|\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428240228 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 3 3 2 2 3 2 F := [10 x y z + 12 y + 11 y z + 9 x , 19 x y + 7 x z + 16 x y - y , 2 2 3 2 -14 x z - 14 y z - 7 x z - 7 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [4 x y - 20 z - 11 x z - 7, 12 x y z - 7 y z - 1, 4 2 3 2 12 x - 15 x y z + 3 x - 8 x y ] > Problem := [F,G]; 2 4 3 3 Problem := [[10 x y z + 12 y + 11 y z + 9 x , 3 2 2 3 2 2 2 3 2 19 x y + 7 x z + 16 x y - y , -14 x z - 14 y z - 7 x z - 7 x], [ 2 3 4 x y - 20 z - 11 x z - 7, 12 x y z - 7 y z - 1, 4 2 3 2 12 x - 15 x y z + 3 x - 8 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.5MB, alloc=32.3MB, time=0.50 memory used=46.3MB, alloc=36.3MB, time=0.76 memory used=66.7MB, alloc=60.3MB, time=1.01 memory used=108.4MB, alloc=60.3MB, time=1.61 memory used=149.1MB, alloc=60.3MB, time=2.21 memory used=190.5MB, alloc=68.3MB, time=2.65 memory used=237.3MB, alloc=68.3MB, time=3.20 memory used=280.3MB, alloc=68.3MB, time=3.55 memory used=321.3MB, alloc=92.3MB, time=3.90 memory used=392.2MB, alloc=92.3MB, time=4.74 memory used=460.0MB, alloc=92.3MB, time=5.55 memory used=529.1MB, alloc=116.3MB, time=6.37 memory used=597.0MB, alloc=372.3MB, time=7.38 memory used=691.9MB, alloc=372.3MB, time=8.49 memory used=781.9MB, alloc=372.3MB, time=9.36 memory used=833.9MB, alloc=372.3MB, time=9.59 memory used=887.1MB, alloc=372.3MB, time=10.25 memory used=949.9MB, alloc=372.3MB, time=10.74 memory used=1009.3MB, alloc=372.3MB, time=11.54 memory used=1082.0MB, alloc=372.3MB, time=12.06 memory used=1185.8MB, alloc=372.3MB, time=13.32 memory used=1265.3MB, alloc=396.3MB, time=14.20 memory used=1390.4MB, alloc=396.3MB, time=15.20 memory used=1502.6MB, alloc=396.3MB, time=16.71 memory used=1556.2MB, alloc=396.3MB, time=16.98 memory used=1610.0MB, alloc=396.3MB, time=17.41 memory used=1685.7MB, alloc=396.3MB, time=18.01 memory used=1744.2MB, alloc=396.3MB, time=18.28 memory used=1804.3MB, alloc=396.3MB, time=19.02 memory used=1849.8MB, alloc=396.3MB, time=19.20 memory used=1909.9MB, alloc=420.3MB, time=19.66 memory used=1980.2MB, alloc=420.3MB, time=19.92 memory used=2031.5MB, alloc=420.3MB, time=20.14 memory used=2090.2MB, alloc=420.3MB, time=20.36 memory used=2160.6MB, alloc=420.3MB, time=20.58 memory used=2229.9MB, alloc=420.3MB, time=20.80 memory used=2274.9MB, alloc=420.3MB, time=20.99 memory used=2324.5MB, alloc=420.3MB, time=21.18 memory used=2379.4MB, alloc=420.3MB, time=21.35 memory used=2440.7MB, alloc=420.3MB, time=21.58 memory used=2521.5MB, alloc=420.3MB, time=22.15 memory used=2590.9MB, alloc=420.3MB, time=22.40 memory used=2641.8MB, alloc=420.3MB, time=22.62 memory used=2703.5MB, alloc=420.3MB, time=22.84 memory used=2776.7MB, alloc=420.3MB, time=23.06 memory used=2839.0MB, alloc=420.3MB, time=23.26 memory used=2885.0MB, alloc=420.3MB, time=23.48 memory used=2935.8MB, alloc=420.3MB, time=23.67 memory used=2991.9MB, alloc=420.3MB, time=23.88 memory used=3055.1MB, alloc=420.3MB, time=24.07 memory used=3155.4MB, alloc=420.3MB, time=29.23 memory used=3216.0MB, alloc=420.3MB, time=29.44 memory used=3281.3MB, alloc=420.3MB, time=29.68 memory used=3332.5MB, alloc=420.3MB, time=29.92 memory used=3392.6MB, alloc=420.3MB, time=30.17 memory used=3461.6MB, alloc=420.3MB, time=30.41 memory used=3673.6MB, alloc=420.3MB, time=31.47 memory used=3803.6MB, alloc=420.3MB, time=33.21 memory used=3864.6MB, alloc=420.3MB, time=33.42 memory used=3965.2MB, alloc=420.3MB, time=34.25 memory used=4089.3MB, alloc=420.3MB, time=35.72 memory used=4233.2MB, alloc=420.3MB, time=36.97 memory used=4371.8MB, alloc=420.3MB, time=38.40 memory used=4512.0MB, alloc=420.3MB, time=40.76 memory used=4650.9MB, alloc=420.3MB, time=43.65 memory used=4799.1MB, alloc=420.3MB, time=47.02 memory used=4865.5MB, alloc=420.3MB, time=47.33 memory used=4921.4MB, alloc=420.3MB, time=47.58 memory used=4971.9MB, alloc=420.3MB, time=47.82 memory used=5031.9MB, alloc=420.3MB, time=48.06 memory used=5100.3MB, alloc=420.3MB, time=48.31 memory used=5145.3MB, alloc=420.3MB, time=48.51 memory used=5188.5MB, alloc=420.3MB, time=48.72 memory used=5235.6MB, alloc=420.3MB, time=48.95 memory used=5287.8MB, alloc=420.3MB, time=49.18 memory used=5345.7MB, alloc=420.3MB, time=49.38 memory used=5425.1MB, alloc=420.3MB, time=50.13 memory used=5485.8MB, alloc=420.3MB, time=50.42 memory used=5534.9MB, alloc=420.3MB, time=50.68 memory used=5586.6MB, alloc=420.3MB, time=50.93 memory used=5649.5MB, alloc=420.3MB, time=51.18 memory used=5715.7MB, alloc=420.3MB, time=51.41 memory used=5757.0MB, alloc=444.3MB, time=51.63 memory used=5815.0MB, alloc=444.3MB, time=51.88 memory used=5880.6MB, alloc=444.3MB, time=52.16 memory used=5955.8MB, alloc=444.3MB, time=52.41 memory used=6099.2MB, alloc=444.3MB, time=60.04 memory used=6173.8MB, alloc=444.3MB, time=60.36 memory used=6246.4MB, alloc=444.3MB, time=60.63 memory used=6311.5MB, alloc=444.3MB, time=60.88 memory used=6392.4MB, alloc=444.3MB, time=61.14 memory used=6636.9MB, alloc=444.3MB, time=62.58 memory used=6739.8MB, alloc=444.3MB, time=63.98 memory used=6833.6MB, alloc=444.3MB, time=64.62 memory used=6921.5MB, alloc=444.3MB, time=65.32 memory used=7007.2MB, alloc=444.3MB, time=65.87 memory used=7085.7MB, alloc=444.3MB, time=66.24 memory used=7173.1MB, alloc=444.3MB, time=67.27 memory used=7238.4MB, alloc=444.3MB, time=67.54 memory used=7326.1MB, alloc=444.3MB, time=68.25 memory used=7399.7MB, alloc=444.3MB, time=68.59 memory used=7454.2MB, alloc=444.3MB, time=68.87 memory used=7521.0MB, alloc=444.3MB, time=69.17 memory used=7600.3MB, alloc=444.3MB, time=69.48 memory used=7663.6MB, alloc=468.3MB, time=69.78 memory used=7725.9MB, alloc=468.3MB, time=70.07 memory used=7795.1MB, alloc=468.3MB, time=70.34 memory used=7871.6MB, alloc=468.3MB, time=70.62 memory used=7957.0MB, alloc=468.3MB, time=70.91 memory used=8052.9MB, alloc=468.3MB, time=71.20 memory used=8160.8MB, alloc=468.3MB, time=71.49 memory used=8316.7MB, alloc=468.3MB, time=72.52 memory used=8389.5MB, alloc=468.3MB, time=72.86 memory used=8479.0MB, alloc=468.3MB, time=73.20 memory used=8575.4MB, alloc=468.3MB, time=73.53 memory used=8637.8MB, alloc=468.3MB, time=73.80 memory used=8706.7MB, alloc=468.3MB, time=74.07 memory used=8783.0MB, alloc=468.3MB, time=74.36 memory used=8866.5MB, alloc=468.3MB, time=74.66 memory used=8960.0MB, alloc=468.3MB, time=74.95 memory used=9066.0MB, alloc=468.3MB, time=75.24 memory used=9265.4MB, alloc=468.3MB, time=83.15 memory used=9355.6MB, alloc=468.3MB, time=83.50 memory used=9424.6MB, alloc=468.3MB, time=83.79 memory used=9507.3MB, alloc=468.3MB, time=84.09 memory used=9608.7MB, alloc=468.3MB, time=84.41 memory used=9782.1MB, alloc=468.3MB, time=84.95 memory used=10022.2MB, alloc=468.3MB, time=86.58 memory used=10176.6MB, alloc=468.3MB, time=88.01 memory used=10264.5MB, alloc=468.3MB, time=88.54 memory used=10356.8MB, alloc=468.3MB, time=88.92 memory used=10479.5MB, alloc=468.3MB, time=92.30 memory used=10562.5MB, alloc=468.3MB, time=92.69 memory used=10698.7MB, alloc=468.3MB, time=94.36 memory used=10895.3MB, alloc=468.3MB, time=95.81 memory used=11067.9MB, alloc=468.3MB, time=98.99 memory used=11136.1MB, alloc=468.3MB, time=100.14 memory used=11230.0MB, alloc=468.3MB, time=101.48 memory used=11331.6MB, alloc=468.3MB, time=102.77 memory used=11439.1MB, alloc=468.3MB, time=103.53 memory used=11526.3MB, alloc=468.3MB, time=104.03 memory used=11623.5MB, alloc=468.3MB, time=105.89 memory used=11699.7MB, alloc=468.3MB, time=106.26 memory used=11801.2MB, alloc=468.3MB, time=107.42 memory used=11935.4MB, alloc=468.3MB, time=108.76 memory used=12054.6MB, alloc=492.3MB, time=110.09 memory used=12149.6MB, alloc=492.3MB, time=110.56 memory used=12232.8MB, alloc=492.3MB, time=110.99 memory used=12311.4MB, alloc=492.3MB, time=111.40 memory used=12406.0MB, alloc=492.3MB, time=111.82 memory used=12515.8MB, alloc=492.3MB, time=112.23 memory used=12583.0MB, alloc=492.3MB, time=112.57 memory used=12681.2MB, alloc=492.3MB, time=113.43 memory used=12777.7MB, alloc=492.3MB, time=113.92 memory used=12873.1MB, alloc=492.3MB, time=114.38 memory used=12949.2MB, alloc=492.3MB, time=114.79 memory used=13039.0MB, alloc=492.3MB, time=115.23 memory used=13147.1MB, alloc=492.3MB, time=115.66 memory used=13225.1MB, alloc=492.3MB, time=116.01 memory used=13297.5MB, alloc=492.3MB, time=116.34 memory used=13441.5MB, alloc=492.3MB, time=125.45 memory used=13523.9MB, alloc=492.3MB, time=125.86 memory used=13629.8MB, alloc=492.3MB, time=126.31 memory used=13698.8MB, alloc=492.3MB, time=126.66 memory used=13777.4MB, alloc=492.3MB, time=127.01 memory used=13869.6MB, alloc=492.3MB, time=127.41 memory used=14036.3MB, alloc=492.3MB, time=128.51 memory used=14119.9MB, alloc=492.3MB, time=129.62 memory used=14190.5MB, alloc=492.3MB, time=130.96 memory used=14347.9MB, alloc=492.3MB, time=133.17 memory used=14440.7MB, alloc=492.3MB, time=133.60 memory used=14513.3MB, alloc=492.3MB, time=133.98 memory used=14603.6MB, alloc=492.3MB, time=134.37 memory used=14822.0MB, alloc=492.3MB, time=135.53 memory used=14969.3MB, alloc=492.3MB, time=136.71 memory used=15103.3MB, alloc=492.3MB, time=137.86 memory used=15227.3MB, alloc=492.3MB, time=139.14 memory used=15311.9MB, alloc=492.3MB, time=139.61 memory used=15419.5MB, alloc=492.3MB, time=140.37 memory used=15501.0MB, alloc=492.3MB, time=140.80 memory used=15633.6MB, alloc=492.3MB, time=144.67 memory used=15715.6MB, alloc=492.3MB, time=145.08 memory used=15803.8MB, alloc=492.3MB, time=146.08 memory used=15889.2MB, alloc=492.3MB, time=147.08 memory used=15998.5MB, alloc=516.3MB, time=148.41 memory used=16121.0MB, alloc=516.3MB, time=149.34 memory used=16208.6MB, alloc=516.3MB, time=150.41 memory used=16344.3MB, alloc=516.3MB, time=151.56 memory used=16390.6MB, alloc=516.3MB, time=152.46 memory used=16523.3MB, alloc=516.3MB, time=153.74 memory used=16615.8MB, alloc=516.3MB, time=154.21 |\^/| 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(); 1428240528 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 F := [16 y z + 12 y + 6 y z + 6 y, 15 y z + 12 x y + 5 z - 18 x, 2 -20 x y z - 8 z + 9 z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 4 3 2 G := [-20 y z + 3 x y + 14 z - 4 z, 8 x z - 17 y + 5 z + 11 z , 2 2 4 2 2 -7 x y + 18 z - 6 x y - 2 z ] > Problem := [F,G]; 3 3 2 2 2 2 Problem := [[16 y z + 12 y + 6 y z + 6 y, 15 y z + 12 x y + 5 z - 18 x, 2 3 2 3 -20 x y z - 8 z + 9 z], [-20 y z + 3 x y + 14 z - 4 z, 3 4 3 2 2 2 4 2 2 8 x z - 17 y + 5 z + 11 z , -7 x y + 18 z - 6 x y - 2 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.52 memory used=46.7MB, alloc=32.3MB, time=0.83 memory used=65.3MB, alloc=56.3MB, time=1.11 memory used=117.9MB, alloc=60.8MB, time=1.68 memory used=140.8MB, alloc=60.8MB, time=1.99 memory used=166.3MB, alloc=60.8MB, time=2.43 memory used=214.1MB, alloc=60.8MB, time=3.57 memory used=239.6MB, alloc=60.8MB, time=3.92 memory used=280.7MB, alloc=60.8MB, time=4.24 memory used=327.3MB, alloc=60.8MB, time=4.70 memory used=367.7MB, alloc=60.8MB, time=5.23 memory used=407.9MB, alloc=60.8MB, time=5.83 memory used=444.0MB, alloc=84.8MB, time=6.38 memory used=507.2MB, alloc=92.8MB, time=7.33 memory used=568.0MB, alloc=116.8MB, time=8.28 memory used=646.3MB, alloc=116.8MB, time=9.02 memory used=694.6MB, alloc=116.8MB, time=9.23 memory used=801.2MB, alloc=116.8MB, time=10.74 memory used=884.7MB, alloc=117.2MB, time=11.47 memory used=921.2MB, alloc=117.2MB, time=11.61 memory used=966.4MB, alloc=117.2MB, time=11.74 memory used=1009.5MB, alloc=117.2MB, time=11.87 memory used=1041.4MB, alloc=117.2MB, time=11.97 memory used=1077.1MB, alloc=117.2MB, time=12.08 memory used=1116.9MB, alloc=117.2MB, time=12.19 memory used=1162.0MB, alloc=117.2MB, time=12.31 memory used=1228.9MB, alloc=123.1MB, time=19.51 memory used=1285.1MB, alloc=123.1MB, time=21.16 memory used=1329.1MB, alloc=123.1MB, time=21.31 memory used=1366.6MB, alloc=123.1MB, time=21.45 memory used=1399.5MB, alloc=123.1MB, time=21.58 memory used=1435.6MB, alloc=123.1MB, time=21.72 memory used=1476.5MB, alloc=123.1MB, time=21.85 memory used=1520.6MB, alloc=123.1MB, time=22.00 memory used=1569.7MB, alloc=123.1MB, time=22.14 memory used=1612.4MB, alloc=147.1MB, time=22.29 memory used=1652.0MB, alloc=147.1MB, time=22.41 memory used=1693.0MB, alloc=147.1MB, time=22.54 memory used=1736.8MB, alloc=147.1MB, time=22.67 memory used=1782.1MB, alloc=147.1MB, time=22.81 memory used=1831.1MB, alloc=147.1MB, time=22.94 memory used=1881.6MB, alloc=147.1MB, time=23.07 memory used=1935.8MB, alloc=147.1MB, time=23.21 memory used=1991.4MB, alloc=147.1MB, time=23.35 memory used=2050.7MB, alloc=147.1MB, time=23.48 memory used=2111.3MB, alloc=147.1MB, time=23.62 memory used=2175.6MB, alloc=147.1MB, time=23.77 memory used=2243.7MB, alloc=147.1MB, time=23.91 memory used=2315.5MB, alloc=147.1MB, time=24.05 memory used=2390.6MB, alloc=147.1MB, time=24.20 memory used=2405.4MB, alloc=155.8MB, time=24.29 memory used=2415.8MB, alloc=155.8MB, time=24.39 memory used=2423.1MB, alloc=155.8MB, time=24.48 memory used=2430.7MB, alloc=155.8MB, time=24.59 memory used=2439.0MB, alloc=155.8MB, time=24.68 memory used=2447.5MB, alloc=155.8MB, time=24.76 memory used=2456.0MB, alloc=155.8MB, time=24.85 memory used=2464.5MB, alloc=155.8MB, time=24.94 memory used=2472.9MB, alloc=155.8MB, time=25.02 memory used=2481.4MB, alloc=155.8MB, time=25.10 memory used=2489.9MB, alloc=155.8MB, time=25.19 memory used=2498.4MB, alloc=155.8MB, time=25.27 memory used=2506.9MB, alloc=155.8MB, time=25.36 memory used=2515.4MB, alloc=155.8MB, time=25.44 memory used=2523.9MB, alloc=155.8MB, time=25.52 memory used=2532.4MB, alloc=155.8MB, time=25.60 memory used=2540.9MB, alloc=155.8MB, time=25.69 memory used=2549.3MB, alloc=155.8MB, time=25.77 memory used=2557.8MB, alloc=155.8MB, time=25.86 memory used=2566.3MB, alloc=155.8MB, time=25.97 memory used=2574.8MB, alloc=155.8MB, time=26.04 memory used=2583.3MB, alloc=155.8MB, time=26.13 memory used=2591.7MB, alloc=155.8MB, time=26.22 memory used=2600.2MB, alloc=155.8MB, time=26.31 memory used=2608.7MB, alloc=155.8MB, time=26.40 memory used=2617.1MB, alloc=155.8MB, time=26.50 memory used=2625.6MB, alloc=155.8MB, time=26.58 memory used=2634.0MB, alloc=155.8MB, time=26.67 memory used=2642.5MB, alloc=155.8MB, time=26.75 memory used=2650.9MB, alloc=155.8MB, time=26.83 memory used=2659.4MB, alloc=155.8MB, time=26.91 memory used=2667.8MB, alloc=155.8MB, time=26.99 memory used=2676.2MB, alloc=155.8MB, time=27.07 memory used=2684.6MB, alloc=155.8MB, time=27.15 memory used=2693.1MB, alloc=155.8MB, time=27.22 memory used=2701.5MB, alloc=155.8MB, time=27.31 memory used=2709.9MB, alloc=155.8MB, time=27.40 memory used=2718.2MB, alloc=155.8MB, time=27.50 memory used=2726.6MB, alloc=155.8MB, time=27.60 memory used=2735.0MB, alloc=155.8MB, time=27.69 memory used=2743.4MB, alloc=155.8MB, time=27.76 memory used=2751.7MB, alloc=155.8MB, time=27.84 memory used=2760.0MB, alloc=155.8MB, time=27.91 memory used=2768.4MB, alloc=155.8MB, time=27.99 memory used=2776.7MB, alloc=155.8MB, time=28.08 memory used=2785.1MB, alloc=155.8MB, time=28.17 memory used=2796.1MB, alloc=155.8MB, time=28.27 memory used=2804.6MB, alloc=155.8MB, time=28.35 memory used=2815.4MB, alloc=155.8MB, time=28.43 memory used=2826.4MB, alloc=155.8MB, time=28.51 memory used=2837.4MB, alloc=155.8MB, time=28.58 memory used=2848.3MB, alloc=155.8MB, time=28.66 memory used=2859.3MB, alloc=155.8MB, time=28.74 memory used=2870.2MB, alloc=155.8MB, time=28.82 memory used=2881.1MB, alloc=155.8MB, time=28.91 memory used=2891.9MB, alloc=155.8MB, time=29.00 memory used=2902.8MB, alloc=155.8MB, time=29.08 memory used=2913.6MB, alloc=155.8MB, time=29.16 memory used=2924.3MB, alloc=155.8MB, time=29.24 memory used=2935.1MB, alloc=155.8MB, time=29.34 memory used=2945.8MB, alloc=155.8MB, time=29.42 memory used=2956.4MB, alloc=155.8MB, time=29.49 memory used=2967.1MB, alloc=155.8MB, time=29.59 memory used=2977.7MB, alloc=155.8MB, time=29.69 memory used=2988.3MB, alloc=155.8MB, time=29.78 memory used=2998.8MB, alloc=155.8MB, time=29.87 memory used=3009.3MB, alloc=155.8MB, time=29.95 memory used=3019.8MB, alloc=155.8MB, time=30.04 memory used=3030.2MB, alloc=155.8MB, time=30.13 memory used=3040.7MB, alloc=155.8MB, time=30.21 memory used=3053.5MB, alloc=155.8MB, time=30.30 memory used=3066.4MB, alloc=155.8MB, time=30.38 memory used=3079.2MB, alloc=155.8MB, time=30.49 memory used=3092.0MB, alloc=155.8MB, time=30.56 memory used=3104.6MB, alloc=155.8MB, time=30.65 memory used=3117.2MB, alloc=155.8MB, time=30.74 memory used=3129.8MB, alloc=155.8MB, time=30.82 memory used=3142.2MB, alloc=155.8MB, time=30.92 memory used=3154.6MB, alloc=155.8MB, time=31.02 memory used=3167.0MB, alloc=155.8MB, time=31.11 memory used=3179.2MB, alloc=155.8MB, time=31.20 memory used=3191.4MB, alloc=155.8MB, time=31.28 memory used=3203.4MB, alloc=155.8MB, time=31.38 memory used=3215.6MB, alloc=155.8MB, time=31.47 memory used=3229.7MB, alloc=155.8MB, time=31.55 memory used=3243.9MB, alloc=155.8MB, time=31.63 memory used=3257.9MB, alloc=155.8MB, time=31.71 memory used=3271.9MB, alloc=155.8MB, time=31.80 memory used=3285.7MB, alloc=155.8MB, time=31.90 memory used=3299.3MB, alloc=155.8MB, time=32.00 memory used=3312.8MB, alloc=155.8MB, time=32.10 memory used=3326.2MB, alloc=155.8MB, time=32.20 memory used=3339.7MB, alloc=155.8MB, time=32.31 memory used=3354.7MB, alloc=155.8MB, time=32.40 memory used=3369.8MB, alloc=155.8MB, time=32.50 memory used=3384.7MB, alloc=155.8MB, time=32.58 memory used=3399.3MB, alloc=155.8MB, time=32.66 memory used=3413.8MB, alloc=155.8MB, time=32.74 memory used=3430.0MB, alloc=155.8MB, time=32.85 memory used=3446.0MB, alloc=155.8MB, time=32.93 memory used=3461.8MB, alloc=155.8MB, time=33.02 memory used=3477.2MB, alloc=155.8MB, time=33.12 memory used=3494.1MB, alloc=155.8MB, time=33.21 memory used=3510.6MB, alloc=155.8MB, time=33.29 memory used=3526.9MB, alloc=155.8MB, time=33.40 memory used=3544.2MB, alloc=155.8MB, time=33.50 memory used=3561.1MB, alloc=155.8MB, time=33.59 memory used=3579.0MB, alloc=155.8MB, time=33.68 memory used=3596.5MB, alloc=155.8MB, time=33.76 memory used=3614.4MB, alloc=155.8MB, time=33.86 memory used=3633.0MB, alloc=155.8MB, time=33.94 memory used=3651.9MB, alloc=155.8MB, time=34.02 memory used=3671.1MB, alloc=155.8MB, time=34.11 memory used=3690.9MB, alloc=155.8MB, time=34.21 memory used=3711.5MB, alloc=155.8MB, time=34.30 memory used=3729.1MB, alloc=155.8MB, time=34.40 memory used=3835.2MB, alloc=155.8MB, time=35.48 memory used=3978.9MB, alloc=155.8MB, time=36.22 memory used=4094.3MB, alloc=411.8MB, time=37.44 memory used=4247.2MB, alloc=411.8MB, time=39.18 memory used=4300.4MB, alloc=411.8MB, time=39.35 memory used=4364.8MB, alloc=411.8MB, time=39.54 memory used=4409.7MB, alloc=411.8MB, time=39.69 memory used=4457.1MB, alloc=411.8MB, time=39.84 memory used=4512.8MB, alloc=411.8MB, time=39.98 memory used=4592.8MB, alloc=411.8MB, time=45.89 memory used=4664.9MB, alloc=411.8MB, time=48.82 memory used=4726.2MB, alloc=411.8MB, time=49.02 memory used=4768.5MB, alloc=411.8MB, time=49.20 memory used=4817.4MB, alloc=411.8MB, time=49.38 memory used=4873.6MB, alloc=411.8MB, time=49.57 memory used=4937.4MB, alloc=411.8MB, time=49.75 memory used=4995.1MB, alloc=411.8MB, time=49.92 memory used=5032.9MB, alloc=411.8MB, time=50.06 memory used=5072.5MB, alloc=411.8MB, time=50.20 memory used=5114.0MB, alloc=411.8MB, time=50.33 memory used=5156.8MB, alloc=411.8MB, time=50.47 memory used=5200.8MB, alloc=411.8MB, time=50.62 memory used=5248.4MB, alloc=411.8MB, time=50.76 memory used=5297.2MB, alloc=411.8MB, time=50.91 memory used=5349.6MB, alloc=411.8MB, time=51.05 memory used=5403.2MB, alloc=411.8MB, time=51.20 memory used=5460.4MB, alloc=411.8MB, time=51.35 memory used=5518.6MB, alloc=411.8MB, time=51.50 memory used=5580.4MB, alloc=411.8MB, time=51.66 memory used=5643.1MB, alloc=411.8MB, time=51.81 memory used=5709.3MB, alloc=411.8MB, time=51.97 memory used=5913.5MB, alloc=411.8MB, time=52.49 memory used=6062.4MB, alloc=411.8MB, time=52.78 memory used=6222.7MB, alloc=411.8MB, time=53.08 memory used=6396.0MB, alloc=411.8MB, time=53.38 memory used=6583.5MB, alloc=411.8MB, time=53.71 memory used=6790.0MB, alloc=411.8MB, time=54.04 memory used=7022.9MB, alloc=411.8MB, time=54.38 memory used=7272.3MB, alloc=411.8MB, time=56.02 memory used=7388.0MB, alloc=411.8MB, time=57.61 memory used=7516.3MB, alloc=411.8MB, time=58.78 memory used=7582.0MB, alloc=411.8MB, time=59.14 memory used=7626.6MB, alloc=411.8MB, time=59.33 memory used=7681.6MB, alloc=411.8MB, time=59.53 memory used=7742.1MB, alloc=435.8MB, time=59.88 memory used=7805.7MB, alloc=435.8MB, time=60.12 memory used=7882.4MB, alloc=435.8MB, time=61.81 memory used=7966.3MB, alloc=435.8MB, time=62.93 memory used=8040.4MB, alloc=435.8MB, time=63.17 memory used=8093.8MB, alloc=435.8MB, time=63.38 memory used=8145.1MB, alloc=435.8MB, time=63.59 memory used=8198.0MB, alloc=435.8MB, time=63.79 memory used=8256.0MB, alloc=435.8MB, time=64.00 memory used=8319.1MB, alloc=435.8MB, time=64.20 memory used=8399.4MB, alloc=435.8MB, time=82.93 memory used=8482.2MB, alloc=435.8MB, time=86.46 memory used=8532.5MB, alloc=435.8MB, time=86.66 memory used=8581.8MB, alloc=435.8MB, time=86.87 memory used=8631.9MB, alloc=435.8MB, time=87.06 memory used=8682.6MB, alloc=435.8MB, time=87.26 memory used=8733.6MB, alloc=435.8MB, time=87.46 memory used=8786.7MB, alloc=435.8MB, time=87.66 memory used=8842.2MB, alloc=435.8MB, time=87.87 memory used=8900.6MB, alloc=435.8MB, time=88.07 memory used=8961.4MB, alloc=435.8MB, time=88.29 memory used=9025.0MB, alloc=435.8MB, time=88.50 memory used=9091.6MB, alloc=435.8MB, time=88.70 memory used=9161.8MB, alloc=435.8MB, time=88.92 memory used=9236.2MB, alloc=435.8MB, time=89.13 memory used=9306.3MB, alloc=435.8MB, time=89.34 memory used=9356.3MB, alloc=435.8MB, time=89.51 memory used=9404.3MB, alloc=459.8MB, time=107.61 |\^/| 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(); 1428240828 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 F := [-18 x y z - 7 y + 4 x z + 4 x, -15 x - 20 x z + 7 x z - 16 x, 4 2 2 3 2 16 x + 4 y z - 3 y z - 17 x y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 2 2 G := [-y z + 20 x y + 4 z + 6 x, x y z + 13 y z + 15 y - 4 z , 3 3 2 3 19 x y + 19 x z + 5 x y z + 2 z ] > Problem := [F,G]; 2 3 4 2 Problem := [[-18 x y z - 7 y + 4 x z + 4 x, -15 x - 20 x z + 7 x z - 16 x, 4 2 2 3 2 3 2 3 16 x + 4 y z - 3 y z - 17 x y], [-y z + 20 x y + 4 z + 6 x, 2 2 2 2 3 3 2 3 x y z + 13 y z + 15 y - 4 z , 19 x y + 19 x z + 5 x y z + 2 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.18 memory used=59.3MB, alloc=36.3MB, time=1.06 memory used=112.0MB, alloc=36.3MB, time=1.72 memory used=134.3MB, alloc=36.3MB, time=1.96 memory used=153.3MB, alloc=36.3MB, time=2.12 memory used=169.7MB, alloc=60.3MB, time=10.25 memory used=194.1MB, alloc=84.3MB, time=13.77 memory used=225.0MB, alloc=84.3MB, time=13.87 memory used=255.3MB, alloc=84.3MB, time=13.96 memory used=285.4MB, alloc=84.3MB, time=14.04 memory used=315.4MB, alloc=84.3MB, time=14.13 memory used=345.2MB, alloc=84.3MB, time=14.21 memory used=374.9MB, alloc=84.3MB, time=14.30 memory used=404.6MB, alloc=84.3MB, time=14.38 memory used=437.1MB, alloc=84.3MB, time=14.47 memory used=469.5MB, alloc=84.3MB, time=14.55 memory used=501.7MB, alloc=84.3MB, time=14.64 memory used=533.6MB, alloc=84.3MB, time=14.72 memory used=565.3MB, alloc=84.3MB, time=14.81 memory used=599.8MB, alloc=84.3MB, time=14.90 memory used=634.0MB, alloc=84.3MB, time=15.00 memory used=667.8MB, alloc=84.3MB, time=15.09 memory used=701.3MB, alloc=84.3MB, time=15.18 memory used=737.2MB, alloc=84.3MB, time=15.28 memory used=772.7MB, alloc=84.3MB, time=15.36 memory used=807.8MB, alloc=84.3MB, time=15.45 memory used=845.2MB, alloc=84.3MB, time=15.54 memory used=882.0MB, alloc=84.3MB, time=15.64 memory used=920.8MB, alloc=84.3MB, time=15.73 memory used=958.8MB, alloc=84.3MB, time=15.82 memory used=998.5MB, alloc=84.3MB, time=15.92 memory used=1037.4MB, alloc=84.3MB, time=16.01 memory used=1077.7MB, alloc=84.3MB, time=16.12 memory used=1119.2MB, alloc=84.3MB, time=16.20 memory used=1159.3MB, alloc=84.3MB, time=16.30 memory used=1200.3MB, alloc=84.3MB, time=16.39 memory used=1243.7MB, alloc=84.3MB, time=16.49 memory used=1287.0MB, alloc=84.3MB, time=16.58 memory used=1331.7MB, alloc=84.3MB, time=16.67 memory used=1376.8MB, alloc=84.3MB, time=16.77 memory used=1422.8MB, alloc=84.3MB, time=16.86 memory used=1470.8MB, alloc=84.3MB, time=16.94 memory used=1520.5MB, alloc=84.3MB, time=17.03 memory used=1569.4MB, alloc=84.3MB, time=17.47 memory used=1593.7MB, alloc=107.8MB, time=29.52 memory used=1597.6MB, alloc=107.8MB, time=29.87 memory used=1597.6MB, alloc=363.8MB, time=29.90 memory used=1827.2MB, alloc=363.8MB, time=39.87 memory used=2022.0MB, alloc=363.8MB, time=40.12 memory used=2218.6MB, alloc=363.8MB, time=40.39 memory used=2423.6MB, alloc=363.8MB, time=40.66 memory used=2523.2MB, alloc=363.8MB, time=52.11 memory used=2554.7MB, alloc=363.8MB, time=52.19 memory used=2584.8MB, alloc=363.8MB, time=52.28 memory used=2614.9MB, alloc=363.8MB, time=52.38 memory used=2648.1MB, alloc=363.8MB, time=52.48 memory used=2681.2MB, alloc=363.8MB, time=52.56 memory used=2714.1MB, alloc=363.8MB, time=52.64 memory used=2746.7MB, alloc=363.8MB, time=52.72 memory used=2779.2MB, alloc=363.8MB, time=52.81 memory used=2811.5MB, alloc=363.8MB, time=52.90 memory used=2846.7MB, alloc=363.8MB, time=53.00 memory used=2881.5MB, alloc=363.8MB, time=53.10 memory used=2915.9MB, alloc=363.8MB, time=53.19 memory used=2950.2MB, alloc=363.8MB, time=53.28 memory used=2987.0MB, alloc=363.8MB, time=53.37 memory used=3023.4MB, alloc=363.8MB, time=53.46 memory used=3059.5MB, alloc=363.8MB, time=53.57 memory used=3097.9MB, alloc=363.8MB, time=53.66 memory used=3135.8MB, alloc=363.8MB, time=53.76 memory used=3175.8MB, alloc=363.8MB, time=53.85 memory used=3214.9MB, alloc=363.8MB, time=53.94 memory used=3253.5MB, alloc=363.8MB, time=54.04 memory used=3293.9MB, alloc=363.8MB, time=54.13 memory used=3335.9MB, alloc=363.8MB, time=54.23 memory used=3376.8MB, alloc=363.8MB, time=54.34 memory used=3419.0MB, alloc=363.8MB, time=54.43 memory used=3462.0MB, alloc=363.8MB, time=54.53 memory used=3505.8MB, alloc=363.8MB, time=54.63 memory used=3549.9MB, alloc=363.8MB, time=54.73 memory used=3596.0MB, alloc=363.8MB, time=54.83 memory used=3643.1MB, alloc=363.8MB, time=54.92 memory used=3690.5MB, alloc=363.8MB, time=55.01 memory used=3738.7MB, alloc=363.8MB, time=55.11 memory used=3788.5MB, alloc=363.8MB, time=55.21 memory used=3840.7MB, alloc=363.8MB, time=55.32 memory used=4134.2MB, alloc=363.8MB, time=77.44 memory used=4326.0MB, alloc=363.8MB, time=77.70 memory used=4519.1MB, alloc=363.8MB, time=77.97 memory used=4719.1MB, alloc=363.8MB, time=78.25 memory used=4851.5MB, alloc=363.8MB, time=81.19 memory used=4906.9MB, alloc=363.8MB, time=83.67 memory used=4938.8MB, alloc=363.8MB, time=83.73 memory used=4971.1MB, alloc=363.8MB, time=83.80 memory used=5004.8MB, alloc=363.8MB, time=83.87 memory used=5038.6MB, alloc=363.8MB, time=83.94 memory used=5073.7MB, alloc=363.8MB, time=84.01 memory used=5109.7MB, alloc=363.8MB, time=84.09 memory used=5145.9MB, alloc=363.8MB, time=84.16 memory used=5182.8MB, alloc=363.8MB, time=84.24 memory used=5264.2MB, alloc=363.8MB, time=90.66 memory used=5304.7MB, alloc=363.8MB, time=121.26 memory used=5337.5MB, alloc=387.8MB, time=142.59 |\^/| 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(); 1428241128 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 4 2 F := [-2 x z - 10 y z + 11 x + 15 x z, 20 x z + 20 z - 9 x + 19 y z, 2 2 2 2 13 x y + 9 x y + 17 x y z + 18 x z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 3 G := [9 y z + 10 x z + 18 x + 3 y, 2 x y - 2 y z - 12 x - 5 y, 3 2 2 15 x z - 3 x y + 5 x y z + 19 z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-2 x z - 10 y z + 11 x + 15 x z, 2 2 4 2 2 2 2 2 20 x z + 20 z - 9 x + 19 y z, 13 x y + 9 x y + 17 x y z + 18 x z ], 3 2 3 3 3 [9 y z + 10 x z + 18 x + 3 y, 2 x y - 2 y z - 12 x - 5 y, 3 2 2 15 x z - 3 x y + 5 x y z + 19 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=27.7MB, alloc=34.3MB, time=0.42 memory used=41.6MB, alloc=34.3MB, time=0.46 memory used=60.3MB, alloc=34.3MB, time=0.60 memory used=85.2MB, alloc=39.2MB, time=0.85 memory used=101.3MB, alloc=39.2MB, time=0.90 memory used=110.5MB, alloc=39.2MB, time=0.93 memory used=120.8MB, alloc=39.2MB, time=0.97 memory used=132.3MB, alloc=39.2MB, time=1.01 memory used=145.4MB, alloc=39.2MB, time=1.04 memory used=160.0MB, alloc=39.2MB, time=1.08 memory used=175.4MB, alloc=39.2MB, time=1.12 memory used=184.0MB, alloc=39.2MB, time=1.16 memory used=192.5MB, alloc=39.2MB, time=1.18 memory used=201.0MB, alloc=39.2MB, time=1.22 memory used=209.7MB, alloc=39.2MB, time=1.25 memory used=219.1MB, alloc=39.2MB, time=1.28 memory used=229.1MB, alloc=39.2MB, time=1.31 memory used=239.6MB, alloc=39.2MB, time=1.34 memory used=250.6MB, alloc=39.2MB, time=1.38 memory used=262.2MB, alloc=39.2MB, time=1.41 memory used=274.9MB, alloc=39.2MB, time=1.44 memory used=288.4MB, alloc=39.2MB, time=1.47 memory used=302.4MB, alloc=39.2MB, time=1.51 memory used=317.3MB, alloc=39.2MB, time=1.54 memory used=336.3MB, alloc=39.2MB, time=1.77 memory used=355.7MB, alloc=39.2MB, time=1.83 memory used=370.4MB, alloc=39.2MB, time=1.88 memory used=380.4MB, alloc=39.2MB, time=1.92 memory used=391.3MB, alloc=39.2MB, time=1.95 memory used=403.7MB, alloc=39.2MB, time=1.99 memory used=417.2MB, alloc=39.2MB, time=2.03 memory used=432.4MB, alloc=39.2MB, time=2.07 memory used=445.7MB, alloc=39.2MB, time=2.10 memory used=453.8MB, alloc=39.2MB, time=2.14 memory used=462.1MB, alloc=39.2MB, time=2.17 memory used=470.9MB, alloc=39.2MB, time=2.20 memory used=480.2MB, alloc=39.2MB, time=2.23 memory used=490.0MB, alloc=39.2MB, time=2.26 memory used=500.9MB, alloc=39.2MB, time=2.29 memory used=511.7MB, alloc=39.2MB, time=2.33 memory used=523.6MB, alloc=39.2MB, time=2.36 memory used=535.7MB, alloc=39.2MB, time=2.39 memory used=549.0MB, alloc=39.2MB, time=2.43 memory used=563.3MB, alloc=39.2MB, time=2.46 memory used=578.1MB, alloc=39.2MB, time=2.50 memory used=594.0MB, alloc=39.2MB, time=2.53 memory used=619.8MB, alloc=39.2MB, time=5.62 memory used=649.3MB, alloc=39.2MB, time=8.84 memory used=665.6MB, alloc=39.2MB, time=8.89 memory used=675.7MB, alloc=39.2MB, time=8.93 memory used=687.9MB, alloc=39.2MB, time=8.97 memory used=702.3MB, alloc=39.2MB, time=9.01 memory used=711.1MB, alloc=63.2MB, time=9.06 memory used=734.6MB, alloc=63.2MB, time=9.12 memory used=762.9MB, alloc=63.2MB, time=9.18 memory used=795.7MB, alloc=63.2MB, time=9.25 memory used=830.8MB, alloc=63.2MB, time=9.32 memory used=850.9MB, alloc=63.2MB, time=9.37 memory used=872.0MB, alloc=63.2MB, time=9.41 memory used=894.8MB, alloc=63.2MB, time=9.46 memory used=919.0MB, alloc=63.2MB, time=9.51 memory used=945.4MB, alloc=63.2MB, time=9.56 memory used=972.8MB, alloc=63.2MB, time=9.62 memory used=1002.6MB, alloc=63.2MB, time=9.67 memory used=1034.4MB, alloc=63.2MB, time=9.72 memory used=1068.2MB, alloc=63.2MB, time=9.78 memory used=1115.1MB, alloc=81.9MB, time=9.86 memory used=1126.2MB, alloc=81.9MB, time=9.89 memory used=1137.5MB, alloc=81.9MB, time=9.93 memory used=1149.9MB, alloc=81.9MB, time=9.97 memory used=1189.7MB, alloc=81.9MB, time=10.54 memory used=1250.2MB, alloc=81.9MB, time=16.71 memory used=1279.3MB, alloc=81.9MB, time=16.79 memory used=1306.4MB, alloc=81.9MB, time=16.87 memory used=1330.3MB, alloc=81.9MB, time=16.94 memory used=1358.1MB, alloc=81.9MB, time=17.02 memory used=1390.2MB, alloc=81.9MB, time=17.09 memory used=1422.8MB, alloc=81.9MB, time=17.17 memory used=1441.9MB, alloc=81.9MB, time=17.22 memory used=1462.3MB, alloc=81.9MB, time=17.27 memory used=1484.0MB, alloc=81.9MB, time=17.33 memory used=1507.1MB, alloc=81.9MB, time=17.39 memory used=1531.3MB, alloc=81.9MB, time=17.45 memory used=1557.5MB, alloc=81.9MB, time=17.51 memory used=1585.4MB, alloc=81.9MB, time=17.57 memory used=1614.6MB, alloc=81.9MB, time=17.62 memory used=1646.5MB, alloc=81.9MB, time=17.69 memory used=1680.4MB, alloc=81.9MB, time=17.75 memory used=1706.4MB, alloc=81.9MB, time=17.81 memory used=1718.6MB, alloc=81.9MB, time=17.85 memory used=1731.5MB, alloc=81.9MB, time=17.91 memory used=1785.0MB, alloc=81.9MB, time=18.45 memory used=1828.2MB, alloc=81.9MB, time=19.48 memory used=1866.8MB, alloc=81.9MB, time=19.61 memory used=1896.5MB, alloc=81.9MB, time=19.71 memory used=1916.7MB, alloc=81.9MB, time=19.79 memory used=1937.9MB, alloc=81.9MB, time=19.89 memory used=1962.8MB, alloc=81.9MB, time=19.98 memory used=1989.6MB, alloc=81.9MB, time=20.05 memory used=2016.0MB, alloc=81.9MB, time=20.15 memory used=2039.6MB, alloc=81.9MB, time=20.24 memory used=2066.5MB, alloc=81.9MB, time=20.32 memory used=2093.0MB, alloc=81.9MB, time=20.40 memory used=2113.2MB, alloc=81.9MB, time=20.47 memory used=2129.4MB, alloc=81.9MB, time=20.55 memory used=2146.5MB, alloc=81.9MB, time=20.62 memory used=2163.9MB, alloc=81.9MB, time=20.68 memory used=2181.6MB, alloc=81.9MB, time=20.75 memory used=2199.6MB, alloc=81.9MB, time=20.81 memory used=2217.9MB, alloc=81.9MB, time=20.89 memory used=2237.2MB, alloc=81.9MB, time=20.96 memory used=2259.2MB, alloc=81.9MB, time=21.04 memory used=2282.1MB, alloc=81.9MB, time=21.11 memory used=2305.2MB, alloc=81.9MB, time=21.18 memory used=2328.7MB, alloc=81.9MB, time=21.26 memory used=2352.4MB, alloc=81.9MB, time=21.32 memory used=2376.4MB, alloc=81.9MB, time=21.39 memory used=2400.7MB, alloc=81.9MB, time=21.47 memory used=2423.7MB, alloc=81.9MB, time=21.54 memory used=2442.3MB, alloc=81.9MB, time=21.60 memory used=2462.7MB, alloc=81.9MB, time=21.66 memory used=2483.4MB, alloc=81.9MB, time=21.72 memory used=2504.1MB, alloc=81.9MB, time=21.79 memory used=2524.9MB, alloc=81.9MB, time=21.85 memory used=2545.9MB, alloc=81.9MB, time=21.91 memory used=2566.7MB, alloc=81.9MB, time=21.97 memory used=2588.5MB, alloc=81.9MB, time=22.03 memory used=2610.2MB, alloc=81.9MB, time=22.10 memory used=2633.7MB, alloc=81.9MB, time=22.16 memory used=2656.7MB, alloc=81.9MB, time=22.22 memory used=2680.0MB, alloc=81.9MB, time=22.28 memory used=2703.9MB, alloc=81.9MB, time=22.34 memory used=2719.7MB, alloc=105.9MB, time=22.43 memory used=2748.9MB, alloc=105.9MB, time=22.50 memory used=2778.9MB, alloc=105.9MB, time=22.57 memory used=2811.8MB, alloc=105.9MB, time=22.65 memory used=2845.4MB, alloc=105.9MB, time=22.72 memory used=2879.0MB, alloc=105.9MB, time=22.80 memory used=2913.4MB, alloc=105.9MB, time=22.88 memory used=2949.3MB, alloc=105.9MB, time=22.95 memory used=2987.2MB, alloc=105.9MB, time=23.03 memory used=3026.4MB, alloc=105.9MB, time=23.10 memory used=3067.2MB, alloc=105.9MB, time=23.19 memory used=3110.0MB, alloc=105.9MB, time=23.26 memory used=3155.5MB, alloc=105.9MB, time=23.35 memory used=3203.6MB, alloc=105.9MB, time=23.43 memory used=3255.3MB, alloc=105.9MB, time=23.51 memory used=3321.4MB, alloc=105.9MB, time=24.06 memory used=3364.0MB, alloc=105.9MB, time=24.30 memory used=3406.1MB, alloc=105.9MB, time=24.49 memory used=3432.5MB, alloc=107.8MB, time=24.79 memory used=3483.5MB, alloc=107.8MB, time=24.89 memory used=3515.2MB, alloc=107.8MB, time=24.99 memory used=3566.4MB, alloc=107.8MB, time=25.10 memory used=3604.3MB, alloc=107.8MB, time=25.93 memory used=3626.7MB, alloc=107.8MB, time=26.00 memory used=3650.5MB, alloc=107.8MB, time=26.06 memory used=3675.7MB, alloc=107.8MB, time=26.13 memory used=3705.7MB, alloc=107.8MB, time=26.20 memory used=3749.4MB, alloc=107.8MB, time=26.28 memory used=3796.5MB, alloc=107.8MB, time=26.36 memory used=3839.6MB, alloc=107.8MB, time=26.44 memory used=3854.1MB, alloc=107.8MB, time=26.49 memory used=3868.9MB, alloc=107.8MB, time=26.54 memory used=3883.9MB, alloc=107.8MB, time=26.58 memory used=3899.1MB, alloc=107.8MB, time=26.63 memory used=3915.0MB, alloc=107.8MB, time=26.70 memory used=3936.4MB, alloc=107.8MB, time=26.77 memory used=3959.0MB, alloc=107.8MB, time=26.84 memory used=3983.1MB, alloc=107.8MB, time=26.90 memory used=4008.6MB, alloc=107.8MB, time=26.98 memory used=4043.9MB, alloc=107.8MB, time=27.05 memory used=4088.2MB, alloc=107.8MB, time=27.14 memory used=4135.4MB, alloc=107.8MB, time=27.23 memory used=4168.0MB, alloc=107.8MB, time=27.30 memory used=4182.3MB, alloc=107.8MB, time=27.34 memory used=4197.0MB, alloc=107.8MB, time=27.39 memory used=4211.8MB, alloc=107.8MB, time=27.44 memory used=4227.0MB, alloc=107.8MB, time=27.48 memory used=4244.3MB, alloc=107.8MB, time=27.78 memory used=4320.0MB, alloc=363.8MB, time=29.27 memory used=4361.3MB, alloc=363.8MB, time=29.39 memory used=4400.1MB, alloc=363.8MB, time=29.52 memory used=4446.6MB, alloc=363.8MB, time=29.65 memory used=4492.0MB, alloc=363.8MB, time=29.77 memory used=4538.5MB, alloc=363.8MB, time=29.90 memory used=4572.7MB, alloc=363.8MB, time=30.01 memory used=4604.9MB, alloc=363.8MB, time=30.11 memory used=4637.8MB, alloc=363.8MB, time=30.22 memory used=4674.2MB, alloc=363.8MB, time=30.33 memory used=4712.1MB, alloc=363.8MB, time=30.44 memory used=4751.2MB, alloc=363.8MB, time=30.55 memory used=4795.0MB, alloc=363.8MB, time=30.65 memory used=4839.7MB, alloc=363.8MB, time=30.76 memory used=4880.3MB, alloc=363.8MB, time=30.87 memory used=4915.7MB, alloc=363.8MB, time=30.95 memory used=4952.7MB, alloc=363.8MB, time=31.04 memory used=4990.5MB, alloc=363.8MB, time=31.13 memory used=5031.7MB, alloc=363.8MB, time=31.23 memory used=5074.3MB, alloc=363.8MB, time=31.32 memory used=5117.0MB, alloc=363.8MB, time=31.42 memory used=5156.9MB, alloc=363.8MB, time=31.51 memory used=5186.6MB, alloc=363.8MB, time=31.58 memory used=5216.3MB, alloc=363.8MB, time=31.65 memory used=5247.0MB, alloc=363.8MB, time=31.73 memory used=5279.9MB, alloc=363.8MB, time=31.80 memory used=5313.4MB, alloc=363.8MB, time=31.88 memory used=5347.9MB, alloc=363.8MB, time=31.95 memory used=5384.1MB, alloc=363.8MB, time=32.03 memory used=5421.1MB, alloc=363.8MB, time=32.11 memory used=5459.1MB, alloc=363.8MB, time=32.19 memory used=5498.9MB, alloc=363.8MB, time=32.27 memory used=5541.6MB, alloc=363.8MB, time=32.35 memory used=5586.3MB, alloc=363.8MB, time=32.43 memory used=5632.8MB, alloc=363.8MB, time=32.51 memory used=5682.8MB, alloc=363.8MB, time=32.59 memory used=5737.8MB, alloc=363.8MB, time=32.67 memory used=5795.4MB, alloc=363.8MB, time=33.39 memory used=5836.1MB, alloc=363.8MB, time=33.52 memory used=5901.6MB, alloc=363.8MB, time=33.97 memory used=5943.1MB, alloc=363.8MB, time=34.06 memory used=6010.5MB, alloc=363.8MB, time=34.22 memory used=6138.2MB, alloc=363.8MB, time=35.26 memory used=6221.6MB, alloc=363.8MB, time=35.39 memory used=6434.3MB, alloc=363.8MB, time=35.81 memory used=6528.8MB, alloc=363.8MB, time=36.00 memory used=6707.2MB, alloc=363.8MB, time=37.47 memory used=6790.9MB, alloc=363.8MB, time=69.75 memory used=6836.4MB, alloc=387.8MB, time=105.79 memory used=6891.1MB, alloc=387.8MB, time=143.03 |\^/| 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(); 1428241428 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 2 4 2 F := [12 x y + 4 x z - y z - 10 z , 15 x y z - z + x - y, 2 3 2 3 -19 x y z + 14 y z - 5 x z - 18 y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 4 G := [7 x + 4 y z - 15 x y z - 13 x , 18 x z + 20 z - 3 x z - 11 y, 3 2 2 2 y z - 4 x z - 11 y z + 3 x y] > Problem := [F,G]; 3 2 2 3 2 2 4 2 Problem := [[12 x y + 4 x z - y z - 10 z , 15 x y z - z + x - y, 2 3 2 3 4 3 2 -19 x y z + 14 y z - 5 x z - 18 y ], [7 x + 4 y z - 15 x y z - 13 x , 2 2 4 3 2 2 18 x z + 20 z - 3 x z - 11 y, 2 y z - 4 x z - 11 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=4.5MB, alloc=32.3MB, time=0.18 memory used=27.3MB, alloc=32.4MB, time=0.57 memory used=50.0MB, alloc=36.4MB, time=0.86 memory used=92.6MB, alloc=36.4MB, time=1.35 memory used=131.0MB, alloc=36.4MB, time=1.71 memory used=156.1MB, alloc=36.4MB, time=1.93 memory used=166.2MB, alloc=36.4MB, time=1.97 memory used=179.2MB, alloc=36.4MB, time=2.01 memory used=188.9MB, alloc=36.4MB, time=2.04 memory used=198.2MB, alloc=36.4MB, time=2.07 memory used=209.3MB, alloc=36.4MB, time=2.11 memory used=273.7MB, alloc=37.8MB, time=2.99 memory used=285.3MB, alloc=61.8MB, time=3.05 memory used=313.3MB, alloc=61.8MB, time=3.11 memory used=335.7MB, alloc=61.8MB, time=3.17 memory used=391.4MB, alloc=61.8MB, time=3.58 memory used=444.9MB, alloc=62.3MB, time=16.89 memory used=471.7MB, alloc=86.3MB, time=23.04 memory used=515.7MB, alloc=110.3MB, time=49.10 memory used=583.3MB, alloc=110.3MB, time=119.90 |\^/| 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(); 1428241728 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 3 4 F := [7 x y - 6 x y + 2 y z + 2 x y, -x y - 4 z + 17 x y z - 11, 4 4 3 3 16 x + 8 z + 4 x - 4 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 G := [3 y z - 9 x z - 3 y + 10 z , -14 x y z - 7 x z + 12 y z + 14 y, 3 2 2 2 -20 x y + 13 x y z - 3 x z + 11 z ] > Problem := [F,G]; 3 3 2 2 2 3 4 Problem := [[7 x y - 6 x y + 2 y z + 2 x y, -x y - 4 z + 17 x y z - 11, 4 4 3 3 3 2 2 16 x + 8 z + 4 x - 4 z ], [3 y z - 9 x z - 3 y + 10 z , 2 2 2 3 2 2 2 -14 x y z - 7 x z + 12 y z + 14 y, -20 x y + 13 x y z - 3 x z + 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=24.6MB, alloc=32.3MB, time=0.49 memory used=49.2MB, alloc=32.3MB, time=0.81 memory used=68.0MB, alloc=32.3MB, time=0.95 memory used=81.9MB, alloc=32.3MB, time=1.03 memory used=109.1MB, alloc=61.2MB, time=1.46 memory used=151.1MB, alloc=61.2MB, time=2.07 memory used=187.4MB, alloc=61.2MB, time=2.69 memory used=221.3MB, alloc=62.6MB, time=2.79 memory used=247.3MB, alloc=62.6MB, time=2.87 memory used=264.8MB, alloc=62.6MB, time=2.93 memory used=284.3MB, alloc=62.6MB, time=2.99 memory used=305.5MB, alloc=62.6MB, time=3.06 memory used=329.1MB, alloc=62.6MB, time=3.13 memory used=355.1MB, alloc=62.6MB, time=3.19 memory used=383.6MB, alloc=62.6MB, time=3.26 memory used=399.9MB, alloc=62.6MB, time=3.31 memory used=414.8MB, alloc=62.6MB, time=3.37 memory used=430.8MB, alloc=62.6MB, time=3.42 memory used=447.3MB, alloc=62.6MB, time=3.48 memory used=464.6MB, alloc=62.6MB, time=3.53 memory used=482.8MB, alloc=62.6MB, time=3.59 memory used=502.0MB, alloc=62.6MB, time=3.65 memory used=522.3MB, alloc=62.6MB, time=3.70 memory used=543.8MB, alloc=62.6MB, time=3.76 memory used=566.6MB, alloc=62.6MB, time=3.82 memory used=590.6MB, alloc=62.6MB, time=3.88 memory used=616.2MB, alloc=62.6MB, time=3.94 memory used=643.6MB, alloc=62.6MB, time=4.00 memory used=680.8MB, alloc=62.6MB, time=4.44 memory used=715.2MB, alloc=62.6MB, time=4.54 memory used=740.4MB, alloc=62.6MB, time=4.62 memory used=758.0MB, alloc=62.6MB, time=4.68 memory used=777.8MB, alloc=62.6MB, time=4.75 memory used=800.3MB, alloc=62.6MB, time=4.83 memory used=825.5MB, alloc=62.6MB, time=4.90 memory used=853.4MB, alloc=62.6MB, time=4.97 memory used=880.2MB, alloc=62.6MB, time=5.04 memory used=895.8MB, alloc=62.6MB, time=5.10 memory used=911.4MB, alloc=62.6MB, time=5.16 memory used=927.5MB, alloc=62.6MB, time=5.22 memory used=945.1MB, alloc=62.6MB, time=5.27 memory used=962.9MB, alloc=62.6MB, time=5.33 memory used=982.1MB, alloc=62.6MB, time=5.39 memory used=1001.8MB, alloc=62.6MB, time=5.45 memory used=1023.3MB, alloc=62.6MB, time=5.50 memory used=1045.4MB, alloc=62.6MB, time=5.56 memory used=1068.9MB, alloc=62.6MB, time=5.62 memory used=1093.9MB, alloc=62.6MB, time=5.68 memory used=1120.7MB, alloc=62.6MB, time=5.74 memory used=1152.8MB, alloc=62.6MB, time=5.84 memory used=1199.4MB, alloc=62.6MB, time=15.19 memory used=1248.6MB, alloc=62.6MB, time=18.49 memory used=1302.4MB, alloc=62.6MB, time=18.98 memory used=1331.3MB, alloc=62.6MB, time=19.08 memory used=1350.5MB, alloc=62.6MB, time=19.15 memory used=1373.8MB, alloc=62.6MB, time=19.22 memory used=1401.1MB, alloc=62.6MB, time=19.29 memory used=1419.6MB, alloc=62.6MB, time=19.36 memory used=1435.9MB, alloc=62.6MB, time=19.42 memory used=1452.7MB, alloc=62.6MB, time=19.48 memory used=1470.4MB, alloc=62.6MB, time=19.53 memory used=1489.7MB, alloc=62.6MB, time=19.59 memory used=1509.9MB, alloc=62.6MB, time=19.66 memory used=1531.9MB, alloc=62.6MB, time=19.72 memory used=1554.7MB, alloc=62.6MB, time=19.78 memory used=1579.4MB, alloc=62.6MB, time=19.85 memory used=1604.6MB, alloc=62.6MB, time=19.91 memory used=1631.9MB, alloc=62.6MB, time=19.98 memory used=1658.0MB, alloc=62.6MB, time=20.04 memory used=1673.6MB, alloc=86.6MB, time=20.11 memory used=1700.5MB, alloc=86.6MB, time=20.18 memory used=1729.2MB, alloc=86.6MB, time=20.25 memory used=1758.3MB, alloc=86.6MB, time=20.32 memory used=1789.1MB, alloc=86.6MB, time=20.39 memory used=1821.6MB, alloc=86.6MB, time=20.46 memory used=1855.7MB, alloc=86.6MB, time=20.54 memory used=1891.3MB, alloc=86.6MB, time=20.61 memory used=1928.1MB, alloc=86.6MB, time=20.70 memory used=1966.2MB, alloc=86.6MB, time=20.77 memory used=2006.6MB, alloc=86.6MB, time=20.85 memory used=2049.2MB, alloc=86.6MB, time=20.93 memory used=2093.4MB, alloc=86.6MB, time=21.02 memory used=2140.0MB, alloc=86.6MB, time=21.10 memory used=2188.1MB, alloc=86.6MB, time=21.17 memory used=2229.5MB, alloc=107.8MB, time=21.26 memory used=2241.9MB, alloc=107.8MB, time=21.31 memory used=2254.5MB, alloc=107.8MB, time=21.36 memory used=2267.6MB, alloc=107.8MB, time=21.42 memory used=2281.2MB, alloc=107.8MB, time=21.47 memory used=2295.1MB, alloc=107.8MB, time=21.54 memory used=2309.5MB, alloc=107.8MB, time=21.60 memory used=2326.9MB, alloc=107.8MB, time=21.90 memory used=2390.1MB, alloc=107.8MB, time=22.10 memory used=2424.2MB, alloc=107.8MB, time=22.22 memory used=2463.7MB, alloc=107.8MB, time=22.34 memory used=2511.2MB, alloc=107.8MB, time=22.45 memory used=2551.3MB, alloc=107.8MB, time=22.56 memory used=2581.1MB, alloc=107.8MB, time=22.65 memory used=2613.0MB, alloc=107.8MB, time=22.74 memory used=2647.7MB, alloc=107.8MB, time=22.82 memory used=2685.8MB, alloc=107.8MB, time=22.93 memory used=2727.7MB, alloc=107.8MB, time=23.03 memory used=2774.2MB, alloc=107.8MB, time=23.12 memory used=2834.5MB, alloc=107.8MB, time=24.23 memory used=2895.1MB, alloc=107.8MB, time=24.40 memory used=2937.9MB, alloc=107.8MB, time=24.54 memory used=2969.6MB, alloc=107.8MB, time=24.65 memory used=3006.5MB, alloc=107.8MB, time=24.77 memory used=3046.5MB, alloc=107.8MB, time=24.89 memory used=3089.5MB, alloc=107.8MB, time=25.02 memory used=3137.5MB, alloc=107.8MB, time=25.15 memory used=3184.9MB, alloc=107.8MB, time=25.27 memory used=3212.8MB, alloc=107.8MB, time=25.37 memory used=3239.2MB, alloc=107.8MB, time=25.46 memory used=3267.9MB, alloc=107.8MB, time=25.54 memory used=3297.1MB, alloc=107.8MB, time=25.64 memory used=3326.9MB, alloc=107.8MB, time=25.74 memory used=3357.2MB, alloc=107.8MB, time=25.84 memory used=3388.4MB, alloc=107.8MB, time=25.95 memory used=3422.7MB, alloc=107.8MB, time=26.05 memory used=3457.9MB, alloc=107.8MB, time=26.15 memory used=3493.5MB, alloc=107.8MB, time=26.26 memory used=3529.5MB, alloc=107.8MB, time=26.35 memory used=3566.6MB, alloc=107.8MB, time=26.45 memory used=3606.3MB, alloc=107.8MB, time=26.55 memory used=3647.0MB, alloc=107.8MB, time=26.67 memory used=3688.4MB, alloc=107.8MB, time=26.77 memory used=3732.8MB, alloc=107.8MB, time=26.88 memory used=3777.9MB, alloc=107.8MB, time=26.98 memory used=3826.7MB, alloc=107.8MB, time=27.09 memory used=3875.5MB, alloc=107.8MB, time=27.19 memory used=3921.6MB, alloc=107.8MB, time=27.29 memory used=3949.3MB, alloc=107.8MB, time=27.37 memory used=3973.0MB, alloc=107.8MB, time=27.44 memory used=3998.3MB, alloc=107.8MB, time=27.51 memory used=4023.6MB, alloc=107.8MB, time=27.58 memory used=4048.8MB, alloc=107.8MB, time=27.65 memory used=4073.8MB, alloc=107.8MB, time=27.72 memory used=4099.3MB, alloc=107.8MB, time=27.79 memory used=4126.9MB, alloc=107.8MB, time=27.87 memory used=4154.7MB, alloc=107.8MB, time=27.95 memory used=4182.4MB, alloc=107.8MB, time=28.02 memory used=4210.4MB, alloc=107.8MB, time=28.09 memory used=4240.1MB, alloc=107.8MB, time=28.17 memory used=4269.9MB, alloc=107.8MB, time=28.24 memory used=4300.1MB, alloc=107.8MB, time=28.31 memory used=4331.4MB, alloc=107.8MB, time=28.38 memory used=4363.5MB, alloc=107.8MB, time=28.46 memory used=4396.4MB, alloc=107.8MB, time=28.53 memory used=4430.0MB, alloc=107.8MB, time=28.60 memory used=4464.8MB, alloc=107.8MB, time=28.69 memory used=4500.7MB, alloc=107.8MB, time=28.77 memory used=4537.6MB, alloc=107.8MB, time=28.84 memory used=4576.6MB, alloc=107.8MB, time=28.92 memory used=4616.8MB, alloc=107.8MB, time=29.00 memory used=4658.9MB, alloc=107.8MB, time=29.07 memory used=4722.2MB, alloc=107.8MB, time=30.15 memory used=4777.3MB, alloc=107.8MB, time=30.31 memory used=4809.1MB, alloc=107.8MB, time=30.44 memory used=4843.1MB, alloc=107.8MB, time=30.55 memory used=4881.5MB, alloc=107.8MB, time=30.66 memory used=4922.8MB, alloc=107.8MB, time=30.79 memory used=4967.3MB, alloc=107.8MB, time=30.92 memory used=5016.3MB, alloc=107.8MB, time=31.05 memory used=5053.9MB, alloc=107.8MB, time=31.17 memory used=5079.6MB, alloc=107.8MB, time=31.27 memory used=5107.5MB, alloc=107.8MB, time=31.37 memory used=5136.4MB, alloc=107.8MB, time=31.48 memory used=5165.9MB, alloc=107.8MB, time=31.57 memory used=5195.9MB, alloc=107.8MB, time=31.68 memory used=5226.4MB, alloc=107.8MB, time=31.78 memory used=5257.8MB, alloc=107.8MB, time=31.89 memory used=5292.3MB, alloc=107.8MB, time=32.00 memory used=5327.7MB, alloc=107.8MB, time=32.10 memory used=5363.4MB, alloc=107.8MB, time=32.20 memory used=5399.7MB, alloc=107.8MB, time=32.31 memory used=5439.8MB, alloc=107.8MB, time=32.41 memory used=5480.3MB, alloc=107.8MB, time=32.53 memory used=5521.0MB, alloc=107.8MB, time=32.63 memory used=5562.8MB, alloc=107.8MB, time=32.74 memory used=5607.0MB, alloc=107.8MB, time=32.86 memory used=5652.2MB, alloc=107.8MB, time=32.96 memory used=5701.0MB, alloc=107.8MB, time=33.08 memory used=5749.8MB, alloc=107.8MB, time=33.19 memory used=5789.8MB, alloc=107.8MB, time=33.29 memory used=5815.3MB, alloc=107.8MB, time=33.36 memory used=5839.5MB, alloc=107.8MB, time=33.44 memory used=5864.8MB, alloc=107.8MB, time=33.51 memory used=5890.1MB, alloc=107.8MB, time=33.58 memory used=5915.1MB, alloc=107.8MB, time=33.65 memory used=5940.1MB, alloc=107.8MB, time=33.72 memory used=5965.6MB, alloc=107.8MB, time=33.79 memory used=5993.0MB, alloc=107.8MB, time=33.87 memory used=6020.8MB, alloc=107.8MB, time=33.94 memory used=6048.3MB, alloc=107.8MB, time=34.01 memory used=6076.3MB, alloc=107.8MB, time=34.09 memory used=6105.7MB, alloc=107.8MB, time=34.16 memory used=6135.4MB, alloc=107.8MB, time=34.23 memory used=6165.6MB, alloc=107.8MB, time=34.30 memory used=6196.5MB, alloc=107.8MB, time=34.39 memory used=6228.4MB, alloc=107.8MB, time=34.46 memory used=6261.1MB, alloc=107.8MB, time=34.53 memory used=6294.6MB, alloc=107.8MB, time=34.61 memory used=6330.6MB, alloc=107.8MB, time=34.69 memory used=6366.9MB, alloc=107.8MB, time=34.76 memory used=6405.0MB, alloc=107.8MB, time=34.84 memory used=6444.1MB, alloc=107.8MB, time=34.91 memory used=6484.6MB, alloc=107.8MB, time=34.99 memory used=6531.0MB, alloc=107.8MB, time=35.38 memory used=6609.3MB, alloc=107.8MB, time=66.37 memory used=6663.8MB, alloc=107.8MB, time=83.22 memory used=6758.7MB, alloc=107.8MB, time=84.11 memory used=6838.2MB, alloc=107.8MB, time=84.70 memory used=6873.9MB, alloc=107.8MB, time=84.83 memory used=6916.9MB, alloc=107.8MB, time=84.96 memory used=6958.0MB, alloc=107.8MB, time=85.08 memory used=6985.8MB, alloc=107.8MB, time=85.18 memory used=7016.9MB, alloc=107.8MB, time=85.29 memory used=7050.3MB, alloc=107.8MB, time=85.39 memory used=7085.7MB, alloc=107.8MB, time=85.50 memory used=7124.3MB, alloc=107.8MB, time=85.61 memory used=7165.1MB, alloc=107.8MB, time=85.72 memory used=7209.2MB, alloc=107.8MB, time=85.82 memory 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memory used=7943.3MB, alloc=107.8MB, time=87.63 memory used=7985.0MB, alloc=107.8MB, time=87.71 memory used=8028.8MB, alloc=107.8MB, time=87.80 memory used=8072.7MB, alloc=107.8MB, time=87.90 memory used=8118.1MB, alloc=107.8MB, time=88.01 memory used=8165.6MB, alloc=107.8MB, time=88.11 memory used=8216.5MB, alloc=107.8MB, time=88.20 memory used=8240.3MB, alloc=107.8MB, time=88.28 memory used=8250.4MB, alloc=107.8MB, time=88.33 memory used=8258.9MB, alloc=107.8MB, time=88.39 memory used=8266.7MB, alloc=107.8MB, time=88.46 memory used=8275.2MB, alloc=107.8MB, time=88.53 memory used=8283.6MB, alloc=107.8MB, time=88.58 memory used=8292.0MB, alloc=107.8MB, time=88.66 memory used=8300.4MB, alloc=107.8MB, time=88.73 memory used=8308.8MB, alloc=107.8MB, time=88.78 memory used=8317.1MB, alloc=107.8MB, time=88.85 memory used=8325.4MB, alloc=107.8MB, time=88.90 memory used=8333.7MB, alloc=107.8MB, time=88.95 memory used=8341.9MB, alloc=107.8MB, time=89.00 memory used=8350.4MB, alloc=107.8MB, time=89.09 memory used=8360.3MB, alloc=107.8MB, time=89.16 memory used=8368.8MB, alloc=107.8MB, time=89.22 memory used=8378.6MB, alloc=107.8MB, time=89.27 memory used=8388.7MB, alloc=107.8MB, time=89.32 memory used=8398.7MB, alloc=107.8MB, time=89.39 memory used=8408.6MB, alloc=107.8MB, time=89.47 memory used=8418.5MB, alloc=107.8MB, time=89.52 memory used=8428.4MB, alloc=107.8MB, time=89.58 memory used=8438.2MB, alloc=107.8MB, time=89.63 memory used=8447.9MB, alloc=107.8MB, time=89.70 memory used=8457.5MB, alloc=107.8MB, time=89.78 memory used=8467.1MB, alloc=107.8MB, time=89.83 memory used=8476.7MB, alloc=107.8MB, time=89.90 memory used=8486.4MB, alloc=107.8MB, time=89.95 memory used=8497.4MB, alloc=107.8MB, time=90.00 memory used=8508.6MB, alloc=107.8MB, time=90.06 memory used=8519.7MB, alloc=107.8MB, time=90.12 memory used=8530.7MB, alloc=107.8MB, time=90.19 memory used=8541.6MB, alloc=107.8MB, time=90.24 memory used=8552.3MB, alloc=107.8MB, time=90.29 memory used=8563.0MB, alloc=107.8MB, time=90.34 memory used=8573.6MB, alloc=107.8MB, time=90.39 memory used=8584.3MB, alloc=107.8MB, time=90.47 memory used=8596.1MB, alloc=107.8MB, time=90.52 memory used=8608.0MB, alloc=107.8MB, time=90.57 memory used=8619.8MB, alloc=107.8MB, time=90.64 memory used=8631.4MB, alloc=107.8MB, time=90.70 memory used=8642.8MB, alloc=107.8MB, time=90.75 memory used=8654.4MB, alloc=107.8MB, time=90.81 memory used=8666.8MB, alloc=107.8MB, time=90.87 memory used=8678.1MB, alloc=107.8MB, time=90.94 memory used=8690.2MB, alloc=107.8MB, time=91.03 memory used=8703.4MB, alloc=107.8MB, time=91.11 memory used=8716.5MB, alloc=107.8MB, time=91.18 memory used=8729.4MB, alloc=107.8MB, time=91.26 memory used=8742.3MB, alloc=107.8MB, time=91.31 memory used=8755.4MB, alloc=107.8MB, time=91.39 memory used=8768.8MB, alloc=107.8MB, time=91.45 memory used=8782.5MB, alloc=107.8MB, time=91.54 memory used=8796.4MB, alloc=107.8MB, time=91.60 memory used=8811.2MB, alloc=107.8MB, time=91.65 memory 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memory used=9775.2MB, alloc=131.8MB, time=99.96 memory used=9813.1MB, alloc=131.8MB, time=100.09 memory used=9855.3MB, alloc=131.8MB, time=100.23 memory used=9901.9MB, alloc=131.8MB, time=100.37 memory used=9952.9MB, alloc=131.8MB, time=100.51 memory used=10010.2MB, alloc=131.8MB, time=100.65 memory used=10053.3MB, alloc=131.8MB, time=100.77 memory used=10087.0MB, alloc=131.8MB, time=100.87 memory used=10147.4MB, alloc=131.8MB, time=101.31 memory used=10193.4MB, alloc=131.8MB, time=101.49 memory used=10241.7MB, alloc=131.8MB, time=101.64 memory used=10295.9MB, alloc=131.8MB, time=101.81 memory used=10329.4MB, alloc=131.8MB, time=101.93 memory used=10366.6MB, alloc=131.8MB, time=102.05 memory used=10408.5MB, alloc=131.8MB, time=102.19 memory used=10455.1MB, alloc=131.8MB, time=102.33 memory used=10506.0MB, alloc=131.8MB, time=102.47 memory used=10563.1MB, alloc=131.8MB, time=102.61 memory used=10604.5MB, alloc=131.8MB, time=102.71 memory used=10638.0MB, alloc=131.8MB, time=102.82 memory 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used=12006.9MB, alloc=131.8MB, time=124.53 memory used=12019.4MB, alloc=131.8MB, time=124.63 memory used=12032.7MB, alloc=131.8MB, time=124.72 memory used=12045.9MB, alloc=131.8MB, time=124.81 memory used=12059.5MB, alloc=131.8MB, time=124.92 memory used=12073.7MB, alloc=131.8MB, time=125.03 memory used=12109.9MB, alloc=131.8MB, time=126.31 memory used=12175.8MB, alloc=131.8MB, time=126.54 memory used=12213.2MB, alloc=131.8MB, time=126.69 memory used=12254.1MB, alloc=131.8MB, time=126.85 memory used=12301.7MB, alloc=131.8MB, time=127.01 memory used=12356.7MB, alloc=131.8MB, time=127.18 memory used=12408.3MB, alloc=131.8MB, time=127.34 memory used=12438.3MB, alloc=131.8MB, time=127.47 memory used=12470.4MB, alloc=131.8MB, time=127.62 memory used=12504.7MB, alloc=131.8MB, time=127.75 memory used=12540.0MB, alloc=131.8MB, time=127.89 memory used=12576.3MB, alloc=131.8MB, time=128.03 memory used=12613.5MB, alloc=131.8MB, time=128.16 memory used=12652.1MB, alloc=131.8MB, time=128.29 memory used=12694.3MB, alloc=131.8MB, time=128.44 memory used=12737.8MB, alloc=131.8MB, time=128.58 memory used=12782.3MB, alloc=131.8MB, time=128.73 memory used=12831.5MB, alloc=131.8MB, time=128.87 memory used=12881.5MB, alloc=131.8MB, time=129.01 memory used=12932.2MB, alloc=131.8MB, time=129.16 memory used=12987.8MB, alloc=131.8MB, time=129.29 memory used=13043.9MB, alloc=131.8MB, time=129.44 memory used=13088.3MB, alloc=131.8MB, time=129.57 memory used=13116.1MB, alloc=131.8MB, time=129.67 memory used=13144.9MB, alloc=155.8MB, time=129.80 memory used=13184.8MB, alloc=155.8MB, time=129.93 memory used=13227.4MB, alloc=155.8MB, time=130.06 memory used=13270.8MB, alloc=155.8MB, time=130.18 memory used=13314.8MB, alloc=155.8MB, time=130.31 memory used=13361.9MB, alloc=155.8MB, time=130.44 memory used=13409.2MB, alloc=155.8MB, time=130.57 memory used=13457.3MB, alloc=155.8MB, time=130.70 memory used=13507.4MB, alloc=155.8MB, time=130.83 memory used=13558.7MB, alloc=155.8MB, time=130.96 memory used=13612.0MB, alloc=155.8MB, time=131.10 memory used=13669.3MB, alloc=155.8MB, time=131.23 memory used=13726.3MB, alloc=155.8MB, time=131.36 memory used=13785.4MB, alloc=155.8MB, time=131.49 memory used=13846.8MB, alloc=155.8MB, time=131.62 memory used=13911.7MB, alloc=155.8MB, time=131.75 memory used=13978.6MB, alloc=155.8MB, time=131.89 memory used=14048.9MB, alloc=155.8MB, time=132.03 memory used=14123.1MB, alloc=155.8MB, time=132.17 memory used=14202.4MB, alloc=155.8MB, time=132.31 memory used=14302.9MB, alloc=155.8MB, time=133.67 memory used=14361.7MB, alloc=155.8MB, time=133.88 memory used=14425.0MB, alloc=155.8MB, time=134.09 memory used=14500.3MB, alloc=155.8MB, time=134.30 memory used=14564.3MB, alloc=155.8MB, time=134.50 memory used=14608.7MB, alloc=155.8MB, time=134.67 memory used=14657.3MB, alloc=155.8MB, time=134.83 memory used=14708.0MB, alloc=155.8MB, time=134.99 memory used=14764.2MB, alloc=155.8MB, time=135.18 memory used=14822.4MB, alloc=155.8MB, time=135.36 memory used=14886.2MB, alloc=155.8MB, time=135.53 memory used=14951.9MB, alloc=155.8MB, time=135.70 memory used=15023.2MB, alloc=155.8MB, time=135.88 memory used=15096.6MB, alloc=155.8MB, time=136.06 memory used=15174.5MB, alloc=155.8MB, time=136.24 memory used=15237.8MB, alloc=155.8MB, time=136.40 memory used=15277.7MB, alloc=155.8MB, time=136.53 memory used=15320.8MB, alloc=155.8MB, time=136.66 memory used=15364.2MB, alloc=155.8MB, time=136.79 memory used=15407.7MB, alloc=155.8MB, time=136.92 memory used=15451.6MB, alloc=155.8MB, time=137.05 memory used=15498.6MB, alloc=155.8MB, time=137.18 memory used=15546.1MB, alloc=155.8MB, time=137.31 memory used=15594.2MB, alloc=155.8MB, time=137.44 memory used=15644.4MB, alloc=155.8MB, time=137.57 memory used=15695.7MB, alloc=155.8MB, time=137.70 memory used=15749.2MB, alloc=155.8MB, time=137.84 memory used=15806.6MB, alloc=155.8MB, time=137.97 memory used=15863.7MB, alloc=155.8MB, time=138.11 memory used=15923.0MB, alloc=155.8MB, time=138.26 memory used=15986.9MB, alloc=155.8MB, time=138.40 memory used=16053.2MB, alloc=155.8MB, time=138.54 memory used=16120.7MB, alloc=155.8MB, time=138.69 memory used=16192.8MB, alloc=155.8MB, time=138.83 memory used=16268.9MB, alloc=155.8MB, time=138.98 memory used=16348.7MB, alloc=155.8MB, time=139.11 |\^/| 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(); 1428242028 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [-15 x z - 13 y - 2 x - 14 z, -x y + 15 x y z - 2 x z - 9 x z, 2 2 2 2 16 x y z + 15 x y + 19 y + 14 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 G := [-9 x z - 5 x - 11 x z, -10 x y z - 17 x y z + 17 y z + 16 y , 2 2 11 x z + 15 y + 8] > Problem := [F,G]; 2 2 3 2 2 Problem := [[-15 x z - 13 y - 2 x - 14 z, -x y + 15 x y z - 2 x z - 9 x z, 2 2 2 2 3 3 16 x y z + 15 x y + 19 y + 14 z ], [-9 x z - 5 x - 11 x z, 2 2 2 2 2 2 -10 x y z - 17 x y z + 17 y z + 16 y , 11 x z + 15 y + 8]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=47.0MB, alloc=32.3MB, time=0.82 memory used=64.3MB, alloc=60.3MB, time=1.10 memory used=105.7MB, alloc=68.3MB, time=1.74 memory used=146.4MB, alloc=92.3MB, time=2.36 memory used=209.4MB, alloc=92.3MB, time=3.35 memory used=277.6MB, alloc=92.3MB, time=4.31 memory used=342.9MB, alloc=116.3MB, time=5.12 memory used=409.5MB, alloc=372.3MB, time=6.15 memory used=495.5MB, alloc=372.3MB, time=7.13 memory used=587.3MB, alloc=372.3MB, time=8.41 memory used=677.2MB, alloc=396.3MB, time=9.73 memory used=778.7MB, alloc=396.3MB, time=10.82 memory used=887.5MB, alloc=396.3MB, time=12.04 memory used=987.7MB, alloc=420.3MB, time=13.29 memory used=1102.5MB, alloc=420.3MB, time=14.37 memory used=1198.6MB, alloc=420.3MB, time=15.22 memory used=1327.9MB, alloc=420.3MB, time=17.03 memory used=1458.3MB, alloc=444.3MB, time=19.09 memory used=1581.4MB, alloc=468.3MB, time=21.24 memory used=1705.7MB, alloc=468.3MB, time=23.49 memory used=1824.3MB, alloc=492.3MB, time=25.55 memory used=1948.2MB, alloc=492.3MB, time=28.08 memory used=2051.5MB, alloc=492.3MB, time=30.21 memory used=2152.8MB, alloc=492.3MB, time=32.13 memory used=2242.3MB, alloc=492.3MB, time=33.73 memory used=2336.2MB, alloc=516.3MB, time=35.01 memory used=2422.0MB, alloc=516.3MB, time=36.43 memory used=2502.0MB, alloc=516.3MB, time=37.72 memory used=2567.5MB, alloc=516.3MB, time=38.77 memory used=2660.6MB, alloc=516.3MB, time=40.01 memory used=2734.6MB, alloc=516.3MB, time=41.56 memory used=2796.8MB, alloc=516.3MB, time=42.74 memory used=2865.3MB, alloc=516.3MB, time=43.86 memory used=2925.8MB, alloc=540.3MB, time=44.91 memory used=2982.3MB, alloc=540.3MB, time=46.25 memory used=3032.4MB, alloc=540.3MB, time=47.37 memory used=3082.2MB, alloc=540.3MB, time=48.48 memory used=3121.8MB, alloc=540.3MB, time=49.43 memory used=3351.5MB, alloc=540.3MB, time=52.76 memory used=3576.0MB, alloc=564.3MB, time=56.21 memory used=3757.0MB, alloc=588.3MB, time=59.03 memory used=3937.6MB, alloc=588.3MB, time=62.34 memory used=4120.3MB, alloc=612.3MB, time=65.68 memory used=4306.5MB, alloc=612.3MB, time=68.91 memory used=4457.7MB, alloc=612.3MB, time=71.49 memory used=4625.1MB, alloc=612.3MB, time=74.70 memory used=4794.4MB, alloc=636.3MB, time=77.57 memory used=4985.4MB, alloc=636.3MB, time=80.12 memory used=5154.0MB, alloc=636.3MB, time=82.70 memory used=5306.8MB, alloc=636.3MB, time=84.98 memory used=5513.6MB, alloc=636.3MB, time=87.35 memory used=5647.6MB, alloc=636.3MB, time=90.00 memory used=5809.7MB, alloc=636.3MB, time=92.79 memory used=5922.1MB, alloc=636.3MB, time=95.12 memory used=6030.4MB, alloc=636.3MB, time=97.20 memory used=6160.4MB, alloc=660.3MB, time=100.03 memory used=6266.1MB, alloc=660.3MB, time=102.54 memory used=6370.5MB, alloc=660.3MB, time=105.12 memory used=6468.7MB, alloc=660.3MB, time=107.10 memory used=6697.7MB, alloc=660.3MB, time=109.79 memory used=6891.1MB, alloc=660.3MB, time=111.71 memory used=7184.3MB, alloc=684.3MB, time=115.67 |\^/| 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(); 1428242328 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 F := [-17 x y + 5 x - 6 y z - 9, -6 x y + 14 z - 19 x y + 14 y z, 3 2 2 3 x z + 13 x z - 2 y z + 3 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 2 G := [-17 x y + 13 x z + 18 z + 8 z, -7 x z - 4 y z + 3 x + 14 y, 2 4 2 6 x y z - 8 y - 17 y z + 9 y z] > Problem := [F,G]; 3 3 2 3 Problem := [[-17 x y + 5 x - 6 y z - 9, -6 x y + 14 z - 19 x y + 14 y z, 3 2 2 3 2 2 3 x z + 13 x z - 2 y z + 3 x z], [-17 x y + 13 x z + 18 z + 8 z, 3 3 2 2 4 2 -7 x z - 4 y z + 3 x + 14 y, 6 x y z - 8 y - 17 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=3.8MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.51 memory used=46.1MB, alloc=56.3MB, time=0.83 memory used=88.3MB, alloc=60.3MB, time=1.46 memory used=128.6MB, alloc=60.3MB, time=1.84 memory used=162.8MB, alloc=60.3MB, time=2.22 memory used=209.9MB, alloc=68.3MB, time=2.97 memory used=246.9MB, alloc=92.3MB, time=3.36 memory used=313.6MB, alloc=92.3MB, time=4.35 memory used=377.5MB, alloc=116.3MB, time=5.30 memory used=439.5MB, alloc=116.3MB, time=6.17 memory used=499.7MB, alloc=372.3MB, time=7.00 memory used=594.7MB, alloc=396.3MB, time=8.18 memory used=701.1MB, alloc=396.3MB, time=9.22 memory used=782.9MB, alloc=396.3MB, time=9.76 memory used=884.6MB, alloc=396.3MB, time=10.77 memory used=1020.0MB, alloc=396.3MB, time=12.40 memory used=1144.8MB, alloc=420.3MB, time=14.04 memory used=1252.4MB, alloc=420.3MB, time=15.59 memory used=1376.3MB, alloc=420.3MB, time=16.96 memory used=1490.4MB, alloc=444.3MB, time=18.34 memory used=1585.6MB, alloc=444.3MB, time=19.74 memory used=1686.8MB, alloc=468.3MB, time=21.29 memory used=1783.1MB, alloc=468.3MB, time=22.94 memory used=1869.1MB, alloc=468.3MB, time=24.31 memory used=1960.8MB, alloc=468.3MB, time=25.74 memory used=2055.9MB, alloc=468.3MB, time=27.20 memory used=2151.5MB, alloc=468.3MB, time=27.84 memory used=2248.7MB, alloc=468.3MB, time=28.53 memory used=2361.3MB, alloc=468.3MB, time=29.77 memory used=2465.5MB, alloc=468.3MB, time=31.32 memory used=2547.5MB, alloc=468.3MB, time=33.85 memory used=2651.4MB, alloc=492.3MB, time=36.02 memory used=2734.0MB, alloc=492.3MB, time=38.30 memory used=2799.4MB, alloc=492.3MB, time=39.43 memory used=2858.6MB, alloc=492.3MB, time=40.47 memory used=2914.1MB, alloc=492.3MB, time=41.54 memory used=2976.1MB, alloc=492.3MB, time=42.76 memory used=3031.8MB, alloc=492.3MB, time=43.82 memory used=3089.9MB, alloc=492.3MB, time=44.89 memory used=3152.7MB, alloc=492.3MB, time=45.79 memory used=3233.1MB, alloc=492.3MB, time=46.50 memory used=3337.2MB, alloc=492.3MB, time=48.03 memory used=3428.2MB, alloc=492.3MB, time=48.60 memory used=3530.5MB, alloc=492.3MB, time=49.34 memory used=3632.3MB, alloc=492.3MB, time=50.02 memory used=3715.7MB, alloc=492.3MB, time=50.88 memory used=3930.4MB, alloc=516.3MB, time=53.87 memory used=4069.9MB, alloc=516.3MB, time=55.18 memory used=4174.0MB, alloc=516.3MB, time=55.88 memory used=4397.9MB, alloc=548.3MB, time=58.32 memory used=4560.6MB, alloc=548.3MB, time=59.53 memory used=4690.2MB, alloc=548.3MB, time=60.46 memory used=4842.6MB, alloc=548.3MB, time=61.63 memory used=4981.1MB, alloc=548.3MB, time=63.32 memory used=5101.5MB, alloc=548.3MB, time=63.98 memory used=5215.4MB, alloc=548.3MB, time=64.59 memory used=5348.9MB, alloc=548.3MB, time=65.48 memory used=5583.7MB, alloc=548.3MB, time=67.99 memory used=5776.3MB, alloc=548.3MB, time=70.66 memory used=5935.8MB, alloc=572.3MB, time=73.41 memory used=6078.4MB, alloc=572.3MB, time=74.60 memory used=6221.0MB, alloc=572.3MB, time=75.74 memory used=6374.0MB, alloc=572.3MB, time=77.43 memory used=6494.1MB, alloc=572.3MB, time=78.11 memory used=6623.2MB, alloc=572.3MB, time=79.11 memory used=6736.6MB, alloc=572.3MB, time=79.80 memory used=6876.4MB, alloc=572.3MB, time=80.86 memory used=7112.6MB, alloc=572.3MB, time=83.32 memory used=7225.5MB, alloc=572.3MB, time=84.06 memory used=7355.1MB, alloc=572.3MB, time=84.96 memory used=7516.3MB, alloc=572.3MB, time=86.50 memory used=7629.4MB, alloc=572.3MB, time=87.23 memory used=7757.6MB, alloc=572.3MB, time=88.17 memory used=7985.8MB, alloc=572.3MB, time=90.69 memory used=8186.3MB, alloc=596.3MB, time=93.33 memory used=8357.8MB, alloc=596.3MB, time=95.49 memory used=8527.0MB, alloc=596.3MB, time=97.97 memory used=8688.6MB, alloc=620.3MB, time=101.19 memory used=8820.2MB, alloc=620.3MB, time=103.95 memory used=8970.4MB, alloc=644.3MB, time=107.02 memory used=9077.5MB, alloc=644.3MB, time=109.10 memory used=9180.5MB, alloc=668.3MB, time=110.95 memory used=9301.0MB, alloc=668.3MB, time=113.61 memory used=9390.8MB, alloc=668.3MB, time=115.55 memory used=9479.3MB, alloc=668.3MB, time=117.45 memory used=9826.8MB, alloc=692.3MB, time=121.84 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428242628 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 2 F := [9 x y z - 13 x z - 4 z + 13 z, 19 x z - 6 x y z + 18 y z + 14 x z , 3 2 2 7 x y - 2 y z + 7 y z + 15] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 2 G := [10 x y z + 15 y z - 3 z - 18 z , -15 x y z + 3 x z + y z - 6 x, 2 2 3 2 5 x y z - 8 x y z - 8 x z - y z ] > Problem := [F,G]; 2 2 2 Problem := [[9 x y z - 13 x z - 4 z + 13 z, 3 2 3 2 3 2 2 19 x z - 6 x y z + 18 y z + 14 x z , 7 x y - 2 y z + 7 y z + 15], [ 2 3 3 2 2 2 10 x y z + 15 y z - 3 z - 18 z , -15 x y z + 3 x z + y z - 6 x, 2 2 3 2 5 x y z - 8 x y z - 8 x z - y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.18 memory used=25.7MB, alloc=32.3MB, time=0.50 memory used=44.4MB, alloc=56.3MB, time=0.78 memory used=79.8MB, alloc=60.3MB, time=1.28 memory used=123.7MB, alloc=68.3MB, time=1.89 memory used=165.2MB, alloc=92.3MB, time=2.48 memory used=231.6MB, alloc=92.3MB, time=3.40 memory used=297.0MB, alloc=92.3MB, time=4.15 memory used=332.7MB, alloc=92.3MB, time=4.31 memory used=380.7MB, alloc=92.3MB, time=4.71 memory used=421.0MB, alloc=92.3MB, time=5.12 memory used=501.2MB, alloc=93.5MB, time=6.22 memory used=565.5MB, alloc=117.5MB, time=7.17 memory used=635.2MB, alloc=373.5MB, time=8.12 memory used=723.3MB, alloc=397.5MB, time=9.31 memory used=822.9MB, alloc=397.5MB, time=10.26 memory used=904.9MB, alloc=397.5MB, time=10.98 memory used=952.1MB, alloc=397.5MB, time=11.17 memory used=1004.2MB, alloc=397.5MB, time=11.34 memory used=1052.4MB, alloc=397.5MB, time=11.51 memory used=1156.4MB, alloc=397.5MB, time=12.55 memory used=1232.0MB, alloc=397.5MB, time=13.05 memory used=1286.0MB, alloc=397.5MB, time=13.27 memory used=1357.9MB, alloc=397.5MB, time=13.83 memory used=1404.8MB, alloc=397.5MB, time=14.02 memory used=1458.2MB, alloc=397.5MB, time=14.23 memory used=1500.6MB, alloc=397.5MB, time=14.38 memory used=1541.2MB, alloc=397.5MB, time=14.57 memory used=1609.9MB, alloc=397.5MB, time=14.97 memory used=1657.7MB, alloc=397.5MB, time=15.16 memory used=1706.4MB, alloc=397.5MB, time=15.34 memory used=1755.1MB, alloc=397.5MB, time=15.51 memory used=1793.9MB, alloc=397.5MB, time=15.67 memory used=1851.7MB, alloc=397.5MB, time=16.10 memory used=1911.9MB, alloc=397.5MB, time=16.42 memory used=1957.9MB, alloc=397.5MB, time=16.59 memory used=2008.5MB, alloc=397.5MB, time=16.77 memory used=2046.1MB, alloc=397.5MB, time=16.92 memory used=2110.0MB, alloc=397.5MB, time=17.34 memory used=2223.2MB, alloc=421.5MB, time=18.88 memory used=2335.8MB, alloc=445.5MB, time=20.51 memory used=2441.7MB, alloc=445.5MB, time=22.21 memory used=2554.3MB, alloc=445.5MB, time=23.87 memory used=2648.6MB, alloc=469.5MB, time=25.36 memory used=2748.1MB, alloc=469.5MB, time=27.06 memory used=2846.3MB, alloc=469.5MB, time=28.36 memory used=2960.4MB, alloc=469.5MB, time=29.39 memory used=3095.8MB, alloc=469.5MB, time=32.70 memory used=3171.2MB, alloc=469.5MB, time=33.04 memory used=3257.0MB, alloc=469.5MB, time=33.42 memory used=3389.1MB, alloc=469.5MB, time=36.80 memory used=3462.4MB, alloc=469.5MB, time=37.17 memory used=3585.5MB, alloc=469.5MB, time=38.38 memory used=3703.4MB, alloc=469.5MB, time=40.14 memory used=3790.9MB, alloc=469.5MB, time=41.41 memory used=3908.6MB, alloc=469.5MB, time=42.84 memory used=4010.5MB, alloc=469.5MB, time=43.57 memory used=4131.2MB, alloc=493.5MB, time=45.13 memory used=4199.4MB, alloc=493.5MB, time=46.29 memory used=4270.7MB, alloc=493.5MB, time=47.57 memory used=4340.5MB, alloc=493.5MB, time=48.82 memory used=4401.8MB, alloc=493.5MB, time=49.89 memory used=4474.0MB, alloc=493.5MB, time=51.32 memory used=4525.5MB, alloc=493.5MB, time=52.42 memory used=4596.9MB, alloc=493.5MB, time=53.91 memory used=4647.5MB, alloc=493.5MB, time=54.93 memory used=4719.0MB, alloc=493.5MB, time=56.58 memory used=4763.7MB, alloc=493.5MB, time=57.56 memory used=4831.0MB, alloc=493.5MB, time=59.10 memory used=5021.3MB, alloc=517.5MB, time=61.84 memory used=5152.4MB, alloc=517.5MB, time=62.98 memory used=5255.6MB, alloc=517.5MB, time=63.65 memory used=5362.7MB, alloc=517.5MB, time=64.39 memory used=5477.1MB, alloc=517.5MB, time=65.17 memory used=5575.9MB, alloc=517.5MB, time=66.03 memory used=5704.0MB, alloc=517.5MB, time=66.80 memory used=5845.1MB, alloc=541.5MB, time=86.78 memory used=6000.6MB, alloc=541.5MB, time=89.05 memory used=6107.7MB, alloc=541.5MB, time=89.63 memory used=6205.8MB, alloc=541.5MB, time=90.18 memory used=6326.3MB, alloc=541.5MB, time=90.77 memory used=6442.5MB, alloc=541.5MB, time=91.32 memory used=6522.4MB, alloc=541.5MB, time=91.87 memory used=6607.9MB, alloc=541.5MB, time=92.38 memory used=6701.9MB, alloc=541.5MB, time=92.87 memory used=6804.0MB, alloc=541.5MB, time=93.38 memory used=6915.0MB, alloc=541.5MB, time=93.89 memory used=7036.5MB, alloc=541.5MB, time=94.39 memory used=7210.5MB, alloc=541.5MB, time=95.01 memory used=7374.2MB, alloc=541.5MB, time=95.71 memory used=7549.1MB, alloc=541.5MB, time=96.56 memory used=7766.3MB, alloc=541.5MB, time=118.94 memory used=7882.1MB, alloc=541.5MB, time=119.56 memory used=7971.1MB, alloc=541.5MB, time=120.14 memory used=8079.3MB, alloc=541.5MB, time=120.73 memory used=8207.3MB, alloc=541.5MB, time=121.29 memory used=8297.5MB, alloc=541.5MB, time=121.79 memory used=8378.8MB, alloc=541.5MB, time=122.29 memory used=8468.5MB, alloc=541.5MB, time=122.80 memory used=8564.9MB, alloc=541.5MB, time=123.32 memory used=8670.8MB, alloc=541.5MB, time=123.86 memory used=8786.6MB, alloc=541.5MB, time=124.38 memory used=8927.0MB, alloc=541.5MB, time=124.93 memory used=9160.4MB, alloc=541.5MB, time=125.61 memory used=9469.8MB, alloc=541.5MB, time=128.83 memory used=9658.7MB, alloc=541.5MB, time=131.97 memory used=9749.0MB, alloc=541.5MB, time=132.56 memory used=9862.4MB, alloc=541.5MB, time=133.18 memory used=9944.8MB, alloc=541.5MB, time=133.68 memory used=10037.0MB, alloc=541.5MB, time=134.17 memory used=10242.5MB, alloc=565.5MB, time=136.98 memory used=10370.9MB, alloc=565.5MB, time=137.75 memory used=10558.8MB, alloc=565.5MB, time=148.17 memory used=10708.9MB, alloc=565.5MB, time=149.16 memory used=10819.9MB, alloc=565.5MB, time=149.81 memory used=10939.3MB, alloc=565.5MB, time=150.45 memory used=11026.8MB, alloc=565.5MB, time=151.03 memory used=11125.5MB, alloc=565.5MB, time=151.62 memory used=11238.0MB, alloc=565.5MB, time=152.25 memory used=11363.8MB, alloc=565.5MB, time=152.82 |\^/| 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(); 1428242928 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 4 3 F := [7 x z - 18 y z + 10 z , -x - 3 y z - x y, 2 2 2 -20 x z - 3 x y z - 10 x y z - x y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 3 3 2 G := [-8 x y z - 12 y z + y - 10 x, -17 y z - 17 x - 14 y + 8 y z , 2 2 -5 x y z - 7 x y - 2 x y z - 4] > Problem := [F,G]; 2 2 3 2 4 3 Problem := [[7 x z - 18 y z + 10 z , -x - 3 y z - x y, 2 2 2 2 2 2 3 -20 x z - 3 x y z - 10 x y z - x y], [-8 x y z - 12 y z + y - 10 x, 3 3 3 2 2 2 -17 y z - 17 x - 14 y + 8 y z , -5 x y z - 7 x y - 2 x y z - 4]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=23.5MB, alloc=32.3MB, time=0.45 memory used=41.4MB, alloc=56.3MB, time=0.72 memory used=77.8MB, alloc=60.3MB, time=1.01 memory used=110.8MB, alloc=60.3MB, time=1.24 memory used=148.2MB, alloc=60.3MB, time=1.77 memory used=199.1MB, alloc=68.3MB, time=2.40 memory used=239.3MB, alloc=68.3MB, time=2.76 memory used=278.4MB, alloc=68.3MB, time=3.18 memory used=323.6MB, alloc=68.3MB, time=3.72 memory used=368.8MB, alloc=68.3MB, time=4.27 memory used=398.1MB, alloc=68.3MB, time=4.43 memory used=424.7MB, alloc=92.3MB, time=4.87 memory used=467.8MB, alloc=92.3MB, time=5.04 memory used=513.5MB, alloc=92.3MB, time=5.50 memory used=558.6MB, alloc=92.3MB, time=5.81 memory used=611.5MB, alloc=92.3MB, time=6.22 memory used=679.7MB, alloc=92.3MB, time=6.89 memory used=727.1MB, alloc=92.3MB, time=7.21 memory used=759.8MB, alloc=92.3MB, time=7.32 memory used=792.5MB, alloc=92.3MB, time=7.43 memory used=825.0MB, alloc=92.3MB, time=7.53 memory used=856.0MB, alloc=92.3MB, time=7.62 memory used=898.6MB, alloc=92.3MB, time=8.01 memory used=932.5MB, alloc=92.3MB, time=8.13 memory used=965.5MB, alloc=92.3MB, time=8.25 memory used=997.4MB, alloc=92.3MB, time=8.36 memory used=1030.5MB, alloc=92.3MB, time=8.46 memory used=1079.4MB, alloc=92.3MB, time=10.91 memory used=1119.3MB, alloc=92.3MB, time=11.04 memory used=1150.5MB, alloc=92.3MB, time=11.16 memory used=1182.6MB, alloc=92.3MB, time=11.24 memory used=1214.8MB, alloc=92.3MB, time=11.33 memory used=1244.9MB, alloc=92.3MB, time=11.42 memory used=1285.4MB, alloc=107.8MB, time=11.52 memory used=1335.1MB, alloc=107.8MB, time=12.25 memory used=1368.1MB, alloc=107.8MB, time=12.36 memory used=1399.1MB, alloc=107.8MB, time=12.45 memory used=1460.2MB, alloc=107.8MB, time=13.12 memory used=1494.8MB, alloc=107.8MB, time=13.24 memory used=1528.2MB, alloc=107.8MB, time=13.36 memory used=1558.4MB, alloc=107.8MB, time=13.47 memory used=1591.7MB, alloc=107.8MB, time=13.58 memory used=1618.8MB, alloc=107.8MB, time=13.67 memory used=1650.2MB, alloc=107.8MB, time=13.77 memory used=1685.0MB, alloc=107.8MB, time=13.87 memory used=1711.9MB, alloc=107.8MB, time=13.95 memory used=1737.0MB, alloc=107.8MB, time=14.04 memory used=1763.2MB, alloc=107.8MB, time=14.14 memory used=1799.8MB, alloc=107.8MB, time=14.37 memory used=1844.7MB, alloc=107.8MB, time=14.57 memory used=1879.5MB, alloc=107.8MB, time=14.67 memory used=1925.7MB, alloc=107.8MB, time=19.13 memory used=1975.3MB, alloc=107.8MB, time=34.88 memory used=2013.8MB, alloc=107.8MB, time=35.41 memory used=2049.2MB, alloc=107.8MB, time=35.52 memory used=2076.1MB, alloc=107.8MB, time=35.62 memory used=2106.0MB, alloc=107.8MB, time=35.72 memory used=2138.2MB, alloc=107.8MB, time=35.81 memory used=2172.3MB, alloc=107.8MB, time=35.92 memory used=2208.9MB, alloc=107.8MB, time=36.01 memory used=2233.8MB, alloc=107.8MB, time=36.10 memory used=2258.0MB, alloc=107.8MB, time=36.18 memory used=2283.0MB, alloc=107.8MB, time=36.28 memory used=2309.9MB, alloc=107.8MB, time=36.38 memory used=2338.7MB, alloc=107.8MB, time=36.50 memory used=2369.4MB, alloc=107.8MB, time=36.59 memory used=2403.5MB, alloc=107.8MB, time=36.69 memory used=2444.1MB, alloc=107.8MB, time=36.80 memory used=2484.9MB, alloc=107.8MB, time=36.90 memory used=2525.2MB, alloc=107.8MB, time=37.00 memory used=2564.8MB, alloc=107.8MB, time=37.10 memory used=2604.4MB, alloc=107.8MB, time=37.19 memory used=2640.1MB, alloc=107.8MB, time=37.27 memory used=2652.9MB, alloc=107.8MB, time=37.36 memory used=2664.8MB, alloc=107.8MB, time=37.45 memory used=2676.4MB, alloc=107.8MB, time=37.52 memory used=2688.4MB, alloc=107.8MB, time=37.60 memory used=2700.6MB, alloc=107.8MB, time=37.68 memory used=2713.6MB, alloc=107.8MB, time=37.75 memory used=2726.7MB, alloc=107.8MB, time=37.82 memory used=2740.2MB, alloc=107.8MB, time=37.88 memory used=2754.2MB, alloc=107.8MB, time=37.96 memory used=2769.0MB, alloc=107.8MB, time=38.02 memory used=2784.6MB, alloc=107.8MB, time=38.10 memory used=2801.1MB, alloc=107.8MB, time=38.21 memory used=2819.1MB, alloc=107.8MB, time=38.30 memory used=2877.3MB, alloc=107.8MB, time=40.14 memory used=2908.9MB, alloc=107.8MB, time=40.25 memory used=2940.9MB, alloc=107.8MB, time=40.34 memory used=2975.0MB, alloc=107.8MB, time=40.43 memory used=3003.0MB, alloc=107.8MB, time=40.50 memory used=3033.9MB, alloc=107.8MB, time=40.58 memory used=3071.2MB, alloc=107.8MB, time=40.71 memory used=3131.0MB, alloc=107.8MB, time=41.41 memory used=3216.8MB, alloc=107.8MB, time=44.17 memory used=3249.2MB, alloc=107.8MB, time=44.29 memory used=3291.5MB, alloc=131.8MB, time=50.48 memory used=3351.7MB, alloc=131.8MB, time=72.92 memory used=3403.0MB, alloc=131.8MB, time=73.15 memory used=3450.2MB, alloc=131.8MB, time=73.29 memory used=3487.1MB, alloc=131.8MB, time=73.42 memory used=3527.1MB, alloc=131.8MB, time=73.55 memory used=3572.3MB, alloc=131.8MB, time=73.70 memory used=3619.9MB, alloc=131.8MB, time=73.84 memory used=3669.8MB, alloc=131.8MB, time=73.98 memory used=3722.3MB, alloc=131.8MB, time=74.11 memory used=3759.5MB, alloc=131.8MB, time=74.23 memory used=3791.0MB, alloc=131.8MB, time=74.33 memory used=3823.1MB, alloc=131.8MB, time=74.42 memory used=3856.9MB, alloc=131.8MB, time=74.54 memory used=3891.7MB, alloc=131.8MB, time=74.64 memory used=3927.3MB, alloc=131.8MB, time=74.74 memory used=3963.9MB, alloc=131.8MB, time=74.84 memory used=4004.0MB, alloc=131.8MB, time=74.95 memory used=4044.9MB, alloc=131.8MB, time=75.06 memory used=4086.6MB, alloc=131.8MB, time=75.16 memory used=4130.8MB, alloc=131.8MB, time=75.28 memory used=4180.4MB, alloc=131.8MB, time=75.39 memory used=4231.3MB, alloc=131.8MB, time=75.53 memory used=4285.9MB, alloc=131.8MB, time=75.66 memory used=4341.4MB, alloc=131.8MB, time=75.78 memory used=4398.2MB, alloc=131.8MB, time=75.90 memory used=4458.8MB, alloc=131.8MB, time=76.02 memory used=4520.6MB, alloc=131.8MB, time=76.16 memory used=4586.1MB, alloc=131.8MB, time=76.28 memory used=4653.1MB, alloc=131.8MB, time=76.41 memory used=4672.9MB, alloc=131.8MB, time=76.48 memory used=4686.2MB, alloc=131.8MB, time=76.56 memory used=4694.6MB, alloc=131.8MB, time=76.63 memory used=4703.7MB, alloc=131.8MB, time=76.71 memory used=4710.4MB, alloc=131.8MB, time=76.80 memory used=4716.6MB, alloc=131.8MB, time=76.86 memory used=4723.1MB, alloc=131.8MB, time=76.95 memory used=4729.9MB, alloc=131.8MB, time=77.04 memory used=4736.8MB, alloc=131.8MB, time=77.11 memory used=4743.6MB, alloc=131.8MB, time=77.18 memory used=4750.5MB, alloc=131.8MB, time=77.27 memory used=4757.3MB, alloc=131.8MB, time=77.35 memory used=4764.2MB, alloc=131.8MB, time=77.42 memory used=4771.1MB, alloc=131.8MB, time=77.48 memory used=4778.1MB, alloc=131.8MB, time=77.55 memory used=4785.1MB, alloc=131.8MB, time=77.63 memory used=4792.1MB, alloc=131.8MB, time=77.70 memory used=4799.1MB, alloc=131.8MB, time=77.77 memory used=4806.0MB, alloc=131.8MB, time=77.84 memory used=4813.0MB, alloc=131.8MB, time=77.91 memory used=4820.0MB, alloc=131.8MB, time=78.00 memory used=4827.0MB, alloc=131.8MB, time=78.06 memory used=4834.1MB, alloc=131.8MB, time=78.13 memory used=4841.1MB, alloc=131.8MB, time=78.21 memory used=4848.1MB, alloc=131.8MB, time=78.29 memory used=4855.1MB, alloc=131.8MB, time=78.35 memory used=4862.1MB, alloc=131.8MB, time=78.44 memory used=4869.1MB, alloc=131.8MB, time=78.52 memory used=4876.2MB, alloc=131.8MB, time=78.60 memory used=4883.2MB, alloc=131.8MB, time=78.67 memory used=4890.2MB, alloc=131.8MB, time=78.73 memory used=4897.3MB, alloc=131.8MB, time=78.83 memory used=4904.3MB, alloc=131.8MB, time=78.91 memory used=4911.3MB, alloc=131.8MB, time=78.98 memory used=4918.4MB, alloc=131.8MB, time=79.04 memory used=4925.4MB, alloc=131.8MB, time=79.12 memory used=4932.5MB, alloc=131.8MB, time=79.20 memory used=4939.5MB, alloc=131.8MB, time=79.27 memory used=4946.6MB, alloc=131.8MB, time=79.35 memory used=4953.6MB, alloc=131.8MB, time=79.42 memory used=4960.7MB, alloc=131.8MB, time=79.50 memory used=4967.7MB, alloc=131.8MB, time=79.58 memory used=4974.8MB, alloc=131.8MB, time=79.65 memory used=4981.9MB, alloc=131.8MB, time=79.74 memory used=4988.9MB, alloc=131.8MB, time=79.80 memory used=4996.0MB, alloc=131.8MB, time=79.87 memory used=5003.1MB, alloc=131.8MB, time=79.94 memory used=5010.1MB, alloc=131.8MB, time=80.00 memory used=5017.2MB, alloc=131.8MB, time=80.08 memory used=5024.3MB, alloc=131.8MB, time=80.14 memory used=5031.3MB, alloc=131.8MB, time=80.24 memory used=5038.4MB, alloc=131.8MB, time=80.32 memory used=5045.5MB, alloc=131.8MB, time=80.41 memory used=5052.6MB, alloc=131.8MB, time=80.51 memory used=5059.6MB, alloc=131.8MB, time=80.59 memory used=5066.7MB, alloc=131.8MB, time=80.66 memory used=5073.8MB, alloc=131.8MB, time=80.74 memory used=5080.8MB, alloc=131.8MB, time=80.82 memory used=5088.2MB, alloc=131.8MB, time=80.88 memory used=5095.5MB, alloc=131.8MB, time=80.96 memory used=5105.7MB, alloc=131.8MB, time=81.06 memory used=5113.1MB, alloc=131.8MB, time=81.15 memory used=5123.4MB, alloc=131.8MB, time=81.23 memory used=5130.9MB, alloc=131.8MB, time=81.32 memory used=5141.1MB, alloc=131.8MB, time=81.39 memory used=5148.6MB, alloc=131.8MB, time=81.48 memory used=5158.8MB, alloc=131.8MB, time=81.56 memory used=5169.4MB, alloc=131.8MB, time=81.63 memory used=5180.0MB, alloc=131.8MB, time=81.73 memory used=5190.7MB, alloc=131.8MB, time=81.83 memory used=5201.2MB, alloc=131.8MB, time=81.92 memory used=5211.8MB, alloc=131.8MB, time=82.02 memory used=5222.4MB, alloc=131.8MB, time=82.09 memory used=5233.0MB, alloc=131.8MB, time=82.16 memory used=5243.6MB, alloc=131.8MB, time=82.23 memory used=5254.2MB, alloc=131.8MB, time=82.31 memory used=5264.7MB, alloc=131.8MB, time=82.38 memory used=5275.3MB, alloc=131.8MB, time=82.49 memory used=5285.9MB, alloc=131.8MB, time=82.55 memory used=5296.4MB, alloc=131.8MB, time=82.65 memory used=5307.0MB, alloc=131.8MB, time=82.72 memory used=5317.5MB, alloc=131.8MB, time=82.82 memory used=5328.0MB, alloc=131.8MB, time=82.94 memory used=5338.6MB, alloc=131.8MB, time=83.01 memory used=5349.1MB, alloc=131.8MB, time=83.09 memory used=5359.6MB, alloc=131.8MB, time=83.18 memory used=5370.1MB, alloc=131.8MB, time=83.28 memory used=5380.6MB, alloc=131.8MB, time=83.36 memory used=5391.1MB, alloc=131.8MB, time=83.45 memory used=5401.5MB, alloc=131.8MB, time=83.53 memory used=5412.0MB, alloc=131.8MB, time=83.61 memory used=5422.4MB, alloc=131.8MB, time=83.69 memory used=5432.9MB, alloc=131.8MB, time=83.80 memory used=5443.3MB, alloc=131.8MB, time=83.89 memory used=5453.7MB, alloc=131.8MB, time=83.96 memory used=5464.1MB, alloc=131.8MB, time=84.06 memory used=5474.5MB, alloc=131.8MB, time=84.16 memory used=5484.9MB, alloc=131.8MB, time=84.23 memory used=5495.3MB, alloc=131.8MB, time=84.31 memory used=5505.6MB, alloc=131.8MB, time=84.39 memory used=5516.0MB, alloc=131.8MB, time=84.47 memory used=5526.3MB, alloc=131.8MB, time=84.53 memory used=5536.6MB, alloc=131.8MB, time=84.63 memory used=5547.0MB, alloc=131.8MB, time=84.71 memory used=5557.3MB, alloc=131.8MB, time=84.77 memory used=5567.5MB, alloc=131.8MB, time=84.84 memory used=5577.3MB, alloc=131.8MB, time=84.94 memory used=5587.0MB, alloc=131.8MB, time=85.02 memory used=5597.2MB, alloc=131.8MB, time=85.09 memory used=5607.4MB, alloc=131.8MB, time=85.16 memory used=5617.6MB, alloc=131.8MB, time=85.25 memory used=5627.8MB, alloc=131.8MB, time=85.34 memory used=5637.9MB, alloc=131.8MB, time=85.43 memory used=5648.1MB, alloc=131.8MB, time=85.52 memory used=5658.2MB, alloc=131.8MB, time=85.62 memory used=5668.3MB, alloc=131.8MB, time=85.69 memory used=5678.4MB, alloc=131.8MB, time=85.79 memory used=5688.4MB, alloc=131.8MB, time=85.86 memory used=5698.5MB, alloc=131.8MB, time=85.96 memory used=5708.5MB, alloc=131.8MB, time=86.05 memory used=5718.9MB, alloc=131.8MB, time=86.14 memory used=5729.1MB, alloc=131.8MB, time=86.21 memory used=5741.7MB, alloc=131.8MB, time=86.33 memory used=5752.1MB, alloc=131.8MB, time=86.41 memory used=5764.9MB, alloc=131.8MB, time=86.49 memory used=5775.4MB, alloc=131.8MB, time=86.57 memory used=5787.9MB, alloc=131.8MB, time=86.63 memory used=5801.0MB, alloc=131.8MB, time=86.70 memory used=5814.1MB, alloc=131.8MB, time=86.79 memory used=5827.1MB, alloc=131.8MB, time=86.87 memory used=5840.1MB, alloc=131.8MB, time=86.95 memory used=5853.0MB, alloc=131.8MB, time=87.05 memory used=5865.9MB, alloc=131.8MB, time=87.14 memory used=5878.7MB, alloc=131.8MB, time=87.21 memory used=5891.5MB, alloc=131.8MB, time=87.31 memory used=5904.3MB, alloc=131.8MB, time=87.39 memory used=5917.0MB, alloc=131.8MB, time=87.48 memory used=5929.7MB, alloc=131.8MB, time=87.56 memory used=5942.3MB, alloc=131.8MB, time=87.64 memory used=5954.8MB, alloc=131.8MB, time=87.70 memory used=5967.3MB, alloc=131.8MB, time=87.78 memory used=5979.8MB, alloc=131.8MB, time=87.86 memory used=5992.2MB, alloc=131.8MB, time=87.94 memory used=6004.5MB, alloc=131.8MB, time=88.03 memory used=6016.8MB, alloc=131.8MB, time=88.12 memory used=6029.5MB, alloc=131.8MB, time=88.19 memory used=6041.9MB, alloc=131.8MB, time=88.28 memory used=6056.4MB, alloc=131.8MB, time=88.36 memory used=6069.1MB, alloc=131.8MB, time=88.45 memory used=6083.4MB, alloc=131.8MB, time=88.51 memory used=6098.3MB, alloc=131.8MB, time=88.61 memory used=6113.1MB, alloc=131.8MB, time=88.68 memory used=6127.9MB, alloc=131.8MB, time=88.76 memory used=6142.5MB, alloc=131.8MB, time=88.83 memory used=6157.0MB, alloc=131.8MB, time=88.92 memory used=6171.4MB, alloc=131.8MB, time=88.98 memory used=6185.7MB, alloc=131.8MB, time=89.06 memory used=6199.9MB, alloc=131.8MB, time=89.16 memory used=6214.0MB, alloc=131.8MB, time=89.24 memory used=6228.0MB, alloc=131.8MB, time=89.35 memory used=6242.3MB, alloc=131.8MB, time=89.45 memory used=6258.3MB, alloc=131.8MB, time=89.56 memory used=6272.7MB, alloc=131.8MB, time=89.64 memory used=6288.2MB, alloc=131.8MB, time=89.72 memory used=6304.3MB, alloc=131.8MB, time=89.80 memory used=6320.1MB, alloc=131.8MB, time=89.89 memory used=6336.0MB, alloc=131.8MB, time=89.96 memory used=6351.5MB, alloc=131.8MB, time=90.04 memory used=6367.4MB, alloc=131.8MB, time=90.16 memory used=6384.6MB, alloc=131.8MB, time=90.24 memory used=6402.1MB, alloc=131.8MB, time=90.34 memory used=6419.3MB, alloc=131.8MB, time=90.43 memory used=6436.3MB, alloc=131.8MB, time=90.53 memory used=6453.0MB, alloc=131.8MB, time=90.62 memory used=6469.9MB, alloc=131.8MB, time=90.72 memory used=6487.8MB, alloc=131.8MB, time=90.80 memory used=6505.9MB, alloc=131.8MB, time=90.90 memory used=6523.6MB, alloc=131.8MB, time=91.00 memory used=6541.5MB, alloc=131.8MB, time=91.09 memory used=6560.0MB, alloc=131.8MB, time=91.16 memory used=6578.6MB, alloc=131.8MB, time=91.25 memory used=6597.1MB, alloc=131.8MB, time=91.34 memory used=6614.2MB, alloc=131.8MB, time=91.44 memory used=6629.9MB, alloc=131.8MB, time=91.51 memory used=6645.9MB, alloc=131.8MB, time=91.60 memory used=6662.0MB, alloc=131.8MB, time=91.68 memory used=6678.4MB, alloc=131.8MB, time=91.77 memory used=6695.1MB, alloc=131.8MB, time=91.84 memory used=6710.2MB, alloc=131.8MB, time=91.94 memory used=6725.0MB, alloc=131.8MB, time=92.02 memory used=6739.9MB, alloc=131.8MB, time=92.11 memory used=6755.0MB, alloc=131.8MB, time=92.20 memory used=6864.8MB, alloc=387.8MB, time=93.61 memory used=6951.4MB, alloc=387.8MB, time=94.42 memory used=7038.2MB, alloc=387.8MB, time=95.17 memory used=7124.7MB, alloc=387.8MB, time=96.34 memory used=7213.8MB, alloc=387.8MB, time=97.82 memory used=7301.5MB, alloc=387.8MB, time=99.60 memory used=7388.8MB, alloc=387.8MB, time=101.64 memory used=7476.9MB, alloc=387.8MB, time=104.07 memory used=7564.0MB, alloc=387.8MB, time=106.79 memory used=7652.5MB, alloc=387.8MB, time=109.53 memory used=7740.0MB, alloc=387.8MB, time=112.99 memory used=7828.5MB, alloc=387.8MB, time=116.33 memory used=7916.5MB, alloc=387.8MB, time=120.81 memory used=7984.8MB, alloc=387.8MB, time=121.30 memory used=8037.5MB, alloc=387.8MB, time=122.19 memory used=8080.4MB, alloc=387.8MB, time=122.32 memory used=8121.4MB, alloc=387.8MB, time=122.44 memory used=8207.9MB, alloc=411.8MB, time=124.05 memory used=8287.1MB, alloc=411.8MB, time=124.70 memory used=8351.1MB, alloc=411.8MB, time=125.20 memory used=8426.3MB, alloc=411.8MB, time=133.85 memory used=8505.8MB, alloc=411.8MB, time=154.44 memory used=8563.0MB, alloc=411.8MB, time=154.64 memory used=8616.7MB, alloc=411.8MB, time=154.82 memory used=8683.2MB, alloc=411.8MB, time=155.03 memory used=8740.3MB, alloc=411.8MB, time=155.21 memory used=8782.3MB, alloc=411.8MB, time=155.35 memory used=8825.1MB, alloc=411.8MB, time=155.50 memory used=8870.9MB, alloc=411.8MB, time=155.65 memory used=8922.1MB, alloc=411.8MB, time=155.80 memory used=8975.9MB, alloc=411.8MB, time=155.96 memory used=9032.3MB, alloc=411.8MB, time=156.11 memory used=9091.1MB, alloc=411.8MB, time=156.27 memory used=9156.1MB, alloc=411.8MB, time=156.44 memory used=9223.5MB, alloc=411.8MB, time=156.62 memory used=9293.4MB, alloc=411.8MB, time=156.78 memory used=9492.3MB, alloc=411.8MB, time=157.34 memory used=9638.6MB, alloc=411.8MB, time=157.66 memory used=9795.1MB, alloc=411.8MB, time=157.99 memory used=9963.0MB, alloc=411.8MB, time=158.33 memory used=10146.7MB, alloc=411.8MB, time=158.68 memory used=10341.6MB, alloc=411.8MB, time=159.05 memory used=10552.8MB, alloc=411.8MB, time=159.45 memory used=10779.5MB, alloc=411.8MB, time=159.85 memory used=11020.9MB, alloc=411.8MB, time=160.26 memory used=11257.7MB, alloc=411.8MB, time=160.66 memory used=11437.6MB, alloc=411.8MB, time=161.00 memory used=11623.1MB, alloc=411.8MB, time=161.33 memory used=11819.8MB, alloc=411.8MB, time=161.68 memory used=12024.9MB, alloc=411.8MB, time=162.05 memory used=12237.1MB, alloc=411.8MB, time=162.41 memory used=12463.1MB, alloc=411.8MB, time=162.78 memory used=12701.0MB, alloc=411.8MB, time=163.16 memory used=12950.7MB, alloc=411.8MB, time=163.55 memory used=13167.6MB, alloc=411.8MB, time=163.90 memory used=13379.0MB, alloc=411.8MB, time=164.24 memory used=13673.7MB, alloc=411.8MB, time=165.68 memory used=13754.8MB, alloc=411.8MB, time=166.22 memory used=13833.4MB, alloc=411.8MB, time=166.43 memory used=13912.9MB, alloc=411.8MB, time=166.66 |\^/| 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(); 1428243228 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 4 3 F := [18 x z - 8 y z - 14 z + 3 x, 16 x + 19 z - 12 y - 4 y z, 4 3 -17 x + 16 x z - 9 y z - 12] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 3 2 3 2 G := [-2 x + 13 x y - 9 y + 5 x z, 6 x z - 10 x y z - 8 y z - 19 x y , 4 3 2 10 x - 7 x z + 6 x y z - 18 y] > Problem := [F,G]; 3 2 2 4 4 3 Problem := [[18 x z - 8 y z - 14 z + 3 x, 16 x + 19 z - 12 y - 4 y z, 4 3 4 2 2 3 -17 x + 16 x z - 9 y z - 12], [-2 x + 13 x y - 9 y + 5 x z, 3 2 3 2 4 3 2 6 x z - 10 x y z - 8 y z - 19 x y , 10 x - 7 x z + 6 x y z - 18 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.19 memory used=28.4MB, alloc=34.4MB, time=0.44 memory used=43.6MB, alloc=34.4MB, time=0.49 memory used=56.2MB, alloc=34.4MB, time=0.52 memory used=72.0MB, alloc=34.4MB, time=0.56 memory used=84.1MB, alloc=34.4MB, time=0.59 memory used=94.6MB, alloc=34.4MB, time=0.62 memory used=106.6MB, alloc=34.4MB, time=0.66 memory used=127.7MB, alloc=34.4MB, time=0.83 memory used=140.9MB, alloc=34.4MB, time=0.87 memory used=154.3MB, alloc=34.4MB, time=0.91 memory used=171.0MB, alloc=34.4MB, time=0.95 memory used=180.9MB, alloc=34.4MB, time=0.98 memory used=191.4MB, alloc=34.4MB, time=1.02 memory used=203.6MB, alloc=34.4MB, time=1.05 memory used=229.6MB, alloc=35.1MB, time=2.47 memory used=243.2MB, alloc=35.1MB, time=2.51 memory used=257.1MB, alloc=35.1MB, time=2.55 memory used=272.5MB, alloc=35.1MB, time=2.59 memory used=282.3MB, alloc=35.1MB, time=2.62 memory used=293.1MB, alloc=35.1MB, time=2.65 memory used=305.3MB, alloc=35.1MB, time=2.69 memory used=318.3MB, alloc=35.1MB, time=2.72 memory used=332.4MB, alloc=35.1MB, time=2.75 memory used=348.0MB, alloc=35.1MB, time=2.79 memory used=362.5MB, alloc=35.1MB, time=2.82 memory used=371.6MB, alloc=35.1MB, time=2.85 memory used=381.0MB, alloc=35.1MB, time=2.87 memory used=391.2MB, alloc=35.1MB, time=2.90 memory used=402.1MB, alloc=35.1MB, time=2.93 memory used=418.3MB, alloc=35.1MB, time=3.03 memory used=433.1MB, alloc=35.1MB, time=3.14 memory used=448.7MB, alloc=35.1MB, time=3.33 memory used=461.0MB, alloc=35.1MB, time=3.37 memory used=471.7MB, alloc=35.1MB, time=3.40 memory used=490.0MB, alloc=35.1MB, time=3.64 memory used=514.5MB, alloc=39.2MB, time=3.95 memory used=531.7MB, alloc=39.2MB, time=4.15 memory used=544.3MB, alloc=39.2MB, time=4.19 memory used=553.9MB, alloc=39.2MB, time=4.23 memory used=564.8MB, alloc=39.2MB, time=4.26 memory used=589.2MB, alloc=39.2MB, time=4.48 memory used=616.0MB, alloc=63.2MB, time=4.74 memory used=650.5MB, alloc=63.2MB, time=5.22 memory used=700.7MB, alloc=72.2MB, time=6.24 memory used=741.5MB, alloc=96.2MB, time=13.59 memory used=773.5MB, alloc=120.2MB, time=15.03 memory used=832.3MB, alloc=144.2MB, time=15.22 memory used=862.5MB, alloc=168.2MB, time=25.34 memory used=904.1MB, alloc=168.2MB, time=25.85 memory used=1029.5MB, alloc=428.2MB, time=27.30 memory used=1228.7MB, alloc=428.2MB, time=28.61 memory used=1403.7MB, alloc=428.2MB, time=30.23 memory used=1493.3MB, alloc=428.2MB, time=30.46 memory used=1583.9MB, alloc=428.2MB, time=30.63 memory used=1666.9MB, alloc=428.2MB, time=30.76 memory used=1776.7MB, alloc=428.2MB, time=31.68 memory used=1943.1MB, alloc=428.2MB, time=34.31 memory used=2125.6MB, alloc=428.2MB, time=39.66 memory used=2307.2MB, alloc=428.2MB, time=44.86 memory used=2492.9MB, alloc=428.2MB, time=50.49 memory used=2652.8MB, alloc=428.2MB, time=55.41 memory used=2782.4MB, alloc=428.2MB, time=56.66 memory used=2883.8MB, alloc=428.2MB, time=60.81 memory used=2958.1MB, alloc=428.2MB, time=61.04 memory used=3040.7MB, alloc=428.2MB, time=61.27 memory used=3112.7MB, alloc=428.2MB, time=61.45 memory used=3173.8MB, alloc=428.2MB, time=61.62 memory used=3243.1MB, alloc=428.2MB, time=61.79 memory used=3321.4MB, alloc=428.2MB, time=61.96 memory used=3410.2MB, alloc=428.2MB, time=62.14 memory used=3641.9MB, alloc=428.2MB, time=62.66 memory used=3808.4MB, alloc=428.2MB, time=62.95 memory used=4016.0MB, alloc=428.2MB, time=64.78 memory used=4100.0MB, alloc=428.2MB, time=65.01 memory used=4166.1MB, alloc=428.2MB, time=65.18 memory used=4233.4MB, alloc=428.2MB, time=65.35 memory used=4312.4MB, alloc=428.2MB, time=65.51 memory used=4404.5MB, alloc=428.2MB, time=65.69 memory used=4585.5MB, alloc=428.2MB, time=66.00 memory used=4705.3MB, alloc=428.2MB, time=67.07 memory used=4797.6MB, alloc=428.2MB, time=67.32 memory used=4889.7MB, alloc=428.2MB, time=68.19 memory used=5066.6MB, alloc=428.2MB, time=70.24 memory used=5155.2MB, alloc=428.2MB, time=70.62 memory used=5254.1MB, alloc=428.2MB, time=71.72 memory used=5406.3MB, alloc=428.2MB, time=73.28 memory used=5511.3MB, alloc=428.2MB, time=74.79 memory used=5592.9MB, alloc=428.2MB, time=75.07 memory used=5656.1MB, alloc=428.2MB, time=75.28 memory used=5796.0MB, alloc=428.2MB, time=76.45 memory used=5863.4MB, alloc=428.2MB, time=76.70 memory used=5930.6MB, alloc=428.2MB, time=76.94 memory used=5988.4MB, alloc=428.2MB, time=77.16 memory used=6057.6MB, alloc=428.2MB, time=77.38 memory used=6140.8MB, alloc=428.2MB, time=77.62 memory used=6202.6MB, alloc=428.2MB, time=78.00 memory used=6290.2MB, alloc=428.2MB, time=78.53 memory used=6369.5MB, alloc=428.2MB, time=78.79 memory used=6424.7MB, alloc=428.2MB, time=79.01 memory used=6486.9MB, alloc=428.2MB, time=79.24 memory used=6561.1MB, alloc=428.2MB, time=79.48 memory used=6632.9MB, alloc=428.2MB, time=79.68 memory used=6723.2MB, alloc=428.2MB, time=84.77 memory used=6799.5MB, alloc=428.2MB, time=85.04 memory used=6863.5MB, alloc=428.2MB, time=85.25 memory used=6938.4MB, alloc=428.2MB, time=85.47 memory used=6991.7MB, alloc=428.2MB, time=85.68 memory used=7053.2MB, alloc=428.2MB, time=85.85 memory used=7140.1MB, alloc=428.2MB, time=86.35 memory used=7228.0MB, alloc=428.2MB, time=86.95 memory used=7346.3MB, alloc=428.2MB, time=88.34 memory used=7437.3MB, alloc=428.2MB, time=89.91 memory used=7501.9MB, alloc=428.2MB, time=90.12 memory used=7626.0MB, alloc=428.2MB, time=91.53 memory used=7790.3MB, alloc=428.2MB, time=92.94 memory used=7867.1MB, alloc=452.2MB, time=127.68 memory used=7939.3MB, alloc=476.2MB, time=139.10 memory used=8035.3MB, alloc=476.2MB, time=139.45 memory used=8129.2MB, alloc=476.2MB, time=139.80 memory used=8229.0MB, alloc=476.2MB, time=140.16 memory used=8329.8MB, alloc=476.2MB, time=140.52 memory used=8431.4MB, alloc=476.2MB, time=140.86 memory used=8533.9MB, alloc=476.2MB, time=141.22 memory used=8637.3MB, alloc=476.2MB, time=141.58 memory used=8741.5MB, alloc=476.2MB, time=141.93 memory used=8846.7MB, alloc=476.2MB, time=142.29 memory used=8958.0MB, alloc=476.2MB, time=142.65 memory used=9070.1MB, alloc=476.2MB, time=143.00 memory used=9164.1MB, alloc=476.2MB, time=143.33 memory used=9243.1MB, alloc=476.2MB, time=143.64 memory used=9315.3MB, alloc=500.2MB, time=143.94 memory used=9395.4MB, alloc=500.2MB, time=144.28 memory used=9476.9MB, alloc=500.2MB, time=144.62 memory used=9553.9MB, alloc=500.2MB, time=144.95 memory used=9626.7MB, alloc=500.2MB, time=145.26 memory used=9700.4MB, alloc=500.2MB, time=145.58 memory used=9774.8MB, alloc=500.2MB, time=145.89 memory used=9849.2MB, alloc=500.2MB, time=146.20 memory used=9918.4MB, alloc=500.2MB, time=146.51 memory used=9987.7MB, alloc=500.2MB, time=146.81 memory used=10058.3MB, alloc=500.2MB, time=147.11 memory used=10129.2MB, alloc=500.2MB, time=147.42 memory used=10200.3MB, alloc=500.2MB, time=147.72 memory used=10271.5MB, alloc=500.2MB, time=148.02 memory used=10343.0MB, alloc=500.2MB, time=148.33 memory used=10414.9MB, alloc=500.2MB, time=148.64 memory used=10492.7MB, alloc=500.2MB, time=148.96 memory used=10570.7MB, alloc=500.2MB, time=149.27 memory used=10648.8MB, alloc=500.2MB, time=149.57 memory used=10727.2MB, alloc=500.2MB, time=149.88 memory used=10805.8MB, alloc=500.2MB, time=150.20 memory used=10884.5MB, alloc=500.2MB, time=150.52 memory used=10963.4MB, alloc=500.2MB, time=150.85 memory used=11042.5MB, alloc=500.2MB, time=151.15 memory used=11121.7MB, alloc=500.2MB, time=151.46 memory used=11201.1MB, alloc=500.2MB, time=151.77 memory used=11280.6MB, alloc=500.2MB, time=152.08 memory used=11360.3MB, alloc=500.2MB, time=152.38 memory used=11440.3MB, alloc=500.2MB, time=152.70 memory used=11526.4MB, alloc=500.2MB, time=153.03 memory used=11612.5MB, alloc=500.2MB, time=153.35 memory used=11698.8MB, alloc=500.2MB, time=153.67 memory used=11785.3MB, alloc=500.2MB, time=153.98 memory used=11871.8MB, alloc=500.2MB, time=154.29 memory used=11958.5MB, alloc=500.2MB, time=154.61 memory used=12045.2MB, alloc=500.2MB, time=154.93 memory used=12132.0MB, alloc=500.2MB, time=155.25 memory used=12218.9MB, alloc=500.2MB, time=155.57 memory used=12305.9MB, alloc=500.2MB, time=155.88 memory used=12393.2MB, alloc=500.2MB, time=156.19 memory used=12486.5MB, alloc=500.2MB, time=156.52 memory used=12579.9MB, alloc=500.2MB, time=156.84 memory used=12673.3MB, alloc=500.2MB, time=157.16 memory used=12766.7MB, alloc=500.2MB, time=157.48 memory used=12860.2MB, alloc=500.2MB, time=157.80 memory used=12953.7MB, alloc=500.2MB, time=158.12 memory used=13047.1MB, alloc=500.2MB, time=158.44 memory used=13140.9MB, alloc=500.2MB, time=158.77 memory used=13240.5MB, alloc=500.2MB, time=159.09 memory used=13340.2MB, alloc=500.2MB, time=159.41 memory used=13439.8MB, alloc=500.2MB, time=159.73 memory used=13539.4MB, alloc=500.2MB, time=160.04 memory used=13638.9MB, alloc=500.2MB, time=160.36 memory used=13738.4MB, alloc=500.2MB, time=160.68 memory used=13837.7MB, alloc=500.2MB, time=161.01 memory used=13937.2MB, alloc=500.2MB, time=161.34 memory used=14042.5MB, alloc=500.2MB, time=161.67 memory used=14147.7MB, alloc=500.2MB, time=161.99 memory used=14252.8MB, alloc=500.2MB, time=162.31 memory used=14357.6MB, alloc=500.2MB, time=162.65 memory used=14462.3MB, alloc=500.2MB, time=162.97 memory used=14567.0MB, alloc=500.2MB, time=163.30 memory used=14677.5MB, alloc=500.2MB, time=163.62 memory used=14787.7MB, alloc=500.2MB, time=163.96 memory used=14897.6MB, alloc=500.2MB, time=164.30 memory used=15007.2MB, alloc=500.2MB, time=164.62 memory used=15116.7MB, alloc=500.2MB, time=164.96 memory used=15231.8MB, alloc=500.2MB, time=165.30 memory used=15346.5MB, alloc=500.2MB, time=165.63 memory used=15460.8MB, alloc=500.2MB, time=165.96 memory used=15574.9MB, alloc=500.2MB, time=166.31 memory used=15694.3MB, alloc=500.2MB, time=166.64 memory used=15813.3MB, alloc=500.2MB, time=166.97 memory used=15931.7MB, alloc=500.2MB, time=167.31 memory used=16049.8MB, alloc=500.2MB, time=167.65 memory used=16173.0MB, alloc=500.2MB, time=167.99 memory used=16295.5MB, alloc=500.2MB, time=168.31 memory used=16417.3MB, alloc=500.2MB, time=168.65 memory used=16538.7MB, alloc=500.2MB, time=168.99 memory used=16664.8MB, alloc=500.2MB, time=169.32 memory used=16790.2MB, alloc=500.2MB, time=169.66 memory used=16914.8MB, alloc=500.2MB, time=170.01 memory used=17044.0MB, alloc=500.2MB, time=170.34 memory used=17172.4MB, alloc=500.2MB, time=170.70 memory used=17305.1MB, alloc=500.2MB, time=171.05 memory used=17436.8MB, alloc=500.2MB, time=171.40 memory used=17572.5MB, alloc=500.2MB, time=171.75 memory used=17701.9MB, alloc=500.2MB, time=172.08 memory used=17792.3MB, alloc=500.2MB, time=172.35 memory used=17871.5MB, alloc=500.2MB, time=172.61 memory used=17944.5MB, alloc=500.2MB, time=172.86 memory used=18013.9MB, alloc=500.2MB, time=173.11 memory used=18083.6MB, alloc=500.2MB, time=173.36 memory used=18153.1MB, alloc=500.2MB, time=173.60 memory used=18217.9MB, alloc=500.2MB, time=173.84 memory used=18283.2MB, alloc=500.2MB, time=174.08 memory used=18348.4MB, alloc=500.2MB, time=174.32 memory used=18413.3MB, alloc=500.2MB, time=174.57 memory used=18482.5MB, alloc=500.2MB, time=174.81 memory used=18551.1MB, alloc=500.2MB, time=175.06 memory used=18619.3MB, alloc=500.2MB, time=175.30 memory used=18686.9MB, alloc=500.2MB, time=175.54 memory used=18754.1MB, alloc=500.2MB, time=175.78 memory used=18825.4MB, alloc=500.2MB, time=176.02 memory used=18896.0MB, alloc=500.2MB, time=176.26 memory used=18965.9MB, alloc=500.2MB, time=176.52 memory used=19035.4MB, alloc=500.2MB, time=176.77 memory used=19108.5MB, alloc=500.2MB, time=177.02 memory used=19181.0MB, alloc=500.2MB, time=177.27 memory used=19252.6MB, alloc=500.2MB, time=177.51 memory used=19323.5MB, alloc=500.2MB, time=177.76 memory used=19397.9MB, alloc=500.2MB, time=178.02 memory used=19471.4MB, alloc=500.2MB, time=178.26 memory used=19544.0MB, alloc=500.2MB, time=178.51 memory used=19619.8MB, alloc=500.2MB, time=178.76 memory used=19694.5MB, alloc=500.2MB, time=179.01 memory used=19768.2MB, alloc=500.2MB, time=179.25 memory used=19844.6MB, alloc=500.2MB, time=179.52 memory used=19920.0MB, alloc=500.2MB, time=179.77 memory used=19997.8MB, alloc=500.2MB, time=180.02 memory used=20074.2MB, alloc=500.2MB, time=180.27 memory used=20153.0MB, alloc=500.2MB, time=180.52 memory used=20233.6MB, alloc=500.2MB, time=180.77 |\^/| 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(); 1428243528 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 3 F := [11 x z + 16 x z + 11 y z + 6 x z, -12 x y + 9 x + 17 x y - 10 x, 2 4 -6 x y z + 8 z + 20 x z - 17 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [16 x z + 16 y z - 5 z - 8 y, -13 x y z + 17 y z + 5 x y + 12 x, 2 2 2 -20 x y - x y - 2 z ] > Problem := [F,G]; 2 2 3 2 Problem := [[11 x z + 16 x z + 11 y z + 6 x z, 3 3 2 4 -12 x y + 9 x + 17 x y - 10 x, -6 x y z + 8 z + 20 x z - 17 x], [ 3 2 3 2 16 x z + 16 y z - 5 z - 8 y, -13 x y z + 17 y z + 5 x y + 12 x, 2 2 2 -20 x y - x y - 2 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.52 memory used=47.2MB, alloc=56.3MB, time=0.85 memory used=88.4MB, alloc=60.3MB, time=1.49 memory used=129.7MB, alloc=60.3MB, time=2.08 memory used=168.7MB, alloc=84.3MB, time=2.68 memory used=232.8MB, alloc=92.3MB, time=3.65 memory used=298.4MB, alloc=92.3MB, time=4.57 memory used=362.6MB, alloc=116.3MB, time=5.51 memory used=444.6MB, alloc=372.3MB, time=6.81 memory used=528.7MB, alloc=396.3MB, time=8.16 memory used=612.6MB, alloc=396.3MB, time=8.91 memory used=712.7MB, alloc=396.3MB, time=10.09 memory used=821.1MB, alloc=420.3MB, time=11.76 memory used=955.9MB, alloc=420.3MB, time=13.82 memory used=1081.4MB, alloc=444.3MB, time=15.84 memory used=1209.9MB, alloc=468.3MB, time=17.78 memory used=1354.5MB, alloc=468.3MB, time=19.60 memory used=1475.0MB, alloc=468.3MB, time=20.80 memory used=1565.0MB, alloc=468.3MB, time=21.17 memory used=1635.4MB, alloc=468.3MB, time=21.46 memory used=1727.5MB, alloc=468.3MB, time=22.12 memory used=1827.8MB, alloc=468.3MB, time=28.60 memory used=1921.0MB, alloc=468.3MB, time=34.59 memory used=1989.4MB, alloc=468.3MB, time=34.88 memory used=2078.2MB, alloc=468.3MB, time=35.20 memory used=2142.5MB, alloc=468.3MB, time=35.46 memory used=2205.0MB, alloc=468.3MB, time=35.74 memory used=2275.7MB, alloc=468.3MB, time=36.00 memory used=2355.3MB, alloc=468.3MB, time=36.26 memory used=2450.9MB, alloc=468.3MB, time=36.53 memory used=2704.2MB, alloc=468.3MB, time=39.37 memory used=2888.8MB, alloc=468.3MB, time=41.76 memory used=3054.9MB, alloc=468.3MB, time=44.35 memory used=3221.5MB, alloc=492.3MB, time=48.56 memory used=3425.2MB, alloc=492.3MB, time=55.27 memory used=3629.5MB, alloc=492.3MB, time=63.92 memory used=3827.9MB, alloc=492.3MB, time=72.31 memory used=3961.2MB, alloc=492.3MB, time=73.45 memory used=4059.3MB, alloc=492.3MB, time=74.84 memory used=4179.1MB, alloc=492.3MB, time=85.77 memory used=4259.4MB, alloc=492.3MB, time=86.12 memory used=4359.7MB, alloc=492.3MB, time=86.48 memory used=4437.9MB, alloc=492.3MB, time=86.79 memory used=4512.6MB, alloc=492.3MB, time=87.09 memory used=4599.7MB, alloc=492.3MB, time=87.41 memory used=4738.6MB, alloc=492.3MB, time=87.79 memory used=4866.2MB, alloc=492.3MB, time=89.22 memory used=5012.5MB, alloc=492.3MB, time=91.36 memory used=5163.9MB, alloc=492.3MB, time=93.35 memory used=5277.7MB, alloc=492.3MB, time=94.86 memory used=5377.5MB, alloc=516.3MB, time=96.50 memory used=5514.7MB, alloc=516.3MB, time=97.76 memory used=5661.0MB, alloc=516.3MB, time=100.14 memory used=5777.7MB, alloc=516.3MB, time=101.90 memory used=5887.9MB, alloc=516.3MB, time=103.23 memory used=5997.0MB, alloc=516.3MB, time=106.09 memory used=6096.2MB, alloc=516.3MB, time=106.86 memory used=6214.6MB, alloc=516.3MB, time=108.35 memory used=6314.4MB, alloc=540.3MB, time=110.44 memory used=6400.5MB, alloc=540.3MB, time=112.20 memory used=6483.9MB, alloc=540.3MB, time=113.99 memory used=6556.2MB, alloc=540.3MB, time=115.41 memory used=6625.0MB, alloc=540.3MB, time=116.94 memory used=6681.2MB, alloc=540.3MB, time=118.01 memory used=6723.5MB, alloc=540.3MB, time=118.92 memory used=6789.5MB, alloc=540.3MB, time=120.12 memory used=6849.2MB, alloc=540.3MB, time=121.43 memory used=6894.8MB, alloc=540.3MB, time=122.44 memory used=6933.5MB, alloc=540.3MB, time=123.30 memory used=6973.7MB, alloc=540.3MB, time=124.23 memory used=7155.2MB, alloc=564.3MB, time=127.51 memory used=7371.5MB, alloc=588.3MB, time=131.34 memory used=7572.4MB, alloc=612.3MB, time=135.32 memory used=7828.9MB, alloc=636.3MB, time=139.63 memory used=8059.4MB, alloc=636.3MB, time=142.88 memory used=8212.3MB, alloc=660.3MB, time=145.27 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428243828 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 2 F := [8 x y + 17 y z - 4 x y - 15 x z, 8 x z + 13 x z + 2 x y z + 11 y z , 4 20 z + 11 x y z + 16 z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [16 x y z - 20 x z - 3 z + x, -10 x z + 4 x y - 8 y z + 17 y z, 3 2 -12 x z + 15 x z - x y - 4 x z] > Problem := [F,G]; 3 2 Problem := [[8 x y + 17 y z - 4 x y - 15 x z, 3 2 2 2 4 8 x z + 13 x z + 2 x y z + 11 y z , 20 z + 11 x y z + 16 z], [ 2 2 2 2 2 2 16 x y z - 20 x z - 3 z + x, -10 x z + 4 x y - 8 y z + 17 y z, 3 2 -12 x z + 15 x z - x y - 4 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.54 memory used=46.0MB, alloc=56.3MB, time=0.87 memory used=87.2MB, alloc=60.3MB, time=1.51 memory used=127.0MB, alloc=60.3MB, time=2.10 memory used=166.8MB, alloc=84.3MB, time=2.71 memory used=229.1MB, alloc=92.3MB, time=3.67 memory used=291.1MB, alloc=116.3MB, time=4.67 memory used=369.7MB, alloc=116.3MB, time=5.86 memory used=440.0MB, alloc=396.3MB, time=7.03 memory used=547.9MB, alloc=396.3MB, time=8.64 memory used=659.0MB, alloc=420.3MB, time=10.31 memory used=789.2MB, alloc=444.3MB, time=12.49 memory used=927.2MB, alloc=468.3MB, time=14.90 memory used=1043.2MB, alloc=468.3MB, time=16.74 memory used=1160.7MB, alloc=468.3MB, time=18.87 memory used=1260.8MB, alloc=468.3MB, time=20.64 memory used=1361.4MB, alloc=492.3MB, time=22.52 memory used=1460.8MB, alloc=492.3MB, time=24.47 memory used=1557.8MB, alloc=492.3MB, time=26.35 memory used=1645.2MB, alloc=492.3MB, time=28.15 memory used=1719.0MB, alloc=492.3MB, time=29.63 memory used=1784.4MB, alloc=492.3MB, time=30.97 memory used=1851.1MB, alloc=516.3MB, time=32.34 memory used=1907.3MB, alloc=516.3MB, time=33.51 memory used=1959.4MB, alloc=516.3MB, time=34.65 memory used=2013.4MB, alloc=516.3MB, time=35.91 memory used=2069.9MB, alloc=516.3MB, time=37.28 memory used=2121.0MB, alloc=516.3MB, time=38.70 memory used=2320.3MB, alloc=540.3MB, time=42.74 memory used=2515.4MB, alloc=564.3MB, time=46.50 memory used=2691.2MB, alloc=588.3MB, time=50.01 memory used=2866.4MB, alloc=612.3MB, time=53.39 memory used=2989.7MB, alloc=636.3MB, time=55.85 memory used=3132.8MB, alloc=660.3MB, time=59.03 memory used=3259.0MB, alloc=660.3MB, time=61.72 memory used=3361.4MB, alloc=660.3MB, time=64.14 memory used=3437.9MB, alloc=660.3MB, time=66.00 memory used=3530.6MB, alloc=660.3MB, time=68.25 memory used=3866.2MB, alloc=684.3MB, time=73.72 memory used=4207.0MB, alloc=708.3MB, time=81.06 memory used=4555.1MB, alloc=732.3MB, time=87.85 memory used=4907.7MB, alloc=756.3MB, time=95.48 memory used=5268.3MB, alloc=780.3MB, time=103.79 memory used=5569.9MB, alloc=804.3MB, time=109.43 memory used=5844.3MB, alloc=828.3MB, time=116.44 |\^/| 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(); 1428244128 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [-18 x y z + 3 x z - 14 x z - 15 y , 3 2 2 2 2 3 2 3 20 x y - 14 x y z + 18 y z - 20 z , -20 x y z - 10 x z - 18 x y + y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [5 x y z - 14 x y + 19 x z + 11 x, -8 x y z - 15 y z - y z + 13, 2 2 2 20 x y + 8 x y z - 6 x y] > Problem := [F,G]; 2 3 2 2 Problem := [[-18 x y z + 3 x z - 14 x z - 15 y , 3 2 2 2 2 3 2 3 20 x y - 14 x y z + 18 y z - 20 z , -20 x y z - 10 x z - 18 x y + y ] 2 2 2 3 2 , [5 x y z - 14 x y + 19 x z + 11 x, -8 x y z - 15 y z - y z + 13, 2 2 2 20 x y + 8 x y z - 6 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=24.8MB, alloc=32.3MB, time=0.45 memory used=44.2MB, alloc=56.3MB, time=0.71 memory used=84.8MB, alloc=60.3MB, time=1.22 memory used=129.3MB, alloc=60.3MB, time=2.47 memory used=158.4MB, alloc=60.3MB, time=2.76 memory used=181.0MB, alloc=60.3MB, time=2.82 memory used=227.1MB, alloc=60.3MB, time=3.33 memory used=272.9MB, alloc=68.5MB, time=3.82 memory used=293.6MB, alloc=68.5MB, time=3.90 memory used=317.4MB, alloc=68.5MB, time=3.97 memory used=334.7MB, alloc=68.5MB, time=4.04 memory used=359.2MB, alloc=68.5MB, time=4.21 memory used=384.7MB, alloc=68.6MB, time=4.31 memory used=409.4MB, alloc=68.6MB, time=4.40 memory used=427.7MB, alloc=68.6MB, time=4.47 memory used=447.4MB, alloc=68.6MB, time=4.54 memory used=479.3MB, alloc=69.2MB, time=5.38 memory used=501.1MB, alloc=69.2MB, time=5.46 memory used=521.1MB, alloc=69.2MB, time=5.53 memory used=543.6MB, alloc=69.2MB, time=5.59 memory used=592.2MB, alloc=69.2MB, time=6.24 memory used=641.4MB, alloc=69.2MB, time=6.79 memory used=691.7MB, alloc=69.2MB, time=7.61 memory used=735.2MB, alloc=93.2MB, time=8.29 memory used=802.4MB, alloc=93.2MB, time=9.00 memory used=847.6MB, alloc=93.2MB, time=9.39 memory used=920.8MB, alloc=93.2MB, time=10.23 memory used=999.1MB, alloc=93.2MB, time=10.94 memory used=1055.5MB, alloc=93.2MB, time=13.42 memory used=1088.1MB, alloc=93.2MB, time=13.55 memory used=1113.4MB, alloc=93.2MB, time=13.66 memory used=1143.6MB, alloc=93.2MB, time=13.77 memory used=1179.4MB, alloc=93.2MB, time=13.88 memory used=1207.7MB, alloc=93.2MB, time=13.99 memory used=1230.1MB, alloc=93.2MB, time=14.08 memory used=1253.8MB, alloc=93.2MB, time=14.19 memory used=1279.3MB, alloc=93.2MB, time=14.29 memory used=1306.5MB, alloc=93.2MB, time=14.39 memory used=1336.6MB, alloc=93.2MB, time=14.48 memory used=1369.7MB, alloc=93.2MB, time=14.59 memory used=1418.2MB, alloc=107.8MB, time=14.71 memory used=1467.7MB, alloc=107.8MB, time=15.70 memory used=1503.6MB, alloc=107.8MB, time=15.83 memory used=1529.8MB, alloc=107.8MB, time=15.94 memory used=1560.7MB, alloc=107.8MB, time=16.05 memory used=1595.4MB, alloc=107.8MB, time=16.19 memory used=1617.7MB, alloc=107.8MB, time=16.28 memory used=1641.7MB, alloc=107.8MB, time=16.40 memory used=1669.2MB, alloc=107.8MB, time=16.49 memory used=1719.3MB, alloc=107.8MB, time=16.86 memory used=1786.4MB, alloc=131.8MB, time=17.72 memory used=1862.0MB, alloc=131.8MB, time=20.32 memory used=1933.5MB, alloc=387.8MB, time=21.53 memory used=2031.5MB, alloc=411.8MB, time=22.49 memory used=2149.1MB, alloc=411.8MB, time=23.96 memory used=2231.7MB, alloc=435.8MB, time=24.77 memory used=2349.4MB, alloc=435.8MB, time=26.10 memory used=2447.1MB, alloc=435.8MB, time=27.82 memory used=2566.8MB, alloc=459.8MB, time=28.96 memory used=2698.2MB, alloc=459.8MB, time=30.50 memory used=2803.0MB, alloc=483.8MB, time=32.01 memory used=2903.3MB, alloc=483.8MB, time=33.17 memory used=3003.2MB, alloc=483.8MB, time=34.33 memory used=3100.8MB, alloc=507.8MB, time=35.54 memory used=3205.9MB, alloc=507.8MB, time=36.08 memory used=3319.4MB, alloc=507.8MB, time=36.76 memory used=3428.1MB, alloc=507.8MB, time=37.51 memory used=3529.7MB, alloc=507.8MB, time=38.10 memory used=3630.8MB, alloc=507.8MB, time=38.56 memory used=3736.3MB, alloc=507.8MB, time=39.67 memory used=3844.1MB, alloc=507.8MB, time=40.37 memory used=3968.7MB, alloc=507.8MB, time=42.24 memory used=4057.2MB, alloc=507.8MB, time=42.62 memory used=4186.8MB, alloc=507.8MB, time=47.95 memory used=4289.8MB, alloc=507.8MB, time=49.13 memory used=4375.0MB, alloc=507.8MB, time=49.46 memory used=4481.4MB, alloc=507.8MB, time=49.91 memory used=4615.6MB, alloc=507.8MB, time=56.08 memory used=4706.1MB, alloc=507.8MB, time=56.43 memory used=4780.0MB, alloc=507.8MB, time=56.73 memory used=4893.9MB, alloc=507.8MB, time=57.39 memory used=4996.8MB, alloc=507.8MB, time=57.77 memory used=5173.0MB, alloc=507.8MB, time=60.35 memory used=5300.4MB, alloc=507.8MB, time=62.24 memory used=5428.5MB, alloc=507.8MB, time=64.09 memory used=5583.9MB, alloc=507.8MB, time=66.40 memory used=5698.5MB, alloc=507.8MB, time=68.14 memory used=5783.8MB, alloc=507.8MB, time=68.53 memory used=5901.8MB, alloc=531.8MB, time=69.82 memory used=6056.4MB, alloc=531.8MB, time=72.30 memory used=6186.3MB, alloc=531.8MB, time=73.70 memory used=6336.8MB, alloc=531.8MB, time=76.50 memory used=6407.9MB, alloc=531.8MB, time=77.80 memory used=6460.0MB, alloc=531.8MB, time=78.63 memory used=6545.1MB, alloc=531.8MB, time=79.79 memory used=6604.0MB, alloc=531.8MB, time=80.87 memory used=6660.9MB, alloc=531.8MB, time=81.77 memory used=6711.7MB, alloc=531.8MB, time=82.52 memory used=6764.5MB, alloc=531.8MB, time=83.54 memory used=6813.2MB, alloc=531.8MB, time=84.53 memory used=6856.2MB, alloc=531.8MB, time=85.44 memory used=7039.0MB, alloc=555.8MB, time=87.56 memory used=7258.1MB, alloc=579.8MB, time=89.87 memory used=7398.7MB, alloc=579.8MB, time=90.69 memory used=7528.5MB, alloc=579.8MB, time=91.98 memory used=7663.1MB, alloc=579.8MB, time=93.13 memory used=7777.8MB, alloc=579.8MB, time=93.75 memory used=7895.1MB, alloc=579.8MB, time=94.33 memory used=8026.3MB, alloc=579.8MB, time=95.23 memory used=8142.6MB, alloc=579.8MB, time=95.86 memory used=8272.9MB, alloc=579.8MB, time=98.83 memory used=8394.8MB, alloc=579.8MB, time=99.44 memory used=8497.3MB, alloc=579.8MB, time=99.99 memory used=8627.3MB, alloc=579.8MB, time=100.89 memory used=8765.4MB, alloc=579.8MB, time=101.73 memory used=8893.2MB, alloc=579.8MB, time=102.99 memory used=9036.5MB, alloc=579.8MB, time=106.46 memory used=9169.2MB, alloc=579.8MB, time=111.18 memory used=9298.2MB, alloc=579.8MB, time=111.83 memory used=9387.1MB, alloc=579.8MB, time=112.36 memory used=9494.4MB, alloc=579.8MB, time=112.90 memory used=9625.8MB, alloc=579.8MB, time=113.44 memory used=9865.4MB, alloc=579.8MB, time=114.61 memory used=10066.1MB, alloc=579.8MB, time=115.62 memory used=10328.8MB, alloc=579.8MB, time=116.41 memory used=10507.1MB, alloc=579.8MB, time=117.70 memory used=10617.6MB, alloc=579.8MB, time=118.31 memory used=10766.1MB, alloc=579.8MB, time=119.29 memory used=10883.2MB, alloc=579.8MB, time=119.94 memory used=10993.8MB, alloc=579.8MB, time=120.53 |\^/| 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(); 1428244428 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 2 2 F := [-4 x y - 18 x y z + 14 x , -17 x y z + 6 y z + 20 x y - 5 x y , 2 2 3 2 2 10 y z + 11 y z - y - 16 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 G := [-16 x y z + 18 y + 9 z - 20, -10 x y z - 8 x z + 6 x z + 18 x y, 2 3 3 -5 x y z + 20 y z + 11 y + 13] > Problem := [F,G]; 2 2 2 3 Problem := [[-4 x y - 18 x y z + 14 x , 2 3 2 2 2 2 3 2 2 -17 x y z + 6 y z + 20 x y - 5 x y , 10 y z + 11 y z - y - 16 z ], [ 3 2 2 2 2 3 -16 x y z + 18 y + 9 z - 20, -10 x y z - 8 x z + 6 x z + 18 x y, 2 3 3 -5 x y z + 20 y z + 11 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=29.9MB, alloc=34.3MB, time=0.46 memory used=44.3MB, alloc=34.3MB, time=0.50 memory used=56.9MB, alloc=34.3MB, time=0.53 memory used=69.6MB, alloc=34.3MB, time=0.57 memory used=84.2MB, alloc=34.3MB, time=0.60 memory used=106.9MB, alloc=34.3MB, time=0.92 memory used=125.5MB, alloc=34.3MB, time=0.98 memory used=137.4MB, alloc=34.3MB, time=1.02 memory used=147.4MB, alloc=34.3MB, time=1.05 memory used=159.2MB, alloc=34.3MB, time=1.09 memory used=173.0MB, alloc=34.3MB, time=1.12 memory used=185.6MB, alloc=34.3MB, time=1.16 memory used=194.3MB, alloc=34.3MB, time=1.19 memory used=203.7MB, alloc=34.3MB, time=1.22 memory used=215.7MB, alloc=34.3MB, time=1.28 memory used=235.7MB, alloc=34.7MB, time=1.43 memory used=248.9MB, alloc=34.7MB, time=1.47 memory used=258.8MB, alloc=34.7MB, time=1.50 memory used=270.4MB, alloc=34.7MB, time=1.53 memory used=283.8MB, alloc=34.7MB, time=1.57 memory used=297.0MB, alloc=34.7MB, time=1.61 memory used=306.1MB, alloc=34.7MB, time=1.64 memory used=315.3MB, alloc=34.7MB, time=1.67 memory used=325.6MB, alloc=34.7MB, time=1.70 memory used=347.7MB, alloc=34.7MB, time=2.91 memory used=370.3MB, alloc=34.7MB, time=6.74 memory used=393.2MB, alloc=34.7MB, time=7.27 memory used=413.7MB, alloc=34.7MB, time=7.37 memory used=423.6MB, alloc=34.7MB, time=7.41 memory used=435.5MB, alloc=34.7MB, time=7.45 memory used=450.0MB, alloc=34.7MB, time=7.48 memory used=458.5MB, alloc=58.7MB, time=7.53 memory used=482.5MB, alloc=58.7MB, time=7.59 memory used=511.8MB, alloc=58.7MB, time=7.65 memory used=546.2MB, alloc=58.7MB, time=7.71 memory used=572.8MB, alloc=58.7MB, time=7.76 memory used=593.8MB, alloc=58.7MB, time=7.81 memory used=617.0MB, alloc=58.7MB, time=7.85 memory used=641.9MB, alloc=58.7MB, time=7.90 memory used=668.2MB, alloc=58.7MB, time=7.95 memory used=697.2MB, alloc=58.7MB, time=7.99 memory used=730.0MB, alloc=58.7MB, time=8.04 memory used=773.3MB, alloc=81.9MB, time=8.35 memory used=816.1MB, alloc=81.9MB, time=8.47 memory used=840.7MB, alloc=81.9MB, time=8.55 memory used=871.0MB, alloc=81.9MB, time=8.63 memory used=906.2MB, alloc=81.9MB, time=8.72 memory used=927.4MB, alloc=81.9MB, time=8.79 memory used=949.9MB, alloc=81.9MB, time=8.86 memory used=974.5MB, alloc=81.9MB, time=8.92 memory used=1002.7MB, alloc=81.9MB, time=9.00 memory used=1033.8MB, alloc=81.9MB, time=9.07 memory used=1069.1MB, alloc=81.9MB, time=9.15 memory used=1103.3MB, alloc=81.9MB, time=9.47 memory used=1139.5MB, alloc=81.9MB, time=9.58 memory used=1164.7MB, alloc=81.9MB, time=9.66 memory used=1195.9MB, alloc=81.9MB, time=9.74 memory used=1229.1MB, alloc=81.9MB, time=9.82 memory used=1249.6MB, alloc=81.9MB, time=9.89 memory used=1272.1MB, alloc=81.9MB, time=9.96 memory used=1297.6MB, alloc=81.9MB, time=10.03 memory used=1325.2MB, alloc=81.9MB, time=10.10 memory used=1356.1MB, alloc=81.9MB, time=10.17 memory used=1391.4MB, alloc=81.9MB, time=10.24 memory used=1430.0MB, alloc=81.9MB, time=12.68 memory used=1475.3MB, alloc=81.9MB, time=22.94 memory used=1527.1MB, alloc=81.9MB, time=23.50 memory used=1555.3MB, alloc=81.9MB, time=23.59 memory used=1583.1MB, alloc=81.9MB, time=23.66 memory used=1606.5MB, alloc=81.9MB, time=23.73 memory used=1633.7MB, alloc=81.9MB, time=23.80 memory used=1665.2MB, alloc=81.9MB, time=23.87 memory used=1701.0MB, alloc=81.9MB, time=23.96 memory used=1724.3MB, alloc=81.9MB, time=24.01 memory used=1744.6MB, alloc=81.9MB, time=24.07 memory used=1765.7MB, alloc=81.9MB, time=24.12 memory used=1788.1MB, alloc=81.9MB, time=24.18 memory used=1811.8MB, alloc=81.9MB, time=24.24 memory used=1836.9MB, alloc=81.9MB, time=24.30 memory used=1863.1MB, alloc=81.9MB, time=24.35 memory used=1891.3MB, alloc=81.9MB, time=24.41 memory used=1921.4MB, alloc=81.9MB, time=24.46 memory used=1952.8MB, alloc=81.9MB, time=24.51 memory used=1987.1MB, alloc=81.9MB, time=24.57 memory used=2024.7MB, alloc=81.9MB, time=24.64 memory used=2035.7MB, alloc=81.9MB, time=24.68 memory used=2047.2MB, alloc=81.9MB, time=24.72 memory used=2058.7MB, alloc=81.9MB, time=24.76 memory used=2070.8MB, alloc=81.9MB, time=24.80 memory used=2083.6MB, alloc=81.9MB, time=24.84 memory used=2139.1MB, alloc=81.9MB, time=26.97 memory used=2168.7MB, alloc=81.9MB, time=27.05 memory used=2194.1MB, alloc=81.9MB, time=27.12 memory used=2226.4MB, alloc=81.9MB, time=27.21 memory used=2254.4MB, alloc=81.9MB, time=27.27 memory used=2276.1MB, alloc=81.9MB, time=27.33 memory used=2300.2MB, alloc=81.9MB, time=27.38 memory used=2328.3MB, alloc=81.9MB, time=27.44 memory used=2373.9MB, alloc=81.9MB, time=27.86 memory used=2431.3MB, alloc=81.9MB, time=35.38 memory used=2466.8MB, alloc=105.9MB, time=47.86 memory used=2512.1MB, alloc=105.9MB, time=77.05 memory used=2567.3MB, alloc=105.9MB, time=82.65 memory used=2614.4MB, alloc=105.9MB, time=82.78 memory used=2649.9MB, alloc=105.9MB, time=82.88 memory used=2687.8MB, alloc=105.9MB, time=83.00 memory used=2732.3MB, alloc=105.9MB, time=83.11 memory used=2784.1MB, alloc=105.9MB, time=83.22 memory used=2826.1MB, alloc=105.9MB, time=83.31 memory used=2855.5MB, alloc=105.9MB, time=83.38 memory used=2886.2MB, alloc=105.9MB, time=83.46 memory used=2919.3MB, alloc=105.9MB, time=83.53 memory used=2954.9MB, alloc=105.9MB, time=83.62 memory used=2991.4MB, alloc=105.9MB, time=83.69 memory used=3030.1MB, alloc=105.9MB, time=83.77 memory used=3071.3MB, alloc=105.9MB, time=83.85 memory used=3114.7MB, alloc=105.9MB, time=83.93 memory used=3160.3MB, alloc=105.9MB, time=84.02 memory used=3208.3MB, alloc=105.9MB, time=84.11 memory used=3259.5MB, alloc=105.9MB, time=84.20 memory used=3318.6MB, alloc=105.9MB, time=84.29 memory used=3347.6MB, alloc=107.8MB, time=84.36 memory used=3358.8MB, alloc=107.8MB, time=84.40 memory used=3370.5MB, alloc=107.8MB, time=84.45 memory used=3382.2MB, alloc=107.8MB, time=84.50 memory used=3393.8MB, alloc=107.8MB, time=84.57 memory used=3405.3MB, alloc=107.8MB, time=84.62 memory used=3416.7MB, alloc=107.8MB, time=84.72 memory used=3428.3MB, alloc=107.8MB, time=84.76 memory used=3440.8MB, alloc=107.8MB, time=84.81 memory used=3453.5MB, alloc=107.8MB, time=84.86 memory used=3466.1MB, alloc=107.8MB, time=84.90 memory used=3478.5MB, alloc=107.8MB, time=84.95 memory used=3492.3MB, alloc=107.8MB, time=85.00 memory used=3505.9MB, alloc=107.8MB, time=85.06 memory used=3519.5MB, alloc=107.8MB, time=85.11 memory used=3534.1MB, alloc=107.8MB, time=85.20 memory used=3548.5MB, alloc=107.8MB, time=85.25 memory used=3562.8MB, alloc=107.8MB, time=85.30 memory used=3577.8MB, alloc=107.8MB, time=85.35 memory used=3592.7MB, alloc=107.8MB, time=85.43 memory used=3608.2MB, alloc=107.8MB, time=85.48 memory used=3624.6MB, alloc=107.8MB, time=85.56 memory used=3640.7MB, alloc=107.8MB, time=85.60 memory used=3657.8MB, alloc=107.8MB, time=85.65 memory used=3675.4MB, alloc=107.8MB, time=85.70 memory used=3693.2MB, alloc=107.8MB, time=85.75 memory used=3711.5MB, alloc=107.8MB, time=85.81 memory used=3731.1MB, alloc=107.8MB, time=85.86 memory used=3789.8MB, alloc=107.8MB, time=86.31 memory used=3861.4MB, alloc=107.8MB, time=87.81 memory used=3916.3MB, alloc=107.8MB, time=87.99 memory used=3991.7MB, alloc=107.8MB, time=90.85 memory used=4034.7MB, alloc=107.8MB, time=90.96 memory used=4085.3MB, alloc=107.8MB, time=91.50 memory used=4152.7MB, alloc=107.8MB, time=92.19 memory used=4216.7MB, alloc=107.8MB, time=92.83 memory used=4263.0MB, alloc=107.8MB, time=93.10 memory used=4316.6MB, alloc=107.8MB, time=93.69 memory used=4350.2MB, alloc=107.8MB, time=93.83 memory used=4393.4MB, alloc=107.8MB, time=93.96 memory used=4427.3MB, alloc=107.8MB, time=94.08 memory used=4453.5MB, alloc=107.8MB, time=94.19 memory used=4482.4MB, alloc=107.8MB, time=94.30 memory used=4514.8MB, alloc=107.8MB, time=94.41 memory used=4549.2MB, alloc=107.8MB, time=94.52 memory used=4586.6MB, alloc=107.8MB, time=94.64 memory used=4628.0MB, alloc=107.8MB, time=94.75 memory used=4673.0MB, alloc=107.8MB, time=94.87 memory used=4708.9MB, alloc=107.8MB, time=94.97 memory used=4732.6MB, alloc=107.8MB, time=95.06 memory used=4757.0MB, alloc=107.8MB, time=95.14 memory used=4782.1MB, alloc=107.8MB, time=95.22 memory used=4808.7MB, alloc=107.8MB, time=95.30 memory used=4837.0MB, alloc=107.8MB, time=95.38 memory used=4866.9MB, alloc=107.8MB, time=95.46 memory used=4898.9MB, alloc=107.8MB, time=95.55 memory used=4931.9MB, alloc=107.8MB, time=95.63 memory used=4967.2MB, alloc=107.8MB, time=95.72 memory used=5020.1MB, alloc=107.8MB, time=96.30 memory used=5055.1MB, alloc=107.8MB, time=96.44 memory used=5094.9MB, alloc=107.8MB, time=96.58 memory used=5135.8MB, alloc=107.8MB, time=96.71 memory used=5161.7MB, alloc=107.8MB, time=96.82 memory used=5190.4MB, alloc=107.8MB, time=96.92 memory used=5222.2MB, alloc=107.8MB, time=97.03 memory used=5256.4MB, alloc=107.8MB, time=97.14 memory used=5293.9MB, alloc=107.8MB, time=97.26 memory used=5334.7MB, alloc=107.8MB, time=97.37 memory used=5379.6MB, alloc=107.8MB, time=97.49 memory used=5420.8MB, alloc=107.8MB, time=97.60 memory used=5444.7MB, alloc=107.8MB, time=97.68 memory used=5469.2MB, alloc=107.8MB, time=97.76 memory used=5496.0MB, alloc=107.8MB, time=97.85 memory used=5523.3MB, alloc=107.8MB, time=97.94 memory used=5552.1MB, alloc=107.8MB, time=98.02 memory used=5582.0MB, alloc=107.8MB, time=98.11 memory used=5614.2MB, alloc=107.8MB, time=98.20 memory used=5648.1MB, alloc=107.8MB, time=98.28 memory used=5684.1MB, alloc=107.8MB, time=98.37 memory used=5743.9MB, alloc=107.8MB, time=107.48 memory used=5791.0MB, alloc=107.8MB, time=123.83 memory used=5833.0MB, alloc=107.8MB, time=124.49 memory used=5868.4MB, alloc=107.8MB, time=124.61 memory used=5899.9MB, alloc=107.8MB, time=124.73 memory used=5937.0MB, alloc=107.8MB, time=124.84 memory used=5980.1MB, alloc=107.8MB, time=124.95 memory used=6014.2MB, alloc=107.8MB, time=125.06 memory used=6038.7MB, alloc=107.8MB, time=125.15 memory used=6064.8MB, alloc=107.8MB, time=125.23 memory used=6093.4MB, alloc=107.8MB, time=125.33 memory used=6123.1MB, alloc=107.8MB, time=125.42 memory used=6155.6MB, alloc=107.8MB, time=125.52 memory used=6189.1MB, alloc=107.8MB, time=125.61 memory used=6223.6MB, alloc=107.8MB, time=125.71 memory used=6260.6MB, alloc=107.8MB, time=125.81 memory used=6300.7MB, alloc=107.8MB, time=125.90 memory used=6341.5MB, alloc=107.8MB, time=126.00 memory used=6385.1MB, alloc=107.8MB, time=126.10 memory used=6431.6MB, alloc=107.8MB, time=126.20 memory used=6463.0MB, alloc=107.8MB, time=126.29 memory used=6471.0MB, alloc=107.8MB, time=126.34 memory used=6479.7MB, alloc=107.8MB, time=126.40 memory used=6488.3MB, alloc=107.8MB, time=126.46 memory used=6497.0MB, alloc=107.8MB, time=126.56 memory used=6505.7MB, alloc=107.8MB, time=126.63 memory used=6514.4MB, alloc=107.8MB, time=126.69 memory used=6523.1MB, alloc=107.8MB, time=126.76 memory used=6531.8MB, alloc=107.8MB, time=126.81 memory used=6540.5MB, alloc=107.8MB, time=126.87 memory used=6549.1MB, alloc=107.8MB, time=126.94 memory used=6557.8MB, alloc=107.8MB, time=127.01 memory used=6566.5MB, alloc=107.8MB, time=127.07 memory used=6575.2MB, alloc=107.8MB, time=127.17 memory used=6583.9MB, alloc=107.8MB, time=127.24 memory used=6592.8MB, alloc=107.8MB, time=127.32 memory used=6603.4MB, alloc=107.8MB, time=127.40 memory used=6612.3MB, alloc=107.8MB, time=127.49 memory used=6622.8MB, alloc=107.8MB, time=127.57 memory used=6633.6MB, alloc=107.8MB, time=127.67 memory used=6644.3MB, alloc=107.8MB, time=127.75 memory used=6655.1MB, alloc=107.8MB, time=127.80 memory used=6665.8MB, alloc=107.8MB, time=127.86 memory used=6676.5MB, alloc=107.8MB, time=127.98 memory used=6687.1MB, alloc=107.8MB, time=128.04 memory used=6697.7MB, alloc=107.8MB, time=128.12 memory used=6708.3MB, alloc=107.8MB, time=128.18 memory used=6718.9MB, alloc=107.8MB, time=128.26 memory used=6729.4MB, alloc=107.8MB, time=128.34 memory used=6740.2MB, alloc=107.8MB, time=128.40 memory used=6752.4MB, alloc=107.8MB, time=128.47 memory used=6764.9MB, alloc=107.8MB, time=128.57 memory used=6777.3MB, alloc=107.8MB, time=128.64 memory used=6789.6MB, alloc=107.8MB, time=128.71 memory used=6801.9MB, alloc=107.8MB, time=128.78 memory used=6814.1MB, alloc=107.8MB, time=128.84 memory used=6826.2MB, alloc=107.8MB, time=128.90 memory used=6838.2MB, alloc=107.8MB, time=128.96 memory used=6850.4MB, alloc=107.8MB, time=129.02 memory used=6863.9MB, alloc=107.8MB, time=129.08 memory used=6877.6MB, alloc=107.8MB, time=129.17 memory used=6891.2MB, alloc=107.8MB, time=129.25 memory used=6904.6MB, alloc=107.8MB, time=129.30 memory used=6917.9MB, alloc=107.8MB, time=129.38 memory used=6931.5MB, alloc=107.8MB, time=129.47 memory used=6945.9MB, alloc=107.8MB, time=129.53 memory used=6960.5MB, alloc=107.8MB, time=129.62 memory used=6974.8MB, alloc=107.8MB, time=129.70 memory used=6989.4MB, alloc=107.8MB, time=129.76 memory used=7004.5MB, alloc=107.8MB, time=129.83 memory used=7019.8MB, alloc=107.8MB, time=129.90 memory used=7035.2MB, alloc=107.8MB, time=129.96 memory used=7051.0MB, alloc=107.8MB, time=130.03 memory used=7067.2MB, alloc=107.8MB, time=130.09 memory used=7083.6MB, alloc=107.8MB, time=130.19 memory used=7101.4MB, alloc=107.8MB, time=130.28 memory used=7118.8MB, alloc=107.8MB, time=130.38 memory used=7137.3MB, alloc=107.8MB, time=130.46 memory used=7155.7MB, alloc=107.8MB, time=130.53 memory used=7174.7MB, alloc=107.8MB, time=130.62 memory used=7194.5MB, alloc=107.8MB, time=130.70 memory used=7259.5MB, alloc=107.8MB, time=131.28 memory used=7294.7MB, alloc=107.8MB, time=131.40 memory used=7344.7MB, alloc=107.8MB, time=131.80 memory used=7362.7MB, alloc=107.8MB, time=131.87 memory used=7407.2MB, alloc=107.8MB, time=131.98 memory used=7443.3MB, alloc=107.8MB, time=132.09 memory used=7461.4MB, alloc=107.8MB, time=132.17 memory used=7504.8MB, alloc=107.8MB, time=132.28 memory used=7557.4MB, alloc=107.8MB, time=135.91 memory used=7601.6MB, alloc=107.8MB, time=136.07 memory used=7634.5MB, alloc=107.8MB, time=136.19 memory used=7676.6MB, alloc=107.8MB, time=136.32 memory used=7712.5MB, alloc=107.8MB, time=136.42 memory used=7741.2MB, alloc=107.8MB, time=136.52 memory used=7772.0MB, alloc=107.8MB, time=136.61 memory used=7806.0MB, alloc=107.8MB, time=136.71 memory used=7843.3MB, alloc=107.8MB, time=136.80 memory used=7885.0MB, alloc=107.8MB, time=136.90 memory used=7930.2MB, alloc=107.8MB, time=136.99 memory used=7969.0MB, alloc=107.8MB, time=137.09 memory used=7979.1MB, alloc=107.8MB, time=137.15 memory used=7989.5MB, alloc=107.8MB, time=137.21 memory used=8000.1MB, alloc=107.8MB, time=137.28 memory used=8011.1MB, alloc=107.8MB, time=137.34 memory used=8022.3MB, alloc=107.8MB, time=137.40 memory used=8033.8MB, alloc=107.8MB, time=137.47 memory used=8045.8MB, alloc=107.8MB, time=137.56 memory used=8058.3MB, alloc=107.8MB, time=137.62 memory used=8071.4MB, alloc=107.8MB, time=137.68 memory used=8084.9MB, alloc=107.8MB, time=137.74 memory used=8099.2MB, alloc=107.8MB, time=137.83 memory used=8169.2MB, alloc=107.8MB, time=139.29 memory used=8199.7MB, alloc=107.8MB, time=139.42 memory used=8236.9MB, alloc=107.8MB, time=139.55 memory used=8280.2MB, alloc=107.8MB, time=139.69 memory used=8311.6MB, alloc=107.8MB, time=139.80 memory used=8335.7MB, alloc=107.8MB, time=139.91 memory used=8363.1MB, alloc=107.8MB, time=140.02 memory used=8391.9MB, alloc=107.8MB, time=140.12 memory used=8421.9MB, alloc=107.8MB, time=140.22 memory used=8453.1MB, alloc=107.8MB, time=140.33 memory used=8485.8MB, alloc=107.8MB, time=140.45 memory used=8522.4MB, alloc=107.8MB, time=140.55 memory used=8560.4MB, alloc=107.8MB, time=140.66 memory used=8599.6MB, alloc=107.8MB, time=140.79 memory used=8640.3MB, alloc=107.8MB, time=140.90 memory used=8685.0MB, alloc=107.8MB, time=141.02 memory used=8715.0MB, alloc=131.8MB, time=141.13 memory used=8747.1MB, alloc=131.8MB, time=141.24 memory used=8780.5MB, alloc=131.8MB, time=141.34 memory used=8815.4MB, alloc=131.8MB, time=141.44 memory used=8854.0MB, alloc=131.8MB, time=141.55 memory used=8893.4MB, alloc=131.8MB, time=141.66 memory used=8933.2MB, alloc=131.8MB, time=141.77 memory used=8973.8MB, alloc=131.8MB, time=141.88 memory used=9017.9MB, alloc=131.8MB, time=141.99 memory used=9062.6MB, alloc=131.8MB, time=142.11 memory used=9108.2MB, alloc=131.8MB, time=142.23 memory used=9156.8MB, alloc=131.8MB, time=142.34 memory used=9206.0MB, alloc=131.8MB, time=142.47 memory used=9259.3MB, alloc=131.8MB, time=142.59 memory used=9312.2MB, alloc=131.8MB, time=142.71 memory used=9368.8MB, alloc=131.8MB, time=142.83 memory used=9428.9MB, alloc=131.8MB, time=142.96 memory used=9491.6MB, alloc=131.8MB, time=143.09 memory used=9556.8MB, alloc=131.8MB, time=143.21 memory used=9623.6MB, alloc=131.8MB, time=143.33 memory used=9661.8MB, alloc=131.8MB, time=143.42 memory used=9669.6MB, alloc=131.8MB, time=143.48 memory used=9677.6MB, alloc=131.8MB, time=143.53 memory used=9684.2MB, alloc=131.8MB, time=143.61 memory used=9690.8MB, alloc=131.8MB, time=143.67 memory used=9697.3MB, alloc=131.8MB, time=143.76 memory used=9704.7MB, alloc=131.8MB, time=143.82 memory used=9711.6MB, alloc=131.8MB, time=143.88 memory used=9719.6MB, alloc=131.8MB, time=143.94 memory used=9727.0MB, alloc=131.8MB, time=143.99 memory used=9735.1MB, alloc=131.8MB, time=144.06 memory used=9742.7MB, alloc=131.8MB, time=144.11 memory used=9750.3MB, alloc=131.8MB, time=144.19 memory used=9759.2MB, alloc=131.8MB, time=144.24 memory used=9768.0MB, alloc=131.8MB, time=144.32 memory used=9776.6MB, alloc=131.8MB, time=144.38 memory used=9785.1MB, alloc=131.8MB, time=144.44 memory used=9793.5MB, alloc=131.8MB, time=144.49 memory used=9802.7MB, alloc=131.8MB, time=144.55 memory used=9812.4MB, alloc=131.8MB, time=144.64 memory used=9821.8MB, alloc=131.8MB, time=144.70 memory used=9831.6MB, alloc=131.8MB, time=144.84 memory used=9841.6MB, alloc=131.8MB, time=144.91 memory used=9851.8MB, alloc=131.8MB, time=145.00 memory used=9861.9MB, alloc=131.8MB, time=145.06 memory used=9930.6MB, alloc=131.8MB, time=145.55 memory used=9965.2MB, alloc=131.8MB, time=145.90 memory used=9980.1MB, alloc=131.8MB, time=145.98 memory used=10034.4MB, alloc=131.8MB, time=146.10 memory used=10049.6MB, alloc=131.8MB, time=146.18 memory used=10114.9MB, alloc=131.8MB, time=146.33 memory used=10177.3MB, alloc=131.8MB, time=146.93 memory used=10242.3MB, alloc=131.8MB, time=147.07 memory used=10315.0MB, alloc=131.8MB, time=174.43 |\^/| 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(); 1428244728 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 2 F := [-20 x y z + 13 x y z - 7 y z + 12 y, 16 x z + 9 x z - 11 y - 9 z , 2 2 -15 x y z + 5 y z + 7 y z + 10 y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 4 2 3 G := [-14 x y z - 20 x z + 20 y z + 10 z , -10 y - 6 x z + 14 y + 20, 2 2 2 13 x z - 2 y z + 16 y z + 11 x z] > Problem := [F,G]; 2 2 2 Problem := [[-20 x y z + 13 x y z - 7 y z + 12 y, 3 2 2 2 2 2 16 x z + 9 x z - 11 y - 9 z , -15 x y z + 5 y z + 7 y z + 10 y], [ 2 2 2 3 4 2 3 -14 x y z - 20 x z + 20 y z + 10 z , -10 y - 6 x z + 14 y + 20, 2 2 2 13 x z - 2 y z + 16 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=0.18 memory used=24.8MB, alloc=32.3MB, time=0.46 memory used=43.4MB, alloc=32.3MB, time=0.63 memory used=63.4MB, alloc=32.3MB, time=0.87 memory used=85.2MB, alloc=36.3MB, time=1.16 memory used=108.6MB, alloc=60.3MB, time=1.43 memory used=138.1MB, alloc=60.3MB, time=1.50 memory used=173.8MB, alloc=60.3MB, time=1.72 memory used=203.2MB, alloc=60.3MB, time=1.80 memory used=238.7MB, alloc=60.3MB, time=2.63 memory used=273.9MB, alloc=60.3MB, time=3.28 memory used=298.0MB, alloc=60.3MB, time=3.34 memory used=329.8MB, alloc=60.3MB, time=3.56 memory used=357.2MB, alloc=60.3MB, time=3.69 memory used=404.0MB, alloc=68.3MB, time=4.22 memory used=448.5MB, alloc=68.3MB, time=4.80 memory used=495.0MB, alloc=68.3MB, time=5.35 memory used=540.7MB, alloc=92.3MB, time=5.97 memory used=607.3MB, alloc=92.3MB, time=6.92 memory used=665.3MB, alloc=92.3MB, time=7.46 memory used=731.2MB, alloc=116.3MB, time=8.34 memory used=798.2MB, alloc=116.3MB, time=9.15 memory used=847.9MB, alloc=116.3MB, time=9.35 memory used=896.5MB, alloc=116.3MB, time=9.63 memory used=972.3MB, alloc=116.3MB, time=10.60 memory used=1081.6MB, alloc=373.8MB, time=11.78 memory used=1177.6MB, alloc=373.8MB, time=13.51 memory used=1249.9MB, alloc=373.8MB, time=14.16 memory used=1289.7MB, alloc=373.8MB, time=14.33 memory used=1330.1MB, alloc=373.8MB, time=14.48 memory used=1383.0MB, alloc=373.8MB, time=15.93 memory used=1423.7MB, alloc=373.8MB, time=16.08 memory used=1456.7MB, alloc=373.8MB, time=16.22 memory used=1497.2MB, alloc=373.8MB, time=16.36 memory used=1544.6MB, alloc=373.8MB, time=16.51 memory used=1572.0MB, alloc=397.8MB, time=16.66 memory used=1616.2MB, alloc=397.8MB, time=16.80 memory used=1666.5MB, alloc=397.8MB, time=16.95 memory used=1723.0MB, alloc=397.8MB, time=17.10 memory used=1786.1MB, alloc=397.8MB, time=17.25 memory used=1878.1MB, alloc=397.8MB, time=17.45 memory used=2042.7MB, alloc=397.8MB, time=22.70 memory used=2095.3MB, alloc=397.8MB, time=22.88 memory used=2149.0MB, alloc=397.8MB, time=23.06 memory used=2215.1MB, alloc=397.8MB, time=23.25 memory used=2262.4MB, alloc=397.8MB, time=23.40 memory used=2304.4MB, alloc=397.8MB, time=23.54 memory used=2349.2MB, alloc=397.8MB, time=23.72 memory used=2398.5MB, alloc=397.8MB, time=23.86 memory used=2451.5MB, alloc=397.8MB, time=24.01 memory used=2509.3MB, alloc=397.8MB, time=24.15 memory used=2571.8MB, alloc=397.8MB, time=24.31 memory used=2638.7MB, alloc=397.8MB, time=24.48 memory used=2837.2MB, alloc=397.8MB, time=24.89 memory used=2995.6MB, alloc=397.8MB, time=25.18 memory used=3187.6MB, alloc=397.8MB, time=27.25 memory used=3235.6MB, alloc=397.8MB, time=27.41 memory used=3299.2MB, alloc=397.8MB, time=27.59 memory used=3347.8MB, alloc=397.8MB, time=27.73 memory used=3391.7MB, alloc=397.8MB, time=27.88 memory used=3440.4MB, alloc=397.8MB, time=28.04 memory used=3495.6MB, alloc=397.8MB, time=28.19 memory used=3556.4MB, alloc=397.8MB, time=28.36 memory used=3623.5MB, alloc=397.8MB, time=28.52 memory used=3798.6MB, alloc=397.8MB, time=28.96 memory used=3852.5MB, alloc=397.8MB, time=29.10 memory used=3999.8MB, alloc=397.8MB, time=30.72 memory used=4055.3MB, alloc=397.8MB, time=30.92 memory used=4123.1MB, alloc=397.8MB, time=31.53 memory used=4196.9MB, alloc=397.8MB, time=32.13 memory used=4300.8MB, alloc=397.8MB, time=33.25 memory used=4400.9MB, alloc=397.8MB, time=34.70 memory used=4516.0MB, alloc=421.8MB, time=36.02 memory used=4607.3MB, alloc=421.8MB, time=36.65 memory used=4678.6MB, alloc=421.8MB, time=38.06 memory used=4765.7MB, alloc=421.8MB, time=38.89 memory used=4881.5MB, alloc=445.8MB, time=40.22 memory used=5006.9MB, alloc=445.8MB, time=41.81 memory used=5141.7MB, alloc=469.8MB, time=43.85 memory used=5244.7MB, alloc=469.8MB, time=45.18 memory used=5350.7MB, alloc=469.8MB, time=46.36 memory used=5463.3MB, alloc=469.8MB, time=47.43 memory used=5577.7MB, alloc=469.8MB, time=48.54 memory used=5669.1MB, alloc=469.8MB, time=49.64 memory used=5765.4MB, alloc=469.8MB, time=50.99 memory used=5835.6MB, alloc=469.8MB, time=52.05 memory used=5897.4MB, alloc=469.8MB, time=53.04 memory used=5965.9MB, alloc=469.8MB, time=54.15 memory used=6041.5MB, alloc=493.8MB, time=55.24 memory used=6143.0MB, alloc=493.8MB, time=58.36 memory used=6228.7MB, alloc=493.8MB, time=58.77 memory used=6340.7MB, alloc=493.8MB, time=59.64 memory used=6455.2MB, alloc=493.8MB, time=62.49 memory used=6569.2MB, alloc=493.8MB, time=63.67 memory used=6633.3MB, alloc=493.8MB, time=64.60 memory used=6732.0MB, alloc=493.8MB, time=65.54 memory used=6844.7MB, alloc=493.8MB, time=66.56 memory used=6914.3MB, alloc=493.8MB, time=67.77 memory used=6959.4MB, alloc=493.8MB, time=68.66 memory used=7012.6MB, alloc=493.8MB, time=69.72 memory used=7053.5MB, alloc=493.8MB, time=70.63 memory used=7191.2MB, alloc=517.8MB, time=71.93 memory used=7300.9MB, alloc=517.8MB, time=72.62 memory used=7416.9MB, alloc=517.8MB, time=75.13 memory used=7538.2MB, alloc=517.8MB, time=75.99 memory used=7689.0MB, alloc=517.8MB, time=89.50 memory used=7795.8MB, alloc=517.8MB, time=91.75 memory used=7902.1MB, alloc=517.8MB, time=92.28 memory used=7980.2MB, alloc=517.8MB, time=92.72 memory used=8077.6MB, alloc=517.8MB, time=93.16 memory used=8231.1MB, alloc=517.8MB, time=94.16 memory used=8353.8MB, alloc=517.8MB, time=94.93 memory used=8506.3MB, alloc=517.8MB, time=110.05 memory used=8601.7MB, alloc=517.8MB, time=110.56 memory used=8702.2MB, alloc=517.8MB, time=111.05 memory used=8783.1MB, alloc=517.8MB, time=111.49 memory used=8883.8MB, alloc=517.8MB, time=111.98 memory used=9038.2MB, alloc=517.8MB, time=112.73 memory used=9147.1MB, alloc=517.8MB, time=113.37 memory used=9261.1MB, alloc=517.8MB, time=114.80 memory used=9379.0MB, alloc=517.8MB, time=115.63 memory used=9627.2MB, alloc=517.8MB, time=119.15 memory used=9885.3MB, alloc=517.8MB, time=122.43 memory used=10036.8MB, alloc=517.8MB, time=124.50 memory used=10251.7MB, alloc=541.8MB, time=126.41 memory used=10496.1MB, alloc=541.8MB, time=129.95 memory used=10685.9MB, alloc=565.8MB, time=132.81 memory used=10867.4MB, alloc=589.8MB, time=135.85 memory used=11013.7MB, alloc=613.8MB, time=136.83 memory used=11129.3MB, alloc=613.8MB, time=137.57 memory used=11274.6MB, alloc=613.8MB, time=138.31 memory used=11401.8MB, alloc=613.8MB, time=139.30 memory used=11562.1MB, alloc=613.8MB, time=140.17 memory used=11673.0MB, alloc=613.8MB, time=140.94 memory used=11823.5MB, alloc=613.8MB, time=141.70 memory used=11966.3MB, alloc=613.8MB, time=147.84 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428245028 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 4 2 2 2 F := [14 x y z - 8 x y - 15 x z - 16 z, 16 y + 7 x y + 18 y z + 17 y z , 3 2 2 3 2 -9 x y + 8 y z - 17 y z - 15 y z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 4 4 2 G := [5 x y - 13 x - 6 y z - 9 z , -7 y - 13 z + 14 x - 3, 3 2 2 4 2 -18 x y + 16 x y + 10 z - 13 y z] > Problem := [F,G]; 2 3 3 Problem := [[14 x y z - 8 x y - 15 x z - 16 z, 4 2 2 2 3 2 2 3 2 16 y + 7 x y + 18 y z + 17 y z , -9 x y + 8 y z - 17 y z - 15 y z ], 2 2 3 2 3 4 4 2 [5 x y - 13 x - 6 y z - 9 z , -7 y - 13 z + 14 x - 3, 3 2 2 4 2 -18 x y + 16 x y + 10 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=4.4MB, alloc=32.3MB, time=0.19 memory used=24.7MB, alloc=32.3MB, time=0.46 memory used=51.3MB, alloc=56.3MB, time=0.76 memory used=84.2MB, alloc=56.3MB, time=1.28 memory used=113.5MB, alloc=56.3MB, time=1.86 memory used=154.7MB, alloc=60.3MB, time=2.10 memory used=210.2MB, alloc=62.0MB, time=2.83 memory used=246.8MB, alloc=62.0MB, time=3.31 memory used=274.9MB, alloc=62.0MB, time=3.39 memory used=300.1MB, alloc=62.0MB, time=3.45 memory used=322.6MB, alloc=62.0MB, time=3.51 memory used=349.3MB, alloc=62.0MB, time=3.57 memory used=383.6MB, alloc=62.0MB, time=3.77 memory used=424.3MB, alloc=62.0MB, time=4.53 memory used=449.3MB, alloc=62.0MB, time=4.61 memory used=475.2MB, alloc=62.0MB, time=4.68 memory used=501.9MB, alloc=62.0MB, time=4.74 memory used=521.6MB, alloc=62.0MB, time=4.80 memory used=543.6MB, alloc=62.0MB, time=4.85 memory used=568.3MB, alloc=62.0MB, time=4.91 memory used=596.4MB, alloc=62.0MB, time=4.98 memory used=628.0MB, alloc=62.0MB, time=5.04 memory used=649.6MB, alloc=83.8MB, time=5.12 memory used=663.3MB, alloc=83.8MB, time=5.16 memory used=677.3MB, alloc=83.8MB, time=5.21 memory used=692.3MB, alloc=83.8MB, time=5.26 memory used=708.3MB, alloc=83.8MB, time=5.31 memory used=725.9MB, alloc=83.8MB, time=5.37 memory used=774.9MB, alloc=83.8MB, time=6.41 memory used=802.6MB, alloc=83.8MB, time=6.50 memory used=827.6MB, alloc=83.8MB, time=6.57 memory used=849.5MB, alloc=83.8MB, time=6.63 memory used=874.9MB, alloc=83.8MB, time=6.69 memory used=943.7MB, alloc=83.8MB, time=7.26 memory used=989.2MB, alloc=107.8MB, time=21.26 memory used=1023.4MB, alloc=131.8MB, time=76.00 memory used=1064.4MB, alloc=155.8MB, time=127.92 memory used=1106.3MB, alloc=155.8MB, time=129.35 |\^/| 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(); 1428245328 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 4 2 F := [8 x y + 11 x y z - 7 y z - 12 x , -18 x y + 7 z + 10 x z + 6 z, 2 2 3 4 2 -19 x z + 15 x y + 12 y - 10 x y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [-3 y z - 13 y z - 6 x z - 20 x z, 3 2 3 2 2 3 2 2 3 2 x z + 10 x y z - 10 x z - 12 y z , 16 x y - 7 x z + y - 14 y z ] > Problem := [F,G]; 3 2 2 2 Problem := [[8 x y + 11 x y z - 7 y z - 12 x , 3 4 2 2 2 3 4 2 -18 x y + 7 z + 10 x z + 6 z, -19 x z + 15 x y + 12 y - 10 x y], [ 2 2 3 2 3 2 3 2 2 -3 y z - 13 y z - 6 x z - 20 x z, x z + 10 x y z - 10 x z - 12 y z , 3 2 2 3 2 16 x y - 7 x z + 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=4.6MB, alloc=32.3MB, time=0.18 memory used=25.8MB, alloc=32.3MB, time=0.48 memory used=45.6MB, alloc=56.3MB, time=0.75 memory used=87.8MB, alloc=56.3MB, time=1.54 memory used=228.4MB, alloc=68.3MB, time=2.71 memory used=271.6MB, alloc=70.0MB, time=3.16 memory used=313.4MB, alloc=70.0MB, time=3.59 memory used=335.1MB, alloc=70.0MB, time=3.66 memory used=357.4MB, alloc=70.0MB, time=3.73 memory used=376.4MB, alloc=70.0MB, time=3.79 memory used=406.6MB, alloc=70.0MB, time=3.97 memory used=429.6MB, alloc=70.0MB, time=4.10 memory used=452.3MB, alloc=70.0MB, time=4.19 memory used=475.8MB, alloc=70.0MB, time=4.28 memory used=498.9MB, alloc=70.0MB, time=4.44 memory used=524.6MB, alloc=81.9MB, time=4.53 memory used=557.0MB, alloc=81.9MB, time=4.61 memory used=580.3MB, alloc=81.9MB, time=4.68 memory used=603.6MB, alloc=81.9MB, time=4.76 memory used=635.3MB, alloc=81.9MB, time=4.84 memory used=658.8MB, alloc=81.9MB, time=4.91 memory used=688.9MB, alloc=83.8MB, time=5.24 memory used=708.6MB, alloc=83.8MB, time=5.30 memory used=729.4MB, alloc=83.8MB, time=5.36 memory used=751.4MB, alloc=83.8MB, time=5.43 memory used=780.6MB, alloc=83.8MB, time=5.50 memory used=818.0MB, alloc=83.8MB, time=5.57 memory used=858.0MB, alloc=83.8MB, time=5.66 memory used=900.6MB, alloc=83.8MB, time=5.74 memory used=923.1MB, alloc=83.8MB, time=5.80 memory used=935.8MB, alloc=83.8MB, time=5.85 memory used=948.6MB, alloc=83.8MB, time=5.89 memory used=961.7MB, alloc=83.8MB, time=5.98 memory used=975.0MB, alloc=83.8MB, time=6.04 memory used=990.3MB, alloc=83.8MB, time=6.10 memory used=1009.2MB, alloc=83.8MB, time=6.20 memory used=1029.3MB, alloc=83.8MB, time=6.26 memory used=1050.5MB, alloc=83.8MB, time=6.34 memory used=1072.8MB, alloc=83.8MB, time=6.42 memory used=1107.1MB, alloc=83.8MB, time=6.50 memory used=1145.2MB, alloc=83.8MB, time=6.58 memory used=1185.9MB, alloc=83.8MB, time=6.65 memory used=1228.9MB, alloc=83.8MB, time=6.74 memory used=1241.5MB, alloc=83.8MB, time=6.79 memory used=1254.2MB, alloc=83.8MB, time=6.83 memory used=1267.1MB, alloc=83.8MB, time=6.88 memory used=1280.2MB, alloc=83.8MB, time=6.92 memory used=1293.5MB, alloc=83.8MB, time=7.03 memory used=1349.9MB, alloc=83.8MB, time=8.98 memory used=1379.9MB, alloc=83.8MB, time=9.10 memory used=1401.5MB, alloc=83.8MB, time=9.17 memory used=1426.5MB, alloc=83.8MB, time=9.25 memory used=1443.2MB, alloc=83.8MB, time=9.32 memory used=1462.6MB, alloc=83.8MB, time=9.39 memory used=1484.9MB, alloc=83.8MB, time=9.45 memory used=1510.4MB, alloc=83.8MB, time=9.52 memory used=1539.1MB, alloc=83.8MB, time=9.59 memory used=1551.4MB, alloc=83.8MB, time=9.66 memory used=1605.9MB, alloc=83.8MB, time=10.85 memory used=1644.9MB, alloc=83.8MB, time=11.33 memory used=1686.1MB, alloc=107.8MB, time=11.84 memory used=1740.7MB, alloc=131.8MB, time=15.73 memory used=1794.5MB, alloc=155.8MB, time=27.76 memory used=1848.1MB, alloc=155.8MB, time=27.90 memory used=1905.4MB, alloc=155.8MB, time=28.05 memory used=1963.6MB, alloc=155.8MB, time=28.20 memory used=2022.1MB, alloc=155.8MB, time=28.35 memory used=2081.0MB, alloc=155.8MB, time=28.49 memory used=2145.5MB, alloc=155.8MB, time=28.64 memory used=2210.4MB, alloc=155.8MB, time=28.78 memory used=2275.4MB, alloc=155.8MB, time=28.95 memory used=2346.2MB, alloc=155.8MB, time=29.11 memory used=2416.8MB, alloc=155.8MB, time=29.28 memory used=2482.0MB, alloc=155.8MB, time=29.44 memory used=2526.9MB, alloc=155.8MB, time=29.55 memory used=2566.2MB, alloc=155.8MB, time=29.65 memory used=2602.9MB, alloc=179.8MB, time=29.77 memory used=2647.7MB, alloc=179.8MB, time=29.89 memory used=2693.3MB, alloc=179.8MB, time=30.00 memory used=2743.9MB, alloc=179.8MB, time=30.12 memory used=2794.2MB, alloc=179.8MB, time=30.25 memory used=2844.2MB, alloc=179.8MB, time=30.38 memory used=2899.1MB, alloc=179.8MB, time=30.50 memory used=2953.2MB, alloc=179.8MB, time=30.62 memory used=3006.8MB, alloc=179.8MB, time=30.76 memory used=3064.7MB, alloc=179.8MB, time=30.89 memory used=3121.7MB, alloc=179.8MB, time=31.01 memory used=3182.5MB, alloc=179.8MB, time=31.15 memory used=3242.1MB, alloc=179.8MB, time=31.28 memory used=3304.8MB, alloc=179.8MB, time=31.41 memory used=3365.8MB, alloc=179.8MB, time=31.53 memory used=3429.1MB, alloc=179.8MB, time=31.66 memory used=3494.2MB, alloc=179.8MB, time=31.79 memory used=3564.5MB, alloc=179.8MB, time=31.92 memory used=3634.4MB, alloc=179.8MB, time=32.06 memory used=3706.5MB, alloc=179.8MB, time=32.20 memory used=3784.5MB, alloc=179.8MB, time=32.34 memory used=3865.6MB, alloc=179.8MB, time=32.49 memory used=3949.4MB, alloc=179.8MB, time=47.87 memory used=4036.2MB, alloc=179.8MB, time=48.12 memory used=4112.7MB, alloc=179.8MB, time=48.30 memory used=4194.8MB, alloc=179.8MB, time=48.49 memory used=4277.7MB, alloc=179.8MB, time=48.66 memory used=4366.6MB, alloc=179.8MB, time=48.86 memory used=4455.9MB, alloc=179.8MB, time=49.04 memory used=4551.1MB, alloc=179.8MB, time=49.25 memory used=4646.2MB, alloc=179.8MB, time=49.45 memory used=4715.6MB, alloc=179.8MB, time=49.61 memory used=4767.2MB, alloc=179.8MB, time=49.73 memory used=4814.0MB, alloc=179.8MB, time=49.85 memory used=4863.5MB, alloc=179.8MB, time=49.97 memory used=4914.4MB, alloc=179.8MB, time=50.10 memory used=4964.9MB, alloc=179.8MB, time=50.23 memory used=5015.0MB, alloc=179.8MB, time=50.35 memory used=5064.9MB, alloc=179.8MB, time=50.47 memory used=5119.2MB, alloc=179.8MB, time=50.59 memory used=5173.2MB, alloc=179.8MB, time=50.72 memory used=5231.5MB, alloc=179.8MB, time=50.85 memory used=5288.9MB, alloc=179.8MB, time=50.98 memory used=5345.3MB, alloc=179.8MB, time=51.11 memory used=5405.6MB, alloc=179.8MB, time=51.24 memory used=5469.1MB, alloc=179.8MB, time=51.38 memory used=5530.9MB, alloc=179.8MB, time=51.51 memory used=5595.4MB, alloc=179.8MB, time=51.64 memory used=5661.6MB, alloc=179.8MB, time=51.77 memory used=5729.2MB, alloc=179.8MB, time=51.91 memory used=5801.0MB, alloc=179.8MB, time=52.05 memory used=5875.2MB, alloc=179.8MB, time=52.19 memory used=5952.8MB, alloc=179.8MB, time=52.33 memory used=6032.6MB, alloc=179.8MB, time=52.46 memory used=6118.6MB, alloc=179.8MB, time=52.94 memory used=6138.0MB, alloc=179.8MB, time=53.80 memory used=6138.0MB, alloc=435.8MB, time=53.84 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428245628 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 F := [18 x + 9 y z - 8 x z + 3, -7 x z + 13 y + 2 y , 2 2 2 -18 x y + 16 y z - 20 x y + 12 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 4 3 2 G := [-20 x y - 10 y z - 14 y + 5, -18 x + 12 y + 3 y z - 6 x z , 2 2 3 -3 x z + 9 y z - 4 y z + 5 x] > Problem := [F,G]; 3 2 3 3 2 Problem := [[18 x + 9 y z - 8 x z + 3, -7 x z + 13 y + 2 y , 2 2 2 3 3 2 -18 x y + 16 y z - 20 x y + 12 z ], [-20 x y - 10 y z - 14 y + 5, 4 4 3 2 2 2 3 -18 x + 12 y + 3 y z - 6 x z , -3 x z + 9 y z - 4 y z + 5 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=24.6MB, alloc=32.3MB, time=0.47 memory used=45.7MB, alloc=36.5MB, time=0.77 memory used=65.3MB, alloc=37.5MB, time=0.92 memory used=78.8MB, alloc=37.5MB, time=0.99 memory used=90.4MB, alloc=37.5MB, time=1.03 memory used=106.5MB, alloc=37.5MB, time=1.26 memory used=122.0MB, alloc=37.5MB, time=1.34 memory used=138.3MB, alloc=37.5MB, time=1.46 memory used=160.7MB, alloc=61.5MB, time=1.74 memory used=195.7MB, alloc=61.5MB, time=2.18 memory used=236.3MB, alloc=61.5MB, time=2.61 memory used=281.8MB, alloc=62.1MB, time=3.77 memory used=306.2MB, alloc=62.1MB, time=3.84 memory used=331.0MB, alloc=62.1MB, time=3.90 memory used=355.1MB, alloc=62.1MB, time=3.96 memory used=404.7MB, alloc=70.1MB, time=4.49 memory used=442.0MB, alloc=70.1MB, time=4.75 memory used=465.3MB, alloc=70.1MB, time=4.85 memory used=490.1MB, alloc=70.1MB, time=4.93 memory used=507.9MB, alloc=70.1MB, time=5.00 memory used=529.2MB, alloc=70.1MB, time=5.07 memory used=554.0MB, alloc=70.1MB, time=5.14 memory used=590.5MB, alloc=70.1MB, time=5.87 memory used=615.1MB, alloc=70.1MB, time=5.96 memory used=634.7MB, alloc=70.1MB, time=6.03 memory used=659.3MB, alloc=70.1MB, time=6.11 memory used=680.5MB, alloc=70.1MB, time=6.18 memory used=698.3MB, alloc=70.1MB, time=6.24 memory used=718.5MB, alloc=70.1MB, time=6.30 memory used=747.6MB, alloc=70.1MB, time=6.47 memory used=771.4MB, alloc=70.1MB, time=6.63 memory used=807.5MB, alloc=70.1MB, time=7.49 memory used=844.0MB, alloc=94.1MB, time=8.14 memory used=891.4MB, alloc=94.1MB, time=8.29 memory used=921.6MB, alloc=94.1MB, time=8.42 memory used=955.3MB, alloc=94.1MB, time=8.55 memory used=992.8MB, alloc=94.1MB, time=8.68 memory used=1034.3MB, alloc=94.1MB, time=8.82 memory used=1082.0MB, alloc=94.1MB, time=8.95 memory used=1113.7MB, alloc=94.1MB, time=9.06 memory used=1139.0MB, alloc=94.1MB, time=9.17 memory used=1162.2MB, alloc=94.1MB, time=9.27 memory used=1189.4MB, alloc=94.1MB, time=9.37 memory used=1217.9MB, alloc=94.1MB, time=9.48 memory used=1247.3MB, alloc=94.1MB, time=9.59 memory used=1277.3MB, alloc=94.1MB, time=9.71 memory used=1308.1MB, alloc=94.1MB, time=9.82 memory used=1339.6MB, alloc=94.1MB, time=9.91 memory used=1371.7MB, alloc=94.1MB, time=10.02 memory used=1404.5MB, alloc=94.1MB, time=10.13 memory used=1437.9MB, alloc=94.1MB, time=10.24 memory used=1472.0MB, alloc=94.1MB, time=10.36 memory used=1507.3MB, alloc=94.1MB, time=10.46 memory used=1547.8MB, alloc=94.1MB, time=10.57 memory used=1589.6MB, alloc=94.1MB, time=10.69 memory used=1632.1MB, alloc=94.1MB, time=10.80 memory used=1675.3MB, alloc=94.1MB, time=10.92 memory used=1719.0MB, alloc=94.1MB, time=11.04 memory used=1762.5MB, alloc=94.1MB, time=11.16 memory used=1789.3MB, alloc=118.1MB, time=11.26 memory used=1820.0MB, alloc=118.1MB, time=11.35 memory used=1850.3MB, alloc=118.1MB, time=11.45 memory used=1882.7MB, alloc=118.1MB, time=11.54 memory used=1915.4MB, alloc=118.1MB, time=11.64 memory used=1948.3MB, alloc=118.1MB, time=11.72 memory used=1981.4MB, alloc=118.1MB, time=11.82 memory used=2015.5MB, alloc=118.1MB, time=11.92 memory used=2054.9MB, alloc=118.1MB, time=12.02 memory used=2095.2MB, alloc=118.1MB, time=12.12 memory used=2135.7MB, alloc=118.1MB, time=12.23 memory used=2176.4MB, alloc=118.1MB, time=12.33 memory used=2217.2MB, alloc=118.1MB, time=12.44 memory used=2258.2MB, alloc=118.1MB, time=12.54 memory used=2299.2MB, alloc=118.1MB, time=12.64 memory used=2340.4MB, alloc=118.1MB, time=12.74 memory used=2382.6MB, alloc=118.1MB, time=12.84 memory used=2429.7MB, alloc=118.1MB, time=12.95 memory used=2477.8MB, alloc=118.1MB, time=13.07 memory used=2525.8MB, alloc=118.1MB, time=13.18 memory used=2573.7MB, alloc=118.1MB, time=13.29 memory used=2621.6MB, alloc=118.1MB, time=13.41 memory used=2670.6MB, alloc=118.1MB, time=13.52 memory used=2723.7MB, alloc=118.1MB, time=13.64 memory used=2777.7MB, alloc=118.1MB, time=13.75 memory used=2831.3MB, alloc=118.1MB, time=13.87 memory used=2885.8MB, alloc=118.1MB, time=13.99 memory used=2943.9MB, alloc=118.1MB, time=14.10 memory used=3002.6MB, alloc=118.1MB, time=14.22 memory used=3061.9MB, alloc=118.1MB, time=14.34 memory used=3124.0MB, alloc=118.1MB, time=14.46 memory used=3187.7MB, alloc=118.1MB, time=14.58 memory used=3253.5MB, alloc=118.1MB, time=14.71 memory used=3320.6MB, alloc=118.1MB, time=14.83 memory used=3376.2MB, alloc=131.8MB, time=14.95 memory used=3391.2MB, alloc=131.8MB, time=15.01 memory used=3399.7MB, alloc=131.8MB, time=15.09 memory used=3404.0MB, alloc=131.8MB, time=15.14 memory used=3408.5MB, alloc=131.8MB, time=15.20 memory used=3413.7MB, alloc=131.8MB, time=15.24 memory used=3419.0MB, alloc=131.8MB, time=15.34 memory used=3424.2MB, alloc=131.8MB, time=15.38 memory used=3429.4MB, alloc=131.8MB, time=15.42 memory used=3434.6MB, alloc=131.8MB, time=15.47 memory used=3439.8MB, alloc=131.8MB, time=15.52 memory used=3445.0MB, alloc=131.8MB, time=15.56 memory used=3450.2MB, alloc=131.8MB, time=15.67 memory used=3455.3MB, alloc=131.8MB, time=15.74 memory used=3460.4MB, alloc=131.8MB, time=15.78 memory used=3465.5MB, alloc=131.8MB, time=15.84 memory used=3470.6MB, alloc=131.8MB, time=15.90 memory used=3475.7MB, alloc=131.8MB, time=15.99 memory used=3480.7MB, alloc=131.8MB, time=16.04 memory used=3485.7MB, alloc=131.8MB, time=16.10 memory used=3490.7MB, alloc=131.8MB, time=16.16 memory used=3495.7MB, alloc=131.8MB, time=16.22 memory used=3500.7MB, alloc=131.8MB, time=16.26 memory used=3505.6MB, alloc=131.8MB, time=16.30 memory used=3510.5MB, alloc=131.8MB, time=16.39 memory used=3515.4MB, alloc=131.8MB, time=16.43 memory used=3520.3MB, alloc=131.8MB, time=16.51 memory used=3525.2MB, alloc=131.8MB, time=16.55 memory used=3530.0MB, alloc=131.8MB, time=16.61 memory used=3534.9MB, alloc=131.8MB, time=16.68 memory used=3539.7MB, alloc=131.8MB, time=16.76 memory used=3544.5MB, alloc=131.8MB, time=16.85 memory used=3550.7MB, alloc=131.8MB, time=16.94 memory used=3556.3MB, alloc=131.8MB, time=17.00 memory used=3563.4MB, alloc=131.8MB, time=17.07 memory used=3569.6MB, alloc=131.8MB, time=17.13 memory used=3575.1MB, alloc=131.8MB, time=17.20 memory used=3582.0MB, alloc=131.8MB, time=17.29 memory used=3588.2MB, alloc=131.8MB, time=17.35 memory used=3595.8MB, alloc=131.8MB, time=17.40 memory used=3602.0MB, alloc=131.8MB, time=17.46 memory used=3609.3MB, alloc=131.8MB, time=17.52 memory used=3615.6MB, alloc=131.8MB, time=17.58 memory used=3622.7MB, alloc=131.8MB, time=17.63 memory used=3629.4MB, alloc=131.8MB, time=17.68 memory used=3635.8MB, alloc=131.8MB, time=17.73 memory used=3642.5MB, alloc=131.8MB, time=17.77 memory used=3650.3MB, alloc=131.8MB, time=17.83 memory used=3657.2MB, alloc=131.8MB, time=17.90 memory used=3665.7MB, alloc=131.8MB, time=17.96 memory used=3674.0MB, alloc=131.8MB, time=18.03 memory used=3682.2MB, alloc=131.8MB, time=18.10 memory used=3690.3MB, alloc=131.8MB, time=18.19 memory used=3698.3MB, alloc=131.8MB, time=18.23 memory used=3706.3MB, alloc=131.8MB, time=18.33 memory used=3714.1MB, alloc=131.8MB, time=18.38 memory used=3723.5MB, alloc=131.8MB, time=18.46 memory used=3731.9MB, alloc=131.8MB, time=18.50 memory used=3740.8MB, alloc=131.8MB, time=18.58 memory used=3749.9MB, alloc=131.8MB, time=18.62 memory used=3759.1MB, alloc=131.8MB, time=18.72 memory used=3768.3MB, alloc=131.8MB, time=18.77 memory used=3778.4MB, alloc=131.8MB, time=18.86 memory used=3848.5MB, alloc=131.8MB, time=20.16 memory used=3902.3MB, alloc=131.8MB, time=20.34 memory used=3953.2MB, alloc=131.8MB, time=20.50 memory used=4014.8MB, alloc=131.8MB, time=20.68 memory used=4081.0MB, alloc=131.8MB, time=20.85 memory used=4119.6MB, alloc=131.8MB, time=20.98 memory used=4157.3MB, alloc=131.8MB, time=21.12 memory used=4199.9MB, alloc=131.8MB, time=21.25 memory used=4244.2MB, alloc=131.8MB, time=21.39 memory used=4290.2MB, alloc=131.8MB, time=21.52 memory used=4337.8MB, alloc=131.8MB, time=21.64 memory used=4387.2MB, alloc=131.8MB, time=21.78 memory used=4443.5MB, alloc=131.8MB, time=21.92 memory used=4501.4MB, alloc=131.8MB, time=22.07 memory used=4560.9MB, alloc=131.8MB, time=22.22 memory used=4622.0MB, alloc=131.8MB, time=22.37 memory used=4685.5MB, alloc=131.8MB, time=22.51 memory used=4752.0MB, alloc=131.8MB, time=22.67 memory used=4791.2MB, alloc=131.8MB, time=22.77 memory used=4823.4MB, alloc=131.8MB, time=22.87 memory used=4855.7MB, alloc=131.8MB, time=22.96 memory used=4888.3MB, alloc=131.8MB, time=23.05 memory used=4921.1MB, alloc=131.8MB, time=23.15 memory used=4954.1MB, alloc=131.8MB, time=23.24 memory used=4987.3MB, alloc=131.8MB, time=23.35 memory used=5021.6MB, alloc=131.8MB, time=23.45 memory used=5061.0MB, alloc=131.8MB, time=23.55 memory used=5101.4MB, alloc=131.8MB, time=23.65 memory used=5142.0MB, alloc=131.8MB, time=23.76 memory used=5182.8MB, alloc=131.8MB, time=23.86 memory used=5223.7MB, alloc=131.8MB, time=23.96 memory used=5264.6MB, alloc=131.8MB, time=24.07 memory used=5305.7MB, alloc=131.8MB, time=24.18 memory used=5346.9MB, alloc=131.8MB, time=24.29 memory used=5389.2MB, alloc=131.8MB, time=24.40 memory used=5436.3MB, alloc=131.8MB, time=24.50 memory used=5484.3MB, alloc=131.8MB, time=24.62 memory used=5532.3MB, alloc=131.8MB, time=24.73 memory used=5580.2MB, alloc=131.8MB, time=24.84 memory used=5628.0MB, alloc=131.8MB, time=24.95 memory used=5677.1MB, alloc=131.8MB, time=25.07 memory used=5729.9MB, alloc=131.8MB, time=25.19 memory used=5783.7MB, alloc=131.8MB, time=25.29 memory used=5837.2MB, alloc=131.8MB, time=25.41 memory used=5891.8MB, alloc=131.8MB, time=25.52 memory used=5949.5MB, alloc=131.8MB, time=25.64 memory used=6007.9MB, alloc=131.8MB, time=25.75 memory used=6067.5MB, alloc=131.8MB, time=25.86 memory used=6128.7MB, alloc=131.8MB, time=25.99 memory used=6192.1MB, alloc=131.8MB, time=26.11 memory used=6257.4MB, alloc=131.8MB, time=26.23 memory used=6324.5MB, alloc=131.8MB, time=26.35 memory used=6362.6MB, alloc=131.8MB, time=26.44 memory used=6377.4MB, alloc=131.8MB, time=26.51 memory used=6385.9MB, alloc=131.8MB, time=26.57 memory used=6390.2MB, alloc=131.8MB, time=26.62 memory used=6394.8MB, alloc=131.8MB, time=26.69 memory used=6399.9MB, alloc=131.8MB, time=26.73 memory used=6405.2MB, alloc=131.8MB, time=26.79 memory used=6410.4MB, alloc=131.8MB, time=26.84 memory used=6415.6MB, alloc=131.8MB, time=26.89 memory used=6420.9MB, alloc=131.8MB, time=26.94 memory used=6426.1MB, alloc=131.8MB, time=26.98 memory used=6431.2MB, alloc=131.8MB, time=27.03 memory used=6436.4MB, alloc=131.8MB, time=27.08 memory used=6441.5MB, alloc=131.8MB, time=27.15 memory used=6446.6MB, alloc=131.8MB, time=27.20 memory used=6451.7MB, alloc=131.8MB, time=27.24 memory used=6456.8MB, alloc=131.8MB, time=27.28 memory used=6461.9MB, alloc=131.8MB, time=27.37 memory used=6466.9MB, alloc=131.8MB, time=27.41 memory used=6471.9MB, alloc=131.8MB, time=27.48 memory used=6476.9MB, alloc=131.8MB, time=27.57 memory used=6481.9MB, alloc=131.8MB, time=27.62 memory used=6486.9MB, alloc=131.8MB, time=27.68 memory used=6491.8MB, alloc=131.8MB, time=27.74 memory used=6496.8MB, alloc=131.8MB, time=27.81 memory used=6501.7MB, alloc=131.8MB, time=27.89 memory used=6506.5MB, alloc=131.8MB, time=27.98 memory used=6511.4MB, alloc=131.8MB, time=28.03 memory used=6516.3MB, alloc=131.8MB, time=28.13 memory used=6521.1MB, alloc=131.8MB, time=28.18 memory used=6525.9MB, alloc=131.8MB, time=28.23 memory used=6530.7MB, alloc=131.8MB, time=28.28 memory used=6537.0MB, alloc=131.8MB, time=28.34 memory used=6542.5MB, alloc=131.8MB, time=28.39 memory used=6549.7MB, alloc=131.8MB, time=28.46 memory used=6555.8MB, alloc=131.8MB, time=28.54 memory used=6561.3MB, alloc=131.8MB, time=28.58 memory used=6568.3MB, alloc=131.8MB, time=28.64 memory used=6574.4MB, alloc=131.8MB, time=28.71 memory used=6582.0MB, alloc=131.8MB, time=28.80 memory used=6588.2MB, alloc=131.8MB, time=28.87 memory used=6595.5MB, alloc=131.8MB, time=28.92 memory used=6601.9MB, alloc=131.8MB, time=28.97 memory used=6608.9MB, alloc=131.8MB, time=29.06 memory used=6615.6MB, alloc=131.8MB, time=29.12 memory used=6622.0MB, alloc=131.8MB, time=29.18 memory used=6628.7MB, alloc=131.8MB, time=29.23 memory used=6636.5MB, alloc=131.8MB, time=29.29 memory used=6643.5MB, alloc=131.8MB, time=29.37 memory used=6651.9MB, alloc=131.8MB, time=29.45 memory used=6660.2MB, alloc=131.8MB, time=29.51 memory used=6668.4MB, alloc=131.8MB, time=29.56 memory used=6676.5MB, alloc=131.8MB, time=29.62 memory used=6684.6MB, alloc=131.8MB, time=29.67 memory used=6692.5MB, alloc=131.8MB, time=29.72 memory used=6700.3MB, alloc=131.8MB, time=29.77 memory used=6709.7MB, alloc=131.8MB, time=29.82 memory used=6718.2MB, alloc=131.8MB, time=29.87 memory used=6727.0MB, alloc=131.8MB, time=29.93 memory used=6736.1MB, alloc=131.8MB, time=29.98 memory used=6745.3MB, alloc=131.8MB, time=30.03 memory used=6754.5MB, alloc=131.8MB, time=30.11 memory used=6764.6MB, alloc=131.8MB, time=30.18 memory used=6865.7MB, alloc=131.8MB, time=51.49 memory used=6935.6MB, alloc=131.8MB, time=91.75 memory used=6990.8MB, alloc=155.8MB, time=131.16 |\^/| 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(); 1428245928 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 2 2 F := [-8 x z - 20 y z - 20 x, 14 x y - 19 y z + 12 x y - 2 x z, 3 3 2 17 x y + 5 y z - 13 y z - 4] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [-14 x z + 14 x y z + 12 y z + 13 x y, 2 4 3 2 4 2 3 -10 x y z - 18 y - 20 y z - 10 x y, -18 x + 10 y z + 16 z - z] > Problem := [F,G]; 3 3 3 3 2 2 Problem := [[-8 x z - 20 y z - 20 x, 14 x y - 19 y z + 12 x y - 2 x z, 3 3 2 17 x y + 5 y z - 13 y z - 4], [ 3 2 2 2 2 -14 x z + 14 x y z + 12 y z + 13 x y, 2 4 3 2 4 2 3 -10 x y z - 18 y - 20 y z - 10 x y, -18 x + 10 y z + 16 z - z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.19 memory used=26.1MB, alloc=32.3MB, time=0.50 memory used=50.3MB, alloc=60.3MB, time=0.86 memory used=96.3MB, alloc=60.3MB, time=1.24 memory used=124.3MB, alloc=60.3MB, time=1.32 memory used=155.5MB, alloc=60.3MB, time=1.48 memory used=197.8MB, alloc=60.3MB, time=2.13 memory used=245.5MB, alloc=60.3MB, time=2.64 memory used=273.4MB, alloc=60.3MB, time=2.71 memory used=301.8MB, alloc=60.3MB, time=2.85 memory used=342.1MB, alloc=60.3MB, time=3.16 memory used=392.6MB, alloc=60.3MB, time=3.80 memory used=436.4MB, alloc=68.3MB, time=4.44 memory used=477.4MB, alloc=68.3MB, time=4.84 memory used=517.9MB, alloc=68.3MB, time=5.28 memory used=561.3MB, alloc=68.3MB, time=5.89 memory used=608.1MB, alloc=68.3MB, time=6.39 memory used=651.0MB, alloc=92.3MB, time=7.84 memory used=685.3MB, alloc=92.3MB, time=7.96 memory used=712.6MB, alloc=92.3MB, time=8.07 memory used=740.4MB, alloc=92.3MB, time=8.20 memory used=769.4MB, alloc=92.3MB, time=8.31 memory used=799.5MB, alloc=92.3MB, time=8.42 memory used=830.5MB, alloc=92.3MB, time=8.54 memory used=862.6MB, alloc=92.3MB, time=8.65 memory used=896.8MB, alloc=92.3MB, time=8.78 memory used=932.9MB, alloc=92.3MB, time=8.90 memory used=973.6MB, alloc=92.3MB, time=9.30 memory used=1021.3MB, alloc=92.3MB, time=11.91 memory used=1050.4MB, alloc=116.3MB, time=14.45 memory used=1113.0MB, alloc=116.3MB, time=16.73 memory used=1173.2MB, alloc=116.3MB, time=16.88 memory used=1233.3MB, alloc=116.3MB, time=17.04 memory used=1293.3MB, alloc=116.3MB, time=17.20 memory used=1356.3MB, alloc=116.3MB, time=17.37 memory used=1419.0MB, alloc=116.3MB, time=17.53 memory used=1484.6MB, alloc=116.3MB, time=17.72 memory used=1544.1MB, alloc=116.3MB, time=17.89 memory used=1588.4MB, alloc=116.3MB, time=18.03 memory used=1627.1MB, alloc=116.3MB, time=18.16 memory used=1661.5MB, alloc=116.3MB, time=18.30 memory used=1694.0MB, alloc=116.3MB, time=18.43 memory used=1727.6MB, alloc=116.3MB, time=18.55 memory used=1761.1MB, alloc=116.3MB, time=18.68 memory used=1794.3MB, alloc=116.3MB, time=18.81 memory used=1827.3MB, alloc=116.3MB, time=18.92 memory used=1860.3MB, alloc=116.3MB, time=19.05 memory used=1892.9MB, alloc=116.3MB, time=19.18 memory used=1925.4MB, alloc=116.3MB, time=19.31 memory used=1960.6MB, alloc=116.3MB, time=19.44 memory used=1995.3MB, alloc=116.3MB, time=19.56 memory used=2029.7MB, alloc=116.3MB, time=19.68 memory used=2063.7MB, alloc=116.3MB, time=19.80 memory used=2100.2MB, alloc=116.3MB, time=19.93 memory used=2136.1MB, alloc=116.3MB, time=20.05 memory used=2171.6MB, alloc=116.3MB, time=20.18 memory used=2209.2MB, alloc=116.3MB, time=20.30 memory used=2246.3MB, alloc=116.3MB, time=20.42 memory used=2285.3MB, alloc=116.3MB, time=20.55 memory used=2323.6MB, alloc=116.3MB, time=20.68 memory used=2363.5MB, alloc=116.3MB, time=20.80 memory used=2402.5MB, alloc=116.3MB, time=20.92 memory used=2442.8MB, alloc=116.3MB, time=21.05 memory used=2482.0MB, alloc=116.3MB, time=21.17 memory used=2522.3MB, alloc=116.3MB, time=21.30 memory used=2563.3MB, alloc=116.3MB, time=21.42 memory used=2604.8MB, alloc=116.3MB, time=21.55 memory used=2648.3MB, alloc=116.3MB, time=21.67 memory used=2691.4MB, alloc=116.3MB, time=21.80 memory used=2735.2MB, alloc=116.3MB, time=21.92 memory used=2780.5MB, alloc=116.3MB, time=22.06 memory used=2827.0MB, alloc=116.3MB, time=22.20 memory used=2874.6MB, alloc=116.3MB, time=22.34 memory used=2927.2MB, alloc=116.3MB, time=23.02 memory used=3013.0MB, alloc=116.3MB, time=24.88 memory used=3075.7MB, alloc=116.3MB, time=53.17 memory used=3120.1MB, alloc=116.3MB, time=79.23 memory used=3176.0MB, alloc=116.3MB, time=119.49 memory used=3246.7MB, alloc=116.3MB, time=121.88 memory used=3307.8MB, alloc=116.3MB, time=122.03 memory used=3368.0MB, alloc=116.3MB, time=122.19 memory used=3405.3MB, alloc=116.3MB, time=122.30 memory used=3443.8MB, alloc=116.3MB, time=122.43 memory used=3492.3MB, alloc=116.3MB, time=122.68 memory used=3578.1MB, alloc=116.3MB, time=154.39 memory used=3637.1MB, alloc=116.3MB, time=159.07 memory used=3692.4MB, alloc=116.3MB, time=159.23 memory used=3756.4MB, alloc=116.3MB, time=159.40 memory used=3834.3MB, alloc=116.3MB, time=164.14 memory used=3891.2MB, alloc=116.3MB, time=165.52 memory used=3939.4MB, alloc=116.3MB, time=166.29 memory used=3999.3MB, alloc=116.3MB, time=166.48 memory used=4037.5MB, alloc=116.3MB, time=166.62 memory used=4075.7MB, alloc=116.3MB, time=166.76 memory used=4120.1MB, alloc=116.3MB, time=166.92 memory used=4167.6MB, alloc=116.3MB, time=167.06 memory used=4218.2MB, alloc=116.3MB, time=167.23 memory used=4274.9MB, alloc=116.3MB, time=167.38 memory used=4332.4MB, alloc=116.3MB, time=167.52 memory used=4363.2MB, alloc=116.3MB, time=167.63 memory used=4393.0MB, alloc=116.3MB, time=167.73 memory used=4423.8MB, alloc=116.3MB, time=167.84 memory used=4459.3MB, alloc=116.3MB, time=167.94 memory used=4495.2MB, alloc=116.3MB, time=168.06 memory used=4531.4MB, alloc=116.3MB, time=168.16 memory used=4568.1MB, alloc=116.3MB, time=168.28 memory used=4609.4MB, alloc=116.3MB, time=168.40 memory used=4651.0MB, alloc=116.3MB, time=168.52 memory used=4692.7MB, alloc=116.3MB, time=168.64 memory used=4739.0MB, alloc=116.3MB, time=168.75 memory used=4785.2MB, alloc=116.3MB, time=168.88 memory used=4835.7MB, alloc=116.3MB, time=169.01 memory used=4885.8MB, alloc=116.3MB, time=169.14 memory used=4939.7MB, alloc=116.3MB, time=169.26 memory used=4997.0MB, alloc=116.3MB, time=169.40 memory used=5057.1MB, alloc=116.3MB, time=169.53 memory used=5127.3MB, alloc=131.8MB, time=169.69 memory used=5134.6MB, alloc=131.8MB, time=169.75 memory used=5141.7MB, alloc=131.8MB, time=169.83 memory used=5148.9MB, alloc=131.8MB, time=169.91 memory used=5156.1MB, alloc=131.8MB, time=169.99 memory used=5163.2MB, alloc=131.8MB, time=170.07 memory used=5170.2MB, alloc=131.8MB, time=170.13 memory used=5177.2MB, alloc=131.8MB, time=170.21 memory used=5184.1MB, alloc=131.8MB, time=170.27 memory used=5190.9MB, alloc=131.8MB, time=170.35 memory used=5197.7MB, alloc=131.8MB, time=170.47 memory used=5204.4MB, alloc=131.8MB, time=170.55 memory used=5211.0MB, alloc=131.8MB, time=170.63 memory used=5217.6MB, alloc=131.8MB, time=170.70 memory used=5224.8MB, alloc=131.8MB, time=170.78 memory used=5233.8MB, alloc=131.8MB, time=170.86 memory used=5241.1MB, alloc=131.8MB, time=170.94 memory used=5249.5MB, alloc=131.8MB, time=171.00 memory used=5258.7MB, alloc=131.8MB, time=171.09 memory used=5267.7MB, alloc=131.8MB, time=171.15 memory used=5276.5MB, alloc=131.8MB, time=171.24 |\^/| 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(); 1428246228 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 3 3 2 F := [-18 x y - z - 5 z - 2, 13 x y z - 2 y - 13 z - 8 z , 3 2 2 2 2 -9 x y - 15 y z + 6 x + 18 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 3 4 2 2 2 G := [9 x - 2 x y - 8 y z - 20 z , -14 z + 14 x y + 7 x y + 4 x , 3 2 2 2 2 15 x z + 17 x y - 14 x z + 11 y z] > Problem := [F,G]; 2 2 4 3 3 3 2 Problem := [[-18 x y - z - 5 z - 2, 13 x y z - 2 y - 13 z - 8 z , 3 2 2 2 2 4 2 2 2 2 3 -9 x y - 15 y z + 6 x + 18 z ], [9 x - 2 x y - 8 y z - 20 z , 4 2 2 2 3 2 2 2 2 -14 z + 14 x y + 7 x y + 4 x , 15 x z + 17 x y - 14 x 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=4.5MB, alloc=32.3MB, time=0.18 memory used=26.9MB, alloc=36.3MB, time=0.53 memory used=56.0MB, alloc=36.3MB, time=0.79 memory used=68.1MB, alloc=36.3MB, time=0.83 memory used=84.6MB, alloc=36.3MB, time=0.95 memory used=97.1MB, alloc=36.3MB, time=1.01 memory used=107.9MB, alloc=36.3MB, time=1.07 memory used=120.0MB, alloc=36.3MB, time=1.11 memory used=131.2MB, alloc=36.3MB, time=1.15 memory used=143.9MB, alloc=36.3MB, time=1.19 memory used=161.8MB, alloc=36.3MB, time=1.36 memory used=176.2MB, alloc=36.3MB, time=1.45 memory used=202.6MB, alloc=36.3MB, time=1.74 memory used=231.8MB, alloc=36.3MB, time=2.05 memory used=255.7MB, alloc=36.3MB, time=2.30 memory used=275.9MB, alloc=60.3MB, time=2.59 memory used=343.9MB, alloc=72.1MB, time=3.19 memory used=399.3MB, alloc=72.1MB, time=3.60 memory used=432.7MB, alloc=72.1MB, time=3.73 memory used=461.2MB, alloc=72.1MB, time=3.81 memory used=510.5MB, alloc=72.1MB, time=4.21 memory used=539.1MB, alloc=72.1MB, time=4.31 memory used=564.5MB, alloc=72.1MB, time=4.39 memory used=593.2MB, alloc=72.1MB, time=4.48 memory used=613.0MB, alloc=72.1MB, time=4.54 memory used=635.1MB, alloc=72.1MB, time=4.60 memory used=660.4MB, alloc=72.1MB, time=4.67 memory used=688.9MB, alloc=72.1MB, time=4.74 memory used=728.0MB, alloc=83.8MB, time=4.84 memory used=737.2MB, alloc=83.8MB, time=4.88 memory used=746.6MB, alloc=83.8MB, time=4.93 memory used=757.1MB, alloc=83.8MB, time=4.98 memory used=822.5MB, alloc=83.8MB, time=5.51 memory used=862.1MB, alloc=83.8MB, time=6.90 memory used=891.3MB, alloc=83.8MB, time=14.56 memory used=931.8MB, alloc=107.8MB, time=38.45 memory used=1578.3MB, alloc=107.8MB, time=42.23 memory used=1597.3MB, alloc=363.8MB, time=43.13 memory used=2114.5MB, alloc=363.8MB, time=48.10 memory used=2151.3MB, alloc=387.8MB, time=49.70 memory used=2792.7MB, alloc=387.8MB, time=58.76 memory used=3264.8MB, alloc=387.8MB, time=69.28 memory used=3349.9MB, alloc=387.8MB, time=72.75 memory used=3448.7MB, alloc=416.5MB, time=76.75 memory used=3453.3MB, alloc=421.1MB, time=76.82 memory used=3457.9MB, alloc=425.7MB, time=76.87 memory used=3462.6MB, alloc=430.3MB, time=76.94 memory used=3467.2MB, alloc=416.5MB, time=77.07 memory used=3554.3MB, alloc=411.8MB, time=77.55 memory used=3665.5MB, alloc=411.8MB, time=78.35 memory used=3743.2MB, alloc=411.8MB, time=78.57 memory used=3805.2MB, alloc=411.8MB, time=78.71 memory used=3923.8MB, alloc=411.8MB, time=79.59 memory used=4000.1MB, alloc=411.8MB, time=79.99 memory used=4096.3MB, alloc=411.8MB, time=80.40 memory used=4177.0MB, alloc=411.8MB, time=80.93 memory used=4259.1MB, alloc=411.8MB, time=81.40 memory used=4338.8MB, alloc=411.8MB, time=81.59 memory used=4430.9MB, alloc=411.8MB, time=82.24 memory used=4504.6MB, alloc=411.8MB, time=82.46 memory used=4582.7MB, alloc=411.8MB, time=82.66 memory used=4665.7MB, alloc=411.8MB, time=82.87 memory used=4753.5MB, alloc=411.8MB, time=83.08 memory used=4846.3MB, alloc=411.8MB, time=83.31 memory used=4919.1MB, alloc=411.8MB, time=83.51 memory used=4978.2MB, alloc=411.8MB, time=83.68 memory used=5032.9MB, alloc=411.8MB, time=83.83 memory used=5088.2MB, alloc=411.8MB, time=84.01 memory used=5146.6MB, alloc=411.8MB, time=84.16 memory used=5231.0MB, alloc=411.8MB, time=84.68 memory used=5315.9MB, alloc=411.8MB, time=105.49 memory used=5387.9MB, alloc=435.8MB, time=154.47 |\^/| 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(); 1428246528 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 4 2 F := [5 y z + 15 z - 9 y, -6 x z - 6 z + 5 x y z - 19 y z , 3 2 2 2 2 y + 11 y z - 17 x - 5 y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 2 G := [16 x - 12 x y + 16 y + 10 z, -15 z - 8 x - 20 y - 2 y, 2 3 3 2 -4 x y z - 17 y z - 17 z + 2 x ] > Problem := [F,G]; 2 3 3 4 2 Problem := [[5 y z + 15 z - 9 y, -6 x z - 6 z + 5 x y z - 19 y z , 3 2 2 2 3 2 2 2 y + 11 y z - 17 x - 5 y ], [16 x - 12 x y + 16 y + 10 z, 4 3 2 2 3 3 2 -15 z - 8 x - 20 y - 2 y, -4 x y z - 17 y z - 17 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=24.3MB, alloc=32.3MB, time=0.47 memory used=47.3MB, alloc=36.3MB, time=0.74 memory used=61.2MB, alloc=36.3MB, time=0.81 memory used=71.1MB, alloc=60.3MB, time=0.86 memory used=109.7MB, alloc=60.3MB, time=1.17 memory used=154.6MB, alloc=68.5MB, time=1.65 memory used=212.2MB, alloc=68.5MB, time=2.94 memory used=257.3MB, alloc=68.5MB, time=3.45 memory used=294.2MB, alloc=68.5MB, time=3.69 memory used=316.0MB, alloc=68.5MB, time=3.77 memory used=340.9MB, alloc=68.5MB, time=3.84 memory used=358.3MB, alloc=68.5MB, time=3.90 memory used=378.5MB, alloc=68.5MB, time=3.96 memory used=410.7MB, alloc=68.5MB, time=4.11 memory used=432.2MB, alloc=68.5MB, time=4.19 memory used=457.5MB, alloc=68.5MB, time=4.26 memory used=474.9MB, alloc=68.5MB, time=4.32 memory used=495.2MB, alloc=68.5MB, time=4.38 memory used=559.6MB, alloc=68.5MB, time=6.42 memory used=583.0MB, alloc=68.5MB, time=6.49 memory used=601.7MB, alloc=68.5MB, time=6.56 memory used=621.9MB, alloc=68.5MB, time=6.63 memory used=645.9MB, alloc=68.5MB, time=6.70 memory used=668.4MB, alloc=68.5MB, time=6.76 memory used=684.2MB, alloc=68.5MB, time=6.84 memory used=701.6MB, alloc=68.5MB, time=6.89 memory used=721.2MB, alloc=68.5MB, time=6.95 memory used=749.4MB, alloc=68.5MB, time=7.14 memory used=780.4MB, alloc=68.5MB, time=7.34 memory used=801.8MB, alloc=68.5MB, time=7.42 memory used=827.1MB, alloc=68.5MB, time=7.51 memory used=846.2MB, alloc=68.5MB, time=7.58 memory used=864.6MB, alloc=68.5MB, time=7.65 memory used=894.1MB, alloc=68.5MB, time=7.79 memory used=916.8MB, alloc=68.5MB, time=7.87 memory used=941.2MB, alloc=68.5MB, time=7.95 memory used=961.5MB, alloc=68.5MB, time=8.03 memory used=979.8MB, alloc=68.5MB, time=8.10 memory used=1012.2MB, alloc=68.5MB, time=9.70 memory used=1066.4MB, alloc=68.5MB, time=10.15 memory used=1089.6MB, alloc=68.5MB, time=10.23 memory used=1108.4MB, alloc=68.5MB, time=10.29 memory used=1130.9MB, alloc=68.5MB, time=10.37 memory used=1156.5MB, alloc=68.5MB, time=10.44 memory used=1173.6MB, alloc=68.5MB, time=10.50 memory used=1190.2MB, alloc=68.5MB, time=10.56 memory used=1208.9MB, alloc=68.5MB, time=10.62 memory used=1230.4MB, alloc=68.5MB, time=10.68 memory used=1259.0MB, alloc=68.5MB, time=10.80 memory used=1290.4MB, alloc=68.5MB, time=11.10 memory used=1311.6MB, alloc=68.5MB, time=11.17 memory used=1333.1MB, alloc=68.5MB, time=11.24 memory used=1372.2MB, alloc=68.5MB, time=11.59 memory used=1425.1MB, alloc=92.5MB, time=17.98 memory used=1486.9MB, alloc=92.5MB, time=19.55 memory used=1527.4MB, alloc=92.5MB, time=19.67 memory used=1560.1MB, alloc=92.5MB, time=19.78 memory used=1600.0MB, alloc=92.5MB, time=19.87 memory used=1646.5MB, alloc=92.5MB, time=19.98 memory used=1676.9MB, alloc=92.5MB, time=20.06 memory used=1706.0MB, alloc=92.5MB, time=20.14 memory used=1737.5MB, alloc=92.5MB, time=20.22 memory used=1771.6MB, alloc=92.5MB, time=20.30 memory used=1808.2MB, alloc=92.5MB, time=20.38 memory used=1847.8MB, alloc=92.5MB, time=20.46 memory used=1889.7MB, alloc=92.5MB, time=20.54 memory used=1936.2MB, alloc=92.5MB, time=20.62 memory used=1959.4MB, alloc=107.8MB, time=20.70 memory used=1972.5MB, alloc=107.8MB, time=20.75 memory used=1983.9MB, alloc=107.8MB, time=20.80 memory used=1995.6MB, alloc=107.8MB, time=20.86 memory used=2007.9MB, alloc=107.8MB, time=20.93 memory used=2080.2MB, alloc=363.8MB, time=21.76 memory used=2140.5MB, alloc=363.8MB, time=22.37 memory used=2212.9MB, alloc=363.8MB, time=23.23 memory used=2273.8MB, alloc=363.8MB, time=23.97 memory used=2317.7MB, alloc=363.8MB, time=24.12 memory used=2342.6MB, alloc=363.8MB, time=24.24 memory used=2370.3MB, alloc=363.8MB, time=24.36 memory used=2401.4MB, alloc=363.8MB, time=24.47 memory used=2437.6MB, alloc=363.8MB, time=24.60 memory used=2474.2MB, alloc=363.8MB, time=24.71 memory used=2499.0MB, alloc=363.8MB, time=24.82 memory used=2521.6MB, alloc=363.8MB, time=24.93 memory used=2544.9MB, alloc=363.8MB, time=25.02 memory used=2569.7MB, alloc=363.8MB, time=25.12 memory used=2596.0MB, alloc=363.8MB, time=25.22 memory used=2624.7MB, alloc=363.8MB, time=25.34 memory used=2655.2MB, alloc=363.8MB, time=25.45 memory used=2688.4MB, alloc=363.8MB, time=25.55 memory used=2724.7MB, alloc=363.8MB, time=25.68 memory used=2774.9MB, alloc=363.8MB, time=29.29 memory used=2834.6MB, alloc=363.8MB, time=38.14 memory used=2864.9MB, alloc=363.8MB, time=38.27 memory used=2899.7MB, alloc=363.8MB, time=38.39 memory used=2927.4MB, alloc=363.8MB, time=38.51 memory used=2951.6MB, alloc=363.8MB, time=38.61 memory used=2978.4MB, alloc=363.8MB, time=38.72 memory used=3008.4MB, alloc=363.8MB, time=38.83 memory used=3041.6MB, alloc=363.8MB, time=38.94 memory used=3077.7MB, alloc=363.8MB, time=39.05 memory used=3112.6MB, alloc=363.8MB, time=39.16 memory used=3134.5MB, alloc=387.8MB, time=39.28 memory used=3169.7MB, alloc=387.8MB, time=39.39 memory used=3208.5MB, alloc=387.8MB, time=39.50 memory used=3249.8MB, alloc=387.8MB, time=39.60 memory used=3295.2MB, alloc=387.8MB, time=39.73 memory used=3346.0MB, alloc=387.8MB, time=39.85 memory used=3411.1MB, alloc=387.8MB, time=40.26 memory used=3490.0MB, alloc=387.8MB, time=40.86 memory used=3585.9MB, alloc=387.8MB, time=41.84 memory used=3646.6MB, alloc=387.8MB, time=42.23 memory used=3693.6MB, alloc=387.8MB, time=42.38 memory used=3729.1MB, alloc=387.8MB, time=42.53 memory used=3784.0MB, alloc=387.8MB, time=42.79 memory used=3831.8MB, alloc=387.8MB, time=42.96 memory used=3867.5MB, alloc=387.8MB, time=43.09 memory used=3966.2MB, alloc=387.8MB, time=45.83 memory used=4008.7MB, alloc=387.8MB, time=45.97 memory used=4051.2MB, alloc=387.8MB, time=46.11 memory used=4096.3MB, alloc=387.8MB, time=46.25 memory used=4129.3MB, alloc=387.8MB, time=46.36 memory used=4169.2MB, alloc=387.8MB, time=46.47 memory used=4223.5MB, alloc=387.8MB, time=46.68 memory used=4276.0MB, alloc=387.8MB, time=47.12 memory used=4338.2MB, alloc=387.8MB, time=48.05 memory used=4397.0MB, alloc=387.8MB, time=48.26 memory used=4432.6MB, alloc=387.8MB, time=48.41 memory used=4475.2MB, alloc=387.8MB, time=48.58 memory used=4525.1MB, alloc=387.8MB, time=48.74 memory used=4569.1MB, alloc=387.8MB, time=48.89 memory used=4598.9MB, alloc=387.8MB, time=49.03 memory used=4630.4MB, alloc=387.8MB, time=49.16 memory used=4663.2MB, alloc=387.8MB, time=49.31 memory used=4699.7MB, alloc=387.8MB, time=49.43 memory used=4737.2MB, alloc=387.8MB, time=49.57 memory used=4778.5MB, alloc=387.8MB, time=49.71 memory used=4820.7MB, alloc=387.8MB, time=49.85 memory used=4866.5MB, alloc=387.8MB, time=50.00 memory used=4913.7MB, alloc=387.8MB, time=50.15 memory used=4963.8MB, alloc=387.8MB, time=50.29 memory used=5013.8MB, alloc=387.8MB, time=50.43 memory used=5048.9MB, alloc=387.8MB, time=50.54 memory used=5075.7MB, alloc=411.8MB, time=50.67 memory used=5116.3MB, alloc=411.8MB, time=50.80 memory used=5160.8MB, alloc=411.8MB, time=50.93 memory used=5205.5MB, alloc=411.8MB, time=51.06 memory used=5252.8MB, alloc=411.8MB, time=51.20 memory used=5303.0MB, alloc=411.8MB, time=51.34 memory used=5355.6MB, alloc=411.8MB, time=51.47 memory used=5411.7MB, alloc=411.8MB, time=51.60 memory used=5472.2MB, alloc=411.8MB, time=51.74 memory used=5566.2MB, alloc=411.8MB, time=67.91 memory used=5648.2MB, alloc=411.8MB, time=87.33 memory used=5712.4MB, alloc=411.8MB, time=87.52 memory used=5760.5MB, alloc=411.8MB, time=87.69 memory used=5819.0MB, alloc=411.8MB, time=87.86 memory used=5889.2MB, alloc=411.8MB, time=88.04 memory used=5947.4MB, alloc=411.8MB, time=88.19 memory used=5990.6MB, alloc=411.8MB, time=88.32 memory used=6037.0MB, alloc=411.8MB, time=88.45 memory used=6086.6MB, alloc=411.8MB, time=88.59 memory used=6139.3MB, alloc=411.8MB, time=88.74 memory used=6195.0MB, alloc=411.8MB, time=88.88 memory used=6255.3MB, alloc=411.8MB, time=89.03 memory used=6319.8MB, alloc=411.8MB, time=89.19 memory used=6388.5MB, alloc=411.8MB, time=89.35 memory used=6462.6MB, alloc=411.8MB, time=89.49 memory used=6652.7MB, alloc=411.8MB, time=89.96 memory used=6817.6MB, alloc=411.8MB, time=90.24 memory used=6995.1MB, alloc=411.8MB, time=91.12 memory used=7057.3MB, alloc=411.8MB, time=91.30 memory used=7153.1MB, alloc=411.8MB, time=93.29 memory used=7284.7MB, alloc=411.8MB, time=96.41 memory used=7348.9MB, alloc=411.8MB, time=96.61 memory used=7396.1MB, alloc=411.8MB, time=96.78 memory used=7450.4MB, alloc=411.8MB, time=96.95 memory used=7513.8MB, alloc=411.8MB, time=97.13 memory used=7587.0MB, alloc=411.8MB, time=97.33 memory used=7631.7MB, alloc=411.8MB, time=97.47 memory used=7673.9MB, alloc=411.8MB, time=97.60 memory used=7718.9MB, alloc=411.8MB, time=97.73 memory used=7765.3MB, alloc=411.8MB, time=97.87 memory used=7815.0MB, alloc=411.8MB, time=98.02 memory used=7867.9MB, alloc=411.8MB, time=98.16 memory used=7924.0MB, alloc=411.8MB, time=98.31 memory used=7983.3MB, alloc=411.8MB, time=98.46 memory used=8045.6MB, alloc=411.8MB, time=98.61 memory used=8110.7MB, alloc=411.8MB, time=98.77 memory used=8180.7MB, alloc=411.8MB, time=98.94 memory used=8254.0MB, alloc=411.8MB, time=99.09 memory used=8428.6MB, alloc=411.8MB, time=99.40 memory used=8582.4MB, alloc=411.8MB, time=99.68 memory used=8756.2MB, alloc=411.8MB, time=99.97 memory used=8958.6MB, alloc=411.8MB, time=100.28 memory used=9058.8MB, alloc=411.8MB, time=114.25 memory used=9117.2MB, alloc=411.8MB, time=114.46 memory used=9171.0MB, alloc=411.8MB, time=114.66 memory used=9215.6MB, alloc=411.8MB, time=114.83 memory used=9265.3MB, alloc=411.8MB, time=115.01 memory used=9321.4MB, alloc=411.8MB, time=115.19 memory used=9384.6MB, alloc=411.8MB, time=115.38 memory used=9452.7MB, alloc=411.8MB, time=115.57 memory used=9506.8MB, alloc=411.8MB, time=115.73 memory used=9543.5MB, alloc=411.8MB, time=115.86 memory used=9583.2MB, alloc=411.8MB, time=116.00 memory used=9622.2MB, alloc=411.8MB, time=116.14 memory used=9664.9MB, alloc=411.8MB, time=116.31 memory used=9708.7MB, alloc=411.8MB, time=116.45 memory used=9753.5MB, alloc=411.8MB, time=116.59 memory used=9799.3MB, alloc=411.8MB, time=116.73 memory used=9846.2MB, alloc=411.8MB, time=116.87 memory used=9896.8MB, alloc=411.8MB, time=117.02 memory used=9948.6MB, alloc=411.8MB, time=117.20 memory used=10001.3MB, alloc=411.8MB, time=117.35 memory used=10055.0MB, alloc=411.8MB, time=117.51 memory used=10112.6MB, alloc=411.8MB, time=117.65 memory used=10171.2MB, alloc=411.8MB, time=117.80 memory used=10230.7MB, alloc=411.8MB, time=117.96 memory used=10294.4MB, alloc=411.8MB, time=118.11 memory used=10358.9MB, alloc=411.8MB, time=118.26 memory used=10424.2MB, alloc=411.8MB, time=118.42 memory used=10493.7MB, alloc=411.8MB, time=118.58 memory used=10588.7MB, alloc=411.8MB, time=118.78 memory used=10728.0MB, alloc=411.8MB, time=119.09 memory used=10869.0MB, alloc=411.8MB, time=119.37 memory used=11020.4MB, alloc=411.8MB, time=119.65 memory used=11180.2MB, alloc=411.8MB, time=119.95 memory used=11347.6MB, alloc=411.8MB, time=120.25 memory used=11525.3MB, alloc=411.8MB, time=120.54 memory used=11712.1MB, alloc=411.8MB, time=120.86 memory used=11909.9MB, alloc=411.8MB, time=121.19 memory used=12122.6MB, alloc=411.8MB, time=121.51 memory used=12348.1MB, alloc=411.8MB, time=121.84 memory used=12591.7MB, alloc=411.8MB, time=122.18 memory used=12807.8MB, alloc=411.8MB, time=122.49 memory used=13066.9MB, alloc=411.8MB, time=124.54 memory used=13194.7MB, alloc=411.8MB, time=125.91 memory used=13317.2MB, alloc=411.8MB, time=127.01 memory used=13444.6MB, alloc=411.8MB, time=128.21 memory used=13568.2MB, alloc=411.8MB, time=129.66 memory used=13690.1MB, alloc=411.8MB, time=131.35 memory used=13813.5MB, alloc=411.8MB, time=133.29 memory used=13934.4MB, alloc=411.8MB, time=135.46 memory used=14057.1MB, alloc=411.8MB, time=137.92 memory used=14181.9MB, alloc=411.8MB, time=140.42 memory used=14301.9MB, alloc=411.8MB, time=143.43 memory used=14425.7MB, alloc=411.8MB, time=146.38 memory used=14547.4MB, alloc=411.8MB, time=149.47 memory used=14670.7MB, alloc=411.8MB, time=153.22 memory used=14793.6MB, alloc=411.8MB, time=156.64 memory used=14903.4MB, alloc=411.8MB, time=159.37 memory used=14972.8MB, alloc=411.8MB, time=159.89 memory used=15036.3MB, alloc=411.8MB, time=160.27 memory used=15165.2MB, alloc=411.8MB, time=163.69 memory used=15225.9MB, alloc=411.8MB, time=163.94 memory used=15277.8MB, alloc=411.8MB, time=164.12 memory used=15320.4MB, alloc=411.8MB, time=164.30 memory used=15369.6MB, alloc=411.8MB, time=164.48 memory used=15425.7MB, alloc=411.8MB, time=164.66 memory used=15490.2MB, alloc=411.8MB, time=164.84 memory used=15530.8MB, alloc=411.8MB, time=165.00 memory used=15566.0MB, alloc=411.8MB, time=165.16 memory used=15604.5MB, alloc=411.8MB, time=165.30 memory used=15644.1MB, alloc=411.8MB, time=165.45 memory used=15686.6MB, alloc=411.8MB, time=165.60 memory used=15730.2MB, alloc=411.8MB, time=165.74 memory used=15776.6MB, alloc=411.8MB, time=165.89 memory used=15826.0MB, alloc=411.8MB, time=166.05 memory used=15876.1MB, alloc=411.8MB, time=166.20 memory used=15929.1MB, alloc=411.8MB, time=166.35 memory used=15984.7MB, alloc=411.8MB, time=166.51 memory used=16042.9MB, alloc=411.8MB, time=166.66 memory used=16103.7MB, alloc=411.8MB, time=166.82 memory used=16171.2MB, alloc=411.8MB, time=166.98 memory used=16337.7MB, alloc=411.8MB, time=167.29 memory used=16491.6MB, alloc=411.8MB, time=167.58 memory used=16665.1MB, alloc=411.8MB, time=167.88 memory used=16870.4MB, alloc=411.8MB, time=168.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428246828 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 2 F := [-3 x z + 8 y z + 7 x y, -7 x z - 18 y z + 15 z + 5 z , 2 2 -8 x y - 15 x y z - 13 y z - z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 2 2 3 G := [-12 x y z - 3 z - 17 x z + 4 x y z, -9 x y - 11 y z - 6 z - 8 z, 2 2 3 3 -17 x y - 20 x z + 7 x + 15 x z] > Problem := [F,G]; 2 2 2 3 2 3 2 Problem := [[-3 x z + 8 y z + 7 x y, -7 x z - 18 y z + 15 z + 5 z , 2 2 2 4 2 -8 x y - 15 x y z - 13 y z - z], [-12 x y z - 3 z - 17 x z + 4 x y z, 2 2 2 3 2 2 3 3 -9 x y - 11 y z - 6 z - 8 z, -17 x y - 20 x z + 7 x + 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=0.18 memory used=25.0MB, alloc=32.3MB, time=0.49 memory used=43.7MB, alloc=56.3MB, time=0.78 memory used=79.9MB, alloc=56.3MB, time=1.00 memory used=110.7MB, alloc=56.3MB, time=1.15 memory used=142.9MB, alloc=56.3MB, time=1.29 memory used=184.3MB, alloc=60.3MB, time=1.71 memory used=226.4MB, alloc=60.3MB, time=2.30 memory used=271.3MB, alloc=68.3MB, time=2.91 memory used=315.6MB, alloc=92.3MB, time=3.50 memory used=386.3MB, alloc=92.3MB, time=4.34 memory used=431.6MB, alloc=92.3MB, time=4.97 memory used=467.4MB, alloc=92.3MB, time=5.12 memory used=498.2MB, alloc=92.3MB, time=5.24 memory used=528.7MB, alloc=92.3MB, time=5.34 memory used=554.1MB, alloc=92.3MB, time=5.44 memory used=591.5MB, alloc=92.3MB, time=5.58 memory used=637.7MB, alloc=92.3MB, time=7.46 memory used=679.2MB, alloc=92.3MB, time=7.66 memory used=706.3MB, alloc=92.3MB, time=7.77 memory used=741.7MB, alloc=92.3MB, time=7.89 memory used=771.1MB, alloc=92.3MB, time=7.99 memory used=795.1MB, alloc=92.3MB, time=8.09 memory used=822.1MB, alloc=92.3MB, time=8.20 memory used=852.3MB, alloc=92.3MB, time=8.29 memory used=887.6MB, alloc=92.3MB, time=8.41 memory used=959.4MB, alloc=99.6MB, time=9.01 memory used=1019.4MB, alloc=99.6MB, time=13.53 memory used=1050.8MB, alloc=99.6MB, time=13.65 memory used=1075.7MB, alloc=99.6MB, time=13.77 memory used=1106.5MB, alloc=99.6MB, time=13.88 memory used=1143.2MB, alloc=99.6MB, time=14.02 memory used=1164.9MB, alloc=99.6MB, time=14.13 memory used=1187.4MB, alloc=123.6MB, time=14.24 memory used=1227.3MB, alloc=123.6MB, time=14.36 memory used=1273.0MB, alloc=123.6MB, time=14.48 memory used=1324.1MB, alloc=123.6MB, time=14.60 memory used=1393.5MB, alloc=131.8MB, time=14.75 memory used=1403.7MB, alloc=131.8MB, time=14.82 memory used=1414.9MB, alloc=131.8MB, time=14.89 memory used=1426.8MB, alloc=131.8MB, time=14.98 memory used=1438.9MB, alloc=131.8MB, time=15.05 memory used=1451.9MB, alloc=131.8MB, time=15.13 memory used=1517.1MB, alloc=131.8MB, time=15.64 memory used=1568.2MB, alloc=131.8MB, time=15.78 memory used=1620.1MB, alloc=131.8MB, time=15.93 memory used=1716.0MB, alloc=131.8MB, time=16.90 memory used=1780.9MB, alloc=387.8MB, time=17.82 memory used=1875.1MB, alloc=387.8MB, time=19.03 memory used=1966.2MB, alloc=411.8MB, time=20.15 memory used=2082.7MB, alloc=411.8MB, time=22.21 memory used=2133.5MB, alloc=411.8MB, time=22.40 memory used=2188.5MB, alloc=411.8MB, time=22.57 memory used=2257.6MB, alloc=411.8MB, time=23.02 memory used=2324.7MB, alloc=411.8MB, time=23.65 memory used=2381.6MB, alloc=411.8MB, time=24.02 memory used=2480.4MB, alloc=411.8MB, time=25.79 memory used=2609.6MB, alloc=411.8MB, time=26.77 memory used=2731.0MB, alloc=411.8MB, time=27.83 memory used=2857.8MB, alloc=411.8MB, time=30.42 memory used=2974.3MB, alloc=411.8MB, time=31.84 memory used=3086.7MB, alloc=435.8MB, time=33.14 memory used=3208.1MB, alloc=435.8MB, time=34.75 memory used=3337.6MB, alloc=459.8MB, time=36.43 memory used=3481.1MB, alloc=459.8MB, time=37.63 memory used=3549.6MB, alloc=459.8MB, time=37.90 memory used=3656.1MB, alloc=459.8MB, time=41.10 memory used=3720.2MB, alloc=459.8MB, time=41.39 memory used=3791.0MB, alloc=459.8MB, time=41.64 memory used=3886.4MB, alloc=459.8MB, time=42.25 memory used=4020.1MB, alloc=459.8MB, time=44.26 memory used=4109.0MB, alloc=483.8MB, time=45.66 memory used=4216.6MB, alloc=483.8MB, time=47.35 memory used=4308.8MB, alloc=507.8MB, time=48.61 memory used=4410.5MB, alloc=507.8MB, time=49.81 memory used=4489.8MB, alloc=531.8MB, time=50.89 memory used=4575.9MB, alloc=531.8MB, time=52.35 memory used=4632.2MB, alloc=531.8MB, time=53.35 memory used=4703.0MB, alloc=531.8MB, time=54.48 memory used=4762.0MB, alloc=531.8MB, time=55.37 memory used=4810.6MB, alloc=531.8MB, time=56.24 memory used=4867.1MB, alloc=531.8MB, time=57.16 memory used=4938.3MB, alloc=531.8MB, time=58.54 memory used=4994.0MB, alloc=531.8MB, time=59.71 memory used=5039.3MB, alloc=531.8MB, time=60.69 memory used=5236.0MB, alloc=555.8MB, time=63.24 memory used=5451.9MB, alloc=579.8MB, time=65.97 memory used=5575.3MB, alloc=603.8MB, time=66.72 memory used=5678.1MB, alloc=603.8MB, time=67.38 memory used=5814.5MB, alloc=603.8MB, time=68.07 memory used=5915.8MB, alloc=603.8MB, time=68.69 memory used=6015.5MB, alloc=603.8MB, time=69.28 memory used=6156.9MB, alloc=603.8MB, time=70.49 memory used=6278.7MB, alloc=603.8MB, time=71.25 memory used=6389.7MB, alloc=603.8MB, time=71.93 memory used=6526.5MB, alloc=627.8MB, time=72.64 memory used=6629.8MB, alloc=627.8MB, time=73.26 memory used=6755.3MB, alloc=627.8MB, time=73.89 memory used=6961.3MB, alloc=627.8MB, time=93.32 memory used=7103.5MB, alloc=627.8MB, time=94.09 memory used=7213.9MB, alloc=627.8MB, time=94.73 memory used=7354.9MB, alloc=627.8MB, time=95.41 memory used=7618.1MB, alloc=627.8MB, time=96.43 memory used=7783.4MB, alloc=627.8MB, time=97.17 memory used=7998.9MB, alloc=627.8MB, time=98.55 memory used=8127.8MB, alloc=627.8MB, time=99.30 memory used=8275.3MB, alloc=627.8MB, time=100.04 memory used=8382.4MB, alloc=627.8MB, time=100.73 memory used=8512.8MB, alloc=627.8MB, time=101.39 memory used=8676.9MB, alloc=627.8MB, time=102.67 memory used=8806.4MB, alloc=627.8MB, time=103.49 memory used=8954.0MB, alloc=627.8MB, time=104.27 memory used=9061.1MB, alloc=627.8MB, time=104.90 memory used=9191.7MB, alloc=627.8MB, time=105.52 memory used=9394.1MB, alloc=627.8MB, time=125.33 memory used=9532.4MB, alloc=627.8MB, time=126.06 memory used=9650.9MB, alloc=627.8MB, time=126.73 memory used=9799.9MB, alloc=627.8MB, time=127.48 memory used=10024.4MB, alloc=627.8MB, time=128.31 memory used=10188.4MB, alloc=627.8MB, time=129.01 memory used=10408.2MB, alloc=627.8MB, time=130.14 memory used=10550.4MB, alloc=627.8MB, time=130.83 memory used=10721.6MB, alloc=627.8MB, time=141.24 memory used=10856.6MB, alloc=627.8MB, time=141.98 memory used=10980.6MB, alloc=627.8MB, time=142.65 memory used=11149.8MB, alloc=627.8MB, time=143.35 memory used=11293.5MB, alloc=627.8MB, time=144.09 memory used=11607.4MB, alloc=627.8MB, time=147.53 memory used=11843.5MB, alloc=627.8MB, time=153.55 memory used=11960.8MB, alloc=627.8MB, time=154.22 memory used=12108.8MB, alloc=627.8MB, time=154.92 memory used=12395.3MB, alloc=627.8MB, time=158.19 |\^/| 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(); 1428247129 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 3 2 2 3 F := [19 x z + 9 y - y z + 7 y , 13 x y z - 5 x z - y , 4 2 -2 y + 12 x z + 10 x y + 4 z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 2 3 G := [-x y + 13 y z + 3 x y - 8 z, 7 x y + 19 x y z - 3 x y , 4 2 2 2 -16 x + 12 x y z - 3 y z - 14 y ] > Problem := [F,G]; 3 4 2 2 3 2 2 3 Problem := [[19 x z + 9 y - y z + 7 y , 13 x y z - 5 x z - y , 4 2 2 2 2 2 2 -2 y + 12 x z + 10 x y + 4 z], [-x y + 13 y z + 3 x y - 8 z, 2 2 2 3 4 2 2 2 7 x y + 19 x y z - 3 x y , -16 x + 12 x y z - 3 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=0.18 memory used=24.0MB, alloc=32.3MB, time=0.49 memory used=43.3MB, alloc=56.3MB, time=0.79 memory used=82.3MB, alloc=59.2MB, time=1.00 memory used=127.3MB, alloc=63.2MB, time=1.43 memory used=173.2MB, alloc=63.2MB, time=1.98 memory used=224.1MB, alloc=71.2MB, time=2.52 memory used=250.2MB, alloc=71.2MB, time=2.61 memory used=271.0MB, alloc=71.2MB, time=2.68 memory used=304.0MB, alloc=71.2MB, time=3.02 memory used=339.1MB, alloc=71.2MB, time=3.22 memory used=366.5MB, alloc=71.2MB, time=3.29 memory used=387.7MB, alloc=71.2MB, time=3.37 memory used=413.2MB, alloc=71.2MB, time=3.44 memory used=443.4MB, alloc=71.2MB, time=3.51 memory used=463.9MB, alloc=71.2MB, time=3.57 memory used=483.7MB, alloc=71.2MB, time=3.62 memory used=527.6MB, alloc=71.2MB, time=4.05 memory used=570.8MB, alloc=71.2MB, time=4.66 memory used=618.5MB, alloc=95.2MB, time=5.26 memory used=681.9MB, alloc=95.2MB, time=5.96 memory used=731.2MB, alloc=95.2MB, time=6.23 memory used=773.0MB, alloc=95.2MB, time=6.42 memory used=813.5MB, alloc=95.2MB, time=6.66 memory used=868.2MB, alloc=95.2MB, time=7.00 memory used=900.5MB, alloc=95.2MB, time=7.12 memory used=942.7MB, alloc=95.2MB, time=7.32 memory used=983.1MB, alloc=95.2MB, time=7.46 memory used=1032.2MB, alloc=95.2MB, time=8.34 memory used=1063.9MB, alloc=95.2MB, time=8.47 memory used=1148.4MB, alloc=95.2MB, time=9.46 memory used=1231.2MB, alloc=351.2MB, time=10.45 memory used=1282.7MB, alloc=351.2MB, time=11.16 memory used=1334.6MB, alloc=351.2MB, time=13.03 memory used=1365.2MB, alloc=351.2MB, time=13.14 memory used=1396.0MB, alloc=351.2MB, time=13.27 memory used=1435.7MB, alloc=351.2MB, time=13.53 memory used=1467.9MB, alloc=351.2MB, time=13.72 memory used=1518.8MB, alloc=351.2MB, time=14.20 memory used=1596.5MB, alloc=351.2MB, time=15.21 memory used=1662.6MB, alloc=375.2MB, time=15.92 memory used=1754.6MB, alloc=375.2MB, time=17.18 memory used=1829.3MB, alloc=375.2MB, time=17.93 memory used=1890.6MB, alloc=375.2MB, time=18.16 memory used=1923.7MB, alloc=375.2MB, time=18.32 memory used=1963.5MB, alloc=375.2MB, time=18.52 memory used=2009.9MB, alloc=375.2MB, time=18.71 memory used=2056.5MB, alloc=399.2MB, time=18.95 memory used=2098.5MB, alloc=399.2MB, time=19.14 memory used=2144.2MB, alloc=399.2MB, time=19.31 memory used=2195.7MB, alloc=399.2MB, time=19.49 memory used=2251.3MB, alloc=399.2MB, time=19.65 memory used=2312.6MB, alloc=399.2MB, time=19.83 memory used=2379.5MB, alloc=399.2MB, time=20.02 memory used=2453.8MB, alloc=399.2MB, time=20.19 memory used=2497.1MB, alloc=399.2MB, time=20.32 memory used=2539.3MB, alloc=399.2MB, time=20.45 memory used=2584.1MB, alloc=399.2MB, time=20.59 memory used=2652.6MB, alloc=399.2MB, time=20.96 memory used=2712.8MB, alloc=399.2MB, time=21.18 memory used=2781.4MB, alloc=399.2MB, time=21.39 memory used=2829.7MB, alloc=399.2MB, time=21.57 memory used=2878.8MB, alloc=399.2MB, time=21.74 memory used=2936.1MB, alloc=399.2MB, time=21.93 memory used=3016.8MB, alloc=399.2MB, time=23.36 memory used=3134.9MB, alloc=399.2MB, time=26.36 memory used=3188.8MB, alloc=399.2MB, time=26.54 memory used=3248.8MB, alloc=399.2MB, time=26.78 memory used=3318.1MB, alloc=399.2MB, time=26.95 memory used=3360.8MB, alloc=399.2MB, time=27.10 memory used=3409.0MB, alloc=399.2MB, time=27.25 memory used=3462.5MB, alloc=399.2MB, time=27.43 memory used=3521.5MB, alloc=399.2MB, time=27.57 memory used=3589.8MB, alloc=399.2MB, time=27.72 memory used=3720.3MB, alloc=399.2MB, time=29.03 memory used=3827.3MB, alloc=399.2MB, time=36.18 memory used=3886.6MB, alloc=399.2MB, time=36.39 memory used=3934.2MB, alloc=399.2MB, time=36.59 memory used=3991.4MB, alloc=399.2MB, time=36.77 memory used=4060.0MB, alloc=399.2MB, time=36.97 memory used=4106.2MB, alloc=399.2MB, time=37.12 memory used=4147.3MB, alloc=399.2MB, time=37.28 memory used=4192.0MB, alloc=399.2MB, time=37.44 memory used=4240.0MB, alloc=399.2MB, time=37.63 memory used=4292.4MB, alloc=399.2MB, time=37.79 memory used=4348.9MB, alloc=399.2MB, time=37.94 memory used=4410.4MB, alloc=399.2MB, time=38.11 memory used=4476.9MB, alloc=399.2MB, time=38.27 memory used=4651.0MB, alloc=399.2MB, time=39.09 memory used=4770.2MB, alloc=399.2MB, time=40.23 memory used=4875.8MB, alloc=399.2MB, time=41.94 memory used=4993.2MB, alloc=399.2MB, time=43.58 memory used=5120.3MB, alloc=423.2MB, time=45.02 memory used=5240.0MB, alloc=423.2MB, time=46.43 memory used=5385.5MB, alloc=423.2MB, time=48.56 memory used=5524.7MB, alloc=447.2MB, time=49.53 memory used=5655.1MB, alloc=447.2MB, time=50.86 memory used=5731.1MB, alloc=447.2MB, time=51.17 memory used=5788.9MB, alloc=447.2MB, time=51.50 memory used=5859.4MB, alloc=447.2MB, time=51.76 memory used=5944.5MB, alloc=447.2MB, time=52.02 memory used=6002.7MB, alloc=447.2MB, time=52.26 memory used=6056.8MB, alloc=447.2MB, time=52.53 memory used=6119.5MB, alloc=447.2MB, time=52.86 memory used=6210.8MB, alloc=447.2MB, time=53.45 memory used=6282.1MB, alloc=447.2MB, time=53.72 memory used=6344.1MB, alloc=447.2MB, time=53.98 memory used=6419.5MB, alloc=447.2MB, time=54.26 memory used=6503.5MB, alloc=447.2MB, time=54.52 memory used=6556.4MB, alloc=447.2MB, time=54.73 memory used=6613.5MB, alloc=447.2MB, time=54.97 memory used=6722.8MB, alloc=447.2MB, time=64.65 memory used=6795.4MB, alloc=447.2MB, time=64.97 memory used=6866.3MB, alloc=447.2MB, time=65.26 memory used=6943.7MB, alloc=447.2MB, time=65.52 memory used=6997.0MB, alloc=447.2MB, time=65.75 memory used=7057.3MB, alloc=447.2MB, time=66.02 memory used=7124.9MB, alloc=447.2MB, time=66.26 memory used=7199.5MB, alloc=447.2MB, time=66.50 memory used=7282.2MB, alloc=447.2MB, time=66.76 memory used=7395.3MB, alloc=447.2MB, time=67.06 memory used=7533.8MB, alloc=447.2MB, time=67.47 memory used=7694.4MB, alloc=447.2MB, time=67.82 memory used=7994.1MB, alloc=447.2MB, time=69.45 memory used=8104.7MB, alloc=447.2MB, time=70.83 memory used=8167.5MB, alloc=447.2MB, time=71.13 memory used=8244.7MB, alloc=447.2MB, time=71.55 memory used=8325.9MB, alloc=447.2MB, time=73.25 memory used=8386.8MB, alloc=447.2MB, time=73.53 memory used=8483.1MB, alloc=471.2MB, time=74.68 memory used=8621.9MB, alloc=471.2MB, time=75.94 memory used=8706.5MB, alloc=471.2MB, time=76.27 memory used=8773.6MB, alloc=471.2MB, time=76.59 memory used=8855.2MB, alloc=471.2MB, time=76.90 memory used=8946.0MB, alloc=471.2MB, time=77.20 memory used=9037.1MB, alloc=471.2MB, time=77.88 memory used=9123.5MB, alloc=471.2MB, time=78.26 memory used=9200.7MB, alloc=471.2MB, time=78.60 memory used=9272.0MB, alloc=471.2MB, time=78.91 memory used=9360.7MB, alloc=471.2MB, time=79.23 memory used=9439.8MB, alloc=471.2MB, time=79.52 memory used=9563.0MB, alloc=471.2MB, time=87.76 memory used=9641.5MB, alloc=471.2MB, time=88.11 memory used=9721.7MB, alloc=471.2MB, time=88.45 memory used=9808.6MB, alloc=471.2MB, time=88.76 memory used=9868.2MB, alloc=471.2MB, time=89.06 memory used=9935.0MB, alloc=471.2MB, time=89.36 memory used=10010.0MB, alloc=471.2MB, time=89.64 memory used=10093.8MB, alloc=471.2MB, time=89.93 memory used=10187.2MB, alloc=471.2MB, time=90.22 memory used=10408.6MB, alloc=471.2MB, time=90.67 memory used=10637.1MB, alloc=471.2MB, time=92.86 memory used=10766.5MB, alloc=471.2MB, time=94.44 memory used=10948.4MB, alloc=471.2MB, time=96.96 memory used=11119.5MB, alloc=471.2MB, time=100.84 memory used=11289.4MB, alloc=471.2MB, time=106.71 memory used=11444.7MB, alloc=471.2MB, time=113.59 memory used=11566.7MB, alloc=471.2MB, time=118.44 memory used=11650.7MB, alloc=471.2MB, time=119.78 memory used=11718.7MB, alloc=471.2MB, time=120.92 memory used=11784.9MB, alloc=495.2MB, time=122.07 memory used=11884.1MB, alloc=495.2MB, time=123.10 memory used=11991.8MB, alloc=495.2MB, time=123.88 memory used=12230.9MB, alloc=495.2MB, time=142.57 memory used=12404.6MB, alloc=495.2MB, time=147.66 memory used=12533.6MB, alloc=495.2MB, time=148.66 memory used=12621.2MB, alloc=495.2MB, time=149.94 memory used=12712.5MB, alloc=519.2MB, time=150.90 memory used=12778.5MB, alloc=519.2MB, time=151.91 memory used=12905.0MB, alloc=519.2MB, time=153.98 memory used=13018.7MB, alloc=519.2MB, time=154.61 memory used=13150.2MB, alloc=519.2MB, time=157.99 memory used=13249.5MB, alloc=519.2MB, time=158.45 memory used=13379.7MB, alloc=519.2MB, time=159.49 memory used=13435.6MB, alloc=519.2MB, time=160.47 memory used=13492.5MB, alloc=519.2MB, time=161.19 memory used=13543.9MB, alloc=519.2MB, time=162.88 |\^/| 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(); 1428247429 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 3 2 4 F := [-14 x y z - 4 x z + 3 z + 5, 2 x z - 19 x y z + 3 z - 15 x y z, 2 2 2 3 -19 x z - 14 x y z - 8 y z + 11 x y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 2 G := [18 x z + 16 x z - 6 y - 20, 9 x y z - 12 y z + 18 x z + 10 y z , 3 2 2 2 6 x y - 16 x y + 2 x y - 13 x y z] > Problem := [F,G]; 2 3 4 Problem := [[-14 x y z - 4 x z + 3 z + 5, 3 2 4 2 x z - 19 x y z + 3 z - 15 x y z, 2 2 2 3 2 2 2 -19 x z - 14 x y z - 8 y z + 11 x y z], [18 x z + 16 x z - 6 y - 20, 2 3 2 2 9 x y z - 12 y z + 18 x z + 10 y z , 3 2 2 2 6 x y - 16 x y + 2 x y - 13 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=32.3MB, time=0.82 memory used=65.4MB, alloc=56.3MB, time=1.11 memory used=106.9MB, alloc=68.3MB, time=1.72 memory used=147.7MB, alloc=92.3MB, time=2.33 memory used=211.3MB, alloc=92.3MB, time=3.29 memory used=273.0MB, alloc=116.3MB, time=4.21 memory used=361.7MB, alloc=116.3MB, time=5.23 memory used=438.0MB, alloc=372.3MB, time=6.42 memory used=520.6MB, alloc=396.3MB, time=7.68 memory used=625.5MB, alloc=396.3MB, time=8.65 memory used=718.7MB, alloc=396.3MB, time=9.69 memory used=818.0MB, alloc=420.3MB, time=11.30 memory used=951.2MB, alloc=444.3MB, time=13.25 memory used=1084.9MB, alloc=468.3MB, time=15.34 memory used=1208.7MB, alloc=468.3MB, time=17.40 memory used=1330.5MB, alloc=492.3MB, time=19.29 memory used=1452.5MB, alloc=492.3MB, time=21.33 memory used=1556.9MB, alloc=492.3MB, time=23.06 memory used=1642.8MB, alloc=492.3MB, time=24.56 memory used=1755.7MB, alloc=492.3MB, time=25.98 memory used=1864.6MB, alloc=492.3MB, time=26.62 memory used=1984.0MB, alloc=492.3MB, time=31.42 memory used=2135.3MB, alloc=492.3MB, time=32.78 memory used=2215.9MB, alloc=492.3MB, time=33.16 memory used=2327.5MB, alloc=492.3MB, time=33.73 memory used=2500.7MB, alloc=492.3MB, time=39.44 memory used=2585.3MB, alloc=492.3MB, time=39.90 memory used=2674.7MB, alloc=492.3MB, time=40.39 memory used=2813.9MB, alloc=492.3MB, time=41.98 memory used=2923.7MB, alloc=516.3MB, time=43.32 memory used=3047.4MB, alloc=516.3MB, time=46.33 memory used=3178.9MB, alloc=516.3MB, time=47.46 memory used=3271.7MB, alloc=516.3MB, time=49.20 memory used=3338.7MB, alloc=516.3MB, time=50.40 memory used=3415.0MB, alloc=516.3MB, time=52.04 memory used=3482.1MB, alloc=516.3MB, time=53.59 memory used=3552.8MB, alloc=516.3MB, time=55.13 memory used=3621.4MB, alloc=516.3MB, time=56.64 memory used=3684.6MB, alloc=516.3MB, time=58.05 memory used=3728.3MB, alloc=516.3MB, time=58.99 memory used=3933.0MB, alloc=540.3MB, time=62.89 memory used=4144.4MB, alloc=564.3MB, time=66.46 memory used=4281.5MB, alloc=588.3MB, time=67.57 memory used=4437.8MB, alloc=588.3MB, time=68.82 memory used=4562.2MB, alloc=588.3MB, time=69.56 memory used=4716.4MB, alloc=588.3MB, time=70.62 memory used=4849.5MB, alloc=588.3MB, time=71.38 memory used=4961.3MB, alloc=588.3MB, time=72.07 memory used=5140.7MB, alloc=588.3MB, time=87.03 memory used=5259.7MB, alloc=588.3MB, time=87.78 memory used=5397.9MB, alloc=588.3MB, time=88.52 memory used=5504.0MB, alloc=588.3MB, time=89.15 memory used=5609.7MB, alloc=588.3MB, time=89.76 memory used=5735.2MB, alloc=588.3MB, time=90.38 memory used=5922.9MB, alloc=588.3MB, time=91.66 memory used=6053.3MB, alloc=588.3MB, time=92.44 memory used=6167.1MB, alloc=588.3MB, time=93.12 memory used=6321.7MB, alloc=588.3MB, time=94.15 memory used=6442.5MB, alloc=588.3MB, time=94.86 memory used=6621.5MB, alloc=588.3MB, time=109.80 memory used=6745.3MB, alloc=588.3MB, time=110.54 memory used=6870.4MB, alloc=588.3MB, time=111.25 memory used=6996.6MB, alloc=588.3MB, time=111.91 memory used=7097.1MB, alloc=588.3MB, time=112.51 memory used=7215.6MB, alloc=588.3MB, time=113.10 memory used=7432.0MB, alloc=588.3MB, time=114.54 memory used=7712.9MB, alloc=588.3MB, time=123.39 memory used=7829.6MB, alloc=588.3MB, time=124.06 memory used=7963.7MB, alloc=588.3MB, time=124.73 memory used=8058.8MB, alloc=588.3MB, time=125.29 memory used=8178.7MB, alloc=588.3MB, time=125.88 memory used=8405.3MB, alloc=588.3MB, time=129.21 memory used=8697.0MB, alloc=612.3MB, time=136.43 memory used=8837.8MB, alloc=612.3MB, time=137.41 memory used=9011.7MB, alloc=612.3MB, time=138.29 memory used=9247.1MB, alloc=612.3MB, time=144.08 |\^/| 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(); 1428247729 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 3 2 2 2 F := [-9 x - 2 x z + 13 x y - 4 y , -2 x z - 8 x y z + 19 x z - 14 y z , 3 3 2 2 6 x z - 8 y z + 13 y z - 19 x ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 4 2 2 2 3 3 [7 z - 14 x + 3 x z - 19, -3 x y z - 19 y , 9 x y + 12 y z - x - 20 z] > Problem := [F,G]; 4 2 2 2 3 Problem := [[-9 x - 2 x z + 13 x y - 4 y , 3 2 2 2 3 3 2 2 -2 x z - 8 x y z + 19 x z - 14 y z , 6 x z - 8 y z + 13 y z - 19 x ], 4 2 2 2 3 3 [7 z - 14 x + 3 x z - 19, -3 x y z - 19 y , 9 x y + 12 y z - x - 20 z] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.19 memory used=26.1MB, alloc=32.3MB, time=0.51 memory used=46.5MB, alloc=56.3MB, time=0.83 memory used=88.1MB, alloc=60.3MB, time=1.46 memory used=128.1MB, alloc=60.3MB, time=2.05 memory used=167.0MB, alloc=84.3MB, time=2.65 memory used=229.5MB, alloc=92.3MB, time=3.64 memory used=295.2MB, alloc=116.3MB, time=4.65 memory used=361.5MB, alloc=116.3MB, time=5.69 memory used=423.2MB, alloc=372.3MB, time=6.68 memory used=513.6MB, alloc=396.3MB, time=8.04 memory used=625.7MB, alloc=420.3MB, time=9.89 memory used=754.0MB, alloc=444.3MB, time=11.96 memory used=884.6MB, alloc=468.3MB, time=14.19 memory used=992.4MB, alloc=468.3MB, time=15.93 memory used=1107.3MB, alloc=468.3MB, time=17.84 memory used=1197.3MB, alloc=468.3MB, time=19.31 memory used=1299.6MB, alloc=492.3MB, time=20.64 memory used=1390.0MB, alloc=492.3MB, time=22.04 memory used=1473.1MB, alloc=492.3MB, time=23.39 memory used=1558.1MB, alloc=492.3MB, time=24.70 memory used=1652.8MB, alloc=492.3MB, time=26.22 memory used=1724.0MB, alloc=492.3MB, time=27.54 memory used=1789.3MB, alloc=492.3MB, time=28.77 memory used=1860.8MB, alloc=492.3MB, time=30.11 memory used=1923.8MB, alloc=516.3MB, time=31.26 memory used=2011.1MB, alloc=516.3MB, time=32.33 memory used=2070.7MB, alloc=516.3MB, time=33.71 memory used=2130.6MB, alloc=516.3MB, time=35.10 memory used=2198.3MB, alloc=516.3MB, time=36.78 memory used=2266.3MB, alloc=516.3MB, time=38.36 memory used=2316.5MB, alloc=516.3MB, time=39.51 memory used=2506.8MB, alloc=540.3MB, time=42.95 memory used=2677.3MB, alloc=564.3MB, time=45.40 memory used=2861.9MB, alloc=588.3MB, time=48.65 memory used=3028.2MB, alloc=612.3MB, time=51.73 memory used=3168.6MB, alloc=636.3MB, time=54.06 memory used=3320.6MB, alloc=660.3MB, time=56.90 memory used=3419.4MB, alloc=660.3MB, time=58.83 memory used=3544.2MB, alloc=660.3MB, time=61.30 memory used=3641.6MB, alloc=660.3MB, time=63.35 memory used=3734.2MB, alloc=660.3MB, time=65.29 memory used=4107.5MB, alloc=684.3MB, time=71.34 memory used=4305.1MB, alloc=708.3MB, time=74.59 memory used=4478.3MB, alloc=732.3MB, time=75.90 memory used=4644.3MB, alloc=732.3MB, time=77.21 memory used=4807.3MB, alloc=732.3MB, time=78.55 memory used=5014.8MB, alloc=732.3MB, time=81.69 memory used=5216.5MB, alloc=732.3MB, time=83.01 memory used=5365.3MB, alloc=732.3MB, time=84.25 memory used=5581.1MB, alloc=732.3MB, time=87.36 memory used=5759.9MB, alloc=732.3MB, time=88.78 memory used=5944.7MB, alloc=732.3MB, time=90.17 memory used=6099.8MB, alloc=732.3MB, time=91.50 memory used=6312.2MB, alloc=732.3MB, time=94.65 memory used=6509.5MB, alloc=732.3MB, time=95.98 memory used=6665.1MB, alloc=732.3MB, time=97.21 memory used=6832.8MB, alloc=732.3MB, time=98.45 memory used=7068.7MB, alloc=756.3MB, time=115.06 memory used=7283.9MB, alloc=756.3MB, time=116.49 memory used=7474.5MB, alloc=756.3MB, time=117.85 |\^/| 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(); 1428248029 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 3 2 F := [-15 x y z + 8 y z - 14 y - 2 z, 17 x y - 2 x z + 5 y z + 8 x z, 4 2 2 2 15 x - 9 x y - 19 x y z - 8 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 4 3 G := [-12 x y z - 15 y z + 20 x y z - 6 x y, 8 x z - 2 x z + 6 y - 15 y z, 4 2 2 2 5 x - 18 y z - 11 x y + 5 x z] > Problem := [F,G]; 2 3 Problem := [[-15 x y z + 8 y z - 14 y - 2 z, 3 3 3 2 4 2 2 2 17 x y - 2 x z + 5 y z + 8 x z, 15 x - 9 x y - 19 x y z - 8 x], [ 2 3 3 3 4 3 -12 x y z - 15 y z + 20 x y z - 6 x y, 8 x z - 2 x z + 6 y - 15 y z, 4 2 2 2 5 x - 18 y z - 11 x y + 5 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.18 memory used=23.8MB, alloc=32.3MB, time=0.48 memory used=49.4MB, alloc=56.3MB, time=0.81 memory used=83.8MB, alloc=56.9MB, time=1.29 memory used=115.2MB, alloc=56.9MB, time=1.42 memory used=156.0MB, alloc=60.9MB, time=1.72 memory used=203.5MB, alloc=68.9MB, time=2.31 memory used=248.5MB, alloc=68.9MB, time=2.91 memory used=291.0MB, alloc=68.9MB, time=3.50 memory used=338.6MB, alloc=92.9MB, time=4.08 memory used=387.0MB, alloc=92.9MB, time=4.22 memory used=416.5MB, alloc=92.9MB, time=4.33 memory used=451.7MB, alloc=92.9MB, time=4.44 memory used=493.2MB, alloc=92.9MB, time=4.56 memory used=539.4MB, alloc=92.9MB, time=4.69 memory used=565.2MB, alloc=92.9MB, time=4.79 memory used=591.5MB, alloc=92.9MB, time=4.88 memory used=618.0MB, alloc=92.9MB, time=4.97 memory used=645.4MB, alloc=92.9MB, time=5.07 memory used=675.9MB, alloc=92.9MB, time=5.17 memory used=707.3MB, alloc=92.9MB, time=5.27 memory used=739.5MB, alloc=92.9MB, time=5.38 memory used=774.9MB, alloc=92.9MB, time=5.47 memory used=811.1MB, alloc=92.9MB, time=5.58 memory used=850.9MB, alloc=92.9MB, time=5.68 memory used=891.0MB, alloc=92.9MB, time=5.78 memory used=934.6MB, alloc=92.9MB, time=5.88 memory used=981.4MB, alloc=92.9MB, time=6.00 memory used=1012.2MB, alloc=92.9MB, time=6.08 memory used=1035.0MB, alloc=92.9MB, time=6.15 memory used=1059.1MB, alloc=92.9MB, time=6.22 memory used=1083.1MB, alloc=92.9MB, time=6.30 memory used=1106.8MB, alloc=92.9MB, time=6.37 memory used=1130.8MB, alloc=92.9MB, time=6.45 memory used=1156.9MB, alloc=92.9MB, time=6.54 memory used=1182.9MB, alloc=92.9MB, time=6.62 memory used=1211.3MB, alloc=92.9MB, time=6.70 memory used=1239.3MB, alloc=92.9MB, time=6.77 memory used=1269.3MB, alloc=92.9MB, time=6.85 memory used=1298.8MB, alloc=92.9MB, time=6.92 memory used=1329.8MB, alloc=92.9MB, time=7.00 memory used=1362.1MB, alloc=92.9MB, time=7.07 memory used=1395.5MB, alloc=92.9MB, time=7.15 memory used=1431.2MB, alloc=92.9MB, time=7.23 memory used=1468.5MB, alloc=92.9MB, time=7.31 memory used=1507.8MB, alloc=92.9MB, time=7.38 memory used=1556.9MB, alloc=92.9MB, time=7.62 memory used=1616.8MB, alloc=94.4MB, time=8.02 memory used=1649.0MB, alloc=94.4MB, time=8.14 memory used=1682.6MB, alloc=94.4MB, time=8.26 memory used=1722.4MB, alloc=94.4MB, time=8.39 memory used=1766.6MB, alloc=94.4MB, time=8.51 memory used=1799.3MB, alloc=94.4MB, time=8.61 memory used=1824.1MB, alloc=94.4MB, time=8.72 memory used=1850.3MB, alloc=94.4MB, time=8.82 memory used=1877.3MB, alloc=94.4MB, time=8.93 memory used=1907.6MB, alloc=94.4MB, time=9.03 memory used=1938.7MB, alloc=94.4MB, time=9.13 memory used=1970.7MB, alloc=94.4MB, time=9.23 memory used=2006.0MB, alloc=94.4MB, time=9.34 memory used=2042.1MB, alloc=94.4MB, time=9.45 memory used=2081.5MB, alloc=94.4MB, time=9.56 memory used=2121.6MB, alloc=94.4MB, time=9.66 memory used=2165.0MB, alloc=94.4MB, time=9.76 memory used=2208.7MB, alloc=94.4MB, time=9.88 memory used=2247.4MB, alloc=94.4MB, time=9.97 memory used=2269.3MB, alloc=94.4MB, time=10.05 memory used=2293.2MB, alloc=94.4MB, time=10.12 memory used=2317.2MB, alloc=94.4MB, time=10.20 memory used=2341.0MB, alloc=94.4MB, time=10.30 memory used=2364.8MB, alloc=94.4MB, time=10.37 memory used=2391.2MB, alloc=94.4MB, time=10.44 memory used=2417.3MB, alloc=94.4MB, time=10.53 memory used=2443.3MB, alloc=94.4MB, time=10.61 memory used=2471.2MB, alloc=94.4MB, time=10.70 memory used=2499.3MB, alloc=94.4MB, time=10.79 memory used=2528.5MB, alloc=94.4MB, time=10.86 memory used=2560.0MB, alloc=94.4MB, time=10.94 memory used=2593.0MB, alloc=94.4MB, time=11.01 memory used=2626.8MB, alloc=94.4MB, time=11.09 memory used=2661.0MB, alloc=94.4MB, time=11.17 memory used=2697.4MB, alloc=94.4MB, time=11.26 memory used=2736.1MB, alloc=94.4MB, time=11.34 memory used=2777.6MB, alloc=94.4MB, time=11.42 memory used=2848.0MB, alloc=94.4MB, time=25.22 memory used=2895.1MB, alloc=118.4MB, time=54.76 memory used=2945.5MB, alloc=142.4MB, time=94.94 |\^/| 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(); 1428248329 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 3 2 2 F := [11 y z - 5 z - 8 y z + 18 z , 8 x y z - 11 x y z + 19 y z + 7 x, 2 2 2 4 16 x y z - 11 y z + 19 z - 17 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 2 G := [-3 y - 2 x - 12 x y + 13 z, 19 x y - 13 x + 6 x y z - 6 y z, 3 3 -18 x y - 16 x y z - y + 11 y] > Problem := [F,G]; 3 4 2 3 Problem := [[11 y z - 5 z - 8 y z + 18 z , 2 2 2 2 2 4 8 x y z - 11 x y z + 19 y z + 7 x, 16 x y z - 11 y z + 19 z - 17 x z] 4 2 2 2 3 2 , [-3 y - 2 x - 12 x y + 13 z, 19 x y - 13 x + 6 x y z - 6 y z, 3 3 -18 x y - 16 x y z - y + 11 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=25.2MB, alloc=32.3MB, time=0.48 memory used=44.9MB, alloc=32.3MB, time=0.75 memory used=64.3MB, alloc=60.3MB, time=1.05 memory used=105.5MB, alloc=68.3MB, time=1.65 memory used=150.5MB, alloc=68.3MB, time=2.15 memory used=195.8MB, alloc=92.3MB, time=2.75 memory used=263.9MB, alloc=92.3MB, time=3.68 memory used=328.7MB, alloc=92.3MB, time=4.48 memory used=394.7MB, alloc=116.3MB, time=5.39 memory used=455.6MB, alloc=116.3MB, time=5.91 memory used=524.8MB, alloc=372.3MB, time=6.81 memory used=629.5MB, alloc=372.3MB, time=8.52 memory used=714.1MB, alloc=396.3MB, time=9.51 memory used=819.9MB, alloc=396.3MB, time=10.86 memory used=926.9MB, alloc=420.3MB, time=12.46 memory used=1037.3MB, alloc=444.3MB, time=13.97 memory used=1140.2MB, alloc=444.3MB, time=15.28 memory used=1237.9MB, alloc=468.3MB, time=16.63 memory used=1360.1MB, alloc=468.3MB, time=17.88 memory used=1452.4MB, alloc=468.3MB, time=19.07 memory used=1536.3MB, alloc=468.3MB, time=20.38 memory used=1631.8MB, alloc=468.3MB, time=21.96 memory used=1733.0MB, alloc=468.3MB, time=23.11 memory used=1812.8MB, alloc=468.3MB, time=24.22 memory used=1891.5MB, alloc=492.3MB, time=25.49 memory used=1962.3MB, alloc=492.3MB, time=26.76 memory used=2017.2MB, alloc=492.3MB, time=27.77 memory used=2135.5MB, alloc=492.3MB, time=29.01 memory used=2248.1MB, alloc=492.3MB, time=30.75 memory used=2348.6MB, alloc=492.3MB, time=31.44 memory used=2455.1MB, alloc=492.3MB, time=32.26 memory used=2571.4MB, alloc=492.3MB, time=33.19 memory used=2648.1MB, alloc=492.3MB, time=34.40 memory used=2709.6MB, alloc=492.3MB, time=35.59 memory used=2780.2MB, alloc=492.3MB, time=36.79 memory used=2835.7MB, alloc=492.3MB, time=37.86 memory used=2906.3MB, alloc=492.3MB, time=38.79 memory used=2977.5MB, alloc=492.3MB, time=40.00 memory used=3021.2MB, alloc=492.3MB, time=40.83 memory used=3239.6MB, alloc=516.3MB, time=44.20 memory used=3445.6MB, alloc=540.3MB, time=47.53 memory used=3660.3MB, alloc=564.3MB, time=50.16 memory used=3830.9MB, alloc=588.3MB, time=52.70 memory used=4002.4MB, alloc=588.3MB, time=55.54 memory used=4141.1MB, alloc=612.3MB, time=58.02 memory used=4299.4MB, alloc=612.3MB, time=60.36 memory used=4421.7MB, alloc=612.3MB, time=62.67 memory used=4550.4MB, alloc=612.3MB, time=65.05 memory used=4747.8MB, alloc=636.3MB, time=67.44 memory used=4910.5MB, alloc=636.3MB, time=70.01 memory used=5083.2MB, alloc=636.3MB, time=73.03 memory used=5219.0MB, alloc=636.3MB, time=75.40 memory used=5335.0MB, alloc=636.3MB, time=78.04 memory used=5426.3MB, alloc=636.3MB, time=79.94 memory used=5527.2MB, alloc=636.3MB, time=82.09 memory used=5611.1MB, alloc=660.3MB, time=83.98 memory used=5928.8MB, alloc=684.3MB, time=89.20 memory used=6281.9MB, alloc=708.3MB, time=94.20 memory used=6648.5MB, alloc=732.3MB, time=99.03 memory used=6893.6MB, alloc=756.3MB, time=101.98 memory used=7104.6MB, alloc=756.3MB, time=103.68 memory used=7472.8MB, alloc=780.3MB, time=108.70 memory used=7833.6MB, alloc=804.3MB, time=114.99 memory used=8066.9MB, alloc=828.3MB, time=119.58 memory used=8443.8MB, alloc=852.3MB, time=123.83 |\^/| 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(); 1428248629 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [3 x + 13 z - 2 x - 18, x z + 6 x - 20 z - 10, 2 2 -10 x y z - 16 x z - 6 y + 16 z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 3 G := [2 x + x y + 8 y z - 13 y z, -11 x y - 20 y z + 2 x y - 8, 3 3 2 -18 x z + 5 y z + 6 x y z + 3 x ] > Problem := [F,G]; 3 2 2 Problem := [[3 x + 13 z - 2 x - 18, x z + 6 x - 20 z - 10, 2 2 4 2 2 2 -10 x y z - 16 x z - 6 y + 16 z], [2 x + x y + 8 y z - 13 y z, 3 3 3 3 2 -11 x y - 20 y z + 2 x y - 8, -18 x z + 5 y z + 6 x y z + 3 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.51 memory used=46.0MB, alloc=32.3MB, time=0.77 memory used=66.6MB, alloc=56.3MB, time=0.98 memory used=114.2MB, alloc=68.6MB, time=1.59 memory used=159.1MB, alloc=68.6MB, time=2.12 memory used=199.8MB, alloc=68.6MB, time=2.74 memory used=244.8MB, alloc=92.6MB, time=3.34 memory used=309.9MB, alloc=92.6MB, time=3.94 memory used=372.5MB, alloc=92.6MB, time=4.50 memory used=441.5MB, alloc=92.6MB, time=5.41 memory used=507.7MB, alloc=92.6MB, time=6.04 memory used=566.3MB, alloc=92.6MB, time=6.50 memory used=635.8MB, alloc=348.6MB, time=7.33 memory used=702.3MB, alloc=372.6MB, time=8.23 memory used=795.3MB, alloc=372.6MB, time=9.13 memory used=890.1MB, alloc=372.6MB, time=10.28 memory used=978.1MB, alloc=372.6MB, time=11.51 memory used=1058.3MB, alloc=372.6MB, time=12.13 memory used=1120.2MB, alloc=372.6MB, time=12.55 memory used=1181.7MB, alloc=372.6MB, time=12.96 memory used=1272.4MB, alloc=396.6MB, time=14.76 memory used=1388.7MB, alloc=396.6MB, time=15.71 memory used=1493.4MB, alloc=396.6MB, time=16.54 memory used=1603.5MB, alloc=396.6MB, time=17.88 memory used=1671.6MB, alloc=396.6MB, time=18.25 memory used=1731.4MB, alloc=396.6MB, time=18.62 memory used=1838.2MB, alloc=396.6MB, time=19.91 memory used=1945.5MB, alloc=396.6MB, time=21.55 memory used=2000.0MB, alloc=396.6MB, time=21.85 memory used=2119.0MB, alloc=420.6MB, time=23.31 memory used=2232.7MB, alloc=420.6MB, time=24.24 memory used=2304.1MB, alloc=420.6MB, time=24.54 memory used=2384.3MB, alloc=420.6MB, time=24.95 memory used=2459.6MB, alloc=420.6MB, time=25.25 memory used=2533.6MB, alloc=420.6MB, time=25.64 memory used=2608.1MB, alloc=420.6MB, time=25.99 memory used=2685.6MB, alloc=420.6MB, time=26.37 memory used=2787.1MB, alloc=420.6MB, time=27.30 memory used=2914.8MB, alloc=420.6MB, time=28.38 memory used=3007.1MB, alloc=420.6MB, time=28.94 memory used=3122.3MB, alloc=420.6MB, time=30.21 memory used=3253.8MB, alloc=420.6MB, time=31.92 memory used=3336.6MB, alloc=420.6MB, time=32.48 memory used=3462.9MB, alloc=420.6MB, time=33.98 memory used=3571.6MB, alloc=420.6MB, time=35.43 memory used=3695.7MB, alloc=444.6MB, time=37.09 memory used=3799.7MB, alloc=444.6MB, time=38.78 memory used=3895.3MB, alloc=444.6MB, time=40.38 memory used=4032.5MB, alloc=468.6MB, time=42.02 memory used=4120.9MB, alloc=468.6MB, time=43.51 memory used=4212.2MB, alloc=468.6MB, time=44.99 memory used=4321.5MB, alloc=468.6MB, time=46.37 memory used=4410.4MB, alloc=468.6MB, time=47.83 memory used=4510.4MB, alloc=492.6MB, time=49.32 memory used=4618.8MB, alloc=492.6MB, time=50.85 memory used=4729.5MB, alloc=492.6MB, time=51.42 memory used=4859.6MB, alloc=492.6MB, time=52.70 memory used=4978.5MB, alloc=492.6MB, time=53.49 memory used=5104.5MB, alloc=492.6MB, time=54.66 memory used=5181.8MB, alloc=492.6MB, time=55.01 memory used=5313.1MB, alloc=492.6MB, time=56.25 memory used=5399.2MB, alloc=492.6MB, time=56.68 memory used=5520.3MB, alloc=492.6MB, time=57.52 memory used=5629.9MB, alloc=492.6MB, time=58.72 memory used=5738.4MB, alloc=492.6MB, time=60.04 memory used=5811.1MB, alloc=492.6MB, time=61.43 memory used=5881.9MB, alloc=492.6MB, time=62.73 memory used=5959.0MB, alloc=492.6MB, time=64.30 memory used=6046.2MB, alloc=492.6MB, time=65.67 memory used=6124.2MB, alloc=492.6MB, time=66.84 memory used=6193.9MB, alloc=516.6MB, time=67.81 memory used=6246.5MB, alloc=516.6MB, time=68.77 memory used=6360.6MB, alloc=516.6MB, time=69.78 memory used=6412.7MB, alloc=516.6MB, time=70.89 memory used=6470.4MB, alloc=540.6MB, time=71.79 memory used=6579.4MB, alloc=540.6MB, time=72.75 memory used=6791.6MB, alloc=540.6MB, time=75.06 memory used=6950.9MB, alloc=540.6MB, time=76.36 memory used=7092.5MB, alloc=540.6MB, time=77.69 memory used=7281.0MB, alloc=540.6MB, time=80.34 memory used=7465.1MB, alloc=564.6MB, time=83.11 memory used=7691.9MB, alloc=564.6MB, time=86.14 memory used=7933.2MB, alloc=588.6MB, time=88.68 memory used=8176.0MB, alloc=612.6MB, time=91.16 memory used=8375.6MB, alloc=612.6MB, time=92.50 memory used=8581.5MB, alloc=612.6MB, time=95.32 memory used=8806.8MB, alloc=636.6MB, time=98.14 memory used=9020.2MB, alloc=636.6MB, time=100.82 memory used=9206.0MB, alloc=636.6MB, time=103.29 memory used=9461.2MB, alloc=660.6MB, time=105.40 memory used=9648.1MB, alloc=684.6MB, time=108.64 memory used=9777.3MB, alloc=684.6MB, time=111.06 memory used=9904.9MB, alloc=684.6MB, time=113.33 memory used=10021.3MB, alloc=684.6MB, time=115.40 memory used=10231.6MB, alloc=684.6MB, time=117.70 memory used=10315.2MB, alloc=684.6MB, time=118.88 memory used=10443.7MB, alloc=684.6MB, time=120.92 memory used=10577.8MB, alloc=684.6MB, time=123.80 memory used=10694.2MB, alloc=684.6MB, time=125.85 memory used=10806.2MB, alloc=684.6MB, time=127.90 |\^/| 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(); 1428248929 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 2 F := [-7 x z - 16 y z + 19 z + 2 y z, -12 x + 10 x y z - 19 x z + 4 y z, 2 2 2 2 -4 x y z + 20 y z - 10 x y + 15 x y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 3 3 3 3 G := [-17 x z + 17 y z + 15 y - 10 z , -3 x y + 18 x - 6 y + 6 x z, 2 2 3 3 2 -11 x y + 9 x y - 3 z + 20 x ] > Problem := [F,G]; 2 2 3 Problem := [[-7 x z - 16 y z + 19 z + 2 y z, 4 2 -12 x + 10 x y z - 19 x z + 4 y z, 2 2 2 2 -4 x y z + 20 y z - 10 x y + 15 x y z], [ 2 2 2 2 3 3 3 3 3 -17 x z + 17 y z + 15 y - 10 z , -3 x y + 18 x - 6 y + 6 x z, 2 2 3 3 2 -11 x y + 9 x 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=0.18 memory used=25.3MB, alloc=32.3MB, time=0.47 memory used=46.7MB, alloc=32.3MB, time=0.75 memory used=65.5MB, alloc=56.3MB, time=1.04 memory used=112.6MB, alloc=68.4MB, time=1.63 memory used=145.0MB, alloc=68.4MB, time=1.77 memory used=183.3MB, alloc=68.4MB, time=2.39 memory used=219.0MB, alloc=68.4MB, time=2.55 memory used=246.3MB, alloc=68.4MB, time=2.71 memory used=292.7MB, alloc=68.4MB, time=3.23 memory used=332.3MB, alloc=68.4MB, time=3.88 memory used=354.0MB, alloc=68.4MB, time=3.95 memory used=394.4MB, alloc=68.4MB, time=4.49 memory used=435.3MB, alloc=92.4MB, time=5.10 memory used=505.2MB, alloc=92.4MB, time=6.40 memory used=573.1MB, alloc=92.4MB, time=7.27 memory used=643.0MB, alloc=92.4MB, time=8.08 memory used=674.8MB, alloc=92.4MB, time=8.20 memory used=710.0MB, alloc=92.4MB, time=8.31 memory used=753.0MB, alloc=92.4MB, time=8.50 memory used=782.1MB, alloc=92.4MB, time=8.62 memory used=814.7MB, alloc=92.4MB, time=8.73 memory used=873.0MB, alloc=93.5MB, time=12.11 memory used=906.3MB, alloc=93.5MB, time=12.24 memory used=934.3MB, alloc=93.5MB, time=12.34 memory used=961.2MB, alloc=93.5MB, time=12.44 memory used=993.3MB, alloc=93.5MB, time=12.55 memory used=1030.6MB, alloc=93.5MB, time=12.67 memory used=1060.8MB, alloc=93.5MB, time=12.78 memory used=1083.0MB, alloc=93.5MB, time=12.86 memory used=1106.9MB, alloc=93.5MB, time=12.96 memory used=1132.0MB, alloc=93.5MB, time=13.04 memory used=1159.2MB, alloc=93.5MB, time=13.14 memory used=1189.1MB, alloc=93.5MB, time=13.26 memory used=1241.8MB, alloc=93.5MB, time=13.60 memory used=1306.0MB, alloc=349.5MB, time=14.76 memory used=1358.4MB, alloc=349.5MB, time=15.59 memory used=1385.4MB, alloc=373.5MB, time=15.72 memory used=1463.8MB, alloc=373.5MB, time=16.46 memory used=1543.0MB, alloc=373.5MB, time=17.37 memory used=1600.6MB, alloc=373.5MB, time=17.68 memory used=1667.8MB, alloc=373.5MB, time=19.00 memory used=1710.9MB, alloc=373.5MB, time=19.15 memory used=1800.5MB, alloc=373.5MB, time=20.28 memory used=1895.7MB, alloc=373.5MB, time=22.12 memory used=1938.1MB, alloc=373.5MB, time=22.26 memory used=2005.0MB, alloc=373.5MB, time=24.12 memory used=2048.4MB, alloc=373.5MB, time=24.29 memory used=2091.8MB, alloc=373.5MB, time=24.44 memory used=2133.6MB, alloc=373.5MB, time=24.59 memory used=2167.2MB, alloc=373.5MB, time=24.71 memory used=2206.3MB, alloc=373.5MB, time=24.83 memory used=2251.8MB, alloc=373.5MB, time=24.96 memory used=2317.0MB, alloc=373.5MB, time=25.30 memory used=2361.0MB, alloc=373.5MB, time=25.58 memory used=2436.0MB, alloc=373.5MB, time=29.73 memory used=2477.6MB, alloc=373.5MB, time=29.90 memory used=2518.9MB, alloc=373.5MB, time=30.05 memory used=2568.0MB, alloc=373.5MB, time=30.22 memory used=2599.3MB, alloc=373.5MB, time=30.34 memory used=2633.5MB, alloc=373.5MB, time=30.46 memory used=2670.9MB, alloc=373.5MB, time=30.59 memory used=2712.4MB, alloc=373.5MB, time=30.73 memory used=2758.6MB, alloc=373.5MB, time=30.87 memory used=2810.0MB, alloc=373.5MB, time=31.01 memory used=2988.2MB, alloc=373.5MB, time=32.36 memory used=3075.0MB, alloc=397.5MB, time=33.55 memory used=3193.6MB, alloc=421.5MB, time=34.74 memory used=3274.2MB, alloc=421.5MB, time=35.16 memory used=3371.5MB, alloc=421.5MB, time=36.71 memory used=3447.9MB, alloc=421.5MB, time=37.11 memory used=3526.6MB, alloc=421.5MB, time=38.08 memory used=3641.5MB, alloc=421.5MB, time=39.50 memory used=3777.0MB, alloc=421.5MB, time=40.82 memory used=3877.9MB, alloc=445.5MB, time=42.17 memory used=3991.9MB, alloc=469.5MB, time=43.92 memory used=4093.0MB, alloc=469.5MB, time=45.45 memory used=4203.7MB, alloc=469.5MB, time=47.35 memory used=4314.7MB, alloc=469.5MB, time=49.62 memory used=4424.5MB, alloc=493.5MB, time=50.94 memory used=4527.4MB, alloc=493.5MB, time=52.47 memory used=4638.7MB, alloc=493.5MB, time=53.72 memory used=4752.5MB, alloc=493.5MB, time=55.91 memory used=4852.4MB, alloc=493.5MB, time=56.64 memory used=4964.8MB, alloc=493.5MB, time=57.52 memory used=5089.8MB, alloc=493.5MB, time=58.82 memory used=5166.9MB, alloc=493.5MB, time=59.93 memory used=5282.5MB, alloc=493.5MB, time=61.95 memory used=5391.1MB, alloc=517.5MB, time=63.02 memory used=5459.4MB, alloc=517.5MB, time=64.02 memory used=5531.7MB, alloc=517.5MB, time=65.15 memory used=5581.9MB, alloc=517.5MB, time=66.09 memory used=5629.1MB, alloc=517.5MB, time=66.99 memory used=5686.0MB, alloc=517.5MB, time=67.87 memory used=5780.8MB, alloc=517.5MB, time=68.95 memory used=5892.2MB, alloc=517.5MB, time=69.53 memory used=5974.9MB, alloc=517.5MB, time=70.02 memory used=6095.1MB, alloc=517.5MB, time=70.70 memory used=6188.3MB, alloc=517.5MB, time=71.23 memory used=6337.8MB, alloc=517.5MB, time=74.97 memory used=6438.0MB, alloc=517.5MB, time=75.50 memory used=6532.0MB, alloc=517.5MB, time=75.97 memory used=6637.5MB, alloc=517.5MB, time=76.54 memory used=6752.1MB, alloc=517.5MB, time=78.79 memory used=6851.4MB, alloc=517.5MB, time=79.35 memory used=6946.8MB, alloc=517.5MB, time=79.86 memory used=7069.8MB, alloc=517.5MB, time=80.71 memory used=7246.5MB, alloc=517.5MB, time=88.17 memory used=7300.4MB, alloc=517.5MB, time=88.87 memory used=7392.0MB, alloc=517.5MB, time=89.39 memory used=7496.3MB, alloc=517.5MB, time=89.89 memory used=7568.8MB, alloc=517.5MB, time=90.32 memory used=7655.8MB, alloc=517.5MB, time=90.76 memory used=7783.3MB, alloc=517.5MB, time=91.32 memory used=7906.4MB, alloc=517.5MB, time=93.21 memory used=7999.2MB, alloc=517.5MB, time=93.69 memory used=8106.9MB, alloc=517.5MB, time=94.34 memory used=8225.9MB, alloc=517.5MB, time=94.97 memory used=8340.8MB, alloc=517.5MB, time=102.24 memory used=8448.5MB, alloc=517.5MB, time=102.91 memory used=8548.9MB, alloc=517.5MB, time=103.40 memory used=8630.9MB, alloc=517.5MB, time=103.86 memory used=8713.0MB, alloc=517.5MB, time=104.30 memory used=8812.2MB, alloc=517.5MB, time=104.74 memory used=8941.7MB, alloc=517.5MB, time=105.53 memory used=9035.5MB, alloc=517.5MB, time=106.03 memory used=9152.2MB, alloc=517.5MB, time=106.85 memory used=9246.1MB, alloc=517.5MB, time=107.35 memory used=9368.2MB, alloc=517.5MB, time=113.76 memory used=9459.6MB, alloc=517.5MB, time=114.31 memory used=9564.0MB, alloc=517.5MB, time=114.84 memory used=9636.8MB, alloc=517.5MB, time=115.30 memory used=9725.4MB, alloc=517.5MB, time=115.72 memory used=9838.7MB, alloc=517.5MB, time=116.62 memory used=9956.8MB, alloc=517.5MB, time=118.53 memory used=10046.1MB, alloc=517.5MB, time=119.02 memory used=10180.4MB, alloc=517.5MB, time=120.92 memory used=10269.6MB, alloc=517.5MB, time=121.41 memory used=10350.3MB, alloc=517.5MB, time=122.45 memory used=10591.0MB, alloc=517.5MB, time=127.68 memory used=10845.1MB, alloc=541.5MB, time=133.61 memory used=11113.8MB, alloc=541.5MB, time=140.87 memory used=11375.1MB, alloc=541.5MB, time=145.67 memory used=11627.2MB, alloc=541.5MB, time=156.37 memory used=11732.7MB, alloc=541.5MB, time=156.92 memory used=11824.6MB, alloc=541.5MB, time=157.44 memory used=11967.4MB, alloc=541.5MB, time=161.51 memory used=12075.3MB, alloc=541.5MB, time=162.14 memory used=12180.5MB, alloc=541.5MB, time=162.70 memory used=12268.2MB, alloc=541.5MB, time=163.19 memory used=12462.5MB, alloc=565.5MB, time=165.16 memory used=12742.5MB, alloc=565.5MB, time=170.33 memory used=12928.2MB, alloc=565.5MB, time=176.66 |\^/| 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(); 1428249229 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [12 x y + 17 x z - 14 x z + 11 y z, x y - 15 y z + 5 y + 19 z, 2 2 2 2 17 x y + 13 x z + 7 x - 12 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 G := [2 x y z - 14 x - 18 z - 19 z, 11 y z - 19 y - 7 x + 5, 3 2 2 2 2 x z - 8 x z + 20 x y z - 3 x y] > Problem := [F,G]; 3 3 2 Problem := [[12 x y + 17 x z - 14 x z + 11 y z, x y - 15 y z + 5 y + 19 z, 2 2 2 2 2 3 2 17 x y + 13 x z + 7 x - 12 y z], [2 x y z - 14 x - 18 z - 19 z, 3 2 3 2 2 2 2 11 y z - 19 y - 7 x + 5, x z - 8 x z + 20 x y z - 3 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=46.1MB, alloc=60.3MB, time=0.81 memory used=86.8MB, alloc=60.3MB, time=1.38 memory used=126.0MB, alloc=60.3MB, time=1.95 memory used=163.8MB, alloc=84.3MB, time=2.53 memory used=227.0MB, alloc=92.3MB, time=3.50 memory used=298.0MB, alloc=116.3MB, time=4.44 memory used=377.7MB, alloc=116.3MB, time=8.62 memory used=458.8MB, alloc=140.3MB, time=12.90 memory used=560.1MB, alloc=144.7MB, time=13.78 memory used=647.9MB, alloc=144.7MB, time=14.25 memory used=708.9MB, alloc=144.7MB, time=14.41 memory used=757.1MB, alloc=144.7MB, time=14.57 memory used=811.2MB, alloc=144.7MB, time=14.74 memory used=878.2MB, alloc=144.7MB, time=14.97 memory used=967.0MB, alloc=144.7MB, time=15.45 memory used=1028.2MB, alloc=144.7MB, time=15.63 memory used=1076.7MB, alloc=144.7MB, time=15.79 memory used=1131.1MB, alloc=144.7MB, time=15.95 memory used=1247.0MB, alloc=144.7MB, time=16.90 memory used=1378.6MB, alloc=144.7MB, time=17.64 memory used=1490.5MB, alloc=144.7MB, time=18.41 memory used=1551.0MB, alloc=144.7MB, time=18.59 memory used=1673.7MB, alloc=144.7MB, time=19.63 memory used=1799.0MB, alloc=144.7MB, time=20.38 memory used=1915.0MB, alloc=144.7MB, time=20.91 memory used=2045.1MB, alloc=400.7MB, time=22.32 memory used=2155.4MB, alloc=400.7MB, time=23.02 memory used=2270.4MB, alloc=400.7MB, time=23.52 memory used=2389.1MB, alloc=400.7MB, time=24.40 memory used=2445.1MB, alloc=400.7MB, time=24.61 memory used=2505.5MB, alloc=400.7MB, time=24.79 memory used=2611.9MB, alloc=400.7MB, time=26.29 memory used=2716.8MB, alloc=424.7MB, time=27.75 memory used=2844.8MB, alloc=448.7MB, time=29.74 memory used=2977.4MB, alloc=448.7MB, time=31.99 memory used=3106.4MB, alloc=472.7MB, time=34.05 memory used=3226.9MB, alloc=496.7MB, time=36.02 memory used=3347.7MB, alloc=496.7MB, time=38.18 memory used=3469.1MB, alloc=496.7MB, time=40.13 memory used=3584.3MB, alloc=496.7MB, time=41.94 memory used=3684.4MB, alloc=496.7MB, time=43.77 memory used=3775.1MB, alloc=520.7MB, time=45.53 memory used=3868.5MB, alloc=520.7MB, time=47.24 memory used=3953.1MB, alloc=520.7MB, time=48.89 memory used=4041.5MB, alloc=520.7MB, time=50.65 memory used=4123.9MB, alloc=520.7MB, time=52.23 memory used=4191.2MB, alloc=520.7MB, time=53.53 memory used=4277.1MB, alloc=520.7MB, time=55.46 memory used=4342.0MB, alloc=520.7MB, time=56.70 memory used=4403.2MB, alloc=520.7MB, time=57.98 memory used=4461.8MB, alloc=520.7MB, time=59.11 memory used=4534.5MB, alloc=544.7MB, time=60.39 memory used=4594.8MB, alloc=544.7MB, time=61.48 memory used=4656.4MB, alloc=544.7MB, time=62.47 memory used=4718.0MB, alloc=544.7MB, time=63.97 memory used=4775.2MB, alloc=544.7MB, time=65.37 memory used=4826.8MB, alloc=544.7MB, time=66.63 memory used=5051.5MB, alloc=568.7MB, time=71.33 memory used=5277.9MB, alloc=592.7MB, time=76.43 memory used=5449.9MB, alloc=616.7MB, time=79.52 memory used=5667.8MB, alloc=640.7MB, time=83.40 memory used=5900.9MB, alloc=664.7MB, time=86.35 memory used=6065.8MB, alloc=664.7MB, time=89.80 memory used=6223.6MB, alloc=688.7MB, time=93.51 memory used=6411.1MB, alloc=688.7MB, time=98.43 memory used=6565.0MB, alloc=688.7MB, time=102.08 memory used=6665.5MB, alloc=688.7MB, time=104.51 memory used=6789.9MB, alloc=712.7MB, time=106.56 memory used=6912.8MB, alloc=712.7MB, time=108.79 memory used=7047.9MB, alloc=736.7MB, time=111.65 memory used=7264.6MB, alloc=736.7MB, time=113.16 memory used=7432.0MB, alloc=736.7MB, time=118.51 memory used=7604.3MB, alloc=760.7MB, time=119.74 memory used=7833.0MB, alloc=760.7MB, time=121.04 memory used=8023.7MB, alloc=760.7MB, time=122.23 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428249529 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 4 2 F := [16 x y + 19 x y z + 3 x y z , 13 x y z - 11 y + 16 z + 7 z , 3 2 2 -9 x y + 2 x y z + 14 x y z - 19 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 3 2 3 G := [13 x y z - 7 y z + 4 z - 9 z , -10 x y z + 5 x y , 3 2 2 3 8 x y + 2 x y z + 15 x y - 15 y ] > Problem := [F,G]; 3 2 2 2 4 4 2 Problem := [[16 x y + 19 x y z + 3 x y z , 13 x y z - 11 y + 16 z + 7 z , 3 2 2 2 3 4 3 -9 x y + 2 x y z + 14 x y z - 19 x], [13 x y z - 7 y z + 4 z - 9 z , 2 3 3 2 2 3 -10 x y z + 5 x y , 8 x y + 2 x 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=4.4MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.1MB, alloc=56.3MB, time=0.82 memory used=88.9MB, alloc=60.3MB, time=1.45 memory used=129.8MB, alloc=60.3MB, time=2.05 memory used=169.0MB, alloc=84.3MB, time=2.65 memory used=231.2MB, alloc=92.3MB, time=3.58 memory used=295.5MB, alloc=116.3MB, time=4.52 memory used=368.2MB, alloc=116.3MB, time=5.63 memory used=444.0MB, alloc=396.3MB, time=6.90 memory used=551.9MB, alloc=396.3MB, time=8.56 memory used=664.4MB, alloc=420.3MB, time=10.07 memory used=797.2MB, alloc=420.3MB, time=12.11 memory used=926.9MB, alloc=444.3MB, time=14.20 memory used=1062.3MB, alloc=468.3MB, time=16.70 memory used=1177.8MB, alloc=492.3MB, time=18.79 memory used=1300.0MB, alloc=492.3MB, time=21.11 memory used=1400.1MB, alloc=492.3MB, time=23.13 memory used=1499.4MB, alloc=492.3MB, time=25.14 memory used=1598.5MB, alloc=516.3MB, time=27.17 memory used=1681.2MB, alloc=516.3MB, time=28.90 memory used=1763.9MB, alloc=516.3MB, time=30.74 memory used=1838.9MB, alloc=516.3MB, time=32.35 memory used=1905.3MB, alloc=516.3MB, time=33.85 memory used=1969.3MB, alloc=516.3MB, time=35.39 memory used=2030.9MB, alloc=516.3MB, time=37.00 memory used=2092.0MB, alloc=516.3MB, time=38.57 memory used=2149.3MB, alloc=516.3MB, time=40.01 memory used=2202.6MB, alloc=516.3MB, time=41.28 memory used=2255.3MB, alloc=540.3MB, time=42.60 memory used=2305.6MB, alloc=540.3MB, time=44.01 memory used=2528.0MB, alloc=564.3MB, time=48.30 memory used=2759.6MB, alloc=588.3MB, time=53.07 memory used=2968.9MB, alloc=612.3MB, time=57.85 memory used=3148.3MB, alloc=636.3MB, time=59.83 memory used=3307.2MB, alloc=636.3MB, time=61.14 memory used=3469.8MB, alloc=636.3MB, time=62.81 memory used=3595.4MB, alloc=636.3MB, time=63.55 memory used=3780.9MB, alloc=660.3MB, time=67.82 memory used=3930.8MB, alloc=684.3MB, time=70.55 memory used=4061.7MB, alloc=708.3MB, time=73.00 memory used=4223.8MB, alloc=708.3MB, time=77.16 memory used=4339.2MB, alloc=708.3MB, time=79.65 memory used=4436.3MB, alloc=708.3MB, time=81.68 memory used=4546.4MB, alloc=732.3MB, time=83.95 memory used=4663.2MB, alloc=732.3MB, time=86.78 memory used=5045.0MB, alloc=756.3MB, time=94.53 memory used=5449.6MB, alloc=780.3MB, time=102.36 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428249829 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 F := [-14 x z + 20 y z - 17 x + 3, 6 x z + 10 x y + 4 y z + 11 x z, 3 2 2 15 x z + 19 y z + 19 y - 10 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 3 4 3 G := [-13 x z - 18 x z - y z - 17 z , 19 x z - 3 z - 3 z + 17 y z, 3 3 -4 x z + 7 x y z - 18 z - 12 x] > Problem := [F,G]; 2 2 2 3 2 2 Problem := [[-14 x z + 20 y z - 17 x + 3, 6 x z + 10 x y + 4 y z + 11 x z, 3 2 2 3 3 2 2 2 15 x z + 19 y z + 19 y - 10 y z], [-13 x z - 18 x z - y z - 17 z , 3 4 3 3 3 19 x z - 3 z - 3 z + 17 y z, -4 x z + 7 x y z - 18 z - 12 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.18 memory used=24.7MB, alloc=32.3MB, time=0.47 memory used=49.0MB, alloc=33.2MB, time=0.74 memory used=59.0MB, alloc=33.2MB, time=0.77 memory used=75.1MB, alloc=33.2MB, time=0.97 memory used=89.4MB, alloc=33.2MB, time=1.02 memory used=102.2MB, alloc=33.2MB, time=1.05 memory used=127.0MB, alloc=37.2MB, time=1.32 memory used=149.3MB, alloc=61.2MB, time=1.64 memory used=206.9MB, alloc=61.2MB, time=4.23 memory used=252.9MB, alloc=61.3MB, time=4.43 memory used=275.9MB, alloc=61.3MB, time=4.50 memory used=304.3MB, alloc=61.3MB, time=4.58 memory used=337.4MB, alloc=61.3MB, time=4.65 memory used=357.6MB, alloc=61.3MB, time=4.72 memory used=379.1MB, alloc=61.3MB, time=4.78 memory used=402.5MB, alloc=61.3MB, time=4.84 memory used=428.2MB, alloc=61.3MB, time=4.90 memory used=456.6MB, alloc=61.3MB, time=4.96 memory used=487.1MB, alloc=61.3MB, time=5.03 memory used=515.4MB, alloc=61.3MB, time=5.09 memory used=549.6MB, alloc=61.3MB, time=5.31 memory used=598.8MB, alloc=61.3MB, time=7.69 memory used=637.1MB, alloc=61.3MB, time=7.86 memory used=663.4MB, alloc=61.3MB, time=7.93 memory used=690.9MB, alloc=61.3MB, time=8.00 memory used=710.4MB, alloc=61.3MB, time=8.06 memory used=732.4MB, alloc=61.3MB, time=8.12 memory used=756.8MB, alloc=61.3MB, time=8.18 memory used=783.8MB, alloc=61.3MB, time=8.24 memory used=814.1MB, alloc=61.3MB, time=8.31 memory used=845.1MB, alloc=61.3MB, time=8.37 memory used=866.2MB, alloc=61.3MB, time=8.42 memory used=884.1MB, alloc=61.3MB, time=8.48 memory used=903.0MB, alloc=61.3MB, time=8.53 memory used=922.0MB, alloc=61.3MB, time=8.58 memory used=942.2MB, alloc=61.3MB, time=8.62 memory used=963.5MB, alloc=61.3MB, time=8.67 memory used=985.9MB, alloc=61.3MB, time=8.72 memory used=1009.3MB, alloc=61.3MB, time=8.78 memory used=1033.5MB, alloc=61.3MB, time=8.83 memory used=1059.3MB, alloc=61.3MB, time=8.88 memory used=1086.0MB, alloc=61.3MB, time=8.93 memory used=1114.4MB, alloc=61.3MB, time=8.98 memory used=1144.3MB, alloc=61.3MB, time=9.03 memory used=1187.6MB, alloc=81.9MB, time=9.12 memory used=1204.4MB, alloc=81.9MB, time=9.16 memory used=1218.3MB, alloc=81.9MB, time=9.21 memory used=1251.1MB, alloc=81.9MB, time=9.51 memory used=1296.3MB, alloc=81.9MB, time=10.23 memory used=1323.9MB, alloc=81.9MB, time=10.33 memory used=1353.5MB, alloc=81.9MB, time=10.42 memory used=1379.1MB, alloc=81.9MB, time=10.49 memory used=1400.9MB, alloc=81.9MB, time=10.55 memory used=1426.8MB, alloc=81.9MB, time=10.62 memory used=1484.2MB, alloc=81.9MB, time=16.68 memory used=1508.1MB, alloc=105.9MB, time=29.90 memory used=1539.0MB, alloc=129.9MB, time=38.08 memory used=1617.6MB, alloc=129.9MB, time=80.07 memory used=2640.4MB, alloc=385.9MB, time=88.36 memory used=2680.3MB, alloc=385.9MB, time=90.39 memory used=3187.9MB, alloc=385.9MB, time=96.53 memory used=3459.4MB, alloc=385.9MB, time=100.21 memory used=3974.9MB, alloc=385.9MB, time=106.82 memory used=4469.3MB, alloc=385.9MB, time=119.03 memory used=5274.1MB, alloc=409.9MB, time=123.54 memory used=5313.3MB, alloc=409.9MB, time=125.43 memory used=5412.3MB, alloc=409.9MB, time=127.50 memory used=5447.5MB, alloc=438.5MB, time=128.57 memory used=5452.1MB, alloc=443.1MB, time=128.62 memory used=5456.8MB, alloc=447.8MB, time=128.71 memory used=5461.4MB, alloc=452.4MB, time=128.81 memory used=5466.0MB, alloc=438.5MB, time=128.94 memory used=5572.3MB, alloc=433.9MB, time=129.73 memory used=5659.3MB, alloc=433.9MB, time=129.94 memory used=5738.4MB, alloc=433.9MB, time=130.09 memory used=5827.6MB, alloc=433.9MB, time=130.43 memory used=5921.6MB, alloc=433.9MB, time=131.80 memory used=6022.7MB, alloc=433.9MB, time=132.05 memory used=6087.9MB, alloc=433.9MB, time=132.24 memory used=6158.8MB, alloc=433.9MB, time=132.43 memory used=6236.7MB, alloc=433.9MB, time=132.62 memory used=6322.2MB, alloc=433.9MB, time=132.81 memory used=6416.8MB, alloc=433.9MB, time=133.01 memory used=6520.2MB, alloc=433.9MB, time=133.23 memory used=6614.1MB, alloc=433.9MB, time=133.44 memory used=6672.4MB, alloc=433.9MB, time=133.58 memory used=6732.5MB, alloc=433.9MB, time=133.71 memory used=6795.8MB, alloc=433.9MB, time=133.86 memory used=6860.9MB, alloc=433.9MB, time=134.01 memory used=6929.3MB, alloc=433.9MB, time=134.16 memory used=7000.6MB, alloc=433.9MB, time=134.32 memory used=7076.3MB, alloc=433.9MB, time=134.46 memory used=7155.6MB, alloc=433.9MB, time=134.62 memory used=7237.6MB, alloc=433.9MB, time=134.79 memory used=7324.5MB, alloc=433.9MB, time=134.94 memory used=7415.7MB, alloc=433.9MB, time=135.10 memory used=7513.7MB, alloc=433.9MB, time=135.27 memory used=7617.9MB, alloc=433.9MB, time=135.45 |\^/| 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(); 1428250129 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [x z - 2 x z - 2 y z - 2 y z, -20 x z + 10 y + 17 x + 5, 2 2 2 2 3 2 20 x y + 16 x z + 12 x y - 17 x y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 4 3 2 G := [16 y z + 3 x y + y z + 15, 13 x + 10 x - 8 x + 4 x, 3 2 4 y z - 9 x y z + 3 x y + 20 z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[x z - 2 x z - 2 y z - 2 y z, -20 x z + 10 y + 17 x + 5, 2 2 2 2 3 2 2 2 2 2 20 x y + 16 x z + 12 x y - 17 x y z], [16 y z + 3 x y + y z + 15, 4 3 2 3 2 13 x + 10 x - 8 x + 4 x, 4 y z - 9 x y z + 3 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=0.17 memory used=26.0MB, alloc=32.3MB, time=0.49 memory used=45.7MB, alloc=56.3MB, time=0.79 memory used=85.7MB, alloc=60.3MB, time=1.37 memory used=125.4MB, alloc=84.3MB, time=1.97 memory used=162.8MB, alloc=84.3MB, time=2.51 memory used=229.3MB, alloc=92.3MB, time=3.43 memory used=291.6MB, alloc=92.3MB, time=4.34 memory used=352.2MB, alloc=116.3MB, time=5.26 memory used=428.0MB, alloc=372.3MB, time=6.28 memory used=519.2MB, alloc=396.3MB, time=7.51 memory used=619.4MB, alloc=396.3MB, time=8.68 memory used=732.4MB, alloc=396.3MB, time=10.02 memory used=833.3MB, alloc=420.3MB, time=11.54 memory used=963.6MB, alloc=444.3MB, time=13.52 memory used=1084.1MB, alloc=468.3MB, time=15.45 memory used=1204.0MB, alloc=468.3MB, time=17.42 memory used=1294.5MB, alloc=492.3MB, time=18.63 memory used=1402.0MB, alloc=492.3MB, time=20.29 memory used=1484.5MB, alloc=492.3MB, time=21.74 memory used=1570.0MB, alloc=492.3MB, time=22.98 memory used=1648.5MB, alloc=492.3MB, time=24.26 memory used=1732.1MB, alloc=492.3MB, time=25.58 memory used=1799.4MB, alloc=516.3MB, time=26.80 memory used=1860.0MB, alloc=516.3MB, time=27.79 memory used=1923.7MB, alloc=516.3MB, time=29.16 memory used=1987.9MB, alloc=516.3MB, time=30.29 memory used=2047.1MB, alloc=516.3MB, time=31.20 memory used=2116.1MB, alloc=516.3MB, time=32.66 memory used=2186.9MB, alloc=516.3MB, time=34.13 memory used=2227.9MB, alloc=516.3MB, time=35.23 memory used=2427.4MB, alloc=540.3MB, time=38.68 memory used=2590.2MB, alloc=564.3MB, time=40.47 memory used=2773.1MB, alloc=564.3MB, time=42.85 memory used=3007.0MB, alloc=564.3MB, time=45.58 memory used=3197.2MB, alloc=588.3MB, time=49.48 memory used=3436.4MB, alloc=588.3MB, time=52.43 memory used=3614.9MB, alloc=612.3MB, time=55.63 memory used=3775.3MB, alloc=612.3MB, time=58.64 memory used=3929.0MB, alloc=636.3MB, time=61.59 memory used=4178.6MB, alloc=636.3MB, time=64.62 memory used=4378.6MB, alloc=636.3MB, time=67.58 memory used=4549.4MB, alloc=660.3MB, time=69.71 memory used=4739.0MB, alloc=660.3MB, time=71.50 memory used=4944.8MB, alloc=660.3MB, time=73.49 memory used=5131.0MB, alloc=660.3MB, time=74.79 memory used=5325.5MB, alloc=660.3MB, time=77.74 memory used=5509.8MB, alloc=660.3MB, time=79.21 memory used=5695.6MB, alloc=660.3MB, time=80.60 memory used=5838.2MB, alloc=660.3MB, time=81.50 memory used=6032.1MB, alloc=660.3MB, time=82.88 memory used=6173.5MB, alloc=660.3MB, time=83.75 memory used=6369.5MB, alloc=660.3MB, time=90.52 memory used=6517.2MB, alloc=660.3MB, time=91.35 memory used=6685.3MB, alloc=660.3MB, time=93.68 memory used=6832.2MB, alloc=660.3MB, time=110.00 memory used=6999.7MB, alloc=660.3MB, time=111.41 memory used=7165.7MB, alloc=660.3MB, time=112.32 memory used=7283.8MB, alloc=660.3MB, time=113.11 memory used=7434.6MB, 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(); 1428250429 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 F := [5 x y z - 16 x z - 19 x y z - 11 x z , 3 2 3 2 3 4 2 -20 x y + 8 x y + 10 y - 18 y , 11 x z - 15 z + 2 x z - 19 y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 3 2 G := [-3 x z + 6 x z - 13 x z + 8 z , 4 x + 13 x y - 15 x z - 11 z, 4 2 2 8 x - 18 y z - 8 x + 14 y z] > Problem := [F,G]; 2 2 2 2 3 Problem := [[5 x y z - 16 x z - 19 x y z - 11 x z , 3 2 3 2 3 4 2 -20 x y + 8 x y + 10 y - 18 y , 11 x z - 15 z + 2 x z - 19 y], [ 3 2 2 2 3 3 2 -3 x z + 6 x z - 13 x z + 8 z , 4 x + 13 x y - 15 x z - 11 z, 4 2 2 8 x - 18 y z - 8 x + 14 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=67.5MB, alloc=56.3MB, time=1.10 memory used=107.4MB, alloc=60.3MB, time=1.68 memory used=147.8MB, alloc=60.3MB, time=2.23 memory used=188.2MB, alloc=92.3MB, time=2.85 memory used=250.7MB, alloc=92.3MB, time=3.71 memory used=312.5MB, alloc=92.3MB, time=4.58 memory used=375.0MB, alloc=116.3MB, time=5.47 memory used=454.1MB, alloc=116.3MB, time=6.63 memory used=528.4MB, alloc=372.3MB, time=7.73 memory used=619.0MB, alloc=396.3MB, time=8.91 memory used=730.9MB, alloc=420.3MB, time=10.41 memory used=869.6MB, alloc=444.3MB, time=12.36 memory used=999.2MB, alloc=444.3MB, time=14.16 memory used=1143.1MB, alloc=468.3MB, time=16.25 memory used=1257.7MB, alloc=468.3MB, time=18.01 memory used=1358.7MB, alloc=468.3MB, time=19.40 memory used=1460.8MB, alloc=492.3MB, time=20.95 memory used=1561.3MB, alloc=492.3MB, time=22.54 memory used=1662.7MB, alloc=492.3MB, time=23.95 memory used=1777.0MB, alloc=492.3MB, time=25.33 memory used=1873.1MB, alloc=492.3MB, time=26.54 memory used=1958.9MB, alloc=492.3MB, time=27.62 memory used=2046.5MB, alloc=492.3MB, time=29.22 memory used=2156.4MB, alloc=516.3MB, time=30.53 memory used=2272.9MB, alloc=516.3MB, time=31.66 memory used=2358.2MB, alloc=516.3MB, time=32.84 memory used=2448.1MB, alloc=516.3MB, time=33.86 memory used=2525.9MB, alloc=516.3MB, time=35.19 memory used=2589.4MB, alloc=516.3MB, time=36.38 memory used=2655.1MB, alloc=516.3MB, time=37.71 memory used=2716.1MB, alloc=516.3MB, time=39.02 memory used=2770.0MB, alloc=516.3MB, time=40.06 memory used=2818.8MB, alloc=516.3MB, time=41.03 memory used=2878.9MB, alloc=516.3MB, time=42.33 memory used=2927.6MB, alloc=516.3MB, time=43.37 memory used=3125.8MB, alloc=540.3MB, time=46.55 memory used=3302.2MB, alloc=564.3MB, time=49.39 memory used=3500.0MB, alloc=588.3MB, time=52.59 memory used=3672.2MB, alloc=588.3MB, time=55.14 memory used=3867.0MB, alloc=612.3MB, time=58.18 memory used=4050.7MB, alloc=612.3MB, time=61.39 memory used=4205.1MB, alloc=636.3MB, time=64.49 memory used=4344.0MB, alloc=636.3MB, time=67.23 memory used=4536.8MB, alloc=636.3MB, time=69.72 memory used=4723.7MB, alloc=636.3MB, time=72.39 memory used=4866.4MB, alloc=636.3MB, time=75.01 memory used=4997.4MB, alloc=660.3MB, time=77.40 memory used=5207.6MB, alloc=660.3MB, time=79.33 memory used=5394.2MB, alloc=660.3MB, time=81.11 memory used=5542.5MB, alloc=660.3MB, time=83.19 memory used=5643.0MB, alloc=660.3MB, time=85.22 memory used=5799.4MB, alloc=660.3MB, time=87.84 memory used=5946.3MB, alloc=660.3MB, time=90.24 memory used=6046.6MB, alloc=684.3MB, time=92.42 memory used=6150.0MB, alloc=684.3MB, time=94.68 memory used=6263.3MB, alloc=684.3MB, time=96.85 memory used=6389.3MB, alloc=684.3MB, time=99.10 memory used=6521.7MB, alloc=684.3MB, time=101.31 memory used=6866.8MB, alloc=708.3MB, time=106.66 memory used=7241.7MB, alloc=732.3MB, time=113.30 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428250729 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [-15 y - 4 y z - 5 z - 4 z, -9 x y z + y + 16 x + y, 3 2 6 x z - 20 x y + 3 y z - 2] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 2 2 2 3 G := [2 x y + 20 z + 18 y - x, 20 x y - 13 x y + 10 x z - 14 x z , 3 2 2 -7 x y - 9 x y - 5 x + 4 x] > Problem := [F,G]; 3 2 2 3 Problem := [[-15 y - 4 y z - 5 z - 4 z, -9 x y z + y + 16 x + y, 3 2 2 3 2 6 x z - 20 x y + 3 y z - 2], [2 x y + 20 z + 18 y - x, 3 2 2 2 2 3 3 2 2 20 x y - 13 x y + 10 x z - 14 x z , -7 x y - 9 x y - 5 x + 4 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=23.8MB, alloc=32.3MB, time=0.48 memory used=43.5MB, alloc=60.3MB, time=0.78 memory used=86.2MB, alloc=60.3MB, time=1.19 memory used=127.1MB, alloc=60.3MB, time=1.50 memory used=171.9MB, alloc=60.3MB, time=2.09 memory used=220.7MB, alloc=62.0MB, time=2.58 memory used=264.3MB, alloc=62.0MB, time=3.01 memory used=295.0MB, alloc=62.0MB, time=3.33 memory used=321.6MB, alloc=62.0MB, time=3.40 memory used=340.3MB, alloc=62.0MB, time=3.45 memory used=362.2MB, alloc=62.0MB, time=3.51 memory used=387.7MB, alloc=62.0MB, time=3.56 memory used=425.7MB, alloc=81.9MB, time=3.66 memory used=438.7MB, alloc=81.9MB, time=3.70 memory used=453.1MB, alloc=81.9MB, time=3.76 memory used=494.8MB, alloc=81.9MB, time=4.26 memory used=520.9MB, alloc=81.9MB, time=4.33 memory used=539.5MB, alloc=81.9MB, time=4.40 memory used=560.7MB, alloc=81.9MB, time=4.46 memory used=585.5MB, alloc=81.9MB, time=4.52 memory used=623.0MB, alloc=81.9MB, time=4.61 memory used=636.0MB, alloc=81.9MB, time=4.66 memory used=650.6MB, alloc=81.9MB, time=4.71 memory used=684.4MB, alloc=81.9MB, time=5.00 memory used=721.5MB, alloc=81.9MB, time=5.20 memory used=747.5MB, alloc=81.9MB, time=5.26 memory used=771.0MB, alloc=81.9MB, time=5.32 memory used=816.0MB, alloc=81.9MB, time=5.78 memory used=850.8MB, alloc=81.9MB, time=6.14 memory used=907.6MB, alloc=81.9MB, time=6.82 memory used=947.2MB, alloc=81.9MB, time=7.24 memory used=969.1MB, alloc=81.9MB, time=7.33 memory used=993.2MB, alloc=81.9MB, time=7.40 memory used=1010.3MB, alloc=81.9MB, time=7.46 memory used=1030.2MB, alloc=81.9MB, time=7.52 memory used=1053.8MB, alloc=81.9MB, time=7.59 memory used=1091.8MB, alloc=81.9MB, time=7.68 memory used=1105.1MB, alloc=81.9MB, time=7.74 memory used=1119.7MB, alloc=81.9MB, time=7.79 memory used=1155.1MB, alloc=81.9MB, time=8.08 memory used=1180.3MB, alloc=81.9MB, time=8.18 memory used=1210.3MB, alloc=81.9MB, time=8.37 memory used=1233.5MB, alloc=81.9MB, time=8.44 memory used=1262.5MB, alloc=81.9MB, time=8.53 memory used=1286.6MB, alloc=81.9MB, time=8.61 memory used=1324.0MB, alloc=81.9MB, time=8.95 memory used=1372.6MB, alloc=81.9MB, time=9.54 memory used=1410.4MB, alloc=81.9MB, time=10.06 memory used=1449.0MB, alloc=81.9MB, time=10.63 memory used=1488.3MB, alloc=105.9MB, time=11.16 memory used=1519.6MB, alloc=105.9MB, time=11.46 memory used=1566.4MB, alloc=105.9MB, time=11.76 memory used=1616.6MB, alloc=105.9MB, time=12.06 memory used=1655.3MB, alloc=105.9MB, time=12.25 memory used=1712.2MB, alloc=105.9MB, time=13.51 memory used=1747.5MB, alloc=105.9MB, time=13.66 memory used=1778.3MB, alloc=105.9MB, time=13.78 memory used=1812.3MB, alloc=105.9MB, time=13.93 memory used=1852.2MB, alloc=105.9MB, time=14.08 memory used=1888.1MB, alloc=105.9MB, time=14.21 memory used=1911.7MB, alloc=105.9MB, time=14.31 memory used=1935.4MB, alloc=105.9MB, time=14.41 memory used=1959.2MB, alloc=105.9MB, time=14.51 memory used=1983.9MB, alloc=129.9MB, time=14.63 memory used=2026.1MB, alloc=129.9MB, time=14.76 memory used=2072.4MB, alloc=129.9MB, time=14.92 memory used=2124.4MB, alloc=129.9MB, time=15.06 memory used=2178.1MB, alloc=129.9MB, time=15.20 memory used=2237.5MB, alloc=129.9MB, time=15.36 memory used=2298.5MB, alloc=129.9MB, time=15.51 memory used=2356.2MB, alloc=129.9MB, time=15.66 memory used=2392.8MB, alloc=129.9MB, time=15.77 memory used=2424.2MB, alloc=129.9MB, time=15.87 memory used=2458.5MB, alloc=129.9MB, time=15.97 memory used=2493.5MB, alloc=129.9MB, time=16.07 memory used=2528.6MB, alloc=129.9MB, time=16.18 memory used=2567.9MB, alloc=129.9MB, time=16.29 memory used=2607.0MB, alloc=129.9MB, time=16.40 memory used=2645.9MB, alloc=129.9MB, time=16.50 memory used=2688.6MB, alloc=129.9MB, time=16.61 memory used=2730.9MB, alloc=129.9MB, time=16.72 memory used=2776.7MB, alloc=129.9MB, time=16.84 memory used=2822.2MB, alloc=129.9MB, time=16.95 memory used=2870.0MB, alloc=129.9MB, time=17.06 memory used=2920.1MB, alloc=129.9MB, time=17.17 memory used=2974.6MB, alloc=129.9MB, time=17.29 memory used=3030.5MB, alloc=129.9MB, time=17.42 memory used=3089.8MB, alloc=129.9MB, time=17.53 memory used=3153.6MB, alloc=129.9MB, time=17.65 memory used=3199.8MB, alloc=131.8MB, time=17.88 memory used=3268.4MB, alloc=131.8MB, time=18.25 memory used=3335.2MB, alloc=131.8MB, time=19.68 memory used=3393.9MB, alloc=131.8MB, time=19.89 memory used=3443.8MB, alloc=131.8MB, time=20.07 memory used=3505.0MB, alloc=131.8MB, time=20.25 memory used=3551.0MB, alloc=131.8MB, time=20.40 memory used=3588.0MB, alloc=131.8MB, time=20.54 memory used=3626.7MB, alloc=131.8MB, time=20.69 memory used=3671.2MB, alloc=131.8MB, time=20.84 memory used=3717.5MB, alloc=131.8MB, time=20.99 memory used=3765.6MB, alloc=131.8MB, time=21.14 memory used=3819.2MB, alloc=131.8MB, time=21.28 memory used=3874.8MB, alloc=131.8MB, time=21.43 memory used=3935.2MB, alloc=131.8MB, time=21.59 memory used=3994.7MB, alloc=131.8MB, time=21.74 memory used=4030.9MB, alloc=131.8MB, time=21.85 memory used=4061.7MB, alloc=131.8MB, time=21.95 memory used=4095.7MB, alloc=131.8MB, time=22.05 memory used=4130.7MB, alloc=131.8MB, time=22.16 memory used=4165.6MB, alloc=131.8MB, time=22.27 memory used=4201.1MB, alloc=131.8MB, time=22.38 memory used=4239.7MB, alloc=131.8MB, time=22.49 memory used=4278.6MB, alloc=131.8MB, time=22.60 memory used=4318.0MB, alloc=131.8MB, time=22.71 memory used=4359.5MB, alloc=131.8MB, time=22.82 memory used=4402.0MB, alloc=131.8MB, time=22.92 memory used=4446.5MB, alloc=131.8MB, time=23.03 memory used=4494.7MB, alloc=131.8MB, time=23.15 memory used=4545.3MB, alloc=131.8MB, time=23.27 memory used=4597.7MB, alloc=131.8MB, time=23.39 memory used=4651.6MB, alloc=131.8MB, time=23.51 memory used=4708.5MB, alloc=131.8MB, time=23.62 memory used=4769.5MB, alloc=131.8MB, time=23.75 memory used=4838.2MB, alloc=131.8MB, time=23.89 memory used=4909.4MB, alloc=131.8MB, time=24.38 memory used=4976.6MB, alloc=131.8MB, time=26.39 memory used=5040.9MB, alloc=131.8MB, time=59.59 memory used=5101.2MB, alloc=131.8MB, time=95.27 memory used=5165.3MB, alloc=131.8MB, time=139.67 |\^/| 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(); 1428251029 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 2 2 2 2 2 F := [15 x y + 9 y - 9 y z - 10 x z , -x y z + 11 y z + 7 y z - 7 z , 4 2 2 -7 z + 15 x z - 10 y - 9 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 2 2 2 G := [-4 x z - 18 y z - 6 z + 13 x, 19 x y + 10 x z - 8 x z + 17 y z, 2 2 2 2 -7 x z - 13 x y z - 20 x z + 5 x ] > Problem := [F,G]; 3 4 2 2 2 Problem := [[15 x y + 9 y - 9 y z - 10 x z , 2 2 2 2 4 2 2 -x y z + 11 y z + 7 y z - 7 z , -7 z + 15 x z - 10 y - 9 y z], [ 3 3 2 3 2 2 2 2 -4 x z - 18 y z - 6 z + 13 x, 19 x y + 10 x z - 8 x z + 17 y z, 2 2 2 2 -7 x z - 13 x y z - 20 x z + 5 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.18 memory used=25.8MB, alloc=32.3MB, time=0.49 memory used=45.5MB, alloc=32.3MB, time=0.78 memory used=64.4MB, alloc=56.3MB, time=1.07 memory used=105.6MB, alloc=68.3MB, time=1.69 memory used=147.2MB, alloc=68.3MB, time=2.28 memory used=188.8MB, alloc=68.3MB, time=2.84 memory used=231.2MB, alloc=92.3MB, time=3.43 memory used=287.7MB, alloc=92.3MB, time=3.78 memory used=331.3MB, alloc=92.3MB, time=3.98 memory used=385.2MB, alloc=92.3MB, time=4.38 memory used=442.3MB, alloc=92.3MB, time=5.05 memory used=487.3MB, alloc=92.3MB, time=5.32 memory used=554.6MB, alloc=92.3MB, time=5.98 memory used=631.8MB, alloc=92.3MB, time=7.55 memory used=693.6MB, alloc=92.3MB, time=8.16 memory used=732.2MB, alloc=92.3MB, time=8.44 memory used=802.8MB, alloc=92.3MB, time=9.33 memory used=861.1MB, alloc=92.3MB, time=9.94 memory used=918.7MB, alloc=348.3MB, time=10.76 memory used=980.1MB, alloc=348.3MB, time=11.54 memory used=1040.8MB, alloc=372.3MB, time=12.27 memory used=1113.6MB, alloc=372.3MB, time=12.85 memory used=1163.5MB, alloc=372.3MB, time=13.20 memory used=1227.1MB, alloc=372.3MB, time=13.75 memory used=1276.3MB, alloc=372.3MB, time=14.07 memory used=1320.3MB, alloc=372.3MB, time=14.21 memory used=1406.9MB, alloc=372.3MB, time=15.21 memory used=1464.6MB, alloc=372.3MB, time=15.67 memory used=1544.9MB, alloc=372.3MB, time=16.50 memory used=1623.6MB, alloc=396.3MB, time=17.73 memory used=1734.1MB, alloc=396.3MB, time=19.31 memory used=1845.8MB, alloc=420.3MB, time=20.77 memory used=1958.9MB, alloc=420.3MB, time=22.40 memory used=2083.4MB, alloc=444.3MB, time=23.74 memory used=2226.5MB, alloc=444.3MB, time=25.68 memory used=2350.2MB, alloc=444.3MB, time=27.42 memory used=2441.5MB, alloc=444.3MB, time=28.24 memory used=2531.6MB, alloc=444.3MB, time=28.98 memory used=2615.4MB, alloc=444.3MB, time=29.53 memory used=2755.2MB, alloc=468.3MB, time=31.18 memory used=2890.5MB, alloc=468.3MB, time=32.66 memory used=3022.9MB, alloc=468.3MB, time=34.13 memory used=3121.3MB, alloc=468.3MB, time=35.60 memory used=3212.4MB, alloc=492.3MB, time=36.85 memory used=3336.6MB, alloc=492.3MB, time=38.04 memory used=3457.1MB, alloc=492.3MB, time=39.14 memory used=3573.2MB, alloc=492.3MB, time=39.84 memory used=3683.3MB, alloc=492.3MB, time=40.49 memory used=3796.3MB, alloc=492.3MB, time=41.20 memory used=3907.2MB, alloc=492.3MB, time=41.82 memory used=4006.8MB, alloc=492.3MB, time=42.36 memory used=4107.0MB, alloc=492.3MB, time=43.36 memory used=4215.8MB, alloc=492.3MB, time=44.04 memory used=4317.3MB, alloc=492.3MB, time=45.28 memory used=4423.4MB, alloc=492.3MB, time=45.94 memory used=4519.5MB, alloc=492.3MB, time=46.37 memory used=4595.2MB, alloc=492.3MB, time=46.74 memory used=4709.5MB, alloc=492.3MB, time=47.36 memory used=4801.9MB, alloc=492.3MB, time=47.78 memory used=4875.5MB, alloc=492.3MB, time=48.16 memory used=4990.8MB, alloc=492.3MB, time=49.72 memory used=5075.7MB, alloc=492.3MB, time=50.10 memory used=5178.1MB, alloc=492.3MB, time=50.84 memory used=5297.7MB, alloc=492.3MB, time=51.94 memory used=5384.6MB, alloc=492.3MB, time=52.38 memory used=5465.9MB, alloc=492.3MB, time=52.77 memory used=5541.9MB, alloc=492.3MB, time=53.17 memory used=5635.6MB, alloc=492.3MB, time=53.58 memory used=5715.9MB, alloc=492.3MB, time=53.94 memory used=5818.9MB, alloc=492.3MB, time=54.80 memory used=5915.4MB, alloc=492.3MB, time=55.22 memory used=5984.4MB, alloc=492.3MB, time=55.60 memory used=6068.8MB, alloc=492.3MB, time=55.98 memory used=6164.8MB, alloc=492.3MB, time=56.37 memory used=6260.2MB, alloc=492.3MB, time=59.06 memory used=6345.0MB, alloc=492.3MB, time=59.45 memory used=6437.5MB, alloc=492.3MB, time=59.83 memory used=6531.7MB, alloc=492.3MB, time=60.88 memory used=6621.9MB, alloc=492.3MB, time=61.34 memory used=6708.6MB, alloc=492.3MB, time=61.75 memory used=6783.6MB, alloc=492.3MB, time=62.15 memory used=6876.2MB, alloc=492.3MB, time=62.55 memory used=6960.7MB, alloc=492.3MB, time=62.88 memory used=7062.3MB, alloc=492.3MB, time=63.78 memory used=7160.8MB, alloc=492.3MB, time=64.21 memory used=7228.9MB, alloc=492.3MB, time=64.58 memory used=7312.7MB, alloc=492.3MB, time=64.96 memory used=7410.4MB, alloc=492.3MB, time=65.34 memory used=7542.6MB, alloc=492.3MB, time=70.30 memory used=7628.3MB, alloc=492.3MB, time=70.69 memory used=7712.8MB, alloc=492.3MB, time=71.08 memory used=7799.6MB, alloc=492.3MB, time=71.42 memory used=7869.1MB, alloc=492.3MB, time=71.73 memory used=7977.6MB, alloc=492.3MB, time=72.73 memory used=8074.7MB, alloc=492.3MB, time=73.15 memory used=8146.5MB, alloc=492.3MB, time=73.53 memory used=8226.2MB, alloc=492.3MB, time=73.96 memory used=8325.1MB, alloc=492.3MB, time=74.35 memory used=8402.3MB, alloc=492.3MB, time=75.21 memory used=8504.9MB, alloc=492.3MB, time=75.70 memory used=8597.5MB, alloc=492.3MB, time=76.13 memory used=8669.7MB, alloc=492.3MB, time=76.49 memory used=8758.1MB, alloc=492.3MB, time=76.89 memory used=8852.3MB, alloc=492.3MB, time=77.29 memory used=8984.1MB, alloc=492.3MB, time=82.26 memory used=9069.1MB, alloc=492.3MB, time=82.66 memory used=9157.4MB, alloc=492.3MB, time=83.03 memory used=9238.8MB, alloc=492.3MB, time=83.38 memory used=9309.5MB, alloc=492.3MB, time=83.71 memory used=9425.1MB, alloc=492.3MB, time=84.44 memory used=9538.9MB, alloc=492.3MB, time=86.11 memory used=9619.7MB, alloc=492.3MB, time=86.54 memory used=9722.4MB, alloc=492.3MB, time=86.98 memory used=9787.2MB, alloc=492.3MB, time=87.39 memory used=9860.6MB, alloc=492.3MB, time=87.79 memory used=9942.3MB, alloc=492.3MB, time=88.16 memory used=10033.4MB, alloc=492.3MB, time=88.56 memory used=10136.6MB, alloc=492.3MB, time=88.95 memory used=10220.2MB, alloc=516.3MB, time=89.31 memory used=10294.5MB, alloc=516.3MB, time=89.66 memory used=10375.3MB, alloc=516.3MB, time=90.00 memory used=10465.5MB, alloc=516.3MB, time=90.36 memory used=10595.5MB, alloc=516.3MB, time=92.00 memory used=10696.7MB, alloc=516.3MB, time=92.48 memory used=10808.2MB, alloc=516.3MB, time=92.93 memory used=10890.8MB, alloc=516.3MB, time=93.38 memory used=10985.5MB, alloc=516.3MB, time=93.80 memory used=11095.9MB, alloc=516.3MB, time=94.23 memory used=11218.9MB, alloc=516.3MB, time=94.64 memory used=11309.1MB, alloc=516.3MB, time=95.01 memory used=11385.1MB, alloc=516.3MB, time=95.37 memory used=11469.2MB, alloc=516.3MB, time=95.73 memory used=11563.5MB, alloc=516.3MB, time=96.08 memory used=11753.8MB, alloc=516.3MB, time=107.58 memory used=11855.6MB, alloc=516.3MB, time=108.03 memory used=11956.6MB, alloc=516.3MB, time=108.45 memory used=12070.6MB, alloc=516.3MB, time=108.86 memory used=12147.8MB, alloc=516.3MB, time=109.22 memory used=12236.0MB, alloc=516.3MB, time=109.61 memory used=12337.9MB, alloc=516.3MB, time=109.96 memory used=12542.7MB, alloc=516.3MB, time=112.07 memory used=12656.3MB, alloc=516.3MB, time=113.90 memory used=12756.5MB, alloc=516.3MB, time=115.54 memory used=12885.5MB, alloc=516.3MB, time=117.59 memory used=13013.5MB, alloc=516.3MB, time=121.83 memory used=13113.0MB, alloc=516.3MB, time=122.26 memory used=13208.9MB, alloc=516.3MB, time=122.66 memory used=13301.0MB, alloc=516.3MB, time=123.04 memory used=13443.0MB, alloc=516.3MB, time=123.92 memory used=13574.7MB, alloc=516.3MB, time=124.38 memory used=13649.6MB, alloc=516.3MB, time=125.62 memory used=13830.2MB, alloc=516.3MB, time=127.18 memory used=13989.1MB, alloc=516.3MB, time=129.72 memory used=14120.3MB, alloc=516.3MB, time=134.20 memory used=14209.6MB, alloc=516.3MB, time=134.61 memory used=14311.0MB, alloc=516.3MB, time=135.02 memory used=14391.6MB, alloc=516.3MB, time=135.38 memory used=14507.0MB, alloc=516.3MB, time=136.73 memory used=14674.0MB, alloc=516.3MB, time=138.14 memory used=14813.4MB, alloc=516.3MB, time=140.23 memory used=14908.3MB, alloc=516.3MB, time=141.48 memory used=15031.0MB, alloc=516.3MB, time=142.47 memory used=15152.6MB, alloc=516.3MB, time=143.35 memory used=15259.5MB, alloc=516.3MB, time=143.88 memory used=15368.4MB, alloc=516.3MB, time=144.53 memory used=15473.0MB, alloc=516.3MB, time=145.06 memory used=15590.3MB, alloc=516.3MB, time=145.76 memory used=15693.2MB, alloc=516.3MB, time=146.38 memory used=15821.4MB, alloc=516.3MB, time=147.27 memory used=15939.2MB, alloc=516.3MB, time=148.38 memory used=16044.2MB, alloc=540.3MB, time=148.89 memory used=16134.0MB, alloc=540.3MB, time=149.36 memory used=16250.9MB, alloc=540.3MB, time=149.83 memory used=16354.3MB, alloc=540.3MB, time=150.26 memory used=16487.4MB, alloc=540.3MB, time=151.25 memory used=16594.6MB, alloc=540.3MB, time=151.74 |\^/| 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(); 1428251329 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [11 x z - 4 x y + 11 x + 17 z, -16 x y z + 12 x z - 13 z - 17 x, 3 2 4 3 -8 x y - 5 x y z - 7 y + 10 y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 4 4 2 2 3 3 G := [-2 x z - 8 x y + y z + 10 z , 9 x - 17 x y + 10 y + 18 z , 3 2 11 x y + 11 z - 14 z + 2] > Problem := [F,G]; 2 2 Problem := [[11 x z - 4 x y + 11 x + 17 z, 2 3 2 3 2 4 3 -16 x y z + 12 x z - 13 z - 17 x, -8 x y - 5 x y z - 7 y + 10 y ], [ 3 3 3 4 4 2 2 3 3 -2 x z - 8 x y + y z + 10 z , 9 x - 17 x y + 10 y + 18 z , 3 2 11 x y + 11 z - 14 z + 2]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=27.9MB, alloc=33.2MB, time=0.46 memory used=41.4MB, alloc=33.2MB, time=0.50 memory used=54.0MB, alloc=33.2MB, time=0.53 memory used=63.1MB, alloc=33.2MB, time=0.56 memory used=74.1MB, alloc=33.2MB, time=0.59 memory used=87.5MB, alloc=33.2MB, time=0.62 memory used=98.4MB, alloc=33.2MB, time=0.64 memory used=118.8MB, alloc=33.2MB, time=0.92 memory used=140.1MB, alloc=57.2MB, time=1.14 memory used=168.9MB, alloc=57.5MB, time=1.21 memory used=195.9MB, alloc=57.5MB, time=1.27 memory used=228.8MB, alloc=58.5MB, time=1.41 memory used=259.4MB, alloc=58.5MB, time=1.48 memory used=288.4MB, alloc=58.5MB, time=2.52 memory used=348.6MB, alloc=60.4MB, time=4.70 memory used=377.8MB, alloc=60.4MB, time=4.78 memory used=402.2MB, alloc=60.4MB, time=4.84 memory used=427.5MB, alloc=60.4MB, time=4.90 memory used=457.2MB, alloc=60.4MB, time=4.96 memory used=492.2MB, alloc=60.4MB, time=5.02 memory used=514.0MB, alloc=60.4MB, time=5.07 memory used=534.3MB, alloc=60.4MB, time=5.12 memory used=556.4MB, alloc=60.4MB, time=5.17 memory used=579.6MB, alloc=60.4MB, time=5.22 memory used=604.7MB, alloc=60.4MB, time=5.27 memory used=630.5MB, alloc=60.4MB, time=5.31 memory used=658.5MB, alloc=60.4MB, time=5.36 memory used=688.9MB, alloc=60.4MB, time=5.41 memory used=722.9MB, alloc=60.4MB, time=5.46 memory used=746.3MB, alloc=83.8MB, time=5.52 memory used=790.5MB, alloc=83.8MB, time=5.68 memory used=819.5MB, alloc=83.8MB, time=5.75 memory used=853.4MB, alloc=83.8MB, time=5.94 memory used=881.7MB, alloc=83.8MB, time=6.02 memory used=908.2MB, alloc=83.8MB, time=6.09 memory used=962.9MB, alloc=83.8MB, time=9.51 memory used=1000.9MB, alloc=83.8MB, time=9.66 memory used=1030.0MB, alloc=83.8MB, time=9.74 memory used=1053.0MB, alloc=83.8MB, time=9.82 memory used=1080.5MB, alloc=83.8MB, time=9.88 memory used=1112.2MB, alloc=83.8MB, time=9.96 memory used=1141.9MB, alloc=83.8MB, time=10.04 memory used=1161.0MB, alloc=83.8MB, time=10.09 memory used=1181.8MB, alloc=83.8MB, time=10.15 memory used=1203.9MB, alloc=83.8MB, time=10.20 memory used=1228.0MB, alloc=83.8MB, time=10.26 memory used=1253.7MB, alloc=83.8MB, time=10.32 memory used=1280.2MB, alloc=83.8MB, time=10.38 memory used=1309.6MB, alloc=83.8MB, time=10.43 memory used=1341.7MB, alloc=83.8MB, time=10.50 memory used=1381.3MB, alloc=83.8MB, time=10.56 memory used=1433.3MB, alloc=83.8MB, time=11.05 memory used=1492.0MB, alloc=83.8MB, time=14.89 memory used=1518.7MB, alloc=83.8MB, time=14.98 memory used=1544.2MB, alloc=83.8MB, time=15.05 memory used=1566.2MB, alloc=83.8MB, time=15.12 memory used=1592.1MB, alloc=83.8MB, time=15.20 memory used=1621.3MB, alloc=83.8MB, time=15.28 memory used=1654.5MB, alloc=83.8MB, time=15.36 memory used=1673.0MB, alloc=83.8MB, time=15.41 memory used=1691.7MB, alloc=83.8MB, time=15.47 memory used=1711.6MB, alloc=83.8MB, time=15.54 memory used=1732.8MB, alloc=83.8MB, time=15.61 memory used=1755.2MB, alloc=83.8MB, time=15.67 memory used=1779.0MB, alloc=83.8MB, time=15.73 memory used=1804.4MB, alloc=83.8MB, time=15.78 memory used=1830.7MB, alloc=83.8MB, time=15.85 memory used=1858.2MB, alloc=83.8MB, time=15.91 memory used=1888.1MB, alloc=83.8MB, time=15.97 memory used=1920.5MB, alloc=83.8MB, time=16.03 memory used=1936.5MB, alloc=83.8MB, time=16.08 memory used=1945.2MB, alloc=83.8MB, time=16.16 memory used=1954.3MB, alloc=83.8MB, time=16.21 memory used=1963.7MB, alloc=83.8MB, time=16.31 memory used=1973.5MB, alloc=83.8MB, time=16.38 memory used=2033.5MB, alloc=83.8MB, time=16.91 memory used=2080.7MB, alloc=83.8MB, time=17.91 memory used=2107.3MB, alloc=83.8MB, time=18.00 memory used=2129.8MB, alloc=83.8MB, time=18.07 memory used=2168.8MB, alloc=83.8MB, time=18.30 memory used=2206.5MB, alloc=83.8MB, time=19.17 memory used=2231.3MB, alloc=83.8MB, time=19.25 memory used=2259.5MB, alloc=83.8MB, time=19.38 memory used=2302.1MB, alloc=83.8MB, time=19.78 memory used=2346.6MB, alloc=83.8MB, time=20.38 memory used=2388.0MB, alloc=83.8MB, time=20.87 memory used=2412.0MB, alloc=83.8MB, time=20.99 memory used=2444.7MB, alloc=83.8MB, time=21.18 memory used=2462.3MB, alloc=107.8MB, time=21.27 memory used=2503.9MB, alloc=107.8MB, time=21.38 memory used=2535.4MB, alloc=107.8MB, time=21.48 memory used=2568.4MB, alloc=107.8MB, time=21.58 memory used=2616.2MB, alloc=107.8MB, time=21.78 memory used=2657.7MB, alloc=107.8MB, time=21.90 memory used=2689.4MB, alloc=107.8MB, time=22.00 memory used=2723.0MB, alloc=107.8MB, time=22.10 memory used=2788.1MB, alloc=107.8MB, time=26.14 memory used=2831.1MB, alloc=107.8MB, time=26.27 memory used=2860.5MB, alloc=107.8MB, time=26.38 memory used=2894.0MB, alloc=107.8MB, time=26.48 memory used=2932.6MB, alloc=107.8MB, time=26.58 memory used=2977.0MB, alloc=107.8MB, time=26.70 memory used=3014.7MB, alloc=107.8MB, time=26.80 memory used=3040.4MB, alloc=107.8MB, time=26.87 memory used=3067.6MB, alloc=107.8MB, time=26.95 memory used=3096.7MB, alloc=107.8MB, time=27.03 memory used=3127.6MB, alloc=107.8MB, time=27.11 memory used=3160.2MB, alloc=107.8MB, time=27.19 memory used=3194.7MB, alloc=107.8MB, time=27.27 memory used=3231.3MB, alloc=107.8MB, time=27.35 memory used=3270.7MB, alloc=107.8MB, time=27.44 memory used=3312.2MB, alloc=107.8MB, time=27.52 memory used=3355.3MB, alloc=107.8MB, time=27.61 memory used=3401.6MB, alloc=107.8MB, time=27.70 memory used=3420.6MB, alloc=107.8MB, time=27.78 memory used=3430.8MB, alloc=107.8MB, time=27.86 memory used=3441.2MB, alloc=107.8MB, time=27.92 memory used=3451.7MB, alloc=107.8MB, time=27.98 memory used=3462.5MB, alloc=107.8MB, time=28.06 memory used=3473.7MB, alloc=107.8MB, time=28.15 memory used=3485.2MB, alloc=107.8MB, time=28.21 memory used=3497.1MB, alloc=107.8MB, time=28.27 memory used=3508.9MB, alloc=107.8MB, time=28.37 memory used=3579.8MB, alloc=107.8MB, time=28.84 memory used=3612.6MB, alloc=107.8MB, time=28.96 memory used=3656.9MB, alloc=107.8MB, time=29.07 memory used=3685.1MB, alloc=107.8MB, time=29.18 memory used=3716.4MB, alloc=107.8MB, time=29.27 memory used=3778.8MB, alloc=107.8MB, time=33.89 memory used=3818.3MB, alloc=107.8MB, time=34.01 memory used=3856.1MB, alloc=107.8MB, time=34.12 memory used=3886.9MB, alloc=107.8MB, time=34.22 memory used=3922.8MB, alloc=107.8MB, time=34.32 memory used=3963.5MB, alloc=107.8MB, time=34.41 memory used=4010.7MB, alloc=107.8MB, time=34.52 memory used=4038.2MB, alloc=107.8MB, time=34.60 memory used=4064.2MB, alloc=107.8MB, time=34.69 memory used=4091.8MB, alloc=107.8MB, time=34.77 memory used=4121.4MB, alloc=107.8MB, time=34.87 memory used=4152.8MB, alloc=107.8MB, time=34.95 memory used=4185.9MB, alloc=107.8MB, time=35.03 memory used=4220.7MB, alloc=107.8MB, time=35.13 memory used=4257.9MB, alloc=107.8MB, time=35.22 memory used=4297.7MB, alloc=107.8MB, time=35.30 memory used=4339.5MB, alloc=107.8MB, time=35.39 memory used=4383.0MB, alloc=107.8MB, time=35.48 memory used=4439.5MB, alloc=107.8MB, time=35.59 memory used=4449.5MB, alloc=107.8MB, time=35.63 memory used=4459.9MB, alloc=107.8MB, time=35.72 memory used=4470.4MB, alloc=107.8MB, time=35.79 memory used=4481.1MB, alloc=107.8MB, time=35.85 memory used=4492.0MB, alloc=107.8MB, time=35.90 memory used=4503.2MB, alloc=107.8MB, time=35.99 memory used=4514.8MB, alloc=107.8MB, time=36.06 memory used=4526.6MB, alloc=107.8MB, time=36.17 memory used=4539.1MB, alloc=107.8MB, time=36.23 memory used=4631.8MB, alloc=107.8MB, time=38.73 memory used=4670.8MB, alloc=107.8MB, time=39.55 memory used=4744.9MB, alloc=107.8MB, time=40.32 memory used=4818.2MB, alloc=107.8MB, time=40.94 memory used=4889.9MB, alloc=107.8MB, time=41.49 memory used=4960.4MB, alloc=107.8MB, time=42.30 memory used=5033.1MB, alloc=107.8MB, time=43.38 memory used=5104.9MB, alloc=107.8MB, time=44.80 memory used=5178.8MB, alloc=107.8MB, time=46.27 memory used=5252.8MB, alloc=107.8MB, time=47.95 memory used=5326.0MB, alloc=107.8MB, time=49.84 memory used=5400.9MB, alloc=107.8MB, time=52.07 memory used=5474.9MB, alloc=107.8MB, time=54.17 memory used=5549.7MB, alloc=107.8MB, time=56.71 memory used=5625.8MB, alloc=107.8MB, time=59.43 memory used=5701.0MB, alloc=107.8MB, time=62.36 memory used=5774.9MB, alloc=107.8MB, time=65.60 memory used=5851.3MB, alloc=107.8MB, time=68.41 memory used=5922.0MB, alloc=107.8MB, time=70.35 memory used=5977.2MB, alloc=107.8MB, time=71.55 memory used=6035.4MB, alloc=107.8MB, time=72.03 memory used=6116.3MB, alloc=107.8MB, time=72.65 memory used=6169.9MB, alloc=107.8MB, time=73.09 memory used=6220.0MB, alloc=107.8MB, time=74.38 memory used=6247.7MB, alloc=107.8MB, time=74.48 memory used=6282.1MB, alloc=107.8MB, time=74.58 memory used=6306.1MB, alloc=107.8MB, time=74.68 memory used=6359.2MB, alloc=107.8MB, time=75.12 memory used=6415.4MB, alloc=363.8MB, time=75.80 memory used=6470.9MB, alloc=363.8MB, time=76.35 memory used=6525.1MB, alloc=363.8MB, time=78.39 memory used=6555.6MB, alloc=387.8MB, time=78.54 memory used=6602.1MB, alloc=387.8MB, time=78.72 memory used=6642.4MB, alloc=387.8MB, time=78.85 memory used=6684.1MB, alloc=387.8MB, time=78.98 memory used=6742.2MB, alloc=387.8MB, time=79.21 memory used=6808.2MB, alloc=387.8MB, time=81.97 memory used=6852.4MB, alloc=387.8MB, time=82.12 memory used=6900.0MB, alloc=387.8MB, time=82.28 memory used=6936.0MB, alloc=387.8MB, time=82.41 memory used=6980.2MB, alloc=387.8MB, time=82.54 memory used=7071.4MB, alloc=387.8MB, time=83.23 memory used=7142.2MB, alloc=387.8MB, time=83.91 memory used=7232.6MB, alloc=387.8MB, time=85.62 memory used=7311.7MB, alloc=387.8MB, time=86.24 memory used=7408.1MB, alloc=387.8MB, time=87.18 memory used=7468.0MB, alloc=387.8MB, time=89.39 memory used=7508.3MB, alloc=387.8MB, time=89.55 memory used=7552.3MB, alloc=387.8MB, time=89.70 memory used=7587.2MB, alloc=387.8MB, time=89.83 memory used=7636.3MB, alloc=387.8MB, time=91.65 memory used=7689.6MB, alloc=387.8MB, time=92.20 memory used=7728.9MB, alloc=387.8MB, time=92.35 memory used=7769.6MB, alloc=387.8MB, time=92.48 memory used=7804.5MB, alloc=387.8MB, time=92.60 memory used=7885.8MB, alloc=387.8MB, time=93.60 memory used=7968.8MB, alloc=411.8MB, time=95.06 memory used=8033.9MB, alloc=411.8MB, time=95.31 memory used=8086.4MB, alloc=411.8MB, time=95.52 memory used=8144.2MB, alloc=411.8MB, time=95.72 memory used=8181.6MB, alloc=411.8MB, time=95.90 memory used=8223.5MB, alloc=411.8MB, time=96.08 memory used=8271.6MB, alloc=411.8MB, time=96.26 memory used=8324.7MB, alloc=411.8MB, time=96.45 memory used=8381.9MB, alloc=411.8MB, time=96.64 memory used=8445.4MB, alloc=411.8MB, time=96.83 memory used=8491.7MB, alloc=411.8MB, time=97.00 memory used=8526.8MB, alloc=411.8MB, time=97.14 memory used=8563.7MB, alloc=411.8MB, time=97.33 memory used=8603.7MB, alloc=411.8MB, time=97.51 memory used=8645.9MB, alloc=411.8MB, time=97.66 memory used=8691.4MB, alloc=411.8MB, time=97.81 memory used=8739.8MB, alloc=411.8MB, time=97.96 memory used=8813.1MB, alloc=411.8MB, time=98.76 memory used=8860.9MB, alloc=411.8MB, time=98.97 memory used=8923.9MB, alloc=411.8MB, time=99.19 memory used=8965.1MB, alloc=411.8MB, time=99.37 memory used=9005.5MB, alloc=411.8MB, time=99.54 memory used=9050.9MB, alloc=411.8MB, time=99.72 memory used=9100.9MB, alloc=411.8MB, time=99.91 memory used=9157.5MB, alloc=411.8MB, time=100.10 memory used=9218.7MB, alloc=411.8MB, time=100.29 memory used=9275.3MB, alloc=411.8MB, time=100.47 memory used=9310.6MB, alloc=411.8MB, time=100.62 memory used=9347.4MB, alloc=411.8MB, time=100.77 memory used=9386.1MB, alloc=411.8MB, time=100.93 memory used=9428.2MB, alloc=411.8MB, time=101.09 memory used=9472.9MB, alloc=411.8MB, time=101.25 memory used=9520.7MB, alloc=411.8MB, time=101.41 memory used=9595.8MB, alloc=411.8MB, time=112.70 memory used=9680.9MB, alloc=411.8MB, time=127.42 memory used=9803.7MB, alloc=411.8MB, time=128.30 memory used=9861.8MB, alloc=411.8MB, time=128.53 memory used=9905.1MB, alloc=411.8MB, time=128.72 memory used=9955.4MB, alloc=411.8MB, time=128.90 memory used=10015.6MB, alloc=411.8MB, time=129.09 memory used=10066.5MB, alloc=411.8MB, time=129.27 memory used=10102.5MB, alloc=411.8MB, time=129.42 memory used=10141.1MB, alloc=411.8MB, time=129.59 memory used=10182.7MB, alloc=411.8MB, time=129.73 memory used=10227.4MB, alloc=411.8MB, time=129.89 memory used=10275.2MB, alloc=411.8MB, time=130.06 memory used=10325.9MB, alloc=411.8MB, time=130.22 memory used=10381.1MB, alloc=411.8MB, time=130.39 memory used=10438.9MB, alloc=411.8MB, time=130.56 memory used=10501.0MB, alloc=411.8MB, time=130.73 memory used=10704.2MB, alloc=411.8MB, time=131.24 memory used=10868.3MB, alloc=411.8MB, time=131.54 memory used=11099.5MB, alloc=411.8MB, time=132.49 memory used=11151.5MB, alloc=411.8MB, time=132.70 memory used=11211.7MB, alloc=411.8MB, time=132.91 memory used=11250.0MB, alloc=411.8MB, time=133.08 memory used=11291.5MB, alloc=411.8MB, time=133.25 memory used=11337.6MB, alloc=411.8MB, time=133.44 memory used=11388.6MB, alloc=411.8MB, time=133.62 memory used=11445.2MB, alloc=411.8MB, time=133.81 memory used=11508.6MB, alloc=411.8MB, time=133.99 memory used=11558.0MB, alloc=411.8MB, time=134.16 memory used=11592.9MB, alloc=411.8MB, time=134.31 memory used=11629.6MB, alloc=411.8MB, time=134.46 memory used=11668.7MB, alloc=411.8MB, time=134.61 memory used=11710.1MB, alloc=411.8MB, time=134.78 memory used=11754.5MB, alloc=411.8MB, time=134.94 memory used=11802.8MB, alloc=411.8MB, time=135.10 memory used=11875.8MB, alloc=411.8MB, time=135.90 memory used=11925.1MB, alloc=411.8MB, time=136.11 memory used=11986.7MB, alloc=411.8MB, time=136.32 memory used=12032.8MB, alloc=411.8MB, time=136.51 memory used=12074.2MB, alloc=411.8MB, time=136.69 memory used=12119.6MB, alloc=411.8MB, time=136.87 memory used=12169.9MB, alloc=411.8MB, time=137.05 memory used=12226.2MB, alloc=411.8MB, time=137.25 memory used=12289.5MB, alloc=411.8MB, time=137.44 memory used=12347.7MB, alloc=411.8MB, time=137.62 memory used=12382.7MB, alloc=411.8MB, time=137.76 memory used=12419.5MB, alloc=411.8MB, time=137.90 memory used=12458.6MB, alloc=411.8MB, time=138.07 memory used=12500.1MB, alloc=411.8MB, time=138.21 memory used=12544.9MB, alloc=411.8MB, time=138.40 memory used=12593.3MB, alloc=411.8MB, time=138.56 memory used=12668.0MB, alloc=411.8MB, time=146.19 memory used=12754.2MB, alloc=411.8MB, time=164.90 memory used=12876.9MB, alloc=411.8MB, time=165.78 memory used=12941.6MB, alloc=411.8MB, time=166.06 memory used=12988.0MB, alloc=411.8MB, time=166.25 memory used=13037.2MB, alloc=411.8MB, time=166.43 memory used=13096.3MB, alloc=411.8MB, time=166.62 memory used=13150.5MB, alloc=411.8MB, time=166.81 memory used=13186.9MB, alloc=411.8MB, time=166.96 memory used=13225.4MB, alloc=411.8MB, time=167.12 memory used=13266.7MB, alloc=411.8MB, time=167.28 memory used=13311.2MB, alloc=411.8MB, time=167.44 memory used=13358.6MB, alloc=411.8MB, time=167.60 memory used=13409.2MB, alloc=411.8MB, time=167.77 memory used=13463.9MB, alloc=411.8MB, time=167.94 memory used=13521.7MB, alloc=411.8MB, time=168.10 memory used=13583.4MB, alloc=411.8MB, time=168.26 memory used=13789.4MB, alloc=411.8MB, time=168.61 memory used=13954.6MB, alloc=411.8MB, time=168.91 memory used=14173.5MB, alloc=411.8MB, time=169.41 memory used=14241.3MB, alloc=411.8MB, time=173.35 memory used=14319.9MB, alloc=411.8MB, time=173.86 memory used=14364.8MB, alloc=411.8MB, time=174.04 memory used=14424.4MB, alloc=411.8MB, time=174.23 memory used=14469.5MB, alloc=411.8MB, time=174.40 memory used=14510.5MB, alloc=411.8MB, time=174.55 memory used=14556.8MB, alloc=411.8MB, time=174.70 memory used=14608.8MB, alloc=411.8MB, time=174.88 memory used=14667.2MB, alloc=411.8MB, time=175.04 memory used=14786.0MB, alloc=411.8MB, time=175.46 memory used=14856.3MB, alloc=411.8MB, time=176.02 memory used=14973.7MB, alloc=411.8MB, time=177.32 memory used=15099.3MB, alloc=435.8MB, time=184.98 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428251629 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 3 2 2 2 3 2 2 F := [-14 y + 4 z + 11 y - 13 y z, -7 x z + 7 y z - 20 x y + 13 y z, 3 2 2 3 -17 x z + 19 x z - 2 x - 11 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 3 3 2 G := [14 x y - y - 17 y z - 18 y z, -12 x - 16 x z - 20 x z - 15 x y, 2 2 8 x z - 16 y z + 2 y z + 19 x] > Problem := [F,G]; 4 4 3 2 Problem := [[-14 y + 4 z + 11 y - 13 y z, 2 2 3 2 2 3 2 2 3 -7 x z + 7 y z - 20 x y + 13 y z, -17 x z + 19 x z - 2 x - 11 y z] 3 3 2 4 3 3 2 , [14 x y - y - 17 y z - 18 y z, -12 x - 16 x z - 20 x z - 15 x y, 2 2 8 x z - 16 y z + 2 y z + 19 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=25.1MB, alloc=32.3MB, time=0.45 memory used=41.2MB, alloc=32.3MB, time=0.62 memory used=59.9MB, alloc=32.3MB, time=0.80 memory used=79.6MB, alloc=56.3MB, time=1.10 memory used=120.4MB, alloc=60.3MB, time=1.55 memory used=153.5MB, alloc=62.2MB, time=1.68 memory used=188.8MB, alloc=62.2MB, time=2.65 memory used=229.3MB, alloc=62.2MB, time=3.09 memory used=256.4MB, alloc=62.2MB, time=3.18 memory used=301.7MB, alloc=62.2MB, time=3.72 memory used=344.1MB, alloc=62.2MB, time=4.19 memory used=385.5MB, alloc=62.2MB, time=4.41 memory used=416.4MB, alloc=62.2MB, time=4.68 memory used=458.4MB, alloc=62.2MB, time=5.05 memory used=491.0MB, alloc=62.2MB, time=5.44 memory used=533.3MB, alloc=70.2MB, time=6.07 memory used=575.0MB, alloc=94.2MB, time=6.69 memory used=640.7MB, alloc=94.2MB, time=7.52 memory used=678.2MB, alloc=94.2MB, time=7.64 memory used=711.3MB, alloc=94.2MB, time=7.75 memory used=751.7MB, alloc=94.2MB, time=7.99 memory used=788.6MB, alloc=94.2MB, time=8.10 memory used=821.5MB, alloc=94.2MB, time=8.81 memory used=882.2MB, alloc=94.2MB, time=10.60 memory used=912.3MB, alloc=94.2MB, time=10.70 memory used=949.0MB, alloc=94.2MB, time=10.81 memory used=976.5MB, alloc=94.2MB, time=10.89 memory used=1009.8MB, alloc=94.2MB, time=11.03 memory used=1060.1MB, alloc=94.2MB, time=11.44 memory used=1119.0MB, alloc=94.2MB, time=12.32 memory used=1162.2MB, alloc=94.2MB, time=12.64 memory used=1246.6MB, alloc=94.2MB, time=13.72 memory used=1309.3MB, alloc=94.2MB, time=14.81 memory used=1371.4MB, alloc=94.2MB, time=15.52 memory used=1437.7MB, alloc=350.2MB, time=16.37 memory used=1488.5MB, alloc=350.2MB, time=16.80 memory used=1522.7MB, alloc=350.2MB, time=17.03 memory used=1589.4MB, alloc=350.2MB, time=17.91 memory used=1653.6MB, alloc=374.2MB, time=18.78 memory used=1709.0MB, alloc=374.2MB, time=19.25 memory used=1771.9MB, alloc=374.2MB, time=19.80 memory used=1852.8MB, alloc=374.2MB, time=20.61 memory used=1934.9MB, alloc=374.2MB, time=21.47 memory used=2004.1MB, alloc=374.2MB, time=22.08 memory used=2067.8MB, alloc=374.2MB, time=22.64 memory used=2149.1MB, alloc=398.2MB, time=23.84 memory used=2247.8MB, alloc=398.2MB, time=24.82 memory used=2310.5MB, alloc=398.2MB, time=25.07 memory used=2380.4MB, alloc=398.2MB, time=25.79 memory used=2452.1MB, alloc=398.2MB, time=27.20 memory used=2510.8MB, alloc=398.2MB, time=27.43 memory used=2610.8MB, alloc=398.2MB, time=28.67 memory used=2709.0MB, alloc=398.2MB, time=31.26 memory used=2764.8MB, alloc=398.2MB, time=31.55 memory used=2846.1MB, alloc=398.2MB, time=32.28 memory used=2967.4MB, alloc=422.2MB, time=33.61 memory used=3069.9MB, alloc=422.2MB, time=34.38 memory used=3162.1MB, alloc=422.2MB, time=35.89 memory used=3276.9MB, alloc=422.2MB, time=37.16 memory used=3394.9MB, alloc=422.2MB, time=38.65 memory used=3523.9MB, alloc=446.2MB, time=40.44 memory used=3651.9MB, alloc=470.2MB, time=42.45 memory used=3754.8MB, alloc=470.2MB, time=44.06 memory used=3864.2MB, alloc=470.2MB, time=45.56 memory used=3959.4MB, alloc=470.2MB, time=47.13 memory used=4070.3MB, alloc=494.2MB, time=48.39 memory used=4173.7MB, alloc=494.2MB, time=48.85 memory used=4289.6MB, alloc=494.2MB, time=49.79 memory used=4376.7MB, alloc=494.2MB, time=50.15 memory used=4480.2MB, alloc=494.2MB, time=50.63 memory used=4593.4MB, alloc=494.2MB, time=52.06 memory used=4693.7MB, alloc=494.2MB, time=52.57 memory used=4802.8MB, alloc=494.2MB, time=55.13 memory used=4888.5MB, alloc=494.2MB, time=55.45 memory used=4991.0MB, alloc=494.2MB, time=56.13 memory used=5094.3MB, alloc=494.2MB, time=56.71 memory used=5209.7MB, alloc=494.2MB, time=57.44 memory used=5298.8MB, alloc=494.2MB, time=57.79 memory used=5405.1MB, alloc=494.2MB, time=59.10 memory used=5498.5MB, alloc=494.2MB, time=59.65 memory used=5604.8MB, alloc=494.2MB, time=60.25 memory used=5725.3MB, alloc=494.2MB, time=61.52 memory used=5822.9MB, alloc=494.2MB, time=62.02 memory used=5934.0MB, alloc=494.2MB, time=62.73 memory used=6020.8MB, alloc=494.2MB, time=63.08 memory used=6113.6MB, alloc=494.2MB, time=63.40 memory used=6211.1MB, alloc=494.2MB, time=63.84 memory used=6312.1MB, alloc=494.2MB, time=64.50 memory used=6415.8MB, alloc=494.2MB, time=65.07 memory used=6507.1MB, alloc=494.2MB, time=65.44 memory used=6610.1MB, alloc=494.2MB, time=65.97 memory used=6694.7MB, alloc=494.2MB, time=66.30 memory used=6810.4MB, alloc=494.2MB, time=68.18 memory used=6903.4MB, alloc=494.2MB, time=68.53 memory used=6981.3MB, alloc=494.2MB, time=68.84 memory used=7089.2MB, alloc=494.2MB, time=70.20 memory used=7186.3MB, alloc=494.2MB, time=70.62 memory used=7259.4MB, alloc=494.2MB, time=71.01 memory used=7346.8MB, alloc=494.2MB, time=71.39 memory used=7451.7MB, alloc=494.2MB, time=71.78 memory used=7534.9MB, alloc=494.2MB, time=72.11 memory used=7599.5MB, alloc=494.2MB, time=72.42 memory used=7670.8MB, alloc=494.2MB, time=72.75 memory used=7748.4MB, alloc=494.2MB, time=73.06 memory used=7834.6MB, alloc=494.2MB, time=73.38 memory used=7930.2MB, alloc=494.2MB, time=73.70 memory used=8052.8MB, alloc=494.2MB, time=74.94 memory used=8149.0MB, alloc=494.2MB, time=75.37 memory used=8227.6MB, alloc=494.2MB, time=75.76 memory used=8310.4MB, alloc=494.2MB, time=76.14 memory used=8410.3MB, alloc=494.2MB, time=76.52 memory used=8510.2MB, alloc=494.2MB, time=76.89 memory used=8573.1MB, alloc=494.2MB, time=77.23 memory used=8642.1MB, alloc=494.2MB, time=77.58 memory used=8717.9MB, alloc=494.2MB, time=77.90 memory used=8800.8MB, alloc=494.2MB, time=78.23 memory used=8892.7MB, alloc=494.2MB, time=78.56 memory used=8997.0MB, alloc=494.2MB, time=78.88 memory used=9130.3MB, alloc=494.2MB, time=86.66 memory used=9213.5MB, alloc=494.2MB, time=87.04 memory used=9311.2MB, alloc=494.2MB, time=87.45 memory used=9379.4MB, alloc=494.2MB, time=87.79 memory used=9459.6MB, alloc=494.2MB, time=88.12 memory used=9553.2MB, alloc=494.2MB, time=88.47 memory used=9661.9MB, alloc=494.2MB, time=88.83 memory used=9886.6MB, alloc=494.2MB, time=90.21 memory used=9970.2MB, alloc=494.2MB, time=90.61 memory used=10056.9MB, alloc=494.2MB, time=90.99 memory used=10164.8MB, alloc=494.2MB, time=91.38 memory used=10234.9MB, alloc=494.2MB, time=91.70 memory used=10305.6MB, alloc=494.2MB, time=92.01 memory used=10386.6MB, alloc=494.2MB, time=92.32 memory used=10495.7MB, alloc=494.2MB, time=93.37 memory used=10590.5MB, alloc=494.2MB, time=93.77 memory used=10665.4MB, alloc=494.2MB, time=94.16 memory used=10760.4MB, alloc=494.2MB, time=94.51 memory used=10858.0MB, alloc=494.2MB, time=94.85 memory used=10923.9MB, alloc=494.2MB, time=95.17 memory used=10998.5MB, alloc=494.2MB, time=95.46 memory used=11084.7MB, alloc=494.2MB, time=95.76 memory used=11215.4MB, alloc=494.2MB, time=100.84 memory used=11300.5MB, alloc=494.2MB, time=101.19 memory used=11389.9MB, alloc=494.2MB, time=101.52 memory used=11463.4MB, alloc=494.2MB, time=101.82 memory used=11552.0MB, alloc=494.2MB, time=102.13 memory used=11709.5MB, alloc=494.2MB, time=102.69 memory used=11798.5MB, alloc=494.2MB, time=103.06 memory used=11934.5MB, alloc=494.2MB, time=104.29 memory used=12061.5MB, alloc=494.2MB, time=106.50 memory used=12225.4MB, alloc=494.2MB, time=111.32 memory used=12312.8MB, alloc=494.2MB, time=111.70 memory used=12402.8MB, alloc=494.2MB, time=112.08 memory used=12475.3MB, alloc=494.2MB, time=112.42 memory used=12569.3MB, alloc=494.2MB, time=112.76 memory used=12704.7MB, alloc=494.2MB, time=114.31 memory used=12858.1MB, alloc=494.2MB, time=116.99 memory used=12961.5MB, alloc=494.2MB, time=118.77 memory used=13049.2MB, alloc=494.2MB, time=119.14 memory used=13121.4MB, alloc=494.2MB, time=119.49 memory used=13253.8MB, alloc=518.2MB, time=120.87 memory used=13419.1MB, alloc=518.2MB, time=123.28 memory used=13554.9MB, alloc=518.2MB, time=124.91 memory used=13662.9MB, alloc=518.2MB, time=125.41 memory used=13803.2MB, alloc=518.2MB, time=126.53 memory used=13913.1MB, alloc=518.2MB, time=127.20 memory used=14008.7MB, alloc=518.2MB, time=127.63 memory used=14113.8MB, alloc=518.2MB, time=128.03 memory used=14219.4MB, alloc=518.2MB, time=128.56 memory used=14367.3MB, alloc=518.2MB, time=130.70 memory used=14466.6MB, alloc=518.2MB, time=131.12 memory used=14575.6MB, alloc=518.2MB, time=131.70 memory used=14694.8MB, alloc=518.2MB, time=135.13 memory used=14796.2MB, alloc=518.2MB, time=135.55 memory used=14881.5MB, alloc=518.2MB, time=135.89 memory used=15004.8MB, alloc=518.2MB, time=136.75 memory used=15125.8MB, alloc=518.2MB, time=137.61 memory used=15220.4MB, alloc=518.2MB, time=138.02 memory used=15321.0MB, alloc=518.2MB, time=138.40 memory used=15424.1MB, alloc=518.2MB, time=138.89 memory used=15535.1MB, alloc=518.2MB, time=139.63 memory used=15644.6MB, alloc=518.2MB, time=140.32 memory used=15747.0MB, alloc=518.2MB, time=140.72 memory used=15851.2MB, alloc=518.2MB, time=141.33 memory used=15946.0MB, alloc=518.2MB, time=141.73 memory used=16066.7MB, alloc=518.2MB, time=143.61 memory used=16169.0MB, alloc=518.2MB, time=144.03 memory used=16253.1MB, alloc=518.2MB, time=144.39 memory used=16371.9MB, alloc=518.2MB, time=145.67 memory used=16473.2MB, alloc=518.2MB, time=146.13 memory used=16557.0MB, alloc=518.2MB, time=146.53 memory used=16661.1MB, alloc=518.2MB, time=146.96 memory used=16773.4MB, alloc=518.2MB, time=147.35 memory used=16844.0MB, alloc=518.2MB, time=147.70 memory used=16921.4MB, alloc=518.2MB, time=148.05 memory used=17006.7MB, alloc=518.2MB, time=148.43 memory used=17100.8MB, alloc=518.2MB, time=148.82 memory used=17204.1MB, alloc=518.2MB, time=149.20 memory used=17322.9MB, alloc=518.2MB, time=149.56 memory used=17471.6MB, alloc=518.2MB, time=150.98 memory used=17563.4MB, alloc=518.2MB, time=151.40 memory used=17654.1MB, alloc=518.2MB, time=151.82 memory used=17764.4MB, alloc=518.2MB, time=152.24 memory used=17860.0MB, alloc=518.2MB, time=152.63 memory used=17930.4MB, alloc=518.2MB, time=152.98 memory used=18007.8MB, alloc=518.2MB, time=153.33 memory used=18093.1MB, alloc=518.2MB, time=153.68 memory used=18188.7MB, alloc=518.2MB, time=154.03 memory used=18294.8MB, alloc=518.2MB, time=154.40 memory used=18452.3MB, alloc=518.2MB, time=159.46 memory used=18574.6MB, alloc=518.2MB, time=162.49 memory used=18674.8MB, alloc=518.2MB, time=162.90 memory used=18761.8MB, alloc=518.2MB, time=163.26 memory used=18845.6MB, alloc=518.2MB, time=163.60 memory used=18944.1MB, alloc=518.2MB, time=163.99 memory used=19061.5MB, alloc=518.2MB, time=164.37 memory used=19231.3MB, alloc=518.2MB, time=164.82 memory used=19383.5MB, alloc=518.2MB, time=166.01 memory used=19464.3MB, alloc=518.2MB, time=166.42 |\^/| 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(); 1428251929 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 2 F := [-5 x y z - 15 x y + 15 y z - 15 y , x y z - 13 x y z - 2 y + 10 z , 3 2 2 2 3 x y + 8 y z - 16 x z + 15 y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 2 G := [-19 x y - 8 x y z + 12 y z - 20 x z , 17 y z - 9 x - 18 x z - 16 x, 2 2 7 x z - 6 y - 18 z - 15] > Problem := [F,G]; 2 2 2 2 Problem := [[-5 x y z - 15 x y + 15 y z - 15 y , 2 2 2 2 3 2 2 2 x y z - 13 x y z - 2 y + 10 z , 3 x y + 8 y z - 16 x z + 15 y], [ 3 2 3 2 3 2 -19 x y - 8 x y z + 12 y z - 20 x z , 17 y z - 9 x - 18 x z - 16 x, 2 2 7 x z - 6 y - 18 z - 15]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.5MB, alloc=32.3MB, time=0.50 memory used=44.4MB, alloc=56.3MB, time=0.80 memory used=86.2MB, alloc=60.3MB, time=1.42 memory used=128.3MB, alloc=68.3MB, time=1.98 memory used=175.4MB, alloc=92.3MB, time=2.57 memory used=240.8MB, alloc=92.3MB, time=3.38 memory used=307.2MB, alloc=348.3MB, time=4.29 memory used=374.7MB, alloc=348.3MB, time=5.21 memory used=448.1MB, alloc=372.3MB, time=6.19 memory used=539.3MB, alloc=372.3MB, time=7.48 memory used=613.6MB, alloc=372.3MB, time=8.21 memory used=692.0MB, alloc=372.3MB, time=9.70 memory used=728.5MB, alloc=372.3MB, time=9.85 memory used=769.0MB, alloc=372.3MB, time=10.00 memory used=833.4MB, alloc=372.3MB, time=10.46 memory used=926.7MB, alloc=396.3MB, time=12.03 memory used=1049.9MB, alloc=396.3MB, time=13.36 memory used=1174.7MB, alloc=396.3MB, time=16.24 memory used=1308.6MB, alloc=396.3MB, time=19.67 memory used=1434.6MB, alloc=396.3MB, time=20.89 memory used=1557.4MB, alloc=396.3MB, time=23.38 memory used=1684.1MB, alloc=396.3MB, time=27.17 memory used=1754.9MB, alloc=396.3MB, time=27.68 memory used=1837.7MB, alloc=396.3MB, time=29.22 memory used=1887.2MB, alloc=396.3MB, time=29.39 memory used=1945.6MB, alloc=396.3MB, time=29.56 memory used=1995.5MB, alloc=396.3MB, time=29.71 memory used=2037.8MB, alloc=396.3MB, time=29.85 memory used=2088.9MB, alloc=396.3MB, time=29.99 memory used=2213.3MB, alloc=396.3MB, time=31.18 memory used=2345.1MB, alloc=396.3MB, time=32.61 memory used=2448.1MB, alloc=420.3MB, time=34.24 memory used=2561.6MB, alloc=420.3MB, time=35.92 memory used=2644.3MB, alloc=420.3MB, time=37.05 memory used=2698.9MB, alloc=420.3MB, time=37.28 memory used=2768.9MB, alloc=420.3MB, time=37.73 memory used=2852.5MB, alloc=420.3MB, time=38.49 memory used=2950.3MB, alloc=420.3MB, time=39.94 memory used=3083.4MB, alloc=420.3MB, time=41.88 memory used=3138.5MB, alloc=420.3MB, time=42.11 memory used=3238.7MB, alloc=420.3MB, time=42.91 memory used=3371.5MB, alloc=444.3MB, time=44.12 memory used=3514.6MB, alloc=444.3MB, time=46.01 memory used=3619.7MB, alloc=444.3MB, time=47.55 memory used=3733.5MB, alloc=468.3MB, time=49.23 memory used=3831.4MB, alloc=468.3MB, time=50.77 memory used=3916.4MB, alloc=468.3MB, time=52.09 memory used=4007.5MB, alloc=468.3MB, time=53.49 memory used=4097.2MB, alloc=468.3MB, time=54.79 memory used=4191.7MB, alloc=492.3MB, time=56.07 memory used=4301.3MB, alloc=492.3MB, time=57.06 memory used=4379.0MB, alloc=492.3MB, time=58.49 memory used=4451.5MB, alloc=492.3MB, time=59.73 memory used=4531.5MB, alloc=516.3MB, time=60.85 memory used=4605.2MB, alloc=516.3MB, time=62.14 memory used=4666.9MB, alloc=516.3MB, time=63.16 memory used=4729.2MB, alloc=516.3MB, time=64.11 memory used=4785.9MB, alloc=516.3MB, time=65.11 memory used=4843.5MB, alloc=516.3MB, time=66.35 memory used=4891.7MB, alloc=516.3MB, time=67.25 memory used=4979.1MB, alloc=516.3MB, time=68.98 memory used=5115.2MB, alloc=516.3MB, time=71.40 memory used=5180.3MB, alloc=516.3MB, time=72.43 memory used=5255.7MB, alloc=516.3MB, time=74.05 memory used=5304.5MB, alloc=516.3MB, time=74.97 memory used=5528.2MB, alloc=540.3MB, time=77.43 memory used=5711.5MB, alloc=564.3MB, time=79.39 memory used=5937.2MB, alloc=564.3MB, time=82.09 memory used=6136.2MB, alloc=588.3MB, time=85.08 memory used=6306.5MB, alloc=588.3MB, time=88.19 memory used=6454.6MB, alloc=588.3MB, time=90.61 memory used=6670.0MB, alloc=612.3MB, time=93.40 memory used=6851.2MB, alloc=612.3MB, time=94.38 memory used=6976.1MB, alloc=612.3MB, time=95.18 memory used=7112.5MB, alloc=612.3MB, time=95.97 memory used=7285.9MB, alloc=612.3MB, time=97.78 memory used=7455.1MB, alloc=612.3MB, time=98.74 memory used=7584.4MB, alloc=612.3MB, time=99.57 memory used=7720.8MB, alloc=612.3MB, time=100.34 memory used=7899.5MB, alloc=612.3MB, time=143.76 memory used=8060.3MB, alloc=612.3MB, time=157.03 memory used=8215.0MB, alloc=612.3MB, time=157.87 memory used=8335.3MB, alloc=612.3MB, time=158.63 memory used=8452.8MB, alloc=612.3MB, time=159.41 memory used=8587.5MB, alloc=612.3MB, time=160.19 memory used=8728.1MB, alloc=612.3MB, time=160.91 |\^/| 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(); 1428252229 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 4 2 2 3 2 2 F := [4 y + 3 y z - 18 z - 14, 13 x z + 15 y z + 7 x z - 8 y z, 3 3 2 2 6 x y + x + 12 x y + 20 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 3 2 3 G := [-10 x z + 8 z - 18 y + y, 2 x z - 17 x y - 2 z + 20 x z, 3 3 2 -18 x z - 6 y z - 11 x y + 4 z] > Problem := [F,G]; 4 3 4 2 2 3 2 2 Problem := [[4 y + 3 y z - 18 z - 14, 13 x z + 15 y z + 7 x z - 8 y z, 3 3 2 2 2 2 4 3 6 x y + x + 12 x y + 20 y z], [-10 x z + 8 z - 18 y + y, 3 2 3 3 3 2 2 x z - 17 x y - 2 z + 20 x z, -18 x z - 6 y z - 11 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=4.4MB, alloc=32.3MB, time=0.17 memory used=23.9MB, alloc=32.3MB, time=0.44 memory used=43.6MB, alloc=32.3MB, time=0.74 memory used=64.7MB, alloc=57.9MB, time=0.93 memory used=100.7MB, alloc=59.5MB, time=1.06 memory used=139.3MB, alloc=59.5MB, time=1.57 memory used=178.5MB, alloc=63.5MB, time=1.81 memory used=223.1MB, alloc=63.5MB, time=2.35 memory used=270.8MB, alloc=71.5MB, time=2.94 memory used=315.3MB, alloc=71.5MB, time=3.50 memory used=360.9MB, alloc=71.5MB, time=4.08 memory used=402.5MB, alloc=95.5MB, time=4.57 memory used=463.1MB, alloc=95.5MB, time=4.94 memory used=508.6MB, alloc=95.5MB, time=5.11 memory used=549.6MB, alloc=95.5MB, time=5.54 memory used=617.8MB, alloc=95.5MB, time=27.83 memory used=679.8MB, alloc=95.5MB, time=32.05 memory used=730.3MB, alloc=95.5MB, time=32.36 memory used=767.0MB, alloc=95.5MB, time=32.48 memory used=802.8MB, alloc=95.5MB, time=32.60 memory used=829.4MB, alloc=95.5MB, time=32.70 memory used=858.9MB, alloc=95.5MB, time=32.80 memory used=890.9MB, alloc=95.5MB, time=32.91 memory used=926.3MB, alloc=95.5MB, time=33.02 memory used=965.3MB, alloc=95.5MB, time=33.12 memory used=1006.4MB, alloc=95.5MB, time=33.23 memory used=1045.4MB, alloc=95.5MB, time=33.33 memory used=1069.1MB, alloc=95.5MB, time=33.41 memory used=1091.7MB, alloc=95.5MB, time=33.49 memory used=1115.8MB, alloc=95.5MB, time=33.57 memory used=1140.3MB, alloc=95.5MB, time=33.68 memory used=1166.9MB, alloc=95.5MB, time=33.76 memory used=1193.8MB, alloc=95.5MB, time=33.84 memory used=1221.1MB, alloc=95.5MB, time=33.94 memory used=1250.4MB, alloc=95.5MB, time=34.03 memory used=1280.1MB, alloc=95.5MB, time=34.11 memory used=1310.0MB, alloc=95.5MB, time=34.19 memory used=1341.9MB, alloc=95.5MB, time=34.28 memory used=1374.1MB, alloc=95.5MB, time=34.36 memory used=1408.2MB, alloc=95.5MB, time=34.45 memory used=1442.5MB, alloc=95.5MB, time=34.52 memory used=1478.5MB, alloc=95.5MB, time=34.62 memory used=1516.4MB, alloc=95.5MB, time=34.71 memory used=1556.0MB, alloc=95.5MB, time=34.79 memory used=1595.7MB, alloc=95.5MB, time=34.88 memory used=1638.1MB, alloc=95.5MB, time=34.97 memory used=1682.0MB, alloc=95.5MB, time=35.06 memory used=1713.9MB, alloc=107.8MB, time=35.15 memory used=1723.1MB, alloc=107.8MB, time=35.21 memory used=1731.6MB, alloc=107.8MB, time=35.28 memory used=1740.2MB, alloc=107.8MB, time=35.37 memory used=1749.9MB, alloc=107.8MB, time=35.43 memory used=1759.8MB, alloc=107.8MB, time=35.49 memory used=1769.7MB, alloc=107.8MB, time=35.58 memory used=1779.5MB, alloc=107.8MB, time=35.66 memory used=1789.3MB, alloc=107.8MB, time=35.72 memory used=1798.9MB, alloc=107.8MB, time=35.80 memory used=1808.5MB, alloc=107.8MB, time=35.86 memory used=1818.0MB, alloc=107.8MB, time=35.92 memory used=1827.6MB, alloc=107.8MB, time=35.99 memory used=1838.2MB, alloc=107.8MB, time=36.06 memory used=1848.9MB, alloc=107.8MB, time=36.13 memory used=1859.5MB, alloc=107.8MB, time=36.19 memory used=1870.0MB, alloc=107.8MB, time=36.27 memory used=1880.4MB, alloc=107.8MB, time=36.33 memory used=1890.9MB, alloc=107.8MB, time=36.40 memory used=1902.1MB, alloc=107.8MB, time=36.47 memory used=1913.4MB, alloc=107.8MB, time=36.55 memory used=1924.5MB, alloc=107.8MB, time=36.61 memory used=1936.7MB, alloc=107.8MB, time=36.69 memory used=1948.6MB, alloc=107.8MB, time=36.77 memory used=1960.3MB, alloc=107.8MB, time=36.83 memory used=1973.0MB, alloc=107.8MB, time=36.92 memory used=1985.3MB, alloc=107.8MB, time=37.02 memory used=1998.4MB, alloc=107.8MB, time=37.10 memory used=2011.1MB, alloc=107.8MB, time=37.16 memory used=2024.4MB, alloc=107.8MB, time=37.24 memory used=2038.2MB, alloc=107.8MB, time=37.34 memory used=2052.2MB, alloc=107.8MB, time=37.42 memory used=2065.7MB, alloc=107.8MB, time=37.50 memory used=2079.7MB, alloc=107.8MB, time=37.57 memory used=2094.6MB, alloc=107.8MB, time=37.67 memory used=2146.2MB, alloc=107.8MB, time=37.99 memory used=2189.8MB, alloc=107.8MB, time=38.28 memory used=2253.6MB, alloc=107.8MB, time=38.82 memory used=2309.8MB, alloc=107.8MB, time=39.68 memory used=2341.5MB, alloc=107.8MB, time=39.77 memory used=2414.9MB, alloc=107.8MB, time=40.40 memory used=2488.2MB, alloc=107.8MB, time=41.15 memory used=2555.1MB, alloc=107.8MB, time=41.80 memory used=2624.9MB, alloc=107.8MB, time=42.63 memory used=2693.9MB, alloc=107.8MB, time=43.59 memory used=2762.6MB, alloc=107.8MB, time=44.68 memory used=2831.6MB, alloc=107.8MB, time=45.97 memory used=2899.7MB, alloc=107.8MB, time=47.42 memory used=2967.5MB, alloc=107.8MB, time=49.06 memory used=3037.0MB, alloc=107.8MB, time=50.67 memory used=3104.6MB, alloc=107.8MB, time=52.65 memory used=3174.2MB, alloc=107.8MB, time=54.71 memory used=3243.2MB, alloc=107.8MB, time=57.28 memory used=3311.3MB, alloc=107.8MB, time=59.76 memory used=3379.2MB, alloc=107.8MB, time=62.44 memory used=3445.0MB, alloc=107.8MB, time=65.28 memory used=3512.0MB, alloc=107.8MB, time=68.36 memory used=3580.1MB, alloc=107.8MB, time=71.70 memory used=3649.5MB, alloc=107.8MB, time=75.19 memory used=3718.4MB, alloc=107.8MB, time=78.32 memory used=3789.1MB, alloc=107.8MB, time=82.18 memory used=3859.7MB, alloc=107.8MB, time=86.18 memory used=3931.0MB, alloc=107.8MB, time=90.34 memory used=4002.5MB, alloc=107.8MB, time=94.27 memory used=4077.9MB, alloc=107.8MB, time=96.76 memory used=4140.9MB, alloc=107.8MB, time=98.59 memory used=4172.1MB, alloc=107.8MB, time=98.70 memory used=4200.8MB, alloc=107.8MB, time=98.81 memory used=4237.1MB, alloc=107.8MB, time=98.91 memory used=4259.9MB, alloc=107.8MB, time=98.99 memory used=4285.8MB, alloc=107.8MB, time=99.09 memory used=4322.7MB, alloc=107.8MB, time=99.28 memory used=4372.1MB, alloc=107.8MB, time=99.55 memory used=4432.9MB, alloc=107.8MB, time=108.88 memory used=4470.9MB, alloc=107.8MB, time=109.03 memory used=4500.8MB, alloc=107.8MB, time=109.15 memory used=4527.1MB, alloc=107.8MB, time=109.25 memory used=4557.7MB, alloc=107.8MB, time=109.37 memory used=4594.0MB, alloc=107.8MB, time=109.47 memory used=4622.7MB, alloc=107.8MB, time=109.56 memory used=4644.1MB, alloc=107.8MB, time=109.65 memory used=4667.4MB, alloc=107.8MB, time=109.74 memory used=4692.0MB, alloc=107.8MB, time=109.83 memory used=4718.8MB, alloc=107.8MB, time=109.95 memory used=4747.4MB, alloc=107.8MB, time=110.06 memory used=4777.6MB, alloc=107.8MB, time=110.15 memory used=4809.6MB, alloc=107.8MB, time=110.24 memory used=4843.8MB, alloc=107.8MB, time=110.32 memory used=4887.2MB, alloc=107.8MB, time=110.43 memory used=4898.1MB, alloc=107.8MB, time=110.50 memory used=4909.7MB, alloc=107.8MB, time=110.59 memory used=4955.3MB, alloc=107.8MB, time=110.92 memory used=5029.3MB, alloc=107.8MB, time=111.65 memory used=5117.1MB, alloc=107.8MB, time=113.06 memory used=5211.7MB, alloc=131.8MB, time=114.52 memory used=5255.8MB, alloc=131.8MB, time=114.69 memory used=5302.3MB, alloc=131.8MB, time=114.84 memory used=5355.7MB, alloc=131.8MB, time=115.00 memory used=5387.7MB, alloc=131.8MB, time=115.12 memory used=5423.8MB, alloc=131.8MB, time=115.24 memory used=5462.8MB, alloc=131.8MB, time=115.37 memory used=5504.3MB, alloc=131.8MB, time=115.49 memory used=5549.5MB, alloc=131.8MB, time=115.62 memory used=5599.3MB, alloc=131.8MB, time=115.75 memory used=5651.3MB, alloc=131.8MB, time=115.88 memory used=5707.3MB, alloc=131.8MB, time=116.02 memory used=5746.4MB, alloc=131.8MB, time=116.13 memory used=5755.0MB, alloc=131.8MB, time=116.22 memory used=5762.4MB, alloc=131.8MB, time=116.31 memory used=5769.7MB, alloc=131.8MB, time=116.41 memory used=5777.1MB, alloc=131.8MB, time=116.49 memory used=5784.5MB, alloc=131.8MB, time=116.59 memory used=5791.9MB, alloc=131.8MB, time=116.68 memory used=5799.3MB, alloc=131.8MB, time=116.77 memory used=5807.1MB, alloc=131.8MB, time=116.87 memory used=5814.8MB, alloc=131.8MB, time=116.94 memory used=5824.2MB, alloc=131.8MB, time=117.01 memory used=5832.1MB, alloc=131.8MB, time=117.09 memory used=5841.7MB, alloc=131.8MB, time=117.17 memory used=5849.8MB, alloc=131.8MB, time=117.24 memory used=5859.3MB, alloc=131.8MB, time=117.34 memory used=5869.4MB, alloc=131.8MB, time=117.41 memory used=5879.5MB, alloc=131.8MB, time=117.49 memory used=5889.6MB, alloc=131.8MB, time=117.61 memory used=5899.8MB, alloc=131.8MB, time=117.72 memory used=5909.9MB, alloc=131.8MB, time=117.79 memory used=5920.1MB, alloc=131.8MB, time=117.88 memory used=5930.3MB, alloc=131.8MB, time=117.98 memory used=5940.5MB, alloc=131.8MB, time=118.10 memory used=5950.7MB, alloc=131.8MB, time=118.17 memory used=5961.0MB, alloc=131.8MB, time=118.28 memory used=5971.2MB, alloc=131.8MB, time=118.38 memory used=5981.4MB, alloc=131.8MB, time=118.46 memory used=5991.7MB, alloc=131.8MB, time=118.55 memory used=6001.9MB, alloc=131.8MB, time=118.63 memory used=6012.2MB, alloc=131.8MB, time=118.71 memory used=6022.5MB, alloc=131.8MB, time=118.79 memory used=6032.7MB, alloc=131.8MB, time=118.88 memory used=6043.0MB, alloc=131.8MB, time=118.96 memory used=6053.7MB, alloc=131.8MB, time=119.04 memory used=6064.2MB, alloc=131.8MB, time=119.14 memory used=6076.3MB, alloc=131.8MB, time=119.22 memory used=6087.2MB, alloc=131.8MB, time=119.30 memory used=6099.4MB, alloc=131.8MB, time=119.39 memory used=6112.2MB, alloc=131.8MB, time=119.49 memory used=6124.9MB, alloc=131.8MB, time=119.58 memory used=6137.7MB, alloc=131.8MB, time=119.67 memory used=6150.4MB, alloc=131.8MB, time=119.77 memory used=6163.1MB, alloc=131.8MB, time=119.87 memory used=6175.8MB, alloc=131.8MB, time=119.98 memory used=6188.4MB, alloc=131.8MB, time=120.07 memory used=6201.0MB, alloc=131.8MB, time=120.17 memory used=6213.6MB, alloc=131.8MB, time=120.27 memory used=6226.2MB, alloc=131.8MB, time=120.36 memory used=6239.2MB, alloc=131.8MB, time=120.44 memory used=6253.6MB, alloc=131.8MB, time=120.56 memory used=6266.8MB, alloc=131.8MB, time=120.64 memory used=6280.9MB, alloc=131.8MB, time=120.72 memory used=6295.7MB, alloc=131.8MB, time=120.80 memory used=6310.4MB, alloc=131.8MB, time=120.91 memory used=6325.0MB, alloc=131.8MB, time=121.01 memory used=6339.5MB, alloc=131.8MB, time=121.11 memory used=6354.5MB, alloc=131.8MB, time=121.21 memory used=6370.6MB, alloc=131.8MB, time=121.31 memory used=6385.7MB, alloc=131.8MB, time=121.41 memory used=6401.3MB, alloc=131.8MB, time=121.49 memory used=6417.6MB, alloc=131.8MB, time=121.59 memory used=6433.7MB, alloc=131.8MB, time=121.67 memory used=6450.3MB, alloc=131.8MB, time=121.77 memory used=6467.7MB, alloc=131.8MB, time=121.86 memory used=6485.5MB, alloc=131.8MB, time=121.94 memory used=6503.1MB, alloc=131.8MB, time=122.03 memory used=6520.4MB, alloc=131.8MB, time=122.12 memory used=6538.2MB, alloc=131.8MB, time=122.23 memory used=6556.2MB, alloc=131.8MB, time=122.34 memory used=6574.7MB, alloc=131.8MB, time=122.42 memory used=6593.6MB, alloc=131.8MB, time=122.51 memory used=6611.9MB, alloc=131.8MB, time=122.62 memory used=6625.5MB, alloc=131.8MB, time=122.69 memory used=6638.4MB, alloc=131.8MB, time=122.80 memory used=6651.5MB, alloc=131.8MB, time=122.90 memory used=6664.7MB, alloc=131.8MB, time=123.00 memory used=6677.8MB, alloc=131.8MB, time=123.10 memory used=6691.3MB, alloc=131.8MB, time=123.20 memory used=6705.2MB, alloc=131.8MB, time=123.30 memory used=6775.9MB, alloc=131.8MB, time=123.90 memory used=6847.2MB, alloc=131.8MB, time=126.30 memory used=6934.8MB, alloc=131.8MB, time=127.13 memory used=6974.9MB, alloc=131.8MB, time=127.29 memory used=7026.3MB, alloc=131.8MB, time=127.44 memory used=7065.5MB, alloc=131.8MB, time=127.58 memory used=7099.5MB, alloc=131.8MB, time=127.69 memory used=7137.8MB, alloc=131.8MB, time=127.82 memory used=7180.3MB, alloc=131.8MB, time=127.94 memory used=7226.8MB, alloc=131.8MB, time=128.07 memory used=7277.3MB, alloc=131.8MB, time=128.20 memory used=7331.8MB, alloc=131.8MB, time=128.33 memory used=7373.8MB, alloc=131.8MB, time=128.45 memory used=7381.6MB, alloc=131.8MB, time=128.51 memory used=7389.6MB, alloc=131.8MB, time=128.59 memory used=7397.9MB, alloc=131.8MB, time=128.67 memory used=7406.1MB, alloc=131.8MB, time=128.77 memory used=7415.6MB, alloc=131.8MB, time=128.87 memory used=7424.1MB, alloc=131.8MB, time=128.97 memory used=7433.7MB, alloc=131.8MB, time=129.06 memory used=7443.7MB, alloc=131.8MB, time=129.14 memory used=7453.8MB, alloc=131.8MB, time=129.25 memory used=7463.9MB, alloc=131.8MB, time=129.33 memory used=7473.9MB, alloc=131.8MB, time=129.44 memory used=7484.0MB, alloc=131.8MB, time=129.52 memory used=7494.1MB, alloc=131.8MB, time=129.63 memory used=7504.2MB, alloc=131.8MB, time=129.74 memory used=7514.3MB, alloc=131.8MB, time=129.83 memory used=7524.4MB, alloc=131.8MB, time=129.93 memory used=7534.5MB, alloc=131.8MB, time=130.04 memory used=7544.9MB, alloc=131.8MB, time=130.15 memory used=7556.6MB, alloc=131.8MB, time=130.24 memory used=7567.2MB, alloc=131.8MB, time=130.32 memory used=7578.6MB, alloc=131.8MB, time=130.44 memory used=7590.7MB, alloc=131.8MB, time=130.54 memory used=7602.6MB, alloc=131.8MB, time=130.63 memory used=7614.5MB, alloc=131.8MB, time=130.72 memory used=7626.3MB, alloc=131.8MB, time=130.82 memory used=7638.6MB, alloc=131.8MB, time=130.91 memory used=7651.8MB, alloc=131.8MB, time=131.00 memory used=7664.2MB, alloc=131.8MB, time=131.09 memory used=7677.0MB, alloc=131.8MB, time=131.19 memory used=7690.5MB, alloc=131.8MB, time=131.27 memory used=7703.8MB, alloc=131.8MB, time=131.40 memory used=7717.5MB, alloc=131.8MB, time=131.48 memory used=7732.0MB, alloc=131.8MB, time=131.56 memory used=7746.7MB, alloc=131.8MB, time=131.66 memory used=7761.4MB, alloc=131.8MB, time=131.77 memory used=7776.3MB, alloc=131.8MB, time=131.86 memory used=7791.8MB, alloc=131.8MB, time=131.96 memory used=7807.5MB, alloc=131.8MB, time=132.06 memory used=7823.6MB, alloc=131.8MB, time=132.17 memory used=7839.8MB, alloc=131.8MB, time=132.30 memory used=7856.3MB, alloc=131.8MB, time=132.40 memory used=7873.3MB, alloc=131.8MB, time=132.49 memory used=7890.4MB, alloc=131.8MB, time=132.59 memory used=7908.3MB, alloc=131.8MB, time=132.69 memory used=7926.5MB, alloc=131.8MB, time=132.78 memory used=8019.1MB, alloc=131.8MB, time=133.74 memory used=8105.8MB, alloc=131.8MB, time=134.23 memory used=8195.9MB, alloc=131.8MB, time=134.62 memory used=8269.1MB, alloc=387.8MB, time=135.43 memory used=8347.9MB, alloc=387.8MB, time=136.11 memory used=8444.6MB, alloc=387.8MB, time=140.87 memory used=8486.7MB, alloc=387.8MB, time=141.03 memory used=8526.0MB, alloc=387.8MB, time=141.18 memory used=8560.5MB, alloc=387.8MB, time=141.32 memory used=8601.5MB, alloc=387.8MB, time=141.46 memory used=8649.0MB, alloc=387.8MB, time=141.60 memory used=8691.3MB, alloc=387.8MB, time=141.74 memory used=8720.1MB, alloc=387.8MB, time=141.85 memory used=8751.0MB, alloc=387.8MB, time=141.97 memory used=8784.2MB, alloc=387.8MB, time=142.08 memory used=8819.5MB, alloc=387.8MB, time=142.24 memory used=8857.6MB, alloc=387.8MB, time=142.36 memory used=8898.6MB, alloc=387.8MB, time=142.49 memory used=8941.8MB, alloc=387.8MB, time=142.61 memory used=8989.4MB, alloc=387.8MB, time=142.73 memory used=9088.3MB, alloc=411.8MB, time=158.38 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428252529 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 3 2 2 F := [7 y z - 18 x - 11 x z - 16 y z , 5 x y - 9 y + 16 x + 14 y , 3 2 -18 x + 8 x - 11 y z + 10] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-10 x y z + 16 y z + 7 x y + 17 x y z, 2 2 3 2 2 2 3 -11 x y z - 5 x y - 14 y + 10 x , -5 x y z + 3 x y + 14 y + 11] > Problem := [F,G]; 3 3 2 2 2 2 3 2 2 Problem := [[7 y z - 18 x - 11 x z - 16 y z , 5 x y - 9 y + 16 x + 14 y , 3 2 2 3 2 -18 x + 8 x - 11 y z + 10], [-10 x y z + 16 y z + 7 x y + 17 x y z, 2 2 3 2 2 2 3 -11 x y z - 5 x y - 14 y + 10 x , -5 x y z + 3 x y + 14 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=0.18 memory used=23.9MB, alloc=32.3MB, time=0.46 memory used=42.9MB, alloc=32.3MB, time=0.73 memory used=61.7MB, alloc=60.3MB, time=0.98 memory used=103.6MB, alloc=68.3MB, time=1.51 memory used=144.9MB, alloc=68.3MB, time=2.06 memory used=187.5MB, alloc=68.3MB, time=2.60 memory used=233.4MB, alloc=92.3MB, time=3.17 memory used=302.3MB, alloc=92.3MB, time=3.98 memory used=354.4MB, alloc=92.3MB, time=4.34 memory used=420.4MB, alloc=92.3MB, time=5.12 memory used=480.4MB, alloc=372.3MB, time=5.76 memory used=574.5MB, alloc=372.3MB, time=6.92 memory used=643.0MB, alloc=372.3MB, time=7.38 memory used=705.2MB, alloc=372.3MB, time=7.79 memory used=794.5MB, alloc=372.3MB, time=8.81 memory used=873.6MB, alloc=396.3MB, time=9.55 memory used=983.7MB, alloc=396.3MB, time=10.71 memory used=1081.3MB, alloc=396.3MB, time=11.42 memory used=1160.4MB, alloc=396.3MB, time=11.93 memory used=1275.3MB, alloc=396.3MB, time=13.17 memory used=1393.0MB, alloc=420.3MB, time=14.50 memory used=1511.6MB, alloc=420.3MB, time=16.00 memory used=1619.7MB, alloc=444.3MB, time=17.47 memory used=1722.1MB, alloc=444.3MB, time=18.17 memory used=1803.9MB, alloc=444.3MB, time=18.59 memory used=1887.1MB, alloc=444.3MB, time=18.97 memory used=1972.4MB, alloc=444.3MB, time=19.51 memory used=2072.7MB, alloc=444.3MB, time=20.17 memory used=2153.1MB, alloc=444.3MB, time=20.57 memory used=2238.1MB, alloc=444.3MB, time=20.98 memory used=2312.7MB, alloc=444.3MB, time=21.34 memory used=2447.0MB, alloc=444.3MB, time=22.64 memory used=2542.2MB, alloc=444.3MB, time=23.32 memory used=2617.6MB, alloc=444.3MB, time=23.75 memory used=2693.5MB, alloc=444.3MB, time=24.16 memory used=2795.0MB, alloc=444.3MB, time=25.09 memory used=2889.5MB, alloc=444.3MB, time=25.88 memory used=2962.6MB, alloc=468.3MB, time=26.20 memory used=3029.8MB, alloc=468.3MB, time=26.50 memory used=3117.4MB, alloc=468.3MB, time=26.83 memory used=3230.2MB, alloc=468.3MB, time=27.67 memory used=3320.0MB, alloc=468.3MB, time=28.03 memory used=3385.7MB, alloc=468.3MB, time=28.34 memory used=3469.4MB, alloc=468.3MB, time=28.66 memory used=3596.5MB, alloc=468.3MB, time=35.54 memory used=3710.2MB, alloc=492.3MB, time=94.96 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428252829 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 F := [-5 y - 9 x z + 3 y + 1, -11 x y z - 9 y z - 7, 2 2 3 19 x y z - 12 x z - 11 y + 7 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 4 2 G := [-10 x z + 16 y + 12 z - 19 z, 12 x y + 14 z + 7 y + 6 y z, 2 2 2 20 x z + 18 y z - 2 y z ] > Problem := [F,G]; 4 2 3 2 2 Problem := [[-5 y - 9 x z + 3 y + 1, -11 x y z - 9 y z - 7, 2 2 3 3 2 2 19 x y z - 12 x z - 11 y + 7 x], [-10 x z + 16 y + 12 z - 19 z, 2 2 4 2 2 2 2 12 x y + 14 z + 7 y + 6 y z, 20 x z + 18 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=4.4MB, alloc=32.3MB, time=0.18 memory used=25.3MB, alloc=32.3MB, time=0.48 memory used=45.5MB, alloc=56.3MB, time=0.78 memory used=89.0MB, alloc=60.3MB, time=1.36 memory used=131.6MB, alloc=60.3MB, time=1.96 memory used=169.6MB, alloc=84.3MB, time=2.52 memory used=237.3MB, alloc=92.3MB, time=3.43 memory used=305.3MB, alloc=92.3MB, time=4.20 memory used=367.4MB, alloc=116.3MB, time=5.15 memory used=448.6MB, alloc=372.3MB, time=5.96 memory used=511.5MB, alloc=372.3MB, time=6.45 memory used=551.6MB, alloc=372.3MB, time=6.60 memory used=596.6MB, alloc=372.3MB, time=6.73 memory used=628.3MB, alloc=372.3MB, time=6.83 memory used=675.7MB, alloc=372.3MB, time=7.11 memory used=722.1MB, alloc=372.3MB, time=7.36 memory used=770.2MB, alloc=372.3MB, time=8.34 memory used=819.4MB, alloc=372.3MB, time=8.62 memory used=857.1MB, alloc=372.3MB, time=8.75 memory used=907.2MB, alloc=372.3MB, time=8.89 memory used=938.0MB, alloc=372.3MB, time=9.00 memory used=972.0MB, alloc=372.3MB, time=9.10 memory used=1009.4MB, alloc=372.3MB, time=9.20 memory used=1051.4MB, alloc=372.3MB, time=9.35 memory used=1100.7MB, alloc=372.3MB, time=9.47 memory used=1173.8MB, alloc=372.3MB, time=9.79 memory used=1227.2MB, alloc=372.3MB, time=10.11 memory used=1318.0MB, alloc=396.3MB, time=11.29 memory used=1418.4MB, alloc=396.3MB, time=12.53 memory used=1535.6MB, alloc=420.3MB, time=13.98 memory used=1660.9MB, alloc=420.3MB, time=15.83 memory used=1779.7MB, alloc=444.3MB, time=17.54 memory used=1901.9MB, alloc=444.3MB, time=19.23 memory used=2014.3MB, alloc=444.3MB, time=20.88 memory used=2143.8MB, alloc=468.3MB, time=22.35 memory used=2255.5MB, alloc=468.3MB, time=23.46 memory used=2369.2MB, alloc=468.3MB, time=26.45 memory used=2460.9MB, alloc=468.3MB, time=26.85 memory used=2591.1MB, alloc=468.3MB, time=30.22 memory used=2683.1MB, alloc=468.3MB, time=30.68 memory used=2811.3MB, alloc=468.3MB, time=34.24 memory used=2934.1MB, alloc=468.3MB, time=35.19 memory used=3050.7MB, alloc=468.3MB, time=36.53 memory used=3170.5MB, alloc=468.3MB, time=47.51 memory used=3241.0MB, alloc=468.3MB, time=47.82 memory used=3321.9MB, alloc=468.3MB, time=48.13 memory used=3415.7MB, alloc=468.3MB, time=48.80 memory used=3515.0MB, alloc=468.3MB, time=49.57 memory used=3611.7MB, alloc=468.3MB, time=50.95 memory used=3700.6MB, alloc=468.3MB, time=52.43 memory used=3797.5MB, alloc=492.3MB, time=54.17 memory used=3871.3MB, alloc=492.3MB, time=55.46 memory used=3957.0MB, alloc=492.3MB, time=57.04 memory used=4081.8MB, alloc=492.3MB, time=58.14 memory used=4210.5MB, alloc=492.3MB, time=61.91 memory used=4299.1MB, alloc=492.3MB, time=62.34 memory used=4402.2MB, alloc=492.3MB, time=62.88 memory used=4524.8MB, alloc=492.3MB, time=66.66 memory used=4610.3MB, alloc=492.3MB, time=67.07 memory used=4731.7MB, alloc=492.3MB, time=70.97 memory used=4833.6MB, alloc=492.3MB, time=71.48 memory used=4917.3MB, alloc=492.3MB, time=71.87 memory used=4996.0MB, alloc=492.3MB, time=73.04 memory used=5061.8MB, alloc=492.3MB, time=74.00 memory used=5196.4MB, alloc=492.3MB, time=87.30 memory used=5278.2MB, alloc=492.3MB, time=87.75 memory used=5370.0MB, alloc=492.3MB, time=88.19 memory used=5441.6MB, alloc=492.3MB, time=88.58 memory used=5515.6MB, alloc=492.3MB, time=88.94 memory used=5609.4MB, alloc=492.3MB, time=89.55 memory used=5686.1MB, alloc=492.3MB, time=90.96 memory used=5763.9MB, alloc=492.3MB, time=93.13 memory used=5847.2MB, alloc=492.3MB, time=93.60 memory used=5925.0MB, alloc=492.3MB, time=93.99 memory used=6000.8MB, alloc=492.3MB, time=94.37 memory used=6124.5MB, alloc=492.3MB, time=95.01 memory used=6215.0MB, alloc=492.3MB, time=95.49 memory used=6285.9MB, alloc=492.3MB, time=95.91 memory used=6391.5MB, alloc=492.3MB, time=96.52 memory used=6484.4MB, alloc=492.3MB, time=96.97 memory used=6554.6MB, alloc=492.3MB, time=97.39 memory used=6660.3MB, alloc=492.3MB, time=99.75 memory used=6769.8MB, alloc=492.3MB, time=109.66 memory used=6851.6MB, alloc=492.3MB, time=110.08 memory used=6935.2MB, alloc=516.3MB, time=110.50 memory used=7015.3MB, alloc=516.3MB, time=110.93 memory used=7109.6MB, alloc=516.3MB, time=111.34 memory used=7219.8MB, alloc=516.3MB, time=111.75 memory used=7476.8MB, alloc=516.3MB, time=112.48 memory used=7634.1MB, alloc=516.3MB, time=112.98 memory used=7895.8MB, alloc=516.3MB, time=113.82 memory used=7987.7MB, alloc=516.3MB, time=114.24 memory used=8114.5MB, alloc=516.3MB, time=114.96 memory used=8210.7MB, alloc=516.3MB, time=115.43 memory used=8320.6MB, alloc=516.3MB, time=115.88 memory used=8523.7MB, alloc=516.3MB, time=129.31 memory used=8625.7MB, alloc=516.3MB, time=129.78 memory used=8715.2MB, alloc=516.3MB, time=130.21 memory used=8799.3MB, alloc=516.3MB, time=130.63 memory used=8896.8MB, alloc=516.3MB, time=131.06 memory used=9009.9MB, alloc=516.3MB, time=131.48 memory used=9239.4MB, alloc=516.3MB, time=132.04 memory used=9394.9MB, alloc=516.3MB, time=132.54 memory used=9682.7MB, alloc=516.3MB, time=133.42 memory used=9773.7MB, alloc=516.3MB, time=133.87 memory used=9903.1MB, alloc=516.3MB, time=134.57 memory used=10000.0MB, alloc=516.3MB, time=135.05 memory used=10105.6MB, alloc=516.3MB, time=135.53 memory used=10320.8MB, alloc=516.3MB, time=149.06 memory used=10415.1MB, alloc=516.3MB, time=149.55 memory used=10514.2MB, alloc=516.3MB, time=149.98 memory used=10594.3MB, alloc=516.3MB, time=150.38 memory used=10686.4MB, alloc=516.3MB, time=150.80 memory used=10792.6MB, alloc=516.3MB, time=151.24 memory used=10915.3MB, alloc=516.3MB, time=151.67 memory used=11071.2MB, alloc=516.3MB, time=152.17 memory used=11225.3MB, alloc=516.3MB, time=152.65 memory used=11407.6MB, alloc=516.3MB, time=153.17 memory used=11509.1MB, alloc=516.3MB, time=154.37 memory used=11572.2MB, alloc=516.3MB, time=155.38 memory used=11642.8MB, alloc=516.3MB, time=156.51 memory used=11719.1MB, alloc=516.3MB, time=157.61 |\^/| 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(); 1428253129 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 2 F := [-15 x y z + 15 x z - 19 x y + 5 y z, 7 x y - 11 x z + 11 y - 12 y, 2 2 2 2 -17 x z + 20 x y z + 20 y z + 7 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 3 G := [-8 x y + 16 z - 8 x z + x, 10 x y z - 19 y z + 8 x - 3 y, 2 2 2 2 -8 y z + 14 y z + 13 x - 11 x] > Problem := [F,G]; 2 2 2 2 Problem := [[-15 x y z + 15 x z - 19 x y + 5 y z, 2 2 2 2 2 2 2 2 7 x y - 11 x z + 11 y - 12 y, -17 x z + 20 x y z + 20 y z + 7 x z], 3 3 2 3 3 [-8 x y + 16 z - 8 x z + x, 10 x y z - 19 y z + 8 x - 3 y, 2 2 2 2 -8 y z + 14 y z + 13 x - 11 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.52 memory used=44.6MB, alloc=56.3MB, time=0.80 memory used=89.6MB, alloc=62.3MB, time=1.21 memory used=136.8MB, alloc=62.3MB, time=1.57 memory used=183.6MB, alloc=62.3MB, time=2.32 memory used=246.5MB, alloc=62.3MB, time=3.05 memory used=307.3MB, alloc=62.3MB, time=4.67 memory used=349.6MB, alloc=62.3MB, time=5.21 memory used=390.4MB, alloc=62.3MB, time=5.72 memory used=422.1MB, alloc=62.3MB, time=5.96 memory used=450.9MB, alloc=62.3MB, time=6.08 memory used=480.2MB, alloc=62.3MB, time=6.28 memory used=520.2MB, alloc=62.3MB, time=6.69 memory used=561.2MB, alloc=70.3MB, time=7.31 memory used=600.4MB, alloc=94.3MB, time=7.89 memory used=656.0MB, alloc=94.3MB, time=8.35 memory used=707.0MB, alloc=94.3MB, time=8.73 memory used=774.9MB, alloc=94.3MB, time=9.74 memory used=840.3MB, alloc=94.3MB, time=10.84 memory used=885.4MB, alloc=94.3MB, time=11.00 memory used=927.2MB, alloc=94.3MB, time=11.42 memory used=966.8MB, alloc=94.3MB, time=11.64 memory used=1016.6MB, alloc=95.4MB, time=12.43 memory used=1060.7MB, alloc=95.4MB, time=12.59 memory used=1093.0MB, alloc=95.4MB, time=12.72 memory used=1118.1MB, alloc=95.4MB, time=12.83 memory used=1146.7MB, alloc=95.4MB, time=12.96 memory used=1188.6MB, alloc=95.4MB, time=13.45 memory used=1229.4MB, alloc=95.4MB, time=13.60 memory used=1270.1MB, alloc=95.4MB, time=13.86 memory used=1315.9MB, alloc=95.4MB, time=14.75 memory used=1351.2MB, alloc=95.4MB, time=14.88 memory used=1375.2MB, alloc=95.4MB, time=15.00 memory used=1401.4MB, alloc=95.4MB, time=15.11 memory used=1430.7MB, alloc=95.4MB, time=15.22 memory used=1465.4MB, alloc=95.4MB, time=15.67 memory used=1511.0MB, alloc=95.4MB, time=15.83 memory used=1544.2MB, alloc=95.4MB, time=16.01 memory used=1621.3MB, alloc=95.4MB, time=16.84 memory used=1691.8MB, alloc=95.4MB, time=18.40 memory used=1747.5MB, alloc=95.4MB, time=19.48 memory used=1784.0MB, alloc=95.4MB, time=19.61 memory used=1809.7MB, alloc=95.4MB, time=19.73 memory used=1845.4MB, alloc=95.4MB, time=20.53 memory used=1884.1MB, alloc=95.4MB, time=20.68 memory used=1909.5MB, alloc=95.4MB, time=20.79 memory used=1938.5MB, alloc=95.4MB, time=20.91 memory used=1977.3MB, alloc=119.4MB, time=24.49 memory used=2034.5MB, alloc=143.4MB, time=31.08 memory used=2153.4MB, alloc=143.4MB, time=32.72 memory used=2261.4MB, alloc=399.4MB, time=36.60 memory used=2351.0MB, alloc=399.4MB, time=36.88 memory used=2414.5MB, alloc=423.4MB, time=69.20 memory used=2474.5MB, alloc=447.4MB, time=104.06 memory used=2528.6MB, alloc=471.4MB, time=104.26 memory used=2577.8MB, alloc=495.4MB, time=104.46 memory used=2644.2MB, alloc=519.4MB, time=104.69 memory used=2720.0MB, alloc=519.4MB, time=104.93 memory used=2798.8MB, alloc=519.4MB, time=105.17 memory used=2877.8MB, alloc=519.4MB, time=105.43 memory used=2957.0MB, alloc=519.4MB, time=105.68 memory used=3036.5MB, alloc=519.4MB, time=105.94 memory used=3116.1MB, alloc=519.4MB, time=106.19 memory used=3195.9MB, alloc=519.4MB, time=106.42 memory used=3275.8MB, alloc=519.4MB, time=106.66 memory used=3355.9MB, alloc=519.4MB, time=106.91 memory used=3436.6MB, alloc=519.4MB, time=107.16 memory used=3526.0MB, alloc=519.4MB, time=107.43 memory used=3615.6MB, alloc=519.4MB, time=107.70 memory used=3705.4MB, alloc=519.4MB, time=107.95 memory used=3795.3MB, alloc=519.4MB, time=108.23 memory used=3885.5MB, alloc=519.4MB, time=108.49 memory used=3975.7MB, alloc=519.4MB, time=108.73 memory used=4066.1MB, alloc=519.4MB, time=108.98 memory used=4156.7MB, alloc=519.4MB, time=109.25 memory used=4247.3MB, alloc=519.4MB, time=109.49 memory used=4338.1MB, alloc=519.4MB, time=109.76 memory used=4429.0MB, alloc=519.4MB, time=110.01 memory used=4520.0MB, alloc=519.4MB, time=110.26 memory used=4611.1MB, alloc=519.4MB, time=110.52 memory used=4702.3MB, alloc=519.4MB, time=110.78 memory used=4794.0MB, alloc=519.4MB, time=111.04 memory used=4894.4MB, alloc=519.4MB, time=111.29 memory used=4995.0MB, alloc=519.4MB, time=111.58 memory used=5095.6MB, alloc=519.4MB, time=111.84 memory used=5196.3MB, alloc=519.4MB, time=112.09 memory used=5297.0MB, alloc=519.4MB, time=112.36 memory used=5397.7MB, alloc=519.4MB, time=112.62 memory used=5498.5MB, alloc=519.4MB, time=112.89 memory used=5599.3MB, alloc=519.4MB, time=113.16 memory used=5700.0MB, alloc=519.4MB, time=113.41 memory used=5800.8MB, alloc=519.4MB, time=113.68 memory used=5901.8MB, alloc=519.4MB, time=113.97 memory used=6011.7MB, alloc=519.4MB, time=114.23 memory used=6121.5MB, alloc=519.4MB, time=114.49 memory used=6231.2MB, alloc=519.4MB, time=114.75 memory used=6340.9MB, alloc=519.4MB, time=115.02 memory used=6450.4MB, alloc=519.4MB, time=115.30 memory used=6559.8MB, alloc=519.4MB, time=115.58 memory used=6669.1MB, alloc=519.4MB, time=115.83 memory used=6778.3MB, alloc=519.4MB, time=116.09 memory used=6887.6MB, alloc=519.4MB, time=116.39 memory used=7005.5MB, alloc=519.4MB, time=116.67 memory used=7123.2MB, alloc=519.4MB, time=116.97 memory used=7240.7MB, alloc=519.4MB, time=117.26 memory used=7357.9MB, alloc=519.4MB, time=117.54 memory used=7474.9MB, alloc=519.4MB, time=117.80 memory used=7591.5MB, alloc=519.4MB, time=118.06 memory used=7708.2MB, alloc=519.4MB, time=118.35 memory used=7833.2MB, alloc=519.4MB, time=118.65 memory used=7957.7MB, alloc=519.4MB, time=118.95 memory used=8081.9MB, alloc=519.4MB, time=119.24 memory used=8205.6MB, alloc=519.4MB, time=119.52 memory used=8328.8MB, alloc=519.4MB, time=119.81 memory used=8451.9MB, alloc=519.4MB, time=120.08 memory used=8582.9MB, alloc=519.4MB, time=120.38 memory used=8713.3MB, alloc=519.4MB, time=120.66 memory used=8843.0MB, alloc=519.4MB, time=120.93 memory used=8972.2MB, alloc=519.4MB, time=121.23 memory used=9100.8MB, alloc=519.4MB, time=121.52 memory used=9237.0MB, alloc=519.4MB, time=121.81 memory used=9372.4MB, alloc=519.4MB, time=122.09 memory used=9507.1MB, alloc=519.4MB, time=122.41 memory used=9649.0MB, alloc=519.4MB, time=122.69 memory used=9789.8MB, alloc=519.4MB, time=122.99 memory used=9929.6MB, alloc=519.4MB, time=123.29 memory used=10066.1MB, alloc=519.4MB, time=123.58 memory used=10165.1MB, alloc=519.4MB, time=123.81 memory used=10250.2MB, alloc=519.4MB, time=124.02 memory used=10330.2MB, alloc=519.4MB, time=124.21 memory used=10404.9MB, alloc=519.4MB, time=124.40 memory used=10472.6MB, alloc=519.4MB, time=124.58 memory used=10540.9MB, alloc=519.4MB, time=124.76 memory used=10609.2MB, alloc=519.4MB, time=124.94 memory used=10678.4MB, alloc=519.4MB, time=125.12 memory used=10747.5MB, alloc=519.4MB, time=125.31 memory used=10816.3MB, alloc=519.4MB, time=125.48 memory used=10884.6MB, alloc=519.4MB, time=125.66 memory used=10952.5MB, alloc=519.4MB, time=125.83 memory used=11020.3MB, alloc=519.4MB, time=126.01 memory used=11094.8MB, alloc=519.4MB, time=126.20 memory used=11168.9MB, alloc=519.4MB, time=126.38 memory used=11242.4MB, alloc=519.4MB, time=126.57 memory used=11315.4MB, alloc=519.4MB, time=126.75 memory used=11387.8MB, alloc=519.4MB, time=126.93 memory used=11459.7MB, alloc=519.4MB, time=127.11 memory used=11531.0MB, alloc=519.4MB, time=127.29 memory used=11602.0MB, alloc=519.4MB, time=127.48 memory used=11679.2MB, alloc=519.4MB, time=127.67 memory used=11755.7MB, alloc=519.4MB, time=127.86 memory used=11831.5MB, alloc=519.4MB, time=128.04 memory used=11906.6MB, alloc=519.4MB, time=128.22 memory used=11981.1MB, alloc=519.4MB, time=128.40 memory used=12061.3MB, alloc=519.4MB, time=128.60 memory used=12140.7MB, alloc=519.4MB, time=128.78 memory used=12219.1MB, alloc=519.4MB, time=128.97 memory used=12296.7MB, alloc=519.4MB, time=129.15 memory used=12373.4MB, alloc=519.4MB, time=129.34 memory used=12455.3MB, alloc=519.4MB, time=129.54 memory used=12536.1MB, alloc=519.4MB, time=129.73 memory used=12615.8MB, alloc=519.4MB, time=129.92 memory used=12700.3MB, alloc=519.4MB, time=130.11 memory used=12783.4MB, alloc=519.4MB, time=130.31 memory used=12865.2MB, alloc=519.4MB, time=130.50 memory used=12951.1MB, alloc=519.4MB, time=130.68 memory used=13035.6MB, alloc=519.4MB, time=130.89 memory used=13123.7MB, alloc=519.4MB, time=131.08 memory used=13209.9MB, alloc=519.4MB, time=131.27 memory used=13299.3MB, alloc=519.4MB, time=131.47 memory used=13386.5MB, alloc=519.4MB, time=131.67 memory used=13476.3MB, alloc=519.4MB, time=131.87 memory used=13568.2MB, alloc=519.4MB, time=132.07 memory used=13657.2MB, alloc=519.4MB, time=132.27 memory used=13747.6MB, alloc=519.4MB, time=132.47 memory used=13839.0MB, alloc=519.4MB, time=132.68 memory used=13934.5MB, alloc=519.4MB, time=132.88 memory used=14029.3MB, alloc=519.4MB, time=133.08 memory used=14126.0MB, alloc=519.4MB, time=133.30 memory used=14223.2MB, alloc=519.4MB, time=133.50 memory used=14322.2MB, alloc=519.4MB, time=133.70 memory used=14422.9MB, alloc=519.4MB, time=133.90 memory used=14527.7MB, alloc=519.4MB, time=134.11 memory used=14634.1MB, alloc=519.4MB, time=134.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428253429 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 2 2 3 2 2 F := [-13 x y z + y + 18 y z + 5, 3 x z + 17 z - 7 x - 9 z , 2 2 3 4 3 -16 x y + 5 x y - 13 y - 9 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-10 x y + 2 x z - 17 x z, -17 x z + 5 x y + 8 x z + 3 x, 2 2 2 -19 x y - 7 x y z + 13 x - 19 y] > Problem := [F,G]; 2 4 2 2 2 2 3 2 2 Problem := [[-13 x y z + y + 18 y z + 5, 3 x z + 17 z - 7 x - 9 z , 2 2 3 4 3 2 2 -16 x y + 5 x y - 13 y - 9 y z], [-10 x y + 2 x z - 17 x z, 2 2 2 2 2 -17 x z + 5 x y + 8 x z + 3 x, -19 x y - 7 x y z + 13 x - 19 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=24.6MB, alloc=32.3MB, time=0.45 memory used=45.8MB, alloc=36.3MB, time=0.73 memory used=65.1MB, alloc=60.3MB, time=1.00 memory used=107.0MB, alloc=60.3MB, time=1.45 memory used=151.4MB, alloc=60.3MB, time=1.95 memory used=204.1MB, alloc=68.3MB, time=2.54 memory used=246.7MB, alloc=68.3MB, time=3.12 memory used=287.4MB, alloc=68.3MB, time=3.59 memory used=332.4MB, alloc=92.3MB, time=4.16 memory used=393.5MB, alloc=92.3MB, time=4.88 memory used=458.0MB, alloc=92.3MB, time=5.65 memory used=515.8MB, alloc=92.3MB, time=6.31 memory used=580.0MB, alloc=116.3MB, time=7.18 memory used=638.9MB, alloc=116.3MB, time=7.98 memory used=707.2MB, alloc=116.3MB, time=8.53 memory used=768.4MB, alloc=116.3MB, time=8.96 memory used=823.9MB, alloc=116.3MB, time=9.42 memory used=879.4MB, alloc=116.3MB, time=9.74 memory used=927.8MB, alloc=116.3MB, time=9.94 memory used=980.8MB, alloc=116.3MB, time=10.31 memory used=1033.8MB, alloc=116.3MB, time=10.70 memory used=1081.2MB, alloc=116.3MB, time=10.90 memory used=1131.2MB, alloc=116.3MB, time=11.32 memory used=1212.3MB, alloc=116.3MB, time=12.17 memory used=1293.0MB, alloc=116.3MB, time=13.30 memory used=1363.8MB, alloc=116.3MB, time=13.85 memory used=1434.9MB, alloc=116.3MB, time=14.54 memory used=1523.9MB, alloc=140.5MB, time=15.34 memory used=1612.4MB, alloc=140.5MB, time=16.03 memory used=1687.0MB, alloc=140.5MB, time=16.51 memory used=1756.9MB, alloc=140.5MB, time=16.97 memory used=1823.7MB, alloc=140.5MB, time=17.37 memory used=1890.8MB, alloc=140.5MB, time=17.68 memory used=1958.4MB, alloc=140.5MB, time=18.20 memory used=2027.2MB, alloc=396.5MB, time=19.31 memory used=2098.8MB, alloc=396.5MB, time=19.77 memory used=2212.6MB, alloc=396.5MB, time=20.88 memory used=2319.1MB, alloc=396.5MB, time=22.38 memory used=2430.4MB, alloc=420.5MB, time=23.89 memory used=2556.1MB, alloc=420.5MB, time=25.49 memory used=2686.2MB, alloc=444.5MB, time=27.02 memory used=2786.7MB, alloc=444.5MB, time=27.71 memory used=2874.7MB, alloc=444.5MB, time=28.60 memory used=2950.0MB, alloc=444.5MB, time=28.91 memory used=3037.9MB, alloc=444.5MB, time=29.40 memory used=3127.5MB, alloc=444.5MB, time=29.95 memory used=3217.7MB, alloc=444.5MB, time=30.59 memory used=3302.6MB, alloc=444.5MB, time=31.20 memory used=3394.2MB, alloc=444.5MB, time=31.80 memory used=3522.9MB, alloc=444.5MB, time=33.30 memory used=3646.7MB, alloc=444.5MB, time=34.44 memory used=3777.5MB, alloc=444.5MB, time=36.26 memory used=3896.3MB, alloc=468.5MB, time=37.96 memory used=4042.5MB, alloc=468.5MB, time=39.57 memory used=4186.2MB, alloc=468.5MB, time=41.45 memory used=4280.9MB, alloc=468.5MB, time=42.74 memory used=4360.3MB, alloc=468.5MB, time=43.08 memory used=4526.7MB, alloc=468.5MB, time=45.02 memory used=4687.0MB, alloc=468.5MB, time=46.67 memory used=4831.3MB, alloc=492.5MB, time=49.20 memory used=4918.1MB, alloc=492.5MB, time=49.52 memory used=5033.0MB, alloc=492.5MB, time=50.17 memory used=5197.7MB, alloc=492.5MB, time=51.62 memory used=5325.5MB, alloc=492.5MB, time=53.38 memory used=5442.2MB, alloc=492.5MB, time=55.05 memory used=5531.9MB, alloc=492.5MB, time=56.51 memory used=5612.8MB, alloc=492.5MB, time=57.99 memory used=5689.0MB, alloc=492.5MB, time=59.29 memory used=5769.3MB, alloc=516.5MB, time=60.60 memory used=5842.4MB, alloc=516.5MB, time=61.85 memory used=5913.3MB, alloc=516.5MB, time=63.22 memory used=6054.3MB, alloc=516.5MB, time=64.51 memory used=6172.1MB, alloc=516.5MB, time=65.62 memory used=6292.3MB, alloc=516.5MB, time=66.84 memory used=6366.5MB, alloc=516.5MB, time=68.78 memory used=6440.0MB, alloc=516.5MB, time=69.82 memory used=6545.2MB, alloc=516.5MB, time=71.22 memory used=6639.5MB, alloc=516.5MB, time=71.69 memory used=6730.5MB, alloc=516.5MB, time=72.20 memory used=6818.4MB, alloc=516.5MB, time=72.65 memory used=6917.1MB, alloc=516.5MB, time=73.43 memory used=7022.2MB, alloc=516.5MB, time=74.01 memory used=7088.2MB, alloc=516.5MB, time=76.24 memory used=7190.4MB, alloc=516.5MB, time=76.90 memory used=7279.9MB, alloc=516.5MB, time=77.33 memory used=7491.2MB, alloc=516.5MB, time=78.07 memory used=7724.4MB, alloc=516.5MB, time=79.05 memory used=7799.0MB, alloc=516.5MB, time=80.12 memory used=7877.6MB, alloc=516.5MB, time=81.05 memory used=7935.1MB, alloc=516.5MB, time=82.14 memory used=7967.7MB, alloc=516.5MB, time=83.00 memory used=8040.7MB, alloc=516.5MB, time=84.37 memory used=8105.5MB, alloc=516.5MB, time=85.39 memory used=8148.6MB, alloc=516.5MB, time=86.69 memory used=8277.1MB, alloc=540.5MB, time=88.37 memory used=8385.0MB, alloc=540.5MB, time=89.25 memory used=8501.0MB, alloc=540.5MB, time=90.89 memory used=8616.0MB, alloc=540.5MB, time=91.75 memory used=8726.1MB, alloc=540.5MB, time=92.62 memory used=8843.7MB, alloc=540.5MB, time=94.26 memory used=8947.7MB, alloc=540.5MB, time=95.02 memory used=9062.0MB, alloc=540.5MB, time=95.93 memory used=9172.8MB, alloc=540.5MB, time=96.89 memory used=9288.1MB, alloc=540.5MB, time=98.30 memory used=9429.9MB, alloc=540.5MB, time=100.06 memory used=9547.7MB, alloc=540.5MB, time=101.83 memory used=9660.4MB, alloc=540.5MB, time=102.92 memory used=9868.3MB, alloc=540.5MB, time=106.44 memory used=10029.2MB, alloc=540.5MB, time=109.81 memory used=10141.1MB, alloc=540.5MB, time=110.97 memory used=10357.7MB, alloc=540.5MB, time=116.71 memory used=10614.3MB, alloc=540.5MB, time=122.99 memory used=10785.8MB, alloc=564.5MB, time=126.76 memory used=11030.0MB, alloc=564.5MB, time=131.48 memory used=11242.8MB, alloc=588.5MB, 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(); 1428253729 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 2 3 3 F := [-16 x z - 14 y z - 4 y z + 10 y , -11 x y z + 8 x z - 11 y - 13, 2 -2 x z - 4 y + 4 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 3 G := [12 x y + 3 y z - 5 y z - 19 z , 16 x y - 9 x z + 4 z , 2 2 2 -18 x z - 16 y - 6 y z - 11 x] > Problem := [F,G]; 2 2 3 3 2 Problem := [[-16 x z - 14 y z - 4 y z + 10 y , 2 3 3 2 -11 x y z + 8 x z - 11 y - 13, -2 x z - 4 y + 4 x], [ 3 2 2 2 2 2 2 3 12 x y + 3 y z - 5 y z - 19 z , 16 x y - 9 x z + 4 z , 2 2 2 -18 x z - 16 y - 6 y z - 11 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.0MB, alloc=32.3MB, time=0.73 memory used=46.8MB, alloc=36.3MB, time=1.29 memory used=69.2MB, alloc=60.3MB, time=1.78 memory used=112.8MB, alloc=68.3MB, time=2.84 memory used=155.9MB, alloc=68.3MB, time=3.54 memory used=195.1MB, alloc=68.3MB, time=4.00 memory used=230.4MB, alloc=68.3MB, time=5.06 memory used=252.9MB, alloc=68.3MB, time=5.20 memory used=292.9MB, alloc=68.3MB, time=5.99 memory used=326.3MB, alloc=68.3MB, time=6.58 memory used=382.9MB, alloc=68.3MB, time=7.43 memory used=435.3MB, alloc=68.3MB, time=8.08 memory used=487.7MB, alloc=68.3MB, time=9.16 memory used=548.7MB, alloc=68.3MB, time=10.86 memory used=595.3MB, alloc=68.3MB, time=11.53 memory used=646.1MB, alloc=68.3MB, time=12.23 memory used=696.6MB, alloc=68.3MB, time=13.28 memory used=756.4MB, alloc=68.3MB, time=15.09 memory used=808.9MB, alloc=68.3MB, time=15.67 memory used=857.4MB, alloc=68.3MB, time=16.46 memory used=907.2MB, alloc=68.3MB, time=17.52 memory used=959.5MB, alloc=68.3MB, time=19.06 memory used=1002.3MB, alloc=68.3MB, time=19.92 memory used=1030.7MB, alloc=68.3MB, time=20.25 memory used=1084.5MB, alloc=68.3MB, time=21.17 memory used=1137.1MB, alloc=92.3MB, time=21.99 memory used=1204.0MB, alloc=92.3MB, time=23.56 memory used=1268.1MB, alloc=92.3MB, time=25.02 memory used=1329.3MB, alloc=348.3MB, time=26.38 memory used=1392.7MB, alloc=372.3MB, time=27.88 memory used=1450.4MB, alloc=372.3MB, time=29.27 memory used=1539.7MB, alloc=372.3MB, time=31.15 memory used=1609.2MB, alloc=372.3MB, time=32.23 memory used=1704.3MB, alloc=372.3MB, time=33.64 memory used=1800.3MB, alloc=396.3MB, time=35.59 memory used=1889.5MB, alloc=396.3MB, time=38.11 memory used=1953.0MB, alloc=396.3MB, time=41.39 memory used=2041.1MB, alloc=396.3MB, time=46.35 memory used=2090.9MB, alloc=396.3MB, time=46.67 memory used=2152.2MB, alloc=396.3MB, time=46.99 memory used=2216.5MB, alloc=396.3MB, time=47.56 memory used=2293.9MB, alloc=396.3MB, time=49.97 memory used=2344.2MB, alloc=396.3MB, time=50.27 memory used=2397.5MB, alloc=396.3MB, time=50.57 memory used=2441.7MB, alloc=396.3MB, time=50.81 memory used=2494.2MB, alloc=396.3MB, time=51.07 memory used=2557.4MB, alloc=396.3MB, time=51.35 memory used=2680.9MB, alloc=396.3MB, time=59.53 memory used=2732.1MB, alloc=396.3MB, time=59.85 memory used=2793.1MB, alloc=396.3MB, time=60.21 memory used=2838.7MB, alloc=396.3MB, time=60.48 memory used=2882.4MB, alloc=396.3MB, time=60.73 memory used=2931.0MB, alloc=396.3MB, time=61.00 memory used=2986.7MB, alloc=396.3MB, time=61.28 memory used=3048.9MB, alloc=396.3MB, time=61.56 memory used=3245.7MB, alloc=396.3MB, time=62.39 memory used=3346.7MB, alloc=396.3MB, time=63.27 memory used=3400.4MB, alloc=396.3MB, time=63.57 memory used=3489.5MB, alloc=396.3MB, time=65.05 memory used=3611.8MB, alloc=396.3MB, time=66.73 memory used=3739.8MB, alloc=396.3MB, time=68.98 memory used=3840.5MB, alloc=396.3MB, time=71.29 memory used=3953.2MB, alloc=420.3MB, time=73.66 memory used=4071.7MB, alloc=420.3MB, time=76.31 memory used=4189.7MB, alloc=444.3MB, time=79.15 memory used=4298.2MB, alloc=444.3MB, time=80.42 memory used=4398.4MB, alloc=444.3MB, time=81.47 memory used=4500.7MB, alloc=444.3MB, time=82.70 memory used=4598.9MB, alloc=444.3MB, time=84.96 memory used=4689.8MB, alloc=444.3MB, time=85.65 memory used=4760.5MB, alloc=444.3MB, time=86.08 memory used=4840.9MB, alloc=444.3MB, time=86.75 memory used=4911.2MB, alloc=444.3MB, time=87.18 memory used=5004.6MB, alloc=444.3MB, time=91.21 memory used=5071.9MB, alloc=444.3MB, time=91.62 memory used=5168.5MB, alloc=444.3MB, time=92.64 memory used=5240.0MB, alloc=444.3MB, time=93.14 memory used=5324.1MB, alloc=444.3MB, time=93.90 memory used=5397.3MB, alloc=444.3MB, time=94.35 memory used=5501.6MB, alloc=444.3MB, time=109.59 memory used=5586.3MB, alloc=444.3MB, time=110.23 memory used=5648.5MB, alloc=444.3MB, time=110.66 memory used=5711.2MB, alloc=444.3MB, time=111.06 memory used=5787.6MB, alloc=444.3MB, time=111.48 memory used=5854.4MB, alloc=444.3MB, time=111.86 memory used=5904.6MB, alloc=444.3MB, time=112.19 memory used=5958.9MB, alloc=444.3MB, time=112.53 memory used=6019.0MB, alloc=444.3MB, time=112.89 memory used=6085.9MB, alloc=444.3MB, time=113.23 memory used=6160.2MB, alloc=444.3MB, time=113.63 memory used=6265.3MB, alloc=444.3MB, time=116.24 memory used=6329.2MB, alloc=444.3MB, time=116.70 memory used=6391.5MB, alloc=468.3MB, time=117.19 memory used=6485.3MB, alloc=468.3MB, time=117.73 memory used=6586.3MB, alloc=468.3MB, time=118.25 memory used=6648.0MB, alloc=468.3MB, time=118.70 memory used=6711.9MB, alloc=468.3MB, time=119.14 memory used=6780.0MB, alloc=468.3MB, time=119.58 memory used=6853.6MB, alloc=468.3MB, time=120.01 memory used=6932.6MB, alloc=468.3MB, time=120.47 memory used=7016.8MB, alloc=468.3MB, time=120.94 memory used=7109.6MB, alloc=468.3MB, time=121.39 memory used=7206.8MB, alloc=468.3MB, time=121.85 memory used=7311.6MB, alloc=468.3MB, time=122.36 memory used=7394.8MB, alloc=468.3MB, time=122.78 memory used=7450.8MB, alloc=468.3MB, time=123.13 memory used=7509.0MB, alloc=468.3MB, time=123.49 memory used=7569.7MB, alloc=468.3MB, time=123.85 memory used=7632.1MB, alloc=468.3MB, time=124.21 memory used=7698.7MB, alloc=468.3MB, time=124.57 memory used=7768.3MB, alloc=468.3MB, time=124.93 memory used=7842.2MB, alloc=468.3MB, time=125.29 memory used=7920.4MB, alloc=468.3MB, time=125.66 memory used=8003.3MB, alloc=468.3MB, time=126.03 memory used=8126.9MB, alloc=468.3MB, time=128.78 memory used=8206.2MB, alloc=468.3MB, time=129.32 memory used=8291.6MB, alloc=468.3MB, time=129.86 memory used=8393.0MB, alloc=468.3MB, time=130.41 memory used=8474.0MB, alloc=468.3MB, time=130.90 memory used=8535.2MB, alloc=468.3MB, time=131.36 memory used=8602.0MB, alloc=468.3MB, time=131.80 memory used=8674.5MB, alloc=468.3MB, time=132.26 memory used=8752.6MB, alloc=468.3MB, time=132.72 memory used=8836.0MB, alloc=468.3MB, time=133.20 memory used=8924.5MB, alloc=468.3MB, time=133.68 memory used=9018.2MB, alloc=468.3MB, time=134.13 memory used=9118.9MB, alloc=468.3MB, time=134.62 memory used=9222.0MB, alloc=468.3MB, time=135.10 memory used=9281.1MB, alloc=468.3MB, time=135.47 memory used=9337.8MB, alloc=468.3MB, time=135.86 memory used=9396.2MB, alloc=468.3MB, time=136.22 memory used=9459.2MB, alloc=468.3MB, time=136.58 memory used=9523.8MB, alloc=468.3MB, time=136.96 memory used=9592.0MB, alloc=468.3MB, time=137.34 memory used=9662.7MB, alloc=468.3MB, time=137.73 memory used=9737.1MB, alloc=468.3MB, time=138.11 memory used=9816.5MB, alloc=468.3MB, time=138.50 memory used=9909.3MB, alloc=468.3MB, time=139.03 |\^/| 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(); 1428254029 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 2 3 F := [19 x z + 16 x y + 9 x , -18 y z + 7 x z + 13 y - 3 x y, 2 2 2 -7 x y z + 5 x y - 14 x z + 20 y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 G := [-4 y z + 11 z - 5 x + 6 y , 9 x - 16 x y - 10 y - 9 z, 3 3 2 -x z - 14 y z + 3 x y z + 13 x ] > Problem := [F,G]; 3 2 2 3 3 2 3 Problem := [[19 x z + 16 x y + 9 x , -18 y z + 7 x z + 13 y - 3 x y, 2 2 2 2 3 2 2 -7 x y z + 5 x y - 14 x z + 20 y], [-4 y z + 11 z - 5 x + 6 y , 2 2 3 3 2 9 x - 16 x y - 10 y - 9 z, -x z - 14 y z + 3 x y z + 13 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.87 memory used=45.1MB, alloc=56.3MB, time=1.26 memory used=85.3MB, alloc=61.4MB, time=2.01 memory used=129.9MB, alloc=69.4MB, time=3.00 memory used=172.8MB, alloc=69.4MB, time=3.69 memory used=218.6MB, alloc=69.4MB, time=4.48 memory used=261.3MB, alloc=69.4MB, time=5.47 memory used=304.3MB, alloc=93.4MB, time=6.54 memory used=376.5MB, alloc=93.4MB, time=7.98 memory used=427.7MB, alloc=93.4MB, time=8.74 memory used=476.0MB, alloc=93.4MB, time=9.50 memory used=542.0MB, alloc=93.4MB, time=10.72 memory used=605.9MB, alloc=349.4MB, time=12.01 memory used=665.3MB, alloc=349.4MB, time=13.36 memory used=744.7MB, alloc=373.4MB, time=14.71 memory used=843.2MB, alloc=373.4MB, time=16.55 memory used=928.6MB, alloc=397.4MB, time=18.43 memory used=1053.5MB, alloc=397.4MB, time=20.80 memory used=1125.9MB, alloc=397.4MB, time=21.85 memory used=1226.9MB, alloc=421.4MB, time=23.91 memory used=1353.0MB, alloc=421.4MB, time=26.20 memory used=1455.6MB, alloc=421.4MB, time=27.46 memory used=1524.8MB, alloc=421.4MB, time=28.67 memory used=1598.4MB, alloc=421.4MB, time=29.34 memory used=1667.5MB, alloc=421.4MB, time=30.59 memory used=1746.9MB, alloc=421.4MB, time=31.88 memory used=1818.8MB, alloc=421.4MB, time=32.58 memory used=1899.1MB, alloc=421.4MB, time=33.89 memory used=1966.2MB, alloc=421.4MB, time=34.39 memory used=2040.4MB, alloc=421.4MB, time=35.61 memory used=2113.8MB, alloc=421.4MB, time=36.18 memory used=2203.5MB, alloc=421.4MB, time=37.84 memory used=2327.7MB, alloc=445.4MB, time=41.78 memory used=2408.4MB, alloc=445.4MB, time=42.69 memory used=2545.7MB, alloc=445.4MB, time=44.97 memory used=2680.9MB, alloc=445.4MB, time=47.06 memory used=2786.2MB, alloc=445.4MB, time=49.15 memory used=2883.1MB, alloc=469.4MB, time=51.21 memory used=2993.3MB, alloc=469.4MB, time=53.79 memory used=3086.8MB, alloc=469.4MB, time=55.90 memory used=3190.0MB, alloc=469.4MB, time=58.13 memory used=3319.1MB, alloc=469.4MB, time=60.32 memory used=3399.7MB, alloc=469.4MB, time=62.21 memory used=3477.4MB, alloc=469.4MB, time=64.22 memory used=3555.6MB, alloc=493.4MB, time=66.20 memory used=3680.4MB, alloc=493.4MB, time=70.56 memory used=3823.8MB, alloc=493.4MB, time=75.25 memory used=3927.0MB, alloc=493.4MB, time=77.56 memory used=4029.1MB, alloc=493.4MB, time=79.73 memory used=4122.5MB, alloc=493.4MB, time=81.66 memory used=4212.4MB, alloc=493.4MB, time=84.14 memory used=4270.9MB, alloc=493.4MB, time=85.97 memory used=4388.9MB, alloc=493.4MB, time=87.79 memory used=4470.1MB, alloc=493.4MB, time=88.38 memory used=4570.9MB, alloc=493.4MB, time=89.61 memory used=4671.1MB, alloc=493.4MB, time=90.86 memory used=4748.1MB, alloc=493.4MB, time=91.46 memory used=4836.0MB, alloc=493.4MB, time=93.22 memory used=4963.8MB, alloc=517.4MB, time=95.20 memory used=5096.4MB, alloc=517.4MB, time=97.01 memory used=5171.3MB, alloc=517.4MB, time=99.12 memory used=5214.0MB, alloc=517.4MB, time=100.49 memory used=5283.1MB, alloc=517.4MB, time=102.44 memory used=5330.2MB, alloc=517.4MB, time=103.94 memory used=5375.4MB, alloc=517.4MB, time=105.43 memory used=5433.2MB, alloc=517.4MB, time=106.80 memory used=5551.0MB, alloc=517.4MB, time=108.00 memory used=5661.2MB, alloc=517.4MB, time=109.76 memory used=5772.2MB, alloc=517.4MB, time=111.36 memory used=5880.3MB, alloc=517.4MB, time=113.28 memory used=6015.0MB, alloc=517.4MB, time=118.95 memory used=6116.7MB, alloc=517.4MB, time=119.81 memory used=6201.5MB, alloc=517.4MB, time=120.51 memory used=6313.5MB, alloc=517.4MB, time=122.02 memory used=6415.8MB, alloc=517.4MB, time=122.80 memory used=6531.2MB, alloc=517.4MB, time=124.47 memory used=6616.7MB, alloc=517.4MB, time=125.23 memory used=6710.8MB, alloc=517.4MB, time=125.96 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428254329 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 F := [-5 x z + 18 x y z - 3 x y z - 16, 9 y z - 17 y z - 11 y - 15 z, 3 2 -11 x z + 8 x z - 7 y z + 6 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 4 2 G := [-8 x y z + 14 x z + 3 y - 12 y , -15 x y + 8 y - 4 z , 2 2 2 2 3 18 x y + 8 y z + 18 y - 14 y] > Problem := [F,G]; 3 2 2 Problem := [[-5 x z + 18 x y z - 3 x y z - 16, 3 2 3 2 9 y z - 17 y z - 11 y - 15 z, -11 x z + 8 x z - 7 y z + 6 x], [ 2 2 3 2 2 2 4 2 -8 x y z + 14 x z + 3 y - 12 y , -15 x y + 8 y - 4 z , 2 2 2 2 3 18 x y + 8 y z + 18 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=25.1MB, alloc=32.3MB, time=0.84 memory used=56.2MB, alloc=36.3MB, time=1.51 memory used=74.6MB, alloc=36.3MB, time=1.85 memory used=100.7MB, alloc=36.3MB, time=2.38 memory used=126.1MB, alloc=36.3MB, time=2.87 memory used=145.2MB, alloc=36.3MB, time=3.15 memory used=168.7MB, alloc=36.3MB, time=3.60 memory used=191.3MB, alloc=36.3MB, time=3.97 memory used=210.1MB, alloc=36.3MB, time=4.21 memory used=221.9MB, alloc=36.3MB, time=4.28 memory used=232.8MB, alloc=36.3MB, time=4.34 memory used=250.3MB, alloc=36.3MB, time=4.68 memory used=262.7MB, alloc=36.3MB, time=4.78 memory used=274.9MB, alloc=36.3MB, time=5.06 memory used=285.8MB, alloc=36.3MB, time=5.13 memory used=298.3MB, alloc=36.3MB, time=5.21 memory used=309.7MB, alloc=36.3MB, time=5.28 memory used=321.2MB, alloc=36.3MB, time=5.36 memory used=332.5MB, alloc=36.3MB, time=5.43 memory used=356.2MB, alloc=36.3MB, time=6.10 memory used=376.6MB, alloc=60.3MB, time=6.61 memory used=421.9MB, alloc=68.3MB, time=7.73 memory used=469.3MB, alloc=92.3MB, time=9.45 memory used=529.3MB, alloc=96.1MB, time=9.75 memory used=584.1MB, alloc=96.1MB, time=10.02 memory used=637.3MB, alloc=96.1MB, time=10.27 memory used=674.9MB, alloc=96.1MB, time=10.48 memory used=704.5MB, alloc=96.1MB, time=10.66 memory used=734.4MB, alloc=96.1MB, time=10.85 memory used=766.4MB, alloc=96.1MB, time=11.03 memory used=799.4MB, alloc=96.1MB, time=11.21 memory used=833.2MB, alloc=96.1MB, time=11.39 memory used=868.0MB, alloc=96.1MB, time=11.58 memory used=905.8MB, alloc=96.1MB, time=11.78 memory used=944.5MB, alloc=96.1MB, time=11.98 memory used=984.1MB, alloc=96.1MB, time=12.17 memory used=1026.8MB, alloc=96.1MB, time=12.37 memory used=1070.3MB, alloc=96.1MB, time=12.57 memory used=1117.0MB, alloc=96.1MB, time=12.77 memory used=1164.4MB, alloc=96.1MB, time=12.97 memory used=1213.4MB, alloc=96.1MB, time=13.16 memory used=1247.1MB, alloc=96.1MB, time=13.34 memory used=1274.4MB, alloc=96.1MB, time=13.49 memory used=1299.1MB, alloc=96.1MB, time=13.64 memory used=1323.2MB, alloc=96.1MB, time=13.79 memory used=1350.0MB, alloc=96.1MB, time=13.95 memory used=1376.9MB, alloc=96.1MB, time=14.12 memory used=1403.7MB, alloc=96.1MB, time=14.27 memory used=1430.6MB, alloc=96.1MB, time=14.42 memory used=1457.6MB, alloc=96.1MB, time=14.57 memory used=1487.2MB, alloc=96.1MB, time=14.73 memory used=1516.8MB, alloc=96.1MB, time=14.90 memory used=1546.3MB, alloc=96.1MB, time=15.06 memory used=1575.8MB, alloc=96.1MB, time=15.22 memory used=1607.8MB, alloc=96.1MB, time=15.40 memory used=1639.7MB, alloc=96.1MB, time=15.56 memory used=1671.4MB, alloc=96.1MB, time=15.71 memory used=1703.1MB, alloc=96.1MB, time=15.86 memory used=1737.0MB, alloc=96.1MB, time=16.03 memory used=1770.8MB, alloc=96.1MB, time=16.19 memory used=1806.7MB, alloc=96.1MB, time=16.35 memory used=1842.3MB, alloc=96.1MB, time=16.53 memory used=1879.8MB, alloc=96.1MB, time=16.68 memory used=1916.9MB, alloc=96.1MB, time=16.87 memory used=1955.7MB, alloc=96.1MB, time=17.04 memory used=1996.1MB, alloc=96.1MB, time=17.21 memory used=2035.6MB, alloc=96.1MB, time=17.40 memory used=2076.4MB, alloc=96.1MB, time=17.58 memory used=2118.2MB, alloc=96.1MB, time=17.75 memory used=2162.6MB, alloc=96.1MB, time=17.93 memory used=2207.2MB, alloc=96.1MB, time=18.12 memory used=2253.3MB, alloc=96.1MB, time=18.31 memory used=2301.7MB, alloc=96.1MB, time=18.49 memory used=2349.6MB, alloc=96.1MB, time=18.66 memory used=2375.5MB, alloc=96.1MB, time=18.78 memory used=2401.5MB, alloc=96.1MB, time=18.90 memory used=2428.8MB, alloc=96.1MB, time=19.02 memory used=2457.1MB, alloc=96.1MB, time=19.14 memory used=2517.0MB, alloc=96.1MB, time=20.26 memory used=2573.3MB, alloc=96.1MB, time=20.54 memory used=2627.4MB, alloc=96.1MB, time=20.80 memory used=2672.4MB, alloc=96.1MB, time=21.02 memory used=2702.9MB, alloc=96.1MB, time=21.20 memory used=2732.6MB, alloc=96.1MB, time=21.39 memory used=2762.3MB, alloc=96.1MB, time=21.57 memory used=2794.8MB, alloc=96.1MB, time=21.76 memory used=2828.3MB, alloc=96.1MB, time=21.94 memory used=2862.8MB, alloc=96.1MB, time=22.14 memory used=2900.3MB, alloc=96.1MB, time=22.35 memory used=2938.6MB, alloc=96.1MB, time=22.54 memory used=2978.0MB, alloc=96.1MB, time=22.75 memory used=3020.4MB, alloc=96.1MB, time=22.96 memory used=3063.7MB, alloc=96.1MB, time=23.17 memory used=3110.1MB, alloc=96.1MB, time=23.39 memory used=3157.3MB, alloc=96.1MB, time=23.60 memory used=3207.7MB, alloc=96.1MB, time=23.83 memory used=3245.8MB, alloc=96.1MB, time=24.00 memory used=3274.2MB, alloc=96.1MB, time=24.16 memory used=3300.2MB, alloc=96.1MB, time=24.32 memory used=3326.6MB, alloc=96.1MB, time=24.46 memory used=3353.4MB, alloc=96.1MB, time=24.62 memory used=3380.2MB, alloc=96.1MB, time=24.76 memory used=3407.1MB, alloc=96.1MB, time=24.92 memory used=3433.9MB, alloc=96.1MB, time=25.08 memory used=3461.0MB, alloc=96.1MB, time=25.24 memory used=3490.6MB, alloc=96.1MB, time=25.39 memory used=3520.1MB, alloc=96.1MB, time=25.55 memory used=3549.6MB, alloc=96.1MB, time=25.70 memory used=3579.2MB, alloc=96.1MB, time=25.86 memory used=3611.2MB, alloc=96.1MB, time=26.03 memory used=3643.1MB, alloc=96.1MB, time=26.19 memory used=3674.9MB, alloc=96.1MB, time=26.35 memory used=3706.6MB, alloc=96.1MB, time=26.51 memory used=3740.5MB, alloc=96.1MB, time=26.69 memory used=3774.3MB, alloc=96.1MB, time=26.86 memory used=3810.3MB, alloc=96.1MB, time=27.03 memory used=3845.9MB, alloc=96.1MB, time=27.20 memory used=3883.5MB, alloc=96.1MB, time=27.37 memory used=3920.7MB, alloc=96.1MB, time=27.54 memory used=3959.6MB, alloc=96.1MB, time=27.71 memory used=4000.1MB, alloc=96.1MB, time=27.89 memory used=4039.8MB, alloc=96.1MB, time=28.06 memory used=4080.7MB, alloc=96.1MB, time=28.23 memory used=4122.6MB, alloc=96.1MB, time=28.41 memory used=4167.2MB, alloc=96.1MB, time=28.58 memory used=4212.0MB, alloc=96.1MB, time=28.75 memory used=4258.3MB, alloc=96.1MB, time=28.94 memory used=4307.0MB, alloc=96.1MB, time=29.12 memory used=4356.0MB, alloc=96.1MB, time=29.30 memory used=4383.3MB, alloc=96.1MB, time=29.43 memory used=4409.1MB, alloc=96.1MB, time=29.55 memory used=4435.5MB, alloc=96.1MB, time=29.67 memory used=4463.5MB, alloc=96.1MB, time=29.79 memory used=4514.3MB, alloc=120.1MB, time=49.88 memory used=4578.7MB, alloc=144.1MB, time=97.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428254629 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 4 3 F := [9 x y - 6 x y z + 17 x z - 18 x y, 2 x y z + 19 y z - 9 z - 18 z , 2 2 4 20 x y + 8 y + 10 y z - 19] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [-20 x y z - 11 x z - 19 y + 10 z , 2 2 2 2 11 x y - 16 x y z - 13 x z - 8 x z, 3 3 2 2 2 11 x y + 8 x z - 11 x z + 9 y z] > Problem := [F,G]; 2 2 2 Problem := [[9 x y - 6 x y z + 17 x z - 18 x y, 2 3 4 3 2 2 4 2 x y z + 19 y z - 9 z - 18 z , 20 x y + 8 y + 10 y z - 19], [ 2 3 2 2 -20 x y z - 11 x z - 19 y + 10 z , 2 2 2 2 11 x y - 16 x y z - 13 x z - 8 x z, 3 3 2 2 2 11 x y + 8 x z - 11 x z + 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.2MB, alloc=32.3MB, time=0.82 memory used=49.8MB, alloc=60.3MB, time=1.33 memory used=94.5MB, alloc=60.4MB, time=1.98 memory used=135.1MB, alloc=60.9MB, time=4.33 memory used=162.9MB, alloc=60.9MB, time=4.46 memory used=184.8MB, alloc=60.9MB, time=4.57 memory used=211.9MB, alloc=60.9MB, time=4.68 memory used=244.3MB, alloc=60.9MB, time=4.81 memory used=264.9MB, alloc=60.9MB, time=4.90 memory used=284.7MB, alloc=60.9MB, time=4.99 memory used=306.0MB, alloc=60.9MB, time=5.08 memory used=328.9MB, alloc=60.9MB, time=5.17 memory used=353.3MB, alloc=60.9MB, time=5.27 memory used=380.1MB, alloc=60.9MB, time=5.37 memory used=408.4MB, alloc=60.9MB, time=5.47 memory used=439.1MB, alloc=60.9MB, time=5.58 memory used=471.9MB, alloc=60.9MB, time=5.68 memory used=492.7MB, alloc=83.8MB, time=5.80 memory used=506.0MB, alloc=83.8MB, time=5.87 memory used=519.6MB, alloc=83.8MB, time=5.96 memory used=532.9MB, alloc=83.8MB, time=6.07 memory used=547.6MB, alloc=83.8MB, time=6.16 memory used=563.0MB, alloc=83.8MB, time=6.24 memory used=579.1MB, alloc=83.8MB, time=6.32 memory used=622.1MB, alloc=83.8MB, time=6.75 memory used=662.4MB, alloc=83.8MB, time=7.31 memory used=710.0MB, alloc=83.8MB, time=8.37 memory used=761.6MB, alloc=83.8MB, time=9.13 memory used=809.2MB, alloc=83.8MB, time=15.56 memory used=848.4MB, alloc=83.8MB, time=16.49 memory used=881.8MB, alloc=83.8MB, time=16.67 memory used=901.6MB, alloc=83.8MB, time=16.79 memory used=929.3MB, alloc=83.8MB, time=17.04 memory used=974.0MB, alloc=83.8MB, time=17.49 memory used=1021.9MB, alloc=83.8MB, time=24.50 memory used=1055.8MB, alloc=83.8MB, time=24.67 memory used=1082.4MB, alloc=83.8MB, time=24.82 memory used=1100.5MB, alloc=83.8MB, time=24.94 memory used=1137.6MB, alloc=83.8MB, time=25.92 memory used=1186.4MB, alloc=83.8MB, time=29.66 memory used=1230.2MB, alloc=83.8MB, time=48.48 memory used=1257.7MB, alloc=107.8MB, time=59.50 memory used=1316.7MB, alloc=107.8MB, time=60.42 memory used=1358.8MB, alloc=107.8MB, time=60.63 memory used=1392.4MB, alloc=107.8MB, time=60.82 memory used=1431.0MB, alloc=107.8MB, time=61.00 memory used=1486.8MB, alloc=107.8MB, time=61.57 memory used=1564.8MB, alloc=107.8MB, time=64.65 memory used=1636.7MB, alloc=107.8MB, time=65.71 memory used=1704.4MB, alloc=107.8MB, time=67.21 memory used=1771.8MB, alloc=107.8MB, time=68.57 memory used=1801.2MB, alloc=107.8MB, time=68.75 memory used=1832.1MB, alloc=107.8MB, time=68.95 memory used=1870.7MB, alloc=107.8MB, time=69.14 memory used=1893.2MB, alloc=107.8MB, time=69.29 memory used=1916.3MB, alloc=131.8MB, time=69.47 memory used=1957.7MB, alloc=131.8MB, time=69.69 memory used=2005.6MB, alloc=131.8MB, time=69.94 memory used=2060.4MB, alloc=131.8MB, time=70.16 memory used=2119.2MB, alloc=131.8MB, time=70.41 memory used=2152.0MB, alloc=131.8MB, time=70.58 memory used=2187.3MB, alloc=131.8MB, time=70.73 memory used=2226.2MB, alloc=131.8MB, time=70.89 memory used=2287.2MB, alloc=131.8MB, time=71.58 memory used=2334.1MB, alloc=131.8MB, time=71.84 memory used=2385.9MB, alloc=131.8MB, time=72.09 memory used=2422.3MB, alloc=131.8MB, time=72.32 memory used=2464.0MB, alloc=131.8MB, time=72.56 memory used=2512.5MB, alloc=131.8MB, time=72.78 memory used=2567.3MB, alloc=131.8MB, time=73.04 memory used=2623.7MB, alloc=131.8MB, time=73.28 memory used=2656.5MB, alloc=131.8MB, time=73.45 memory used=2692.6MB, alloc=131.8MB, time=73.61 memory used=2731.4MB, alloc=131.8MB, time=73.77 memory used=2813.1MB, alloc=131.8MB, time=103.75 memory used=2864.8MB, alloc=131.8MB, time=162.39 |\^/| 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(); 1428254929 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-8 x y z - 7 y z + 19 x z - 19 z , 2 3 2 2 4 3 2 2 10 x y z - 10 x z - 12 x y + 16 x z , -4 x + 6 x z + 10 x z - 20 x z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 2 G := [5 y z - 6 y z - 5 y + 19 z, 15 x y z - 18 y z - 15 x + 12 x z, 3 3 3 -x y - x y + 3 x - 19 z] > Problem := [F,G]; 2 2 2 Problem := [[-8 x y z - 7 y z + 19 x z - 19 z , 2 3 2 2 4 3 2 2 10 x y z - 10 x z - 12 x y + 16 x z , -4 x + 6 x z + 10 x z - 20 x z 3 3 2 2 2 2 2 ], [5 y z - 6 y z - 5 y + 19 z, 15 x y z - 18 y z - 15 x + 12 x z, 3 3 3 -x y - x y + 3 x - 19 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=45.8MB, alloc=56.3MB, time=1.36 memory used=84.4MB, alloc=60.3MB, time=2.35 memory used=127.5MB, alloc=68.3MB, time=3.40 memory used=166.7MB, alloc=68.3MB, time=4.15 memory used=212.9MB, alloc=92.3MB, time=5.10 memory used=282.4MB, alloc=92.3MB, time=6.57 memory used=348.7MB, alloc=92.3MB, time=8.18 memory used=403.1MB, alloc=372.3MB, time=9.55 memory used=493.1MB, alloc=372.3MB, time=11.86 memory used=529.7MB, alloc=372.3MB, time=12.12 memory used=602.9MB, alloc=372.3MB, time=13.56 memory used=706.8MB, alloc=372.3MB, time=15.50 memory used=808.6MB, alloc=396.3MB, time=17.54 memory used=950.7MB, alloc=396.3MB, time=20.54 memory used=1062.1MB, alloc=396.3MB, time=23.60 memory used=1165.8MB, alloc=420.3MB, time=25.79 memory used=1274.8MB, alloc=420.3MB, time=30.05 memory used=1335.3MB, alloc=420.3MB, time=30.43 memory used=1397.3MB, alloc=420.3MB, time=30.78 memory used=1463.8MB, alloc=420.3MB, time=31.13 memory used=1510.3MB, alloc=420.3MB, time=31.44 memory used=1563.5MB, alloc=420.3MB, time=31.73 memory used=1623.6MB, alloc=420.3MB, time=32.02 memory used=1690.9MB, alloc=420.3MB, time=32.33 memory used=1843.8MB, alloc=420.3MB, time=36.00 memory used=1909.6MB, alloc=420.3MB, time=36.39 memory used=1967.4MB, alloc=420.3MB, time=36.74 memory used=2041.2MB, alloc=420.3MB, time=37.09 memory used=2086.9MB, alloc=420.3MB, time=37.36 memory used=2138.6MB, alloc=420.3MB, time=37.68 memory used=2196.7MB, alloc=420.3MB, time=37.97 memory used=2262.3MB, alloc=420.3MB, time=38.28 memory used=2335.5MB, alloc=420.3MB, time=38.58 memory used=2479.8MB, alloc=420.3MB, time=39.46 memory used=2542.1MB, alloc=420.3MB, time=39.78 memory used=2704.8MB, alloc=420.3MB, time=42.83 memory used=2840.7MB, alloc=420.3MB, time=45.14 memory used=2901.1MB, alloc=420.3MB, time=45.52 memory used=2988.7MB, alloc=420.3MB, time=46.87 memory used=3120.2MB, alloc=444.3MB, time=49.25 memory used=3256.8MB, alloc=444.3MB, time=52.68 memory used=3388.1MB, alloc=468.3MB, time=56.00 memory used=3493.0MB, alloc=468.3MB, time=58.74 memory used=3613.9MB, alloc=468.3MB, time=61.88 memory used=3727.9MB, alloc=468.3MB, time=64.31 memory used=3833.3MB, alloc=492.3MB, time=66.50 memory used=3964.9MB, alloc=492.3MB, time=68.40 memory used=4080.7MB, alloc=492.3MB, time=69.44 memory used=4214.6MB, alloc=492.3MB, time=72.02 memory used=4289.8MB, alloc=492.3MB, time=73.77 memory used=4393.8MB, alloc=492.3MB, time=76.56 memory used=4467.2MB, alloc=492.3MB, time=78.61 memory used=4572.6MB, alloc=492.3MB, time=82.15 memory used=4625.1MB, alloc=492.3MB, time=83.65 memory used=4708.2MB, alloc=492.3MB, time=86.24 memory used=4798.4MB, alloc=516.3MB, time=88.76 memory used=4932.4MB, alloc=516.3MB, time=90.33 memory used=5052.9MB, alloc=516.3MB, time=92.26 memory used=5179.4MB, alloc=516.3MB, time=93.74 memory used=5304.9MB, alloc=516.3MB, time=94.97 memory used=5409.0MB, alloc=516.3MB, time=96.36 memory used=5561.1MB, alloc=516.3MB, time=136.92 memory used=5652.0MB, alloc=516.3MB, time=137.63 memory used=5760.8MB, alloc=516.3MB, time=138.36 memory used=5834.7MB, alloc=516.3MB, time=138.97 memory used=5923.5MB, alloc=516.3MB, time=139.56 memory used=6061.5MB, alloc=516.3MB, time=144.36 memory used=6164.5MB, alloc=540.3MB, time=145.28 memory used=6267.3MB, alloc=540.3MB, time=146.15 memory used=6393.6MB, alloc=540.3MB, time=147.03 memory used=6529.5MB, alloc=540.3MB, time=147.92 memory used=6610.9MB, alloc=540.3MB, time=148.67 memory used=6694.4MB, alloc=540.3MB, time=149.41 memory used=6784.0MB, alloc=540.3MB, time=150.18 memory used=6881.7MB, alloc=540.3MB, time=150.97 memory used=6987.2MB, alloc=540.3MB, time=151.74 memory used=7095.5MB, alloc=540.3MB, time=152.52 memory used=7211.3MB, alloc=540.3MB, time=153.29 memory used=7334.6MB, alloc=540.3MB, time=154.08 memory used=7470.2MB, alloc=540.3MB, time=154.87 memory used=7612.2MB, alloc=540.3MB, time=155.69 memory used=7710.8MB, alloc=540.3MB, time=156.42 memory used=7782.6MB, alloc=540.3MB, time=157.03 |\^/| 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(); 1428255229 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 3 2 2 F := [-7 y - 17 x - 13 x z + 13 y z , 13 x - 9 x y + 4 y z + 17 z, 3 2 2 20 x z - 12 x y z - 11 x + 17 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 3 G := [4 x y z + 8 x y - 5 x - 13 y, -7 x y z + 17 y z + 13 x y + 7 y , 3 2 19 x y - 8 x z - 13 z - 5] > Problem := [F,G]; 4 3 2 2 3 2 2 Problem := [[-7 y - 17 x - 13 x z + 13 y z , 13 x - 9 x y + 4 y z + 17 z, 3 2 2 2 2 2 20 x z - 12 x y z - 11 x + 17 x z], [4 x y z + 8 x y - 5 x - 13 y, 2 3 2 3 3 2 -7 x y z + 17 y z + 13 x y + 7 y , 19 x y - 8 x z - 13 z - 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.88 memory used=47.2MB, alloc=32.3MB, time=1.40 memory used=66.1MB, alloc=56.3MB, time=1.90 memory used=108.6MB, alloc=60.3MB, time=2.75 memory used=150.0MB, alloc=60.3MB, time=3.58 memory used=191.5MB, alloc=60.3MB, time=4.22 memory used=234.9MB, alloc=60.3MB, time=5.48 memory used=261.6MB, alloc=60.3MB, time=6.23 memory used=289.7MB, alloc=84.3MB, time=8.67 memory used=325.9MB, alloc=108.3MB, time=11.39 memory used=546.1MB, alloc=140.3MB, time=19.07 memory used=667.8MB, alloc=140.3MB, time=32.40 memory used=742.9MB, alloc=140.3MB, time=32.67 memory used=821.0MB, alloc=140.3MB, time=32.92 memory used=900.3MB, alloc=140.3MB, time=33.18 memory used=980.4MB, alloc=140.3MB, time=33.45 memory used=1063.7MB, alloc=140.3MB, time=33.74 memory used=1146.9MB, alloc=140.3MB, time=34.02 memory used=1231.9MB, alloc=140.3MB, time=34.30 memory used=1301.4MB, alloc=140.3MB, time=34.53 memory used=1364.7MB, alloc=140.3MB, time=34.73 memory used=1425.8MB, alloc=140.3MB, time=34.93 memory used=1485.7MB, alloc=140.3MB, time=35.14 memory used=1544.4MB, alloc=140.3MB, time=35.33 memory used=1601.2MB, alloc=140.3MB, time=35.52 memory used=1658.0MB, alloc=140.3MB, time=35.70 memory used=1712.7MB, alloc=140.3MB, time=35.88 memory used=1765.6MB, alloc=140.3MB, time=36.06 memory used=1815.2MB, alloc=140.3MB, time=36.23 memory used=1877.9MB, alloc=140.3MB, time=48.24 memory used=1956.2MB, alloc=140.3MB, time=48.49 memory used=2034.5MB, alloc=140.3MB, time=48.77 memory used=2114.0MB, alloc=140.3MB, time=49.05 memory used=2194.3MB, alloc=140.3MB, time=49.34 memory used=2275.2MB, alloc=140.3MB, time=49.61 memory used=2358.7MB, alloc=140.3MB, time=49.90 memory used=2444.2MB, alloc=140.3MB, time=50.15 memory used=2516.8MB, alloc=140.3MB, time=50.38 memory used=2580.8MB, alloc=140.3MB, time=50.59 memory used=2642.1MB, alloc=140.3MB, time=50.81 memory used=2702.3MB, alloc=140.3MB, time=51.01 memory used=2759.4MB, alloc=140.3MB, time=51.21 memory used=2816.9MB, alloc=140.3MB, time=51.40 memory used=2874.1MB, alloc=140.3MB, time=51.59 memory used=2929.7MB, alloc=140.3MB, time=51.78 memory used=2982.3MB, alloc=140.3MB, time=51.95 memory used=3032.1MB, alloc=140.3MB, time=52.12 memory used=3087.4MB, alloc=140.3MB, time=57.75 memory used=3190.4MB, alloc=140.3MB, time=98.99 memory used=3247.4MB, alloc=140.3MB, time=99.17 memory used=3302.7MB, alloc=140.3MB, time=99.35 memory used=3358.3MB, alloc=140.3MB, time=99.52 memory used=3414.1MB, alloc=140.3MB, time=99.69 memory used=3469.7MB, alloc=140.3MB, time=103.14 memory used=3557.0MB, alloc=140.3MB, time=116.67 memory used=3623.4MB, alloc=140.3MB, time=116.89 memory used=3688.0MB, alloc=140.3MB, time=117.12 memory used=3757.1MB, alloc=140.3MB, time=117.34 memory used=3825.3MB, alloc=140.3MB, time=117.57 memory used=3892.8MB, alloc=140.3MB, time=117.80 memory used=3964.5MB, alloc=140.3MB, time=118.03 memory used=4035.1MB, alloc=140.3MB, time=118.27 memory used=4104.9MB, alloc=140.3MB, time=118.50 memory used=4178.4MB, alloc=140.3MB, time=118.76 memory used=4250.6MB, alloc=140.3MB, time=118.99 memory used=4326.3MB, alloc=140.3MB, time=119.23 memory used=4400.4MB, alloc=140.3MB, time=119.50 memory used=4477.5MB, alloc=140.3MB, time=119.74 memory used=4552.8MB, alloc=140.3MB, time=119.97 memory used=4618.6MB, alloc=140.3MB, time=120.20 memory used=4677.3MB, alloc=140.3MB, time=120.40 memory used=4732.3MB, alloc=140.3MB, time=120.59 memory used=4786.6MB, alloc=140.3MB, time=120.78 memory used=4839.8MB, alloc=140.3MB, time=120.96 memory used=4891.7MB, alloc=140.3MB, time=121.16 memory used=4945.4MB, alloc=140.3MB, time=121.35 memory used=4997.6MB, alloc=140.3MB, time=121.55 memory used=5049.0MB, alloc=140.3MB, time=121.73 memory used=5101.4MB, alloc=140.3MB, time=121.92 memory used=5152.3MB, alloc=140.3MB, time=122.10 memory used=5204.1MB, alloc=140.3MB, time=122.28 memory used=5255.9MB, alloc=140.3MB, time=122.46 memory used=5305.1MB, alloc=140.3MB, time=122.63 memory used=5354.2MB, alloc=140.3MB, time=122.81 memory used=5404.4MB, alloc=140.3MB, time=122.98 memory used=5452.9MB, alloc=140.3MB, time=123.16 memory used=5500.5MB, alloc=140.3MB, time=123.32 memory used=5545.9MB, alloc=140.3MB, time=123.48 memory used=5589.7MB, alloc=140.3MB, time=123.64 memory used=5634.5MB, alloc=140.3MB, time=123.80 memory used=5703.9MB, alloc=140.3MB, time=140.42 memory used=5771.8MB, alloc=140.3MB, time=140.64 memory used=5836.6MB, alloc=140.3MB, time=140.88 memory used=5906.1MB, alloc=140.3MB, time=141.12 memory used=5974.8MB, alloc=140.3MB, time=141.34 memory used=6042.7MB, alloc=140.3MB, time=141.57 memory used=6114.9MB, alloc=140.3MB, time=141.83 memory used=6186.1MB, alloc=140.3MB, time=142.06 memory used=6256.3MB, alloc=140.3MB, time=142.30 memory used=6330.4MB, alloc=140.3MB, time=142.56 memory used=6403.0MB, alloc=140.3MB, time=142.82 memory used=6474.8MB, alloc=140.3MB, time=143.09 memory used=6549.5MB, alloc=140.3MB, time=143.33 memory used=6623.0MB, alloc=140.3MB, time=143.56 memory used=6699.2MB, alloc=140.3MB, time=143.83 memory used=6774.7MB, alloc=140.3MB, time=144.06 memory used=6835.8MB, alloc=140.3MB, time=144.26 memory used=6891.0MB, alloc=140.3MB, time=144.47 memory used=6945.6MB, alloc=140.3MB, time=144.66 memory used=6999.4MB, alloc=140.3MB, time=144.85 memory used=7052.0MB, alloc=140.3MB, time=145.03 memory used=7106.4MB, alloc=140.3MB, time=145.22 memory used=7159.3MB, alloc=140.3MB, time=145.40 memory used=7211.3MB, alloc=140.3MB, time=145.59 memory used=7261.4MB, alloc=140.3MB, time=145.77 memory used=7313.2MB, alloc=140.3MB, time=145.96 memory used=7362.6MB, alloc=140.3MB, time=146.14 memory used=7413.3MB, alloc=140.3MB, time=146.33 memory used=7464.0MB, alloc=140.3MB, time=146.50 memory used=7514.6MB, alloc=140.3MB, time=146.68 memory used=7564.3MB, alloc=140.3MB, time=146.85 memory used=7612.9MB, alloc=140.3MB, time=147.03 memory used=7661.2MB, alloc=140.3MB, time=147.20 memory used=7708.2MB, alloc=140.3MB, time=147.36 memory used=7753.8MB, alloc=140.3MB, time=147.52 memory used=7798.7MB, alloc=140.3MB, time=147.67 memory used=7848.0MB, alloc=140.3MB, 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(); 1428255529 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 3 F := [-9 y + 16 z - 15 y - 13, 15 x z + 3 x y + 3 z + 5 x y, 4 2 2 17 x + 5 x z - 11 y z - 19 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 4 2 G := [-y z - 10 x y z - 6 y - 11 z, 19 x y + 15 z - 4 y z + 16 z , 2 3 2 2 2 4 x y z + 15 x z + 9 y z + 17 x z ] > Problem := [F,G]; 4 2 3 2 3 Problem := [[-9 y + 16 z - 15 y - 13, 15 x z + 3 x y + 3 z + 5 x y, 4 2 2 2 2 3 17 x + 5 x z - 11 y z - 19 x z], [-y z - 10 x y z - 6 y - 11 z, 3 4 2 2 3 2 2 2 19 x y + 15 z - 4 y z + 16 z , 4 x y z + 15 x z + 9 y z + 17 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=24.7MB, alloc=32.3MB, time=0.82 memory used=41.0MB, alloc=32.3MB, time=1.02 memory used=60.2MB, alloc=32.3MB, time=1.44 memory used=80.4MB, alloc=60.3MB, time=1.93 memory used=117.8MB, alloc=60.3MB, time=2.75 memory used=162.5MB, alloc=68.3MB, time=3.82 memory used=196.6MB, alloc=68.3MB, time=4.27 memory used=233.2MB, alloc=68.3MB, time=4.87 memory used=272.3MB, alloc=68.3MB, time=5.99 memory used=299.9MB, alloc=68.3MB, time=6.34 memory used=322.8MB, alloc=68.3MB, time=6.51 memory used=345.0MB, alloc=68.3MB, time=6.64 memory used=361.0MB, alloc=81.9MB, time=6.82 memory used=392.7MB, alloc=81.9MB, time=6.96 memory used=416.2MB, alloc=81.9MB, time=7.06 memory used=439.8MB, alloc=81.9MB, time=7.19 memory used=472.4MB, alloc=81.9MB, time=7.33 memory used=496.0MB, alloc=81.9MB, time=7.43 memory used=536.7MB, alloc=81.9MB, time=8.13 memory used=583.1MB, alloc=81.9MB, time=9.09 memory used=636.5MB, alloc=105.9MB, time=9.97 memory used=704.9MB, alloc=105.9MB, time=11.23 memory used=753.8MB, alloc=105.9MB, time=11.83 memory used=784.1MB, alloc=105.9MB, time=12.00 memory used=822.5MB, alloc=105.9MB, time=12.20 memory used=856.0MB, alloc=105.9MB, time=12.37 memory used=881.1MB, alloc=105.9MB, time=12.52 memory used=908.9MB, alloc=105.9MB, time=12.68 memory used=940.6MB, alloc=105.9MB, time=12.83 memory used=975.5MB, alloc=105.9MB, time=13.00 memory used=1013.2MB, alloc=105.9MB, time=13.17 memory used=1055.0MB, alloc=105.9MB, time=13.35 memory used=1090.9MB, alloc=105.9MB, time=13.50 memory used=1113.4MB, alloc=105.9MB, time=13.62 memory used=1137.7MB, alloc=105.9MB, time=13.75 memory used=1163.0MB, alloc=105.9MB, time=13.87 memory used=1189.7MB, alloc=105.9MB, time=14.00 memory used=1218.2MB, alloc=105.9MB, time=14.15 memory used=1253.0MB, alloc=105.9MB, time=14.56 memory used=1311.9MB, alloc=105.9MB, time=25.01 memory used=1347.2MB, alloc=105.9MB, time=25.20 memory used=1377.4MB, alloc=105.9MB, time=25.35 memory used=1414.7MB, alloc=105.9MB, time=25.51 memory used=1452.0MB, alloc=105.9MB, time=25.67 memory used=1476.5MB, alloc=105.9MB, time=25.79 memory used=1503.7MB, alloc=105.9MB, time=25.92 memory used=1533.2MB, alloc=105.9MB, time=26.05 memory used=1565.3MB, alloc=105.9MB, time=26.18 memory used=1601.2MB, alloc=105.9MB, time=26.32 memory used=1641.2MB, alloc=105.9MB, time=26.46 memory used=1678.1MB, alloc=107.8MB, time=26.60 memory used=1759.0MB, alloc=107.8MB, time=28.08 memory used=1818.2MB, alloc=107.8MB, time=28.98 memory used=1853.7MB, alloc=107.8MB, time=29.23 memory used=1891.8MB, alloc=107.8MB, time=29.83 memory used=1921.9MB, alloc=107.8MB, time=30.01 memory used=1968.8MB, alloc=107.8MB, time=30.52 memory used=2013.9MB, alloc=107.8MB, time=31.75 memory used=2044.0MB, alloc=107.8MB, time=31.96 memory used=2075.4MB, alloc=107.8MB, time=32.18 memory used=2114.0MB, alloc=107.8MB, time=32.40 memory used=2136.8MB, alloc=131.8MB, time=32.60 memory used=2173.6MB, alloc=131.8MB, time=32.81 memory used=2215.4MB, alloc=131.8MB, time=33.03 memory used=2262.5MB, alloc=131.8MB, time=33.28 memory used=2314.9MB, alloc=131.8MB, time=33.51 memory used=2374.0MB, alloc=131.8MB, time=33.77 memory used=2415.6MB, alloc=131.8MB, time=33.97 memory used=2448.8MB, alloc=131.8MB, time=34.13 memory used=2482.4MB, alloc=131.8MB, time=34.31 memory used=2518.6MB, alloc=131.8MB, time=34.48 memory used=2557.2MB, alloc=131.8MB, time=34.66 memory used=2597.9MB, alloc=131.8MB, time=34.84 memory used=2640.4MB, alloc=131.8MB, time=35.02 memory used=2686.6MB, alloc=131.8MB, time=35.21 memory used=2735.6MB, alloc=131.8MB, time=35.40 memory used=2787.9MB, alloc=131.8MB, time=35.60 memory used=2849.2MB, alloc=131.8MB, time=36.84 memory used=2928.1MB, alloc=131.8MB, time=57.20 memory used=2975.0MB, alloc=131.8MB, time=57.46 memory used=3022.2MB, alloc=131.8MB, time=57.69 memory used=3076.3MB, alloc=131.8MB, time=57.92 memory used=3110.9MB, alloc=131.8MB, time=58.10 memory used=3149.6MB, alloc=131.8MB, time=58.28 memory used=3192.5MB, alloc=131.8MB, time=58.47 memory used=3240.7MB, alloc=131.8MB, time=58.67 memory used=3293.8MB, alloc=131.8MB, time=58.87 memory used=3352.5MB, alloc=131.8MB, time=59.08 memory used=3377.6MB, alloc=131.8MB, time=59.23 memory used=3387.8MB, alloc=131.8MB, time=59.34 memory used=3397.9MB, alloc=131.8MB, time=59.47 memory used=3408.8MB, alloc=131.8MB, time=59.58 memory used=3418.8MB, alloc=131.8MB, time=59.71 memory used=3430.0MB, alloc=131.8MB, time=59.83 memory used=3441.3MB, alloc=131.8MB, time=59.97 memory used=3453.2MB, alloc=131.8MB, time=60.08 memory used=3465.0MB, alloc=131.8MB, time=60.21 memory used=3477.5MB, alloc=131.8MB, time=60.32 memory used=3490.6MB, alloc=131.8MB, time=60.44 memory used=3503.9MB, alloc=131.8MB, time=60.56 memory used=3517.9MB, alloc=131.8MB, time=60.68 memory used=3604.6MB, alloc=131.8MB, time=63.73 memory used=3669.9MB, alloc=131.8MB, time=66.19 memory used=3713.3MB, alloc=131.8MB, time=66.40 memory used=3764.5MB, alloc=131.8MB, time=66.77 memory used=3808.6MB, alloc=131.8MB, time=66.97 memory used=3891.7MB, alloc=131.8MB, time=68.15 memory used=3965.7MB, alloc=387.8MB, time=69.81 memory used=4058.0MB, alloc=387.8MB, time=71.05 memory used=4147.7MB, alloc=387.8MB, time=72.02 memory used=4236.2MB, alloc=387.8MB, time=73.18 memory used=4323.6MB, alloc=387.8MB, time=74.59 memory used=4414.2MB, alloc=387.8MB, time=76.14 memory used=4504.0MB, alloc=387.8MB, time=77.84 memory used=4592.5MB, alloc=387.8MB, time=79.64 memory used=4680.7MB, alloc=387.8MB, time=81.61 memory used=4771.3MB, alloc=387.8MB, time=83.97 memory used=4860.4MB, alloc=387.8MB, time=86.22 memory used=4950.0MB, alloc=387.8MB, time=88.60 memory used=5087.3MB, alloc=387.8MB, time=92.86 memory used=5173.0MB, alloc=387.8MB, time=94.38 memory used=5260.3MB, alloc=387.8MB, time=95.28 memory used=5351.4MB, alloc=387.8MB, time=96.32 memory used=5442.6MB, alloc=387.8MB, time=97.73 memory used=5533.2MB, alloc=387.8MB, time=99.20 memory used=5622.6MB, alloc=387.8MB, time=100.98 memory used=5714.6MB, alloc=387.8MB, time=102.80 memory used=5805.2MB, alloc=387.8MB, time=104.73 memory used=5895.0MB, alloc=387.8MB, time=106.81 memory used=5985.6MB, alloc=387.8MB, time=109.08 memory used=6078.3MB, alloc=387.8MB, time=111.72 memory used=6179.2MB, alloc=387.8MB, time=115.53 memory used=6286.2MB, alloc=387.8MB, time=118.57 memory used=6328.5MB, alloc=387.8MB, time=118.81 memory used=6377.2MB, alloc=387.8MB, time=119.33 memory used=6418.5MB, alloc=387.8MB, time=119.58 memory used=6459.0MB, alloc=387.8MB, time=119.79 memory used=6560.6MB, alloc=387.8MB, time=121.40 memory used=6650.9MB, alloc=411.8MB, time=122.14 memory used=6802.9MB, alloc=411.8MB, time=124.28 memory used=6922.7MB, alloc=411.8MB, time=126.02 memory used=6997.5MB, alloc=411.8MB, time=126.70 memory used=7067.5MB, alloc=411.8MB, time=130.57 memory used=7121.9MB, alloc=411.8MB, time=130.86 memory used=7225.7MB, alloc=411.8MB, time=133.09 memory used=7333.0MB, alloc=411.8MB, time=136.33 memory used=7414.4MB, alloc=411.8MB, time=137.51 memory used=7461.7MB, alloc=411.8MB, time=137.77 memory used=7507.4MB, alloc=411.8MB, time=138.01 memory used=7574.0MB, alloc=411.8MB, time=138.44 memory used=7626.6MB, alloc=411.8MB, time=138.75 memory used=7666.3MB, alloc=411.8MB, time=138.98 memory used=7717.1MB, alloc=411.8MB, time=139.23 memory used=7860.8MB, alloc=411.8MB, time=141.51 memory used=7965.8MB, alloc=435.8MB, time=142.48 memory used=8144.9MB, alloc=435.8MB, time=145.41 memory used=8301.9MB, alloc=435.8MB, time=147.22 memory used=8457.9MB, alloc=435.8MB, time=151.69 memory used=8584.1MB, alloc=435.8MB, time=153.47 memory used=8644.8MB, alloc=435.8MB, time=153.84 memory used=8701.5MB, alloc=435.8MB, time=154.18 memory used=8774.1MB, alloc=435.8MB, time=154.55 memory used=8958.0MB, alloc=435.8MB, time=155.54 memory used=9167.7MB, alloc=435.8MB, time=156.27 memory used=9574.4MB, alloc=435.8MB, time=165.34 memory used=9632.0MB, alloc=435.8MB, time=165.66 |\^/| 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(); 1428255830 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [13 x y - 16 x y z + 3 y z - 15 y z, 2 4 4 3 3 2 4 2 -15 x y z - 14 y - 12 z - 16 x , -14 x z + 9 x y z - y - 7 x ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 G := [-7 x y + 10 y - 15 x y z + 4 x z , 2 2 2 3 2 3 -11 x y + x y z + 18 y z + 13 x y, -10 z + 15 x y - 19 x + 9 y] > Problem := [F,G]; 2 2 2 3 Problem := [[13 x y - 16 x y z + 3 y z - 15 y z, 2 4 4 3 3 2 4 2 -15 x y z - 14 y - 12 z - 16 x , -14 x z + 9 x y z - y - 7 x ], [ 2 2 4 2 -7 x y + 10 y - 15 x y z + 4 x z , 2 2 2 3 2 3 -11 x y + x y z + 18 y z + 13 x y, -10 z + 15 x y - 19 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=0.32 memory used=26.2MB, alloc=32.3MB, time=0.89 memory used=44.6MB, alloc=56.3MB, time=1.36 memory used=84.0MB, alloc=60.3MB, time=2.23 memory used=128.6MB, alloc=68.3MB, time=3.27 memory used=174.9MB, alloc=68.3MB, time=4.23 memory used=212.9MB, alloc=68.3MB, time=4.77 memory used=232.4MB, alloc=68.3MB, time=4.90 memory used=254.4MB, alloc=68.3MB, time=5.03 memory used=272.0MB, alloc=68.3MB, time=5.14 memory used=302.6MB, alloc=68.3MB, time=5.57 memory used=322.5MB, alloc=68.3MB, time=5.70 memory used=344.9MB, alloc=68.3MB, time=5.82 memory used=362.9MB, alloc=68.3MB, time=5.93 memory used=395.7MB, alloc=68.3MB, time=9.50 memory used=419.3MB, alloc=68.3MB, time=9.64 memory used=437.1MB, alloc=68.3MB, time=9.75 memory used=457.7MB, alloc=68.3MB, time=9.86 memory used=476.7MB, alloc=68.3MB, time=9.96 memory used=521.9MB, alloc=68.3MB, time=11.14 memory used=558.2MB, alloc=68.3MB, time=11.84 memory used=604.4MB, alloc=92.3MB, time=12.68 memory used=687.7MB, alloc=92.3MB, time=13.98 memory used=770.5MB, alloc=92.3MB, time=16.08 memory used=836.0MB, alloc=92.3MB, time=17.64 memory used=875.4MB, alloc=92.3MB, time=18.24 memory used=950.1MB, alloc=92.3MB, time=19.55 memory used=1026.8MB, alloc=92.3MB, time=21.14 memory used=1060.0MB, alloc=92.3MB, time=21.36 memory used=1088.1MB, alloc=92.3MB, time=21.54 memory used=1118.7MB, alloc=92.3MB, time=21.71 memory used=1141.1MB, alloc=92.3MB, time=21.86 memory used=1167.5MB, alloc=92.3MB, time=22.01 memory used=1199.8MB, alloc=92.3MB, time=22.18 memory used=1283.8MB, alloc=116.3MB, time=23.38 memory used=1368.8MB, alloc=116.3MB, time=24.66 memory used=1416.3MB, alloc=116.3MB, time=25.20 memory used=1472.8MB, alloc=116.3MB, time=46.52 memory used=1519.3MB, alloc=116.3MB, time=48.75 memory used=1558.4MB, alloc=116.3MB, time=48.99 memory used=1604.9MB, alloc=116.3MB, time=49.23 memory used=1636.5MB, alloc=116.3MB, time=49.41 memory used=1673.1MB, alloc=116.3MB, time=49.61 memory used=1715.2MB, alloc=116.3MB, time=49.82 memory used=1763.5MB, alloc=116.3MB, time=50.04 memory used=1806.5MB, alloc=131.8MB, time=50.26 memory used=1817.2MB, alloc=131.8MB, time=50.39 memory used=1828.1MB, alloc=131.8MB, time=50.53 memory used=1839.7MB, alloc=131.8MB, time=50.69 memory used=1852.0MB, alloc=131.8MB, time=50.84 memory used=1865.2MB, alloc=131.8MB, time=50.97 memory used=1879.4MB, alloc=131.8MB, time=51.11 memory used=1942.9MB, alloc=131.8MB, time=52.09 memory used=1992.0MB, alloc=131.8MB, time=52.42 memory used=2082.9MB, alloc=131.8MB, time=53.98 memory used=2157.3MB, alloc=387.8MB, time=55.78 memory used=2244.6MB, alloc=411.8MB, time=57.68 memory used=2361.3MB, alloc=411.8MB, time=60.23 memory used=2476.3MB, alloc=435.8MB, time=62.77 memory used=2598.3MB, alloc=435.8MB, time=69.38 memory used=2657.8MB, alloc=435.8MB, time=69.71 memory used=2715.6MB, alloc=435.8MB, time=70.00 memory used=2788.3MB, alloc=435.8MB, time=70.79 memory used=2860.7MB, alloc=435.8MB, time=71.38 memory used=2956.2MB, alloc=435.8MB, time=74.94 memory used=3015.7MB, alloc=435.8MB, time=75.25 memory used=3109.8MB, alloc=435.8MB, time=78.91 memory used=3171.7MB, alloc=435.8MB, time=79.25 memory used=3237.4MB, alloc=435.8MB, time=79.90 memory used=3308.3MB, alloc=435.8MB, time=80.97 memory used=3379.5MB, alloc=435.8MB, time=81.60 memory used=3495.6MB, alloc=435.8MB, time=84.14 memory used=3632.1MB, alloc=435.8MB, time=101.58 memory used=3686.8MB, alloc=435.8MB, time=101.94 memory used=3749.3MB, alloc=435.8MB, time=102.29 memory used=3795.4MB, alloc=459.8MB, time=102.59 memory used=3860.8MB, alloc=459.8MB, time=102.90 memory used=3947.0MB, alloc=459.8MB, time=103.62 memory used=4074.3MB, alloc=459.8MB, time=105.38 memory used=4211.6MB, alloc=459.8MB, time=108.06 memory used=4306.5MB, alloc=459.8MB, time=109.26 memory used=4393.6MB, alloc=459.8MB, time=110.17 memory used=4473.1MB, alloc=459.8MB, time=111.03 memory used=4580.1MB, alloc=459.8MB, time=115.48 memory used=4649.1MB, alloc=459.8MB, time=115.90 memory used=4728.2MB, alloc=459.8MB, time=116.78 memory used=4806.4MB, alloc=459.8MB, time=117.49 memory used=4886.4MB, alloc=459.8MB, time=120.28 memory used=4963.9MB, alloc=459.8MB, time=121.13 memory used=5042.6MB, alloc=459.8MB, time=121.86 memory used=5114.8MB, alloc=459.8MB, time=123.67 memory used=5191.7MB, alloc=459.8MB, time=126.12 memory used=5279.7MB, alloc=459.8MB, time=127.70 memory used=5352.3MB, alloc=459.8MB, time=128.18 memory used=5419.9MB, alloc=459.8MB, time=128.81 memory used=5502.3MB, alloc=459.8MB, time=129.63 memory used=5574.6MB, alloc=459.8MB, time=130.77 |\^/| 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(); 1428256130 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [18 y z - 11 x - 18 x y, -10 x y z + 20 x z - 11 y z - z , 4 3 2 2 3 -7 x + 6 x y + 14 x z + 20 y z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 2 2 G := [-16 x z - 17 x z - 10 x - 11 z, 6 x - 19 x y + 7 y + 4 z , 3 3 4 16 x z - 16 x y - 16 z - 8 x z] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[18 y z - 11 x - 18 x y, -10 x y z + 20 x z - 11 y z - z , 4 3 2 2 3 3 2 -7 x + 6 x y + 14 x z + 20 y z ], [-16 x z - 17 x z - 10 x - 11 z, 4 2 2 2 3 3 4 6 x - 19 x y + 7 y + 4 z , 16 x z - 16 x y - 16 z - 8 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.9MB, alloc=32.3MB, time=0.85 memory used=45.5MB, alloc=56.3MB, time=1.38 memory used=86.8MB, alloc=60.3MB, time=2.43 memory used=127.7MB, alloc=60.3MB, time=3.48 memory used=164.6MB, alloc=60.3MB, time=4.08 memory used=203.0MB, alloc=84.3MB, time=5.09 memory used=237.3MB, alloc=84.3MB, time=5.91 memory used=305.4MB, alloc=92.3MB, time=7.49 memory used=368.9MB, alloc=372.3MB, time=9.02 memory used=446.6MB, alloc=372.3MB, time=9.99 memory used=503.7MB, alloc=372.3MB, time=10.82 memory used=598.9MB, alloc=372.3MB, time=12.59 memory used=683.2MB, alloc=372.3MB, time=14.43 memory used=768.2MB, alloc=396.3MB, time=16.58 memory used=853.6MB, alloc=396.3MB, time=17.72 memory used=921.2MB, alloc=396.3MB, time=18.67 memory used=983.7MB, alloc=396.3MB, time=19.19 memory used=1103.2MB, alloc=396.3MB, time=21.61 memory used=1194.6MB, alloc=396.3MB, time=23.17 memory used=1254.3MB, alloc=396.3MB, time=23.60 memory used=1302.7MB, alloc=396.3MB, time=23.91 memory used=1374.6MB, alloc=396.3MB, time=25.31 memory used=1434.2MB, alloc=396.3MB, time=25.87 memory used=1485.8MB, alloc=396.3MB, time=26.21 memory used=1604.1MB, alloc=420.3MB, time=28.48 memory used=1722.7MB, alloc=420.3MB, time=31.01 memory used=1810.7MB, alloc=420.3MB, time=32.71 memory used=1946.3MB, alloc=420.3MB, time=35.32 memory used=2056.1MB, alloc=444.3MB, time=38.27 memory used=2166.4MB, alloc=444.3MB, time=41.24 memory used=2259.6MB, alloc=468.3MB, time=43.68 memory used=2376.6MB, alloc=468.3MB, time=46.37 memory used=2481.1MB, alloc=468.3MB, time=48.72 memory used=2570.0MB, alloc=468.3MB, time=51.47 memory used=2665.1MB, alloc=468.3MB, time=53.66 memory used=2740.0MB, alloc=468.3MB, time=54.22 memory used=2802.4MB, alloc=468.3MB, time=54.70 memory used=2878.3MB, alloc=468.3MB, time=55.22 memory used=2969.5MB, alloc=468.3MB, time=55.78 memory used=3123.9MB, alloc=468.3MB, time=56.78 memory used=3335.3MB, alloc=468.3MB, time=59.74 memory used=3433.9MB, alloc=468.3MB, time=62.16 memory used=3528.7MB, alloc=492.3MB, time=63.15 memory used=3627.1MB, alloc=492.3MB, time=63.98 memory used=3714.1MB, alloc=492.3MB, time=64.58 memory used=3820.3MB, alloc=492.3MB, time=66.23 memory used=3905.3MB, alloc=492.3MB, time=66.78 memory used=4003.8MB, alloc=492.3MB, time=67.57 memory used=4119.3MB, alloc=492.3MB, time=68.74 memory used=4245.1MB, alloc=492.3MB, time=70.78 memory used=4330.5MB, alloc=492.3MB, time=71.38 memory used=4419.5MB, alloc=492.3MB, time=71.93 memory used=4559.9MB, alloc=492.3MB, time=75.33 memory used=4650.4MB, alloc=492.3MB, time=75.93 memory used=4725.5MB, alloc=492.3MB, time=76.47 memory used=4872.9MB, alloc=492.3MB, time=77.88 memory used=4976.6MB, alloc=492.3MB, time=81.16 memory used=5060.6MB, alloc=492.3MB, time=83.00 memory used=5182.4MB, alloc=492.3MB, time=85.73 memory used=5273.0MB, alloc=492.3MB, time=86.36 memory used=5347.2MB, alloc=492.3MB, time=86.89 memory used=5505.0MB, alloc=492.3MB, time=88.90 memory used=5591.7MB, alloc=492.3MB, time=90.49 memory used=5713.0MB, alloc=492.3MB, time=92.38 memory used=5822.9MB, alloc=492.3MB, time=94.13 memory used=5909.9MB, alloc=492.3MB, time=96.10 memory used=5982.7MB, alloc=492.3MB, time=98.20 memory used=6034.1MB, alloc=492.3MB, time=99.95 memory used=6085.7MB, alloc=492.3MB, time=101.49 memory used=6164.7MB, alloc=492.3MB, time=104.21 memory used=6218.0MB, alloc=516.3MB, time=105.80 memory used=6273.7MB, alloc=516.3MB, time=107.45 memory used=6484.6MB, alloc=540.3MB, time=111.95 memory used=6708.0MB, alloc=564.3MB, time=117.21 memory used=6895.2MB, alloc=588.3MB, time=121.35 memory used=7052.4MB, alloc=612.3MB, time=125.11 |\^/| 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(); 1428256430 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 F := [16 x y - 18 x + x - 19 y z, -15 y z - 10 y z - 17 x y - 2 x, 2 2 4 2 9 x z - 14 y + 4 y z - 15 x y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 4 2 G := [17 x y - 20 y z + 14 x z + 4 z , -17 x y z + 5 y - 3 x y z - 16 y z, 2 2 2 2 -5 y z + 6 x y - 8 y + y z] > Problem := [F,G]; 3 3 2 3 2 Problem := [[16 x y - 18 x + x - 19 y z, -15 y z - 10 y z - 17 x y - 2 x, 2 2 4 2 3 2 2 2 9 x z - 14 y + 4 y z - 15 x y], [17 x y - 20 y z + 14 x z + 4 z , 2 4 2 2 2 2 2 -17 x y z + 5 y - 3 x y z - 16 y z, -5 y z + 6 x y - 8 y + y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.31 memory used=25.1MB, alloc=32.3MB, time=0.84 memory used=43.7MB, alloc=56.3MB, time=1.26 memory used=86.5MB, alloc=60.3MB, time=2.02 memory used=120.8MB, alloc=60.3MB, time=2.29 memory used=163.9MB, alloc=60.3MB, time=2.84 memory used=203.1MB, alloc=60.3MB, time=3.22 memory used=259.9MB, alloc=61.4MB, time=4.07 memory used=302.7MB, alloc=69.4MB, time=5.12 memory used=344.2MB, alloc=69.4MB, time=5.96 memory used=383.7MB, alloc=69.4MB, time=6.62 memory used=404.2MB, alloc=69.4MB, time=6.75 memory used=420.7MB, alloc=69.4MB, time=6.87 memory used=459.2MB, alloc=69.4MB, time=7.37 memory used=519.2MB, alloc=93.4MB, time=8.89 memory used=590.0MB, alloc=93.4MB, time=10.12 memory used=623.9MB, alloc=93.4MB, time=10.29 memory used=679.3MB, alloc=93.4MB, time=11.02 memory used=744.6MB, alloc=93.4MB, time=12.27 memory used=802.5MB, alloc=93.4MB, time=13.28 memory used=861.0MB, alloc=93.4MB, time=14.49 memory used=929.6MB, alloc=117.4MB, time=15.63 memory used=988.1MB, alloc=117.4MB, time=16.06 memory used=1048.3MB, alloc=117.4MB, time=16.64 memory used=1100.1MB, alloc=117.4MB, time=16.96 memory used=1155.9MB, alloc=117.4MB, time=17.50 memory used=1201.7MB, alloc=117.4MB, time=17.75 memory used=1242.0MB, alloc=117.4MB, time=17.97 memory used=1278.5MB, alloc=117.4MB, time=18.18 memory used=1321.9MB, alloc=117.4MB, time=18.38 memory used=1373.6MB, alloc=117.4MB, time=18.60 memory used=1434.4MB, alloc=117.4MB, time=20.20 memory used=1473.0MB, alloc=117.4MB, time=20.42 memory used=1520.5MB, alloc=117.4MB, time=20.64 memory used=1565.8MB, alloc=117.4MB, time=20.94 memory used=1619.4MB, alloc=117.4MB, time=21.59 memory used=1661.5MB, alloc=117.4MB, time=21.81 memory used=1718.7MB, alloc=117.4MB, time=22.29 memory used=1777.3MB, alloc=117.4MB, time=22.74 memory used=1840.8MB, alloc=117.4MB, time=24.03 memory used=1883.4MB, alloc=117.4MB, time=24.26 memory used=1927.9MB, alloc=117.4MB, time=24.49 memory used=1967.7MB, alloc=117.4MB, time=24.68 memory used=2026.0MB, alloc=117.4MB, time=25.37 memory used=2067.1MB, alloc=117.4MB, time=25.63 memory used=2112.5MB, alloc=117.4MB, time=25.88 memory used=2159.3MB, alloc=117.4MB, time=26.11 memory used=2191.2MB, alloc=117.4MB, time=26.30 memory used=2227.7MB, alloc=117.4MB, time=26.51 memory used=2268.7MB, alloc=117.4MB, time=26.72 memory used=2316.2MB, alloc=117.4MB, time=26.92 memory used=2383.0MB, alloc=117.9MB, time=27.65 memory used=2420.2MB, alloc=117.9MB, time=27.89 memory used=2468.4MB, alloc=117.9MB, time=28.14 memory used=2510.4MB, alloc=117.9MB, time=28.37 memory used=2543.1MB, alloc=117.9MB, time=28.57 memory used=2580.0MB, alloc=117.9MB, time=28.77 memory used=2622.1MB, alloc=117.9MB, time=28.98 memory used=2670.4MB, alloc=117.9MB, time=29.19 memory used=2857.8MB, alloc=120.7MB, time=52.24 memory used=2913.6MB, alloc=120.7MB, time=52.88 memory used=2959.0MB, alloc=120.7MB, time=53.13 memory used=2992.8MB, alloc=120.7MB, time=53.32 memory used=3032.1MB, alloc=120.7MB, time=53.54 memory used=3078.2MB, alloc=120.7MB, time=53.75 memory used=3130.0MB, alloc=120.7MB, time=53.97 memory used=3164.6MB, alloc=120.7MB, time=54.15 memory used=3194.8MB, alloc=120.7MB, time=54.34 memory used=3226.5MB, alloc=120.7MB, time=54.52 memory used=3260.6MB, alloc=120.7MB, time=54.70 memory used=3297.2MB, alloc=120.7MB, time=54.91 memory used=3336.0MB, alloc=120.7MB, time=55.10 memory used=3377.8MB, alloc=120.7MB, time=55.30 memory used=3421.8MB, alloc=120.7MB, time=55.48 memory used=3468.8MB, alloc=120.7MB, time=55.66 memory used=3519.8MB, alloc=120.7MB, time=55.84 memory used=3548.2MB, alloc=131.8MB, time=56.00 memory used=3558.9MB, alloc=131.8MB, time=56.12 memory used=3570.1MB, alloc=131.8MB, time=56.26 memory used=3614.4MB, alloc=131.8MB, time=57.70 memory used=3668.0MB, alloc=131.8MB, time=58.00 memory used=3701.4MB, alloc=131.8MB, time=58.22 memory used=3740.4MB, alloc=131.8MB, time=58.46 memory used=3785.6MB, alloc=131.8MB, time=58.71 memory used=3837.2MB, alloc=131.8MB, time=58.96 memory used=3879.6MB, alloc=155.8MB, time=59.20 memory used=3920.5MB, alloc=155.8MB, time=59.45 memory used=3965.4MB, alloc=155.8MB, time=59.69 memory used=4014.8MB, alloc=155.8MB, time=59.93 memory used=4065.8MB, alloc=155.8MB, time=60.20 memory used=4121.2MB, alloc=155.8MB, time=60.45 memory used=4180.8MB, alloc=155.8MB, time=60.72 memory used=4244.5MB, alloc=155.8MB, time=60.98 memory used=4312.1MB, alloc=155.8MB, time=61.24 memory used=4386.2MB, alloc=155.8MB, time=61.51 memory used=4447.4MB, alloc=155.8MB, time=61.76 memory used=4485.5MB, alloc=155.8MB, time=61.94 memory used=4524.9MB, alloc=155.8MB, time=62.12 memory used=4566.1MB, alloc=155.8MB, time=62.32 memory used=4609.0MB, alloc=155.8MB, time=62.51 memory used=4654.0MB, alloc=155.8MB, time=62.69 memory used=4700.9MB, alloc=155.8MB, time=62.88 memory used=4750.2MB, alloc=155.8MB, time=63.07 memory used=4803.4MB, alloc=155.8MB, time=63.25 memory used=4859.1MB, alloc=155.8MB, time=63.45 memory used=4931.2MB, alloc=155.8MB, time=64.99 memory used=5006.6MB, alloc=155.8MB, time=65.38 memory used=5058.7MB, alloc=155.8MB, time=65.67 memory used=5122.7MB, alloc=155.8MB, time=66.00 memory used=5197.8MB, alloc=155.8MB, time=66.31 memory used=5240.3MB, alloc=155.8MB, time=66.55 memory used=5283.7MB, alloc=155.8MB, time=66.80 memory used=5330.2MB, alloc=155.8MB, time=67.05 memory used=5380.5MB, alloc=155.8MB, time=67.31 memory used=5435.5MB, alloc=155.8MB, time=67.57 memory used=5494.9MB, alloc=155.8MB, time=67.84 memory used=5558.3MB, alloc=155.8MB, time=68.10 memory used=5625.7MB, alloc=155.8MB, time=68.36 memory used=5696.7MB, alloc=155.8MB, time=68.62 memory used=5767.3MB, alloc=155.8MB, time=68.88 memory used=5806.2MB, alloc=155.8MB, time=69.06 memory used=5845.1MB, alloc=155.8MB, time=69.24 memory used=5886.6MB, alloc=155.8MB, time=69.42 memory used=5930.2MB, alloc=155.8MB, time=69.61 memory used=5975.5MB, alloc=155.8MB, time=69.80 memory used=6022.1MB, alloc=155.8MB, time=69.99 memory used=6071.8MB, alloc=155.8MB, time=70.18 memory used=6123.7MB, alloc=155.8MB, time=70.38 memory used=6178.4MB, alloc=155.8MB, time=70.58 memory used=6237.3MB, alloc=155.8MB, time=70.78 memory used=6333.1MB, alloc=155.8MB, time=108.44 memory used=6532.3MB, alloc=411.8MB, time=118.00 memory used=6606.1MB, alloc=411.8MB, time=118.66 memory used=6663.0MB, alloc=411.8MB, time=118.94 memory used=6715.0MB, alloc=411.8MB, time=119.20 memory used=6776.7MB, alloc=411.8MB, time=119.46 memory used=6850.2MB, alloc=411.8MB, time=119.74 memory used=6898.7MB, alloc=411.8MB, time=119.96 memory used=6942.5MB, alloc=411.8MB, time=120.17 memory used=6988.4MB, alloc=411.8MB, time=120.40 memory used=7037.9MB, alloc=411.8MB, time=120.61 memory used=7091.3MB, alloc=411.8MB, time=120.83 memory used=7148.0MB, alloc=411.8MB, time=121.04 memory used=7209.2MB, alloc=411.8MB, time=121.27 memory used=7275.7MB, alloc=411.8MB, time=121.51 memory used=7346.4MB, alloc=411.8MB, time=121.74 memory used=7552.7MB, alloc=411.8MB, time=122.52 memory used=7665.2MB, alloc=411.8MB, time=126.37 memory used=7722.3MB, alloc=411.8MB, time=126.64 memory used=7789.9MB, alloc=411.8MB, time=126.92 memory used=7839.4MB, alloc=411.8MB, time=127.13 memory used=7892.2MB, alloc=411.8MB, time=127.34 memory used=8027.6MB, alloc=411.8MB, time=129.65 memory used=8172.5MB, alloc=411.8MB, time=132.07 memory used=8291.1MB, alloc=411.8MB, time=152.81 memory used=8356.7MB, alloc=411.8MB, time=153.70 memory used=8408.8MB, alloc=411.8MB, time=153.98 memory used=8456.9MB, alloc=411.8MB, time=154.24 memory used=8515.1MB, alloc=411.8MB, time=154.51 memory used=8580.2MB, alloc=411.8MB, time=154.78 memory used=8617.6MB, alloc=411.8MB, time=154.98 memory used=8658.3MB, alloc=411.8MB, time=155.19 memory used=8702.2MB, alloc=411.8MB, time=155.40 memory used=8750.0MB, alloc=411.8MB, time=155.61 memory used=8802.3MB, alloc=411.8MB, time=155.83 memory used=8859.3MB, alloc=411.8MB, time=156.06 memory used=8920.0MB, alloc=411.8MB, time=156.29 memory used=9054.9MB, alloc=411.8MB, time=157.32 memory used=9191.1MB, alloc=411.8MB, time=159.24 memory used=9291.1MB, alloc=411.8MB, time=160.91 memory used=9401.7MB, alloc=435.8MB, time=163.35 memory used=9508.3MB, alloc=435.8MB, time=165.79 memory used=9609.9MB, alloc=459.8MB, time=168.35 memory used=9704.1MB, alloc=459.8MB, time=170.69 memory used=9802.1MB, alloc=483.8MB, time=173.13 memory used=9923.9MB, alloc=483.8MB, time=174.68 memory used=10011.9MB, alloc=483.8MB, time=175.38 memory used=10105.3MB, alloc=483.8MB, time=176.14 memory used=10192.5MB, alloc=483.8MB, time=176.79 memory used=10278.5MB, alloc=483.8MB, time=177.40 memory used=10378.4MB, alloc=483.8MB, time=178.19 memory used=10490.7MB, alloc=483.8MB, time=180.73 memory used=10567.3MB, alloc=483.8MB, time=181.25 memory used=10647.6MB, alloc=483.8MB, time=181.76 memory used=10722.1MB, alloc=483.8MB, time=182.23 memory used=10786.9MB, alloc=483.8MB, time=182.66 memory used=10863.7MB, alloc=483.8MB, time=183.09 |\^/| 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(); 1428256730 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 4 4 F := [9 x y + 4 x y - 4 x z + 11 z , -9 x + 10 x y z - 9 y + 16 z , 4 3 3 2 15 y + 18 y z - 4 y z - 5 x ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 4 3 2 G := [-18 x y z + 14 x z - 12 y - 14 z, -3 x y + 8 y + 15 y - 15 z , 2 2 -8 x y z + x y - 4 x z - 11 x] > Problem := [F,G]; 3 2 4 2 4 4 Problem := [[9 x y + 4 x y - 4 x z + 11 z , -9 x + 10 x y z - 9 y + 16 z , 4 3 3 2 2 2 3 15 y + 18 y z - 4 y z - 5 x ], [-18 x y z + 14 x z - 12 y - 14 z, 2 2 4 3 2 2 2 -3 x y + 8 y + 15 y - 15 z , -8 x y z + x y - 4 x z - 11 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=24.6MB, alloc=32.3MB, time=0.77 memory used=47.1MB, alloc=36.3MB, time=1.27 memory used=67.2MB, alloc=36.3MB, time=1.56 memory used=83.4MB, alloc=36.3MB, time=1.76 memory used=94.1MB, alloc=60.3MB, time=1.88 memory used=137.9MB, alloc=60.3MB, time=2.92 memory used=179.0MB, alloc=60.8MB, time=3.60 memory used=225.1MB, alloc=68.8MB, time=4.86 memory used=271.3MB, alloc=68.8MB, time=5.92 memory used=316.9MB, alloc=68.8MB, time=6.78 memory used=336.0MB, alloc=92.8MB, time=6.91 memory used=381.0MB, alloc=92.8MB, time=7.19 memory used=436.4MB, alloc=92.8MB, time=11.97 memory used=471.0MB, alloc=92.8MB, time=12.13 memory used=505.7MB, alloc=92.8MB, time=12.28 memory used=549.6MB, alloc=92.8MB, time=12.61 memory used=597.3MB, alloc=92.8MB, time=13.08 memory used=641.5MB, alloc=92.8MB, time=13.49 memory used=696.4MB, alloc=92.8MB, time=18.15 memory used=731.4MB, alloc=92.8MB, time=18.31 memory used=771.3MB, alloc=92.8MB, time=18.60 memory used=815.4MB, alloc=92.8MB, time=18.90 memory used=862.8MB, alloc=92.8MB, time=21.08 memory used=913.3MB, alloc=92.8MB, time=27.48 memory used=947.4MB, alloc=92.8MB, time=27.65 memory used=985.2MB, alloc=92.8MB, time=27.80 memory used=1015.7MB, alloc=92.8MB, time=27.92 memory used=1065.7MB, alloc=92.8MB, time=28.62 memory used=1116.9MB, alloc=92.8MB, time=31.25 memory used=1156.6MB, alloc=92.8MB, time=31.60 memory used=1195.6MB, alloc=92.8MB, time=31.96 memory used=1250.5MB, alloc=92.8MB, time=32.89 memory used=1290.5MB, alloc=92.8MB, time=33.78 memory used=1359.2MB, alloc=92.8MB, time=35.06 memory used=1419.0MB, alloc=92.8MB, time=37.35 memory used=1451.7MB, alloc=92.8MB, time=39.35 memory used=1488.6MB, alloc=92.8MB, time=39.76 memory used=1528.0MB, alloc=95.6MB, time=40.04 memory used=1562.4MB, alloc=95.6MB, time=40.21 memory used=1601.9MB, alloc=95.7MB, time=40.39 memory used=1635.4MB, alloc=95.7MB, time=40.55 memory used=1683.0MB, alloc=95.7MB, time=41.20 memory used=1718.7MB, alloc=95.7MB, time=44.66 memory used=1758.4MB, alloc=95.7MB, time=45.03 memory used=1806.4MB, alloc=95.7MB, time=48.73 memory used=1833.8MB, alloc=95.7MB, time=48.89 memory used=1896.3MB, alloc=351.7MB, time=50.21 memory used=1960.1MB, alloc=375.7MB, time=51.80 memory used=2050.3MB, alloc=375.7MB, time=53.88 memory used=2116.7MB, alloc=375.7MB, time=54.80 memory used=2170.9MB, alloc=375.7MB, time=55.32 memory used=2215.0MB, alloc=375.7MB, time=55.55 memory used=2248.6MB, alloc=375.7MB, time=55.76 memory used=2292.4MB, alloc=375.7MB, time=56.26 memory used=2345.8MB, alloc=375.7MB, time=56.88 memory used=2385.7MB, alloc=375.7MB, time=57.14 memory used=2429.4MB, alloc=375.7MB, time=57.36 memory used=2461.0MB, alloc=375.7MB, time=57.57 memory used=2507.5MB, alloc=375.7MB, time=58.09 memory used=2561.3MB, alloc=375.7MB, time=60.57 memory used=2622.9MB, alloc=375.7MB, time=67.37 memory used=2662.4MB, alloc=375.7MB, time=67.59 memory used=2699.6MB, alloc=375.7MB, time=67.80 memory used=2745.8MB, alloc=375.7MB, time=68.03 memory used=2779.5MB, alloc=375.7MB, time=68.23 memory used=2809.7MB, alloc=375.7MB, time=68.41 memory used=2844.2MB, alloc=375.7MB, time=68.62 memory used=2885.2MB, alloc=375.7MB, time=68.80 memory used=2939.4MB, alloc=375.7MB, time=69.41 memory used=2982.4MB, alloc=375.7MB, time=69.66 memory used=3016.7MB, alloc=375.7MB, time=69.87 memory used=3066.5MB, alloc=375.7MB, time=70.42 memory used=3107.7MB, alloc=375.7MB, time=70.69 memory used=3152.3MB, alloc=375.7MB, time=70.92 memory used=3184.5MB, alloc=375.7MB, time=71.12 memory used=3254.7MB, alloc=399.7MB, time=88.22 memory used=3329.7MB, alloc=399.7MB, time=88.74 memory used=3378.7MB, alloc=399.7MB, time=89.01 memory used=3443.1MB, alloc=399.7MB, time=89.28 memory used=3495.0MB, alloc=399.7MB, time=89.51 memory used=3540.8MB, alloc=399.7MB, time=89.71 memory used=3592.8MB, alloc=399.7MB, time=89.93 memory used=3653.0MB, alloc=399.7MB, time=90.14 memory used=3727.1MB, alloc=399.7MB, time=91.10 memory used=3802.5MB, alloc=399.7MB, time=91.86 memory used=3862.6MB, alloc=399.7MB, time=92.11 memory used=3942.4MB, alloc=399.7MB, time=92.47 memory used=4028.9MB, alloc=399.7MB, time=94.27 memory used=4102.0MB, alloc=399.7MB, time=95.00 memory used=4161.5MB, alloc=399.7MB, time=95.31 memory used=4215.3MB, alloc=399.7MB, time=95.59 memory used=4262.1MB, alloc=399.7MB, time=95.82 memory used=4317.6MB, alloc=399.7MB, time=96.08 memory used=4384.3MB, alloc=399.7MB, time=96.35 memory used=4469.0MB, alloc=399.7MB, time=109.06 memory used=4529.5MB, alloc=399.7MB, time=109.34 memory used=4575.8MB, alloc=399.7MB, time=109.60 memory used=4632.8MB, alloc=399.7MB, time=109.86 memory used=4700.6MB, alloc=399.7MB, time=110.13 memory used=4749.5MB, alloc=399.7MB, time=110.35 memory used=4790.1MB, alloc=399.7MB, time=110.55 memory used=4834.0MB, alloc=399.7MB, time=110.75 memory used=4881.8MB, alloc=399.7MB, time=110.96 memory used=4933.3MB, alloc=399.7MB, time=111.17 memory used=4989.7MB, alloc=399.7MB, time=111.38 memory used=5050.5MB, alloc=399.7MB, time=111.61 memory used=5116.3MB, alloc=399.7MB, time=111.83 memory used=5188.0MB, alloc=399.7MB, time=112.06 memory used=5345.3MB, alloc=399.7MB, time=112.73 memory used=5448.8MB, alloc=399.7MB, time=114.03 memory used=5503.9MB, alloc=399.7MB, time=114.28 memory used=5558.6MB, alloc=399.7MB, time=114.49 memory used=5606.9MB, alloc=399.7MB, time=114.69 memory used=5683.4MB, alloc=399.7MB, time=115.65 memory used=5764.5MB, alloc=399.7MB, time=116.81 memory used=5875.9MB, alloc=399.7MB, time=123.67 memory used=5930.8MB, alloc=399.7MB, time=123.95 memory used=5987.3MB, alloc=399.7MB, time=124.19 memory used=6091.2MB, alloc=399.7MB, time=126.11 memory used=6211.9MB, alloc=399.7MB, time=128.69 memory used=6327.7MB, alloc=399.7MB, time=131.07 memory used=6443.3MB, alloc=399.7MB, time=134.48 memory used=6557.5MB, alloc=399.7MB, time=138.73 memory used=6673.3MB, alloc=399.7MB, time=143.88 memory used=6788.4MB, alloc=399.7MB, time=150.19 memory used=6904.4MB, alloc=399.7MB, time=157.75 memory used=7020.9MB, alloc=399.7MB, time=165.90 memory used=7136.4MB, alloc=399.7MB, time=175.01 memory used=7253.2MB, alloc=399.7MB, time=185.10 memory used=7361.3MB, alloc=399.7MB, time=191.34 memory used=7423.6MB, alloc=399.7MB, time=191.69 memory used=7476.5MB, alloc=399.7MB, time=191.96 memory used=7541.8MB, alloc=399.7MB, time=192.53 memory used=7595.9MB, alloc=399.7MB, time=192.83 memory used=7644.2MB, alloc=399.7MB, time=193.08 |\^/| 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(); 1428257030 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 4 2 F := [4 y + 10 y z + 5 y z + 14, 17 x z + 11 x y z + 14 z + 9 y z , 3 2 3 -14 x z + 13 x y + 2 y + 15 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 3 2 G := [17 x z - 8 x z + 2 x z + 4 x , 11 y - 10 y - 17 y z + 15, 3 3 2 -10 x y - 15 x z + 2 x y ] > Problem := [F,G]; 3 2 3 2 4 2 Problem := [[4 y + 10 y z + 5 y z + 14, 17 x z + 11 x y z + 14 z + 9 y z , 3 2 3 3 2 2 3 2 -14 x z + 13 x y + 2 y + 15 x z], [17 x z - 8 x z + 2 x z + 4 x , 3 2 3 3 2 11 y - 10 y - 17 y z + 15, -10 x y - 15 x z + 2 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.88 memory used=46.8MB, alloc=32.3MB, time=1.41 memory used=66.0MB, alloc=56.3MB, time=1.95 memory used=106.5MB, alloc=60.3MB, time=3.02 memory used=146.7MB, alloc=60.3MB, time=4.05 memory used=187.5MB, alloc=68.3MB, time=5.11 memory used=224.6MB, alloc=92.3MB, time=6.12 memory used=288.4MB, alloc=92.3MB, time=7.51 memory used=348.8MB, alloc=116.3MB, time=9.13 memory used=415.6MB, alloc=116.3MB, time=10.67 memory used=483.1MB, alloc=372.3MB, time=12.44 memory used=572.2MB, alloc=396.3MB, time=14.64 memory used=684.8MB, alloc=396.3MB, time=17.25 memory used=794.1MB, alloc=396.3MB, time=19.68 memory used=903.7MB, alloc=420.3MB, time=22.38 memory used=1020.1MB, alloc=420.3MB, time=24.27 memory used=1136.2MB, alloc=420.3MB, time=26.23 memory used=1245.7MB, alloc=420.3MB, time=28.42 memory used=1376.9MB, alloc=444.3MB, time=31.38 memory used=1475.1MB, alloc=444.3MB, time=33.70 memory used=1600.7MB, alloc=444.3MB, time=36.97 memory used=1711.9MB, alloc=468.3MB, time=39.94 memory used=1832.4MB, alloc=468.3MB, time=43.28 memory used=1955.6MB, alloc=468.3MB, time=49.77 memory used=2044.2MB, alloc=468.3MB, time=50.54 memory used=2125.3MB, alloc=468.3MB, time=51.15 memory used=2249.2MB, alloc=468.3MB, time=53.71 memory used=2337.5MB, alloc=492.3MB, time=54.39 memory used=2434.5MB, alloc=492.3MB, time=54.99 memory used=2507.4MB, alloc=492.3MB, time=55.54 memory used=2595.9MB, alloc=492.3MB, time=56.10 memory used=2704.4MB, alloc=492.3MB, time=56.67 memory used=2775.9MB, alloc=492.3MB, time=57.13 memory used=2871.5MB, alloc=492.3MB, time=58.35 memory used=2970.9MB, alloc=492.3MB, time=59.01 memory used=3060.7MB, alloc=492.3MB, time=59.58 memory used=3138.0MB, alloc=492.3MB, time=60.11 memory used=3232.7MB, alloc=492.3MB, time=60.66 memory used=3337.0MB, alloc=492.3MB, time=61.19 memory used=3402.4MB, alloc=492.3MB, time=61.63 memory used=3532.7MB, alloc=492.3MB, time=81.90 memory used=3619.7MB, alloc=492.3MB, time=82.46 memory used=3719.0MB, alloc=492.3MB, time=83.02 memory used=3794.7MB, alloc=492.3MB, time=83.48 memory used=3869.9MB, alloc=492.3MB, time=83.93 memory used=3957.4MB, alloc=492.3MB, time=84.39 memory used=4060.1MB, alloc=492.3MB, time=84.87 memory used=4281.0MB, alloc=492.3MB, time=86.47 memory used=4381.4MB, alloc=492.3MB, time=87.10 memory used=4454.7MB, alloc=492.3MB, time=87.61 memory used=4538.0MB, alloc=492.3MB, time=88.16 memory used=4639.3MB, alloc=492.3MB, time=88.70 memory used=4727.0MB, alloc=492.3MB, time=89.20 memory used=4795.2MB, alloc=492.3MB, time=89.63 memory used=4906.0MB, alloc=492.3MB, time=90.85 memory used=5005.1MB, alloc=492.3MB, time=91.44 memory used=5077.5MB, alloc=492.3MB, time=91.99 memory used=5164.4MB, alloc=492.3MB, time=92.51 memory used=5271.0MB, alloc=492.3MB, time=93.09 memory used=5347.3MB, alloc=492.3MB, time=93.54 memory used=5433.8MB, alloc=492.3MB, time=97.40 memory used=5561.8MB, alloc=492.3MB, time=113.99 memory used=5647.6MB, alloc=492.3MB, time=114.53 memory used=5739.6MB, alloc=492.3MB, time=115.03 memory used=5811.1MB, alloc=492.3MB, time=115.45 memory used=5893.6MB, alloc=492.3MB, time=115.90 memory used=5990.0MB, alloc=492.3MB, time=116.36 memory used=6202.9MB, alloc=492.3MB, time=117.40 memory used=6319.9MB, alloc=492.3MB, time=119.66 memory used=6415.6MB, alloc=492.3MB, time=122.27 memory used=6531.0MB, alloc=492.3MB, time=124.50 memory used=6635.7MB, alloc=492.3MB, time=127.11 memory used=6692.3MB, alloc=492.3MB, time=128.45 memory used=6786.3MB, alloc=492.3MB, time=131.14 memory used=6889.3MB, alloc=492.3MB, time=132.10 memory used=6983.6MB, alloc=492.3MB, time=132.88 memory used=7065.9MB, alloc=492.3MB, time=133.49 memory used=7159.9MB, alloc=492.3MB, time=134.44 memory used=7270.5MB, alloc=492.3MB, time=137.04 memory used=7362.2MB, alloc=516.3MB, time=137.81 memory used=7465.4MB, alloc=516.3MB, time=138.52 memory used=7548.5MB, alloc=516.3MB, time=139.16 memory used=7649.0MB, alloc=516.3MB, time=139.83 memory used=7766.6MB, alloc=516.3MB, time=140.49 memory used=7855.4MB, alloc=516.3MB, time=141.08 memory used=7929.6MB, alloc=516.3MB, time=141.62 memory used=8010.9MB, alloc=516.3MB, time=142.17 memory used=8100.2MB, alloc=516.3MB, time=142.75 memory used=8200.5MB, alloc=516.3MB, time=143.29 memory used=8326.6MB, alloc=516.3MB, time=145.02 memory used=8428.6MB, alloc=516.3MB, time=145.71 memory used=8513.8MB, alloc=516.3MB, time=146.36 memory used=8615.2MB, alloc=516.3MB, time=147.04 memory used=8736.0MB, alloc=516.3MB, time=147.72 memory used=8819.9MB, alloc=516.3MB, time=148.31 memory used=8895.4MB, alloc=516.3MB, time=148.85 memory used=8977.1MB, alloc=516.3MB, time=149.40 memory used=9068.0MB, alloc=516.3MB, time=149.94 |\^/| 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(); 1428257330 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 3 2 2 F := [-8 x - 5 x y z - 2 x z - 8 z , -3 y z + 8 x z + 16 x y z - 9 x z , 3 2 2 -11 y z + 5 x y - x y - 20 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 2 3 G := [9 x y - 15 x y z - 4 y - 7 x , y z - 4 x z - 2 y - 4, 3 2 2 -11 x y + 11 x z - 20 y z - 19 z] > Problem := [F,G]; 4 2 2 3 Problem := [[-8 x - 5 x y z - 2 x z - 8 z , 3 2 2 3 2 2 -3 y z + 8 x z + 16 x y z - 9 x z , -11 y z + 5 x y - x y - 20 x], [ 2 2 2 3 2 3 2 3 9 x y - 15 x y z - 4 y - 7 x , y z - 4 x z - 2 y - 4, 3 2 2 -11 x y + 11 x z - 20 y z - 19 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.31 memory used=23.5MB, alloc=32.3MB, time=0.80 memory used=47.9MB, alloc=36.3MB, time=1.26 memory used=59.3MB, alloc=36.3MB, time=1.32 memory used=74.8MB, alloc=37.5MB, time=1.46 memory used=87.8MB, alloc=37.5MB, time=1.52 memory used=96.3MB, alloc=37.5MB, time=1.57 memory used=105.7MB, alloc=37.5MB, time=1.63 memory used=116.5MB, alloc=37.5MB, time=1.68 memory used=128.9MB, alloc=37.5MB, time=1.74 memory used=140.7MB, alloc=37.5MB, time=1.79 memory used=148.3MB, alloc=37.5MB, time=1.84 memory used=156.5MB, alloc=37.5MB, time=1.88 memory used=165.4MB, alloc=37.5MB, time=1.93 memory used=175.5MB, alloc=37.5MB, time=1.97 memory used=199.7MB, alloc=61.5MB, time=4.46 memory used=235.2MB, alloc=61.5MB, time=5.29 memory used=265.2MB, alloc=61.5MB, time=5.43 memory used=288.6MB, alloc=61.5MB, time=5.54 memory used=315.3MB, alloc=61.5MB, time=5.65 memory used=347.0MB, alloc=61.5MB, time=5.77 memory used=382.8MB, alloc=61.5MB, time=5.90 memory used=403.7MB, alloc=61.5MB, time=5.98 memory used=423.2MB, alloc=61.5MB, time=6.06 memory used=443.6MB, alloc=61.5MB, time=6.14 memory used=465.8MB, alloc=61.5MB, time=6.23 memory used=488.7MB, alloc=61.5MB, time=6.31 memory used=513.3MB, alloc=61.5MB, time=6.41 memory used=539.8MB, alloc=61.5MB, time=6.50 memory used=566.8MB, alloc=61.5MB, time=6.60 memory used=595.7MB, alloc=61.5MB, time=6.69 memory used=626.3MB, alloc=61.5MB, time=6.79 memory used=658.4MB, alloc=61.5MB, time=6.90 memory used=692.1MB, alloc=61.5MB, time=7.00 memory used=727.4MB, alloc=61.5MB, time=7.11 memory used=752.2MB, alloc=81.9MB, time=7.22 memory used=763.5MB, alloc=83.8MB, time=7.29 memory used=776.0MB, alloc=83.8MB, time=7.36 memory used=788.8MB, alloc=83.8MB, time=7.43 memory used=801.4MB, alloc=83.8MB, time=7.50 memory used=814.0MB, alloc=83.8MB, time=7.56 memory used=827.5MB, alloc=83.8MB, time=7.63 memory used=840.9MB, alloc=83.8MB, time=7.71 memory used=854.4MB, alloc=83.8MB, time=7.78 memory used=868.3MB, alloc=83.8MB, time=7.86 memory used=882.6MB, alloc=83.8MB, time=7.94 memory used=897.4MB, alloc=83.8MB, time=8.01 memory used=912.8MB, alloc=83.8MB, time=8.09 memory used=928.3MB, alloc=83.8MB, time=8.16 memory used=944.7MB, alloc=83.8MB, time=8.24 memory used=961.8MB, alloc=83.8MB, time=8.33 memory used=979.2MB, alloc=83.8MB, time=8.40 memory used=997.0MB, alloc=83.8MB, time=8.48 memory used=1016.1MB, alloc=83.8MB, time=8.56 memory used=1073.9MB, alloc=83.8MB, time=9.93 memory used=1116.8MB, alloc=83.8MB, time=10.86 memory used=1162.5MB, alloc=83.8MB, time=11.86 memory used=1198.1MB, alloc=83.8MB, time=12.51 memory used=1226.4MB, alloc=107.8MB, time=13.08 memory used=1265.7MB, alloc=107.8MB, time=13.30 memory used=1300.6MB, alloc=107.8MB, time=13.49 memory used=1343.7MB, alloc=107.8MB, time=13.71 memory used=1374.7MB, alloc=107.8MB, time=13.88 memory used=1402.0MB, alloc=107.8MB, time=14.04 memory used=1430.6MB, alloc=107.8MB, time=14.20 memory used=1461.9MB, alloc=107.8MB, time=14.36 memory used=1497.0MB, alloc=107.8MB, time=14.54 memory used=1533.9MB, alloc=107.8MB, time=14.71 memory used=1575.0MB, alloc=107.8MB, time=14.88 memory used=1618.5MB, alloc=107.8MB, time=15.08 memory used=1656.7MB, alloc=107.8MB, time=15.26 memory used=1679.7MB, alloc=107.8MB, time=15.39 memory used=1704.5MB, alloc=107.8MB, time=15.51 memory used=1730.0MB, alloc=107.8MB, time=15.64 memory used=1756.9MB, alloc=107.8MB, time=15.76 memory used=1785.1MB, alloc=107.8MB, time=15.89 memory used=1815.6MB, alloc=107.8MB, time=16.02 memory used=1847.7MB, alloc=107.8MB, time=16.14 memory used=1891.1MB, alloc=107.8MB, time=16.78 memory used=1935.8MB, alloc=107.8MB, time=17.03 memory used=1969.3MB, alloc=107.8MB, time=17.23 memory used=2011.5MB, alloc=107.8MB, time=17.45 memory used=2046.2MB, alloc=107.8MB, time=17.63 memory used=2073.5MB, alloc=107.8MB, time=17.81 memory used=2101.8MB, alloc=107.8MB, time=17.97 memory used=2132.9MB, alloc=107.8MB, time=18.13 memory used=2167.9MB, alloc=107.8MB, time=18.30 memory used=2204.4MB, alloc=107.8MB, time=18.47 memory used=2244.0MB, alloc=107.8MB, time=18.65 memory used=2288.3MB, alloc=107.8MB, time=18.84 memory used=2329.8MB, alloc=107.8MB, time=19.01 memory used=2353.8MB, alloc=107.8MB, time=19.13 memory used=2378.2MB, alloc=107.8MB, time=19.26 memory used=2403.7MB, alloc=107.8MB, time=19.38 memory used=2430.3MB, alloc=107.8MB, time=19.51 memory used=2458.5MB, alloc=107.8MB, time=19.63 memory used=2488.4MB, alloc=107.8MB, time=19.76 memory used=2520.4MB, alloc=107.8MB, time=19.88 memory used=2559.8MB, alloc=107.8MB, time=20.17 memory used=2621.4MB, alloc=107.8MB, time=53.15 memory used=2670.0MB, alloc=107.8MB, time=60.73 memory used=2706.0MB, alloc=107.8MB, time=60.93 memory used=2741.0MB, alloc=107.8MB, time=61.12 memory used=2770.1MB, alloc=107.8MB, time=61.27 memory used=2803.2MB, alloc=107.8MB, time=61.44 memory used=2839.8MB, alloc=107.8MB, time=61.63 memory used=2881.4MB, alloc=107.8MB, time=61.81 memory used=2924.9MB, alloc=107.8MB, time=62.00 memory used=2949.6MB, alloc=107.8MB, time=62.13 memory used=2972.5MB, alloc=107.8MB, time=62.26 memory used=2998.2MB, alloc=107.8MB, time=62.38 memory used=3024.8MB, alloc=107.8MB, time=62.52 memory used=3052.1MB, alloc=107.8MB, time=62.66 memory used=3080.1MB, alloc=107.8MB, time=62.79 memory used=3108.7MB, alloc=107.8MB, time=62.93 memory used=3138.0MB, alloc=107.8MB, time=63.07 memory used=3170.4MB, alloc=107.8MB, time=63.22 memory used=3203.5MB, alloc=107.8MB, time=63.38 memory used=3237.3MB, alloc=107.8MB, time=63.53 memory used=3271.7MB, alloc=107.8MB, time=63.69 memory used=3306.8MB, alloc=107.8MB, time=63.84 memory used=3344.9MB, alloc=107.8MB, time=64.01 memory used=3383.7MB, alloc=107.8MB, time=64.16 memory used=3423.1MB, alloc=107.8MB, time=64.33 memory used=3463.3MB, alloc=107.8MB, time=64.48 memory used=3506.3MB, alloc=107.8MB, time=64.65 memory used=3550.1MB, alloc=107.8MB, time=64.83 memory used=3573.0MB, alloc=107.8MB, time=64.95 memory used=3579.3MB, alloc=107.8MB, time=65.04 memory used=3587.5MB, alloc=107.8MB, time=65.12 memory used=3593.6MB, alloc=107.8MB, time=65.23 memory used=3602.1MB, alloc=107.8MB, time=65.32 memory used=3608.2MB, alloc=107.8MB, time=65.43 memory used=3616.6MB, alloc=107.8MB, time=65.52 memory used=3625.4MB, alloc=107.8MB, time=65.62 memory used=3634.2MB, alloc=107.8MB, time=65.72 memory used=3642.9MB, alloc=107.8MB, time=65.83 memory used=3651.7MB, alloc=107.8MB, time=65.93 memory used=3660.5MB, alloc=107.8MB, time=66.04 memory used=3669.4MB, alloc=107.8MB, time=66.14 memory used=3678.2MB, alloc=107.8MB, time=66.25 memory used=3687.0MB, alloc=107.8MB, time=66.35 memory used=3695.9MB, alloc=107.8MB, time=66.44 memory used=3704.7MB, alloc=107.8MB, time=66.56 memory used=3713.6MB, alloc=107.8MB, time=66.65 memory used=3722.4MB, alloc=107.8MB, time=66.75 memory used=3731.3MB, alloc=107.8MB, time=66.84 memory used=3740.2MB, alloc=107.8MB, time=66.93 memory used=3749.1MB, alloc=107.8MB, time=67.04 memory used=3758.0MB, alloc=107.8MB, time=67.13 memory used=3766.9MB, alloc=107.8MB, time=67.24 memory used=3775.8MB, alloc=107.8MB, time=67.34 memory used=3784.7MB, alloc=107.8MB, time=67.43 memory used=3793.6MB, alloc=107.8MB, time=67.53 memory used=3802.5MB, alloc=107.8MB, time=67.62 memory used=3811.4MB, alloc=107.8MB, time=67.71 memory used=3820.3MB, alloc=107.8MB, time=67.83 memory used=3829.3MB, alloc=107.8MB, time=67.92 memory used=3838.2MB, alloc=107.8MB, time=68.05 memory used=3847.1MB, alloc=107.8MB, time=68.17 memory used=3856.1MB, alloc=107.8MB, time=68.26 memory used=3865.0MB, alloc=107.8MB, time=68.36 memory used=3873.9MB, alloc=107.8MB, time=68.47 memory used=3882.9MB, alloc=107.8MB, time=68.59 memory used=3891.8MB, alloc=107.8MB, time=68.70 memory used=3900.7MB, alloc=107.8MB, time=68.79 memory used=3909.7MB, alloc=107.8MB, time=68.89 memory used=3918.6MB, alloc=107.8MB, time=69.00 memory used=3927.5MB, alloc=107.8MB, time=69.10 memory used=3936.5MB, alloc=107.8MB, time=69.20 memory used=3945.4MB, alloc=107.8MB, time=69.30 memory used=3954.3MB, alloc=107.8MB, time=69.41 memory used=3963.2MB, alloc=107.8MB, time=69.51 memory used=3972.2MB, alloc=107.8MB, time=69.62 memory used=3981.1MB, alloc=107.8MB, time=69.72 memory used=3990.0MB, alloc=107.8MB, time=69.80 memory used=3999.2MB, alloc=107.8MB, time=69.90 memory used=4010.7MB, alloc=107.8MB, time=69.99 memory used=4020.0MB, alloc=107.8MB, time=70.09 memory used=4031.5MB, alloc=107.8MB, time=70.21 memory used=4043.3MB, alloc=107.8MB, time=70.31 memory used=4055.1MB, alloc=107.8MB, time=70.41 memory used=4066.9MB, alloc=107.8MB, time=70.52 memory used=4078.7MB, alloc=107.8MB, time=70.62 memory used=4090.5MB, alloc=107.8MB, time=70.72 memory used=4102.2MB, alloc=107.8MB, time=70.82 memory used=4113.9MB, alloc=107.8MB, time=70.92 memory used=4125.7MB, alloc=107.8MB, time=71.01 memory used=4137.3MB, alloc=107.8MB, time=71.11 memory used=4149.0MB, alloc=107.8MB, time=71.21 memory used=4160.7MB, alloc=107.8MB, time=71.30 memory used=4172.3MB, alloc=107.8MB, time=71.41 memory used=4183.9MB, alloc=107.8MB, time=71.52 memory used=4195.4MB, alloc=107.8MB, time=71.61 memory used=4207.0MB, alloc=107.8MB, time=71.71 memory used=4218.5MB, alloc=107.8MB, time=71.81 memory used=4230.0MB, alloc=107.8MB, time=71.91 memory used=4241.5MB, alloc=107.8MB, time=72.01 memory used=4252.9MB, alloc=107.8MB, time=72.11 memory used=4264.3MB, alloc=107.8MB, time=72.24 memory used=4275.7MB, alloc=107.8MB, time=72.41 memory used=4287.3MB, alloc=107.8MB, time=72.55 memory used=4301.1MB, alloc=107.8MB, time=72.66 memory used=4312.8MB, alloc=107.8MB, time=72.77 memory used=4326.4MB, alloc=107.8MB, time=72.88 memory used=4340.4MB, alloc=107.8MB, time=72.98 memory used=4354.3MB, alloc=107.8MB, time=73.10 memory used=4368.1MB, alloc=107.8MB, time=73.21 memory used=4381.9MB, alloc=107.8MB, time=73.31 memory used=4395.6MB, alloc=107.8MB, time=73.42 memory used=4409.2MB, alloc=107.8MB, time=73.51 memory used=4422.8MB, alloc=107.8MB, time=73.62 memory used=4436.3MB, alloc=107.8MB, time=73.75 memory used=4449.7MB, alloc=107.8MB, time=73.86 memory used=4463.1MB, alloc=107.8MB, time=73.96 memory used=4476.7MB, alloc=107.8MB, time=74.06 memory used=4492.2MB, alloc=107.8MB, time=74.16 memory used=4507.9MB, alloc=107.8MB, time=74.29 memory used=4523.4MB, alloc=107.8MB, time=74.40 memory used=4538.9MB, alloc=107.8MB, time=74.50 memory used=4554.2MB, alloc=107.8MB, time=74.61 memory used=4569.4MB, alloc=107.8MB, time=74.71 memory used=4584.5MB, alloc=107.8MB, time=74.83 memory used=4599.4MB, alloc=107.8MB, time=74.96 memory used=4614.5MB, alloc=107.8MB, time=75.07 memory used=4631.2MB, alloc=107.8MB, time=75.19 memory used=4648.1MB, alloc=107.8MB, time=75.30 memory used=4664.8MB, alloc=107.8MB, time=75.39 memory used=4681.4MB, alloc=107.8MB, time=75.51 memory used=4697.6MB, alloc=107.8MB, time=75.62 memory used=4714.2MB, alloc=107.8MB, time=75.72 memory used=4731.7MB, alloc=107.8MB, time=75.88 memory used=4749.4MB, alloc=107.8MB, time=75.98 memory used=4766.8MB, alloc=107.8MB, time=76.10 memory used=4784.5MB, alloc=107.8MB, time=76.22 memory used=4802.7MB, alloc=107.8MB, time=76.33 memory used=4821.1MB, alloc=107.8MB, time=76.45 memory used=4839.7MB, alloc=107.8MB, time=76.56 memory used=4858.8MB, alloc=107.8MB, time=76.67 memory used=4875.6MB, alloc=107.8MB, time=76.78 memory used=4891.5MB, alloc=107.8MB, time=76.89 memory used=4906.2MB, alloc=107.8MB, time=76.98 memory used=4919.3MB, alloc=107.8MB, time=77.09 memory used=4931.5MB, alloc=107.8MB, time=77.18 memory used=4944.4MB, alloc=107.8MB, time=77.28 memory used=4957.8MB, alloc=107.8MB, time=77.39 memory used=4971.7MB, alloc=107.8MB, time=77.49 memory used=4984.8MB, alloc=107.8MB, time=77.60 memory used=4999.2MB, alloc=107.8MB, time=77.70 memory used=5013.9MB, alloc=107.8MB, time=77.83 memory used=5029.0MB, alloc=107.8MB, time=77.95 memory used=5047.2MB, alloc=107.8MB, time=78.21 memory used=5103.3MB, alloc=107.8MB, time=86.38 memory used=5136.7MB, alloc=131.8MB, time=86.61 memory used=5176.3MB, alloc=131.8MB, time=86.85 memory used=5218.1MB, alloc=131.8MB, time=87.09 memory used=5263.4MB, alloc=131.8MB, time=87.35 memory used=5312.5MB, alloc=131.8MB, time=87.62 memory used=5365.2MB, alloc=131.8MB, time=87.88 memory used=5422.5MB, alloc=131.8MB, time=88.16 memory used=5469.3MB, alloc=131.8MB, time=88.40 memory used=5503.2MB, alloc=131.8MB, time=88.62 memory used=5535.3MB, alloc=155.8MB, time=88.83 memory used=5577.4MB, alloc=155.8MB, time=89.05 memory used=5622.8MB, alloc=155.8MB, time=89.31 memory used=5669.7MB, alloc=155.8MB, time=89.57 memory used=5718.0MB, alloc=155.8MB, time=89.81 memory used=5767.8MB, alloc=155.8MB, time=90.07 memory used=5819.1MB, alloc=155.8MB, time=90.33 memory used=5871.7MB, alloc=155.8MB, time=90.57 memory used=5925.9MB, alloc=155.8MB, time=90.83 memory used=5982.0MB, alloc=155.8MB, time=91.11 memory used=6047.9MB, alloc=155.8MB, time=91.42 memory used=6116.1MB, alloc=155.8MB, time=91.70 memory used=6186.2MB, alloc=155.8MB, time=92.00 memory used=6257.9MB, alloc=155.8MB, time=92.31 memory used=6331.4MB, alloc=155.8MB, time=92.61 memory used=6406.6MB, alloc=155.8MB, time=92.91 memory used=6483.4MB, alloc=155.8MB, time=93.22 memory used=6561.9MB, alloc=155.8MB, time=93.51 memory used=6621.5MB, alloc=155.8MB, time=93.76 memory used=6657.0MB, alloc=179.8MB, time=93.95 memory used=6700.0MB, alloc=179.8MB, time=94.15 memory used=6744.8MB, alloc=179.8MB, time=94.35 memory used=6792.2MB, alloc=179.8MB, time=94.56 memory used=6840.1MB, alloc=179.8MB, time=94.77 memory used=6888.4MB, alloc=179.8MB, time=94.98 memory used=6937.3MB, alloc=179.8MB, time=95.18 memory used=6986.6MB, alloc=179.8MB, time=95.39 memory used=7036.3MB, alloc=179.8MB, time=95.59 memory used=7086.6MB, alloc=179.8MB, time=95.80 memory used=7137.2MB, alloc=179.8MB, time=96.01 memory used=7188.3MB, alloc=179.8MB, time=96.23 memory used=7239.9MB, alloc=179.8MB, time=96.43 memory used=7291.9MB, alloc=179.8MB, time=96.63 memory used=7344.3MB, alloc=179.8MB, time=96.84 memory used=7397.1MB, alloc=179.8MB, time=97.06 memory used=7450.4MB, alloc=179.8MB, time=97.27 memory used=7504.0MB, alloc=179.8MB, time=97.49 memory used=7558.1MB, alloc=179.8MB, time=97.70 memory used=7612.5MB, alloc=179.8MB, time=97.92 memory used=7667.3MB, alloc=179.8MB, time=98.13 memory used=7722.6MB, alloc=179.8MB, time=98.34 memory used=7778.2MB, alloc=179.8MB, time=98.57 memory used=7835.2MB, alloc=179.8MB, time=98.80 memory used=7904.7MB, alloc=179.8MB, time=99.04 memory used=7962.9MB, alloc=179.8MB, time=99.26 memory used=8033.1MB, alloc=179.8MB, time=99.51 memory used=8105.1MB, alloc=179.8MB, time=99.76 memory used=8177.7MB, alloc=179.8MB, time=100.02 memory used=8250.8MB, alloc=179.8MB, time=100.28 memory used=8324.3MB, alloc=179.8MB, time=100.54 memory used=8398.4MB, alloc=179.8MB, time=100.79 memory used=8472.9MB, alloc=179.8MB, time=101.05 memory used=8547.9MB, alloc=179.8MB, time=101.30 memory used=8623.4MB, alloc=179.8MB, time=101.57 memory used=8699.3MB, alloc=179.8MB, time=101.83 memory used=8775.7MB, alloc=179.8MB, time=102.09 memory used=8852.5MB, alloc=179.8MB, time=102.34 memory used=8929.6MB, alloc=179.8MB, time=102.59 memory used=9007.2MB, alloc=179.8MB, time=102.85 memory used=9085.2MB, alloc=179.8MB, time=103.10 memory used=9163.6MB, alloc=179.8MB, time=103.36 memory used=9242.3MB, alloc=179.8MB, time=103.61 memory used=9321.4MB, alloc=179.8MB, time=103.87 memory used=9400.9MB, alloc=179.8MB, time=104.12 memory used=9480.6MB, alloc=179.8MB, time=104.38 memory used=9560.7MB, alloc=179.8MB, time=104.64 memory used=9641.2MB, alloc=179.8MB, time=104.91 memory used=9723.2MB, alloc=179.8MB, time=105.18 memory used=9819.3MB, alloc=179.8MB, time=105.48 memory used=9916.9MB, alloc=179.8MB, time=105.78 memory used=10014.9MB, alloc=179.8MB, time=106.08 memory used=10113.2MB, alloc=179.8MB, time=106.38 memory used=10211.9MB, alloc=179.8MB, time=106.68 memory used=10254.6MB, alloc=179.8MB, time=106.86 memory used=10256.0MB, alloc=179.8MB, time=106.95 memory used=10256.7MB, alloc=179.8MB, time=107.04 memory used=10257.4MB, alloc=435.8MB, time=107.11 memory used=10391.6MB, alloc=435.8MB, time=107.83 memory used=10514.2MB, alloc=435.8MB, time=108.24 memory used=10630.9MB, alloc=435.8MB, time=108.66 memory used=10748.0MB, alloc=435.8MB, time=109.08 memory used=10866.8MB, alloc=435.8MB, time=109.49 memory used=10999.7MB, alloc=435.8MB, time=109.94 memory used=11134.4MB, alloc=435.8MB, time=110.39 memory used=11269.3MB, alloc=435.8MB, time=110.84 memory used=11404.5MB, alloc=435.8MB, time=111.28 memory used=11539.7MB, alloc=435.8MB, time=111.72 memory used=11675.0MB, alloc=435.8MB, time=112.17 memory used=11810.4MB, alloc=435.8MB, time=112.63 memory used=11947.4MB, alloc=435.8MB, time=113.08 memory used=12098.2MB, alloc=435.8MB, time=113.56 memory used=12250.4MB, alloc=435.8MB, time=114.05 memory used=12402.4MB, alloc=435.8MB, time=114.53 memory used=12554.1MB, alloc=435.8MB, time=115.00 memory used=12705.5MB, alloc=435.8MB, time=115.49 memory used=12858.2MB, alloc=435.8MB, time=115.97 memory used=13023.9MB, alloc=435.8MB, time=116.47 memory used=13190.5MB, alloc=435.8MB, time=116.98 memory used=13356.4MB, alloc=435.8MB, time=117.48 memory used=13521.5MB, alloc=435.8MB, time=118.00 memory used=13688.2MB, alloc=435.8MB, time=118.50 memory used=13865.0MB, alloc=435.8MB, time=119.02 memory used=14043.0MB, alloc=435.8MB, time=119.54 memory used=14219.6MB, alloc=435.8MB, time=120.07 memory used=14410.2MB, alloc=435.8MB, time=120.62 memory used=14598.9MB, alloc=435.8MB, time=121.17 memory used=14787.2MB, alloc=435.8MB, time=121.71 memory used=14984.6MB, alloc=435.8MB, time=122.26 memory used=15180.9MB, alloc=435.8MB, time=122.83 memory used=15388.7MB, alloc=435.8MB, time=123.41 memory used=15594.5MB, alloc=435.8MB, time=123.97 memory used=15806.3MB, alloc=435.8MB, time=124.56 memory used=16028.6MB, alloc=435.8MB, time=125.16 memory used=16258.0MB, alloc=435.8MB, time=125.78 memory used=16492.7MB, alloc=435.8MB, time=126.39 memory used=16730.8MB, alloc=435.8MB, time=127.00 memory used=16972.6MB, alloc=435.8MB, time=127.61 memory used=17222.5MB, alloc=435.8MB, time=128.23 memory used=17459.6MB, alloc=435.8MB, time=128.82 memory used=17658.6MB, alloc=435.8MB, time=129.32 memory used=17839.9MB, alloc=435.8MB, time=129.78 memory used=18028.9MB, alloc=435.8MB, time=130.23 memory used=18299.5MB, alloc=435.8MB, time=132.01 memory used=18395.6MB, alloc=435.8MB, time=132.36 memory used=18498.7MB, alloc=435.8MB, time=133.50 memory used=18610.7MB, alloc=435.8MB, time=142.09 memory used=18686.9MB, alloc=435.8MB, time=142.50 memory used=18771.5MB, alloc=435.8MB, time=142.91 memory used=18873.1MB, alloc=435.8MB, time=143.33 memory used=18956.2MB, alloc=435.8MB, time=143.72 memory used=19016.5MB, alloc=435.8MB, time=144.04 memory used=19073.2MB, alloc=435.8MB, time=144.35 memory used=19134.6MB, alloc=435.8MB, time=144.67 memory used=19199.2MB, alloc=435.8MB, time=144.96 memory used=19266.3MB, alloc=435.8MB, time=145.28 memory used=19336.2MB, alloc=435.8MB, time=145.62 memory used=19409.0MB, alloc=435.8MB, time=145.95 memory used=19492.8MB, alloc=435.8MB, time=146.31 memory used=19580.0MB, alloc=435.8MB, time=146.65 memory used=19670.3MB, alloc=435.8MB, time=147.03 memory used=19763.4MB, alloc=435.8MB, time=147.38 memory used=19859.4MB, alloc=435.8MB, time=147.76 memory used=19958.1MB, alloc=435.8MB, time=148.14 memory used=20058.5MB, alloc=435.8MB, time=148.50 memory used=20121.9MB, alloc=435.8MB, time=148.76 memory used=20173.1MB, alloc=435.8MB, time=148.97 memory used=20217.9MB, alloc=435.8MB, time=149.17 memory used=20265.3MB, alloc=435.8MB, time=149.38 memory used=20313.2MB, alloc=435.8MB, time=149.59 memory used=20361.6MB, alloc=435.8MB, time=149.80 memory used=20410.4MB, alloc=435.8MB, time=150.01 memory used=20459.7MB, alloc=435.8MB, time=150.22 memory used=20509.5MB, alloc=435.8MB, time=150.43 memory used=20559.7MB, alloc=435.8MB, time=150.64 memory used=20610.4MB, alloc=435.8MB, time=150.85 memory used=20661.5MB, alloc=435.8MB, time=151.06 memory used=20713.0MB, alloc=435.8MB, time=151.28 memory used=20765.0MB, alloc=435.8MB, time=151.49 memory used=20817.4MB, alloc=435.8MB, time=151.70 memory used=20870.3MB, alloc=435.8MB, time=151.91 memory used=20923.5MB, alloc=435.8MB, time=152.13 memory used=20977.2MB, alloc=435.8MB, time=152.34 memory used=21031.2MB, alloc=435.8MB, time=152.56 memory used=21085.7MB, alloc=435.8MB, time=152.77 memory used=21140.5MB, alloc=435.8MB, time=152.99 memory used=21195.8MB, alloc=435.8MB, time=153.21 memory used=21252.4MB, alloc=435.8MB, time=153.43 memory used=21321.4MB, alloc=435.8MB, time=153.68 memory used=21379.3MB, alloc=435.8MB, time=153.90 memory used=21449.1MB, alloc=435.8MB, time=154.15 memory used=21520.7MB, alloc=435.8MB, time=154.40 memory used=21592.8MB, alloc=435.8MB, time=154.66 memory used=21665.5MB, alloc=435.8MB, time=154.92 memory used=21738.6MB, alloc=435.8MB, time=155.18 memory used=21812.3MB, alloc=435.8MB, time=155.44 memory used=21886.5MB, alloc=435.8MB, time=155.70 memory used=21961.1MB, alloc=435.8MB, time=155.96 memory used=22036.2MB, alloc=435.8MB, time=156.21 memory used=22111.8MB, alloc=435.8MB, time=156.48 memory used=22187.8MB, alloc=435.8MB, time=156.74 memory used=22264.2MB, alloc=435.8MB, time=157.00 memory used=22341.1MB, alloc=435.8MB, time=157.26 memory used=22418.4MB, alloc=435.8MB, time=157.52 memory used=22496.0MB, alloc=435.8MB, time=157.78 memory used=22574.1MB, alloc=435.8MB, time=158.04 memory used=22652.6MB, alloc=435.8MB, time=158.31 memory used=22731.4MB, alloc=435.8MB, time=158.57 memory used=22810.5MB, alloc=435.8MB, time=158.83 memory used=22890.0MB, alloc=435.8MB, time=159.09 memory used=22969.9MB, alloc=435.8MB, time=159.35 memory used=23050.1MB, alloc=435.8MB, time=159.63 memory used=23131.8MB, alloc=435.8MB, time=159.91 memory used=23227.7MB, alloc=435.8MB, time=160.21 memory used=23325.1MB, alloc=435.8MB, time=160.51 memory used=23422.8MB, alloc=435.8MB, time=160.82 memory used=23520.9MB, alloc=435.8MB, time=161.12 memory used=23619.4MB, alloc=435.8MB, time=161.43 |\^/| 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(); 1428257630 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [4 x y + 5 x z + 9 x z - 18 z, -18 y z - 6 y z - 16, 3 3 2 10 x y - 17 y z - 4 x z - y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 G := [-12 y z - 13 x z + 10 y z + 20 x, -13 x y z - 12 x z + 9 x y - 8 z, 3 2 3 2 -9 x y + x y z + 2 y z + 17 x y] > Problem := [F,G]; 2 2 2 Problem := [[4 x y + 5 x z + 9 x z - 18 z, -18 y z - 6 y z - 16, 3 3 2 3 2 2 10 x y - 17 y z - 4 x z - y], [-12 y z - 13 x z + 10 y z + 20 x, 2 2 2 3 2 3 2 -13 x y z - 12 x z + 9 x y - 8 z, -9 x y + x y z + 2 y z + 17 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=25.7MB, alloc=32.3MB, time=0.86 memory used=45.1MB, alloc=56.3MB, time=1.37 memory used=85.4MB, alloc=60.3MB, time=2.41 memory used=125.1MB, alloc=60.3MB, time=3.42 memory used=165.6MB, alloc=84.3MB, time=4.50 memory used=233.6MB, alloc=92.3MB, time=5.94 memory used=302.6MB, alloc=92.3MB, time=7.50 memory used=371.1MB, alloc=116.3MB, time=9.17 memory used=447.5MB, alloc=372.3MB, time=11.25 memory used=540.9MB, alloc=372.3MB, time=13.50 memory used=625.8MB, alloc=396.3MB, time=15.44 memory used=742.1MB, alloc=396.3MB, time=18.04 memory used=863.7MB, alloc=396.3MB, time=20.80 memory used=976.0MB, alloc=420.3MB, time=23.76 memory used=1109.5MB, alloc=444.3MB, time=27.14 memory used=1223.0MB, alloc=444.3MB, time=29.82 memory used=1363.8MB, alloc=444.3MB, time=32.48 memory used=1499.8MB, alloc=444.3MB, time=35.12 memory used=1636.2MB, alloc=444.3MB, time=37.52 memory used=1740.4MB, alloc=444.3MB, time=39.10 memory used=1859.4MB, alloc=444.3MB, time=41.13 memory used=1995.0MB, alloc=468.3MB, time=44.15 memory used=2080.9MB, alloc=468.3MB, time=46.46 memory used=2188.5MB, alloc=468.3MB, time=49.07 memory used=2277.5MB, alloc=468.3MB, time=51.50 memory used=2416.3MB, alloc=468.3MB, time=53.65 memory used=2516.2MB, alloc=468.3MB, time=55.13 memory used=2608.0MB, alloc=468.3MB, time=56.09 memory used=2703.7MB, alloc=468.3MB, time=58.10 memory used=2797.9MB, alloc=468.3MB, time=60.44 memory used=2907.2MB, alloc=492.3MB, time=62.69 memory used=2972.0MB, alloc=492.3MB, time=64.65 memory used=3061.2MB, alloc=492.3MB, time=66.62 memory used=3166.6MB, alloc=492.3MB, time=69.01 memory used=3301.6MB, alloc=492.3MB, time=71.17 memory used=3424.7MB, alloc=492.3MB, time=73.58 memory used=3539.6MB, alloc=492.3MB, time=75.83 memory used=3604.5MB, alloc=492.3MB, time=77.67 memory used=3666.3MB, alloc=492.3MB, time=79.52 memory used=3745.2MB, alloc=492.3MB, time=82.17 memory used=3812.8MB, alloc=492.3MB, time=84.34 memory used=3869.7MB, alloc=492.3MB, time=86.08 memory used=3944.7MB, alloc=516.3MB, time=89.04 memory used=4001.8MB, alloc=516.3MB, time=90.71 memory used=4062.1MB, alloc=516.3MB, time=92.64 memory used=4116.6MB, alloc=516.3MB, time=94.37 memory used=4156.5MB, alloc=516.3MB, time=95.75 memory used=4193.5MB, alloc=516.3MB, time=97.19 memory used=4403.4MB, alloc=540.3MB, time=101.34 memory used=4616.1MB, alloc=564.3MB, time=106.73 memory used=4778.8MB, alloc=588.3MB, time=110.87 |\^/| 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(); 1428257930 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 3 F := [10 x z + 9 x y - 10 x z + 5 y , 4 x y z + 15 x z - 14 x + 11, 4 2 3 2 -2 x + 5 x y z - 12 y + 10 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 3 2 2 2 G := [14 x y z + 8 y + 13 y z + 7 y, 12 x y - 10 x y + 3 y z - 17 x z, 2 2 20 x + 12 y z + 16 z - 6] > Problem := [F,G]; 3 2 2 2 2 3 3 Problem := [[10 x z + 9 x y - 10 x z + 5 y , 4 x y z + 15 x z - 14 x + 11, 4 2 3 2 2 4 2 -2 x + 5 x y z - 12 y + 10 y z], [14 x y z + 8 y + 13 y z + 7 y, 3 2 2 2 2 2 12 x y - 10 x y + 3 y z - 17 x z, 20 x + 12 y z + 16 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=4.4MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=36.3MB, time=0.84 memory used=45.9MB, alloc=36.3MB, time=1.12 memory used=65.4MB, alloc=36.3MB, time=1.54 memory used=88.0MB, alloc=36.3MB, time=1.94 memory used=110.6MB, alloc=36.6MB, time=3.08 memory used=125.7MB, alloc=36.6MB, time=3.16 memory used=134.1MB, alloc=36.6MB, time=3.22 memory used=151.0MB, alloc=36.6MB, time=3.42 memory used=171.3MB, alloc=38.1MB, time=3.60 memory used=189.9MB, alloc=38.1MB, time=4.45 memory used=198.2MB, alloc=38.1MB, time=4.51 memory used=207.8MB, alloc=38.1MB, time=4.57 memory used=231.2MB, alloc=62.1MB, time=5.05 memory used=274.6MB, alloc=63.4MB, time=6.96 memory used=316.1MB, alloc=63.4MB, time=7.42 memory used=362.4MB, alloc=71.4MB, time=8.14 memory used=385.2MB, alloc=71.4MB, time=8.26 memory used=415.1MB, alloc=71.4MB, time=8.56 memory used=444.4MB, alloc=71.4MB, time=8.72 memory used=472.0MB, alloc=71.4MB, time=8.86 memory used=508.5MB, alloc=71.4MB, time=10.62 memory used=534.6MB, alloc=71.4MB, time=10.76 memory used=554.5MB, alloc=71.4MB, time=10.86 memory used=580.1MB, alloc=71.4MB, time=10.97 memory used=603.4MB, alloc=71.4MB, time=11.07 memory used=640.6MB, alloc=71.4MB, time=11.70 memory used=684.2MB, alloc=71.4MB, time=12.91 memory used=706.1MB, alloc=71.4MB, time=13.02 memory used=729.3MB, alloc=71.4MB, time=13.13 memory used=774.9MB, alloc=71.4MB, time=13.92 memory used=815.1MB, alloc=95.4MB, time=14.95 memory used=882.0MB, alloc=95.4MB, time=16.49 memory used=919.4MB, alloc=95.4MB, time=16.94 memory used=969.5MB, alloc=95.4MB, time=17.59 memory used=1012.2MB, alloc=95.4MB, time=17.95 memory used=1063.6MB, alloc=95.4MB, time=22.26 memory used=1098.9MB, alloc=95.4MB, time=22.45 memory used=1130.2MB, alloc=95.4MB, time=22.63 memory used=1157.7MB, alloc=95.4MB, time=22.78 memory used=1190.0MB, alloc=95.4MB, time=22.94 memory used=1227.9MB, alloc=95.4MB, time=23.12 memory used=1258.1MB, alloc=95.4MB, time=23.25 memory used=1281.0MB, alloc=95.4MB, time=23.39 memory used=1305.8MB, alloc=95.4MB, time=23.54 memory used=1332.1MB, alloc=95.4MB, time=23.69 memory used=1361.0MB, alloc=95.4MB, time=23.85 memory used=1390.6MB, alloc=95.4MB, time=23.98 memory used=1422.3MB, alloc=95.4MB, time=24.12 memory used=1458.2MB, alloc=95.4MB, time=24.26 memory used=1496.6MB, alloc=95.4MB, time=24.40 memory used=1514.9MB, alloc=107.8MB, time=24.54 memory used=1563.4MB, alloc=107.8MB, time=25.12 memory used=1630.9MB, alloc=107.8MB, time=26.99 memory used=1688.8MB, alloc=107.8MB, time=28.08 memory used=1759.5MB, alloc=107.8MB, time=29.42 memory used=1829.3MB, alloc=107.8MB, time=30.94 memory used=1898.2MB, alloc=107.8MB, time=33.40 memory used=1967.8MB, alloc=107.8MB, time=36.52 memory used=2036.8MB, alloc=107.8MB, time=40.13 memory used=2106.7MB, alloc=107.8MB, time=44.00 memory used=2172.7MB, alloc=107.8MB, time=46.33 memory used=2235.5MB, alloc=131.8MB, time=47.57 memory used=2298.5MB, alloc=131.8MB, time=51.06 memory used=2341.0MB, alloc=131.8MB, time=51.32 memory used=2389.8MB, alloc=131.8MB, time=51.57 memory used=2424.7MB, alloc=131.8MB, time=51.76 memory used=2466.0MB, alloc=131.8MB, time=51.97 memory used=2515.4MB, alloc=131.8MB, time=52.19 memory used=2545.6MB, alloc=131.8MB, time=52.36 memory used=2619.2MB, alloc=131.8MB, time=56.50 memory used=2661.9MB, alloc=131.8MB, time=56.75 memory used=2712.7MB, alloc=131.8MB, time=56.99 memory used=2747.1MB, alloc=131.8MB, time=57.18 memory used=2785.4MB, alloc=131.8MB, time=57.37 memory used=2830.2MB, alloc=131.8MB, time=57.58 memory used=2886.3MB, alloc=131.8MB, time=57.81 memory used=2964.6MB, alloc=387.8MB, time=59.25 memory used=3020.4MB, alloc=387.8MB, time=59.77 memory used=3063.1MB, alloc=387.8MB, time=59.97 memory used=3130.1MB, alloc=387.8MB, time=61.52 memory used=3200.1MB, alloc=387.8MB, time=62.25 memory used=3284.1MB, alloc=387.8MB, time=65.03 memory used=3334.5MB, alloc=387.8MB, time=65.35 memory used=3372.1MB, alloc=387.8MB, time=65.57 memory used=3412.9MB, alloc=387.8MB, time=65.78 memory used=3470.2MB, alloc=387.8MB, time=69.38 memory used=3512.0MB, alloc=387.8MB, time=69.63 memory used=3549.3MB, alloc=387.8MB, time=69.86 memory used=3597.3MB, alloc=387.8MB, time=70.10 memory used=3629.1MB, alloc=387.8MB, time=70.29 memory used=3663.1MB, alloc=387.8MB, time=70.48 memory used=3723.8MB, alloc=387.8MB, time=71.39 memory used=3814.7MB, alloc=387.8MB, time=72.66 memory used=3870.6MB, alloc=387.8MB, time=74.02 memory used=3930.1MB, alloc=387.8MB, time=74.56 memory used=3991.2MB, alloc=387.8MB, time=75.98 memory used=4050.9MB, alloc=387.8MB, time=76.50 memory used=4107.5MB, alloc=387.8MB, time=77.84 memory used=4193.8MB, alloc=387.8MB, time=79.28 memory used=4261.0MB, alloc=387.8MB, time=81.84 memory used=4307.2MB, alloc=387.8MB, time=82.16 memory used=4345.5MB, alloc=387.8MB, time=82.43 memory used=4403.2MB, alloc=411.8MB, time=89.53 memory used=4479.5MB, alloc=411.8MB, time=90.95 memory used=4532.2MB, alloc=411.8MB, time=91.28 memory used=4599.9MB, alloc=411.8MB, time=91.62 memory used=4642.7MB, alloc=411.8MB, time=91.89 memory used=4732.1MB, alloc=411.8MB, time=104.68 memory used=4779.6MB, alloc=411.8MB, time=104.99 memory used=4833.5MB, alloc=411.8MB, time=105.31 memory used=4897.7MB, alloc=411.8MB, time=105.64 memory used=4961.9MB, alloc=411.8MB, time=105.95 memory used=5003.2MB, alloc=411.8MB, time=106.21 memory used=5048.2MB, alloc=411.8MB, time=106.48 memory used=5097.6MB, alloc=411.8MB, time=106.75 memory used=5151.9MB, alloc=411.8MB, time=107.04 memory used=5238.6MB, alloc=411.8MB, time=108.60 memory used=5310.0MB, alloc=411.8MB, time=109.03 memory used=5398.0MB, alloc=411.8MB, time=109.90 memory used=5461.6MB, alloc=411.8MB, time=111.66 memory used=5523.7MB, alloc=411.8MB, time=112.06 memory used=5598.3MB, alloc=411.8MB, time=113.25 memory used=5720.5MB, alloc=411.8MB, time=115.32 memory used=5849.4MB, alloc=411.8MB, time=117.72 memory used=5977.2MB, alloc=411.8MB, time=123.66 memory used=6066.7MB, alloc=411.8MB, time=127.35 memory used=6151.4MB, alloc=411.8MB, time=131.97 memory used=6204.3MB, alloc=411.8MB, time=132.30 memory used=6317.4MB, alloc=411.8MB, time=134.30 memory used=6443.6MB, alloc=411.8MB, time=136.71 memory used=6565.5MB, alloc=411.8MB, time=140.47 memory used=6688.4MB, alloc=411.8MB, time=146.36 memory used=6760.2MB, alloc=411.8MB, time=148.08 memory used=6849.0MB, alloc=411.8MB, time=149.51 memory used=6958.7MB, alloc=435.8MB, time=151.13 memory used=7119.7MB, alloc=435.8MB, time=153.39 memory used=7274.6MB, alloc=435.8MB, time=160.20 memory used=7400.9MB, alloc=459.8MB, time=163.91 memory used=7507.5MB, alloc=459.8MB, time=165.04 memory used=7604.7MB, alloc=459.8MB, time=167.35 memory used=7673.6MB, alloc=459.8MB, time=167.76 memory used=7758.0MB, alloc=459.8MB, time=168.63 memory used=7856.8MB, alloc=459.8MB, time=170.20 memory used=7974.2MB, alloc=459.8MB, time=173.17 memory used=8048.7MB, alloc=459.8MB, time=173.81 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428258230 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 F := [4 x z + 13 x y + 10 z - 10, -6 x y z + 8 x y + 18 x z + 2 y , 3 2 2 4 2 -x z + 19 x y + 19 z - 11 x ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 4 2 G := [-4 x y z - 20 x z - 9 y z - 16 y, 9 x + 20 y - 7 y z - 13 y, 2 2 4 7 x y z - 20 x y z + 19 z - 7 y z] > Problem := [F,G]; 2 2 3 2 2 2 2 Problem := [[4 x z + 13 x y + 10 z - 10, -6 x y z + 8 x y + 18 x z + 2 y , 3 2 2 4 2 2 2 2 -x z + 19 x y + 19 z - 11 x ], [-4 x y z - 20 x z - 9 y z - 16 y, 4 4 2 2 2 4 9 x + 20 y - 7 y z - 13 y, 7 x y z - 20 x y z + 19 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=4.5MB, alloc=32.3MB, time=0.31 memory used=25.4MB, alloc=32.3MB, time=0.84 memory used=45.0MB, alloc=56.3MB, time=1.33 memory used=95.0MB, alloc=60.4MB, time=2.68 memory used=157.9MB, alloc=70.9MB, time=3.95 memory used=182.8MB, alloc=70.9MB, time=4.08 memory used=206.1MB, alloc=70.9MB, time=4.21 memory used=234.7MB, alloc=70.9MB, time=4.33 memory used=254.0MB, alloc=70.9MB, time=4.43 memory used=274.2MB, alloc=70.9MB, time=4.53 memory used=297.1MB, alloc=70.9MB, time=4.63 memory used=331.1MB, alloc=70.9MB, time=4.93 memory used=358.1MB, alloc=70.9MB, time=5.08 memory used=379.7MB, alloc=70.9MB, time=5.21 memory used=407.7MB, alloc=70.9MB, time=5.34 memory used=429.9MB, alloc=70.9MB, time=5.45 memory used=449.3MB, alloc=70.9MB, time=5.55 memory used=471.5MB, alloc=70.9MB, time=5.65 memory used=496.8MB, alloc=70.9MB, time=5.74 memory used=531.2MB, alloc=70.9MB, time=6.06 memory used=555.2MB, alloc=70.9MB, time=6.19 memory used=579.9MB, alloc=70.9MB, time=6.31 memory used=608.4MB, alloc=70.9MB, time=6.45 memory used=627.2MB, alloc=70.9MB, time=6.54 memory used=647.2MB, alloc=70.9MB, time=6.63 memory used=669.5MB, alloc=70.9MB, time=6.73 memory used=694.7MB, alloc=70.9MB, time=6.83 memory used=731.9MB, alloc=70.9MB, time=18.38 memory used=765.2MB, alloc=70.9MB, time=23.93 memory used=823.3MB, alloc=70.9MB, time=24.98 memory used=862.0MB, alloc=70.9MB, time=25.47 memory used=883.1MB, alloc=70.9MB, time=25.61 memory used=908.2MB, alloc=70.9MB, time=25.76 memory used=935.6MB, alloc=70.9MB, time=25.91 memory used=952.6MB, alloc=70.9MB, time=26.02 memory used=969.0MB, alloc=70.9MB, time=26.14 memory used=986.7MB, alloc=70.9MB, time=26.27 memory used=1005.7MB, alloc=70.9MB, time=26.39 memory used=1025.7MB, alloc=70.9MB, time=26.52 memory used=1046.6MB, alloc=70.9MB, time=26.65 memory used=1068.5MB, alloc=70.9MB, time=26.78 memory used=1091.4MB, alloc=70.9MB, time=26.90 memory used=1115.2MB, alloc=70.9MB, time=27.02 memory used=1139.9MB, alloc=70.9MB, time=27.15 memory used=1165.5MB, alloc=70.9MB, time=27.28 memory used=1192.0MB, alloc=70.9MB, time=27.41 memory used=1218.5MB, alloc=70.9MB, time=27.55 memory used=1235.0MB, alloc=94.9MB, time=27.67 memory used=1260.4MB, alloc=94.9MB, time=27.79 memory used=1285.6MB, alloc=94.9MB, time=27.91 memory used=1312.2MB, alloc=94.9MB, time=28.04 memory used=1339.6MB, alloc=94.9MB, time=28.18 memory used=1367.8MB, alloc=94.9MB, time=28.31 memory used=1396.5MB, alloc=94.9MB, time=28.44 memory used=1425.9MB, alloc=94.9MB, time=28.57 memory used=1456.0MB, alloc=94.9MB, time=28.69 memory used=1486.6MB, alloc=94.9MB, time=28.84 memory used=1517.9MB, alloc=94.9MB, time=28.97 memory used=1549.8MB, alloc=94.9MB, time=29.10 memory used=1582.6MB, alloc=94.9MB, time=29.24 memory used=1619.5MB, alloc=94.9MB, time=29.39 memory used=1657.5MB, alloc=94.9MB, time=29.53 memory used=1696.2MB, alloc=94.9MB, time=29.69 memory used=1735.6MB, alloc=94.9MB, time=29.84 memory used=1775.6MB, alloc=94.9MB, time=29.99 memory used=1816.4MB, alloc=94.9MB, time=30.15 memory used=1857.8MB, alloc=94.9MB, time=30.30 memory used=1899.9MB, alloc=94.9MB, time=30.46 memory used=1942.6MB, alloc=94.9MB, time=30.61 memory used=1986.0MB, alloc=94.9MB, time=30.77 memory used=2030.0MB, alloc=94.9MB, time=30.93 memory used=2074.6MB, alloc=94.9MB, time=31.08 memory used=2119.8MB, alloc=94.9MB, time=31.25 memory used=2167.9MB, alloc=94.9MB, time=31.41 memory used=2218.0MB, alloc=107.8MB, time=31.61 memory used=2228.9MB, alloc=107.8MB, time=31.70 memory used=2233.9MB, alloc=107.8MB, time=31.76 memory used=2238.5MB, alloc=107.8MB, time=31.85 memory used=2243.3MB, alloc=107.8MB, time=31.94 memory used=2248.2MB, alloc=107.8MB, time=32.06 memory used=2253.3MB, alloc=107.8MB, time=32.14 memory used=2258.4MB, alloc=107.8MB, time=32.23 memory used=2263.4MB, alloc=107.8MB, time=32.29 memory used=2268.5MB, alloc=107.8MB, time=32.39 memory used=2269.1MB, alloc=107.8MB, time=32.47 memory used=2273.7MB, alloc=107.8MB, time=32.56 memory used=2274.1MB, alloc=107.8MB, time=32.63 memory used=2278.8MB, alloc=107.8MB, time=32.70 memory used=2279.2MB, alloc=107.8MB, time=32.76 memory used=2283.9MB, alloc=107.8MB, time=32.84 memory used=2284.3MB, alloc=107.8MB, time=32.95 memory used=2284.5MB, alloc=107.8MB, time=33.01 memory used=2289.1MB, alloc=107.8MB, time=33.09 memory used=2289.5MB, alloc=107.8MB, time=33.19 memory used=2289.7MB, alloc=107.8MB, time=33.27 memory used=2294.1MB, alloc=363.8MB, time=33.34 memory used=2430.9MB, alloc=363.8MB, time=34.06 memory used=2576.2MB, alloc=363.8MB, time=34.52 memory used=2731.9MB, alloc=363.8MB, time=35.00 memory used=2891.7MB, alloc=363.8MB, time=35.48 memory used=3061.6MB, alloc=363.8MB, time=35.99 memory used=3241.6MB, alloc=363.8MB, time=36.50 memory used=3425.1MB, alloc=363.8MB, time=37.03 memory used=3618.3MB, alloc=363.8MB, time=37.57 memory used=3821.0MB, alloc=363.8MB, time=38.14 memory used=4033.1MB, alloc=363.8MB, time=38.73 memory used=4254.4MB, alloc=363.8MB, time=39.33 memory used=4484.3MB, alloc=363.8MB, time=39.93 memory used=4729.5MB, alloc=363.8MB, time=40.55 memory used=4969.2MB, alloc=363.8MB, time=41.17 memory used=5196.8MB, alloc=363.8MB, time=41.76 memory used=5379.5MB, alloc=363.8MB, time=42.25 memory used=5564.4MB, alloc=363.8MB, time=42.75 memory used=5756.7MB, alloc=363.8MB, time=43.24 memory used=5953.6MB, alloc=363.8MB, time=43.76 memory used=6155.6MB, alloc=363.8MB, time=44.28 memory used=6365.9MB, alloc=363.8MB, time=44.81 memory used=6585.4MB, alloc=363.8MB, time=45.36 memory used=6811.9MB, alloc=363.8MB, time=45.91 memory used=7044.9MB, alloc=363.8MB, time=46.47 memory used=7289.2MB, alloc=363.8MB, time=47.05 memory used=7536.3MB, alloc=363.8MB, time=47.62 memory used=7765.5MB, alloc=363.8MB, time=48.15 memory used=7987.8MB, alloc=363.8MB, time=48.66 memory used=8208.3MB, alloc=363.8MB, time=49.14 memory used=8461.2MB, alloc=363.8MB, time=51.49 memory used=8529.7MB, alloc=363.8MB, time=53.01 memory used=8597.7MB, alloc=363.8MB, time=54.40 memory used=8668.5MB, alloc=363.8MB, time=55.91 memory used=8726.2MB, alloc=363.8MB, time=57.21 memory used=8797.0MB, alloc=363.8MB, time=59.45 memory used=8857.8MB, alloc=363.8MB, time=61.22 memory used=8907.8MB, alloc=363.8MB, time=63.17 memory used=8970.1MB, alloc=387.8MB, time=64.56 memory used=9041.1MB, alloc=387.8MB, time=74.26 memory used=9100.9MB, alloc=411.8MB, time=74.65 memory used=9155.9MB, alloc=411.8MB, time=75.00 memory used=9197.0MB, alloc=411.8MB, time=75.28 memory used=9243.5MB, alloc=411.8MB, time=75.61 memory used=9296.6MB, alloc=411.8MB, time=75.93 memory used=9353.9MB, alloc=411.8MB, time=76.26 memory used=9415.6MB, alloc=411.8MB, time=76.60 memory used=9481.5MB, alloc=411.8MB, time=76.94 memory used=9541.7MB, alloc=435.8MB, time=77.30 memory used=9592.2MB, alloc=459.8MB, time=77.62 memory used=9647.9MB, alloc=459.8MB, time=77.97 memory used=9705.6MB, alloc=459.8MB, time=78.31 memory used=9766.9MB, alloc=459.8MB, time=78.64 memory used=9830.3MB, alloc=459.8MB, time=78.98 memory used=9896.0MB, alloc=459.8MB, time=79.34 memory used=9963.8MB, alloc=459.8MB, time=79.70 memory used=10033.8MB, alloc=459.8MB, time=80.06 memory used=10105.8MB, alloc=459.8MB, time=80.43 memory used=10180.0MB, alloc=459.8MB, time=80.79 memory used=10256.3MB, alloc=459.8MB, time=81.16 memory used=10335.9MB, alloc=459.8MB, time=81.54 memory used=10428.8MB, alloc=459.8MB, time=81.95 memory used=10525.4MB, alloc=459.8MB, time=82.35 memory used=10624.7MB, alloc=459.8MB, time=82.79 memory used=10726.6MB, alloc=459.8MB, time=83.23 memory used=10831.1MB, alloc=459.8MB, time=83.65 memory used=10938.2MB, alloc=459.8MB, time=84.09 memory used=11017.5MB, alloc=459.8MB, time=84.43 memory used=11066.2MB, alloc=483.8MB, time=84.70 memory used=11124.9MB, alloc=483.8MB, time=84.99 memory used=11187.6MB, alloc=483.8MB, time=85.30 memory used=11251.6MB, alloc=483.8MB, time=85.60 memory used=11317.5MB, alloc=483.8MB, time=85.90 memory used=11384.3MB, alloc=483.8MB, time=86.20 memory used=11451.9MB, alloc=483.8MB, time=86.51 memory used=11520.2MB, alloc=483.8MB, time=86.82 memory used=11589.3MB, alloc=483.8MB, time=87.13 memory used=11659.1MB, alloc=483.8MB, time=87.43 memory used=11729.7MB, alloc=483.8MB, time=87.74 memory used=11800.9MB, alloc=483.8MB, time=88.05 memory used=11872.9MB, alloc=483.8MB, time=88.36 memory used=11945.7MB, alloc=483.8MB, time=88.68 memory used=12019.1MB, alloc=483.8MB, time=88.99 memory used=12093.2MB, alloc=483.8MB, time=89.31 memory used=12168.0MB, alloc=483.8MB, time=89.62 memory used=12243.5MB, alloc=483.8MB, time=89.94 memory used=12319.7MB, alloc=483.8MB, time=90.26 memory used=12396.5MB, alloc=483.8MB, time=90.57 memory used=12474.0MB, alloc=483.8MB, time=90.89 memory used=12552.1MB, alloc=483.8MB, time=91.20 memory used=12630.9MB, alloc=483.8MB, time=91.53 memory used=12710.4MB, alloc=483.8MB, time=91.86 memory used=12790.4MB, alloc=483.8MB, time=92.18 memory used=12871.1MB, alloc=483.8MB, time=92.50 memory used=12952.5MB, alloc=483.8MB, time=92.83 memory used=13034.4MB, alloc=483.8MB, time=93.15 memory used=13116.9MB, alloc=483.8MB, time=93.48 memory used=13200.0MB, alloc=483.8MB, time=93.80 memory used=13283.7MB, alloc=483.8MB, time=94.13 memory used=13368.0MB, alloc=483.8MB, time=94.46 memory used=13452.8MB, alloc=483.8MB, time=94.79 memory used=13538.2MB, alloc=483.8MB, time=95.13 memory used=13624.2MB, alloc=483.8MB, time=95.46 memory used=13710.7MB, alloc=483.8MB, time=95.79 memory used=13797.8MB, alloc=483.8MB, time=96.13 memory used=13885.4MB, alloc=483.8MB, time=96.46 memory used=13973.5MB, alloc=483.8MB, time=96.79 memory used=14062.2MB, alloc=483.8MB, time=97.13 memory used=14151.4MB, alloc=483.8MB, time=97.46 memory used=14241.0MB, alloc=483.8MB, time=97.80 memory used=14331.2MB, alloc=483.8MB, time=98.14 memory used=14422.0MB, alloc=483.8MB, time=98.49 memory used=14515.3MB, alloc=483.8MB, time=98.83 memory used=14608.4MB, alloc=483.8MB, time=99.18 memory used=14720.0MB, alloc=483.8MB, time=99.56 memory used=14816.4MB, alloc=483.8MB, time=99.92 memory used=14929.5MB, alloc=483.8MB, time=100.31 memory used=15046.7MB, alloc=483.8MB, time=100.70 memory used=15164.6MB, alloc=483.8MB, time=101.09 memory used=15283.1MB, alloc=483.8MB, time=101.49 memory used=15403.4MB, alloc=483.8MB, time=101.89 memory used=15551.1MB, alloc=483.8MB, time=102.37 memory used=15702.2MB, alloc=483.8MB, time=102.85 memory used=15848.1MB, alloc=483.8MB, time=103.33 memory used=16015.1MB, alloc=483.8MB, time=103.91 memory used=16128.8MB, alloc=483.8MB, time=104.37 memory used=16243.1MB, alloc=483.8MB, time=104.82 memory used=16344.5MB, alloc=483.8MB, time=105.24 memory used=16464.5MB, alloc=483.8MB, time=105.69 memory used=16568.4MB, alloc=483.8MB, time=106.12 memory used=16689.5MB, alloc=483.8MB, time=106.59 memory used=16815.1MB, alloc=483.8MB, time=107.06 memory used=16941.1MB, alloc=483.8MB, time=107.53 memory used=17067.6MB, alloc=483.8MB, time=108.02 memory used=17194.6MB, alloc=483.8MB, time=108.50 memory used=17321.9MB, alloc=483.8MB, time=108.98 memory used=17449.7MB, alloc=483.8MB, time=109.45 memory used=17577.8MB, alloc=483.8MB, time=109.93 memory used=17706.4MB, alloc=483.8MB, time=110.41 memory used=17835.3MB, alloc=483.8MB, time=110.89 memory used=17964.6MB, alloc=483.8MB, time=111.36 memory used=18094.3MB, alloc=483.8MB, time=111.83 memory used=18224.2MB, alloc=483.8MB, time=112.32 memory used=18354.5MB, alloc=483.8MB, time=112.79 memory used=18485.0MB, alloc=483.8MB, time=113.26 memory used=18615.9MB, alloc=483.8MB, time=113.73 memory used=18747.0MB, alloc=483.8MB, time=114.21 memory used=18878.4MB, alloc=483.8MB, time=114.68 memory used=19010.0MB, alloc=483.8MB, time=115.16 memory used=19141.8MB, alloc=483.8MB, time=115.65 memory used=19277.2MB, alloc=483.8MB, time=116.14 memory used=19411.3MB, alloc=483.8MB, time=116.63 memory used=19565.3MB, alloc=483.8MB, time=117.16 memory used=19703.0MB, alloc=483.8MB, time=117.65 memory used=19857.5MB, alloc=483.8MB, time=118.18 memory used=20017.1MB, alloc=483.8MB, time=118.73 memory used=20176.8MB, alloc=483.8MB, time=119.26 memory used=20336.7MB, alloc=483.8MB, time=119.80 memory used=20496.7MB, alloc=483.8MB, time=120.33 memory used=20656.8MB, alloc=483.8MB, time=120.87 memory used=20817.0MB, alloc=483.8MB, time=121.42 memory used=20977.2MB, alloc=483.8MB, time=121.96 memory used=21137.4MB, alloc=483.8MB, time=122.50 memory used=21297.7MB, alloc=483.8MB, time=123.04 memory used=21457.9MB, alloc=483.8MB, time=123.57 memory used=21618.0MB, alloc=483.8MB, time=124.11 memory used=21782.1MB, alloc=483.8MB, time=124.66 memory used=21965.0MB, alloc=483.8MB, time=125.24 memory used=22130.6MB, alloc=483.8MB, time=125.79 memory used=22311.3MB, alloc=483.8MB, time=126.37 memory used=22497.3MB, alloc=483.8MB, time=126.95 memory used=22683.1MB, alloc=483.8MB, time=127.54 memory used=22868.5MB, alloc=483.8MB, time=128.13 memory used=23053.6MB, alloc=483.8MB, time=128.71 memory used=23238.2MB, alloc=483.8MB, time=129.29 memory used=23422.4MB, alloc=483.8MB, time=129.85 memory used=23606.2MB, alloc=483.8MB, time=130.44 memory used=23793.8MB, alloc=483.8MB, time=131.03 memory used=23998.4MB, alloc=483.8MB, time=131.65 memory used=24206.3MB, alloc=483.8MB, time=132.28 memory used=24413.3MB, alloc=483.8MB, time=132.89 memory used=24619.5MB, alloc=483.8MB, time=133.50 memory used=24824.6MB, alloc=483.8MB, time=134.11 memory used=25028.7MB, alloc=483.8MB, time=134.73 memory used=25236.5MB, alloc=483.8MB, time=135.34 memory used=25459.2MB, alloc=483.8MB, time=135.98 memory used=25684.8MB, alloc=483.8MB, time=136.63 memory used=25908.7MB, alloc=483.8MB, time=137.27 memory used=26130.8MB, alloc=483.8MB, time=137.92 memory used=26356.3MB, alloc=483.8MB, time=138.56 memory used=26594.5MB, alloc=483.8MB, time=139.23 memory used=26814.2MB, alloc=483.8MB, time=139.84 memory used=27004.0MB, alloc=483.8MB, time=140.41 memory used=27195.9MB, alloc=483.8MB, time=140.97 memory used=27399.1MB, alloc=483.8MB, time=141.56 memory used=27593.0MB, alloc=483.8MB, time=142.11 memory used=27787.3MB, alloc=483.8MB, time=142.68 memory used=27984.9MB, alloc=483.8MB, time=143.26 memory used=28159.5MB, alloc=483.8MB, time=143.78 memory used=28323.2MB, alloc=483.8MB, time=144.29 memory used=28495.8MB, alloc=483.8MB, time=144.80 memory used=28666.8MB, alloc=483.8MB, time=145.31 memory used=28835.7MB, alloc=483.8MB, time=145.82 memory used=29007.9MB, alloc=483.8MB, time=146.33 memory used=29187.3MB, alloc=483.8MB, time=146.85 memory used=29368.7MB, alloc=483.8MB, time=147.37 memory used=29547.3MB, alloc=483.8MB, time=147.88 memory used=29728.4MB, alloc=483.8MB, time=148.40 memory used=29913.5MB, alloc=483.8MB, time=148.93 memory used=30100.3MB, alloc=483.8MB, time=149.48 memory used=30291.3MB, alloc=483.8MB, time=150.00 memory used=30485.4MB, alloc=483.8MB, time=150.54 memory used=30685.5MB, alloc=483.8MB, time=151.09 memory used=30886.3MB, alloc=483.8MB, time=151.64 memory used=31095.8MB, alloc=483.8MB, time=152.19 memory used=31312.2MB, alloc=483.8MB, time=152.76 memory used=31533.3MB, alloc=483.8MB, time=153.33 |\^/| 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(); 1428258530 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 F := [-x z - 6 y z + 10 x y + 12 y z, 12 x y z + 4 x z - 4 x - 15 z, 3 3 -16 x y + 17 x y - 17 y + 20] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 3 3 2 G := [-20 x z - 16 y z - 9 x y + 2 y , 7 y z + 8 y z - 9 y + 8 y z , 2 2 2 3 8 x y + 8 x z + 17 y + 13 x z] > Problem := [F,G]; 3 3 2 2 Problem := [[-x z - 6 y z + 10 x y + 12 y z, 2 2 3 3 12 x y z + 4 x z - 4 x - 15 z, -16 x y + 17 x y - 17 y + 20], [ 3 3 2 2 2 3 3 2 -20 x z - 16 y z - 9 x y + 2 y , 7 y z + 8 y z - 9 y + 8 y z , 2 2 2 3 8 x y + 8 x z + 17 y + 13 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=24.2MB, alloc=32.3MB, time=0.80 memory used=43.3MB, alloc=36.3MB, time=1.27 memory used=62.1MB, alloc=60.3MB, time=1.76 memory used=105.7MB, alloc=60.4MB, time=2.33 memory used=132.3MB, alloc=60.4MB, time=2.44 memory used=156.2MB, alloc=60.4MB, time=2.53 memory used=185.2MB, alloc=60.4MB, time=2.62 memory used=213.0MB, alloc=60.4MB, time=2.91 memory used=262.0MB, alloc=60.4MB, time=3.98 memory used=308.2MB, alloc=60.4MB, time=4.64 memory used=348.0MB, alloc=60.4MB, time=5.20 memory used=374.5MB, alloc=60.4MB, time=5.31 memory used=396.1MB, alloc=60.4MB, time=5.41 memory used=419.2MB, alloc=60.4MB, time=5.51 memory used=447.0MB, alloc=60.4MB, time=5.61 memory used=473.6MB, alloc=60.4MB, time=5.71 memory used=491.2MB, alloc=60.4MB, time=5.78 memory used=510.7MB, alloc=60.4MB, time=5.86 memory used=531.9MB, alloc=60.4MB, time=5.93 memory used=555.2MB, alloc=60.4MB, time=6.01 memory used=590.1MB, alloc=60.4MB, time=6.32 memory used=623.9MB, alloc=61.1MB, time=6.76 memory used=649.1MB, alloc=61.1MB, time=6.87 memory used=671.8MB, alloc=61.1MB, time=6.96 memory used=698.9MB, alloc=61.1MB, time=7.06 memory used=728.7MB, alloc=61.1MB, time=7.17 memory used=746.7MB, alloc=61.1MB, time=7.24 memory used=766.0MB, alloc=61.1MB, time=7.32 memory used=787.2MB, alloc=61.1MB, time=7.39 memory used=811.1MB, alloc=61.1MB, time=7.47 memory used=849.0MB, alloc=61.1MB, time=7.84 memory used=898.0MB, alloc=69.1MB, time=8.85 memory used=943.9MB, alloc=93.1MB, time=9.87 memory used=1009.9MB, alloc=93.1MB, time=11.38 memory used=1073.9MB, alloc=93.1MB, time=12.67 memory used=1116.6MB, alloc=93.1MB, time=13.12 memory used=1161.8MB, alloc=93.1MB, time=13.59 memory used=1196.8MB, alloc=93.1MB, time=13.80 memory used=1224.8MB, alloc=93.1MB, time=13.97 memory used=1256.1MB, alloc=93.1MB, time=14.13 memory used=1295.8MB, alloc=93.1MB, time=14.43 memory used=1326.5MB, alloc=93.1MB, time=14.60 memory used=1355.2MB, alloc=93.1MB, time=14.76 memory used=1399.2MB, alloc=93.1MB, time=15.20 memory used=1428.6MB, alloc=93.1MB, time=15.37 memory used=1465.5MB, alloc=93.1MB, time=15.59 memory used=1507.3MB, alloc=93.1MB, time=15.93 memory used=1540.9MB, alloc=93.1MB, time=16.12 memory used=1566.5MB, alloc=93.1MB, time=16.27 memory used=1606.4MB, alloc=93.1MB, time=16.63 memory used=1637.0MB, alloc=93.1MB, time=16.80 memory used=1676.6MB, alloc=93.1MB, time=17.16 memory used=1724.4MB, alloc=93.1MB, time=18.02 memory used=1765.9MB, alloc=93.1MB, time=18.25 memory used=1790.4MB, alloc=93.1MB, time=18.43 memory used=1820.1MB, alloc=93.1MB, time=18.60 memory used=1853.4MB, alloc=93.1MB, time=18.78 memory used=1892.5MB, alloc=93.1MB, time=18.96 memory used=1915.8MB, alloc=117.1MB, time=19.13 memory used=1951.8MB, alloc=117.1MB, time=19.32 memory used=1991.4MB, alloc=117.1MB, time=19.51 memory used=2034.8MB, alloc=117.1MB, time=19.71 memory used=2083.0MB, alloc=117.1MB, time=19.91 memory used=2135.9MB, alloc=117.1MB, time=20.12 memory used=2194.8MB, alloc=117.1MB, time=20.32 memory used=2239.4MB, alloc=117.1MB, time=20.49 memory used=2273.4MB, alloc=117.1MB, time=20.62 memory used=2331.8MB, alloc=117.1MB, time=21.33 memory used=2382.2MB, alloc=117.1MB, time=21.59 memory used=2429.6MB, alloc=117.1MB, time=21.83 memory used=2489.4MB, alloc=117.1MB, time=22.07 memory used=2525.4MB, alloc=117.1MB, time=22.27 memory used=2562.5MB, alloc=117.1MB, time=22.47 memory used=2604.3MB, alloc=117.1MB, time=22.66 memory used=2649.8MB, alloc=117.1MB, time=22.85 memory used=2700.3MB, alloc=117.1MB, time=23.06 memory used=2755.8MB, alloc=117.1MB, time=23.26 memory used=2814.4MB, alloc=117.1MB, time=23.46 memory used=2848.3MB, alloc=117.1MB, time=23.60 memory used=2883.3MB, alloc=117.1MB, time=23.74 memory used=2972.7MB, alloc=117.2MB, time=65.98 memory used=3085.3MB, alloc=117.2MB, time=72.73 memory used=3136.0MB, alloc=117.2MB, time=72.99 memory used=3182.5MB, alloc=117.2MB, time=73.22 memory used=3223.0MB, alloc=117.2MB, time=73.43 memory used=3270.8MB, alloc=117.2MB, time=73.64 memory used=3325.1MB, alloc=117.2MB, time=73.85 memory used=3381.8MB, alloc=117.2MB, time=74.07 memory used=3414.1MB, alloc=117.2MB, time=74.23 memory used=3448.4MB, alloc=117.2MB, time=74.39 memory used=3484.1MB, alloc=117.2MB, time=74.55 memory used=3522.4MB, alloc=117.2MB, time=74.73 memory used=3563.5MB, alloc=117.2MB, time=74.89 memory used=3605.5MB, alloc=117.2MB, time=75.07 memory used=3650.1MB, alloc=117.2MB, time=75.24 memory used=3697.3MB, alloc=117.2MB, time=75.41 memory used=3747.0MB, alloc=117.2MB, time=75.59 memory used=3799.2MB, alloc=117.2MB, time=75.76 memory used=3853.5MB, alloc=117.2MB, time=75.95 memory used=3911.9MB, alloc=117.2MB, time=76.13 memory used=3976.7MB, alloc=117.2MB, time=76.33 memory used=3989.0MB, alloc=131.8MB, time=76.46 memory used=3998.1MB, alloc=131.8MB, time=76.57 memory used=4007.1MB, alloc=131.8MB, time=76.70 memory used=4016.4MB, alloc=131.8MB, time=76.81 memory used=4025.7MB, alloc=131.8MB, time=76.92 memory used=4034.9MB, alloc=131.8MB, time=77.04 memory used=4044.0MB, alloc=131.8MB, time=77.14 memory used=4053.2MB, alloc=131.8MB, time=77.25 memory used=4062.2MB, alloc=131.8MB, time=77.37 memory used=4071.3MB, alloc=131.8MB, time=77.48 memory used=4080.3MB, alloc=131.8MB, time=77.62 memory used=4089.5MB, alloc=131.8MB, time=77.72 memory used=4100.0MB, alloc=131.8MB, time=77.83 memory used=4109.2MB, alloc=131.8MB, time=77.93 memory used=4119.4MB, alloc=131.8MB, time=78.04 memory used=4129.9MB, alloc=131.8MB, time=78.14 memory used=4140.3MB, alloc=131.8MB, time=78.26 memory used=4150.6MB, alloc=131.8MB, time=78.38 memory used=4160.9MB, alloc=131.8MB, time=78.49 memory used=4171.1MB, alloc=131.8MB, time=78.60 memory used=4181.4MB, alloc=131.8MB, time=78.72 memory used=4192.8MB, alloc=131.8MB, time=78.84 memory used=4204.3MB, alloc=131.8MB, time=78.98 memory used=4215.8MB, alloc=131.8MB, time=79.11 memory used=4227.1MB, alloc=131.8MB, time=79.21 memory used=4238.2MB, alloc=131.8MB, time=79.35 memory used=4249.6MB, alloc=131.8MB, time=79.47 memory used=4261.7MB, alloc=131.8MB, time=79.60 memory used=4273.9MB, alloc=131.8MB, time=79.71 memory used=4285.9MB, alloc=131.8MB, time=79.82 memory used=4298.0MB, alloc=131.8MB, time=79.94 memory used=4310.6MB, alloc=131.8MB, time=80.05 memory used=4323.4MB, alloc=131.8MB, time=80.16 memory used=4336.2MB, alloc=131.8MB, time=80.27 memory used=4349.3MB, alloc=131.8MB, time=80.37 memory used=4362.7MB, alloc=131.8MB, time=80.52 memory used=4376.3MB, alloc=131.8MB, time=80.63 memory used=4390.2MB, alloc=131.8MB, time=80.74 memory used=4405.0MB, alloc=131.8MB, time=80.85 memory used=4419.6MB, alloc=131.8MB, time=80.98 memory used=4434.7MB, alloc=131.8MB, time=81.13 memory used=4450.2MB, alloc=131.8MB, time=81.25 memory used=4466.2MB, alloc=131.8MB, time=81.37 memory used=4536.3MB, alloc=131.8MB, time=82.28 memory used=4577.9MB, alloc=131.8MB, time=82.52 memory used=4629.7MB, alloc=131.8MB, time=82.76 memory used=4683.2MB, alloc=131.8MB, time=82.99 memory used=4717.7MB, alloc=131.8MB, time=83.19 memory used=4756.6MB, alloc=131.8MB, time=83.38 memory used=4799.3MB, alloc=131.8MB, time=83.58 memory used=4845.5MB, alloc=131.8MB, time=83.79 memory used=4896.4MB, alloc=131.8MB, time=84.00 memory used=4953.1MB, alloc=131.8MB, time=84.21 memory used=5005.4MB, alloc=131.8MB, time=84.40 memory used=5038.3MB, alloc=131.8MB, time=84.54 memory used=5079.0MB, alloc=131.8MB, time=84.79 memory used=5149.8MB, alloc=131.8MB, time=85.80 memory used=5195.7MB, alloc=131.8MB, time=86.05 memory used=5246.3MB, alloc=131.8MB, time=86.28 memory used=5302.4MB, alloc=131.8MB, time=86.51 memory used=5337.2MB, alloc=131.8MB, time=86.70 memory used=5374.9MB, alloc=131.8MB, time=86.88 memory used=5416.8MB, alloc=131.8MB, time=87.08 memory used=5462.4MB, alloc=131.8MB, time=87.28 memory used=5513.0MB, alloc=131.8MB, time=87.50 memory used=5570.0MB, alloc=131.8MB, time=87.72 memory used=5625.5MB, alloc=131.8MB, time=87.92 memory used=5659.0MB, alloc=131.8MB, time=88.06 memory used=5694.4MB, alloc=131.8MB, time=88.20 memory used=5782.2MB, alloc=131.8MB, time=118.30 memory used=5895.7MB, alloc=131.8MB, time=138.98 memory used=5952.9MB, alloc=131.8MB, time=139.30 memory used=6001.6MB, alloc=131.8MB, time=139.52 memory used=6040.1MB, alloc=131.8MB, time=139.73 memory used=6085.5MB, alloc=131.8MB, time=139.94 memory used=6137.3MB, alloc=131.8MB, time=140.17 memory used=6197.0MB, alloc=131.8MB, time=140.39 memory used=6232.3MB, alloc=131.8MB, time=140.56 memory used=6265.4MB, alloc=131.8MB, time=140.72 memory used=6300.8MB, alloc=131.8MB, time=140.88 memory used=6337.2MB, alloc=131.8MB, time=141.04 memory used=6376.3MB, alloc=131.8MB, time=141.21 memory used=6418.1MB, alloc=131.8MB, time=141.38 memory used=6460.7MB, alloc=131.8MB, time=141.56 memory used=6505.9MB, alloc=131.8MB, time=141.74 memory used=6553.6MB, alloc=131.8MB, time=141.91 memory used=6603.8MB, alloc=131.8MB, time=142.09 memory used=6656.3MB, alloc=131.8MB, time=142.28 memory used=6712.9MB, alloc=131.8MB, time=142.46 memory used=6771.3MB, alloc=131.8MB, time=142.64 memory used=6815.8MB, alloc=131.8MB, time=142.80 memory used=6825.4MB, alloc=131.8MB, time=142.92 memory used=6834.3MB, alloc=131.8MB, time=143.04 memory used=6843.7MB, alloc=131.8MB, time=143.14 memory used=6853.0MB, alloc=131.8MB, time=143.25 memory used=6862.3MB, alloc=131.8MB, time=143.35 memory used=6871.5MB, alloc=131.8MB, time=143.47 memory used=6880.7MB, alloc=131.8MB, time=143.57 memory used=6889.8MB, alloc=131.8MB, time=143.67 memory used=6899.0MB, alloc=131.8MB, time=143.77 memory used=6908.0MB, alloc=131.8MB, time=143.88 memory used=6917.1MB, alloc=131.8MB, time=143.99 memory used=6926.3MB, alloc=131.8MB, time=144.13 memory used=6936.8MB, alloc=131.8MB, time=144.24 memory used=6946.0MB, alloc=131.8MB, time=144.34 memory used=6956.3MB, alloc=131.8MB, time=144.46 memory used=6966.8MB, alloc=131.8MB, time=144.56 memory used=6977.2MB, alloc=131.8MB, time=144.69 memory used=6987.6MB, alloc=131.8MB, time=144.79 memory used=6997.9MB, alloc=131.8MB, time=144.89 memory used=7008.1MB, alloc=131.8MB, time=145.00 memory used=7018.4MB, alloc=131.8MB, time=145.10 memory used=7029.9MB, alloc=131.8MB, time=145.21 memory used=7041.4MB, alloc=131.8MB, time=145.32 memory used=7052.9MB, alloc=131.8MB, time=145.43 memory used=7064.2MB, alloc=131.8MB, time=145.56 memory used=7075.4MB, alloc=131.8MB, time=145.67 memory used=7086.7MB, alloc=131.8MB, time=145.78 memory used=7098.9MB, alloc=131.8MB, time=145.92 memory used=7111.1MB, alloc=131.8MB, time=146.04 memory used=7123.1MB, alloc=131.8MB, time=146.15 memory used=7135.2MB, alloc=131.8MB, time=146.27 memory used=7147.9MB, alloc=131.8MB, time=146.38 memory used=7160.6MB, alloc=131.8MB, time=146.49 memory used=7173.5MB, alloc=131.8MB, time=146.65 memory used=7186.5MB, alloc=131.8MB, time=146.77 memory used=7199.9MB, alloc=131.8MB, time=146.90 memory used=7213.6MB, alloc=131.8MB, time=147.01 memory used=7227.5MB, alloc=131.8MB, time=147.15 memory used=7242.3MB, alloc=131.8MB, time=147.26 memory used=7257.1MB, alloc=131.8MB, time=147.37 memory used=7272.1MB, alloc=131.8MB, time=147.50 memory used=7287.7MB, alloc=131.8MB, time=147.63 memory used=7303.7MB, alloc=131.8MB, time=147.73 memory used=7368.4MB, alloc=131.8MB, time=148.29 memory used=7417.4MB, alloc=131.8MB, time=148.48 memory used=7502.4MB, alloc=131.8MB, time=150.05 memory used=7608.3MB, alloc=131.8MB, time=173.68 memory used=7656.8MB, alloc=131.8MB, time=173.94 memory used=7698.6MB, alloc=131.8MB, time=174.16 memory used=7739.5MB, alloc=131.8MB, time=174.36 memory used=7787.6MB, alloc=131.8MB, time=174.58 memory used=7843.3MB, alloc=131.8MB, time=174.82 memory used=7884.9MB, alloc=131.8MB, time=175.01 memory used=7917.6MB, alloc=131.8MB, time=175.17 memory used=7951.6MB, alloc=131.8MB, time=175.33 memory used=7988.1MB, alloc=131.8MB, time=175.50 memory used=8027.0MB, alloc=131.8MB, time=175.69 memory used=8068.3MB, alloc=131.8MB, time=175.86 memory used=8111.8MB, alloc=131.8MB, time=176.03 memory used=8159.0MB, alloc=131.8MB, time=176.21 memory used=8208.1MB, alloc=131.8MB, time=176.38 memory used=8260.5MB, alloc=131.8MB, time=176.56 memory used=8316.0MB, alloc=131.8MB, time=176.74 memory used=8377.2MB, alloc=131.8MB, time=176.93 memory used=8387.1MB, alloc=131.8MB, time=177.07 memory used=8396.0MB, alloc=131.8MB, time=177.18 memory used=8405.9MB, alloc=131.8MB, time=177.31 memory used=8416.0MB, alloc=131.8MB, time=177.42 memory used=8426.0MB, alloc=131.8MB, time=177.53 memory used=8435.9MB, alloc=131.8MB, time=177.66 memory used=8445.7MB, alloc=131.8MB, time=177.77 memory used=8455.6MB, alloc=131.8MB, time=177.88 memory used=8466.3MB, alloc=131.8MB, time=178.00 memory used=8477.0MB, alloc=131.8MB, time=178.11 memory used=8487.6MB, alloc=131.8MB, time=178.22 memory used=8498.3MB, alloc=131.8MB, time=178.33 memory used=8509.5MB, alloc=131.8MB, time=178.45 memory used=8520.8MB, alloc=131.8MB, time=178.57 memory used=8532.1MB, alloc=131.8MB, time=178.68 memory used=8543.8MB, alloc=131.8MB, time=178.80 memory used=8555.7MB, alloc=131.8MB, time=178.91 memory used=8567.8MB, alloc=131.8MB, time=179.01 memory used=8580.2MB, alloc=131.8MB, time=179.13 memory used=8593.4MB, alloc=131.8MB, time=179.24 memory used=8606.7MB, alloc=131.8MB, time=179.36 memory used=8620.1MB, alloc=131.8MB, time=179.47 memory used=8634.1MB, alloc=131.8MB, time=179.58 memory used=8648.5MB, alloc=131.8MB, time=179.70 memory used=8730.5MB, alloc=387.8MB, time=181.01 memory used=8804.7MB, alloc=387.8MB, time=181.89 memory used=8896.6MB, alloc=387.8MB, time=183.90 |\^/| 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(); 1428258830 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [7 x y - 8 x y z + 3 x y z - 7 x, 7 x y z - 18 x y z + 4 x , 2 3 2 5 x y z - 15 y z + y z - 17 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 2 G := [18 x y z + 18 x y - 6 x y - 7 x, 7 z - 14 x z - 11 x y z + 18 y z , 2 2 -16 x y z + 3 x + 10 y z + 14 y] > Problem := [F,G]; 3 2 2 2 2 Problem := [[7 x y - 8 x y z + 3 x y z - 7 x, 7 x y z - 18 x y z + 4 x , 2 3 2 2 2 2 5 x y z - 15 y z + y z - 17 z ], [18 x y z + 18 x y - 6 x y - 7 x, 4 2 2 2 2 7 z - 14 x z - 11 x y z + 18 y z , -16 x y z + 3 x + 10 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=0.30 memory used=26.7MB, alloc=32.3MB, time=0.85 memory used=46.5MB, alloc=32.3MB, time=1.35 memory used=64.9MB, alloc=56.3MB, time=1.85 memory used=106.3MB, alloc=60.3MB, time=2.88 memory used=141.7MB, alloc=63.4MB, time=3.14 memory used=172.6MB, alloc=63.4MB, time=4.11 memory used=215.9MB, alloc=63.4MB, time=4.90 memory used=247.2MB, alloc=63.4MB, time=5.55 memory used=282.9MB, alloc=63.4MB, time=6.38 memory used=327.5MB, alloc=95.4MB, time=7.67 memory used=399.3MB, alloc=95.4MB, time=9.36 memory used=462.7MB, alloc=95.4MB, time=10.95 memory used=528.7MB, alloc=95.4MB, time=12.60 memory used=570.5MB, alloc=95.4MB, time=13.17 memory used=634.9MB, alloc=119.4MB, time=14.73 memory used=703.9MB, alloc=119.4MB, time=16.25 memory used=759.7MB, alloc=119.4MB, time=16.77 memory used=818.0MB, alloc=119.4MB, time=19.97 memory used=856.8MB, alloc=119.4MB, time=20.20 memory used=927.9MB, alloc=119.4MB, time=21.54 memory used=1017.4MB, alloc=119.4MB, time=22.81 memory used=1115.0MB, alloc=119.4MB, time=25.76 memory used=1187.6MB, alloc=375.4MB, time=28.56 memory used=1270.3MB, alloc=399.4MB, time=30.62 memory used=1356.7MB, alloc=399.4MB, time=34.11 memory used=1406.1MB, alloc=399.4MB, time=34.40 memory used=1460.7MB, alloc=399.4MB, time=34.67 memory used=1501.1MB, alloc=399.4MB, time=34.90 memory used=1564.4MB, alloc=399.4MB, time=35.33 memory used=1622.6MB, alloc=399.4MB, time=35.78 memory used=1679.4MB, alloc=399.4MB, time=36.12 memory used=1763.7MB, alloc=399.4MB, time=44.54 memory used=1811.1MB, alloc=399.4MB, time=44.83 memory used=1868.9MB, alloc=399.4MB, time=45.11 memory used=1909.6MB, alloc=399.4MB, time=45.36 memory used=1951.4MB, alloc=399.4MB, time=45.60 memory used=1999.8MB, alloc=399.4MB, time=45.83 memory used=2056.1MB, alloc=399.4MB, time=46.07 memory used=2183.6MB, alloc=399.4MB, time=48.22 memory used=2234.0MB, alloc=399.4MB, time=48.51 memory used=2284.0MB, alloc=399.4MB, time=48.78 memory used=2346.8MB, alloc=423.4MB, time=49.76 memory used=2419.5MB, alloc=423.4MB, time=50.55 memory used=2552.3MB, alloc=423.4MB, time=53.19 memory used=2636.6MB, alloc=423.4MB, time=58.52 memory used=2700.9MB, alloc=423.4MB, time=58.96 memory used=2825.4MB, alloc=423.4MB, time=61.90 memory used=2952.6MB, alloc=447.4MB, time=65.15 memory used=3056.4MB, alloc=447.4MB, time=67.02 memory used=3185.0MB, alloc=447.4MB, time=70.03 memory used=3313.2MB, alloc=471.4MB, time=73.19 memory used=3419.7MB, alloc=471.4MB, time=76.17 memory used=3533.4MB, alloc=495.4MB, time=78.72 memory used=3626.3MB, alloc=495.4MB, time=80.92 memory used=3711.8MB, alloc=495.4MB, time=82.83 memory used=3807.1MB, alloc=495.4MB, time=85.42 memory used=3903.7MB, alloc=495.4MB, time=88.12 memory used=3983.9MB, alloc=495.4MB, time=90.56 memory used=4064.7MB, alloc=519.4MB, time=92.68 memory used=4150.7MB, alloc=519.4MB, time=96.01 memory used=4267.1MB, alloc=519.4MB, time=99.33 memory used=4328.9MB, alloc=519.4MB, time=101.06 memory used=4410.4MB, alloc=519.4MB, time=103.34 memory used=4486.1MB, alloc=519.4MB, time=105.58 memory used=4550.3MB, alloc=519.4MB, time=107.72 memory used=4615.7MB, alloc=519.4MB, time=110.02 memory used=4672.3MB, alloc=519.4MB, time=112.01 memory used=4756.5MB, alloc=519.4MB, time=113.62 memory used=4876.8MB, alloc=519.4MB, time=116.52 memory used=4987.8MB, alloc=519.4MB, time=118.71 memory used=5095.7MB, alloc=519.4MB, time=125.75 memory used=5199.7MB, alloc=519.4MB, time=126.76 memory used=5292.1MB, alloc=519.4MB, time=128.84 memory used=5381.9MB, alloc=519.4MB, time=136.03 memory used=5475.0MB, alloc=519.4MB, time=136.81 memory used=5592.8MB, alloc=519.4MB, time=138.17 memory used=5720.1MB, alloc=519.4MB, time=145.93 memory used=5815.3MB, alloc=519.4MB, time=146.70 memory used=5934.8MB, alloc=519.4MB, time=149.16 memory used=6046.2MB, alloc=519.4MB, time=151.47 memory used=6158.9MB, alloc=519.4MB, time=153.28 memory used=6253.1MB, alloc=519.4MB, time=155.24 memory used=6336.2MB, alloc=519.4MB, time=158.76 memory used=6387.0MB, alloc=519.4MB, time=160.69 memory used=6635.8MB, alloc=543.4MB, time=167.82 |\^/| 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(); 1428259130 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 3 4 2 F := [15 x y z - 8 x z + z + 17 y z, -x y + 14 z - 11 x y + 14 z, 3 2 -8 y z - 2 x y z - 12 x + 11 x y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 3 2 G := [16 x y - 4 x y z - 17 y - 19, -17 x y - 19 y z + 12 x z + 12 x y, 2 2 2 -5 x y + 9 x y z + 13 x z + y z] > Problem := [F,G]; 2 3 4 3 4 2 Problem := [[15 x y z - 8 x z + z + 17 y z, -x y + 14 z - 11 x y + 14 z, 3 2 2 2 2 2 -8 y z - 2 x y z - 12 x + 11 x y], [16 x y - 4 x y z - 17 y - 19, 2 2 3 2 2 2 2 -17 x y - 19 y z + 12 x z + 12 x y, -5 x y + 9 x y z + 13 x z + y z] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=24.7MB, alloc=32.3MB, time=0.80 memory used=45.6MB, alloc=32.3MB, time=1.27 memory used=65.2MB, alloc=56.7MB, time=1.64 memory used=108.9MB, alloc=60.7MB, time=3.01 memory used=143.7MB, alloc=60.7MB, time=3.83 memory used=186.3MB, alloc=64.3MB, time=4.26 memory used=208.8MB, alloc=64.3MB, time=4.39 memory used=236.5MB, alloc=64.3MB, time=4.52 memory used=273.1MB, alloc=64.3MB, time=4.89 memory used=303.3MB, alloc=64.3MB, time=5.04 memory used=327.2MB, alloc=64.3MB, time=5.18 memory used=356.6MB, alloc=64.3MB, time=5.30 memory used=431.8MB, alloc=64.3MB, time=15.28 memory used=459.8MB, alloc=64.3MB, time=15.43 memory used=488.2MB, alloc=64.3MB, time=15.56 memory used=510.8MB, alloc=64.3MB, time=15.67 memory used=531.9MB, alloc=64.3MB, time=15.78 memory used=556.3MB, alloc=64.3MB, time=15.88 memory used=583.5MB, alloc=64.3MB, time=16.00 memory used=611.8MB, alloc=64.3MB, time=16.12 memory used=630.1MB, alloc=64.3MB, time=16.21 memory used=667.5MB, alloc=64.3MB, time=16.78 memory used=699.5MB, alloc=64.3MB, time=16.93 memory used=720.5MB, alloc=64.3MB, time=17.05 memory used=745.0MB, alloc=64.3MB, time=17.18 memory used=773.4MB, alloc=64.3MB, time=17.31 memory used=804.0MB, alloc=64.3MB, time=17.45 memory used=822.6MB, alloc=64.3MB, time=17.56 memory used=843.1MB, alloc=64.3MB, time=17.66 memory used=873.8MB, alloc=64.3MB, time=18.20 memory used=912.6MB, alloc=64.3MB, time=18.39 memory used=936.6MB, alloc=64.3MB, time=18.52 memory used=959.0MB, alloc=64.3MB, time=18.64 memory used=985.0MB, alloc=64.3MB, time=18.77 memory used=1015.6MB, alloc=64.3MB, time=18.89 memory used=1040.0MB, alloc=64.3MB, time=19.01 memory used=1059.1MB, alloc=64.3MB, time=19.12 memory used=1080.2MB, alloc=64.3MB, time=19.21 memory used=1124.0MB, alloc=64.3MB, time=30.50 memory used=1171.1MB, alloc=64.3MB, time=37.50 memory used=1194.1MB, alloc=64.3MB, time=37.62 memory used=1222.8MB, alloc=64.3MB, time=37.75 memory used=1246.4MB, alloc=64.3MB, time=37.87 memory used=1266.3MB, alloc=64.3MB, time=37.97 memory used=1288.2MB, alloc=64.3MB, time=38.08 memory used=1312.7MB, alloc=64.3MB, time=38.19 memory used=1340.2MB, alloc=64.3MB, time=38.30 memory used=1370.8MB, alloc=64.3MB, time=38.41 memory used=1395.1MB, alloc=64.3MB, time=38.51 memory used=1412.8MB, alloc=64.3MB, time=38.59 memory used=1431.5MB, alloc=64.3MB, time=38.67 memory used=1452.1MB, alloc=64.3MB, time=38.76 memory used=1484.8MB, alloc=64.3MB, time=39.05 memory used=1517.4MB, alloc=64.3MB, time=39.60 memory used=1554.3MB, alloc=64.3MB, time=41.05 memory used=1580.9MB, alloc=64.3MB, time=41.17 memory used=1602.1MB, alloc=64.3MB, time=41.27 memory used=1646.3MB, alloc=64.3MB, time=42.04 memory used=1700.8MB, alloc=64.3MB, time=46.77 memory used=1724.3MB, alloc=64.3MB, time=46.89 memory used=1750.2MB, alloc=64.3MB, time=47.01 memory used=1770.3MB, alloc=64.3MB, time=47.12 memory used=1793.6MB, alloc=64.3MB, time=47.23 memory used=1822.2MB, alloc=64.3MB, time=47.35 memory used=1862.0MB, alloc=64.3MB, time=48.12 memory used=1904.9MB, alloc=64.3MB, time=48.92 memory used=1945.0MB, alloc=64.3MB, time=49.99 memory used=1989.9MB, alloc=72.3MB, time=50.89 memory used=2033.6MB, alloc=72.3MB, time=51.73 memory used=2064.9MB, alloc=72.3MB, time=52.46 memory used=2084.6MB, alloc=72.3MB, time=52.58 memory used=2126.0MB, alloc=72.3MB, time=53.34 memory used=2168.5MB, alloc=96.3MB, time=54.32 memory used=2230.9MB, alloc=96.3MB, time=55.45 memory used=2269.8MB, alloc=96.3MB, time=55.77 memory used=2322.9MB, alloc=96.3MB, time=57.03 memory used=2351.5MB, alloc=96.3MB, time=57.22 memory used=2385.9MB, alloc=96.3MB, time=57.41 memory used=2426.9MB, alloc=96.3MB, time=57.61 memory used=2455.4MB, alloc=96.3MB, time=57.77 memory used=2478.3MB, alloc=96.3MB, time=57.94 memory used=2503.2MB, alloc=96.3MB, time=58.11 memory used=2531.2MB, alloc=96.3MB, time=58.27 memory used=2560.2MB, alloc=96.3MB, time=58.43 memory used=2592.4MB, alloc=96.3MB, time=58.59 memory used=2625.4MB, alloc=96.3MB, time=58.75 memory used=2661.6MB, alloc=96.3MB, time=58.93 memory used=2698.8MB, alloc=96.3MB, time=59.10 memory used=2737.9MB, alloc=96.3MB, time=59.28 memory used=2770.1MB, alloc=96.3MB, time=59.42 memory used=2791.6MB, alloc=96.3MB, time=59.55 memory used=2813.0MB, alloc=96.3MB, time=59.68 memory used=2835.7MB, alloc=96.3MB, time=59.81 memory used=2858.3MB, alloc=96.3MB, time=59.96 memory used=2883.0MB, alloc=96.3MB, time=60.09 memory used=2907.4MB, alloc=96.3MB, time=60.22 memory used=2933.7MB, alloc=96.3MB, time=60.35 memory used=2961.6MB, alloc=96.3MB, time=60.48 memory used=2990.8MB, alloc=96.3MB, time=60.61 memory used=3021.0MB, alloc=96.3MB, time=60.74 memory used=3052.2MB, alloc=96.3MB, time=60.88 memory used=3085.9MB, alloc=96.3MB, time=61.03 memory used=3122.4MB, alloc=96.3MB, time=61.16 memory used=3164.5MB, alloc=96.3MB, time=61.73 memory used=3196.0MB, alloc=96.3MB, time=61.94 memory used=3228.2MB, alloc=107.8MB, time=62.41 memory used=3247.9MB, alloc=107.8MB, time=62.55 memory used=3291.9MB, alloc=107.8MB, time=62.73 memory used=3331.9MB, alloc=107.8MB, time=64.41 memory used=3375.7MB, alloc=107.8MB, time=64.66 memory used=3405.3MB, alloc=107.8MB, time=64.84 memory used=3440.9MB, alloc=107.8MB, time=65.03 memory used=3481.8MB, alloc=107.8MB, time=65.23 memory used=3506.3MB, alloc=107.8MB, time=65.39 memory used=3531.0MB, alloc=107.8MB, time=65.55 memory used=3556.2MB, alloc=107.8MB, time=65.71 memory used=3584.5MB, alloc=107.8MB, time=65.87 memory used=3613.8MB, alloc=107.8MB, time=66.03 memory used=3646.2MB, alloc=107.8MB, time=66.19 memory used=3679.5MB, alloc=107.8MB, time=66.37 memory used=3715.9MB, alloc=107.8MB, time=66.53 memory used=3755.3MB, alloc=107.8MB, time=66.70 memory used=3793.8MB, alloc=107.8MB, time=66.87 memory used=3822.3MB, alloc=107.8MB, time=67.01 memory used=3844.0MB, alloc=131.8MB, time=67.16 memory used=3878.6MB, alloc=131.8MB, time=67.31 memory used=3916.4MB, alloc=131.8MB, time=67.47 memory used=3956.4MB, alloc=131.8MB, time=67.63 memory used=3998.0MB, alloc=131.8MB, time=67.79 memory used=4042.5MB, alloc=131.8MB, time=67.94 memory used=4091.1MB, alloc=131.8MB, time=68.12 memory used=4143.8MB, alloc=131.8MB, time=68.29 memory used=4206.1MB, alloc=131.8MB, time=68.87 memory used=4254.5MB, alloc=131.8MB, time=69.18 memory used=4272.6MB, alloc=131.8MB, time=69.55 memory used=4292.3MB, alloc=131.8MB, time=69.69 memory used=4352.5MB, alloc=131.8MB, time=69.91 memory used=4408.6MB, alloc=131.8MB, time=70.82 memory used=4446.0MB, alloc=131.8MB, time=71.11 memory used=4464.9MB, alloc=131.8MB, time=71.25 memory used=4516.5MB, alloc=131.8MB, time=71.46 memory used=4588.1MB, alloc=131.8MB, time=116.05 memory used=4658.6MB, alloc=131.8MB, time=143.69 memory used=4711.0MB, alloc=131.8MB, time=143.93 memory used=4752.2MB, alloc=131.8MB, time=144.12 memory used=4802.8MB, alloc=131.8MB, time=144.34 memory used=4863.4MB, alloc=131.8MB, time=144.56 memory used=4903.8MB, alloc=131.8MB, time=144.72 memory used=4940.2MB, alloc=131.8MB, time=144.87 memory used=4979.5MB, alloc=131.8MB, time=145.03 memory used=5020.2MB, alloc=131.8MB, time=145.19 memory used=5064.0MB, alloc=131.8MB, time=145.35 memory used=5110.8MB, alloc=131.8MB, time=145.52 memory used=5160.6MB, alloc=131.8MB, time=145.70 memory used=5215.2MB, alloc=131.8MB, time=145.86 memory used=5272.4MB, alloc=131.8MB, time=146.04 memory used=5335.5MB, alloc=131.8MB, time=146.23 memory used=5379.2MB, alloc=131.8MB, time=146.38 memory used=5388.2MB, alloc=131.8MB, time=146.48 memory used=5396.7MB, alloc=131.8MB, time=146.58 memory used=5406.0MB, alloc=131.8MB, time=146.67 memory used=5415.3MB, alloc=131.8MB, time=146.78 memory used=5424.5MB, alloc=131.8MB, time=146.88 memory used=5433.8MB, alloc=131.8MB, time=146.98 memory used=5443.0MB, alloc=131.8MB, time=147.08 memory used=5452.1MB, alloc=131.8MB, time=147.18 memory used=5461.3MB, alloc=131.8MB, time=147.28 memory used=5470.4MB, alloc=131.8MB, time=147.37 memory used=5479.4MB, alloc=131.8MB, time=147.47 memory used=5488.6MB, alloc=131.8MB, time=147.56 memory used=5499.3MB, alloc=131.8MB, time=147.66 memory used=5510.0MB, alloc=131.8MB, time=147.76 memory used=5520.7MB, alloc=131.8MB, time=147.87 memory used=5531.3MB, alloc=131.8MB, time=147.97 memory used=5541.8MB, alloc=131.8MB, time=148.08 memory used=5552.3MB, alloc=131.8MB, time=148.18 memory used=5562.7MB, alloc=131.8MB, time=148.27 memory used=5573.0MB, alloc=131.8MB, time=148.38 memory used=5583.4MB, alloc=131.8MB, time=148.48 memory used=5595.1MB, alloc=131.8MB, time=148.58 memory used=5606.8MB, alloc=131.8MB, time=148.68 memory used=5618.4MB, alloc=131.8MB, time=148.79 memory used=5629.9MB, alloc=131.8MB, time=148.91 memory used=5641.2MB, alloc=131.8MB, time=149.04 memory used=5652.8MB, alloc=131.8MB, time=149.16 memory used=5665.2MB, alloc=131.8MB, time=149.27 memory used=5677.7MB, alloc=131.8MB, time=149.38 memory used=5690.0MB, alloc=131.8MB, time=149.48 memory used=5703.6MB, alloc=131.8MB, time=149.59 memory used=5716.9MB, alloc=131.8MB, time=149.69 memory used=5730.1MB, alloc=131.8MB, time=149.80 memory used=5744.0MB, alloc=131.8MB, time=149.90 memory used=5757.8MB, alloc=131.8MB, time=150.01 memory used=5772.5MB, alloc=131.8MB, time=150.12 memory used=5786.9MB, alloc=131.8MB, time=150.22 memory used=5801.7MB, alloc=131.8MB, time=150.33 memory used=5817.1MB, alloc=131.8MB, time=150.44 memory used=5833.0MB, alloc=131.8MB, time=150.55 memory used=5849.2MB, alloc=131.8MB, time=150.67 memory used=5866.0MB, alloc=131.8MB, time=150.78 memory used=5883.7MB, alloc=131.8MB, time=150.89 memory used=5902.4MB, alloc=131.8MB, time=151.00 memory used=5970.1MB, alloc=131.8MB, time=152.44 memory used=6017.0MB, alloc=131.8MB, time=152.68 memory used=6090.0MB, alloc=131.8MB, time=157.57 memory used=6140.5MB, alloc=131.8MB, time=157.81 memory used=6192.5MB, alloc=131.8MB, time=158.03 memory used=6241.1MB, alloc=131.8MB, time=158.23 memory used=6282.2MB, alloc=131.8MB, time=158.39 memory used=6329.4MB, alloc=131.8MB, time=158.56 memory used=6385.3MB, alloc=131.8MB, time=158.74 memory used=6420.6MB, alloc=131.8MB, time=158.88 memory used=6463.1MB, alloc=131.8MB, time=159.59 memory used=6535.4MB, alloc=131.8MB, time=172.22 memory used=6615.0MB, alloc=131.8MB, time=184.69 memory used=6665.7MB, alloc=131.8MB, time=184.93 memory used=6709.4MB, alloc=131.8MB, time=185.12 memory used=6763.6MB, alloc=131.8MB, time=185.35 memory used=6816.1MB, alloc=131.8MB, time=185.54 memory used=6851.0MB, alloc=131.8MB, time=185.70 memory used=6889.7MB, alloc=131.8MB, time=185.87 memory used=6931.3MB, alloc=131.8MB, time=186.03 memory used=6975.9MB, alloc=131.8MB, time=186.19 memory used=7024.7MB, alloc=131.8MB, time=186.36 memory used=7077.6MB, alloc=131.8MB, time=186.54 memory used=7134.4MB, alloc=131.8MB, time=186.72 memory used=7199.3MB, alloc=131.8MB, time=186.91 memory used=7230.8MB, alloc=131.8MB, time=187.04 memory used=7239.9MB, alloc=131.8MB, time=187.14 memory used=7248.8MB, alloc=131.8MB, time=187.24 memory used=7257.6MB, alloc=131.8MB, time=187.36 memory used=7266.6MB, alloc=131.8MB, time=187.47 memory used=7276.7MB, alloc=131.8MB, time=187.57 memory used=7286.8MB, alloc=131.8MB, time=187.68 memory used=7296.8MB, alloc=131.8MB, time=187.78 memory used=7306.8MB, alloc=131.8MB, time=187.88 memory used=7316.7MB, alloc=131.8MB, time=187.99 memory used=7327.8MB, alloc=131.8MB, time=188.11 memory used=7338.8MB, alloc=131.8MB, time=188.22 memory used=7349.6MB, alloc=131.8MB, time=188.33 memory used=7360.5MB, alloc=131.8MB, time=188.45 memory used=7372.1MB, alloc=131.8MB, time=188.56 memory used=7383.7MB, alloc=131.8MB, time=188.67 memory used=7395.2MB, alloc=131.8MB, time=188.78 memory used=7407.3MB, alloc=131.8MB, time=188.89 memory used=7419.5MB, alloc=131.8MB, time=189.00 memory used=7432.2MB, alloc=131.8MB, time=189.11 memory used=7444.9MB, alloc=131.8MB, time=189.22 memory used=7457.9MB, alloc=131.8MB, time=189.33 memory used=7471.4MB, alloc=131.8MB, time=189.44 memory used=7485.4MB, alloc=131.8MB, time=189.56 memory used=7500.0MB, alloc=131.8MB, time=189.67 memory used=7515.4MB, alloc=131.8MB, time=189.78 memory used=7531.2MB, alloc=131.8MB, time=189.92 memory used=7582.6MB, alloc=131.8MB, time=190.33 memory used=7658.0MB, alloc=131.8MB, time=197.97 memory used=7706.5MB, alloc=131.8MB, time=198.20 memory used=7756.7MB, alloc=131.8MB, time=198.44 memory used=7812.8MB, alloc=131.8MB, time=198.65 memory used=7848.9MB, alloc=131.8MB, time=198.80 memory used=7889.3MB, alloc=131.8MB, time=198.97 memory used=7934.5MB, alloc=131.8MB, time=199.14 memory used=7985.4MB, alloc=131.8MB, time=199.31 memory used=8042.2MB, alloc=131.8MB, time=199.50 memory used=8108.5MB, alloc=131.8MB, time=199.70 memory used=8118.6MB, alloc=131.8MB, time=199.80 memory used=8129.3MB, alloc=131.8MB, time=199.91 memory used=8139.9MB, alloc=131.8MB, time=200.03 memory used=8150.9MB, alloc=131.8MB, time=200.14 memory used=8162.2MB, alloc=131.8MB, time=200.25 memory used=8174.4MB, alloc=131.8MB, time=200.36 memory used=8187.1MB, alloc=131.8MB, time=200.46 |\^/| 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(); 1428259430 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 F := [11 y - 11 y z - 12 x - 1, -3 x y z + 4 x y - 2 x y + 19 z, 3 2 -13 y z + 14 y z - 10] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 4 3 4 3 3 4 [7 x - 10 x - 18 y, -z - 16 y z + 18 z + 13, -x y - x y + 16 y - x z] > Problem := [F,G]; 4 2 2 2 3 Problem := [[11 y - 11 y z - 12 x - 1, -3 x y z + 4 x y - 2 x y + 19 z, 3 2 -13 y z + 14 y z - 10], 4 3 4 3 3 4 [7 x - 10 x - 18 y, -z - 16 y z + 18 z + 13, -x y - x y + 16 y - x z] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.31 memory used=24.0MB, alloc=32.3MB, time=0.83 memory used=43.1MB, alloc=56.3MB, time=1.32 memory used=79.5MB, alloc=60.3MB, time=2.09 memory used=126.2MB, alloc=68.3MB, time=3.17 memory used=164.1MB, alloc=68.3MB, time=3.36 memory used=185.8MB, alloc=68.3MB, time=3.50 memory used=214.7MB, alloc=68.3MB, time=3.80 memory used=252.6MB, alloc=68.3MB, time=4.01 memory used=274.6MB, alloc=68.3MB, time=4.13 memory used=302.0MB, alloc=68.3MB, time=4.40 memory used=336.8MB, alloc=68.3MB, time=5.45 memory used=361.9MB, alloc=68.3MB, time=5.58 memory used=399.5MB, alloc=68.3MB, time=6.20 memory used=442.9MB, alloc=68.3MB, time=7.20 memory used=484.0MB, alloc=68.3MB, time=7.81 memory used=533.6MB, alloc=68.3MB, time=8.74 memory used=579.0MB, alloc=68.3MB, time=13.34 memory used=610.9MB, alloc=68.3MB, time=13.51 memory used=641.2MB, alloc=68.3MB, time=13.69 memory used=667.7MB, alloc=68.3MB, time=13.84 memory used=684.9MB, alloc=68.3MB, time=13.97 memory used=702.3MB, alloc=68.3MB, time=14.10 memory used=719.7MB, alloc=68.3MB, time=14.24 memory used=791.2MB, alloc=68.3MB, time=15.82 memory used=853.4MB, alloc=68.3MB, time=21.66 memory used=882.6MB, alloc=92.3MB, time=72.45 memory used=917.7MB, alloc=116.3MB, time=72.64 memory used=963.5MB, alloc=140.3MB, time=153.75 |\^/| 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(); 1428259730 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 F := [16 x y z - 9 y z - 13 y + 17, 7 x y + 19 y + 11 x - 6 x y, 2 2 -10 x y z + 9 x y z - 17 x y + 17 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 3 2 G := [-13 x y - 4 x y z - 7 y , 13 x + 4 y - 10 z + 9 z, 2 2 11 x y z - 2 y z + 18 y z - 20 z] > Problem := [F,G]; 2 3 2 3 2 Problem := [[16 x y z - 9 y z - 13 y + 17, 7 x y + 19 y + 11 x - 6 x y, 2 2 3 3 -10 x y z + 9 x y z - 17 x y + 17 x], [-13 x y - 4 x y z - 7 y , 4 3 2 2 2 13 x + 4 y - 10 z + 9 z, 11 x y z - 2 y z + 18 y z - 20 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.1MB, alloc=40.3MB, time=0.99 memory used=56.8MB, alloc=68.3MB, time=1.69 memory used=101.7MB, alloc=68.3MB, time=2.83 memory used=151.1MB, alloc=76.3MB, time=4.11 memory used=200.0MB, alloc=100.3MB, time=5.33 memory used=270.4MB, alloc=100.3MB, time=7.14 memory used=340.4MB, alloc=124.3MB, time=8.92 memory used=413.6MB, alloc=124.3MB, time=10.88 memory used=489.2MB, alloc=380.3MB, time=12.74 memory used=586.0MB, alloc=404.3MB, time=15.08 memory used=708.9MB, alloc=428.3MB, time=17.82 memory used=852.7MB, alloc=452.3MB, time=21.41 memory used=967.7MB, alloc=452.3MB, time=24.02 memory used=1098.8MB, alloc=476.3MB, time=27.30 memory used=1194.7MB, alloc=476.3MB, time=29.49 memory used=1290.2MB, alloc=476.3MB, time=32.01 memory used=1381.0MB, alloc=500.3MB, time=34.07 memory used=1478.6MB, alloc=500.3MB, time=37.09 memory used=1552.6MB, alloc=500.3MB, time=39.08 memory used=1649.0MB, alloc=500.3MB, time=41.70 memory used=1741.5MB, alloc=500.3MB, time=44.77 memory used=1822.7MB, alloc=500.3MB, time=46.68 memory used=1892.6MB, alloc=500.3MB, time=48.71 memory used=1958.4MB, alloc=500.3MB, time=50.34 memory used=2046.7MB, alloc=500.3MB, time=52.87 memory used=2113.5MB, alloc=500.3MB, time=55.23 memory used=2170.2MB, alloc=500.3MB, time=57.14 memory used=2225.0MB, alloc=500.3MB, time=58.79 memory used=2290.4MB, alloc=524.3MB, time=60.70 memory used=2342.1MB, alloc=524.3MB, time=62.56 memory used=2383.4MB, alloc=524.3MB, time=64.07 memory used=2433.3MB, alloc=524.3MB, time=65.80 memory used=2636.7MB, alloc=548.3MB, time=72.14 memory used=2851.8MB, alloc=572.3MB, time=76.84 memory used=3068.0MB, alloc=572.3MB, time=81.80 memory used=3265.1MB, alloc=572.3MB, time=86.05 memory used=3492.1MB, alloc=596.3MB, time=91.34 memory used=3652.8MB, alloc=596.3MB, time=95.96 memory used=3792.1MB, alloc=596.3MB, time=100.37 memory used=3961.9MB, alloc=620.3MB, time=105.23 memory used=4100.7MB, alloc=620.3MB, time=109.63 memory used=4225.7MB, alloc=620.3MB, time=113.68 memory used=4348.4MB, alloc=644.3MB, time=117.73 |\^/| 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(); 1428260030 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 3 2 2 3 3 F := [-5 z - 8 x - 7 y , 3 x z + 5 x y + 11 x + 8 y , 2 4 2 3 13 x y z + 14 z - x y + 6 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 3 2 G := [13 x y + 20 x y z + 5 y - 4 y , 20 x z - 4 y z - 4 x y + 5 x z, 2 2 2 -18 x z - 19 x - 4 z - 16 x] > Problem := [F,G]; 4 3 2 3 2 2 3 3 Problem := [[-5 z - 8 x - 7 y , 3 x z + 5 x y + 11 x + 8 y , 2 4 2 3 2 2 2 4 2 13 x y z + 14 z - x y + 6 z ], [13 x y + 20 x y z + 5 y - 4 y , 3 2 2 2 2 20 x z - 4 y z - 4 x y + 5 x z, -18 x z - 19 x - 4 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=4.3MB, alloc=32.3MB, time=0.31 memory used=24.3MB, alloc=32.3MB, time=0.80 memory used=43.9MB, alloc=32.3MB, time=1.26 memory used=62.4MB, alloc=56.3MB, time=1.65 memory used=110.7MB, alloc=70.3MB, time=2.42 memory used=140.9MB, alloc=70.3MB, time=2.60 memory used=177.0MB, alloc=70.3MB, time=2.91 memory used=205.6MB, alloc=70.3MB, time=3.04 memory used=239.1MB, alloc=70.3MB, time=3.27 memory used=272.4MB, alloc=70.3MB, time=3.91 memory used=302.7MB, alloc=70.3MB, time=4.05 memory used=334.1MB, alloc=70.3MB, time=4.36 memory used=364.3MB, alloc=70.3MB, time=4.64 memory used=411.7MB, alloc=70.3MB, time=5.56 memory used=456.9MB, alloc=70.3MB, time=6.42 memory used=497.4MB, alloc=70.3MB, time=6.88 memory used=558.0MB, alloc=70.3MB, time=7.82 memory used=618.8MB, alloc=70.3MB, time=8.46 memory used=680.2MB, alloc=70.3MB, time=9.75 memory used=740.8MB, alloc=70.3MB, time=10.35 memory used=802.0MB, alloc=70.3MB, time=11.03 memory used=851.6MB, alloc=70.3MB, time=12.22 memory used=895.3MB, alloc=70.3MB, time=13.23 memory used=940.5MB, alloc=70.3MB, time=14.39 memory used=985.9MB, alloc=70.3MB, time=15.41 memory used=1032.8MB, alloc=70.3MB, time=16.39 memory used=1075.5MB, alloc=94.3MB, time=17.32 memory used=1143.3MB, alloc=94.3MB, time=18.71 memory used=1204.0MB, alloc=96.7MB, time=19.39 memory used=1276.7MB, alloc=96.7MB, time=21.27 memory used=1342.7MB, alloc=96.7MB, time=22.99 memory used=1404.1MB, alloc=96.7MB, time=23.97 memory used=1445.3MB, alloc=96.7MB, time=24.41 memory used=1485.5MB, alloc=96.7MB, time=24.86 memory used=1515.0MB, alloc=96.7MB, time=25.04 memory used=1549.3MB, alloc=96.7MB, time=25.30 memory used=1580.7MB, alloc=96.7MB, time=25.49 memory used=1606.0MB, alloc=96.7MB, time=25.64 memory used=1642.0MB, alloc=96.7MB, time=26.01 memory used=1683.0MB, alloc=96.7MB, time=26.51 memory used=1720.4MB, alloc=96.7MB, time=26.89 memory used=1755.2MB, alloc=96.7MB, time=27.10 memory used=1781.6MB, alloc=96.7MB, time=27.27 memory used=1819.1MB, alloc=96.7MB, time=27.53 memory used=1845.3MB, alloc=96.7MB, time=27.69 memory used=1881.9MB, alloc=96.7MB, time=28.05 memory used=1919.5MB, alloc=96.7MB, time=28.36 memory used=1946.6MB, alloc=96.7MB, time=28.52 memory used=1983.6MB, alloc=96.7MB, time=28.80 memory used=2012.5MB, alloc=96.7MB, time=28.97 memory used=2048.2MB, alloc=96.7MB, time=29.34 memory used=2076.0MB, alloc=96.7MB, time=29.51 memory used=2114.6MB, alloc=96.7MB, time=29.85 memory used=2142.4MB, alloc=96.7MB, time=30.01 memory used=2179.3MB, alloc=96.7MB, time=30.30 memory used=2207.8MB, alloc=96.7MB, time=30.46 memory used=2245.9MB, alloc=96.7MB, time=30.88 memory used=2273.8MB, alloc=96.7MB, time=31.04 memory used=2311.9MB, alloc=96.7MB, time=31.48 memory used=2353.2MB, alloc=96.7MB, time=31.88 memory used=2383.1MB, alloc=96.7MB, time=32.06 memory used=2410.9MB, alloc=96.7MB, time=32.21 memory used=2436.0MB, alloc=96.7MB, time=32.37 memory used=2478.4MB, alloc=120.7MB, time=32.82 memory used=2527.2MB, alloc=120.7MB, time=33.07 memory used=2567.4MB, alloc=120.7MB, time=33.26 memory used=2632.9MB, alloc=120.7MB, time=34.76 memory used=2676.7MB, alloc=120.7MB, time=34.98 memory used=2731.2MB, alloc=120.7MB, time=35.52 memory used=2776.4MB, alloc=120.7MB, time=35.89 memory used=2794.0MB, alloc=131.8MB, time=36.36 memory used=2849.4MB, alloc=131.8MB, time=36.59 memory used=2875.1MB, alloc=131.8MB, time=36.76 memory used=2929.6MB, alloc=131.8MB, time=36.98 memory used=2988.9MB, alloc=131.8MB, time=37.86 memory used=3040.6MB, alloc=131.8MB, time=38.10 memory used=3078.2MB, alloc=131.8MB, time=38.30 memory used=3124.4MB, alloc=131.8MB, time=38.51 memory used=3187.7MB, alloc=131.8MB, time=39.06 memory used=3236.1MB, alloc=131.8MB, time=39.29 memory used=3276.1MB, alloc=131.8MB, time=39.50 memory used=3319.8MB, alloc=131.8MB, time=39.70 memory used=3390.6MB, alloc=131.8MB, time=41.76 memory used=3436.0MB, alloc=131.8MB, time=41.99 memory used=3483.3MB, alloc=131.8MB, time=42.20 memory used=3530.9MB, alloc=131.8MB, time=42.63 memory used=3577.7MB, alloc=131.8MB, time=43.10 memory used=3613.7MB, alloc=131.8MB, time=43.66 memory used=3668.5MB, alloc=131.8MB, time=43.89 memory used=3694.4MB, alloc=131.8MB, time=44.06 memory used=3748.6MB, alloc=131.8MB, time=44.29 memory used=3806.2MB, alloc=131.8MB, time=45.14 memory used=3853.3MB, alloc=131.8MB, time=45.36 memory used=3908.0MB, alloc=131.8MB, time=45.77 memory used=3957.8MB, alloc=131.8MB, time=46.01 memory used=3998.7MB, alloc=131.8MB, time=46.22 memory used=4066.3MB, alloc=131.8MB, time=48.15 memory used=4110.4MB, alloc=131.8MB, time=48.36 memory used=4157.1MB, alloc=131.8MB, time=48.56 memory used=4215.8MB, alloc=131.8MB, time=49.43 memory used=4270.5MB, alloc=131.8MB, time=49.86 memory used=4314.1MB, alloc=131.8MB, time=50.08 memory used=4370.6MB, alloc=131.8MB, time=50.42 memory used=4421.8MB, alloc=131.8MB, time=50.82 memory used=4476.0MB, alloc=131.8MB, time=51.17 memory used=4527.8MB, alloc=131.8MB, time=51.50 memory used=4584.2MB, alloc=131.8MB, time=52.01 memory used=4638.9MB, alloc=131.8MB, time=52.46 memory used=4683.5MB, alloc=131.8MB, time=52.68 memory used=4739.9MB, alloc=131.8MB, time=53.02 memory used=4794.5MB, alloc=131.8MB, time=53.55 memory used=4848.5MB, alloc=131.8MB, time=54.09 memory used=4898.0MB, alloc=131.8MB, time=54.58 memory used=4946.0MB, alloc=131.8MB, time=54.82 memory used=5003.0MB, alloc=131.8MB, time=55.52 memory used=5061.5MB, alloc=131.8MB, time=56.04 memory used=5110.9MB, alloc=131.8MB, time=56.29 memory used=5148.9MB, alloc=131.8MB, time=56.50 memory used=5196.9MB, alloc=131.8MB, time=56.71 memory used=5258.7MB, alloc=131.8MB, time=57.19 memory used=5309.8MB, alloc=131.8MB, time=57.44 memory used=5347.6MB, alloc=131.8MB, time=57.64 memory used=5392.8MB, alloc=131.8MB, time=57.86 memory used=5459.0MB, alloc=131.8MB, time=59.39 memory used=5502.9MB, alloc=131.8MB, time=59.60 memory used=5554.6MB, alloc=131.8MB, time=59.99 memory used=5607.9MB, alloc=131.8MB, time=60.27 memory used=5651.6MB, alloc=131.8MB, time=60.49 memory used=5709.8MB, alloc=131.8MB, time=60.92 memory used=5757.8MB, alloc=131.8MB, time=61.16 memory used=5797.6MB, alloc=131.8MB, time=61.36 memory used=5870.7MB, alloc=131.8MB, time=63.44 memory used=5915.5MB, alloc=131.8MB, time=63.66 memory used=5963.5MB, alloc=131.8MB, time=63.88 memory used=6018.0MB, alloc=131.8MB, time=64.32 memory used=6065.8MB, alloc=131.8MB, time=64.56 memory used=6104.6MB, alloc=131.8MB, time=64.76 memory used=6162.5MB, alloc=131.8MB, time=65.31 memory used=6209.0MB, alloc=131.8MB, time=65.53 memory used=6263.6MB, alloc=131.8MB, time=67.31 memory used=6327.2MB, alloc=131.8MB, time=67.80 memory used=6370.3MB, alloc=131.8MB, time=68.02 memory used=6419.7MB, alloc=131.8MB, time=68.44 memory used=6468.3MB, alloc=131.8MB, time=69.11 memory used=6522.9MB, alloc=131.8MB, time=69.35 memory used=6577.9MB, alloc=131.8MB, time=69.98 memory used=6632.9MB, alloc=131.8MB, time=70.79 memory used=6740.0MB, alloc=131.8MB, time=72.64 memory used=6828.2MB, alloc=131.8MB, time=75.43 memory used=6901.2MB, alloc=387.8MB, time=76.81 memory used=7009.5MB, alloc=387.8MB, time=80.30 memory used=7112.0MB, alloc=387.8MB, time=82.57 memory used=7185.2MB, alloc=387.8MB, time=84.31 memory used=7236.5MB, alloc=387.8MB, time=85.07 memory used=7328.5MB, alloc=387.8MB, time=86.47 memory used=7435.3MB, alloc=411.8MB, time=87.70 memory used=7581.9MB, alloc=411.8MB, time=91.27 memory used=7664.2MB, alloc=411.8MB, time=92.10 memory used=7749.8MB, alloc=411.8MB, time=93.02 memory used=7827.0MB, alloc=411.8MB, time=93.93 memory used=7900.9MB, alloc=411.8MB, time=94.42 memory used=7978.4MB, alloc=411.8MB, time=95.41 memory used=8059.4MB, alloc=411.8MB, time=96.62 memory used=8174.3MB, alloc=411.8MB, time=98.90 memory used=8301.1MB, alloc=435.8MB, time=100.81 memory used=8382.3MB, alloc=435.8MB, time=101.55 memory used=8451.8MB, alloc=435.8MB, time=102.03 memory used=8520.7MB, alloc=435.8MB, time=102.49 memory used=8596.9MB, alloc=435.8MB, time=103.19 memory used=8672.8MB, alloc=435.8MB, time=103.92 memory used=8740.3MB, alloc=435.8MB, time=104.35 memory used=8824.4MB, alloc=435.8MB, time=105.51 memory used=8891.3MB, alloc=435.8MB, time=105.88 memory used=8943.3MB, alloc=435.8MB, time=106.20 memory used=9007.3MB, alloc=435.8MB, time=106.53 memory used=9082.4MB, alloc=435.8MB, time=106.87 memory used=9129.3MB, alloc=435.8MB, time=107.14 memory used=9178.2MB, alloc=435.8MB, time=107.41 memory used=9233.6MB, alloc=435.8MB, time=107.68 memory used=9298.8MB, alloc=435.8MB, time=107.95 memory used=9377.3MB, alloc=435.8MB, time=108.86 memory used=9436.1MB, alloc=435.8MB, time=109.22 memory used=9493.5MB, alloc=435.8MB, time=109.55 memory used=9564.2MB, alloc=435.8MB, time=109.90 memory used=9625.8MB, alloc=435.8MB, time=110.21 memory used=9671.9MB, alloc=435.8MB, time=110.48 memory used=9723.8MB, alloc=435.8MB, time=110.75 memory used=9782.0MB, alloc=435.8MB, time=111.03 memory used=9862.7MB, alloc=435.8MB, time=112.20 memory used=9923.1MB, alloc=435.8MB, time=112.56 memory used=9993.8MB, alloc=435.8MB, time=112.91 memory used=10041.3MB, alloc=435.8MB, time=113.17 memory used=10099.8MB, alloc=435.8MB, time=113.45 memory used=10178.9MB, alloc=435.8MB, time=114.53 memory used=10242.7MB, alloc=435.8MB, time=114.89 memory used=10297.0MB, alloc=435.8MB, time=115.22 memory used=10363.4MB, alloc=435.8MB, time=115.57 memory used=10435.1MB, alloc=435.8MB, time=115.90 memory used=10480.3MB, alloc=435.8MB, time=116.16 memory used=10529.9MB, alloc=435.8MB, time=116.43 memory used=10585.4MB, alloc=435.8MB, time=116.70 memory used=10649.9MB, alloc=435.8MB, time=116.97 memory used=10728.0MB, alloc=435.8MB, time=118.06 memory used=10789.5MB, alloc=435.8MB, time=118.42 memory used=10845.2MB, alloc=435.8MB, time=118.74 memory used=10913.5MB, alloc=435.8MB, time=119.08 memory used=10981.2MB, alloc=435.8MB, time=119.40 memory used=11026.8MB, alloc=435.8MB, time=119.66 memory used=11077.5MB, alloc=435.8MB, time=119.95 memory used=11134.9MB, alloc=435.8MB, time=120.22 memory used=11215.0MB, alloc=435.8MB, time=121.80 memory used=11282.5MB, alloc=435.8MB, time=122.19 memory used=11340.8MB, alloc=435.8MB, time=122.52 memory used=11410.2MB, alloc=435.8MB, time=122.86 memory used=11457.6MB, alloc=435.8MB, time=123.13 memory used=11512.0MB, alloc=435.8MB, time=123.42 memory used=11575.4MB, alloc=435.8MB, time=123.70 memory used=11658.9MB, alloc=435.8MB, time=124.53 memory used=11736.4MB, alloc=435.8MB, time=125.78 memory used=11804.6MB, alloc=435.8MB, time=126.17 memory used=11855.4MB, alloc=435.8MB, time=126.48 memory used=11916.6MB, alloc=435.8MB, time=126.83 memory used=11991.1MB, alloc=435.8MB, time=127.18 memory used=12043.0MB, alloc=435.8MB, time=127.46 memory used=12090.8MB, alloc=435.8MB, time=127.72 memory used=12144.1MB, alloc=435.8MB, time=127.99 memory used=12204.6MB, alloc=435.8MB, time=128.26 memory used=12283.7MB, alloc=435.8MB, time=129.33 memory used=12349.9MB, alloc=435.8MB, time=129.70 memory used=12402.7MB, alloc=435.8MB, time=130.03 memory used=12467.7MB, alloc=435.8MB, time=130.35 memory used=12541.9MB, alloc=435.8MB, time=130.69 memory used=12587.7MB, alloc=435.8MB, time=130.96 memory used=12636.7MB, alloc=435.8MB, time=131.23 memory used=12691.6MB, alloc=435.8MB, time=131.50 memory used=12755.8MB, alloc=435.8MB, time=131.77 memory used=12840.6MB, alloc=435.8MB, time=133.45 memory used=12895.1MB, alloc=435.8MB, time=133.78 memory used=12968.2MB, alloc=435.8MB, time=134.13 memory used=13016.1MB, alloc=435.8MB, time=134.43 memory used=13069.2MB, alloc=435.8MB, time=134.70 memory used=13130.2MB, alloc=435.8MB, time=134.97 memory used=13210.8MB, alloc=435.8MB, time=135.64 memory used=13284.7MB, alloc=435.8MB, time=136.48 memory used=13345.8MB, alloc=435.8MB, time=136.82 memory used=13421.9MB, alloc=435.8MB, time=137.49 memory used=13483.4MB, alloc=435.8MB, time=137.85 memory used=13549.3MB, alloc=435.8MB, time=139.00 memory used=13624.0MB, alloc=435.8MB, time=139.47 memory used=13696.8MB, alloc=435.8MB, time=139.88 memory used=13750.0MB, alloc=435.8MB, time=140.23 memory used=13801.1MB, alloc=435.8MB, time=140.56 memory used=13858.3MB, alloc=435.8MB, time=140.91 memory used=13923.2MB, alloc=435.8MB, time=141.26 memory used=13995.8MB, alloc=435.8MB, time=141.62 memory used=14070.8MB, alloc=435.8MB, time=141.98 memory used=14116.1MB, alloc=435.8MB, time=142.25 memory used=14160.5MB, alloc=435.8MB, time=142.52 memory used=14207.1MB, alloc=435.8MB, time=142.79 memory used=14257.8MB, alloc=435.8MB, time=143.06 memory used=14312.0MB, alloc=435.8MB, time=143.33 memory used=14368.9MB, alloc=435.8MB, time=143.61 memory used=14429.8MB, alloc=435.8MB, time=143.89 memory used=14496.4MB, alloc=435.8MB, time=144.17 memory used=14569.7MB, alloc=435.8MB, time=144.45 memory used=14658.3MB, alloc=435.8MB, time=145.77 memory used=14720.9MB, alloc=435.8MB, time=146.15 memory used=14787.9MB, alloc=435.8MB, time=146.53 memory used=14836.9MB, alloc=435.8MB, time=146.86 memory used=14892.5MB, alloc=435.8MB, time=147.18 memory used=14953.9MB, alloc=435.8MB, time=147.52 memory used=15023.0MB, alloc=435.8MB, time=147.86 memory used=15099.9MB, alloc=435.8MB, time=148.22 memory used=15155.6MB, alloc=435.8MB, time=148.52 memory used=15199.8MB, alloc=435.8MB, time=148.79 memory used=15246.4MB, alloc=435.8MB, time=149.08 memory used=15295.0MB, alloc=435.8MB, time=149.35 memory used=15347.4MB, alloc=435.8MB, time=149.62 memory used=15403.0MB, alloc=435.8MB, time=149.90 memory used=15462.9MB, alloc=435.8MB, time=150.19 memory used=15527.6MB, alloc=435.8MB, time=150.47 memory used=15597.2MB, alloc=435.8MB, time=150.77 memory used=15692.6MB, alloc=435.8MB, time=159.81 memory used=15769.5MB, alloc=435.8MB, time=160.28 memory used=15821.3MB, alloc=435.8MB, time=160.61 memory used=15884.5MB, alloc=435.8MB, time=160.95 memory used=15960.2MB, alloc=435.8MB, time=161.31 memory used=16006.8MB, alloc=435.8MB, time=161.58 memory used=16054.4MB, alloc=435.8MB, time=161.85 memory used=16105.9MB, alloc=435.8MB, time=162.13 memory used=16161.6MB, alloc=435.8MB, time=162.42 memory used=16223.6MB, alloc=435.8MB, time=162.71 memory used=16290.2MB, alloc=435.8MB, time=163.00 memory used=16363.3MB, alloc=435.8MB, time=163.29 memory used=16579.8MB, alloc=435.8MB, time=164.13 memory used=16674.8MB, alloc=435.8MB, time=165.26 memory used=16737.0MB, alloc=435.8MB, time=165.62 memory used=16821.6MB, alloc=435.8MB, time=167.83 memory used=16883.6MB, alloc=435.8MB, time=168.20 memory used=16954.3MB, alloc=435.8MB, time=168.58 memory used=17000.5MB, alloc=435.8MB, time=168.92 memory used=17049.9MB, alloc=435.8MB, time=169.25 memory used=17105.5MB, alloc=435.8MB, time=169.58 memory used=17167.1MB, alloc=435.8MB, time=169.94 memory used=17234.5MB, alloc=435.8MB, time=170.28 memory used=17307.6MB, alloc=435.8MB, time=170.63 memory used=17384.2MB, alloc=435.8MB, time=170.98 memory used=17432.4MB, alloc=435.8MB, time=171.25 memory used=17473.1MB, alloc=435.8MB, time=171.55 memory used=17515.6MB, alloc=435.8MB, time=171.81 memory used=17561.6MB, alloc=435.8MB, time=172.09 memory used=17607.9MB, alloc=435.8MB, time=172.36 memory used=17657.2MB, alloc=435.8MB, time=172.62 memory used=17709.5MB, alloc=435.8MB, time=172.90 memory used=17761.9MB, alloc=435.8MB, time=173.16 memory used=17816.6MB, alloc=435.8MB, time=173.43 memory used=17873.7MB, alloc=435.8MB, time=173.71 memory used=17935.0MB, alloc=435.8MB, time=173.99 memory used=17998.2MB, alloc=435.8MB, time=174.27 memory used=18064.9MB, alloc=435.8MB, time=174.56 memory used=18136.7MB, alloc=435.8MB, time=174.84 memory used=18211.4MB, alloc=435.8MB, time=175.14 memory used=18416.0MB, alloc=435.8MB, time=177.29 memory used=18481.2MB, alloc=435.8MB, time=177.71 memory used=18550.2MB, alloc=435.8MB, time=178.11 |\^/| 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(); 1428260330 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 2 F := [-10 x y + 13 z - 16 x + 2 y z, 4 y z + 16 x z + 17 y z - 14 y, 2 3 18 x y - 5 z + 15 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 G := [-11 x y - 18 x z - 20 x y + 20 y , -2 x y z - 3 x + 10 y - 19, 3 2 4 -15 x z - 16 x y z - 6 y + 9 x] > Problem := [F,G]; 3 3 2 Problem := [[-10 x y + 13 z - 16 x + 2 y z, 2 2 2 2 2 3 4 y z + 16 x z + 17 y z - 14 y, 18 x y - 5 z + 15 y z], [ 3 3 3 2 2 -11 x y - 18 x z - 20 x y + 20 y , -2 x y z - 3 x + 10 y - 19, 3 2 4 -15 x z - 16 x y z - 6 y + 9 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=25.2MB, alloc=34.3MB, time=0.60 memory used=42.4MB, alloc=34.3MB, time=0.71 memory used=59.1MB, alloc=34.3MB, time=1.03 memory used=78.0MB, alloc=34.3MB, time=1.34 memory used=101.9MB, alloc=38.3MB, time=2.13 memory used=113.9MB, alloc=38.3MB, time=2.19 memory used=129.3MB, alloc=38.3MB, time=2.38 memory used=153.9MB, alloc=38.3MB, time=2.82 memory used=196.6MB, alloc=62.3MB, time=3.50 memory used=239.1MB, alloc=62.3MB, time=12.80 memory used=280.9MB, alloc=62.3MB, time=14.21 memory used=315.4MB, alloc=62.3MB, time=14.33 memory used=336.0MB, alloc=62.3MB, time=14.43 memory used=356.3MB, alloc=62.3MB, time=14.52 memory used=377.8MB, alloc=62.3MB, time=14.62 memory used=400.5MB, alloc=62.3MB, time=14.72 memory used=424.8MB, alloc=62.3MB, time=14.81 memory used=450.8MB, alloc=62.3MB, time=14.92 memory used=477.7MB, alloc=62.3MB, time=15.02 memory used=511.4MB, alloc=62.3MB, time=15.19 memory used=665.9MB, alloc=62.3MB, time=17.73 memory used=693.8MB, alloc=62.3MB, time=17.98 memory used=831.8MB, alloc=62.3MB, time=20.21 memory used=869.4MB, alloc=62.3MB, time=35.68 memory used=891.1MB, alloc=86.3MB, time=56.23 memory used=923.9MB, alloc=110.3MB, time=96.22 memory used=980.9MB, alloc=110.3MB, time=155.05 |\^/| 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(); 1428260630 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 F := [-8 x y + 8 y z - 8 z - 7 z, 19 x z - 20 x + 6 y z, 2 2 2 -15 x z - 18 y + 2 z + 11] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 4 2 2 2 G := [12 x z - 11 y z + 17 x z + 19 y , -12 x - 6 x y z + 7 x y + x , 2 3 2 2 10 x y z - 17 y + 6 y z - 16 x ] > Problem := [F,G]; 2 2 2 3 3 2 Problem := [[-8 x y + 8 y z - 8 z - 7 z, 19 x z - 20 x + 6 y z, 2 2 2 3 2 2 2 3 -15 x z - 18 y + 2 z + 11], [12 x z - 11 y z + 17 x z + 19 y , 4 2 2 2 2 3 2 2 -12 x - 6 x y z + 7 x y + x , 10 x y z - 17 y + 6 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=4.5MB, alloc=32.3MB, time=0.31 memory used=27.1MB, alloc=32.3MB, time=0.90 memory used=46.5MB, alloc=56.3MB, time=1.40 memory used=88.4MB, alloc=60.3MB, time=2.37 memory used=132.9MB, alloc=68.3MB, time=3.46 memory used=176.7MB, alloc=68.3MB, time=4.68 memory used=218.4MB, alloc=68.3MB, time=5.29 memory used=253.6MB, alloc=68.3MB, time=5.93 memory used=298.1MB, alloc=92.3MB, time=7.04 memory used=362.0MB, alloc=92.3MB, time=8.06 memory used=426.2MB, alloc=92.3MB, time=8.97 memory used=507.2MB, alloc=92.3MB, time=10.49 memory used=573.8MB, alloc=92.3MB, time=11.88 memory used=613.8MB, alloc=92.3MB, time=12.20 memory used=647.9MB, alloc=92.3MB, time=12.44 memory used=680.2MB, alloc=92.3MB, time=12.64 memory used=716.9MB, alloc=92.3MB, time=12.93 memory used=750.5MB, alloc=92.3MB, time=13.17 memory used=784.8MB, alloc=92.3MB, time=13.39 memory used=830.9MB, alloc=92.3MB, time=14.27 memory used=861.2MB, alloc=92.3MB, time=14.46 memory used=891.0MB, alloc=92.3MB, time=14.64 memory used=927.8MB, alloc=92.3MB, time=14.83 memory used=953.7MB, alloc=116.3MB, time=15.01 memory used=990.3MB, alloc=116.3MB, time=15.20 memory used=1032.2MB, alloc=116.3MB, time=15.40 memory used=1079.0MB, alloc=116.3MB, time=15.61 memory used=1131.5MB, alloc=116.3MB, time=15.82 memory used=1190.7MB, alloc=116.3MB, time=16.05 memory used=1228.9MB, alloc=116.3MB, time=16.22 memory used=1263.1MB, alloc=116.3MB, time=16.38 memory used=1298.2MB, alloc=116.3MB, time=16.57 memory used=1335.9MB, alloc=116.3MB, time=16.73 memory used=1377.1MB, alloc=116.3MB, time=16.89 memory used=1420.8MB, alloc=116.3MB, time=17.04 memory used=1468.5MB, alloc=116.3MB, time=17.21 memory used=1532.0MB, alloc=116.3MB, time=18.08 memory used=1579.3MB, alloc=116.3MB, time=18.32 memory used=1630.4MB, alloc=116.3MB, time=18.55 memory used=1667.7MB, alloc=116.3MB, time=18.75 memory used=1709.3MB, alloc=116.3MB, time=18.94 memory used=1755.6MB, alloc=116.3MB, time=19.16 memory used=1808.3MB, alloc=116.3MB, time=19.37 memory used=1867.3MB, alloc=116.3MB, time=19.60 memory used=1907.9MB, alloc=116.3MB, time=19.77 memory used=1940.7MB, alloc=116.3MB, time=19.93 memory used=1976.7MB, alloc=116.3MB, time=20.08 memory used=2014.9MB, alloc=116.3MB, time=20.25 memory used=2054.9MB, alloc=116.3MB, time=20.40 memory used=2098.4MB, alloc=116.3MB, time=20.56 memory used=2145.6MB, alloc=116.3MB, time=20.72 memory used=2219.6MB, alloc=116.3MB, time=46.22 memory used=2333.2MB, alloc=116.4MB, time=49.65 memory used=2379.2MB, alloc=116.4MB, time=49.87 memory used=2421.5MB, alloc=116.4MB, time=50.07 memory used=2473.1MB, alloc=116.4MB, time=50.29 memory used=2527.6MB, alloc=116.4MB, time=50.50 memory used=2560.1MB, alloc=116.4MB, time=50.65 memory used=2595.1MB, alloc=116.4MB, time=50.81 memory used=2633.3MB, alloc=116.4MB, time=50.96 memory used=2674.5MB, alloc=116.4MB, time=51.13 memory used=2718.6MB, alloc=116.4MB, time=51.29 memory used=2765.6MB, alloc=116.4MB, time=51.45 memory used=2815.3MB, alloc=116.4MB, time=51.62 memory used=2867.8MB, alloc=116.4MB, time=51.79 memory used=2924.1MB, alloc=116.4MB, time=51.99 memory used=2985.5MB, alloc=116.4MB, time=52.18 memory used=3000.3MB, alloc=131.8MB, time=52.32 memory used=3009.8MB, alloc=131.8MB, time=52.43 memory used=3018.6MB, alloc=131.8MB, time=52.55 memory used=3027.3MB, alloc=131.8MB, time=52.66 memory used=3036.0MB, alloc=131.8MB, time=52.78 memory used=3044.9MB, alloc=131.8MB, time=52.89 memory used=3055.1MB, alloc=131.8MB, time=53.00 memory used=3065.4MB, alloc=131.8MB, time=53.11 memory used=3075.7MB, alloc=131.8MB, time=53.24 memory used=3085.9MB, alloc=131.8MB, time=53.36 memory used=3096.1MB, alloc=131.8MB, time=53.49 memory used=3106.2MB, alloc=131.8MB, time=53.60 memory used=3116.3MB, alloc=131.8MB, time=53.72 memory used=3126.3MB, alloc=131.8MB, time=53.84 memory used=3136.4MB, alloc=131.8MB, time=53.97 memory used=3147.7MB, alloc=131.8MB, time=54.10 memory used=3159.1MB, alloc=131.8MB, time=54.23 memory used=3170.3MB, alloc=131.8MB, time=54.34 memory used=3181.6MB, alloc=131.8MB, time=54.46 memory used=3192.7MB, alloc=131.8MB, time=54.57 memory used=3203.9MB, alloc=131.8MB, time=54.68 memory used=3216.0MB, alloc=131.8MB, time=54.79 memory used=3228.2MB, alloc=131.8MB, time=54.91 memory used=3240.2MB, alloc=131.8MB, time=55.05 memory used=3252.4MB, alloc=131.8MB, time=55.16 memory used=3265.0MB, alloc=131.8MB, time=55.29 memory used=3277.8MB, alloc=131.8MB, time=55.41 memory used=3290.8MB, alloc=131.8MB, time=55.53 memory used=3304.0MB, alloc=131.8MB, time=55.66 memory used=3317.5MB, alloc=131.8MB, time=55.78 memory used=3331.4MB, alloc=131.8MB, time=55.91 memory used=3345.6MB, alloc=131.8MB, time=56.04 memory used=3360.7MB, alloc=131.8MB, time=56.19 memory used=3375.9MB, alloc=131.8MB, time=56.32 memory used=3391.3MB, alloc=131.8MB, time=56.43 memory used=3407.4MB, alloc=131.8MB, time=56.60 memory used=3424.1MB, alloc=131.8MB, time=56.71 memory used=3445.4MB, alloc=131.8MB, time=57.04 memory used=3501.9MB, alloc=131.8MB, time=57.33 memory used=3547.5MB, alloc=131.8MB, time=57.54 memory used=3592.8MB, alloc=131.8MB, time=57.75 memory used=3659.0MB, alloc=131.8MB, time=58.19 memory used=3710.2MB, alloc=131.8MB, time=58.43 memory used=3751.1MB, alloc=131.8MB, time=58.63 memory used=3799.7MB, alloc=131.8MB, time=58.83 memory used=3872.4MB, alloc=131.8MB, time=63.14 memory used=3919.4MB, alloc=131.8MB, time=63.37 memory used=3970.1MB, alloc=131.8MB, time=63.58 memory used=4017.5MB, alloc=131.8MB, time=63.76 memory used=4055.5MB, alloc=131.8MB, time=63.92 memory used=4099.1MB, alloc=131.8MB, time=64.09 memory used=4147.6MB, alloc=131.8MB, time=64.26 memory used=4204.6MB, alloc=131.8MB, time=64.43 memory used=4225.1MB, alloc=131.8MB, time=64.56 memory used=4236.5MB, alloc=131.8MB, time=64.69 memory used=4321.4MB, alloc=131.8MB, time=66.60 memory used=4382.7MB, alloc=131.8MB, time=67.12 memory used=4426.1MB, alloc=131.8MB, time=67.33 memory used=4476.1MB, alloc=131.8MB, time=67.53 memory used=4513.0MB, alloc=131.8MB, time=67.69 memory used=4557.9MB, alloc=131.8MB, time=67.86 memory used=4626.1MB, alloc=131.8MB, time=69.12 memory used=4674.9MB, alloc=131.8MB, time=69.37 memory used=4715.2MB, alloc=131.8MB, time=69.58 memory used=4766.0MB, alloc=131.8MB, time=69.79 memory used=4817.6MB, alloc=131.8MB, time=70.00 memory used=4851.8MB, alloc=131.8MB, time=70.16 memory used=4888.8MB, alloc=131.8MB, time=70.33 memory used=4930.0MB, alloc=131.8MB, time=70.51 memory used=4973.8MB, alloc=131.8MB, time=70.69 memory used=5021.4MB, alloc=131.8MB, time=70.87 memory used=5074.0MB, alloc=131.8MB, time=71.05 memory used=5131.2MB, alloc=131.8MB, time=71.25 memory used=5182.3MB, alloc=131.8MB, time=71.43 memory used=5191.9MB, alloc=131.8MB, time=71.54 memory used=5201.9MB, alloc=131.8MB, time=71.66 memory used=5212.2MB, alloc=131.8MB, time=71.80 memory used=5222.3MB, alloc=131.8MB, time=71.92 memory used=5232.5MB, alloc=131.8MB, time=72.04 memory used=5243.4MB, alloc=131.8MB, time=72.16 memory used=5254.3MB, alloc=131.8MB, time=72.28 memory used=5265.2MB, alloc=131.8MB, time=72.42 memory used=5276.6MB, alloc=131.8MB, time=72.55 memory used=5288.0MB, alloc=131.8MB, time=72.68 memory used=5300.2MB, alloc=131.8MB, time=72.80 memory used=5312.3MB, alloc=131.8MB, time=72.92 memory used=5324.7MB, alloc=131.8MB, time=73.04 memory used=5337.5MB, alloc=131.8MB, time=73.16 memory used=5350.8MB, alloc=131.8MB, time=73.27 memory used=5364.6MB, alloc=131.8MB, time=73.41 memory used=5378.9MB, alloc=131.8MB, time=73.52 memory used=5394.0MB, alloc=131.8MB, time=73.64 memory used=5469.7MB, alloc=131.8MB, time=74.92 memory used=5548.2MB, alloc=131.8MB, time=76.04 memory used=5641.6MB, alloc=387.8MB, time=79.10 memory used=5744.0MB, alloc=387.8MB, time=80.12 memory used=5851.9MB, alloc=387.8MB, time=81.76 memory used=5975.0MB, alloc=387.8MB, time=83.22 memory used=6083.4MB, alloc=387.8MB, time=84.99 memory used=6157.3MB, alloc=387.8MB, time=85.81 memory used=6207.5MB, alloc=387.8MB, time=86.23 memory used=6261.8MB, alloc=387.8MB, time=86.83 memory used=6307.0MB, alloc=387.8MB, time=87.11 memory used=6353.2MB, alloc=387.8MB, time=87.38 memory used=6387.5MB, alloc=387.8MB, time=87.61 memory used=6427.2MB, alloc=387.8MB, time=87.83 memory used=6473.7MB, alloc=387.8MB, time=88.07 memory used=6528.3MB, alloc=387.8MB, time=88.32 memory used=6559.9MB, alloc=387.8MB, time=88.50 memory used=6591.4MB, alloc=387.8MB, time=88.67 memory used=6625.7MB, alloc=387.8MB, time=88.85 memory used=6670.3MB, alloc=387.8MB, time=89.36 memory used=6719.8MB, alloc=387.8MB, time=89.67 memory used=6767.3MB, alloc=387.8MB, time=89.95 memory used=6801.0MB, alloc=387.8MB, time=90.17 memory used=6841.1MB, alloc=387.8MB, time=90.41 memory used=6888.0MB, alloc=387.8MB, time=90.66 memory used=6942.5MB, alloc=387.8MB, time=90.92 memory used=6976.1MB, alloc=387.8MB, time=91.12 memory used=7007.7MB, alloc=387.8MB, time=91.31 memory used=7042.7MB, alloc=387.8MB, time=91.50 memory used=7085.5MB, alloc=387.8MB, time=92.65 memory used=7150.9MB, alloc=387.8MB, time=98.69 memory used=7190.2MB, alloc=387.8MB, time=98.94 memory used=7234.6MB, alloc=387.8MB, time=99.19 memory used=7284.6MB, alloc=387.8MB, time=99.45 memory used=7315.9MB, alloc=387.8MB, time=99.64 memory used=7349.7MB, alloc=387.8MB, time=99.84 memory used=7386.6MB, alloc=387.8MB, time=100.05 memory used=7427.0MB, alloc=387.8MB, time=100.25 memory used=7471.8MB, alloc=387.8MB, time=100.46 memory used=7520.6MB, alloc=387.8MB, time=100.68 memory used=7572.9MB, alloc=387.8MB, time=100.91 memory used=7758.6MB, alloc=387.8MB, time=101.73 memory used=7937.0MB, alloc=387.8MB, time=104.16 memory used=7983.8MB, alloc=387.8MB, time=104.42 memory used=8035.9MB, alloc=387.8MB, time=104.83 memory used=8081.9MB, alloc=387.8MB, time=105.08 memory used=8123.0MB, alloc=387.8MB, time=105.29 memory used=8159.1MB, alloc=387.8MB, time=105.49 memory used=8201.6MB, alloc=387.8MB, time=105.69 memory used=8252.2MB, alloc=387.8MB, time=105.91 memory used=8322.9MB, alloc=387.8MB, time=107.26 memory used=8365.4MB, alloc=387.8MB, time=107.51 memory used=8406.6MB, alloc=387.8MB, time=107.75 memory used=8458.0MB, alloc=387.8MB, time=108.01 memory used=8496.7MB, alloc=387.8MB, time=108.23 memory used=8528.5MB, alloc=387.8MB, time=108.43 memory used=8563.0MB, alloc=387.8MB, time=108.62 memory used=8600.5MB, alloc=387.8MB, time=108.82 memory used=8641.1MB, alloc=387.8MB, time=109.03 memory used=8685.8MB, alloc=387.8MB, time=109.25 memory used=8733.4MB, alloc=387.8MB, time=109.48 memory used=8785.1MB, alloc=387.8MB, time=109.71 memory used=8842.4MB, alloc=387.8MB, time=109.94 memory used=8992.5MB, alloc=387.8MB, time=110.45 memory used=9174.0MB, alloc=387.8MB, time=110.98 memory used=9259.6MB, alloc=387.8MB, time=111.76 memory used=9326.2MB, alloc=387.8MB, time=113.19 memory used=9387.9MB, alloc=387.8MB, time=113.89 memory used=9501.5MB, alloc=387.8MB, time=115.66 memory used=9614.6MB, alloc=387.8MB, time=117.30 memory used=9700.0MB, alloc=387.8MB, time=119.22 memory used=9794.4MB, alloc=411.8MB, time=121.86 memory used=9897.0MB, alloc=411.8MB, time=135.02 memory used=9978.2MB, alloc=411.8MB, time=135.46 memory used=10053.2MB, alloc=411.8MB, time=136.25 memory used=10136.7MB, alloc=411.8MB, time=139.95 memory used=10189.9MB, alloc=411.8MB, time=140.30 memory used=10252.5MB, alloc=411.8MB, time=140.64 memory used=10302.6MB, alloc=411.8MB, time=140.94 memory used=10349.3MB, alloc=411.8MB, time=141.23 |\^/| 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(); 1428260930 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [-19 x z - 17 x y - 16 z, -16 x y z - 18 x z + 12 x z - 18 x y z, 3 2 2 2 3 7 x y + 14 y z + 10 x y + 10 y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 3 G := [15 x y z - 4 y z + 2 x - 9, 18 x + 2 x y z + 10 x y + 14 x y z, 2 4 2 2 11 x y z + 5 y - 8 x y + 10 x z] > Problem := [F,G]; 3 2 Problem := [[-19 x z - 17 x y - 16 z, 2 2 2 2 -16 x y z - 18 x z + 12 x z - 18 x y z, 3 2 2 2 3 2 2 2 7 x y + 14 y z + 10 x y + 10 y ], [15 x y z - 4 y z + 2 x - 9, 4 2 3 2 4 2 2 18 x + 2 x y z + 10 x y + 14 x y z, 11 x y z + 5 y - 8 x y + 10 x z] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.4MB, alloc=44.3MB, time=1.02 memory used=58.3MB, alloc=44.3MB, time=1.68 memory used=83.0MB, alloc=68.3MB, time=2.33 memory used=130.5MB, alloc=76.3MB, time=3.54 memory used=178.6MB, alloc=76.3MB, time=4.76 memory used=230.1MB, alloc=100.3MB, time=6.00 memory used=299.4MB, alloc=100.3MB, time=7.65 memory used=363.9MB, alloc=124.3MB, time=9.20 memory used=425.6MB, alloc=380.3MB, time=10.77 memory used=527.0MB, alloc=404.3MB, time=13.07 memory used=651.4MB, alloc=404.3MB, time=16.04 memory used=767.7MB, alloc=428.3MB, time=18.87 memory used=881.5MB, alloc=452.3MB, time=21.77 memory used=980.9MB, alloc=452.3MB, time=24.35 memory used=1088.0MB, alloc=452.3MB, time=27.30 memory used=1158.1MB, alloc=452.3MB, time=29.29 memory used=1237.4MB, alloc=476.3MB, time=31.24 memory used=1318.1MB, alloc=476.3MB, time=33.58 memory used=1391.6MB, alloc=476.3MB, time=35.80 memory used=1466.9MB, alloc=476.3MB, time=38.06 memory used=1530.0MB, alloc=476.3MB, time=39.84 memory used=1595.7MB, alloc=476.3MB, time=41.91 memory used=1664.2MB, alloc=476.3MB, time=44.06 memory used=1725.3MB, alloc=476.3MB, time=46.02 memory used=1777.1MB, alloc=476.3MB, time=47.61 memory used=1845.0MB, alloc=476.3MB, time=49.53 memory used=1889.4MB, alloc=476.3MB, time=50.99 memory used=1938.1MB, alloc=500.3MB, time=52.59 memory used=2137.3MB, alloc=524.3MB, time=57.69 memory used=2340.3MB, alloc=548.3MB, time=62.12 memory used=2528.9MB, alloc=548.3MB, time=66.52 memory used=2707.4MB, alloc=572.3MB, time=71.25 memory used=2882.2MB, alloc=596.3MB, time=75.98 memory used=3052.6MB, alloc=596.3MB, time=80.07 memory used=3230.4MB, alloc=620.3MB, time=85.91 memory used=3373.0MB, alloc=644.3MB, time=89.89 memory used=3503.2MB, alloc=644.3MB, time=94.41 memory used=3621.2MB, alloc=644.3MB, time=98.06 memory used=3743.2MB, alloc=644.3MB, time=102.40 memory used=3806.8MB, alloc=644.3MB, time=104.90 memory used=3901.4MB, alloc=668.3MB, time=108.09 memory used=4242.9MB, alloc=692.3MB, time=117.10 |\^/| 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(); 1428261230 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 F := [-4 y - 18 y z - 20 y - 4 z, 17 x + 3 x y z + 11 y - 8, 3 2 2 2 2 2 18 x y + 19 x y + x y z - 18 y z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 2 G := [6 y z - 6 x z + 3 x - 14 x z, -16 x y - 5 x z - 11 x z - 8 z, 2 3 11 x y z - 5 z - 18 x z + 8] > Problem := [F,G]; 3 2 2 4 3 Problem := [[-4 y - 18 y z - 20 y - 4 z, 17 x + 3 x y z + 11 y - 8, 3 2 2 2 2 2 3 2 2 18 x y + 19 x y + x y z - 18 y z ], [6 y z - 6 x z + 3 x - 14 x z, 2 2 3 2 2 3 -16 x y - 5 x z - 11 x z - 8 z, 11 x y z - 5 z - 18 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=0.32 memory used=25.9MB, alloc=32.4MB, time=0.75 memory used=45.4MB, alloc=35.2MB, time=0.97 memory used=60.6MB, alloc=35.2MB, time=1.03 memory used=72.0MB, alloc=35.2MB, time=1.09 memory used=83.3MB, alloc=35.2MB, time=1.14 memory used=96.3MB, alloc=35.2MB, time=1.19 memory used=111.3MB, alloc=35.2MB, time=1.25 memory used=125.9MB, alloc=35.2MB, time=1.30 memory used=135.5MB, alloc=35.2MB, time=1.34 memory used=156.0MB, alloc=35.2MB, time=1.81 memory used=178.4MB, alloc=63.2MB, time=2.40 memory used=216.4MB, alloc=63.9MB, time=2.57 memory used=239.1MB, alloc=63.9MB, time=2.68 memory used=266.6MB, alloc=63.9MB, time=2.79 memory used=299.5MB, alloc=63.9MB, time=2.90 memory used=325.0MB, alloc=63.9MB, time=3.00 memory used=344.7MB, alloc=63.9MB, time=3.09 memory used=366.3MB, alloc=63.9MB, time=3.17 memory used=389.5MB, alloc=63.9MB, time=3.27 memory used=414.6MB, alloc=63.9MB, time=3.36 memory used=441.7MB, alloc=63.9MB, time=3.46 memory used=471.3MB, alloc=63.9MB, time=3.56 memory used=503.4MB, alloc=63.9MB, time=3.65 memory used=538.2MB, alloc=63.9MB, time=3.75 memory used=559.5MB, alloc=63.9MB, time=3.82 memory used=595.2MB, alloc=64.0MB, time=4.21 memory used=624.8MB, alloc=64.0MB, time=4.35 memory used=649.2MB, alloc=64.0MB, time=4.48 memory used=679.3MB, alloc=64.0MB, time=4.61 memory used=713.1MB, alloc=64.0MB, time=4.74 memory used=732.7MB, alloc=64.0MB, time=4.84 memory used=753.0MB, alloc=64.0MB, time=4.95 memory used=775.5MB, alloc=64.0MB, time=5.05 memory used=799.3MB, alloc=64.0MB, time=5.15 memory used=824.8MB, alloc=64.0MB, time=5.26 memory used=852.6MB, alloc=64.0MB, time=5.37 memory used=882.7MB, alloc=64.0MB, time=5.48 memory used=915.9MB, alloc=64.0MB, time=5.60 memory used=947.0MB, alloc=64.0MB, time=5.71 memory used=965.3MB, alloc=64.0MB, time=5.78 memory used=1015.1MB, alloc=65.8MB, time=11.09 memory used=1041.1MB, alloc=65.8MB, time=11.23 memory used=1070.3MB, alloc=65.8MB, time=11.37 memory used=1091.4MB, alloc=65.8MB, time=11.48 memory used=1115.9MB, alloc=65.8MB, time=11.60 memory used=1143.4MB, alloc=65.8MB, time=11.71 memory used=1173.9MB, alloc=65.8MB, time=11.84 memory used=1207.5MB, alloc=65.8MB, time=11.97 memory used=1231.1MB, alloc=65.8MB, time=12.06 memory used=1250.1MB, alloc=65.8MB, time=12.15 memory used=1269.6MB, alloc=65.8MB, time=12.24 memory used=1290.7MB, alloc=65.8MB, time=12.32 memory used=1312.1MB, alloc=65.8MB, time=12.41 memory used=1334.9MB, alloc=65.8MB, time=12.50 memory used=1359.1MB, alloc=65.8MB, time=12.59 memory used=1384.5MB, alloc=65.8MB, time=12.67 memory used=1410.4MB, alloc=65.8MB, time=12.77 memory used=1438.3MB, alloc=65.8MB, time=12.86 memory used=1467.4MB, alloc=65.8MB, time=12.97 memory used=1497.5MB, alloc=65.8MB, time=13.05 memory used=1529.0MB, alloc=65.8MB, time=13.16 memory used=1562.7MB, alloc=65.8MB, time=13.25 memory used=1596.1MB, alloc=81.9MB, time=13.37 memory used=1607.5MB, alloc=83.8MB, time=13.44 memory used=1619.4MB, alloc=83.8MB, time=13.51 memory used=1631.5MB, alloc=83.8MB, time=13.59 memory used=1643.6MB, alloc=83.8MB, time=13.66 memory used=1656.6MB, alloc=83.8MB, time=13.74 memory used=1670.2MB, alloc=83.8MB, time=13.82 memory used=1715.3MB, alloc=83.8MB, time=14.72 memory used=1748.7MB, alloc=83.8MB, time=14.96 memory used=1775.3MB, alloc=83.8MB, time=15.07 memory used=1800.6MB, alloc=83.8MB, time=15.18 memory used=1831.3MB, alloc=83.8MB, time=15.32 memory used=1860.3MB, alloc=83.8MB, time=15.42 memory used=1880.5MB, alloc=83.8MB, time=15.50 memory used=1902.7MB, alloc=83.8MB, time=15.57 memory used=1927.4MB, alloc=83.8MB, time=15.65 memory used=1968.6MB, alloc=83.8MB, time=16.23 memory used=2028.0MB, alloc=83.8MB, time=33.54 memory used=2074.1MB, alloc=83.8MB, time=55.80 memory used=2108.3MB, alloc=83.8MB, time=56.04 memory used=2131.6MB, alloc=83.8MB, time=56.17 memory used=2161.2MB, alloc=83.8MB, time=56.32 memory used=2186.1MB, alloc=83.8MB, time=56.43 memory used=2204.1MB, alloc=83.8MB, time=56.53 memory used=2224.3MB, alloc=83.8MB, time=56.64 memory used=2245.7MB, alloc=83.8MB, time=56.76 memory used=2268.4MB, alloc=83.8MB, time=56.87 memory used=2293.9MB, alloc=83.8MB, time=56.99 memory used=2320.6MB, alloc=83.8MB, time=57.12 memory used=2348.6MB, alloc=83.8MB, time=57.25 memory used=2377.8MB, alloc=83.8MB, time=57.38 memory used=2409.8MB, alloc=83.8MB, time=57.51 memory used=2433.2MB, alloc=83.8MB, time=57.60 memory used=2448.6MB, alloc=83.8MB, time=57.68 memory used=2464.3MB, alloc=83.8MB, time=57.75 memory used=2480.5MB, alloc=83.8MB, time=57.84 memory used=2497.0MB, alloc=83.8MB, time=57.92 memory used=2513.6MB, alloc=83.8MB, time=58.03 memory used=2530.6MB, alloc=83.8MB, time=58.12 memory used=2547.9MB, alloc=83.8MB, time=58.21 memory used=2567.2MB, alloc=83.8MB, time=58.29 memory used=2586.9MB, alloc=83.8MB, time=58.37 memory used=2606.9MB, alloc=83.8MB, time=58.46 memory used=2627.1MB, alloc=83.8MB, time=58.55 memory used=2647.5MB, alloc=83.8MB, time=58.63 memory used=2668.2MB, alloc=83.8MB, time=58.72 memory used=2689.0MB, alloc=83.8MB, time=58.82 memory used=2710.1MB, alloc=83.8MB, time=58.91 memory used=2731.5MB, alloc=83.8MB, time=59.01 memory used=2755.1MB, alloc=83.8MB, time=59.10 memory used=2779.1MB, alloc=83.8MB, time=59.19 memory used=2803.3MB, alloc=83.8MB, time=59.29 memory used=2827.7MB, alloc=83.8MB, time=59.38 memory used=2852.2MB, alloc=83.8MB, time=59.47 memory used=2876.9MB, alloc=83.8MB, time=59.56 memory used=2902.0MB, alloc=83.8MB, time=59.65 memory used=2929.3MB, alloc=83.8MB, time=59.74 memory used=2956.9MB, alloc=83.8MB, time=59.84 memory used=2984.7MB, alloc=83.8MB, time=59.93 memory used=3012.5MB, alloc=83.8MB, time=60.03 memory used=3040.5MB, alloc=83.8MB, time=60.13 memory used=3071.1MB, alloc=83.8MB, time=60.23 memory used=3101.8MB, alloc=83.8MB, time=60.33 memory used=3132.5MB, alloc=83.8MB, time=60.44 memory used=3172.8MB, alloc=83.8MB, time=60.55 memory used=3183.5MB, alloc=83.8MB, time=60.62 memory used=3194.5MB, alloc=83.8MB, time=60.69 memory used=3204.5MB, alloc=83.8MB, time=60.77 memory used=3214.6MB, alloc=83.8MB, time=60.89 memory used=3224.7MB, alloc=83.8MB, time=60.98 memory used=3234.8MB, alloc=83.8MB, time=61.06 memory used=3244.9MB, alloc=83.8MB, time=61.14 memory used=3255.0MB, alloc=83.8MB, time=61.23 memory used=3265.1MB, alloc=83.8MB, time=61.29 memory used=3275.1MB, alloc=83.8MB, time=61.37 memory used=3285.2MB, alloc=83.8MB, time=61.43 memory used=3295.3MB, alloc=83.8MB, time=61.52 memory used=3305.3MB, alloc=83.8MB, time=61.63 memory used=3315.3MB, alloc=83.8MB, time=61.72 memory 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used=9945.0MB, alloc=363.8MB, time=96.28 memory used=9988.8MB, alloc=363.8MB, time=96.41 memory used=10034.4MB, alloc=363.8MB, time=96.54 memory used=10080.8MB, alloc=363.8MB, time=96.67 memory used=10127.9MB, alloc=363.8MB, time=96.81 memory used=10176.3MB, alloc=363.8MB, time=96.94 memory used=10226.5MB, alloc=363.8MB, time=97.07 memory used=10301.9MB, alloc=363.8MB, time=97.28 memory used=10457.6MB, alloc=363.8MB, time=97.88 memory used=10604.6MB, alloc=363.8MB, time=98.22 memory used=10692.3MB, alloc=363.8MB, time=160.03 |\^/| 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(); 1428261530 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 4 2 F := [5 x y z - 19 y - 4 y + 4 z, 13 y z - 2 z - y z + x z, 2 2 6 x y z + y z - 13] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 G := [-10 x y + 5 y z - 12 y z - 10, 18 x y - 12 x y + z - 4 z, 3 2 2 17 y - 10 y z - 14 y - 15 x] > Problem := [F,G]; 2 3 3 4 2 Problem := [[5 x y z - 19 y - 4 y + 4 z, 13 y z - 2 z - y z + x z, 2 2 2 2 2 6 x y z + y z - 13], [-10 x y + 5 y z - 12 y z - 10, 2 2 3 3 2 2 18 x y - 12 x y + z - 4 z, 17 y - 10 y z - 14 y - 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=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=45.6MB, alloc=56.3MB, time=1.33 memory used=84.9MB, alloc=60.3MB, time=2.25 memory used=127.1MB, alloc=60.3MB, time=3.06 memory used=166.6MB, alloc=60.3MB, time=3.69 memory used=213.2MB, alloc=68.3MB, time=4.70 memory used=255.0MB, alloc=92.3MB, time=5.63 memory used=325.5MB, alloc=92.3MB, time=6.98 memory used=369.4MB, alloc=92.3MB, time=7.77 memory used=406.8MB, alloc=92.3MB, time=8.08 memory used=472.7MB, alloc=348.3MB, time=9.59 memory used=549.4MB, alloc=348.3MB, time=11.15 memory used=618.8MB, alloc=348.3MB, time=13.13 memory used=653.8MB, alloc=348.3MB, time=13.48 memory used=685.9MB, alloc=348.3MB, time=13.71 memory used=727.0MB, alloc=348.3MB, time=14.71 memory used=754.7MB, alloc=348.3MB, time=14.89 memory used=784.0MB, alloc=348.3MB, time=15.06 memory used=815.3MB, alloc=348.3MB, time=15.34 memory used=851.5MB, alloc=348.3MB, time=15.82 memory used=899.7MB, alloc=348.3MB, time=16.88 memory used=928.2MB, alloc=372.3MB, time=17.09 memory used=975.8MB, alloc=372.3MB, time=17.30 memory used=1055.3MB, alloc=372.3MB, time=18.66 memory used=1145.7MB, alloc=372.3MB, time=20.42 memory used=1220.6MB, alloc=372.3MB, time=21.86 memory used=1301.4MB, alloc=372.3MB, time=23.86 memory used=1391.2MB, alloc=396.3MB, time=25.90 memory used=1497.7MB, alloc=420.3MB, time=28.51 memory used=1608.1MB, alloc=420.3MB, time=30.40 memory used=1717.1MB, alloc=420.3MB, time=32.73 memory used=1833.8MB, alloc=420.3MB, time=34.72 memory used=1922.7MB, alloc=420.3MB, time=35.94 memory used=1998.7MB, alloc=420.3MB, time=36.72 memory used=2070.8MB, alloc=420.3MB, time=37.51 memory used=2146.3MB, alloc=420.3MB, time=38.32 memory used=2268.1MB, alloc=444.3MB, time=40.77 memory used=2398.1MB, alloc=444.3MB, time=43.62 memory used=2498.1MB, alloc=444.3MB, time=46.20 memory used=2614.7MB, alloc=468.3MB, time=48.41 memory used=2707.8MB, alloc=468.3MB, time=50.96 memory used=2806.1MB, alloc=468.3MB, time=53.16 memory used=2889.9MB, alloc=468.3MB, time=55.51 memory used=2998.1MB, alloc=468.3MB, time=56.81 memory used=3092.9MB, alloc=468.3MB, time=58.06 memory used=3186.3MB, alloc=468.3MB, time=58.94 memory used=3269.0MB, alloc=468.3MB, time=60.41 memory used=3360.4MB, alloc=468.3MB, time=61.25 memory used=3458.7MB, alloc=468.3MB, time=62.21 memory used=3552.5MB, alloc=468.3MB, time=63.12 memory used=3630.8MB, alloc=468.3MB, time=63.79 memory used=3733.2MB, alloc=468.3MB, time=68.03 memory used=3805.9MB, alloc=468.3MB, time=68.53 memory used=3902.2MB, alloc=468.3MB, time=69.29 memory used=3989.1MB, alloc=468.3MB, time=70.03 memory used=4089.0MB, alloc=468.3MB, time=74.40 memory used=4163.2MB, alloc=468.3MB, time=74.99 memory used=4234.2MB, alloc=468.3MB, time=75.49 memory used=4330.7MB, alloc=468.3MB, time=76.28 memory used=4420.4MB, alloc=468.3MB, time=77.14 memory used=4519.8MB, alloc=468.3MB, time=81.41 memory used=4599.3MB, alloc=468.3MB, time=82.01 memory used=4671.4MB, alloc=468.3MB, time=82.54 memory used=4775.2MB, alloc=468.3MB, time=84.01 memory used=4851.7MB, alloc=468.3MB, time=84.62 memory used=4940.7MB, alloc=468.3MB, time=85.35 memory used=5032.8MB, alloc=468.3MB, time=86.92 memory used=5119.6MB, alloc=468.3MB, time=87.55 memory used=5209.3MB, alloc=468.3MB, time=88.26 memory used=5298.4MB, alloc=468.3MB, time=89.62 memory used=5387.8MB, alloc=468.3MB, time=90.39 memory used=5477.5MB, alloc=468.3MB, time=91.11 memory used=5564.8MB, alloc=468.3MB, time=92.51 memory used=5697.8MB, alloc=468.3MB, time=94.82 memory used=5799.5MB, alloc=468.3MB, time=97.84 memory used=5895.1MB, alloc=492.3MB, time=100.90 memory used=6004.2MB, alloc=492.3MB, time=104.22 memory used=6092.8MB, alloc=492.3MB, time=106.00 memory used=6236.0MB, alloc=492.3MB, time=109.53 memory used=6355.3MB, alloc=492.3MB, time=117.49 memory used=6447.2MB, alloc=492.3MB, time=118.10 memory used=6517.9MB, alloc=492.3MB, time=118.62 memory used=6639.9MB, alloc=492.3MB, time=120.49 memory used=6737.6MB, alloc=492.3MB, time=122.30 memory used=6849.6MB, alloc=492.3MB, time=125.39 memory used=6925.0MB, alloc=492.3MB, time=127.78 memory used=7003.5MB, alloc=492.3MB, time=130.00 memory used=7066.9MB, alloc=492.3MB, time=131.99 memory used=7133.4MB, alloc=492.3MB, time=134.22 memory used=7190.9MB, alloc=492.3MB, time=136.14 memory used=7301.8MB, alloc=516.3MB, time=137.49 memory used=7396.2MB, alloc=516.3MB, time=138.22 memory used=7519.0MB, alloc=516.3MB, time=139.35 memory used=7613.8MB, alloc=516.3MB, time=140.08 |\^/| 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(); 1428261830 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 F := [-5 z + 11 x y z + 15, 3 x y + y z + 5 x y - 17 y z, 2 2 3 2 2 -17 x y + 3 y + 17 x + 10 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 3 2 2 G := [-18 x z + 11 y - 11 z - 17 z, 6 x z + 20 x y - 15 y z - 17 y , 2 2 3 -14 x y z - x y z + 18 y z + 20 y] > Problem := [F,G]; 4 3 2 Problem := [[-5 z + 11 x y z + 15, 3 x y + y z + 5 x y - 17 y z, 2 2 3 2 2 2 3 2 -17 x y + 3 y + 17 x + 10 z ], [-18 x z + 11 y - 11 z - 17 z, 2 2 3 2 2 2 2 3 6 x z + 20 x y - 15 y z - 17 y , -14 x y z - x y z + 18 y z + 20 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.8MB, alloc=32.3MB, time=0.86 memory used=43.7MB, alloc=56.3MB, time=1.35 memory used=88.4MB, alloc=60.3MB, time=2.30 memory used=124.3MB, alloc=60.3MB, time=2.87 memory used=155.2MB, alloc=60.3MB, time=3.11 memory used=191.3MB, alloc=60.3MB, time=3.70 memory used=221.1MB, alloc=60.3MB, time=4.02 memory used=267.9MB, alloc=70.2MB, time=5.68 memory used=290.5MB, alloc=70.2MB, time=5.79 memory used=325.6MB, alloc=70.2MB, time=6.18 memory used=370.0MB, alloc=70.2MB, time=7.20 memory used=412.9MB, alloc=70.2MB, time=8.22 memory used=454.3MB, alloc=94.2MB, time=9.23 memory used=511.2MB, alloc=94.2MB, time=9.98 memory used=562.1MB, alloc=94.2MB, time=11.24 memory used=608.2MB, alloc=94.2MB, time=11.57 memory used=639.8MB, alloc=94.2MB, time=11.72 memory used=679.3MB, alloc=94.2MB, time=11.98 memory used=729.6MB, alloc=94.2MB, time=12.54 memory used=765.8MB, alloc=94.2MB, time=12.73 memory used=800.4MB, alloc=94.2MB, time=13.06 memory used=849.7MB, alloc=94.2MB, time=15.32 memory used=882.5MB, alloc=94.2MB, time=15.50 memory used=915.5MB, alloc=94.2MB, time=15.66 memory used=950.6MB, alloc=94.2MB, time=15.81 memory used=976.8MB, alloc=94.2MB, time=15.93 memory used=1013.5MB, alloc=94.2MB, time=16.23 memory used=1081.5MB, alloc=94.2MB, time=18.53 memory used=1114.8MB, alloc=94.2MB, time=18.69 memory used=1145.3MB, alloc=94.2MB, time=18.84 memory used=1183.7MB, alloc=94.2MB, time=19.00 memory used=1208.5MB, alloc=94.2MB, time=19.13 memory used=1236.2MB, alloc=94.2MB, time=19.25 memory used=1276.1MB, alloc=94.2MB, time=19.93 memory used=1308.4MB, alloc=94.2MB, time=20.15 memory used=1345.3MB, alloc=94.2MB, time=20.68 memory used=1434.2MB, alloc=94.2MB, time=22.18 memory used=1510.1MB, alloc=94.2MB, time=23.43 memory used=1585.0MB, alloc=94.2MB, time=25.67 memory used=1661.3MB, alloc=94.2MB, time=28.59 memory used=1727.0MB, alloc=94.2MB, time=30.99 memory used=1787.7MB, alloc=94.2MB, time=32.49 memory used=1822.5MB, alloc=94.2MB, time=32.67 memory used=1848.2MB, alloc=94.2MB, time=32.82 memory used=1881.1MB, alloc=94.2MB, time=32.98 memory used=1913.0MB, alloc=94.2MB, time=33.12 memory used=1937.0MB, alloc=94.2MB, time=33.24 memory used=1984.8MB, alloc=94.2MB, time=33.86 memory used=2058.6MB, alloc=94.2MB, time=35.21 memory used=2109.2MB, alloc=94.2MB, time=36.52 memory used=2142.0MB, alloc=94.2MB, time=36.73 memory used=2175.1MB, alloc=94.2MB, time=37.04 memory used=2235.0MB, alloc=374.2MB, time=38.43 memory used=2305.6MB, alloc=374.2MB, time=39.68 memory used=2392.7MB, alloc=374.2MB, time=41.56 memory used=2433.5MB, alloc=374.2MB, time=41.80 memory used=2480.3MB, alloc=374.2MB, time=42.05 memory used=2515.2MB, alloc=374.2MB, time=42.24 memory used=2551.3MB, alloc=374.2MB, time=42.42 memory used=2593.9MB, alloc=374.2MB, time=42.63 memory used=2644.7MB, alloc=374.2MB, time=42.83 memory used=2715.8MB, alloc=374.2MB, time=44.00 memory used=2794.1MB, alloc=374.2MB, time=46.48 memory used=2831.5MB, alloc=374.2MB, time=46.72 memory used=2881.0MB, alloc=374.2MB, time=46.98 memory used=2916.2MB, alloc=374.2MB, time=47.18 memory used=2950.4MB, alloc=374.2MB, time=47.37 memory used=2988.1MB, alloc=374.2MB, time=47.56 memory used=3030.3MB, alloc=374.2MB, time=47.76 memory used=3077.1MB, alloc=374.2MB, time=47.97 memory used=3129.3MB, alloc=374.2MB, time=48.20 memory used=3354.0MB, alloc=374.2MB, time=50.22 memory used=3431.4MB, alloc=374.2MB, time=51.51 memory used=3469.7MB, alloc=374.2MB, time=51.71 memory used=3506.0MB, alloc=374.2MB, time=51.89 memory used=3565.2MB, alloc=374.2MB, time=55.35 memory used=3602.9MB, alloc=374.2MB, time=55.58 memory used=3645.1MB, alloc=374.2MB, time=55.81 memory used=3687.6MB, alloc=374.2MB, time=56.03 memory used=3717.6MB, alloc=374.2MB, time=56.21 memory used=3751.4MB, alloc=374.2MB, time=56.40 memory used=3788.6MB, alloc=374.2MB, time=56.59 memory used=3829.6MB, alloc=374.2MB, time=56.79 memory used=3876.2MB, alloc=374.2MB, time=56.98 memory used=3979.0MB, alloc=374.2MB, time=60.68 memory used=4018.7MB, alloc=374.2MB, time=60.93 memory used=4056.6MB, alloc=374.2MB, time=61.15 memory used=4104.8MB, alloc=374.2MB, time=61.38 memory used=4134.2MB, alloc=374.2MB, time=61.57 memory used=4166.4MB, alloc=374.2MB, time=61.77 memory used=4202.0MB, alloc=374.2MB, time=61.95 memory used=4241.4MB, alloc=374.2MB, time=62.15 memory used=4285.4MB, alloc=374.2MB, time=62.34 memory used=4388.7MB, alloc=374.2MB, time=63.02 memory used=4436.7MB, alloc=374.2MB, time=63.49 memory used=4477.5MB, alloc=374.2MB, time=63.71 memory used=4544.7MB, alloc=374.2MB, time=64.58 memory used=4624.6MB, alloc=398.2MB, time=66.72 memory used=4735.4MB, alloc=398.2MB, time=69.40 memory used=4821.2MB, alloc=398.2MB, time=71.06 memory used=4886.1MB, alloc=398.2MB, time=71.99 memory used=4949.4MB, alloc=398.2MB, time=72.86 memory used=5052.3MB, alloc=422.2MB, time=74.96 memory used=5140.3MB, alloc=422.2MB, time=77.56 memory used=5269.7MB, alloc=422.2MB, time=79.64 memory used=5395.1MB, alloc=446.2MB, time=82.15 memory used=5506.2MB, alloc=446.2MB, time=84.79 memory used=5608.4MB, alloc=446.2MB, time=87.38 memory used=5709.5MB, alloc=470.2MB, time=89.93 memory used=5799.6MB, alloc=470.2MB, time=92.33 memory used=5905.8MB, alloc=470.2MB, time=94.50 memory used=6042.6MB, alloc=470.2MB, time=96.70 memory used=6144.2MB, alloc=470.2MB, time=98.39 memory used=6257.4MB, alloc=470.2MB, time=100.24 memory used=6332.4MB, alloc=470.2MB, time=100.73 memory used=6419.3MB, alloc=470.2MB, time=101.39 memory used=6509.3MB, alloc=470.2MB, time=102.88 memory used=6612.0MB, alloc=470.2MB, time=104.00 memory used=6714.9MB, alloc=470.2MB, time=105.85 memory used=6806.4MB, alloc=470.2MB, time=106.64 memory used=6879.7MB, alloc=470.2MB, time=107.18 memory used=6979.4MB, alloc=470.2MB, time=111.21 memory used=7053.7MB, alloc=470.2MB, time=111.73 memory used=7127.3MB, alloc=470.2MB, time=112.20 memory used=7200.7MB, alloc=470.2MB, time=112.74 memory used=7314.4MB, alloc=470.2MB, time=114.69 memory used=7391.1MB, alloc=470.2MB, time=115.30 memory used=7486.7MB, alloc=470.2MB, time=116.02 memory used=7590.8MB, alloc=470.2MB, time=126.66 memory used=7658.0MB, alloc=470.2MB, time=127.17 memory used=7739.8MB, alloc=470.2MB, time=127.67 memory used=7810.8MB, alloc=494.2MB, time=128.15 memory used=7883.5MB, alloc=494.2MB, time=128.62 memory used=7966.7MB, alloc=494.2MB, time=129.09 memory used=8062.8MB, alloc=494.2MB, time=129.57 memory used=8174.6MB, alloc=494.2MB, time=130.06 memory used=8393.6MB, alloc=494.2MB, time=131.28 memory used=8482.2MB, alloc=494.2MB, time=131.84 memory used=8573.7MB, alloc=494.2MB, time=132.36 memory used=8687.4MB, alloc=494.2MB, time=133.38 memory used=8777.3MB, alloc=494.2MB, time=133.94 memory used=8867.3MB, alloc=494.2MB, time=134.46 memory used=9092.7MB, alloc=494.2MB, time=169.81 memory used=9181.8MB, alloc=494.2MB, time=170.39 memory used=9270.2MB, alloc=494.2MB, time=170.97 memory used=9374.1MB, alloc=494.2MB, time=171.53 memory used=9440.0MB, alloc=494.2MB, time=171.99 memory used=9514.4MB, alloc=494.2MB, time=172.44 memory used=9595.6MB, alloc=494.2MB, time=172.91 memory used=9686.3MB, alloc=494.2MB, time=173.38 memory used=9786.3MB, alloc=494.2MB, time=173.85 memory used=9898.8MB, alloc=494.2MB, time=174.35 memory used=10070.7MB, alloc=494.2MB, time=175.00 memory used=10226.8MB, alloc=494.2MB, time=175.61 memory used=10385.9MB, alloc=494.2MB, time=176.82 memory used=10469.8MB, alloc=494.2MB, time=177.38 memory used=10564.2MB, alloc=494.2MB, time=177.92 |\^/| 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(); 1428262130 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 3 2 F := [5 x - 19 z + 7 x y - 17 x, -11 x y z + 3 x z + 5 y + 11 y z , 3 2 3 19 x z - x z - 18 z - 20 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 2 3 G := [-10 x y + 6 y - 19 x z - 20 x, 19 x z - 4 x + 7 x y + 8 z , 3 3 3 2 17 x y + 14 x y + 17 x z - 13 z ] > Problem := [F,G]; 4 3 2 2 3 2 Problem := [[5 x - 19 z + 7 x y - 17 x, -11 x y z + 3 x z + 5 y + 11 y z , 3 2 3 3 3 19 x z - x z - 18 z - 20 x z], [-10 x y + 6 y - 19 x z - 20 x, 2 2 3 2 3 3 3 3 2 19 x z - 4 x + 7 x y + 8 z , 17 x y + 14 x y + 17 x z - 13 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.9MB, alloc=44.7MB, time=0.95 memory used=58.9MB, alloc=44.7MB, time=1.59 memory used=87.3MB, alloc=68.7MB, time=2.26 memory used=137.6MB, alloc=76.7MB, time=3.05 memory used=185.9MB, alloc=78.4MB, time=3.69 memory used=229.0MB, alloc=78.4MB, time=4.05 memory used=282.4MB, alloc=78.4MB, time=4.99 memory used=337.1MB, alloc=78.4MB, time=6.00 memory used=399.5MB, alloc=78.4MB, time=7.16 memory used=451.0MB, alloc=78.4MB, time=8.19 memory used=518.6MB, alloc=78.4MB, time=9.21 memory used=569.6MB, alloc=102.4MB, time=10.40 memory used=625.7MB, alloc=102.4MB, time=11.71 memory used=700.1MB, alloc=102.4MB, time=12.71 memory used=741.4MB, alloc=102.4MB, time=12.98 memory used=781.2MB, alloc=102.4MB, time=13.30 memory used=825.8MB, alloc=102.4MB, time=13.70 memory used=862.6MB, alloc=102.4MB, time=13.90 memory used=896.8MB, alloc=102.4MB, time=14.07 memory used=938.2MB, alloc=102.4MB, time=14.40 memory used=975.5MB, alloc=102.4MB, time=14.60 memory used=1009.8MB, alloc=102.4MB, time=14.77 memory used=1061.5MB, alloc=102.4MB, time=16.38 memory used=1095.8MB, alloc=102.4MB, time=16.58 memory used=1132.3MB, alloc=102.4MB, time=16.76 memory used=1195.4MB, alloc=102.4MB, time=18.99 memory used=1249.6MB, alloc=102.4MB, time=27.06 memory used=1288.6MB, alloc=102.4MB, time=27.26 memory used=1316.0MB, alloc=102.4MB, time=27.43 memory used=1348.9MB, alloc=102.4MB, time=27.61 memory used=1387.3MB, alloc=102.4MB, time=27.79 memory used=1429.4MB, alloc=102.4MB, time=27.97 memory used=1453.9MB, alloc=102.4MB, time=28.11 memory used=1479.9MB, alloc=102.4MB, time=28.24 memory used=1508.2MB, alloc=102.4MB, time=28.39 memory used=1538.4MB, alloc=102.4MB, time=28.54 memory used=1571.2MB, alloc=102.4MB, time=28.69 memory used=1607.6MB, alloc=102.4MB, time=28.84 memory used=1652.3MB, alloc=102.4MB, time=29.13 memory used=1745.5MB, alloc=102.4MB, time=33.69 memory used=1779.8MB, alloc=102.4MB, time=33.90 memory used=1812.9MB, alloc=102.4MB, time=34.08 memory used=1855.5MB, alloc=102.4MB, time=34.46 memory used=1952.3MB, alloc=126.4MB, time=36.54 memory used=2066.5MB, alloc=126.9MB, time=38.47 memory used=2180.8MB, alloc=127.2MB, time=40.98 memory used=2296.4MB, alloc=127.2MB, time=44.42 memory used=2411.6MB, alloc=127.3MB, time=48.76 memory used=2527.0MB, alloc=127.4MB, time=54.00 memory used=2643.0MB, alloc=127.6MB, time=59.93 memory used=2749.1MB, alloc=383.6MB, time=64.43 memory used=2864.5MB, alloc=383.6MB, time=66.88 memory used=2971.6MB, alloc=383.6MB, time=68.90 memory used=3080.7MB, alloc=383.6MB, time=71.55 memory used=3189.6MB, alloc=383.6MB, time=75.10 memory used=3297.9MB, alloc=383.6MB, time=79.48 memory used=3406.6MB, alloc=383.6MB, time=84.61 memory used=3516.0MB, alloc=383.6MB, time=90.15 memory used=3627.6MB, alloc=383.6MB, time=96.82 memory used=3736.1MB, alloc=383.6MB, time=100.28 memory used=3809.3MB, alloc=383.6MB, time=101.79 memory used=3855.8MB, alloc=383.6MB, time=102.02 memory used=3902.3MB, alloc=383.6MB, time=102.39 memory used=3997.5MB, alloc=383.6MB, time=103.53 memory used=4111.5MB, alloc=383.6MB, time=105.30 memory used=4199.2MB, alloc=383.6MB, time=107.15 memory used=4258.5MB, alloc=407.6MB, time=107.90 memory used=4313.9MB, alloc=407.6MB, time=108.20 memory used=4368.0MB, alloc=407.6MB, time=108.46 memory used=4418.0MB, alloc=407.6MB, time=108.69 memory used=4487.3MB, alloc=407.6MB, time=109.28 memory used=4610.3MB, alloc=407.6MB, time=136.49 memory used=4684.4MB, alloc=407.6MB, time=137.08 memory used=4737.2MB, alloc=407.6MB, time=137.38 memory used=4788.8MB, alloc=407.6MB, time=137.68 memory used=4851.4MB, alloc=407.6MB, time=137.98 memory used=4919.5MB, alloc=407.6MB, time=138.30 memory used=4957.9MB, alloc=407.6MB, time=138.54 memory used=4999.5MB, alloc=407.6MB, time=138.78 memory used=5043.3MB, alloc=407.6MB, time=139.02 memory used=5090.2MB, alloc=407.6MB, time=139.26 memory used=5141.0MB, alloc=407.6MB, time=139.50 memory used=5195.5MB, alloc=407.6MB, time=139.74 memory used=5253.5MB, alloc=407.6MB, time=139.99 memory used=5315.0MB, alloc=407.6MB, time=140.24 memory used=5379.9MB, alloc=407.6MB, time=140.50 memory used=5448.0MB, alloc=407.6MB, time=140.77 memory used=5521.2MB, alloc=407.6MB, time=141.03 memory used=5665.9MB, alloc=407.6MB, time=141.74 memory used=5812.0MB, alloc=407.6MB, time=142.20 memory used=5974.4MB, alloc=407.6MB, time=142.66 memory used=6158.6MB, alloc=407.6MB, time=143.15 memory used=6399.3MB, alloc=407.6MB, time=144.13 memory used=6489.9MB, alloc=407.6MB, time=172.13 memory used=6583.6MB, alloc=407.6MB, time=173.99 memory used=6643.1MB, alloc=407.6MB, time=174.31 memory used=6691.0MB, alloc=407.6MB, time=174.60 memory used=6748.2MB, alloc=407.6MB, time=174.90 memory used=6816.3MB, alloc=407.6MB, time=175.21 memory used=6868.8MB, alloc=407.6MB, time=175.47 memory used=6909.0MB, alloc=407.6MB, time=175.71 memory used=6951.0MB, alloc=407.6MB, time=175.94 memory used=6996.5MB, alloc=407.6MB, time=176.18 memory used=7045.7MB, alloc=407.6MB, time=176.43 memory used=7096.4MB, alloc=407.6MB, time=176.68 memory used=7150.6MB, alloc=407.6MB, time=176.94 memory used=7208.5MB, alloc=407.6MB, time=177.19 memory used=7270.0MB, alloc=407.6MB, time=177.45 memory used=7334.9MB, alloc=407.6MB, time=177.71 memory used=7403.1MB, alloc=407.6MB, time=177.97 memory used=7474.7MB, alloc=407.6MB, time=178.25 memory used=7617.9MB, alloc=407.6MB, time=178.72 memory used=7764.4MB, alloc=407.6MB, time=179.17 memory used=7924.7MB, alloc=407.6MB, time=179.63 memory used=8102.9MB, alloc=407.6MB, time=180.12 memory used=8308.4MB, alloc=407.6MB, time=180.63 memory used=8470.6MB, alloc=407.6MB, time=182.54 memory used=8629.5MB, alloc=407.6MB, time=185.12 memory used=8700.8MB, alloc=407.6MB, time=185.88 memory used=8815.3MB, alloc=407.6MB, time=188.94 memory used=8868.2MB, alloc=407.6MB, time=189.25 memory used=8923.1MB, alloc=407.6MB, time=189.67 memory used=8979.1MB, alloc=407.6MB, time=190.28 memory used=9059.1MB, alloc=407.6MB, time=191.02 memory used=9134.5MB, alloc=407.6MB, time=191.38 memory used=9197.7MB, alloc=407.6MB, time=192.34 |\^/| 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(); 1428262430 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 3 F := [15 x z - x z + 15 x y - 6 y , -16 x z - 15 z + 20 x y + 18 y z, 4 3 3 -17 x - 8 x y - 8 y z - x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 4 2 3 G := [12 y z - 4 y z - 10 y + 9 y z, -9 x + 16 x y z - 19 x y + 20, 3 2 2 3 2 15 x y + x z + 16 y - 4 y ] > Problem := [F,G]; 2 2 3 2 2 Problem := [[15 x z - x z + 15 x y - 6 y , 2 3 4 3 3 -16 x z - 15 z + 20 x y + 18 y z, -17 x - 8 x y - 8 y z - x z], [ 2 2 3 2 4 2 3 12 y z - 4 y z - 10 y + 9 y z, -9 x + 16 x y z - 19 x y + 20, 3 2 2 3 2 15 x y + x z + 16 y - 4 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=34.7MB, alloc=44.7MB, time=0.83 memory used=61.3MB, alloc=44.7MB, time=1.18 memory used=92.0MB, alloc=44.7MB, time=2.67 memory used=115.6MB, alloc=44.7MB, time=2.80 memory used=129.8MB, alloc=68.7MB, time=2.91 memory used=158.7MB, alloc=68.7MB, time=3.06 memory used=193.8MB, alloc=68.7MB, time=3.21 memory used=229.8MB, alloc=68.7MB, time=3.38 memory used=252.7MB, alloc=68.7MB, time=3.50 memory used=276.2MB, alloc=68.7MB, time=3.64 memory used=302.4MB, alloc=68.7MB, time=3.79 memory used=330.1MB, alloc=68.7MB, time=3.92 memory used=361.3MB, alloc=68.7MB, time=4.07 memory used=393.7MB, alloc=68.7MB, time=4.20 memory used=429.6MB, alloc=68.7MB, time=4.35 memory used=466.5MB, alloc=68.7MB, time=4.50 memory used=506.9MB, alloc=68.7MB, time=4.68 memory used=534.7MB, alloc=68.7MB, time=4.79 memory used=555.4MB, alloc=68.7MB, time=4.89 memory used=575.4MB, alloc=68.7MB, time=4.99 memory used=596.0MB, alloc=68.7MB, time=5.09 memory used=618.1MB, alloc=68.7MB, time=5.19 memory used=640.9MB, alloc=68.7MB, time=5.30 memory used=664.1MB, alloc=68.7MB, time=5.40 memory used=688.9MB, alloc=68.7MB, time=5.49 memory used=714.0MB, alloc=68.7MB, time=5.60 memory used=741.5MB, alloc=68.7MB, time=5.71 memory used=768.6MB, alloc=68.7MB, time=5.82 memory used=797.7MB, alloc=68.7MB, time=5.93 memory used=828.5MB, alloc=68.7MB, time=6.04 memory used=860.8MB, alloc=68.7MB, time=6.15 memory used=894.1MB, alloc=68.7MB, time=6.26 memory used=929.8MB, alloc=68.7MB, time=6.38 memory used=966.9MB, alloc=68.7MB, time=6.49 memory used=1008.2MB, alloc=68.7MB, time=6.95 memory used=1040.9MB, alloc=68.7MB, time=7.21 memory used=1087.2MB, alloc=71.4MB, time=8.65 memory used=1114.7MB, alloc=71.4MB, time=8.80 memory used=1149.5MB, alloc=71.4MB, time=8.98 memory used=1187.8MB, alloc=71.4MB, time=9.16 memory used=1210.1MB, alloc=71.4MB, time=9.30 memory used=1234.9MB, alloc=71.4MB, time=9.43 memory used=1261.2MB, alloc=71.4MB, time=9.57 memory used=1288.6MB, alloc=71.4MB, time=9.70 memory used=1317.6MB, alloc=71.4MB, time=9.84 memory used=1349.0MB, alloc=71.4MB, time=9.98 memory used=1382.4MB, alloc=71.4MB, time=10.12 memory used=1418.6MB, alloc=71.4MB, time=10.28 memory used=1458.8MB, alloc=71.4MB, time=10.44 memory used=1491.1MB, alloc=71.4MB, time=10.57 memory used=1510.5MB, alloc=71.4MB, time=10.66 memory used=1530.4MB, alloc=71.4MB, time=10.76 memory used=1550.9MB, alloc=71.4MB, time=10.85 memory used=1573.3MB, alloc=71.4MB, time=10.96 memory used=1596.0MB, alloc=71.4MB, time=11.05 memory used=1618.8MB, alloc=71.4MB, time=11.15 memory used=1644.2MB, alloc=71.4MB, time=11.25 memory used=1669.3MB, alloc=71.4MB, time=11.35 memory used=1694.9MB, alloc=71.4MB, time=11.46 memory used=1721.5MB, alloc=71.4MB, time=11.56 memory used=1750.6MB, alloc=71.4MB, time=11.67 memory used=1779.8MB, alloc=71.4MB, time=11.78 memory used=1810.3MB, alloc=71.4MB, time=11.90 memory used=1842.2MB, alloc=71.4MB, time=12.00 memory used=1875.8MB, alloc=71.4MB, time=12.12 memory used=1911.9MB, alloc=71.4MB, time=12.22 memory used=1955.5MB, alloc=71.4MB, time=12.53 memory used=1989.4MB, alloc=71.4MB, time=12.92 memory used=2029.3MB, alloc=71.4MB, time=20.09 memory used=2072.2MB, alloc=71.4MB, time=42.90 memory used=2113.7MB, alloc=71.4MB, time=70.74 memory used=2175.1MB, alloc=71.4MB, time=72.24 memory used=2210.1MB, alloc=71.4MB, time=72.40 memory used=2234.7MB, alloc=71.4MB, time=72.53 memory used=2261.9MB, alloc=71.4MB, time=72.67 memory used=2293.7MB, alloc=71.4MB, time=72.83 memory used=2330.1MB, alloc=71.4MB, time=72.98 memory used=2364.1MB, alloc=71.4MB, time=73.12 memory used=2385.1MB, alloc=71.4MB, time=73.22 memory used=2406.2MB, alloc=71.4MB, time=73.33 memory used=2429.5MB, alloc=71.4MB, time=73.43 memory used=2453.7MB, alloc=71.4MB, time=73.54 memory used=2478.5MB, alloc=71.4MB, time=73.65 memory used=2505.7MB, alloc=71.4MB, time=73.77 memory used=2533.6MB, alloc=71.4MB, time=73.89 memory used=2562.1MB, alloc=71.4MB, time=74.00 memory used=2593.0MB, alloc=71.4MB, time=74.12 memory used=2624.4MB, alloc=71.4MB, time=74.24 memory used=2658.3MB, alloc=71.4MB, time=74.36 memory used=2692.5MB, alloc=71.4MB, time=74.50 memory used=2729.3MB, alloc=71.4MB, time=74.62 memory used=2766.5MB, alloc=71.4MB, time=74.76 memory used=2799.5MB, alloc=81.9MB, time=74.89 memory used=2810.9MB, alloc=91.8MB, time=74.98 memory used=2821.0MB, alloc=91.8MB, time=75.05 memory used=2831.2MB, alloc=91.8MB, time=75.12 memory used=2843.0MB, alloc=91.8MB, time=75.20 memory used=2855.1MB, alloc=91.8MB, time=75.27 memory used=2867.2MB, alloc=91.8MB, time=75.35 memory used=2879.3MB, alloc=91.8MB, time=75.43 memory used=2891.4MB, alloc=91.8MB, time=75.50 memory used=2903.4MB, alloc=91.8MB, time=75.58 memory used=2915.4MB, alloc=91.8MB, time=75.66 memory used=2927.4MB, alloc=91.8MB, time=75.74 memory used=2939.4MB, alloc=91.8MB, time=75.81 memory used=2951.3MB, alloc=91.8MB, time=75.90 memory used=2963.4MB, alloc=91.8MB, time=75.98 memory used=2977.0MB, alloc=91.8MB, time=76.05 memory used=2990.7MB, alloc=91.8MB, time=76.14 memory used=3004.4MB, alloc=91.8MB, time=76.23 memory used=3018.0MB, alloc=91.8MB, time=76.32 memory used=3031.5MB, alloc=91.8MB, time=76.42 memory used=3045.0MB, alloc=91.8MB, time=76.50 memory used=3058.6MB, alloc=91.8MB, time=76.59 memory used=3073.5MB, alloc=91.8MB, time=76.68 memory used=3088.5MB, alloc=91.8MB, time=76.76 memory used=3103.4MB, alloc=91.8MB, time=76.83 memory used=3118.1MB, alloc=91.8MB, time=76.92 memory used=3133.0MB, alloc=91.8MB, time=77.00 memory used=3148.8MB, alloc=91.8MB, time=77.09 memory used=3164.9MB, alloc=91.8MB, time=77.17 memory used=3180.9MB, alloc=91.8MB, time=77.25 memory used=3197.9MB, alloc=91.8MB, time=77.34 memory used=3214.8MB, alloc=91.8MB, time=77.43 memory used=3232.9MB, alloc=91.8MB, time=77.51 memory used=3250.7MB, alloc=91.8MB, time=77.60 memory used=3269.5MB, alloc=91.8MB, time=77.69 memory used=3288.0MB, alloc=91.8MB, time=77.79 memory used=3307.1MB, alloc=91.8MB, time=77.88 memory used=3326.7MB, alloc=91.8MB, time=77.97 memory used=3346.8MB, alloc=91.8MB, time=78.06 memory used=3367.6MB, alloc=91.8MB, time=78.15 memory used=3389.7MB, alloc=91.8MB, time=78.25 memory used=3411.7MB, alloc=91.8MB, time=78.34 memory used=3435.4MB, alloc=91.8MB, time=78.43 memory used=3483.1MB, alloc=91.8MB, time=79.60 memory used=3510.8MB, alloc=91.8MB, time=79.77 memory used=3545.3MB, alloc=91.8MB, time=79.93 memory used=3581.6MB, alloc=91.8MB, time=80.09 memory used=3602.6MB, alloc=91.8MB, time=80.21 memory used=3625.1MB, alloc=91.8MB, time=80.35 memory used=3649.3MB, alloc=91.8MB, time=80.49 memory used=3676.3MB, alloc=91.8MB, time=80.62 memory used=3704.6MB, alloc=91.8MB, time=80.75 memory used=3736.5MB, alloc=91.8MB, time=80.90 memory used=3769.4MB, alloc=91.8MB, time=81.05 memory used=3805.7MB, alloc=91.8MB, time=81.21 memory used=3843.0MB, alloc=91.8MB, time=81.36 memory used=3878.5MB, alloc=91.8MB, time=81.50 memory used=3898.2MB, alloc=91.8MB, time=81.59 memory used=3917.9MB, alloc=91.8MB, time=81.69 memory used=3937.9MB, alloc=91.8MB, time=81.79 memory used=3958.4MB, alloc=91.8MB, time=81.88 memory used=3980.6MB, alloc=91.8MB, time=81.99 memory used=4003.3MB, alloc=91.8MB, time=82.08 memory used=4026.0MB, alloc=91.8MB, time=82.19 memory used=4051.2MB, alloc=91.8MB, time=82.29 memory used=4076.2MB, alloc=91.8MB, time=82.39 memory used=4101.7MB, alloc=91.8MB, time=82.49 memory used=4128.2MB, alloc=91.8MB, time=82.59 memory used=4156.6MB, alloc=91.8MB, time=82.71 memory used=4185.6MB, alloc=91.8MB, time=82.81 memory used=4217.1MB, alloc=91.8MB, time=82.92 memory used=4250.0MB, alloc=91.8MB, time=83.04 memory used=4284.0MB, alloc=91.8MB, time=83.15 memory used=4319.9MB, alloc=91.8MB, time=83.26 memory used=4359.5MB, alloc=91.8MB, time=83.65 memory used=4403.6MB, alloc=91.8MB, time=84.84 memory used=4433.1MB, alloc=91.8MB, time=85.00 memory used=4465.2MB, alloc=91.8MB, time=85.17 memory used=4505.3MB, alloc=91.8MB, time=85.35 memory used=4530.0MB, alloc=91.8MB, time=85.50 memory used=4553.5MB, alloc=91.8MB, time=85.64 memory used=4579.6MB, alloc=91.8MB, time=85.78 memory used=4606.8MB, alloc=91.8MB, time=85.92 memory used=4635.1MB, alloc=91.8MB, time=86.07 memory used=4666.9MB, alloc=91.8MB, time=86.23 memory used=4699.8MB, alloc=91.8MB, time=86.38 memory used=4736.1MB, alloc=91.8MB, time=86.51 memory used=4773.7MB, alloc=91.8MB, time=86.66 memory used=4809.8MB, alloc=91.8MB, time=86.80 memory used=4829.0MB, alloc=91.8MB, time=86.90 memory used=4848.4MB, alloc=91.8MB, time=86.99 memory used=4868.4MB, alloc=91.8MB, time=87.09 memory used=4890.9MB, alloc=91.8MB, time=87.19 memory used=4913.7MB, alloc=91.8MB, time=87.29 memory used=4936.4MB, alloc=91.8MB, time=87.38 memory used=4959.4MB, alloc=91.8MB, time=87.48 memory used=4984.1MB, alloc=91.8MB, time=87.59 memory used=5009.2MB, alloc=91.8MB, time=87.69 memory used=5036.5MB, alloc=91.8MB, time=87.80 memory used=5064.0MB, alloc=91.8MB, time=87.91 memory used=5092.2MB, alloc=91.8MB, time=88.02 memory used=5122.9MB, alloc=91.8MB, time=88.13 memory used=5154.9MB, alloc=91.8MB, time=88.24 memory used=5187.6MB, alloc=91.8MB, time=88.36 memory used=5222.8MB, alloc=91.8MB, time=88.48 memory used=5260.0MB, alloc=91.8MB, time=88.59 memory used=5313.1MB, alloc=91.8MB, time=103.84 memory used=5347.1MB, alloc=91.8MB, time=135.28 memory used=5394.5MB, alloc=91.8MB, time=148.16 memory used=5448.7MB, alloc=91.8MB, time=148.65 memory used=5482.2MB, alloc=91.8MB, time=148.81 memory used=5508.2MB, alloc=91.8MB, time=148.96 memory used=5538.2MB, alloc=91.8MB, time=149.10 memory used=5573.0MB, alloc=91.8MB, time=149.26 memory used=5612.8MB, alloc=91.8MB, time=149.42 memory used=5637.7MB, alloc=91.8MB, time=149.53 memory used=5659.1MB, alloc=91.8MB, time=149.64 memory used=5682.2MB, alloc=91.8MB, time=149.74 memory used=5706.1MB, alloc=91.8MB, time=149.84 memory used=5732.4MB, alloc=91.8MB, time=149.95 memory used=5759.4MB, alloc=91.8MB, time=150.07 memory used=5787.2MB, alloc=91.8MB, time=150.19 memory used=5817.3MB, alloc=91.8MB, time=150.31 memory used=5848.2MB, alloc=91.8MB, time=150.43 memory used=5881.5MB, alloc=91.8MB, time=150.56 memory used=5915.3MB, alloc=91.8MB, time=150.69 memory used=5951.6MB, alloc=91.8MB, time=150.82 memory used=5988.4MB, alloc=91.8MB, time=150.95 memory used=6027.6MB, alloc=91.8MB, time=151.09 memory used=6066.5MB, alloc=91.8MB, time=151.23 memory used=6076.7MB, alloc=91.8MB, time=151.30 memory used=6086.8MB, alloc=91.8MB, time=151.36 memory used=6097.1MB, alloc=91.8MB, time=151.44 memory used=6109.0MB, alloc=91.8MB, time=151.52 memory used=6121.1MB, alloc=91.8MB, time=151.60 memory used=6133.2MB, alloc=91.8MB, time=151.70 memory used=6145.3MB, alloc=91.8MB, time=151.77 memory used=6157.3MB, alloc=91.8MB, time=151.85 memory used=6169.3MB, alloc=91.8MB, time=151.93 memory used=6181.4MB, alloc=91.8MB, time=152.01 memory used=6193.3MB, alloc=91.8MB, time=152.08 memory used=6205.3MB, alloc=91.8MB, time=152.16 memory used=6217.2MB, alloc=91.8MB, time=152.25 memory used=6229.4MB, alloc=91.8MB, time=152.33 memory used=6242.9MB, alloc=91.8MB, time=152.41 memory used=6256.6MB, alloc=91.8MB, time=152.48 memory used=6270.3MB, alloc=91.8MB, time=152.56 memory used=6283.8MB, alloc=91.8MB, time=152.65 memory used=6297.3MB, alloc=91.8MB, time=152.72 memory used=6310.8MB, alloc=91.8MB, time=152.81 memory used=6324.4MB, alloc=91.8MB, time=152.88 memory used=6339.2MB, alloc=91.8MB, time=152.96 memory used=6354.2MB, alloc=91.8MB, time=153.04 memory used=6369.0MB, alloc=91.8MB, time=153.13 memory used=6383.7MB, alloc=91.8MB, time=153.21 memory used=6400.0MB, alloc=91.8MB, time=153.29 memory used=6416.2MB, alloc=91.8MB, time=153.37 memory used=6432.2MB, alloc=91.8MB, time=153.46 memory used=6449.5MB, alloc=91.8MB, time=153.54 memory used=6466.6MB, alloc=91.8MB, time=153.63 memory used=6483.6MB, alloc=91.8MB, time=153.71 memory used=6501.4MB, alloc=91.8MB, time=153.80 memory used=6519.2MB, alloc=91.8MB, time=153.88 memory used=6537.6MB, alloc=91.8MB, time=153.97 memory used=6557.1MB, alloc=91.8MB, time=154.05 memory used=6576.3MB, alloc=91.8MB, time=154.15 memory used=6596.8MB, alloc=91.8MB, time=154.24 memory used=6617.8MB, alloc=91.8MB, time=154.33 memory used=6638.8MB, alloc=91.8MB, time=154.42 memory used=6660.8MB, alloc=91.8MB, time=154.52 memory used=6683.6MB, alloc=91.8MB, time=154.61 memory used=6736.1MB, alloc=91.8MB, time=155.09 memory used=6767.6MB, alloc=91.8MB, time=155.23 memory used=6816.3MB, alloc=91.8MB, time=156.12 memory used=6884.5MB, alloc=91.8MB, time=164.08 memory used=6926.8MB, alloc=91.8MB, time=187.22 memory used=6964.9MB, alloc=91.8MB, time=188.81 memory used=6996.8MB, alloc=91.8MB, time=188.98 memory used=7020.7MB, alloc=91.8MB, time=189.10 memory used=7049.3MB, alloc=91.8MB, time=189.24 memory used=7082.5MB, alloc=91.8MB, time=189.38 memory used=7118.3MB, alloc=91.8MB, time=189.53 memory used=7138.8MB, alloc=91.8MB, time=189.63 memory used=7159.5MB, alloc=91.8MB, time=189.74 memory used=7182.5MB, alloc=91.8MB, time=189.84 memory used=7206.2MB, alloc=91.8MB, time=189.95 memory used=7232.0MB, alloc=91.8MB, time=190.06 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428262730 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 2 2 F := [3 x z + 10 x y - 20 y z, x + 9 x y z - 7 x z - 7, 2 3 3 2 10 x y z + 4 y z + 10 y + 6 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 2 G := [12 x y z + 9 x y - z - 3 x , 13 x y z - 11 y + 4 y - 8 x, 3 2 2 3 -2 x z + 16 x y + 9 z - 7 x] > Problem := [F,G]; 2 2 2 4 2 2 2 Problem := [[3 x z + 10 x y - 20 y z, x + 9 x y z - 7 x z - 7, 2 3 3 2 2 2 3 2 10 x y z + 4 y z + 10 y + 6 y z], [12 x y z + 9 x y - z - 3 x , 2 3 2 3 2 2 3 13 x y z - 11 y + 4 y - 8 x, -2 x z + 16 x y + 9 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=0.31 memory used=27.4MB, alloc=36.4MB, time=0.80 memory used=49.1MB, alloc=36.7MB, time=1.27 memory used=65.9MB, alloc=36.7MB, time=1.36 memory used=76.1MB, alloc=36.7MB, time=1.42 memory used=87.1MB, alloc=36.7MB, time=1.48 memory used=104.4MB, alloc=36.7MB, time=1.66 memory used=119.6MB, alloc=36.7MB, time=1.73 memory used=128.8MB, alloc=36.7MB, time=1.79 memory used=139.8MB, alloc=36.7MB, time=1.85 memory used=162.3MB, alloc=36.7MB, time=5.98 memory used=180.9MB, alloc=36.7MB, time=6.31 memory used=191.2MB, alloc=36.7MB, time=6.37 memory used=204.3MB, alloc=36.7MB, time=6.43 memory used=217.9MB, alloc=36.7MB, time=6.50 memory used=226.6MB, alloc=36.7MB, time=6.55 memory used=235.8MB, alloc=36.7MB, time=6.60 memory used=245.8MB, alloc=36.7MB, time=6.66 memory used=256.8MB, alloc=36.7MB, time=6.71 memory used=268.5MB, alloc=36.7MB, time=6.77 memory used=281.0MB, alloc=36.7MB, time=6.82 memory used=294.8MB, alloc=36.7MB, time=6.88 memory used=308.4MB, alloc=36.7MB, time=6.94 memory used=316.1MB, alloc=36.7MB, time=6.98 memory used=324.2MB, alloc=36.7MB, time=7.03 memory used=332.8MB, alloc=36.7MB, time=7.07 memory used=341.9MB, alloc=36.7MB, time=7.12 memory used=351.9MB, alloc=36.7MB, time=7.16 memory used=371.2MB, alloc=36.7MB, time=7.31 memory used=383.6MB, alloc=36.7MB, time=7.38 memory used=394.5MB, alloc=36.7MB, time=7.44 memory used=410.8MB, alloc=36.7MB, time=7.64 memory used=428.2MB, alloc=36.7MB, time=7.73 memory used=438.6MB, alloc=36.7MB, time=7.79 memory used=450.1MB, alloc=36.7MB, time=7.85 memory used=472.0MB, alloc=36.7MB, time=11.57 memory used=491.5MB, alloc=36.7MB, time=12.51 memory used=501.8MB, alloc=36.7MB, time=12.57 memory used=513.1MB, alloc=36.7MB, time=12.63 memory used=526.7MB, alloc=36.7MB, time=12.70 memory used=536.7MB, alloc=60.7MB, time=12.78 memory used=560.7MB, alloc=60.7MB, time=12.87 memory used=589.8MB, alloc=60.7MB, time=12.97 memory used=623.9MB, alloc=60.7MB, time=13.08 memory used=645.3MB, alloc=60.7MB, time=13.15 memory used=668.2MB, alloc=60.7MB, time=13.22 memory used=707.3MB, alloc=60.7MB, time=13.78 memory used=748.1MB, alloc=60.7MB, time=14.23 memory used=791.2MB, alloc=60.7MB, time=14.74 memory used=825.3MB, alloc=60.7MB, time=15.52 memory used=868.7MB, alloc=60.7MB, time=16.36 memory used=910.7MB, alloc=62.9MB, time=16.82 memory used=942.5MB, alloc=62.9MB, time=16.97 memory used=962.8MB, alloc=62.9MB, time=17.07 memory used=987.4MB, alloc=62.9MB, time=17.18 memory used=1023.2MB, alloc=62.9MB, time=17.53 memory used=1060.3MB, alloc=62.9MB, time=17.70 memory used=1083.4MB, alloc=62.9MB, time=17.82 memory used=1106.4MB, alloc=62.9MB, time=17.93 memory used=1134.0MB, alloc=62.9MB, time=18.03 memory used=1187.9MB, alloc=63.9MB, time=27.46 memory used=1225.6MB, alloc=63.9MB, time=27.73 memory used=1246.1MB, alloc=63.9MB, time=27.83 memory used=1271.0MB, alloc=63.9MB, time=27.95 memory used=1301.0MB, alloc=63.9MB, time=28.07 memory used=1321.3MB, alloc=63.9MB, time=28.17 memory used=1339.3MB, alloc=63.9MB, time=28.26 memory used=1358.9MB, alloc=63.9MB, time=28.35 memory used=1379.8MB, alloc=63.9MB, time=28.45 memory used=1401.9MB, alloc=63.9MB, time=28.54 memory used=1425.9MB, alloc=63.9MB, time=28.64 memory used=1451.8MB, alloc=63.9MB, time=28.75 memory used=1479.5MB, alloc=63.9MB, time=28.85 memory used=1509.9MB, alloc=63.9MB, time=28.96 memory used=1531.5MB, alloc=63.9MB, time=29.04 memory used=1547.6MB, alloc=63.9MB, time=29.11 memory used=1564.2MB, alloc=63.9MB, time=29.18 memory used=1581.6MB, alloc=63.9MB, time=29.26 memory used=1600.3MB, alloc=63.9MB, time=29.33 memory used=1620.2MB, alloc=63.9MB, time=29.41 memory used=1641.1MB, alloc=63.9MB, time=29.48 memory used=1669.9MB, alloc=63.9MB, time=29.69 memory used=1714.7MB, alloc=63.9MB, time=30.41 memory used=1738.1MB, alloc=63.9MB, time=30.53 memory used=1761.7MB, alloc=63.9MB, time=30.63 memory used=1782.7MB, alloc=63.9MB, time=30.72 memory used=1812.7MB, alloc=63.9MB, time=30.95 memory used=1853.2MB, alloc=63.9MB, time=33.26 memory used=1898.6MB, alloc=72.0MB, time=34.09 memory used=1953.1MB, alloc=72.0MB, time=35.04 memory used=2006.6MB, alloc=72.0MB, time=36.20 memory used=2059.8MB, alloc=72.0MB, time=38.25 memory used=2113.6MB, alloc=72.0MB, time=40.72 memory used=2166.7MB, alloc=72.0MB, time=43.64 memory used=2205.9MB, alloc=72.0MB, time=44.62 memory used=2240.0MB, alloc=72.0MB, time=45.14 memory used=2278.6MB, alloc=72.0MB, time=46.50 memory used=2324.0MB, alloc=72.0MB, time=47.44 memory used=2366.0MB, alloc=72.0MB, time=48.40 memory used=2407.1MB, alloc=96.0MB, time=49.38 memory used=2474.8MB, alloc=96.0MB, time=57.22 memory used=2509.9MB, alloc=96.0MB, time=57.42 memory used=2542.9MB, alloc=96.0MB, time=57.60 memory used=2572.6MB, alloc=96.0MB, time=57.75 memory used=2607.0MB, alloc=96.0MB, time=57.92 memory used=2647.3MB, alloc=96.0MB, time=58.10 memory used=2683.5MB, alloc=96.0MB, time=58.26 memory used=2708.0MB, alloc=96.0MB, time=58.40 memory used=2734.5MB, alloc=96.0MB, time=58.53 memory used=2763.4MB, alloc=96.0MB, time=58.68 memory used=2795.6MB, alloc=96.0MB, time=58.81 memory used=2849.1MB, alloc=96.0MB, time=59.52 memory used=2882.2MB, alloc=96.0MB, time=59.69 memory used=2921.1MB, alloc=96.0MB, time=59.94 memory used=2998.1MB, alloc=96.0MB, time=61.45 memory used=3053.4MB, alloc=96.0MB, time=62.11 memory used=3088.2MB, alloc=96.0MB, time=62.29 memory used=3116.2MB, alloc=96.0MB, time=62.44 memory used=3157.4MB, alloc=96.0MB, time=62.90 memory used=3220.5MB, alloc=96.0MB, time=64.75 memory used=3282.7MB, alloc=96.0MB, time=65.94 memory used=3340.5MB, alloc=376.0MB, time=67.71 memory used=3404.4MB, alloc=376.0MB, time=68.30 memory used=3442.8MB, alloc=376.0MB, time=68.55 memory used=3490.9MB, alloc=376.0MB, time=68.80 memory used=3543.2MB, alloc=376.0MB, time=69.05 memory used=3575.7MB, alloc=376.0MB, time=69.26 memory used=3610.9MB, alloc=376.0MB, time=69.47 memory used=3648.8MB, alloc=376.0MB, time=69.69 memory used=3691.2MB, alloc=376.0MB, time=69.92 memory used=3737.3MB, alloc=376.0MB, time=70.13 memory used=3789.5MB, alloc=376.0MB, time=70.36 memory used=3840.3MB, alloc=376.0MB, time=70.57 memory used=3884.1MB, alloc=376.0MB, time=71.48 memory used=3940.3MB, alloc=376.0MB, time=71.79 memory used=3981.2MB, alloc=376.0MB, time=72.05 memory used=4032.5MB, alloc=376.0MB, time=72.32 memory used=4079.8MB, alloc=376.0MB, time=72.57 memory used=4112.5MB, alloc=376.0MB, time=72.79 memory used=4149.4MB, alloc=376.0MB, time=73.01 memory used=4188.8MB, alloc=376.0MB, time=73.24 memory used=4233.4MB, alloc=376.0MB, time=73.46 memory used=4282.4MB, alloc=376.0MB, time=73.70 memory used=4337.2MB, alloc=376.0MB, time=73.93 memory used=4380.1MB, alloc=376.0MB, time=74.12 memory used=4444.2MB, alloc=376.0MB, time=102.32 memory used=4499.1MB, alloc=376.0MB, time=106.75 memory used=4547.7MB, alloc=376.0MB, time=107.00 memory used=4583.6MB, alloc=376.0MB, time=107.22 memory used=4626.8MB, alloc=376.0MB, time=107.44 memory used=4677.0MB, alloc=376.0MB, time=107.68 memory used=4726.4MB, alloc=376.0MB, time=107.90 memory used=4758.2MB, alloc=376.0MB, time=108.08 memory used=4792.2MB, alloc=376.0MB, time=108.26 memory used=4828.5MB, alloc=376.0MB, time=108.44 memory used=4868.4MB, alloc=376.0MB, time=108.62 memory used=4911.1MB, alloc=376.0MB, time=108.82 memory used=4956.3MB, alloc=376.0MB, time=109.00 memory used=5006.8MB, alloc=376.0MB, time=109.19 memory used=5078.7MB, alloc=376.0MB, time=110.26 memory used=5125.6MB, alloc=376.0MB, time=110.53 memory used=5168.8MB, alloc=376.0MB, time=110.79 memory used=5221.8MB, alloc=376.0MB, time=111.04 memory used=5263.3MB, alloc=376.0MB, time=111.26 memory used=5296.2MB, alloc=376.0MB, time=111.47 memory used=5332.1MB, alloc=376.0MB, time=111.67 memory used=5372.0MB, alloc=376.0MB, time=111.89 memory used=5415.3MB, alloc=376.0MB, time=112.12 memory used=5463.1MB, alloc=376.0MB, time=112.35 memory used=5517.1MB, alloc=376.0MB, time=112.58 memory used=5560.6MB, alloc=376.0MB, time=112.77 memory used=5611.8MB, alloc=376.0MB, time=113.76 memory used=5662.0MB, alloc=376.0MB, time=114.05 memory used=5703.9MB, alloc=376.0MB, time=114.29 memory used=5756.3MB, alloc=376.0MB, time=114.57 memory used=5801.0MB, alloc=376.0MB, time=114.80 memory used=5833.9MB, alloc=376.0MB, time=115.01 memory used=5869.8MB, alloc=376.0MB, time=115.22 memory used=5909.6MB, alloc=376.0MB, time=115.44 memory used=5953.0MB, alloc=376.0MB, time=115.65 memory used=6000.9MB, alloc=376.0MB, time=115.88 memory used=6055.2MB, alloc=376.0MB, time=116.11 memory used=6100.2MB, alloc=376.0MB, time=116.30 memory used=6152.9MB, alloc=376.0MB, time=129.26 memory used=6218.8MB, alloc=376.0MB, time=150.28 memory used=6268.2MB, alloc=376.0MB, time=150.55 memory used=6304.9MB, alloc=376.0MB, time=150.77 memory used=6345.2MB, alloc=376.0MB, time=151.00 memory used=6393.2MB, alloc=376.0MB, time=151.23 memory used=6449.1MB, alloc=376.0MB, time=151.47 memory used=6482.5MB, alloc=376.0MB, time=151.65 memory used=6515.4MB, alloc=376.0MB, time=151.83 memory used=6550.7MB, alloc=376.0MB, time=152.02 memory used=6589.1MB, alloc=376.0MB, time=152.20 memory used=6630.1MB, alloc=376.0MB, time=152.38 memory used=6674.7MB, alloc=376.0MB, time=152.57 memory used=6721.8MB, alloc=376.0MB, time=152.76 memory used=6774.6MB, alloc=376.0MB, time=152.96 memory used=6852.2MB, alloc=376.0MB, time=155.26 memory used=6896.0MB, alloc=376.0MB, time=155.49 memory used=6943.2MB, alloc=376.0MB, time=155.72 memory used=6990.3MB, alloc=376.0MB, time=156.48 memory used=7035.4MB, alloc=376.0MB, time=156.72 memory used=7111.3MB, alloc=376.0MB, time=158.08 memory used=7214.0MB, alloc=376.0MB, time=159.75 memory used=7279.4MB, alloc=376.0MB, time=162.12 memory used=7315.5MB, alloc=376.0MB, time=162.35 memory used=7360.2MB, alloc=376.0MB, time=162.58 memory used=7435.9MB, alloc=376.0MB, time=163.82 memory used=7537.1MB, alloc=400.0MB, time=165.69 memory used=7671.5MB, alloc=400.0MB, time=167.74 memory used=7784.1MB, alloc=400.0MB, time=170.30 memory used=7895.0MB, alloc=424.0MB, time=172.86 memory used=7972.3MB, alloc=424.0MB, time=173.58 memory used=8049.4MB, alloc=424.0MB, time=174.29 memory used=8139.1MB, alloc=424.0MB, time=176.26 memory used=8222.6MB, alloc=424.0MB, time=176.76 |\^/| 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(); 1428263030 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 F := [14 x z + 16 y - 3 x + 3 y, -6 x z - 19 x y + 12 y + 20 z , 2 3 3 -12 x y z + 7 x y + 7 x - 7 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 4 2 2 3 2 G := [-20 x y z - 5 y z - 14 x y + 3 y , -4 x - 15 x y + 3 y z + 17 x y, 3 3 -11 y z + 20 y - 17 x z - 20 y] > Problem := [F,G]; 3 3 2 2 2 2 Problem := [[14 x z + 16 y - 3 x + 3 y, -6 x z - 19 x y + 12 y + 20 z , 2 3 3 2 3 2 2 -12 x y z + 7 x y + 7 x - 7 y z], [-20 x y z - 5 y z - 14 x y + 3 y , 4 2 2 3 2 3 3 -4 x - 15 x y + 3 y z + 17 x y, -11 y z + 20 y - 17 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=0.32 memory used=25.7MB, alloc=33.6MB, time=0.77 memory used=41.3MB, alloc=33.6MB, time=0.85 memory used=54.9MB, alloc=33.6MB, time=0.91 memory used=74.4MB, alloc=34.1MB, time=1.03 memory used=86.1MB, alloc=34.1MB, time=1.09 memory used=105.4MB, alloc=34.1MB, time=1.50 memory used=121.9MB, alloc=34.1MB, time=1.60 memory used=135.3MB, alloc=34.1MB, time=1.66 memory used=151.0MB, alloc=34.1MB, time=1.80 memory used=172.7MB, alloc=34.1MB, time=2.17 memory used=185.2MB, alloc=34.1MB, time=2.23 memory used=202.7MB, alloc=34.1MB, time=2.52 memory used=227.7MB, alloc=38.7MB, time=2.83 memory used=242.1MB, alloc=38.7MB, time=2.90 memory used=252.1MB, alloc=38.7MB, time=2.96 memory used=263.7MB, alloc=38.7MB, time=3.01 memory used=277.5MB, alloc=38.7MB, time=3.08 memory used=293.7MB, alloc=38.7MB, time=3.24 memory used=313.4MB, alloc=38.7MB, time=3.44 memory used=328.3MB, alloc=38.7MB, time=3.51 memory used=338.1MB, alloc=38.7MB, time=3.57 memory used=349.9MB, alloc=38.7MB, time=3.63 memory used=363.7MB, alloc=38.7MB, time=3.69 memory used=381.0MB, alloc=38.7MB, time=3.86 memory used=401.7MB, alloc=38.7MB, time=5.85 memory used=425.5MB, alloc=38.7MB, time=6.18 memory used=436.6MB, alloc=38.7MB, time=6.24 memory used=449.9MB, alloc=38.7MB, time=6.31 memory used=463.6MB, alloc=38.7MB, time=6.37 memory used=472.6MB, alloc=38.7MB, time=6.42 memory used=482.6MB, alloc=38.7MB, time=6.48 memory used=493.6MB, alloc=38.7MB, time=6.54 memory used=505.5MB, alloc=38.7MB, time=6.59 memory used=518.3MB, alloc=38.7MB, time=6.65 memory used=532.3MB, alloc=38.7MB, time=6.71 memory used=546.3MB, alloc=38.7MB, time=6.77 memory used=555.6MB, alloc=38.7MB, time=6.81 memory used=564.2MB, alloc=38.7MB, time=6.86 memory used=573.5MB, alloc=38.7MB, time=6.91 memory used=583.4MB, alloc=38.7MB, time=6.95 memory used=600.3MB, alloc=38.7MB, time=7.23 memory used=627.7MB, alloc=38.7MB, time=8.26 memory used=647.9MB, alloc=38.7MB, time=8.49 memory used=660.1MB, alloc=38.7MB, time=8.55 memory used=668.7MB, alloc=38.7MB, time=8.61 memory used=678.8MB, alloc=38.7MB, time=8.66 memory used=691.2MB, alloc=38.7MB, time=8.72 memory used=701.5MB, alloc=38.7MB, time=8.77 memory used=721.1MB, alloc=38.7MB, time=8.98 memory used=731.8MB, alloc=38.7MB, time=9.04 memory used=742.6MB, alloc=38.7MB, time=9.10 memory used=754.7MB, alloc=38.7MB, time=9.16 memory used=771.3MB, alloc=38.7MB, time=9.41 memory used=787.1MB, alloc=38.7MB, time=9.49 memory used=796.5MB, alloc=38.7MB, time=9.55 memory used=808.7MB, alloc=38.7MB, time=9.61 memory used=822.7MB, alloc=38.7MB, time=9.75 memory used=843.5MB, alloc=38.7MB, time=11.39 memory used=861.3MB, alloc=38.7MB, time=11.53 memory used=873.5MB, alloc=38.7MB, time=11.60 memory used=883.9MB, alloc=62.7MB, time=11.68 memory used=909.8MB, alloc=62.7MB, time=11.78 memory used=939.2MB, alloc=62.7MB, time=11.87 memory used=962.0MB, alloc=62.7MB, time=11.94 memory used=1005.8MB, alloc=62.7MB, time=12.99 memory used=1041.8MB, alloc=62.7MB, time=13.42 memory used=1084.2MB, alloc=62.7MB, time=14.10 memory used=1111.9MB, alloc=62.7MB, time=14.22 memory used=1144.0MB, alloc=62.7MB, time=14.40 memory used=1178.9MB, alloc=62.7MB, time=14.93 memory used=1203.2MB, alloc=62.7MB, time=15.04 memory used=1241.3MB, alloc=62.9MB, time=15.35 memory used=1268.2MB, alloc=62.9MB, time=15.47 memory used=1293.8MB, alloc=62.9MB, time=15.57 memory used=1316.4MB, alloc=62.9MB, time=15.67 memory used=1353.6MB, alloc=62.9MB, time=15.93 memory used=1377.8MB, alloc=62.9MB, time=16.04 memory used=1405.8MB, alloc=62.9MB, time=16.15 memory used=1427.0MB, alloc=62.9MB, time=16.24 memory used=1464.8MB, alloc=62.9MB, time=17.18 memory used=1494.2MB, alloc=62.9MB, time=17.31 memory used=1515.6MB, alloc=62.9MB, time=17.40 memory used=1544.3MB, alloc=62.9MB, time=17.51 memory used=1572.3MB, alloc=62.9MB, time=17.80 memory used=1607.1MB, alloc=62.9MB, time=18.64 memory used=1651.3MB, alloc=71.2MB, time=19.36 memory used=1674.0MB, alloc=71.2MB, time=19.48 memory used=1723.8MB, alloc=71.2MB, time=20.29 memory used=1778.6MB, alloc=71.2MB, time=21.18 memory used=1816.6MB, alloc=71.2MB, time=21.74 memory used=1842.7MB, alloc=71.2MB, time=21.90 memory used=1863.6MB, alloc=71.2MB, time=22.02 memory used=1883.2MB, alloc=71.2MB, time=22.13 memory used=1907.7MB, alloc=71.2MB, time=22.39 memory used=1929.4MB, alloc=71.2MB, time=22.53 memory used=1951.4MB, alloc=71.2MB, time=22.65 memory used=1969.2MB, alloc=71.2MB, time=22.77 memory used=2002.2MB, alloc=71.2MB, time=23.74 memory used=2023.3MB, alloc=71.2MB, time=23.88 memory used=2040.1MB, alloc=71.2MB, time=23.98 memory used=2059.8MB, alloc=71.2MB, time=24.09 memory used=2093.0MB, alloc=71.2MB, time=24.49 memory used=2115.7MB, alloc=71.2MB, time=24.62 memory used=2134.6MB, alloc=71.2MB, time=24.74 memory used=2157.9MB, alloc=71.2MB, time=24.87 memory used=2180.8MB, alloc=95.2MB, time=25.01 memory used=2210.4MB, alloc=95.2MB, time=25.15 memory used=2245.6MB, alloc=95.2MB, time=25.30 memory used=2286.8MB, alloc=95.2MB, time=25.47 memory used=2343.2MB, alloc=95.2MB, time=25.91 memory used=2379.2MB, alloc=95.2MB, time=26.10 memory used=2421.8MB, alloc=95.2MB, time=26.29 memory used=2451.3MB, alloc=95.2MB, time=26.45 memory used=2485.8MB, alloc=95.2MB, time=26.60 memory used=2526.9MB, alloc=95.2MB, time=26.78 memory used=2589.4MB, alloc=95.2MB, time=28.88 memory used=2628.2MB, alloc=95.2MB, time=29.05 memory used=2661.7MB, alloc=95.2MB, time=29.21 memory used=2704.9MB, alloc=95.2MB, time=29.39 memory used=2734.8MB, alloc=95.2MB, time=29.51 memory used=2782.5MB, alloc=95.2MB, time=29.90 memory used=2821.1MB, alloc=95.2MB, time=30.08 memory used=2873.2MB, alloc=95.2MB, time=30.41 memory used=2911.8MB, alloc=95.2MB, time=30.59 memory used=2990.3MB, alloc=95.2MB, time=36.15 memory used=3031.3MB, alloc=95.2MB, time=36.33 memory used=3063.3MB, alloc=95.2MB, time=36.49 memory used=3100.0MB, alloc=95.2MB, time=36.66 memory used=3145.3MB, alloc=95.2MB, time=36.83 memory used=3174.8MB, alloc=95.2MB, time=36.95 memory used=3203.7MB, alloc=95.2MB, time=37.07 memory used=3236.6MB, alloc=95.2MB, time=37.19 memory used=3285.5MB, alloc=95.2MB, time=37.50 memory used=3324.3MB, alloc=95.2MB, time=37.68 memory used=3377.8MB, alloc=95.2MB, time=38.05 memory used=3415.6MB, alloc=95.2MB, time=38.24 memory used=3490.0MB, alloc=95.2MB, time=43.92 memory used=3531.5MB, alloc=95.2MB, time=44.12 memory used=3564.9MB, alloc=95.2MB, time=44.29 memory used=3600.4MB, alloc=95.2MB, time=44.45 memory used=3643.8MB, alloc=95.2MB, time=44.62 memory used=3677.8MB, alloc=95.2MB, time=44.75 memory used=3705.1MB, alloc=95.2MB, time=44.87 memory used=3735.8MB, alloc=95.2MB, time=44.99 memory used=3771.6MB, alloc=95.2MB, time=45.12 memory used=3823.0MB, alloc=95.2MB, time=45.52 memory used=3862.1MB, alloc=95.2MB, time=45.71 memory used=3901.9MB, alloc=95.2MB, time=46.06 memory used=3943.3MB, alloc=95.2MB, time=46.26 memory used=3981.7MB, alloc=95.2MB, time=46.42 memory used=4033.9MB, alloc=95.2MB, time=49.05 memory used=4071.6MB, alloc=95.2MB, time=49.23 memory used=4107.0MB, alloc=95.2MB, time=49.39 memory used=4147.6MB, alloc=95.2MB, time=49.54 memory used=4176.8MB, alloc=95.2MB, time=49.66 memory used=4223.9MB, alloc=95.2MB, time=50.02 memory used=4264.0MB, alloc=95.2MB, time=50.20 memory used=4301.8MB, alloc=95.2MB, time=50.56 memory used=4349.1MB, alloc=95.2MB, time=50.97 memory used=4388.9MB, alloc=95.2MB, time=51.14 memory used=4433.4MB, alloc=95.2MB, time=53.43 memory used=4484.3MB, alloc=95.2MB, time=54.27 memory used=4517.6MB, alloc=95.2MB, time=54.44 memory used=4556.5MB, alloc=95.2MB, time=54.60 memory used=4590.9MB, alloc=95.2MB, time=54.73 memory used=4645.5MB, alloc=95.2MB, time=55.47 memory used=4735.0MB, alloc=95.2MB, time=57.37 memory used=4825.3MB, alloc=95.6MB, time=61.61 memory used=4906.6MB, alloc=351.6MB, time=64.11 memory used=4995.0MB, alloc=351.6MB, time=65.76 memory used=5085.7MB, alloc=351.6MB, time=69.66 memory used=5174.1MB, alloc=351.6MB, time=72.41 memory used=5256.1MB, alloc=351.6MB, time=74.14 memory used=5338.0MB, alloc=351.6MB, time=76.48 memory used=5421.4MB, alloc=351.6MB, time=81.09 memory used=5496.2MB, alloc=351.6MB, time=89.48 memory used=5532.9MB, alloc=351.6MB, time=89.68 memory used=5561.9MB, alloc=351.6MB, time=89.84 memory used=5592.9MB, alloc=351.6MB, time=90.00 memory used=5630.0MB, alloc=351.6MB, time=90.17 memory used=5670.4MB, alloc=351.6MB, time=90.34 memory used=5695.3MB, alloc=351.6MB, time=90.47 memory used=5721.1MB, alloc=351.6MB, time=90.59 memory used=5749.3MB, alloc=351.6MB, time=90.72 memory used=5780.0MB, alloc=351.6MB, time=90.86 memory used=5814.8MB, alloc=351.6MB, time=90.99 memory used=5858.4MB, alloc=351.6MB, time=91.44 memory used=5892.1MB, alloc=351.6MB, time=91.80 memory used=5927.7MB, alloc=351.6MB, time=92.37 memory used=6012.2MB, alloc=351.6MB, time=113.25 memory used=6061.1MB, alloc=351.6MB, time=113.68 memory used=6100.9MB, alloc=351.6MB, time=113.89 memory used=6127.2MB, alloc=351.6MB, time=114.05 memory used=6156.4MB, alloc=351.6MB, time=114.20 memory used=6189.6MB, alloc=351.6MB, time=114.39 memory used=6227.2MB, alloc=351.6MB, time=114.57 memory used=6270.1MB, alloc=351.6MB, time=114.75 memory used=6297.8MB, alloc=351.6MB, time=114.89 memory used=6322.0MB, alloc=351.6MB, time=115.02 memory used=6346.9MB, alloc=351.6MB, time=115.16 memory used=6373.8MB, alloc=351.6MB, time=115.29 memory used=6402.1MB, alloc=351.6MB, time=115.43 memory used=6432.4MB, alloc=351.6MB, time=115.56 memory used=6464.5MB, alloc=351.6MB, time=115.70 memory used=6498.1MB, alloc=351.6MB, time=115.84 memory used=6533.5MB, alloc=351.6MB, time=115.98 memory used=6571.9MB, alloc=351.6MB, time=116.12 memory used=6613.3MB, alloc=351.6MB, time=116.27 memory used=6686.2MB, alloc=351.6MB, time=117.06 memory used=6719.9MB, alloc=351.6MB, time=117.28 memory used=6768.6MB, alloc=351.6MB, time=117.87 memory used=6814.0MB, alloc=351.6MB, time=118.09 memory used=6849.8MB, alloc=351.6MB, time=118.25 memory used=6914.6MB, alloc=351.6MB, time=119.84 memory used=6998.2MB, alloc=351.6MB, time=121.23 memory used=7074.5MB, alloc=351.6MB, time=122.88 memory used=7150.4MB, alloc=351.6MB, time=124.72 memory used=7227.2MB, alloc=351.6MB, time=128.16 memory used=7304.4MB, alloc=351.6MB, time=131.54 memory used=7337.2MB, alloc=351.6MB, time=131.73 memory used=7376.1MB, alloc=351.6MB, time=132.06 memory used=7436.0MB, alloc=351.6MB, time=135.65 memory used=7478.2MB, alloc=351.6MB, time=135.92 memory used=7505.5MB, alloc=351.6MB, time=136.08 memory used=7541.7MB, alloc=351.6MB, time=136.26 memory used=7567.4MB, alloc=351.6MB, time=136.40 memory used=7593.2MB, alloc=351.6MB, time=136.55 memory used=7624.6MB, alloc=351.6MB, time=136.71 memory used=7663.0MB, alloc=351.6MB, time=137.19 memory used=7703.3MB, alloc=351.6MB, time=137.56 memory used=7743.6MB, alloc=351.6MB, time=137.87 memory used=7778.4MB, alloc=351.6MB, time=138.07 memory used=7840.8MB, alloc=351.6MB, time=141.92 memory used=7872.2MB, alloc=351.6MB, time=142.10 memory used=7901.0MB, alloc=351.6MB, time=142.26 memory used=7937.9MB, alloc=351.6MB, time=142.44 memory used=7961.2MB, alloc=351.6MB, time=142.58 memory used=7986.8MB, alloc=351.6MB, time=142.72 memory used=8017.2MB, alloc=351.6MB, time=142.87 memory used=8084.7MB, alloc=351.6MB, time=144.01 memory used=8163.3MB, alloc=375.6MB, time=147.16 memory used=8255.1MB, alloc=375.6MB, time=157.77 memory used=8298.8MB, alloc=375.6MB, time=158.00 memory used=8343.5MB, alloc=375.6MB, time=158.21 memory used=8393.8MB, alloc=375.6MB, time=158.44 memory used=8426.8MB, alloc=375.6MB, time=158.61 memory used=8464.1MB, alloc=375.6MB, time=158.80 memory used=8506.5MB, alloc=375.6MB, time=158.98 memory used=8552.9MB, alloc=375.6MB, time=159.15 memory used=8606.6MB, alloc=375.6MB, time=159.34 memory used=8691.7MB, alloc=375.6MB, time=159.99 memory used=8794.1MB, alloc=375.6MB, time=161.76 memory used=8849.6MB, alloc=375.6MB, time=162.67 memory used=8918.9MB, alloc=375.6MB, time=164.04 memory used=9010.5MB, alloc=375.6MB, time=165.71 memory used=9080.8MB, alloc=375.6MB, time=168.20 memory used=9167.3MB, alloc=375.6MB, time=169.41 memory used=9223.4MB, alloc=375.6MB, time=170.18 memory used=9279.8MB, alloc=375.6MB, time=171.20 memory used=9327.3MB, alloc=375.6MB, time=171.51 memory used=9373.2MB, alloc=375.6MB, time=171.77 memory used=9403.6MB, alloc=399.6MB, time=172.01 memory used=9453.7MB, alloc=399.6MB, time=172.28 memory used=9516.2MB, alloc=399.6MB, time=172.56 memory used=9572.5MB, alloc=399.6MB, time=172.82 memory used=9614.9MB, alloc=399.6MB, time=173.04 memory used=9682.5MB, alloc=399.6MB, time=173.82 memory used=9744.2MB, alloc=399.6MB, time=174.14 memory used=9789.2MB, alloc=399.6MB, time=174.41 memory used=9845.6MB, alloc=399.6MB, time=174.70 memory used=9913.6MB, alloc=399.6MB, time=174.98 memory used=9955.9MB, alloc=399.6MB, time=175.19 memory used=10012.8MB, alloc=399.6MB, time=177.44 memory used=10083.6MB, alloc=399.6MB, time=178.29 memory used=10140.3MB, alloc=399.6MB, time=178.59 memory used=10193.1MB, alloc=399.6MB, time=178.83 memory used=10239.7MB, alloc=399.6MB, time=179.04 memory used=10297.6MB, alloc=399.6MB, time=179.27 memory used=10368.6MB, alloc=399.6MB, time=180.25 memory used=10423.5MB, alloc=399.6MB, time=180.55 memory used=10514.3MB, alloc=399.6MB, time=182.00 memory used=10570.4MB, alloc=399.6MB, time=182.29 memory used=10643.5MB, alloc=399.6MB, time=183.11 memory used=10705.1MB, alloc=399.6MB, time=183.44 memory used=10760.4MB, alloc=399.6MB, time=183.92 |\^/| 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(); 1428263330 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 3 2 2 2 F := [9 x y + 15 x y z + y z - 6 y z , 13 x y + 19 y z - 8 y z + 15, 4 -20 z - 2 x y z + 2 x z + 14 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [19 x y z - 13 x y z - 2 x - 18 y z , 4 2 2 2 2 2 13 x + 19 x y z + 16 x z - 5 y z, 14 x y z - 13 x y - 8 x z - 17 x] > Problem := [F,G]; 3 2 2 2 3 Problem := [[9 x y + 15 x y z + y z - 6 y z , 3 2 2 2 4 13 x y + 19 y z - 8 y z + 15, -20 z - 2 x y z + 2 x z + 14 x], [ 2 2 3 2 19 x y z - 13 x y z - 2 x - 18 y z , 4 2 2 2 2 2 13 x + 19 x y z + 16 x z - 5 y z, 14 x y z - 13 x y - 8 x z - 17 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.0MB, alloc=32.3MB, time=0.82 memory used=41.9MB, alloc=32.3MB, time=1.03 memory used=61.7MB, alloc=32.3MB, time=1.44 memory used=82.3MB, alloc=32.3MB, time=1.92 memory used=102.4MB, alloc=60.3MB, time=2.45 memory used=140.3MB, alloc=62.8MB, time=2.89 memory used=172.9MB, alloc=62.8MB, time=3.20 memory used=206.8MB, alloc=62.8MB, time=3.46 memory used=238.2MB, alloc=62.8MB, time=3.70 memory used=270.6MB, alloc=62.8MB, time=5.31 memory used=304.9MB, alloc=62.8MB, time=5.86 memory used=327.7MB, alloc=62.8MB, time=5.95 memory used=361.8MB, alloc=62.8MB, time=6.19 memory used=389.0MB, alloc=62.8MB, time=6.30 memory used=425.1MB, alloc=62.8MB, time=6.70 memory used=451.7MB, alloc=62.8MB, time=6.82 memory used=491.9MB, alloc=62.8MB, time=8.97 memory used=519.1MB, alloc=62.8MB, time=9.09 memory used=541.8MB, alloc=62.8MB, time=9.18 memory used=574.0MB, alloc=62.8MB, time=9.39 memory used=604.1MB, alloc=62.8MB, time=9.83 memory used=634.3MB, alloc=62.8MB, time=10.16 memory used=660.8MB, alloc=62.8MB, time=10.38 memory used=686.4MB, alloc=62.8MB, time=10.50 memory used=723.5MB, alloc=62.8MB, time=11.12 memory used=758.5MB, alloc=62.8MB, time=11.59 memory used=804.5MB, alloc=62.8MB, time=12.43 memory used=847.0MB, alloc=70.8MB, time=13.49 memory used=889.0MB, alloc=70.8MB, time=14.37 memory used=931.8MB, alloc=70.8MB, time=15.38 memory used=961.4MB, alloc=94.8MB, time=15.78 memory used=1005.8MB, alloc=94.8MB, time=16.16 memory used=1042.4MB, alloc=94.8MB, time=16.34 memory used=1073.7MB, alloc=94.8MB, time=16.49 memory used=1119.6MB, alloc=94.8MB, time=16.89 memory used=1159.2MB, alloc=94.8MB, time=17.07 memory used=1188.9MB, alloc=94.8MB, time=17.22 memory used=1240.8MB, alloc=94.8MB, time=20.83 memory used=1277.1MB, alloc=94.8MB, time=21.01 memory used=1310.4MB, alloc=94.8MB, time=21.16 memory used=1352.8MB, alloc=94.8MB, time=21.32 memory used=1379.5MB, alloc=94.8MB, time=21.43 memory used=1409.8MB, alloc=94.8MB, time=21.56 memory used=1447.0MB, alloc=94.8MB, time=21.68 memory used=1492.1MB, alloc=94.8MB, time=22.01 memory used=1535.2MB, alloc=94.8MB, time=22.74 memory used=1571.5MB, alloc=94.8MB, time=22.89 memory used=1624.8MB, alloc=94.8MB, time=24.19 memory used=1657.7MB, alloc=94.8MB, time=24.35 memory used=1696.7MB, alloc=94.8MB, time=24.50 memory used=1724.7MB, alloc=94.8MB, time=24.61 memory used=1776.2MB, alloc=94.8MB, time=25.73 memory used=1812.7MB, alloc=94.8MB, time=25.91 memory used=1847.5MB, alloc=94.8MB, time=26.07 memory used=1880.3MB, alloc=94.8MB, time=26.20 memory used=1932.3MB, alloc=94.8MB, time=27.67 memory used=1984.4MB, alloc=94.8MB, time=29.11 memory used=2022.3MB, alloc=94.8MB, time=29.30 memory used=2058.5MB, alloc=94.8MB, time=29.46 memory used=2089.5MB, alloc=94.8MB, time=29.62 memory used=2127.4MB, alloc=94.8MB, time=29.77 memory used=2163.7MB, alloc=94.8MB, time=29.91 memory used=2214.6MB, alloc=94.8MB, time=31.12 memory used=2247.0MB, alloc=94.8MB, time=31.28 memory used=2285.9MB, alloc=94.8MB, time=31.43 memory used=2313.8MB, alloc=94.8MB, time=31.55 memory used=2378.6MB, alloc=94.8MB, time=32.51 memory used=2454.4MB, alloc=94.8MB, time=33.69 memory used=2531.1MB, alloc=94.8MB, time=36.00 memory used=2608.3MB, alloc=94.8MB, time=39.47 memory used=2686.0MB, alloc=94.8MB, time=43.85 memory used=2760.3MB, alloc=94.8MB, time=47.32 memory used=2797.5MB, alloc=94.8MB, time=47.50 memory used=2837.6MB, alloc=94.8MB, time=48.45 memory used=2869.8MB, alloc=94.8MB, time=48.61 memory used=2904.2MB, alloc=94.8MB, time=48.75 memory used=2962.0MB, alloc=94.8MB, time=50.43 memory used=3004.4MB, alloc=94.8MB, time=50.87 memory used=3038.6MB, alloc=94.8MB, time=51.06 memory used=3071.2MB, alloc=94.8MB, time=51.22 memory used=3100.8MB, alloc=94.8MB, time=51.38 memory used=3137.1MB, alloc=94.8MB, time=51.54 memory used=3173.0MB, alloc=94.8MB, time=51.69 memory used=3216.4MB, alloc=94.8MB, time=52.89 memory used=3249.7MB, alloc=94.8MB, time=53.06 memory used=3283.4MB, alloc=94.8MB, time=53.23 memory used=3315.7MB, alloc=94.8MB, time=53.37 memory used=3344.0MB, alloc=94.8MB, time=53.49 memory used=3385.1MB, alloc=94.8MB, time=53.94 memory used=3417.5MB, alloc=94.8MB, time=54.25 memory used=3452.4MB, alloc=107.8MB, time=54.78 memory used=3499.3MB, alloc=107.8MB, time=54.97 memory used=3537.2MB, alloc=107.8MB, time=55.14 memory used=3583.6MB, alloc=107.8MB, time=55.34 memory used=3632.5MB, alloc=107.8MB, time=56.26 memory used=3705.2MB, alloc=107.8MB, time=58.14 memory used=3768.0MB, alloc=107.8MB, time=59.64 memory used=3823.6MB, alloc=107.8MB, time=60.67 memory used=3881.9MB, alloc=131.8MB, time=66.27 memory used=3926.7MB, alloc=131.8MB, time=66.53 memory used=3974.6MB, alloc=131.8MB, time=66.77 memory used=4016.4MB, alloc=131.8MB, time=66.98 memory used=4052.3MB, alloc=131.8MB, time=67.17 memory used=4093.4MB, alloc=131.8MB, time=67.36 memory used=4140.6MB, alloc=131.8MB, time=67.58 memory used=4193.7MB, alloc=131.8MB, time=67.79 memory used=4243.7MB, alloc=131.8MB, time=68.01 memory used=4252.8MB, alloc=131.8MB, time=68.12 memory used=4262.8MB, alloc=131.8MB, time=68.24 memory used=4272.7MB, alloc=131.8MB, time=68.36 memory used=4282.7MB, alloc=131.8MB, time=68.48 memory used=4293.5MB, alloc=131.8MB, time=68.60 memory used=4304.3MB, alloc=131.8MB, time=68.74 memory used=4315.2MB, alloc=131.8MB, time=68.85 memory used=4326.6MB, alloc=131.8MB, time=69.00 memory used=4338.2MB, alloc=131.8MB, time=69.14 memory used=4350.3MB, alloc=131.8MB, time=69.27 memory used=4363.3MB, alloc=131.8MB, time=69.41 memory used=4376.1MB, alloc=131.8MB, time=69.55 memory used=4389.3MB, alloc=131.8MB, time=69.67 memory used=4403.5MB, alloc=131.8MB, time=69.80 memory used=4418.0MB, alloc=131.8MB, time=69.94 memory used=4433.1MB, alloc=131.8MB, time=70.07 memory used=4449.0MB, alloc=131.8MB, time=70.20 memory used=4524.0MB, alloc=131.8MB, time=72.22 memory used=4574.2MB, alloc=131.8MB, time=72.46 memory used=4610.1MB, alloc=131.8MB, time=72.65 memory used=4650.4MB, alloc=131.8MB, time=72.84 memory used=4698.8MB, alloc=131.8MB, time=73.05 memory used=4753.9MB, alloc=131.8MB, time=73.28 memory used=4764.0MB, alloc=131.8MB, time=73.40 memory used=4775.5MB, alloc=131.8MB, time=73.52 memory used=4787.2MB, alloc=131.8MB, time=73.66 memory used=4799.7MB, alloc=131.8MB, time=73.78 memory used=4874.7MB, alloc=131.8MB, time=75.15 memory used=4944.4MB, alloc=131.8MB, time=76.02 memory used=5024.7MB, alloc=387.8MB, time=77.36 memory used=5078.7MB, alloc=387.8MB, time=77.78 memory used=5120.4MB, alloc=387.8MB, time=78.03 memory used=5192.8MB, alloc=387.8MB, time=81.74 memory used=5239.3MB, alloc=387.8MB, time=82.02 memory used=5278.2MB, alloc=387.8MB, time=82.27 memory used=5328.9MB, alloc=387.8MB, time=82.53 memory used=5368.0MB, alloc=387.8MB, time=82.75 memory used=5401.1MB, alloc=387.8MB, time=82.94 memory used=5437.2MB, alloc=387.8MB, time=83.13 memory used=5477.2MB, alloc=387.8MB, time=83.34 memory used=5521.2MB, alloc=387.8MB, time=83.55 memory used=5569.1MB, alloc=387.8MB, time=83.77 memory used=5621.7MB, alloc=387.8MB, time=83.99 memory used=5807.6MB, alloc=387.8MB, time=84.84 memory used=5960.8MB, alloc=387.8MB, time=87.28 memory used=6010.5MB, alloc=387.8MB, time=87.58 memory used=6047.4MB, alloc=387.8MB, time=87.81 memory used=6092.2MB, alloc=387.8MB, time=88.05 memory used=6138.3MB, alloc=387.8MB, time=88.27 memory used=6171.2MB, alloc=387.8MB, time=88.45 memory used=6228.5MB, alloc=387.8MB, time=89.81 memory used=6271.5MB, alloc=387.8MB, time=90.06 memory used=6315.3MB, alloc=387.8MB, time=90.30 memory used=6351.8MB, alloc=387.8MB, time=90.48 memory used=6405.8MB, alloc=387.8MB, time=90.96 memory used=6464.6MB, alloc=387.8MB, time=91.62 memory used=6506.6MB, alloc=387.8MB, time=91.81 memory used=6603.3MB, alloc=387.8MB, time=94.01 memory used=6651.5MB, alloc=387.8MB, time=94.72 memory used=6726.8MB, alloc=387.8MB, time=96.08 memory used=6802.0MB, alloc=387.8MB, time=98.60 memory used=6882.6MB, alloc=411.8MB, time=100.66 memory used=6981.8MB, alloc=411.8MB, time=102.53 memory used=7052.4MB, alloc=411.8MB, time=104.73 memory used=7100.1MB, alloc=411.8MB, time=105.03 memory used=7165.6MB, alloc=411.8MB, time=105.54 memory used=7230.4MB, alloc=411.8MB, time=107.81 memory used=7279.5MB, alloc=411.8MB, time=108.09 memory used=7348.6MB, alloc=411.8MB, time=109.35 memory used=7417.7MB, alloc=411.8MB, time=110.31 memory used=7526.3MB, alloc=435.8MB, time=112.49 memory used=7666.1MB, alloc=435.8MB, time=114.92 memory used=7810.0MB, alloc=459.8MB, time=117.60 memory used=7934.6MB, alloc=459.8MB, time=120.57 memory used=8058.9MB, alloc=459.8MB, time=122.54 memory used=8136.5MB, alloc=459.8MB, time=123.49 memory used=8258.3MB, alloc=483.8MB, time=126.01 memory used=8357.8MB, alloc=483.8MB, time=128.50 memory used=8447.6MB, alloc=483.8MB, time=130.74 memory used=8578.9MB, alloc=483.8MB, time=132.44 memory used=8659.8MB, alloc=483.8MB, time=132.96 memory used=8748.7MB, alloc=483.8MB, time=133.74 memory used=8838.4MB, alloc=483.8MB, time=137.59 memory used=8916.3MB, alloc=483.8MB, time=138.10 memory used=8987.5MB, alloc=483.8MB, time=138.54 memory used=9074.2MB, alloc=483.8MB, time=139.26 memory used=9148.0MB, alloc=483.8MB, time=139.76 memory used=9240.6MB, alloc=483.8MB, time=140.58 memory used=9330.9MB, alloc=483.8MB, time=144.57 memory used=9408.7MB, alloc=483.8MB, time=145.07 memory used=9475.4MB, alloc=483.8MB, time=145.50 memory used=9568.1MB, alloc=483.8MB, time=146.21 memory used=9641.6MB, alloc=483.8MB, time=146.70 memory used=9739.3MB, alloc=483.8MB, time=149.15 memory used=9811.4MB, alloc=483.8MB, time=149.59 memory used=9896.8MB, alloc=483.8MB, time=150.63 memory used=9987.7MB, alloc=483.8MB, time=151.43 memory used=10076.2MB, alloc=483.8MB, time=152.10 memory used=10177.1MB, alloc=483.8MB, time=159.87 memory used=10252.4MB, alloc=483.8MB, time=160.37 memory used=10320.5MB, alloc=483.8MB, time=160.82 memory used=10387.7MB, alloc=483.8MB, time=161.23 memory used=10470.2MB, alloc=483.8MB, time=161.66 memory used=10573.2MB, alloc=483.8MB, time=162.61 memory used=10669.9MB, alloc=483.8MB, time=165.18 memory used=10747.3MB, alloc=507.8MB, time=165.79 |\^/| 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(); 1428263630 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 3 2 F := [9 x y z - 9 x + 7 x y z + 2 x z , x z - 3 z - 13 y - 5, 3 3 2 17 x y + 19 x z + 15 y z + 8 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 G := [3 x + 12 x z - 16 z, -12 x z - 4 x y - 14 x z - 15 y , 4 3 -12 z - 9 y + 15 x z - z] > Problem := [F,G]; 2 3 2 3 3 2 Problem := [[9 x y z - 9 x + 7 x y z + 2 x z , x z - 3 z - 13 y - 5, 3 3 2 4 2 17 x y + 19 x z + 15 y z + 8 y z], [3 x + 12 x z - 16 z, 3 2 2 4 3 -12 x z - 4 x y - 14 x z - 15 y , -12 z - 9 y + 15 x z - z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=25.7MB, alloc=32.3MB, time=0.88 memory used=45.6MB, alloc=60.3MB, time=1.40 memory used=86.6MB, alloc=60.3MB, time=2.40 memory used=130.9MB, alloc=68.3MB, time=3.48 memory used=170.4MB, alloc=68.3MB, time=4.52 memory used=209.8MB, alloc=92.3MB, time=5.38 memory used=278.1MB, alloc=92.3MB, time=6.94 memory used=347.3MB, alloc=92.3MB, time=8.60 memory used=408.8MB, alloc=372.3MB, time=10.21 memory used=501.8MB, alloc=372.3MB, time=12.55 memory used=592.6MB, alloc=372.3MB, time=14.42 memory used=681.4MB, alloc=396.3MB, time=16.73 memory used=797.6MB, alloc=396.3MB, time=19.22 memory used=917.5MB, alloc=396.3MB, time=21.79 memory used=1027.8MB, alloc=420.3MB, time=24.37 memory used=1162.5MB, alloc=420.3MB, time=27.10 memory used=1287.5MB, alloc=420.3MB, time=30.43 memory used=1400.0MB, alloc=444.3MB, time=33.39 memory used=1519.0MB, alloc=444.3MB, time=36.38 memory used=1628.9MB, alloc=444.3MB, time=39.56 memory used=1724.2MB, alloc=468.3MB, time=42.11 memory used=1814.0MB, alloc=468.3MB, time=44.62 memory used=1904.3MB, alloc=468.3MB, time=47.23 memory used=2034.2MB, alloc=468.3MB, time=50.06 memory used=2130.8MB, alloc=468.3MB, time=50.79 memory used=2216.1MB, alloc=468.3MB, time=51.52 memory used=2292.1MB, alloc=468.3MB, time=52.05 memory used=2412.6MB, alloc=468.3MB, time=55.11 memory used=2507.1MB, alloc=468.3MB, time=56.30 memory used=2617.4MB, alloc=468.3MB, time=59.19 memory used=2762.2MB, alloc=468.3MB, time=62.36 memory used=2859.8MB, alloc=468.3MB, time=65.24 memory used=2994.0MB, alloc=468.3MB, time=67.47 memory used=3082.0MB, alloc=468.3MB, time=70.04 memory used=3167.1MB, alloc=468.3MB, time=72.86 memory used=3253.3MB, alloc=492.3MB, time=75.63 memory used=3332.3MB, alloc=492.3MB, time=78.16 memory used=3399.7MB, alloc=492.3MB, time=80.47 memory used=3472.0MB, alloc=492.3MB, time=82.59 memory used=3540.7MB, alloc=492.3MB, time=84.87 memory used=3610.6MB, alloc=492.3MB, time=86.86 memory used=3669.3MB, alloc=492.3MB, time=88.80 memory used=3730.4MB, alloc=492.3MB, time=90.90 memory used=3789.7MB, alloc=492.3MB, time=92.73 memory used=3839.7MB, alloc=492.3MB, time=94.52 memory used=3897.2MB, alloc=492.3MB, time=96.40 memory used=3938.3MB, alloc=492.3MB, time=97.94 memory used=3984.6MB, alloc=492.3MB, time=99.50 memory used=4038.6MB, alloc=492.3MB, time=101.29 memory used=4103.2MB, alloc=516.3MB, time=103.17 memory used=4172.9MB, alloc=516.3MB, time=104.47 memory used=4224.5MB, alloc=516.3MB, time=106.02 memory used=4267.1MB, alloc=516.3MB, time=107.80 memory used=4422.6MB, alloc=516.3MB, time=110.62 memory used=4584.1MB, alloc=516.3MB, time=113.57 memory used=4781.7MB, alloc=540.3MB, time=118.85 memory used=4997.9MB, alloc=540.3MB, time=124.90 memory used=5199.7MB, alloc=564.3MB, time=129.69 memory used=5389.7MB, alloc=588.3MB, time=134.20 |\^/| 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(); 1428263930 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 3 4 3 2 F := [-x z + 7 z - 2 x y - 2 y , -16 x - 17 y + 4 x - 12 x z, 2 3 11 x y z - 20 y + x z + 18 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 3 G := [19 z - 14 z - 5 x y + 12 z , -x y + 13 y - 17 z, 3 10 y z - 16 x y - 3 x z + 14 y] > Problem := [F,G]; 3 4 2 3 4 3 2 Problem := [[-x z + 7 z - 2 x y - 2 y , -16 x - 17 y + 4 x - 12 x z, 2 3 4 3 2 11 x y z - 20 y + x z + 18 x], [19 z - 14 z - 5 x y + 12 z , 3 3 -x y + 13 y - 17 z, 10 y z - 16 x y - 3 x z + 14 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.32 memory used=24.8MB, alloc=32.3MB, time=0.84 memory used=45.1MB, alloc=32.3MB, time=1.14 memory used=64.0MB, alloc=32.3MB, time=1.43 memory used=93.9MB, alloc=37.2MB, time=2.13 memory used=116.1MB, alloc=37.2MB, time=2.78 memory used=132.5MB, alloc=61.2MB, time=3.04 memory used=173.9MB, alloc=61.2MB, time=3.80 memory used=217.0MB, alloc=61.2MB, time=4.60 memory used=252.5MB, alloc=61.2MB, time=5.32 memory used=296.6MB, alloc=69.2MB, time=6.35 memory used=343.4MB, alloc=69.2MB, time=7.44 memory used=392.6MB, alloc=93.2MB, time=8.41 memory used=450.9MB, alloc=93.2MB, time=8.98 memory used=497.5MB, alloc=93.2MB, time=9.27 memory used=538.6MB, alloc=93.2MB, time=9.59 memory used=585.4MB, alloc=93.2MB, time=9.90 memory used=628.1MB, alloc=93.2MB, time=10.16 memory used=665.4MB, alloc=93.2MB, time=10.36 memory used=710.2MB, alloc=93.2MB, time=10.73 memory used=765.7MB, alloc=93.2MB, time=11.35 memory used=797.7MB, alloc=93.2MB, time=11.55 memory used=835.6MB, alloc=93.2MB, time=11.73 memory used=867.5MB, alloc=93.2MB, time=11.89 memory used=906.5MB, alloc=93.2MB, time=12.27 memory used=947.3MB, alloc=93.2MB, time=12.50 memory used=980.3MB, alloc=93.2MB, time=12.69 memory used=1018.8MB, alloc=93.2MB, time=12.87 memory used=1045.0MB, alloc=93.2MB, time=13.01 memory used=1093.8MB, alloc=93.2MB, time=14.38 memory used=1126.8MB, alloc=93.2MB, time=14.56 memory used=1176.5MB, alloc=93.2MB, time=15.07 memory used=1212.2MB, alloc=93.2MB, time=15.28 memory used=1247.5MB, alloc=93.2MB, time=15.47 memory used=1284.6MB, alloc=93.2MB, time=15.64 memory used=1311.5MB, alloc=93.2MB, time=15.80 memory used=1362.2MB, alloc=93.2MB, time=16.18 memory used=1394.0MB, alloc=93.2MB, time=16.38 memory used=1431.4MB, alloc=93.2MB, time=16.56 memory used=1465.1MB, alloc=93.2MB, time=16.73 memory used=1492.6MB, alloc=93.2MB, time=16.88 memory used=1542.4MB, alloc=93.2MB, time=18.58 memory used=1578.5MB, alloc=93.2MB, time=18.76 memory used=1606.1MB, alloc=93.2MB, time=18.92 memory used=1655.9MB, alloc=93.2MB, time=19.46 memory used=1700.3MB, alloc=93.2MB, time=19.70 memory used=1733.4MB, alloc=93.2MB, time=19.89 memory used=1772.8MB, alloc=93.2MB, time=20.07 memory used=1799.2MB, alloc=93.2MB, time=20.22 memory used=1851.8MB, alloc=93.2MB, time=20.69 memory used=1881.9MB, alloc=93.2MB, time=20.87 memory used=1921.9MB, alloc=93.2MB, time=21.05 memory used=1951.0MB, alloc=93.2MB, time=21.20 memory used=1999.6MB, alloc=93.2MB, time=22.46 memory used=2035.0MB, alloc=93.2MB, time=22.66 memory used=2063.7MB, alloc=93.2MB, time=22.81 memory used=2116.2MB, alloc=93.3MB, time=23.23 memory used=2147.3MB, alloc=93.3MB, time=23.41 memory used=2187.9MB, alloc=93.3MB, time=23.61 memory used=2213.8MB, alloc=93.3MB, time=23.76 memory used=2265.2MB, alloc=93.3MB, time=24.18 memory used=2294.7MB, alloc=93.3MB, time=24.36 memory used=2334.1MB, alloc=93.3MB, time=24.55 memory used=2362.0MB, alloc=93.3MB, time=24.70 memory used=2410.3MB, alloc=93.3MB, time=26.37 memory used=2446.5MB, alloc=93.3MB, time=26.55 memory used=2475.0MB, alloc=93.3MB, time=26.72 memory used=2537.8MB, alloc=93.3MB, time=27.71 memory used=2607.0MB, alloc=93.3MB, time=29.60 memory used=2672.5MB, alloc=349.3MB, time=31.12 memory used=2754.7MB, alloc=349.3MB, time=33.73 memory used=2786.9MB, alloc=349.3MB, time=33.93 memory used=2815.1MB, alloc=349.3MB, time=34.10 memory used=2843.5MB, alloc=349.3MB, time=34.27 memory used=2892.3MB, alloc=349.3MB, time=36.20 memory used=2928.6MB, alloc=349.3MB, time=36.43 memory used=2958.8MB, alloc=349.3MB, time=36.60 memory used=2986.2MB, alloc=349.3MB, time=36.77 memory used=3055.9MB, alloc=373.3MB, time=37.79 memory used=3156.3MB, alloc=373.3MB, time=40.21 memory used=3247.8MB, alloc=373.3MB, time=42.02 memory used=3294.8MB, alloc=373.3MB, time=42.39 memory used=3336.2MB, alloc=373.3MB, time=42.65 memory used=3391.3MB, alloc=373.3MB, time=44.58 memory used=3432.3MB, alloc=373.3MB, time=44.92 memory used=3487.7MB, alloc=373.3MB, time=45.40 memory used=3571.2MB, alloc=373.3MB, time=45.80 memory used=3676.0MB, alloc=373.3MB, time=46.63 memory used=3795.8MB, alloc=373.3MB, time=47.05 memory used=3891.2MB, alloc=373.3MB, time=47.35 memory used=4075.4MB, alloc=373.3MB, time=48.00 memory used=4197.0MB, alloc=373.3MB, time=49.04 memory used=4243.0MB, alloc=373.3MB, time=49.47 memory used=4287.5MB, alloc=373.3MB, time=50.67 memory used=4337.2MB, alloc=373.3MB, time=51.22 memory used=4376.7MB, alloc=373.3MB, time=51.48 memory used=4417.3MB, alloc=373.3MB, time=51.87 memory used=4513.8MB, alloc=373.3MB, time=52.28 memory used=4599.3MB, alloc=373.3MB, time=53.06 memory used=4733.0MB, alloc=373.3MB, time=53.48 memory used=4826.2MB, alloc=373.3MB, time=53.77 memory used=5013.6MB, alloc=373.3MB, time=54.25 memory used=5161.7MB, alloc=373.3MB, time=56.59 memory used=5237.3MB, alloc=373.3MB, time=58.41 memory used=5291.8MB, alloc=373.3MB, time=59.83 memory used=5334.7MB, alloc=373.3MB, time=60.37 memory used=5388.9MB, alloc=373.3MB, time=60.79 memory used=5434.8MB, alloc=373.3MB, time=61.61 memory used=5517.4MB, alloc=397.3MB, time=63.62 memory used=5617.9MB, alloc=397.3MB, time=65.06 memory used=5709.5MB, alloc=397.3MB, time=66.07 memory used=5765.3MB, alloc=397.3MB, time=66.43 memory used=5817.3MB, alloc=397.3MB, time=66.76 memory used=5898.8MB, alloc=397.3MB, time=67.61 memory used=5968.8MB, alloc=397.3MB, time=68.04 memory used=6016.5MB, alloc=397.3MB, time=68.38 memory used=6078.8MB, alloc=397.3MB, time=68.81 memory used=6168.1MB, alloc=397.3MB, time=69.72 memory used=6223.7MB, alloc=397.3MB, time=70.09 memory used=6275.0MB, alloc=397.3MB, time=70.43 memory used=6351.4MB, alloc=397.3MB, time=71.29 memory used=6432.0MB, alloc=397.3MB, time=71.76 memory used=6477.8MB, alloc=397.3MB, time=72.08 memory used=6535.7MB, alloc=397.3MB, time=72.42 memory used=6617.9MB, alloc=397.3MB, time=73.33 memory used=6681.9MB, alloc=397.3MB, time=73.94 memory used=6753.3MB, alloc=397.3MB, time=74.41 memory used=6832.7MB, alloc=397.3MB, time=75.28 memory used=6896.4MB, alloc=397.3MB, time=75.94 memory used=6958.6MB, alloc=397.3MB, time=76.33 memory used=7049.2MB, alloc=397.3MB, time=79.45 memory used=7144.9MB, alloc=397.3MB, time=83.73 memory used=7265.4MB, alloc=397.3MB, time=85.77 memory used=7334.8MB, alloc=397.3MB, time=87.97 memory used=7388.9MB, alloc=397.3MB, time=88.32 memory used=7445.2MB, alloc=397.3MB, time=88.66 memory used=7486.5MB, alloc=397.3MB, time=88.99 memory used=7550.1MB, alloc=421.3MB, time=100.41 memory used=7631.9MB, alloc=421.3MB, time=103.79 memory used=7711.0MB, alloc=421.3MB, time=104.21 memory used=7771.4MB, alloc=421.3MB, time=104.58 memory used=7827.3MB, alloc=421.3MB, time=104.93 memory used=7884.9MB, alloc=421.3MB, time=105.26 memory used=7948.8MB, alloc=421.3MB, time=105.61 memory used=8020.1MB, alloc=421.3MB, time=105.97 memory used=8247.9MB, alloc=421.3MB, time=110.71 memory used=8431.8MB, alloc=421.3MB, time=132.50 |\^/| 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(); 1428264230 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 F := [10 x y z + 18 x y + x y + 6 z, 10 x y z + 20 y z - 15 y - 11 z , 3 2 2 5 x y + 9 x y z + 2 x z + 4 z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 4 2 2 G := [11 x z - 13 z + 18 z, -11 x y - 10 y + 18 x z - y z, 2 2 2 3 2 6 x y + 7 x y z + x - 6 y z ] > Problem := [F,G]; 2 2 Problem := [[10 x y z + 18 x y + x y + 6 z, 2 3 3 2 3 2 2 10 x y z + 20 y z - 15 y - 11 z , 5 x y + 9 x y z + 2 x z + 4 z], [ 3 3 2 2 4 2 2 11 x z - 13 z + 18 z, -11 x y - 10 y + 18 x z - y z, 2 2 2 3 2 6 x y + 7 x y z + x - 6 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.32 memory used=26.5MB, alloc=32.3MB, time=0.90 memory used=47.1MB, alloc=32.3MB, time=1.47 memory used=66.3MB, alloc=56.3MB, time=2.01 memory used=105.8MB, alloc=60.3MB, time=3.08 memory used=144.2MB, alloc=84.3MB, time=4.15 memory used=207.9MB, alloc=92.3MB, time=5.87 memory used=273.1MB, alloc=116.3MB, time=7.55 memory used=349.8MB, alloc=116.3MB, time=9.57 memory used=413.8MB, alloc=372.3MB, time=10.91 memory used=504.5MB, alloc=396.3MB, time=13.01 memory used=621.5MB, alloc=420.3MB, time=15.68 memory used=741.9MB, alloc=420.3MB, time=18.78 memory used=868.1MB, alloc=444.3MB, time=21.83 memory used=981.2MB, alloc=444.3MB, time=24.73 memory used=1086.0MB, alloc=444.3MB, time=27.41 memory used=1195.6MB, alloc=468.3MB, time=30.25 memory used=1296.2MB, alloc=468.3MB, time=32.85 memory used=1399.8MB, alloc=468.3MB, time=35.53 memory used=1489.7MB, alloc=468.3MB, time=37.81 memory used=1579.0MB, alloc=468.3MB, time=40.03 memory used=1667.4MB, alloc=468.3MB, time=42.70 memory used=1735.2MB, alloc=468.3MB, time=44.55 memory used=1813.0MB, alloc=468.3MB, time=46.82 memory used=1889.5MB, alloc=492.3MB, time=49.15 memory used=1964.9MB, alloc=492.3MB, time=51.21 memory used=2039.7MB, alloc=492.3MB, time=53.38 memory used=2110.9MB, alloc=492.3MB, time=55.52 memory used=2177.3MB, alloc=492.3MB, time=57.34 memory used=2245.7MB, alloc=492.3MB, time=59.69 memory used=2303.3MB, alloc=492.3MB, time=61.23 memory used=2366.5MB, alloc=492.3MB, time=62.93 memory used=2423.4MB, alloc=492.3MB, time=64.86 memory used=2499.8MB, alloc=492.3MB, time=66.24 memory used=2589.8MB, alloc=492.3MB, time=67.60 memory used=2686.5MB, alloc=492.3MB, time=69.26 memory used=2792.6MB, alloc=492.3MB, time=70.53 memory used=2879.6MB, alloc=492.3MB, time=71.33 memory used=2969.6MB, alloc=492.3MB, time=73.37 memory used=3057.2MB, alloc=492.3MB, time=74.16 memory used=3137.5MB, alloc=492.3MB, time=74.86 memory used=3204.5MB, alloc=492.3MB, time=76.66 memory used=3430.1MB, alloc=516.3MB, time=81.63 memory used=3653.6MB, alloc=516.3MB, time=87.00 memory used=3882.1MB, alloc=516.3MB, time=90.81 memory used=4118.5MB, alloc=516.3MB, time=94.90 memory used=4347.6MB, alloc=516.3MB, time=100.13 memory used=4575.9MB, alloc=516.3MB, time=106.77 memory used=4693.1MB, alloc=516.3MB, time=108.21 memory used=4855.7MB, alloc=516.3MB, time=111.27 memory used=4946.6MB, alloc=516.3MB, time=112.11 memory used=5040.6MB, alloc=516.3MB, time=112.89 memory used=5135.8MB, alloc=516.3MB, time=113.65 memory used=5209.1MB, alloc=516.3MB, time=114.32 memory used=5321.4MB, alloc=516.3MB, time=117.28 memory used=5418.0MB, alloc=516.3MB, time=118.10 memory used=5496.5MB, alloc=516.3MB, time=118.83 memory used=5588.6MB, alloc=516.3MB, time=119.53 memory used=5780.9MB, alloc=516.3MB, time=122.63 memory used=6028.5MB, alloc=540.3MB, time=128.33 memory used=6277.5MB, alloc=540.3MB, time=133.30 memory used=6543.7MB, alloc=540.3MB, time=137.39 |\^/| 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(); 1428264530 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 3 F := [14 x y z - 16 y - 2 y z + 15 x y, 10 y z + 18 x y z + 17 z + 17 x y, 2 2 3 2 2 5 y z - 13 y z - 5 x y + 11 y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 3 2 G := [18 x y z + 7 y z + 10 z + 18, -12 x y z + 12 x z - 19 x + 4 x y, 2 2 3 2 -10 y z + 7 x - 14 x y + 6 x] > Problem := [F,G]; 2 3 2 Problem := [[14 x y z - 16 y - 2 y z + 15 x y, 3 3 2 2 3 2 2 10 y z + 18 x y z + 17 z + 17 x y, 5 y z - 13 y z - 5 x y + 11 y ], [ 2 3 2 2 2 3 2 18 x y z + 7 y z + 10 z + 18, -12 x y z + 12 x z - 19 x + 4 x y, 2 2 3 2 -10 y z + 7 x - 14 x y + 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=24.4MB, alloc=32.3MB, time=0.83 memory used=43.0MB, alloc=56.3MB, time=1.32 memory used=87.6MB, alloc=60.3MB, time=1.91 memory used=135.8MB, alloc=65.8MB, time=2.65 memory used=171.9MB, alloc=65.8MB, time=3.60 memory used=203.3MB, alloc=65.8MB, time=4.14 memory used=243.1MB, alloc=65.8MB, time=4.71 memory used=279.4MB, alloc=65.8MB, time=5.70 memory used=310.9MB, alloc=65.8MB, time=6.28 memory used=363.1MB, alloc=65.8MB, time=8.69 memory used=398.6MB, alloc=65.8MB, time=18.87 memory used=429.6MB, alloc=65.8MB, time=19.04 memory used=452.7MB, alloc=65.8MB, time=19.17 memory used=478.7MB, alloc=65.8MB, time=19.29 memory used=528.5MB, alloc=65.8MB, time=20.00 memory used=576.9MB, alloc=65.8MB, time=25.80 memory used=605.1MB, alloc=65.8MB, time=25.94 memory used=625.9MB, alloc=65.8MB, time=26.06 memory used=664.0MB, alloc=65.8MB, time=26.90 memory used=707.2MB, alloc=65.8MB, time=27.73 memory used=739.9MB, alloc=65.8MB, time=28.19 memory used=769.1MB, alloc=65.8MB, time=28.62 memory used=809.0MB, alloc=65.8MB, time=29.58 memory used=851.2MB, alloc=97.8MB, time=30.47 memory used=915.1MB, alloc=97.8MB, time=32.05 memory used=979.1MB, alloc=121.8MB, time=33.64 memory used=1040.1MB, alloc=121.8MB, time=34.23 memory used=1092.1MB, alloc=121.8MB, time=34.56 memory used=1135.6MB, alloc=121.8MB, time=34.79 memory used=1194.6MB, alloc=121.8MB, time=36.10 memory used=1250.0MB, alloc=121.8MB, time=36.53 memory used=1296.1MB, alloc=121.8MB, time=36.77 memory used=1338.7MB, alloc=121.8MB, time=36.97 memory used=1391.2MB, alloc=121.8MB, time=38.03 memory used=1459.8MB, alloc=121.8MB, time=38.85 memory used=1503.6MB, alloc=121.8MB, time=39.09 memory used=1548.9MB, alloc=121.8MB, time=39.31 memory used=1588.0MB, alloc=121.8MB, time=39.51 memory used=1653.5MB, alloc=121.8MB, time=51.47 memory used=1708.3MB, alloc=121.8MB, time=54.08 memory used=1749.6MB, alloc=121.8MB, time=54.30 memory used=1795.0MB, alloc=121.8MB, time=54.52 memory used=1847.7MB, alloc=121.8MB, time=54.73 memory used=1880.1MB, alloc=121.8MB, time=54.89 memory used=1917.0MB, alloc=121.8MB, time=55.06 memory used=1957.2MB, alloc=121.8MB, time=55.23 memory used=2001.7MB, alloc=121.8MB, time=55.40 memory used=2053.0MB, alloc=121.8MB, time=55.58 memory used=2118.8MB, alloc=127.1MB, time=56.31 memory used=2168.6MB, alloc=127.1MB, time=56.57 memory used=2206.7MB, alloc=127.1MB, time=56.78 memory used=2249.3MB, alloc=127.1MB, time=56.98 memory used=2317.2MB, alloc=127.1MB, time=63.54 memory used=2360.8MB, alloc=127.1MB, time=63.75 memory used=2406.0MB, alloc=127.1MB, time=63.96 memory used=2452.1MB, alloc=127.1MB, time=64.15 memory used=2486.0MB, alloc=127.1MB, time=64.31 memory used=2526.2MB, alloc=127.1MB, time=64.47 memory used=2605.6MB, alloc=127.1MB, time=66.04 memory used=2658.0MB, alloc=127.1MB, time=66.64 memory used=2701.3MB, alloc=127.1MB, time=66.84 memory used=2741.8MB, alloc=127.1MB, time=67.03 memory used=2793.1MB, alloc=127.1MB, time=67.62 memory used=2838.1MB, alloc=127.1MB, time=67.87 memory used=2885.8MB, alloc=127.1MB, time=68.11 memory used=2927.9MB, alloc=127.1MB, time=68.33 memory used=2962.0MB, alloc=127.1MB, time=68.52 memory used=3002.0MB, alloc=127.1MB, time=68.71 memory used=3048.2MB, alloc=127.1MB, time=68.91 memory used=3117.1MB, alloc=127.1MB, time=86.78 memory used=3171.2MB, alloc=127.1MB, time=103.83 memory used=3217.4MB, alloc=127.1MB, time=104.07 memory used=3253.5MB, alloc=127.1MB, time=104.26 memory used=3291.2MB, alloc=127.1MB, time=104.46 memory used=3334.9MB, alloc=127.1MB, time=104.67 memory used=3384.1MB, alloc=127.1MB, time=104.88 memory used=3429.8MB, alloc=127.1MB, time=105.09 memory used=3458.2MB, alloc=127.1MB, time=105.24 memory used=3488.6MB, alloc=127.1MB, time=105.39 memory used=3521.3MB, alloc=127.1MB, time=105.55 memory used=3556.3MB, alloc=127.1MB, time=105.72 memory used=3591.9MB, alloc=127.1MB, time=105.88 memory used=3629.6MB, alloc=127.1MB, time=106.04 memory used=3669.5MB, alloc=127.1MB, time=106.22 memory used=3712.9MB, alloc=127.1MB, time=106.39 memory used=3758.2MB, alloc=127.1MB, time=106.56 memory used=3806.6MB, alloc=127.1MB, time=106.74 memory used=3856.5MB, alloc=127.1MB, time=106.92 memory used=3910.1MB, alloc=127.1MB, time=107.11 memory used=3939.4MB, alloc=131.8MB, time=107.26 memory used=3948.5MB, alloc=131.8MB, time=107.38 memory used=3957.4MB, alloc=131.8MB, time=107.49 memory used=3967.2MB, alloc=131.8MB, time=107.61 memory used=3977.1MB, alloc=131.8MB, time=107.73 memory used=3987.0MB, alloc=131.8MB, time=107.84 memory used=3996.7MB, alloc=131.8MB, time=107.97 memory used=4006.3MB, alloc=131.8MB, time=108.09 memory used=4016.1MB, alloc=131.8MB, time=108.20 memory used=4026.5MB, alloc=131.8MB, time=108.31 memory used=4037.1MB, alloc=131.8MB, time=108.43 memory used=4047.6MB, alloc=131.8MB, time=108.56 memory used=4058.9MB, alloc=131.8MB, time=108.68 memory used=4070.1MB, alloc=131.8MB, time=108.80 memory used=4081.2MB, alloc=131.8MB, time=108.91 memory used=4092.9MB, alloc=131.8MB, time=109.03 memory used=4104.5MB, alloc=131.8MB, time=109.16 memory used=4116.9MB, alloc=131.8MB, time=109.28 memory used=4129.0MB, alloc=131.8MB, time=109.40 memory used=4141.4MB, alloc=131.8MB, time=109.54 memory used=4154.4MB, alloc=131.8MB, time=109.69 memory used=4167.6MB, alloc=131.8MB, time=109.81 memory used=4181.2MB, alloc=131.8MB, time=109.93 memory used=4195.2MB, alloc=131.8MB, time=110.05 memory used=4209.9MB, alloc=131.8MB, time=110.16 memory used=4225.3MB, alloc=131.8MB, time=110.29 memory used=4335.6MB, alloc=131.8MB, time=112.67 memory used=4431.3MB, alloc=131.8MB, time=114.11 memory used=4528.2MB, alloc=131.8MB, time=116.52 memory used=4625.3MB, alloc=131.8MB, time=119.77 memory used=4722.0MB, alloc=131.8MB, time=123.73 memory used=4820.0MB, alloc=131.8MB, time=128.30 memory used=4906.4MB, alloc=131.8MB, time=131.28 memory used=4951.5MB, alloc=131.8MB, time=131.52 memory used=4986.0MB, alloc=131.8MB, time=131.71 memory used=5040.1MB, alloc=131.8MB, time=132.86 memory used=5080.5MB, alloc=131.8MB, time=133.08 memory used=5127.1MB, alloc=131.8MB, time=133.57 memory used=5202.0MB, alloc=131.8MB, time=135.25 memory used=5241.7MB, alloc=131.8MB, time=135.46 memory used=5285.5MB, alloc=131.8MB, time=135.66 memory used=5319.5MB, alloc=131.8MB, time=135.83 memory used=5359.0MB, alloc=131.8MB, time=136.12 memory used=5414.1MB, alloc=131.8MB, time=136.73 memory used=5455.1MB, alloc=131.8MB, time=136.97 memory used=5500.3MB, alloc=131.8MB, time=137.20 memory used=5530.9MB, alloc=131.8MB, time=137.40 memory used=5566.0MB, alloc=131.8MB, time=137.60 memory used=5606.1MB, alloc=131.8MB, time=137.80 memory used=5652.0MB, alloc=131.8MB, time=137.99 memory used=5702.6MB, alloc=131.8MB, time=138.56 memory used=5762.7MB, alloc=155.8MB, time=156.58 memory used=5834.2MB, alloc=155.8MB, time=173.69 memory used=5892.4MB, alloc=155.8MB, time=173.98 memory used=5943.7MB, alloc=155.8MB, time=174.22 memory used=6007.4MB, alloc=155.8MB, time=174.49 memory used=6069.5MB, alloc=155.8MB, time=174.73 memory used=6110.4MB, alloc=155.8MB, time=174.92 memory used=6154.5MB, alloc=155.8MB, time=175.12 memory used=6203.5MB, alloc=155.8MB, time=175.32 memory used=6255.7MB, alloc=155.8MB, time=175.52 memory used=6312.7MB, alloc=155.8MB, time=175.74 memory used=6372.6MB, alloc=155.8MB, time=175.95 memory used=6438.4MB, alloc=155.8MB, time=176.17 memory used=6508.2MB, alloc=155.8MB, time=176.39 memory used=6568.7MB, alloc=155.8MB, time=176.60 memory used=6578.3MB, alloc=155.8MB, time=176.76 memory used=6586.7MB, alloc=155.8MB, time=176.88 memory used=6596.2MB, alloc=155.8MB, time=177.02 memory used=6605.9MB, alloc=155.8MB, time=177.15 memory used=6615.6MB, alloc=155.8MB, time=177.27 memory used=6625.2MB, alloc=155.8MB, time=177.41 memory used=6634.8MB, alloc=155.8MB, time=177.53 memory used=6644.3MB, alloc=155.8MB, time=177.68 memory used=6653.7MB, alloc=155.8MB, time=177.81 memory used=6663.2MB, alloc=155.8MB, time=177.94 memory used=6673.8MB, alloc=155.8MB, time=178.06 memory used=6684.5MB, alloc=155.8MB, time=178.19 memory used=6695.1MB, alloc=155.8MB, time=178.36 memory used=6705.5MB, alloc=155.8MB, time=178.49 memory used=6715.9MB, alloc=155.8MB, time=178.62 memory used=6726.4MB, alloc=155.8MB, time=178.75 memory used=6737.8MB, alloc=155.8MB, time=178.89 memory used=6749.1MB, alloc=155.8MB, time=179.01 memory used=6759.2MB, alloc=155.8MB, time=179.15 memory used=6771.3MB, alloc=155.8MB, time=179.28 memory used=6783.5MB, alloc=155.8MB, time=179.41 memory used=6795.4MB, alloc=155.8MB, time=179.55 memory used=6808.2MB, alloc=155.8MB, time=179.67 memory used=6820.8MB, alloc=155.8MB, time=179.81 memory used=6834.2MB, alloc=155.8MB, time=179.94 memory used=6847.2MB, alloc=155.8MB, time=180.07 memory used=6860.8MB, alloc=155.8MB, time=180.22 memory used=6874.9MB, alloc=155.8MB, time=180.36 memory used=6889.4MB, alloc=155.8MB, time=180.49 memory used=6903.9MB, alloc=155.8MB, time=180.63 memory used=6919.2MB, alloc=155.8MB, time=180.76 memory used=6934.7MB, alloc=155.8MB, time=180.90 memory used=6951.2MB, alloc=155.8MB, time=181.04 memory used=7031.2MB, alloc=411.8MB, time=182.73 memory used=7144.3MB, alloc=411.8MB, time=185.57 memory used=7257.6MB, alloc=411.8MB, time=188.41 memory used=7356.5MB, alloc=411.8MB, time=190.76 memory used=7414.7MB, alloc=411.8MB, time=191.29 memory used=7465.7MB, alloc=411.8MB, time=191.57 memory used=7509.8MB, alloc=411.8MB, time=191.81 memory used=7592.4MB, alloc=411.8MB, time=192.69 memory used=7650.9MB, alloc=411.8MB, time=193.08 memory used=7703.0MB, alloc=411.8MB, time=193.39 memory used=7744.6MB, alloc=411.8MB, time=193.67 memory used=7793.8MB, alloc=411.8MB, time=193.96 memory used=7852.2MB, alloc=411.8MB, time=194.26 memory used=7900.3MB, alloc=411.8MB, time=194.52 memory used=7937.5MB, alloc=411.8MB, time=194.74 memory used=7978.5MB, alloc=411.8MB, time=194.97 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428264830 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 4 2 2 3 2 2 F := [17 x + 2 x z - 8 z + 11, -17 x y - 3 x y - 5 y z + 8 x y, 3 3 -5 x z - 5 z + 17 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 2 2 G := [-15 x z + 10 x y z - 2 y + 5 z , -11 x + 15 y z + x z + 14 y z, 2 2 2 2 2 2 -3 x y - 14 x z + 2 x + 6 z ] > Problem := [F,G]; 4 3 4 2 2 3 2 2 Problem := [[17 x + 2 x z - 8 z + 11, -17 x y - 3 x y - 5 y z + 8 x y, 3 3 3 2 2 -5 x z - 5 z + 17 y z], [-15 x z + 10 x y z - 2 y + 5 z , 4 3 2 2 2 2 2 2 2 2 -11 x + 15 y z + x z + 14 y z, -3 x y - 14 x z + 2 x + 6 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=24.4MB, alloc=32.3MB, time=0.82 memory used=47.2MB, alloc=32.3MB, time=1.18 memory used=76.9MB, alloc=36.3MB, time=1.87 memory used=99.4MB, alloc=36.3MB, time=2.45 memory used=119.0MB, alloc=60.3MB, time=2.99 memory used=160.5MB, alloc=60.3MB, time=3.78 memory used=184.3MB, alloc=60.3MB, time=3.89 memory used=208.7MB, alloc=60.3MB, time=4.00 memory used=244.0MB, alloc=61.3MB, time=4.85 memory used=269.3MB, alloc=61.3MB, time=5.00 memory used=289.9MB, alloc=61.3MB, time=5.12 memory used=314.2MB, alloc=61.3MB, time=5.25 memory used=343.3MB, alloc=61.3MB, time=5.38 memory used=367.5MB, alloc=61.3MB, time=5.50 memory used=382.4MB, alloc=61.3MB, time=5.60 memory used=398.2MB, alloc=61.3MB, time=5.70 memory used=415.0MB, alloc=61.3MB, time=5.80 memory used=434.3MB, alloc=61.3MB, time=5.91 memory used=454.7MB, alloc=61.3MB, time=6.02 memory used=475.6MB, alloc=61.3MB, time=6.13 memory used=497.1MB, alloc=61.3MB, time=6.24 memory used=519.1MB, alloc=61.3MB, time=6.35 memory used=542.2MB, alloc=61.3MB, time=6.46 memory used=568.0MB, alloc=61.3MB, time=6.58 memory used=594.8MB, alloc=61.3MB, time=6.69 memory used=622.0MB, alloc=61.3MB, time=6.81 memory used=649.7MB, alloc=61.3MB, time=6.92 memory used=676.6MB, alloc=61.3MB, time=7.04 memory used=690.9MB, alloc=61.3MB, time=7.12 memory used=705.2MB, alloc=85.3MB, time=7.22 memory used=732.4MB, alloc=85.3MB, time=7.35 memory used=760.9MB, alloc=85.3MB, time=7.47 memory used=789.6MB, alloc=85.3MB, time=7.60 memory used=819.2MB, alloc=85.3MB, time=7.73 memory used=850.6MB, alloc=85.3MB, time=7.85 memory used=882.9MB, alloc=85.3MB, time=7.98 memory used=916.3MB, alloc=85.3MB, time=8.10 memory used=951.3MB, alloc=85.3MB, time=8.24 memory used=989.0MB, alloc=85.3MB, time=8.38 memory used=1027.8MB, alloc=85.3MB, time=8.51 memory used=1068.3MB, alloc=85.3MB, time=8.65 memory used=1110.9MB, alloc=85.3MB, time=8.79 memory used=1155.6MB, alloc=85.3MB, time=8.93 memory used=1203.2MB, alloc=85.3MB, time=9.07 memory used=1261.2MB, alloc=85.3MB, time=9.99 memory used=1308.6MB, alloc=86.7MB, time=10.24 memory used=1351.6MB, alloc=86.7MB, time=10.45 memory used=1398.7MB, alloc=86.7MB, time=10.65 memory used=1428.5MB, alloc=86.7MB, time=10.81 memory used=1462.1MB, alloc=86.7MB, time=10.98 memory used=1497.7MB, alloc=86.7MB, time=11.15 memory used=1538.3MB, alloc=86.7MB, time=11.34 memory used=1580.7MB, alloc=86.7MB, time=11.55 memory used=1628.2MB, alloc=86.7MB, time=11.74 memory used=1678.0MB, alloc=86.7MB, time=11.95 memory used=1719.4MB, alloc=86.7MB, time=12.11 memory used=1746.6MB, alloc=86.7MB, time=12.24 memory used=1775.1MB, alloc=86.7MB, time=12.35 memory used=1803.7MB, alloc=86.7MB, time=12.48 memory used=1832.4MB, alloc=86.7MB, time=12.60 memory used=1862.3MB, alloc=86.7MB, time=12.73 memory used=1893.5MB, alloc=86.7MB, time=12.85 memory used=1925.8MB, alloc=86.7MB, time=12.98 memory used=1961.4MB, alloc=86.7MB, time=13.11 memory used=1997.5MB, alloc=86.7MB, time=13.24 memory used=2035.0MB, alloc=86.7MB, time=13.37 memory used=2074.0MB, alloc=86.7MB, time=13.50 memory used=2116.1MB, alloc=86.7MB, time=13.64 memory used=2159.6MB, alloc=86.7MB, time=13.77 memory used=2205.7MB, alloc=86.7MB, time=13.92 memory used=2255.1MB, alloc=86.7MB, time=14.06 memory used=2323.3MB, alloc=86.7MB, time=34.38 memory used=2372.0MB, alloc=86.7MB, time=74.84 memory used=2435.1MB, alloc=86.7MB, time=78.75 memory used=2478.9MB, alloc=86.7MB, time=78.97 memory used=2512.2MB, alloc=86.7MB, time=79.16 memory used=2550.9MB, alloc=86.7MB, time=79.36 memory used=2596.8MB, alloc=86.7MB, time=79.56 memory used=2645.4MB, alloc=86.7MB, time=79.75 memory used=2673.1MB, alloc=86.7MB, time=79.87 memory used=2701.1MB, alloc=86.7MB, time=80.01 memory used=2731.6MB, alloc=86.7MB, time=80.14 memory used=2763.2MB, alloc=86.7MB, time=80.28 memory used=2796.0MB, alloc=86.7MB, time=80.43 memory used=2830.0MB, alloc=86.7MB, time=80.57 memory used=2867.7MB, alloc=86.7MB, time=80.71 memory used=2906.6MB, alloc=86.7MB, time=80.86 memory used=2946.6MB, alloc=86.7MB, time=81.01 memory used=2987.7MB, alloc=86.7MB, time=81.17 memory used=3032.9MB, alloc=86.7MB, time=81.33 memory used=3079.0MB, alloc=86.7MB, time=81.50 memory used=3126.4MB, alloc=86.7MB, time=81.66 memory used=3174.8MB, alloc=86.7MB, time=81.82 memory used=3227.6MB, alloc=107.8MB, time=82.03 memory used=3236.9MB, alloc=107.8MB, time=82.12 memory used=3246.0MB, alloc=107.8MB, time=82.20 memory used=3255.5MB, alloc=107.8MB, time=82.29 memory used=3265.4MB, alloc=107.8MB, time=82.38 memory used=3275.4MB, alloc=107.8MB, time=82.46 memory used=3285.3MB, alloc=107.8MB, time=82.56 memory used=3295.3MB, alloc=107.8MB, time=82.67 memory used=3305.3MB, alloc=107.8MB, time=82.77 memory used=3315.4MB, alloc=107.8MB, time=82.89 memory used=3325.5MB, alloc=107.8MB, time=82.97 memory used=3335.6MB, alloc=107.8MB, time=83.07 memory used=3345.7MB, alloc=107.8MB, time=83.18 memory used=3355.8MB, alloc=107.8MB, time=83.28 memory used=3366.0MB, alloc=107.8MB, time=83.37 memory used=3376.2MB, alloc=107.8MB, time=83.45 memory used=3386.5MB, alloc=107.8MB, time=83.54 memory used=3396.7MB, alloc=107.8MB, time=83.67 memory used=3407.0MB, alloc=107.8MB, time=83.75 memory used=3417.3MB, alloc=107.8MB, time=83.84 memory used=3427.6MB, alloc=107.8MB, time=83.95 memory used=3438.0MB, alloc=107.8MB, time=84.05 memory used=3448.3MB, alloc=107.8MB, time=84.14 memory used=3458.7MB, alloc=107.8MB, time=84.23 memory used=3469.1MB, alloc=107.8MB, time=84.31 memory used=3479.6MB, alloc=107.8MB, time=84.38 memory used=3490.0MB, alloc=107.8MB, time=84.48 memory used=3500.5MB, alloc=107.8MB, time=84.57 memory used=3511.0MB, alloc=107.8MB, time=84.66 memory used=3521.5MB, alloc=107.8MB, time=84.74 memory used=3532.0MB, alloc=107.8MB, time=84.83 memory used=3542.6MB, alloc=107.8MB, time=84.92 memory used=3553.1MB, alloc=107.8MB, time=85.01 memory used=3563.7MB, alloc=107.8MB, time=85.10 memory used=3574.3MB, alloc=107.8MB, time=85.20 memory used=3584.9MB, alloc=107.8MB, time=85.29 memory used=3595.5MB, alloc=107.8MB, time=85.38 memory used=3606.2MB, alloc=107.8MB, time=85.47 memory used=3616.8MB, alloc=107.8MB, time=85.54 memory used=3627.5MB, alloc=107.8MB, time=85.64 memory used=3638.1MB, alloc=107.8MB, time=85.72 memory used=3648.8MB, alloc=107.8MB, time=85.80 memory used=3659.5MB, alloc=107.8MB, time=85.88 memory used=3670.5MB, alloc=107.8MB, time=85.97 memory used=3681.4MB, alloc=107.8MB, time=86.07 memory used=3695.3MB, alloc=107.8MB, time=86.17 memory used=3706.4MB, alloc=107.8MB, time=86.28 memory used=3720.4MB, alloc=107.8MB, time=86.38 memory used=3734.7MB, alloc=107.8MB, time=86.46 memory used=3749.1MB, alloc=107.8MB, time=86.56 memory used=3763.5MB, alloc=107.8MB, time=86.66 memory used=3777.8MB, alloc=107.8MB, time=86.75 memory used=3792.3MB, alloc=107.8MB, time=86.84 memory used=3806.7MB, alloc=107.8MB, time=86.94 memory used=3821.1MB, alloc=107.8MB, time=87.03 memory used=3835.5MB, alloc=107.8MB, time=87.14 memory used=3849.9MB, alloc=107.8MB, time=87.22 memory used=3864.4MB, alloc=107.8MB, time=87.30 memory used=3878.8MB, alloc=107.8MB, time=87.39 memory used=3893.2MB, alloc=107.8MB, time=87.48 memory used=3907.7MB, alloc=107.8MB, time=87.57 memory used=3922.1MB, alloc=107.8MB, time=87.66 memory used=3936.6MB, alloc=107.8MB, time=87.76 memory used=3951.0MB, alloc=107.8MB, time=87.85 memory used=3965.4MB, alloc=107.8MB, time=87.94 memory used=3979.8MB, alloc=107.8MB, time=88.03 memory used=3994.2MB, alloc=107.8MB, time=88.13 memory used=4008.7MB, alloc=107.8MB, time=88.23 memory used=4023.1MB, alloc=107.8MB, time=88.32 memory used=4037.5MB, alloc=107.8MB, time=88.42 memory used=4051.9MB, alloc=107.8MB, time=88.51 memory used=4066.2MB, alloc=107.8MB, time=88.60 memory used=4080.9MB, alloc=107.8MB, time=88.69 memory used=4098.5MB, alloc=107.8MB, time=88.78 memory used=4113.4MB, alloc=107.8MB, time=88.87 memory used=4130.7MB, alloc=107.8MB, time=88.98 memory used=4148.6MB, alloc=107.8MB, time=89.07 memory used=4166.4MB, alloc=107.8MB, time=89.17 memory used=4184.2MB, alloc=107.8MB, time=89.27 memory used=4201.9MB, alloc=107.8MB, time=89.36 memory used=4219.6MB, alloc=107.8MB, time=89.46 memory used=4237.3MB, alloc=107.8MB, time=89.56 memory used=4254.9MB, alloc=107.8MB, time=89.65 memory used=4272.5MB, alloc=107.8MB, time=89.75 memory used=4290.0MB, alloc=107.8MB, time=89.84 memory used=4307.5MB, alloc=107.8MB, time=89.93 memory used=4324.9MB, alloc=107.8MB, time=90.03 memory used=4342.3MB, alloc=107.8MB, time=90.12 memory used=4359.6MB, alloc=107.8MB, time=90.22 memory used=4377.2MB, alloc=107.8MB, time=90.31 memory used=4397.4MB, alloc=107.8MB, time=90.40 memory used=4418.0MB, alloc=107.8MB, time=90.50 memory used=4438.4MB, alloc=107.8MB, time=90.60 memory used=4458.7MB, alloc=107.8MB, time=90.70 memory used=4478.9MB, alloc=107.8MB, time=90.80 memory used=4499.0MB, alloc=107.8MB, time=90.91 memory used=4519.0MB, alloc=107.8MB, time=91.01 memory used=4538.9MB, alloc=107.8MB, time=91.11 memory used=4558.7MB, alloc=107.8MB, time=91.21 memory used=4578.3MB, alloc=107.8MB, time=91.31 memory used=4598.3MB, alloc=107.8MB, time=91.41 memory used=4620.4MB, alloc=107.8MB, time=91.52 memory used=4642.8MB, alloc=107.8MB, time=91.62 memory used=4663.5MB, alloc=107.8MB, time=91.72 memory used=4679.2MB, alloc=107.8MB, time=91.81 memory used=4694.4MB, alloc=107.8MB, time=91.90 memory used=4709.2MB, alloc=107.8MB, time=91.98 memory used=4721.9MB, alloc=107.8MB, time=92.07 memory used=4736.7MB, alloc=107.8MB, time=92.16 memory used=4751.8MB, alloc=107.8MB, time=92.25 memory used=4766.9MB, alloc=107.8MB, time=92.34 memory used=4781.8MB, alloc=107.8MB, time=92.42 memory used=4796.5MB, alloc=107.8MB, time=92.52 memory used=4811.2MB, alloc=107.8MB, time=92.60 memory used=4825.7MB, alloc=107.8MB, time=92.70 memory used=4840.1MB, alloc=107.8MB, time=92.79 memory used=4854.4MB, alloc=107.8MB, time=92.88 memory used=4869.0MB, alloc=107.8MB, time=92.96 memory used=4885.4MB, alloc=107.8MB, time=93.06 memory used=4901.9MB, alloc=107.8MB, time=93.16 memory used=4918.3MB, alloc=107.8MB, time=93.26 memory used=4934.5MB, alloc=107.8MB, time=93.35 memory used=4950.5MB, alloc=107.8MB, time=93.44 memory used=4966.2MB, alloc=107.8MB, time=93.53 memory used=4982.2MB, alloc=107.8MB, time=93.61 memory used=4999.6MB, alloc=107.8MB, time=93.70 memory used=5017.1MB, alloc=107.8MB, time=93.79 memory used=5034.4MB, alloc=107.8MB, time=93.88 memory used=5051.3MB, alloc=107.8MB, time=93.98 memory used=5068.4MB, alloc=107.8MB, time=94.07 memory used=5084.7MB, alloc=107.8MB, time=94.16 memory used=5102.2MB, alloc=107.8MB, time=94.25 memory used=5120.0MB, alloc=107.8MB, time=94.34 memory used=5139.3MB, alloc=107.8MB, time=94.44 memory used=5158.1MB, alloc=107.8MB, time=94.52 memory used=5175.7MB, alloc=107.8MB, time=94.62 memory used=5195.7MB, alloc=107.8MB, time=94.70 memory used=5216.1MB, alloc=107.8MB, time=94.80 memory used=5236.3MB, alloc=107.8MB, time=94.89 memory used=5257.4MB, alloc=107.8MB, time=94.99 memory used=5278.5MB, alloc=107.8MB, time=95.08 memory used=5300.7MB, alloc=107.8MB, time=95.18 memory used=5368.1MB, alloc=107.8MB, time=96.35 memory used=5407.3MB, alloc=107.8MB, time=96.56 memory used=5458.5MB, alloc=107.8MB, time=96.78 memory used=5489.1MB, alloc=107.8MB, time=96.97 memory used=5520.2MB, alloc=107.8MB, time=97.12 memory used=5555.2MB, alloc=107.8MB, time=97.30 memory used=5592.2MB, alloc=107.8MB, time=97.49 memory used=5634.0MB, alloc=107.8MB, time=97.69 memory used=5678.1MB, alloc=107.8MB, time=97.86 memory used=5726.1MB, alloc=107.8MB, time=98.07 memory used=5776.6MB, alloc=107.8MB, time=98.27 memory used=5803.8MB, alloc=107.8MB, time=98.39 memory used=5831.3MB, alloc=107.8MB, time=98.51 memory used=5859.9MB, alloc=107.8MB, time=98.64 memory used=5888.5MB, alloc=107.8MB, time=98.77 memory used=5918.0MB, alloc=107.8MB, time=98.89 memory used=5949.6MB, alloc=107.8MB, time=99.02 memory used=5981.9MB, alloc=107.8MB, time=99.15 memory used=6015.0MB, alloc=107.8MB, time=99.27 memory used=6049.5MB, alloc=107.8MB, time=99.40 memory used=6085.5MB, alloc=107.8MB, time=99.53 memory used=6123.4MB, alloc=107.8MB, time=99.67 memory used=6163.0MB, alloc=107.8MB, time=99.80 memory used=6205.6MB, alloc=107.8MB, time=99.94 memory used=6249.9MB, alloc=107.8MB, time=100.09 memory used=6296.6MB, alloc=107.8MB, time=100.23 memory used=6353.9MB, alloc=107.8MB, time=100.61 memory used=6452.1MB, alloc=107.8MB, time=102.07 memory used=6491.9MB, alloc=107.8MB, time=102.26 memory used=6540.2MB, alloc=107.8MB, time=102.80 memory used=6603.9MB, alloc=107.8MB, time=104.33 memory used=6668.1MB, alloc=107.8MB, time=105.88 memory used=6735.3MB, alloc=107.8MB, time=107.97 memory used=6770.6MB, alloc=107.8MB, time=108.18 memory used=6816.0MB, alloc=107.8MB, time=108.69 memory used=6875.3MB, alloc=107.8MB, time=110.01 memory used=6920.6MB, alloc=107.8MB, time=110.26 memory used=6947.1MB, alloc=131.8MB, time=110.46 memory used=6990.6MB, alloc=131.8MB, time=110.71 memory used=7044.6MB, alloc=131.8MB, time=110.96 memory used=7094.0MB, alloc=131.8MB, time=111.19 memory used=7126.9MB, alloc=131.8MB, time=111.38 memory used=7162.7MB, alloc=131.8MB, time=111.58 memory used=7201.9MB, alloc=131.8MB, time=111.76 memory used=7245.3MB, alloc=131.8MB, time=111.96 memory used=7290.6MB, alloc=131.8MB, time=112.16 memory used=7340.5MB, alloc=131.8MB, time=112.37 memory used=7394.4MB, alloc=131.8MB, time=112.57 memory used=7452.0MB, alloc=131.8MB, time=112.78 memory used=7500.8MB, alloc=131.8MB, time=112.97 memory used=7532.2MB, alloc=131.8MB, time=113.11 memory used=7564.6MB, alloc=131.8MB, time=113.26 memory used=7599.2MB, alloc=131.8MB, time=113.40 memory used=7635.7MB, alloc=131.8MB, time=113.54 memory used=7674.1MB, alloc=131.8MB, time=113.68 memory used=7734.9MB, alloc=131.8MB, time=114.77 memory used=7791.2MB, alloc=131.8MB, time=115.08 memory used=7833.2MB, alloc=131.8MB, time=115.31 memory used=7884.2MB, alloc=131.8MB, time=115.55 memory used=7938.1MB, alloc=131.8MB, time=115.79 memory used=7970.5MB, alloc=131.8MB, time=115.99 memory used=8006.0MB, alloc=131.8MB, time=116.20 memory used=8043.4MB, alloc=131.8MB, time=116.41 memory used=8083.9MB, alloc=131.8MB, time=116.62 memory used=8127.5MB, alloc=131.8MB, time=116.84 memory used=8175.2MB, alloc=131.8MB, time=117.04 memory used=8226.2MB, alloc=131.8MB, time=117.26 memory used=8280.9MB, alloc=131.8MB, time=117.48 memory used=8337.4MB, alloc=131.8MB, time=117.71 memory used=8369.3MB, alloc=131.8MB, time=117.86 memory used=8401.1MB, alloc=131.8MB, time=118.00 memory used=8434.5MB, alloc=131.8MB, time=118.15 memory used=8468.8MB, alloc=131.8MB, time=118.29 memory used=8505.5MB, alloc=131.8MB, time=118.45 memory used=8560.6MB, alloc=131.8MB, time=125.23 memory used=8651.7MB, alloc=131.8MB, time=153.24 memory used=8758.4MB, alloc=131.8MB, time=155.15 memory used=8812.9MB, alloc=131.8MB, time=155.51 memory used=8865.5MB, alloc=131.8MB, time=155.74 memory used=8901.4MB, alloc=131.8MB, time=155.95 memory used=8941.4MB, alloc=131.8MB, time=156.16 memory used=8987.5MB, alloc=131.8MB, time=156.36 memory used=9039.6MB, alloc=131.8MB, time=156.58 memory used=9097.9MB, alloc=131.8MB, time=156.81 memory used=9139.0MB, alloc=131.8MB, time=156.99 memory used=9169.9MB, alloc=131.8MB, time=157.15 memory used=9202.2MB, alloc=131.8MB, time=157.31 memory used=9235.3MB, alloc=131.8MB, time=157.47 memory used=9271.6MB, alloc=131.8MB, time=157.63 memory used=9308.6MB, alloc=131.8MB, time=157.79 memory used=9346.5MB, alloc=131.8MB, time=157.95 memory used=9387.6MB, alloc=131.8MB, time=158.11 memory used=9429.4MB, alloc=131.8MB, time=158.28 memory used=9472.1MB, alloc=131.8MB, time=158.45 memory used=9517.9MB, alloc=131.8MB, time=158.63 memory used=9564.4MB, alloc=131.8MB, time=158.80 memory used=9613.9MB, alloc=131.8MB, time=158.98 memory used=9664.3MB, alloc=131.8MB, time=159.16 memory used=9717.8MB, alloc=131.8MB, time=159.34 memory used=9771.8MB, alloc=131.8MB, time=159.52 memory used=9828.9MB, alloc=131.8MB, time=159.71 memory used=9886.6MB, alloc=131.8MB, time=159.89 memory used=9906.6MB, alloc=131.8MB, time=160.02 memory used=9915.0MB, alloc=131.8MB, time=160.12 memory used=9922.3MB, alloc=131.8MB, time=160.22 memory used=9930.2MB, alloc=131.8MB, time=160.33 memory used=9938.2MB, alloc=131.8MB, time=160.43 memory used=9946.2MB, alloc=131.8MB, time=160.53 memory used=9954.2MB, alloc=131.8MB, time=160.64 memory used=9962.2MB, alloc=131.8MB, time=160.74 memory used=9970.1MB, alloc=131.8MB, time=160.84 memory used=9978.1MB, alloc=131.8MB, time=160.97 memory used=9986.1MB, alloc=131.8MB, time=161.07 memory used=9994.1MB, alloc=131.8MB, time=161.17 memory used=10002.0MB, alloc=131.8MB, time=161.28 memory used=10010.0MB, alloc=131.8MB, time=161.38 memory used=10018.0MB, alloc=131.8MB, time=161.48 memory used=10025.9MB, alloc=131.8MB, time=161.59 memory used=10033.9MB, alloc=131.8MB, time=161.69 memory used=10041.8MB, alloc=131.8MB, time=161.79 memory used=10049.8MB, alloc=131.8MB, time=161.90 memory used=10057.7MB, alloc=131.8MB, time=162.03 memory used=10065.7MB, alloc=131.8MB, time=162.13 memory used=10073.6MB, alloc=131.8MB, time=162.23 memory used=10081.6MB, alloc=131.8MB, time=162.33 memory used=10089.5MB, alloc=131.8MB, time=162.46 memory used=10097.4MB, alloc=131.8MB, time=162.56 memory used=10105.3MB, alloc=131.8MB, time=162.66 memory used=10113.2MB, alloc=131.8MB, time=162.77 memory used=10121.1MB, alloc=131.8MB, time=162.87 memory used=10129.0MB, alloc=131.8MB, time=162.98 memory used=10137.1MB, alloc=131.8MB, time=163.09 memory used=10145.1MB, alloc=131.8MB, time=163.22 memory used=10155.2MB, alloc=131.8MB, time=163.33 memory used=10163.4MB, alloc=131.8MB, time=163.43 memory used=10173.5MB, alloc=131.8MB, time=163.55 memory used=10183.9MB, alloc=131.8MB, time=163.68 memory used=10194.3MB, alloc=131.8MB, time=163.78 memory used=10204.7MB, alloc=131.8MB, time=163.89 memory used=10215.0MB, alloc=131.8MB, time=164.00 memory used=10225.4MB, alloc=131.8MB, time=164.11 memory used=10235.7MB, alloc=131.8MB, time=164.23 memory used=10246.0MB, alloc=131.8MB, time=164.39 memory used=10256.3MB, alloc=131.8MB, time=164.50 memory used=10266.5MB, alloc=131.8MB, time=164.65 memory used=10276.7MB, alloc=131.8MB, time=164.76 memory used=10286.9MB, alloc=131.8MB, time=164.87 memory used=10297.1MB, alloc=131.8MB, time=165.00 memory used=10307.2MB, alloc=131.8MB, time=165.10 memory used=10317.3MB, alloc=131.8MB, time=165.21 memory used=10327.4MB, alloc=131.8MB, time=165.31 memory used=10337.5MB, alloc=131.8MB, time=165.42 memory used=10347.5MB, alloc=131.8MB, time=165.54 memory used=10357.5MB, alloc=131.8MB, time=165.65 memory used=10367.4MB, alloc=131.8MB, time=165.76 memory used=10377.4MB, alloc=131.8MB, time=165.87 memory used=10387.6MB, alloc=131.8MB, time=165.99 memory used=10399.6MB, alloc=131.8MB, time=166.11 memory used=10409.9MB, alloc=131.8MB, time=166.22 memory used=10421.6MB, alloc=131.8MB, time=166.33 memory used=10433.7MB, alloc=131.8MB, time=166.44 memory used=10445.8MB, alloc=131.8MB, time=166.55 memory used=10457.9MB, alloc=131.8MB, time=166.66 memory used=10469.8MB, alloc=131.8MB, time=166.77 memory used=10481.7MB, alloc=131.8MB, time=166.89 memory used=10493.6MB, alloc=131.8MB, time=166.99 memory used=10505.3MB, alloc=131.8MB, time=167.10 memory used=10517.0MB, alloc=131.8MB, time=167.22 memory used=10528.7MB, alloc=131.8MB, time=167.33 memory used=10540.2MB, alloc=131.8MB, time=167.44 memory used=10552.0MB, alloc=131.8MB, time=167.54 memory used=10565.4MB, alloc=131.8MB, time=167.67 memory used=10577.2MB, alloc=131.8MB, time=167.77 memory used=10590.2MB, alloc=131.8MB, time=167.88 memory used=10603.6MB, alloc=131.8MB, time=167.99 memory used=10616.8MB, alloc=131.8MB, time=168.10 memory used=10629.9MB, alloc=131.8MB, time=168.23 memory used=10642.9MB, alloc=131.8MB, time=168.34 memory used=10655.8MB, alloc=131.8MB, time=168.44 memory used=10668.9MB, alloc=131.8MB, time=168.57 memory used=10683.3MB, alloc=131.8MB, time=168.68 memory used=10697.9MB, alloc=131.8MB, time=168.80 memory used=10712.2MB, alloc=131.8MB, time=168.92 memory used=10726.4MB, alloc=131.8MB, time=169.03 memory used=10740.3MB, alloc=131.8MB, time=169.14 memory used=10754.5MB, alloc=131.8MB, time=169.26 memory used=10769.6MB, alloc=131.8MB, time=169.38 memory used=10784.8MB, alloc=131.8MB, time=169.50 memory used=10799.7MB, alloc=131.8MB, time=169.62 memory used=10814.8MB, alloc=131.8MB, time=169.75 memory used=10830.5MB, alloc=131.8MB, time=169.87 memory used=10846.2MB, alloc=131.8MB, time=169.99 memory used=10862.1MB, alloc=131.8MB, time=170.11 memory used=10878.2MB, alloc=131.8MB, time=170.25 memory used=10894.7MB, alloc=131.8MB, time=170.36 memory used=10911.5MB, alloc=131.8MB, time=170.47 memory used=10928.5MB, alloc=131.8MB, time=170.60 memory used=10945.9MB, alloc=131.8MB, time=170.74 memory used=10963.7MB, alloc=131.8MB, time=170.88 memory used=10981.8MB, alloc=131.8MB, time=170.99 memory used=11000.5MB, alloc=131.8MB, time=171.10 memory used=11019.9MB, alloc=131.8MB, time=171.24 memory used=11097.3MB, alloc=131.8MB, time=172.24 memory used=11144.9MB, alloc=131.8MB, time=172.44 memory used=11225.1MB, alloc=131.8MB, time=173.89 memory used=11316.1MB, alloc=387.8MB, time=177.07 |\^/| 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(); 1428265131 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 F := [5 x z + 6 z - 7 y - 14, -16 x y - 12 x y z + 11 x y z + 11 y , 3 2 2 -4 x z - 7 x y z + 17 y - 12 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 3 3 2 2 G := [7 y + 15 y z + 18 x - 13 z , 14 x z - 20 x y - 20 x y + 20 y z, 3 2 2 2 19 x y + 5 x y z - 15 x y + 19 x ] > Problem := [F,G]; 3 2 3 2 2 Problem := [[5 x z + 6 z - 7 y - 14, -16 x y - 12 x y z + 11 x y z + 11 y , 3 2 2 4 3 3 3 -4 x z - 7 x y z + 17 y - 12 y z], [7 y + 15 y z + 18 x - 13 z , 3 2 2 3 2 2 2 14 x z - 20 x y - 20 x y + 20 y z, 19 x y + 5 x y z - 15 x y + 19 x ] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=24.1MB, alloc=32.3MB, time=0.78 memory used=44.5MB, alloc=60.3MB, time=1.27 memory used=87.1MB, alloc=60.3MB, time=2.06 memory used=137.0MB, alloc=68.3MB, time=2.94 memory used=183.7MB, alloc=68.3MB, time=4.02 memory used=215.0MB, alloc=68.3MB, time=4.49 memory used=238.4MB, alloc=68.3MB, time=4.61 memory used=273.8MB, alloc=68.3MB, time=5.11 memory used=314.0MB, alloc=68.3MB, time=5.96 memory used=360.0MB, alloc=68.3MB, time=6.94 memory used=406.8MB, alloc=92.3MB, time=7.89 memory used=478.8MB, alloc=92.3MB, time=9.36 memory used=545.0MB, alloc=372.3MB, time=10.95 memory used=607.0MB, alloc=372.3MB, time=11.62 memory used=670.8MB, alloc=372.3MB, time=12.28 memory used=732.0MB, alloc=372.3MB, time=12.92 memory used=794.3MB, alloc=372.3MB, time=14.59 memory used=871.9MB, alloc=372.3MB, time=15.75 memory used=981.5MB, alloc=372.3MB, time=17.77 memory used=1058.8MB, alloc=372.3MB, time=19.25 memory used=1158.1MB, alloc=372.3MB, time=21.27 memory used=1249.1MB, alloc=396.3MB, time=23.36 memory used=1350.9MB, alloc=396.3MB, time=25.11 memory used=1412.2MB, alloc=396.3MB, time=25.61 memory used=1477.1MB, alloc=396.3MB, time=26.28 memory used=1531.9MB, alloc=396.3MB, time=26.72 memory used=1599.2MB, alloc=396.3MB, time=29.20 memory used=1650.4MB, alloc=396.3MB, time=29.49 memory used=1750.3MB, alloc=396.3MB, time=31.28 memory used=1822.7MB, alloc=396.3MB, time=32.74 memory used=1930.2MB, alloc=396.3MB, time=34.49 memory used=2036.4MB, alloc=420.3MB, time=37.20 memory used=2138.4MB, alloc=444.3MB, time=39.71 memory used=2272.8MB, alloc=444.3MB, time=42.15 memory used=2371.5MB, alloc=444.3MB, time=43.46 memory used=2448.5MB, alloc=444.3MB, time=44.04 memory used=2533.6MB, alloc=444.3MB, time=45.27 memory used=2614.8MB, alloc=444.3MB, time=46.18 memory used=2741.9MB, alloc=444.3MB, time=49.55 memory used=2807.2MB, alloc=444.3MB, time=49.97 memory used=2966.3MB, alloc=444.3MB, time=52.94 memory used=3113.1MB, alloc=468.3MB, time=55.91 memory used=3238.7MB, alloc=468.3MB, time=59.35 memory used=3340.3MB, alloc=468.3MB, time=61.56 memory used=3439.5MB, alloc=468.3MB, time=63.76 memory used=3553.2MB, alloc=468.3MB, time=65.15 memory used=3650.8MB, alloc=468.3MB, time=66.34 memory used=3756.4MB, alloc=468.3MB, time=67.64 memory used=3840.6MB, alloc=468.3MB, time=69.43 memory used=3938.3MB, alloc=468.3MB, time=71.57 memory used=4031.4MB, alloc=468.3MB, time=74.34 memory used=4157.0MB, alloc=468.3MB, time=79.49 memory used=4228.2MB, alloc=468.3MB, time=80.02 memory used=4307.5MB, alloc=492.3MB, time=80.58 memory used=4381.1MB, alloc=492.3MB, time=81.05 memory used=4473.9MB, alloc=492.3MB, time=81.55 memory used=4684.7MB, alloc=492.3MB, time=83.00 memory used=4801.3MB, alloc=492.3MB, time=84.80 memory used=4885.1MB, alloc=492.3MB, time=86.46 memory used=4981.4MB, alloc=492.3MB, time=88.40 memory used=5106.7MB, alloc=492.3MB, time=90.21 memory used=5190.6MB, alloc=492.3MB, time=90.88 memory used=5283.0MB, alloc=492.3MB, time=91.54 memory used=5360.4MB, alloc=492.3MB, time=92.14 memory used=5450.1MB, alloc=492.3MB, time=93.06 memory used=5534.3MB, alloc=492.3MB, time=93.73 memory used=5622.3MB, alloc=492.3MB, time=94.38 memory used=5705.6MB, alloc=492.3MB, time=94.96 memory used=5792.7MB, alloc=492.3MB, time=100.42 memory used=5893.4MB, alloc=492.3MB, time=101.84 memory used=5978.3MB, alloc=492.3MB, time=102.45 memory used=6055.7MB, alloc=492.3MB, time=103.03 memory used=6151.9MB, alloc=492.3MB, time=103.64 memory used=6357.0MB, alloc=492.3MB, time=104.61 memory used=6502.9MB, alloc=492.3MB, time=106.36 memory used=6593.1MB, alloc=492.3MB, time=107.00 memory used=6666.6MB, alloc=492.3MB, time=107.55 memory used=6761.1MB, alloc=492.3MB, time=108.45 memory used=6844.4MB, alloc=492.3MB, time=109.07 memory used=6931.2MB, alloc=492.3MB, time=109.66 memory used=7022.4MB, alloc=492.3MB, time=111.91 memory used=7116.5MB, alloc=492.3MB, time=112.56 memory used=7189.5MB, alloc=492.3MB, time=113.12 memory used=7316.2MB, alloc=492.3MB, time=113.96 memory used=7402.6MB, alloc=492.3MB, time=114.62 memory used=7505.9MB, alloc=492.3MB, time=115.42 memory used=7612.4MB, alloc=492.3MB, time=117.10 memory used=7699.4MB, alloc=492.3MB, time=117.75 memory used=7788.4MB, alloc=492.3MB, time=118.38 memory used=7857.0MB, alloc=492.3MB, time=119.94 memory used=7935.7MB, alloc=492.3MB, time=121.61 memory used=7996.4MB, alloc=492.3MB, time=123.28 memory used=8109.0MB, alloc=492.3MB, time=126.61 memory used=8195.0MB, alloc=492.3MB, time=127.22 memory used=8316.8MB, alloc=492.3MB, time=128.84 memory used=8397.3MB, alloc=492.3MB, time=132.15 memory used=8469.7MB, alloc=492.3MB, time=134.01 memory used=8557.8MB, alloc=492.3MB, time=136.02 memory used=8661.5MB, alloc=492.3MB, time=139.85 memory used=8770.8MB, alloc=492.3MB, time=146.25 memory used=8849.4MB, alloc=492.3MB, time=150.95 memory used=8896.6MB, alloc=492.3MB, time=152.38 memory used=8961.1MB, alloc=492.3MB, time=153.72 memory used=9003.2MB, alloc=492.3MB, time=155.01 memory used=9050.4MB, alloc=492.3MB, time=156.43 memory used=9081.9MB, alloc=492.3MB, time=157.50 memory used=9155.7MB, alloc=492.3MB, time=159.16 memory used=9198.9MB, alloc=516.3MB, time=160.49 memory used=9392.0MB, alloc=516.3MB, time=163.87 memory used=9512.8MB, alloc=516.3MB, time=165.44 memory used=9668.8MB, alloc=516.3MB, time=167.86 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428265430 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 3 F := [8 x y + 20 y z - 6 x y - 19 x z, -x z - 15 y z - 18 y + 10 y, 2 2 8 x y - 15 x y z - 9 x - 20 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 3 2 3 3 G := [-9 z - 2 x + 13 y + 5 z , -15 x y + 10 x z + 7 y + 3 z , 3 4 2 2 5 x y - 14 y + 12 y z + 9 y z ] > Problem := [F,G]; 3 2 Problem := [[8 x y + 20 y z - 6 x y - 19 x z, 2 2 2 2 3 2 2 -x z - 15 y z - 18 y + 10 y, 8 x y - 15 x y z - 9 x - 20 x z], [ 4 3 3 2 3 2 3 3 -9 z - 2 x + 13 y + 5 z , -15 x y + 10 x z + 7 y + 3 z , 3 4 2 2 5 x y - 14 y + 12 y z + 9 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=24.5MB, alloc=32.3MB, time=0.83 memory used=42.2MB, alloc=56.3MB, time=1.31 memory used=95.6MB, alloc=60.3MB, time=2.22 memory used=140.1MB, alloc=60.3MB, time=3.54 memory used=180.5MB, alloc=60.3MB, time=4.49 memory used=222.4MB, alloc=60.3MB, time=5.38 memory used=263.7MB, alloc=60.3MB, time=6.29 memory used=299.9MB, alloc=60.3MB, time=6.87 memory used=329.6MB, alloc=60.3MB, time=8.12 memory used=354.1MB, alloc=60.3MB, time=8.44 memory used=382.6MB, alloc=60.3MB, time=8.90 memory used=418.6MB, alloc=60.3MB, time=9.61 memory used=447.6MB, alloc=60.3MB, time=10.29 memory used=472.1MB, alloc=60.3MB, time=10.58 memory used=500.4MB, alloc=68.0MB, time=10.80 memory used=523.5MB, alloc=68.0MB, time=10.91 memory used=545.5MB, alloc=68.0MB, time=11.01 memory used=584.6MB, alloc=68.0MB, time=11.59 memory used=631.7MB, alloc=68.0MB, time=12.59 memory used=670.8MB, alloc=92.0MB, time=13.57 memory used=721.1MB, alloc=92.0MB, time=14.47 memory used=788.7MB, alloc=100.0MB, time=16.00 memory used=854.8MB, alloc=100.0MB, time=17.45 memory used=897.9MB, alloc=100.0MB, time=18.37 memory used=956.3MB, alloc=100.0MB, time=19.57 memory used=1005.4MB, alloc=100.0MB, time=20.64 memory used=1061.2MB, alloc=100.0MB, time=21.58 memory used=1113.9MB, alloc=100.0MB, time=24.36 memory used=1159.0MB, alloc=100.0MB, time=25.93 memory used=1196.0MB, alloc=100.0MB, time=27.28 memory used=1227.3MB, alloc=100.0MB, time=27.54 memory used=1315.6MB, alloc=124.0MB, time=29.63 memory used=1364.9MB, alloc=124.0MB, time=30.92 memory used=1404.8MB, alloc=124.0MB, time=31.17 memory used=1451.5MB, alloc=124.0MB, time=31.41 memory used=1506.7MB, alloc=124.0MB, time=31.67 memory used=1548.0MB, alloc=124.0MB, time=31.88 memory used=1597.5MB, alloc=124.0MB, time=44.08 memory used=1624.5MB, alloc=131.8MB, time=47.96 memory used=1626.1MB, alloc=131.8MB, time=48.07 memory used=1633.7MB, alloc=131.8MB, time=48.20 memory used=1635.7MB, alloc=387.8MB, time=48.31 memory used=1707.4MB, alloc=411.8MB, time=53.55 memory used=1767.0MB, alloc=411.8MB, time=53.76 memory used=1829.3MB, alloc=411.8MB, time=53.96 memory used=1892.5MB, alloc=411.8MB, time=54.17 memory used=1957.5MB, alloc=411.8MB, time=54.37 memory used=2025.9MB, alloc=411.8MB, time=54.58 memory used=2095.9MB, alloc=411.8MB, time=54.80 memory used=2168.8MB, alloc=411.8MB, time=55.01 memory used=2284.9MB, alloc=411.8MB, time=55.60 memory used=2380.8MB, alloc=411.8MB, time=57.46 memory used=2487.9MB, alloc=411.8MB, time=60.28 memory used=2554.3MB, alloc=411.8MB, time=60.83 memory used=2650.5MB, alloc=411.8MB, time=64.81 memory used=2740.1MB, alloc=411.8MB, time=68.03 memory used=2844.4MB, alloc=411.8MB, time=70.49 memory used=2904.6MB, alloc=411.8MB, time=73.39 memory used=3005.2MB, alloc=435.8MB, time=74.86 memory used=3144.3MB, alloc=459.8MB, time=77.11 memory used=3287.1MB, alloc=459.8MB, time=80.59 memory used=3413.3MB, alloc=483.8MB, time=83.68 memory used=3527.5MB, alloc=483.8MB, time=86.11 memory used=3635.6MB, alloc=483.8MB, time=88.28 memory used=3718.6MB, alloc=483.8MB, time=88.94 memory used=3836.2MB, alloc=483.8MB, time=89.63 memory used=4036.5MB, alloc=483.8MB, time=100.76 memory used=4122.8MB, alloc=483.8MB, time=101.24 memory used=4247.3MB, alloc=483.8MB, time=101.90 memory used=4459.4MB, alloc=483.8MB, time=102.70 memory used=4743.3MB, alloc=483.8MB, time=104.16 memory used=4999.2MB, alloc=483.8MB, time=104.87 memory used=5211.1MB, alloc=483.8MB, time=105.47 memory used=5433.9MB, alloc=483.8MB, time=106.05 memory used=5581.4MB, alloc=483.8MB, time=109.21 memory used=5756.7MB, alloc=483.8MB, time=119.14 memory used=5855.7MB, alloc=483.8MB, time=119.77 memory used=5961.3MB, alloc=483.8MB, time=120.44 memory used=6202.9MB, alloc=483.8MB, time=121.24 memory used=6449.0MB, alloc=483.8MB, time=122.55 memory used=6747.6MB, alloc=483.8MB, time=123.37 memory used=6941.5MB, alloc=483.8MB, time=123.96 memory used=7180.2MB, alloc=483.8MB, time=124.59 memory used=7449.0MB, alloc=483.8MB, time=126.31 memory used=7623.9MB, alloc=483.8MB, time=137.35 memory used=7709.5MB, alloc=483.8MB, time=138.12 memory used=7853.5MB, alloc=483.8MB, time=138.85 memory used=7953.4MB, alloc=483.8MB, time=140.22 memory used=8034.0MB, alloc=483.8MB, time=140.69 memory used=8100.2MB, alloc=483.8MB, time=141.13 memory used=8186.2MB, alloc=483.8MB, time=141.57 memory used=8270.2MB, alloc=483.8MB, time=142.41 memory used=8355.2MB, alloc=483.8MB, time=143.74 memory used=8435.1MB, alloc=483.8MB, time=144.20 memory used=8502.7MB, alloc=483.8MB, time=144.64 memory used=8587.3MB, alloc=483.8MB, time=145.07 |\^/| 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(); 1428265731 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 3 4 F := [12 x y - 15 x y + 18 y z + 10 x , -8 x y z + 17 x z + 9 y + 9 y z, 4 3 3 3 -7 x + 6 x z + 13 y z + 14 y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 3 4 G := [-5 x y - 15 x y z + 9 y z + 9 y , 13 x y z - 12 x z - 5 z - 15, 2 2 4 2 x y - 14 y + y z] > Problem := [F,G]; 3 3 2 2 Problem := [[12 x y - 15 x y + 18 y z + 10 x , 2 3 4 4 3 3 3 -8 x y z + 17 x z + 9 y + 9 y z, -7 x + 6 x z + 13 y z + 14 y ], [ 3 2 3 3 2 3 4 -5 x y - 15 x y z + 9 y z + 9 y , 13 x y z - 12 x z - 5 z - 15, 2 2 4 2 x y - 14 y + y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=28.6MB, alloc=34.3MB, time=0.81 memory used=53.4MB, alloc=38.3MB, time=1.41 memory used=76.3MB, alloc=38.3MB, time=1.81 memory used=92.5MB, alloc=38.3MB, time=1.97 memory used=111.7MB, alloc=38.3MB, time=2.11 memory used=122.3MB, alloc=38.3MB, time=2.17 memory used=139.5MB, alloc=38.3MB, time=2.36 memory used=155.4MB, alloc=38.3MB, time=2.45 memory used=166.6MB, alloc=38.3MB, time=2.51 memory used=192.4MB, alloc=38.3MB, time=5.10 memory used=207.2MB, alloc=38.3MB, time=5.19 memory used=219.6MB, alloc=38.3MB, time=5.25 memory used=230.9MB, alloc=38.3MB, time=5.31 memory used=239.9MB, alloc=38.3MB, time=5.36 memory used=250.2MB, alloc=38.3MB, time=5.42 memory used=261.4MB, alloc=38.3MB, time=5.47 memory used=274.1MB, alloc=38.3MB, time=5.53 memory used=287.3MB, alloc=38.3MB, time=5.59 memory used=295.2MB, alloc=38.3MB, time=5.63 memory used=303.3MB, alloc=38.3MB, time=5.68 memory used=312.4MB, alloc=38.3MB, time=5.72 memory used=322.4MB, alloc=38.3MB, time=5.77 memory used=338.1MB, alloc=38.3MB, time=6.07 memory used=350.0MB, alloc=38.3MB, time=6.26 memory used=360.6MB, alloc=38.3MB, time=6.32 memory used=372.2MB, alloc=38.3MB, time=6.43 memory used=395.6MB, alloc=38.3MB, time=6.94 memory used=418.4MB, alloc=38.3MB, time=7.65 memory used=429.2MB, alloc=38.3MB, time=7.71 memory used=438.3MB, alloc=38.3MB, time=7.76 memory used=449.2MB, alloc=38.3MB, time=7.82 memory used=476.8MB, alloc=62.3MB, time=8.31 memory used=534.4MB, alloc=62.3MB, time=9.45 memory used=596.9MB, alloc=70.3MB, time=12.78 memory used=652.5MB, alloc=70.3MB, time=15.40 memory used=693.4MB, alloc=70.3MB, time=16.88 memory used=718.9MB, alloc=70.3MB, time=17.00 memory used=743.6MB, alloc=70.3MB, time=17.12 memory used=771.8MB, alloc=70.3MB, time=17.23 memory used=802.2MB, alloc=70.3MB, time=17.50 memory used=829.8MB, alloc=70.3MB, time=17.64 memory used=866.9MB, alloc=70.3MB, time=17.93 memory used=899.5MB, alloc=70.3MB, time=19.28 memory used=941.6MB, alloc=70.3MB, time=21.38 memory used=970.1MB, alloc=70.3MB, time=21.51 memory used=992.6MB, alloc=70.3MB, time=21.61 memory used=1020.4MB, alloc=70.3MB, time=21.73 memory used=1051.2MB, alloc=70.3MB, time=21.84 memory used=1070.8MB, alloc=70.3MB, time=21.93 memory used=1092.3MB, alloc=70.3MB, time=22.02 memory used=1126.1MB, alloc=70.3MB, time=22.43 memory used=1179.0MB, alloc=70.3MB, time=24.00 memory used=1214.6MB, alloc=70.3MB, time=25.38 memory used=1238.3MB, alloc=70.3MB, time=25.51 memory used=1260.6MB, alloc=70.3MB, time=25.63 memory used=1287.5MB, alloc=70.3MB, time=25.74 memory used=1307.0MB, alloc=70.3MB, time=25.83 memory used=1329.9MB, alloc=70.3MB, time=26.02 memory used=1380.2MB, alloc=70.3MB, time=30.82 memory used=1405.6MB, alloc=70.3MB, time=30.96 memory used=1426.4MB, alloc=70.3MB, time=31.07 memory used=1448.7MB, alloc=70.3MB, time=31.18 memory used=1476.0MB, alloc=70.3MB, time=31.30 memory used=1501.4MB, alloc=70.3MB, time=31.41 memory used=1518.9MB, alloc=70.3MB, time=31.50 memory used=1537.8MB, alloc=70.3MB, time=31.59 memory used=1559.0MB, alloc=70.3MB, time=31.68 memory used=1583.7MB, alloc=70.3MB, time=31.78 memory used=1620.6MB, alloc=70.3MB, time=32.40 memory used=1659.3MB, alloc=70.3MB, time=32.96 memory used=1704.4MB, alloc=70.3MB, time=33.98 memory used=1742.0MB, alloc=70.3MB, time=34.30 memory used=1775.6MB, alloc=70.3MB, time=34.65 memory used=1805.4MB, alloc=70.3MB, time=35.07 memory used=1842.6MB, alloc=70.3MB, time=35.72 memory used=1891.8MB, alloc=70.3MB, time=36.71 memory used=1935.5MB, alloc=70.3MB, time=38.42 memory used=1981.1MB, alloc=70.3MB, time=39.68 memory used=2030.3MB, alloc=94.3MB, time=40.58 memory used=2085.1MB, alloc=94.3MB, time=43.28 memory used=2161.3MB, alloc=350.3MB, time=44.40 memory used=2218.7MB, alloc=350.3MB, time=45.23 memory used=2247.7MB, alloc=350.3MB, time=45.41 memory used=2284.9MB, alloc=350.3MB, time=45.61 memory used=2308.3MB, alloc=350.3MB, time=45.77 memory used=2334.3MB, alloc=350.3MB, time=45.93 memory used=2364.3MB, alloc=350.3MB, time=46.09 memory used=2399.5MB, alloc=350.3MB, time=46.26 memory used=2429.6MB, alloc=350.3MB, time=46.57 memory used=2469.9MB, alloc=350.3MB, time=46.94 memory used=2505.2MB, alloc=350.3MB, time=47.13 memory used=2528.7MB, alloc=350.3MB, time=47.29 memory used=2557.1MB, alloc=350.3MB, time=47.45 memory used=2605.6MB, alloc=350.3MB, time=49.95 memory used=2635.6MB, alloc=350.3MB, time=50.13 memory used=2666.0MB, alloc=350.3MB, time=50.30 memory used=2692.6MB, alloc=350.3MB, time=50.44 memory used=2738.5MB, alloc=350.3MB, time=51.06 memory used=2765.5MB, alloc=350.3MB, time=51.25 memory used=2798.0MB, alloc=350.3MB, time=51.45 memory used=2833.7MB, alloc=374.3MB, time=51.67 memory used=2869.2MB, alloc=374.3MB, time=51.88 memory used=2910.6MB, alloc=374.3MB, time=52.09 memory used=2957.6MB, alloc=374.3MB, time=52.30 memory used=3011.3MB, alloc=374.3MB, time=52.53 memory used=3065.8MB, alloc=374.3MB, time=52.73 memory used=3099.2MB, alloc=374.3MB, time=52.90 memory used=3135.4MB, alloc=374.3MB, time=53.06 memory used=3174.9MB, alloc=374.3MB, time=53.22 memory used=3231.8MB, alloc=374.3MB, time=53.99 memory used=3283.6MB, alloc=374.3MB, time=54.28 memory used=3341.1MB, alloc=374.3MB, time=54.54 memory used=3378.0MB, alloc=374.3MB, time=54.76 memory used=3418.4MB, alloc=374.3MB, time=54.96 memory used=3465.3MB, alloc=374.3MB, time=55.17 memory used=3518.9MB, alloc=374.3MB, time=55.40 memory used=3575.4MB, alloc=374.3MB, time=55.61 memory used=3609.7MB, alloc=374.3MB, time=55.77 memory used=3645.4MB, alloc=374.3MB, time=55.96 memory used=3684.7MB, alloc=374.3MB, time=56.13 memory used=3739.7MB, alloc=374.3MB, time=59.65 memory used=3807.9MB, alloc=374.3MB, time=69.97 memory used=3851.7MB, alloc=374.3MB, time=70.18 memory used=3903.6MB, alloc=374.3MB, time=70.40 memory used=3948.4MB, alloc=374.3MB, time=70.59 memory used=3985.1MB, alloc=374.3MB, time=70.76 memory used=4026.6MB, alloc=374.3MB, time=70.93 memory used=4072.8MB, alloc=374.3MB, time=71.10 memory used=4127.8MB, alloc=374.3MB, time=71.29 memory used=4203.2MB, alloc=374.3MB, time=71.95 memory used=4258.5MB, alloc=374.3MB, time=72.47 memory used=4312.0MB, alloc=374.3MB, time=72.72 memory used=4379.4MB, alloc=374.3MB, time=73.69 memory used=4425.4MB, alloc=374.3MB, time=73.93 memory used=4475.7MB, alloc=374.3MB, time=74.17 memory used=4513.4MB, alloc=374.3MB, time=74.37 memory used=4558.0MB, alloc=374.3MB, time=74.59 memory used=4611.5MB, alloc=374.3MB, time=74.79 memory used=4655.0MB, alloc=374.3MB, time=74.97 memory used=4713.7MB, alloc=374.3MB, time=75.52 memory used=4766.4MB, alloc=374.3MB, time=75.77 memory used=4805.5MB, alloc=374.3MB, time=75.96 memory used=4864.9MB, alloc=374.3MB, time=76.38 memory used=4930.7MB, alloc=374.3MB, time=81.15 memory used=4989.1MB, alloc=374.3MB, time=82.28 memory used=5038.2MB, alloc=374.3MB, time=82.51 memory used=5080.4MB, alloc=374.3MB, time=82.69 memory used=5123.5MB, alloc=374.3MB, time=82.87 memory used=5182.9MB, alloc=374.3MB, time=83.64 memory used=5232.3MB, alloc=374.3MB, time=83.89 memory used=5294.6MB, alloc=374.3MB, time=84.81 memory used=5341.6MB, alloc=374.3MB, time=85.06 memory used=5393.8MB, alloc=374.3MB, time=85.30 memory used=5430.7MB, alloc=374.3MB, time=85.50 memory used=5474.3MB, alloc=374.3MB, time=85.71 memory used=5525.9MB, alloc=374.3MB, time=85.93 memory used=5574.0MB, alloc=374.3MB, time=86.12 memory used=5633.9MB, alloc=374.3MB, time=86.76 memory used=5679.5MB, alloc=374.3MB, time=87.01 memory used=5730.5MB, alloc=374.3MB, time=87.25 memory used=5767.6MB, alloc=374.3MB, time=87.45 memory used=5811.4MB, alloc=374.3MB, time=87.65 memory used=5864.2MB, alloc=374.3MB, time=87.86 memory used=5911.1MB, alloc=374.3MB, time=88.04 memory used=5981.0MB, alloc=374.3MB, time=104.26 memory used=6048.2MB, alloc=374.3MB, time=105.06 memory used=6089.1MB, alloc=374.3MB, time=105.27 memory used=6142.2MB, alloc=374.3MB, time=105.50 memory used=6186.5MB, alloc=374.3MB, time=105.69 memory used=6223.5MB, alloc=374.3MB, time=105.85 memory used=6265.3MB, alloc=374.3MB, time=106.01 memory used=6312.3MB, alloc=374.3MB, time=106.19 memory used=6364.4MB, alloc=374.3MB, time=106.37 memory used=6458.4MB, alloc=374.3MB, time=107.57 memory used=6510.0MB, alloc=374.3MB, time=107.84 memory used=6560.0MB, alloc=374.3MB, time=108.09 memory used=6611.0MB, alloc=374.3MB, time=108.34 memory used=6645.9MB, alloc=374.3MB, time=108.54 memory used=6685.3MB, alloc=374.3MB, time=108.75 memory used=6728.4MB, alloc=374.3MB, time=108.96 memory used=6775.5MB, alloc=374.3MB, time=109.18 memory used=6829.2MB, alloc=374.3MB, time=109.40 memory used=6888.0MB, alloc=374.3MB, time=109.63 memory used=6925.6MB, alloc=374.3MB, time=109.80 memory used=6958.0MB, alloc=374.3MB, time=109.96 memory used=6992.8MB, alloc=374.3MB, time=110.12 memory used=7030.6MB, alloc=374.3MB, time=110.29 memory used=7071.2MB, alloc=374.3MB, time=110.46 memory used=7132.6MB, alloc=374.3MB, time=111.24 memory used=7180.7MB, alloc=374.3MB, time=111.50 memory used=7236.3MB, alloc=374.3MB, time=111.75 memory used=7271.5MB, alloc=374.3MB, time=111.95 memory used=7312.4MB, alloc=374.3MB, time=112.16 memory used=7359.5MB, alloc=374.3MB, time=112.36 memory used=7414.8MB, alloc=374.3MB, time=112.57 memory used=7455.5MB, alloc=374.3MB, time=112.74 memory used=7525.6MB, alloc=374.3MB, time=122.85 memory used=7579.6MB, alloc=374.3MB, time=123.12 memory used=7620.6MB, alloc=374.3MB, time=123.33 memory used=7674.8MB, alloc=374.3MB, time=123.55 memory used=7714.3MB, alloc=374.3MB, time=123.72 memory used=7751.9MB, alloc=374.3MB, time=123.89 memory used=7794.1MB, alloc=374.3MB, time=124.06 memory used=7840.2MB, alloc=374.3MB, time=124.23 memory used=7894.4MB, alloc=374.3MB, time=124.41 memory used=7981.6MB, alloc=374.3MB, time=125.51 memory used=8024.3MB, alloc=374.3MB, time=125.75 memory used=8081.7MB, alloc=374.3MB, time=126.01 memory used=8121.2MB, alloc=374.3MB, time=126.23 memory used=8157.0MB, alloc=374.3MB, time=126.43 memory used=8197.1MB, alloc=374.3MB, time=126.63 memory used=8241.2MB, alloc=374.3MB, time=126.83 memory used=8290.7MB, alloc=374.3MB, time=127.04 memory used=8345.3MB, alloc=374.3MB, time=127.26 memory used=8399.6MB, alloc=374.3MB, time=127.48 memory used=8431.3MB, alloc=374.3MB, time=127.63 memory used=8464.3MB, alloc=374.3MB, time=127.80 memory used=8499.5MB, alloc=374.3MB, time=127.98 memory used=8537.3MB, alloc=374.3MB, time=128.15 memory used=8579.2MB, alloc=374.3MB, time=128.31 memory used=8641.1MB, alloc=374.3MB, time=129.66 memory used=8698.3MB, alloc=374.3MB, time=129.97 memory used=8747.2MB, alloc=374.3MB, time=130.23 memory used=8801.6MB, alloc=374.3MB, time=130.48 memory used=8836.6MB, alloc=374.3MB, time=130.68 memory used=8874.2MB, alloc=374.3MB, time=130.89 memory used=8917.1MB, alloc=374.3MB, time=131.11 memory used=8963.9MB, alloc=374.3MB, time=131.32 memory used=9016.0MB, alloc=374.3MB, time=131.54 memory used=9073.3MB, alloc=374.3MB, time=131.78 memory used=9116.2MB, alloc=374.3MB, time=131.97 memory used=9148.7MB, alloc=374.3MB, time=132.13 memory used=9182.9MB, alloc=374.3MB, time=132.30 memory used=9219.8MB, alloc=374.3MB, time=132.47 memory used=9259.9MB, alloc=374.3MB, time=132.64 memory used=9304.1MB, alloc=374.3MB, time=132.81 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428266031 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 3 2 F := [-20 x - 19 x z - 17 x z - 20 z, -2 x y - 8 x z - 2 x y + 2, 3 3 17 x y + 6 z + 4 y z - 6 z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [18 x y - 19 x z + 13 x y, 20 y z + 11 x y z + 13 z, 2 2 2 3 2 7 x y + 8 x y z + 15 x z - 2 x z] > Problem := [F,G]; 4 2 3 3 2 Problem := [[-20 x - 19 x z - 17 x z - 20 z, -2 x y - 8 x z - 2 x y + 2, 3 3 2 2 17 x y + 6 z + 4 y z - 6 z], [18 x y - 19 x z + 13 x y, 3 2 2 2 3 2 20 y z + 11 x y z + 13 z, 7 x y + 8 x y z + 15 x z - 2 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.87 memory used=46.8MB, alloc=32.3MB, time=1.39 memory used=65.7MB, alloc=56.3MB, time=1.91 memory used=106.0MB, alloc=60.3MB, time=2.94 memory used=146.1MB, alloc=60.3MB, time=3.96 memory used=188.3MB, alloc=92.3MB, time=5.05 memory used=252.3MB, alloc=92.3MB, time=6.69 memory used=315.7MB, alloc=92.3MB, time=8.35 memory used=378.3MB, alloc=116.3MB, time=9.98 memory used=452.8MB, alloc=116.3MB, time=11.91 memory used=526.3MB, alloc=372.3MB, time=13.85 memory used=609.3MB, alloc=396.3MB, time=16.00 memory used=710.2MB, alloc=420.3MB, time=18.73 memory used=829.4MB, alloc=420.3MB, time=21.65 memory used=960.5MB, alloc=444.3MB, time=24.84 memory used=1075.5MB, alloc=444.3MB, time=27.55 memory used=1176.2MB, alloc=444.3MB, time=30.18 memory used=1270.4MB, alloc=468.3MB, time=32.43 memory used=1367.7MB, alloc=468.3MB, time=35.05 memory used=1450.2MB, alloc=468.3MB, time=37.10 memory used=1538.6MB, alloc=468.3MB, time=39.26 memory used=1631.0MB, alloc=468.3MB, time=41.95 memory used=1723.3MB, alloc=492.3MB, time=44.21 memory used=1816.6MB, alloc=492.3MB, time=47.09 memory used=1901.7MB, alloc=492.3MB, time=49.57 memory used=1980.2MB, alloc=492.3MB, time=51.75 memory used=2051.0MB, alloc=492.3MB, time=53.70 memory used=2134.8MB, alloc=492.3MB, time=55.81 memory used=2208.2MB, alloc=492.3MB, time=58.13 memory used=2265.9MB, alloc=492.3MB, time=59.78 memory used=2325.8MB, alloc=492.3MB, time=61.42 memory used=2395.7MB, alloc=492.3MB, time=63.78 memory used=2447.9MB, alloc=492.3MB, time=65.60 memory used=2506.4MB, alloc=516.3MB, time=67.41 memory used=2554.7MB, alloc=516.3MB, time=68.93 memory used=2610.5MB, alloc=516.3MB, time=70.88 memory used=2661.1MB, alloc=516.3MB, time=72.73 memory used=2712.4MB, alloc=516.3MB, time=74.67 memory used=2900.3MB, alloc=540.3MB, time=79.53 memory used=3094.7MB, alloc=540.3MB, time=84.35 memory used=3256.8MB, alloc=564.3MB, time=88.96 memory used=3435.4MB, alloc=588.3MB, time=94.08 memory used=3625.5MB, alloc=588.3MB, time=99.05 memory used=3803.8MB, alloc=612.3MB, time=103.49 memory used=3959.8MB, alloc=612.3MB, time=108.73 memory used=4106.7MB, alloc=612.3MB, time=112.63 memory used=4265.1MB, alloc=612.3MB, time=117.51 memory used=4404.3MB, alloc=612.3MB, time=121.72 |\^/| 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(); 1428266331 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 2 2 2 3 2 F := [2 x y + 10 y z + 16 z + 12 y z, 14 x z - 12 x + 7 x y z + 6 y z , 3 -9 x z - 5 x y - 17 z + 20] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 4 G := [-3 x y z - 19 x y z - 8 x y - 3 y , 4 x z + 5 z + 11 x y z - 7 x, 2 3 2 19 x y z + 12 x - 4 x + 19 x] > Problem := [F,G]; 2 2 3 4 2 Problem := [[2 x y + 10 y z + 16 z + 12 y z, 2 2 3 2 3 14 x z - 12 x + 7 x y z + 6 y z , -9 x z - 5 x y - 17 z + 20], [ 2 2 2 2 2 2 4 -3 x y z - 19 x y z - 8 x y - 3 y , 4 x z + 5 z + 11 x y z - 7 x, 2 3 2 19 x y z + 12 x - 4 x + 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=4.4MB, alloc=32.3MB, time=0.31 memory used=26.5MB, alloc=32.3MB, time=0.90 memory used=45.6MB, alloc=56.3MB, time=1.39 memory used=84.3MB, alloc=60.3MB, time=2.34 memory used=127.2MB, alloc=68.3MB, time=3.35 memory used=176.2MB, alloc=68.3MB, time=4.27 memory used=221.1MB, alloc=68.3MB, time=5.24 memory used=264.6MB, alloc=92.3MB, time=6.31 memory used=330.3MB, alloc=92.3MB, time=7.90 memory used=394.4MB, alloc=116.3MB, time=9.55 memory used=479.0MB, alloc=116.3MB, time=11.22 memory used=565.5MB, alloc=372.3MB, time=13.30 memory used=618.7MB, alloc=372.3MB, time=14.68 memory used=666.8MB, alloc=396.3MB, time=19.05 memory used=741.7MB, alloc=396.3MB, time=19.85 memory used=853.2MB, alloc=396.3MB, time=21.72 memory used=968.0MB, alloc=420.3MB, time=24.36 memory used=1102.6MB, alloc=444.3MB, time=27.56 memory used=1237.5MB, alloc=444.3MB, time=29.69 memory used=1344.8MB, alloc=444.3MB, time=30.90 memory used=1435.8MB, alloc=444.3MB, time=31.57 memory used=1536.8MB, alloc=444.3MB, time=32.73 memory used=1608.9MB, alloc=444.3MB, time=33.12 memory used=1696.1MB, alloc=444.3MB, time=33.84 memory used=1767.4MB, alloc=444.3MB, time=34.21 memory used=1841.0MB, alloc=444.3MB, time=35.37 memory used=2006.3MB, alloc=444.3MB, time=38.44 memory used=2156.4MB, alloc=444.3MB, time=40.85 memory used=2256.3MB, alloc=444.3MB, time=41.75 memory used=2351.3MB, alloc=444.3MB, time=42.99 memory used=2450.0MB, alloc=444.3MB, time=44.54 memory used=2530.8MB, alloc=444.3MB, time=45.05 memory used=2613.8MB, alloc=444.3MB, time=45.83 memory used=2686.6MB, alloc=444.3MB, time=46.30 memory used=2767.4MB, alloc=444.3MB, time=48.28 memory used=2940.7MB, alloc=444.3MB, time=50.96 memory used=3086.6MB, alloc=468.3MB, time=53.97 memory used=3203.7MB, alloc=468.3MB, time=56.57 memory used=3303.1MB, alloc=468.3MB, time=59.05 memory used=3413.3MB, alloc=468.3MB, time=61.71 memory used=3510.5MB, alloc=468.3MB, time=64.21 memory used=3729.5MB, alloc=492.3MB, time=67.12 memory used=3834.3MB, alloc=492.3MB, time=71.04 memory used=3925.6MB, alloc=492.3MB, time=75.28 memory used=4067.8MB, alloc=492.3MB, time=94.32 memory used=4180.3MB, alloc=492.3MB, time=99.60 memory used=4258.4MB, alloc=492.3MB, time=100.07 memory used=4578.2MB, alloc=492.3MB, time=104.74 memory used=4687.5MB, alloc=492.3MB, time=106.46 memory used=4793.2MB, alloc=492.3MB, time=108.11 memory used=4896.1MB, alloc=516.3MB, time=109.68 memory used=5047.3MB, alloc=516.3MB, time=111.44 memory used=5247.3MB, alloc=516.3MB, time=115.67 memory used=5331.4MB, alloc=516.3MB, time=118.11 memory used=5413.2MB, alloc=516.3MB, time=120.42 memory used=5493.9MB, alloc=516.3MB, time=122.54 memory used=5631.0MB, alloc=540.3MB, time=124.56 memory used=5767.2MB, alloc=540.3MB, time=125.94 memory used=5905.8MB, alloc=540.3MB, time=128.17 memory used=6032.4MB, alloc=540.3MB, time=129.13 memory used=6157.4MB, alloc=540.3MB, time=130.14 memory used=6278.4MB, alloc=540.3MB, time=132.25 memory used=6401.3MB, alloc=540.3MB, time=133.05 memory used=6497.7MB, alloc=540.3MB, time=133.70 memory used=6609.4MB, alloc=540.3MB, time=134.36 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428266631 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 4 3 F := [14 x z + 7 y z - 14 x z + 9 x, -11 x y - 20 z + 5 x y z + 7 y , 4 2 -10 x + 9 x y z + 19 x + 13 x y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 2 2 G := [-19 x y + 4 x y z - 8 x y z + 4 x z, x y - 20 y z + 18 x y + 7 z , 3 2 2 16 x z + 12 x y + 7 y z + 18 z] > Problem := [F,G]; 3 3 2 Problem := [[14 x z + 7 y z - 14 x z + 9 x, 3 4 3 4 2 -11 x y - 20 z + 5 x y z + 7 y , -10 x + 9 x y z + 19 x + 13 x y], [ 3 2 2 3 3 2 2 -19 x y + 4 x y z - 8 x y z + 4 x z, x y - 20 y z + 18 x y + 7 z , 3 2 2 16 x z + 12 x y + 7 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=4.6MB, alloc=32.3MB, time=0.32 memory used=26.0MB, alloc=32.5MB, time=0.90 memory used=46.4MB, alloc=34.3MB, time=1.00 memory used=57.6MB, alloc=34.3MB, time=1.06 memory used=69.6MB, alloc=34.3MB, time=1.12 memory used=83.8MB, alloc=34.3MB, time=1.18 memory used=99.0MB, alloc=34.3MB, time=1.24 memory used=107.8MB, alloc=34.3MB, time=1.29 memory used=117.1MB, alloc=34.3MB, time=1.34 memory used=127.2MB, alloc=34.3MB, time=1.39 memory used=138.4MB, alloc=34.3MB, time=1.44 memory used=150.3MB, alloc=34.3MB, time=1.50 memory used=163.1MB, alloc=34.3MB, time=1.55 memory used=177.1MB, alloc=34.3MB, time=1.60 memory used=200.8MB, alloc=34.3MB, time=3.51 memory used=216.0MB, alloc=34.3MB, time=3.58 memory used=231.3MB, alloc=34.3MB, time=3.65 memory used=241.9MB, alloc=34.3MB, time=3.70 memory used=252.9MB, alloc=34.3MB, time=3.76 memory used=265.4MB, alloc=34.3MB, time=3.82 memory used=279.7MB, alloc=34.3MB, time=3.88 memory used=295.4MB, alloc=34.3MB, time=3.93 memory used=306.5MB, alloc=34.3MB, time=3.98 memory used=315.4MB, alloc=34.3MB, time=4.02 memory used=324.8MB, alloc=34.3MB, time=4.07 memory used=334.9MB, alloc=34.3MB, time=4.11 memory used=345.9MB, alloc=34.3MB, time=4.15 memory used=357.9MB, alloc=34.3MB, time=4.20 memory used=370.9MB, alloc=34.3MB, time=4.25 memory used=394.3MB, alloc=34.3MB, time=4.73 memory used=415.2MB, alloc=34.3MB, time=5.25 memory used=431.8MB, alloc=58.3MB, time=5.48 memory used=474.2MB, alloc=62.3MB, time=5.98 memory used=499.7MB, alloc=62.3MB, time=6.07 memory used=542.1MB, alloc=64.8MB, time=7.21 memory used=563.8MB, alloc=64.8MB, time=7.34 memory used=587.6MB, alloc=64.8MB, time=7.46 memory used=614.9MB, alloc=64.8MB, time=7.59 memory used=646.6MB, alloc=64.8MB, time=7.72 memory used=666.9MB, alloc=64.8MB, time=7.82 memory used=683.5MB, alloc=64.8MB, time=7.91 memory used=702.6MB, alloc=64.8MB, time=8.01 memory used=722.3MB, alloc=64.8MB, time=8.11 memory used=742.6MB, alloc=64.8MB, time=8.21 memory used=763.6MB, alloc=64.8MB, time=8.31 memory used=787.4MB, alloc=64.8MB, time=8.41 memory used=811.7MB, alloc=64.8MB, time=8.52 memory used=836.6MB, alloc=64.8MB, time=8.63 memory used=862.5MB, alloc=64.8MB, time=8.74 memory used=890.4MB, alloc=64.8MB, time=8.86 memory used=919.1MB, alloc=64.8MB, time=8.98 memory used=950.9MB, alloc=64.8MB, time=9.09 memory used=978.5MB, alloc=64.8MB, time=9.19 memory used=994.3MB, alloc=64.8MB, time=9.26 memory used=1009.6MB, alloc=64.8MB, time=9.33 memory used=1025.4MB, alloc=64.8MB, time=9.39 memory used=1041.2MB, alloc=64.8MB, time=9.47 memory used=1057.1MB, alloc=64.8MB, time=9.55 memory used=1072.9MB, alloc=64.8MB, time=9.62 memory used=1089.3MB, alloc=64.8MB, time=9.69 memory used=1107.1MB, alloc=64.8MB, time=9.77 memory used=1125.4MB, alloc=64.8MB, time=9.85 memory used=1143.6MB, alloc=64.8MB, time=9.92 memory used=1162.2MB, alloc=64.8MB, time=10.02 memory used=1182.3MB, alloc=64.8MB, time=10.11 memory used=1202.6MB, alloc=64.8MB, time=10.19 memory used=1222.5MB, alloc=64.8MB, time=10.27 memory used=1244.8MB, alloc=64.8MB, time=10.35 memory used=1266.7MB, alloc=64.8MB, time=10.43 memory used=1289.0MB, alloc=64.8MB, time=10.50 memory used=1312.1MB, alloc=64.8MB, time=10.58 memory used=1336.5MB, alloc=64.8MB, time=10.66 memory used=1361.3MB, alloc=64.8MB, time=10.74 memory used=1387.9MB, alloc=64.8MB, time=10.83 memory used=1414.7MB, alloc=64.8MB, time=10.92 memory used=1442.8MB, alloc=64.8MB, time=11.00 memory used=1472.5MB, alloc=64.8MB, time=11.09 memory used=1512.8MB, alloc=64.8MB, time=12.26 memory used=1540.4MB, alloc=64.8MB, time=12.40 memory used=1562.9MB, alloc=64.8MB, time=12.52 memory used=1590.4MB, alloc=64.8MB, time=12.64 memory used=1621.1MB, alloc=64.8MB, time=12.77 memory used=1646.0MB, alloc=64.8MB, time=12.89 memory used=1663.5MB, alloc=64.8MB, time=12.99 memory used=1682.4MB, alloc=64.8MB, time=13.10 memory used=1702.0MB, alloc=64.8MB, time=13.20 memory used=1722.2MB, alloc=64.8MB, time=13.31 memory used=1743.3MB, alloc=64.8MB, time=13.42 memory used=1766.7MB, alloc=64.8MB, time=13.53 memory used=1791.0MB, alloc=64.8MB, time=13.64 memory used=1815.9MB, alloc=64.8MB, time=13.75 memory used=1843.8MB, alloc=64.8MB, time=13.86 memory used=1872.1MB, alloc=64.8MB, time=13.97 memory used=1900.9MB, alloc=64.8MB, time=14.08 memory used=1932.6MB, alloc=64.8MB, time=14.21 memory used=1961.2MB, alloc=64.8MB, time=14.32 memory used=1976.7MB, alloc=64.8MB, time=14.40 memory used=1991.4MB, alloc=64.8MB, time=14.47 memory used=2006.9MB, alloc=64.8MB, time=14.54 memory used=2022.8MB, alloc=64.8MB, time=14.62 memory used=2038.5MB, alloc=64.8MB, time=14.70 memory used=2054.7MB, alloc=64.8MB, time=14.78 memory used=2072.8MB, alloc=64.8MB, time=14.88 memory used=2091.2MB, alloc=64.8MB, time=14.95 memory used=2109.5MB, alloc=64.8MB, time=15.04 memory used=2127.7MB, alloc=64.8MB, time=15.12 memory used=2146.3MB, alloc=64.8MB, time=15.20 memory used=2166.3MB, alloc=64.8MB, time=15.29 memory used=2186.6MB, alloc=64.8MB, time=15.38 memory used=2207.2MB, alloc=64.8MB, time=15.46 memory used=2229.0MB, alloc=64.8MB, time=15.54 memory used=2251.0MB, alloc=64.8MB, time=15.63 memory used=2274.8MB, alloc=64.8MB, time=15.72 memory used=2298.1MB, alloc=64.8MB, time=15.80 memory used=2323.0MB, alloc=64.8MB, time=15.89 memory used=2349.0MB, alloc=64.8MB, time=15.98 memory used=2375.1MB, alloc=64.8MB, time=16.07 memory used=2402.8MB, alloc=64.8MB, time=16.15 memory used=2431.8MB, alloc=64.8MB, time=16.23 memory used=2462.2MB, alloc=64.8MB, time=16.33 memory used=2510.2MB, alloc=64.8MB, time=30.23 memory used=2621.6MB, alloc=64.8MB, time=32.86 memory used=2655.3MB, alloc=64.8MB, time=33.22 memory used=2683.9MB, alloc=64.8MB, time=33.35 memory used=2704.2MB, alloc=64.8MB, time=33.45 memory used=2727.5MB, alloc=64.8MB, time=33.56 memory used=2754.8MB, alloc=64.8MB, time=33.67 memory used=2785.6MB, alloc=64.8MB, time=33.79 memory used=2812.4MB, alloc=64.8MB, time=33.90 memory used=2830.1MB, alloc=64.8MB, time=33.98 memory used=2848.6MB, alloc=64.8MB, time=34.06 memory used=2868.5MB, alloc=64.8MB, time=34.15 memory used=2888.9MB, alloc=64.8MB, time=34.23 memory used=2910.8MB, alloc=64.8MB, time=34.32 memory used=2934.1MB, alloc=64.8MB, time=34.42 memory used=2958.8MB, alloc=64.8MB, time=34.51 memory used=2984.8MB, alloc=64.8MB, time=34.61 memory used=3011.9MB, alloc=64.8MB, time=34.71 memory used=3041.1MB, alloc=64.8MB, time=34.80 memory used=3070.9MB, alloc=64.8MB, time=34.90 memory used=3102.4MB, alloc=64.8MB, time=34.99 memory used=3130.1MB, alloc=81.9MB, time=35.11 memory used=3141.5MB, alloc=81.9MB, time=35.18 memory used=3153.2MB, alloc=81.9MB, time=35.25 memory used=3165.5MB, alloc=81.9MB, time=35.34 memory used=3178.3MB, alloc=81.9MB, time=35.43 memory used=3191.3MB, alloc=81.9MB, time=35.52 memory used=3204.6MB, alloc=81.9MB, time=35.62 memory used=3218.9MB, alloc=81.9MB, time=35.74 memory used=3233.6MB, alloc=81.9MB, time=35.81 memory used=3274.2MB, alloc=81.9MB, time=36.30 memory used=3304.6MB, alloc=81.9MB, time=36.65 memory used=3333.1MB, alloc=81.9MB, time=36.78 memory used=3364.3MB, alloc=81.9MB, time=37.49 memory used=3393.2MB, alloc=81.9MB, time=37.63 memory used=3417.7MB, alloc=81.9MB, time=37.74 memory used=3444.4MB, alloc=81.9MB, time=37.84 memory used=3480.3MB, alloc=81.9MB, time=38.39 memory used=3532.2MB, alloc=81.9MB, time=52.69 memory used=3562.2MB, alloc=81.9MB, time=53.31 memory used=3590.9MB, alloc=81.9MB, time=53.43 memory used=3609.6MB, alloc=81.9MB, time=53.53 memory used=3631.5MB, alloc=81.9MB, time=53.63 memory used=3656.5MB, alloc=81.9MB, time=53.75 memory used=3684.8MB, alloc=81.9MB, time=53.86 memory used=3715.6MB, alloc=81.9MB, time=53.97 memory used=3733.2MB, alloc=81.9MB, time=54.06 memory used=3751.0MB, alloc=81.9MB, time=54.14 memory used=3768.9MB, alloc=81.9MB, time=54.21 memory used=3788.0MB, alloc=81.9MB, time=54.30 memory used=3807.7MB, alloc=81.9MB, time=54.38 memory used=3828.6MB, alloc=81.9MB, time=54.48 memory used=3851.1MB, alloc=81.9MB, time=54.56 memory used=3874.9MB, alloc=81.9MB, time=54.65 memory used=3900.1MB, alloc=81.9MB, time=54.73 memory used=3926.5MB, alloc=81.9MB, time=54.82 memory used=3953.9MB, alloc=81.9MB, time=54.91 memory used=3983.3MB, alloc=81.9MB, time=55.01 memory used=4013.1MB, alloc=81.9MB, time=55.11 memory used=4048.9MB, alloc=81.9MB, time=55.21 memory used=4060.2MB, alloc=81.9MB, time=55.28 memory used=4071.7MB, alloc=81.9MB, time=55.37 memory used=4083.5MB, alloc=81.9MB, time=55.46 memory used=4095.8MB, alloc=81.9MB, time=55.53 memory used=4108.5MB, alloc=81.9MB, time=55.60 memory used=4121.0MB, alloc=81.9MB, time=55.69 memory used=4134.8MB, alloc=81.9MB, time=55.77 memory used=4148.9MB, alloc=81.9MB, time=55.85 memory used=4163.8MB, alloc=81.9MB, time=55.92 memory used=4213.1MB, alloc=81.9MB, time=56.68 memory used=4248.4MB, alloc=81.9MB, time=57.05 memory used=4283.4MB, alloc=81.9MB, time=58.23 memory used=4318.8MB, alloc=81.9MB, time=58.40 memory used=4338.9MB, alloc=81.9MB, time=58.52 memory used=4359.3MB, alloc=81.9MB, time=58.65 memory used=4382.0MB, alloc=81.9MB, time=58.78 memory used=4407.5MB, alloc=81.9MB, time=58.91 memory used=4435.8MB, alloc=81.9MB, time=59.04 memory used=4464.1MB, alloc=81.9MB, time=59.17 memory used=4480.5MB, alloc=81.9MB, time=59.27 memory used=4497.8MB, alloc=81.9MB, time=59.37 memory used=4515.6MB, alloc=81.9MB, time=59.47 memory used=4533.7MB, alloc=81.9MB, time=59.57 memory used=4553.3MB, alloc=81.9MB, time=59.68 memory used=4574.3MB, alloc=81.9MB, time=59.78 memory used=4595.2MB, alloc=81.9MB, time=59.89 memory used=4617.4MB, alloc=81.9MB, time=60.00 memory used=4640.9MB, alloc=81.9MB, time=60.12 memory used=4666.3MB, alloc=81.9MB, time=60.23 memory used=4693.7MB, alloc=81.9MB, time=60.34 memory used=4722.3MB, alloc=81.9MB, time=60.46 memory used=4751.9MB, alloc=81.9MB, time=60.57 memory used=4769.1MB, alloc=81.9MB, time=60.65 memory used=4785.8MB, alloc=81.9MB, time=60.73 memory used=4818.3MB, alloc=81.9MB, time=61.81 memory used=4851.9MB, alloc=81.9MB, time=61.97 memory used=4870.8MB, alloc=81.9MB, time=62.10 memory used=4891.8MB, alloc=81.9MB, time=62.22 memory used=4914.8MB, alloc=81.9MB, time=62.35 memory used=4940.6MB, alloc=81.9MB, time=62.49 memory used=4969.2MB, alloc=81.9MB, time=62.63 memory used=4996.2MB, alloc=81.9MB, time=62.76 memory used=5012.2MB, alloc=81.9MB, time=62.86 memory used=5029.8MB, alloc=81.9MB, time=62.97 memory used=5047.7MB, alloc=81.9MB, time=63.08 memory used=5065.9MB, alloc=81.9MB, time=63.19 memory used=5085.4MB, alloc=81.9MB, time=63.30 memory used=5106.4MB, alloc=81.9MB, time=63.40 memory used=5128.8MB, alloc=81.9MB, time=63.51 memory used=5152.4MB, alloc=81.9MB, time=63.61 memory used=5177.0MB, alloc=81.9MB, time=63.73 memory used=5202.6MB, alloc=81.9MB, time=63.85 memory used=5230.8MB, alloc=81.9MB, time=63.97 memory used=5259.9MB, alloc=81.9MB, time=64.09 memory used=5286.3MB, alloc=81.9MB, time=64.20 memory used=5302.6MB, alloc=81.9MB, time=64.28 memory used=5319.9MB, alloc=81.9MB, time=64.37 memory used=5363.1MB, alloc=81.9MB, time=78.08 memory used=5393.8MB, alloc=81.9MB, time=78.71 memory used=5417.8MB, alloc=81.9MB, time=78.84 memory used=5444.5MB, alloc=81.9MB, time=78.96 memory used=5462.9MB, alloc=81.9MB, time=79.07 memory used=5483.1MB, alloc=81.9MB, time=79.18 memory used=5506.2MB, alloc=81.9MB, time=79.29 memory used=5532.1MB, alloc=81.9MB, time=79.42 memory used=5560.4MB, alloc=81.9MB, time=79.53 memory used=5585.9MB, alloc=81.9MB, time=79.64 memory used=5601.9MB, alloc=81.9MB, time=79.75 memory used=5618.6MB, alloc=81.9MB, time=79.84 memory used=5637.1MB, alloc=81.9MB, time=79.92 memory used=5657.2MB, alloc=81.9MB, time=80.01 memory used=5679.4MB, alloc=81.9MB, time=80.10 memory used=5709.7MB, alloc=81.9MB, time=80.30 memory used=5741.5MB, alloc=81.9MB, time=80.95 memory used=5764.0MB, alloc=81.9MB, time=81.06 memory used=5796.6MB, alloc=81.9MB, time=81.35 memory used=5829.5MB, alloc=81.9MB, time=81.79 memory used=5858.2MB, alloc=81.9MB, time=81.94 memory used=5880.5MB, alloc=81.9MB, time=82.06 memory used=5908.4MB, alloc=81.9MB, time=82.20 memory used=5932.5MB, alloc=81.9MB, time=82.31 memory used=5951.9MB, alloc=81.9MB, time=82.42 memory used=5976.4MB, alloc=81.9MB, time=82.60 memory used=6015.3MB, alloc=81.9MB, time=83.11 memory used=6036.5MB, alloc=81.9MB, time=83.25 memory used=6060.4MB, alloc=81.9MB, time=83.38 memory used=6090.4MB, alloc=81.9MB, time=83.51 memory used=6108.7MB, alloc=81.9MB, time=83.62 memory used=6128.3MB, alloc=81.9MB, time=83.72 memory used=6161.4MB, alloc=81.9MB, time=86.44 memory used=6193.3MB, alloc=81.9MB, time=87.35 memory used=6220.2MB, alloc=81.9MB, time=87.48 memory used=6239.2MB, alloc=81.9MB, time=87.58 memory used=6262.2MB, alloc=81.9MB, time=87.70 memory used=6288.8MB, alloc=81.9MB, time=87.81 memory used=6317.2MB, alloc=81.9MB, time=88.03 memory used=6347.7MB, alloc=81.9MB, time=88.63 memory used=6370.3MB, alloc=81.9MB, time=88.75 memory used=6405.4MB, alloc=81.9MB, time=89.50 memory used=6452.5MB, alloc=81.9MB, time=102.45 memory used=6478.7MB, alloc=81.9MB, time=102.59 memory used=6504.7MB, alloc=81.9MB, time=102.71 memory used=6526.9MB, alloc=81.9MB, time=102.83 memory used=6545.5MB, alloc=81.9MB, time=102.94 memory used=6566.2MB, alloc=81.9MB, time=103.05 memory used=6589.6MB, alloc=81.9MB, time=103.15 memory used=6616.2MB, alloc=81.9MB, time=103.26 memory used=6645.5MB, alloc=81.9MB, time=103.37 memory used=6662.1MB, alloc=81.9MB, time=103.46 memory used=6679.0MB, alloc=81.9MB, time=103.56 memory used=6697.3MB, alloc=81.9MB, time=103.66 memory used=6717.0MB, alloc=81.9MB, time=103.75 memory used=6743.9MB, alloc=81.9MB, time=104.05 memory used=6784.6MB, alloc=81.9MB, time=104.73 memory used=6824.0MB, alloc=81.9MB, time=105.42 memory used=6848.1MB, alloc=81.9MB, time=105.58 memory used=6881.5MB, alloc=81.9MB, time=106.02 memory used=6918.1MB, alloc=81.9MB, time=107.21 memory used=6941.9MB, alloc=105.9MB, time=107.37 memory used=6974.9MB, alloc=105.9MB, time=107.55 memory used=7015.8MB, alloc=105.9MB, time=107.74 memory used=7062.9MB, alloc=105.9MB, time=107.93 memory used=7090.3MB, alloc=105.9MB, time=108.09 memory used=7118.4MB, alloc=105.9MB, time=108.25 memory used=7149.7MB, alloc=105.9MB, time=108.40 memory used=7182.4MB, alloc=105.9MB, time=108.56 memory used=7218.3MB, alloc=105.9MB, time=108.72 memory used=7257.3MB, alloc=105.9MB, time=108.87 memory used=7299.4MB, alloc=105.9MB, time=109.04 memory used=7344.4MB, alloc=105.9MB, time=109.21 memory used=7392.2MB, alloc=105.9MB, time=109.38 memory used=7426.5MB, alloc=105.9MB, time=109.51 memory used=7451.1MB, alloc=105.9MB, time=109.61 memory used=7476.5MB, alloc=105.9MB, time=109.73 memory used=7503.0MB, alloc=105.9MB, time=109.84 memory used=7531.6MB, alloc=105.9MB, time=109.95 memory used=7561.7MB, alloc=105.9MB, time=110.08 memory used=7593.2MB, alloc=105.9MB, time=110.19 memory used=7625.7MB, alloc=105.9MB, time=110.30 memory used=7659.4MB, alloc=105.9MB, time=110.41 memory used=7695.5MB, alloc=105.9MB, time=110.53 memory used=7734.0MB, alloc=105.9MB, time=110.64 memory used=7793.8MB, alloc=105.9MB, time=111.99 memory used=7827.5MB, alloc=105.9MB, time=112.18 memory used=7868.4MB, alloc=105.9MB, time=112.36 memory used=7917.6MB, alloc=105.9MB, time=112.55 memory used=7946.3MB, alloc=105.9MB, time=112.71 memory used=7975.6MB, alloc=105.9MB, time=112.86 memory used=8007.1MB, alloc=105.9MB, time=113.02 memory used=8040.1MB, alloc=105.9MB, time=113.18 memory used=8075.9MB, alloc=105.9MB, time=113.32 memory used=8114.6MB, alloc=105.9MB, time=113.48 memory used=8156.7MB, alloc=105.9MB, time=113.63 memory used=8201.7MB, alloc=105.9MB, time=113.80 memory used=8249.6MB, alloc=105.9MB, time=113.95 memory used=8285.6MB, alloc=105.9MB, time=114.09 memory used=8310.5MB, alloc=105.9MB, time=114.20 memory used=8337.7MB, alloc=105.9MB, time=114.31 memory used=8364.5MB, alloc=105.9MB, time=114.42 memory used=8393.2MB, alloc=105.9MB, time=114.53 memory used=8423.4MB, alloc=105.9MB, time=114.65 memory used=8454.8MB, alloc=105.9MB, time=114.76 memory used=8487.5MB, alloc=105.9MB, time=114.88 memory used=8522.4MB, alloc=105.9MB, time=114.99 memory used=8559.8MB, alloc=105.9MB, time=115.11 memory used=8599.1MB, alloc=105.9MB, time=115.22 memory used=8747.7MB, alloc=105.9MB, time=131.10 memory used=8794.6MB, alloc=105.9MB, time=131.48 memory used=8831.3MB, alloc=105.9MB, time=131.64 memory used=8865.5MB, alloc=105.9MB, time=131.79 memory used=8906.4MB, alloc=105.9MB, time=131.95 memory used=8953.6MB, alloc=105.9MB, time=132.11 memory used=8980.9MB, alloc=105.9MB, time=132.22 memory used=9009.8MB, alloc=105.9MB, time=132.34 memory used=9040.9MB, alloc=105.9MB, time=132.46 memory used=9074.3MB, alloc=105.9MB, time=132.59 memory used=9110.7MB, alloc=105.9MB, time=132.71 memory used=9149.2MB, alloc=105.9MB, time=132.84 memory used=9192.2MB, alloc=105.9MB, time=132.97 memory used=9244.5MB, alloc=105.9MB, time=133.11 memory used=9256.0MB, alloc=107.8MB, time=133.20 memory used=9265.1MB, alloc=107.8MB, time=133.29 memory used=9274.5MB, alloc=107.8MB, time=133.37 memory used=9324.0MB, alloc=107.8MB, time=133.70 memory used=9372.7MB, alloc=107.8MB, time=134.48 memory used=9411.5MB, alloc=107.8MB, time=134.64 memory used=9459.9MB, alloc=107.8MB, time=135.32 memory used=9512.5MB, alloc=107.8MB, time=135.78 memory used=9553.7MB, alloc=107.8MB, time=135.97 memory used=9585.9MB, alloc=107.8MB, time=136.14 memory used=9627.4MB, alloc=107.8MB, time=136.29 memory used=9672.5MB, alloc=107.8MB, time=136.82 memory used=9709.7MB, alloc=107.8MB, time=136.99 memory used=9751.2MB, alloc=107.8MB, time=137.19 memory used=9800.7MB, alloc=107.8MB, time=137.61 memory used=9889.0MB, alloc=107.8MB, time=150.69 memory used=9930.5MB, alloc=107.8MB, time=152.14 memory used=9972.3MB, alloc=107.8MB, time=152.34 memory used=10002.3MB, alloc=107.8MB, time=152.51 memory used=10032.0MB, alloc=107.8MB, time=152.67 memory used=10064.9MB, alloc=107.8MB, time=152.84 memory used=10101.8MB, alloc=107.8MB, time=153.01 memory used=10141.3MB, alloc=107.8MB, time=153.19 memory used=10185.0MB, alloc=107.8MB, time=153.37 memory used=10223.4MB, alloc=107.8MB, time=153.53 memory used=10247.3MB, alloc=107.8MB, time=153.65 memory used=10272.0MB, alloc=107.8MB, time=153.78 memory used=10298.2MB, alloc=107.8MB, time=153.91 memory used=10324.9MB, alloc=107.8MB, time=154.04 memory used=10352.1MB, alloc=107.8MB, time=154.17 memory used=10379.9MB, alloc=107.8MB, time=154.31 memory used=10409.9MB, alloc=107.8MB, time=154.44 memory used=10440.4MB, alloc=107.8MB, time=154.57 memory used=10471.4MB, alloc=107.8MB, time=154.69 memory used=10504.8MB, alloc=107.8MB, time=154.82 memory used=10538.6MB, alloc=107.8MB, time=154.96 memory used=10574.8MB, alloc=107.8MB, time=155.09 memory used=10611.4MB, alloc=107.8MB, time=155.22 memory used=10648.3MB, alloc=107.8MB, time=155.36 memory used=10687.3MB, alloc=107.8MB, time=155.49 memory used=10728.8MB, alloc=107.8MB, time=155.63 memory used=10770.3MB, alloc=107.8MB, time=155.77 memory used=10814.0MB, alloc=107.8MB, time=155.92 memory used=10859.8MB, alloc=107.8MB, time=156.06 memory used=10897.5MB, alloc=107.8MB, time=156.20 memory used=10908.3MB, alloc=107.8MB, time=156.30 memory used=10917.8MB, alloc=107.8MB, time=156.39 memory used=10925.7MB, alloc=107.8MB, time=156.50 memory used=10933.5MB, alloc=107.8MB, time=156.58 memory used=10941.8MB, alloc=107.8MB, time=156.67 memory used=10950.1MB, alloc=107.8MB, time=156.76 memory used=10958.3MB, alloc=107.8MB, time=156.85 memory used=10966.6MB, alloc=107.8MB, time=156.94 memory used=10974.8MB, alloc=107.8MB, time=157.03 memory used=10983.0MB, alloc=107.8MB, time=157.12 memory used=10991.1MB, alloc=107.8MB, time=157.21 memory used=10999.5MB, alloc=107.8MB, time=157.30 memory used=11009.4MB, alloc=107.8MB, time=157.39 memory used=11017.8MB, alloc=107.8MB, time=157.48 memory used=11027.6MB, alloc=107.8MB, time=157.58 memory used=11037.7MB, alloc=107.8MB, time=157.67 memory used=11047.6MB, alloc=107.8MB, time=157.75 memory used=11057.6MB, alloc=107.8MB, time=157.85 memory used=11067.5MB, alloc=107.8MB, time=157.94 memory used=11077.3MB, alloc=107.8MB, time=158.05 memory used=11087.1MB, alloc=107.8MB, time=158.15 memory used=11096.9MB, alloc=107.8MB, time=158.23 memory used=11106.6MB, alloc=107.8MB, time=158.32 memory used=11116.2MB, alloc=107.8MB, time=158.40 memory used=11125.8MB, alloc=107.8MB, time=158.49 memory used=11135.6MB, alloc=107.8MB, time=158.59 memory used=11146.8MB, alloc=107.8MB, time=158.69 memory used=11158.0MB, alloc=107.8MB, time=158.81 memory used=11169.2MB, alloc=107.8MB, time=158.91 memory used=11180.3MB, alloc=107.8MB, time=159.01 memory used=11191.4MB, alloc=107.8MB, time=159.10 memory used=11202.3MB, alloc=107.8MB, time=159.19 memory used=11213.1MB, alloc=107.8MB, time=159.30 memory used=11223.8MB, alloc=107.8MB, time=159.39 memory used=11234.7MB, alloc=107.8MB, time=159.50 memory used=11246.7MB, alloc=107.8MB, time=159.59 memory used=11258.8MB, alloc=107.8MB, time=159.68 memory used=11270.8MB, alloc=107.8MB, time=159.80 memory used=11282.7MB, alloc=107.8MB, time=159.89 memory used=11294.6MB, alloc=107.8MB, time=159.98 memory used=11307.5MB, alloc=107.8MB, time=160.08 memory used=11320.4MB, alloc=107.8MB, time=160.19 memory used=11333.1MB, alloc=107.8MB, time=160.30 memory used=11345.8MB, alloc=107.8MB, time=160.42 memory used=11359.3MB, alloc=107.8MB, time=160.51 memory used=11372.8MB, alloc=107.8MB, time=160.60 memory used=11386.1MB, alloc=107.8MB, time=160.70 memory used=11400.1MB, alloc=107.8MB, time=160.79 memory used=11413.9MB, alloc=107.8MB, time=160.88 memory used=11428.6MB, alloc=107.8MB, time=160.98 memory used=11443.0MB, alloc=107.8MB, time=161.07 memory used=11457.8MB, alloc=107.8MB, time=161.16 memory used=11472.9MB, alloc=107.8MB, time=161.28 memory used=11488.5MB, alloc=107.8MB, time=161.38 memory used=11504.6MB, alloc=107.8MB, time=161.48 memory used=11520.6MB, alloc=107.8MB, time=161.57 memory used=11538.1MB, alloc=107.8MB, time=161.67 memory used=11600.5MB, alloc=107.8MB, time=173.46 memory used=11635.3MB, alloc=107.8MB, time=173.64 memory used=11674.4MB, alloc=107.8MB, time=173.82 memory used=11701.0MB, alloc=107.8MB, time=173.97 memory used=11731.5MB, alloc=107.8MB, time=174.13 memory used=11765.2MB, alloc=107.8MB, time=174.29 memory used=11801.5MB, alloc=107.8MB, time=174.46 memory used=11841.8MB, alloc=107.8MB, time=174.64 memory used=11886.3MB, alloc=107.8MB, time=174.81 memory used=11918.5MB, alloc=107.8MB, time=174.96 memory used=11941.8MB, alloc=107.8MB, time=175.07 memory used=11965.4MB, alloc=107.8MB, time=175.19 memory used=11989.8MB, alloc=107.8MB, time=175.31 memory used=12016.5MB, alloc=107.8MB, time=175.43 memory used=12043.7MB, alloc=107.8MB, time=175.55 memory used=12071.4MB, alloc=107.8MB, time=175.68 memory used=12099.8MB, alloc=107.8MB, time=175.80 memory used=12130.1MB, alloc=107.8MB, time=175.93 memory used=12161.1MB, alloc=107.8MB, time=176.05 memory used=12192.6MB, alloc=107.8MB, time=176.17 memory used=12226.2MB, alloc=107.8MB, time=176.30 memory used=12260.3MB, alloc=107.8MB, time=176.43 memory used=12296.8MB, alloc=107.8MB, time=176.56 memory used=12333.6MB, alloc=107.8MB, time=176.70 memory used=12372.7MB, alloc=107.8MB, time=176.83 memory used=12411.9MB, alloc=107.8MB, time=176.97 memory used=12453.4MB, alloc=107.8MB, time=177.11 memory used=12495.1MB, alloc=107.8MB, time=177.24 memory used=12538.6MB, alloc=107.8MB, time=177.38 memory used=12585.4MB, alloc=107.8MB, time=177.53 memory used=12595.1MB, alloc=107.8MB, time=177.61 memory used=12604.2MB, alloc=107.8MB, time=177.71 memory used=12612.1MB, alloc=107.8MB, time=177.79 memory used=12619.7MB, alloc=107.8MB, time=177.88 memory used=12628.0MB, alloc=107.8MB, time=177.97 memory used=12636.3MB, alloc=107.8MB, time=178.05 memory used=12644.5MB, alloc=107.8MB, time=178.15 memory used=12652.8MB, alloc=107.8MB, time=178.26 memory used=12661.0MB, alloc=107.8MB, time=178.39 memory used=12669.2MB, alloc=107.8MB, time=178.49 memory used=12677.4MB, alloc=107.8MB, time=178.57 memory used=12685.7MB, alloc=107.8MB, time=178.67 memory used=12695.7MB, alloc=107.8MB, time=178.75 memory used=12704.1MB, alloc=107.8MB, time=178.84 memory used=12713.8MB, alloc=107.8MB, time=178.93 memory used=12723.9MB, alloc=107.8MB, time=179.02 memory used=12733.9MB, alloc=107.8MB, time=179.11 memory used=12743.8MB, alloc=107.8MB, time=179.19 memory used=12753.8MB, alloc=107.8MB, time=179.28 memory used=12763.6MB, alloc=107.8MB, time=179.37 memory used=12773.4MB, alloc=107.8MB, time=179.47 memory used=12783.2MB, alloc=107.8MB, time=179.56 memory used=12792.9MB, alloc=107.8MB, time=179.65 memory used=12802.6MB, alloc=107.8MB, time=179.74 memory used=12812.2MB, alloc=107.8MB, time=179.84 memory used=12821.9MB, alloc=107.8MB, time=179.96 memory used=12833.1MB, alloc=107.8MB, time=180.05 memory used=12844.4MB, alloc=107.8MB, time=180.17 memory used=12855.6MB, alloc=107.8MB, time=180.26 memory used=12866.7MB, alloc=107.8MB, time=180.36 memory used=12877.8MB, alloc=107.8MB, time=180.45 memory used=12888.7MB, alloc=107.8MB, time=180.56 memory used=12899.5MB, alloc=107.8MB, time=180.65 memory used=12910.3MB, alloc=107.8MB, time=180.76 memory used=12921.1MB, alloc=107.8MB, time=180.85 memory used=12933.2MB, alloc=107.8MB, time=180.94 memory used=12945.3MB, alloc=107.8MB, time=181.03 memory used=12957.3MB, alloc=107.8MB, time=181.12 memory used=12969.3MB, alloc=107.8MB, time=181.21 memory used=12980.9MB, alloc=107.8MB, time=181.30 memory used=12992.9MB, alloc=107.8MB, time=181.39 memory used=13005.5MB, alloc=107.8MB, time=181.48 memory used=13018.2MB, alloc=107.8MB, time=181.58 memory used=13030.8MB, alloc=107.8MB, time=181.68 memory used=13044.6MB, alloc=107.8MB, time=181.78 memory used=13058.1MB, alloc=107.8MB, time=181.88 memory used=13071.3MB, alloc=107.8MB, time=181.98 memory used=13085.5MB, alloc=107.8MB, time=182.06 memory used=13099.4MB, alloc=107.8MB, time=182.15 memory used=13114.2MB, alloc=107.8MB, time=182.25 memory used=13128.7MB, alloc=107.8MB, time=182.34 memory used=13143.4MB, alloc=107.8MB, time=182.44 memory used=13158.9MB, alloc=107.8MB, time=182.54 memory used=13174.6MB, alloc=107.8MB, time=182.64 memory used=13190.5MB, alloc=107.8MB, time=182.73 memory used=13207.1MB, alloc=107.8MB, time=182.84 memory used=13224.2MB, alloc=107.8MB, time=182.93 memory used=13326.0MB, alloc=107.8MB, time=184.70 memory used=13401.4MB, alloc=107.8MB, time=185.65 memory used=13478.9MB, alloc=107.8MB, time=186.40 memory used=13556.6MB, alloc=107.8MB, time=187.37 memory used=13634.8MB, alloc=107.8MB, time=188.60 memory used=13708.2MB, alloc=107.8MB, time=190.61 memory used=13750.0MB, alloc=107.8MB, time=191.25 memory used=13783.8MB, alloc=107.8MB, time=191.46 memory used=13827.6MB, alloc=107.8MB, time=192.09 memory used=13863.0MB, alloc=107.8MB, time=192.29 memory used=13890.4MB, alloc=107.8MB, time=192.46 memory used=13925.5MB, alloc=107.8MB, time=192.64 |\^/| 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(); 1428266931 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 3 2 F := [-12 x y + 4 y - 12 x y z + 10 x y, -18 x z + 4 y z - 2 x z - 9 x y, 2 2 3 6 x z + 13 x + 10 y + 8] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 3 2 3 4 G := [x - 16 y + 5 y + 19 y z , -11 x y + 14 z + 4 x y z + 16 z, 4 2 2 -18 z + 4 x z - 17 x + 2 x z] > Problem := [F,G]; 2 2 4 Problem := [[-12 x y + 4 y - 12 x y z + 10 x y, 2 2 3 2 2 2 3 -18 x z + 4 y z - 2 x z - 9 x y, 6 x z + 13 x + 10 y + 8], [ 4 4 3 2 3 4 x - 16 y + 5 y + 19 y z , -11 x y + 14 z + 4 x y z + 16 z, 4 2 2 -18 z + 4 x z - 17 x + 2 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=25.8MB, alloc=32.5MB, time=0.82 memory used=78.8MB, alloc=77.7MB, time=1.98 memory used=128.6MB, alloc=81.9MB, time=3.78 memory used=164.8MB, alloc=81.9MB, time=3.95 memory used=195.4MB, alloc=81.9MB, time=4.08 memory used=246.9MB, alloc=82.0MB, time=4.97 memory used=290.6MB, alloc=82.0MB, time=6.17 memory used=322.1MB, alloc=82.0MB, time=6.31 memory used=369.3MB, alloc=82.0MB, time=7.16 memory used=407.5MB, alloc=82.0MB, time=7.38 memory used=462.6MB, alloc=82.0MB, time=9.96 memory used=506.4MB, alloc=82.0MB, time=11.27 memory used=540.6MB, alloc=82.0MB, time=11.44 memory used=566.5MB, alloc=82.0MB, time=11.56 memory used=595.2MB, alloc=82.0MB, time=11.68 memory used=652.4MB, alloc=82.0MB, time=12.84 memory used=702.7MB, alloc=82.0MB, time=13.58 memory used=735.1MB, alloc=82.0MB, time=13.74 memory used=771.5MB, alloc=82.0MB, time=14.00 memory used=802.6MB, alloc=82.0MB, time=14.16 memory used=846.7MB, alloc=82.0MB, time=17.40 memory used=878.7MB, alloc=82.0MB, time=17.58 memory used=909.1MB, alloc=82.0MB, time=17.72 memory used=932.9MB, alloc=82.0MB, time=17.84 memory used=960.7MB, alloc=82.0MB, time=17.97 memory used=993.6MB, alloc=82.0MB, time=18.10 memory used=1022.3MB, alloc=82.0MB, time=18.22 memory used=1042.7MB, alloc=82.0MB, time=18.32 memory used=1064.8MB, alloc=82.0MB, time=18.41 memory used=1089.6MB, alloc=82.0MB, time=18.51 memory used=1126.8MB, alloc=82.0MB, time=18.74 memory used=1156.4MB, alloc=82.0MB, time=18.89 memory used=1199.6MB, alloc=82.0MB, time=20.39 memory used=1229.6MB, alloc=82.0MB, time=20.53 memory used=1253.8MB, alloc=82.0MB, time=20.65 memory used=1280.7MB, alloc=82.0MB, time=20.78 memory used=1313.6MB, alloc=82.0MB, time=20.91 memory used=1334.9MB, alloc=82.0MB, time=20.99 memory used=1378.1MB, alloc=82.0MB, time=21.59 memory used=1409.3MB, alloc=82.0MB, time=21.75 memory used=1436.1MB, alloc=82.0MB, time=21.88 memory used=1470.2MB, alloc=82.0MB, time=22.03 memory used=1494.0MB, alloc=82.0MB, time=22.15 memory used=1516.8MB, alloc=82.0MB, time=22.27 memory used=1557.0MB, alloc=82.0MB, time=25.24 memory used=1601.1MB, alloc=82.0MB, time=29.23 memory used=1631.4MB, alloc=82.0MB, time=29.38 memory used=1658.1MB, alloc=82.0MB, time=29.51 memory used=1681.5MB, alloc=82.0MB, time=29.64 memory used=1708.3MB, alloc=82.0MB, time=29.78 memory used=1739.2MB, alloc=82.0MB, time=29.90 memory used=1774.1MB, alloc=82.0MB, time=30.05 memory used=1800.2MB, alloc=82.0MB, time=30.15 memory used=1820.1MB, alloc=82.0MB, time=30.25 memory used=1841.4MB, alloc=82.0MB, time=30.34 memory used=1863.3MB, alloc=82.0MB, time=30.43 memory used=1887.1MB, alloc=82.0MB, time=30.54 memory used=1913.0MB, alloc=82.0MB, time=30.64 memory used=1940.9MB, alloc=82.0MB, time=30.73 memory used=1972.0MB, alloc=82.0MB, time=30.84 memory used=2007.6MB, alloc=82.0MB, time=31.28 memory used=2034.6MB, alloc=82.0MB, time=31.56 memory used=2071.4MB, alloc=82.0MB, time=32.02 memory used=2099.9MB, alloc=82.0MB, time=32.17 memory used=2143.3MB, alloc=82.0MB, time=33.72 memory used=2174.1MB, alloc=82.0MB, time=33.87 memory used=2199.8MB, alloc=82.0MB, time=34.00 memory used=2226.5MB, alloc=82.0MB, time=34.13 memory used=2258.8MB, alloc=82.0MB, time=34.25 memory used=2282.3MB, alloc=82.0MB, time=34.35 memory used=2312.0MB, alloc=82.0MB, time=34.64 memory used=2375.7MB, alloc=82.0MB, time=37.62 memory used=2415.9MB, alloc=82.0MB, time=37.83 memory used=2438.2MB, alloc=82.0MB, time=37.98 memory used=2465.5MB, alloc=82.0MB, time=38.12 memory used=2498.2MB, alloc=82.0MB, time=38.27 memory used=2518.4MB, alloc=82.0MB, time=38.38 memory used=2551.2MB, alloc=82.0MB, time=42.99 memory used=2602.9MB, alloc=82.0MB, time=49.11 memory used=2628.6MB, alloc=82.0MB, time=49.26 memory used=2655.2MB, alloc=82.0MB, time=49.41 memory used=2686.6MB, alloc=82.0MB, time=49.55 memory used=2713.4MB, alloc=82.0MB, time=49.70 memory used=2732.6MB, alloc=82.0MB, time=49.81 memory used=2752.9MB, alloc=82.0MB, time=49.93 memory used=2774.3MB, alloc=82.0MB, time=50.06 memory used=2798.1MB, alloc=82.0MB, time=50.18 memory used=2823.0MB, alloc=82.0MB, time=50.32 memory used=2848.9MB, alloc=82.0MB, time=50.44 memory used=2875.9MB, alloc=82.0MB, time=50.57 memory used=2905.6MB, alloc=82.0MB, time=50.71 memory used=2936.2MB, alloc=82.0MB, time=50.85 memory used=2967.9MB, alloc=82.0MB, time=50.99 memory used=3002.4MB, alloc=82.0MB, time=51.13 memory used=3025.4MB, alloc=82.0MB, time=51.25 memory used=3042.3MB, alloc=106.0MB, time=51.37 memory used=3071.4MB, alloc=106.0MB, time=51.49 memory used=3102.0MB, alloc=106.0MB, time=51.62 memory used=3133.4MB, alloc=106.0MB, time=51.75 memory used=3167.5MB, alloc=106.0MB, time=51.88 memory used=3202.1MB, alloc=106.0MB, time=52.01 memory used=3237.2MB, alloc=106.0MB, time=52.14 memory used=3275.1MB, alloc=106.0MB, time=52.27 memory used=3313.4MB, alloc=106.0MB, time=52.41 memory used=3352.2MB, alloc=106.0MB, time=52.54 memory used=3393.6MB, alloc=106.0MB, time=52.68 memory used=3435.5MB, alloc=106.0MB, time=52.82 memory used=3480.0MB, alloc=106.0MB, time=52.97 memory used=3524.8MB, alloc=106.0MB, time=53.11 memory used=3572.1MB, alloc=106.0MB, time=53.26 memory used=3619.7MB, alloc=106.0MB, time=53.41 memory used=3669.7MB, alloc=106.0MB, time=53.55 memory used=3722.1MB, alloc=106.0MB, time=53.71 memory used=3776.7MB, alloc=106.0MB, time=53.86 memory used=3831.7MB, alloc=106.0MB, time=54.02 memory used=3881.1MB, alloc=115.8MB, time=54.18 memory used=3893.8MB, alloc=115.8MB, time=54.27 memory used=3901.8MB, alloc=115.8MB, time=54.36 memory used=3909.9MB, alloc=115.8MB, time=54.50 memory used=3918.9MB, alloc=115.8MB, time=54.59 memory used=3927.8MB, alloc=115.8MB, time=54.70 memory used=3936.7MB, alloc=115.8MB, time=54.79 memory used=3945.6MB, alloc=115.8MB, time=54.89 memory used=3954.5MB, alloc=115.8MB, time=54.98 memory used=3963.3MB, alloc=115.8MB, time=55.07 memory used=3972.1MB, alloc=115.8MB, time=55.15 memory used=3980.9MB, alloc=115.8MB, time=55.23 memory used=3989.7MB, alloc=115.8MB, time=55.33 memory used=3998.4MB, alloc=115.8MB, time=55.42 memory used=4007.1MB, alloc=115.8MB, time=55.51 memory used=4015.8MB, alloc=115.8MB, time=55.59 memory used=4024.5MB, alloc=115.8MB, time=55.67 memory used=4033.1MB, alloc=115.8MB, time=55.77 memory used=4041.7MB, alloc=115.8MB, time=55.88 memory used=4050.3MB, alloc=115.8MB, time=55.97 memory used=4058.8MB, alloc=115.8MB, time=56.06 memory used=4067.6MB, alloc=115.8MB, time=56.16 memory used=4077.9MB, alloc=115.8MB, time=56.26 memory used=4086.8MB, alloc=115.8MB, time=56.34 memory used=4096.9MB, alloc=115.8MB, time=56.42 memory used=4107.4MB, alloc=115.8MB, time=56.51 memory used=4117.8MB, alloc=115.8MB, time=56.59 memory used=4128.1MB, alloc=115.8MB, time=56.69 memory used=4138.4MB, alloc=115.8MB, time=56.77 memory used=4148.6MB, alloc=115.8MB, time=56.85 memory used=4158.8MB, alloc=115.8MB, time=56.94 memory used=4168.9MB, alloc=115.8MB, time=57.05 memory used=4178.9MB, alloc=115.8MB, time=57.15 memory used=4188.9MB, alloc=115.8MB, time=57.26 memory used=4198.8MB, alloc=115.8MB, time=57.35 memory used=4209.0MB, alloc=115.8MB, time=57.44 memory used=4220.5MB, alloc=115.8MB, time=57.52 memory used=4232.1MB, alloc=115.8MB, time=57.63 memory used=4243.7MB, alloc=115.8MB, time=57.75 memory used=4255.1MB, alloc=115.8MB, time=57.84 memory used=4266.4MB, alloc=115.8MB, time=57.94 memory used=4277.7MB, alloc=115.8MB, time=58.04 memory used=4288.8MB, alloc=115.8MB, time=58.14 memory used=4299.8MB, alloc=115.8MB, time=58.23 memory used=4311.0MB, alloc=115.8MB, time=58.36 memory used=4323.3MB, alloc=115.8MB, time=58.47 memory used=4335.7MB, alloc=115.8MB, time=58.55 memory used=4348.1MB, alloc=115.8MB, time=58.64 memory used=4360.2MB, alloc=115.8MB, time=58.72 memory used=4372.1MB, alloc=115.8MB, time=58.82 memory used=4384.2MB, alloc=115.8MB, time=58.91 memory used=4397.1MB, alloc=115.8MB, time=59.03 memory used=4410.1MB, alloc=115.8MB, time=59.12 memory used=4422.8MB, alloc=115.8MB, time=59.21 memory used=4435.8MB, alloc=115.8MB, time=59.29 memory used=4449.1MB, alloc=115.8MB, time=59.40 memory used=4462.5MB, alloc=115.8MB, time=59.49 memory used=4476.1MB, alloc=115.8MB, time=59.59 memory used=4489.8MB, alloc=115.8MB, time=59.69 memory used=4503.9MB, alloc=115.8MB, time=59.78 memory used=4518.2MB, alloc=115.8MB, time=59.89 memory used=4532.7MB, alloc=115.8MB, time=59.99 memory used=4548.2MB, alloc=115.8MB, time=60.10 memory used=4563.6MB, alloc=115.8MB, time=60.19 memory used=4579.7MB, alloc=115.8MB, time=60.28 memory used=4596.0MB, alloc=115.8MB, time=60.38 memory 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memory used=6047.5MB, alloc=115.8MB, time=100.13 memory used=6078.6MB, alloc=115.8MB, time=100.30 memory used=6113.1MB, alloc=115.8MB, time=100.49 memory used=6151.8MB, alloc=115.8MB, time=100.68 memory used=6194.7MB, alloc=115.8MB, time=100.89 memory used=6240.3MB, alloc=115.8MB, time=101.09 memory used=6290.2MB, alloc=115.8MB, time=101.29 memory used=6343.1MB, alloc=115.8MB, time=101.49 memory used=6372.5MB, alloc=115.8MB, time=101.63 memory used=6400.3MB, alloc=115.8MB, time=101.76 memory used=6428.9MB, alloc=115.8MB, time=101.90 memory used=6458.1MB, alloc=115.8MB, time=102.03 memory used=6489.9MB, alloc=115.8MB, time=102.17 memory used=6522.1MB, alloc=115.8MB, time=102.30 memory used=6554.8MB, alloc=115.8MB, time=102.44 memory used=6590.2MB, alloc=115.8MB, time=102.58 memory used=6626.0MB, alloc=115.8MB, time=102.73 memory used=6662.2MB, alloc=115.8MB, time=102.87 memory used=6701.0MB, alloc=115.8MB, time=103.02 memory used=6740.2MB, alloc=115.8MB, time=103.17 memory 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used=16043.0MB, alloc=395.8MB, time=194.47 memory used=16258.2MB, alloc=395.8MB, time=194.97 memory used=16485.5MB, alloc=395.8MB, time=195.47 memory used=16730.2MB, alloc=395.8MB, time=196.00 memory used=16953.7MB, alloc=395.8MB, time=196.49 memory used=17138.2MB, alloc=395.8MB, time=196.90 memory used=17337.3MB, alloc=395.8MB, time=197.33 memory used=17542.0MB, alloc=395.8MB, time=198.50 memory used=17611.5MB, alloc=395.8MB, time=199.40 memory used=17676.7MB, alloc=395.8MB, time=199.69 |\^/| 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(); 1428267231 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 2 F := [4 x y z - 9 x z + 5 x z + 3, 3 x y - 14 x z - 9 x - 3 y, 2 2 2 2 4 -9 x z - 13 y z - 15 z + 3 x y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 3 2 2 2 3 G := [-14 x z + 4 y + 3 x y - 4 y z, 6 x z - 16 x y z + 6 y z + 17 z , 2 4 6 x y z + 12 z - 20 y z - z] > Problem := [F,G]; 2 3 2 3 2 2 Problem := [[4 x y z - 9 x z + 5 x z + 3, 3 x y - 14 x z - 9 x - 3 y, 2 2 2 2 4 -9 x z - 13 y z - 15 z + 3 x y z], [ 2 2 4 2 2 3 2 2 2 3 -14 x z + 4 y + 3 x y - 4 y z, 6 x z - 16 x y z + 6 y z + 17 z , 2 4 6 x y z + 12 z - 20 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=4.4MB, alloc=32.3MB, time=0.31 memory used=24.5MB, alloc=32.3MB, time=0.84 memory used=42.7MB, alloc=56.3MB, time=1.33 memory used=85.4MB, alloc=62.8MB, time=3.01 memory used=125.8MB, alloc=67.2MB, time=3.25 memory used=164.2MB, alloc=67.2MB, time=3.76 memory used=202.4MB, alloc=67.2MB, time=4.89 memory used=230.6MB, alloc=67.2MB, time=5.03 memory used=254.1MB, alloc=67.2MB, time=5.15 memory used=277.2MB, alloc=67.2MB, time=5.25 memory used=304.0MB, alloc=67.2MB, time=5.36 memory used=332.7MB, alloc=67.2MB, time=5.48 memory used=353.1MB, alloc=67.2MB, time=5.56 memory used=383.5MB, alloc=67.2MB, time=5.94 memory used=408.8MB, alloc=67.2MB, time=6.25 memory used=435.3MB, alloc=67.2MB, time=6.41 memory used=475.2MB, alloc=81.9MB, time=7.05 memory used=502.6MB, alloc=81.9MB, time=7.16 memory used=538.9MB, alloc=81.9MB, time=7.32 memory used=565.8MB, alloc=81.9MB, time=7.44 memory used=606.2MB, alloc=83.8MB, time=8.84 memory used=625.3MB, alloc=83.8MB, time=8.93 memory used=647.2MB, alloc=83.8MB, time=9.04 memory used=680.6MB, alloc=83.8MB, time=9.16 memory used=717.0MB, alloc=83.8MB, time=9.29 memory used=756.1MB, alloc=83.8MB, time=9.41 memory used=798.1MB, alloc=83.8MB, time=9.52 memory used=827.3MB, alloc=83.8MB, time=9.62 memory used=840.1MB, alloc=83.8MB, time=9.69 memory used=853.0MB, alloc=83.8MB, time=9.76 memory used=867.7MB, alloc=83.8MB, time=9.87 memory used=886.2MB, alloc=83.8MB, time=9.96 memory used=905.9MB, alloc=83.8MB, time=10.06 memory used=934.6MB, alloc=83.8MB, time=10.18 memory used=969.4MB, alloc=83.8MB, time=10.30 memory used=1007.1MB, alloc=83.8MB, time=10.45 memory used=1047.4MB, alloc=83.8MB, time=10.57 memory used=1090.6MB, alloc=83.8MB, time=10.69 memory used=1104.1MB, alloc=83.8MB, time=10.76 memory used=1116.9MB, alloc=83.8MB, time=10.83 memory used=1129.9MB, alloc=83.8MB, time=10.90 memory used=1184.8MB, alloc=83.8MB, time=13.55 memory used=1228.0MB, alloc=83.8MB, time=14.57 memory used=1271.5MB, alloc=107.8MB, time=15.58 memory used=1340.8MB, alloc=107.8MB, time=17.08 memory used=1404.2MB, alloc=363.8MB, time=18.62 memory used=1462.8MB, alloc=363.8MB, time=19.50 memory used=1495.6MB, alloc=363.8MB, time=19.70 memory used=1526.2MB, alloc=363.8MB, time=19.88 memory used=1559.8MB, alloc=363.8MB, time=20.29 memory used=1591.2MB, alloc=363.8MB, time=20.57 memory used=1629.9MB, alloc=363.8MB, time=20.92 memory used=1658.8MB, alloc=363.8MB, time=21.07 memory used=1696.5MB, alloc=363.8MB, time=21.27 memory used=1732.1MB, alloc=363.8MB, time=21.81 memory used=1774.3MB, alloc=363.8MB, time=22.07 memory used=1802.4MB, alloc=363.8MB, time=22.26 memory used=1831.3MB, alloc=363.8MB, time=22.46 memory used=1867.9MB, alloc=363.8MB, time=22.94 memory used=1907.2MB, alloc=363.8MB, time=23.31 memory used=1937.0MB, alloc=363.8MB, time=23.47 memory used=1974.1MB, alloc=363.8MB, time=23.67 memory used=2003.8MB, alloc=363.8MB, time=23.83 memory used=2057.7MB, alloc=363.8MB, time=28.04 memory used=2087.1MB, alloc=363.8MB, time=28.22 memory used=2114.3MB, alloc=363.8MB, time=28.39 memory used=2142.4MB, alloc=363.8MB, time=28.56 memory used=2190.0MB, alloc=363.8MB, time=28.97 memory used=2217.8MB, alloc=363.8MB, time=29.16 memory used=2247.0MB, alloc=363.8MB, time=29.34 memory used=2294.4MB, alloc=363.8MB, time=29.81 memory used=2322.6MB, alloc=363.8MB, time=30.00 memory used=2352.4MB, alloc=363.8MB, time=30.18 memory used=2405.5MB, alloc=363.8MB, time=34.31 memory used=2434.9MB, alloc=363.8MB, time=34.50 memory used=2463.3MB, alloc=363.8MB, time=34.67 memory used=2489.8MB, alloc=363.8MB, time=34.83 memory used=2535.6MB, alloc=363.8MB, time=35.25 memory used=2564.4MB, alloc=363.8MB, time=35.45 memory used=2594.3MB, alloc=363.8MB, time=35.62 memory used=2637.6MB, alloc=363.8MB, time=36.09 memory used=2668.6MB, alloc=387.8MB, time=36.30 memory used=2714.3MB, alloc=387.8MB, time=36.54 memory used=2786.1MB, alloc=387.8MB, time=40.67 memory used=2830.5MB, alloc=387.8MB, time=40.89 memory used=2926.2MB, alloc=387.8MB, time=45.80 memory used=2977.4MB, alloc=387.8MB, time=46.07 memory used=3019.5MB, alloc=387.8MB, time=46.28 memory used=3117.6MB, alloc=387.8MB, time=51.10 memory used=3163.9MB, alloc=387.8MB, time=51.34 memory used=3221.7MB, alloc=387.8MB, time=52.07 memory used=3316.9MB, alloc=387.8MB, time=54.03 memory used=3390.5MB, alloc=387.8MB, time=55.33 memory used=3455.6MB, alloc=387.8MB, time=55.75 memory used=3514.9MB, alloc=387.8MB, time=56.11 memory used=3574.4MB, alloc=387.8MB, time=57.34 memory used=3640.4MB, alloc=387.8MB, time=57.77 memory used=3701.5MB, alloc=387.8MB, time=58.14 memory used=3756.7MB, alloc=387.8MB, time=59.29 memory used=3824.9MB, alloc=387.8MB, time=59.75 memory used=3886.5MB, alloc=387.8MB, time=60.14 memory used=3940.1MB, alloc=387.8MB, time=60.55 memory used=4026.7MB, alloc=411.8MB, time=68.92 memory used=4122.6MB, alloc=411.8MB, time=90.78 memory used=4204.1MB, alloc=411.8MB, time=91.21 memory used=4256.9MB, alloc=411.8MB, time=91.54 memory used=4305.9MB, alloc=411.8MB, time=91.85 memory used=4361.7MB, alloc=411.8MB, time=92.17 memory used=4475.5MB, alloc=411.8MB, time=121.54 memory used=4560.8MB, alloc=411.8MB, time=122.79 memory used=4633.5MB, alloc=411.8MB, time=123.17 memory used=4680.1MB, alloc=411.8MB, time=123.46 memory used=4730.5MB, alloc=411.8MB, time=123.76 memory used=4793.1MB, alloc=411.8MB, time=124.30 memory used=4899.4MB, alloc=411.8MB, time=125.82 memory used=4979.8MB, alloc=411.8MB, time=127.38 memory used=5032.6MB, alloc=411.8MB, time=127.71 memory used=5082.6MB, alloc=411.8MB, time=128.01 memory used=5141.1MB, alloc=411.8MB, time=128.32 memory used=5206.9MB, alloc=411.8MB, time=128.65 memory used=5247.7MB, alloc=411.8MB, time=128.92 memory used=5287.5MB, alloc=411.8MB, time=129.18 memory used=5329.2MB, alloc=411.8MB, time=129.44 memory used=5374.5MB, alloc=411.8MB, time=129.70 memory used=5421.1MB, alloc=411.8MB, time=129.95 memory used=5470.7MB, alloc=411.8MB, time=130.22 memory used=5523.8MB, alloc=411.8MB, time=130.50 memory used=5580.3MB, alloc=411.8MB, time=130.78 memory used=5640.1MB, alloc=411.8MB, time=131.06 memory used=5704.3MB, alloc=411.8MB, time=131.35 memory used=5757.5MB, alloc=411.8MB, time=131.60 memory used=5802.5MB, alloc=411.8MB, time=131.82 memory used=5837.8MB, alloc=411.8MB, time=132.02 memory used=5874.4MB, alloc=411.8MB, time=132.24 memory used=5912.6MB, alloc=411.8MB, time=132.45 memory used=5953.4MB, alloc=411.8MB, time=132.67 memory used=5995.4MB, alloc=411.8MB, time=132.89 memory used=6039.7MB, alloc=411.8MB, time=133.10 memory used=6087.1MB, alloc=411.8MB, time=133.31 memory used=6137.1MB, alloc=411.8MB, time=133.52 memory used=6217.2MB, alloc=411.8MB, time=135.37 memory used=6277.9MB, alloc=411.8MB, time=135.73 memory used=6325.3MB, alloc=411.8MB, time=136.05 memory used=6382.2MB, alloc=411.8MB, time=136.37 memory used=6449.0MB, alloc=411.8MB, time=136.70 memory used=6494.9MB, alloc=411.8MB, time=136.97 memory used=6533.4MB, alloc=411.8MB, time=137.23 memory used=6574.9MB, alloc=411.8MB, time=137.50 memory used=6619.9MB, alloc=411.8MB, time=137.77 memory used=6666.4MB, alloc=411.8MB, time=138.03 memory used=6715.8MB, alloc=411.8MB, time=138.31 memory used=6768.9MB, alloc=411.8MB, time=138.58 memory used=6825.3MB, alloc=411.8MB, time=138.87 memory used=6885.2MB, alloc=411.8MB, time=139.14 memory used=6949.4MB, alloc=411.8MB, time=139.43 memory used=7005.2MB, alloc=411.8MB, time=139.69 memory used=7052.0MB, alloc=411.8MB, time=139.92 memory used=7087.9MB, alloc=411.8MB, time=140.13 memory used=7125.0MB, alloc=411.8MB, time=140.35 memory used=7163.5MB, alloc=411.8MB, time=140.57 memory used=7204.3MB, alloc=411.8MB, time=140.79 memory used=7246.7MB, alloc=411.8MB, time=141.02 memory used=7291.3MB, alloc=411.8MB, time=141.24 memory used=7339.0MB, alloc=411.8MB, time=141.45 memory used=7389.5MB, alloc=411.8MB, time=141.66 memory used=7474.1MB, alloc=411.8MB, time=168.78 memory used=7670.7MB, alloc=411.8MB, time=175.32 memory used=7726.1MB, alloc=411.8MB, time=175.64 memory used=7776.3MB, alloc=411.8MB, time=175.94 memory used=7819.3MB, alloc=411.8MB, time=176.22 memory used=7868.1MB, alloc=411.8MB, time=176.51 memory used=7923.4MB, alloc=411.8MB, time=176.79 memory used=7985.2MB, alloc=411.8MB, time=177.08 memory used=8044.1MB, alloc=411.8MB, time=177.35 memory used=8081.2MB, alloc=411.8MB, time=177.58 memory used=8118.5MB, alloc=411.8MB, time=177.81 memory used=8158.6MB, alloc=411.8MB, time=178.03 memory used=8200.7MB, alloc=411.8MB, time=178.26 memory used=8244.6MB, alloc=411.8MB, time=178.50 memory used=8291.6MB, alloc=411.8MB, time=178.73 memory used=8340.3MB, alloc=411.8MB, time=178.96 memory used=8392.8MB, alloc=411.8MB, time=179.21 memory used=8447.6MB, alloc=411.8MB, time=179.45 memory used=8505.6MB, alloc=411.8MB, time=179.70 memory used=8567.4MB, alloc=411.8MB, time=179.95 memory used=8649.6MB, alloc=411.8MB, time=180.25 memory used=8848.8MB, alloc=411.8MB, time=182.40 memory used=8899.5MB, alloc=411.8MB, time=182.73 memory used=8949.4MB, alloc=411.8MB, time=183.04 memory used=9008.1MB, alloc=411.8MB, time=183.36 memory used=9073.3MB, alloc=411.8MB, time=183.68 memory used=9114.2MB, alloc=411.8MB, time=183.95 memory used=9152.9MB, alloc=411.8MB, time=184.22 memory used=9194.6MB, alloc=411.8MB, time=184.48 memory used=9237.8MB, alloc=411.8MB, time=184.75 memory used=9284.1MB, alloc=411.8MB, time=185.01 memory used=9333.7MB, alloc=411.8MB, time=185.29 memory used=9386.9MB, alloc=411.8MB, time=185.58 memory used=9443.3MB, alloc=411.8MB, time=185.87 memory used=9502.8MB, alloc=411.8MB, time=186.15 memory used=9567.5MB, alloc=411.8MB, time=186.44 memory used=9621.1MB, alloc=411.8MB, time=186.69 memory used=9665.7MB, alloc=411.8MB, time=186.93 memory used=9701.0MB, alloc=411.8MB, time=187.14 memory used=9737.6MB, alloc=411.8MB, time=187.37 memory used=9775.8MB, alloc=411.8MB, time=187.58 |\^/| 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(); 1428267531 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 2 F := [5 x - 3 y z + 8 y z + 5 y, 9 y - 20 x z - 11 y + 16 z , 2 2 3 2 y z - 6 x + 19 y + 3 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; G := 3 3 3 3 2 2 2 [-5 x + 14 y + 15 z , 15 y - 4 y z + 12, -y z - 14 x z - 6 y z + 4 y] > Problem := [F,G]; 4 2 2 3 2 2 Problem := [[5 x - 3 y z + 8 y z + 5 y, 9 y - 20 x z - 11 y + 16 z , 2 2 3 2 y z - 6 x + 19 y + 3 x], 3 3 3 3 2 2 2 [-5 x + 14 y + 15 z , 15 y - 4 y z + 12, -y z - 14 x z - 6 y z + 4 y] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.32 memory used=24.3MB, alloc=32.3MB, time=0.73 memory used=44.5MB, alloc=33.3MB, time=1.02 memory used=56.4MB, alloc=33.3MB, time=1.09 memory used=71.9MB, alloc=33.3MB, time=1.20 memory used=88.1MB, alloc=33.3MB, time=1.31 memory used=109.5MB, alloc=33.3MB, time=2.56 memory used=121.6MB, alloc=33.3MB, time=2.62 memory used=137.6MB, alloc=33.3MB, time=2.76 memory used=151.6MB, alloc=33.3MB, time=2.82 memory used=166.9MB, alloc=33.3MB, time=2.92 memory used=184.5MB, alloc=33.3MB, time=3.07 memory used=204.5MB, alloc=33.3MB, time=4.26 memory used=216.5MB, alloc=33.3MB, time=4.32 memory used=234.4MB, alloc=33.3MB, time=4.62 memory used=260.2MB, alloc=61.3MB, time=6.36 memory used=302.6MB, alloc=62.8MB, time=16.20 memory used=330.8MB, alloc=62.8MB, time=16.31 memory used=356.8MB, alloc=62.8MB, time=16.40 memory used=384.6MB, alloc=62.8MB, time=16.49 memory used=429.8MB, alloc=63.4MB, time=17.08 memory used=472.7MB, alloc=63.4MB, time=17.98 memory used=517.4MB, alloc=63.4MB, time=18.94 memory used=558.1MB, alloc=63.4MB, time=19.57 memory used=603.3MB, alloc=71.4MB, time=20.53 memory used=645.5MB, alloc=71.4MB, time=21.35 memory used=673.5MB, alloc=71.4MB, time=21.50 memory used=693.6MB, alloc=71.4MB, time=21.61 memory used=718.5MB, alloc=71.4MB, time=21.72 memory used=747.2MB, alloc=71.4MB, time=21.85 memory used=763.2MB, alloc=71.4MB, time=21.95 memory used=780.2MB, alloc=71.4MB, time=22.04 memory used=799.1MB, alloc=71.4MB, time=22.15 memory used=819.6MB, alloc=71.4MB, time=22.26 memory used=841.6MB, alloc=71.4MB, time=22.37 memory used=865.7MB, alloc=71.4MB, time=22.47 memory used=892.4MB, alloc=71.4MB, time=22.58 memory used=919.8MB, alloc=71.4MB, time=22.69 memory used=948.8MB, alloc=71.4MB, time=23.04 memory used=972.5MB, alloc=71.4MB, time=23.18 memory used=997.3MB, alloc=71.4MB, time=23.29 memory used=1021.5MB, alloc=71.4MB, time=23.41 memory used=1039.3MB, alloc=71.4MB, time=23.51 memory used=1060.1MB, alloc=71.4MB, time=23.61 memory used=1095.4MB, alloc=71.4MB, time=28.00 memory used=1123.6MB, alloc=71.4MB, time=28.37 memory used=1145.8MB, alloc=71.4MB, time=28.49 memory used=1166.8MB, alloc=71.4MB, time=28.60 memory used=1192.2MB, alloc=71.4MB, time=28.72 memory used=1215.6MB, alloc=71.4MB, time=28.82 memory used=1232.1MB, alloc=71.4MB, time=28.91 memory used=1250.7MB, alloc=71.4MB, time=28.99 memory used=1271.8MB, alloc=71.4MB, time=29.09 memory used=1299.4MB, alloc=71.4MB, time=29.27 memory used=1343.8MB, alloc=71.4MB, time=30.22 memory used=1368.1MB, alloc=71.4MB, time=30.36 memory used=1386.5MB, alloc=71.4MB, time=30.49 memory used=1408.7MB, alloc=71.4MB, time=30.63 memory used=1434.7MB, alloc=71.4MB, time=30.77 memory used=1462.0MB, alloc=71.4MB, time=30.89 memory used=1476.8MB, alloc=95.4MB, time=31.02 memory used=1506.3MB, alloc=95.4MB, time=31.16 memory used=1539.6MB, alloc=95.4MB, time=31.31 memory used=1576.0MB, alloc=95.4MB, time=31.46 memory used=1616.9MB, alloc=95.4MB, time=31.63 memory used=1662.0MB, alloc=95.4MB, time=31.79 memory used=1712.3MB, alloc=95.4MB, time=31.97 memory used=1741.3MB, alloc=95.4MB, time=32.08 memory used=1769.6MB, alloc=95.4MB, time=32.20 memory used=1799.9MB, alloc=95.4MB, time=32.30 memory used=1844.7MB, alloc=95.4MB, time=35.46 memory used=1900.9MB, alloc=95.4MB, time=65.82 memory used=1946.6MB, alloc=95.4MB, time=70.52 memory used=1986.3MB, alloc=95.4MB, time=70.70 memory used=2023.3MB, alloc=95.4MB, time=70.86 memory used=2068.9MB, alloc=95.4MB, time=71.04 memory used=2107.2MB, alloc=95.4MB, time=71.20 memory used=2136.6MB, alloc=95.4MB, time=71.31 memory used=2169.2MB, alloc=95.4MB, time=71.43 memory used=2204.5MB, alloc=95.4MB, time=71.55 memory used=2243.5MB, alloc=95.4MB, time=71.68 memory used=2285.9MB, alloc=95.4MB, time=71.81 memory used=2333.1MB, alloc=95.4MB, time=71.95 memory used=2367.2MB, alloc=107.8MB, time=72.08 memory used=2378.2MB, alloc=107.8MB, time=72.15 memory used=2389.8MB, alloc=107.8MB, time=72.25 memory used=2450.8MB, alloc=107.8MB, time=73.04 memory used=2489.4MB, alloc=107.8MB, time=73.21 memory used=2518.9MB, alloc=107.8MB, time=73.80 memory used=2543.1MB, alloc=107.8MB, time=73.92 memory used=2569.8MB, alloc=107.8MB, time=74.05 memory used=2599.0MB, alloc=107.8MB, time=74.18 memory used=2630.8MB, alloc=107.8MB, time=74.30 memory used=2681.8MB, alloc=107.8MB, time=74.67 memory used=2780.9MB, alloc=107.8MB, time=77.59 memory used=2827.7MB, alloc=107.8MB, time=77.88 memory used=2861.2MB, alloc=107.8MB, time=78.03 memory used=2905.9MB, alloc=107.8MB, time=78.21 memory used=2936.7MB, alloc=107.8MB, time=78.34 memory used=2967.3MB, alloc=107.8MB, time=78.47 memory used=3002.3MB, alloc=107.8MB, time=78.59 memory used=3088.6MB, alloc=107.8MB, time=79.75 memory used=3159.3MB, alloc=107.8MB, time=80.91 memory used=3234.3MB, alloc=107.8MB, time=81.69 memory used=3310.6MB, alloc=107.8MB, time=82.50 memory used=3386.7MB, alloc=107.8MB, time=83.39 memory used=3462.3MB, alloc=107.8MB, time=84.43 memory used=3535.8MB, alloc=107.8MB, time=85.78 memory used=3609.1MB, alloc=107.8MB, time=87.29 memory used=3683.5MB, alloc=107.8MB, time=89.05 memory used=3759.9MB, alloc=107.8MB, time=90.72 memory used=3834.4MB, alloc=107.8MB, time=92.75 memory used=3907.8MB, alloc=107.8MB, time=95.02 memory used=3985.4MB, alloc=107.8MB, time=97.06 memory used=4065.2MB, alloc=107.8MB, time=100.66 memory used=4148.8MB, alloc=107.8MB, time=102.35 memory used=4195.9MB, alloc=107.8MB, time=102.83 memory used=4226.2MB, alloc=107.8MB, time=102.99 memory used=4264.5MB, alloc=107.8MB, time=103.17 memory used=4296.1MB, alloc=107.8MB, time=103.31 memory used=4322.7MB, alloc=107.8MB, time=103.44 memory used=4352.3MB, alloc=107.8MB, time=103.57 memory used=4386.3MB, alloc=107.8MB, time=103.71 memory used=4426.0MB, alloc=107.8MB, time=103.85 memory used=4520.0MB, alloc=107.8MB, time=105.21 memory used=4596.0MB, alloc=107.8MB, time=106.17 memory used=4652.7MB, alloc=107.8MB, time=106.99 memory used=4686.2MB, alloc=107.8MB, time=107.18 memory used=4736.7MB, alloc=107.8MB, time=113.40 memory used=4766.5MB, alloc=107.8MB, time=113.57 memory used=4797.8MB, alloc=107.8MB, time=113.71 memory used=4858.3MB, alloc=363.8MB, time=115.06 memory used=4918.5MB, alloc=387.8MB, time=116.25 memory used=4984.8MB, alloc=387.8MB, time=117.43 memory used=5076.1MB, alloc=387.8MB, time=120.86 memory used=5122.9MB, alloc=387.8MB, time=121.12 memory used=5193.1MB, alloc=387.8MB, time=127.84 memory used=5233.3MB, alloc=387.8MB, time=128.06 memory used=5277.1MB, alloc=387.8MB, time=128.27 memory used=5357.0MB, alloc=387.8MB, time=129.49 memory used=5439.2MB, alloc=387.8MB, time=130.92 memory used=5505.1MB, alloc=387.8MB, time=131.71 memory used=5540.6MB, alloc=387.8MB, time=131.92 memory used=5585.9MB, alloc=387.8MB, time=132.14 memory used=5618.9MB, alloc=387.8MB, time=132.32 memory used=5650.4MB, alloc=387.8MB, time=132.49 memory used=5688.0MB, alloc=387.8MB, time=132.66 memory used=5779.4MB, alloc=387.8MB, time=133.97 memory used=5872.5MB, alloc=387.8MB, time=135.18 memory used=5967.8MB, alloc=411.8MB, time=136.82 memory used=6043.8MB, alloc=411.8MB, time=138.81 memory used=6095.9MB, alloc=411.8MB, time=139.13 memory used=6153.9MB, alloc=411.8MB, time=139.44 memory used=6203.2MB, alloc=411.8MB, time=139.70 memory used=6245.3MB, alloc=411.8MB, time=139.95 memory used=6292.8MB, alloc=411.8MB, time=140.21 memory used=6346.9MB, alloc=411.8MB, time=140.47 memory used=6406.2MB, alloc=411.8MB, time=140.74 memory used=6476.5MB, alloc=411.8MB, time=141.03 memory used=6649.1MB, alloc=411.8MB, time=141.86 memory used=6826.4MB, alloc=411.8MB, time=142.43 memory used=7049.8MB, alloc=411.8MB, time=143.06 memory used=7174.8MB, alloc=411.8MB, time=144.13 memory used=7246.8MB, alloc=411.8MB, time=144.92 memory used=7314.3MB, alloc=411.8MB, time=145.25 memory used=7387.6MB, alloc=411.8MB, time=179.28 |\^/| 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(); 1428267831 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 F := [13 x - 12 z, 11 x z + 6 y z - 2 z - 4 y , 2 2 3 17 y z + 7 x + x y z - 3 x y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 4 2 G := [6 x z + 10 x z + 5 z - 18, 14 x y - 9 y - 2 x y z - x , 4 2 -2 x - 14 x y + 8 y z + 10] > Problem := [F,G]; 2 3 2 3 2 Problem := [[13 x - 12 z, 11 x z + 6 y z - 2 z - 4 y , 2 2 3 2 2 3 17 y z + 7 x + x y z - 3 x y], [6 x z + 10 x z + 5 z - 18, 3 4 2 4 2 14 x y - 9 y - 2 x y z - x , -2 x - 14 x y + 8 y z + 10]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.84 memory used=45.8MB, alloc=36.3MB, time=1.29 memory used=64.5MB, alloc=60.3MB, time=1.77 memory used=108.9MB, alloc=68.3MB, time=2.82 memory used=152.0MB, alloc=68.3MB, time=3.69 memory used=199.8MB, alloc=68.3MB, time=4.66 memory used=245.4MB, alloc=68.3MB, time=5.46 memory used=290.0MB, alloc=92.3MB, time=6.49 memory used=357.3MB, alloc=92.3MB, time=7.97 memory used=419.9MB, alloc=92.3MB, time=9.38 memory used=486.1MB, alloc=92.3MB, time=10.55 memory used=546.8MB, alloc=116.3MB, time=11.89 memory used=602.8MB, alloc=372.3MB, time=13.28 memory used=697.3MB, alloc=372.3MB, time=15.26 memory used=750.2MB, alloc=372.3MB, time=15.79 memory used=837.6MB, alloc=372.3MB, time=17.49 memory used=938.9MB, alloc=396.3MB, time=19.48 memory used=996.9MB, alloc=396.3MB, time=19.82 memory used=1060.2MB, alloc=396.3MB, time=20.12 memory used=1102.8MB, alloc=396.3MB, time=20.40 memory used=1150.6MB, alloc=396.3MB, time=20.66 memory used=1205.7MB, alloc=396.3MB, time=20.94 memory used=1270.8MB, alloc=396.3MB, time=21.22 memory used=1314.3MB, alloc=396.3MB, time=21.45 memory used=1378.5MB, alloc=396.3MB, time=22.06 memory used=1431.3MB, alloc=396.3MB, time=22.37 memory used=1485.3MB, alloc=396.3MB, time=22.67 memory used=1531.5MB, alloc=396.3MB, time=22.93 memory used=1587.6MB, alloc=396.3MB, time=23.21 memory used=1662.5MB, alloc=396.3MB, time=25.22 memory used=1719.1MB, alloc=396.3MB, time=25.55 memory used=1772.2MB, alloc=396.3MB, time=25.84 memory used=1822.2MB, alloc=396.3MB, time=26.09 memory used=1939.9MB, alloc=396.3MB, time=28.47 memory used=2016.4MB, alloc=396.3MB, time=29.44 memory used=2122.5MB, alloc=396.3MB, time=31.55 memory used=2180.8MB, alloc=420.3MB, time=31.97 memory used=2247.5MB, alloc=420.3MB, time=32.35 memory used=2308.9MB, alloc=420.3MB, time=32.71 memory used=2363.8MB, alloc=420.3MB, time=33.04 memory used=2431.7MB, alloc=420.3MB, time=33.39 memory used=2515.6MB, alloc=420.3MB, time=34.19 memory used=2586.8MB, alloc=420.3MB, time=34.57 memory used=2640.5MB, alloc=420.3MB, time=34.92 memory used=2722.0MB, alloc=420.3MB, time=36.81 memory used=2783.3MB, alloc=420.3MB, time=37.17 memory used=2917.1MB, alloc=420.3MB, time=39.35 memory used=3074.1MB, alloc=420.3MB, time=42.43 memory used=3216.1MB, alloc=420.3MB, time=46.91 memory used=3317.1MB, alloc=420.3MB, time=48.24 memory used=3401.5MB, alloc=420.3MB, time=49.16 memory used=3475.1MB, alloc=420.3MB, time=49.71 memory used=3548.5MB, alloc=420.3MB, time=50.96 memory used=3699.8MB, alloc=420.3MB, time=54.10 memory used=3841.6MB, alloc=444.3MB, time=56.44 memory used=3960.4MB, alloc=444.3MB, time=58.59 memory used=4060.4MB, alloc=444.3MB, time=62.38 memory used=4186.0MB, alloc=444.3MB, time=64.45 memory used=4345.9MB, alloc=444.3MB, time=66.05 memory used=4470.2MB, alloc=444.3MB, time=68.46 memory used=4546.0MB, alloc=444.3MB, time=69.63 memory used=4612.3MB, alloc=444.3MB, time=70.21 memory used=4688.5MB, alloc=468.3MB, time=71.50 memory used=4832.3MB, alloc=468.3MB, time=73.91 memory used=4923.7MB, alloc=468.3MB, time=76.36 memory used=5013.9MB, alloc=468.3MB, time=78.77 memory used=5085.1MB, alloc=468.3MB, time=80.62 memory used=5169.8MB, alloc=492.3MB, time=82.77 memory used=5237.0MB, alloc=492.3MB, time=84.74 memory used=5295.6MB, alloc=492.3MB, time=86.53 memory used=5352.3MB, alloc=492.3MB, time=88.04 memory used=5411.5MB, alloc=492.3MB, time=89.45 memory used=5484.4MB, alloc=492.3MB, time=91.04 memory used=5531.1MB, alloc=492.3MB, time=92.50 memory used=5576.7MB, alloc=492.3MB, time=93.86 memory used=5647.5MB, alloc=492.3MB, time=95.63 memory used=5697.0MB, alloc=492.3MB, time=96.85 memory used=5756.6MB, alloc=492.3MB, time=98.46 memory used=5801.6MB, alloc=492.3MB, time=99.87 memory used=5863.8MB, alloc=492.3MB, time=101.20 memory used=6052.1MB, alloc=516.3MB, time=104.69 memory used=6265.3MB, alloc=540.3MB, time=109.45 memory used=6465.1MB, alloc=564.3MB, time=114.43 memory used=6682.0MB, alloc=588.3MB, time=118.66 memory used=6826.9MB, alloc=612.3MB, time=123.15 memory used=6991.4MB, alloc=636.3MB, time=127.36 memory used=7151.7MB, alloc=636.3MB, time=131.79 memory used=7328.0MB, alloc=660.3MB, time=136.12 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428268131 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 2 2 F := [-y z + y - 20 y z - 7 z, 7 x y - 5 y z - 8 y - 9 x, 2 2 2 2 2 -7 x y - 16 x y z - 11 y z + 19] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 G := [10 x y + 2 x y z + 12 x z + 17 z , 2 3 2 2 2 -19 x y z + 11 x z - 3 y z - 19 y z, 3 2 2 2 3 20 x y - 7 x y + 6 x y z - y z ] > Problem := [F,G]; 2 2 3 2 3 2 2 2 Problem := [[-y z + y - 20 y z - 7 z, 7 x y - 5 y z - 8 y - 9 x, 2 2 2 2 2 -7 x y - 16 x y z - 11 y z + 19], [ 3 2 2 3 10 x y + 2 x y z + 12 x z + 17 z , 2 3 2 2 2 -19 x y z + 11 x z - 3 y z - 19 y z, 3 2 2 2 3 20 x y - 7 x y + 6 x y z - y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.4MB, alloc=32.3MB, time=0.83 memory used=49.1MB, alloc=36.3MB, time=1.33 memory used=69.0MB, alloc=60.3MB, time=1.87 memory used=134.0MB, alloc=62.3MB, time=2.95 memory used=184.8MB, alloc=62.5MB, time=3.38 memory used=212.9MB, alloc=62.5MB, time=3.51 memory used=240.3MB, alloc=62.5MB, time=3.63 memory used=274.2MB, alloc=62.5MB, time=3.76 memory used=298.8MB, alloc=62.5MB, time=3.86 memory used=321.5MB, alloc=62.5MB, time=3.96 memory used=369.4MB, alloc=62.5MB, time=4.37 memory used=400.7MB, alloc=62.5MB, time=4.51 memory used=425.7MB, alloc=62.5MB, time=4.62 memory used=456.5MB, alloc=62.5MB, time=4.75 memory used=484.9MB, alloc=62.5MB, time=4.86 memory used=505.5MB, alloc=62.5MB, time=4.96 memory used=552.5MB, alloc=62.5MB, time=5.68 memory used=580.6MB, alloc=62.5MB, time=5.82 memory used=608.6MB, alloc=62.5MB, time=5.93 memory used=630.5MB, alloc=62.5MB, time=6.02 memory used=660.3MB, alloc=62.5MB, time=6.23 memory used=701.6MB, alloc=62.5MB, time=6.55 memory used=727.6MB, alloc=62.5MB, time=6.67 memory used=751.1MB, alloc=62.5MB, time=6.79 memory used=778.8MB, alloc=62.5MB, time=6.90 memory used=811.0MB, alloc=62.5MB, time=7.03 memory used=829.4MB, alloc=62.5MB, time=7.11 memory used=848.3MB, alloc=62.5MB, time=7.20 memory used=868.3MB, alloc=62.5MB, time=7.29 memory used=890.3MB, alloc=62.5MB, time=7.38 memory used=914.2MB, alloc=62.5MB, time=7.47 memory used=938.6MB, alloc=62.5MB, time=7.57 memory used=964.8MB, alloc=62.5MB, time=7.67 memory used=993.0MB, alloc=62.5MB, time=7.77 memory used=1022.9MB, alloc=62.5MB, time=7.87 memory used=1054.7MB, alloc=62.5MB, time=7.98 memory used=1090.0MB, alloc=81.9MB, time=8.13 memory used=1101.3MB, alloc=81.9MB, time=8.21 memory used=1112.3MB, alloc=81.9MB, time=8.28 memory used=1124.1MB, alloc=81.9MB, time=8.36 memory used=1136.0MB, alloc=81.9MB, time=8.44 memory used=1147.8MB, alloc=81.9MB, time=8.51 memory used=1160.7MB, alloc=81.9MB, time=8.59 memory used=1173.4MB, alloc=81.9MB, time=8.68 memory used=1186.3MB, alloc=81.9MB, time=8.79 memory used=1199.8MB, alloc=81.9MB, time=8.88 memory used=1213.9MB, alloc=81.9MB, time=8.97 memory used=1228.0MB, alloc=81.9MB, time=9.05 memory used=1242.7MB, alloc=81.9MB, time=9.13 memory used=1258.0MB, alloc=81.9MB, time=9.21 memory used=1273.1MB, alloc=81.9MB, time=9.30 memory used=1289.0MB, alloc=81.9MB, time=9.39 memory used=1305.6MB, alloc=81.9MB, time=9.47 memory used=1325.4MB, alloc=81.9MB, time=9.68 memory used=1372.1MB, alloc=81.9MB, time=10.13 memory used=1399.2MB, alloc=81.9MB, time=10.27 memory used=1421.8MB, alloc=81.9MB, time=10.38 memory used=1448.8MB, alloc=81.9MB, time=10.51 memory used=1481.2MB, alloc=81.9MB, time=10.65 memory used=1501.4MB, alloc=81.9MB, time=10.75 memory used=1519.7MB, alloc=81.9MB, time=10.85 memory used=1539.5MB, alloc=81.9MB, time=10.95 memory used=1561.3MB, alloc=81.9MB, time=11.04 memory used=1583.8MB, alloc=81.9MB, time=11.14 memory used=1608.0MB, alloc=81.9MB, time=11.25 memory used=1634.3MB, alloc=81.9MB, time=11.35 memory used=1662.3MB, alloc=81.9MB, time=11.47 memory used=1692.0MB, alloc=81.9MB, time=11.57 memory used=1723.4MB, alloc=81.9MB, time=11.68 memory used=1764.3MB, alloc=81.9MB, time=11.82 memory used=1775.9MB, alloc=83.8MB, time=11.90 memory used=1787.8MB, alloc=83.8MB, time=11.98 memory used=1800.1MB, alloc=83.8MB, time=12.06 memory used=1813.0MB, alloc=83.8MB, time=12.13 memory used=1826.1MB, alloc=83.8MB, time=12.21 memory used=1840.2MB, alloc=83.8MB, time=12.29 memory used=1854.1MB, alloc=83.8MB, time=12.37 memory used=1869.0MB, alloc=83.8MB, time=12.46 memory used=1883.8MB, alloc=83.8MB, time=12.57 memory used=1899.2MB, alloc=83.8MB, time=12.66 memory used=1915.0MB, alloc=83.8MB, time=12.74 memory used=1931.5MB, alloc=83.8MB, time=12.81 memory used=1948.6MB, alloc=83.8MB, time=12.89 memory used=1966.5MB, alloc=83.8MB, time=12.97 memory used=1985.4MB, alloc=83.8MB, time=13.05 memory used=2048.0MB, alloc=83.8MB, time=13.85 memory used=2116.2MB, alloc=83.8MB, time=14.91 memory used=2140.5MB, alloc=83.8MB, time=15.03 memory used=2168.4MB, alloc=83.8MB, time=15.15 memory used=2188.2MB, alloc=83.8MB, time=15.25 memory used=2217.2MB, alloc=83.8MB, time=15.57 memory used=2244.0MB, alloc=83.8MB, time=15.98 memory used=2285.2MB, alloc=83.8MB, time=17.00 memory used=2329.0MB, alloc=83.8MB, time=18.09 memory used=2369.7MB, alloc=107.8MB, time=19.78 memory used=2403.3MB, alloc=107.8MB, time=19.97 memory used=2437.1MB, alloc=107.8MB, time=20.15 memory used=2476.2MB, alloc=107.8MB, time=20.34 memory used=2521.3MB, alloc=107.8MB, time=20.52 memory used=2557.8MB, alloc=107.8MB, time=20.68 memory used=2585.4MB, alloc=107.8MB, time=20.84 memory used=2615.1MB, alloc=107.8MB, time=21.00 memory used=2649.1MB, alloc=107.8MB, time=21.14 memory used=2695.5MB, alloc=107.8MB, time=22.05 memory used=2735.7MB, alloc=107.8MB, time=22.25 memory used=2772.1MB, alloc=107.8MB, time=22.45 memory used=2817.9MB, alloc=107.8MB, time=22.65 memory used=2851.2MB, alloc=107.8MB, time=22.82 memory used=2893.5MB, alloc=107.8MB, time=23.45 memory used=2947.8MB, alloc=131.8MB, time=45.99 memory used=2965.1MB, alloc=131.8MB, time=70.37 memory used=2965.2MB, alloc=387.8MB, time=70.43 |\^/| 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(); 1428268431 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 3 3 2 F := [-19 x y z + 10 x + 12 z + 10 y , -17 x y + 6 y z - 19 x z - 10 z, 2 2 2 2 12 x y + 14 x y z + 5 x y z + 4 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 2 G := [-10 x z + 8 z - 18 x y - 15 z, -9 y z - 20 x + 12 y z + 6 z , 3 2 12 x z - 7 x y + 20 x y z + 10 x z] > Problem := [F,G]; 2 3 3 2 Problem := [[-19 x y z + 10 x + 12 z + 10 y , 3 3 2 2 2 2 2 -17 x y + 6 y z - 19 x z - 10 z, 12 x y + 14 x y z + 5 x y z + 4 x], 2 3 2 2 3 2 [-10 x z + 8 z - 18 x y - 15 z, -9 y z - 20 x + 12 y z + 6 z , 3 2 12 x z - 7 x y + 20 x y z + 10 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.31 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=45.4MB, alloc=32.3MB, time=1.23 memory used=67.6MB, alloc=36.3MB, time=1.78 memory used=87.0MB, alloc=60.3MB, time=2.28 memory used=116.8MB, alloc=60.3MB, time=2.95 memory used=160.2MB, alloc=60.7MB, time=3.48 memory used=185.7MB, alloc=60.7MB, time=3.59 memory used=210.6MB, alloc=60.7MB, time=3.75 memory used=240.1MB, alloc=60.9MB, time=3.89 memory used=264.7MB, alloc=60.9MB, time=3.99 memory used=297.9MB, alloc=60.9MB, time=4.95 memory used=321.4MB, alloc=60.9MB, time=5.05 memory used=363.7MB, alloc=60.9MB, time=5.67 memory used=398.6MB, alloc=60.9MB, time=6.67 memory used=419.6MB, alloc=60.9MB, time=6.76 memory used=456.3MB, alloc=60.9MB, time=7.28 memory used=491.4MB, alloc=60.9MB, time=8.01 memory used=529.8MB, alloc=60.9MB, time=8.54 memory used=562.5MB, alloc=62.0MB, time=8.85 memory used=582.4MB, alloc=62.0MB, time=8.96 memory used=608.8MB, alloc=62.0MB, time=9.08 memory used=626.9MB, alloc=62.0MB, time=9.18 memory used=645.3MB, alloc=62.0MB, time=9.28 memory used=675.8MB, alloc=62.0MB, time=9.52 memory used=697.0MB, alloc=62.0MB, time=9.64 memory used=719.8MB, alloc=62.0MB, time=9.76 memory used=743.0MB, alloc=62.0MB, time=9.87 memory used=760.3MB, alloc=62.0MB, time=9.96 memory used=782.8MB, alloc=62.0MB, time=10.20 memory used=816.7MB, alloc=62.0MB, time=12.51 memory used=841.2MB, alloc=62.0MB, time=12.63 memory used=857.6MB, alloc=62.0MB, time=12.73 memory used=877.5MB, alloc=62.0MB, time=12.83 memory used=900.2MB, alloc=62.0MB, time=12.93 memory used=936.3MB, alloc=62.0MB, time=13.90 memory used=959.0MB, alloc=62.0MB, time=14.01 memory used=980.9MB, alloc=62.0MB, time=14.21 memory used=1008.3MB, alloc=62.0MB, time=14.36 memory used=1031.1MB, alloc=62.0MB, time=14.48 memory used=1060.0MB, alloc=62.0MB, time=14.70 memory used=1081.0MB, alloc=62.0MB, time=14.82 memory used=1104.3MB, alloc=62.0MB, time=14.93 memory used=1141.4MB, alloc=62.0MB, time=23.41 memory used=1168.6MB, alloc=62.0MB, time=24.04 memory used=1190.5MB, alloc=62.0MB, time=24.15 memory used=1212.0MB, alloc=62.0MB, time=24.27 memory used=1228.5MB, alloc=62.0MB, time=24.36 memory used=1247.4MB, alloc=62.0MB, time=24.47 memory used=1269.1MB, alloc=62.0MB, time=24.57 memory used=1293.4MB, alloc=62.0MB, time=24.68 memory used=1314.8MB, alloc=62.0MB, time=24.77 memory used=1329.5MB, alloc=62.0MB, time=24.85 memory used=1345.9MB, alloc=62.0MB, time=24.93 memory used=1369.9MB, alloc=62.0MB, time=25.22 memory used=1408.5MB, alloc=62.0MB, time=25.85 memory used=1450.9MB, alloc=86.0MB, time=36.24 memory used=1494.7MB, alloc=86.0MB, time=67.65 memory used=1542.9MB, alloc=86.0MB, time=69.85 memory used=1585.8MB, alloc=86.0MB, time=70.05 memory used=1614.1MB, alloc=86.0MB, time=70.20 memory used=1646.3MB, alloc=86.0MB, time=70.36 memory used=1683.5MB, alloc=86.0MB, time=70.52 memory used=1726.2MB, alloc=86.0MB, time=70.69 memory used=1764.0MB, alloc=86.0MB, time=70.83 memory used=1789.6MB, alloc=86.0MB, time=70.94 memory used=1817.4MB, alloc=86.0MB, time=71.06 memory used=1847.7MB, alloc=86.0MB, time=71.18 memory used=1879.2MB, alloc=86.0MB, time=71.30 memory used=1913.4MB, alloc=86.0MB, time=71.42 memory used=1952.6MB, alloc=86.0MB, time=71.56 memory used=2027.1MB, alloc=94.0MB, time=72.93 memory used=2091.4MB, alloc=94.0MB, time=74.24 memory used=2155.4MB, alloc=94.0MB, time=75.49 memory used=2194.7MB, alloc=94.0MB, time=75.87 memory used=2239.7MB, alloc=94.0MB, time=76.53 memory used=2268.6MB, alloc=94.0MB, time=76.71 memory used=2304.1MB, alloc=94.0MB, time=76.90 memory used=2326.3MB, alloc=94.0MB, time=77.06 memory used=2350.8MB, alloc=118.0MB, time=77.24 memory used=2396.5MB, alloc=118.0MB, time=77.47 memory used=2451.1MB, alloc=118.0MB, time=77.68 memory used=2496.7MB, alloc=118.0MB, time=77.86 memory used=2531.8MB, alloc=118.0MB, time=78.03 memory used=2571.2MB, alloc=118.0MB, time=78.19 memory used=2629.6MB, alloc=118.0MB, time=78.86 memory used=2681.5MB, alloc=118.0MB, time=79.10 memory used=2719.9MB, alloc=118.0MB, time=79.31 memory used=2766.1MB, alloc=118.0MB, time=79.52 memory used=2820.5MB, alloc=118.0MB, time=79.73 memory used=2866.8MB, alloc=118.0MB, time=79.93 memory used=2901.9MB, alloc=118.0MB, time=80.08 memory used=2941.6MB, alloc=118.0MB, time=80.23 memory used=3013.4MB, alloc=118.0MB, time=84.21 memory used=3056.3MB, alloc=118.0MB, time=84.42 memory used=3112.2MB, alloc=118.0MB, time=84.66 memory used=3147.9MB, alloc=118.0MB, time=84.82 memory used=3188.7MB, alloc=118.0MB, time=85.00 memory used=3237.9MB, alloc=118.0MB, time=85.18 memory used=3299.8MB, alloc=118.0MB, time=85.83 memory used=3372.1MB, alloc=118.0MB, time=86.83 memory used=3420.6MB, alloc=118.0MB, time=87.07 memory used=3463.6MB, alloc=118.0MB, time=87.29 memory used=3503.7MB, alloc=118.0MB, time=87.49 memory used=3551.7MB, alloc=118.0MB, time=87.70 memory used=3608.1MB, alloc=118.0MB, time=87.92 memory used=3647.8MB, alloc=118.0MB, time=88.10 memory used=3682.9MB, alloc=118.0MB, time=88.27 memory used=3722.2MB, alloc=118.0MB, time=88.45 memory used=3788.2MB, alloc=118.0MB, time=92.41 memory used=3832.7MB, alloc=118.0MB, time=92.64 memory used=3887.0MB, alloc=118.0MB, time=92.88 memory used=3927.5MB, alloc=118.0MB, time=93.06 memory used=3966.5MB, alloc=118.0MB, time=93.23 memory used=4012.6MB, alloc=118.0MB, time=93.40 memory used=4072.7MB, alloc=118.0MB, time=93.75 memory used=4144.0MB, alloc=118.0MB, time=96.23 memory used=4228.0MB, alloc=118.0MB, time=100.19 memory used=4275.8MB, alloc=118.0MB, time=100.42 memory used=4312.9MB, alloc=118.0MB, time=100.65 memory used=4357.5MB, alloc=118.0MB, time=100.87 memory used=4409.8MB, alloc=118.0MB, time=101.11 memory used=4458.4MB, alloc=118.0MB, time=101.33 memory used=4489.9MB, alloc=118.0MB, time=101.50 memory used=4523.0MB, alloc=118.0MB, time=101.67 memory used=4558.9MB, alloc=118.0MB, time=101.86 memory used=4597.5MB, alloc=118.0MB, time=102.04 memory used=4637.2MB, alloc=118.0MB, time=102.23 memory used=4680.5MB, alloc=118.0MB, time=102.42 memory used=4726.6MB, alloc=118.0MB, time=102.61 memory used=4774.9MB, alloc=118.0MB, time=102.81 memory used=4825.3MB, alloc=118.0MB, time=103.01 memory used=4879.4MB, alloc=118.0MB, time=103.21 memory used=4940.0MB, alloc=118.0MB, time=103.42 memory used=4961.2MB, alloc=131.8MB, time=103.58 memory used=4971.1MB, alloc=131.8MB, time=103.71 memory used=4979.9MB, alloc=131.8MB, time=103.84 memory used=4989.7MB, alloc=131.8MB, time=103.98 memory used=4999.3MB, alloc=131.8MB, time=104.11 memory used=5008.9MB, 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used=6017.0MB, alloc=131.8MB, time=114.30 memory used=6063.0MB, alloc=131.8MB, time=114.48 memory used=6111.2MB, alloc=131.8MB, time=114.67 memory used=6161.9MB, alloc=131.8MB, time=114.86 memory used=6215.8MB, alloc=131.8MB, time=115.06 memory used=6274.6MB, alloc=131.8MB, time=115.26 memory used=6302.4MB, alloc=131.8MB, time=115.41 memory used=6313.2MB, alloc=131.8MB, time=115.53 memory used=6321.8MB, alloc=131.8MB, time=115.64 memory used=6331.2MB, alloc=131.8MB, time=115.79 memory used=6340.9MB, alloc=131.8MB, time=115.92 memory used=6350.5MB, alloc=131.8MB, time=116.06 memory used=6360.1MB, alloc=131.8MB, time=116.20 memory used=6369.6MB, alloc=131.8MB, time=116.32 memory used=6379.0MB, alloc=131.8MB, time=116.45 memory used=6388.6MB, alloc=131.8MB, time=116.59 memory used=6399.2MB, alloc=131.8MB, time=116.71 memory used=6410.0MB, alloc=131.8MB, time=116.83 memory used=6420.6MB, alloc=131.8MB, time=116.97 memory used=6431.2MB, alloc=131.8MB, time=117.08 memory used=6441.6MB, 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time=152.15 memory used=8897.5MB, alloc=131.8MB, time=152.29 memory used=8909.5MB, alloc=131.8MB, time=152.43 memory used=8921.3MB, alloc=131.8MB, time=152.58 memory used=8933.1MB, alloc=131.8MB, time=152.73 memory used=8944.8MB, alloc=131.8MB, time=152.89 memory used=8956.7MB, alloc=131.8MB, time=153.04 memory used=8969.8MB, alloc=131.8MB, time=153.19 memory used=8983.2MB, alloc=131.8MB, time=153.34 memory used=8996.3MB, alloc=131.8MB, time=153.49 memory used=9009.3MB, alloc=131.8MB, time=153.63 memory used=9022.5MB, alloc=131.8MB, time=153.77 memory used=9036.7MB, alloc=131.8MB, time=153.91 memory used=9051.0MB, alloc=131.8MB, time=154.07 memory used=9065.1MB, alloc=131.8MB, time=154.21 memory used=9079.3MB, alloc=131.8MB, time=154.38 memory used=9094.2MB, alloc=131.8MB, time=154.53 memory used=9109.2MB, alloc=131.8MB, time=154.70 memory used=9124.2MB, alloc=131.8MB, time=154.86 memory used=9139.8MB, alloc=131.8MB, time=155.00 memory used=9155.3MB, alloc=131.8MB, time=155.15 memory used=9171.8MB, alloc=131.8MB, time=155.31 memory used=9188.1MB, alloc=131.8MB, time=155.47 memory used=9204.9MB, alloc=131.8MB, time=155.63 memory used=9222.2MB, alloc=131.8MB, time=155.78 memory used=9240.0MB, alloc=131.8MB, time=155.93 memory used=9258.6MB, alloc=131.8MB, time=156.07 memory used=9277.6MB, alloc=131.8MB, time=156.24 memory used=9349.7MB, alloc=131.8MB, time=158.40 memory used=9389.4MB, alloc=131.8MB, time=158.66 memory used=9427.3MB, alloc=131.8MB, time=158.89 memory used=9473.2MB, alloc=131.8MB, time=159.13 memory used=9523.1MB, alloc=131.8MB, time=159.39 memory used=9551.9MB, alloc=131.8MB, time=159.57 memory used=9581.6MB, alloc=131.8MB, time=159.77 memory used=9613.8MB, alloc=131.8MB, time=159.97 memory used=9649.1MB, alloc=131.8MB, time=160.16 memory used=9685.6MB, alloc=131.8MB, time=160.36 memory used=9725.2MB, alloc=131.8MB, time=160.57 memory used=9765.9MB, alloc=131.8MB, time=160.78 memory used=9809.6MB, alloc=131.8MB, time=161.00 memory used=9856.4MB, alloc=131.8MB, time=161.22 memory used=9906.2MB, alloc=131.8MB, time=161.45 memory used=9958.9MB, alloc=131.8MB, time=161.69 memory used=9995.8MB, alloc=131.8MB, time=161.89 memory used=10004.9MB, alloc=131.8MB, time=162.03 memory used=10012.5MB, alloc=131.8MB, time=162.20 memory used=10020.5MB, alloc=131.8MB, time=162.34 memory used=10029.1MB, alloc=131.8MB, time=162.48 memory used=10037.7MB, alloc=131.8MB, time=162.62 memory used=10046.2MB, alloc=131.8MB, time=162.74 memory used=10054.8MB, alloc=131.8MB, time=162.89 memory used=10063.3MB, alloc=131.8MB, time=163.04 memory used=10071.9MB, alloc=131.8MB, time=163.19 memory used=10080.4MB, alloc=131.8MB, time=163.32 memory used=10089.0MB, alloc=131.8MB, time=163.47 memory used=10097.5MB, alloc=131.8MB, time=163.61 memory used=10106.1MB, alloc=131.8MB, time=163.77 memory used=10114.6MB, alloc=131.8MB, time=163.91 memory used=10123.3MB, alloc=131.8MB, time=164.07 memory used=10132.0MB, alloc=131.8MB, time=164.23 memory used=10142.2MB, alloc=131.8MB, time=164.38 memory used=10151.1MB, alloc=131.8MB, time=164.51 memory used=10161.3MB, alloc=131.8MB, time=164.66 memory used=10171.8MB, alloc=131.8MB, time=164.80 memory used=10182.4MB, alloc=131.8MB, time=164.94 memory used=10192.9MB, alloc=131.8MB, time=165.09 memory used=10203.4MB, alloc=131.8MB, time=165.24 memory used=10213.8MB, alloc=131.8MB, time=165.37 memory used=10224.2MB, alloc=131.8MB, time=165.51 memory used=10234.6MB, alloc=131.8MB, time=165.65 memory used=10244.9MB, alloc=131.8MB, time=165.80 memory used=10255.2MB, alloc=131.8MB, time=165.94 memory used=10265.5MB, alloc=131.8MB, time=166.07 memory used=10276.0MB, alloc=131.8MB, time=166.23 memory used=10287.9MB, alloc=131.8MB, time=166.39 memory used=10300.0MB, alloc=131.8MB, time=166.54 memory used=10312.1MB, alloc=131.8MB, time=166.69 memory used=10324.1MB, alloc=131.8MB, time=166.83 memory used=10336.0MB, alloc=131.8MB, time=166.98 memory used=10347.8MB, alloc=131.8MB, time=167.12 memory used=10359.5MB, alloc=131.8MB, time=167.28 memory used=10371.5MB, alloc=131.8MB, time=167.41 memory used=10384.7MB, alloc=131.8MB, time=167.58 memory used=10398.1MB, alloc=131.8MB, time=167.72 memory used=10411.3MB, alloc=131.8MB, time=167.88 memory used=10424.4MB, alloc=131.8MB, time=168.03 memory used=10437.3MB, alloc=131.8MB, time=168.17 memory used=10450.5MB, alloc=131.8MB, time=168.33 memory used=10464.6MB, alloc=131.8MB, time=168.49 memory used=10478.7MB, alloc=131.8MB, time=168.65 memory used=10492.7MB, alloc=131.8MB, time=168.79 memory used=10506.9MB, alloc=131.8MB, time=168.96 memory used=10521.6MB, alloc=131.8MB, time=169.10 memory used=10536.5MB, alloc=131.8MB, time=169.25 |\^/| 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(); 1428268731 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 F := [7 x y z + 6 y z - 12 x y z + 18 x, -2 x y - 11 x y - 18 x y - 3 y z, 3 9 x z - 12 x z - 12 x - 12] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 3 2 G := [10 x z + 7 x y - 13 x y z - 17 x z, -x z - 4 x z + 5 x y + 5 x z, 2 2 2 3 16 x y z + 8 y z - 12 y + 8 y z] > Problem := [F,G]; 2 3 Problem := [[7 x y z + 6 y z - 12 x y z + 18 x, 3 3 3 -2 x y - 11 x y - 18 x y - 3 y z, 9 x z - 12 x z - 12 x - 12], [ 3 2 2 2 3 3 2 10 x z + 7 x y - 13 x y z - 17 x z, -x z - 4 x z + 5 x y + 5 x z, 2 2 2 3 16 x y z + 8 y z - 12 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=24.7MB, alloc=32.3MB, time=0.83 memory used=46.3MB, alloc=36.3MB, time=1.30 memory used=65.5MB, alloc=60.3MB, time=1.67 memory used=109.4MB, alloc=60.3MB, time=2.58 memory used=141.2MB, alloc=60.3MB, time=3.35 memory used=185.1MB, alloc=68.3MB, time=4.27 memory used=230.3MB, alloc=68.3MB, time=5.10 memory used=280.8MB, alloc=68.3MB, time=6.23 memory used=322.9MB, alloc=92.3MB, time=6.93 memory used=388.5MB, alloc=92.3MB, time=8.40 memory used=440.0MB, alloc=92.3MB, time=9.28 memory used=498.9MB, alloc=92.3MB, time=10.22 memory used=575.8MB, alloc=94.5MB, time=13.06 memory used=605.8MB, alloc=94.5MB, time=13.23 memory used=663.7MB, alloc=94.5MB, time=13.98 memory used=729.4MB, alloc=118.5MB, time=15.61 memory used=793.3MB, alloc=374.5MB, time=17.24 memory used=877.1MB, alloc=374.5MB, time=19.11 memory used=975.3MB, alloc=398.5MB, time=21.05 memory used=1072.8MB, alloc=398.5MB, time=22.77 memory used=1178.1MB, alloc=398.5MB, time=24.62 memory used=1284.9MB, alloc=398.5MB, time=26.56 memory used=1366.1MB, alloc=398.5MB, time=27.64 memory used=1413.3MB, alloc=398.5MB, time=27.98 memory used=1465.9MB, alloc=398.5MB, time=28.31 memory used=1507.1MB, alloc=398.5MB, time=28.61 memory used=1578.7MB, alloc=398.5MB, time=29.34 memory used=1629.9MB, alloc=398.5MB, time=29.68 memory used=1679.1MB, alloc=398.5MB, time=30.00 memory used=1741.9MB, alloc=398.5MB, time=33.23 memory used=1797.0MB, alloc=398.5MB, time=33.58 memory used=1839.9MB, alloc=398.5MB, time=33.90 memory used=1903.7MB, alloc=398.5MB, time=34.44 memory used=2012.4MB, alloc=398.5MB, time=36.53 memory used=2122.0MB, alloc=398.5MB, time=38.15 memory used=2239.6MB, alloc=398.5MB, time=42.12 memory used=2349.9MB, alloc=398.5MB, time=46.00 memory used=2405.3MB, alloc=398.5MB, time=46.72 memory used=2478.1MB, alloc=398.5MB, time=47.71 memory used=2574.8MB, alloc=422.5MB, time=49.18 memory used=2691.3MB, alloc=422.5MB, time=51.84 memory used=2764.8MB, alloc=422.5MB, time=52.37 memory used=2822.2MB, alloc=422.5MB, time=52.75 memory used=2892.6MB, alloc=422.5MB, time=53.41 memory used=2957.2MB, alloc=422.5MB, time=53.87 memory used=3012.3MB, alloc=422.5MB, time=54.25 memory used=3088.9MB, alloc=422.5MB, time=56.80 memory used=3146.8MB, alloc=422.5MB, time=57.20 memory used=3214.3MB, alloc=422.5MB, time=57.70 memory used=3327.5MB, alloc=422.5MB, time=59.97 memory used=3433.1MB, alloc=422.5MB, time=62.08 memory used=3544.2MB, alloc=446.5MB, time=64.54 memory used=3639.7MB, alloc=446.5MB, time=66.59 memory used=3723.1MB, alloc=446.5MB, time=68.72 memory used=3815.1MB, alloc=446.5MB, time=71.12 memory used=3911.9MB, alloc=446.5MB, time=72.40 memory used=3985.3MB, alloc=446.5MB, time=73.00 memory used=4052.5MB, alloc=446.5MB, time=73.50 memory used=4138.4MB, alloc=470.5MB, time=74.46 memory used=4222.8MB, alloc=470.5MB, time=75.03 memory used=4328.7MB, alloc=470.5MB, time=78.09 memory used=4467.4MB, alloc=470.5MB, time=80.14 memory used=4549.2MB, alloc=470.5MB, time=82.13 memory used=4685.1MB, alloc=470.5MB, time=83.09 memory used=4758.8MB, alloc=470.5MB, time=83.70 memory used=4840.5MB, alloc=470.5MB, time=84.30 memory used=4930.8MB, alloc=470.5MB, time=84.88 memory used=5033.5MB, alloc=470.5MB, time=86.39 memory used=5134.6MB, alloc=470.5MB, time=87.12 memory used=5207.2MB, alloc=470.5MB, time=87.73 memory used=5298.2MB, alloc=470.5MB, time=88.36 memory used=5397.2MB, alloc=470.5MB, time=94.94 memory used=5502.1MB, alloc=470.5MB, time=95.75 memory used=5591.7MB, alloc=470.5MB, time=96.34 memory used=5662.1MB, alloc=470.5MB, time=96.88 memory used=5779.8MB, alloc=470.5MB, time=98.41 memory used=5861.8MB, alloc=470.5MB, time=100.34 memory used=5973.8MB, alloc=470.5MB, time=101.46 memory used=6080.0MB, alloc=470.5MB, time=103.07 memory used=6197.2MB, alloc=470.5MB, time=105.62 memory used=6268.8MB, alloc=470.5MB, time=106.17 memory used=6348.8MB, alloc=470.5MB, time=106.71 memory used=6477.0MB, alloc=470.5MB, time=108.85 memory used=6574.3MB, alloc=470.5MB, time=111.03 memory used=6636.3MB, alloc=470.5MB, time=112.85 memory used=6707.8MB, alloc=494.5MB, time=115.00 memory used=6791.0MB, alloc=494.5MB, time=116.44 memory used=6886.8MB, alloc=494.5MB, time=117.11 memory used=6973.9MB, alloc=494.5MB, time=117.74 memory used=7080.2MB, alloc=494.5MB, time=119.51 memory used=7146.0MB, alloc=494.5MB, time=121.37 memory used=7207.3MB, alloc=494.5MB, time=124.36 memory used=7276.3MB, alloc=494.5MB, time=128.44 memory used=7338.7MB, alloc=494.5MB, time=131.01 memory used=7403.9MB, alloc=494.5MB, time=132.25 memory used=7478.9MB, alloc=494.5MB, time=134.71 memory used=7573.2MB, alloc=494.5MB, time=135.51 memory used=7687.4MB, alloc=494.5MB, time=137.93 memory used=7757.2MB, alloc=494.5MB, time=139.50 memory used=7854.2MB, alloc=494.5MB, time=141.42 memory used=7920.0MB, alloc=494.5MB, time=142.83 memory used=7968.1MB, alloc=494.5MB, time=144.53 memory used=8020.3MB, alloc=494.5MB, time=146.34 memory used=8059.1MB, alloc=494.5MB, time=147.60 memory used=8103.3MB, alloc=494.5MB, time=148.89 memory used=8291.0MB, alloc=518.5MB, time=153.36 memory used=8501.1MB, alloc=542.5MB, time=158.19 |\^/| 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(); 1428269031 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 3 3 2 F := [8 x y z + 6 y z + 8 z - x z, -18 x - 14 x y - 13 x z - 9 x z , 3 2 2 -11 x y - 20 x z - 6 x y - 6 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 3 G := [4 x y + y z - 7 x y z + 17 y , 6 x y z - 3 y z + 16 z + 8 z, 3 2 2 2 x z - 9 x y z - 12 y z + 10 x] > Problem := [F,G]; 2 2 3 Problem := [[8 x y z + 6 y z + 8 z - x z, 4 3 3 2 3 2 2 -18 x - 14 x y - 13 x z - 9 x z , -11 x y - 20 x z - 6 x y - 6 x], [ 2 2 3 2 2 3 3 4 x y + y z - 7 x y z + 17 y , 6 x y z - 3 y z + 16 z + 8 z, 3 2 2 2 x z - 9 x y z - 12 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=0.31 memory used=26.7MB, alloc=32.3MB, time=0.90 memory used=46.6MB, alloc=60.3MB, time=1.39 memory used=87.7MB, alloc=60.3MB, time=2.47 memory used=128.6MB, alloc=68.3MB, time=3.53 memory used=172.3MB, alloc=92.3MB, time=4.59 memory used=238.4MB, alloc=92.3MB, time=5.94 memory used=301.5MB, alloc=92.3MB, time=7.47 memory used=361.9MB, alloc=116.3MB, time=8.97 memory used=430.9MB, alloc=372.3MB, time=10.68 memory used=514.7MB, alloc=372.3MB, time=12.18 memory used=598.2MB, alloc=372.3MB, time=14.12 memory used=665.1MB, alloc=372.3MB, time=15.38 memory used=758.0MB, alloc=372.3MB, time=16.83 memory used=840.3MB, alloc=396.3MB, time=18.59 memory used=949.3MB, alloc=396.3MB, time=21.05 memory used=1043.5MB, alloc=396.3MB, time=22.84 memory used=1136.6MB, alloc=420.3MB, time=24.45 memory used=1214.1MB, alloc=420.3MB, time=25.36 memory used=1277.4MB, alloc=420.3MB, time=25.70 memory used=1349.9MB, alloc=420.3MB, time=26.50 memory used=1473.6MB, alloc=420.3MB, time=28.83 memory used=1601.2MB, alloc=444.3MB, time=32.32 memory used=1726.9MB, alloc=444.3MB, time=35.71 memory used=1822.3MB, alloc=468.3MB, time=37.83 memory used=1923.5MB, alloc=468.3MB, time=40.33 memory used=2023.2MB, alloc=468.3MB, time=42.97 memory used=2128.1MB, alloc=468.3MB, time=45.09 memory used=2220.0MB, alloc=468.3MB, time=47.11 memory used=2299.3MB, alloc=492.3MB, time=49.05 memory used=2392.5MB, alloc=492.3MB, time=51.45 memory used=2473.9MB, alloc=492.3MB, time=53.79 memory used=2554.5MB, alloc=492.3MB, time=56.11 memory used=2628.2MB, alloc=492.3MB, time=58.14 memory used=2688.5MB, alloc=492.3MB, time=59.68 memory used=2759.9MB, alloc=492.3MB, time=61.69 memory used=2865.3MB, alloc=492.3MB, time=63.65 memory used=2959.9MB, alloc=492.3MB, time=65.41 memory used=3055.4MB, alloc=492.3MB, time=67.16 memory used=3122.2MB, alloc=492.3MB, time=68.90 memory used=3194.4MB, alloc=516.3MB, time=73.30 memory used=3291.9MB, alloc=516.3MB, time=74.81 memory used=3362.4MB, alloc=516.3MB, time=76.58 memory used=3418.1MB, alloc=516.3MB, time=77.89 memory used=3480.7MB, alloc=516.3MB, time=80.04 memory used=3520.6MB, alloc=516.3MB, time=81.46 memory used=3563.5MB, alloc=516.3MB, time=83.07 memory used=3759.8MB, alloc=516.3MB, time=89.01 memory used=3975.8MB, alloc=540.3MB, time=96.16 memory used=4179.8MB, alloc=540.3MB, time=99.99 memory used=4357.4MB, alloc=564.3MB, time=104.01 memory used=4532.2MB, alloc=564.3MB, time=108.78 memory used=4708.4MB, alloc=588.3MB, time=113.82 memory used=4874.8MB, alloc=612.3MB, time=118.33 memory used=5077.9MB, alloc=612.3MB, time=121.59 memory used=5282.6MB, alloc=612.3MB, time=126.48 memory used=5421.5MB, alloc=612.3MB, time=127.94 memory used=5602.2MB, alloc=612.3MB, time=130.02 memory used=5736.2MB, alloc=612.3MB, time=131.25 memory used=5906.2MB, alloc=612.3MB, time=133.04 memory used=6073.8MB, alloc=612.3MB, time=140.99 memory used=6207.0MB, alloc=612.3MB, time=142.17 memory used=6361.3MB, alloc=612.3MB, time=143.73 memory used=6511.3MB, alloc=612.3MB, time=145.04 memory used=6677.0MB, alloc=612.3MB, time=147.07 memory used=6811.4MB, alloc=612.3MB, time=148.29 memory used=6986.7MB, alloc=612.3MB, time=156.50 memory used=7118.0MB, alloc=612.3MB, time=157.69 memory used=7258.4MB, alloc=612.3MB, time=159.13 memory used=7424.2MB, alloc=612.3MB, time=161.17 memory used=7583.4MB, alloc=612.3MB, time=162.54 memory used=7739.5MB, alloc=612.3MB, time=164.26 memory used=7911.9MB, alloc=612.3MB, time=172.30 memory used=8042.5MB, alloc=612.3MB, time=173.53 memory used=8177.1MB, alloc=612.3MB, time=174.67 memory used=8334.7MB, alloc=612.3MB, time=176.84 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428269331 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 2 F := [19 x y z + 17 x y - 13 y + 18 y, 8 z - 19 y z + 10 y - 12 x, 3 4 3 x z + 20 z + y + 4] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 3 3 2 G := [-18 x z - 2 y - x y - 5 x y, -16 x y + 13 x z - 20 x z + 7 x, 2 3 2 15 x y z + 6 x - 17 x z - 7 z ] > Problem := [F,G]; 2 2 2 4 2 2 Problem := [[19 x y z + 17 x y - 13 y + 18 y, 8 z - 19 y z + 10 y - 12 x, 3 4 3 3 4 2 x z + 20 z + y + 4], [-18 x z - 2 y - x y - 5 x y, 3 3 2 2 3 2 -16 x y + 13 x z - 20 x z + 7 x, 15 x y z + 6 x - 17 x z - 7 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=24.7MB, alloc=32.3MB, time=0.84 memory used=43.3MB, alloc=56.3MB, time=1.33 memory used=86.1MB, alloc=61.1MB, time=1.90 memory used=119.1MB, alloc=61.1MB, time=2.09 memory used=157.6MB, alloc=61.1MB, time=2.62 memory used=201.0MB, alloc=61.1MB, time=3.31 memory used=235.7MB, alloc=61.1MB, time=4.00 memory used=281.2MB, alloc=69.1MB, time=4.97 memory used=325.9MB, alloc=69.1MB, time=5.98 memory used=370.8MB, alloc=69.1MB, time=7.02 memory used=390.1MB, alloc=93.1MB, time=7.18 memory used=431.0MB, alloc=93.1MB, time=7.48 memory used=470.8MB, alloc=93.1MB, time=7.73 memory used=514.8MB, alloc=93.1MB, time=8.17 memory used=551.2MB, alloc=93.1MB, time=8.37 memory used=584.1MB, alloc=93.1MB, time=8.55 memory used=624.2MB, alloc=93.1MB, time=8.76 memory used=662.5MB, alloc=93.1MB, time=8.94 memory used=688.9MB, alloc=93.1MB, time=9.08 memory used=718.5MB, alloc=93.1MB, time=9.22 memory used=750.9MB, alloc=93.1MB, time=9.36 memory used=788.1MB, alloc=93.1MB, time=9.51 memory used=832.9MB, alloc=93.1MB, time=9.97 memory used=869.7MB, alloc=93.1MB, time=10.17 memory used=902.6MB, alloc=93.1MB, time=10.34 memory used=942.6MB, alloc=93.1MB, time=10.53 memory used=981.3MB, alloc=93.1MB, time=10.70 memory used=1008.0MB, alloc=93.1MB, time=10.84 memory used=1037.1MB, alloc=93.1MB, time=10.98 memory used=1069.9MB, alloc=93.1MB, time=11.13 memory used=1106.9MB, alloc=93.1MB, time=11.27 memory used=1160.5MB, alloc=93.1MB, time=12.15 memory used=1194.3MB, alloc=93.1MB, time=12.35 memory used=1236.3MB, alloc=93.1MB, time=12.54 memory used=1263.4MB, alloc=93.1MB, time=12.68 memory used=1295.0MB, alloc=93.1MB, time=12.82 memory used=1333.0MB, alloc=93.1MB, time=12.98 memory used=1380.4MB, alloc=93.1MB, time=13.46 memory used=1415.6MB, alloc=93.1MB, time=13.65 memory used=1455.0MB, alloc=93.1MB, time=13.82 memory used=1495.1MB, alloc=93.1MB, time=14.19 memory used=1530.9MB, alloc=93.1MB, time=14.37 memory used=1589.0MB, alloc=93.1MB, time=15.13 memory used=1632.5MB, alloc=93.1MB, time=17.15 memory used=1676.5MB, alloc=93.1MB, time=17.41 memory used=1705.6MB, alloc=93.1MB, time=17.60 memory used=1738.8MB, alloc=93.1MB, time=17.81 memory used=1778.0MB, alloc=93.1MB, time=18.01 memory used=1818.9MB, alloc=93.1MB, time=18.21 memory used=1842.8MB, alloc=117.1MB, time=18.40 memory used=1879.2MB, alloc=117.1MB, time=18.61 memory used=1920.3MB, alloc=117.1MB, time=18.82 memory used=1963.9MB, alloc=117.1MB, time=19.03 memory used=2009.8MB, alloc=117.1MB, time=19.25 memory used=2061.5MB, alloc=117.1MB, time=19.51 memory used=2115.3MB, alloc=117.1MB, time=19.76 memory used=2171.7MB, alloc=117.1MB, time=20.01 memory used=2233.4MB, alloc=117.1MB, time=20.27 memory used=2294.0MB, alloc=117.1MB, time=20.51 memory used=2327.0MB, alloc=117.1MB, time=20.66 memory used=2357.3MB, alloc=117.1MB, time=20.81 memory used=2389.5MB, alloc=117.1MB, time=20.97 memory used=2422.4MB, alloc=117.1MB, time=21.12 memory used=2455.7MB, alloc=117.1MB, time=21.29 memory used=2489.9MB, alloc=117.1MB, time=21.45 memory used=2527.9MB, alloc=117.1MB, time=21.61 memory used=2566.7MB, alloc=117.1MB, time=21.78 memory used=2605.7MB, alloc=117.1MB, time=21.94 memory used=2644.9MB, alloc=117.1MB, time=22.12 memory used=2684.9MB, alloc=117.1MB, time=22.28 memory used=2728.7MB, alloc=117.1MB, time=22.46 memory used=2773.1MB, alloc=117.1MB, time=22.63 memory used=2817.5MB, alloc=117.1MB, time=22.81 memory used=2862.7MB, alloc=117.1MB, time=22.98 memory used=2911.1MB, alloc=117.1MB, time=23.16 memory used=2960.1MB, alloc=117.1MB, time=23.34 memory used=3009.9MB, alloc=117.1MB, time=23.53 memory used=3062.0MB, alloc=117.1MB, time=23.72 memory used=3115.4MB, alloc=117.1MB, time=23.90 memory used=3171.0MB, alloc=117.1MB, time=24.09 memory used=3228.0MB, alloc=117.1MB, time=24.27 memory used=3287.2MB, alloc=117.1MB, time=24.47 memory used=3349.0MB, alloc=117.1MB, time=24.67 memory used=3419.5MB, alloc=121.9MB, time=24.89 memory used=3436.6MB, alloc=131.8MB, time=25.01 memory used=3447.7MB, alloc=131.8MB, time=25.10 memory used=3454.2MB, alloc=131.8MB, time=25.19 memory used=3460.5MB, alloc=131.8MB, time=25.28 memory used=3467.0MB, alloc=131.8MB, time=25.41 memory used=3474.6MB, alloc=131.8MB, time=25.49 memory used=3482.0MB, alloc=131.8MB, time=25.58 memory used=3489.4MB, alloc=131.8MB, time=25.67 memory used=3496.8MB, alloc=131.8MB, time=25.76 memory used=3504.1MB, alloc=131.8MB, time=25.84 memory used=3511.3MB, alloc=131.8MB, time=25.92 memory used=3518.5MB, alloc=131.8MB, time=26.03 memory used=3525.6MB, alloc=131.8MB, time=26.11 memory used=3532.7MB, alloc=131.8MB, time=26.19 memory used=3539.7MB, alloc=131.8MB, time=26.30 memory used=3546.7MB, alloc=131.8MB, time=26.39 memory used=3553.6MB, alloc=131.8MB, time=26.48 memory used=3561.4MB, alloc=131.8MB, time=26.58 memory used=3568.7MB, alloc=131.8MB, time=26.67 memory used=3577.3MB, alloc=131.8MB, time=26.76 memory used=3585.0MB, alloc=131.8MB, time=26.84 memory used=3593.8MB, alloc=131.8MB, time=26.93 memory used=3601.8MB, alloc=131.8MB, time=27.02 memory used=3609.9MB, alloc=131.8MB, time=27.11 memory used=3619.3MB, alloc=131.8MB, time=27.20 memory used=3628.7MB, alloc=131.8MB, time=27.29 memory used=3637.8MB, alloc=131.8MB, time=27.38 memory used=3646.8MB, alloc=131.8MB, time=27.48 memory used=3655.7MB, alloc=131.8MB, time=27.57 memory used=3665.5MB, alloc=131.8MB, time=27.66 memory used=3674.6MB, alloc=131.8MB, time=27.75 memory used=3684.2MB, alloc=131.8MB, time=27.84 memory used=3694.0MB, alloc=131.8MB, time=27.93 memory used=3704.2MB, alloc=131.8MB, time=28.02 memory used=3714.7MB, alloc=131.8MB, time=28.12 memory used=3725.2MB, alloc=131.8MB, time=28.22 memory used=3736.8MB, alloc=131.8MB, time=28.31 memory used=3748.5MB, alloc=131.8MB, time=28.40 memory used=3760.3MB, alloc=131.8MB, time=28.49 memory used=3840.7MB, alloc=131.8MB, time=85.73 memory used=3907.9MB, alloc=131.8MB, time=161.57 memory used=3984.1MB, alloc=131.8MB, time=179.33 memory used=4036.6MB, alloc=131.8MB, time=179.61 memory used=4078.7MB, alloc=131.8MB, time=179.83 memory used=4124.6MB, alloc=131.8MB, time=180.05 memory used=4178.4MB, alloc=131.8MB, time=180.30 memory used=4239.9MB, alloc=131.8MB, time=180.54 memory used=4275.3MB, alloc=131.8MB, time=180.70 memory used=4309.7MB, alloc=131.8MB, time=180.87 memory used=4347.7MB, alloc=131.8MB, time=181.04 memory used=4387.3MB, alloc=131.8MB, time=181.22 memory used=4428.4MB, alloc=131.8MB, time=181.40 memory used=4473.3MB, alloc=131.8MB, time=181.58 memory used=4519.6MB, alloc=131.8MB, time=181.77 memory used=4567.5MB, alloc=131.8MB, time=181.96 memory used=4618.8MB, alloc=131.8MB, time=182.15 memory used=4671.7MB, alloc=131.8MB, time=182.35 memory used=4728.5MB, alloc=131.8MB, time=182.55 memory used=4786.7MB, alloc=131.8MB, time=182.77 memory used=4848.6MB, alloc=131.8MB, time=182.98 memory used=4883.6MB, alloc=131.8MB, time=183.14 memory used=4892.1MB, alloc=131.8MB, time=183.24 memory used=4900.3MB, alloc=131.8MB, time=183.32 memory used=4906.3MB, alloc=131.8MB, time=183.41 memory used=4914.8MB, alloc=131.8MB, time=183.50 memory used=4921.0MB, alloc=131.8MB, time=183.59 memory used=4929.6MB, alloc=131.8MB, time=183.69 memory used=4935.8MB, alloc=131.8MB, time=183.78 memory used=4944.4MB, alloc=131.8MB, time=183.88 memory used=4953.2MB, alloc=131.8MB, time=183.98 memory used=4962.1MB, alloc=131.8MB, time=184.10 memory used=4971.0MB, alloc=131.8MB, time=184.19 memory used=4979.9MB, alloc=131.8MB, time=184.29 memory used=4988.9MB, alloc=131.8MB, time=184.39 memory used=4997.8MB, alloc=131.8MB, time=184.49 memory used=5006.7MB, alloc=131.8MB, time=184.61 memory used=5015.7MB, alloc=131.8MB, time=184.70 memory used=5024.7MB, alloc=131.8MB, time=184.79 memory used=5033.6MB, alloc=131.8MB, time=184.88 memory used=5042.6MB, alloc=131.8MB, time=184.98 memory used=5051.6MB, alloc=131.8MB, time=185.07 memory used=5060.6MB, alloc=131.8MB, time=185.16 memory used=5069.6MB, alloc=131.8MB, time=185.27 memory used=5078.6MB, alloc=131.8MB, time=185.37 memory used=5087.6MB, alloc=131.8MB, time=185.47 memory used=5096.7MB, alloc=131.8MB, time=185.56 memory used=5105.7MB, alloc=131.8MB, time=185.66 memory used=5114.7MB, alloc=131.8MB, time=185.76 memory used=5123.8MB, alloc=131.8MB, time=185.85 memory used=5132.8MB, alloc=131.8MB, time=185.94 memory used=5141.9MB, alloc=131.8MB, time=186.04 memory used=5150.9MB, alloc=131.8MB, time=186.13 memory used=5160.0MB, alloc=131.8MB, time=186.22 memory used=5169.0MB, alloc=131.8MB, time=186.31 memory used=5178.1MB, alloc=131.8MB, time=186.47 memory used=5187.1MB, alloc=131.8MB, time=186.56 memory used=5196.2MB, alloc=131.8MB, time=186.65 memory used=5205.3MB, alloc=131.8MB, time=186.74 memory used=5214.3MB, alloc=131.8MB, time=186.83 memory used=5223.4MB, alloc=131.8MB, time=186.94 memory used=5232.5MB, alloc=131.8MB, time=187.05 memory used=5241.5MB, alloc=131.8MB, time=187.17 memory used=5250.6MB, alloc=131.8MB, time=187.29 memory used=5259.6MB, alloc=131.8MB, time=187.39 memory used=5268.7MB, alloc=131.8MB, time=187.48 memory used=5277.7MB, alloc=131.8MB, time=187.60 memory used=5286.8MB, alloc=131.8MB, time=187.69 memory used=5295.8MB, alloc=131.8MB, time=187.79 memory used=5304.9MB, alloc=131.8MB, time=187.88 memory used=5313.9MB, alloc=131.8MB, time=187.98 memory used=5323.0MB, alloc=131.8MB, time=188.07 memory used=5332.0MB, alloc=131.8MB, time=188.16 memory used=5341.3MB, alloc=131.8MB, time=188.26 memory used=5353.1MB, alloc=131.8MB, time=188.36 memory used=5362.5MB, alloc=131.8MB, time=188.45 memory used=5374.1MB, alloc=131.8MB, time=188.55 memory used=5386.1MB, alloc=131.8MB, time=188.66 memory used=5398.1MB, alloc=131.8MB, time=188.77 memory used=5410.0MB, alloc=131.8MB, time=188.87 memory used=5422.0MB, alloc=131.8MB, time=188.97 memory used=5433.9MB, alloc=131.8MB, time=189.08 memory used=5445.8MB, alloc=131.8MB, time=189.18 memory used=5457.7MB, alloc=131.8MB, time=189.28 memory used=5469.6MB, alloc=131.8MB, time=189.38 memory used=5481.4MB, alloc=131.8MB, time=189.48 memory used=5493.3MB, alloc=131.8MB, time=189.59 memory used=5505.1MB, alloc=131.8MB, time=189.70 memory used=5516.9MB, alloc=131.8MB, time=189.80 memory used=5528.6MB, alloc=131.8MB, time=189.90 memory used=5540.3MB, alloc=131.8MB, time=190.00 memory used=5552.0MB, alloc=131.8MB, time=190.10 memory used=5563.7MB, alloc=131.8MB, time=190.20 memory used=5575.4MB, alloc=131.8MB, time=190.30 memory used=5587.0MB, alloc=131.8MB, time=190.40 memory used=5598.5MB, alloc=131.8MB, time=190.50 memory used=5610.1MB, alloc=131.8MB, time=190.59 memory used=5621.9MB, alloc=131.8MB, time=190.69 memory used=5636.0MB, alloc=131.8MB, time=190.81 memory used=5647.9MB, alloc=131.8MB, time=190.90 memory used=5661.7MB, alloc=131.8MB, time=191.01 memory used=5675.9MB, alloc=131.8MB, time=191.11 memory used=5690.0MB, alloc=131.8MB, time=191.23 memory used=5704.1MB, alloc=131.8MB, time=191.34 memory used=5718.1MB, alloc=131.8MB, time=191.45 memory used=5732.0MB, alloc=131.8MB, time=191.55 memory used=5745.9MB, alloc=131.8MB, time=191.69 memory used=5759.7MB, alloc=131.8MB, time=191.79 memory used=5773.4MB, alloc=131.8MB, time=191.89 memory used=5787.1MB, alloc=131.8MB, time=191.99 memory used=5800.6MB, alloc=131.8MB, time=192.09 memory used=5814.1MB, alloc=131.8MB, time=192.20 memory used=5827.9MB, alloc=131.8MB, time=192.31 memory used=5843.5MB, alloc=131.8MB, time=192.42 memory used=5859.4MB, alloc=131.8MB, time=192.52 memory used=5875.2MB, alloc=131.8MB, time=192.63 memory used=5890.8MB, alloc=131.8MB, time=192.74 memory used=5906.3MB, alloc=131.8MB, time=192.84 memory used=5921.6MB, alloc=131.8MB, time=192.94 memory used=5936.8MB, alloc=131.8MB, time=193.05 memory used=5951.9MB, alloc=131.8MB, time=193.16 memory used=5967.2MB, alloc=131.8MB, time=193.27 memory used=5984.0MB, alloc=131.8MB, time=193.37 memory used=6001.1MB, alloc=131.8MB, time=193.48 memory used=6017.9MB, alloc=131.8MB, time=193.59 memory used=6034.6MB, alloc=131.8MB, time=193.71 memory used=6051.4MB, alloc=131.8MB, time=193.81 memory used=6069.4MB, alloc=131.8MB, time=193.92 memory used=6087.6MB, alloc=131.8MB, time=194.03 memory used=6105.4MB, alloc=131.8MB, time=194.15 memory used=6123.3MB, alloc=131.8MB, time=194.26 memory used=6142.2MB, alloc=131.8MB, time=194.37 memory used=6161.1MB, alloc=131.8MB, time=194.48 memory used=6179.9MB, alloc=131.8MB, time=194.59 memory used=6198.4MB, alloc=131.8MB, time=194.70 memory used=6215.1MB, alloc=131.8MB, time=194.81 memory used=6230.9MB, alloc=131.8MB, time=194.91 memory used=6243.6MB, alloc=131.8MB, time=195.00 memory used=6256.9MB, alloc=131.8MB, time=195.10 memory used=6269.5MB, alloc=131.8MB, time=195.24 memory used=6282.4MB, alloc=131.8MB, time=195.33 memory used=6295.8MB, alloc=131.8MB, time=195.43 memory used=6309.5MB, alloc=131.8MB, time=195.53 memory used=6323.5MB, alloc=131.8MB, time=195.63 memory used=6337.5MB, alloc=131.8MB, time=195.75 memory used=6351.9MB, alloc=131.8MB, time=195.88 memory used=6366.8MB, alloc=131.8MB, time=195.98 memory used=6381.9MB, alloc=131.8MB, time=196.08 memory used=6397.5MB, alloc=131.8MB, time=196.18 memory used=6467.4MB, alloc=131.8MB, time=196.75 memory used=6513.8MB, alloc=131.8MB, time=196.96 memory used=6581.3MB, alloc=131.8MB, time=199.49 memory used=6654.6MB, alloc=131.8MB, time=210.39 memory used=6702.3MB, alloc=131.8MB, time=210.63 memory used=6758.3MB, alloc=131.8MB, time=210.86 memory used=6809.5MB, alloc=131.8MB, time=211.08 memory used=6849.0MB, alloc=131.8MB, time=211.25 memory used=6892.4MB, alloc=131.8MB, time=211.43 memory used=6940.5MB, alloc=131.8MB, time=211.62 memory used=6994.6MB, alloc=131.8MB, time=211.81 memory used=7054.4MB, alloc=131.8MB, time=212.02 memory used=7121.6MB, alloc=131.8MB, time=212.24 memory used=7136.9MB, alloc=131.8MB, time=212.36 memory used=7146.3MB, alloc=131.8MB, time=212.46 memory used=7155.9MB, alloc=131.8MB, time=212.55 memory used=7166.3MB, alloc=131.8MB, time=212.65 memory used=7176.8MB, alloc=131.8MB, time=212.75 memory used=7187.3MB, alloc=131.8MB, time=212.85 memory used=7197.8MB, alloc=131.8MB, time=212.97 memory used=7209.1MB, alloc=131.8MB, time=213.07 memory used=7220.3MB, alloc=131.8MB, time=213.17 memory used=7231.6MB, alloc=131.8MB, time=213.29 memory used=7243.5MB, alloc=131.8MB, time=213.39 memory used=7255.3MB, alloc=131.8MB, time=213.49 memory used=7268.0MB, alloc=131.8MB, time=213.60 memory used=7280.6MB, alloc=131.8MB, time=213.70 memory used=7293.4MB, alloc=131.8MB, time=213.82 memory used=7306.9MB, alloc=131.8MB, time=213.92 memory used=7320.9MB, alloc=131.8MB, time=214.02 memory used=7335.0MB, alloc=131.8MB, time=214.12 memory used=7350.0MB, alloc=131.8MB, time=214.23 memory used=7365.5MB, alloc=131.8MB, time=214.33 memory used=7460.1MB, alloc=131.8MB, time=217.52 memory used=7555.3MB, alloc=131.8MB, time=222.08 memory used=7602.3MB, alloc=131.8MB, time=222.32 memory used=7657.1MB, alloc=131.8MB, time=222.58 |\^/| 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(); 1428269631 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 3 3 F := [11 y z + 14 x + 3 y z - 15, 2 x y - 6 x y z + 9 y + 20 z , 2 2 2 2 3 y z + 2 x z + 2 x - 5 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 4 2 3 G := [4 x y z - 14 z + 4 z - 10, -7 x + 11 x y z + 15 y z + 11 x y, 2 3 2 9 x y z - 14 y z - 15 x y z - 8 y z ] > Problem := [F,G]; 3 3 3 2 3 3 Problem := [[11 y z + 14 x + 3 y z - 15, 2 x y - 6 x y z + 9 y + 20 z , 2 2 2 2 2 4 3 3 y z + 2 x z + 2 x - 5 x z], [4 x y z - 14 z + 4 z - 10, 4 2 3 -7 x + 11 x y z + 15 y z + 11 x y, 2 3 2 9 x y z - 14 y z - 15 x y z - 8 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=25.6MB, alloc=32.3MB, time=0.84 memory used=44.9MB, alloc=32.3MB, time=1.35 memory used=63.7MB, alloc=32.3MB, time=1.67 memory used=80.9MB, alloc=56.3MB, time=2.10 memory used=121.7MB, alloc=60.3MB, time=2.75 memory used=166.6MB, alloc=68.3MB, time=3.69 memory used=209.2MB, alloc=68.3MB, time=4.71 memory used=249.5MB, alloc=68.3MB, time=5.63 memory used=282.9MB, alloc=68.3MB, time=6.09 memory used=322.9MB, alloc=92.3MB, time=7.05 memory used=397.0MB, alloc=92.3MB, time=8.77 memory used=460.8MB, alloc=92.3MB, time=10.36 memory used=508.3MB, alloc=92.3MB, time=11.23 memory used=551.9MB, alloc=92.3MB, time=11.88 memory used=615.1MB, alloc=372.3MB, time=13.25 memory used=698.3MB, alloc=372.3MB, time=15.26 memory used=752.8MB, alloc=372.3MB, time=16.34 memory used=802.4MB, alloc=372.3MB, time=16.74 memory used=852.9MB, alloc=372.3MB, time=17.49 memory used=946.1MB, alloc=372.3MB, time=19.50 memory used=1035.0MB, alloc=396.3MB, time=21.15 memory used=1156.3MB, alloc=396.3MB, time=23.41 memory used=1267.5MB, alloc=420.3MB, time=25.91 memory used=1367.5MB, alloc=444.3MB, time=28.01 memory used=1469.3MB, alloc=444.3MB, time=30.74 memory used=1575.0MB, alloc=444.3MB, time=31.87 memory used=1653.0MB, alloc=444.3MB, time=33.42 memory used=1739.2MB, alloc=444.3MB, time=34.09 memory used=1826.6MB, alloc=444.3MB, time=35.42 memory used=1918.0MB, alloc=444.3MB, time=37.34 memory used=1985.8MB, alloc=444.3MB, time=37.80 memory used=2077.4MB, alloc=444.3MB, time=38.91 memory used=2152.5MB, alloc=444.3MB, time=39.53 memory used=2234.7MB, alloc=444.3MB, time=40.22 memory used=2355.8MB, alloc=468.3MB, time=42.67 memory used=2473.3MB, alloc=468.3MB, time=45.14 memory used=2614.1MB, alloc=468.3MB, time=47.72 memory used=2750.9MB, alloc=468.3MB, time=50.73 memory used=2826.9MB, alloc=468.3MB, time=52.74 memory used=2903.5MB, alloc=468.3MB, time=54.86 memory used=2983.4MB, alloc=468.3MB, time=56.95 memory used=3051.0MB, alloc=468.3MB, time=58.66 memory used=3119.4MB, alloc=492.3MB, time=60.30 memory used=3191.7MB, alloc=492.3MB, time=62.65 memory used=3272.4MB, alloc=492.3MB, time=65.26 memory used=3386.5MB, alloc=492.3MB, time=69.65 memory used=3467.9MB, alloc=492.3MB, time=71.36 memory used=3594.7MB, alloc=492.3MB, time=73.53 memory used=3677.7MB, alloc=492.3MB, time=75.49 memory used=3726.3MB, alloc=492.3MB, time=76.96 memory used=3801.2MB, alloc=492.3MB, time=78.68 memory used=3857.6MB, alloc=492.3MB, time=79.95 memory used=3922.2MB, alloc=492.3MB, time=81.66 memory used=3964.4MB, alloc=492.3MB, time=83.24 memory used=4155.7MB, alloc=516.3MB, time=88.01 memory used=4345.1MB, alloc=540.3MB, time=92.87 memory used=4497.6MB, alloc=564.3MB, time=97.09 memory used=4728.4MB, alloc=588.3MB, time=101.38 memory used=4919.5MB, alloc=588.3MB, time=105.13 memory used=5122.4MB, alloc=588.3MB, time=108.97 memory used=5265.1MB, alloc=588.3MB, time=110.95 memory used=5480.4MB, alloc=612.3MB, time=116.20 memory used=5711.9MB, alloc=612.3MB, time=121.45 memory used=5860.8MB, alloc=612.3MB, time=125.84 memory used=6067.4MB, alloc=636.3MB, time=130.43 memory used=6170.9MB, alloc=636.3MB, time=133.75 memory used=6286.7MB, alloc=636.3MB, time=137.44 memory used=6394.8MB, alloc=636.3MB, time=141.18 memory used=6530.2MB, alloc=636.3MB, time=145.51 memory used=6621.6MB, alloc=636.3MB, time=148.44 memory used=6695.6MB, alloc=636.3MB, time=151.37 memory used=6788.9MB, alloc=636.3MB, time=154.83 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428269931 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 2 2 F := [-14 x y + x y z - 6 x - x z, -4 x z + 10 x + 20 y - 3 y, 3 2 -13 y - 17 y z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 2 2 2 G := [-19 x z - 9 x y - 20 z + 17, -9 x y - 2 x z + 13 x z + 10 y , 2 2 2 2 2 12 x y - 14 x y z - 5 y z - 16 y z ] > Problem := [F,G]; 2 2 2 3 2 2 2 2 Problem := [[-14 x y + x y z - 6 x - x z, -4 x z + 10 x + 20 y - 3 y, 3 2 2 2 3 -13 y - 17 y z ], [-19 x z - 9 x y - 20 z + 17, 3 2 2 2 2 -9 x y - 2 x z + 13 x z + 10 y , 2 2 2 2 2 12 x y - 14 x y z - 5 y z - 16 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.9MB, alloc=32.3MB, time=0.87 memory used=45.3MB, alloc=56.3MB, time=1.33 memory used=86.6MB, alloc=60.3MB, time=2.28 memory used=127.0MB, alloc=60.3MB, time=3.30 memory used=161.0MB, alloc=60.3MB, time=4.08 memory used=201.1MB, alloc=60.3MB, time=4.85 memory used=238.0MB, alloc=60.3MB, time=5.47 memory used=288.3MB, alloc=92.4MB, time=6.55 memory used=361.0MB, alloc=92.4MB, time=8.14 memory used=426.0MB, alloc=92.4MB, time=9.58 memory used=473.1MB, alloc=92.4MB, time=10.29 memory used=517.8MB, alloc=92.4MB, time=10.92 memory used=579.3MB, alloc=372.4MB, time=12.25 memory used=671.5MB, alloc=372.4MB, time=14.44 memory used=764.6MB, alloc=396.4MB, time=16.47 memory used=885.1MB, alloc=396.4MB, time=19.18 memory used=992.9MB, alloc=420.4MB, time=21.98 memory used=1113.8MB, alloc=420.4MB, time=24.64 memory used=1246.5MB, alloc=420.4MB, time=26.76 memory used=1342.0MB, alloc=420.4MB, time=28.41 memory used=1479.2MB, alloc=444.4MB, time=31.52 memory used=1578.8MB, alloc=444.4MB, time=32.70 memory used=1665.8MB, alloc=444.4MB, time=33.75 memory used=1800.8MB, alloc=444.4MB, time=36.32 memory used=1914.3MB, alloc=468.4MB, time=39.22 memory used=2016.4MB, alloc=468.4MB, time=41.57 memory used=2130.6MB, alloc=468.4MB, time=43.90 memory used=2238.4MB, alloc=468.4MB, time=46.39 memory used=2336.4MB, alloc=492.4MB, time=48.94 memory used=2427.4MB, alloc=492.4MB, time=51.62 memory used=2510.5MB, alloc=492.4MB, time=53.64 memory used=2579.0MB, alloc=492.4MB, time=55.29 memory used=2655.1MB, alloc=516.4MB, time=57.13 memory used=2738.1MB, alloc=516.4MB, time=59.13 memory used=2830.2MB, alloc=516.4MB, time=60.94 memory used=2904.7MB, alloc=516.4MB, time=63.17 memory used=2968.2MB, alloc=516.4MB, time=64.81 memory used=3047.2MB, alloc=516.4MB, time=66.80 memory used=3112.0MB, alloc=516.4MB, time=68.36 memory used=3171.7MB, alloc=516.4MB, time=70.01 memory used=3249.4MB, alloc=540.4MB, time=71.47 memory used=3321.8MB, alloc=540.4MB, time=74.05 memory used=3375.1MB, alloc=540.4MB, time=75.68 memory used=3422.7MB, alloc=540.4MB, time=77.27 memory used=3623.0MB, alloc=564.4MB, time=82.15 memory used=3812.5MB, alloc=588.4MB, time=86.28 memory used=4050.9MB, alloc=588.4MB, time=90.42 memory used=4248.7MB, alloc=588.4MB, time=95.35 memory used=4445.2MB, alloc=612.4MB, time=99.66 memory used=4643.0MB, alloc=636.4MB, time=104.70 memory used=4845.9MB, alloc=660.4MB, time=109.91 memory used=5013.0MB, alloc=660.4MB, time=114.45 memory used=5208.5MB, alloc=660.4MB, time=118.91 memory used=5343.7MB, alloc=660.4MB, time=122.07 memory used=5465.9MB, alloc=660.4MB, time=125.50 memory used=5611.7MB, alloc=684.4MB, time=128.97 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428270231 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 F := [-20 x y z - 19 x y z + 10 x - 13 z , 20 x z + 8 y z - 20 y z, 2 3 -3 y z + 17 z + 9 x y - 3 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 G := [-15 x z - 2 y - 11 y , -14 x y - 18 x y z + 7 x - 10 z, 2 2 2 2 4 x y z + 16 y z + 19 x z - 20 z] > Problem := [F,G]; 2 2 3 2 2 2 Problem := [[-20 x y z - 19 x y z + 10 x - 13 z , 20 x z + 8 y z - 20 y z, 2 3 2 2 3 2 -3 y z + 17 z + 9 x y - 3 x z], [-15 x z - 2 y - 11 y , 2 2 2 2 2 2 2 -14 x y - 18 x y z + 7 x - 10 z, 4 x y z + 16 y z + 19 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=4.5MB, alloc=32.3MB, time=0.32 memory used=25.9MB, alloc=32.3MB, time=0.89 memory used=45.7MB, alloc=60.3MB, time=1.42 memory used=86.6MB, alloc=60.3MB, time=2.50 memory used=127.3MB, alloc=60.3MB, time=3.57 memory used=161.3MB, alloc=84.3MB, time=4.41 memory used=224.0MB, alloc=92.3MB, time=6.10 memory used=287.2MB, alloc=116.3MB, time=7.66 memory used=363.5MB, alloc=116.3MB, time=9.60 memory used=443.5MB, alloc=140.3MB, time=11.80 memory used=515.5MB, alloc=140.3MB, time=13.76 memory used=582.9MB, alloc=396.3MB, time=15.57 memory used=686.1MB, alloc=396.3MB, time=18.14 memory used=792.3MB, alloc=420.3MB, time=20.29 memory used=922.9MB, alloc=420.3MB, time=23.79 memory used=1050.1MB, alloc=444.3MB, time=27.22 memory used=1173.8MB, alloc=468.3MB, time=30.48 memory used=1290.8MB, alloc=468.3MB, time=33.15 memory used=1426.9MB, alloc=468.3MB, time=36.98 memory used=1548.3MB, alloc=492.3MB, time=40.27 memory used=1661.4MB, alloc=492.3MB, time=45.37 memory used=1783.4MB, alloc=492.3MB, time=48.82 memory used=1883.6MB, alloc=492.3MB, time=51.76 memory used=1977.5MB, alloc=492.3MB, time=54.46 memory used=2091.7MB, alloc=492.3MB, time=57.87 memory used=2183.4MB, alloc=492.3MB, time=60.56 memory used=2292.3MB, alloc=492.3MB, time=62.80 memory used=2371.4MB, alloc=492.3MB, time=65.00 memory used=2503.9MB, alloc=516.3MB, time=67.14 memory used=2592.4MB, alloc=516.3MB, time=67.84 memory used=2712.0MB, alloc=516.3MB, time=68.84 memory used=2805.2MB, alloc=516.3MB, time=69.58 memory used=2948.1MB, alloc=516.3MB, time=98.98 memory used=3070.6MB, alloc=516.3MB, time=100.93 memory used=3177.7MB, alloc=516.3MB, time=101.68 memory used=3254.8MB, alloc=516.3MB, time=102.36 memory used=3338.8MB, alloc=516.3MB, time=103.03 memory used=3437.4MB, alloc=516.3MB, time=103.77 memory used=3552.3MB, alloc=516.3MB, time=104.62 memory used=3746.1MB, alloc=516.3MB, time=105.98 memory used=3901.1MB, alloc=516.3MB, time=106.83 memory used=4086.2MB, alloc=516.3MB, time=107.83 memory used=4248.1MB, alloc=516.3MB, time=110.09 memory used=4394.8MB, alloc=516.3MB, time=112.66 memory used=4529.9MB, alloc=516.3MB, time=114.96 memory used=4599.5MB, alloc=516.3MB, time=117.11 memory used=4708.8MB, alloc=516.3MB, time=118.11 memory used=4837.8MB, alloc=516.3MB, time=130.09 memory used=4935.7MB, alloc=516.3MB, time=130.89 memory used=5014.5MB, alloc=516.3MB, time=131.59 memory used=5106.9MB, alloc=516.3MB, time=132.30 memory used=5282.5MB, alloc=516.3MB, time=134.06 memory used=5371.9MB, alloc=516.3MB, time=137.36 memory used=5438.2MB, alloc=516.3MB, time=139.53 memory used=5521.7MB, alloc=516.3MB, time=141.91 memory used=5579.3MB, alloc=540.3MB, time=143.87 |\^/| 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(); 1428270531 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [5 x y z + 6 x z - 16 y z - 14, 7 x z + 10 x y z - 2 x + 13, 2 2 3 2 2 4 x z - 10 x - 20 x z + 2 x z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 3 2 2 G := [-11 z + 14 y - 2 y z + 9 y z , -2 y z + 18 x y + 15 y z + 8 x, 4 2 2 2 2 x - 11 y z + 16 x y + 16 y z ] > Problem := [F,G]; 2 2 3 2 Problem := [[5 x y z + 6 x z - 16 y z - 14, 7 x z + 10 x y z - 2 x + 13, 2 2 3 2 2 4 3 2 2 4 x z - 10 x - 20 x z + 2 x z ], [-11 z + 14 y - 2 y z + 9 y z , 3 2 2 4 2 2 2 2 -2 y z + 18 x y + 15 y z + 8 x, x - 11 y z + 16 x 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=4.4MB, alloc=32.3MB, time=0.32 memory used=23.8MB, alloc=32.3MB, time=0.84 memory used=41.8MB, alloc=56.3MB, time=1.34 memory used=77.7MB, alloc=60.3MB, time=2.26 memory used=120.9MB, alloc=68.3MB, time=3.36 memory used=165.7MB, alloc=68.3MB, time=4.47 memory used=204.5MB, alloc=92.3MB, time=5.15 memory used=261.2MB, alloc=92.3MB, time=5.68 memory used=322.2MB, alloc=92.3MB, time=6.62 memory used=377.3MB, alloc=92.3MB, time=7.33 memory used=461.2MB, alloc=93.4MB, time=8.76 memory used=517.0MB, alloc=93.4MB, time=9.36 memory used=570.4MB, alloc=93.4MB, time=9.95 memory used=639.0MB, alloc=93.4MB, time=11.57 memory used=687.0MB, alloc=93.4MB, time=12.16 memory used=742.9MB, alloc=93.4MB, time=12.90 memory used=808.9MB, alloc=93.4MB, time=14.37 memory used=870.2MB, alloc=93.4MB, time=15.44 memory used=920.3MB, alloc=93.4MB, time=16.21 memory used=984.2MB, alloc=349.4MB, time=17.72 memory used=1055.2MB, alloc=373.4MB, time=19.32 memory used=1135.0MB, alloc=373.4MB, time=20.68 memory used=1235.7MB, alloc=373.4MB, time=22.87 memory used=1307.3MB, alloc=373.4MB, time=24.31 memory used=1344.4MB, alloc=373.4MB, time=24.54 memory used=1402.1MB, alloc=373.4MB, time=25.46 memory used=1439.6MB, alloc=373.4MB, time=25.70 memory used=1563.7MB, alloc=373.4MB, time=29.90 memory used=1625.2MB, alloc=373.4MB, time=30.62 memory used=1686.9MB, alloc=373.4MB, time=31.10 memory used=1777.5MB, alloc=373.4MB, time=32.76 memory used=1852.4MB, alloc=397.4MB, time=34.79 memory used=1963.7MB, alloc=421.4MB, time=37.46 memory used=2088.4MB, alloc=421.4MB, time=40.23 memory used=2208.7MB, alloc=445.4MB, time=43.23 memory used=2340.7MB, alloc=445.4MB, time=46.10 memory used=2433.3MB, alloc=445.4MB, time=48.46 memory used=2558.9MB, alloc=445.4MB, time=50.43 memory used=2666.2MB, alloc=445.4MB, time=51.90 memory used=2765.8MB, alloc=445.4MB, time=53.47 memory used=2866.7MB, alloc=445.4MB, time=54.60 memory used=2927.1MB, alloc=445.4MB, time=55.08 memory used=2999.9MB, alloc=445.4MB, time=55.56 memory used=3080.8MB, alloc=445.4MB, time=56.62 memory used=3160.6MB, alloc=469.4MB, time=57.21 memory used=3243.8MB, alloc=469.4MB, time=57.75 memory used=3359.4MB, alloc=469.4MB, time=66.65 memory used=3453.4MB, alloc=469.4MB, time=67.26 memory used=3534.6MB, alloc=469.4MB, time=67.77 memory used=3610.4MB, alloc=469.4MB, time=68.27 memory used=3715.4MB, alloc=469.4MB, time=71.94 memory used=3838.8MB, alloc=469.4MB, time=72.72 memory used=3922.4MB, alloc=469.4MB, time=73.32 memory used=3991.1MB, alloc=469.4MB, time=73.85 memory used=4067.5MB, alloc=469.4MB, time=74.41 memory used=4151.6MB, alloc=469.4MB, time=74.95 memory used=4243.5MB, alloc=469.4MB, time=75.50 memory used=4345.5MB, alloc=469.4MB, time=76.09 memory used=4436.4MB, alloc=469.4MB, time=76.63 memory used=4494.0MB, alloc=469.4MB, time=77.09 memory used=4552.5MB, alloc=469.4MB, time=77.56 memory used=4614.2MB, alloc=469.4MB, time=78.01 memory used=4676.6MB, alloc=469.4MB, time=78.49 memory used=4742.6MB, alloc=469.4MB, time=78.95 memory used=4812.0MB, alloc=469.4MB, time=79.43 memory used=4884.6MB, alloc=469.4MB, time=79.91 memory used=4960.3MB, alloc=469.4MB, time=80.40 memory used=5038.8MB, alloc=469.4MB, time=80.89 memory used=5119.8MB, alloc=469.4MB, time=81.37 memory used=5205.9MB, alloc=469.4MB, time=81.87 memory used=5296.3MB, alloc=469.4MB, time=82.37 memory used=5390.2MB, alloc=469.4MB, time=82.87 memory used=5489.3MB, alloc=469.4MB, time=83.37 memory used=5575.6MB, alloc=469.4MB, time=83.83 memory used=5654.6MB, alloc=469.4MB, time=84.27 memory used=5712.5MB, alloc=469.4MB, time=84.70 memory used=5769.8MB, alloc=469.4MB, time=85.09 memory used=5830.7MB, alloc=469.4MB, time=85.47 memory used=5895.8MB, alloc=469.4MB, time=85.86 memory used=6005.9MB, alloc=469.4MB, time=89.76 memory used=6125.4MB, alloc=469.4MB, time=90.49 memory used=6195.0MB, alloc=469.4MB, time=91.04 memory used=6264.3MB, alloc=469.4MB, time=91.56 memory used=6342.0MB, alloc=469.4MB, time=92.12 memory used=6427.5MB, alloc=469.4MB, time=92.66 memory used=6523.1MB, alloc=469.4MB, time=93.22 memory used=6626.5MB, alloc=469.4MB, time=93.79 memory used=6704.8MB, alloc=469.4MB, time=94.30 memory used=6762.2MB, alloc=469.4MB, time=94.77 memory used=6821.8MB, alloc=469.4MB, time=95.23 memory used=6883.8MB, alloc=469.4MB, time=95.68 memory used=6949.3MB, alloc=469.4MB, time=96.16 memory used=7015.4MB, alloc=469.4MB, time=96.62 memory used=7084.8MB, alloc=469.4MB, time=97.09 memory used=7157.5MB, alloc=469.4MB, time=97.58 memory used=7233.1MB, alloc=469.4MB, time=98.08 memory used=7311.6MB, alloc=469.4MB, time=98.57 memory used=7395.4MB, alloc=469.4MB, time=99.08 memory used=7481.4MB, alloc=469.4MB, time=99.59 memory used=7571.5MB, alloc=469.4MB, time=100.08 memory used=7667.3MB, alloc=469.4MB, time=100.59 memory used=7765.6MB, alloc=469.4MB, time=101.08 memory used=7849.3MB, alloc=469.4MB, time=101.53 memory used=7923.5MB, alloc=469.4MB, time=101.97 memory used=7981.3MB, alloc=469.4MB, time=102.36 memory used=8039.6MB, alloc=469.4MB, time=102.78 memory used=8101.1MB, alloc=469.4MB, time=103.18 memory used=8167.6MB, alloc=469.4MB, time=103.58 memory used=8285.3MB, alloc=493.4MB, time=191.77 |\^/| 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(); 1428270831 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 2 2 2 2 F := [9 x y z + 13 x y z - x z - 9 y , -9 x + 17 x y - 11 x z - 8 x y , 3 2 2 2 x y - 2 x y z - 20 x y + 7 y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 G := [4 x - 10 x z + 4 x y, 13 x z + 13 x y + 13 y z + 8 y, 4 3 2 2 20 x - 11 x y - 11 x y + 13 y ] > Problem := [F,G]; 2 2 2 Problem := [[9 x y z + 13 x y z - x z - 9 y , 4 2 2 2 2 2 3 2 2 -9 x + 17 x y - 11 x z - 8 x y , 2 x y - 2 x y z - 20 x y + 7 y], [ 4 3 3 4 x - 10 x z + 4 x y, 13 x z + 13 x y + 13 y z + 8 y, 4 3 2 2 20 x - 11 x y - 11 x 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=4.4MB, alloc=32.3MB, time=0.31 memory used=26.1MB, alloc=32.3MB, time=0.88 memory used=45.8MB, alloc=32.3MB, time=1.39 memory used=64.6MB, alloc=56.3MB, time=1.89 memory used=107.5MB, alloc=68.3MB, time=2.99 memory used=151.5MB, alloc=68.3MB, time=4.00 memory used=194.4MB, alloc=92.3MB, time=5.03 memory used=261.3MB, alloc=92.3MB, time=6.59 memory used=335.8MB, alloc=92.3MB, time=8.17 memory used=403.8MB, alloc=116.3MB, time=9.86 memory used=464.1MB, alloc=116.3MB, time=11.27 memory used=543.4MB, alloc=372.3MB, time=12.86 memory used=643.9MB, alloc=372.3MB, time=15.04 memory used=733.7MB, alloc=396.3MB, time=17.24 memory used=848.0MB, alloc=396.3MB, time=20.02 memory used=982.4MB, alloc=420.3MB, time=22.59 memory used=1073.8MB, alloc=420.3MB, time=23.90 memory used=1216.3MB, alloc=420.3MB, time=27.25 memory used=1340.6MB, alloc=444.3MB, time=30.34 memory used=1457.0MB, alloc=444.3MB, time=33.17 memory used=1578.6MB, alloc=468.3MB, time=36.09 memory used=1699.1MB, alloc=468.3MB, time=38.86 memory used=1819.2MB, alloc=468.3MB, time=42.15 memory used=1913.6MB, alloc=468.3MB, time=44.60 memory used=2025.6MB, alloc=492.3MB, time=47.09 memory used=2143.8MB, alloc=492.3MB, time=48.25 memory used=2219.7MB, alloc=492.3MB, time=48.81 memory used=2325.0MB, alloc=492.3MB, time=49.63 memory used=2437.2MB, alloc=492.3MB, time=50.59 memory used=2513.6MB, alloc=492.3MB, time=51.18 memory used=2661.8MB, alloc=492.3MB, time=65.16 memory used=2757.4MB, alloc=492.3MB, time=65.80 memory used=2842.5MB, alloc=492.3MB, time=66.32 memory used=2923.6MB, alloc=492.3MB, time=66.81 memory used=3035.5MB, alloc=492.3MB, time=67.84 memory used=3122.3MB, alloc=492.3MB, time=68.46 memory used=3214.7MB, alloc=492.3MB, time=69.04 memory used=3326.6MB, alloc=492.3MB, time=70.15 memory used=3407.5MB, alloc=492.3MB, time=70.75 memory used=3516.9MB, alloc=492.3MB, time=74.69 memory used=3648.8MB, alloc=492.3MB, time=85.31 memory used=3737.3MB, alloc=492.3MB, time=85.88 memory used=3815.1MB, alloc=492.3MB, time=86.40 memory used=3917.3MB, alloc=492.3MB, time=87.34 memory used=4050.7MB, alloc=492.3MB, time=89.31 memory used=4145.3MB, alloc=492.3MB, time=89.99 memory used=4236.6MB, alloc=492.3MB, time=90.60 memory used=4307.3MB, alloc=492.3MB, time=91.16 memory used=4390.6MB, alloc=492.3MB, time=91.73 memory used=4488.0MB, alloc=492.3MB, time=92.32 memory used=4588.7MB, alloc=492.3MB, time=92.91 memory used=4649.2MB, alloc=492.3MB, time=93.41 memory used=4716.5MB, alloc=492.3MB, time=93.87 memory used=4789.3MB, alloc=492.3MB, time=94.35 memory used=4869.5MB, alloc=492.3MB, time=94.82 memory used=4978.9MB, alloc=492.3MB, time=96.40 memory used=5072.2MB, alloc=492.3MB, time=97.08 memory used=5163.4MB, alloc=492.3MB, time=97.71 memory used=5235.3MB, alloc=492.3MB, time=98.29 memory used=5318.9MB, alloc=492.3MB, time=98.87 memory used=5416.5MB, alloc=492.3MB, time=99.46 memory used=5515.8MB, alloc=492.3MB, time=100.05 memory used=5577.5MB, alloc=492.3MB, time=100.51 memory used=5644.8MB, alloc=492.3MB, time=101.00 memory used=5717.4MB, alloc=492.3MB, time=101.50 memory used=5797.7MB, alloc=492.3MB, time=101.98 memory used=5911.3MB, alloc=492.3MB, time=117.35 memory used=6076.0MB, alloc=492.3MB, time=154.33 memory used=6158.9MB, alloc=492.3MB, time=154.92 memory used=6249.5MB, alloc=492.3MB, time=155.50 memory used=6318.6MB, alloc=492.3MB, time=156.02 memory used=6399.5MB, alloc=492.3MB, time=156.52 memory used=6495.1MB, alloc=492.3MB, time=157.03 memory used=6785.3MB, alloc=492.3MB, time=160.05 memory used=6898.5MB, alloc=492.3MB, time=163.30 memory used=7037.8MB, alloc=492.3MB, time=167.83 memory used=7120.7MB, alloc=492.3MB, time=168.38 memory used=7242.6MB, alloc=492.3MB, time=170.90 memory used=7340.3MB, alloc=492.3MB, time=173.60 memory used=7441.5MB, alloc=492.3MB, time=176.44 memory used=7543.0MB, alloc=516.3MB, time=179.00 memory used=7656.1MB, alloc=516.3MB, time=180.54 |\^/| 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(); 1428271131 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 F := [-15 z + 18 x z + 11 x z + 16 z , -12 x z + 19 x y z - 11 z, 2 2 2 4 13 x y - 14 x y z + z - 16 z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [19 x z - 20 x y - 4 x y z, -3 x y z + 7 x z - 18 x z - 10 y z, 2 2 3 3 7 x y - 19 x y + 3 x z + x y z] > Problem := [F,G]; 4 2 2 2 3 Problem := [[-15 z + 18 x z + 11 x z + 16 z , -12 x z + 19 x y z - 11 z, 2 2 2 4 2 2 2 13 x y - 14 x y z + z - 16 z], [19 x z - 20 x y - 4 x y z, 2 3 2 2 2 3 3 -3 x y z + 7 x z - 18 x z - 10 y z, 7 x y - 19 x y + 3 x z + x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.32 memory used=25.3MB, alloc=32.3MB, time=0.88 memory used=45.4MB, alloc=32.3MB, time=1.41 memory used=64.1MB, alloc=56.3MB, time=1.93 memory used=104.2MB, alloc=60.3MB, time=2.95 memory used=146.4MB, alloc=60.3MB, time=3.92 memory used=186.8MB, alloc=68.3MB, time=4.89 memory used=226.2MB, alloc=92.3MB, time=5.93 memory used=292.3MB, alloc=92.3MB, time=7.54 memory used=357.1MB, alloc=92.3MB, time=9.08 memory used=424.2MB, alloc=116.3MB, time=10.74 memory used=496.9MB, alloc=372.3MB, time=12.37 memory used=586.7MB, alloc=372.3MB, time=13.97 memory used=669.7MB, alloc=372.3MB, time=15.54 memory used=719.1MB, alloc=372.3MB, time=16.16 memory used=771.5MB, alloc=372.3MB, time=16.78 memory used=821.3MB, alloc=372.3MB, time=17.36 memory used=871.6MB, alloc=372.3MB, time=17.88 memory used=909.9MB, alloc=372.3MB, time=18.10 memory used=955.6MB, alloc=372.3MB, time=18.45 memory used=993.6MB, alloc=372.3MB, time=18.67 memory used=1046.9MB, alloc=372.3MB, time=20.02 memory used=1085.0MB, alloc=372.3MB, time=20.24 memory used=1127.0MB, alloc=372.3MB, time=20.61 memory used=1174.2MB, alloc=372.3MB, time=21.00 memory used=1210.4MB, alloc=372.3MB, time=21.21 memory used=1260.3MB, alloc=372.3MB, time=21.56 memory used=1296.3MB, alloc=372.3MB, time=21.77 memory used=1348.2MB, alloc=372.3MB, time=23.13 memory used=1386.9MB, alloc=372.3MB, time=23.32 memory used=1431.0MB, alloc=372.3MB, time=23.66 memory used=1468.6MB, alloc=372.3MB, time=23.87 memory used=1515.8MB, alloc=372.3MB, time=24.20 memory used=1553.1MB, alloc=372.3MB, time=24.41 memory used=1610.0MB, alloc=372.3MB, time=25.84 memory used=1647.4MB, alloc=372.3MB, time=26.05 memory used=1714.8MB, alloc=372.3MB, time=27.07 memory used=1796.9MB, alloc=372.3MB, time=29.06 memory used=1833.0MB, alloc=372.3MB, time=29.27 memory used=1869.9MB, alloc=372.3MB, time=29.46 memory used=1942.7MB, alloc=372.3MB, time=30.52 memory used=2026.8MB, alloc=396.3MB, time=31.76 memory used=2142.0MB, alloc=396.3MB, time=34.39 memory used=2251.7MB, alloc=420.3MB, time=37.12 memory used=2366.5MB, alloc=420.3MB, time=39.85 memory used=2496.2MB, alloc=420.3MB, time=43.25 memory used=2624.5MB, alloc=444.3MB, time=46.64 memory used=2767.6MB, alloc=444.3MB, time=49.37 memory used=2849.1MB, alloc=444.3MB, time=50.70 memory used=2928.5MB, alloc=444.3MB, time=51.81 memory used=3056.6MB, alloc=444.3MB, time=54.11 memory used=3148.9MB, alloc=468.3MB, time=56.03 memory used=3262.4MB, alloc=468.3MB, time=57.80 memory used=3375.4MB, alloc=468.3MB, time=59.31 memory used=3505.4MB, alloc=468.3MB, time=61.39 memory used=3596.3MB, alloc=468.3MB, time=62.44 memory used=3675.5MB, alloc=468.3MB, time=62.92 memory used=3754.0MB, alloc=468.3MB, time=63.60 memory used=3836.4MB, alloc=468.3MB, time=64.12 memory used=3902.5MB, alloc=468.3MB, time=64.52 memory used=3994.4MB, alloc=468.3MB, time=66.36 memory used=4069.3MB, alloc=468.3MB, time=66.78 memory used=4208.9MB, alloc=468.3MB, time=68.58 memory used=4293.6MB, alloc=468.3MB, time=69.23 memory used=4418.4MB, alloc=468.3MB, time=72.29 memory used=4513.3MB, alloc=468.3MB, time=73.32 memory used=4597.3MB, alloc=468.3MB, time=74.02 memory used=4676.9MB, alloc=468.3MB, time=74.63 memory used=4755.6MB, alloc=468.3MB, time=75.17 memory used=4838.0MB, alloc=468.3MB, time=76.64 memory used=4909.0MB, alloc=468.3MB, time=77.11 memory used=5001.3MB, alloc=468.3MB, time=78.10 memory used=5083.9MB, alloc=468.3MB, time=78.97 memory used=5158.7MB, alloc=468.3MB, time=79.44 memory used=5238.5MB, alloc=468.3MB, time=80.08 memory used=5322.9MB, alloc=468.3MB, time=81.51 memory used=5395.5MB, alloc=468.3MB, time=81.99 memory used=5484.4MB, alloc=468.3MB, time=82.59 memory used=5564.3MB, alloc=468.3MB, time=83.10 memory used=5642.8MB, alloc=468.3MB, time=83.72 memory used=5718.2MB, alloc=468.3MB, time=84.21 memory used=5797.7MB, alloc=468.3MB, time=85.72 memory used=5869.2MB, alloc=468.3MB, time=86.17 memory used=5977.1MB, alloc=468.3MB, time=87.27 memory used=6059.6MB, alloc=468.3MB, time=87.91 memory used=6194.9MB, alloc=468.3MB, time=89.90 memory used=6300.7MB, alloc=468.3MB, time=91.71 memory used=6392.5MB, alloc=468.3MB, time=92.54 memory used=6501.4MB, alloc=468.3MB, time=94.44 memory used=6613.1MB, alloc=468.3MB, time=96.02 memory used=6759.9MB, alloc=468.3MB, time=99.04 memory used=6863.9MB, alloc=468.3MB, time=100.89 memory used=6974.5MB, alloc=468.3MB, time=102.51 memory used=7098.4MB, alloc=468.3MB, time=104.82 memory used=7229.0MB, alloc=492.3MB, time=107.31 memory used=7343.8MB, alloc=492.3MB, time=108.58 memory used=7478.8MB, alloc=492.3MB, time=110.39 memory used=7612.5MB, alloc=492.3MB, time=112.77 memory used=7744.6MB, alloc=492.3MB, time=115.67 memory used=7874.8MB, alloc=492.3MB, time=117.80 memory used=7965.8MB, alloc=492.3MB, time=119.52 memory used=8084.0MB, alloc=492.3MB, time=123.12 memory used=8164.0MB, alloc=492.3MB, time=125.42 memory used=8232.0MB, alloc=492.3MB, time=127.41 memory used=8325.8MB, alloc=492.3MB, time=130.30 memory used=8408.9MB, alloc=516.3MB, time=133.06 memory used=8489.5MB, alloc=516.3MB, time=135.70 memory used=8551.5MB, alloc=516.3MB, time=137.47 memory used=8623.3MB, alloc=516.3MB, time=139.95 memory used=8693.4MB, alloc=516.3MB, time=141.96 memory used=8752.1MB, alloc=516.3MB, time=143.69 memory used=8802.3MB, alloc=516.3MB, time=145.35 memory used=8866.3MB, alloc=516.3MB, time=147.01 memory used=8922.6MB, alloc=540.3MB, time=148.42 memory used=9119.6MB, alloc=564.3MB, time=152.97 memory used=9319.8MB, alloc=588.3MB, time=158.46 memory used=9490.2MB, alloc=612.3MB, time=162.57 |\^/| 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(); 1428271431 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 F := [7 x y - 3 x - 3 y z - 2 y, 19 x y - 17 y - 7 x - 7, 2 3 2 2 11 x y z + x + 17 x z - 8 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 G := [10 x z - 10 x + 15 x y z, -14 x y z + 13 x y z - x , 4 4 2 -12 y + 18 z - 13 x y - 10 y ] > Problem := [F,G]; 3 3 2 2 Problem := [[7 x y - 3 x - 3 y z - 2 y, 19 x y - 17 y - 7 x - 7, 2 3 2 2 3 3 11 x y z + x + 17 x z - 8 z ], [10 x z - 10 x + 15 x y z, 2 2 3 4 4 2 -14 x y z + 13 x y z - x , -12 y + 18 z - 13 x y - 10 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.8MB, alloc=32.3MB, time=0.88 memory used=44.8MB, alloc=32.3MB, time=1.37 memory used=64.1MB, alloc=60.3MB, time=1.90 memory used=105.3MB, alloc=60.3MB, time=2.99 memory used=146.1MB, alloc=60.3MB, time=4.02 memory used=185.8MB, alloc=84.3MB, time=5.09 memory used=226.1MB, alloc=84.3MB, time=6.19 memory used=287.0MB, alloc=116.3MB, time=7.87 memory used=368.8MB, alloc=372.3MB, time=10.13 memory used=459.6MB, alloc=396.3MB, time=12.48 memory used=566.7MB, alloc=396.3MB, time=15.50 memory used=681.0MB, alloc=420.3MB, time=18.56 memory used=804.4MB, alloc=444.3MB, time=21.97 memory used=935.6MB, alloc=444.3MB, time=25.61 memory used=1067.1MB, alloc=468.3MB, time=29.42 memory used=1195.4MB, alloc=468.3MB, time=33.45 memory used=1325.4MB, alloc=492.3MB, time=37.66 memory used=1432.2MB, alloc=492.3MB, time=41.20 memory used=1538.4MB, alloc=492.3MB, time=44.66 memory used=1648.8MB, alloc=492.3MB, time=48.50 memory used=1742.1MB, alloc=492.3MB, time=51.52 memory used=1825.7MB, alloc=492.3MB, time=54.27 memory used=1907.0MB, alloc=492.3MB, time=57.19 memory used=1993.8MB, alloc=492.3MB, time=60.35 memory used=2075.6MB, alloc=492.3MB, time=63.39 memory used=2158.5MB, alloc=492.3MB, time=66.48 memory used=2223.8MB, alloc=516.3MB, time=68.82 memory used=2283.8MB, alloc=516.3MB, time=71.14 memory used=2346.6MB, alloc=516.3MB, time=73.32 memory used=2407.4MB, alloc=516.3MB, time=75.88 memory used=2448.4MB, alloc=516.3MB, time=77.26 memory used=2501.9MB, alloc=516.3MB, time=79.65 memory used=2548.4MB, alloc=516.3MB, time=81.72 memory used=2601.1MB, alloc=516.3MB, time=83.96 memory used=2810.0MB, alloc=540.3MB, time=91.32 memory used=3021.3MB, alloc=564.3MB, time=98.26 memory used=3230.7MB, alloc=588.3MB, time=105.13 memory used=3449.5MB, alloc=612.3MB, time=112.92 memory used=3633.6MB, alloc=612.3MB, time=119.30 memory used=3814.8MB, alloc=636.3MB, time=126.12 |\^/| 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(); 1428271731 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 3 F := [5 x y z - 8 x - 19 x y + 19 x, 12 y z - 18 x y - 13 y - 2 z, 3 2 2 19 x z + 6 x z - 15 y z - 10 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 4 2 2 G := [-12 x y z + 12 y z - x - 14 y z, -y z - 18 z + 19 y z + 5 x , 3 3 2 2 -2 x y - 11 y z - 9 x z - 2 y z ] > Problem := [F,G]; 2 3 2 2 2 2 3 Problem := [[5 x y z - 8 x - 19 x y + 19 x, 12 y z - 18 x y - 13 y - 2 z, 3 2 2 2 2 2 19 x z + 6 x z - 15 y z - 10 y z], [-12 x y z + 12 y z - x - 14 y z, 3 4 2 2 3 3 2 2 -y z - 18 z + 19 y z + 5 x , -2 x y - 11 y z - 9 x z - 2 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.88 memory used=45.9MB, alloc=56.3MB, time=1.39 memory used=85.4MB, alloc=60.3MB, time=2.40 memory used=127.4MB, alloc=68.3MB, time=3.45 memory used=164.5MB, alloc=68.3MB, time=4.22 memory used=189.8MB, alloc=68.3MB, time=4.47 memory used=222.8MB, alloc=68.3MB, time=5.09 memory used=274.5MB, alloc=68.3MB, time=6.18 memory used=326.0MB, alloc=68.3MB, time=8.08 memory used=368.1MB, alloc=92.3MB, time=9.13 memory used=424.3MB, alloc=92.3MB, time=10.27 memory used=486.3MB, alloc=92.3MB, time=11.29 memory used=535.3MB, alloc=92.3MB, time=11.99 memory used=601.2MB, alloc=92.3MB, time=13.22 memory used=663.0MB, alloc=92.3MB, time=14.47 memory used=723.8MB, alloc=116.3MB, time=16.10 memory used=785.5MB, alloc=372.3MB, time=17.64 memory used=869.9MB, alloc=396.3MB, time=19.85 memory used=983.7MB, alloc=420.3MB, time=22.49 memory used=1096.4MB, alloc=420.3MB, time=25.10 memory used=1210.5MB, alloc=444.3MB, time=27.80 memory used=1320.0MB, alloc=444.3MB, time=30.00 memory used=1417.8MB, alloc=444.3MB, time=31.16 memory used=1509.2MB, alloc=444.3MB, time=32.42 memory used=1592.9MB, alloc=444.3MB, time=33.04 memory used=1674.8MB, alloc=444.3MB, time=34.84 memory used=1756.5MB, alloc=444.3MB, time=35.90 memory used=1836.0MB, alloc=444.3MB, time=36.41 memory used=1915.4MB, alloc=444.3MB, time=37.22 memory used=1997.8MB, alloc=444.3MB, time=39.01 memory used=2090.3MB, alloc=444.3MB, time=40.39 memory used=2176.7MB, alloc=444.3MB, time=41.43 memory used=2260.0MB, alloc=444.3MB, time=42.11 memory used=2364.0MB, alloc=444.3MB, time=44.14 memory used=2445.7MB, alloc=444.3MB, time=44.80 memory used=2513.1MB, alloc=444.3MB, time=45.25 memory used=2601.3MB, alloc=444.3MB, time=45.92 memory used=2699.4MB, alloc=444.3MB, time=48.89 memory used=2782.0MB, alloc=444.3MB, time=49.89 memory used=2937.0MB, alloc=444.3MB, time=53.47 memory used=3089.1MB, alloc=444.3MB, time=57.99 memory used=3213.9MB, alloc=468.3MB, time=60.73 memory used=3346.4MB, alloc=468.3MB, time=65.11 memory used=3512.9MB, alloc=468.3MB, time=67.37 memory used=3637.9MB, alloc=468.3MB, time=71.00 memory used=3720.9MB, alloc=468.3MB, time=73.23 memory used=3781.9MB, alloc=468.3MB, time=74.72 memory used=3860.2MB, alloc=468.3MB, time=77.06 memory used=3928.5MB, alloc=468.3MB, time=78.85 memory used=4006.6MB, alloc=492.3MB, time=81.11 memory used=4075.5MB, alloc=492.3MB, time=83.02 memory used=4204.7MB, alloc=492.3MB, time=85.11 memory used=4308.8MB, alloc=492.3MB, time=87.21 memory used=4411.4MB, alloc=492.3MB, time=88.12 memory used=4525.1MB, alloc=492.3MB, time=90.63 memory used=4610.7MB, alloc=492.3MB, time=92.73 memory used=4675.1MB, alloc=492.3MB, time=94.50 memory used=4757.2MB, alloc=492.3MB, time=97.00 memory used=4825.8MB, alloc=492.3MB, time=98.52 memory used=4879.4MB, alloc=492.3MB, time=99.97 memory used=4994.7MB, alloc=492.3MB, time=101.75 memory used=5088.2MB, alloc=516.3MB, time=102.53 memory used=5174.3MB, alloc=516.3MB, time=103.24 memory used=5283.6MB, alloc=516.3MB, time=103.95 memory used=5393.3MB, alloc=516.3MB, time=105.06 memory used=5504.6MB, alloc=516.3MB, time=108.60 memory used=5607.3MB, alloc=516.3MB, time=109.36 memory used=5713.3MB, alloc=516.3MB, time=110.69 memory used=5811.8MB, alloc=516.3MB, time=111.48 memory used=5911.1MB, alloc=516.3MB, time=112.23 memory used=6023.4MB, alloc=516.3MB, time=113.60 memory used=6128.1MB, alloc=516.3MB, time=114.44 memory used=6217.3MB, alloc=516.3MB, time=115.16 memory used=6321.4MB, alloc=516.3MB, time=115.89 memory used=6438.1MB, alloc=516.3MB, time=123.00 memory used=6538.2MB, alloc=516.3MB, time=123.71 memory used=6627.5MB, alloc=516.3MB, time=124.36 memory used=6747.2MB, alloc=516.3MB, time=126.09 memory used=6843.9MB, alloc=516.3MB, time=126.84 memory used=6935.6MB, alloc=516.3MB, time=127.58 memory used=7050.1MB, alloc=516.3MB, time=128.35 memory used=7136.1MB, alloc=516.3MB, time=129.02 memory used=7215.8MB, alloc=516.3MB, time=129.63 memory used=7327.0MB, alloc=516.3MB, time=131.12 memory used=7424.5MB, alloc=516.3MB, time=131.90 memory used=7525.1MB, alloc=516.3MB, time=132.66 memory used=7632.9MB, alloc=516.3MB, time=133.67 memory used=7750.4MB, alloc=516.3MB, time=140.64 memory used=7857.7MB, alloc=516.3MB, time=141.74 memory used=7951.0MB, alloc=516.3MB, time=142.46 memory used=8064.5MB, alloc=516.3MB, time=143.53 memory used=8160.4MB, alloc=516.3MB, time=144.28 memory used=8277.8MB, alloc=516.3MB, time=147.72 memory used=8371.8MB, alloc=516.3MB, time=148.40 memory used=8492.4MB, alloc=516.3MB, time=149.76 memory used=8611.3MB, alloc=516.3MB, time=151.30 memory used=8711.2MB, alloc=516.3MB, time=152.06 memory used=8804.5MB, alloc=516.3MB, time=152.78 memory used=8904.8MB, alloc=516.3MB, time=153.45 memory used=9017.9MB, alloc=516.3MB, time=154.75 memory used=9135.6MB, alloc=516.3MB, time=156.01 memory used=9233.3MB, alloc=516.3MB, time=156.73 memory used=9348.9MB, alloc=516.3MB, time=159.90 memory used=9461.3MB, alloc=516.3MB, time=161.34 memory used=9560.2MB, alloc=516.3MB, time=162.42 memory used=9683.3MB, alloc=516.3MB, time=163.54 memory used=9820.2MB, alloc=516.3MB, time=165.22 memory used=9920.3MB, alloc=516.3MB, time=166.00 memory used=10013.5MB, alloc=516.3MB, time=166.71 memory used=10114.1MB, alloc=516.3MB, time=167.39 memory used=10230.7MB, alloc=516.3MB, time=169.21 memory used=10332.5MB, alloc=516.3MB, time=169.99 memory used=10418.7MB, alloc=516.3MB, time=170.69 memory used=10525.4MB, alloc=516.3MB, time=171.40 |\^/| 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(); 1428272031 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [16 y z - 7 x y + x y z - 9 x , 15 y z - 6 y z - 20 x - 4 z, 2 4 2 2 2 x y z + 12 y + 13 y z - 14] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 2 G := [16 x y + 11 x + 19 x y + 2 y, 16 x y + 20 x z + 3 x z - 7 x, 3 2 3 7 x z - 2 y z + 6 z + 11 x z] > Problem := [F,G]; 3 2 2 3 Problem := [[16 y z - 7 x y + x y z - 9 x , 15 y z - 6 y z - 20 x - 4 z, 2 4 2 2 2 2 2 2 x y z + 12 y + 13 y z - 14], [16 x y + 11 x + 19 x y + 2 y, 3 2 2 2 3 2 3 16 x y + 20 x z + 3 x z - 7 x, 7 x z - 2 y z + 6 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=0.31 memory used=25.0MB, alloc=32.3MB, time=0.84 memory used=44.9MB, alloc=60.3MB, time=1.39 memory used=88.1MB, alloc=60.3MB, time=2.43 memory used=129.8MB, alloc=60.3MB, time=3.42 memory used=171.3MB, alloc=60.3MB, time=4.42 memory used=214.0MB, alloc=92.3MB, time=5.48 memory used=281.2MB, alloc=92.3MB, time=6.62 memory used=327.5MB, alloc=92.3MB, time=7.44 memory used=380.8MB, alloc=92.3MB, time=8.20 memory used=428.9MB, alloc=92.3MB, time=9.07 memory used=490.7MB, alloc=92.3MB, time=10.30 memory used=556.0MB, alloc=92.3MB, time=11.95 memory used=608.2MB, alloc=116.3MB, time=13.40 memory used=690.2MB, alloc=116.3MB, time=15.26 memory used=760.7MB, alloc=116.3MB, time=16.27 memory used=820.1MB, alloc=117.1MB, time=18.51 memory used=859.9MB, alloc=117.1MB, time=18.72 memory used=910.1MB, alloc=117.1MB, time=19.30 memory used=953.7MB, alloc=117.1MB, time=19.67 memory used=995.9MB, alloc=131.8MB, time=20.21 memory used=1049.9MB, alloc=131.8MB, time=20.45 memory used=1079.9MB, alloc=131.8MB, time=20.64 memory used=1132.7MB, alloc=131.8MB, time=20.86 memory used=1209.9MB, alloc=131.8MB, time=22.58 memory used=1262.8MB, alloc=387.8MB, time=23.79 memory used=1352.6MB, alloc=411.8MB, time=25.89 memory used=1459.6MB, alloc=411.8MB, time=28.45 memory used=1538.7MB, alloc=411.8MB, time=29.37 memory used=1610.4MB, alloc=411.8MB, time=33.26 memory used=1655.5MB, alloc=411.8MB, time=33.54 memory used=1770.9MB, alloc=411.8MB, time=35.91 memory used=1886.4MB, alloc=435.8MB, time=37.93 memory used=2025.3MB, alloc=435.8MB, time=41.50 memory used=2121.1MB, alloc=435.8MB, time=43.44 memory used=2195.1MB, alloc=435.8MB, time=44.01 memory used=2270.4MB, alloc=435.8MB, time=46.70 memory used=2370.7MB, alloc=435.8MB, time=48.10 memory used=2445.2MB, alloc=435.8MB, time=48.88 memory used=2586.6MB, alloc=435.8MB, time=51.76 memory used=2726.6MB, alloc=459.8MB, time=54.43 memory used=2844.4MB, alloc=483.8MB, time=57.61 memory used=2938.9MB, alloc=483.8MB, time=60.10 memory used=3036.6MB, alloc=483.8MB, time=62.54 memory used=3120.1MB, alloc=483.8MB, time=64.73 memory used=3249.7MB, alloc=483.8MB, time=66.80 memory used=3345.7MB, alloc=483.8MB, time=68.57 memory used=3469.6MB, alloc=507.8MB, time=71.07 memory used=3567.2MB, alloc=507.8MB, time=73.63 memory used=3637.6MB, alloc=507.8MB, time=75.30 memory used=3721.2MB, alloc=507.8MB, time=77.83 memory used=3797.3MB, alloc=507.8MB, time=80.23 memory used=3858.1MB, alloc=507.8MB, time=82.14 memory used=3936.9MB, alloc=507.8MB, time=84.60 memory used=4005.3MB, alloc=507.8MB, time=86.78 memory used=4087.0MB, alloc=507.8MB, time=89.23 memory used=4158.5MB, alloc=507.8MB, time=91.50 memory used=4224.9MB, alloc=507.8MB, time=93.38 memory used=4288.5MB, alloc=531.8MB, time=94.89 memory used=4343.8MB, alloc=531.8MB, time=96.85 memory used=4439.2MB, alloc=531.8MB, time=98.78 memory used=4580.0MB, alloc=531.8MB, time=100.52 memory used=4703.0MB, alloc=531.8MB, time=105.13 memory used=4812.1MB, alloc=531.8MB, time=106.07 memory used=4932.4MB, alloc=531.8MB, time=107.57 memory used=5045.7MB, alloc=531.8MB, time=108.97 memory used=5163.2MB, alloc=531.8MB, time=113.67 memory used=5269.7MB, alloc=531.8MB, time=115.18 memory used=5379.8MB, alloc=531.8MB, time=116.33 memory used=5502.9MB, alloc=531.8MB, time=117.19 memory used=5704.0MB, alloc=531.8MB, time=118.99 memory used=5984.7MB, alloc=531.8MB, time=120.25 memory used=6265.4MB, alloc=531.8MB, time=121.39 memory used=6460.7MB, alloc=531.8MB, time=123.62 memory used=6570.9MB, alloc=531.8MB, time=124.67 memory used=6665.6MB, alloc=531.8MB, time=125.42 memory used=6792.1MB, alloc=531.8MB, time=132.68 memory used=6881.5MB, alloc=531.8MB, time=133.36 memory used=6995.2MB, alloc=531.8MB, time=135.06 memory used=7152.2MB, alloc=531.8MB, time=136.44 memory used=7352.1MB, alloc=531.8MB, time=137.43 memory used=7481.6MB, alloc=531.8MB, time=139.72 memory used=7675.1MB, alloc=555.8MB, time=144.05 memory used=7810.1MB, alloc=555.8MB, time=145.89 memory used=7998.0MB, alloc=555.8MB, time=148.76 memory used=8137.0MB, alloc=555.8MB, time=151.64 memory used=8285.2MB, alloc=555.8MB, time=154.50 memory used=8422.2MB, alloc=555.8MB, time=155.78 memory used=8569.1MB, alloc=555.8MB, time=159.51 memory used=8788.6MB, alloc=555.8MB, time=163.69 memory used=8976.7MB, alloc=579.8MB, time=168.71 |\^/| 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(); 1428272331 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 3 3 2 2 F := [-4 x - x y + 9 x z + x y , 15 x y - 6 x y z - 11 y z - 7 z, 4 2 -5 x + 11 x y z - 2 y + 10 y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 G := [14 y - 20 y z - 17 x z - 15 x y z, 3 2 2 2 3 -8 x z + 8 x y z - 6 y z + 18 y z , 2 2 2 2 15 x y z + 5 x y z + 4 x y + 7 x ] > Problem := [F,G]; 4 3 3 3 3 2 2 Problem := [[-4 x - x y + 9 x z + x y , 15 x y - 6 x y z - 11 y z - 7 z, 4 2 4 3 2 -5 x + 11 x y z - 2 y + 10 y], [14 y - 20 y z - 17 x z - 15 x y z, 3 2 2 2 3 -8 x z + 8 x y z - 6 y z + 18 y z , 2 2 2 2 15 x y z + 5 x y z + 4 x y + 7 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.5MB, alloc=32.3MB, time=0.88 memory used=45.2MB, alloc=36.3MB, time=1.35 memory used=65.2MB, alloc=60.3MB, time=1.84 memory used=109.4MB, alloc=68.3MB, time=2.84 memory used=153.8MB, alloc=68.3MB, time=3.90 memory used=199.1MB, alloc=92.3MB, time=4.84 memory used=263.6MB, alloc=92.3MB, time=6.01 memory used=340.2MB, alloc=95.6MB, time=7.95 memory used=407.5MB, alloc=95.6MB, time=9.54 memory used=444.4MB, alloc=95.6MB, time=9.95 memory used=486.5MB, alloc=95.6MB, time=10.53 memory used=532.4MB, alloc=95.6MB, time=11.11 memory used=587.3MB, alloc=95.6MB, time=11.89 memory used=648.8MB, alloc=95.6MB, time=13.03 memory used=710.3MB, alloc=351.6MB, time=14.55 memory used=782.4MB, alloc=375.6MB, time=15.96 memory used=870.2MB, alloc=399.6MB, time=18.01 memory used=989.7MB, alloc=423.6MB, time=20.48 memory used=1112.8MB, alloc=423.6MB, time=22.28 memory used=1210.7MB, alloc=423.6MB, time=24.33 memory used=1321.7MB, alloc=447.6MB, time=26.73 memory used=1424.6MB, alloc=447.6MB, time=28.96 memory used=1517.4MB, alloc=447.6MB, time=31.00 memory used=1611.9MB, alloc=447.6MB, time=32.90 memory used=1697.7MB, alloc=471.6MB, time=35.15 memory used=1808.1MB, alloc=471.6MB, time=36.80 memory used=1932.8MB, alloc=471.6MB, time=38.23 memory used=2049.8MB, alloc=471.6MB, time=40.04 memory used=2168.7MB, alloc=471.6MB, time=41.40 memory used=2276.6MB, alloc=471.6MB, time=42.44 memory used=2384.0MB, alloc=471.6MB, time=45.56 memory used=2453.9MB, alloc=471.6MB, time=47.56 memory used=2541.7MB, alloc=471.6MB, time=49.72 memory used=2643.4MB, alloc=471.6MB, time=52.33 memory used=2716.7MB, alloc=471.6MB, time=53.79 memory used=2777.7MB, alloc=471.6MB, time=56.19 memory used=2848.1MB, alloc=471.6MB, time=58.10 memory used=2892.0MB, alloc=471.6MB, time=59.44 memory used=2988.1MB, alloc=471.6MB, time=60.91 memory used=3089.2MB, alloc=471.6MB, time=63.25 memory used=3177.9MB, alloc=471.6MB, time=64.07 memory used=3273.1MB, alloc=471.6MB, time=65.49 memory used=3331.1MB, alloc=471.6MB, time=67.03 memory used=3388.8MB, alloc=471.6MB, time=68.54 memory used=3447.0MB, alloc=471.6MB, time=70.17 memory used=3527.9MB, alloc=471.6MB, time=71.45 memory used=3586.7MB, alloc=471.6MB, time=72.99 memory used=3673.1MB, alloc=495.6MB, time=74.25 memory used=3715.2MB, alloc=495.6MB, time=75.70 memory used=3901.0MB, alloc=519.6MB, time=80.05 memory used=4087.5MB, alloc=543.6MB, time=84.20 memory used=4246.5MB, alloc=567.6MB, time=88.09 memory used=4411.2MB, alloc=567.6MB, time=92.38 memory used=4590.7MB, alloc=591.6MB, time=95.92 memory used=4737.3MB, alloc=591.6MB, time=99.88 memory used=4868.3MB, alloc=591.6MB, time=103.42 memory used=5051.5MB, alloc=615.6MB, time=106.79 memory used=5237.1MB, alloc=615.6MB, time=110.87 memory used=5450.2MB, alloc=615.6MB, time=114.40 memory used=5612.9MB, alloc=615.6MB, time=116.90 memory used=5811.3MB, alloc=615.6MB, time=121.60 memory used=5985.8MB, alloc=615.6MB, time=127.26 memory used=6165.2MB, alloc=615.6MB, time=133.26 memory used=6288.0MB, alloc=615.6MB, time=136.73 memory used=6421.6MB, alloc=639.6MB, time=140.36 memory used=6612.8MB, alloc=639.6MB, time=143.80 memory used=6802.1MB, alloc=639.6MB, time=147.62 memory used=6984.8MB, alloc=639.6MB, time=150.96 memory used=7173.6MB, alloc=639.6MB, time=154.21 memory used=7289.4MB, alloc=639.6MB, time=157.85 memory used=7445.2MB, alloc=663.6MB, time=160.99 memory used=7635.5MB, alloc=663.6MB, time=165.41 |\^/| 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(); 1428272631 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [10 x y z + 6 x y + 19 x y, -6 x y z + 17 z - 8 x - 3 z, 3 2 2 -9 x y + 2 x z + 7] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 4 3 G := [-17 x y z - 17 x z - x z + y , 18 x - 3 x - 8 z - 5, 3 2 15 x y + 20 x z - 4 x z + 13 y z] > Problem := [F,G]; 2 2 2 3 2 Problem := [[10 x y z + 6 x y + 19 x y, -6 x y z + 17 z - 8 x - 3 z, 3 2 2 2 2 2 2 -9 x y + 2 x z + 7], [-17 x y z - 17 x z - x z + y , 4 3 3 2 18 x - 3 x - 8 z - 5, 15 x y + 20 x z - 4 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=4.3MB, alloc=32.3MB, time=0.30 memory used=24.1MB, alloc=32.3MB, time=0.82 memory used=42.7MB, alloc=56.3MB, time=1.32 memory used=87.8MB, alloc=60.3MB, time=2.22 memory used=131.7MB, alloc=68.3MB, time=3.18 memory used=173.0MB, alloc=68.3MB, time=4.21 memory used=214.9MB, alloc=68.3MB, time=4.92 memory used=245.7MB, alloc=68.3MB, time=5.23 memory used=270.4MB, alloc=68.3MB, time=5.36 memory used=287.2MB, alloc=68.3MB, time=5.47 memory used=305.6MB, alloc=68.3MB, time=5.58 memory used=326.9MB, alloc=68.3MB, time=5.68 memory used=351.1MB, alloc=68.3MB, time=5.80 memory used=372.1MB, alloc=68.3MB, time=5.90 memory used=387.2MB, alloc=68.3MB, time=5.99 memory used=403.5MB, alloc=68.3MB, time=6.08 memory used=421.7MB, alloc=68.3MB, time=6.17 memory used=474.6MB, alloc=68.3MB, time=7.06 memory used=516.5MB, alloc=68.3MB, time=7.76 memory used=541.4MB, alloc=68.3MB, time=8.13 memory used=575.4MB, alloc=68.3MB, time=8.73 memory used=619.4MB, alloc=68.3MB, time=9.45 memory used=645.2MB, alloc=68.3MB, time=9.71 memory used=690.3MB, alloc=92.3MB, time=10.67 memory used=753.5MB, alloc=92.3MB, time=12.25 memory used=818.5MB, alloc=92.3MB, time=13.71 memory used=863.9MB, alloc=92.3MB, time=14.30 memory used=931.4MB, alloc=116.3MB, time=15.38 memory used=1013.0MB, alloc=116.3MB, time=16.57 memory used=1098.1MB, alloc=116.3MB, time=17.88 memory used=1181.9MB, alloc=116.3MB, time=19.35 memory used=1248.2MB, alloc=372.3MB, time=20.75 memory used=1337.6MB, alloc=396.3MB, time=22.87 memory used=1443.0MB, alloc=396.3MB, time=25.09 memory used=1508.3MB, alloc=396.3MB, time=25.69 memory used=1565.5MB, alloc=396.3MB, time=26.04 memory used=1603.8MB, alloc=396.3MB, time=26.32 memory used=1650.4MB, alloc=396.3MB, time=26.62 memory used=1717.5MB, alloc=396.3MB, time=27.14 memory used=1768.2MB, alloc=396.3MB, time=27.46 memory used=1815.3MB, alloc=396.3MB, time=27.76 memory used=1858.2MB, alloc=396.3MB, time=28.06 memory used=1926.4MB, alloc=396.3MB, time=36.33 memory used=2019.2MB, alloc=396.3MB, time=39.44 memory used=2073.1MB, alloc=396.3MB, time=39.80 memory used=2115.6MB, alloc=396.3MB, time=40.09 memory used=2158.1MB, alloc=396.3MB, time=40.40 memory used=2207.0MB, alloc=396.3MB, time=40.70 memory used=2263.2MB, alloc=396.3MB, time=41.01 memory used=2324.1MB, alloc=396.3MB, time=41.34 memory used=2359.5MB, alloc=396.3MB, time=41.58 memory used=2394.2MB, alloc=420.3MB, time=41.86 memory used=2444.8MB, alloc=420.3MB, time=42.14 memory used=2499.9MB, alloc=420.3MB, time=42.44 memory used=2558.4MB, alloc=420.3MB, time=42.73 memory used=2621.5MB, alloc=420.3MB, time=43.02 memory used=2689.2MB, alloc=420.3MB, time=43.31 memory used=2761.0MB, alloc=420.3MB, time=43.61 memory used=2838.1MB, alloc=420.3MB, time=43.91 memory used=2921.2MB, alloc=420.3MB, time=44.22 memory used=3090.7MB, alloc=420.3MB, time=44.99 memory used=3243.2MB, alloc=420.3MB, time=45.46 memory used=3381.9MB, alloc=420.3MB, time=46.37 memory used=3449.1MB, alloc=420.3MB, time=46.73 memory used=3509.4MB, alloc=420.3MB, time=47.05 memory used=3595.4MB, alloc=420.3MB, time=47.68 memory used=3666.5MB, alloc=420.3MB, time=48.07 memory used=3724.4MB, alloc=420.3MB, time=48.40 memory used=3784.8MB, alloc=420.3MB, time=48.73 memory used=3874.1MB, alloc=420.3MB, time=49.34 memory used=3939.6MB, alloc=420.3MB, time=49.71 memory used=4003.0MB, alloc=420.3MB, time=50.06 memory used=4061.2MB, alloc=420.3MB, time=50.39 memory used=4162.1MB, alloc=420.3MB, time=63.04 memory used=4256.1MB, alloc=420.3MB, time=63.81 memory used=4320.3MB, alloc=420.3MB, time=64.18 memory used=4379.8MB, alloc=420.3MB, time=64.50 memory used=4451.2MB, alloc=420.3MB, time=64.85 memory used=4532.1MB, alloc=420.3MB, time=65.20 memory used=4579.4MB, alloc=420.3MB, time=65.48 memory used=4628.3MB, alloc=420.3MB, time=65.74 memory used=4681.3MB, alloc=420.3MB, time=66.01 memory used=4737.7MB, alloc=420.3MB, time=66.28 memory used=4799.0MB, alloc=420.3MB, time=66.56 memory used=4865.0MB, alloc=420.3MB, time=66.84 memory used=4935.0MB, alloc=420.3MB, time=67.13 memory used=5009.3MB, alloc=420.3MB, time=67.43 memory used=5090.2MB, alloc=420.3MB, time=67.73 memory used=5300.2MB, alloc=420.3MB, time=68.30 memory used=5452.5MB, alloc=420.3MB, time=68.76 memory used=5672.0MB, alloc=420.3MB, time=71.18 memory used=5843.0MB, alloc=420.3MB, time=85.09 memory used=5918.3MB, alloc=420.3MB, time=85.52 memory used=5978.1MB, alloc=420.3MB, time=85.86 memory used=6037.0MB, alloc=420.3MB, time=86.19 memory used=6107.2MB, alloc=420.3MB, time=86.52 memory used=6185.3MB, alloc=420.3MB, time=86.86 memory used=6230.7MB, alloc=420.3MB, time=87.13 memory used=6279.3MB, alloc=420.3MB, time=87.39 memory used=6330.5MB, alloc=420.3MB, time=87.67 memory used=6385.0MB, alloc=420.3MB, time=87.95 memory used=6443.6MB, alloc=420.3MB, time=88.25 memory used=6507.2MB, alloc=420.3MB, time=88.53 memory used=6575.1MB, alloc=420.3MB, time=88.82 memory used=6646.9MB, alloc=420.3MB, time=89.12 memory used=6723.9MB, alloc=420.3MB, time=89.42 memory used=6806.6MB, alloc=420.3MB, time=89.72 memory used=6950.2MB, alloc=420.3MB, time=90.19 memory used=7103.0MB, alloc=420.3MB, time=90.65 memory used=7329.6MB, alloc=420.3MB, time=93.52 memory used=7464.0MB, alloc=420.3MB, time=95.74 memory used=7589.6MB, alloc=420.3MB, time=97.67 memory used=7704.1MB, alloc=420.3MB, time=103.57 memory used=7823.8MB, alloc=420.3MB, time=105.57 memory used=7939.4MB, alloc=420.3MB, time=119.36 memory used=8094.5MB, alloc=420.3MB, time=120.70 memory used=8166.6MB, alloc=420.3MB, time=121.21 memory used=8236.2MB, alloc=420.3MB, time=121.62 memory used=8380.8MB, alloc=420.3MB, time=122.44 memory used=8487.5MB, alloc=420.3MB, time=122.85 memory used=8706.5MB, alloc=420.3MB, time=124.19 memory used=8880.9MB, alloc=420.3MB, time=124.74 memory used=9086.0MB, alloc=420.3MB, time=125.34 memory used=9286.4MB, alloc=420.3MB, time=125.90 memory used=9506.0MB, alloc=420.3MB, time=126.47 memory used=9694.0MB, alloc=420.3MB, time=128.09 memory used=9758.8MB, alloc=420.3MB, time=128.70 memory used=9890.8MB, alloc=444.3MB, time=163.13 memory used=10097.7MB, alloc=444.3MB, time=163.88 memory used=10273.6MB, alloc=444.3MB, time=166.75 memory used=10377.2MB, alloc=444.3MB, time=171.90 memory used=10443.1MB, alloc=444.3MB, time=172.30 memory used=10594.0MB, alloc=444.3MB, time=177.26 memory used=10690.8MB, alloc=444.3MB, time=178.11 memory used=10781.3MB, alloc=444.3MB, time=186.90 memory used=10906.2MB, alloc=444.3MB, time=189.06 |\^/| 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(); 1428272931 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 3 4 3 F := [16 x y + 5 x z + 15 x - 8 x y, 14 x y z - 18 y z + 19 z + 11 x , 3 2 2 2 19 x y + 17 x y z + 6 x y z - 5 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 2 2 G := [3 x y + 4 x z - 6 x y z - 3 z, 3 x - x z - 19 x y - x z, 2 18 y z - 20 x - 18 z - 12] > Problem := [F,G]; 2 2 2 2 2 Problem := [[16 x y + 5 x z + 15 x - 8 x y, 2 3 4 3 3 2 2 2 14 x y z - 18 y z + 19 z + 11 x , 19 x y + 17 x y z + 6 x y z - 5 z ] 3 2 4 3 2 2 , [3 x y + 4 x z - 6 x y z - 3 z, 3 x - x z - 19 x y - x z, 2 18 y z - 20 x - 18 z - 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.89 memory used=45.5MB, alloc=56.3MB, time=1.39 memory used=87.7MB, alloc=60.3MB, time=2.47 memory used=127.4MB, alloc=60.3MB, time=3.50 memory used=165.4MB, alloc=84.3MB, time=4.52 memory used=232.4MB, alloc=92.3MB, time=6.18 memory used=289.3MB, alloc=348.3MB, time=7.53 memory used=358.9MB, alloc=372.3MB, time=9.17 memory used=447.6MB, alloc=372.3MB, time=11.40 memory used=533.8MB, alloc=396.3MB, time=13.78 memory used=647.1MB, alloc=396.3MB, time=16.77 memory used=761.5MB, alloc=420.3MB, time=19.40 memory used=884.5MB, alloc=420.3MB, time=22.63 memory used=1018.3MB, alloc=444.3MB, time=26.33 memory used=1133.1MB, alloc=444.3MB, time=29.08 memory used=1237.6MB, alloc=444.3MB, time=30.61 memory used=1318.4MB, alloc=444.3MB, time=31.75 memory used=1418.5MB, alloc=468.3MB, time=34.40 memory used=1573.8MB, alloc=468.3MB, time=37.54 memory used=1719.4MB, alloc=468.3MB, time=40.63 memory used=1814.7MB, alloc=468.3MB, time=43.44 memory used=1932.2MB, alloc=492.3MB, time=47.06 memory used=2041.8MB, alloc=492.3MB, time=50.48 memory used=2155.4MB, alloc=492.3MB, time=52.85 memory used=2242.7MB, alloc=492.3MB, time=55.27 memory used=2348.6MB, alloc=492.3MB, time=57.72 memory used=2479.8MB, alloc=492.3MB, time=59.75 memory used=2566.4MB, alloc=492.3MB, time=62.03 memory used=2662.2MB, alloc=516.3MB, time=64.19 memory used=2777.0MB, alloc=516.3MB, time=66.28 memory used=2857.4MB, alloc=516.3MB, time=69.16 memory used=2937.0MB, alloc=516.3MB, time=71.60 memory used=2995.8MB, alloc=516.3MB, time=73.34 memory used=3050.7MB, alloc=516.3MB, time=75.03 memory used=3115.2MB, alloc=540.3MB, time=76.61 memory used=3156.7MB, alloc=540.3MB, time=77.88 memory used=3378.2MB, alloc=564.3MB, time=84.84 memory used=3546.5MB, alloc=588.3MB, time=89.58 memory used=3725.0MB, alloc=612.3MB, time=93.69 memory used=3899.9MB, alloc=612.3MB, time=98.59 memory used=4057.2MB, alloc=636.3MB, time=103.51 memory used=4196.7MB, alloc=636.3MB, time=107.70 memory used=4336.4MB, alloc=636.3MB, time=112.36 memory used=4461.9MB, alloc=660.3MB, time=115.94 memory used=4594.1MB, alloc=660.3MB, time=120.99 memory used=4689.0MB, alloc=660.3MB, time=124.41 memory used=4790.6MB, alloc=660.3MB, time=127.64 memory used=4893.2MB, alloc=684.3MB, time=131.36 |\^/| 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(); 1428273231 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 3 2 3 F := [-6 x + 14 x y + 8 y + z , -5 x z - 7 x y z - 9 y z , 2 2 2 2 3 17 x z - 10 y z - 19 z + 9 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [17 x y z + 6 x z + 2 x y z - 9 x y, 3 2 2 2 2 4 2 19 x y + 19 x y z - 6 y z + 8 y z, -7 z + 18 x y z - 13 y - 11 y] > Problem := [F,G]; 4 3 2 2 3 2 3 Problem := [[-6 x + 14 x y + 8 y + z , -5 x z - 7 x y z - 9 y z , 2 2 2 2 3 17 x z - 10 y z - 19 z + 9 y z], [ 2 3 17 x y z + 6 x z + 2 x y z - 9 x y, 3 2 2 2 2 4 2 19 x y + 19 x y z - 6 y z + 8 y z, -7 z + 18 x y z - 13 y - 11 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=24.5MB, alloc=32.3MB, time=0.81 memory used=43.3MB, alloc=60.3MB, time=1.30 memory used=96.1MB, alloc=60.3MB, time=2.65 memory used=144.2MB, alloc=61.9MB, time=3.67 memory used=169.0MB, alloc=61.9MB, time=3.78 memory used=199.6MB, alloc=61.9MB, time=3.90 memory used=228.8MB, alloc=61.9MB, time=4.02 memory used=250.1MB, alloc=61.9MB, time=4.11 memory used=273.2MB, alloc=61.9MB, time=4.21 memory used=298.9MB, alloc=61.9MB, time=4.31 memory used=327.3MB, alloc=61.9MB, time=4.41 memory used=359.0MB, alloc=61.9MB, time=4.52 memory used=393.2MB, alloc=61.9MB, time=4.63 memory used=413.4MB, alloc=61.9MB, time=4.71 memory used=433.7MB, alloc=61.9MB, time=4.79 memory used=473.6MB, alloc=61.9MB, time=5.31 memory used=501.4MB, alloc=61.9MB, time=5.42 memory used=524.3MB, alloc=61.9MB, time=5.51 memory used=573.4MB, alloc=61.9MB, time=7.06 memory used=601.1MB, alloc=61.9MB, time=7.19 memory used=623.9MB, alloc=61.9MB, time=7.30 memory used=652.6MB, alloc=61.9MB, time=7.42 memory used=684.3MB, alloc=61.9MB, time=7.54 memory used=703.4MB, alloc=61.9MB, time=7.62 memory used=722.3MB, alloc=61.9MB, time=7.71 memory used=742.3MB, alloc=61.9MB, time=7.79 memory used=764.5MB, alloc=61.9MB, time=7.88 memory used=787.8MB, alloc=61.9MB, time=7.97 memory used=812.1MB, alloc=61.9MB, time=8.06 memory used=839.2MB, alloc=61.9MB, time=8.16 memory used=867.3MB, alloc=61.9MB, time=8.26 memory used=896.2MB, alloc=61.9MB, time=8.36 memory used=927.8MB, alloc=61.9MB, time=8.47 memory used=960.4MB, alloc=61.9MB, time=8.57 memory used=988.9MB, alloc=81.9MB, time=8.71 memory used=1000.5MB, alloc=83.8MB, time=8.78 memory used=1011.3MB, alloc=83.8MB, time=8.86 memory used=1022.5MB, alloc=83.8MB, time=8.94 memory used=1033.7MB, alloc=83.8MB, time=9.02 memory used=1045.0MB, alloc=83.8MB, time=9.09 memory used=1056.3MB, alloc=83.8MB, time=9.17 memory used=1067.7MB, alloc=83.8MB, time=9.24 memory used=1079.1MB, alloc=83.8MB, time=9.31 memory used=1090.6MB, alloc=83.8MB, time=9.39 memory used=1102.4MB, alloc=83.8MB, time=9.47 memory used=1115.9MB, alloc=83.8MB, time=9.54 memory used=1128.0MB, alloc=83.8MB, time=9.63 memory used=1141.5MB, alloc=83.8MB, time=9.71 memory used=1155.5MB, alloc=83.8MB, time=9.79 memory used=1169.5MB, alloc=83.8MB, time=9.87 memory used=1183.5MB, alloc=83.8MB, time=9.94 memory used=1197.6MB, alloc=83.8MB, time=10.01 memory used=1211.7MB, alloc=83.8MB, time=10.09 memory used=1225.8MB, alloc=83.8MB, time=10.16 memory used=1239.9MB, alloc=83.8MB, time=10.24 memory used=1254.4MB, alloc=83.8MB, time=10.32 memory used=1270.5MB, alloc=83.8MB, time=10.40 memory used=1286.9MB, alloc=83.8MB, time=10.49 memory used=1303.4MB, alloc=83.8MB, time=10.56 memory used=1319.8MB, alloc=83.8MB, time=10.65 memory used=1336.1MB, alloc=83.8MB, time=10.73 memory used=1352.4MB, alloc=83.8MB, time=10.81 memory used=1369.1MB, alloc=83.8MB, time=10.91 memory used=1387.2MB, alloc=83.8MB, time=11.00 memory used=1405.6MB, alloc=83.8MB, time=11.08 memory used=1424.0MB, alloc=83.8MB, time=11.16 memory used=1442.2MB, alloc=83.8MB, time=11.24 memory used=1460.8MB, alloc=83.8MB, time=11.33 memory used=1480.4MB, alloc=83.8MB, time=11.41 memory used=1500.4MB, alloc=83.8MB, time=11.50 memory used=1520.6MB, alloc=83.8MB, time=11.59 memory used=1541.8MB, alloc=83.8MB, time=11.68 memory used=1561.7MB, alloc=83.8MB, time=11.77 memory used=1584.1MB, alloc=83.8MB, time=11.86 memory used=1606.8MB, alloc=83.8MB, time=11.95 memory used=1629.5MB, alloc=83.8MB, time=12.04 memory used=1653.1MB, alloc=83.8MB, time=12.13 memory used=1672.6MB, alloc=83.8MB, time=12.21 memory used=1688.8MB, alloc=83.8MB, time=12.29 memory used=1704.8MB, alloc=83.8MB, time=12.37 memory used=1721.1MB, alloc=83.8MB, time=12.44 memory used=1737.9MB, alloc=83.8MB, time=12.52 memory used=1755.3MB, alloc=83.8MB, time=12.60 memory used=1773.1MB, alloc=83.8MB, time=12.68 memory used=1791.3MB, alloc=83.8MB, time=12.75 memory used=1810.1MB, alloc=83.8MB, time=12.83 memory used=1866.1MB, alloc=83.8MB, time=13.99 memory used=1896.3MB, alloc=83.8MB, time=14.12 memory used=1918.7MB, alloc=83.8MB, time=14.24 memory used=1945.6MB, alloc=83.8MB, time=14.37 memory used=1977.6MB, alloc=83.8MB, time=23.02 memory used=2002.9MB, alloc=107.8MB, time=53.31 memory used=2403.6MB, alloc=107.8MB, time=59.54 memory used=2423.5MB, alloc=363.8MB, time=60.99 memory used=2754.6MB, alloc=363.8MB, time=69.12 memory used=3055.3MB, alloc=363.8MB, time=77.04 memory used=3366.5MB, alloc=363.8MB, time=93.08 memory used=3507.7MB, alloc=387.8MB, time=99.64 memory used=3512.7MB, alloc=391.3MB, time=99.84 memory used=3516.1MB, alloc=394.7MB, time=99.92 memory used=3519.5MB, alloc=398.1MB, time=99.99 memory used=3523.0MB, alloc=401.6MB, time=100.08 memory used=3526.4MB, alloc=391.3MB, time=100.19 memory used=3584.0MB, alloc=387.8MB, time=100.64 memory used=3642.7MB, alloc=387.8MB, time=100.89 memory used=3689.8MB, alloc=387.8MB, time=101.07 memory used=3749.1MB, alloc=387.8MB, time=101.27 memory used=3988.8MB, alloc=387.8MB, time=102.67 memory used=4053.7MB, alloc=387.8MB, time=103.53 memory used=4177.3MB, alloc=387.8MB, time=105.09 memory used=4265.2MB, alloc=387.8MB, time=105.33 memory used=4336.1MB, alloc=387.8MB, time=107.62 memory used=4404.0MB, alloc=387.8MB, time=107.88 memory used=4453.7MB, alloc=387.8MB, time=108.10 memory used=4503.2MB, alloc=387.8MB, time=108.33 memory used=4559.4MB, alloc=387.8MB, time=108.55 memory used=4622.5MB, alloc=387.8MB, time=108.76 memory used=4694.3MB, alloc=387.8MB, time=109.02 memory used=4749.8MB, alloc=387.8MB, time=109.22 memory used=4791.7MB, alloc=387.8MB, time=109.37 memory used=4836.9MB, alloc=387.8MB, time=109.52 memory used=4885.3MB, alloc=387.8MB, time=109.69 memory used=4936.9MB, alloc=387.8MB, time=109.84 memory used=4992.4MB, alloc=387.8MB, time=110.01 memory used=5055.8MB, alloc=387.8MB, time=110.44 memory used=5128.7MB, alloc=387.8MB, time=110.77 memory used=5195.2MB, alloc=387.8MB, time=112.44 memory used=5260.1MB, alloc=387.8MB, time=112.72 memory used=5314.9MB, alloc=387.8MB, time=112.96 memory used=5363.4MB, alloc=387.8MB, time=113.15 memory used=5418.1MB, alloc=387.8MB, time=113.36 memory used=5479.7MB, alloc=387.8MB, time=113.58 memory used=5550.2MB, alloc=387.8MB, time=113.83 memory used=5611.3MB, alloc=387.8MB, time=114.03 memory used=5653.2MB, alloc=387.8MB, time=114.18 memory used=5697.2MB, alloc=387.8MB, time=114.34 memory used=5745.0MB, alloc=387.8MB, time=114.50 memory used=5796.5MB, alloc=387.8MB, time=114.66 memory used=5850.8MB, alloc=387.8MB, time=114.83 memory used=5912.0MB, alloc=387.8MB, time=115.18 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428273531 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 2 2 3 2 F := [-9 x y + 5 x y z + 19 z - 18 y z, -3 x y - 8 x z + 13 y - 14 y z, 4 -2 y - 4 x y z + 3 y z - 15 z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 2 G := [16 x z - 9 x - 6 x y z, 12 x z + 4 x y - 12 x y - 3 x, 2 2 2 -3 x y z + 10 x z - 20 y + 6 x] > Problem := [F,G]; 3 2 4 2 Problem := [[-9 x y + 5 x y z + 19 z - 18 y z, 2 2 3 2 4 -3 x y - 8 x z + 13 y - 14 y z, -2 y - 4 x y z + 3 y z - 15 z], [ 2 2 3 3 2 2 16 x z - 9 x - 6 x y z, 12 x z + 4 x y - 12 x y - 3 x, 2 2 2 -3 x y z + 10 x z - 20 y + 6 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=24.6MB, alloc=32.3MB, time=0.80 memory used=45.5MB, alloc=60.3MB, time=1.32 memory used=91.9MB, alloc=64.0MB, time=1.74 memory used=131.2MB, alloc=64.0MB, time=2.14 memory used=169.7MB, alloc=64.0MB, time=2.95 memory used=233.9MB, alloc=73.1MB, time=5.02 memory used=277.8MB, alloc=73.1MB, time=6.08 memory used=317.0MB, alloc=73.1MB, time=6.57 memory used=358.8MB, alloc=73.1MB, time=7.31 memory used=401.0MB, alloc=73.1MB, time=8.14 memory used=444.7MB, alloc=97.1MB, time=9.14 memory used=508.8MB, alloc=97.1MB, time=10.40 memory used=572.7MB, alloc=97.1MB, time=11.49 memory used=622.5MB, alloc=97.1MB, time=11.83 memory used=662.4MB, alloc=97.1MB, time=12.39 memory used=717.2MB, alloc=97.1MB, time=13.09 memory used=753.1MB, alloc=97.1MB, time=13.31 memory used=792.9MB, alloc=97.1MB, time=13.68 memory used=830.4MB, alloc=97.1MB, time=13.91 memory used=871.3MB, alloc=97.1MB, time=15.06 memory used=905.8MB, alloc=97.1MB, time=15.27 memory used=950.0MB, alloc=97.1MB, time=15.86 memory used=995.6MB, alloc=97.1MB, time=16.41 memory used=1039.9MB, alloc=97.1MB, time=16.67 memory used=1064.5MB, alloc=97.1MB, time=16.84 memory used=1094.0MB, alloc=97.1MB, time=17.01 memory used=1133.8MB, alloc=97.1MB, time=17.37 memory used=1184.1MB, alloc=97.1MB, time=17.98 memory used=1221.0MB, alloc=97.1MB, time=18.20 memory used=1246.2MB, alloc=97.1MB, time=18.38 memory used=1276.9MB, alloc=97.1MB, time=18.55 memory used=1316.4MB, alloc=97.1MB, time=18.92 memory used=1372.5MB, alloc=97.1MB, time=23.55 memory used=1400.3MB, alloc=97.1MB, time=23.74 memory used=1434.2MB, alloc=97.1MB, time=23.93 memory used=1456.8MB, alloc=97.1MB, time=24.10 memory used=1487.6MB, alloc=97.1MB, time=24.35 memory used=1551.7MB, alloc=97.1MB, time=26.16 memory used=1614.9MB, alloc=353.1MB, time=28.00 memory used=1699.0MB, alloc=377.1MB, time=30.13 memory used=1793.8MB, alloc=377.1MB, time=32.78 memory used=1852.2MB, alloc=377.1MB, time=34.22 memory used=1945.2MB, alloc=377.1MB, time=35.90 memory used=2041.6MB, alloc=377.1MB, time=38.56 memory used=2130.9MB, alloc=401.1MB, time=40.62 memory used=2246.0MB, alloc=425.1MB, time=43.18 memory used=2334.6MB, alloc=425.1MB, time=44.29 memory used=2452.3MB, alloc=425.1MB, time=46.80 memory used=2553.7MB, alloc=425.1MB, time=48.10 memory used=2641.9MB, alloc=425.1MB, time=50.72 memory used=2766.7MB, alloc=425.1MB, time=53.51 memory used=2889.0MB, alloc=449.1MB, time=55.09 memory used=3003.2MB, alloc=449.1MB, time=56.65 memory used=3103.0MB, alloc=449.1MB, time=58.09 memory used=3201.6MB, alloc=449.1MB, time=59.00 memory used=3375.4MB, alloc=449.1MB, time=80.93 memory used=3445.3MB, alloc=449.1MB, time=81.44 memory used=3524.5MB, alloc=449.1MB, time=81.92 memory used=3579.9MB, alloc=449.1MB, time=82.37 memory used=3643.6MB, alloc=449.1MB, time=82.81 memory used=3716.1MB, alloc=449.1MB, time=83.26 memory used=3799.6MB, alloc=449.1MB, time=83.73 memory used=3870.9MB, alloc=449.1MB, time=84.13 memory used=3922.0MB, alloc=449.1MB, time=84.49 memory used=3977.4MB, alloc=449.1MB, time=84.86 memory used=4036.4MB, alloc=449.1MB, time=85.22 memory used=4116.5MB, alloc=449.1MB, time=85.74 memory used=4267.3MB, alloc=449.1MB, time=88.50 memory used=4396.3MB, alloc=449.1MB, time=91.77 memory used=4532.1MB, alloc=449.1MB, time=94.25 memory used=4639.5MB, alloc=449.1MB, time=97.43 memory used=4745.3MB, alloc=449.1MB, time=99.85 memory used=4845.0MB, alloc=473.1MB, time=102.03 memory used=4916.2MB, alloc=473.1MB, time=103.85 memory used=4985.8MB, alloc=473.1MB, time=105.74 memory used=5058.6MB, alloc=473.1MB, time=107.75 memory used=5125.4MB, alloc=473.1MB, time=109.57 memory used=5191.4MB, alloc=473.1MB, time=111.07 memory used=5300.1MB, alloc=473.1MB, time=112.78 memory used=5415.8MB, alloc=497.1MB, time=114.32 memory used=5535.2MB, alloc=497.1MB, time=116.29 memory used=5631.2MB, alloc=497.1MB, time=117.95 memory used=5684.4MB, alloc=497.1MB, time=119.75 memory used=5730.8MB, alloc=497.1MB, time=121.12 memory used=5795.5MB, alloc=497.1MB, time=122.33 memory used=5865.8MB, alloc=497.1MB, time=124.16 memory used=5922.9MB, alloc=497.1MB, time=125.71 memory used=5979.0MB, alloc=497.1MB, time=130.40 memory used=6108.8MB, alloc=497.1MB, time=164.31 memory used=6194.8MB, alloc=497.1MB, time=165.04 memory used=6271.4MB, alloc=497.1MB, time=165.76 |\^/| 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(); 1428273831 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 4 2 2 F := [-20 x y + 15 x z + 5 x z + 4, 20 y + 16 y z - 15 z + 13, 3 2 2 2 -9 x y - 14 x y z - 10 x y - 18 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 4 2 2 G := [15 x - 3 x z + 7 x z - 9 y, 18 x - 17 x y + 10 x z - 2 x y, 2 2 -3 x y z - x y z - 12 y + 4] > Problem := [F,G]; 3 2 2 3 4 2 2 Problem := [[-20 x y + 15 x z + 5 x z + 4, 20 y + 16 y z - 15 z + 13, 3 2 2 2 4 3 2 -9 x y - 14 x y z - 10 x y - 18 y z], [15 x - 3 x z + 7 x z - 9 y, 4 2 2 2 2 18 x - 17 x y + 10 x z - 2 x y, -3 x y z - x y z - 12 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=0.31 memory used=26.2MB, alloc=32.3MB, time=0.88 memory used=47.0MB, alloc=32.3MB, time=1.42 memory used=65.9MB, alloc=56.3MB, time=1.96 memory used=107.2MB, alloc=60.3MB, time=3.05 memory used=144.5MB, alloc=84.3MB, time=4.06 memory used=209.7MB, alloc=92.3MB, time=5.73 memory used=276.5MB, alloc=116.3MB, time=7.33 memory used=346.1MB, alloc=116.3MB, time=8.92 memory used=419.9MB, alloc=372.3MB, time=10.62 memory used=517.1MB, alloc=396.3MB, time=12.63 memory used=635.9MB, alloc=396.3MB, time=15.24 memory used=748.7MB, alloc=420.3MB, time=17.83 memory used=893.4MB, alloc=420.3MB, time=20.84 memory used=1032.2MB, alloc=444.3MB, time=23.99 memory used=1145.5MB, alloc=468.3MB, time=26.99 memory used=1265.1MB, alloc=468.3MB, time=29.94 memory used=1378.9MB, alloc=468.3MB, time=32.79 memory used=1495.7MB, alloc=468.3MB, time=35.91 memory used=1602.5MB, alloc=492.3MB, time=38.06 memory used=1700.1MB, alloc=492.3MB, time=40.70 memory used=1809.7MB, alloc=492.3MB, time=43.21 memory used=1902.3MB, alloc=492.3MB, time=45.85 memory used=1982.7MB, alloc=492.3MB, time=47.92 memory used=2119.3MB, alloc=492.3MB, time=49.82 memory used=2213.2MB, alloc=492.3MB, time=51.39 memory used=2352.3MB, alloc=492.3MB, time=53.26 memory used=2500.5MB, alloc=492.3MB, time=61.05 memory used=2579.7MB, alloc=516.3MB, time=61.71 memory used=2694.4MB, alloc=516.3MB, time=62.39 memory used=2770.3MB, alloc=516.3MB, time=62.96 memory used=2857.3MB, alloc=516.3MB, time=63.52 memory used=2956.6MB, alloc=516.3MB, time=64.09 memory used=3071.9MB, alloc=516.3MB, time=64.67 memory used=3284.1MB, alloc=516.3MB, time=65.72 memory used=3447.8MB, alloc=516.3MB, time=66.40 memory used=3658.6MB, alloc=516.3MB, time=69.98 memory used=3894.8MB, alloc=516.3MB, time=73.33 memory used=4065.6MB, alloc=516.3MB, time=77.99 memory used=4312.0MB, alloc=516.3MB, time=80.89 memory used=4531.1MB, alloc=516.3MB, time=84.44 memory used=4646.5MB, alloc=516.3MB, time=87.55 memory used=4751.1MB, alloc=516.3MB, time=88.37 memory used=4853.5MB, alloc=516.3MB, time=89.05 memory used=4955.2MB, alloc=516.3MB, time=91.19 memory used=5046.4MB, alloc=516.3MB, time=91.82 memory used=5149.3MB, alloc=516.3MB, time=92.66 memory used=5234.6MB, alloc=516.3MB, time=94.36 memory used=5330.9MB, alloc=516.3MB, time=96.08 memory used=5407.2MB, alloc=516.3MB, time=98.43 memory used=5573.7MB, alloc=516.3MB, time=105.73 memory used=5663.1MB, alloc=516.3MB, time=106.45 memory used=5758.4MB, alloc=540.3MB, time=107.18 memory used=5845.8MB, alloc=540.3MB, time=107.86 memory used=5950.1MB, alloc=540.3MB, time=108.56 memory used=6074.3MB, alloc=540.3MB, time=109.28 memory used=6297.0MB, alloc=540.3MB, time=110.29 memory used=6452.7MB, alloc=540.3MB, time=111.13 memory used=6638.6MB, alloc=540.3MB, time=112.01 memory used=6803.6MB, alloc=540.3MB, time=114.26 memory used=7037.6MB, alloc=540.3MB, time=117.20 memory used=7117.3MB, alloc=540.3MB, time=119.32 memory used=7295.1MB, alloc=540.3MB, time=122.08 memory used=7343.6MB, alloc=540.3MB, time=123.91 memory used=7408.1MB, alloc=540.3MB, time=125.97 memory used=7467.2MB, alloc=540.3MB, time=127.76 memory used=7544.1MB, alloc=540.3MB, time=129.51 memory used=7687.8MB, alloc=540.3MB, time=131.32 memory used=7806.1MB, alloc=540.3MB, time=132.39 memory used=7915.3MB, alloc=540.3MB, time=133.19 memory used=8001.2MB, alloc=540.3MB, time=133.85 memory used=8123.0MB, alloc=540.3MB, time=136.16 memory used=8218.2MB, alloc=540.3MB, time=136.91 memory used=8342.2MB, alloc=540.3MB, time=138.05 memory used=8465.9MB, alloc=540.3MB, time=139.90 memory used=8537.3MB, alloc=540.3MB, time=141.74 memory used=8604.7MB, alloc=540.3MB, time=143.36 memory used=8665.7MB, alloc=540.3MB, time=144.94 memory used=8835.3MB, alloc=540.3MB, time=147.53 memory used=8933.9MB, alloc=540.3MB, time=148.33 memory used=9049.9MB, alloc=540.3MB, time=149.15 memory used=9154.7MB, alloc=540.3MB, time=151.35 memory used=9260.6MB, alloc=540.3MB, time=152.17 memory used=9350.6MB, alloc=540.3MB, time=152.86 memory used=9465.6MB, alloc=540.3MB, time=154.04 memory used=9629.5MB, alloc=540.3MB, time=156.77 memory used=9821.9MB, alloc=540.3MB, time=167.20 memory used=9922.4MB, alloc=564.3MB, time=168.08 memory used=10033.3MB, alloc=564.3MB, time=168.92 |\^/| 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(); 1428274131 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 F := [11 x z + 6 x z + 16 z + 15 z, 14 x y + 5 x + 4 x + 13 y, 4 4 8 x + 6 z - x y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [14 x y z - 5 x y z - 16 y z + 5 x z, 2 2 2 4 2 -19 x z - x y z - 10 y z + 16 x, 13 z + 17 x y z + 7 x + 12 x y] > Problem := [F,G]; 2 2 2 2 3 2 Problem := [[11 x z + 6 x z + 16 z + 15 z, 14 x y + 5 x + 4 x + 13 y, 4 4 2 2 2 2 8 x + 6 z - x y], [14 x y z - 5 x y z - 16 y z + 5 x z, 2 2 2 4 2 -19 x z - x y z - 10 y z + 16 x, 13 z + 17 x y z + 7 x + 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=0.32 memory used=26.3MB, alloc=32.3MB, time=0.89 memory used=47.0MB, alloc=32.3MB, time=1.42 memory used=66.6MB, alloc=56.3MB, time=1.96 memory used=106.3MB, alloc=60.3MB, time=3.03 memory used=145.7MB, alloc=84.3MB, time=4.08 memory used=209.8MB, alloc=92.3MB, time=5.78 memory used=276.8MB, alloc=92.3MB, time=7.06 memory used=338.2MB, alloc=92.3MB, time=8.55 memory used=398.8MB, alloc=116.3MB, time=10.19 memory used=480.8MB, alloc=116.3MB, time=12.47 memory used=557.2MB, alloc=372.3MB, time=14.44 memory used=637.6MB, alloc=396.3MB, time=16.73 memory used=744.4MB, alloc=420.3MB, time=19.60 memory used=871.4MB, alloc=420.3MB, time=22.43 memory used=1015.9MB, alloc=420.3MB, time=25.39 memory used=1084.0MB, alloc=444.3MB, time=36.13 memory used=1185.5MB, alloc=444.3MB, time=60.55 memory used=1263.3MB, alloc=444.3MB, time=60.96 memory used=1343.6MB, alloc=468.3MB, time=69.60 memory used=1442.7MB, alloc=492.3MB, time=160.67 |\^/| 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(); 1428274431 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 4 2 3 F := [-20 x y z - x y + 3 x y - 2 z , 19 x y z + 8 y - 15 x z + 7 y , 2 4 4 2 3 x y z + 20 y - 3 z - 14 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 3 3 2 G := [-4 x y + x y z - 20 x y - 4 y , -10 y z - 3 y - 16 y z - 19 z , 2 2 2 3 -18 x y z + 13 y z - 2 y z - 5 x y] > Problem := [F,G]; 2 3 2 3 Problem := [[-20 x y z - x y + 3 x y - 2 z , 2 4 2 3 2 4 4 2 19 x y z + 8 y - 15 x z + 7 y , 3 x y z + 20 y - 3 z - 14 z ], [ 2 2 2 2 3 3 3 2 -4 x y + x y z - 20 x y - 4 y , -10 y z - 3 y - 16 y z - 19 z , 2 2 2 3 -18 x y z + 13 y z - 2 y z - 5 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.90 memory used=45.7MB, alloc=56.3MB, time=1.38 memory used=88.3MB, alloc=60.3MB, time=2.36 memory used=132.1MB, alloc=68.3MB, time=3.31 memory used=176.5MB, alloc=68.3MB, time=4.46 memory used=218.9MB, alloc=68.3MB, time=5.26 memory used=265.5MB, alloc=69.3MB, time=6.16 memory used=303.4MB, alloc=70.1MB, time=6.40 memory used=340.3MB, alloc=70.1MB, time=6.61 memory used=366.9MB, alloc=94.1MB, time=12.78 memory used=407.8MB, alloc=94.1MB, time=14.62 memory used=455.4MB, alloc=94.1MB, time=15.98 memory used=528.3MB, alloc=94.1MB, time=38.80 memory used=584.0MB, alloc=94.2MB, time=42.41 memory used=637.8MB, alloc=94.2MB, time=42.73 memory used=707.9MB, alloc=94.2MB, time=44.27 memory used=766.2MB, alloc=94.2MB, time=45.06 memory used=820.2MB, alloc=94.2MB, time=46.21 memory used=858.2MB, alloc=94.2MB, time=46.38 memory used=892.5MB, alloc=94.2MB, time=46.53 memory used=960.4MB, alloc=94.2MB, time=48.05 memory used=1023.2MB, alloc=94.2MB, time=49.21 memory used=1065.9MB, alloc=94.2MB, time=49.76 memory used=1108.2MB, alloc=94.2MB, time=50.08 memory used=1145.9MB, alloc=94.2MB, time=50.49 memory used=1194.9MB, alloc=94.2MB, time=51.02 memory used=1236.4MB, alloc=94.2MB, time=51.47 memory used=1274.3MB, alloc=94.2MB, time=51.81 memory used=1316.2MB, alloc=94.2MB, time=52.32 memory used=1349.0MB, alloc=94.2MB, time=52.47 memory used=1388.0MB, alloc=94.2MB, time=52.67 memory used=1428.4MB, alloc=94.2MB, time=52.85 memory used=1462.0MB, alloc=94.2MB, time=53.02 memory used=1521.1MB, alloc=98.0MB, time=55.60 memory used=1552.3MB, alloc=98.0MB, time=55.79 memory used=1581.5MB, alloc=98.0MB, time=55.98 memory used=1613.4MB, alloc=98.0MB, time=56.16 memory used=1651.0MB, alloc=98.0MB, time=56.36 memory used=1690.3MB, alloc=98.0MB, time=56.57 memory used=1721.4MB, alloc=122.0MB, time=56.77 memory used=1757.0MB, alloc=122.0MB, time=56.98 memory used=1794.0MB, alloc=122.0MB, time=57.18 memory used=1833.3MB, alloc=122.0MB, time=57.38 memory used=1874.5MB, alloc=122.0MB, time=57.58 memory used=1920.5MB, alloc=122.0MB, time=57.79 memory used=1968.4MB, alloc=122.0MB, time=57.99 memory used=2018.1MB, alloc=122.0MB, time=58.19 memory used=2073.3MB, alloc=122.0MB, time=58.40 memory used=2129.8MB, alloc=122.0MB, time=58.63 memory used=2179.6MB, alloc=122.0MB, time=58.83 memory used=2233.4MB, alloc=122.0MB, time=59.04 memory used=2283.8MB, alloc=122.0MB, time=59.23 memory used=2315.4MB, alloc=122.0MB, time=59.37 memory used=2345.3MB, alloc=122.0MB, time=59.52 memory used=2377.9MB, alloc=122.0MB, time=59.66 memory used=2410.8MB, alloc=122.0MB, time=59.81 memory used=2443.8MB, alloc=122.0MB, time=59.95 memory used=2477.1MB, alloc=122.0MB, time=60.11 memory used=2511.0MB, alloc=122.0MB, time=60.25 memory used=2548.7MB, alloc=122.0MB, time=60.40 memory used=2587.0MB, alloc=122.0MB, time=60.56 memory used=2625.4MB, alloc=122.0MB, time=60.71 memory used=2663.9MB, alloc=122.0MB, time=60.87 memory used=2703.0MB, alloc=122.0MB, time=61.03 memory used=2745.6MB, alloc=122.0MB, time=61.18 memory used=2788.7MB, alloc=122.0MB, time=61.34 memory used=2831.9MB, alloc=122.0MB, time=61.50 memory used=2879.4MB, alloc=122.0MB, time=61.67 memory used=2926.6MB, alloc=122.0MB, time=61.83 memory used=2973.7MB, alloc=122.0MB, time=61.98 memory used=3024.8MB, alloc=122.0MB, time=62.15 memory used=3075.4MB, alloc=122.0MB, time=62.33 memory used=3129.7MB, alloc=122.0MB, time=62.50 memory used=3183.8MB, alloc=122.0MB, time=62.67 memory used=3244.0MB, alloc=122.0MB, time=62.85 memory used=3269.7MB, alloc=131.8MB, time=62.99 memory used=3294.1MB, alloc=131.8MB, time=63.12 memory used=3317.8MB, alloc=131.8MB, time=63.24 memory used=3343.2MB, alloc=131.8MB, time=63.36 memory used=3366.4MB, alloc=131.8MB, time=63.47 memory used=3388.9MB, alloc=131.8MB, time=63.59 memory used=3412.8MB, alloc=131.8MB, time=63.72 memory used=3434.7MB, alloc=131.8MB, time=63.83 memory used=3455.7MB, alloc=131.8MB, time=63.94 memory used=3477.9MB, alloc=131.8MB, time=64.06 memory used=3498.3MB, alloc=131.8MB, time=64.17 memory used=3517.9MB, alloc=131.8MB, time=64.29 memory used=3537.8MB, alloc=131.8MB, time=64.40 memory used=3549.5MB, alloc=131.8MB, time=64.51 memory used=3557.6MB, alloc=131.8MB, time=64.60 memory used=3566.5MB, alloc=131.8MB, time=64.69 memory used=3575.4MB, alloc=131.8MB, time=64.79 memory used=3584.1MB, alloc=131.8MB, time=64.88 memory used=3592.7MB, alloc=131.8MB, time=64.98 memory used=3602.2MB, alloc=131.8MB, time=65.07 memory used=3611.0MB, alloc=131.8MB, time=65.18 memory used=3620.6MB, alloc=131.8MB, time=65.29 memory used=3629.9MB, alloc=131.8MB, time=65.38 memory used=3640.0MB, alloc=131.8MB, time=65.47 memory used=3650.3MB, alloc=131.8MB, time=65.56 memory used=3660.6MB, alloc=131.8MB, time=65.69 memory used=3671.3MB, alloc=131.8MB, time=65.78 memory used=3682.9MB, alloc=131.8MB, time=65.87 memory used=3695.1MB, alloc=131.8MB, time=65.98 memory used=3708.0MB, alloc=131.8MB, time=66.07 memory used=3794.8MB, alloc=131.8MB, time=128.88 memory used=3848.9MB, alloc=131.8MB, time=181.74 |\^/| 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(); 1428274731 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 2 F := [-15 x y - 11 y z - 15 z - 3 y, -x y + 11 x y z - 8 y z + 5 x z , 2 3 -2 x y z + 3 x + 6 x z + 20 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 3 2 G := [6 x y z - 17 x z - y + 8 z, -20 x + 2 x y - 11 x + 14 x z , 3 2 -16 x z + 8 x z - 14 z + 13 y] > Problem := [F,G]; 2 2 2 Problem := [[-15 x y - 11 y z - 15 z - 3 y, 3 2 3 2 2 3 -x y + 11 x y z - 8 y z + 5 x z , -2 x y z + 3 x + 6 x z + 20 y z], [ 2 2 4 2 2 3 2 6 x y z - 17 x z - y + 8 z, -20 x + 2 x y - 11 x + 14 x z , 3 2 -16 x z + 8 x z - 14 z + 13 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.1MB, alloc=32.5MB, time=0.85 memory used=47.2MB, alloc=56.5MB, time=1.39 memory used=84.2MB, alloc=60.5MB, time=2.24 memory used=132.3MB, alloc=64.5MB, time=4.22 memory used=159.2MB, alloc=64.5MB, time=4.35 memory used=184.0MB, alloc=64.5MB, time=4.47 memory used=206.4MB, alloc=64.5MB, time=4.57 memory used=234.9MB, alloc=64.5MB, time=4.68 memory used=284.9MB, alloc=64.5MB, time=6.78 memory used=312.7MB, alloc=64.5MB, time=6.92 memory used=338.3MB, alloc=64.5MB, time=7.03 memory used=359.1MB, alloc=64.5MB, time=7.13 memory used=385.4MB, alloc=64.5MB, time=7.25 memory used=433.3MB, alloc=72.5MB, time=8.11 memory used=467.9MB, alloc=72.5MB, time=8.72 memory used=491.0MB, alloc=72.5MB, time=8.83 memory used=512.7MB, alloc=72.5MB, time=8.94 memory used=564.3MB, alloc=72.5MB, time=9.96 memory used=610.4MB, alloc=72.5MB, time=11.02 memory used=655.6MB, alloc=72.5MB, time=11.96 memory used=692.7MB, alloc=96.5MB, time=13.02 memory used=731.7MB, alloc=96.5MB, time=13.22 memory used=762.3MB, alloc=96.5MB, time=13.36 memory used=817.0MB, alloc=96.5MB, time=14.00 memory used=898.9MB, alloc=96.5MB, time=16.19 memory used=983.9MB, alloc=96.5MB, time=17.58 memory used=1072.1MB, alloc=96.5MB, time=20.76 memory used=1141.1MB, alloc=96.5MB, time=22.27 memory used=1204.9MB, alloc=352.5MB, time=23.71 memory used=1276.9MB, alloc=352.5MB, time=26.31 memory used=1309.5MB, alloc=352.5MB, time=26.52 memory used=1339.6MB, alloc=352.5MB, time=26.70 memory used=1365.0MB, alloc=352.5MB, time=26.87 memory used=1397.5MB, alloc=352.5MB, time=27.05 memory used=1445.0MB, alloc=352.5MB, time=27.76 memory used=1472.9MB, alloc=352.5MB, time=27.93 memory used=1544.1MB, alloc=376.5MB, time=29.35 memory used=1646.6MB, alloc=376.5MB, time=31.68 memory used=1718.8MB, alloc=376.5MB, time=32.83 memory used=1803.7MB, alloc=376.5MB, time=35.01 memory used=1892.4MB, alloc=400.5MB, time=37.08 memory used=2012.2MB, alloc=424.5MB, time=39.09 memory used=2086.3MB, alloc=424.5MB, time=39.61 memory used=2184.1MB, alloc=424.5MB, time=44.29 memory used=2240.9MB, alloc=424.5MB, time=44.65 memory used=2303.8MB, alloc=424.5MB, time=44.99 memory used=2364.1MB, alloc=424.5MB, time=45.67 memory used=2436.0MB, alloc=424.5MB, time=46.33 memory used=2542.5MB, alloc=424.5MB, time=48.21 memory used=2676.2MB, alloc=424.5MB, time=50.61 memory used=2807.2MB, alloc=448.5MB, time=52.70 memory used=2924.3MB, alloc=448.5MB, time=54.99 memory used=3017.8MB, alloc=448.5MB, time=56.84 memory used=3157.0MB, alloc=472.5MB, time=59.65 memory used=3246.8MB, alloc=472.5MB, time=61.75 memory used=3330.5MB, alloc=472.5MB, time=63.53 memory used=3409.6MB, alloc=472.5MB, time=65.05 memory used=3492.0MB, alloc=496.5MB, time=67.45 memory used=3552.2MB, alloc=496.5MB, time=69.04 memory used=3671.4MB, alloc=496.5MB, time=70.80 memory used=3792.6MB, alloc=496.5MB, time=74.01 memory used=3892.4MB, alloc=496.5MB, time=74.81 memory used=4016.9MB, alloc=496.5MB, time=76.16 memory used=4125.3MB, alloc=496.5MB, time=78.22 memory used=4258.5MB, alloc=496.5MB, time=80.76 memory used=4355.5MB, alloc=496.5MB, time=81.93 memory used=4456.6MB, alloc=496.5MB, time=82.75 memory used=4540.9MB, alloc=496.5MB, time=83.44 memory used=4647.2MB, alloc=496.5MB, time=84.55 memory used=4740.1MB, alloc=496.5MB, time=85.31 memory used=4811.7MB, alloc=496.5MB, time=85.97 memory used=4935.3MB, alloc=496.5MB, time=89.16 memory used=5013.0MB, alloc=496.5MB, time=89.83 memory used=5108.9MB, alloc=496.5MB, time=90.48 memory used=5205.2MB, alloc=496.5MB, time=91.53 memory used=5304.2MB, alloc=496.5MB, time=92.38 memory used=5403.0MB, alloc=496.5MB, time=94.43 memory used=5509.4MB, alloc=496.5MB, time=95.39 memory used=5604.9MB, alloc=496.5MB, time=96.32 memory used=5701.7MB, alloc=496.5MB, time=97.09 memory used=5808.4MB, alloc=496.5MB, time=97.98 memory used=5911.5MB, alloc=496.5MB, time=98.88 memory used=6027.6MB, alloc=496.5MB, time=100.98 memory used=6107.4MB, alloc=496.5MB, time=101.61 memory used=6223.6MB, alloc=496.5MB, time=103.61 memory used=6328.9MB, alloc=496.5MB, time=106.83 memory used=6411.1MB, alloc=496.5MB, time=110.10 memory used=6530.2MB, alloc=496.5MB, time=112.16 memory used=6633.3MB, alloc=496.5MB, time=116.54 memory used=6722.3MB, alloc=496.5MB, time=118.22 memory used=6817.2MB, alloc=496.5MB, time=119.84 memory used=6922.7MB, alloc=496.5MB, time=122.51 memory used=7010.5MB, alloc=496.5MB, time=126.78 memory used=7077.2MB, alloc=520.5MB, time=128.27 memory used=7173.3MB, alloc=520.5MB, time=130.24 memory used=7247.1MB, alloc=520.5MB, time=132.72 memory used=7326.1MB, alloc=520.5MB, time=135.98 memory used=7410.0MB, alloc=520.5MB, time=137.46 memory used=7480.5MB, alloc=520.5MB, time=139.03 memory used=7732.0MB, alloc=520.5MB, time=146.39 memory used=7967.3MB, alloc=520.5MB, time=152.33 memory used=8107.4MB, alloc=520.5MB, time=156.08 memory used=8206.3MB, alloc=520.5MB, time=156.96 memory used=8347.9MB, alloc=520.5MB, time=159.01 memory used=8445.2MB, alloc=520.5MB, time=159.84 memory used=8539.4MB, alloc=520.5MB, time=161.04 memory used=8644.0MB, alloc=520.5MB, time=161.94 |\^/| 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(); 1428275032 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 3 3 2 F := [-9 y - 14 x z - 4 x + 10, -18 y + 4 y z + 3 y + 16 y z, 3 2 -10 x y - 13 x y - x z + 8 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 4 3 2 G := [-20 x y + 6 y z - 15 x + 15 x z, -2 x z + z + 9 y - 16 y , 2 2 -13 x z + 5 x y - 17 x z + 5 y ] > Problem := [F,G]; 4 4 3 3 2 Problem := [[-9 y - 14 x z - 4 x + 10, -18 y + 4 y z + 3 y + 16 y z, 3 2 2 2 2 -10 x y - 13 x y - x z + 8 y z], [-20 x y + 6 y z - 15 x + 15 x z, 3 4 3 2 2 2 -2 x z + z + 9 y - 16 y , -13 x z + 5 x y - 17 x z + 5 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.0MB, alloc=32.3MB, time=0.83 memory used=46.0MB, alloc=56.3MB, time=1.27 memory used=86.5MB, alloc=61.8MB, time=2.13 memory used=128.5MB, alloc=61.8MB, time=3.20 memory used=155.7MB, alloc=61.8MB, time=3.39 memory used=182.1MB, alloc=61.8MB, time=3.74 memory used=206.4MB, alloc=61.8MB, time=3.86 memory used=245.6MB, alloc=61.8MB, time=4.58 memory used=286.5MB, alloc=61.8MB, time=5.42 memory used=325.6MB, alloc=61.8MB, time=6.74 memory used=365.3MB, alloc=61.8MB, time=7.81 memory used=412.5MB, alloc=93.8MB, time=8.70 memory used=447.4MB, alloc=93.8MB, time=9.17 memory used=485.1MB, alloc=93.8MB, time=9.37 memory used=523.5MB, alloc=93.8MB, time=9.55 memory used=576.0MB, alloc=93.8MB, time=10.01 memory used=611.0MB, alloc=93.8MB, time=10.19 memory used=667.9MB, alloc=93.8MB, time=13.21 memory used=704.5MB, alloc=93.8MB, time=13.39 memory used=734.8MB, alloc=93.8MB, time=13.54 memory used=791.4MB, alloc=93.8MB, time=14.16 memory used=828.9MB, alloc=93.8MB, time=14.37 memory used=868.1MB, alloc=93.8MB, time=14.56 memory used=917.8MB, alloc=93.8MB, time=14.92 memory used=951.2MB, alloc=93.8MB, time=15.09 memory used=1004.1MB, alloc=93.8MB, time=18.16 memory used=1043.5MB, alloc=93.8MB, time=18.36 memory used=1073.5MB, alloc=93.8MB, time=18.51 memory used=1118.2MB, alloc=93.8MB, time=18.86 memory used=1192.7MB, alloc=93.8MB, time=20.22 memory used=1263.7MB, alloc=93.8MB, time=21.53 memory used=1324.8MB, alloc=117.8MB, time=23.16 memory used=1394.3MB, alloc=117.8MB, time=24.15 memory used=1439.0MB, alloc=117.8MB, time=24.37 memory used=1480.1MB, alloc=117.8MB, time=24.74 memory used=1532.3MB, alloc=117.8MB, time=25.03 memory used=1574.7MB, alloc=117.8MB, time=25.25 memory used=1630.1MB, alloc=117.8MB, time=28.44 memory used=1675.1MB, alloc=117.8MB, time=28.68 memory used=1719.7MB, alloc=117.8MB, time=28.88 memory used=1763.6MB, alloc=117.8MB, time=29.26 memory used=1806.4MB, alloc=117.8MB, time=29.68 memory used=1840.4MB, alloc=131.8MB, time=30.26 memory used=1894.5MB, alloc=131.8MB, time=30.50 memory used=1923.1MB, alloc=131.8MB, time=30.69 memory used=1976.8MB, alloc=131.8MB, time=30.94 memory used=2031.4MB, alloc=131.8MB, time=31.88 memory used=2093.5MB, alloc=131.8MB, time=33.29 memory used=2155.7MB, alloc=387.8MB, time=34.29 memory used=2238.1MB, alloc=387.8MB, time=36.29 memory used=2316.2MB, alloc=411.8MB, time=38.27 memory used=2392.9MB, alloc=411.8MB, time=39.38 memory used=2447.5MB, alloc=411.8MB, time=39.82 memory used=2564.2MB, alloc=411.8MB, time=41.96 memory used=2666.0MB, alloc=411.8MB, time=43.30 memory used=2770.3MB, alloc=411.8MB, time=45.52 memory used=2879.1MB, alloc=435.8MB, time=48.09 memory used=3004.3MB, alloc=459.8MB, time=50.85 memory used=3089.0MB, alloc=459.8MB, time=51.55 memory used=3196.9MB, alloc=459.8MB, time=53.11 memory used=3273.8MB, alloc=459.8MB, time=53.54 memory used=3329.8MB, alloc=459.8MB, time=53.87 memory used=3399.7MB, alloc=459.8MB, time=54.25 memory used=3490.1MB, alloc=459.8MB, time=55.28 memory used=3568.7MB, alloc=459.8MB, time=55.70 memory used=3624.3MB, alloc=459.8MB, time=56.03 memory used=3693.4MB, alloc=459.8MB, time=56.38 memory used=3777.0MB, alloc=459.8MB, time=56.92 memory used=3898.2MB, alloc=459.8MB, time=58.55 memory used=4044.5MB, alloc=459.8MB, time=64.43 memory used=4226.8MB, alloc=459.8MB, time=67.05 memory used=4390.9MB, alloc=459.8MB, time=71.19 memory used=4507.6MB, alloc=483.8MB, time=73.72 memory used=4636.6MB, alloc=483.8MB, time=75.56 memory used=4711.7MB, alloc=483.8MB, time=76.02 memory used=4802.9MB, alloc=483.8MB, time=76.92 memory used=4886.3MB, alloc=483.8MB, time=77.43 memory used=4953.6MB, alloc=483.8MB, time=77.85 memory used=5047.4MB, alloc=483.8MB, time=78.58 memory used=5206.3MB, alloc=483.8MB, time=80.92 memory used=5324.7MB, alloc=483.8MB, time=83.20 memory used=5401.6MB, alloc=483.8MB, time=85.25 memory used=5479.8MB, alloc=483.8MB, time=87.38 memory used=5609.0MB, alloc=507.8MB, time=91.53 memory used=5703.5MB, alloc=507.8MB, time=92.60 memory used=5848.0MB, alloc=507.8MB, time=93.82 memory used=6030.3MB, alloc=507.8MB, time=97.10 memory used=6115.5MB, alloc=507.8MB, time=97.71 memory used=6225.0MB, alloc=507.8MB, time=99.29 memory used=6319.3MB, alloc=507.8MB, time=101.23 memory used=6455.7MB, alloc=507.8MB, time=103.66 memory used=6551.8MB, alloc=507.8MB, time=105.75 memory used=6632.1MB, alloc=507.8MB, time=107.92 memory used=6728.3MB, alloc=507.8MB, time=108.70 memory used=6822.4MB, alloc=507.8MB, time=109.29 memory used=6886.8MB, alloc=507.8MB, time=109.78 memory used=6962.8MB, alloc=507.8MB, time=110.30 memory used=7053.4MB, alloc=507.8MB, time=110.84 memory used=7271.2MB, alloc=507.8MB, time=115.20 memory used=7394.6MB, alloc=507.8MB, time=119.04 memory used=7461.5MB, alloc=507.8MB, time=120.93 memory used=7510.8MB, alloc=507.8MB, time=122.62 memory used=7568.1MB, alloc=531.8MB, time=124.33 memory used=7631.8MB, alloc=531.8MB, time=126.16 memory used=7682.6MB, alloc=531.8MB, time=127.73 memory used=7784.7MB, alloc=531.8MB, time=130.54 memory used=7950.0MB, alloc=531.8MB, time=131.63 memory used=8097.4MB, alloc=531.8MB, time=134.38 memory used=8148.0MB, alloc=531.8MB, time=135.95 memory used=8347.2MB, alloc=555.8MB, time=140.44 memory used=8561.3MB, alloc=579.8MB, time=144.69 memory used=8776.3MB, alloc=603.8MB, time=147.74 memory used=8918.6MB, alloc=627.8MB, time=149.11 memory used=9080.1MB, alloc=627.8MB, time=154.47 memory used=9251.1MB, alloc=627.8MB, time=156.95 |\^/| 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(); 1428275332 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 3 2 F := [6 x y + 17 y + 13 y z - 14 z , 6 x y z + 17 y z - 15 z + 19 z, 3 2 2 3 -19 x z - 16 y z - 6 z - 3 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 4 G := [14 x y z - 4 x z - 6 y z - 9 x , 20 x y z - 15 y - 3 x z + 9 y z, 2 y z - 16 x + 5 y] > Problem := [F,G]; 3 3 2 2 Problem := [[6 x y + 17 y + 13 y z - 14 z , 2 3 2 3 2 2 3 6 x y z + 17 y z - 15 z + 19 z, -19 x z - 16 y z - 6 z - 3 x z], [ 2 3 3 3 2 4 14 x y z - 4 x z - 6 y z - 9 x , 20 x y z - 15 y - 3 x z + 9 y z, 2 y z - 16 x + 5 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.90 memory used=45.1MB, alloc=56.3MB, time=1.39 memory used=86.4MB, alloc=60.3MB, time=2.38 memory used=128.9MB, alloc=68.3MB, time=3.41 memory used=171.2MB, alloc=68.3MB, time=4.28 memory used=213.9MB, alloc=92.3MB, time=5.17 memory used=283.2MB, alloc=92.3MB, time=6.40 memory used=357.0MB, alloc=92.3MB, time=8.17 memory used=404.2MB, alloc=92.3MB, time=8.81 memory used=461.8MB, alloc=92.3MB, time=9.76 memory used=503.0MB, alloc=92.3MB, time=10.70 memory used=535.6MB, alloc=92.3MB, time=10.91 memory used=596.9MB, alloc=116.3MB, time=12.35 memory used=662.7MB, alloc=116.3MB, time=13.84 memory used=733.4MB, alloc=372.3MB, time=15.57 memory used=806.3MB, alloc=372.3MB, time=19.63 memory used=851.5MB, alloc=372.3MB, time=20.59 memory used=906.8MB, alloc=372.3MB, time=21.87 memory used=953.3MB, alloc=396.3MB, time=40.73 memory used=996.4MB, alloc=420.3MB, time=73.38 memory used=1034.8MB, alloc=444.3MB, time=108.77 memory used=1089.6MB, alloc=468.3MB, time=152.65 memory used=1174.8MB, alloc=492.3MB, time=202.39 |\^/| 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(); 1428275632 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 2 F := [20 x y + 19 y z - 4 y + 2 z , -18 x z - 16 x z - 19 x y z - 18 x, 2 3 2 2 7 x y + 8 z - 2 x + 14 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 3 4 2 G := [-10 x z - 11 y z + 11 x z + 9 z , 18 x y - 9 z + 6 y + 14 y, 2 2 2 2 2 3 -11 x y - 15 y z + 7 x z + 3 y ] > Problem := [F,G]; 2 2 3 2 2 Problem := [[20 x y + 19 y z - 4 y + 2 z , 2 2 2 2 3 2 2 -18 x z - 16 x z - 19 x y z - 18 x, 7 x y + 8 z - 2 x + 14 z ], [ 3 2 2 2 3 3 4 2 -10 x z - 11 y z + 11 x z + 9 z , 18 x y - 9 z + 6 y + 14 y, 2 2 2 2 2 3 -11 x y - 15 y z + 7 x z + 3 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.6MB, alloc=32.3MB, time=0.31 memory used=25.4MB, alloc=32.3MB, time=0.84 memory used=45.9MB, alloc=33.1MB, time=1.06 memory used=56.0MB, alloc=33.1MB, time=1.11 memory used=73.3MB, alloc=33.1MB, time=1.52 memory used=84.3MB, alloc=33.1MB, time=1.58 memory used=94.2MB, alloc=33.1MB, time=1.64 memory used=103.9MB, alloc=33.1MB, time=1.68 memory used=116.6MB, alloc=33.1MB, time=1.74 memory used=137.4MB, alloc=37.1MB, time=2.16 memory used=155.8MB, alloc=61.1MB, time=2.65 memory used=200.6MB, alloc=61.1MB, time=3.64 memory used=224.5MB, alloc=61.1MB, time=3.74 memory used=255.1MB, alloc=61.1MB, time=3.98 memory used=282.0MB, alloc=61.1MB, time=4.11 memory used=308.2MB, alloc=61.1MB, time=4.21 memory used=329.0MB, alloc=61.1MB, time=4.31 memory used=360.1MB, alloc=61.1MB, time=4.54 memory used=388.2MB, alloc=61.1MB, time=4.66 memory used=408.3MB, alloc=61.1MB, time=4.75 memory used=454.8MB, alloc=61.1MB, time=7.78 memory used=483.7MB, alloc=61.1MB, time=7.91 memory used=504.5MB, alloc=61.1MB, time=8.00 memory used=530.5MB, alloc=61.1MB, time=8.10 memory used=553.1MB, alloc=61.1MB, time=8.19 memory used=572.3MB, alloc=61.1MB, time=8.27 memory used=595.3MB, alloc=61.1MB, time=8.35 memory used=639.1MB, alloc=61.1MB, time=9.16 memory used=674.4MB, alloc=61.6MB, time=11.67 memory used=696.7MB, alloc=61.6MB, time=11.77 memory used=719.5MB, alloc=61.6MB, time=11.87 memory used=746.6MB, alloc=61.6MB, time=11.97 memory used=763.5MB, alloc=61.6MB, time=12.04 memory used=782.9MB, alloc=61.6MB, time=12.12 memory used=807.9MB, alloc=61.6MB, time=12.29 memory used=844.1MB, alloc=61.6MB, time=12.97 memory used=876.1MB, alloc=61.6MB, time=13.32 memory used=905.7MB, alloc=61.6MB, time=13.52 memory used=945.3MB, alloc=61.6MB, time=15.30 memory used=970.6MB, alloc=61.6MB, time=15.42 memory used=991.0MB, alloc=61.6MB, time=15.52 memory used=1025.8MB, alloc=61.6MB, time=15.89 memory used=1068.0MB, alloc=69.6MB, time=16.57 memory used=1111.2MB, alloc=69.6MB, time=17.30 memory used=1152.4MB, alloc=93.6MB, time=18.22 memory used=1217.1MB, alloc=93.6MB, time=19.72 memory used=1266.6MB, alloc=93.6MB, time=20.37 memory used=1304.5MB, alloc=93.6MB, time=20.61 memory used=1354.2MB, alloc=93.6MB, time=22.43 memory used=1382.5MB, alloc=93.6MB, time=22.60 memory used=1413.4MB, alloc=93.6MB, time=22.74 memory used=1458.4MB, alloc=93.6MB, time=23.31 memory used=1494.2MB, alloc=93.6MB, time=23.95 memory used=1537.9MB, alloc=93.6MB, time=24.43 memory used=1604.8MB, alloc=93.6MB, time=26.75 memory used=1635.4MB, alloc=93.6MB, time=26.94 memory used=1661.4MB, alloc=93.6MB, time=27.10 memory used=1694.4MB, alloc=93.6MB, time=27.27 memory used=1723.0MB, alloc=117.6MB, time=27.44 memory used=1759.3MB, alloc=117.6MB, time=27.61 memory used=1803.3MB, alloc=117.6MB, time=27.79 memory used=1862.5MB, alloc=117.6MB, time=28.17 memory used=1910.5MB, alloc=117.6MB, time=28.38 memory used=1993.3MB, alloc=117.6MB, time=29.49 memory used=2097.6MB, alloc=117.6MB, time=30.69 memory used=2195.9MB, alloc=117.6MB, time=32.58 memory used=2286.5MB, alloc=117.6MB, time=34.87 memory used=2329.5MB, alloc=117.6MB, time=35.08 memory used=2380.8MB, alloc=117.6MB, time=35.31 memory used=2417.6MB, alloc=117.6MB, time=35.48 memory used=2455.3MB, alloc=117.6MB, time=35.65 memory used=2500.6MB, alloc=117.6MB, time=35.82 memory used=2558.4MB, alloc=117.6MB, time=36.18 memory used=2602.9MB, alloc=117.6MB, time=36.39 memory used=2687.7MB, alloc=117.6MB, time=37.67 memory used=2761.5MB, alloc=373.6MB, time=39.00 memory used=2843.7MB, alloc=373.6MB, time=40.73 memory used=2904.7MB, alloc=373.6MB, time=41.48 memory used=2989.9MB, alloc=373.6MB, time=42.97 memory used=3065.5MB, alloc=373.6MB, time=44.32 memory used=3139.0MB, alloc=397.6MB, time=45.83 memory used=3193.8MB, alloc=397.6MB, time=46.11 memory used=3240.2MB, alloc=397.6MB, time=46.33 memory used=3299.5MB, alloc=397.6MB, time=46.76 memory used=3411.8MB, alloc=397.6MB, time=48.65 memory used=3498.9MB, alloc=397.6MB, time=52.11 memory used=3556.2MB, alloc=397.6MB, time=52.49 memory used=3613.5MB, alloc=397.6MB, time=52.83 memory used=3659.9MB, alloc=397.6MB, time=53.11 memory used=3703.8MB, alloc=397.6MB, time=53.39 memory used=3755.2MB, alloc=397.6MB, time=53.68 memory used=3837.8MB, alloc=397.6MB, time=56.92 memory used=3888.2MB, alloc=397.6MB, time=57.25 memory used=3945.6MB, alloc=397.6MB, time=57.58 memory used=3987.3MB, alloc=397.6MB, time=57.86 memory used=4036.3MB, alloc=397.6MB, time=58.15 memory used=4112.5MB, alloc=397.6MB, time=69.74 memory used=4192.4MB, alloc=397.6MB, time=70.97 memory used=4239.7MB, alloc=397.6MB, time=71.27 memory used=4299.9MB, alloc=397.6MB, time=71.58 memory used=4349.3MB, alloc=397.6MB, time=71.89 memory used=4389.9MB, alloc=397.6MB, time=72.15 memory used=4434.8MB, alloc=397.6MB, time=72.43 memory used=4484.5MB, alloc=397.6MB, time=72.71 memory used=4539.9MB, alloc=397.6MB, time=73.01 memory used=4602.3MB, alloc=397.6MB, time=73.31 memory used=4644.8MB, alloc=397.6MB, time=73.56 memory used=4705.8MB, alloc=397.6MB, time=74.13 memory used=4756.0MB, alloc=397.6MB, time=74.42 memory used=4802.2MB, alloc=397.6MB, time=74.66 memory used=4875.9MB, alloc=397.6MB, time=78.05 memory used=4924.7MB, alloc=397.6MB, time=78.35 memory used=4971.9MB, alloc=397.6MB, time=78.62 memory used=5032.3MB, alloc=397.6MB, time=78.91 memory used=5073.3MB, alloc=397.6MB, time=79.15 memory used=5111.9MB, alloc=397.6MB, time=79.39 memory used=5153.8MB, alloc=397.6MB, time=79.62 memory used=5200.0MB, alloc=397.6MB, time=79.86 memory used=5249.9MB, alloc=397.6MB, time=80.10 memory used=5305.0MB, alloc=397.6MB, time=80.35 memory used=5364.6MB, alloc=397.6MB, time=80.59 memory used=5553.0MB, alloc=397.6MB, time=81.38 memory used=5680.4MB, alloc=397.6MB, time=82.31 memory used=5752.8MB, alloc=397.6MB, time=85.79 memory used=5803.5MB, alloc=397.6MB, time=86.09 memory used=5847.3MB, alloc=397.6MB, time=86.35 memory used=5903.0MB, alloc=397.6MB, time=86.65 memory used=5952.4MB, alloc=397.6MB, time=86.90 memory used=5988.8MB, alloc=397.6MB, time=87.12 memory used=6029.1MB, alloc=397.6MB, time=87.34 memory used=6073.7MB, alloc=397.6MB, time=87.57 memory used=6122.4MB, alloc=397.6MB, time=87.82 memory used=6174.7MB, alloc=397.6MB, time=88.07 memory used=6231.9MB, alloc=397.6MB, time=88.32 memory used=6297.6MB, alloc=397.6MB, time=88.59 memory used=6451.0MB, alloc=397.6MB, time=89.05 memory used=6621.6MB, alloc=397.6MB, time=101.73 memory used=6674.5MB, alloc=397.6MB, time=102.04 memory used=6715.4MB, alloc=397.6MB, time=102.32 memory used=6765.4MB, alloc=397.6MB, time=102.61 memory used=6825.1MB, alloc=397.6MB, time=102.91 memory used=6871.5MB, alloc=397.6MB, time=103.17 memory used=6907.6MB, alloc=397.6MB, time=103.41 memory used=6945.4MB, alloc=397.6MB, time=103.65 memory used=6986.3MB, alloc=397.6MB, time=103.91 memory used=7028.7MB, alloc=397.6MB, time=104.15 memory used=7074.1MB, alloc=397.6MB, time=104.39 memory used=7122.7MB, alloc=397.6MB, time=104.64 memory used=7174.5MB, alloc=397.6MB, time=104.88 memory used=7229.3MB, alloc=397.6MB, time=105.13 memory used=7286.9MB, alloc=397.6MB, time=105.39 memory used=7349.4MB, alloc=397.6MB, time=105.65 memory used=7520.3MB, alloc=397.6MB, time=106.19 memory used=7669.4MB, alloc=397.6MB, time=106.65 memory used=7839.5MB, alloc=397.6MB, time=107.14 memory used=8101.5MB, alloc=397.6MB, time=108.64 memory used=8155.4MB, alloc=397.6MB, time=108.96 memory used=8227.2MB, alloc=397.6MB, time=113.02 memory used=8286.7MB, alloc=421.6MB, time=145.62 memory used=8636.5MB, alloc=445.6MB, time=153.44 memory used=8847.4MB, alloc=445.6MB, time=159.95 memory used=9209.8MB, alloc=445.6MB, time=171.90 |\^/| 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(); 1428275932 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [6 x y - 9 x z - 18 y z + 16 y, 17 x y z - 4 y + 17 z + 6, 3 2 -18 x y - 18 y z - 2 y z + 6 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 G := [-5 x z + 15 x y + 15 y z + 20 y z, 3 2 2 2 3 2 2 -8 y z + 3 x z + 17 x z - 6 x , -16 y z + 11 x y z - 9 x - 9 z ] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[6 x y - 9 x z - 18 y z + 16 y, 17 x y z - 4 y + 17 z + 6, 3 2 -18 x y - 18 y z - 2 y z + 6 x], [ 2 2 3 2 2 2 3 2 2 2 -5 x z + 15 x y + 15 y z + 20 y z, -8 y z + 3 x z + 17 x z - 6 x , 3 2 2 -16 y z + 11 x y z - 9 x - 9 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.31 memory used=26.1MB, alloc=36.3MB, time=0.89 memory used=52.1MB, alloc=36.3MB, time=1.33 memory used=79.0MB, alloc=60.3MB, time=1.85 memory used=136.2MB, alloc=70.5MB, time=3.24 memory used=191.5MB, alloc=73.3MB, time=4.70 memory used=233.7MB, alloc=74.9MB, time=4.92 memory used=273.8MB, alloc=74.9MB, time=5.12 memory used=311.8MB, alloc=74.9MB, time=5.31 memory used=354.6MB, alloc=74.9MB, time=5.83 memory used=378.1MB, alloc=74.9MB, time=5.96 memory used=409.7MB, alloc=74.9MB, time=6.72 memory used=455.0MB, alloc=74.9MB, time=7.49 memory used=478.8MB, alloc=74.9MB, time=7.62 memory used=510.0MB, alloc=74.9MB, time=7.77 memory used=531.0MB, alloc=74.9MB, time=7.88 memory used=551.5MB, alloc=74.9MB, time=7.99 memory used=573.1MB, alloc=74.9MB, time=8.11 memory used=597.2MB, alloc=74.9MB, time=8.23 memory used=622.7MB, alloc=74.9MB, time=8.34 memory used=650.9MB, alloc=74.9MB, time=8.46 memory used=680.7MB, alloc=74.9MB, time=8.58 memory used=712.7MB, alloc=74.9MB, time=8.71 memory used=735.2MB, alloc=74.9MB, time=8.81 memory used=751.3MB, alloc=74.9MB, time=8.90 memory used=768.2MB, alloc=74.9MB, time=8.98 memory used=785.3MB, alloc=74.9MB, time=9.07 memory used=804.2MB, alloc=74.9MB, time=9.16 memory used=823.4MB, alloc=74.9MB, time=9.24 memory used=842.7MB, alloc=74.9MB, time=9.35 memory used=862.3MB, alloc=74.9MB, time=9.44 memory used=883.7MB, alloc=74.9MB, time=9.53 memory used=905.2MB, alloc=74.9MB, time=9.62 memory used=927.0MB, alloc=74.9MB, time=9.71 memory used=949.2MB, alloc=74.9MB, time=9.81 memory used=972.5MB, alloc=74.9MB, time=9.90 memory used=996.3MB, alloc=74.9MB, time=9.99 memory used=1021.9MB, alloc=74.9MB, time=10.08 memory used=1047.5MB, alloc=74.9MB, time=10.17 memory used=1074.8MB, alloc=74.9MB, time=10.27 memory used=1101.9MB, alloc=74.9MB, time=10.37 memory used=1130.7MB, alloc=74.9MB, time=10.48 memory used=1159.7MB, alloc=74.9MB, time=10.57 memory used=1189.6MB, alloc=74.9MB, time=10.67 memory used=1221.1MB, alloc=74.9MB, time=10.77 memory used=1253.5MB, alloc=74.9MB, time=10.87 memory used=1279.3MB, alloc=83.8MB, time=10.97 memory used=1286.8MB, alloc=83.8MB, time=11.04 memory used=1294.4MB, alloc=83.8MB, time=11.12 memory used=1301.9MB, alloc=83.8MB, time=11.19 memory used=1309.4MB, alloc=83.8MB, time=11.27 memory used=1316.8MB, alloc=83.8MB, time=11.34 memory used=1324.2MB, alloc=83.8MB, time=11.43 memory used=1331.8MB, alloc=83.8MB, time=11.53 memory used=1340.2MB, alloc=83.8MB, time=11.63 memory used=1347.9MB, alloc=83.8MB, time=11.70 memory used=1356.0MB, alloc=83.8MB, time=11.77 memory used=1364.4MB, alloc=83.8MB, time=11.84 memory used=1372.8MB, alloc=83.8MB, time=11.91 memory used=1381.1MB, alloc=83.8MB, time=11.97 memory used=1389.6MB, alloc=83.8MB, time=12.06 memory used=1398.8MB, alloc=83.8MB, time=12.13 memory used=1408.1MB, alloc=83.8MB, time=12.21 memory used=1417.2MB, alloc=83.8MB, time=12.31 memory used=1426.3MB, alloc=83.8MB, time=12.39 memory used=1435.5MB, alloc=83.8MB, time=12.46 memory used=1445.1MB, alloc=83.8MB, time=12.54 memory used=1454.9MB, alloc=83.8MB, time=12.61 memory used=1464.5MB, alloc=83.8MB, time=12.68 memory used=1474.2MB, alloc=83.8MB, time=12.75 memory used=1484.1MB, alloc=83.8MB, time=12.82 memory used=1494.4MB, alloc=83.8MB, time=12.93 memory used=1504.8MB, alloc=83.8MB, time=13.02 memory used=1515.5MB, alloc=83.8MB, time=13.11 memory used=1526.5MB, alloc=83.8MB, time=13.19 memory used=1537.6MB, alloc=83.8MB, time=13.26 memory used=1549.0MB, alloc=83.8MB, time=13.33 memory used=1590.4MB, alloc=83.8MB, time=13.91 memory used=1641.6MB, alloc=83.8MB, time=14.80 memory used=1684.6MB, alloc=83.8MB, time=15.36 memory used=1707.0MB, alloc=83.8MB, time=15.47 memory used=1750.4MB, alloc=83.8MB, time=16.09 memory used=1805.8MB, alloc=83.8MB, time=16.81 memory used=1830.4MB, alloc=83.8MB, time=16.92 memory used=1853.0MB, alloc=83.8MB, time=17.04 memory used=1906.9MB, alloc=83.8MB, time=17.95 memory used=1954.3MB, alloc=83.8MB, time=18.87 memory used=1998.8MB, alloc=107.8MB, time=19.83 memory used=2060.8MB, alloc=107.8MB, time=20.89 memory used=2094.6MB, alloc=107.8MB, time=21.10 memory used=2128.1MB, alloc=107.8MB, time=21.29 memory used=2168.5MB, alloc=107.8MB, time=21.50 memory used=2205.6MB, alloc=107.8MB, time=21.68 memory used=2249.7MB, alloc=107.8MB, time=40.02 memory used=2250.3MB, alloc=107.8MB, time=40.09 memory used=2250.6MB, alloc=107.8MB, time=40.16 memory used=2250.7MB, alloc=107.8MB, time=40.23 memory used=2250.8MB, alloc=107.8MB, time=40.31 memory used=2250.9MB, alloc=107.8MB, time=40.41 memory used=2250.9MB, alloc=107.8MB, time=40.48 memory used=2250.9MB, alloc=107.8MB, time=40.56 memory used=2250.9MB, alloc=363.8MB, time=40.63 |\^/| 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(); 1428276232 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 2 2 F := [-17 x + 20 x y - 6 x y z + 6, -6 x y z - 11 y z - 14 x y z - 10 x , 4 3 3 -13 x + 19 x z - 14 z + 17 y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 2 G := [-12 x y + 12 x z - 20 y + 13 x, 11 x z - 7 x y + 11 y z + 17 x, 2 2 2 2 -11 x y z - 7 y z + 11 x z - 20 x y z] > Problem := [F,G]; 4 3 2 Problem := [[-17 x + 20 x y - 6 x y z + 6, 2 2 2 2 4 3 3 -6 x y z - 11 y z - 14 x y z - 10 x , -13 x + 19 x z - 14 z + 17 y], 2 2 2 2 2 3 2 2 [-12 x y + 12 x z - 20 y + 13 x, 11 x z - 7 x y + 11 y z + 17 x, 2 2 2 2 -11 x y z - 7 y z + 11 x z - 20 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.32 memory used=26.3MB, alloc=32.3MB, time=0.90 memory used=45.2MB, alloc=56.3MB, time=1.41 memory used=84.8MB, alloc=60.3MB, time=2.38 memory used=127.3MB, alloc=68.3MB, time=3.48 memory used=168.5MB, alloc=68.3MB, time=4.50 memory used=209.7MB, alloc=92.3MB, time=5.47 memory used=275.4MB, alloc=92.3MB, time=7.06 memory used=340.8MB, alloc=92.3MB, time=8.66 memory used=405.8MB, alloc=372.3MB, time=10.00 memory used=494.5MB, alloc=372.3MB, time=12.10 memory used=587.9MB, alloc=396.3MB, time=14.21 memory used=703.5MB, alloc=420.3MB, time=17.00 memory used=823.3MB, alloc=420.3MB, time=19.92 memory used=932.6MB, alloc=444.3MB, time=22.45 memory used=1041.9MB, alloc=444.3MB, time=25.12 memory used=1176.4MB, alloc=444.3MB, time=27.38 memory used=1289.2MB, alloc=444.3MB, time=29.55 memory used=1394.6MB, alloc=468.3MB, time=32.06 memory used=1494.8MB, alloc=468.3MB, time=34.49 memory used=1580.9MB, alloc=468.3MB, time=36.72 memory used=1665.0MB, alloc=468.3MB, time=39.03 memory used=1742.3MB, alloc=468.3MB, time=41.34 memory used=1813.1MB, alloc=468.3MB, time=43.39 memory used=1894.6MB, alloc=468.3MB, time=45.49 memory used=1957.4MB, alloc=468.3MB, time=47.36 memory used=2021.4MB, alloc=468.3MB, time=49.32 memory used=2078.4MB, alloc=468.3MB, time=50.97 memory used=2138.3MB, alloc=492.3MB, time=52.77 memory used=2202.6MB, alloc=492.3MB, time=54.42 memory used=2246.7MB, alloc=492.3MB, time=55.82 memory used=2309.4MB, alloc=492.3MB, time=57.43 memory used=2357.3MB, alloc=492.3MB, time=59.29 memory used=2547.7MB, alloc=516.3MB, time=63.95 memory used=2762.5MB, alloc=540.3MB, time=68.48 memory used=2961.9MB, alloc=540.3MB, time=73.27 memory used=3136.5MB, alloc=564.3MB, time=77.89 memory used=3298.8MB, alloc=588.3MB, time=82.35 memory used=3514.9MB, alloc=588.3MB, time=85.99 memory used=3687.5MB, alloc=588.3MB, time=88.30 memory used=3829.3MB, alloc=588.3MB, time=90.06 memory used=4056.0MB, alloc=612.3MB, time=94.19 memory used=4260.9MB, alloc=612.3MB, time=99.52 memory used=4442.4MB, alloc=612.3MB, time=103.23 memory used=4570.9MB, alloc=612.3MB, time=107.00 memory used=4761.4MB, alloc=612.3MB, time=109.96 memory used=4966.7MB, alloc=612.3MB, time=113.33 memory used=5105.6MB, alloc=612.3MB, time=116.86 memory used=5205.3MB, alloc=636.3MB, time=119.90 memory used=5314.8MB, alloc=636.3MB, time=123.36 memory used=5511.9MB, alloc=636.3MB, time=126.85 memory used=5650.2MB, alloc=636.3MB, time=130.07 memory used=5814.0MB, alloc=636.3MB, time=133.20 memory used=6002.0MB, alloc=636.3MB, time=136.35 memory used=6126.2MB, alloc=636.3MB, time=139.81 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428276532 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 F := [18 x + 19 y z - 14 x y + 18 y z, 13 y - 11 y z + 2 x + 9 y z, 2 3 2 5 x y z - 12 y z + 9 x y + 3 x y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 3 4 2 2 G := [4 x - 2 y + 7, 14 x z + 9 z + 6 x y + 14 x z , 3 3 2 2 6 x y + 18 x z - 3 x z - 2 x y z] > Problem := [F,G]; 4 2 3 2 2 Problem := [[18 x + 19 y z - 14 x y + 18 y z, 13 y - 11 y z + 2 x + 9 y z, 2 3 2 4 4 5 x y z - 12 y z + 9 x y + 3 x y], [4 x - 2 y + 7, 3 4 2 2 3 3 2 2 14 x z + 9 z + 6 x y + 14 x z , 6 x y + 18 x z - 3 x z - 2 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.89 memory used=45.8MB, alloc=56.3MB, time=1.38 memory used=86.0MB, alloc=60.3MB, time=2.39 memory used=127.9MB, alloc=68.3MB, time=3.45 memory used=165.1MB, alloc=68.3MB, time=3.99 memory used=208.8MB, alloc=92.3MB, time=4.99 memory used=274.9MB, alloc=92.3MB, time=6.62 memory used=338.7MB, alloc=92.3MB, time=7.56 memory used=376.9MB, alloc=92.3MB, time=7.83 memory used=429.3MB, alloc=92.3MB, time=8.41 memory used=468.4MB, alloc=92.3MB, time=8.66 memory used=512.0MB, alloc=92.3MB, time=9.93 memory used=550.1MB, alloc=92.3MB, time=10.12 memory used=577.4MB, alloc=92.3MB, time=10.28 memory used=610.5MB, alloc=92.3MB, time=10.42 memory used=645.2MB, alloc=92.3MB, time=10.65 memory used=716.6MB, alloc=348.3MB, time=12.19 memory used=784.7MB, alloc=372.3MB, time=13.65 memory used=874.6MB, alloc=372.3MB, time=15.26 memory used=929.2MB, alloc=372.3MB, time=16.19 memory used=1037.1MB, alloc=372.3MB, time=18.23 memory used=1132.2MB, alloc=372.3MB, time=20.85 memory used=1193.6MB, alloc=372.3MB, time=21.80 memory used=1240.0MB, alloc=372.3MB, time=22.24 memory used=1287.5MB, alloc=372.3MB, time=22.58 memory used=1342.5MB, alloc=372.3MB, time=24.21 memory used=1377.9MB, alloc=372.3MB, time=24.43 memory used=1415.5MB, alloc=372.3MB, time=24.63 memory used=1501.1MB, alloc=396.3MB, time=26.09 memory used=1591.7MB, alloc=396.3MB, time=27.42 memory used=1698.3MB, alloc=396.3MB, time=29.39 memory used=1806.8MB, alloc=420.3MB, time=32.23 memory used=1942.4MB, alloc=444.3MB, time=35.47 memory used=2079.5MB, alloc=444.3MB, time=38.24 memory used=2189.5MB, alloc=444.3MB, time=40.77 memory used=2308.2MB, alloc=468.3MB, time=43.48 memory used=2403.2MB, alloc=468.3MB, time=45.78 memory used=2500.7MB, alloc=468.3MB, time=48.33 memory used=2596.5MB, alloc=468.3MB, time=50.82 memory used=2706.1MB, alloc=468.3MB, time=53.08 memory used=2816.5MB, alloc=468.3MB, time=54.51 memory used=2906.3MB, alloc=468.3MB, time=55.26 memory used=2992.4MB, alloc=468.3MB, time=56.01 memory used=3074.6MB, alloc=468.3MB, time=56.64 memory used=3170.7MB, alloc=468.3MB, time=57.64 memory used=3275.0MB, alloc=492.3MB, time=58.91 memory used=3367.6MB, alloc=492.3MB, time=59.53 memory used=3449.5MB, alloc=492.3MB, time=60.08 memory used=3564.3MB, alloc=492.3MB, time=60.98 memory used=3647.1MB, alloc=492.3MB, time=61.58 memory used=3768.3MB, alloc=492.3MB, time=64.39 memory used=3858.1MB, alloc=492.3MB, time=64.97 memory used=3958.0MB, alloc=492.3MB, time=66.22 memory used=4062.2MB, alloc=492.3MB, time=66.89 memory used=4140.3MB, alloc=492.3MB, time=67.45 memory used=4253.7MB, alloc=492.3MB, time=68.42 memory used=4344.1MB, alloc=492.3MB, time=69.02 memory used=4460.1MB, alloc=492.3MB, time=71.90 memory used=4549.1MB, alloc=492.3MB, time=72.50 memory used=4633.7MB, alloc=492.3MB, time=73.01 memory used=4747.9MB, alloc=492.3MB, time=73.91 memory used=4830.0MB, alloc=492.3MB, time=74.44 memory used=4940.9MB, alloc=492.3MB, time=75.34 memory used=5032.7MB, alloc=492.3MB, time=75.95 memory used=5127.7MB, alloc=492.3MB, time=78.18 memory used=5235.6MB, alloc=492.3MB, time=79.38 memory used=5323.3MB, alloc=492.3MB, time=79.94 memory used=5465.7MB, alloc=492.3MB, time=82.46 memory used=5555.8MB, alloc=492.3MB, time=84.37 memory used=5710.6MB, alloc=492.3MB, time=87.88 memory used=5797.5MB, alloc=492.3MB, time=88.44 memory used=5909.2MB, alloc=492.3MB, time=90.12 memory used=6017.6MB, alloc=492.3MB, time=91.86 memory used=6133.6MB, alloc=492.3MB, time=93.02 memory used=6256.7MB, alloc=492.3MB, time=94.44 memory used=6367.0MB, alloc=492.3MB, time=95.51 memory used=6472.3MB, alloc=492.3MB, time=97.41 memory used=6579.4MB, alloc=492.3MB, time=98.68 memory used=6687.0MB, alloc=492.3MB, time=99.57 memory used=6796.8MB, alloc=492.3MB, time=101.23 memory used=6905.3MB, alloc=492.3MB, time=102.11 memory used=7009.9MB, alloc=492.3MB, time=103.81 memory used=7144.7MB, alloc=492.3MB, time=105.92 memory used=7224.2MB, alloc=492.3MB, time=107.73 memory used=7344.9MB, alloc=492.3MB, time=110.05 memory used=7447.4MB, alloc=492.3MB, time=111.86 memory used=7528.4MB, alloc=492.3MB, time=113.78 memory used=7591.2MB, alloc=492.3MB, time=115.67 memory used=7653.9MB, alloc=492.3MB, time=117.38 memory used=7724.1MB, alloc=492.3MB, time=119.38 memory used=7789.4MB, alloc=492.3MB, time=121.34 memory used=7846.9MB, alloc=516.3MB, time=122.88 memory used=7911.9MB, alloc=516.3MB, time=124.98 memory used=7964.8MB, alloc=516.3MB, time=126.71 memory used=8005.3MB, alloc=516.3MB, time=128.10 memory used=8147.7MB, alloc=516.3MB, time=129.90 memory used=8280.3MB, alloc=516.3MB, time=132.55 memory used=8399.7MB, alloc=516.3MB, time=133.64 memory used=8514.8MB, alloc=516.3MB, time=135.98 memory used=8640.7MB, alloc=516.3MB, time=137.18 memory used=8758.3MB, alloc=516.3MB, time=139.78 memory used=8888.3MB, alloc=516.3MB, time=141.09 memory used=9007.6MB, alloc=516.3MB, time=143.08 memory used=9130.4MB, alloc=516.3MB, time=144.24 memory used=9257.5MB, alloc=516.3MB, time=146.48 memory used=9390.6MB, alloc=516.3MB, time=148.58 memory used=9611.2MB, alloc=516.3MB, time=152.97 memory used=9871.2MB, alloc=516.3MB, time=158.75 memory used=9994.2MB, alloc=516.3MB, time=162.40 memory used=10196.1MB, alloc=540.3MB, time=165.42 memory used=10417.4MB, alloc=564.3MB, time=171.45 memory used=10606.0MB, alloc=588.3MB, time=176.58 memory used=10836.0MB, alloc=588.3MB, time=180.63 memory used=10975.3MB, alloc=588.3MB, time=182.13 memory used=11097.9MB, alloc=588.3MB, time=183.19 memory used=11284.1MB, alloc=588.3MB, time=187.93 |\^/| 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(); 1428276832 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 3 4 2 2 2 F := [-8 x + 9 x y - 17 x z + 16 y z, -12 x - 5 x y - 8 y z + 17 x z, 3 2 2 3 3 -19 x y + 16 x z - 13 x + 6 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 2 G := [-20 x z + 16 z - 9 x + 13 y z, 12 x y z - 12 x y z - 19 y z , 3 3 2 2 2 -7 x y - 2 x z + 6 x z + 5 y ] > Problem := [F,G]; 4 3 3 3 Problem := [[-8 x + 9 x y - 17 x z + 16 y z, 4 2 2 2 3 2 2 3 3 -12 x - 5 x y - 8 y z + 17 x z, -19 x y + 16 x z - 13 x + 6 z ], [ 2 3 2 2 2 2 2 -20 x z + 16 z - 9 x + 13 y z, 12 x y z - 12 x y z - 19 y z , 3 3 2 2 2 -7 x y - 2 x z + 6 x z + 5 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.0MB, alloc=32.3MB, time=0.89 memory used=45.2MB, alloc=56.3MB, time=1.41 memory used=86.5MB, alloc=60.3MB, time=2.50 memory used=131.0MB, alloc=92.3MB, time=3.56 memory used=198.9MB, alloc=92.3MB, time=5.16 memory used=264.4MB, alloc=116.3MB, time=6.79 memory used=336.3MB, alloc=372.3MB, time=8.48 memory used=420.2MB, alloc=372.3MB, time=10.18 memory used=510.2MB, alloc=372.3MB, time=11.78 memory used=595.7MB, alloc=396.3MB, time=14.00 memory used=705.9MB, alloc=420.3MB, time=16.72 memory used=835.1MB, alloc=420.3MB, time=19.29 memory used=910.0MB, alloc=420.3MB, time=20.30 memory used=1027.5MB, alloc=420.3MB, time=22.12 memory used=1102.5MB, alloc=420.3MB, time=23.15 memory used=1156.6MB, alloc=420.3MB, time=23.48 memory used=1231.3MB, alloc=420.3MB, time=25.02 memory used=1287.0MB, alloc=420.3MB, time=25.40 memory used=1349.4MB, alloc=420.3MB, time=25.77 memory used=1394.1MB, alloc=420.3MB, time=26.06 memory used=1445.9MB, alloc=420.3MB, time=26.37 memory used=1540.7MB, alloc=420.3MB, time=27.62 memory used=1668.1MB, alloc=444.3MB, time=30.98 memory used=1785.3MB, alloc=468.3MB, time=33.92 memory used=1894.2MB, alloc=468.3MB, time=36.37 memory used=2036.1MB, alloc=492.3MB, time=39.20 memory used=2144.8MB, alloc=492.3MB, time=42.20 memory used=2233.0MB, alloc=492.3MB, time=44.37 memory used=2321.4MB, alloc=516.3MB, time=46.38 memory used=2435.5MB, alloc=516.3MB, time=48.74 memory used=2533.2MB, alloc=516.3MB, time=51.32 memory used=2616.1MB, alloc=516.3MB, time=53.45 memory used=2690.0MB, alloc=516.3MB, time=56.23 memory used=2749.1MB, alloc=516.3MB, time=58.16 memory used=2831.9MB, alloc=540.3MB, time=60.44 memory used=2897.7MB, alloc=540.3MB, time=62.38 memory used=2965.0MB, alloc=540.3MB, time=64.04 memory used=3040.7MB, alloc=540.3MB, time=65.72 memory used=3106.0MB, alloc=540.3MB, time=67.87 memory used=3152.7MB, alloc=540.3MB, time=69.47 memory used=3194.1MB, alloc=540.3MB, time=70.94 memory used=3400.9MB, alloc=564.3MB, time=76.00 memory used=3591.1MB, alloc=588.3MB, time=79.46 memory used=3753.2MB, alloc=588.3MB, time=81.54 memory used=3905.0MB, alloc=588.3MB, time=86.51 memory used=4067.0MB, alloc=588.3MB, time=92.37 memory used=4253.9MB, alloc=588.3MB, time=94.97 memory used=4542.1MB, alloc=588.3MB, time=101.93 memory used=4819.0MB, alloc=612.3MB, time=106.86 memory used=4983.2MB, alloc=636.3MB, time=110.88 memory used=5135.1MB, alloc=636.3MB, time=115.34 memory used=5296.2MB, alloc=660.3MB, time=120.04 memory used=5439.1MB, alloc=660.3MB, time=123.89 memory used=5585.8MB, alloc=660.3MB, time=128.23 memory used=5709.1MB, alloc=660.3MB, time=131.70 memory used=5836.0MB, alloc=684.3MB, time=135.93 memory used=5955.5MB, alloc=684.3MB, time=140.21 memory used=6046.7MB, alloc=684.3MB, time=142.99 memory used=6168.7MB, alloc=684.3MB, time=147.10 memory used=6514.3MB, alloc=708.3MB, time=154.31 memory used=6692.3MB, alloc=708.3MB, time=156.55 memory used=6874.0MB, alloc=708.3MB, time=158.71 memory used=7067.0MB, alloc=708.3MB, time=163.32 memory used=7248.3MB, alloc=708.3MB, time=165.62 memory used=7461.4MB, alloc=708.3MB, time=168.29 memory used=7655.2MB, alloc=708.3MB, 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(); 1428277132 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 3 F := [10 x y z + 3 y z - 6 x z + 2 y , 10 x y + 5 x z - 5 y + 8, 2 4 -18 x y z + 7 y + 7 y - 12 z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-7 x z + 20 y z + z + 6 y, -18 x y z + 9 x y z + 10 y z, 3 3 2 2 8 x y + 3 x z + 9 x z + 3 x ] > Problem := [F,G]; 2 3 2 2 2 2 3 Problem := [[10 x y z + 3 y z - 6 x z + 2 y , 10 x y + 5 x z - 5 y + 8, 2 4 2 2 2 -18 x y z + 7 y + 7 y - 12 z], [-7 x z + 20 y z + z + 6 y, 2 2 3 3 2 2 -18 x y z + 9 x y z + 10 y z, 8 x y + 3 x z + 9 x z + 3 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.0MB, alloc=32.3MB, time=0.88 memory used=47.1MB, alloc=32.3MB, time=1.42 memory used=65.4MB, alloc=56.3MB, time=1.90 memory used=104.9MB, alloc=60.3MB, time=2.92 memory used=143.5MB, alloc=60.3MB, time=3.89 memory used=184.3MB, alloc=92.3MB, time=4.97 memory used=248.8MB, alloc=92.3MB, time=6.53 memory used=313.0MB, alloc=92.3MB, time=8.07 memory used=368.6MB, alloc=92.3MB, time=9.16 memory used=428.2MB, alloc=92.3MB, time=10.34 memory used=489.4MB, alloc=116.3MB, time=11.97 memory used=563.9MB, alloc=116.3MB, time=13.75 memory used=637.7MB, alloc=372.3MB, time=15.61 memory used=723.2MB, alloc=396.3MB, time=17.80 memory used=816.3MB, alloc=396.3MB, time=22.93 memory used=894.4MB, alloc=396.3MB, time=24.95 memory used=986.9MB, alloc=396.3MB, time=54.25 memory used=1053.2MB, alloc=396.3MB, time=61.26 memory used=1100.7MB, alloc=396.3MB, time=61.57 memory used=1187.9MB, alloc=396.3MB, time=62.71 memory used=1286.4MB, alloc=396.3MB, time=66.65 memory used=1335.5MB, alloc=396.3MB, time=66.92 memory used=1380.3MB, alloc=396.3MB, time=67.16 memory used=1473.4MB, alloc=396.3MB, time=68.62 memory used=1577.7MB, alloc=420.3MB, time=71.15 memory used=1669.5MB, alloc=420.3MB, time=72.57 memory used=1768.2MB, alloc=420.3MB, time=74.79 memory used=1824.4MB, alloc=420.3MB, time=75.18 memory used=1895.9MB, alloc=420.3MB, time=75.60 memory used=1939.9MB, alloc=420.3MB, time=75.93 memory used=1988.4MB, alloc=444.3MB, time=76.29 memory used=2059.6MB, alloc=444.3MB, time=76.70 memory used=2142.8MB, alloc=444.3MB, time=77.13 memory used=2238.2MB, alloc=444.3MB, time=77.57 memory used=2297.9MB, alloc=444.3MB, time=77.89 memory used=2350.7MB, alloc=444.3MB, time=78.19 memory used=2409.8MB, alloc=444.3MB, time=78.51 memory used=2472.7MB, alloc=444.3MB, time=78.83 memory used=2538.6MB, alloc=444.3MB, time=79.15 memory used=2611.6MB, alloc=444.3MB, time=79.47 memory used=2691.1MB, alloc=444.3MB, time=79.80 memory used=2778.1MB, alloc=444.3MB, time=80.14 memory used=2891.2MB, alloc=444.3MB, time=130.47 |\^/| 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(); 1428277432 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 3 3 2 2 F := [-13 x + y z - 19 x z - 8 y , 4 y z + 11 x y - 4 x y z + 19 z , 3 3 2 4 x z - y z - 9 y z + 11 z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-17 x y - 14 x y z + 17 y z - 6 z , 4 2 2 2 2 2 2 -2 x - 10 x y + 20 x z + 14 y z , 2 2 2 2 2 19 x y z - 18 y z - 8 x y + 17 x z ] > Problem := [F,G]; 4 3 2 3 3 2 2 Problem := [[-13 x + y z - 19 x z - 8 y , 4 y z + 11 x y - 4 x y z + 19 z , 3 3 2 2 2 2 2 4 x z - y z - 9 y z + 11 z], [-17 x y - 14 x y z + 17 y z - 6 z , 4 2 2 2 2 2 2 -2 x - 10 x y + 20 x z + 14 y z , 2 2 2 2 2 19 x y z - 18 y z - 8 x y + 17 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=25.3MB, alloc=32.3MB, time=0.86 memory used=46.2MB, alloc=36.3MB, time=1.35 memory used=78.3MB, alloc=60.5MB, time=2.05 memory used=106.6MB, alloc=60.5MB, time=2.20 memory used=199.9MB, alloc=61.0MB, time=5.13 memory used=229.6MB, alloc=61.0MB, time=5.40 memory used=255.8MB, alloc=61.0MB, time=5.50 memory used=305.1MB, alloc=61.0MB, time=7.12 memory used=338.1MB, alloc=61.0MB, time=7.31 memory used=361.4MB, alloc=61.0MB, time=7.43 memory used=386.7MB, alloc=61.0MB, time=7.54 memory used=417.3MB, alloc=61.0MB, time=7.67 memory used=444.5MB, alloc=61.0MB, time=7.78 memory used=462.9MB, alloc=61.0MB, time=7.86 memory used=482.1MB, alloc=61.0MB, time=7.96 memory used=503.5MB, alloc=61.0MB, time=8.05 memory used=525.7MB, alloc=61.0MB, time=8.14 memory used=550.2MB, alloc=61.0MB, time=8.24 memory used=575.4MB, alloc=61.0MB, time=8.33 memory used=603.0MB, alloc=61.0MB, time=8.44 memory used=631.2MB, alloc=61.0MB, time=8.54 memory used=661.5MB, alloc=61.0MB, time=8.64 memory used=694.2MB, alloc=61.0MB, time=8.75 memory used=732.3MB, alloc=83.8MB, time=8.91 memory used=744.1MB, alloc=83.8MB, time=8.99 memory used=756.0MB, alloc=83.8MB, time=9.07 memory used=767.8MB, alloc=83.8MB, time=9.15 memory used=779.7MB, alloc=83.8MB, time=9.22 memory used=791.6MB, alloc=83.8MB, time=9.30 memory used=803.7MB, alloc=83.8MB, time=9.37 memory used=816.9MB, alloc=83.8MB, time=9.45 memory used=830.3MB, alloc=83.8MB, time=9.54 memory used=843.7MB, alloc=83.8MB, time=9.61 memory used=857.1MB, alloc=83.8MB, time=9.69 memory used=870.8MB, alloc=83.8MB, time=9.77 memory used=885.3MB, alloc=83.8MB, time=9.86 memory used=900.0MB, alloc=83.8MB, time=9.94 memory used=914.9MB, alloc=83.8MB, time=10.02 memory used=930.6MB, alloc=83.8MB, time=10.09 memory used=946.4MB, alloc=83.8MB, time=10.18 memory used=963.4MB, alloc=83.8MB, time=10.27 memory used=980.2MB, alloc=83.8MB, time=10.35 memory used=998.2MB, alloc=83.8MB, time=10.43 memory used=1016.0MB, alloc=83.8MB, time=10.52 memory used=1034.5MB, alloc=83.8MB, time=10.61 memory used=1053.7MB, alloc=83.8MB, time=10.70 memory used=1073.4MB, alloc=83.8MB, time=10.79 memory used=1094.4MB, alloc=83.8MB, time=10.87 memory used=1115.8MB, alloc=83.8MB, time=10.96 memory used=1138.5MB, alloc=83.8MB, time=11.04 memory used=1187.4MB, alloc=83.8MB, time=11.77 memory used=1215.9MB, alloc=83.8MB, time=12.23 memory used=1247.7MB, alloc=83.8MB, time=12.40 memory used=1273.9MB, alloc=83.8MB, time=12.51 memory used=1295.3MB, alloc=83.8MB, time=13.51 memory used=1324.2MB, alloc=83.8MB, time=13.64 memory used=1356.3MB, alloc=83.8MB, time=13.77 memory used=1391.8MB, alloc=83.8MB, time=13.90 memory used=1430.3MB, alloc=83.8MB, time=14.02 memory used=1472.0MB, alloc=83.8MB, time=14.14 memory used=1501.7MB, alloc=83.8MB, time=14.24 memory used=1566.0MB, alloc=83.8MB, time=23.33 memory used=1602.0MB, alloc=83.8MB, time=23.65 memory used=1628.9MB, alloc=83.8MB, time=23.79 memory used=1648.7MB, alloc=83.8MB, time=23.90 memory used=1672.1MB, alloc=83.8MB, time=24.03 memory used=1698.2MB, alloc=83.8MB, time=24.16 memory used=1727.0MB, alloc=83.8MB, time=24.31 memory used=1755.6MB, alloc=83.8MB, time=24.44 memory used=1773.0MB, alloc=83.8MB, time=24.54 memory used=1789.0MB, alloc=83.8MB, time=24.63 memory used=1806.2MB, alloc=83.8MB, time=24.73 memory used=1824.0MB, alloc=83.8MB, time=24.82 memory used=1842.3MB, alloc=83.8MB, time=24.91 memory used=1861.3MB, alloc=83.8MB, time=25.02 memory used=1882.6MB, alloc=83.8MB, time=25.12 memory used=1904.7MB, alloc=83.8MB, time=25.22 memory used=1927.3MB, alloc=83.8MB, time=25.32 memory used=1950.4MB, alloc=83.8MB, time=25.43 memory used=1974.1MB, alloc=83.8MB, time=25.54 memory used=1998.2MB, alloc=83.8MB, time=25.65 memory used=2023.1MB, alloc=83.8MB, time=25.76 memory used=2050.4MB, alloc=83.8MB, time=25.88 memory used=2078.5MB, alloc=83.8MB, time=25.99 memory used=2107.0MB, alloc=83.8MB, time=26.11 memory used=2136.1MB, alloc=83.8MB, time=26.23 memory used=2165.6MB, alloc=83.8MB, time=26.33 memory used=2190.7MB, alloc=83.8MB, time=26.45 memory used=2200.0MB, alloc=83.8MB, time=26.52 memory used=2210.9MB, alloc=83.8MB, time=26.60 memory used=2221.8MB, alloc=83.8MB, time=26.67 memory used=2232.7MB, alloc=83.8MB, time=26.75 memory used=2243.7MB, alloc=83.8MB, time=26.82 memory used=2254.7MB, alloc=83.8MB, time=26.90 memory used=2265.7MB, alloc=83.8MB, time=26.98 memory used=2276.8MB, alloc=83.8MB, time=27.07 memory used=2288.0MB, alloc=83.8MB, time=27.15 memory used=2299.1MB, alloc=83.8MB, time=27.23 memory used=2310.3MB, alloc=83.8MB, time=27.31 memory used=2321.5MB, alloc=83.8MB, time=27.39 memory used=2332.8MB, alloc=83.8MB, time=27.46 memory used=2344.1MB, alloc=83.8MB, time=27.54 memory used=2355.4MB, alloc=83.8MB, time=27.64 memory used=2366.8MB, alloc=83.8MB, time=27.71 memory used=2378.2MB, alloc=83.8MB, time=27.79 memory used=2389.6MB, alloc=83.8MB, time=27.87 memory used=2401.0MB, alloc=83.8MB, time=27.96 memory used=2412.5MB, alloc=83.8MB, time=28.03 memory used=2423.9MB, alloc=83.8MB, time=28.11 memory used=2435.4MB, alloc=83.8MB, time=28.19 memory used=2446.9MB, alloc=83.8MB, time=28.27 memory used=2458.5MB, alloc=83.8MB, time=28.35 memory used=2470.3MB, alloc=83.8MB, time=28.43 memory used=2484.5MB, alloc=83.8MB, time=28.52 memory used=2496.5MB, alloc=83.8MB, time=28.59 memory used=2510.5MB, alloc=83.8MB, time=28.68 memory used=2525.0MB, alloc=83.8MB, time=28.77 memory used=2539.5MB, alloc=83.8MB, time=28.85 memory used=2554.1MB, alloc=83.8MB, time=28.94 memory used=2568.6MB, alloc=83.8MB, time=29.02 memory used=2583.1MB, alloc=83.8MB, time=29.10 memory used=2597.7MB, alloc=83.8MB, time=29.19 memory used=2612.2MB, alloc=83.8MB, time=29.27 memory used=2626.7MB, alloc=83.8MB, time=29.36 memory used=2641.2MB, alloc=83.8MB, time=29.44 memory used=2655.8MB, alloc=83.8MB, time=29.52 memory used=2670.3MB, alloc=83.8MB, time=29.61 memory used=2684.8MB, alloc=83.8MB, time=29.69 memory used=2699.3MB, alloc=83.8MB, time=29.78 memory used=2714.1MB, alloc=83.8MB, time=29.86 memory used=2731.0MB, alloc=83.8MB, time=29.95 memory used=2748.3MB, alloc=83.8MB, time=30.04 memory used=2765.6MB, alloc=83.8MB, time=30.13 memory used=2782.8MB, alloc=83.8MB, time=30.23 memory used=2800.0MB, alloc=83.8MB, time=30.31 memory used=2817.1MB, alloc=83.8MB, time=30.40 memory used=2834.1MB, alloc=83.8MB, time=30.49 memory used=2851.1MB, alloc=83.8MB, time=30.57 memory used=2868.0MB, alloc=83.8MB, time=30.66 memory used=2885.2MB, alloc=83.8MB, time=30.75 memory used=2904.5MB, alloc=83.8MB, time=30.84 memory used=2923.9MB, alloc=83.8MB, time=30.94 memory used=2943.3MB, alloc=83.8MB, time=31.03 memory used=2962.5MB, alloc=83.8MB, time=31.14 memory used=2981.6MB, alloc=83.8MB, time=31.23 memory used=3000.6MB, alloc=83.8MB, time=31.33 memory used=3019.7MB, alloc=83.8MB, time=31.42 memory used=3040.7MB, alloc=83.8MB, time=31.52 memory used=3061.8MB, alloc=83.8MB, time=31.61 memory used=3082.7MB, alloc=83.8MB, time=31.71 memory used=3103.3MB, alloc=83.8MB, time=31.81 memory used=3124.3MB, alloc=83.8MB, time=31.90 memory used=3146.7MB, alloc=83.8MB, time=31.98 memory used=3169.0MB, alloc=83.8MB, time=32.08 memory used=3191.5MB, alloc=83.8MB, time=32.17 memory used=3211.7MB, alloc=83.8MB, time=32.27 memory used=3227.8MB, alloc=83.8MB, time=32.35 memory used=3243.4MB, alloc=83.8MB, time=32.44 memory used=3259.3MB, alloc=83.8MB, time=32.53 memory used=3275.0MB, alloc=83.8MB, time=32.60 memory used=3290.4MB, alloc=83.8MB, time=32.69 memory used=3306.0MB, alloc=83.8MB, time=32.77 memory used=3322.5MB, alloc=83.8MB, time=32.86 memory used=3339.1MB, alloc=83.8MB, time=32.95 memory used=3355.3MB, alloc=83.8MB, time=33.03 memory used=3371.8MB, alloc=83.8MB, time=33.11 memory used=3389.0MB, alloc=83.8MB, time=33.20 memory used=3406.0MB, alloc=83.8MB, time=33.29 memory used=3423.8MB, alloc=83.8MB, time=33.37 memory used=3441.2MB, alloc=83.8MB, time=33.45 memory used=3459.7MB, alloc=83.8MB, time=33.55 memory used=3478.6MB, alloc=83.8MB, time=33.63 memory used=3498.2MB, alloc=83.8MB, time=33.71 memory used=3518.7MB, alloc=83.8MB, time=33.80 memory used=3598.8MB, alloc=83.8MB, time=35.22 memory used=3646.8MB, alloc=83.8MB, time=36.27 memory used=3687.0MB, alloc=83.8MB, time=37.04 memory used=3731.6MB, alloc=107.8MB, time=38.01 memory used=3800.2MB, alloc=107.8MB, time=39.46 memory used=3856.9MB, alloc=363.8MB, time=40.65 memory used=3911.6MB, alloc=387.8MB, time=68.38 memory used=3961.6MB, alloc=387.8MB, time=149.52 |\^/| 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(); 1428277732 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 2 2 F := [3 x y z + 11 y - 6 x z - 15 y z, -6 x y z + 12 x y - 15 y z - 16 z, 2 2 2 2 4 8 x y + x z - 11 z - 13 z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 3 3 4 G := [-8 x y z + 17 x + x y + 11 z , 2 x y - 17 y z - 16 z - 16, 3 2 2 2 18 x y - 3 x y - 14 x y z + x] > Problem := [F,G]; 2 4 2 Problem := [[3 x y z + 11 y - 6 x z - 15 y z, 2 2 2 2 2 2 2 4 -6 x y z + 12 x y - 15 y z - 16 z, 8 x y + x z - 11 z - 13 z], [ 2 3 2 3 3 3 4 -8 x y z + 17 x + x y + 11 z , 2 x y - 17 y z - 16 z - 16, 3 2 2 2 18 x y - 3 x y - 14 x y z + x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.0MB, alloc=32.3MB, time=0.68 memory used=46.4MB, alloc=32.3MB, time=1.12 memory used=67.4MB, alloc=32.3MB, time=1.45 memory used=81.9MB, alloc=32.3MB, time=1.58 memory used=96.6MB, alloc=32.3MB, time=1.81 memory used=112.2MB, alloc=32.3MB, time=1.94 memory used=126.8MB, alloc=32.3MB, time=2.05 memory used=143.9MB, alloc=32.5MB, time=2.31 memory used=159.7MB, alloc=32.5MB, time=2.51 memory used=178.2MB, alloc=32.5MB, time=2.85 memory used=200.4MB, alloc=60.5MB, time=3.52 memory used=238.9MB, alloc=60.5MB, time=4.09 memory used=280.7MB, alloc=61.9MB, time=4.53 memory used=314.2MB, alloc=61.9MB, time=4.85 memory used=346.4MB, alloc=61.9MB, time=5.04 memory used=379.3MB, alloc=61.9MB, time=5.35 memory used=414.6MB, alloc=61.9MB, time=5.70 memory used=452.6MB, alloc=61.9MB, time=6.00 memory used=490.5MB, alloc=61.9MB, time=6.76 memory used=532.6MB, alloc=70.0MB, time=7.73 memory used=573.1MB, alloc=70.0MB, time=8.46 memory used=602.2MB, alloc=70.0MB, time=8.69 memory used=632.9MB, alloc=70.0MB, time=8.98 memory used=657.8MB, alloc=70.0MB, time=9.12 memory used=679.4MB, alloc=70.0MB, time=9.23 memory used=698.8MB, alloc=70.0MB, time=9.34 memory used=721.5MB, alloc=70.0MB, time=9.45 memory used=751.5MB, alloc=70.0MB, time=9.73 memory used=779.4MB, alloc=70.0MB, time=9.88 memory used=805.8MB, alloc=70.0MB, time=10.01 memory used=826.0MB, alloc=70.0MB, time=10.12 memory used=845.9MB, alloc=70.0MB, time=10.22 memory used=869.0MB, alloc=70.0MB, time=10.32 memory used=905.3MB, alloc=70.0MB, time=11.20 memory used=932.2MB, alloc=70.0MB, time=11.34 memory used=951.7MB, alloc=70.0MB, time=11.45 memory used=978.1MB, alloc=70.0MB, time=11.56 memory used=998.0MB, alloc=70.0MB, time=11.67 memory used=1028.1MB, alloc=70.0MB, time=11.96 memory used=1053.2MB, alloc=70.0MB, time=12.09 memory used=1073.9MB, alloc=70.0MB, time=12.20 memory used=1093.5MB, alloc=70.0MB, time=12.30 memory used=1116.0MB, alloc=70.0MB, time=12.41 memory used=1150.1MB, alloc=70.0MB, time=13.20 memory used=1178.7MB, alloc=70.0MB, time=13.34 memory used=1197.8MB, alloc=70.0MB, time=13.45 memory used=1222.9MB, alloc=70.0MB, time=13.57 memory used=1242.7MB, alloc=70.0MB, time=13.65 memory used=1286.5MB, alloc=70.0MB, time=14.19 memory used=1307.1MB, alloc=70.0MB, time=14.31 memory used=1332.1MB, alloc=70.0MB, time=14.43 memory used=1364.0MB, alloc=70.0MB, time=15.09 memory used=1392.6MB, alloc=70.0MB, time=15.25 memory used=1411.3MB, alloc=70.0MB, time=15.37 memory used=1433.8MB, alloc=70.0MB, time=15.49 memory used=1460.3MB, alloc=70.0MB, time=15.62 memory used=1484.7MB, alloc=70.0MB, time=15.74 memory used=1500.8MB, alloc=70.0MB, time=15.84 memory used=1516.6MB, alloc=70.0MB, time=15.95 memory used=1533.1MB, alloc=94.0MB, time=16.08 memory used=1566.6MB, alloc=94.0MB, time=16.25 memory used=1604.6MB, alloc=94.0MB, time=16.41 memory used=1645.4MB, alloc=94.0MB, time=16.59 memory used=1690.8MB, alloc=94.0MB, time=16.76 memory used=1733.6MB, alloc=94.0MB, time=16.92 memory used=1760.8MB, alloc=94.0MB, time=17.03 memory used=1788.8MB, alloc=94.0MB, time=17.15 memory used=1819.6MB, alloc=94.0MB, time=17.26 memory used=1852.6MB, alloc=94.0MB, time=17.37 memory used=1898.2MB, alloc=94.0MB, time=20.14 memory used=1956.5MB, alloc=94.0MB, time=24.28 memory used=1993.6MB, alloc=94.0MB, time=24.43 memory used=2034.6MB, alloc=94.0MB, time=24.59 memory used=2080.4MB, alloc=94.0MB, time=24.76 memory used=2109.9MB, alloc=94.0MB, time=24.88 memory used=2142.6MB, alloc=94.0MB, time=25.00 memory used=2178.8MB, alloc=94.0MB, time=25.11 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time=52.73 memory used=3164.6MB, alloc=103.3MB, time=52.90 memory used=3202.7MB, alloc=103.3MB, time=53.08 memory used=3245.8MB, alloc=103.3MB, time=53.24 memory used=3292.6MB, alloc=103.3MB, time=53.43 memory used=3328.3MB, alloc=103.3MB, time=53.59 memory used=3354.7MB, alloc=103.3MB, time=53.71 memory used=3381.3MB, alloc=103.3MB, time=53.83 memory used=3409.7MB, alloc=103.3MB, time=53.94 memory used=3438.9MB, alloc=103.3MB, time=54.08 memory used=3470.7MB, alloc=103.3MB, time=54.20 memory used=3503.1MB, alloc=103.3MB, time=54.33 memory used=3536.2MB, alloc=103.3MB, time=54.46 memory used=3572.0MB, alloc=103.3MB, time=54.59 memory used=3608.4MB, alloc=103.3MB, time=54.72 memory used=3647.4MB, alloc=103.3MB, time=54.86 memory used=3686.9MB, alloc=103.3MB, time=54.99 memory used=3729.0MB, alloc=103.3MB, time=55.13 memory used=3771.6MB, alloc=103.3MB, time=55.27 memory used=3816.8MB, alloc=103.3MB, time=55.41 memory used=3864.3MB, alloc=103.3MB, time=55.56 memory used=3915.2MB, 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used=4120.9MB, alloc=107.8MB, time=57.64 memory used=4131.5MB, alloc=107.8MB, time=57.72 memory used=4142.0MB, alloc=107.8MB, time=57.82 memory used=4152.5MB, alloc=107.8MB, time=57.93 memory used=4162.9MB, alloc=107.8MB, time=58.02 memory used=4173.3MB, alloc=107.8MB, time=58.11 memory used=4183.7MB, alloc=107.8MB, time=58.21 memory used=4194.0MB, alloc=107.8MB, time=58.31 memory used=4204.3MB, alloc=107.8MB, time=58.39 memory used=4214.5MB, alloc=107.8MB, time=58.48 memory used=4224.7MB, alloc=107.8MB, time=58.56 memory used=4235.0MB, alloc=107.8MB, time=58.65 memory used=4246.8MB, alloc=107.8MB, time=58.73 memory used=4258.8MB, alloc=107.8MB, time=58.84 memory used=4270.7MB, alloc=107.8MB, time=58.93 memory used=4282.5MB, alloc=107.8MB, time=59.02 memory used=4294.2MB, alloc=107.8MB, time=59.12 memory used=4305.8MB, alloc=107.8MB, time=59.21 memory used=4317.4MB, alloc=107.8MB, time=59.30 memory used=4328.8MB, alloc=107.8MB, time=59.38 memory used=4340.4MB, alloc=107.8MB, time=59.47 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time=61.52 memory used=4668.2MB, alloc=107.8MB, time=61.62 memory used=4780.0MB, alloc=107.8MB, time=63.68 memory used=4860.0MB, alloc=107.8MB, time=64.61 memory used=4940.0MB, alloc=107.8MB, time=66.01 memory used=5022.0MB, alloc=107.8MB, time=67.81 memory used=5101.6MB, alloc=107.8MB, time=70.07 memory used=5181.9MB, alloc=107.8MB, time=72.81 memory used=5263.4MB, alloc=107.8MB, time=75.74 memory used=5344.7MB, alloc=107.8MB, time=79.24 memory used=5423.9MB, alloc=107.8MB, time=82.43 memory used=5473.9MB, alloc=107.8MB, time=82.93 memory used=5512.3MB, alloc=107.8MB, time=83.11 memory used=5544.3MB, alloc=107.8MB, time=83.28 memory used=5594.3MB, alloc=107.8MB, time=84.40 memory used=5635.1MB, alloc=107.8MB, time=84.59 memory used=5674.4MB, alloc=107.8MB, time=84.75 memory used=5725.7MB, alloc=107.8MB, time=85.75 memory used=5779.3MB, alloc=107.8MB, time=86.55 memory used=5812.9MB, alloc=107.8MB, time=86.71 memory used=5849.8MB, alloc=107.8MB, time=86.86 memory used=5880.6MB, 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used=8207.8MB, alloc=363.8MB, time=122.92 memory used=8256.8MB, alloc=363.8MB, time=123.36 memory used=8295.6MB, alloc=363.8MB, time=123.75 memory used=8335.0MB, alloc=363.8MB, time=123.98 memory used=8372.4MB, alloc=363.8MB, time=124.19 memory used=8400.6MB, alloc=363.8MB, time=124.34 memory used=8427.8MB, alloc=363.8MB, time=124.51 memory used=8459.9MB, alloc=363.8MB, time=124.68 memory used=8496.4MB, alloc=363.8MB, time=124.84 memory used=8534.5MB, alloc=363.8MB, time=125.01 memory used=8558.4MB, alloc=363.8MB, time=125.14 memory used=8583.2MB, alloc=363.8MB, time=125.27 memory used=8634.5MB, alloc=363.8MB, time=129.54 memory used=8667.5MB, alloc=363.8MB, time=129.71 memory used=8700.8MB, alloc=363.8MB, time=129.89 memory used=8736.0MB, alloc=363.8MB, time=130.05 memory used=8761.2MB, alloc=363.8MB, time=130.19 memory used=8790.2MB, alloc=363.8MB, time=130.33 memory used=8824.2MB, alloc=363.8MB, time=130.47 memory used=8868.9MB, alloc=363.8MB, time=130.76 memory used=8903.1MB, alloc=363.8MB, time=130.94 memory used=8946.7MB, alloc=363.8MB, time=132.04 memory used=8979.8MB, alloc=363.8MB, time=132.23 memory used=9014.2MB, alloc=363.8MB, time=132.40 memory used=9067.8MB, alloc=363.8MB, time=133.20 memory used=9129.6MB, alloc=363.8MB, time=134.19 memory used=9185.7MB, alloc=363.8MB, time=134.98 memory used=9251.2MB, alloc=363.8MB, time=141.04 memory used=9290.8MB, alloc=363.8MB, time=141.28 memory used=9320.1MB, alloc=363.8MB, time=141.48 memory used=9356.5MB, alloc=363.8MB, time=141.68 memory used=9385.4MB, alloc=363.8MB, time=141.86 memory used=9409.2MB, alloc=363.8MB, time=142.03 memory used=9435.8MB, alloc=363.8MB, time=142.20 memory used=9465.1MB, alloc=363.8MB, time=142.40 memory used=9497.7MB, alloc=363.8MB, time=142.58 memory used=9533.4MB, alloc=363.8MB, time=142.76 memory used=9565.0MB, alloc=363.8MB, time=142.92 memory used=9592.9MB, alloc=363.8MB, time=143.18 memory used=9664.5MB, alloc=363.8MB, time=144.63 memory used=9712.0MB, alloc=387.8MB, time=145.47 memory used=9767.7MB, alloc=387.8MB, time=146.07 memory used=9827.4MB, alloc=387.8MB, time=146.50 memory used=9885.6MB, alloc=387.8MB, time=146.99 memory used=9935.2MB, alloc=387.8MB, time=147.24 memory used=9973.2MB, alloc=387.8MB, time=147.45 memory used=10014.8MB, alloc=387.8MB, time=147.66 memory used=10065.7MB, alloc=387.8MB, time=147.87 memory used=10112.3MB, alloc=387.8MB, time=148.06 memory used=10146.7MB, alloc=387.8MB, time=148.22 memory used=10198.7MB, alloc=387.8MB, time=148.93 memory used=10256.5MB, alloc=387.8MB, time=153.48 memory used=10308.0MB, alloc=387.8MB, time=153.98 memory used=10358.3MB, alloc=387.8MB, time=154.19 memory used=10395.9MB, alloc=387.8MB, time=154.36 memory used=10437.7MB, alloc=387.8MB, time=154.53 memory used=10496.3MB, alloc=387.8MB, time=154.95 memory used=10540.8MB, alloc=387.8MB, time=155.16 memory used=10597.3MB, alloc=387.8MB, time=156.50 memory used=10641.3MB, alloc=387.8MB, time=156.70 memory used=10723.6MB, alloc=387.8MB, time=158.28 memory used=10782.4MB, alloc=387.8MB, time=158.88 memory used=10841.8MB, alloc=387.8MB, time=159.90 memory used=10879.1MB, alloc=387.8MB, time=160.15 memory used=10928.1MB, alloc=387.8MB, time=160.40 memory used=10968.3MB, alloc=387.8MB, time=160.64 memory used=11000.5MB, alloc=387.8MB, time=160.85 memory used=11035.5MB, alloc=387.8MB, time=161.07 memory used=11074.1MB, alloc=387.8MB, time=161.29 memory used=11116.5MB, alloc=387.8MB, time=161.51 memory used=11162.5MB, alloc=387.8MB, time=161.74 memory used=11212.2MB, alloc=387.8MB, time=161.98 memory used=11261.1MB, alloc=387.8MB, time=162.20 memory used=11290.1MB, alloc=387.8MB, time=162.37 memory used=11318.9MB, alloc=387.8MB, time=162.54 memory used=11348.6MB, alloc=387.8MB, time=162.72 memory used=11381.1MB, alloc=387.8MB, time=162.89 memory used=11414.2MB, alloc=387.8MB, time=163.07 memory used=11449.5MB, alloc=387.8MB, time=163.24 memory used=11486.6MB, alloc=387.8MB, time=163.42 memory used=11526.7MB, alloc=387.8MB, time=163.60 memory used=11569.8MB, alloc=387.8MB, time=163.79 memory used=11623.4MB, alloc=387.8MB, time=164.33 memory used=11665.0MB, alloc=387.8MB, time=164.77 memory used=11716.3MB, alloc=387.8MB, time=168.75 memory used=11784.0MB, alloc=387.8MB, time=174.58 memory used=11828.2MB, alloc=387.8MB, time=174.83 memory used=11863.7MB, alloc=387.8MB, time=175.05 memory used=11906.1MB, alloc=387.8MB, time=175.28 memory used=11956.9MB, alloc=387.8MB, time=175.52 memory used=11995.2MB, alloc=387.8MB, time=175.71 memory used=12025.1MB, alloc=387.8MB, time=175.88 memory used=12057.1MB, alloc=387.8MB, time=176.06 memory used=12091.3MB, alloc=387.8MB, time=176.26 memory used=12129.1MB, alloc=387.8MB, time=176.45 memory used=12169.0MB, alloc=387.8MB, time=176.63 memory used=12212.3MB, alloc=387.8MB, time=176.82 memory used=12257.4MB, alloc=387.8MB, time=177.01 memory used=12306.3MB, alloc=387.8MB, time=177.20 memory used=12359.1MB, alloc=387.8MB, time=177.40 memory used=12531.3MB, alloc=387.8MB, time=178.12 memory used=12678.4MB, alloc=387.8MB, time=180.18 memory used=12716.0MB, alloc=387.8MB, time=180.39 memory used=12758.3MB, alloc=387.8MB, time=180.60 memory used=12792.2MB, alloc=387.8MB, time=180.78 memory used=12847.2MB, alloc=387.8MB, time=181.12 memory used=12889.0MB, alloc=387.8MB, time=181.35 memory used=12926.9MB, alloc=387.8MB, time=181.57 memory used=12973.2MB, alloc=387.8MB, time=183.26 |\^/| 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(); 1428278032 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 F := [14 x y z - 15 y z - 9, -19 x z - 14 x z + 12 y - 18 x , 2 3 2 8 x y z + 9 y z - 12 y z + 20] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 3 G := [-19 y z + 18 x y z - 15 z + 16 z , 18 x z - 14 y - 19 y z + 16 z, 2 -18 x y + 5 x y - 7 y z + 19 z] > Problem := [F,G]; 2 2 2 2 3 2 Problem := [[14 x y z - 15 y z - 9, -19 x z - 14 x z + 12 y - 18 x , 2 3 2 3 3 2 8 x y z + 9 y z - 12 y z + 20], [-19 y z + 18 x y z - 15 z + 16 z , 2 2 3 2 18 x z - 14 y - 19 y z + 16 z, -18 x y + 5 x y - 7 y z + 19 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=44.8MB, alloc=56.3MB, time=1.30 memory used=88.0MB, alloc=60.3MB, time=2.31 memory used=130.1MB, alloc=92.3MB, time=3.35 memory used=197.0MB, alloc=92.3MB, time=4.61 memory used=257.5MB, alloc=92.3MB, time=5.46 memory used=289.1MB, alloc=92.3MB, time=5.63 memory used=329.6MB, alloc=92.3MB, time=5.81 memory used=356.1MB, alloc=92.3MB, time=5.95 memory used=386.1MB, alloc=92.3MB, time=6.10 memory used=421.1MB, alloc=92.3MB, time=6.24 memory used=462.5MB, alloc=92.3MB, time=6.39 memory used=510.7MB, alloc=92.3MB, time=6.93 memory used=544.4MB, alloc=92.3MB, time=7.10 memory used=582.2MB, alloc=92.3MB, time=7.27 memory used=608.9MB, alloc=92.3MB, time=7.40 memory used=640.3MB, alloc=92.3MB, time=7.56 memory used=676.4MB, alloc=92.3MB, time=7.72 memory used=718.0MB, alloc=92.3MB, time=7.87 memory used=776.4MB, alloc=92.3MB, time=14.13 memory used=812.0MB, alloc=92.3MB, time=14.31 memory used=841.6MB, alloc=92.3MB, time=14.45 memory used=878.3MB, alloc=92.3MB, time=14.62 memory used=915.4MB, alloc=92.3MB, time=14.76 memory used=940.2MB, alloc=92.3MB, time=14.88 memory used=967.1MB, alloc=92.3MB, time=14.99 memory used=997.2MB, alloc=92.3MB, time=15.11 memory used=1031.7MB, alloc=92.3MB, time=15.24 memory used=1075.8MB, alloc=92.3MB, time=15.59 memory used=1120.6MB, alloc=92.3MB, time=16.13 memory used=1171.6MB, alloc=92.3MB, time=17.26 memory used=1231.2MB, alloc=92.3MB, time=18.04 memory used=1308.2MB, alloc=92.3MB, time=19.21 memory used=1384.8MB, alloc=92.3MB, time=21.50 memory used=1461.4MB, alloc=92.5MB, time=25.26 memory used=1543.5MB, alloc=92.5MB, time=29.05 memory used=1606.9MB, alloc=92.5MB, time=30.57 memory used=1671.4MB, alloc=116.5MB, time=31.90 memory used=1729.0MB, alloc=116.5MB, time=32.49 memory used=1779.6MB, alloc=116.5MB, time=32.92 memory used=1838.1MB, alloc=116.5MB, time=33.68 memory used=1886.9MB, alloc=116.5MB, time=33.95 memory used=1920.0MB, alloc=116.5MB, time=34.16 memory used=1958.9MB, alloc=116.5MB, time=34.38 memory used=2005.7MB, alloc=116.5MB, time=34.61 memory used=2056.2MB, alloc=116.5MB, time=34.86 memory used=2086.9MB, alloc=116.5MB, time=35.03 memory used=2120.4MB, alloc=116.5MB, time=35.20 memory used=2171.7MB, alloc=116.5MB, time=35.77 memory used=2217.5MB, alloc=116.5MB, time=36.03 memory used=2254.7MB, alloc=116.5MB, time=36.26 memory used=2292.4MB, alloc=116.5MB, time=36.49 memory used=2337.4MB, alloc=116.5MB, time=36.73 memory used=2390.4MB, alloc=116.5MB, time=36.97 memory used=2423.2MB, alloc=116.5MB, time=37.14 memory used=2455.9MB, alloc=116.5MB, time=37.31 memory used=2514.8MB, alloc=116.5MB, time=44.25 memory used=2566.6MB, alloc=116.5MB, time=44.60 memory used=2605.2MB, alloc=116.5MB, time=44.83 memory used=2656.9MB, alloc=116.5MB, time=45.09 memory used=2688.8MB, alloc=116.5MB, time=45.27 memory used=2724.2MB, alloc=116.5MB, time=45.44 memory used=2763.5MB, alloc=116.5MB, time=45.64 memory used=2807.8MB, alloc=116.5MB, time=45.83 memory used=2858.0MB, alloc=116.5MB, time=46.04 memory used=2895.6MB, alloc=131.8MB, time=46.23 memory used=2906.4MB, alloc=131.8MB, time=46.36 memory used=2917.7MB, alloc=131.8MB, time=46.48 memory used=2929.8MB, alloc=131.8MB, time=46.60 memory used=2942.2MB, alloc=131.8MB, time=46.73 memory used=2997.6MB, alloc=131.8MB, time=47.28 memory used=3068.2MB, alloc=131.8MB, time=48.87 memory used=3110.0MB, alloc=131.8MB, time=49.09 memory used=3155.1MB, alloc=131.8MB, time=49.29 memory used=3188.7MB, alloc=131.8MB, time=49.45 memory used=3226.6MB, alloc=131.8MB, time=49.62 memory used=3307.3MB, alloc=131.8MB, time=52.08 memory used=3348.4MB, alloc=131.8MB, time=52.30 memory used=3387.1MB, alloc=131.8MB, time=52.51 memory used=3436.5MB, alloc=131.8MB, time=52.74 memory used=3469.2MB, alloc=131.8MB, time=52.94 memory used=3500.7MB, alloc=131.8MB, time=53.12 memory used=3536.0MB, alloc=131.8MB, time=53.29 memory used=3575.3MB, alloc=131.8MB, time=53.47 memory used=3617.9MB, alloc=131.8MB, time=53.65 memory used=3664.1MB, alloc=131.8MB, time=53.84 memory used=3714.2MB, alloc=131.8MB, time=54.04 memory used=3724.7MB, alloc=131.8MB, time=54.19 memory used=3735.6MB, alloc=131.8MB, time=54.35 memory used=3746.8MB, alloc=131.8MB, time=54.47 memory used=3758.8MB, alloc=131.8MB, time=54.60 memory used=3771.2MB, alloc=131.8MB, time=54.73 memory used=3867.1MB, alloc=387.8MB, time=56.05 memory used=3950.0MB, alloc=387.8MB, time=57.39 memory used=3992.4MB, alloc=387.8MB, time=57.86 memory used=4050.0MB, alloc=387.8MB, time=60.43 memory used=4088.1MB, alloc=387.8MB, time=60.68 memory used=4124.3MB, alloc=387.8MB, time=60.90 memory used=4159.1MB, alloc=387.8MB, time=61.11 memory used=4208.7MB, alloc=387.8MB, time=61.68 memory used=4294.3MB, alloc=411.8MB, time=63.53 memory used=4404.7MB, alloc=435.8MB, time=66.05 memory used=4533.0MB, alloc=459.8MB, time=69.10 memory used=4670.4MB, alloc=459.8MB, time=72.20 memory used=4778.0MB, alloc=459.8MB, time=74.57 memory used=4886.4MB, alloc=483.8MB, time=76.65 memory used=4989.5MB, alloc=483.8MB, time=77.53 memory used=5085.4MB, alloc=483.8MB, time=78.50 memory used=5195.5MB, alloc=483.8MB, time=79.85 memory used=5286.6MB, alloc=483.8MB, time=80.62 memory used=5363.2MB, alloc=483.8MB, time=81.12 memory used=5437.0MB, alloc=483.8MB, time=81.58 memory used=5536.5MB, alloc=483.8MB, time=82.42 memory used=5613.5MB, alloc=483.8MB, time=82.91 memory used=5688.3MB, alloc=483.8MB, time=83.37 memory used=5802.1MB, alloc=483.8MB, time=89.81 memory used=5878.4MB, alloc=483.8MB, time=90.29 memory used=5950.8MB, alloc=483.8MB, time=90.73 memory used=6018.5MB, alloc=483.8MB, time=91.13 memory used=6111.8MB, alloc=483.8MB, time=91.70 memory used=6233.7MB, alloc=483.8MB, time=94.24 memory used=6305.4MB, alloc=483.8MB, time=94.68 memory used=6401.3MB, alloc=483.8MB, time=96.13 memory used=6474.4MB, alloc=483.8MB, time=96.56 memory used=6563.1MB, alloc=483.8MB, time=97.21 memory used=6653.5MB, alloc=483.8MB, time=97.88 memory used=6766.1MB, alloc=483.8MB, time=111.80 memory used=6839.6MB, alloc=483.8MB, time=112.31 memory used=6926.5MB, alloc=483.8MB, time=112.81 memory used=6983.7MB, alloc=483.8MB, time=113.22 memory used=7050.0MB, alloc=483.8MB, time=113.65 memory used=7128.0MB, alloc=483.8MB, time=114.08 memory used=7269.3MB, alloc=483.8MB, time=114.89 memory used=7347.7MB, alloc=483.8MB, time=115.42 memory used=7445.2MB, alloc=483.8MB, time=116.34 memory used=7564.5MB, alloc=483.8MB, time=131.67 memory used=7640.3MB, alloc=483.8MB, time=132.19 memory used=7721.0MB, alloc=483.8MB, time=132.67 memory used=7788.1MB, alloc=483.8MB, time=133.12 memory used=7851.2MB, alloc=483.8MB, time=133.53 memory used=7925.3MB, alloc=483.8MB, time=133.94 memory used=8012.0MB, alloc=483.8MB, time=134.37 memory used=8161.3MB, alloc=483.8MB, time=135.77 memory used=8349.3MB, alloc=483.8MB, time=140.24 memory used=8501.6MB, alloc=483.8MB, time=147.64 memory used=8665.2MB, alloc=483.8MB, time=150.62 memory used=8846.0MB, alloc=507.8MB, time=158.44 memory used=8967.4MB, alloc=507.8MB, time=161.37 memory used=9157.3MB, alloc=507.8MB, time=165.69 memory used=9340.5MB, alloc=507.8MB, time=174.62 memory used=9428.4MB, alloc=507.8MB, time=175.13 memory used=9517.4MB, alloc=507.8MB, time=177.81 memory used=9622.6MB, alloc=507.8MB, time=182.44 memory used=9716.0MB, alloc=507.8MB, time=182.99 memory used=9788.6MB, alloc=507.8MB, time=183.45 memory used=9879.7MB, alloc=507.8MB, time=183.93 memory used=10033.2MB, alloc=507.8MB, time=186.52 memory used=10207.4MB, alloc=507.8MB, time=189.36 memory used=10370.9MB, alloc=507.8MB, time=196.53 memory used=10486.6MB, alloc=507.8MB, time=199.85 memory used=10561.0MB, alloc=507.8MB, time=201.74 memory used=10649.0MB, alloc=531.8MB, time=203.76 memory used=10719.5MB, alloc=531.8MB, time=205.98 memory used=10780.7MB, alloc=531.8MB, time=207.78 |\^/| 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(); 1428278332 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 2 F := [-15 x y - 11 y z - 20 y z + 17 y z, 9 x y - 2 x y - 18 x y - 11 y, 3 3 2 2 -9 x y + 14 y z + 5 x z - 8 y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 2 2 2 G := [7 y z + 19 z - y , -11 x - y z + 18 x z - 12, 2 4 -4 x y z - z + 9 x y z + 2 z] > Problem := [F,G]; 3 3 2 Problem := [[-15 x y - 11 y z - 20 y z + 17 y z, 3 2 2 3 3 2 2 9 x y - 2 x y - 18 x y - 11 y, -9 x y + 14 y z + 5 x z - 8 y ], [ 3 3 2 4 2 2 2 7 y z + 19 z - y , -11 x - y z + 18 x z - 12, 2 4 -4 x y z - z + 9 x y z + 2 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.7MB, alloc=32.3MB, time=0.86 memory used=44.9MB, alloc=60.3MB, time=1.38 memory used=80.5MB, alloc=60.3MB, time=2.24 memory used=125.2MB, alloc=68.3MB, time=3.33 memory used=161.9MB, alloc=68.3MB, time=3.83 memory used=195.6MB, alloc=68.3MB, time=4.17 memory used=226.2MB, alloc=69.1MB, time=4.52 memory used=248.0MB, alloc=69.1MB, time=4.63 memory used=269.4MB, alloc=69.1MB, time=4.75 memory used=294.8MB, alloc=69.1MB, time=4.86 memory used=325.0MB, alloc=69.1MB, time=5.37 memory used=351.1MB, alloc=69.1MB, time=5.50 memory used=370.5MB, alloc=69.1MB, time=5.61 memory used=393.1MB, alloc=69.1MB, time=5.72 memory used=417.1MB, alloc=69.1MB, time=5.82 memory used=440.0MB, alloc=69.1MB, time=6.10 memory used=488.8MB, alloc=69.1MB, time=7.15 memory used=534.4MB, alloc=69.1MB, time=8.16 memory used=575.8MB, alloc=93.1MB, time=9.23 memory used=643.7MB, alloc=93.1MB, time=10.67 memory used=707.4MB, alloc=349.1MB, time=12.08 memory used=765.6MB, alloc=349.1MB, time=13.24 memory used=821.9MB, alloc=349.1MB, time=14.32 memory used=892.4MB, alloc=373.1MB, time=15.69 memory used=984.1MB, alloc=373.1MB, time=17.62 memory used=1053.9MB, alloc=373.1MB, time=18.70 memory used=1112.6MB, alloc=373.1MB, time=19.44 memory used=1177.7MB, alloc=373.1MB, time=19.93 memory used=1219.7MB, alloc=373.1MB, time=20.15 memory used=1454.0MB, alloc=373.1MB, time=61.97 memory used=1610.2MB, alloc=373.1MB, time=64.02 memory used=1702.3MB, alloc=373.1MB, time=65.65 memory used=1788.3MB, alloc=373.1MB, time=68.30 memory used=1875.3MB, alloc=373.1MB, time=69.83 memory used=1961.7MB, alloc=397.1MB, time=72.19 memory used=2079.2MB, alloc=397.1MB, time=74.74 memory used=2176.0MB, alloc=421.1MB, time=78.28 memory used=2237.1MB, alloc=421.1MB, time=78.70 memory used=2301.2MB, alloc=421.1MB, time=79.09 memory used=2375.9MB, alloc=421.1MB, time=79.50 memory used=2446.7MB, alloc=421.1MB, time=79.87 memory used=2490.2MB, alloc=421.1MB, time=80.21 memory used=2537.9MB, alloc=421.1MB, time=80.52 memory used=2587.8MB, alloc=421.1MB, time=80.85 memory used=2639.8MB, alloc=421.1MB, time=81.19 memory used=2698.0MB, alloc=421.1MB, time=81.52 memory used=2758.3MB, alloc=421.1MB, time=81.85 memory used=2820.7MB, alloc=421.1MB, time=82.20 memory used=2889.7MB, alloc=421.1MB, time=82.57 memory used=2960.6MB, alloc=421.1MB, time=82.92 memory used=3033.5MB, alloc=421.1MB, time=83.27 memory used=3113.1MB, alloc=421.1MB, time=83.64 memory used=3188.1MB, alloc=445.1MB, time=84.02 memory used=3240.1MB, alloc=445.1MB, time=84.30 memory used=3291.6MB, alloc=445.1MB, time=84.60 memory used=3346.9MB, alloc=445.1MB, time=84.89 memory used=3402.6MB, alloc=445.1MB, time=85.18 memory used=3458.8MB, alloc=445.1MB, time=85.47 memory used=3520.8MB, alloc=445.1MB, time=85.77 memory used=3583.2MB, alloc=445.1MB, time=86.06 memory used=3645.7MB, alloc=445.1MB, time=86.36 memory used=3709.2MB, alloc=445.1MB, time=86.65 memory used=3777.0MB, alloc=445.1MB, time=86.96 memory used=3845.6MB, alloc=445.1MB, time=87.26 memory used=3919.6MB, alloc=445.1MB, time=87.58 memory used=3993.4MB, alloc=445.1MB, time=87.90 memory used=4072.4MB, alloc=445.1MB, time=88.22 memory used=4150.8MB, alloc=445.1MB, time=88.53 memory used=4233.8MB, alloc=445.1MB, time=88.86 memory used=4316.9MB, alloc=445.1MB, time=89.18 memory used=4403.0MB, alloc=445.1MB, time=89.51 memory used=4492.5MB, alloc=445.1MB, time=89.83 memory used=4588.7MB, alloc=445.1MB, time=90.16 memory used=4687.7MB, alloc=445.1MB, time=90.51 memory used=4792.0MB, alloc=445.1MB, time=90.85 memory used=4996.1MB, alloc=445.1MB, time=91.42 memory used=5130.3MB, alloc=445.1MB, time=91.86 memory used=5304.8MB, alloc=445.1MB, time=95.36 memory used=5378.5MB, alloc=445.1MB, time=95.80 memory used=5470.7MB, alloc=445.1MB, time=96.27 memory used=5561.8MB, alloc=445.1MB, time=96.71 memory used=5621.5MB, alloc=445.1MB, time=97.08 memory used=5687.4MB, alloc=445.1MB, time=97.46 memory used=5756.8MB, alloc=445.1MB, time=97.84 memory used=5830.0MB, alloc=445.1MB, time=98.21 memory used=5910.4MB, alloc=445.1MB, time=98.59 memory used=5994.8MB, alloc=445.1MB, time=98.98 memory used=6086.6MB, alloc=445.1MB, time=99.39 memory used=6186.8MB, alloc=445.1MB, time=99.79 memory used=6289.1MB, alloc=445.1MB, time=100.20 memory used=6346.4MB, alloc=445.1MB, time=100.49 memory used=6400.9MB, alloc=445.1MB, time=100.78 memory used=6456.2MB, alloc=445.1MB, time=101.07 memory used=6511.9MB, alloc=445.1MB, time=101.35 memory used=6568.1MB, alloc=445.1MB, time=101.65 memory used=6630.1MB, alloc=445.1MB, time=101.95 memory used=6692.4MB, alloc=445.1MB, time=102.25 memory used=6755.0MB, alloc=445.1MB, time=102.55 memory used=6818.4MB, alloc=445.1MB, time=102.85 memory used=6886.3MB, alloc=445.1MB, time=103.15 memory used=6954.8MB, alloc=445.1MB, time=103.46 memory used=7028.9MB, alloc=445.1MB, time=103.76 memory used=7102.6MB, alloc=445.1MB, time=104.07 memory used=7177.0MB, alloc=445.1MB, time=104.37 memory used=7254.5MB, alloc=445.1MB, time=104.69 memory used=7337.6MB, alloc=445.1MB, time=105.01 memory used=7420.4MB, alloc=445.1MB, time=105.35 memory used=7506.5MB, alloc=445.1MB, time=105.67 memory used=7596.1MB, alloc=445.1MB, time=106.00 memory used=7688.8MB, alloc=445.1MB, time=106.34 memory used=7787.1MB, alloc=445.1MB, time=106.68 memory used=7888.2MB, alloc=445.1MB, time=107.02 memory used=8105.4MB, alloc=445.1MB, time=107.61 memory used=8239.5MB, alloc=445.1MB, time=108.06 memory used=8408.1MB, alloc=445.1MB, time=203.46 |\^/| 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(); 1428278632 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 3 F := [-13 y z - 15 x - 16 y + 10 y z, 16 x - 4 x y - 5 y + z, 2 2 3 -12 x y z - 3 x y z + 3 x - 4 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 G := [-19 x y + 5 x + 13 z , 8 x y z - 9 x z - 4 x z + 18 y z, 2 2 17 x y z - 10 x y z - 11 x z + 16 x] > Problem := [F,G]; 2 2 2 4 2 3 Problem := [[-13 y z - 15 x - 16 y + 10 y z, 16 x - 4 x y - 5 y + z, 2 2 3 3 3 2 -12 x y z - 3 x y z + 3 x - 4 x], [-19 x y + 5 x + 13 z , 2 3 2 2 8 x y z - 9 x z - 4 x z + 18 y z, 17 x y z - 10 x y z - 11 x 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=0.31 memory used=26.1MB, alloc=32.3MB, time=0.87 memory used=47.8MB, alloc=60.3MB, time=1.36 memory used=91.6MB, alloc=60.3MB, time=2.28 memory used=119.6MB, alloc=60.3MB, time=2.40 memory used=155.1MB, alloc=60.9MB, time=2.62 memory used=186.9MB, alloc=60.9MB, time=3.61 memory used=223.2MB, alloc=61.6MB, time=3.89 memory used=246.7MB, alloc=61.6MB, time=3.98 memory used=288.2MB, alloc=61.6MB, time=4.51 memory used=328.9MB, alloc=61.6MB, time=5.21 memory used=351.9MB, alloc=61.6MB, time=5.30 memory used=393.1MB, alloc=61.6MB, time=6.14 memory used=428.6MB, alloc=61.6MB, time=6.95 memory used=471.9MB, alloc=61.6MB, time=7.60 memory used=510.3MB, alloc=62.4MB, time=9.68 memory used=532.4MB, alloc=62.4MB, time=9.80 memory used=554.9MB, alloc=62.4MB, time=9.91 memory used=571.9MB, alloc=62.4MB, time=10.00 memory used=591.8MB, alloc=62.4MB, time=10.10 memory used=615.1MB, alloc=62.4MB, time=10.20 memory used=639.5MB, alloc=62.4MB, time=10.30 memory used=656.1MB, alloc=62.4MB, time=10.39 memory used=671.4MB, alloc=62.4MB, time=10.46 memory used=687.8MB, alloc=62.4MB, time=10.54 memory used=705.8MB, alloc=62.4MB, time=10.62 memory used=725.4MB, alloc=62.4MB, time=10.71 memory used=759.2MB, alloc=62.4MB, time=11.06 memory used=808.8MB, alloc=70.4MB, time=12.64 memory used=849.5MB, alloc=94.4MB, time=13.54 memory used=895.7MB, alloc=94.4MB, time=14.26 memory used=942.4MB, alloc=94.4MB, time=15.01 memory used=1025.9MB, alloc=94.4MB, time=17.97 memory used=1067.7MB, alloc=94.4MB, time=18.71 memory used=1131.1MB, alloc=94.4MB, time=20.26 memory used=1192.9MB, alloc=118.4MB, time=21.70 memory used=1249.3MB, alloc=118.4MB, time=22.12 memory used=1308.3MB, alloc=118.4MB, time=23.38 memory used=1350.5MB, alloc=118.4MB, time=23.61 memory used=1409.0MB, alloc=118.4MB, time=24.28 memory used=1481.7MB, alloc=118.4MB, time=25.73 memory used=1538.7MB, alloc=374.4MB, time=27.16 memory used=1585.7MB, alloc=374.4MB, time=27.59 memory used=1680.3MB, alloc=398.4MB, time=29.35 memory used=1797.2MB, alloc=398.4MB, time=31.85 memory used=1904.9MB, alloc=422.4MB, time=33.84 memory used=1997.0MB, alloc=422.4MB, time=35.26 memory used=2080.2MB, alloc=422.4MB, time=36.05 memory used=2161.7MB, alloc=422.4MB, time=36.83 memory used=2278.4MB, alloc=422.4MB, time=39.10 memory used=2409.4MB, alloc=422.4MB, time=41.33 memory used=2521.9MB, alloc=446.4MB, time=43.96 memory used=2646.1MB, alloc=446.4MB, time=45.58 memory used=2711.5MB, alloc=446.4MB, time=46.05 memory used=2792.8MB, alloc=446.4MB, time=46.70 memory used=2865.1MB, alloc=446.4MB, time=48.80 memory used=2946.8MB, alloc=446.4MB, time=49.79 memory used=3015.8MB, alloc=446.4MB, time=50.20 memory used=3074.5MB, alloc=446.4MB, time=50.58 memory used=3170.5MB, alloc=446.4MB, time=51.58 memory used=3249.7MB, alloc=446.4MB, time=52.12 memory used=3340.6MB, alloc=446.4MB, time=56.86 memory used=3413.8MB, alloc=446.4MB, time=57.35 memory used=3484.2MB, alloc=446.4MB, time=57.78 memory used=3545.6MB, alloc=446.4MB, time=58.17 memory used=3602.9MB, alloc=446.4MB, time=58.53 memory used=3670.6MB, alloc=446.4MB, time=58.92 memory used=3755.9MB, alloc=446.4MB, time=59.80 memory used=3856.6MB, alloc=446.4MB, time=62.46 memory used=3923.2MB, alloc=446.4MB, time=62.89 memory used=3989.2MB, alloc=446.4MB, time=63.30 memory used=4049.0MB, alloc=446.4MB, time=63.67 memory used=4133.2MB, alloc=446.4MB, time=64.67 memory used=4212.4MB, alloc=446.4MB, time=65.26 memory used=4308.4MB, alloc=446.4MB, time=69.92 memory used=4373.5MB, alloc=446.4MB, time=70.36 memory used=4449.5MB, alloc=446.4MB, time=70.81 memory used=4501.5MB, alloc=446.4MB, time=71.17 memory used=4560.8MB, alloc=446.4MB, time=71.54 memory used=4634.0MB, alloc=446.4MB, time=71.92 memory used=4724.8MB, alloc=446.4MB, time=72.70 memory used=4791.0MB, alloc=446.4MB, time=73.14 memory used=4870.1MB, alloc=446.4MB, time=73.76 memory used=4936.3MB, alloc=446.4MB, time=74.23 memory used=5024.1MB, alloc=446.4MB, time=77.14 memory used=5090.4MB, alloc=446.4MB, time=77.59 memory used=5157.7MB, alloc=446.4MB, time=77.98 memory used=5214.7MB, alloc=446.4MB, time=78.34 memory used=5295.9MB, alloc=446.4MB, time=78.89 memory used=5392.0MB, alloc=446.4MB, time=80.58 memory used=5459.4MB, alloc=446.4MB, time=81.03 memory used=5519.6MB, alloc=446.4MB, time=81.42 memory used=5608.1MB, alloc=446.4MB, time=82.10 memory used=5696.1MB, alloc=446.4MB, time=83.65 memory used=5763.5MB, alloc=446.4MB, time=84.07 memory used=5873.3MB, alloc=446.4MB, time=85.48 memory used=6043.5MB, alloc=446.4MB, time=90.53 memory used=6180.5MB, alloc=446.4MB, time=95.14 memory used=6363.8MB, alloc=446.4MB, time=100.54 memory used=6519.0MB, alloc=470.4MB, time=103.61 memory used=6676.7MB, alloc=470.4MB, time=108.38 memory used=6796.9MB, alloc=470.4MB, time=113.25 memory used=6927.8MB, alloc=470.4MB, time=115.26 memory used=7069.3MB, alloc=470.4MB, time=122.04 memory used=7188.9MB, alloc=470.4MB, time=124.27 memory used=7330.2MB, alloc=470.4MB, time=126.23 memory used=7481.4MB, alloc=470.4MB, time=128.33 memory used=7635.7MB, alloc=470.4MB, time=133.38 memory used=7743.0MB, alloc=470.4MB, time=138.07 memory used=7819.8MB, alloc=470.4MB, time=139.91 memory used=7895.6MB, alloc=470.4MB, time=142.24 memory used=7960.7MB, alloc=470.4MB, time=143.94 memory used=8046.8MB, alloc=494.4MB, time=146.47 memory used=8162.5MB, alloc=494.4MB, time=148.54 memory used=8273.2MB, alloc=494.4MB, time=150.58 memory used=8335.0MB, alloc=494.4MB, time=152.12 memory used=8399.0MB, alloc=494.4MB, time=153.58 memory used=8498.8MB, alloc=494.4MB, time=155.25 memory used=8590.7MB, alloc=494.4MB, time=156.07 memory used=8699.3MB, alloc=494.4MB, time=157.32 memory used=8789.1MB, alloc=494.4MB, time=158.02 memory used=8859.1MB, alloc=494.4MB, time=158.64 memory used=8947.7MB, alloc=494.4MB, time=159.29 memory used=9033.8MB, alloc=494.4MB, time=159.92 memory used=9106.9MB, alloc=494.4MB, time=160.86 memory used=9208.4MB, alloc=494.4MB, time=161.66 memory used=9286.4MB, alloc=494.4MB, time=162.31 memory used=9366.2MB, alloc=494.4MB, time=162.94 memory used=9463.1MB, alloc=494.4MB, time=163.58 memory used=9529.3MB, alloc=494.4MB, time=164.14 memory used=9661.3MB, alloc=494.4MB, time=199.40 memory used=9754.4MB, alloc=518.4MB, time=200.15 memory used=9840.3MB, alloc=518.4MB, time=200.85 memory used=9951.1MB, alloc=518.4MB, time=201.56 memory used=10056.0MB, alloc=518.4MB, time=202.23 memory used=10130.9MB, alloc=518.4MB, time=202.80 memory used=10212.0MB, alloc=518.4MB, time=203.39 memory used=10302.2MB, alloc=518.4MB, time=203.99 memory used=10399.0MB, alloc=518.4MB, time=204.59 memory used=10505.0MB, alloc=518.4MB, time=205.21 memory used=10620.0MB, alloc=518.4MB, time=205.85 memory used=10743.7MB, alloc=518.4MB, time=206.50 memory used=10976.1MB, alloc=518.4MB, time=207.62 memory used=11114.1MB, alloc=518.4MB, time=208.33 memory used=11264.0MB, alloc=518.4MB, time=209.04 memory used=11425.4MB, alloc=518.4MB, time=209.77 memory used=11601.1MB, alloc=518.4MB, time=210.53 memory used=11791.9MB, alloc=518.4MB, time=211.31 memory used=12008.4MB, alloc=518.4MB, time=212.10 memory used=12210.9MB, alloc=518.4MB, time=213.34 |\^/| 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(); 1428278932 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 3 2 2 F := [-8 x y + 20 x y z - 15 x + 18 y, 11 x y - 3 y z + 4 x z + 9 y z, 2 2 2 2 -7 x y + x z + 19 x - 9 z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 G := [8 x z + 19 y + 3 x z + 5 z, 3 x y + 20 x z + 4 z + 18, 3 2 2 -19 x y - 4 y z - 8 x z + 9 y z] > Problem := [F,G]; 2 2 2 2 Problem := [[-8 x y + 20 x y z - 15 x + 18 y, 3 3 2 2 2 2 2 2 11 x y - 3 y z + 4 x z + 9 y z, -7 x y + x z + 19 x - 9 z], [ 2 3 3 2 2 8 x z + 19 y + 3 x z + 5 z, 3 x y + 20 x z + 4 z + 18, 3 2 2 -19 x y - 4 y z - 8 x z + 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=24.7MB, alloc=32.3MB, time=0.80 memory used=44.6MB, alloc=60.3MB, time=1.29 memory used=85.8MB, alloc=60.3MB, time=1.79 memory used=142.5MB, alloc=70.6MB, time=3.24 memory used=188.5MB, alloc=70.6MB, time=4.38 memory used=236.2MB, alloc=70.6MB, time=5.40 memory used=285.1MB, alloc=70.6MB, time=6.29 memory used=324.3MB, alloc=70.6MB, time=6.96 memory used=365.5MB, alloc=70.6MB, time=7.87 memory used=413.0MB, alloc=94.6MB, time=8.81 memory used=484.0MB, alloc=94.6MB, time=9.89 memory used=533.6MB, alloc=94.6MB, time=10.46 memory used=585.2MB, alloc=94.6MB, time=11.04 memory used=640.9MB, alloc=94.6MB, time=11.77 memory used=686.9MB, alloc=94.6MB, time=12.08 memory used=734.3MB, alloc=94.6MB, time=12.68 memory used=784.0MB, alloc=94.6MB, time=13.00 memory used=829.2MB, alloc=94.6MB, time=13.58 memory used=906.8MB, alloc=350.6MB, time=15.44 memory used=992.9MB, alloc=350.6MB, time=17.21 memory used=1068.1MB, alloc=350.6MB, time=18.93 memory used=1117.2MB, alloc=350.6MB, time=20.02 memory used=1149.3MB, alloc=350.6MB, time=20.21 memory used=1186.8MB, alloc=350.6MB, time=20.68 memory used=1251.3MB, alloc=350.6MB, time=21.68 memory used=1332.5MB, alloc=350.6MB, time=23.29 memory used=1395.3MB, alloc=374.6MB, time=24.82 memory used=1489.7MB, alloc=374.6MB, time=26.81 memory used=1578.2MB, alloc=374.6MB, time=28.74 memory used=1667.5MB, alloc=398.6MB, time=30.27 memory used=1754.5MB, alloc=398.6MB, time=31.35 memory used=1823.1MB, alloc=398.6MB, time=31.87 memory used=1896.9MB, alloc=398.6MB, time=32.40 memory used=1972.6MB, alloc=398.6MB, time=33.74 memory used=2024.7MB, alloc=398.6MB, time=34.04 memory used=2105.5MB, alloc=398.6MB, time=34.93 memory used=2170.4MB, alloc=398.6MB, time=35.43 memory used=2251.1MB, alloc=398.6MB, time=36.29 memory used=2319.3MB, alloc=398.6MB, time=36.78 memory used=2391.2MB, alloc=398.6MB, time=37.29 memory used=2467.2MB, alloc=398.6MB, time=38.59 memory used=2521.6MB, alloc=398.6MB, time=38.89 memory used=2591.6MB, alloc=398.6MB, time=39.35 memory used=2663.9MB, alloc=398.6MB, time=39.84 memory used=2737.7MB, alloc=398.6MB, time=41.15 memory used=2801.5MB, alloc=398.6MB, time=41.66 memory used=2921.9MB, alloc=398.6MB, time=43.72 memory used=3016.7MB, alloc=398.6MB, time=46.54 memory used=3070.3MB, alloc=398.6MB, time=46.85 memory used=3153.1MB, alloc=398.6MB, time=47.94 memory used=3274.9MB, alloc=422.6MB, time=50.56 memory used=3382.4MB, alloc=422.6MB, time=51.82 memory used=3496.2MB, alloc=422.6MB, time=53.25 memory used=3633.4MB, alloc=422.6MB, time=55.59 memory used=3737.8MB, alloc=422.6MB, time=57.93 memory used=3845.5MB, alloc=422.6MB, time=59.70 memory used=3922.4MB, alloc=422.6MB, time=60.55 memory used=3990.1MB, alloc=422.6MB, time=61.38 memory used=4087.5MB, alloc=422.6MB, time=62.99 memory used=4157.2MB, alloc=422.6MB, time=65.75 memory used=4218.3MB, alloc=422.6MB, time=66.16 memory used=4277.7MB, alloc=422.6MB, time=66.53 memory used=4333.7MB, alloc=422.6MB, time=67.02 memory used=4479.1MB, alloc=422.6MB, time=69.97 memory used=4637.3MB, alloc=422.6MB, time=72.62 memory used=4711.1MB, alloc=446.6MB, time=73.49 memory used=4822.0MB, alloc=446.6MB, time=77.42 memory used=4901.6MB, alloc=446.6MB, time=78.05 memory used=4976.4MB, alloc=446.6MB, time=78.50 memory used=5038.7MB, alloc=446.6MB, time=78.87 memory used=5098.5MB, alloc=446.6MB, time=79.22 memory used=5200.5MB, alloc=446.6MB, time=80.28 memory used=5338.9MB, alloc=446.6MB, time=82.65 memory used=5429.7MB, alloc=446.6MB, time=84.77 memory used=5530.8MB, alloc=470.6MB, time=87.35 memory used=5625.3MB, alloc=470.6MB, time=89.21 memory used=5720.2MB, alloc=470.6MB, time=90.23 memory used=5848.1MB, alloc=470.6MB, time=91.94 memory used=5945.1MB, alloc=470.6MB, time=92.99 memory used=6040.5MB, alloc=470.6MB, time=93.71 memory used=6131.1MB, alloc=470.6MB, time=94.97 memory used=6249.8MB, alloc=470.6MB, time=97.18 memory used=6361.0MB, alloc=470.6MB, time=102.68 memory used=6437.7MB, alloc=470.6MB, time=103.22 memory used=6518.1MB, alloc=470.6MB, time=103.78 memory used=6592.6MB, alloc=470.6MB, time=104.29 memory used=6657.1MB, alloc=470.6MB, time=104.74 memory used=6817.3MB, alloc=470.6MB, time=107.70 memory used=7008.0MB, alloc=470.6MB, time=110.71 memory used=7179.8MB, alloc=470.6MB, time=115.07 memory used=7305.4MB, alloc=470.6MB, time=117.87 memory used=7389.1MB, alloc=470.6MB, time=118.63 memory used=7504.1MB, alloc=470.6MB, time=121.31 memory used=7598.4MB, alloc=470.6MB, time=122.23 memory used=7671.9MB, alloc=470.6MB, time=122.75 memory used=7740.3MB, alloc=470.6MB, time=123.27 memory used=7846.0MB, alloc=470.6MB, time=129.95 memory used=7912.8MB, alloc=470.6MB, time=130.49 memory used=7997.3MB, alloc=470.6MB, time=131.03 memory used=8057.9MB, alloc=494.6MB, time=131.52 memory used=8137.1MB, alloc=494.6MB, time=132.00 memory used=8245.6MB, alloc=494.6MB, time=132.87 memory used=8356.4MB, alloc=494.6MB, time=134.83 memory used=8452.2MB, alloc=494.6MB, time=136.77 memory used=8527.0MB, alloc=494.6MB, time=138.66 memory used=8622.6MB, alloc=494.6MB, time=142.81 memory used=8709.2MB, alloc=494.6MB, time=143.48 memory used=8806.1MB, alloc=494.6MB, time=144.11 memory used=8881.1MB, alloc=494.6MB, time=144.66 memory used=8998.7MB, alloc=494.6MB, time=146.16 memory used=9125.2MB, alloc=494.6MB, time=148.21 memory used=9191.9MB, alloc=494.6MB, time=150.18 memory used=9296.9MB, alloc=494.6MB, time=151.96 memory used=9406.8MB, alloc=494.6MB, time=153.08 memory used=9486.8MB, alloc=494.6MB, time=153.72 memory used=9578.5MB, alloc=494.6MB, time=154.58 memory used=9661.0MB, alloc=494.6MB, time=155.29 memory used=9747.0MB, alloc=494.6MB, time=155.92 memory used=9846.3MB, alloc=494.6MB, time=157.80 memory used=9924.3MB, alloc=494.6MB, time=158.41 memory used=10012.9MB, alloc=494.6MB, time=159.02 memory used=10115.6MB, alloc=494.6MB, time=160.01 memory used=10204.0MB, alloc=494.6MB, time=160.68 memory used=10293.7MB, alloc=494.6MB, time=161.56 memory used=10376.0MB, alloc=494.6MB, time=162.20 memory used=10476.2MB, alloc=494.6MB, time=163.96 memory used=10569.0MB, alloc=494.6MB, time=164.67 memory used=10640.0MB, alloc=494.6MB, time=165.26 memory used=10742.3MB, alloc=494.6MB, time=165.94 memory used=10858.1MB, alloc=494.6MB, time=167.43 memory used=10939.3MB, alloc=494.6MB, time=168.10 memory used=11028.5MB, alloc=494.6MB, time=168.74 memory used=11119.5MB, alloc=494.6MB, time=169.63 memory used=11205.7MB, alloc=494.6MB, time=170.29 memory used=11302.5MB, alloc=494.6MB, time=172.01 memory used=11387.3MB, alloc=494.6MB, time=172.66 memory used=11462.1MB, alloc=494.6MB, time=173.22 memory used=11570.2MB, alloc=494.6MB, time=174.44 memory used=11672.4MB, alloc=494.6MB, time=176.27 memory used=11754.9MB, alloc=494.6MB, time=176.96 memory used=11843.0MB, alloc=494.6MB, time=177.63 memory used=11922.3MB, alloc=494.6MB, time=178.23 |\^/| 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(); 1428279232 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 2 4 F := [-y z + 20 y - 3 y z + 18 z , 19 x y - 6 x y - 14 y - 20 x, 3 3 2 2 -2 x y - 13 x - 7 x y + 3 x ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 2 2 G := [-8 x y z - 14 x - 13 x z - 7 y, -15 x y - 20 x z + 6 y - 15 y, 3 3 4 7 x y + 6 y z + 6 z + 19 x z] > Problem := [F,G]; 2 2 2 2 3 2 2 4 Problem := [[-y z + 20 y - 3 y z + 18 z , 19 x y - 6 x y - 14 y - 20 x, 3 3 2 2 2 3 2 -2 x y - 13 x - 7 x y + 3 x ], [-8 x y z - 14 x - 13 x z - 7 y, 3 2 2 2 3 3 4 -15 x y - 20 x z + 6 y - 15 y, 7 x y + 6 y z + 6 z + 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=4.6MB, alloc=32.3MB, time=0.31 memory used=25.2MB, alloc=36.3MB, time=0.87 memory used=44.8MB, alloc=60.3MB, time=1.38 memory used=79.7MB, alloc=60.3MB, time=2.17 memory used=124.5MB, alloc=68.3MB, time=3.20 memory used=167.9MB, alloc=68.3MB, time=4.10 memory used=211.8MB, alloc=68.3MB, time=5.16 memory used=257.4MB, alloc=92.3MB, time=6.23 memory used=331.4MB, alloc=92.3MB, time=7.79 memory used=395.5MB, alloc=92.3MB, time=9.04 memory used=432.1MB, alloc=92.3MB, time=9.28 memory used=496.1MB, alloc=92.3MB, time=10.47 memory used=560.7MB, alloc=116.3MB, time=12.04 memory used=633.3MB, alloc=372.3MB, time=13.53 memory used=729.0MB, alloc=372.3MB, time=15.60 memory used=821.1MB, alloc=396.3MB, time=17.63 memory used=939.0MB, alloc=396.3MB, time=20.17 memory used=1049.2MB, alloc=396.3MB, time=22.10 memory used=1127.4MB, alloc=396.3MB, time=23.05 memory used=1230.4MB, alloc=420.3MB, time=25.41 memory used=1357.7MB, alloc=420.3MB, time=28.00 memory used=1434.5MB, alloc=420.3MB, time=28.77 memory used=1497.8MB, alloc=420.3MB, time=29.38 memory used=1570.0MB, alloc=420.3MB, time=30.16 memory used=1634.5MB, alloc=420.3MB, time=30.68 memory used=1695.8MB, alloc=420.3MB, time=31.57 memory used=1759.6MB, alloc=420.3MB, time=32.22 memory used=1823.9MB, alloc=420.3MB, time=32.76 memory used=1889.9MB, alloc=420.3MB, time=33.28 memory used=1956.9MB, alloc=420.3MB, time=34.44 memory used=2009.5MB, alloc=420.3MB, time=34.80 memory used=2079.5MB, alloc=444.3MB, time=35.62 memory used=2157.3MB, alloc=444.3MB, time=36.17 memory used=2240.1MB, alloc=444.3MB, time=37.10 memory used=2349.8MB, alloc=444.3MB, time=38.78 memory used=2463.5MB, alloc=444.3MB, time=40.50 memory used=2543.1MB, alloc=444.3MB, time=41.24 memory used=2659.6MB, alloc=444.3MB, time=43.92 memory used=2786.3MB, alloc=444.3MB, time=45.88 memory used=2868.4MB, alloc=444.3MB, time=46.64 memory used=2960.2MB, alloc=444.3MB, time=47.45 memory used=3019.9MB, alloc=444.3MB, time=47.88 memory used=3099.9MB, alloc=444.3MB, time=48.37 memory used=3152.1MB, alloc=444.3MB, time=48.77 memory used=3231.2MB, alloc=444.3MB, time=50.69 memory used=3303.3MB, alloc=444.3MB, time=51.15 memory used=3358.7MB, alloc=444.3MB, time=51.55 memory used=3429.7MB, alloc=444.3MB, time=51.95 memory used=3516.5MB, alloc=444.3MB, time=52.52 memory used=3599.8MB, alloc=444.3MB, time=53.37 memory used=3660.5MB, alloc=444.3MB, time=53.83 memory used=3729.2MB, alloc=444.3MB, time=54.29 memory used=3808.4MB, alloc=444.3MB, time=54.77 memory used=3857.4MB, alloc=444.3MB, time=55.15 memory used=3912.9MB, alloc=444.3MB, time=55.53 memory used=3975.1MB, alloc=444.3MB, time=55.91 memory used=4061.1MB, alloc=444.3MB, time=57.93 memory used=4132.5MB, alloc=444.3MB, time=58.40 memory used=4189.5MB, alloc=444.3MB, time=58.80 memory used=4256.4MB, alloc=444.3MB, time=59.22 memory used=4347.8MB, alloc=444.3MB, time=60.16 memory used=4436.6MB, alloc=444.3MB, time=61.27 memory used=4499.1MB, alloc=444.3MB, time=61.69 memory used=4586.8MB, alloc=444.3MB, time=62.71 memory used=4650.1MB, alloc=444.3MB, time=63.19 memory used=4723.2MB, alloc=444.3MB, time=63.66 memory used=4787.4MB, alloc=444.3MB, time=64.08 memory used=4850.4MB, alloc=444.3MB, time=64.74 memory used=4928.1MB, alloc=444.3MB, time=65.30 memory used=4988.1MB, alloc=444.3MB, time=65.76 memory used=5069.4MB, alloc=444.3MB, time=66.25 memory used=5121.2MB, alloc=444.3MB, time=66.63 memory used=5198.8MB, alloc=444.3MB, time=68.78 memory used=5267.6MB, alloc=444.3MB, time=69.27 memory used=5331.6MB, alloc=444.3MB, time=69.69 memory used=5392.8MB, alloc=444.3MB, time=70.11 memory used=5469.3MB, alloc=444.3MB, time=70.53 memory used=5567.8MB, alloc=444.3MB, time=71.42 memory used=5630.8MB, alloc=444.3MB, time=71.89 memory used=5704.8MB, alloc=444.3MB, time=72.38 memory used=5769.8MB, alloc=444.3MB, time=72.82 memory used=5824.9MB, alloc=444.3MB, time=73.20 memory used=5907.5MB, alloc=444.3MB, time=74.02 memory used=5969.1MB, alloc=444.3MB, time=74.51 memory used=6044.3MB, alloc=444.3MB, time=74.98 memory used=6107.7MB, alloc=444.3MB, time=75.40 memory used=6163.5MB, alloc=444.3MB, time=75.78 memory used=6256.3MB, alloc=444.3MB, time=78.47 memory used=6330.5MB, alloc=444.3MB, time=78.98 memory used=6383.4MB, alloc=444.3MB, time=79.38 memory used=6448.7MB, alloc=444.3MB, time=79.80 memory used=6552.8MB, alloc=444.3MB, time=80.64 memory used=6626.7MB, alloc=444.3MB, time=81.17 memory used=6687.5MB, alloc=444.3MB, time=81.64 memory used=6768.5MB, alloc=444.3MB, time=82.13 memory used=6819.8MB, alloc=444.3MB, time=82.53 memory used=6892.6MB, alloc=444.3MB, time=83.31 memory used=6959.4MB, alloc=444.3MB, time=83.81 memory used=7026.1MB, alloc=444.3MB, time=84.30 memory used=7098.9MB, alloc=444.3MB, time=84.77 memory used=7151.3MB, alloc=444.3MB, time=85.16 memory used=7232.4MB, alloc=444.3MB, time=87.31 memory used=7307.6MB, alloc=444.3MB, time=87.79 memory used=7361.9MB, alloc=444.3MB, time=88.19 memory used=7427.0MB, alloc=444.3MB, time=88.63 memory used=7524.9MB, alloc=444.3MB, time=89.27 memory used=7599.7MB, alloc=444.3MB, time=90.50 memory used=7677.5MB, alloc=444.3MB, time=91.12 memory used=7748.3MB, alloc=444.3MB, time=91.57 memory used=7855.7MB, alloc=444.3MB, time=94.46 memory used=7929.4MB, alloc=444.3MB, time=94.95 memory used=7984.0MB, alloc=444.3MB, time=95.35 memory used=8048.5MB, alloc=444.3MB, time=95.76 memory used=8140.6MB, alloc=444.3MB, time=96.25 memory used=8256.7MB, alloc=444.3MB, time=99.18 memory used=8328.9MB, alloc=444.3MB, time=99.66 memory used=8383.6MB, alloc=444.3MB, time=100.05 memory used=8451.6MB, alloc=444.3MB, time=100.45 memory used=8598.1MB, alloc=444.3MB, time=102.35 memory used=8680.2MB, alloc=444.3MB, time=104.64 memory used=8801.6MB, alloc=444.3MB, time=106.51 memory used=8904.4MB, alloc=444.3MB, time=107.45 memory used=9006.1MB, alloc=468.3MB, time=108.87 memory used=9121.5MB, alloc=468.3MB, time=111.35 memory used=9220.9MB, alloc=468.3MB, time=113.35 memory used=9298.1MB, alloc=468.3MB, time=115.54 memory used=9372.6MB, alloc=468.3MB, time=117.68 memory used=9478.0MB, alloc=468.3MB, time=118.85 memory used=9566.0MB, alloc=468.3MB, time=119.66 memory used=9672.0MB, alloc=468.3MB, time=121.70 memory used=9757.3MB, alloc=468.3MB, time=122.51 memory used=9847.4MB, alloc=468.3MB, time=123.18 memory used=9934.4MB, alloc=468.3MB, time=123.97 memory used=10059.3MB, alloc=468.3MB, time=126.47 memory used=10133.1MB, alloc=468.3MB, time=127.07 memory used=10230.4MB, alloc=468.3MB, time=127.88 memory used=10321.2MB, alloc=468.3MB, time=128.66 memory used=10428.2MB, alloc=468.3MB, time=130.54 memory used=10503.0MB, alloc=468.3MB, time=131.12 memory used=10628.6MB, alloc=468.3MB, time=133.60 memory used=10711.6MB, alloc=468.3MB, time=134.23 memory used=10845.5MB, alloc=468.3MB, time=136.76 memory used=10926.4MB, alloc=468.3MB, time=137.46 memory used=10988.4MB, alloc=468.3MB, time=138.95 memory used=11066.8MB, alloc=468.3MB, time=141.09 memory used=11135.3MB, alloc=468.3MB, time=143.28 memory used=11217.6MB, alloc=468.3MB, time=144.94 memory used=11315.9MB, alloc=468.3MB, time=147.01 memory used=11420.2MB, alloc=492.3MB, time=151.55 memory used=11511.8MB, alloc=492.3MB, time=152.20 memory used=11605.3MB, alloc=492.3MB, time=152.91 memory used=11680.0MB, alloc=492.3MB, time=154.53 memory used=11746.6MB, alloc=492.3MB, time=156.00 memory used=11811.8MB, alloc=492.3MB, time=157.53 memory used=11867.3MB, alloc=492.3MB, time=159.34 memory used=11935.4MB, alloc=492.3MB, time=160.73 memory used=11982.4MB, alloc=492.3MB, time=161.90 memory used=12038.4MB, alloc=492.3MB, time=163.43 memory used=12231.7MB, alloc=516.3MB, time=168.54 memory used=12335.4MB, alloc=516.3MB, time=170.17 memory used=12453.3MB, alloc=516.3MB, time=172.09 memory used=12548.4MB, alloc=516.3MB, time=173.00 memory used=12638.0MB, alloc=516.3MB, time=173.84 memory used=12730.6MB, alloc=540.3MB, time=174.69 memory used=12818.7MB, alloc=540.3MB, time=175.47 memory used=12925.7MB, alloc=540.3MB, time=176.26 memory used=13058.5MB, alloc=540.3MB, time=179.09 memory used=13152.8MB, alloc=540.3MB, time=179.87 memory used=13298.3MB, alloc=540.3MB, time=181.09 memory used=13415.0MB, alloc=540.3MB, time=182.18 memory used=13579.8MB, alloc=540.3MB, time=185.18 memory used=13704.5MB, alloc=540.3MB, time=186.33 memory used=13812.2MB, alloc=540.3MB, time=187.17 memory used=13932.0MB, alloc=540.3MB, time=188.31 memory used=14075.4MB, alloc=540.3MB, time=202.94 |\^/| 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(); 1428279532 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 4 2 F := [-15 x z + 8 y z - z + 19 x y z, 17 y + 9 x z - 8 x y + y z, 3 2 2 -20 x y + 20 x y + 9 x y z + 16 y z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 G := [-12 x y - 10 x z - 15 x z - 9 z, -4 x y z + 5 x z + 11 y z + 5 z , 2 2 7 x y - 11 x y - 14 y z - 10 x] > Problem := [F,G]; 3 2 2 4 4 2 Problem := [[-15 x z + 8 y z - z + 19 x y z, 17 y + 9 x z - 8 x y + y z, 3 2 2 -20 x y + 20 x y + 9 x y z + 16 y z ], [ 3 2 2 2 2 2 2 -12 x y - 10 x z - 15 x z - 9 z, -4 x y z + 5 x z + 11 y z + 5 z , 2 2 7 x y - 11 x y - 14 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=4.5MB, alloc=32.3MB, time=0.32 memory used=25.9MB, alloc=32.3MB, time=0.88 memory used=45.2MB, alloc=56.3MB, time=1.41 memory used=86.2MB, alloc=60.3MB, time=2.45 memory used=127.1MB, alloc=60.3MB, time=3.51 memory used=165.7MB, alloc=84.3MB, time=4.57 memory used=229.8MB, alloc=92.3MB, time=6.21 memory used=296.3MB, alloc=92.3MB, time=7.72 memory used=357.7MB, alloc=116.3MB, time=9.40 memory used=418.0MB, alloc=372.3MB, time=10.87 memory used=500.5MB, alloc=396.3MB, time=13.03 memory used=614.6MB, alloc=420.3MB, time=15.68 memory used=733.4MB, alloc=420.3MB, time=18.73 memory used=867.7MB, alloc=444.3MB, time=22.06 memory used=986.1MB, alloc=468.3MB, time=24.95 memory used=1113.5MB, alloc=468.3MB, time=28.34 memory used=1223.4MB, alloc=468.3MB, time=31.26 memory used=1326.1MB, alloc=492.3MB, time=33.69 memory used=1423.5MB, alloc=492.3MB, time=36.45 memory used=1531.0MB, alloc=492.3MB, time=39.58 memory used=1640.6MB, alloc=492.3MB, time=41.87 memory used=1759.9MB, alloc=492.3MB, time=43.94 memory used=1846.1MB, alloc=492.3MB, time=46.01 memory used=1937.5MB, alloc=516.3MB, time=48.04 memory used=2029.1MB, alloc=516.3MB, time=50.44 memory used=2107.4MB, alloc=516.3MB, time=52.83 memory used=2186.7MB, alloc=516.3MB, time=55.34 memory used=2268.6MB, alloc=516.3MB, time=58.04 memory used=2335.8MB, alloc=516.3MB, time=60.45 memory used=2392.0MB, alloc=516.3MB, time=62.25 memory used=2451.7MB, alloc=516.3MB, time=64.23 memory used=2522.8MB, alloc=516.3MB, time=66.86 memory used=2588.6MB, alloc=516.3MB, time=68.66 memory used=2667.0MB, alloc=516.3MB, time=69.95 memory used=2734.3MB, alloc=516.3MB, time=71.19 memory used=2815.3MB, alloc=516.3MB, time=72.72 memory used=2899.3MB, alloc=516.3MB, time=73.82 memory used=2986.9MB, alloc=516.3MB, time=75.74 memory used=3038.6MB, alloc=516.3MB, time=77.49 memory used=3081.7MB, alloc=516.3MB, time=78.96 memory used=3129.5MB, alloc=516.3MB, time=81.05 memory used=3330.6MB, alloc=540.3MB, time=85.58 memory used=3540.0MB, alloc=564.3MB, time=92.37 memory used=3760.6MB, alloc=588.3MB, time=97.25 memory used=3957.2MB, alloc=612.3MB, time=102.79 memory used=4135.6MB, alloc=612.3MB, time=108.74 memory used=4291.0MB, alloc=612.3MB, time=113.86 memory used=4426.6MB, alloc=636.3MB, time=118.53 memory used=4576.1MB, alloc=636.3MB, time=123.77 memory used=4706.8MB, alloc=636.3MB, time=128.47 memory used=4856.0MB, alloc=636.3MB, time=134.36 memory used=4989.4MB, alloc=660.3MB, time=138.62 memory used=5108.7MB, alloc=660.3MB, time=142.10 memory used=5219.7MB, alloc=660.3MB, time=146.64 memory used=5348.8MB, alloc=660.3MB, time=150.03 memory used=5472.4MB, alloc=660.3MB, time=154.84 memory used=5567.9MB, alloc=660.3MB, time=158.07 memory used=5665.6MB, alloc=660.3MB, 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(); 1428279832 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 2 2 F := [16 x z - 15 y z + 2 x y - 18 y , y z + 6 x z + 18 y - 12, 2 2 2 -9 x y z - 20 x z - 4 z + 7 z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 2 2 2 G := [-18 x z + 20 x y z - 18 y z + 5, -12 x - 20 y z + 8 y z - 19 x y , 2 2 2 3 2 -16 x y z + 17 y z - 12 y + 2 y z] > Problem := [F,G]; 3 2 2 2 3 2 2 2 Problem := [[16 x z - 15 y z + 2 x y - 18 y , y z + 6 x z + 18 y - 12, 2 2 2 3 2 -9 x y z - 20 x z - 4 z + 7 z], [-18 x z + 20 x y z - 18 y z + 5, 4 3 2 2 2 -12 x - 20 y z + 8 y z - 19 x y , 2 2 2 3 2 -16 x y z + 17 y z - 12 y + 2 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.32 memory used=25.2MB, alloc=32.3MB, time=0.88 memory used=43.8MB, alloc=56.3MB, time=1.38 memory used=82.6MB, alloc=60.3MB, time=2.33 memory used=126.3MB, alloc=68.3MB, time=3.35 memory used=169.3MB, alloc=68.3MB, time=4.41 memory used=210.3MB, alloc=92.3MB, time=5.14 memory used=253.6MB, alloc=92.3MB, time=5.45 memory used=307.0MB, alloc=92.3MB, time=6.12 memory used=388.4MB, alloc=92.3MB, time=7.67 memory used=454.2MB, alloc=92.3MB, time=9.04 memory used=516.1MB, alloc=92.3MB, time=10.06 memory used=554.1MB, alloc=92.3MB, time=10.35 memory used=586.5MB, alloc=92.3MB, time=10.61 memory used=639.6MB, alloc=92.3MB, time=11.61 memory used=668.0MB, alloc=92.3MB, time=11.79 memory used=698.2MB, alloc=92.3MB, time=11.95 memory used=733.3MB, alloc=92.3MB, time=12.12 memory used=755.1MB, alloc=92.3MB, time=12.26 memory used=779.9MB, alloc=92.3MB, time=12.39 memory used=809.5MB, alloc=92.3MB, time=12.53 memory used=889.4MB, alloc=92.3MB, time=13.99 memory used=924.5MB, alloc=92.3MB, time=14.29 memory used=962.8MB, alloc=92.3MB, time=14.70 memory used=990.1MB, alloc=116.3MB, time=14.90 memory used=1035.7MB, alloc=116.3MB, time=15.12 memory used=1085.1MB, alloc=116.3MB, time=15.51 memory used=1130.6MB, alloc=116.3MB, time=15.77 memory used=1174.2MB, alloc=116.3MB, time=15.98 memory used=1231.4MB, alloc=116.3MB, time=16.57 memory used=1277.2MB, alloc=116.3MB, time=16.80 memory used=1317.8MB, alloc=116.3MB, time=16.99 memory used=1406.7MB, alloc=116.3MB, time=18.67 memory used=1469.2MB, alloc=372.3MB, time=20.36 memory used=1555.4MB, alloc=396.3MB, time=22.54 memory used=1666.1MB, alloc=420.3MB, time=25.06 memory used=1769.3MB, alloc=420.3MB, time=27.34 memory used=1882.3MB, alloc=444.3MB, time=30.05 memory used=1978.2MB, alloc=444.3MB, time=32.48 memory used=2076.8MB, alloc=444.3MB, time=34.90 memory used=2165.7MB, alloc=444.3MB, time=37.23 memory used=2286.6MB, alloc=468.3MB, time=38.96 memory used=2397.4MB, alloc=468.3MB, time=40.23 memory used=2511.1MB, alloc=468.3MB, time=41.54 memory used=2611.2MB, alloc=468.3MB, time=42.94 memory used=2711.6MB, alloc=468.3MB, time=43.72 memory used=2812.0MB, alloc=468.3MB, time=44.58 memory used=2890.9MB, alloc=468.3MB, time=45.14 memory used=3000.5MB, alloc=468.3MB, time=49.72 memory used=3082.4MB, alloc=468.3MB, time=50.25 memory used=3222.5MB, alloc=468.3MB, time=52.57 memory used=3323.0MB, alloc=468.3MB, time=54.82 memory used=3427.8MB, alloc=468.3MB, time=57.25 memory used=3553.0MB, alloc=468.3MB, time=62.34 memory used=3641.3MB, alloc=468.3MB, time=63.60 memory used=3717.3MB, alloc=468.3MB, time=64.11 memory used=3797.0MB, alloc=468.3MB, time=65.06 memory used=3915.0MB, alloc=468.3MB, time=67.37 memory used=4022.0MB, alloc=468.3MB, time=69.46 memory used=4114.3MB, alloc=468.3MB, time=70.32 memory used=4210.0MB, alloc=468.3MB, time=72.26 memory used=4282.4MB, alloc=468.3MB, time=74.09 memory used=4362.9MB, alloc=492.3MB, time=75.95 memory used=4446.4MB, alloc=492.3MB, time=78.01 memory used=4505.7MB, alloc=492.3MB, time=79.77 memory used=4557.4MB, alloc=492.3MB, time=81.21 memory used=4618.2MB, alloc=492.3MB, time=82.96 memory used=4667.7MB, alloc=492.3MB, time=84.63 memory used=4719.4MB, alloc=492.3MB, time=86.26 memory used=4765.0MB, alloc=492.3MB, time=87.59 memory used=4830.6MB, alloc=492.3MB, time=89.17 memory used=4876.6MB, alloc=492.3MB, time=90.79 memory used=5057.4MB, alloc=516.3MB, time=94.34 memory used=5174.9MB, alloc=516.3MB, time=95.66 memory used=5278.6MB, alloc=516.3MB, time=96.62 memory used=5392.3MB, alloc=516.3MB, time=97.80 memory used=5502.9MB, alloc=516.3MB, time=98.81 memory used=5608.1MB, alloc=516.3MB, time=99.80 memory used=5705.4MB, alloc=516.3MB, time=100.68 memory used=5818.3MB, alloc=516.3MB, time=101.91 memory used=5951.2MB, alloc=516.3MB, time=105.23 memory used=6047.2MB, alloc=516.3MB, time=106.08 memory used=6142.7MB, alloc=516.3MB, time=106.90 memory used=6227.2MB, alloc=516.3MB, time=107.64 memory used=6332.4MB, alloc=516.3MB, time=108.39 memory used=6474.5MB, alloc=516.3MB, time=109.80 memory used=6625.8MB, alloc=516.3MB, time=118.73 memory used=6719.3MB, alloc=516.3MB, time=119.59 memory used=6826.3MB, alloc=516.3MB, time=120.42 memory used=6899.9MB, alloc=516.3MB, time=121.16 memory used=6987.5MB, alloc=516.3MB, time=121.89 memory used=7090.2MB, alloc=516.3MB, time=122.66 memory used=7338.3MB, alloc=516.3MB, time=123.90 memory used=7480.7MB, alloc=516.3MB, time=126.71 memory used=7589.4MB, alloc=516.3MB, time=127.63 memory used=7675.4MB, alloc=540.3MB, time=128.49 memory used=7767.4MB, alloc=540.3MB, time=129.37 memory used=7873.7MB, alloc=540.3MB, time=130.27 memory used=7995.8MB, alloc=540.3MB, time=131.20 memory used=8133.6MB, alloc=540.3MB, time=132.13 memory used=8244.0MB, alloc=540.3MB, time=132.96 memory used=8321.6MB, alloc=540.3MB, time=133.72 memory used=8405.3MB, alloc=540.3MB, time=134.47 memory used=8493.7MB, alloc=540.3MB, time=135.22 memory used=8586.4MB, alloc=540.3MB, time=135.97 memory used=8687.1MB, alloc=540.3MB, time=136.71 memory used=8794.7MB, alloc=540.3MB, time=137.50 memory used=8907.7MB, alloc=540.3MB, time=138.28 memory used=9028.7MB, alloc=540.3MB, time=139.08 memory used=9159.5MB, alloc=540.3MB, time=139.87 memory used=9363.3MB, alloc=540.3MB, time=142.53 memory used=9490.9MB, alloc=540.3MB, time=143.60 memory used=9620.3MB, alloc=540.3MB, time=144.61 memory used=9705.9MB, alloc=540.3MB, time=145.47 memory used=9807.1MB, alloc=540.3MB, time=146.36 memory used=9921.3MB, alloc=540.3MB, time=147.24 memory used=10051.4MB, alloc=540.3MB, time=148.13 memory used=10192.1MB, alloc=540.3MB, time=149.04 memory used=10272.4MB, alloc=540.3MB, time=149.80 memory used=10353.2MB, alloc=540.3MB, time=150.58 memory used=10437.6MB, alloc=540.3MB, time=151.33 memory used=10529.9MB, alloc=540.3MB, time=152.08 memory used=10626.7MB, alloc=540.3MB, time=152.84 memory used=10730.9MB, alloc=540.3MB, time=153.62 memory used=10841.4MB, alloc=540.3MB, time=154.40 memory used=10960.3MB, alloc=540.3MB, time=155.16 memory used=11088.3MB, alloc=540.3MB, time=155.98 memory used=11226.8MB, alloc=540.3MB, time=156.77 memory used=11456.6MB, alloc=540.3MB, time=221.90 |\^/| 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(); 1428280132 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 4 3 2 F := [-10 x z + 4 z + 4 x y - 13 y z , -9 y - 2 x + 8 x y - x z, 2 2 3 2 2 3 x y - 19 x z - 14 y z - 16 y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 G := [4 x y + 17 x y z + 17 x z + 10 z, -18 x - 6 x y - 13 x z + 10 x, 2 3 4 2 10 x y z - 17 y z + 4 z + 2 x y] > Problem := [F,G]; 2 2 4 2 2 4 3 2 Problem := [[-10 x z + 4 z + 4 x y - 13 y z , -9 y - 2 x + 8 x y - x z, 2 2 3 2 2 2 2 3 x y - 19 x z - 14 y z - 16 y], [4 x y + 17 x y z + 17 x z + 10 z, 4 2 3 4 2 -18 x - 6 x y - 13 x z + 10 x, 10 x y z - 17 y z + 4 z + 2 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.4MB, alloc=32.3MB, time=0.79 memory used=47.0MB, alloc=36.3MB, time=1.16 memory used=63.3MB, alloc=36.3MB, time=1.31 memory used=84.7MB, alloc=36.3MB, time=1.65 memory used=96.7MB, alloc=36.3MB, time=1.71 memory used=118.6MB, alloc=36.3MB, time=2.02 memory used=145.3MB, alloc=36.3MB, time=2.43 memory used=166.0MB, alloc=60.3MB, time=2.94 memory used=205.4MB, alloc=60.3MB, time=3.83 memory used=239.2MB, alloc=61.2MB, time=4.03 memory used=263.7MB, alloc=61.2MB, time=4.13 memory used=289.9MB, alloc=61.2MB, time=4.23 memory used=321.3MB, alloc=61.2MB, time=4.33 memory used=340.5MB, alloc=61.2MB, time=4.40 memory used=362.4MB, alloc=61.2MB, time=4.48 memory used=415.7MB, alloc=61.2MB, time=5.17 memory used=464.7MB, alloc=61.2MB, time=5.97 memory used=510.4MB, alloc=62.3MB, time=8.09 memory used=536.6MB, alloc=62.3MB, time=8.21 memory used=556.3MB, alloc=62.3MB, time=8.32 memory used=580.3MB, alloc=62.3MB, time=8.43 memory used=608.0MB, alloc=62.3MB, time=8.56 memory used=633.9MB, alloc=62.3MB, time=8.67 memory used=650.2MB, alloc=62.3MB, time=8.75 memory used=667.5MB, alloc=62.3MB, time=8.84 memory used=686.6MB, alloc=62.3MB, time=8.93 memory used=707.3MB, alloc=62.3MB, time=9.02 memory used=728.7MB, alloc=62.3MB, time=9.11 memory used=752.3MB, alloc=62.3MB, time=9.21 memory used=776.6MB, alloc=62.3MB, time=9.30 memory used=802.8MB, alloc=62.3MB, time=9.41 memory used=830.3MB, alloc=62.3MB, time=9.51 memory used=859.8MB, alloc=62.3MB, time=9.61 memory used=890.9MB, alloc=83.8MB, time=9.76 memory used=903.6MB, alloc=83.8MB, time=9.85 memory used=916.3MB, alloc=83.8MB, time=9.93 memory used=929.5MB, alloc=83.8MB, time=10.01 memory used=943.3MB, alloc=83.8MB, time=10.09 memory used=957.0MB, alloc=83.8MB, time=10.17 memory used=971.8MB, alloc=83.8MB, time=10.25 memory used=987.3MB, alloc=83.8MB, time=10.34 memory used=1003.9MB, alloc=83.8MB, time=10.43 memory used=1044.8MB, alloc=83.8MB, time=10.78 memory used=1067.3MB, alloc=83.8MB, time=10.90 memory used=1092.9MB, alloc=83.8MB, time=11.02 memory used=1112.2MB, alloc=83.8MB, time=11.11 memory used=1151.2MB, alloc=83.8MB, time=11.60 memory used=1174.5MB, alloc=83.8MB, time=11.73 memory used=1199.7MB, alloc=83.8MB, time=11.84 memory used=1221.2MB, alloc=83.8MB, time=11.95 memory used=1260.0MB, alloc=83.8MB, time=12.44 memory used=1311.6MB, alloc=83.8MB, time=13.33 memory used=1355.0MB, alloc=83.8MB, time=14.23 memory used=1398.4MB, alloc=107.8MB, time=15.09 memory used=1478.0MB, alloc=107.8MB, time=16.36 memory used=1543.0MB, alloc=363.8MB, time=17.49 memory used=1618.2MB, alloc=387.8MB, time=18.75 memory used=1681.1MB, alloc=387.8MB, time=19.35 memory used=1735.1MB, alloc=387.8MB, time=19.86 memory used=1783.1MB, alloc=387.8MB, time=20.13 memory used=1837.8MB, alloc=387.8MB, time=20.76 memory used=1897.6MB, alloc=387.8MB, time=21.60 memory used=1950.3MB, alloc=387.8MB, time=22.13 memory used=1992.5MB, alloc=387.8MB, time=22.33 memory used=2031.7MB, alloc=387.8MB, time=22.53 memory used=2102.9MB, alloc=387.8MB, time=24.22 memory used=2147.0MB, alloc=387.8MB, time=24.50 memory used=2181.1MB, alloc=387.8MB, time=24.75 memory used=2219.5MB, alloc=387.8MB, time=25.00 memory used=2264.2MB, alloc=387.8MB, time=25.26 memory used=2312.5MB, alloc=387.8MB, time=25.53 memory used=2367.2MB, alloc=387.8MB, time=25.81 memory used=2397.5MB, alloc=411.8MB, time=26.04 memory used=2438.8MB, alloc=411.8MB, time=26.30 memory used=2481.4MB, alloc=411.8MB, time=26.56 memory used=2527.7MB, alloc=411.8MB, time=26.80 memory used=2576.1MB, alloc=411.8MB, time=27.06 memory used=2629.7MB, alloc=411.8MB, time=27.34 memory used=2684.6MB, alloc=411.8MB, time=27.60 memory used=2741.5MB, alloc=411.8MB, time=27.87 memory used=2801.9MB, alloc=411.8MB, time=28.16 memory used=2868.3MB, alloc=411.8MB, time=28.44 memory used=2936.1MB, alloc=411.8MB, time=28.70 memory used=3007.4MB, alloc=411.8MB, time=28.98 memory used=3072.1MB, alloc=411.8MB, time=29.26 memory used=3108.7MB, alloc=411.8MB, time=29.44 memory used=3146.3MB, alloc=411.8MB, time=29.63 memory used=3185.1MB, alloc=411.8MB, time=29.82 memory used=3224.5MB, alloc=411.8MB, time=30.01 memory used=3266.0MB, alloc=411.8MB, time=30.23 memory used=3307.9MB, alloc=411.8MB, time=30.43 memory used=3353.2MB, alloc=411.8MB, time=30.63 memory used=3397.8MB, alloc=411.8MB, time=30.83 memory used=3445.3MB, alloc=411.8MB, time=31.03 memory used=3495.3MB, alloc=411.8MB, time=31.23 memory used=3547.4MB, alloc=411.8MB, time=31.43 memory used=3600.8MB, alloc=411.8MB, time=31.63 memory used=3656.0MB, alloc=411.8MB, time=31.84 memory used=3714.6MB, alloc=411.8MB, time=32.03 memory used=3794.6MB, alloc=411.8MB, time=33.80 memory used=3867.1MB, alloc=411.8MB, time=34.18 memory used=3919.1MB, alloc=411.8MB, time=34.50 memory used=3981.0MB, alloc=411.8MB, time=34.82 memory used=4053.4MB, alloc=411.8MB, time=35.15 memory used=4113.7MB, alloc=411.8MB, time=35.44 memory used=4156.3MB, alloc=411.8MB, time=35.69 memory used=4201.8MB, alloc=411.8MB, time=35.94 memory used=4248.8MB, alloc=411.8MB, time=36.19 memory used=4297.2MB, alloc=411.8MB, time=36.45 memory used=4350.9MB, alloc=411.8MB, time=36.69 memory used=4405.9MB, alloc=411.8MB, time=36.95 memory used=4466.1MB, alloc=411.8MB, time=37.21 memory used=4527.5MB, alloc=411.8MB, time=37.49 memory used=4594.0MB, alloc=411.8MB, time=37.77 memory used=4662.2MB, alloc=411.8MB, time=38.04 memory used=4734.2MB, alloc=411.8MB, time=38.33 memory used=4796.0MB, alloc=411.8MB, time=38.58 memory used=4833.0MB, alloc=411.8MB, time=38.77 memory used=4871.7MB, alloc=411.8MB, time=38.96 memory used=4910.5MB, alloc=411.8MB, time=39.15 memory used=4950.0MB, alloc=411.8MB, time=39.34 memory used=4991.3MB, alloc=411.8MB, time=39.53 memory used=5034.0MB, alloc=411.8MB, time=39.72 memory used=5078.4MB, alloc=411.8MB, time=39.91 memory used=5123.8MB, alloc=411.8MB, time=40.11 memory used=5171.2MB, alloc=411.8MB, time=40.31 memory used=5220.2MB, alloc=411.8MB, time=40.50 memory used=5272.1MB, alloc=411.8MB, time=40.70 memory used=5325.4MB, alloc=411.8MB, time=40.90 memory used=5380.8MB, alloc=411.8MB, time=41.11 memory used=5439.8MB, alloc=411.8MB, time=41.30 memory used=5528.3MB, alloc=411.8MB, time=67.62 memory used=5614.8MB, alloc=411.8MB, time=139.99 memory used=5676.7MB, alloc=411.8MB, time=209.50 |\^/| 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(); 1428280432 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 2 4 3 2 F := [10 x y + 8 x z + 8 z + 6 x y , -18 x - 2 y z + 19 x y - 13 x z, 2 2 3 3 3 -12 x z - 7 x z + 14 x - 16 y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 4 2 2 2 3 G := [-15 x z + 5 y z + 17 x - 7 x y, 2 x - 13 x z - 5 x z - 12 y , 4 2 2 -19 z - 20 x y - 10 x z - 4] > Problem := [F,G]; 3 2 2 4 2 Problem := [[10 x y + 8 x z + 8 z + 6 x y , 4 3 2 2 2 3 3 3 -18 x - 2 y z + 19 x y - 13 x z, -12 x z - 7 x z + 14 x - 16 y ], [ 3 3 3 4 2 2 2 3 -15 x z + 5 y z + 17 x - 7 x y, 2 x - 13 x z - 5 x z - 12 y , 4 2 2 -19 z - 20 x y - 10 x z - 4]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.32 memory used=48.7MB, alloc=38.3MB, time=1.52 memory used=106.5MB, alloc=38.3MB, time=2.53 memory used=147.1MB, alloc=38.3MB, time=5.13 memory used=165.6MB, alloc=62.3MB, time=6.56 memory used=205.8MB, alloc=62.3MB, time=8.20 memory used=235.8MB, alloc=62.3MB, time=8.32 memory used=269.0MB, alloc=62.3MB, time=8.44 memory used=304.6MB, alloc=62.3MB, time=8.57 memory used=341.9MB, alloc=62.3MB, time=8.69 memory used=368.6MB, alloc=62.3MB, time=8.79 memory used=392.7MB, alloc=62.3MB, time=8.89 memory used=415.4MB, alloc=62.3MB, time=8.99 memory used=437.8MB, alloc=62.3MB, time=9.08 memory used=461.2MB, alloc=62.3MB, time=9.17 memory used=484.8MB, alloc=62.3MB, time=9.26 memory used=509.6MB, alloc=62.3MB, time=9.36 memory used=535.4MB, alloc=62.3MB, time=9.45 memory used=562.2MB, alloc=62.3MB, time=9.55 memory used=590.0MB, alloc=62.3MB, time=9.64 memory used=618.7MB, alloc=62.3MB, time=9.74 memory used=648.2MB, alloc=62.3MB, time=9.85 memory used=678.5MB, alloc=62.3MB, time=9.95 memory used=710.2MB, alloc=62.3MB, time=10.05 memory used=743.1MB, alloc=62.3MB, time=10.15 memory used=777.2MB, alloc=62.3MB, time=10.26 memory used=813.0MB, alloc=62.3MB, time=10.37 memory used=850.7MB, alloc=62.3MB, time=10.48 memory used=889.5MB, alloc=62.3MB, time=10.60 memory used=913.3MB, alloc=62.3MB, time=10.67 memory used=933.7MB, alloc=62.3MB, time=10.74 memory used=954.7MB, alloc=62.3MB, time=10.82 memory used=976.4MB, alloc=62.3MB, time=10.89 memory used=998.7MB, alloc=62.3MB, time=10.96 memory used=1116.7MB, alloc=62.3MB, time=13.30 memory used=1161.1MB, alloc=62.3MB, time=14.37 memory used=1276.9MB, alloc=62.3MB, time=16.93 memory used=1305.7MB, alloc=86.3MB, time=110.18 |\^/| 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(); 1428280732 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 2 2 F := [-20 x + x y + 19 x y z + 15 z, 11 x z + 8 y z - 15 x - 7 x z, 3 2 2 8 x z + 19 x y z + 14 z + 10] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 3 2 G := [16 x z - 4 x y + 6 y - 19 x , 2 y z + 12 x + x y + 5 y, 3 2 12 x z - 20 x y - 20 x + 11 y] > Problem := [F,G]; 4 2 2 2 Problem := [[-20 x + x y + 19 x y z + 15 z, 2 2 2 2 3 2 2 11 x z + 8 y z - 15 x - 7 x z, 8 x z + 19 x y z + 14 z + 10], [ 3 2 3 2 3 3 2 16 x z - 4 x y + 6 y - 19 x , 2 y z + 12 x + x y + 5 y, 3 2 12 x z - 20 x y - 20 x + 11 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=24.8MB, alloc=36.3MB, time=0.81 memory used=47.6MB, alloc=36.3MB, time=1.10 memory used=62.2MB, alloc=36.3MB, time=1.26 memory used=76.1MB, alloc=36.3MB, time=1.38 memory used=94.3MB, alloc=36.3MB, time=1.58 memory used=109.0MB, alloc=36.3MB, time=1.73 memory used=122.6MB, alloc=36.3MB, time=1.85 memory used=143.5MB, alloc=36.3MB, time=2.74 memory used=155.6MB, alloc=36.3MB, time=2.81 memory used=166.8MB, alloc=36.3MB, time=2.86 memory used=183.7MB, alloc=36.3MB, time=3.16 memory used=196.7MB, alloc=36.3MB, time=3.29 memory used=221.7MB, alloc=54.0MB, time=3.56 memory used=235.5MB, alloc=54.0MB, time=3.62 memory used=248.5MB, alloc=54.0MB, time=3.68 memory used=262.3MB, alloc=54.0MB, time=3.73 memory used=272.0MB, alloc=54.0MB, time=3.77 memory used=299.7MB, alloc=54.0MB, time=4.47 memory used=327.9MB, alloc=54.0MB, time=5.24 memory used=353.9MB, alloc=54.0MB, time=6.21 memory used=370.7MB, alloc=54.0MB, time=6.43 memory used=386.1MB, alloc=54.0MB, time=6.54 memory used=404.1MB, alloc=54.0MB, time=6.73 memory used=420.8MB, alloc=54.0MB, time=7.27 memory used=438.7MB, alloc=54.0MB, time=7.53 memory used=450.1MB, alloc=54.0MB, time=7.59 memory used=458.8MB, alloc=54.0MB, time=7.64 memory used=472.0MB, alloc=54.0MB, time=7.77 memory used=496.0MB, alloc=54.0MB, time=8.22 memory used=509.3MB, alloc=78.0MB, time=8.42 memory used=544.5MB, alloc=78.0MB, time=9.09 memory used=585.4MB, alloc=78.0MB, time=9.78 memory used=617.7MB, alloc=78.0MB, time=10.44 memory used=647.9MB, alloc=78.0MB, time=11.06 memory used=680.5MB, alloc=78.0MB, time=11.70 memory used=708.0MB, alloc=78.0MB, time=12.31 memory used=746.3MB, alloc=78.0MB, time=12.91 memory used=779.1MB, alloc=78.0MB, time=13.28 memory used=815.9MB, alloc=78.0MB, time=13.72 memory used=843.5MB, alloc=78.0MB, time=13.97 memory used=876.7MB, alloc=78.0MB, time=14.91 memory used=903.3MB, alloc=78.0MB, time=15.21 memory used=932.4MB, alloc=78.0MB, time=15.63 memory used=960.1MB, alloc=78.0MB, time=15.80 memory used=992.4MB, alloc=78.0MB, time=16.18 memory used=1028.3MB, alloc=78.0MB, time=17.78 memory used=1057.0MB, alloc=78.0MB, time=17.99 memory used=1076.0MB, alloc=78.0MB, time=18.10 memory used=1104.5MB, alloc=78.0MB, time=18.48 memory used=1133.1MB, alloc=78.0MB, time=18.80 memory used=1157.5MB, alloc=78.0MB, time=19.04 memory used=1177.9MB, alloc=78.0MB, time=19.15 memory used=1226.4MB, alloc=78.0MB, time=20.17 memory used=1264.1MB, alloc=78.0MB, time=21.46 memory used=1301.8MB, alloc=78.0MB, time=22.09 memory used=1338.1MB, alloc=78.0MB, time=23.33 memory used=1365.5MB, alloc=78.0MB, time=24.02 memory used=1400.7MB, alloc=78.0MB, time=24.63 memory used=1434.7MB, alloc=78.0MB, time=26.61 memory used=1460.9MB, alloc=78.0MB, time=26.81 memory used=1492.7MB, alloc=78.0MB, time=28.35 memory used=1514.0MB, alloc=78.0MB, time=28.48 memory used=1530.8MB, alloc=78.0MB, time=28.59 memory used=1567.4MB, alloc=78.0MB, time=29.18 memory used=1609.4MB, alloc=102.0MB, time=29.82 memory used=1644.0MB, alloc=102.0MB, time=30.57 memory used=1714.7MB, alloc=102.0MB, time=32.40 memory used=1764.5MB, alloc=102.0MB, time=32.80 memory used=1816.0MB, alloc=102.0MB, time=33.90 memory used=1866.1MB, alloc=102.0MB, time=34.53 memory used=1930.8MB, alloc=102.0MB, time=35.75 memory used=1973.4MB, alloc=102.0MB, time=36.83 memory used=2043.0MB, alloc=102.0MB, time=37.88 memory used=2091.2MB, alloc=102.0MB, time=38.60 memory used=2141.1MB, alloc=102.0MB, time=40.06 memory used=2177.6MB, alloc=102.0MB, time=40.49 memory used=2237.6MB, alloc=102.0MB, time=41.72 memory used=2297.9MB, alloc=102.0MB, time=43.39 memory used=2355.6MB, alloc=102.0MB, time=44.12 memory used=2408.1MB, alloc=102.0MB, time=44.74 memory used=2440.7MB, alloc=102.0MB, time=45.02 memory used=2496.8MB, alloc=102.0MB, time=45.84 memory used=2525.6MB, alloc=102.0MB, time=46.02 memory used=2561.4MB, alloc=126.0MB, time=46.33 memory used=2619.1MB, alloc=126.0MB, time=47.07 memory used=2670.4MB, alloc=126.0MB, time=47.50 memory used=2716.0MB, alloc=126.0MB, time=47.92 memory used=2773.3MB, alloc=126.0MB, time=48.43 memory used=2828.1MB, alloc=126.0MB, time=48.78 memory used=2880.6MB, alloc=126.0MB, time=49.39 memory used=2938.2MB, alloc=126.0MB, time=49.90 memory used=3016.8MB, alloc=126.0MB, time=50.93 memory used=3084.0MB, alloc=126.0MB, time=53.75 memory used=3145.1MB, alloc=126.0MB, time=54.46 memory used=3186.7MB, alloc=126.0MB, time=54.70 memory used=3234.9MB, alloc=126.0MB, time=54.93 memory used=3270.6MB, alloc=126.0MB, time=55.10 memory used=3327.4MB, alloc=126.0MB, time=55.75 memory used=3401.6MB, alloc=126.0MB, time=56.67 memory used=3479.2MB, alloc=382.0MB, time=58.26 memory used=3597.7MB, alloc=382.0MB, time=60.45 memory used=3692.6MB, alloc=382.0MB, time=62.58 memory used=3775.5MB, alloc=382.0MB, time=64.33 memory used=3814.9MB, alloc=382.0MB, time=64.58 memory used=3899.0MB, alloc=382.0MB, time=66.10 memory used=3984.7MB, alloc=406.0MB, time=67.95 memory used=4056.8MB, alloc=406.0MB, time=68.59 memory used=4114.1MB, alloc=406.0MB, time=68.91 memory used=4157.1MB, alloc=406.0MB, time=69.24 memory used=4226.4MB, alloc=406.0MB, time=69.79 memory used=4282.3MB, alloc=406.0MB, time=70.11 memory used=4326.7MB, alloc=406.0MB, time=70.41 memory used=4402.7MB, alloc=406.0MB, time=73.58 memory used=4462.0MB, alloc=406.0MB, time=73.93 memory used=4512.7MB, alloc=406.0MB, time=74.23 memory used=4569.8MB, alloc=406.0MB, time=74.52 memory used=4610.4MB, alloc=406.0MB, time=74.75 memory used=4658.5MB, alloc=406.0MB, time=75.00 memory used=4733.9MB, alloc=406.0MB, time=76.16 memory used=4785.2MB, alloc=406.0MB, time=76.44 memory used=4865.0MB, alloc=406.0MB, time=77.48 memory used=4919.4MB, alloc=406.0MB, time=77.79 memory used=4965.7MB, alloc=406.0MB, time=78.05 memory used=5031.7MB, alloc=406.0MB, time=78.58 memory used=5084.5MB, alloc=406.0MB, time=78.87 memory used=5134.3MB, alloc=406.0MB, time=79.15 memory used=5204.1MB, alloc=406.0MB, time=80.51 memory used=5256.1MB, alloc=406.0MB, time=80.79 memory used=5302.3MB, alloc=406.0MB, time=81.05 memory used=5363.1MB, alloc=406.0MB, time=81.95 memory used=5426.7MB, alloc=406.0MB, time=82.73 memory used=5480.9MB, alloc=406.0MB, time=83.04 memory used=5527.5MB, alloc=406.0MB, time=83.31 memory used=5593.0MB, alloc=406.0MB, time=83.85 memory used=5645.1MB, alloc=406.0MB, time=84.15 memory used=5694.7MB, alloc=406.0MB, time=84.43 memory used=5763.5MB, alloc=406.0MB, time=85.76 memory used=5817.9MB, alloc=406.0MB, time=86.08 memory used=5863.2MB, alloc=406.0MB, time=86.31 memory used=5931.4MB, alloc=406.0MB, time=87.00 memory used=5991.6MB, alloc=406.0MB, time=87.80 memory used=6045.1MB, alloc=406.0MB, time=88.28 memory used=6178.9MB, alloc=406.0MB, time=94.11 memory used=6240.2MB, alloc=406.0MB, time=94.47 memory used=6282.3MB, alloc=406.0MB, time=94.77 memory used=6334.0MB, alloc=406.0MB, time=95.08 memory used=6394.3MB, alloc=406.0MB, time=95.39 memory used=6430.3MB, alloc=406.0MB, time=95.63 memory used=6469.9MB, alloc=406.0MB, time=95.87 memory used=6513.9MB, alloc=406.0MB, time=96.12 memory used=6562.6MB, alloc=406.0MB, time=96.36 memory used=6614.7MB, alloc=406.0MB, time=96.63 memory used=6672.3MB, alloc=406.0MB, time=96.89 memory used=6813.5MB, alloc=406.0MB, time=98.63 memory used=6934.7MB, alloc=406.0MB, time=100.52 memory used=7055.2MB, alloc=406.0MB, time=103.32 memory used=7169.3MB, alloc=406.0MB, time=106.72 memory used=7233.7MB, alloc=406.0MB, time=107.89 memory used=7284.3MB, alloc=406.0MB, time=108.22 memory used=7325.5MB, alloc=406.0MB, time=108.50 memory used=7369.2MB, alloc=406.0MB, time=108.79 memory used=7422.5MB, alloc=406.0MB, time=109.08 memory used=7559.8MB, alloc=406.0MB, time=111.35 memory used=7612.2MB, alloc=430.0MB, time=111.76 memory used=7673.4MB, alloc=430.0MB, time=112.14 memory used=7732.2MB, alloc=430.0MB, time=112.50 memory used=7806.8MB, alloc=430.0MB, time=112.88 memory used=7860.7MB, alloc=430.0MB, time=113.18 memory used=7909.5MB, alloc=430.0MB, time=113.48 memory used=7984.3MB, alloc=430.0MB, time=114.22 memory used=8054.6MB, alloc=430.0MB, time=114.66 memory used=8107.0MB, alloc=430.0MB, time=115.02 memory used=8173.9MB, alloc=430.0MB, time=115.40 memory used=8246.3MB, alloc=430.0MB, time=115.78 memory used=8292.5MB, alloc=430.0MB, time=116.08 memory used=8345.0MB, alloc=430.0MB, time=116.38 memory used=8463.4MB, alloc=430.0MB, time=131.21 memory used=8524.7MB, alloc=430.0MB, time=131.61 memory used=8592.5MB, alloc=430.0MB, time=132.01 memory used=8651.7MB, alloc=430.0MB, time=132.37 memory used=8700.1MB, alloc=430.0MB, time=132.69 memory used=8754.4MB, alloc=430.0MB, time=133.01 memory used=8816.1MB, alloc=430.0MB, time=133.34 memory used=8884.2MB, alloc=430.0MB, time=133.68 memory used=8958.2MB, alloc=430.0MB, time=134.03 memory used=9173.5MB, alloc=430.0MB, time=134.99 memory used=9330.8MB, alloc=430.0MB, time=135.59 memory used=9511.6MB, alloc=430.0MB, time=136.22 memory used=9720.1MB, alloc=430.0MB, time=136.90 memory used=9951.6MB, alloc=430.0MB, time=137.60 memory used=10111.6MB, alloc=430.0MB, time=139.41 memory used=10181.0MB, alloc=430.0MB, time=140.74 memory used=10259.1MB, alloc=430.0MB, time=141.15 memory used=10338.1MB, alloc=430.0MB, time=141.55 memory used=10414.8MB, alloc=430.0MB, time=141.96 memory used=10598.2MB, alloc=430.0MB, time=145.11 memory used=10819.5MB, alloc=430.0MB, time=145.84 memory used=11023.6MB, alloc=430.0MB, time=146.52 memory used=11161.2MB, alloc=430.0MB, time=146.99 memory used=11322.0MB, alloc=430.0MB, time=152.46 memory used=11391.3MB, alloc=430.0MB, time=152.87 memory used=11443.2MB, alloc=430.0MB, time=153.19 memory used=11502.4MB, alloc=430.0MB, time=153.52 memory used=11573.3MB, alloc=430.0MB, time=153.87 memory used=11787.5MB, alloc=430.0MB, time=154.56 memory used=11945.1MB, alloc=430.0MB, time=157.11 memory used=12059.9MB, alloc=430.0MB, time=159.33 memory used=12167.1MB, alloc=430.0MB, time=160.89 memory used=12236.3MB, alloc=430.0MB, time=161.48 memory used=12309.2MB, alloc=430.0MB, time=162.33 memory used=12385.2MB, alloc=430.0MB, time=163.32 memory used=12448.6MB, alloc=430.0MB, time=163.75 memory used=12499.3MB, alloc=430.0MB, time=164.14 memory used=12548.4MB, alloc=430.0MB, time=164.51 memory used=12605.2MB, alloc=430.0MB, time=164.91 memory used=12671.5MB, alloc=430.0MB, time=165.31 memory used=12745.2MB, alloc=430.0MB, time=165.71 memory used=12785.9MB, alloc=454.0MB, time=166.04 memory used=12840.4MB, alloc=454.0MB, time=166.37 memory used=12898.9MB, alloc=454.0MB, time=166.75 memory used=12963.2MB, alloc=454.0MB, time=167.10 memory used=13031.6MB, alloc=454.0MB, time=167.47 memory used=13105.4MB, alloc=454.0MB, time=167.82 memory used=13185.6MB, alloc=454.0MB, time=168.19 memory used=13289.5MB, alloc=454.0MB, time=169.37 memory used=13371.7MB, alloc=454.0MB, time=169.87 memory used=13430.6MB, alloc=454.0MB, time=170.29 memory used=13502.8MB, alloc=454.0MB, time=170.72 memory used=13588.2MB, alloc=454.0MB, time=171.17 memory used=13669.4MB, alloc=454.0MB, time=171.59 memory used=13722.1MB, alloc=454.0MB, time=171.94 memory used=13779.5MB, alloc=454.0MB, time=172.28 memory used=13841.5MB, alloc=454.0MB, time=172.63 memory used=13907.7MB, alloc=454.0MB, time=172.98 memory used=13979.2MB, alloc=454.0MB, time=173.34 memory used=14056.4MB, alloc=454.0MB, time=173.69 memory used=14156.3MB, alloc=454.0MB, time=176.60 memory used=14310.9MB, alloc=454.0MB, time=201.43 memory used=14382.8MB, alloc=454.0MB, time=201.91 memory used=14465.0MB, alloc=454.0MB, time=202.38 memory used=14540.7MB, alloc=454.0MB, time=202.81 memory used=14597.5MB, alloc=454.0MB, time=203.18 memory used=14659.1MB, alloc=454.0MB, time=203.56 memory used=14727.8MB, alloc=454.0MB, time=203.95 memory used=14800.9MB, alloc=454.0MB, time=204.35 memory used=14881.4MB, alloc=454.0MB, time=204.76 memory used=14969.4MB, alloc=454.0MB, time=205.18 memory used=15062.0MB, alloc=454.0MB, time=205.60 memory used=15249.8MB, alloc=454.0MB, time=206.32 memory used=15394.7MB, alloc=454.0MB, time=206.93 memory used=15552.1MB, alloc=454.0MB, time=207.54 memory used=15722.9MB, alloc=454.0MB, time=208.20 memory used=15906.7MB, alloc=454.0MB, time=208.88 memory used=16107.0MB, alloc=454.0MB, time=209.57 memory used=16323.1MB, alloc=454.0MB, time=210.31 memory used=16556.8MB, alloc=454.0MB, time=211.05 memory used=16784.2MB, alloc=454.0MB, time=211.78 memory used=16960.8MB, alloc=454.0MB, time=212.39 |\^/| 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(); 1428281032 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 2 F := [9 y - 2 y z - 15 x z - 18 y, -10 x y - 15 x y - 15 z + 8 z, 2 2 18 x y z - 8 x y z + 4 y z + x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 2 G := [-6 y + 4 y z + 11 z, 13 x y z + 5 y z + 19 y z + 12 y z , 3 2 2 3 -10 x y - 9 x y z - 13 x z + 7 z ] > Problem := [F,G]; 4 2 2 2 3 2 Problem := [[9 y - 2 y z - 15 x z - 18 y, -10 x y - 15 x y - 15 z + 8 z, 2 2 3 2 18 x y z - 8 x y z + 4 y z + x], [-6 y + 4 y z + 11 z, 2 3 3 2 13 x y z + 5 y z + 19 y z + 12 y z , 3 2 2 3 -10 x y - 9 x y z - 13 x z + 7 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=24.6MB, alloc=32.3MB, time=0.85 memory used=42.7MB, alloc=56.3MB, time=1.33 memory used=89.0MB, alloc=60.3MB, time=2.14 memory used=138.6MB, alloc=62.2MB, time=7.12 memory used=163.4MB, alloc=62.2MB, time=7.23 memory used=200.1MB, alloc=62.2MB, time=8.67 memory used=225.3MB, alloc=62.2MB, time=8.79 memory used=253.6MB, alloc=62.2MB, time=16.90 memory used=283.3MB, alloc=62.2MB, time=30.20 memory used=309.2MB, alloc=86.2MB, time=56.17 memory used=335.5MB, alloc=110.2MB, time=86.44 memory used=375.6MB, alloc=110.2MB, time=126.20 memory used=420.2MB, alloc=134.2MB, time=148.81 memory used=460.6MB, alloc=158.2MB, time=192.35 memory used=498.5MB, alloc=182.2MB, time=212.78 memory used=556.3MB, alloc=182.2MB, time=237.23 memory used=643.3MB, alloc=206.2MB, time=240.69 memory used=672.3MB, alloc=230.2MB, time=240.77 memory used=706.9MB, alloc=254.2MB, time=241.43 |\^/| 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(); 1428281332 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 F := [4 y z - 9 x y + 2 x z + 3 y z, 6 x y - 15 x z + 12 y z + 7 x , 3 2 2 2 -17 y z + 6 x y + 2 y z - 15 y z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 4 2 G := [-5 y + 8 x y - 18 z + 8 x y, -4 z + 14 z - 11 y + 11, 2 3 2 -6 x y z + 4 y z - 2 x y + 7 y ] > Problem := [F,G]; 2 3 3 2 2 Problem := [[4 y z - 9 x y + 2 x z + 3 y z, 6 x y - 15 x z + 12 y z + 7 x , 3 2 2 2 4 2 3 -17 y z + 6 x y + 2 y z - 15 y z ], [-5 y + 8 x y - 18 z + 8 x y, 4 2 2 3 2 -4 z + 14 z - 11 y + 11, -6 x y z + 4 y z - 2 x y + 7 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=24.1MB, alloc=32.3MB, time=0.78 memory used=43.2MB, alloc=32.3MB, time=1.13 memory used=64.3MB, alloc=36.3MB, time=1.63 memory used=85.0MB, alloc=60.3MB, time=2.10 memory used=127.5MB, alloc=60.3MB, time=2.91 memory used=172.3MB, alloc=62.0MB, time=3.60 memory used=193.7MB, alloc=62.0MB, time=3.70 memory used=220.6MB, alloc=62.0MB, time=3.81 memory used=244.0MB, alloc=62.0MB, time=3.91 memory used=262.9MB, alloc=62.0MB, time=4.00 memory used=284.6MB, alloc=62.0MB, time=4.09 memory used=314.4MB, alloc=62.0MB, time=4.43 memory used=346.0MB, alloc=62.0MB, time=4.59 memory used=369.9MB, alloc=62.0MB, time=4.70 memory used=399.6MB, alloc=62.0MB, time=4.82 memory used=418.4MB, alloc=62.0MB, time=4.91 memory used=439.2MB, alloc=62.0MB, time=5.00 memory used=463.6MB, alloc=62.0MB, time=5.10 memory used=510.1MB, alloc=62.0MB, time=9.05 memory used=536.3MB, alloc=62.0MB, time=9.17 memory used=556.3MB, alloc=62.0MB, time=9.27 memory used=582.6MB, alloc=62.0MB, time=9.36 memory used=618.3MB, alloc=62.2MB, time=9.91 memory used=641.6MB, alloc=62.2MB, time=10.03 memory used=663.9MB, alloc=62.2MB, time=10.14 memory used=690.3MB, alloc=62.2MB, time=10.26 memory used=717.4MB, alloc=62.2MB, time=10.37 memory used=734.2MB, alloc=62.2MB, time=10.47 memory used=752.4MB, alloc=62.2MB, time=10.56 memory used=771.7MB, alloc=62.2MB, time=10.65 memory used=792.3MB, alloc=62.2MB, time=10.74 memory used=815.0MB, alloc=62.2MB, time=10.84 memory used=839.6MB, alloc=62.2MB, time=10.94 memory used=867.3MB, alloc=62.2MB, time=11.05 memory used=895.6MB, alloc=62.2MB, time=11.15 memory used=912.3MB, alloc=62.2MB, time=11.22 memory used=940.0MB, alloc=62.2MB, time=11.48 memory used=978.6MB, alloc=62.9MB, time=12.03 memory used=1000.2MB, alloc=62.9MB, time=12.14 memory used=1023.2MB, alloc=62.9MB, time=12.26 memory used=1051.1MB, alloc=62.9MB, time=12.37 memory used=1076.7MB, alloc=62.9MB, time=12.48 memory used=1094.3MB, alloc=62.9MB, time=12.58 memory used=1113.4MB, alloc=62.9MB, time=12.67 memory used=1134.0MB, alloc=62.9MB, time=12.77 memory used=1155.9MB, alloc=62.9MB, time=12.87 memory used=1179.7MB, alloc=62.9MB, time=12.96 memory used=1206.0MB, alloc=62.9MB, time=13.06 memory used=1235.3MB, alloc=62.9MB, time=13.17 memory used=1258.6MB, alloc=62.9MB, time=13.25 memory used=1281.3MB, alloc=62.9MB, time=13.46 memory used=1308.1MB, alloc=62.9MB, time=15.04 memory used=1339.9MB, alloc=62.9MB, time=17.49 memory used=1362.1MB, alloc=62.9MB, time=17.57 memory used=1391.3MB, alloc=62.9MB, time=17.80 memory used=1416.9MB, alloc=62.9MB, time=18.00 memory used=1440.2MB, alloc=62.9MB, time=18.20 memory used=1468.2MB, alloc=62.9MB, time=18.33 memory used=1490.7MB, alloc=62.9MB, time=18.43 memory used=1530.2MB, alloc=83.8MB, time=18.86 memory used=1562.3MB, alloc=83.8MB, time=18.98 memory used=1598.1MB, alloc=83.8MB, time=19.13 memory used=1636.0MB, alloc=83.8MB, time=19.25 memory used=1676.5MB, alloc=83.8MB, time=19.38 memory used=1720.3MB, alloc=83.8MB, time=19.51 memory used=1769.0MB, alloc=83.8MB, time=20.57 memory used=1821.6MB, alloc=83.8MB, time=26.62 memory used=1844.9MB, alloc=83.8MB, time=26.75 memory used=1864.1MB, alloc=83.8MB, time=26.86 memory used=1884.6MB, alloc=83.8MB, time=26.96 memory used=1909.9MB, alloc=83.8MB, time=27.09 memory used=1926.3MB, alloc=83.8MB, time=27.17 memory used=1971.2MB, alloc=83.8MB, time=28.00 memory used=2004.8MB, alloc=83.8MB, time=28.19 memory used=2027.2MB, alloc=83.8MB, time=28.46 memory used=2061.3MB, alloc=83.8MB, time=28.66 memory used=2080.9MB, alloc=83.8MB, time=28.97 memory used=2105.4MB, alloc=83.8MB, time=29.85 memory used=2138.9MB, alloc=107.8MB, time=30.14 memory used=2179.5MB, alloc=107.8MB, time=30.35 memory used=2226.2MB, alloc=107.8MB, time=30.84 memory used=2276.9MB, alloc=107.8MB, time=31.11 memory used=2312.9MB, alloc=107.8MB, time=31.31 memory used=2367.3MB, alloc=107.8MB, time=32.83 memory used=2421.5MB, alloc=107.8MB, time=33.27 memory used=2488.3MB, alloc=107.8MB, time=34.85 memory used=2554.4MB, alloc=107.8MB, time=36.57 memory used=2621.5MB, alloc=107.8MB, time=38.06 memory used=2668.4MB, alloc=107.8MB, time=38.66 memory used=2736.5MB, alloc=107.8MB, time=39.83 memory used=2794.0MB, alloc=107.8MB, time=40.73 memory used=2836.5MB, alloc=107.8MB, time=41.75 memory used=2883.0MB, alloc=131.8MB, time=43.19 memory used=2926.7MB, alloc=131.8MB, time=43.45 memory used=2970.2MB, alloc=131.8MB, time=43.70 memory used=3020.4MB, alloc=131.8MB, time=43.96 memory used=3078.3MB, alloc=131.8MB, time=44.22 memory used=3113.8MB, alloc=131.8MB, time=44.43 memory used=3146.1MB, alloc=131.8MB, time=44.64 memory used=3180.9MB, alloc=131.8MB, time=44.84 memory used=3217.0MB, alloc=131.8MB, time=45.04 memory used=3256.3MB, alloc=131.8MB, time=45.25 memory used=3296.7MB, alloc=131.8MB, time=45.47 memory used=3340.7MB, alloc=131.8MB, time=45.69 memory used=3388.1MB, alloc=131.8MB, time=45.91 memory used=3436.3MB, alloc=131.8MB, time=46.12 memory used=3487.8MB, alloc=131.8MB, time=46.34 memory used=3542.4MB, alloc=131.8MB, time=46.57 memory used=3599.9MB, alloc=131.8MB, time=46.81 memory used=3636.5MB, alloc=131.8MB, time=46.98 memory used=3665.6MB, alloc=131.8MB, time=47.13 memory used=3695.5MB, alloc=131.8MB, time=47.28 memory used=3725.8MB, alloc=131.8MB, time=47.42 memory used=3757.4MB, alloc=131.8MB, time=47.58 memory used=3791.6MB, alloc=131.8MB, time=47.74 memory used=3825.1MB, alloc=131.8MB, time=47.90 memory used=3860.5MB, alloc=131.8MB, time=48.05 memory used=3897.3MB, alloc=131.8MB, time=48.21 memory used=3935.2MB, alloc=131.8MB, time=48.37 memory used=3974.5MB, alloc=131.8MB, time=48.54 memory used=4016.9MB, alloc=131.8MB, time=48.71 memory used=4060.7MB, alloc=131.8MB, time=48.88 memory used=4106.5MB, alloc=131.8MB, time=49.04 memory used=4166.7MB, alloc=131.8MB, time=51.46 memory used=4229.7MB, alloc=131.8MB, time=51.79 memory used=4269.0MB, alloc=131.8MB, time=52.04 memory used=4316.4MB, alloc=131.8MB, time=52.28 memory used=4371.4MB, alloc=131.8MB, time=52.54 memory used=4420.7MB, alloc=131.8MB, time=52.78 memory used=4452.1MB, alloc=131.8MB, time=52.99 memory used=4486.1MB, alloc=131.8MB, time=53.19 memory used=4521.5MB, alloc=131.8MB, time=53.40 memory used=4560.5MB, alloc=131.8MB, time=53.60 memory used=4600.6MB, alloc=131.8MB, time=53.81 memory used=4644.1MB, alloc=131.8MB, time=54.01 memory used=4688.7MB, alloc=131.8MB, time=54.21 memory used=4736.4MB, alloc=131.8MB, time=54.42 memory used=4787.7MB, alloc=131.8MB, time=54.63 memory used=4842.2MB, alloc=131.8MB, time=54.85 memory used=4899.8MB, alloc=131.8MB, time=55.08 memory used=4947.2MB, alloc=131.8MB, time=55.28 memory used=4978.0MB, alloc=131.8MB, time=55.43 memory used=5007.2MB, alloc=131.8MB, time=55.58 memory used=5037.4MB, alloc=131.8MB, time=55.74 memory used=5069.3MB, alloc=131.8MB, time=55.90 memory used=5101.4MB, alloc=131.8MB, time=56.05 memory used=5134.9MB, alloc=131.8MB, time=56.21 memory used=5170.6MB, alloc=131.8MB, time=56.37 memory used=5207.8MB, alloc=131.8MB, time=56.55 memory used=5246.1MB, alloc=131.8MB, time=56.71 memory used=5285.3MB, alloc=131.8MB, time=56.88 memory used=5326.9MB, alloc=131.8MB, time=57.04 memory used=5369.9MB, alloc=131.8MB, time=57.20 memory used=5415.2MB, alloc=131.8MB, time=57.37 memory used=5463.5MB, alloc=131.8MB, time=57.54 memory used=5530.8MB, alloc=131.8MB, time=93.74 memory used=5614.3MB, alloc=131.8MB, time=101.29 memory used=5663.9MB, alloc=131.8MB, time=101.56 memory used=5706.4MB, alloc=131.8MB, time=101.78 memory used=5748.2MB, alloc=131.8MB, time=102.00 memory used=5797.4MB, alloc=131.8MB, time=102.23 memory used=5855.8MB, alloc=131.8MB, time=102.46 memory used=5891.0MB, alloc=131.8MB, time=102.63 memory used=5925.4MB, alloc=131.8MB, time=102.79 memory used=5963.1MB, alloc=131.8MB, time=102.96 memory used=6003.5MB, alloc=131.8MB, time=103.13 memory used=6047.2MB, alloc=131.8MB, time=103.29 memory used=6094.3MB, alloc=131.8MB, time=103.46 memory used=6147.1MB, alloc=131.8MB, time=103.64 memory used=6216.2MB, alloc=131.8MB, time=104.05 memory used=6305.7MB, alloc=131.8MB, time=105.71 memory used=6349.7MB, alloc=131.8MB, time=105.98 memory used=6389.8MB, alloc=131.8MB, time=106.20 memory used=6438.1MB, alloc=131.8MB, time=106.44 memory used=6492.9MB, alloc=131.8MB, time=106.70 memory used=6537.4MB, alloc=131.8MB, time=106.92 memory used=6570.5MB, alloc=131.8MB, time=107.11 memory used=6605.2MB, alloc=131.8MB, time=107.30 memory used=6642.2MB, alloc=131.8MB, time=107.50 memory used=6683.2MB, alloc=131.8MB, time=107.70 memory used=6726.4MB, alloc=131.8MB, time=107.89 memory used=6773.5MB, alloc=131.8MB, time=108.09 memory used=6825.2MB, alloc=131.8MB, time=108.29 memory used=6886.4MB, alloc=131.8MB, time=108.75 memory used=6947.8MB, alloc=131.8MB, time=115.85 memory used=7013.0MB, alloc=155.8MB, time=161.39 |\^/| 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(); 1428281632 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 2 2 F := [-3 x y - 5 x y z - 15 y z + 10 x y, 13 y + 6 y z - 11 x z + 2 y , 2 2 2 -7 x y - 2 x y z - 4 y z + 5 y z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [13 x y z + 15 x z + 2 x y z - 18 x y z, 2 3 2 2 2 20 x y z + 10 y z - 14 y z - 18 x z, 3 2 2 2 2 -12 x y + 9 x y - 12 x y z - 12 y ] > Problem := [F,G]; 3 2 2 Problem := [[-3 x y - 5 x y z - 15 y z + 10 x y, 4 3 2 2 2 2 2 13 y + 6 y z - 11 x z + 2 y , -7 x y - 2 x y z - 4 y z + 5 y z ], [ 2 2 2 2 13 x y z + 15 x z + 2 x y z - 18 x y z, 2 3 2 2 2 20 x y z + 10 y z - 14 y z - 18 x z, 3 2 2 2 2 -12 x y + 9 x y - 12 x y z - 12 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=24.9MB, alloc=32.3MB, time=0.84 memory used=44.1MB, alloc=32.3MB, time=1.33 memory used=62.5MB, alloc=60.3MB, time=1.79 memory used=103.9MB, alloc=60.3MB, time=2.77 memory used=145.2MB, alloc=60.3MB, time=3.70 memory used=189.4MB, alloc=68.3MB, time=4.74 memory used=227.8MB, alloc=68.3MB, time=5.55 memory used=267.7MB, alloc=92.3MB, time=6.65 memory used=335.2MB, alloc=92.3MB, time=8.14 memory used=401.6MB, alloc=116.3MB, time=9.70 memory used=466.3MB, alloc=372.3MB, time=11.17 memory used=558.2MB, alloc=396.3MB, time=13.25 memory used=667.8MB, alloc=420.3MB, time=15.75 memory used=769.0MB, alloc=420.3MB, time=18.05 memory used=905.6MB, alloc=420.3MB, time=21.33 memory used=1040.3MB, alloc=444.3MB, time=24.30 memory used=1142.0MB, alloc=444.3MB, time=25.31 memory used=1243.3MB, alloc=444.3MB, time=31.85 memory used=1306.6MB, alloc=444.3MB, time=32.26 memory used=1404.3MB, alloc=444.3MB, time=33.12 memory used=1500.8MB, alloc=444.3MB, time=39.83 memory used=1568.2MB, alloc=444.3MB, time=40.25 memory used=1692.5MB, alloc=444.3MB, time=41.82 memory used=1838.8MB, alloc=444.3MB, time=44.66 memory used=1953.5MB, alloc=444.3MB, time=47.67 memory used=2052.6MB, alloc=468.3MB, time=49.90 memory used=2167.6MB, alloc=468.3MB, time=52.85 memory used=2266.3MB, alloc=468.3MB, time=55.42 memory used=2346.3MB, alloc=492.3MB, time=57.62 memory used=2434.6MB, alloc=492.3MB, time=60.12 memory used=2522.3MB, alloc=492.3MB, time=62.57 memory used=2595.5MB, alloc=492.3MB, time=64.48 memory used=2680.1MB, alloc=492.3MB, time=66.76 memory used=2740.7MB, alloc=492.3MB, time=68.66 memory used=2816.6MB, alloc=492.3MB, time=70.93 memory used=2878.3MB, alloc=492.3MB, time=72.64 memory used=2967.4MB, alloc=492.3MB, time=74.61 memory used=3057.2MB, alloc=492.3MB, time=76.41 memory used=3123.6MB, alloc=516.3MB, time=78.14 memory used=3172.1MB, alloc=516.3MB, time=79.92 memory used=3216.5MB, alloc=516.3MB, time=81.54 memory used=3257.2MB, alloc=516.3MB, time=83.11 memory used=3405.8MB, alloc=516.3MB, time=88.27 memory used=3504.4MB, alloc=516.3MB, time=89.44 memory used=3633.6MB, alloc=516.3MB, time=94.18 memory used=3733.8MB, alloc=516.3MB, time=95.43 memory used=3918.6MB, alloc=516.3MB, time=100.37 memory used=4125.3MB, alloc=540.3MB, time=105.29 memory used=4305.5MB, alloc=564.3MB, time=110.50 memory used=4488.9MB, alloc=588.3MB, time=114.76 memory used=4675.3MB, alloc=612.3MB, time=120.20 memory used=4845.3MB, alloc=636.3MB, time=125.01 memory used=5013.0MB, alloc=636.3MB, time=130.23 memory used=5153.0MB, alloc=660.3MB, time=134.63 memory used=5288.0MB, alloc=660.3MB, time=138.32 memory used=5463.6MB, alloc=684.3MB, time=142.00 memory used=5620.0MB, alloc=684.3MB, time=147.93 memory used=5712.0MB, alloc=708.3MB, time=151.30 memory used=5803.2MB, alloc=708.3MB, time=154.26 memory used=5909.0MB, alloc=708.3MB, time=158.54 |\^/| 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(); 1428281932 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 F := [12 y z - 2 y z + 10 x y + 20 y , -19 x z + 18 x y z - 11 z + 16 x, 4 2 2 12 x + 16 x y z + x - 3 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 G := [10 y z - 4 y z + 14 x y - 2 x, -4 y z - 11 x z - 10 y + 18 y z, 2 2 3 2 2 17 x z - 2 x z + 8 x - 15 y ] > Problem := [F,G]; 3 2 2 2 2 Problem := [[12 y z - 2 y z + 10 x y + 20 y , 2 2 4 2 2 -19 x z + 18 x y z - 11 z + 16 x, 12 x + 16 x y z + x - 3 x z], [ 2 2 2 2 2 2 2 10 y z - 4 y z + 14 x y - 2 x, -4 y z - 11 x z - 10 y + 18 y z, 2 2 3 2 2 17 x z - 2 x 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=4.4MB, alloc=32.3MB, time=0.31 memory used=26.0MB, alloc=32.3MB, time=0.89 memory used=45.2MB, alloc=56.3MB, time=1.39 memory used=86.9MB, alloc=60.3MB, time=2.46 memory used=129.6MB, alloc=68.3MB, time=3.47 memory used=160.9MB, alloc=68.3MB, time=3.81 memory used=207.6MB, alloc=68.3MB, time=4.87 memory used=249.0MB, alloc=92.3MB, time=5.94 memory used=316.8MB, alloc=92.3MB, time=7.31 memory used=382.7MB, alloc=92.3MB, time=8.50 memory used=447.4MB, alloc=92.3MB, time=9.99 memory used=515.4MB, alloc=92.3MB, time=11.59 memory used=582.2MB, alloc=116.3MB, time=13.11 memory used=645.4MB, alloc=116.3MB, time=13.77 memory used=711.6MB, alloc=116.3MB, time=14.58 memory used=759.5MB, alloc=116.3MB, time=15.00 memory used=816.5MB, alloc=116.4MB, time=15.41 memory used=875.3MB, alloc=116.4MB, time=16.09 memory used=940.6MB, alloc=116.4MB, time=16.90 memory used=993.0MB, alloc=116.4MB, time=17.55 memory used=1063.8MB, alloc=116.4MB, time=18.63 memory used=1160.5MB, alloc=373.4MB, time=20.69 memory used=1234.9MB, alloc=373.4MB, time=22.08 memory used=1276.0MB, alloc=373.4MB, time=22.30 memory used=1325.3MB, alloc=373.4MB, time=22.70 memory used=1366.9MB, alloc=373.4MB, time=22.93 memory used=1426.9MB, alloc=373.4MB, time=23.63 memory used=1490.5MB, alloc=373.4MB, time=24.45 memory used=1539.0MB, alloc=373.4MB, time=24.93 memory used=1623.5MB, alloc=373.4MB, time=26.33 memory used=1694.5MB, alloc=373.4MB, time=27.40 memory used=1783.1MB, alloc=373.4MB, time=29.34 memory used=1869.4MB, alloc=397.4MB, time=31.38 memory used=1968.9MB, alloc=397.4MB, time=33.02 memory used=2065.5MB, alloc=397.4MB, time=34.54 memory used=2141.9MB, alloc=397.4MB, time=35.62 memory used=2244.0MB, alloc=397.4MB, time=37.44 memory used=2329.9MB, alloc=397.4MB, time=38.75 memory used=2434.3MB, alloc=397.4MB, time=40.54 memory used=2543.6MB, alloc=421.4MB, time=43.33 memory used=2662.2MB, alloc=445.4MB, time=46.38 memory used=2764.8MB, alloc=469.4MB, time=48.59 memory used=2908.9MB, alloc=469.4MB, time=51.42 memory used=3021.8MB, alloc=469.4MB, time=53.89 memory used=3141.4MB, alloc=493.4MB, time=55.92 memory used=3250.3MB, alloc=493.4MB, time=58.44 memory used=3336.9MB, alloc=493.4MB, time=60.73 memory used=3403.3MB, alloc=493.4MB, time=62.27 memory used=3484.5MB, alloc=493.4MB, time=64.59 memory used=3563.9MB, alloc=493.4MB, time=66.84 memory used=3637.6MB, alloc=493.4MB, time=68.99 memory used=3711.3MB, alloc=517.4MB, time=70.83 memory used=3784.9MB, alloc=517.4MB, time=72.38 memory used=3846.8MB, alloc=517.4MB, time=73.78 memory used=3939.4MB, alloc=517.4MB, time=75.69 memory used=4000.2MB, alloc=517.4MB, time=77.65 memory used=4051.9MB, alloc=517.4MB, time=79.24 memory used=4107.6MB, alloc=517.4MB, time=80.81 memory used=4162.3MB, alloc=517.4MB, time=82.17 memory used=4205.4MB, alloc=517.4MB, time=83.45 memory used=4402.5MB, alloc=541.4MB, time=88.71 memory used=4576.3MB, alloc=565.4MB, time=91.85 memory used=4813.9MB, alloc=565.4MB, time=96.48 memory used=5049.3MB, alloc=589.4MB, time=100.94 memory used=5264.8MB, alloc=613.4MB, time=104.85 memory used=5500.4MB, alloc=613.4MB, time=109.26 memory used=5661.4MB, alloc=613.4MB, time=112.84 memory used=5823.5MB, alloc=637.4MB, time=117.43 memory used=5985.5MB, alloc=661.4MB, time=121.39 memory used=6211.5MB, alloc=661.4MB, time=124.51 memory used=6412.9MB, alloc=661.4MB, time=126.86 memory used=6617.3MB, alloc=661.4MB, time=129.70 memory used=6822.1MB, alloc=661.4MB, time=132.78 memory used=6990.7MB, alloc=661.4MB, time=134.45 memory used=7189.4MB, alloc=661.4MB, time=139.10 memory used=7391.7MB, alloc=661.4MB, time=141.29 memory used=7575.0MB, alloc=661.4MB, time=144.05 memory used=7746.3MB, alloc=661.4MB, time=145.85 memory used=7946.4MB, alloc=661.4MB, time=150.34 memory used=8135.0MB, alloc=661.4MB, time=152.32 memory used=8321.8MB, alloc=661.4MB, time=155.25 memory used=8506.3MB, alloc=661.4MB, time=158.03 memory used=8680.1MB, alloc=661.4MB, time=159.88 memory used=8853.4MB, alloc=661.4MB, time=161.63 memory used=9023.7MB, alloc=661.4MB, time=165.43 memory used=9201.4MB, alloc=661.4MB, time=167.18 memory used=9374.5MB, alloc=661.4MB, time=168.90 memory used=9542.6MB, alloc=661.4MB, time=172.65 |\^/| 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(); 1428282232 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 F := [-x y + 15 y z - 8 x y + 19 y z, 12 y z + 13 z - 13 x z + 12 y, 2 2 2 14 x y - 20 x y + 5 x y z + 20 y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 G := [-17 x y - 10 x z + 13 x z - 20 x, 2 3 3 2 2 2 3 3 2 13 x y z + 13 x z + 9 y z + 19 y , -5 x z + 11 y z - 19 z - 7 x ] > Problem := [F,G]; 3 3 2 2 3 Problem := [[-x y + 15 y z - 8 x y + 19 y z, 12 y z + 13 z - 13 x z + 12 y, 2 2 2 14 x y - 20 x y + 5 x y z + 20 y], [ 3 3 2 2 2 3 3 2 -17 x y - 10 x z + 13 x z - 20 x, 13 x y z + 13 x z + 9 y z + 19 y , 2 2 3 3 2 -5 x z + 11 y z - 19 z - 7 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=25.2MB, alloc=32.3MB, time=0.86 memory used=43.8MB, alloc=56.3MB, time=1.36 memory used=77.1MB, alloc=60.3MB, time=2.12 memory used=152.8MB, alloc=68.3MB, time=7.76 memory used=220.4MB, alloc=70.8MB, time=8.96 memory used=294.9MB, alloc=70.8MB, time=10.39 memory used=344.2MB, alloc=70.8MB, time=11.08 memory used=385.3MB, alloc=70.8MB, time=12.06 memory used=428.7MB, alloc=70.8MB, time=13.04 memory used=469.0MB, alloc=94.8MB, time=14.07 memory used=533.3MB, alloc=94.8MB, time=15.17 memory used=568.3MB, alloc=94.8MB, time=15.36 memory used=626.3MB, alloc=94.8MB, time=16.20 memory used=690.6MB, alloc=94.8MB, time=17.76 memory used=753.1MB, alloc=94.8MB, time=19.10 memory used=810.3MB, alloc=118.8MB, time=20.40 memory used=863.4MB, alloc=374.8MB, time=21.62 memory used=953.3MB, alloc=374.8MB, time=24.68 memory used=1013.9MB, alloc=374.8MB, time=25.01 memory used=1072.2MB, alloc=374.8MB, time=25.33 memory used=1130.7MB, alloc=374.8MB, time=25.64 memory used=1168.0MB, alloc=374.8MB, time=25.90 memory used=1201.0MB, alloc=374.8MB, time=26.14 memory used=1235.2MB, alloc=374.8MB, time=26.38 memory used=1270.9MB, alloc=374.8MB, time=26.62 memory used=1308.5MB, alloc=374.8MB, time=26.86 memory used=1349.2MB, alloc=374.8MB, time=27.13 memory used=1414.6MB, alloc=374.8MB, time=29.38 memory used=1475.0MB, alloc=374.8MB, time=29.71 memory used=1532.6MB, alloc=374.8MB, time=30.03 memory used=1586.0MB, alloc=374.8MB, time=30.33 memory used=1619.9MB, alloc=374.8MB, time=30.56 memory used=1652.4MB, alloc=374.8MB, time=30.80 memory used=1686.1MB, alloc=374.8MB, time=31.04 memory used=1721.6MB, alloc=374.8MB, time=31.27 memory used=1759.0MB, alloc=374.8MB, time=31.52 memory used=1800.6MB, alloc=374.8MB, time=32.00 memory used=1856.2MB, alloc=374.8MB, time=32.85 memory used=1895.4MB, alloc=374.8MB, time=33.06 memory used=1935.6MB, alloc=374.8MB, time=33.26 memory used=1976.2MB, alloc=374.8MB, time=33.48 memory used=2017.6MB, alloc=374.8MB, time=33.69 memory used=2059.5MB, alloc=374.8MB, time=33.91 memory used=2102.8MB, alloc=374.8MB, time=34.13 memory used=2146.9MB, alloc=374.8MB, time=34.33 memory used=2191.8MB, alloc=374.8MB, time=34.56 memory used=2237.4MB, alloc=374.8MB, time=34.78 memory used=2284.3MB, alloc=398.8MB, time=48.85 memory used=2334.8MB, alloc=422.8MB, time=139.83 memory used=2395.1MB, alloc=446.8MB, time=140.17 memory used=2455.2MB, alloc=470.8MB, time=140.51 memory used=2525.6MB, alloc=470.8MB, time=140.87 memory used=2600.6MB, alloc=470.8MB, time=141.25 memory used=2675.6MB, alloc=470.8MB, time=141.62 memory used=2744.5MB, alloc=470.8MB, time=141.96 memory used=2813.3MB, alloc=470.8MB, time=142.31 memory used=2882.1MB, alloc=470.8MB, time=142.65 memory used=2951.0MB, alloc=470.8MB, time=143.01 memory used=3019.8MB, alloc=470.8MB, time=143.39 memory used=3088.8MB, alloc=470.8MB, time=143.75 memory used=3157.9MB, alloc=470.8MB, time=144.09 memory used=3226.8MB, alloc=470.8MB, time=144.44 memory used=3295.9MB, alloc=470.8MB, time=144.79 memory used=3364.8MB, alloc=470.8MB, time=145.16 memory used=3433.9MB, alloc=470.8MB, time=145.50 memory used=3502.9MB, alloc=470.8MB, time=145.86 memory used=3572.0MB, alloc=470.8MB, time=146.20 memory used=3641.1MB, alloc=470.8MB, time=146.54 memory used=3710.1MB, alloc=470.8MB, time=146.88 memory used=3779.2MB, alloc=470.8MB, time=147.22 memory used=3848.2MB, alloc=470.8MB, time=147.58 memory used=3917.0MB, alloc=470.8MB, time=147.92 memory used=3985.6MB, alloc=470.8MB, time=148.26 memory used=4054.7MB, alloc=470.8MB, time=148.63 memory used=4124.0MB, alloc=470.8MB, time=149.00 memory used=4193.3MB, alloc=470.8MB, time=149.35 memory used=4262.6MB, alloc=470.8MB, time=149.71 memory used=4331.8MB, alloc=470.8MB, time=150.06 memory used=4400.9MB, alloc=470.8MB, time=150.42 memory used=4470.0MB, alloc=470.8MB, time=150.76 memory used=4539.0MB, alloc=470.8MB, time=151.08 memory used=4608.0MB, alloc=470.8MB, time=151.44 memory used=4676.8MB, alloc=470.8MB, time=151.78 memory used=4745.9MB, alloc=470.8MB, time=152.15 memory used=4821.5MB, alloc=470.8MB, time=152.53 memory used=4897.0MB, alloc=470.8MB, time=152.87 memory used=4972.3MB, alloc=470.8MB, time=153.25 memory used=5047.6MB, alloc=470.8MB, time=153.61 memory used=5122.8MB, alloc=470.8MB, time=153.99 memory used=5197.8MB, alloc=470.8MB, time=154.35 memory used=5272.7MB, alloc=470.8MB, time=154.70 memory used=5347.5MB, alloc=470.8MB, time=155.05 memory used=5422.2MB, alloc=470.8MB, time=155.42 memory used=5496.7MB, alloc=470.8MB, time=155.76 memory used=5571.1MB, alloc=470.8MB, time=156.13 memory used=5645.3MB, alloc=470.8MB, time=156.46 memory used=5719.6MB, alloc=470.8MB, time=156.84 memory used=5800.2MB, alloc=470.8MB, time=157.20 memory used=5880.7MB, alloc=470.8MB, time=157.59 memory used=5960.9MB, alloc=470.8MB, time=157.97 memory used=6040.9MB, alloc=470.8MB, time=158.32 memory used=6120.8MB, alloc=470.8MB, time=158.67 memory used=6200.4MB, alloc=470.8MB, time=159.06 memory used=6279.8MB, alloc=470.8MB, time=159.40 memory used=6358.9MB, alloc=470.8MB, time=159.79 memory used=6437.8MB, alloc=470.8MB, time=160.14 memory used=6516.8MB, alloc=470.8MB, time=160.50 memory used=6601.7MB, alloc=470.8MB, time=160.89 memory used=6686.4MB, alloc=470.8MB, time=161.28 memory used=6770.8MB, alloc=470.8MB, time=161.68 memory used=6854.9MB, alloc=470.8MB, time=162.08 memory used=6938.6MB, alloc=470.8MB, time=162.47 memory used=7022.0MB, alloc=470.8MB, time=162.87 memory used=7105.1MB, alloc=470.8MB, time=163.22 memory used=7188.1MB, alloc=470.8MB, time=163.59 memory used=7276.8MB, alloc=470.8MB, time=163.99 memory used=7365.1MB, alloc=470.8MB, time=164.39 memory used=7453.0MB, alloc=470.8MB, time=164.80 memory used=7540.5MB, alloc=470.8MB, time=165.16 memory used=7627.5MB, alloc=470.8MB, time=165.55 memory used=7714.0MB, alloc=470.8MB, time=165.91 memory used=7800.3MB, alloc=470.8MB, time=166.31 memory used=7892.1MB, alloc=470.8MB, time=166.68 memory used=7983.3MB, alloc=470.8MB, time=167.07 memory used=8074.0MB, alloc=470.8MB, time=167.44 memory used=8164.0MB, alloc=470.8MB, time=167.79 memory used=8253.7MB, alloc=470.8MB, time=168.17 memory used=8348.6MB, alloc=470.8MB, time=168.54 memory used=8442.7MB, alloc=470.8MB, time=168.94 memory used=8536.1MB, alloc=470.8MB, time=169.33 memory used=8628.8MB, alloc=470.8MB, time=169.70 memory used=8721.1MB, alloc=470.8MB, time=170.10 memory used=8818.0MB, alloc=470.8MB, time=170.51 memory used=8914.1MB, alloc=470.8MB, time=170.91 memory used=9009.3MB, alloc=470.8MB, time=171.28 memory used=9103.9MB, alloc=470.8MB, time=171.65 memory used=9202.8MB, alloc=470.8MB, time=172.03 memory used=9300.6MB, alloc=470.8MB, time=172.43 memory used=9397.7MB, alloc=470.8MB, time=172.81 memory used=9498.7MB, alloc=470.8MB, time=173.18 memory used=9598.6MB, alloc=470.8MB, time=173.56 memory used=9697.4MB, alloc=470.8MB, time=173.97 memory used=9799.8MB, alloc=470.8MB, time=174.38 memory used=9901.1MB, alloc=470.8MB, time=174.79 memory used=10005.6MB, alloc=470.8MB, time=175.17 memory used=10108.7MB, alloc=470.8MB, time=175.56 memory used=10214.8MB, alloc=470.8MB, time=175.95 memory used=10319.3MB, alloc=470.8MB, time=176.34 memory used=10426.3MB, alloc=470.8MB, time=176.76 memory used=10531.4MB, alloc=470.8MB, time=177.18 memory used=10638.8MB, alloc=470.8MB, time=177.60 memory used=10748.2MB, alloc=470.8MB, time=178.03 memory used=10859.3MB, alloc=470.8MB, time=178.46 memory used=10971.6MB, alloc=470.8MB, time=178.86 memory used=11084.8MB, alloc=470.8MB, time=179.25 memory used=11198.5MB, alloc=470.8MB, time=179.68 memory used=11312.2MB, alloc=470.8MB, time=180.12 memory used=11425.6MB, alloc=470.8MB, time=180.55 memory used=11541.4MB, alloc=470.8MB, time=180.99 memory used=11658.7MB, alloc=470.8MB, time=181.40 memory used=11776.4MB, alloc=470.8MB, time=181.80 memory used=11896.3MB, alloc=470.8MB, time=182.24 memory used=12017.6MB, alloc=470.8MB, time=182.64 memory used=12140.0MB, alloc=470.8MB, time=183.05 memory used=12263.6MB, alloc=470.8MB, time=183.46 memory used=12388.3MB, alloc=470.8MB, time=183.87 memory used=12513.9MB, alloc=470.8MB, time=184.27 |\^/| 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(); 1428282532 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 4 2 2 F := [-13 x z + 10 y z - 5 z + 13, 19 x + 7 x y z - x z - 10 x, 3 2 2 5 x y - 3 x y z - 8 x + 3 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 2 2 G := [8 y z + 4 y z + 16 y + 8 z, 11 x + 3 x z - 8 x y z - 17 x y z , 3 2 2 3 2 14 x z - x y - 11 x y + 10 z ] > Problem := [F,G]; 3 2 3 4 2 2 Problem := [[-13 x z + 10 y z - 5 z + 13, 19 x + 7 x y z - x z - 10 x, 3 2 2 3 2 5 x y - 3 x y z - 8 x + 3 x], [8 y z + 4 y z + 16 y + 8 z, 4 3 2 2 3 2 2 3 2 11 x + 3 x z - 8 x y z - 17 x y z , 14 x z - x y - 11 x y + 10 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=27.8MB, alloc=36.6MB, time=0.85 memory used=44.1MB, alloc=36.6MB, time=0.96 memory used=60.6MB, alloc=36.6MB, time=1.21 memory used=73.7MB, alloc=36.6MB, time=1.30 memory used=96.3MB, alloc=38.0MB, time=2.26 memory used=109.5MB, alloc=38.0MB, time=2.33 memory used=121.3MB, alloc=38.0MB, time=2.39 memory used=135.9MB, alloc=38.0MB, time=2.46 memory used=146.9MB, alloc=38.0MB, time=2.52 memory used=155.9MB, alloc=38.0MB, time=2.57 memory used=165.9MB, alloc=38.0MB, time=2.62 memory used=176.7MB, alloc=38.0MB, time=2.68 memory used=189.0MB, alloc=38.0MB, time=2.73 memory used=204.3MB, alloc=38.0MB, time=2.84 memory used=228.8MB, alloc=38.0MB, time=3.32 memory used=258.8MB, alloc=38.0MB, time=4.06 memory used=287.2MB, alloc=38.0MB, time=4.74 memory used=309.0MB, alloc=62.0MB, time=5.58 memory used=351.3MB, alloc=64.9MB, time=5.79 memory used=383.1MB, alloc=64.9MB, time=5.94 memory used=406.2MB, alloc=64.9MB, time=6.07 memory used=454.9MB, alloc=64.9MB, time=7.51 memory used=497.0MB, alloc=64.9MB, time=7.72 memory used=527.1MB, alloc=64.9MB, time=7.86 memory used=551.8MB, alloc=64.9MB, time=8.00 memory used=579.5MB, alloc=64.9MB, time=8.13 memory used=623.8MB, alloc=64.9MB, time=8.82 memory used=664.5MB, alloc=64.9MB, time=9.93 memory used=690.6MB, alloc=64.9MB, time=10.06 memory used=715.8MB, alloc=64.9MB, time=10.18 memory used=746.4MB, alloc=64.9MB, time=10.33 memory used=774.8MB, alloc=64.9MB, time=10.45 memory used=793.8MB, alloc=64.9MB, time=10.55 memory used=814.6MB, alloc=64.9MB, time=10.65 memory used=836.4MB, alloc=64.9MB, time=10.75 memory used=860.2MB, alloc=64.9MB, time=10.85 memory used=884.9MB, alloc=64.9MB, time=10.95 memory used=911.4MB, alloc=64.9MB, time=11.06 memory used=939.7MB, alloc=64.9MB, time=11.17 memory used=970.0MB, alloc=64.9MB, time=11.29 memory used=1003.5MB, alloc=64.9MB, time=11.41 memory used=1042.2MB, alloc=83.8MB, time=11.57 memory used=1054.5MB, alloc=83.8MB, time=11.65 memory used=1067.0MB, alloc=83.8MB, time=11.72 memory used=1079.4MB, alloc=83.8MB, time=11.80 memory used=1091.9MB, alloc=83.8MB, time=11.88 memory used=1105.1MB, alloc=83.8MB, time=11.95 memory used=1118.4MB, alloc=83.8MB, time=12.03 memory used=1132.8MB, alloc=83.8MB, time=12.12 memory used=1147.0MB, alloc=83.8MB, time=12.20 memory used=1162.2MB, alloc=83.8MB, time=12.28 memory used=1177.3MB, alloc=83.8MB, time=12.36 memory used=1192.9MB, alloc=83.8MB, time=12.44 memory used=1209.2MB, alloc=83.8MB, time=12.52 memory used=1226.0MB, alloc=83.8MB, time=12.60 memory used=1243.8MB, alloc=83.8MB, time=12.68 memory used=1262.1MB, alloc=83.8MB, time=12.76 memory used=1281.4MB, alloc=83.8MB, time=12.84 memory used=1302.2MB, alloc=83.8MB, time=12.94 memory used=1360.3MB, alloc=83.8MB, time=13.95 memory used=1402.2MB, alloc=83.8MB, time=14.28 memory used=1437.1MB, alloc=83.8MB, time=20.48 memory used=1461.6MB, alloc=83.8MB, time=41.18 memory used=1757.6MB, alloc=107.8MB, time=45.98 memory used=1914.8MB, alloc=363.8MB, time=50.12 memory used=2179.9MB, alloc=363.8MB, time=56.90 memory used=2476.1MB, alloc=363.8MB, time=69.74 memory used=2583.0MB, alloc=365.3MB, time=73.54 memory used=2584.5MB, alloc=366.7MB, time=73.62 memory used=2585.9MB, alloc=368.1MB, time=73.69 memory used=2587.3MB, alloc=369.6MB, time=73.75 memory used=2588.8MB, alloc=365.3MB, time=73.86 memory used=2636.6MB, alloc=363.8MB, time=74.28 memory used=2680.5MB, alloc=363.8MB, time=74.47 memory used=2714.7MB, alloc=363.8MB, time=74.63 memory used=2752.6MB, alloc=363.8MB, time=74.78 memory used=2800.4MB, alloc=363.8MB, time=74.94 memory used=2866.9MB, alloc=363.8MB, time=75.92 memory used=2910.7MB, alloc=363.8MB, time=76.12 memory used=3015.7MB, alloc=363.8MB, time=77.15 memory used=3082.0MB, alloc=363.8MB, time=77.35 memory used=3156.9MB, alloc=363.8MB, time=83.02 memory used=3217.6MB, alloc=363.8MB, time=84.55 memory used=3255.9MB, alloc=363.8MB, time=84.75 memory used=3291.2MB, alloc=363.8MB, time=84.93 memory used=3330.3MB, alloc=363.8MB, time=85.11 memory used=3374.1MB, alloc=363.8MB, time=85.32 memory used=3430.0MB, alloc=363.8MB, time=85.80 memory used=3505.7MB, alloc=363.8MB, time=86.55 memory used=3541.8MB, alloc=363.8MB, time=86.76 memory used=3578.1MB, alloc=363.8MB, time=86.96 memory used=3618.9MB, alloc=363.8MB, time=87.15 memory used=3664.9MB, alloc=363.8MB, time=87.35 memory used=3714.0MB, alloc=363.8MB, time=87.55 memory used=3764.0MB, alloc=363.8MB, time=88.38 memory used=3810.9MB, alloc=363.8MB, time=88.61 memory used=3845.6MB, alloc=363.8MB, time=88.81 memory used=3884.7MB, alloc=363.8MB, time=89.02 memory used=3928.7MB, alloc=363.8MB, time=89.22 memory used=3978.0MB, alloc=363.8MB, time=89.43 memory used=4018.9MB, alloc=363.8MB, time=89.61 |\^/| 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(); 1428282832 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 4 F := [6 x y z + 11 x y z + 2 y - 20 x y z, -11 x z - z + 6 x y - 11 x z, 3 2 4 y - 11 x + 9 x - 16] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 3 2 G := [-16 x y z - 17 x y + 5 x - 7 y, 10 x z + 13 x y z + 5 y - y z , 2 2 4 2 -11 x y + 16 z - 19 x y + 3 x y z] > Problem := [F,G]; 2 2 4 Problem := [[6 x y z + 11 x y z + 2 y - 20 x y z, 3 4 3 2 -11 x z - z + 6 x y - 11 x z, 4 y - 11 x + 9 x - 16], [ 2 2 2 2 2 2 3 2 -16 x y z - 17 x y + 5 x - 7 y, 10 x z + 13 x y z + 5 y - y z , 2 2 4 2 -11 x y + 16 z - 19 x y + 3 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=25.5MB, alloc=32.3MB, time=0.80 memory used=45.4MB, alloc=32.3MB, time=1.04 memory used=69.9MB, alloc=36.3MB, time=1.57 memory used=83.8MB, alloc=36.3MB, time=1.94 memory used=98.5MB, alloc=37.0MB, time=2.13 memory used=111.1MB, alloc=37.0MB, time=2.20 memory used=121.8MB, alloc=37.0MB, time=2.26 memory used=130.7MB, alloc=37.0MB, time=2.31 memory used=140.7MB, alloc=37.0MB, time=2.38 memory used=152.0MB, alloc=37.0MB, time=2.44 memory used=164.5MB, alloc=37.0MB, time=2.50 memory used=178.4MB, alloc=37.0MB, time=2.56 memory used=188.3MB, alloc=61.0MB, time=2.64 memory used=209.6MB, alloc=61.0MB, time=2.72 memory used=233.5MB, alloc=61.0MB, time=2.81 memory used=260.8MB, alloc=61.0MB, time=2.90 memory used=293.1MB, alloc=61.0MB, time=3.00 memory used=337.9MB, alloc=67.6MB, time=3.68 memory used=367.7MB, alloc=67.6MB, time=4.02 memory used=399.4MB, alloc=67.6MB, time=4.17 memory used=447.9MB, alloc=80.1MB, time=4.92 memory used=472.1MB, alloc=81.9MB, time=5.03 memory used=498.7MB, alloc=81.9MB, time=5.14 memory used=527.8MB, alloc=81.9MB, time=5.24 memory used=559.4MB, alloc=81.9MB, time=5.34 memory used=593.8MB, alloc=81.9MB, time=5.44 memory used=641.6MB, alloc=81.9MB, time=6.67 memory used=669.8MB, alloc=81.9MB, time=6.80 memory used=696.4MB, alloc=81.9MB, time=6.92 memory used=729.7MB, alloc=81.9MB, time=7.05 memory used=750.4MB, alloc=81.9MB, time=7.15 memory used=773.3MB, alloc=81.9MB, time=7.24 memory used=799.1MB, alloc=81.9MB, time=7.33 memory used=829.2MB, alloc=81.9MB, time=7.44 memory used=884.0MB, alloc=81.9MB, time=8.41 memory used=927.7MB, alloc=81.9MB, time=9.30 memory used=961.5MB, alloc=81.9MB, time=9.64 memory used=997.3MB, alloc=81.9MB, time=9.95 memory used=1032.0MB, alloc=81.9MB, time=10.27 memory used=1078.5MB, alloc=81.9MB, time=14.47 memory used=1106.0MB, alloc=81.9MB, time=14.61 memory used=1131.4MB, alloc=81.9MB, time=14.73 memory used=1152.4MB, alloc=81.9MB, time=14.84 memory used=1177.6MB, alloc=81.9MB, time=14.96 memory used=1208.7MB, alloc=81.9MB, time=15.27 memory used=1242.4MB, alloc=81.9MB, time=15.58 memory used=1283.3MB, alloc=81.9MB, time=19.75 memory used=1317.8MB, alloc=81.9MB, time=20.02 memory used=1344.9MB, alloc=81.9MB, time=20.14 memory used=1364.9MB, alloc=81.9MB, time=20.26 memory used=1389.9MB, alloc=81.9MB, time=20.37 memory used=1417.5MB, alloc=81.9MB, time=20.67 memory used=1452.5MB, alloc=81.9MB, time=21.45 memory used=1484.7MB, alloc=81.9MB, time=22.36 memory used=1506.6MB, alloc=81.9MB, time=22.48 memory used=1549.9MB, alloc=81.9MB, time=23.27 memory used=1585.4MB, alloc=81.9MB, time=23.94 memory used=1613.0MB, alloc=81.9MB, time=24.62 memory used=1637.6MB, alloc=105.9MB, time=25.19 memory used=1681.6MB, alloc=105.9MB, time=25.95 memory used=1712.7MB, alloc=105.9MB, time=26.14 memory used=1753.8MB, alloc=105.9MB, time=26.36 memory used=1782.8MB, alloc=105.9MB, time=26.54 memory used=1810.7MB, alloc=105.9MB, time=26.70 memory used=1841.8MB, alloc=105.9MB, time=26.87 memory used=1876.0MB, alloc=105.9MB, time=27.05 memory used=1913.8MB, alloc=105.9MB, time=27.24 memory used=1956.7MB, alloc=105.9MB, time=27.43 memory used=1986.9MB, alloc=105.9MB, time=27.58 memory used=2011.4MB, alloc=105.9MB, time=27.71 memory used=2038.2MB, alloc=105.9MB, time=27.84 memory used=2066.5MB, alloc=105.9MB, time=27.98 memory used=2119.6MB, alloc=105.9MB, time=28.97 memory used=2151.5MB, alloc=105.9MB, time=29.18 memory used=2191.8MB, alloc=105.9MB, time=29.39 memory used=2223.1MB, alloc=105.9MB, time=29.56 memory used=2250.0MB, alloc=105.9MB, time=29.73 memory used=2281.0MB, alloc=105.9MB, time=29.90 memory used=2315.1MB, alloc=105.9MB, time=30.07 memory used=2352.7MB, alloc=105.9MB, time=30.25 memory used=2395.7MB, alloc=105.9MB, time=30.44 memory used=2427.8MB, alloc=105.9MB, time=30.59 memory used=2452.8MB, alloc=105.9MB, time=30.72 memory used=2479.5MB, alloc=105.9MB, time=30.84 memory used=2508.2MB, alloc=105.9MB, time=30.96 memory used=2549.7MB, alloc=105.9MB, time=31.55 memory used=2591.4MB, alloc=107.8MB, time=31.84 memory used=2633.9MB, alloc=107.8MB, time=32.02 memory used=2678.6MB, alloc=107.8MB, time=37.88 memory used=2726.5MB, alloc=107.8MB, time=73.75 memory used=2774.0MB, alloc=107.8MB, time=118.94 memory used=2822.9MB, alloc=107.8MB, time=123.05 memory used=2857.7MB, alloc=107.8MB, time=123.37 memory used=2893.0MB, alloc=107.8MB, time=123.57 memory used=2917.9MB, alloc=107.8MB, time=123.75 memory used=2945.4MB, alloc=107.8MB, time=123.92 memory used=2976.5MB, alloc=107.8MB, time=124.12 memory used=3012.1MB, alloc=107.8MB, time=124.30 memory used=3050.5MB, alloc=107.8MB, time=124.49 memory used=3083.4MB, alloc=107.8MB, time=124.67 memory used=3105.2MB, alloc=107.8MB, time=124.81 memory used=3126.7MB, alloc=107.8MB, time=124.95 memory used=3150.1MB, alloc=107.8MB, time=125.09 memory used=3174.1MB, alloc=107.8MB, time=125.23 memory used=3198.6MB, alloc=107.8MB, time=125.37 memory used=3223.8MB, alloc=107.8MB, time=125.51 memory used=3249.5MB, alloc=131.8MB, time=125.68 memory used=3292.9MB, alloc=131.8MB, time=125.88 memory used=3340.5MB, alloc=131.8MB, time=126.07 memory used=3389.5MB, alloc=131.8MB, time=126.27 memory used=3442.5MB, alloc=131.8MB, time=126.49 memory used=3497.0MB, alloc=131.8MB, time=126.70 memory used=3555.5MB, alloc=131.8MB, time=126.92 memory used=3615.2MB, alloc=131.8MB, time=127.14 memory used=3684.3MB, alloc=131.8MB, time=127.39 memory used=3698.3MB, alloc=131.8MB, time=127.51 memory used=3709.8MB, alloc=131.8MB, time=127.61 memory used=3720.3MB, alloc=131.8MB, time=127.72 memory used=3728.9MB, alloc=131.8MB, time=127.84 memory used=3737.6MB, alloc=131.8MB, time=127.95 memory used=3746.2MB, alloc=131.8MB, time=128.04 memory used=3754.8MB, alloc=131.8MB, time=128.15 memory used=3763.5MB, alloc=131.8MB, time=128.28 memory used=3772.2MB, alloc=131.8MB, time=128.38 memory used=3780.9MB, alloc=131.8MB, time=128.48 memory used=3789.6MB, alloc=131.8MB, time=128.59 memory used=3798.5MB, alloc=131.8MB, time=128.69 memory used=3809.9MB, alloc=131.8MB, time=128.80 memory used=3819.0MB, alloc=131.8MB, time=128.90 memory used=3830.3MB, alloc=131.8MB, time=129.02 memory used=3842.0MB, alloc=131.8MB, time=129.14 memory used=3853.7MB, alloc=131.8MB, time=129.25 memory used=3865.4MB, alloc=131.8MB, time=129.36 memory used=3877.1MB, alloc=131.8MB, time=129.47 memory used=3888.9MB, alloc=131.8MB, time=129.58 memory used=3900.6MB, alloc=131.8MB, time=129.69 memory used=3912.3MB, alloc=131.8MB, time=129.82 memory used=3924.1MB, alloc=131.8MB, time=129.93 memory used=3935.8MB, alloc=131.8MB, time=130.04 memory used=3947.6MB, alloc=131.8MB, time=130.15 memory used=3959.4MB, alloc=131.8MB, time=130.26 memory used=3971.1MB, alloc=131.8MB, time=130.37 memory used=3982.9MB, alloc=131.8MB, time=130.50 memory used=3994.7MB, alloc=131.8MB, time=130.63 memory used=4006.5MB, alloc=131.8MB, time=130.76 memory used=4018.3MB, alloc=131.8MB, time=130.87 memory used=4030.1MB, alloc=131.8MB, time=130.99 memory used=4041.8MB, alloc=131.8MB, time=131.10 memory used=4053.6MB, alloc=131.8MB, time=131.21 memory used=4065.4MB, alloc=131.8MB, time=131.34 memory used=4077.1MB, alloc=131.8MB, time=131.46 memory used=4088.9MB, alloc=131.8MB, time=131.56 memory used=4100.7MB, alloc=131.8MB, time=131.68 memory used=4112.4MB, alloc=131.8MB, time=131.79 memory used=4124.4MB, alloc=131.8MB, time=131.91 memory used=4138.8MB, alloc=131.8MB, time=132.03 memory used=4150.9MB, alloc=131.8MB, time=132.17 memory used=4165.2MB, alloc=131.8MB, time=132.28 memory used=4179.8MB, alloc=131.8MB, time=132.39 memory used=4194.4MB, alloc=131.8MB, time=132.52 memory used=4208.9MB, alloc=131.8MB, time=132.64 memory used=4223.4MB, alloc=131.8MB, time=132.75 memory used=4237.9MB, alloc=131.8MB, time=132.86 memory used=4252.4MB, alloc=131.8MB, time=132.98 memory used=4266.8MB, alloc=131.8MB, time=133.10 memory used=4281.2MB, alloc=131.8MB, time=133.24 memory used=4295.6MB, alloc=131.8MB, time=133.35 memory used=4309.9MB, alloc=131.8MB, time=133.46 memory used=4324.2MB, alloc=131.8MB, time=133.59 memory used=4338.4MB, alloc=131.8MB, time=133.72 memory used=4352.6MB, alloc=131.8MB, time=133.85 memory used=4367.0MB, alloc=131.8MB, time=133.98 memory used=4383.7MB, alloc=131.8MB, time=134.10 memory used=4400.5MB, alloc=131.8MB, time=134.25 memory used=4417.2MB, alloc=131.8MB, time=134.39 memory used=4433.9MB, alloc=131.8MB, time=134.52 memory used=4450.5MB, alloc=131.8MB, time=134.63 memory used=4467.0MB, alloc=131.8MB, time=134.80 memory used=4483.4MB, alloc=131.8MB, time=134.92 memory used=4499.7MB, alloc=131.8MB, time=135.04 memory used=4515.9MB, alloc=131.8MB, time=135.16 memory used=4532.3MB, alloc=131.8MB, time=135.28 memory used=4550.7MB, alloc=131.8MB, time=135.41 memory used=4569.2MB, alloc=131.8MB, time=135.55 memory used=4587.6MB, alloc=131.8MB, time=135.68 memory used=4605.8MB, alloc=131.8MB, time=135.79 memory used=4623.8MB, alloc=131.8MB, time=135.91 memory used=4641.7MB, alloc=131.8MB, time=136.03 memory used=4659.7MB, alloc=131.8MB, time=136.14 memory used=4679.4MB, alloc=131.8MB, time=136.27 memory used=4699.1MB, alloc=131.8MB, time=136.40 memory used=4718.6MB, alloc=131.8MB, time=136.53 memory used=4737.9MB, alloc=131.8MB, time=136.65 memory used=4757.3MB, alloc=131.8MB, time=136.81 memory used=4778.0MB, alloc=131.8MB, time=136.94 memory used=4798.8MB, alloc=131.8MB, time=137.06 memory used=4819.4MB, alloc=131.8MB, time=137.19 memory used=4839.5MB, alloc=131.8MB, time=137.31 memory used=4859.6MB, alloc=131.8MB, time=137.44 memory used=4878.6MB, alloc=131.8MB, time=137.57 memory used=4897.5MB, alloc=131.8MB, time=137.69 memory used=4917.1MB, alloc=131.8MB, time=137.81 memory used=4936.4MB, alloc=131.8MB, time=137.93 memory used=4957.2MB, alloc=131.8MB, time=138.07 memory used=4975.2MB, alloc=131.8MB, time=138.19 memory used=4990.4MB, alloc=131.8MB, time=138.31 memory used=5006.9MB, alloc=131.8MB, time=138.43 memory used=5023.3MB, alloc=131.8MB, time=138.54 memory used=5038.6MB, alloc=131.8MB, time=138.68 memory used=5055.6MB, alloc=131.8MB, time=138.80 memory used=5072.8MB, alloc=131.8MB, time=138.93 memory used=5090.6MB, alloc=131.8MB, time=139.04 memory used=5108.3MB, alloc=131.8MB, time=139.15 memory used=5127.4MB, alloc=131.8MB, time=139.29 memory used=5201.2MB, alloc=387.8MB, time=142.06 memory used=5258.5MB, alloc=387.8MB, time=142.33 memory used=5303.5MB, alloc=387.8MB, time=142.57 memory used=5348.0MB, alloc=387.8MB, time=142.81 memory used=5400.6MB, alloc=387.8MB, time=143.05 memory used=5462.6MB, alloc=387.8MB, time=143.29 memory used=5508.4MB, alloc=387.8MB, time=143.48 memory used=5547.7MB, alloc=387.8MB, time=143.65 memory used=5593.4MB, alloc=387.8MB, time=143.88 memory used=5658.5MB, alloc=387.8MB, time=144.70 memory used=5718.6MB, alloc=387.8MB, time=144.97 memory used=5758.1MB, alloc=387.8MB, time=145.21 memory used=5803.5MB, alloc=387.8MB, time=145.42 memory used=5856.9MB, alloc=387.8MB, time=145.67 memory used=5919.3MB, alloc=387.8MB, time=145.92 memory used=5960.8MB, alloc=387.8MB, time=146.10 memory used=5999.9MB, alloc=387.8MB, time=146.26 memory used=6055.5MB, alloc=387.8MB, time=149.34 memory used=6132.3MB, alloc=387.8MB, time=207.19 |\^/| 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(); 1428283132 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 2 F := [-9 x z - 15 x z - 5 x - 10 x, 5 x y + 8 x y - 19 y - 19 y z, 3 2 2 3 4 -9 x z - 16 x y + 12 x z + 20 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 4 G := [12 x y z + x y z + 12 x - 10 y, 20 x y - 8 x y - 16 z , 3 2 3 y z - 11 x z - 18 x z + 4 y] > Problem := [F,G]; 2 2 3 2 Problem := [[-9 x z - 15 x z - 5 x - 10 x, 2 2 2 2 3 2 2 3 4 5 x y + 8 x y - 19 y - 19 y z, -9 x z - 16 x y + 12 x z + 20 z ], [ 2 2 2 2 2 3 4 12 x y z + x y z + 12 x - 10 y, 20 x y - 8 x y - 16 z , 3 2 3 y z - 11 x z - 18 x z + 4 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.1MB, alloc=32.3MB, time=0.80 memory used=46.3MB, alloc=32.3MB, time=1.28 memory used=67.2MB, alloc=60.3MB, time=1.76 memory used=100.7MB, alloc=60.9MB, time=2.21 memory used=132.3MB, alloc=60.9MB, time=2.95 memory used=165.2MB, alloc=61.6MB, time=3.11 memory used=203.1MB, alloc=61.6MB, time=3.40 memory used=229.7MB, alloc=61.6MB, time=3.51 memory used=262.5MB, alloc=61.6MB, time=3.78 memory used=306.2MB, alloc=69.6MB, time=4.72 memory used=363.1MB, alloc=69.6MB, time=5.76 memory used=413.4MB, alloc=69.6MB, time=7.13 memory used=447.3MB, alloc=69.6MB, time=7.40 memory used=488.1MB, alloc=69.6MB, time=8.12 memory used=531.1MB, alloc=69.6MB, time=9.04 memory used=582.2MB, alloc=69.6MB, time=9.87 memory used=606.1MB, alloc=69.6MB, time=10.05 memory used=649.4MB, alloc=93.6MB, time=10.48 memory used=732.0MB, alloc=93.6MB, time=11.32 memory used=782.6MB, alloc=93.6MB, time=12.14 memory used=815.6MB, alloc=93.6MB, time=12.25 memory used=852.8MB, alloc=93.6MB, time=12.35 memory used=888.8MB, alloc=93.6MB, time=12.46 memory used=915.4MB, alloc=93.6MB, time=12.54 memory used=945.7MB, alloc=93.6MB, time=12.63 memory used=981.3MB, alloc=93.6MB, time=12.72 memory used=1029.4MB, alloc=93.6MB, time=12.96 memory used=1063.6MB, alloc=93.6MB, time=13.07 memory used=1102.2MB, alloc=93.6MB, time=13.18 memory used=1130.4MB, alloc=93.6MB, time=13.27 memory used=1184.9MB, alloc=93.6MB, time=13.72 memory used=1252.3MB, alloc=93.6MB, time=14.58 memory used=1314.5MB, alloc=93.6MB, time=15.32 memory used=1370.9MB, alloc=93.6MB, time=16.19 memory used=1398.6MB, alloc=93.6MB, time=16.30 memory used=1455.3MB, alloc=117.6MB, time=16.95 memory used=1526.3MB, alloc=117.6MB, time=17.56 memory used=1581.1MB, alloc=117.6MB, time=17.76 memory used=1624.2MB, alloc=117.6MB, time=17.89 memory used=1680.1MB, alloc=117.6MB, time=18.13 memory used=1724.7MB, alloc=117.6MB, time=18.27 memory used=1779.5MB, alloc=117.6MB, time=18.57 memory used=1833.2MB, alloc=117.6MB, time=18.92 memory used=1887.4MB, alloc=117.6MB, time=19.11 memory used=1926.6MB, alloc=117.6MB, time=19.24 memory used=2001.7MB, alloc=122.9MB, time=20.02 memory used=2061.5MB, alloc=122.9MB, time=20.22 memory used=2095.6MB, alloc=122.9MB, time=20.38 memory used=2131.8MB, alloc=122.9MB, time=20.55 memory used=2173.0MB, alloc=122.9MB, time=20.71 memory used=2218.8MB, alloc=122.9MB, time=20.89 memory used=2269.1MB, alloc=122.9MB, time=21.05 memory used=2323.6MB, alloc=122.9MB, time=21.22 memory used=2365.3MB, alloc=122.9MB, time=21.37 memory used=2395.0MB, alloc=122.9MB, time=21.52 memory used=2426.1MB, alloc=122.9MB, time=21.66 memory used=2457.7MB, alloc=122.9MB, time=21.79 memory used=2490.9MB, alloc=122.9MB, time=21.91 memory used=2526.9MB, alloc=122.9MB, time=22.05 memory used=2564.9MB, alloc=122.9MB, time=22.19 memory used=2604.8MB, alloc=122.9MB, time=22.32 memory used=2646.3MB, alloc=122.9MB, time=22.46 memory used=2689.5MB, alloc=122.9MB, time=22.60 memory used=2735.3MB, alloc=122.9MB, time=22.75 memory used=2784.4MB, alloc=122.9MB, time=22.89 memory used=2837.3MB, alloc=122.9MB, time=23.03 memory used=2877.6MB, alloc=122.9MB, time=23.15 memory used=2941.5MB, alloc=122.9MB, time=23.89 memory used=3004.4MB, alloc=122.9MB, time=24.12 memory used=3045.4MB, alloc=122.9MB, time=24.29 memory used=3080.6MB, alloc=122.9MB, time=24.45 memory used=3120.8MB, alloc=122.9MB, time=24.61 memory used=3164.3MB, alloc=122.9MB, time=24.77 memory used=3213.5MB, alloc=122.9MB, time=24.94 memory used=3267.5MB, alloc=122.9MB, time=25.11 memory used=3316.7MB, alloc=122.9MB, time=25.27 memory used=3346.9MB, alloc=122.9MB, time=25.41 memory used=3377.0MB, alloc=122.9MB, time=25.55 memory used=3408.5MB, alloc=122.9MB, time=25.70 memory used=3441.9MB, alloc=122.9MB, time=25.84 memory used=3477.7MB, alloc=122.9MB, time=25.98 memory used=3514.2MB, alloc=122.9MB, time=26.11 memory used=3553.7MB, alloc=122.9MB, time=26.26 memory used=3595.5MB, alloc=122.9MB, time=26.40 memory used=3638.6MB, alloc=122.9MB, time=26.54 memory used=3684.6MB, alloc=122.9MB, time=26.67 memory used=3733.4MB, alloc=122.9MB, time=26.81 memory used=3785.9MB, alloc=122.9MB, time=26.94 memory used=3831.4MB, alloc=122.9MB, time=27.05 memory used=3893.6MB, alloc=122.9MB, time=40.67 memory used=3964.6MB, alloc=146.9MB, time=77.82 memory used=4204.4MB, alloc=146.9MB, time=86.70 memory used=4219.5MB, alloc=402.9MB, time=87.25 memory used=4286.9MB, alloc=402.9MB, time=87.53 memory used=4350.8MB, alloc=402.9MB, time=87.75 memory used=4411.9MB, alloc=402.9MB, time=87.95 memory used=4458.3MB, alloc=402.9MB, time=88.12 memory used=4509.5MB, alloc=402.9MB, time=88.30 memory used=4565.6MB, alloc=402.9MB, time=88.49 memory used=4627.8MB, alloc=402.9MB, time=88.69 memory used=4696.4MB, alloc=402.9MB, time=88.89 memory used=4771.1MB, alloc=402.9MB, time=89.08 memory used=4828.1MB, alloc=402.9MB, time=89.25 memory used=4869.4MB, alloc=402.9MB, time=89.39 memory used=4911.2MB, alloc=402.9MB, time=89.52 memory used=4955.0MB, alloc=402.9MB, time=89.66 memory used=5000.9MB, alloc=402.9MB, time=89.80 memory used=5048.6MB, alloc=402.9MB, time=89.94 memory used=5098.1MB, alloc=402.9MB, time=90.08 memory used=5149.2MB, alloc=402.9MB, time=90.23 memory used=5203.5MB, alloc=402.9MB, time=90.37 memory used=5260.7MB, alloc=402.9MB, time=90.52 memory used=5320.3MB, alloc=402.9MB, time=90.67 memory used=5382.0MB, alloc=402.9MB, time=90.81 memory used=5446.7MB, alloc=402.9MB, time=90.97 memory used=5515.0MB, alloc=402.9MB, time=91.12 memory used=5586.9MB, alloc=402.9MB, time=91.28 memory used=5793.9MB, alloc=402.9MB, time=92.24 memory used=5888.5MB, alloc=402.9MB, time=92.57 memory used=5947.0MB, alloc=402.9MB, time=92.80 memory used=5999.3MB, alloc=402.9MB, time=93.00 memory used=6060.3MB, alloc=402.9MB, time=93.22 memory used=6130.3MB, alloc=402.9MB, time=93.44 memory used=6204.2MB, alloc=402.9MB, time=93.66 memory used=6249.2MB, alloc=402.9MB, time=93.84 memory used=6293.0MB, alloc=402.9MB, time=94.01 memory used=6339.7MB, alloc=402.9MB, time=94.18 memory used=6390.9MB, alloc=402.9MB, time=94.37 memory used=6444.6MB, alloc=402.9MB, time=94.55 memory used=6502.2MB, alloc=402.9MB, time=94.73 memory used=6565.0MB, alloc=402.9MB, time=94.92 memory used=6632.2MB, alloc=402.9MB, time=95.11 memory used=6706.7MB, alloc=402.9MB, time=95.29 memory used=6768.2MB, alloc=402.9MB, time=96.00 memory used=6862.0MB, alloc=402.9MB, time=96.32 memory used=6920.1MB, alloc=402.9MB, time=96.57 memory used=6974.5MB, alloc=402.9MB, time=96.79 memory used=7036.3MB, alloc=402.9MB, time=97.01 memory used=7107.1MB, alloc=402.9MB, time=97.22 memory used=7180.0MB, alloc=402.9MB, time=97.45 memory used=7223.2MB, alloc=402.9MB, time=97.64 memory used=7268.5MB, alloc=402.9MB, time=97.81 memory used=7317.7MB, alloc=402.9MB, time=97.98 memory used=7369.3MB, alloc=402.9MB, time=98.15 memory used=7425.3MB, alloc=402.9MB, time=98.33 memory used=7485.0MB, alloc=402.9MB, time=98.53 memory used=7549.8MB, alloc=402.9MB, time=98.72 memory used=7620.0MB, alloc=402.9MB, time=98.90 memory used=7692.8MB, alloc=402.9MB, time=99.08 memory used=7768.8MB, alloc=402.9MB, time=113.08 memory used=7857.1MB, alloc=402.9MB, time=157.26 memory used=8140.9MB, alloc=402.9MB, time=161.87 memory used=8195.5MB, alloc=402.9MB, time=162.07 memory used=8265.9MB, alloc=402.9MB, time=162.28 memory used=8314.7MB, alloc=402.9MB, time=162.47 memory used=8361.5MB, alloc=402.9MB, time=162.64 memory used=8414.4MB, alloc=402.9MB, time=162.82 memory used=8472.0MB, alloc=402.9MB, time=163.00 memory used=8534.4MB, alloc=402.9MB, time=163.19 memory used=8602.9MB, alloc=402.9MB, time=163.38 memory used=8677.4MB, alloc=402.9MB, time=163.58 memory used=8727.7MB, alloc=402.9MB, time=163.74 memory used=8767.7MB, alloc=402.9MB, time=163.89 memory used=8810.2MB, alloc=402.9MB, time=164.04 memory used=8854.8MB, alloc=402.9MB, time=164.18 memory used=8899.6MB, alloc=402.9MB, time=164.33 memory used=8946.4MB, alloc=402.9MB, time=164.47 memory used=8995.1MB, alloc=402.9MB, time=164.62 memory used=9047.2MB, alloc=402.9MB, time=164.77 memory used=9100.8MB, alloc=402.9MB, time=164.92 memory used=9157.4MB, alloc=402.9MB, time=165.07 memory used=9215.1MB, alloc=402.9MB, time=165.23 memory used=9276.7MB, alloc=402.9MB, time=165.38 memory used=9340.1MB, alloc=402.9MB, time=165.53 memory used=9407.7MB, alloc=402.9MB, time=165.69 memory used=9478.2MB, alloc=402.9MB, time=165.85 memory used=9568.6MB, alloc=402.9MB, time=166.03 memory used=9823.5MB, alloc=402.9MB, time=167.43 memory used=9972.1MB, alloc=402.9MB, time=169.37 memory used=10114.9MB, alloc=402.9MB, time=170.70 memory used=10235.8MB, alloc=402.9MB, time=172.21 memory used=10290.0MB, alloc=402.9MB, time=172.39 memory used=10390.1MB, alloc=402.9MB, time=173.54 memory used=10470.7MB, alloc=402.9MB, time=174.03 memory used=10571.4MB, alloc=402.9MB, time=175.06 memory used=10683.9MB, alloc=426.9MB, time=176.46 memory used=10805.5MB, alloc=426.9MB, time=177.92 memory used=10876.3MB, alloc=426.9MB, time=178.25 memory used=10944.1MB, alloc=426.9MB, time=178.58 memory used=11011.7MB, alloc=426.9MB, time=178.91 memory used=11098.3MB, alloc=426.9MB, time=179.71 memory used=11153.6MB, alloc=426.9MB, time=179.98 memory used=11222.3MB, alloc=426.9MB, time=180.26 memory used=11273.8MB, alloc=426.9MB, time=180.50 memory used=11321.5MB, alloc=426.9MB, time=180.77 memory used=11374.8MB, alloc=426.9MB, time=181.01 memory used=11435.4MB, alloc=426.9MB, time=181.25 memory used=11504.1MB, alloc=426.9MB, time=181.49 memory used=11568.3MB, alloc=426.9MB, time=181.72 memory used=11610.4MB, alloc=426.9MB, time=181.91 memory used=11656.6MB, alloc=426.9MB, time=182.13 memory used=11735.7MB, alloc=426.9MB, time=182.70 memory used=11791.0MB, alloc=426.9MB, time=182.97 memory used=11862.9MB, alloc=426.9MB, time=183.25 memory used=11907.0MB, alloc=426.9MB, time=183.48 memory used=11955.9MB, alloc=426.9MB, time=183.72 memory used=12010.9MB, alloc=426.9MB, time=183.95 memory used=12072.9MB, alloc=426.9MB, time=184.19 memory used=12144.0MB, alloc=426.9MB, time=184.43 memory used=12200.2MB, alloc=426.9MB, time=184.64 memory used=12243.0MB, alloc=426.9MB, time=184.83 memory used=12290.9MB, alloc=426.9MB, time=185.04 memory used=12367.0MB, alloc=426.9MB, time=186.02 memory used=12429.2MB, alloc=426.9MB, time=186.26 memory used=12478.3MB, alloc=426.9MB, time=186.49 memory used=12538.1MB, alloc=426.9MB, time=186.72 memory used=12608.6MB, alloc=426.9MB, time=186.97 memory used=12655.2MB, alloc=426.9MB, time=187.20 memory used=12700.7MB, alloc=426.9MB, time=187.39 memory used=12762.6MB, alloc=426.9MB, time=187.64 memory used=12851.0MB, alloc=426.9MB, time=188.52 memory used=12911.2MB, alloc=426.9MB, time=188.78 memory used=12964.9MB, alloc=426.9MB, time=189.01 memory used=13017.3MB, alloc=426.9MB, time=189.24 memory used=13080.7MB, alloc=426.9MB, time=189.47 memory used=13144.0MB, alloc=426.9MB, time=189.69 memory used=13186.3MB, alloc=426.9MB, time=189.88 memory used=13234.7MB, alloc=426.9MB, time=190.08 memory used=13299.6MB, alloc=426.9MB, time=190.56 memory used=13382.0MB, alloc=450.9MB, time=193.63 memory used=13490.0MB, alloc=450.9MB, time=194.05 memory used=13558.5MB, alloc=450.9MB, time=194.37 memory used=13618.6MB, alloc=450.9MB, time=194.67 memory used=13683.2MB, alloc=450.9MB, time=194.97 memory used=13753.8MB, alloc=450.9MB, time=195.27 memory used=13828.8MB, alloc=450.9MB, time=195.58 memory used=13912.4MB, alloc=450.9MB, time=195.90 memory used=14000.5MB, alloc=450.9MB, time=196.22 memory used=14092.8MB, alloc=450.9MB, time=196.53 memory used=14156.6MB, alloc=474.9MB, time=196.82 memory used=14217.9MB, alloc=474.9MB, time=197.11 memory used=14282.9MB, alloc=474.9MB, time=197.40 memory used=14350.4MB, alloc=474.9MB, time=197.68 memory used=14419.3MB, alloc=474.9MB, time=197.97 memory used=14489.5MB, alloc=474.9MB, time=198.26 memory used=14561.0MB, alloc=474.9MB, time=198.53 memory used=14634.2MB, alloc=474.9MB, time=198.82 memory used=14713.7MB, alloc=474.9MB, time=199.12 memory used=14794.9MB, alloc=474.9MB, time=199.41 memory used=14877.1MB, alloc=474.9MB, time=199.71 memory used=14961.2MB, alloc=474.9MB, time=200.00 memory used=15051.3MB, alloc=474.9MB, time=200.30 memory used=15143.0MB, alloc=474.9MB, time=200.61 memory used=15236.1MB, alloc=474.9MB, time=200.91 memory used=15335.6MB, alloc=474.9MB, time=201.21 memory used=15436.4MB, alloc=474.9MB, time=201.53 memory used=15544.4MB, alloc=474.9MB, time=201.84 memory used=15652.8MB, alloc=474.9MB, time=202.14 memory used=15762.5MB, alloc=474.9MB, time=202.47 memory used=15862.4MB, alloc=474.9MB, time=202.76 memory used=15933.8MB, alloc=474.9MB, time=203.01 memory used=15988.4MB, alloc=474.9MB, time=203.23 memory used=16042.5MB, alloc=474.9MB, time=203.48 memory used=16101.6MB, alloc=474.9MB, time=203.70 memory used=16161.5MB, alloc=474.9MB, time=203.93 memory used=16221.1MB, alloc=474.9MB, time=204.16 memory used=16280.5MB, alloc=474.9MB, time=204.38 memory used=16339.9MB, alloc=474.9MB, time=204.61 memory used=16405.3MB, alloc=474.9MB, time=204.84 memory used=16470.4MB, alloc=474.9MB, time=205.07 memory used=16535.1MB, alloc=474.9MB, time=205.29 memory used=16599.5MB, alloc=474.9MB, time=205.52 memory used=16669.5MB, alloc=474.9MB, time=205.75 memory used=16738.9MB, alloc=474.9MB, time=205.99 memory used=16807.8MB, alloc=474.9MB, time=206.23 memory used=16881.8MB, alloc=474.9MB, time=206.46 memory used=16955.0MB, alloc=474.9MB, time=206.70 memory used=17027.9MB, alloc=474.9MB, time=206.93 memory used=17104.0MB, alloc=474.9MB, time=207.16 memory used=17180.3MB, alloc=474.9MB, time=207.40 memory used=17259.3MB, alloc=474.9MB, time=207.63 memory used=17342.5MB, alloc=474.9MB, time=207.87 memory used=17425.0MB, alloc=474.9MB, time=208.10 memory used=17512.8MB, alloc=474.9MB, time=208.36 memory used=17599.9MB, alloc=474.9MB, time=208.60 memory used=17690.6MB, alloc=474.9MB, time=208.83 memory used=17783.6MB, alloc=474.9MB, time=209.07 memory used=17881.7MB, alloc=474.9MB, time=209.32 memory used=17982.4MB, alloc=474.9MB, time=209.56 memory used=18089.1MB, alloc=474.9MB, time=209.80 memory used=18202.7MB, alloc=474.9MB, time=210.25 memory used=18336.2MB, alloc=474.9MB, time=213.34 memory used=18442.3MB, alloc=474.9MB, time=213.75 memory used=18516.9MB, alloc=474.9MB, time=214.09 memory used=18599.1MB, alloc=474.9MB, time=214.44 memory used=18688.5MB, alloc=474.9MB, time=214.79 memory used=18788.8MB, alloc=474.9MB, time=215.14 memory used=18896.0MB, alloc=474.9MB, time=215.50 memory used=19012.0MB, alloc=474.9MB, time=215.86 memory used=19081.0MB, alloc=474.9MB, time=216.15 memory used=19141.0MB, alloc=474.9MB, time=216.42 memory used=19202.2MB, alloc=474.9MB, time=216.72 memory used=19270.1MB, alloc=474.9MB, time=216.99 memory used=19339.3MB, alloc=474.9MB, time=217.28 memory used=19409.8MB, alloc=474.9MB, time=217.56 memory used=19481.5MB, alloc=474.9MB, time=217.84 memory used=19554.7MB, alloc=474.9MB, time=218.13 memory used=19634.8MB, alloc=474.9MB, time=218.42 memory used=19716.2MB, alloc=474.9MB, time=218.70 memory used=19798.7MB, alloc=474.9MB, time=218.99 memory used=19882.8MB, alloc=474.9MB, time=219.29 memory used=19973.2MB, alloc=474.9MB, time=219.58 memory used=20065.0MB, alloc=474.9MB, time=219.89 memory used=20157.9MB, alloc=474.9MB, time=220.17 memory used=20258.0MB, alloc=474.9MB, time=220.46 memory used=20358.7MB, alloc=474.9MB, time=220.76 memory used=20461.0MB, alloc=474.9MB, time=221.05 memory used=20568.7MB, alloc=474.9MB, time=221.34 memory used=20677.4MB, alloc=474.9MB, time=221.64 memory used=20776.2MB, alloc=474.9MB, time=221.93 memory used=20844.5MB, alloc=474.9MB, time=222.16 memory used=20897.6MB, alloc=474.9MB, time=222.38 memory used=20951.7MB, alloc=474.9MB, time=222.61 memory used=21011.0MB, alloc=474.9MB, time=222.83 memory used=21070.8MB, alloc=474.9MB, time=223.05 memory used=21130.4MB, alloc=474.9MB, time=223.27 memory used=21189.8MB, alloc=474.9MB, time=223.50 memory used=21249.0MB, alloc=474.9MB, time=223.72 memory used=21309.0MB, alloc=474.9MB, time=223.94 memory used=21373.1MB, alloc=474.9MB, time=224.19 memory used=21437.8MB, alloc=474.9MB, time=224.42 memory used=21502.0MB, alloc=474.9MB, time=224.65 memory used=21566.8MB, alloc=474.9MB, time=224.88 memory used=21635.3MB, alloc=474.9MB, time=225.16 memory used=21704.1MB, alloc=474.9MB, time=225.40 memory used=21773.0MB, alloc=474.9MB, time=225.64 memory used=21845.5MB, alloc=474.9MB, time=225.86 memory used=21917.9MB, alloc=474.9MB, time=226.09 memory used=21994.9MB, alloc=474.9MB, time=226.31 memory used=22070.7MB, alloc=474.9MB, time=226.55 memory used=22150.5MB, alloc=474.9MB, time=226.78 memory used=22229.8MB, alloc=474.9MB, time=227.00 memory used=22311.1MB, alloc=474.9MB, time=227.23 memory used=22394.6MB, alloc=474.9MB, time=227.47 memory used=22481.3MB, alloc=474.9MB, time=227.70 memory used=22570.2MB, alloc=474.9MB, time=227.94 memory used=22662.6MB, alloc=474.9MB, time=228.18 memory used=22759.0MB, alloc=474.9MB, time=228.43 memory used=22858.0MB, alloc=474.9MB, time=228.68 memory used=22963.2MB, alloc=474.9MB, time=228.92 memory used=23092.7MB, alloc=474.9MB, time=234.90 |\^/| 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(); 1428283432 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 F := [-16 y z - 13 y z - 8 z - 16 z, 6 y z + 13 y z + 11 x, 2 3 -x y z - x y z - 3 z + 11 z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 3 G := [-4 x y - 10 x z - 13 x y z - 2 x, -2 x y - 11 x - 5 x y - 7 y , 2 4 3 20 x y z + 15 y + 10 y z + 6 z] > Problem := [F,G]; 2 2 3 2 2 2 2 Problem := [[-16 y z - 13 y z - 8 z - 16 z, 6 y z + 13 y z + 11 x, 2 3 2 2 2 -x y z - x y z - 3 z + 11 z], [-4 x y - 10 x z - 13 x y z - 2 x, 2 2 3 2 3 2 4 3 -2 x y - 11 x - 5 x y - 7 y , 20 x y z + 15 y + 10 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=4.4MB, alloc=32.3MB, time=0.18 memory used=25.1MB, alloc=32.3MB, time=0.49 memory used=44.4MB, alloc=56.3MB, time=0.78 memory used=87.0MB, alloc=60.3MB, time=1.30 memory used=130.1MB, alloc=68.3MB, time=1.83 memory used=160.5MB, alloc=68.3MB, time=2.03 memory used=202.8MB, alloc=68.3MB, time=2.60 memory used=244.5MB, alloc=92.3MB, time=3.21 memory used=315.3MB, alloc=92.3MB, time=4.31 memory used=360.4MB, alloc=92.3MB, time=4.48 memory used=429.2MB, alloc=92.3MB, time=5.35 memory used=471.1MB, alloc=92.3MB, time=5.58 memory used=515.1MB, alloc=92.3MB, time=5.82 memory used=562.1MB, alloc=92.3MB, time=6.17 memory used=636.1MB, alloc=92.4MB, time=8.26 memory used=668.6MB, alloc=92.4MB, time=8.37 memory used=695.2MB, alloc=92.4MB, time=8.48 memory used=753.9MB, alloc=92.4MB, time=9.14 memory used=815.4MB, alloc=116.4MB, time=10.08 memory used=888.1MB, alloc=116.4MB, time=10.77 memory used=951.8MB, alloc=116.4MB, time=12.30 memory used=1010.5MB, alloc=116.4MB, time=14.10 memory used=1048.7MB, alloc=116.4MB, time=14.25 memory used=1092.0MB, alloc=116.4MB, time=14.38 memory used=1129.9MB, alloc=116.4MB, time=14.50 memory used=1200.8MB, alloc=372.4MB, time=15.49 memory used=1267.3MB, alloc=372.4MB, time=16.01 memory used=1319.5MB, alloc=372.4MB, time=16.44 memory used=1378.5MB, alloc=372.4MB, time=16.85 memory used=1433.1MB, alloc=372.4MB, time=17.39 memory used=1495.6MB, alloc=372.4MB, time=17.94 memory used=1584.3MB, alloc=396.4MB, time=19.39 memory used=1687.6MB, alloc=396.4MB, time=20.94 memory used=1764.1MB, alloc=420.4MB, time=21.64 memory used=1830.2MB, alloc=420.4MB, time=21.88 memory used=1889.5MB, alloc=420.4MB, time=22.09 memory used=1969.8MB, alloc=420.4MB, time=22.52 memory used=2037.4MB, alloc=420.4MB, time=22.77 memory used=2094.9MB, alloc=420.4MB, time=22.99 memory used=2179.4MB, alloc=420.4MB, time=24.67 memory used=2242.6MB, alloc=420.4MB, time=24.89 memory used=2305.8MB, alloc=420.4MB, time=25.10 memory used=2445.2MB, alloc=420.4MB, time=27.17 memory used=2521.1MB, alloc=420.4MB, time=27.73 memory used=2637.4MB, alloc=420.4MB, time=28.89 memory used=2750.9MB, alloc=420.4MB, time=30.49 memory used=2870.2MB, alloc=420.4MB, time=31.80 memory used=2933.7MB, alloc=420.4MB, time=32.08 memory used=2990.1MB, alloc=420.4MB, time=32.30 memory used=3063.4MB, alloc=420.4MB, time=32.73 memory used=3114.9MB, alloc=420.4MB, time=32.95 memory used=3177.0MB, alloc=420.4MB, time=33.18 memory used=3220.1MB, alloc=420.4MB, time=33.37 memory used=3269.2MB, alloc=420.4MB, time=33.59 memory used=3325.2MB, alloc=420.4MB, time=33.78 memory used=3389.7MB, alloc=420.4MB, time=34.04 memory used=3528.8MB, alloc=420.4MB, time=34.53 memory used=3581.7MB, alloc=420.4MB, time=34.76 memory used=3647.8MB, alloc=420.4MB, time=34.99 memory used=3691.3MB, alloc=444.4MB, time=35.21 memory used=3754.5MB, alloc=444.4MB, time=35.43 memory used=3829.7MB, alloc=444.4MB, time=35.65 memory used=3995.2MB, alloc=444.4MB, time=36.00 memory used=4091.1MB, alloc=444.4MB, time=37.08 memory used=4156.6MB, alloc=444.4MB, time=37.34 memory used=4243.6MB, alloc=444.4MB, time=37.62 memory used=4300.7MB, alloc=444.4MB, time=37.85 memory used=4357.6MB, alloc=444.4MB, time=38.07 memory used=4421.7MB, alloc=444.4MB, time=38.28 memory used=4491.1MB, alloc=444.4MB, time=38.50 memory used=4567.4MB, alloc=444.4MB, time=38.74 memory used=4650.9MB, alloc=444.4MB, time=38.97 memory used=4742.6MB, alloc=444.4MB, time=39.20 memory used=4901.6MB, alloc=444.4MB, time=39.63 memory used=5050.1MB, alloc=444.4MB, time=39.96 memory used=5219.1MB, alloc=444.4MB, time=40.31 memory used=5417.8MB, alloc=444.4MB, time=40.67 memory used=5534.3MB, alloc=444.4MB, time=41.86 memory used=5599.5MB, alloc=444.4MB, time=42.14 memory used=5686.5MB, alloc=444.4MB, time=42.41 memory used=5746.8MB, alloc=444.4MB, time=42.67 memory used=5803.2MB, alloc=444.4MB, time=42.88 memory used=5865.3MB, alloc=444.4MB, time=43.11 memory used=5934.3MB, alloc=444.4MB, time=43.33 memory used=6010.8MB, alloc=444.4MB, time=43.57 memory used=6092.7MB, alloc=444.4MB, time=43.80 memory used=6183.3MB, alloc=444.4MB, time=44.04 memory used=6374.0MB, alloc=444.4MB, time=44.44 memory used=6520.2MB, alloc=444.4MB, time=44.77 memory used=6685.9MB, alloc=444.4MB, time=45.12 memory used=6875.9MB, alloc=444.4MB, time=45.48 memory used=7111.2MB, alloc=444.4MB, time=52.01 memory used=7180.9MB, alloc=444.4MB, time=52.29 memory used=7249.3MB, alloc=444.4MB, time=52.56 memory used=7332.1MB, alloc=444.4MB, time=52.84 memory used=7407.7MB, alloc=444.4MB, time=53.09 memory used=7459.5MB, alloc=444.4MB, time=53.30 memory used=7514.3MB, alloc=444.4MB, time=53.52 memory used=7574.6MB, alloc=444.4MB, time=53.74 memory used=7637.6MB, alloc=444.4MB, time=53.99 memory used=7703.4MB, alloc=444.4MB, time=54.24 memory used=7774.4MB, alloc=444.4MB, time=54.47 memory used=7851.2MB, alloc=444.4MB, time=54.71 memory used=7930.6MB, alloc=444.4MB, time=54.95 memory used=8015.7MB, alloc=444.4MB, time=55.18 memory used=8106.6MB, alloc=444.4MB, time=55.42 memory used=8311.2MB, alloc=444.4MB, time=55.82 memory used=8448.1MB, alloc=444.4MB, time=56.15 memory used=8594.0MB, alloc=444.4MB, time=56.49 memory used=8749.8MB, alloc=444.4MB, time=56.88 memory used=8914.7MB, alloc=444.4MB, time=57.23 memory used=9091.7MB, alloc=444.4MB, time=57.59 memory used=9279.6MB, alloc=444.4MB, time=57.96 memory used=9480.5MB, alloc=444.4MB, time=58.34 memory used=9695.0MB, alloc=444.4MB, time=58.72 memory used=9928.1MB, alloc=444.4MB, time=59.11 memory used=10122.5MB, alloc=444.4MB, time=59.47 memory used=10302.6MB, alloc=444.4MB, time=59.81 memory used=10600.0MB, alloc=444.4MB, time=90.12 memory used=10676.7MB, alloc=444.4MB, time=90.44 memory used=10736.9MB, alloc=444.4MB, time=90.71 memory used=10801.2MB, alloc=444.4MB, time=90.98 memory used=10877.2MB, alloc=444.4MB, time=91.24 memory used=10962.7MB, alloc=444.4MB, time=91.52 memory used=11026.2MB, alloc=444.4MB, time=91.75 memory used=11076.3MB, alloc=444.4MB, time=91.97 memory used=11128.7MB, alloc=444.4MB, time=92.20 memory used=11183.1MB, alloc=444.4MB, time=92.42 memory used=11239.7MB, alloc=444.4MB, time=92.64 memory used=11298.3MB, alloc=444.4MB, time=92.85 memory used=11362.6MB, alloc=444.4MB, time=93.09 memory used=11429.1MB, alloc=444.4MB, time=93.32 memory used=11497.6MB, alloc=444.4MB, time=93.55 memory used=11568.1MB, alloc=444.4MB, time=93.77 memory used=11640.8MB, alloc=444.4MB, time=94.00 memory used=11719.2MB, alloc=444.4MB, time=94.24 memory used=11799.8MB, alloc=444.4MB, time=94.46 memory used=11882.3MB, alloc=444.4MB, time=94.73 memory used=11971.4MB, alloc=444.4MB, time=94.97 memory used=12162.5MB, alloc=444.4MB, time=95.36 memory used=12291.9MB, alloc=444.4MB, time=95.69 memory used=12425.8MB, alloc=444.4MB, time=96.00 memory used=12566.9MB, alloc=444.4MB, time=96.33 memory used=12716.4MB, alloc=444.4MB, time=96.66 memory used=12873.8MB, alloc=444.4MB, time=97.00 memory used=13039.0MB, alloc=444.4MB, time=97.35 memory used=13206.9MB, alloc=444.4MB, time=97.69 memory used=13386.7MB, alloc=444.4MB, time=98.05 memory used=13574.1MB, alloc=444.4MB, time=98.41 memory used=13768.3MB, alloc=444.4MB, time=98.78 memory used=13969.0MB, alloc=444.4MB, time=99.15 memory used=14180.8MB, alloc=444.4MB, time=99.54 memory used=14402.9MB, alloc=444.4MB, time=99.94 memory used=14634.5MB, alloc=444.4MB, time=100.32 memory used=14866.7MB, alloc=444.4MB, time=100.71 memory used=15034.3MB, alloc=444.4MB, time=101.04 memory used=15206.9MB, alloc=444.4MB, time=101.37 memory used=15382.3MB, alloc=444.4MB, time=101.72 memory used=15563.5MB, alloc=444.4MB, time=102.06 memory used=15752.0MB, alloc=444.4MB, time=102.40 memory used=15947.6MB, alloc=444.4MB, time=102.76 memory used=16153.3MB, alloc=444.4MB, time=103.12 memory used=16370.1MB, alloc=444.4MB, time=103.49 memory used=16598.7MB, alloc=444.4MB, time=103.86 memory used=16917.9MB, alloc=444.4MB, time=105.90 memory used=17028.4MB, alloc=468.4MB, time=107.53 memory used=17124.3MB, alloc=468.4MB, time=108.87 memory used=17244.5MB, alloc=468.4MB, time=110.57 memory used=17363.6MB, alloc=468.4MB, time=111.47 memory used=17495.4MB, alloc=468.4MB, time=114.77 memory used=17588.5MB, alloc=492.4MB, time=121.85 memory used=17702.2MB, alloc=516.4MB, time=125.04 memory used=17754.8MB, alloc=516.4MB, time=129.20 memory used=17847.0MB, alloc=516.4MB, time=129.67 memory used=17943.4MB, alloc=516.4MB, time=130.16 memory used=18048.4MB, alloc=516.4MB, time=130.62 memory used=18163.0MB, alloc=516.4MB, time=131.08 memory used=18288.7MB, alloc=516.4MB, time=131.56 memory used=18426.1MB, alloc=516.4MB, time=132.04 memory used=18551.3MB, alloc=516.4MB, time=132.49 memory used=18635.5MB, alloc=516.4MB, time=132.89 memory used=18721.5MB, alloc=516.4MB, time=133.28 memory used=18825.2MB, alloc=516.4MB, time=137.03 memory used=18917.7MB, alloc=516.4MB, time=137.51 memory used=19013.9MB, alloc=516.4MB, time=137.98 memory used=19118.8MB, alloc=516.4MB, time=138.43 memory used=19233.4MB, alloc=516.4MB, time=138.88 memory used=19359.1MB, alloc=516.4MB, time=139.35 memory used=19496.5MB, alloc=516.4MB, time=139.82 memory used=19622.0MB, alloc=516.4MB, time=140.29 memory used=19706.0MB, alloc=516.4MB, time=140.69 memory used=19792.0MB, alloc=516.4MB, time=141.09 memory used=19889.7MB, alloc=516.4MB, time=141.56 memory used=20036.0MB, alloc=516.4MB, time=142.85 memory used=20142.2MB, alloc=516.4MB, time=143.31 memory used=20291.8MB, alloc=516.4MB, time=144.21 memory used=20508.7MB, alloc=516.4MB, time=145.90 memory used=20718.9MB, alloc=516.4MB, time=148.43 memory used=20837.6MB, alloc=540.4MB, time=194.41 memory used=20962.0MB, alloc=540.4MB, time=194.95 memory used=21110.2MB, alloc=540.4MB, time=195.45 memory used=21225.3MB, alloc=540.4MB, time=195.90 memory used=21321.1MB, alloc=540.4MB, time=196.32 memory used=21426.3MB, alloc=540.4MB, time=196.75 memory used=21544.7MB, alloc=540.4MB, time=197.18 memory used=21753.0MB, alloc=540.4MB, time=199.27 memory used=22016.3MB, alloc=540.4MB, time=203.22 |\^/| 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(); 1428283732 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 2 F := [-4 y z + 11 y z + 9 x z - 20 x, -11 y z + 5 y + 8 z - 15, 4 3 2 2 5 x - 7 x y - 12 y z + 19 x y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 4 G := [y z + 14 x z + 8 x + 13 y z, 10 y + 2 z + x y - 17, 3 2 2 -20 y z - 6 x - 12 z - 12 x] > Problem := [F,G]; 3 3 2 3 2 2 Problem := [[-4 y z + 11 y z + 9 x z - 20 x, -11 y z + 5 y + 8 z - 15, 4 3 2 2 3 2 2 5 x - 7 x y - 12 y z + 19 x y z], [y z + 14 x z + 8 x + 13 y z, 4 4 3 2 2 10 y + 2 z + x y - 17, -20 y z - 6 x - 12 z - 12 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=50.0MB, alloc=36.3MB, time=0.82 memory used=73.7MB, alloc=60.3MB, time=1.19 memory used=117.4MB, alloc=68.3MB, time=1.71 memory used=164.8MB, alloc=69.0MB, time=2.44 memory used=213.0MB, alloc=69.0MB, time=3.21 memory used=261.1MB, alloc=69.0MB, time=3.72 memory used=307.6MB, alloc=69.0MB, time=4.29 memory used=358.4MB, alloc=69.0MB, time=4.85 memory used=404.0MB, alloc=69.0MB, time=5.54 memory used=450.4MB, alloc=93.0MB, time=6.26 memory used=511.0MB, alloc=93.0MB, time=6.65 memory used=568.7MB, alloc=93.0MB, time=9.80 memory used=643.9MB, alloc=93.0MB, time=12.21 memory used=684.3MB, alloc=93.0MB, time=12.36 memory used=733.8MB, alloc=93.0MB, time=12.55 memory used=823.2MB, alloc=93.0MB, time=18.04 memory used=856.5MB, alloc=93.0MB, time=18.16 memory used=915.9MB, alloc=93.0MB, time=20.01 memory used=979.7MB, alloc=93.0MB, time=21.87 memory used=1023.5MB, alloc=93.0MB, time=22.27 memory used=1093.9MB, alloc=93.0MB, time=23.00 memory used=1156.4MB, alloc=93.0MB, time=23.73 memory used=1224.3MB, alloc=93.0MB, time=24.64 memory used=1292.1MB, alloc=349.0MB, time=25.32 memory used=1340.7MB, alloc=349.0MB, time=25.65 memory used=1400.6MB, alloc=373.0MB, time=26.32 memory used=1495.7MB, alloc=373.0MB, time=28.53 memory used=1539.7MB, alloc=373.0MB, time=28.72 memory used=1589.9MB, alloc=373.0MB, time=28.89 memory used=1626.7MB, alloc=373.0MB, time=29.03 memory used=1669.7MB, alloc=373.0MB, time=29.17 memory used=1719.7MB, alloc=373.0MB, time=29.33 memory used=1775.1MB, alloc=373.0MB, time=29.49 memory used=1808.2MB, alloc=373.0MB, time=29.62 memory used=1851.0MB, alloc=373.0MB, time=30.03 memory used=1927.0MB, alloc=373.0MB, time=30.33 memory used=1979.6MB, alloc=373.0MB, time=30.53 memory used=2018.4MB, alloc=373.0MB, time=30.71 memory used=2063.7MB, alloc=373.0MB, time=30.88 memory used=2116.1MB, alloc=373.0MB, time=31.06 memory used=2168.6MB, alloc=373.0MB, time=31.23 memory used=2202.8MB, alloc=373.0MB, time=31.37 memory used=2258.1MB, alloc=373.0MB, time=34.03 memory used=2341.2MB, alloc=397.0MB, time=66.26 memory used=2412.0MB, alloc=421.0MB, time=113.54 memory used=2498.2MB, alloc=421.0MB, time=190.21 |\^/| 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(); 1428284032 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [-18 x y z - 11 y + 11 x y + 8 y, 3 x y + y z + 14 y - 9 x, 2 2 -13 x y z - 11 x z + 10 y - 3] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 2 G := [7 y z + 11 y z - 14 x z - 13 z, -17 x + 3 y - 5 x z + 3 z , 4 4 2 x - 11 z - x - 18 y z] > Problem := [F,G]; 3 2 2 2 2 Problem := [[-18 x y z - 11 y + 11 x y + 8 y, 3 x y + y z + 14 y - 9 x, 2 2 3 2 -13 x y z - 11 x z + 10 y - 3], [7 y z + 11 y z - 14 x z - 13 z, 4 3 2 4 4 2 -17 x + 3 y - 5 x z + 3 z , x - 11 z - 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=46.0MB, alloc=56.3MB, time=0.79 memory used=84.5MB, alloc=60.3MB, time=1.36 memory used=126.1MB, alloc=68.3MB, time=1.97 memory used=167.6MB, alloc=92.3MB, time=2.54 memory used=235.7MB, alloc=92.3MB, time=3.49 memory used=300.6MB, alloc=92.3MB, time=4.29 memory used=362.7MB, alloc=116.3MB, time=4.96 memory used=425.9MB, alloc=372.3MB, time=5.79 memory used=496.1MB, alloc=372.3MB, time=6.34 memory used=548.4MB, alloc=372.3MB, time=6.55 memory used=596.9MB, alloc=372.3MB, time=6.96 memory used=665.2MB, alloc=372.3MB, time=7.59 memory used=736.5MB, alloc=372.3MB, time=8.07 memory used=842.2MB, alloc=372.3MB, time=9.45 memory used=929.5MB, alloc=372.3MB, time=10.48 memory used=1014.1MB, alloc=396.3MB, time=11.38 memory used=1111.8MB, alloc=396.3MB, time=12.36 memory used=1196.5MB, alloc=396.3MB, time=13.29 memory used=1247.4MB, alloc=396.3MB, time=13.48 memory used=1301.0MB, alloc=396.3MB, time=13.66 memory used=1347.9MB, alloc=396.3MB, time=13.82 memory used=1423.4MB, alloc=396.3MB, time=14.40 memory used=1520.0MB, alloc=396.3MB, time=15.21 memory used=1584.2MB, alloc=396.3MB, time=15.62 memory used=1630.1MB, alloc=396.3MB, time=15.80 memory used=1695.1MB, alloc=396.3MB, time=16.11 memory used=1761.3MB, alloc=396.3MB, time=17.28 memory used=1813.9MB, alloc=396.3MB, time=17.48 memory used=1857.9MB, alloc=396.3MB, time=17.67 memory used=1914.6MB, alloc=396.3MB, time=17.86 memory used=1959.4MB, alloc=396.3MB, time=18.06 memory used=2000.6MB, alloc=396.3MB, time=18.23 memory used=2068.7MB, alloc=396.3MB, time=19.37 memory used=2117.2MB, alloc=396.3MB, time=19.56 memory used=2166.6MB, alloc=396.3MB, time=19.74 memory used=2226.2MB, alloc=396.3MB, time=19.93 memory used=2262.8MB, alloc=396.3MB, time=20.10 memory used=2307.7MB, alloc=396.3MB, time=20.32 memory used=2376.7MB, alloc=396.3MB, time=20.80 memory used=2422.8MB, alloc=396.3MB, time=20.97 memory used=2530.5MB, alloc=396.3MB, time=21.94 memory used=2630.6MB, alloc=420.3MB, time=23.45 memory used=2748.2MB, alloc=444.3MB, time=25.35 memory used=2865.2MB, alloc=444.3MB, time=27.02 memory used=2940.7MB, alloc=468.3MB, time=28.15 memory used=3060.1MB, alloc=468.3MB, time=30.18 memory used=3137.3MB, alloc=468.3MB, time=31.24 memory used=3225.5MB, alloc=492.3MB, time=32.62 memory used=3320.4MB, alloc=492.3MB, time=33.79 memory used=3393.2MB, alloc=492.3MB, time=34.92 memory used=3474.6MB, alloc=492.3MB, time=36.06 memory used=3564.5MB, alloc=492.3MB, time=37.38 memory used=3624.7MB, alloc=492.3MB, time=38.45 memory used=3676.4MB, alloc=492.3MB, time=39.33 memory used=3737.1MB, alloc=492.3MB, time=40.46 memory used=3789.9MB, alloc=492.3MB, time=41.42 memory used=3833.8MB, alloc=492.3MB, time=42.31 memory used=3901.5MB, alloc=516.3MB, time=43.24 memory used=3942.2MB, alloc=516.3MB, time=44.03 memory used=4147.6MB, alloc=540.3MB, time=46.83 memory used=4356.0MB, alloc=564.3MB, time=49.88 memory used=4524.0MB, alloc=588.3MB, time=52.62 memory used=4695.1MB, alloc=612.3MB, time=55.04 memory used=4887.3MB, alloc=612.3MB, time=56.92 memory used=5042.7MB, alloc=612.3MB, time=59.12 memory used=5184.0MB, alloc=612.3MB, time=59.91 memory used=5311.6MB, alloc=612.3MB, time=60.78 memory used=5471.0MB, alloc=612.3MB, time=62.80 memory used=5600.6MB, alloc=612.3MB, time=63.58 memory used=5908.6MB, alloc=612.3MB, time=66.73 memory used=6182.3MB, alloc=612.3MB, time=70.17 memory used=6381.0MB, alloc=636.3MB, time=72.95 memory used=6575.1MB, alloc=636.3MB, time=77.19 memory used=6714.4MB, alloc=636.3MB, time=77.98 memory used=6900.8MB, alloc=636.3MB, time=79.36 memory used=7091.4MB, alloc=636.3MB, time=82.58 memory used=7219.3MB, alloc=636.3MB, time=84.83 memory used=7356.7MB, alloc=636.3MB, time=87.21 memory used=7482.1MB, alloc=636.3MB, time=89.40 memory used=7614.5MB, alloc=636.3MB, time=91.80 memory used=7804.8MB, alloc=660.3MB, time=94.63 memory used=7930.0MB, alloc=660.3MB, time=96.81 memory used=8114.6MB, alloc=660.3MB, time=100.16 memory used=8254.1MB, alloc=660.3MB, time=102.54 memory used=8351.4MB, alloc=660.3MB, time=104.52 memory used=8464.4MB, alloc=660.3MB, time=106.60 memory used=8711.6MB, alloc=660.3MB, time=109.17 memory used=8884.8MB, alloc=660.3MB, time=110.38 memory used=9045.5MB, alloc=660.3MB, time=112.06 memory used=9216.5MB, alloc=660.3MB, time=113.43 memory used=9387.5MB, alloc=660.3MB, time=116.08 memory used=9530.3MB, alloc=660.3MB, time=117.03 memory used=9665.5MB, alloc=660.3MB, time=117.93 memory used=9856.7MB, alloc=684.3MB, time=125.13 memory used=10025.3MB, alloc=684.3MB, time=126.18 memory used=10160.4MB, alloc=684.3MB, time=127.11 memory used=10310.3MB, alloc=684.3MB, time=128.03 memory used=10498.1MB, alloc=684.3MB, time=128.96 memory used=10750.9MB, alloc=684.3MB, time=136.47 memory used=10911.9MB, alloc=684.3MB, time=137.52 memory used=11058.7MB, alloc=684.3MB, time=138.52 memory used=11203.4MB, alloc=684.3MB, time=139.47 memory used=11383.6MB, alloc=684.3MB, time=140.43 memory used=11685.8MB, alloc=684.3MB, time=142.00 memory used=12085.3MB, alloc=684.3MB, time=146.63 memory used=12375.0MB, alloc=708.3MB, time=168.58 memory used=12536.4MB, alloc=708.3MB, time=169.70 memory used=12709.8MB, alloc=708.3MB, time=170.78 memory used=12845.0MB, alloc=708.3MB, time=171.77 memory used=13002.7MB, alloc=708.3MB, time=172.77 memory used=13188.4MB, alloc=708.3MB, time=173.77 memory used=13466.6MB, alloc=708.3MB, time=174.93 memory used=13579.3MB, alloc=708.3MB, time=175.86 memory used=13706.4MB, alloc=708.3MB, time=176.83 memory used=14197.6MB, alloc=732.3MB, time=181.85 |\^/| 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(); 1428284332 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 2 F := [-18 x y z + 3 y - 12 z + 8, -18 x y + 6 x z - 2 x z + 14 x z , 2 2 3 2 2 -20 x y + 6 y z - x z + 16 y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 2 G := [9 y z + 5 z - 19 x y z - 5 y z, 17 x z - 11 x y + 13 x y, 4 2 4 2 11 x - 11 x y z + 3 z - 17 x z] > Problem := [F,G]; 2 2 3 3 2 2 Problem := [[-18 x y z + 3 y - 12 z + 8, -18 x y + 6 x z - 2 x z + 14 x z , 2 2 3 2 2 2 2 4 -20 x y + 6 y z - x z + 16 y ], [9 y z + 5 z - 19 x y z - 5 y z, 2 2 2 4 2 4 2 17 x z - 11 x y + 13 x y, 11 x - 11 x y z + 3 z - 17 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.3MB, alloc=32.3MB, time=0.49 memory used=44.9MB, alloc=32.3MB, time=0.69 memory used=59.0MB, alloc=32.3MB, time=0.76 memory used=77.6MB, alloc=32.3MB, time=0.98 memory used=95.9MB, alloc=56.3MB, time=1.27 memory used=139.2MB, alloc=68.3MB, time=1.90 memory used=176.0MB, alloc=68.3MB, time=2.16 memory used=211.3MB, alloc=68.3MB, time=2.70 memory used=237.6MB, alloc=68.3MB, time=2.78 memory used=257.9MB, alloc=68.3MB, time=2.85 memory used=298.1MB, alloc=68.3MB, time=3.23 memory used=342.3MB, alloc=68.3MB, time=4.47 memory used=367.0MB, alloc=68.3MB, time=4.55 memory used=384.4MB, alloc=68.3MB, time=4.61 memory used=405.9MB, alloc=68.3MB, time=4.68 memory used=431.4MB, alloc=68.3MB, time=4.82 memory used=477.8MB, alloc=68.3MB, time=5.41 memory used=521.6MB, alloc=92.3MB, time=6.01 memory used=587.9MB, alloc=92.3MB, time=6.93 memory used=656.1MB, alloc=92.3MB, time=7.81 memory used=697.4MB, alloc=92.3MB, time=7.96 memory used=723.0MB, alloc=92.3MB, time=8.08 memory used=753.0MB, alloc=92.3MB, time=8.21 memory used=788.1MB, alloc=92.3MB, time=8.33 memory used=817.3MB, alloc=92.3MB, time=8.45 memory used=841.4MB, alloc=92.3MB, time=8.56 memory used=865.4MB, alloc=92.3MB, time=8.67 memory used=891.9MB, alloc=92.3MB, time=8.77 memory used=921.9MB, alloc=92.3MB, time=8.87 memory used=955.3MB, alloc=92.3MB, time=8.97 memory used=995.4MB, alloc=92.3MB, time=9.30 memory used=1029.9MB, alloc=92.3MB, time=9.67 memory used=1078.2MB, alloc=93.4MB, time=9.87 memory used=1105.0MB, alloc=93.4MB, time=9.99 memory used=1133.2MB, alloc=93.4MB, time=10.11 memory used=1166.7MB, alloc=93.4MB, time=10.23 memory used=1197.8MB, alloc=93.4MB, time=10.34 memory used=1224.1MB, alloc=93.4MB, time=10.45 memory used=1247.7MB, alloc=117.4MB, time=10.57 memory used=1290.3MB, alloc=117.4MB, time=10.71 memory used=1340.6MB, alloc=117.4MB, time=10.84 memory used=1398.6MB, alloc=117.4MB, time=11.23 memory used=1469.6MB, alloc=118.5MB, time=13.69 memory used=1520.1MB, alloc=118.5MB, time=13.84 memory used=1561.8MB, alloc=118.5MB, time=13.98 memory used=1613.8MB, alloc=118.5MB, time=14.12 memory used=1657.0MB, alloc=118.5MB, time=14.23 memory used=1701.9MB, alloc=118.5MB, time=14.41 memory used=1775.5MB, alloc=374.5MB, time=15.51 memory used=1884.3MB, alloc=374.5MB, time=16.53 memory used=1990.8MB, alloc=374.5MB, time=19.17 memory used=2102.3MB, alloc=374.5MB, time=23.06 memory used=2177.1MB, alloc=374.5MB, time=23.54 memory used=2244.9MB, alloc=374.5MB, time=24.15 memory used=2316.0MB, alloc=374.5MB, time=24.69 memory used=2394.4MB, alloc=374.5MB, time=25.65 memory used=2441.3MB, alloc=374.5MB, time=25.91 memory used=2495.3MB, alloc=374.5MB, time=26.12 memory used=2542.3MB, alloc=374.5MB, time=26.28 memory used=2597.4MB, alloc=374.5MB, time=26.54 memory used=2639.8MB, alloc=374.5MB, time=26.70 memory used=2681.5MB, alloc=374.5MB, time=26.85 memory used=2744.1MB, alloc=374.5MB, time=28.12 memory used=2783.5MB, alloc=374.5MB, time=28.27 memory used=2859.4MB, alloc=374.5MB, time=28.92 memory used=2957.1MB, alloc=374.5MB, time=30.67 memory used=3050.0MB, alloc=374.5MB, time=31.49 memory used=3123.1MB, alloc=374.5MB, time=32.58 memory used=3176.4MB, alloc=374.5MB, time=33.62 memory used=3212.9MB, alloc=374.5MB, time=33.78 memory used=3251.1MB, alloc=374.5MB, time=33.93 memory used=3290.5MB, alloc=374.5MB, time=34.07 memory used=3343.4MB, alloc=374.5MB, time=35.55 memory used=3384.5MB, alloc=374.5MB, time=35.72 memory used=3416.4MB, alloc=374.5MB, time=35.86 memory used=3456.9MB, alloc=374.5MB, time=36.02 memory used=3492.9MB, alloc=374.5MB, time=36.15 memory used=3534.1MB, alloc=374.5MB, time=36.46 memory used=3610.3MB, alloc=374.5MB, time=37.24 memory used=3680.6MB, alloc=398.5MB, time=38.41 memory used=3785.2MB, alloc=422.5MB, time=39.97 memory used=3903.9MB, alloc=422.5MB, time=41.12 memory used=3977.9MB, alloc=422.5MB, time=41.47 memory used=4052.7MB, alloc=422.5MB, time=42.77 memory used=4117.9MB, alloc=422.5MB, time=43.12 memory used=4242.2MB, alloc=422.5MB, time=44.55 memory used=4349.4MB, alloc=446.5MB, time=47.12 memory used=4421.0MB, alloc=446.5MB, time=47.40 memory used=4555.0MB, alloc=446.5MB, time=48.77 memory used=4690.1MB, alloc=446.5MB, time=50.70 memory used=4797.8MB, alloc=446.5MB, time=51.98 memory used=4895.4MB, alloc=446.5MB, time=53.46 memory used=4992.4MB, alloc=470.5MB, time=54.76 memory used=5128.6MB, alloc=470.5MB, time=56.81 memory used=5223.8MB, alloc=470.5MB, time=57.92 memory used=5309.7MB, alloc=470.5MB, time=59.19 memory used=5393.9MB, alloc=470.5MB, time=60.65 memory used=5528.1MB, alloc=470.5MB, time=62.37 memory used=5627.1MB, alloc=470.5MB, time=62.98 memory used=5709.0MB, alloc=470.5MB, time=63.52 memory used=5807.4MB, alloc=470.5MB, time=64.30 memory used=5882.9MB, alloc=470.5MB, time=64.70 memory used=5966.6MB, alloc=470.5MB, time=65.34 memory used=6071.9MB, alloc=470.5MB, time=67.89 memory used=6142.4MB, alloc=470.5MB, time=68.25 memory used=6214.2MB, alloc=470.5MB, time=68.58 memory used=6296.3MB, alloc=470.5MB, time=69.25 memory used=6402.3MB, alloc=470.5MB, time=70.11 memory used=6484.9MB, alloc=470.5MB, time=70.54 memory used=6575.9MB, alloc=470.5MB, time=71.07 memory used=6652.3MB, alloc=470.5MB, time=71.48 memory used=6749.6MB, alloc=470.5MB, time=73.98 memory used=6822.9MB, alloc=470.5MB, time=74.33 memory used=6900.2MB, alloc=470.5MB, time=74.68 memory used=6991.3MB, alloc=470.5MB, time=75.33 memory used=7069.3MB, alloc=470.5MB, time=75.74 memory used=7153.6MB, alloc=470.5MB, time=76.13 memory used=7220.5MB, alloc=494.5MB, time=76.50 memory used=7300.7MB, alloc=494.5MB, time=76.87 memory used=7398.1MB, alloc=494.5MB, time=77.24 memory used=7489.5MB, alloc=494.5MB, time=77.58 memory used=7604.8MB, alloc=494.5MB, time=78.36 memory used=7695.2MB, alloc=494.5MB, time=78.80 memory used=7791.3MB, alloc=494.5MB, time=79.22 memory used=7868.0MB, alloc=494.5MB, time=79.61 memory used=7959.8MB, alloc=494.5MB, time=80.01 memory used=8058.0MB, alloc=494.5MB, time=80.38 memory used=8167.1MB, alloc=494.5MB, time=84.56 memory used=8262.4MB, alloc=494.5MB, time=85.00 memory used=8357.3MB, alloc=494.5MB, time=85.36 memory used=8442.2MB, alloc=494.5MB, time=85.71 memory used=8528.7MB, alloc=494.5MB, time=86.03 memory used=8644.7MB, alloc=494.5MB, time=86.69 memory used=8741.3MB, alloc=494.5MB, time=87.29 memory used=8857.3MB, alloc=494.5MB, time=87.96 memory used=8952.9MB, alloc=494.5MB, time=88.54 memory used=9073.8MB, alloc=494.5MB, time=91.28 memory used=9166.5MB, alloc=494.5MB, time=91.68 memory used=9267.4MB, alloc=494.5MB, time=92.20 memory used=9371.9MB, alloc=494.5MB, time=92.62 memory used=9479.7MB, alloc=494.5MB, time=93.17 memory used=9617.4MB, alloc=494.5MB, time=98.67 memory used=9712.0MB, alloc=494.5MB, time=99.10 memory used=9797.5MB, alloc=494.5MB, time=99.48 memory used=9900.6MB, alloc=494.5MB, time=99.85 memory used=9972.3MB, alloc=494.5MB, time=100.16 memory used=10054.7MB, alloc=494.5MB, time=100.49 memory used=10178.3MB, alloc=494.5MB, time=101.42 memory used=10279.3MB, alloc=494.5MB, time=101.89 memory used=10380.5MB, alloc=494.5MB, time=102.32 memory used=10471.1MB, alloc=494.5MB, time=102.72 memory used=10545.4MB, alloc=494.5MB, time=103.09 memory used=10628.8MB, alloc=494.5MB, time=103.47 memory used=10724.7MB, alloc=494.5MB, time=103.85 memory used=10827.5MB, alloc=494.5MB, time=104.24 memory used=10905.7MB, alloc=494.5MB, time=104.57 memory used=10998.2MB, alloc=494.5MB, time=105.17 memory used=11095.7MB, alloc=494.5MB, time=105.79 memory used=11224.5MB, alloc=494.5MB, time=106.99 memory used=11312.3MB, alloc=494.5MB, time=107.42 memory used=11418.3MB, alloc=494.5MB, time=107.84 memory used=11491.6MB, alloc=494.5MB, time=108.22 memory used=11570.2MB, alloc=494.5MB, time=108.61 memory used=11659.4MB, alloc=494.5MB, time=108.99 memory used=11762.3MB, alloc=494.5MB, time=109.38 memory used=11849.0MB, alloc=494.5MB, time=109.72 memory used=11925.6MB, alloc=494.5MB, time=110.03 memory used=12028.6MB, alloc=494.5MB, time=110.89 memory used=12169.5MB, alloc=494.5MB, time=122.01 memory used=12288.9MB, alloc=494.5MB, time=122.58 memory used=12367.0MB, alloc=494.5MB, time=122.95 memory used=12463.5MB, alloc=494.5MB, time=123.34 memory used=12562.7MB, alloc=494.5MB, time=123.72 memory used=12631.8MB, alloc=494.5MB, time=124.05 memory used=12709.2MB, alloc=494.5MB, time=124.37 memory used=12795.7MB, alloc=494.5MB, time=124.71 memory used=12894.3MB, alloc=494.5MB, time=125.05 memory used=13080.2MB, alloc=494.5MB, time=126.15 memory used=13165.8MB, alloc=494.5MB, time=126.59 memory used=13269.9MB, alloc=494.5MB, time=127.06 memory used=13350.9MB, alloc=494.5MB, time=127.46 memory used=13425.9MB, alloc=494.5MB, time=127.86 memory used=13512.1MB, alloc=494.5MB, time=128.24 memory used=13610.0MB, alloc=494.5MB, time=128.63 memory used=13707.0MB, alloc=494.5MB, time=129.01 memory used=13785.1MB, alloc=494.5MB, time=129.35 memory used=13877.9MB, alloc=494.5MB, time=130.34 memory used=13999.7MB, alloc=494.5MB, time=130.90 memory used=14094.1MB, alloc=494.5MB, time=131.33 memory used=14194.0MB, alloc=494.5MB, time=131.74 memory used=14265.7MB, alloc=494.5MB, time=132.15 memory used=14346.3MB, alloc=494.5MB, time=132.53 memory used=14438.3MB, alloc=494.5MB, time=132.92 memory used=14544.6MB, alloc=494.5MB, time=133.31 memory used=14625.2MB, alloc=494.5MB, time=133.65 memory used=14701.6MB, alloc=494.5MB, time=134.00 memory used=14864.4MB, alloc=494.5MB, time=155.81 memory used=14979.0MB, alloc=494.5MB, time=156.36 memory used=15060.9MB, alloc=494.5MB, time=156.74 memory used=15149.5MB, alloc=494.5MB, time=157.14 memory used=15254.4MB, alloc=494.5MB, time=157.53 memory used=15341.2MB, alloc=494.5MB, time=157.90 memory used=15410.3MB, alloc=494.5MB, time=158.22 memory used=15485.5MB, alloc=494.5MB, time=158.55 memory used=15567.8MB, alloc=494.5MB, time=158.89 memory used=15658.1MB, alloc=494.5MB, time=159.22 memory used=15756.4MB, alloc=494.5MB, time=159.56 memory used=15893.9MB, alloc=494.5MB, time=159.94 memory used=16143.1MB, alloc=494.5MB, time=161.65 memory used=16301.0MB, alloc=494.5MB, time=164.59 memory used=16439.9MB, alloc=494.5MB, time=169.55 memory used=16564.7MB, alloc=494.5MB, time=171.15 memory used=16709.3MB, alloc=494.5MB, time=174.04 memory used=16849.9MB, alloc=494.5MB, time=179.23 memory used=16952.4MB, alloc=494.5MB, time=180.41 memory used=17109.2MB, alloc=494.5MB, time=182.64 memory used=17264.3MB, alloc=494.5MB, time=187.32 memory used=17381.6MB, alloc=494.5MB, time=190.99 memory used=17477.4MB, alloc=494.5MB, time=192.01 memory used=17592.6MB, alloc=494.5MB, time=193.17 memory used=17731.7MB, alloc=494.5MB, time=195.84 memory used=17858.1MB, alloc=494.5MB, time=200.41 memory used=17979.2MB, alloc=494.5MB, time=201.85 memory used=18071.3MB, alloc=494.5MB, time=202.51 memory used=18159.0MB, alloc=494.5MB, time=203.79 memory used=18220.2MB, alloc=494.5MB, time=204.87 memory used=18300.6MB, alloc=494.5MB, time=205.56 memory used=18423.6MB, alloc=494.5MB, time=206.63 memory used=18529.4MB, alloc=494.5MB, time=207.19 memory used=18647.0MB, alloc=494.5MB, time=208.58 memory used=18759.5MB, alloc=494.5MB, time=209.89 memory used=18819.1MB, alloc=494.5MB, time=210.85 memory used=18876.1MB, alloc=494.5MB, time=211.70 |\^/| 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(); 1428284632 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 3 2 3 2 F := [-9 z - 2 x z - 3 y + 19 x y, -7 x z - 14 x y - 4 y - 6 y , 3 2 2 2 -15 x y + 12 x y - 16 x y z - 13 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 G := [-10 x - 16 x z - 7 x y z - 11 y z , 3 2 2 2 3 2 2 -10 y z - 18 x z + 2 y z + 16 z , 13 x y - x y z + 4 y z - 15 y] > Problem := [F,G]; 4 2 3 3 2 3 2 Problem := [[-9 z - 2 x z - 3 y + 19 x y, -7 x z - 14 x y - 4 y - 6 y , 3 2 2 2 -15 x y + 12 x y - 16 x y z - 13 x z], [ 4 3 2 2 2 3 2 2 2 -10 x - 16 x z - 7 x y z - 11 y z , -10 y z - 18 x z + 2 y z + 16 z , 3 2 2 13 x y - x y z + 4 y z - 15 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=46.2MB, alloc=56.3MB, time=0.81 memory used=84.5MB, alloc=60.6MB, time=1.04 memory used=110.3MB, alloc=60.6MB, time=1.10 memory used=152.3MB, alloc=60.6MB, time=1.67 memory used=194.3MB, alloc=60.6MB, time=2.26 memory used=235.5MB, alloc=63.1MB, time=3.05 memory used=281.3MB, alloc=71.1MB, time=3.97 memory used=328.0MB, alloc=95.1MB, time=4.67 memory used=396.5MB, alloc=95.1MB, time=5.38 memory used=427.8MB, alloc=95.1MB, time=5.49 memory used=469.5MB, alloc=95.1MB, time=5.60 memory used=495.8MB, alloc=95.1MB, time=5.69 memory used=526.2MB, alloc=95.1MB, time=5.78 memory used=571.8MB, alloc=95.1MB, time=6.05 memory used=606.3MB, alloc=95.1MB, time=6.17 memory used=645.8MB, alloc=95.1MB, time=6.29 memory used=676.1MB, alloc=95.1MB, time=6.39 memory used=705.2MB, alloc=95.1MB, time=6.48 memory used=748.0MB, alloc=95.1MB, time=8.56 memory used=838.6MB, alloc=95.1MB, time=15.73 memory used=876.5MB, alloc=95.1MB, time=15.85 memory used=904.0MB, alloc=95.1MB, time=15.95 memory used=937.2MB, alloc=95.1MB, time=16.05 memory used=977.1MB, alloc=95.1MB, time=16.16 memory used=1011.2MB, alloc=95.1MB, time=16.25 memory used=1036.0MB, alloc=95.1MB, time=16.33 memory used=1063.6MB, alloc=95.1MB, time=16.41 memory used=1092.4MB, alloc=95.1MB, time=16.52 memory used=1124.3MB, alloc=95.1MB, time=16.61 memory used=1160.0MB, alloc=95.1MB, time=16.70 memory used=1205.6MB, alloc=95.1MB, time=16.88 memory used=1242.1MB, alloc=95.1MB, time=17.14 memory used=1275.4MB, alloc=95.1MB, time=17.25 memory used=1311.5MB, alloc=95.1MB, time=17.64 memory used=1355.3MB, alloc=95.1MB, time=17.78 memory used=1390.0MB, alloc=95.1MB, time=17.88 memory used=1426.3MB, alloc=95.1MB, time=17.99 memory used=1453.2MB, alloc=95.1MB, time=18.09 memory used=1485.0MB, alloc=95.1MB, time=18.17 memory used=1536.6MB, alloc=95.1MB, time=18.53 memory used=1567.9MB, alloc=95.1MB, time=18.64 memory used=1609.1MB, alloc=95.1MB, time=18.76 memory used=1636.0MB, alloc=95.1MB, time=18.85 memory used=1666.0MB, alloc=95.1MB, time=18.94 memory used=1714.9MB, alloc=95.1MB, time=23.95 memory used=1799.1MB, alloc=95.1MB, time=28.18 memory used=1836.0MB, alloc=95.1MB, time=28.29 memory used=1864.0MB, alloc=95.1MB, time=28.38 memory used=1897.8MB, alloc=95.1MB, time=28.47 memory used=1938.2MB, alloc=95.1MB, time=28.58 memory used=1969.6MB, alloc=95.1MB, time=28.67 memory used=1994.4MB, alloc=95.1MB, time=28.76 memory used=2021.8MB, alloc=95.1MB, time=28.84 memory used=2050.6MB, alloc=95.1MB, time=28.94 memory used=2081.6MB, alloc=95.1MB, time=29.03 memory used=2116.4MB, alloc=95.1MB, time=29.11 memory used=2160.4MB, alloc=95.1MB, time=29.30 memory used=2195.0MB, alloc=95.1MB, time=29.40 memory used=2274.4MB, alloc=95.1MB, time=32.96 memory used=2343.6MB, alloc=95.1MB, time=34.70 memory used=2376.0MB, alloc=95.1MB, time=34.81 memory used=2405.8MB, alloc=95.1MB, time=34.91 memory used=2442.3MB, alloc=95.1MB, time=35.02 memory used=2475.5MB, alloc=95.1MB, time=35.11 memory used=2499.4MB, alloc=95.1MB, time=35.20 memory used=2525.9MB, alloc=95.1MB, time=35.29 memory used=2556.1MB, alloc=95.1MB, time=35.38 memory used=2613.4MB, alloc=95.1MB, time=35.77 memory used=2677.5MB, alloc=95.1MB, time=36.62 memory used=2739.2MB, alloc=95.1MB, time=37.17 memory used=2804.6MB, alloc=119.1MB, time=38.02 memory used=2867.7MB, alloc=375.1MB, time=38.95 memory used=2957.6MB, alloc=399.1MB, time=40.51 memory used=3044.5MB, alloc=399.1MB, time=41.18 memory used=3151.0MB, alloc=399.1MB, time=42.47 memory used=3220.9MB, alloc=399.1MB, time=43.04 memory used=3269.0MB, alloc=399.1MB, time=43.27 memory used=3319.4MB, alloc=399.1MB, time=43.46 memory used=3359.7MB, alloc=399.1MB, time=43.67 memory used=3430.2MB, alloc=399.1MB, time=44.18 memory used=3477.6MB, alloc=399.1MB, time=44.39 memory used=3533.9MB, alloc=399.1MB, time=44.59 memory used=3574.5MB, alloc=399.1MB, time=44.77 memory used=3641.6MB, alloc=423.1MB, time=53.90 memory used=3767.4MB, alloc=423.1MB, time=56.77 memory used=3828.5MB, alloc=423.1MB, time=57.01 memory used=3894.6MB, alloc=423.1MB, time=57.22 memory used=3969.5MB, alloc=423.1MB, time=57.43 memory used=4018.4MB, alloc=423.1MB, time=57.60 memory used=4073.7MB, alloc=423.1MB, time=57.77 memory used=4140.9MB, alloc=423.1MB, time=57.95 memory used=4238.2MB, alloc=423.1MB, time=58.71 memory used=4336.4MB, alloc=423.1MB, time=69.85 memory used=4405.0MB, alloc=423.1MB, time=70.08 memory used=4459.0MB, alloc=423.1MB, time=70.29 memory used=4526.7MB, alloc=423.1MB, time=70.51 memory used=4601.8MB, alloc=423.1MB, time=70.72 memory used=4649.0MB, alloc=423.1MB, time=70.90 memory used=4701.4MB, alloc=423.1MB, time=71.07 memory used=4759.1MB, alloc=423.1MB, time=71.29 memory used=4825.0MB, alloc=423.1MB, time=71.46 memory used=4909.4MB, alloc=423.1MB, time=71.88 memory used=5009.8MB, alloc=423.1MB, time=72.53 memory used=5134.7MB, alloc=423.1MB, time=76.85 memory used=5197.7MB, alloc=423.1MB, time=77.06 memory used=5264.2MB, alloc=423.1MB, time=77.26 memory used=5320.0MB, alloc=423.1MB, time=77.44 memory used=5399.2MB, alloc=423.1MB, time=78.04 memory used=5521.4MB, alloc=423.1MB, time=79.14 memory used=5665.7MB, alloc=423.1MB, time=80.98 memory used=5801.4MB, alloc=423.1MB, time=82.45 memory used=5937.7MB, alloc=423.1MB, time=84.90 memory used=6076.0MB, alloc=423.1MB, time=87.78 memory used=6213.7MB, alloc=423.1MB, time=91.53 memory used=6351.4MB, alloc=423.1MB, time=95.79 memory used=6491.4MB, alloc=423.1MB, time=100.62 memory used=6629.7MB, alloc=423.1MB, time=106.33 memory used=6779.2MB, alloc=423.1MB, time=112.00 memory used=6871.3MB, alloc=423.1MB, time=113.10 memory used=6977.4MB, alloc=423.1MB, time=114.53 memory used=7034.4MB, alloc=423.1MB, time=114.77 memory used=7099.2MB, alloc=423.1MB, time=114.98 memory used=7149.5MB, alloc=423.1MB, time=115.16 memory used=7292.7MB, alloc=423.1MB, time=116.52 memory used=7420.2MB, alloc=447.1MB, time=118.08 memory used=7498.5MB, alloc=447.1MB, time=118.57 memory used=7581.1MB, alloc=447.1MB, time=123.55 memory used=7728.0MB, alloc=447.1MB, time=128.83 memory used=7801.3MB, alloc=447.1MB, time=129.12 memory used=7855.3MB, alloc=447.1MB, time=129.36 memory used=7922.0MB, alloc=447.1MB, time=129.60 memory used=8003.2MB, alloc=447.1MB, time=129.86 memory used=8180.8MB, alloc=447.1MB, time=130.44 memory used=8400.8MB, alloc=447.1MB, time=140.30 memory used=8468.5MB, alloc=447.1MB, time=140.59 memory used=8534.9MB, alloc=447.1MB, time=140.85 memory used=8593.1MB, alloc=447.1MB, time=141.09 memory used=8663.0MB, alloc=447.1MB, time=141.33 memory used=8746.8MB, alloc=447.1MB, time=141.60 memory used=8898.8MB, alloc=447.1MB, time=141.99 memory used=9095.6MB, alloc=447.1MB, time=142.69 memory used=9247.6MB, alloc=447.1MB, time=144.16 memory used=9352.8MB, alloc=447.1MB, time=145.35 memory used=9412.2MB, alloc=447.1MB, time=145.60 memory used=9482.8MB, alloc=447.1MB, time=145.86 memory used=9547.5MB, alloc=447.1MB, time=146.11 memory used=9597.9MB, alloc=447.1MB, time=146.32 memory used=9654.6MB, alloc=447.1MB, time=146.54 memory used=9719.1MB, alloc=447.1MB, time=146.76 memory used=9791.5MB, alloc=447.1MB, time=147.00 memory used=9959.1MB, alloc=471.1MB, time=148.34 memory used=10073.6MB, alloc=471.1MB, time=150.05 memory used=10162.4MB, alloc=471.1MB, time=150.34 memory used=10233.2MB, alloc=471.1MB, time=150.59 memory used=10309.7MB, alloc=471.1MB, time=150.84 memory used=10410.3MB, alloc=471.1MB, time=151.43 memory used=10560.2MB, alloc=471.1MB, time=152.55 memory used=10726.0MB, alloc=471.1MB, time=153.95 memory used=10830.1MB, alloc=471.1MB, time=157.41 memory used=10917.2MB, alloc=471.1MB, time=157.69 memory used=10979.8MB, alloc=471.1MB, time=157.94 memory used=11092.3MB, alloc=471.1MB, time=164.80 memory used=11170.4MB, alloc=471.1MB, time=165.10 memory used=11257.2MB, alloc=471.1MB, time=165.40 memory used=11320.4MB, alloc=471.1MB, time=165.64 memory used=11397.3MB, alloc=471.1MB, time=165.90 memory used=11503.9MB, alloc=471.1MB, time=166.56 memory used=11618.4MB, alloc=471.1MB, time=168.05 memory used=11730.4MB, alloc=495.1MB, time=169.84 memory used=11821.4MB, alloc=495.1MB, time=171.27 memory used=11899.0MB, alloc=495.1MB, time=172.38 memory used=12030.0MB, alloc=495.1MB, time=174.80 memory used=12125.4MB, alloc=495.1MB, time=176.81 memory used=12206.7MB, alloc=519.1MB, time=178.01 memory used=12298.1MB, alloc=519.1MB, time=180.09 memory used=12380.0MB, alloc=519.1MB, time=181.57 memory used=12455.3MB, alloc=543.1MB, time=182.48 memory used=12514.6MB, alloc=543.1MB, time=183.43 memory used=12577.6MB, alloc=543.1MB, time=184.24 memory used=12638.9MB, alloc=543.1MB, time=185.43 memory used=12748.2MB, alloc=543.1MB, time=186.72 memory used=12852.7MB, alloc=543.1MB, time=187.25 memory used=12945.4MB, alloc=543.1MB, time=187.75 memory used=13057.8MB, alloc=543.1MB, time=188.23 memory used=13182.7MB, alloc=543.1MB, time=189.03 memory used=13278.6MB, alloc=543.1MB, time=189.54 memory used=13381.1MB, alloc=543.1MB, time=190.04 memory used=13522.6MB, alloc=567.1MB, time=206.35 memory used=13701.8MB, alloc=567.1MB, time=208.22 memory used=13824.5MB, alloc=567.1MB, time=208.74 |\^/| 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(); 1428284932 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 4 4 2 2 F := [-17 x y + x y - 3 x + 12 z, 14 y - 8 z - 6 x y + 16 y z, 2 2 3 3 x y z - 2 x y + y - 15 x y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 G := [-19 x z + 4 y z + 4 z + 7 x, 12 y z + 2 x y + 9 x y z + 9 x, 3 2 2 x - 19 y z - 14 x - 10 z] > Problem := [F,G]; 3 3 3 4 4 2 2 Problem := [[-17 x y + x y - 3 x + 12 z, 14 y - 8 z - 6 x y + 16 y z, 2 2 3 3 2 2 3 x y z - 2 x y + y - 15 x y], [-19 x z + 4 y z + 4 z + 7 x, 3 2 3 2 12 y z + 2 x y + 9 x y z + 9 x, 2 x - 19 y z - 14 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=32.3MB, time=0.49 memory used=45.1MB, alloc=32.3MB, time=0.64 memory used=59.1MB, alloc=32.3MB, time=0.72 memory used=75.4MB, alloc=32.3MB, time=0.83 memory used=90.6MB, alloc=32.3MB, time=0.92 memory used=106.7MB, alloc=32.3MB, time=1.02 memory used=121.1MB, alloc=32.3MB, time=1.11 memory used=135.7MB, alloc=32.3MB, time=1.18 memory used=154.7MB, alloc=32.3MB, time=1.50 memory used=167.6MB, alloc=32.3MB, time=1.54 memory used=178.0MB, alloc=32.3MB, time=1.57 memory used=194.2MB, alloc=32.3MB, time=1.67 memory used=207.7MB, alloc=32.3MB, time=1.76 memory used=231.1MB, alloc=36.3MB, time=2.10 memory used=247.7MB, alloc=36.4MB, time=2.50 memory used=258.8MB, alloc=36.4MB, time=2.53 memory used=269.6MB, alloc=36.4MB, time=2.57 memory used=292.4MB, alloc=36.4MB, time=2.80 memory used=312.3MB, alloc=60.4MB, time=3.11 memory used=360.2MB, alloc=68.4MB, time=3.71 memory used=394.8MB, alloc=70.1MB, time=3.82 memory used=431.0MB, alloc=71.1MB, time=4.02 memory used=460.3MB, alloc=71.1MB, time=4.17 memory used=509.2MB, alloc=74.9MB, time=7.10 memory used=542.6MB, alloc=74.9MB, time=7.20 memory used=566.0MB, alloc=74.9MB, time=7.29 memory used=588.4MB, alloc=74.9MB, time=7.36 memory used=613.9MB, alloc=74.9MB, time=7.44 memory used=644.3MB, alloc=74.9MB, time=7.55 memory used=695.2MB, alloc=74.9MB, time=8.42 memory used=746.8MB, alloc=74.9MB, time=9.06 memory used=795.8MB, alloc=74.9MB, time=9.99 memory used=846.1MB, alloc=74.9MB, time=11.40 memory used=896.2MB, alloc=74.9MB, time=13.40 memory used=948.0MB, alloc=74.9MB, time=16.10 memory used=993.8MB, alloc=74.9MB, time=17.19 memory used=1027.6MB, alloc=74.9MB, time=17.55 memory used=1067.4MB, alloc=74.9MB, time=17.95 memory used=1101.0MB, alloc=74.9MB, time=18.19 memory used=1137.2MB, alloc=74.9MB, time=19.13 memory used=1158.9MB, alloc=74.9MB, time=19.21 memory used=1180.8MB, alloc=74.9MB, time=19.29 memory used=1197.3MB, alloc=74.9MB, time=19.35 memory used=1216.3MB, alloc=74.9MB, time=19.42 memory used=1237.7MB, alloc=74.9MB, time=19.49 memory used=1261.5MB, alloc=74.9MB, time=19.57 memory used=1283.8MB, alloc=74.9MB, time=19.64 memory used=1298.5MB, alloc=74.9MB, time=19.69 memory used=1314.5MB, alloc=74.9MB, time=19.76 memory used=1337.5MB, alloc=74.9MB, time=19.92 memory used=1362.5MB, alloc=74.9MB, time=20.19 memory used=1386.4MB, alloc=74.9MB, time=20.34 memory used=1405.0MB, alloc=74.9MB, time=20.41 memory used=1442.4MB, alloc=74.9MB, time=20.78 memory used=1464.3MB, alloc=74.9MB, time=20.86 memory used=1485.1MB, alloc=74.9MB, time=20.94 memory used=1512.5MB, alloc=74.9MB, time=21.05 memory used=1547.4MB, alloc=74.9MB, time=21.20 memory used=1565.2MB, alloc=74.9MB, time=21.28 memory used=1586.4MB, alloc=74.9MB, time=21.36 memory used=1622.7MB, alloc=74.9MB, time=23.62 memory used=1654.3MB, alloc=74.9MB, time=23.95 memory used=1673.9MB, alloc=74.9MB, time=24.03 memory used=1699.2MB, alloc=74.9MB, time=24.12 memory used=1715.7MB, alloc=98.9MB, time=24.21 memory used=1747.9MB, alloc=98.9MB, time=24.32 memory used=1786.4MB, alloc=98.9MB, time=24.43 memory used=1832.2MB, alloc=98.9MB, time=24.55 memory used=1867.5MB, alloc=98.9MB, time=24.64 memory used=1895.7MB, alloc=98.9MB, time=24.71 memory used=1925.4MB, alloc=98.9MB, time=24.80 memory used=1958.9MB, alloc=98.9MB, time=24.88 memory used=1997.2MB, alloc=98.9MB, time=24.96 memory used=2065.3MB, alloc=98.9MB, time=25.66 memory used=2125.2MB, alloc=98.9MB, time=25.99 memory used=2167.2MB, alloc=98.9MB, time=26.32 memory used=2211.4MB, alloc=98.9MB, time=26.66 memory used=2248.6MB, alloc=98.9MB, time=26.76 memory used=2290.3MB, alloc=98.9MB, time=26.88 memory used=2357.4MB, alloc=98.9MB, time=28.05 memory used=2435.1MB, alloc=98.9MB, time=28.86 memory used=2485.9MB, alloc=98.9MB, time=29.64 memory used=2519.1MB, alloc=98.9MB, time=29.75 memory used=2572.4MB, alloc=98.9MB, time=31.75 memory used=2609.5MB, alloc=98.9MB, time=31.87 memory used=2637.5MB, alloc=98.9MB, time=31.96 memory used=2680.0MB, alloc=98.9MB, time=32.24 memory used=2714.3MB, alloc=98.9MB, time=32.45 memory used=2749.8MB, alloc=107.8MB, time=32.76 memory used=2793.7MB, alloc=107.8MB, time=32.89 memory used=2830.0MB, alloc=107.8MB, time=33.00 memory used=2873.9MB, alloc=107.8MB, time=33.12 memory used=2928.4MB, alloc=107.8MB, time=33.79 memory used=2985.2MB, alloc=107.8MB, time=34.50 memory used=3026.2MB, alloc=107.8MB, time=34.77 memory used=3071.8MB, alloc=107.8MB, time=35.63 memory used=3100.3MB, alloc=107.8MB, time=35.74 memory used=3139.8MB, alloc=107.8MB, time=35.94 memory used=3179.4MB, alloc=107.8MB, time=36.60 memory used=3232.4MB, alloc=107.8MB, time=37.16 memory used=3294.9MB, alloc=107.8MB, time=37.81 memory used=3353.9MB, alloc=131.8MB, time=38.50 memory used=3417.7MB, alloc=387.8MB, time=39.08 memory used=3514.4MB, alloc=387.8MB, time=40.18 memory used=3598.4MB, alloc=411.8MB, time=41.42 memory used=3707.3MB, alloc=435.8MB, time=42.91 memory used=3802.8MB, alloc=435.8MB, time=43.52 memory used=3875.3MB, alloc=435.8MB, time=43.94 memory used=3959.3MB, alloc=435.8MB, time=44.53 memory used=4032.1MB, alloc=435.8MB, time=44.91 memory used=4121.2MB, alloc=435.8MB, time=47.90 memory used=4182.4MB, alloc=435.8MB, time=48.15 memory used=4265.3MB, alloc=435.8MB, time=48.55 memory used=4353.2MB, alloc=435.8MB, time=50.18 memory used=4432.9MB, alloc=435.8MB, time=50.70 memory used=4510.9MB, alloc=435.8MB, time=51.14 memory used=4592.9MB, alloc=435.8MB, time=51.49 memory used=4698.5MB, alloc=435.8MB, time=56.72 memory used=4758.1MB, alloc=435.8MB, time=56.97 memory used=4818.6MB, alloc=435.8MB, time=57.20 memory used=4888.3MB, alloc=435.8MB, time=57.79 memory used=4961.8MB, alloc=435.8MB, time=58.28 memory used=5022.0MB, alloc=435.8MB, time=58.68 memory used=5104.5MB, alloc=435.8MB, time=59.29 memory used=5191.5MB, alloc=435.8MB, time=59.76 memory used=5272.7MB, alloc=435.8MB, time=61.98 memory used=5368.8MB, alloc=435.8MB, time=65.23 memory used=5421.9MB, alloc=435.8MB, time=65.48 memory used=5487.8MB, alloc=435.8MB, time=65.71 memory used=5568.4MB, alloc=435.8MB, time=66.23 memory used=5638.4MB, alloc=435.8MB, time=66.48 memory used=5721.9MB, alloc=435.8MB, time=67.17 memory used=5794.1MB, alloc=435.8MB, time=67.46 memory used=5877.7MB, alloc=435.8MB, time=71.77 memory used=5965.2MB, alloc=435.8MB, time=74.00 memory used=6018.0MB, alloc=435.8MB, time=74.23 memory used=6080.6MB, alloc=435.8MB, time=74.45 memory used=6147.3MB, alloc=435.8MB, time=75.03 memory used=6216.6MB, alloc=435.8MB, time=75.55 memory used=6280.7MB, alloc=435.8MB, time=75.77 memory used=6344.6MB, alloc=435.8MB, time=76.01 memory used=6426.7MB, alloc=435.8MB, time=76.97 memory used=6502.2MB, alloc=435.8MB, time=77.57 memory used=6653.3MB, alloc=435.8MB, time=79.41 memory used=6796.9MB, alloc=435.8MB, time=83.65 memory used=6939.2MB, alloc=435.8MB, time=87.52 memory used=7067.5MB, alloc=435.8MB, time=90.27 memory used=7197.6MB, alloc=435.8MB, time=95.59 memory used=7328.6MB, alloc=459.8MB, time=97.84 memory used=7478.4MB, alloc=459.8MB, time=103.73 memory used=7595.9MB, alloc=459.8MB, time=107.52 memory used=7680.9MB, alloc=459.8MB, time=109.65 memory used=7778.5MB, alloc=459.8MB, time=111.09 memory used=7851.5MB, alloc=459.8MB, time=111.36 memory used=7985.1MB, alloc=459.8MB, time=113.06 memory used=8129.3MB, alloc=459.8MB, time=117.25 memory used=8244.5MB, alloc=459.8MB, time=121.24 memory used=8418.7MB, alloc=459.8MB, time=122.73 memory used=8585.7MB, alloc=459.8MB, time=126.64 memory used=8736.3MB, alloc=459.8MB, time=131.25 memory used=8835.1MB, alloc=483.8MB, time=132.66 memory used=8938.3MB, alloc=483.8MB, time=133.91 memory used=9057.3MB, alloc=483.8MB, time=135.05 memory used=9139.5MB, alloc=483.8MB, time=136.24 memory used=9251.5MB, alloc=483.8MB, time=137.44 memory used=9348.1MB, alloc=483.8MB, time=138.74 memory used=9447.2MB, alloc=507.8MB, time=139.90 memory used=9538.1MB, alloc=507.8MB, time=140.30 memory used=9642.8MB, alloc=507.8MB, time=140.83 memory used=9736.7MB, alloc=507.8MB, time=141.24 memory used=9846.7MB, alloc=507.8MB, time=145.40 memory used=9943.8MB, alloc=507.8MB, time=145.83 memory used=10030.4MB, alloc=507.8MB, time=146.21 memory used=10126.0MB, alloc=507.8MB, time=146.56 memory used=10196.9MB, alloc=507.8MB, time=146.90 memory used=10279.0MB, alloc=507.8MB, time=147.22 memory used=10392.4MB, alloc=507.8MB, time=147.92 memory used=10484.0MB, alloc=507.8MB, time=148.33 memory used=10594.9MB, alloc=507.8MB, time=148.87 memory used=10682.7MB, alloc=507.8MB, time=149.29 memory used=10792.4MB, alloc=507.8MB, time=149.85 memory used=10881.4MB, alloc=507.8MB, time=150.24 memory used=11004.1MB, alloc=507.8MB, time=154.42 memory used=11091.0MB, alloc=507.8MB, time=154.82 memory used=11190.4MB, alloc=507.8MB, time=155.21 memory used=11269.1MB, alloc=507.8MB, time=155.54 memory used=11344.2MB, alloc=507.8MB, time=155.88 memory used=11432.1MB, alloc=507.8MB, time=156.22 memory used=11564.1MB, alloc=507.8MB, time=157.53 memory used=11629.1MB, alloc=507.8MB, time=158.54 memory used=11752.7MB, alloc=507.8MB, time=161.60 memory used=11842.9MB, alloc=507.8MB, time=161.97 memory used=11925.9MB, alloc=507.8MB, time=162.33 memory used=12002.5MB, alloc=507.8MB, time=162.62 memory used=12100.1MB, alloc=507.8MB, time=163.58 memory used=12159.6MB, alloc=507.8MB, time=164.46 memory used=12232.1MB, alloc=507.8MB, time=165.34 memory used=12355.6MB, alloc=507.8MB, time=166.94 memory used=12471.6MB, alloc=507.8MB, time=167.51 memory used=12585.5MB, alloc=507.8MB, time=168.00 memory used=12655.6MB, alloc=507.8MB, time=168.44 memory used=12734.1MB, alloc=507.8MB, time=168.85 memory used=12827.6MB, alloc=507.8MB, time=169.24 memory used=12954.7MB, alloc=507.8MB, time=170.57 memory used=13075.6MB, alloc=507.8MB, time=171.13 memory used=13176.0MB, alloc=507.8MB, time=171.60 memory used=13247.0MB, alloc=507.8MB, time=172.02 memory used=13330.2MB, alloc=507.8MB, time=172.42 memory used=13430.4MB, alloc=507.8MB, time=172.79 memory used=13561.8MB, alloc=531.8MB, time=219.09 memory used=13689.8MB, alloc=531.8MB, time=220.82 memory used=13783.5MB, alloc=531.8MB, time=221.31 memory used=13891.7MB, alloc=531.8MB, time=221.81 memory used=14013.5MB, alloc=531.8MB, time=222.30 memory used=14128.8MB, alloc=531.8MB, time=222.78 memory used=14211.2MB, alloc=531.8MB, time=223.21 memory used=14292.5MB, alloc=531.8MB, time=223.62 memory used=14379.9MB, alloc=531.8MB, time=224.05 memory used=14473.7MB, alloc=531.8MB, time=224.48 memory used=14575.5MB, alloc=531.8MB, time=224.89 memory used=14685.6MB, alloc=531.8MB, time=225.32 memory used=14806.9MB, alloc=531.8MB, time=225.74 memory used=15076.7MB, alloc=531.8MB, time=228.59 memory used=15179.3MB, alloc=531.8MB, time=229.07 memory used=15293.0MB, alloc=531.8MB, time=229.52 memory used=15412.5MB, alloc=531.8MB, time=230.71 memory used=15557.1MB, alloc=531.8MB, time=231.34 memory used=15662.9MB, alloc=531.8MB, time=231.84 memory used=15754.6MB, alloc=531.8MB, time=232.29 memory used=15866.7MB, alloc=531.8MB, time=232.74 memory used=16022.7MB, alloc=531.8MB, time=234.19 memory used=16160.1MB, alloc=531.8MB, time=234.79 memory used=16251.3MB, alloc=531.8MB, time=235.26 memory used=16347.8MB, alloc=531.8MB, time=235.70 memory used=16468.6MB, alloc=531.8MB, time=236.15 |\^/| 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(); 1428285232 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 3 3 3 F := [-10 y z - 4 z + 13 y + 4 x, 16 x y - 3 x - 14 y + 17 x y, 4 2 -3 y + 4 y z + 11 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 3 G := [-15 x + 15 x z - 5 y z + 10 z, -11 x z - 14 z + 16 x y + 20, 2 3 2 2 -18 x y z + 20 x z + 17 x z - 5 y ] > Problem := [F,G]; 2 2 4 2 3 3 3 Problem := [[-10 y z - 4 z + 13 y + 4 x, 16 x y - 3 x - 14 y + 17 x y, 4 2 4 2 2 2 2 -3 y + 4 y z + 11 x z], [-15 x + 15 x z - 5 y z + 10 z, 2 3 2 3 2 2 -11 x z - 14 z + 16 x y + 20, -18 x y z + 20 x z + 17 x z - 5 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.1MB, alloc=32.3MB, time=0.47 memory used=46.0MB, alloc=60.3MB, time=0.78 memory used=86.9MB, alloc=60.3MB, time=1.06 memory used=157.8MB, alloc=69.5MB, time=1.64 memory used=195.7MB, alloc=69.5MB, time=1.89 memory used=249.2MB, alloc=69.5MB, time=2.29 memory used=315.5MB, alloc=69.5MB, time=2.77 memory used=374.1MB, alloc=69.5MB, time=3.29 memory used=420.6MB, alloc=69.5MB, time=3.92 memory used=450.5MB, alloc=69.5MB, time=4.11 memory used=496.4MB, alloc=69.5MB, time=4.69 memory used=538.4MB, alloc=93.5MB, time=5.29 memory used=600.8MB, alloc=93.5MB, time=6.07 memory used=670.3MB, alloc=93.5MB, time=6.92 memory used=736.1MB, alloc=93.5MB, time=7.57 memory used=770.4MB, alloc=93.5MB, time=7.73 memory used=799.4MB, alloc=93.5MB, time=7.84 memory used=835.6MB, alloc=93.5MB, time=8.01 memory used=876.1MB, alloc=93.5MB, time=8.24 memory used=904.0MB, alloc=93.5MB, time=8.35 memory used=935.2MB, alloc=93.5MB, time=8.46 memory used=961.5MB, alloc=93.5MB, time=8.55 memory used=1003.7MB, alloc=93.5MB, time=8.85 memory used=1033.4MB, alloc=93.5MB, time=8.96 memory used=1062.3MB, alloc=93.5MB, time=9.07 memory used=1092.1MB, alloc=93.5MB, time=9.16 memory used=1134.0MB, alloc=93.5MB, time=9.48 memory used=1167.5MB, alloc=93.5MB, time=9.61 memory used=1194.4MB, alloc=93.5MB, time=9.70 memory used=1227.3MB, alloc=93.5MB, time=9.80 memory used=1263.5MB, alloc=93.5MB, time=10.08 memory used=1295.6MB, alloc=93.5MB, time=10.21 memory used=1330.6MB, alloc=93.5MB, time=10.34 memory used=1356.3MB, alloc=93.5MB, time=10.44 memory used=1380.6MB, alloc=93.5MB, time=10.55 memory used=1408.3MB, alloc=93.5MB, time=10.65 memory used=1439.7MB, alloc=93.5MB, time=10.76 memory used=1474.5MB, alloc=93.5MB, time=10.86 memory used=1510.4MB, alloc=117.5MB, time=10.99 memory used=1543.9MB, alloc=117.5MB, time=11.09 memory used=1581.1MB, alloc=117.5MB, time=11.20 memory used=1621.9MB, alloc=117.5MB, time=11.31 memory used=1677.0MB, alloc=117.5MB, time=11.59 memory used=1729.6MB, alloc=117.5MB, time=11.77 memory used=1776.0MB, alloc=117.5MB, time=11.91 memory used=1817.4MB, alloc=117.5MB, time=12.06 memory used=1868.2MB, alloc=117.5MB, time=12.20 memory used=1926.2MB, alloc=117.5MB, time=12.34 memory used=1959.6MB, alloc=117.5MB, time=12.45 memory used=1996.5MB, alloc=117.5MB, time=12.55 memory used=2037.2MB, alloc=117.5MB, time=12.65 memory used=2091.2MB, alloc=117.5MB, time=13.03 memory used=2152.9MB, alloc=117.5MB, time=13.35 memory used=2195.2MB, alloc=117.5MB, time=13.48 memory used=2251.1MB, alloc=117.5MB, time=13.62 memory used=2285.7MB, alloc=117.5MB, time=13.73 memory used=2326.0MB, alloc=117.5MB, time=13.84 memory used=2374.7MB, alloc=117.5MB, time=13.94 memory used=2434.6MB, alloc=117.5MB, time=14.16 memory used=2493.7MB, alloc=117.5MB, time=14.39 memory used=2536.0MB, alloc=117.5MB, time=14.51 memory used=2597.4MB, alloc=117.5MB, time=14.81 memory used=2643.8MB, alloc=117.5MB, time=14.95 memory used=2699.4MB, alloc=117.5MB, time=15.21 memory used=2755.9MB, alloc=117.5MB, time=15.53 memory used=2807.8MB, alloc=117.5MB, time=15.79 memory used=2869.1MB, alloc=117.5MB, time=16.10 memory used=2914.6MB, alloc=117.5MB, time=16.25 memory used=2962.8MB, alloc=117.5MB, time=16.38 memory used=3019.0MB, alloc=117.5MB, time=16.62 memory used=3064.2MB, alloc=117.5MB, time=16.76 memory used=3120.3MB, alloc=117.5MB, time=17.00 memory used=3165.6MB, alloc=117.5MB, time=17.14 memory used=3213.0MB, alloc=117.5MB, time=17.26 memory used=3283.7MB, alloc=119.2MB, time=18.10 memory used=3339.6MB, alloc=119.2MB, time=18.29 memory used=3375.1MB, alloc=119.2MB, time=18.46 memory used=3417.3MB, alloc=119.2MB, time=18.63 memory used=3463.6MB, alloc=119.2MB, time=18.80 memory used=3514.1MB, alloc=119.2MB, time=18.95 memory used=3571.2MB, alloc=119.2MB, time=19.12 memory used=3611.0MB, alloc=119.2MB, time=19.26 memory used=3642.0MB, alloc=119.2MB, time=19.40 memory used=3671.4MB, alloc=119.2MB, time=19.52 memory used=3702.2MB, alloc=119.2MB, time=19.63 memory used=3736.5MB, alloc=119.2MB, time=19.76 memory used=3772.3MB, alloc=119.2MB, time=19.90 memory used=3808.7MB, alloc=119.2MB, time=20.03 memory used=3845.8MB, alloc=119.2MB, time=20.17 memory used=3883.6MB, alloc=119.2MB, time=20.31 memory used=3922.7MB, alloc=119.2MB, time=20.44 memory used=3965.5MB, alloc=119.2MB, time=20.57 memory used=4009.7MB, alloc=119.2MB, time=20.69 memory used=4054.4MB, alloc=119.2MB, time=20.82 memory used=4100.5MB, alloc=119.2MB, time=20.96 memory used=4150.0MB, alloc=119.2MB, time=21.10 memory used=4200.9MB, alloc=119.2MB, time=21.24 memory used=4252.9MB, alloc=119.2MB, time=21.37 memory used=4308.4MB, alloc=119.2MB, time=21.52 memory used=4355.1MB, alloc=119.2MB, time=21.65 memory used=4382.6MB, alloc=143.2MB, time=21.76 memory used=4421.0MB, alloc=143.2MB, time=21.88 memory used=4460.5MB, alloc=143.2MB, time=22.00 memory used=4500.7MB, alloc=143.2MB, time=22.13 memory used=4545.5MB, alloc=143.2MB, time=22.25 memory used=4589.9MB, alloc=143.2MB, time=22.38 memory used=4634.0MB, alloc=143.2MB, time=22.53 memory used=4682.3MB, alloc=143.2MB, time=22.65 memory used=4730.0MB, alloc=143.2MB, time=22.77 memory used=4781.4MB, alloc=143.2MB, time=22.90 memory used=4832.6MB, alloc=143.2MB, time=23.02 memory used=4885.2MB, alloc=143.2MB, time=23.16 memory used=4941.3MB, alloc=143.2MB, time=23.29 memory used=4999.3MB, alloc=143.2MB, time=23.42 memory used=5059.5MB, alloc=143.2MB, time=23.55 memory used=5122.5MB, alloc=143.2MB, time=23.67 memory used=5189.1MB, alloc=143.2MB, time=23.80 memory used=5285.1MB, alloc=145.1MB, time=24.74 memory used=5349.7MB, alloc=145.1MB, time=24.96 memory used=5405.5MB, alloc=145.1MB, time=25.16 memory used=5473.0MB, alloc=145.1MB, time=25.36 memory used=5549.5MB, alloc=145.1MB, time=25.56 memory used=5608.7MB, alloc=145.1MB, time=25.73 memory used=5653.4MB, alloc=145.1MB, time=25.90 memory used=5700.9MB, alloc=145.1MB, time=26.07 memory used=5749.9MB, alloc=145.1MB, time=26.23 memory used=5801.0MB, alloc=145.1MB, time=26.40 memory used=5856.9MB, alloc=145.1MB, time=26.55 memory used=5914.8MB, alloc=145.1MB, time=26.72 memory used=5978.6MB, alloc=145.1MB, time=26.90 memory used=6043.8MB, alloc=145.1MB, time=27.07 memory used=6114.8MB, alloc=145.1MB, time=27.25 memory used=6186.8MB, alloc=145.1MB, time=27.42 memory used=6264.6MB, alloc=145.1MB, time=27.60 memory used=6340.7MB, alloc=145.1MB, time=27.76 memory used=6379.8MB, alloc=145.1MB, time=27.88 memory used=6419.2MB, alloc=145.1MB, time=28.00 memory used=6459.5MB, alloc=145.1MB, time=28.12 memory used=6500.4MB, alloc=145.1MB, time=28.24 memory used=6544.3MB, alloc=145.1MB, time=28.36 memory used=6588.7MB, alloc=145.1MB, time=28.48 memory used=6633.5MB, alloc=145.1MB, time=28.62 memory used=6680.8MB, alloc=145.1MB, time=28.74 memory used=6729.2MB, alloc=145.1MB, time=28.86 memory used=6779.5MB, alloc=145.1MB, time=28.99 memory used=6830.8MB, alloc=145.1MB, time=29.11 memory used=6884.1MB, alloc=145.1MB, time=29.24 memory used=6939.7MB, alloc=145.1MB, time=29.36 memory used=6997.5MB, alloc=145.1MB, time=29.48 memory used=7058.8MB, alloc=145.1MB, time=29.62 memory used=7122.6MB, alloc=145.1MB, time=29.75 memory used=7190.6MB, alloc=145.1MB, time=29.87 memory used=7273.8MB, alloc=169.1MB, time=60.60 memory used=7340.2MB, alloc=169.1MB, time=124.61 memory used=7421.2MB, alloc=169.1MB, time=222.47 |\^/| 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(); 1428285532 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-7 x y z - 2 x y z + 19 y z + 3 x y, 2 3 2 3 2 2 4 4 19 x y z + 15 x + 14 x y + 13 y , -11 x y + 3 y - 17 z - 9 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 3 3 3 G := [8 x y z - 20 y z + 5 z - 14 y, -19 x z + 17 y z + 3 x + 14 z , 2 2 3 2 x y - 7 x y + 19 z] > Problem := [F,G]; 2 2 Problem := [[-7 x y z - 2 x y z + 19 y z + 3 x y, 2 3 2 3 2 2 4 4 19 x y z + 15 x + 14 x y + 13 y , -11 x y + 3 y - 17 z - 9 y z], [ 2 2 2 3 2 2 3 3 3 8 x y z - 20 y z + 5 z - 14 y, -19 x z + 17 y z + 3 x + 14 z , 2 2 3 2 x y - 7 x y + 19 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=30.1MB, alloc=39.2MB, time=0.41 memory used=50.9MB, alloc=39.2MB, time=0.60 memory used=74.0MB, alloc=39.2MB, time=0.81 memory used=95.9MB, alloc=39.2MB, time=1.08 memory used=114.3MB, alloc=39.2MB, time=1.14 memory used=126.5MB, alloc=39.2MB, time=1.18 memory used=136.5MB, alloc=39.2MB, time=1.23 memory used=155.9MB, alloc=39.2MB, time=1.32 memory used=168.9MB, alloc=39.2MB, time=1.36 memory used=178.1MB, alloc=39.2MB, time=1.39 memory used=204.5MB, alloc=39.2MB, time=3.23 memory used=218.6MB, alloc=39.2MB, time=3.27 memory used=228.4MB, alloc=39.2MB, time=3.31 memory used=240.3MB, alloc=39.2MB, time=3.35 memory used=254.1MB, alloc=39.2MB, time=3.38 memory used=263.2MB, alloc=39.2MB, time=3.42 memory used=271.7MB, alloc=63.2MB, time=3.46 memory used=297.1MB, alloc=63.2MB, time=3.52 memory used=329.1MB, alloc=63.2MB, time=3.58 memory used=362.4MB, alloc=63.2MB, time=3.85 memory used=390.5MB, alloc=63.2MB, time=4.04 memory used=417.9MB, alloc=63.2MB, time=4.12 memory used=446.3MB, alloc=63.2MB, time=4.20 memory used=472.2MB, alloc=83.8MB, time=4.54 memory used=510.3MB, alloc=83.8MB, time=4.63 memory used=536.0MB, alloc=83.8MB, time=4.68 memory used=555.3MB, alloc=83.8MB, time=4.75 memory used=592.7MB, alloc=83.8MB, time=4.84 memory used=618.3MB, alloc=83.8MB, time=4.89 memory used=638.3MB, alloc=83.8MB, time=4.97 memory used=675.6MB, alloc=83.8MB, time=5.05 memory used=701.2MB, alloc=83.8MB, time=5.11 memory used=747.2MB, alloc=83.8MB, time=5.97 memory used=801.0MB, alloc=83.8MB, time=6.68 memory used=856.8MB, alloc=83.8MB, time=7.84 memory used=913.8MB, alloc=83.8MB, time=10.05 memory used=966.0MB, alloc=83.8MB, time=11.77 memory used=1014.0MB, alloc=83.8MB, time=12.58 memory used=1058.3MB, alloc=83.8MB, time=13.03 memory used=1095.5MB, alloc=83.8MB, time=13.26 memory used=1119.3MB, alloc=83.8MB, time=13.34 memory used=1161.8MB, alloc=83.8MB, time=13.81 memory used=1188.1MB, alloc=83.8MB, time=13.90 memory used=1209.8MB, alloc=83.8MB, time=13.98 memory used=1255.1MB, alloc=83.8MB, time=14.38 memory used=1302.9MB, alloc=83.8MB, time=15.01 memory used=1324.1MB, alloc=83.8MB, time=15.09 memory used=1347.4MB, alloc=83.8MB, time=15.17 memory used=1385.7MB, alloc=83.8MB, time=18.00 memory used=1411.4MB, alloc=83.8MB, time=18.09 memory used=1430.9MB, alloc=83.8MB, time=18.16 memory used=1453.3MB, alloc=83.8MB, time=18.24 memory used=1480.5MB, alloc=83.8MB, time=18.31 memory used=1498.5MB, alloc=83.8MB, time=18.38 memory used=1516.2MB, alloc=83.8MB, time=18.46 memory used=1535.9MB, alloc=83.8MB, time=18.52 memory used=1558.4MB, alloc=83.8MB, time=18.59 memory used=1587.7MB, alloc=83.8MB, time=18.85 memory used=1609.8MB, alloc=83.8MB, time=18.94 memory used=1631.0MB, alloc=83.8MB, time=19.12 memory used=1662.3MB, alloc=83.8MB, time=19.21 memory used=1685.5MB, alloc=83.8MB, time=19.28 memory used=1712.6MB, alloc=83.8MB, time=19.51 memory used=1761.3MB, alloc=83.8MB, time=19.98 memory used=1799.5MB, alloc=83.8MB, time=20.14 memory used=1834.9MB, alloc=83.8MB, time=20.44 memory used=1870.6MB, alloc=83.8MB, time=20.73 memory used=1914.9MB, alloc=83.8MB, time=21.32 memory used=1967.2MB, alloc=107.8MB, time=22.04 memory used=2033.7MB, alloc=107.8MB, time=22.59 memory used=2088.0MB, alloc=363.8MB, time=23.20 memory used=2149.1MB, alloc=363.8MB, time=23.90 memory used=2198.3MB, alloc=387.8MB, time=24.27 memory used=2247.5MB, alloc=387.8MB, time=24.44 memory used=2297.8MB, alloc=387.8MB, time=24.59 memory used=2336.4MB, alloc=387.8MB, time=24.73 memory used=2398.9MB, alloc=387.8MB, time=25.12 memory used=2447.3MB, alloc=387.8MB, time=25.27 memory used=2489.9MB, alloc=387.8MB, time=25.41 memory used=2546.0MB, alloc=387.8MB, time=26.21 memory used=2592.8MB, alloc=387.8MB, time=26.37 memory used=2648.5MB, alloc=387.8MB, time=26.61 memory used=2711.2MB, alloc=387.8MB, time=26.94 memory used=2771.0MB, alloc=387.8MB, time=27.48 memory used=2839.4MB, alloc=387.8MB, time=27.71 memory used=2878.4MB, alloc=387.8MB, time=27.87 memory used=2926.3MB, alloc=387.8MB, time=28.03 memory used=2981.7MB, alloc=387.8MB, time=28.19 memory used=3017.3MB, alloc=387.8MB, time=28.33 memory used=3053.5MB, alloc=387.8MB, time=28.46 memory used=3094.1MB, alloc=387.8MB, time=28.60 memory used=3140.4MB, alloc=387.8MB, time=28.73 memory used=3210.3MB, alloc=387.8MB, time=29.29 memory used=3260.8MB, alloc=387.8MB, time=29.49 memory used=3303.5MB, alloc=387.8MB, time=29.64 memory used=3356.3MB, alloc=387.8MB, time=29.81 memory used=3403.3MB, alloc=387.8MB, time=29.98 memory used=3437.7MB, alloc=387.8MB, time=30.11 memory used=3475.6MB, alloc=387.8MB, time=30.24 memory used=3518.2MB, alloc=387.8MB, time=30.37 memory used=3567.3MB, alloc=387.8MB, time=30.51 memory used=3644.3MB, alloc=387.8MB, time=36.19 memory used=3694.7MB, alloc=387.8MB, time=36.34 memory used=3732.4MB, alloc=387.8MB, time=36.48 memory used=3778.9MB, alloc=387.8MB, time=36.62 memory used=3832.4MB, alloc=387.8MB, time=36.76 memory used=3866.9MB, alloc=387.8MB, time=36.87 memory used=3906.2MB, alloc=387.8MB, time=36.98 memory used=3960.5MB, alloc=387.8MB, time=37.49 memory used=4023.7MB, alloc=387.8MB, time=37.84 memory used=4092.3MB, alloc=387.8MB, time=38.48 memory used=4138.8MB, alloc=387.8MB, time=38.65 memory used=4182.8MB, alloc=387.8MB, time=38.81 memory used=4236.8MB, alloc=387.8MB, time=38.99 memory used=4281.9MB, alloc=387.8MB, time=39.14 memory used=4317.2MB, alloc=387.8MB, time=39.27 memory used=4355.9MB, alloc=387.8MB, time=39.40 memory used=4399.2MB, alloc=387.8MB, time=39.53 memory used=4449.0MB, alloc=387.8MB, time=39.65 memory used=4525.8MB, alloc=387.8MB, time=40.29 memory used=4567.8MB, alloc=387.8MB, time=40.46 memory used=4613.1MB, alloc=387.8MB, time=40.62 memory used=4669.3MB, alloc=387.8MB, time=40.77 memory used=4709.7MB, alloc=387.8MB, time=40.91 memory used=4744.9MB, alloc=387.8MB, time=41.05 memory used=4783.8MB, alloc=387.8MB, time=41.18 memory used=4827.8MB, alloc=387.8MB, time=41.31 memory used=4880.5MB, alloc=387.8MB, time=41.59 memory used=4964.8MB, alloc=387.8MB, time=51.44 memory used=5015.0MB, alloc=387.8MB, time=51.61 memory used=5055.0MB, alloc=387.8MB, time=51.76 memory used=5096.1MB, alloc=387.8MB, time=51.90 memory used=5144.8MB, alloc=387.8MB, time=52.04 memory used=5199.9MB, alloc=387.8MB, time=52.19 memory used=5236.7MB, alloc=387.8MB, time=52.30 memory used=5271.4MB, alloc=387.8MB, time=52.41 memory used=5308.8MB, alloc=387.8MB, time=52.55 memory used=5351.3MB, alloc=387.8MB, time=52.66 memory used=5421.7MB, alloc=387.8MB, time=53.25 memory used=5470.4MB, alloc=387.8MB, time=53.45 memory used=5514.5MB, alloc=387.8MB, time=53.60 memory used=5568.9MB, alloc=387.8MB, time=53.77 memory used=5613.6MB, alloc=387.8MB, time=53.91 memory used=5648.6MB, alloc=387.8MB, time=54.04 memory used=5687.7MB, alloc=387.8MB, time=54.17 memory used=5731.3MB, alloc=387.8MB, time=54.30 memory used=5790.7MB, alloc=387.8MB, time=54.89 memory used=5858.9MB, alloc=387.8MB, time=55.12 memory used=5898.8MB, alloc=387.8MB, time=55.29 memory used=5948.1MB, alloc=387.8MB, time=55.46 memory used=6002.9MB, alloc=387.8MB, time=55.62 memory used=6038.3MB, alloc=387.8MB, time=55.76 memory used=6075.2MB, alloc=387.8MB, time=55.89 memory used=6116.6MB, alloc=387.8MB, time=56.03 memory used=6164.0MB, alloc=387.8MB, time=56.16 memory used=6247.2MB, alloc=387.8MB, time=65.46 memory used=6296.9MB, alloc=387.8MB, time=65.64 memory used=6343.9MB, alloc=387.8MB, time=65.80 memory used=6381.3MB, alloc=387.8MB, time=65.93 memory used=6426.3MB, alloc=387.8MB, 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alloc=483.8MB, time=219.14 memory used=25785.1MB, alloc=483.8MB, time=219.40 memory used=25960.1MB, alloc=483.8MB, time=220.29 memory used=26142.8MB, alloc=483.8MB, time=221.12 |\^/| 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(); 1428285832 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 3 2 3 F := [-7 x - 18 x y z - 14 x y - 9 z , 7 y z - 2 x z + 13 y - 5 y, 4 3 4 9 x - 3 x z - 5 z - 13 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 2 G := [9 x - 13 y z + 5 x y - 11 y z, -15 x y - 16 x y - 4 x - 8 x, 3 3 2 -16 x z - 15 y z - 8 x z + 11 y ] > Problem := [F,G]; 4 2 2 3 3 2 3 Problem := [[-7 x - 18 x y z - 14 x y - 9 z , 7 y z - 2 x z + 13 y - 5 y, 4 3 4 4 3 9 x - 3 x z - 5 z - 13 x], [9 x - 13 y z + 5 x y - 11 y z, 2 2 2 2 3 3 2 -15 x y - 16 x y - 4 x - 8 x, -16 x z - 15 y z - 8 x z + 11 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=24.8MB, alloc=32.3MB, time=0.46 memory used=47.3MB, alloc=37.9MB, time=0.63 memory used=66.4MB, alloc=37.9MB, time=0.73 memory used=84.5MB, alloc=37.9MB, time=0.78 memory used=95.0MB, alloc=37.9MB, time=0.82 memory used=107.4MB, alloc=37.9MB, time=0.85 memory used=123.2MB, alloc=37.9MB, time=1.00 memory used=145.3MB, alloc=37.9MB, time=1.38 memory used=160.1MB, alloc=37.9MB, time=1.45 memory used=180.8MB, alloc=37.9MB, time=1.64 memory used=203.0MB, alloc=61.9MB, time=1.92 memory used=249.0MB, alloc=69.9MB, time=2.43 memory used=293.7MB, alloc=69.9MB, time=2.91 memory used=332.4MB, alloc=69.9MB, time=3.12 memory used=359.6MB, alloc=69.9MB, time=3.26 memory used=406.7MB, alloc=69.9MB, time=6.38 memory used=431.6MB, alloc=69.9MB, time=6.47 memory used=458.0MB, alloc=69.9MB, time=6.55 memory used=477.8MB, alloc=69.9MB, time=6.62 memory used=500.5MB, alloc=69.9MB, time=6.70 memory used=526.1MB, alloc=69.9MB, time=6.78 memory used=555.5MB, alloc=69.9MB, time=6.86 memory used=584.5MB, alloc=69.9MB, time=6.93 memory used=601.5MB, alloc=69.9MB, time=6.98 memory used=618.9MB, alloc=69.9MB, time=7.03 memory used=637.9MB, alloc=69.9MB, time=7.09 memory used=657.2MB, alloc=69.9MB, time=7.15 memory used=677.8MB, alloc=69.9MB, time=7.21 memory used=699.7MB, alloc=69.9MB, time=7.27 memory used=722.9MB, alloc=69.9MB, time=7.33 memory used=747.1MB, alloc=69.9MB, time=7.39 memory used=772.3MB, alloc=69.9MB, time=7.45 memory used=798.6MB, alloc=69.9MB, time=7.51 memory used=827.1MB, alloc=69.9MB, time=7.57 memory used=857.2MB, alloc=69.9MB, time=7.63 memory used=898.6MB, alloc=83.8MB, time=7.72 memory used=909.5MB, alloc=83.8MB, time=7.76 memory used=920.6MB, alloc=83.8MB, time=7.82 memory used=931.7MB, alloc=83.8MB, time=7.85 memory used=943.4MB, alloc=83.8MB, time=7.92 memory used=985.3MB, alloc=83.8MB, time=8.28 memory used=1017.3MB, alloc=83.8MB, time=8.61 memory used=1042.5MB, alloc=83.8MB, time=8.69 memory used=1083.2MB, alloc=83.8MB, time=9.14 memory used=1138.7MB, alloc=83.8MB, time=9.71 memory used=1186.1MB, alloc=83.8MB, time=10.34 memory used=1219.7MB, alloc=83.8MB, time=10.63 memory used=1248.6MB, alloc=83.8MB, time=10.79 memory used=1286.4MB, alloc=83.8MB, time=11.15 memory used=1317.8MB, alloc=83.8MB, time=11.25 memory used=1336.9MB, alloc=83.8MB, time=11.32 memory used=1356.4MB, alloc=83.8MB, time=11.40 memory used=1379.2MB, alloc=83.8MB, time=11.48 memory used=1404.8MB, alloc=83.8MB, time=11.58 memory used=1429.9MB, alloc=83.8MB, time=11.66 memory used=1448.3MB, alloc=83.8MB, time=11.73 memory used=1465.3MB, alloc=83.8MB, time=11.81 memory used=1483.9MB, alloc=83.8MB, time=11.88 memory used=1504.4MB, alloc=83.8MB, time=11.95 memory used=1537.1MB, alloc=83.8MB, time=12.98 memory used=1574.7MB, alloc=83.8MB, time=13.15 memory used=1595.4MB, alloc=83.8MB, time=13.24 memory used=1621.5MB, alloc=83.8MB, time=13.32 memory used=1640.7MB, alloc=83.8MB, time=13.40 memory used=1659.0MB, alloc=83.8MB, time=13.47 memory used=1679.7MB, alloc=83.8MB, time=13.54 memory used=1703.9MB, alloc=83.8MB, time=13.61 memory used=1730.4MB, alloc=83.8MB, time=13.77 memory used=1753.6MB, alloc=83.8MB, time=13.92 memory used=1776.5MB, alloc=83.8MB, time=14.00 memory used=1807.0MB, alloc=83.8MB, time=14.23 memory used=1828.4MB, alloc=83.8MB, time=14.29 memory used=1856.6MB, alloc=83.8MB, time=14.38 memory used=1879.0MB, alloc=83.8MB, time=14.45 memory used=1900.2MB, alloc=83.8MB, time=14.51 memory used=1966.4MB, alloc=83.8MB, time=15.56 memory used=2011.5MB, alloc=83.8MB, time=15.83 memory used=2031.2MB, alloc=83.8MB, time=15.92 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time=64.46 memory used=4799.1MB, alloc=131.8MB, time=64.58 memory used=4856.6MB, alloc=131.8MB, time=64.69 memory used=4913.9MB, alloc=131.8MB, time=64.81 memory used=4973.9MB, alloc=131.8MB, time=64.92 memory used=5033.7MB, alloc=131.8MB, time=65.04 memory used=5099.1MB, alloc=131.8MB, time=65.16 memory used=5166.7MB, alloc=131.8MB, time=65.29 memory used=5237.1MB, alloc=131.8MB, time=65.43 memory used=5309.6MB, alloc=131.8MB, time=65.55 memory used=5384.0MB, alloc=131.8MB, time=65.68 memory used=5440.3MB, alloc=131.8MB, time=65.80 memory used=5456.0MB, alloc=131.8MB, time=65.86 memory used=5467.8MB, alloc=131.8MB, time=65.92 memory used=5477.2MB, alloc=131.8MB, time=66.00 memory used=5486.7MB, alloc=131.8MB, time=66.07 memory used=5494.2MB, alloc=131.8MB, time=66.13 memory used=5501.8MB, alloc=131.8MB, time=66.19 memory used=5509.6MB, alloc=131.8MB, time=66.25 memory used=5517.5MB, alloc=131.8MB, time=66.33 memory used=5525.5MB, alloc=131.8MB, time=66.39 memory used=5533.3MB, 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time=79.11 memory used=7792.7MB, alloc=131.8MB, time=79.17 memory used=7807.9MB, alloc=131.8MB, time=79.25 memory used=7823.2MB, alloc=131.8MB, time=79.32 memory used=7838.7MB, alloc=131.8MB, time=79.40 memory used=7854.2MB, alloc=131.8MB, time=79.46 memory used=7869.9MB, alloc=131.8MB, time=79.52 memory used=7885.7MB, alloc=131.8MB, time=79.59 memory used=7901.6MB, alloc=131.8MB, time=79.66 memory used=7917.6MB, alloc=131.8MB, time=79.73 memory used=7933.8MB, alloc=131.8MB, time=79.81 memory used=7950.1MB, alloc=131.8MB, time=79.88 memory used=7966.5MB, alloc=131.8MB, time=79.97 memory used=7983.0MB, alloc=131.8MB, time=80.06 memory used=7999.7MB, alloc=131.8MB, time=80.12 memory used=8016.4MB, alloc=131.8MB, time=80.20 memory used=8033.3MB, alloc=131.8MB, time=80.27 memory used=8050.3MB, alloc=131.8MB, time=80.35 memory used=8067.5MB, alloc=131.8MB, time=80.41 memory used=8084.7MB, alloc=131.8MB, time=80.48 memory used=8101.3MB, alloc=131.8MB, time=80.54 memory used=8114.5MB, alloc=131.8MB, time=80.61 memory used=8128.6MB, alloc=131.8MB, time=80.71 memory used=8144.3MB, alloc=131.8MB, time=80.78 memory used=8161.4MB, alloc=131.8MB, time=80.87 memory used=8182.0MB, alloc=131.8MB, time=80.95 memory used=8203.1MB, alloc=131.8MB, time=81.02 memory used=8224.7MB, alloc=131.8MB, time=81.10 memory used=8246.8MB, alloc=131.8MB, time=81.18 memory used=8269.3MB, alloc=131.8MB, time=81.26 memory used=8292.3MB, alloc=131.8MB, time=81.35 memory used=8315.8MB, alloc=131.8MB, time=81.42 memory used=8339.7MB, alloc=131.8MB, time=81.50 memory used=8364.2MB, alloc=131.8MB, time=81.62 memory used=8389.1MB, alloc=131.8MB, time=81.71 memory used=8414.4MB, alloc=131.8MB, time=81.81 memory used=8440.3MB, alloc=131.8MB, time=81.89 memory used=8466.6MB, alloc=131.8MB, time=81.97 memory used=8491.8MB, alloc=131.8MB, time=82.05 memory used=8503.9MB, alloc=131.8MB, time=82.11 memory used=8516.1MB, alloc=131.8MB, time=82.18 memory used=8528.3MB, alloc=131.8MB, time=82.24 memory used=8541.4MB, alloc=131.8MB, time=82.31 memory used=8555.4MB, alloc=131.8MB, time=82.37 memory used=8569.5MB, alloc=131.8MB, time=82.44 memory used=8583.7MB, alloc=131.8MB, time=82.53 memory used=8598.0MB, alloc=131.8MB, time=82.60 memory used=8612.4MB, alloc=131.8MB, time=82.67 memory used=8627.0MB, alloc=131.8MB, time=82.74 memory used=8641.7MB, alloc=131.8MB, time=82.82 memory used=8656.5MB, alloc=131.8MB, time=82.89 memory used=8671.4MB, alloc=131.8MB, time=82.96 memory used=8686.5MB, alloc=131.8MB, time=83.04 memory used=8701.7MB, alloc=131.8MB, time=83.12 memory used=8717.0MB, alloc=131.8MB, time=83.19 memory used=8732.4MB, alloc=131.8MB, time=83.26 memory used=8747.9MB, alloc=131.8MB, time=83.32 memory used=8763.5MB, alloc=131.8MB, time=83.39 memory used=8779.3MB, alloc=131.8MB, time=83.45 memory used=8795.1MB, alloc=131.8MB, time=83.53 memory used=8811.1MB, alloc=131.8MB, time=83.61 memory used=8827.2MB, alloc=131.8MB, time=83.69 memory used=8843.4MB, alloc=131.8MB, time=83.77 memory used=8859.8MB, alloc=131.8MB, time=83.85 memory used=8876.2MB, alloc=131.8MB, time=83.92 memory used=8892.8MB, alloc=131.8MB, time=83.98 memory used=8909.5MB, alloc=131.8MB, time=84.05 memory used=8926.2MB, alloc=131.8MB, time=84.11 memory used=8943.2MB, alloc=131.8MB, time=84.17 memory used=8960.2MB, alloc=131.8MB, time=84.25 memory used=8977.1MB, alloc=131.8MB, time=84.32 memory used=8990.3MB, alloc=131.8MB, time=84.39 memory used=9003.4MB, alloc=131.8MB, time=84.45 memory used=9128.9MB, alloc=131.8MB, time=86.44 memory used=9246.9MB, alloc=131.8MB, time=87.40 memory used=9333.9MB, alloc=131.8MB, time=87.98 memory used=9388.3MB, alloc=131.8MB, time=88.14 memory used=9448.8MB, alloc=131.8MB, time=88.30 memory used=9490.3MB, alloc=131.8MB, time=88.44 memory used=9539.6MB, alloc=131.8MB, time=88.58 memory used=9598.6MB, alloc=131.8MB, time=88.70 memory used=9672.2MB, alloc=131.8MB, time=89.83 memory used=9732.1MB, alloc=131.8MB, time=89.98 memory used=9779.9MB, alloc=131.8MB, time=90.12 memory used=9839.3MB, alloc=131.8MB, time=90.24 memory used=9881.2MB, alloc=131.8MB, time=90.34 memory used=9991.8MB, alloc=387.8MB, time=91.49 memory used=10062.1MB, alloc=387.8MB, time=91.76 memory used=10111.6MB, alloc=387.8MB, time=91.91 memory used=10164.1MB, alloc=387.8MB, time=92.05 memory used=10229.7MB, alloc=387.8MB, time=92.19 memory used=10270.2MB, alloc=387.8MB, time=92.30 memory used=10313.3MB, alloc=387.8MB, time=92.41 memory used=10361.4MB, alloc=387.8MB, time=92.53 memory used=10427.4MB, alloc=387.8MB, time=92.78 memory used=10500.5MB, alloc=387.8MB, time=107.89 memory used=10568.6MB, alloc=387.8MB, time=131.07 memory used=10678.4MB, alloc=387.8MB, time=133.13 memory used=10773.8MB, alloc=387.8MB, time=133.71 memory used=10821.4MB, alloc=387.8MB, time=133.86 memory used=10880.6MB, alloc=387.8MB, time=134.04 memory used=10933.3MB, alloc=387.8MB, time=134.20 memory used=10971.9MB, alloc=387.8MB, time=134.36 memory used=11012.5MB, alloc=387.8MB, time=134.48 memory used=11055.9MB, alloc=387.8MB, time=134.63 memory used=11104.0MB, alloc=387.8MB, time=134.76 memory used=11154.7MB, alloc=387.8MB, time=134.90 memory used=11208.1MB, alloc=387.8MB, time=135.04 memory used=11266.5MB, alloc=387.8MB, time=135.20 memory used=11327.4MB, alloc=387.8MB, time=135.35 memory used=11391.0MB, alloc=387.8MB, time=135.51 memory used=11446.5MB, alloc=387.8MB, time=135.64 memory used=11479.5MB, alloc=387.8MB, time=135.74 memory used=11511.4MB, alloc=387.8MB, time=135.84 memory used=11545.7MB, alloc=387.8MB, time=135.95 memory used=11580.6MB, alloc=387.8MB, time=136.06 memory used=11616.0MB, alloc=387.8MB, time=136.16 memory used=11652.0MB, alloc=387.8MB, time=136.27 memory used=11688.4MB, alloc=387.8MB, time=136.37 memory used=11725.3MB, alloc=387.8MB, time=136.48 memory used=11762.7MB, alloc=387.8MB, time=136.58 memory used=11804.0MB, alloc=387.8MB, time=136.69 memory used=11845.8MB, alloc=387.8MB, time=136.80 memory used=11888.1MB, alloc=387.8MB, time=136.91 memory used=11930.9MB, alloc=387.8MB, time=137.03 memory used=11974.2MB, alloc=387.8MB, time=137.14 memory used=12017.9MB, alloc=387.8MB, time=137.25 memory used=12062.1MB, alloc=387.8MB, time=137.36 memory used=12106.8MB, alloc=387.8MB, time=137.47 memory used=12155.6MB, alloc=387.8MB, time=137.59 memory used=12204.9MB, alloc=387.8MB, time=137.70 memory used=12254.6MB, alloc=387.8MB, time=137.83 memory used=12304.8MB, alloc=387.8MB, time=137.94 memory used=12355.4MB, alloc=387.8MB, time=138.05 memory used=12406.3MB, alloc=387.8MB, time=138.16 memory used=12457.7MB, alloc=387.8MB, time=138.29 memory used=12513.4MB, alloc=387.8MB, time=138.40 memory used=12569.4MB, alloc=387.8MB, time=138.52 memory used=12625.8MB, alloc=387.8MB, time=138.64 memory used=12682.6MB, alloc=387.8MB, time=138.76 memory used=12739.7MB, alloc=387.8MB, time=138.88 memory used=12801.1MB, alloc=387.8MB, time=139.00 memory used=12862.8MB, alloc=387.8MB, time=139.12 memory used=12924.8MB, alloc=387.8MB, time=139.24 memory used=12987.1MB, alloc=387.8MB, time=139.37 memory used=13180.1MB, alloc=387.8MB, time=139.84 memory used=13319.3MB, alloc=387.8MB, time=140.11 memory used=13460.3MB, alloc=387.8MB, time=140.36 memory used=13609.9MB, alloc=387.8MB, time=140.62 memory used=13763.4MB, alloc=387.8MB, time=140.89 memory used=13924.6MB, alloc=387.8MB, time=141.16 memory used=14088.9MB, alloc=387.8MB, time=141.42 memory used=14259.3MB, alloc=387.8MB, time=141.68 memory used=14439.0MB, alloc=387.8MB, time=141.98 memory used=14626.5MB, alloc=387.8MB, time=142.26 memory used=14820.0MB, alloc=387.8MB, time=142.55 memory used=15024.8MB, alloc=387.8MB, time=142.84 memory used=15239.9MB, alloc=387.8MB, time=143.14 memory used=15465.1MB, alloc=387.8MB, time=143.44 memory used=15705.6MB, alloc=387.8MB, time=143.75 memory used=15939.8MB, alloc=387.8MB, time=144.04 memory used=16079.5MB, alloc=387.8MB, time=145.23 memory used=16180.2MB, alloc=387.8MB, time=146.03 memory used=16325.5MB, alloc=387.8MB, time=148.47 memory used=16537.4MB, alloc=387.8MB, time=151.39 memory used=16627.0MB, alloc=387.8MB, time=151.83 memory used=16701.4MB, alloc=387.8MB, time=152.07 memory used=16775.5MB, alloc=387.8MB, time=152.31 memory used=16849.8MB, alloc=387.8MB, time=154.86 memory used=16913.0MB, alloc=387.8MB, time=189.10 memory used=16961.3MB, alloc=387.8MB, time=193.70 memory used=17040.7MB, alloc=387.8MB, time=194.39 memory used=17106.9MB, alloc=387.8MB, time=195.09 memory used=17169.3MB, alloc=387.8MB, time=195.76 memory used=17237.8MB, alloc=387.8MB, time=196.45 memory used=17291.0MB, alloc=387.8MB, time=196.66 memory used=17333.5MB, alloc=387.8MB, time=196.84 memory used=17375.8MB, alloc=387.8MB, time=197.00 memory used=17417.8MB, alloc=387.8MB, time=197.17 memory used=17460.8MB, alloc=387.8MB, time=197.34 memory used=17503.5MB, alloc=387.8MB, time=197.52 memory used=17546.0MB, alloc=387.8MB, time=197.69 memory used=17589.3MB, alloc=387.8MB, time=197.86 memory used=17632.4MB, alloc=387.8MB, time=198.04 memory used=17676.3MB, alloc=387.8MB, time=198.21 memory used=17719.9MB, alloc=387.8MB, time=198.38 memory used=17764.3MB, alloc=387.8MB, time=198.55 memory used=17808.2MB, alloc=387.8MB, time=198.71 memory used=17853.0MB, alloc=387.8MB, time=198.88 memory used=17898.5MB, alloc=387.8MB, time=199.05 memory used=17943.4MB, alloc=387.8MB, time=199.22 memory used=17988.9MB, alloc=387.8MB, time=199.38 memory used=18034.9MB, alloc=387.8MB, time=199.56 memory used=18080.3MB, alloc=387.8MB, time=199.74 memory used=18126.2MB, alloc=387.8MB, time=199.90 memory used=18172.5MB, alloc=387.8MB, time=200.07 memory used=18219.0MB, alloc=387.8MB, time=200.25 memory used=18265.9MB, alloc=387.8MB, time=200.42 memory used=18312.8MB, alloc=387.8MB, time=200.60 memory used=18359.9MB, alloc=387.8MB, time=200.77 memory used=18407.9MB, alloc=387.8MB, time=200.94 memory used=18455.8MB, alloc=387.8MB, time=201.10 memory used=18504.3MB, alloc=387.8MB, time=201.28 memory used=18553.4MB, alloc=387.8MB, time=201.47 memory used=18602.7MB, alloc=387.8MB, time=201.64 memory used=18652.0MB, alloc=387.8MB, time=201.81 memory used=18702.0MB, alloc=387.8MB, time=201.97 memory used=18752.2MB, alloc=387.8MB, time=202.13 memory used=18802.2MB, alloc=387.8MB, time=202.29 memory used=18853.0MB, alloc=387.8MB, time=202.46 memory used=18903.9MB, alloc=387.8MB, time=202.63 memory used=18955.5MB, alloc=387.8MB, time=202.80 memory used=19007.6MB, alloc=387.8MB, time=202.97 memory used=19059.8MB, alloc=387.8MB, time=203.13 memory used=19111.2MB, alloc=387.8MB, time=203.30 memory used=19239.4MB, alloc=387.8MB, time=204.77 memory used=19308.9MB, alloc=387.8MB, time=205.09 memory used=19350.1MB, alloc=387.8MB, time=205.26 memory used=19398.9MB, alloc=387.8MB, time=205.44 memory used=19456.5MB, alloc=387.8MB, time=205.64 memory used=19502.0MB, alloc=387.8MB, time=205.80 memory used=19537.4MB, alloc=387.8MB, time=205.95 memory used=19575.4MB, alloc=387.8MB, time=206.10 memory used=19616.4MB, alloc=387.8MB, time=206.26 memory used=19660.6MB, alloc=387.8MB, time=206.41 memory used=19708.4MB, alloc=387.8MB, time=206.56 memory used=19759.6MB, alloc=387.8MB, time=206.72 memory used=19815.8MB, alloc=387.8MB, time=206.87 memory used=19869.4MB, alloc=387.8MB, time=207.02 memory used=19902.3MB, alloc=387.8MB, time=207.14 |\^/| 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(); 1428286132 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 3 4 F := [-20 y z - 10 y z + 3 x y - 4 x z, 17 x y - x y - 14 z + 7 x, 3 2 2 -13 y z + 14 x y + 16 x z - 3 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 2 2 2 2 3 G := [-4 x + x y - 10 x z + 8 y , 4 x y + 8 x z - 3 x y + 3 x y z, 2 2 2 2 2 -3 x y z + 14 y z + 15 x y + 17 y ] > Problem := [F,G]; 2 2 3 2 3 3 4 Problem := [[-20 y z - 10 y z + 3 x y - 4 x z, 17 x y - x y - 14 z + 7 x, 3 2 2 4 2 2 2 3 -13 y z + 14 x y + 16 x z - 3 x z], [-4 x + x y - 10 x z + 8 y , 2 2 2 2 3 4 x y + 8 x z - 3 x y + 3 x y z, 2 2 2 2 2 -3 x y z + 14 y z + 15 x y + 17 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=29.1MB, alloc=37.8MB, time=0.47 memory used=47.7MB, alloc=37.9MB, time=0.53 memory used=65.9MB, alloc=38.0MB, time=0.61 memory used=81.0MB, alloc=38.0MB, time=0.65 memory used=108.1MB, alloc=38.2MB, time=2.58 memory used=133.9MB, alloc=38.3MB, time=2.74 memory used=147.6MB, alloc=38.3MB, time=2.78 memory used=158.8MB, alloc=38.3MB, time=2.82 memory used=172.0MB, alloc=38.3MB, time=2.86 memory used=184.3MB, alloc=38.3MB, time=2.89 memory used=193.1MB, alloc=38.3MB, time=2.92 memory used=203.3MB, alloc=38.3MB, time=2.95 memory used=215.5MB, alloc=38.3MB, time=2.99 memory used=235.9MB, alloc=39.1MB, time=3.08 memory used=253.3MB, alloc=39.1MB, time=3.20 memory used=270.5MB, alloc=39.1MB, time=3.25 memory used=295.1MB, alloc=39.1MB, time=5.18 memory used=321.9MB, alloc=39.1MB, time=5.35 memory used=335.7MB, alloc=39.1MB, time=5.39 memory used=346.8MB, alloc=39.1MB, time=5.43 memory used=360.0MB, alloc=39.1MB, time=5.47 memory used=372.4MB, alloc=39.1MB, time=5.50 memory used=381.1MB, alloc=39.1MB, time=5.53 memory used=391.0MB, alloc=39.1MB, time=5.56 memory used=402.9MB, alloc=39.1MB, time=5.60 memory used=423.2MB, alloc=39.1MB, time=5.69 memory used=441.1MB, alloc=39.1MB, time=6.36 memory used=467.8MB, alloc=39.1MB, time=7.69 memory used=483.1MB, alloc=39.1MB, time=7.74 memory used=493.8MB, alloc=39.1MB, time=7.78 memory used=506.9MB, alloc=39.1MB, time=7.82 memory used=520.5MB, alloc=39.1MB, time=7.86 memory used=529.5MB, alloc=39.1MB, time=7.89 memory used=539.3MB, alloc=39.1MB, time=7.92 memory used=550.6MB, alloc=39.1MB, time=7.95 memory used=570.4MB, alloc=39.1MB, time=8.15 memory used=597.2MB, alloc=63.1MB, time=9.27 memory used=651.9MB, alloc=64.2MB, time=12.20 memory used=679.4MB, alloc=64.2MB, time=12.28 memory used=710.1MB, alloc=64.2MB, time=12.36 memory used=733.5MB, alloc=64.2MB, time=12.43 memory used=762.0MB, alloc=64.2MB, time=12.50 memory used=795.8MB, alloc=64.2MB, time=12.70 memory used=825.4MB, alloc=64.2MB, time=12.80 memory used=862.6MB, alloc=64.2MB, time=13.26 memory used=907.6MB, alloc=72.2MB, time=13.84 memory used=953.0MB, alloc=72.2MB, time=14.40 memory used=987.7MB, alloc=72.2MB, time=14.62 memory used=1012.7MB, alloc=72.2MB, time=14.71 memory used=1035.6MB, alloc=72.2MB, time=14.80 memory used=1067.1MB, alloc=72.2MB, time=14.96 memory used=1090.1MB, alloc=72.2MB, time=15.05 memory used=1113.8MB, alloc=72.2MB, time=15.12 memory used=1152.4MB, alloc=72.2MB, time=18.51 memory used=1198.9MB, alloc=72.2MB, time=18.92 memory used=1220.7MB, alloc=72.2MB, time=18.99 memory used=1245.0MB, alloc=72.2MB, time=19.08 memory used=1262.4MB, alloc=72.2MB, time=19.15 memory used=1282.0MB, alloc=72.2MB, time=19.22 memory used=1304.8MB, alloc=72.2MB, time=19.30 memory used=1330.4MB, alloc=72.2MB, time=19.38 memory used=1353.7MB, alloc=72.2MB, time=19.46 memory used=1369.1MB, alloc=72.2MB, time=19.51 memory used=1385.3MB, alloc=72.2MB, time=19.57 memory used=1402.5MB, alloc=72.2MB, time=19.62 memory used=1421.5MB, alloc=72.2MB, time=19.68 memory used=1442.7MB, alloc=72.2MB, time=19.74 memory used=1477.4MB, alloc=72.2MB, time=19.94 memory used=1497.0MB, alloc=72.2MB, time=20.02 memory used=1521.5MB, alloc=72.2MB, time=20.09 memory used=1571.1MB, alloc=72.2MB, time=23.53 memory used=1594.5MB, alloc=72.2MB, time=23.62 memory used=1620.4MB, alloc=72.2MB, time=23.71 memory used=1636.8MB, alloc=72.2MB, time=23.77 memory used=1654.9MB, alloc=72.2MB, time=23.84 memory used=1675.6MB, alloc=72.2MB, time=23.91 memory used=1699.2MB, alloc=72.2MB, time=23.98 memory used=1725.4MB, alloc=72.2MB, time=24.05 memory used=1742.4MB, alloc=72.2MB, time=24.11 memory used=1757.5MB, alloc=72.2MB, time=24.17 memory used=1773.7MB, alloc=72.2MB, time=24.24 memory used=1791.2MB, alloc=72.2MB, time=24.30 memory used=1810.1MB, alloc=72.2MB, time=24.35 memory used=1831.5MB, alloc=72.2MB, time=24.40 memory used=1874.6MB, alloc=72.2MB, time=24.93 memory used=1903.1MB, alloc=72.2MB, time=25.03 memory used=1919.4MB, alloc=72.2MB, time=25.10 memory used=1938.7MB, alloc=72.2MB, time=25.18 memory used=1960.0MB, alloc=72.2MB, time=25.26 memory used=1983.9MB, alloc=72.2MB, time=25.34 memory used=2010.8MB, alloc=72.2MB, time=25.42 memory used=2029.1MB, alloc=96.2MB, time=25.50 memory used=2057.6MB, alloc=96.2MB, time=25.63 memory used=2088.6MB, alloc=96.2MB, time=25.72 memory used=2122.7MB, alloc=96.2MB, time=25.82 memory used=2161.2MB, alloc=96.2MB, time=25.92 memory used=2203.9MB, alloc=96.2MB, time=26.01 memory used=2252.0MB, alloc=96.2MB, time=26.11 memory used=2289.0MB, alloc=96.2MB, time=26.28 memory used=2336.6MB, alloc=96.2MB, time=27.58 memory used=2412.4MB, alloc=96.2MB, time=33.91 memory used=2453.6MB, alloc=96.2MB, time=34.04 memory used=2486.2MB, alloc=96.2MB, time=34.15 memory used=2522.3MB, alloc=96.2MB, time=34.25 memory used=2565.7MB, alloc=96.2MB, time=34.35 memory used=2607.3MB, alloc=96.2MB, time=34.45 memory used=2634.9MB, alloc=96.2MB, time=34.53 memory used=2665.6MB, alloc=96.2MB, time=34.60 memory used=2698.3MB, alloc=96.2MB, time=34.68 memory used=2734.1MB, alloc=96.2MB, time=34.75 memory used=2774.5MB, alloc=96.2MB, time=34.84 memory used=2829.2MB, alloc=96.2MB, time=35.04 memory used=2869.7MB, alloc=96.2MB, time=35.15 memory used=2940.1MB, alloc=96.2MB, time=38.79 memory used=2981.4MB, alloc=96.2MB, time=38.90 memory used=3013.5MB, alloc=96.2MB, time=39.00 memory used=3054.3MB, alloc=96.2MB, time=39.12 memory used=3096.5MB, alloc=96.2MB, time=39.22 memory used=3125.1MB, alloc=96.2MB, time=39.29 memory used=3157.5MB, alloc=96.2MB, time=39.37 memory used=3206.0MB, alloc=96.2MB, time=39.60 memory used=3288.8MB, alloc=96.2MB, time=41.56 memory used=3329.6MB, alloc=96.2MB, time=41.67 memory used=3361.6MB, alloc=96.2MB, time=41.79 memory used=3401.1MB, alloc=96.2MB, time=41.90 memory used=3446.5MB, alloc=96.2MB, time=42.00 memory used=3474.2MB, alloc=96.2MB, time=42.08 memory used=3503.9MB, alloc=96.2MB, time=42.16 memory used=3537.4MB, alloc=96.2MB, time=42.23 memory used=3576.7MB, alloc=96.2MB, time=42.30 memory used=3628.5MB, alloc=96.2MB, time=42.51 memory used=3669.0MB, alloc=96.2MB, time=42.62 memory used=3723.5MB, alloc=96.2MB, time=49.39 memory used=3774.1MB, alloc=96.2MB, time=77.45 memory used=3846.4MB, alloc=96.2MB, time=79.55 memory used=3905.1MB, alloc=96.2MB, time=79.89 memory used=3940.3MB, alloc=96.2MB, time=80.01 memory used=3984.2MB, alloc=96.2MB, time=80.15 memory used=4011.6MB, alloc=96.2MB, time=80.25 memory used=4040.3MB, alloc=96.2MB, time=80.36 memory used=4071.6MB, alloc=96.2MB, time=80.45 memory used=4105.1MB, alloc=96.2MB, time=80.55 memory used=4142.1MB, alloc=96.2MB, time=80.66 memory used=4181.2MB, alloc=96.2MB, time=80.76 memory used=4224.1MB, alloc=96.2MB, time=80.87 memory used=4268.9MB, alloc=96.2MB, time=80.99 memory used=4303.3MB, alloc=96.2MB, time=81.09 memory used=4326.5MB, alloc=96.2MB, time=81.17 memory used=4350.9MB, alloc=96.2MB, time=81.25 memory used=4376.2MB, alloc=96.2MB, time=81.34 memory used=4401.8MB, alloc=96.2MB, time=81.42 memory used=4427.9MB, alloc=96.2MB, time=81.50 memory used=4454.3MB, alloc=96.2MB, time=81.59 memory used=4481.1MB, alloc=96.2MB, time=81.69 memory used=4510.4MB, alloc=96.2MB, time=81.78 memory used=4540.1MB, alloc=96.2MB, time=81.86 memory used=4570.1MB, alloc=96.2MB, time=81.95 memory used=4600.4MB, alloc=96.2MB, time=82.04 memory used=4631.2MB, alloc=96.2MB, time=82.12 memory used=4664.4MB, alloc=96.2MB, time=82.21 memory used=4697.9MB, alloc=96.2MB, time=82.37 memory used=4731.7MB, alloc=96.2MB, time=82.45 memory used=4768.2MB, alloc=96.2MB, time=82.54 memory used=4804.9MB, alloc=96.2MB, time=82.63 memory used=4841.8MB, alloc=96.2MB, time=82.72 memory used=4881.3MB, alloc=96.2MB, time=82.81 memory used=4920.9MB, alloc=96.2MB, time=82.90 memory used=4960.6MB, alloc=96.2MB, time=83.00 memory used=5002.8MB, alloc=96.2MB, time=83.09 memory used=5045.1MB, alloc=96.2MB, time=83.18 memory used=5089.7MB, alloc=96.2MB, time=83.27 memory used=5139.5MB, alloc=97.1MB, time=83.38 memory used=5172.2MB, alloc=107.8MB, time=83.47 memory used=5182.9MB, alloc=107.8MB, time=83.54 memory used=5191.2MB, alloc=107.8MB, time=83.59 memory used=5200.0MB, alloc=107.8MB, time=83.64 memory used=5207.1MB, alloc=107.8MB, time=83.69 memory used=5214.2MB, alloc=107.8MB, time=83.75 memory used=5221.4MB, alloc=107.8MB, time=83.80 memory used=5228.5MB, alloc=107.8MB, time=83.85 memory used=5235.8MB, alloc=107.8MB, time=83.91 memory used=5244.9MB, alloc=107.8MB, time=83.97 memory used=5252.3MB, alloc=107.8MB, time=84.06 memory used=5261.5MB, alloc=107.8MB, time=84.13 memory used=5270.9MB, alloc=107.8MB, time=84.19 memory used=5280.3MB, alloc=107.8MB, time=84.26 memory used=5289.7MB, alloc=107.8MB, time=84.31 memory used=5299.1MB, alloc=107.8MB, time=84.38 memory used=5308.4MB, alloc=107.8MB, time=84.46 memory used=5317.7MB, alloc=107.8MB, time=84.53 memory used=5327.0MB, alloc=107.8MB, time=84.58 memory used=5336.3MB, alloc=107.8MB, time=84.65 memory used=5345.5MB, alloc=107.8MB, time=84.73 memory used=5354.7MB, alloc=107.8MB, time=84.78 memory used=5363.9MB, alloc=107.8MB, time=84.84 memory used=5373.0MB, alloc=107.8MB, time=84.90 memory used=5382.2MB, alloc=107.8MB, time=84.97 memory used=5391.3MB, alloc=107.8MB, time=85.04 memory used=5400.3MB, alloc=107.8MB, time=85.10 memory used=5409.4MB, alloc=107.8MB, time=85.17 memory used=5418.4MB, alloc=107.8MB, time=85.23 memory used=5427.4MB, alloc=107.8MB, time=85.28 memory used=5436.3MB, alloc=107.8MB, time=85.33 memory used=5445.2MB, alloc=107.8MB, time=85.40 memory used=5454.1MB, alloc=107.8MB, time=85.46 memory used=5463.2MB, alloc=107.8MB, time=85.53 memory used=5474.0MB, alloc=107.8MB, time=85.59 memory used=5484.9MB, alloc=107.8MB, time=85.64 memory used=5495.8MB, alloc=107.8MB, time=85.71 memory used=5506.7MB, alloc=107.8MB, time=85.77 memory used=5517.4MB, alloc=107.8MB, time=85.83 memory used=5528.2MB, alloc=107.8MB, time=85.94 memory used=5538.8MB, alloc=107.8MB, time=86.03 memory used=5549.4MB, alloc=107.8MB, time=86.09 memory used=5560.0MB, alloc=107.8MB, time=86.15 memory used=5570.4MB, alloc=107.8MB, time=86.21 memory used=5580.8MB, alloc=107.8MB, time=86.26 memory used=5591.1MB, alloc=107.8MB, time=86.34 memory used=5601.4MB, alloc=107.8MB, time=86.39 memory used=5611.9MB, alloc=107.8MB, time=86.45 memory used=5623.8MB, alloc=107.8MB, time=86.51 memory used=5635.8MB, alloc=107.8MB, time=86.58 memory used=5647.7MB, alloc=107.8MB, time=86.65 memory used=5659.5MB, alloc=107.8MB, time=86.71 memory used=5671.2MB, alloc=107.8MB, time=86.80 memory used=5682.8MB, alloc=107.8MB, time=86.86 memory used=5694.3MB, alloc=107.8MB, time=86.95 memory used=5705.8MB, alloc=107.8MB, time=87.03 memory used=5718.7MB, alloc=107.8MB, time=87.09 memory used=5731.6MB, alloc=107.8MB, time=87.16 memory used=5744.4MB, alloc=107.8MB, time=87.22 memory used=5757.0MB, alloc=107.8MB, time=87.29 memory used=5769.4MB, alloc=107.8MB, time=87.35 memory used=5782.0MB, alloc=107.8MB, time=87.41 memory used=5795.5MB, alloc=107.8MB, time=87.48 memory used=5809.0MB, alloc=107.8MB, time=87.55 memory used=5822.2MB, alloc=107.8MB, time=87.60 memory used=5835.6MB, alloc=107.8MB, time=87.68 memory used=5849.5MB, alloc=107.8MB, time=87.75 memory used=5863.4MB, alloc=107.8MB, time=87.81 memory used=5877.4MB, alloc=107.8MB, time=87.88 memory used=5891.7MB, alloc=107.8MB, time=87.95 memory used=5906.3MB, alloc=107.8MB, time=88.02 memory used=5921.1MB, alloc=107.8MB, time=88.08 memory used=5937.0MB, alloc=107.8MB, time=88.15 memory used=5952.5MB, alloc=107.8MB, time=88.22 memory used=5968.2MB, alloc=107.8MB, time=88.29 memory used=5984.9MB, alloc=107.8MB, time=88.35 memory used=6001.7MB, alloc=107.8MB, time=88.41 memory used=6019.1MB, alloc=107.8MB, time=88.48 memory used=6037.1MB, alloc=107.8MB, time=88.54 memory used=6138.9MB, alloc=107.8MB, time=89.82 memory used=6218.2MB, alloc=107.8MB, time=90.75 memory used=6297.6MB, alloc=107.8MB, time=91.79 memory used=6378.3MB, alloc=107.8MB, time=93.27 memory used=6458.2MB, alloc=107.8MB, time=95.11 memory used=6537.8MB, alloc=107.8MB, time=97.55 memory used=6618.3MB, alloc=107.8MB, time=100.23 memory used=6699.0MB, alloc=107.8MB, time=103.43 memory used=6773.8MB, alloc=107.8MB, time=105.45 memory used=6811.9MB, alloc=107.8MB, time=105.57 memory used=6848.8MB, alloc=107.8MB, time=105.68 memory used=6909.2MB, alloc=107.8MB, time=110.21 memory used=6954.9MB, alloc=107.8MB, time=110.39 memory used=6989.4MB, alloc=107.8MB, time=110.50 memory used=7021.1MB, alloc=107.8MB, time=110.61 memory used=7059.1MB, alloc=107.8MB, time=110.72 memory used=7100.4MB, alloc=107.8MB, time=110.82 memory used=7126.2MB, alloc=107.8MB, time=110.90 memory used=7153.6MB, alloc=107.8MB, time=110.97 memory used=7183.2MB, alloc=107.8MB, time=111.06 memory used=7215.8MB, alloc=107.8MB, time=111.14 memory used=7252.1MB, alloc=107.8MB, time=111.23 memory used=7294.0MB, alloc=107.8MB, time=111.31 memory used=7376.8MB, alloc=107.8MB, time=112.64 memory used=7414.7MB, alloc=107.8MB, time=112.78 memory used=7444.6MB, alloc=107.8MB, time=112.89 memory used=7477.5MB, alloc=107.8MB, time=113.00 memory used=7518.0MB, alloc=107.8MB, time=113.11 memory used=7551.1MB, alloc=107.8MB, time=113.20 memory used=7577.2MB, alloc=107.8MB, time=113.28 memory used=7605.1MB, alloc=107.8MB, time=113.37 memory used=7636.1MB, alloc=107.8MB, time=113.45 memory used=7671.1MB, alloc=107.8MB, time=113.55 memory used=7716.8MB, alloc=107.8MB, time=113.77 memory used=7752.0MB, alloc=107.8MB, time=113.96 memory used=7798.2MB, alloc=107.8MB, time=114.20 memory used=7831.9MB, alloc=107.8MB, time=114.32 memory used=7869.4MB, alloc=107.8MB, time=114.43 memory used=7914.4MB, alloc=107.8MB, time=120.04 memory used=7960.2MB, alloc=131.8MB, time=144.71 memory used=8048.0MB, alloc=131.8MB, time=151.20 memory used=8118.1MB, alloc=131.8MB, time=151.54 memory used=8176.3MB, alloc=131.8MB, time=151.70 memory used=8215.0MB, alloc=131.8MB, time=151.83 memory used=8258.7MB, alloc=131.8MB, time=151.97 memory used=8308.5MB, alloc=131.8MB, time=152.11 memory used=8362.9MB, alloc=131.8MB, time=152.24 memory used=8423.4MB, alloc=131.8MB, time=152.39 memory used=8474.2MB, alloc=131.8MB, time=152.51 memory used=8508.8MB, alloc=131.8MB, time=152.61 memory used=8543.4MB, alloc=131.8MB, time=152.70 memory used=8581.3MB, alloc=131.8MB, time=152.80 memory used=8620.1MB, alloc=131.8MB, time=152.90 memory used=8659.8MB, alloc=131.8MB, time=153.01 memory used=8702.7MB, alloc=131.8MB, time=153.11 memory used=8746.5MB, alloc=131.8MB, time=153.22 memory used=8791.0MB, alloc=131.8MB, time=153.33 memory used=8838.8MB, alloc=131.8MB, time=153.44 memory used=8887.4MB, alloc=131.8MB, time=153.56 memory used=8939.1MB, alloc=131.8MB, time=153.66 memory used=8991.5MB, alloc=131.8MB, time=153.78 memory used=9047.0MB, alloc=131.8MB, time=153.90 memory used=9103.1MB, alloc=131.8MB, time=154.02 memory used=9162.2MB, alloc=131.8MB, time=154.13 memory used=9224.3MB, alloc=131.8MB, time=154.25 memory used=9296.1MB, alloc=131.8MB, time=154.38 memory used=9312.9MB, alloc=131.8MB, time=154.45 memory used=9323.1MB, alloc=131.8MB, time=154.52 memory used=9330.2MB, alloc=131.8MB, time=154.58 memory used=9337.3MB, alloc=131.8MB, time=154.63 memory used=9344.9MB, alloc=131.8MB, time=154.69 memory used=9352.8MB, alloc=131.8MB, time=154.76 memory used=9360.6MB, alloc=131.8MB, time=154.82 memory used=9368.5MB, alloc=131.8MB, time=154.89 memory used=9376.3MB, alloc=131.8MB, time=154.95 memory used=9384.1MB, alloc=131.8MB, time=155.01 memory used=9392.0MB, alloc=131.8MB, time=155.09 memory used=9399.8MB, alloc=131.8MB, time=155.18 memory used=9407.6MB, alloc=131.8MB, time=155.25 memory used=9415.4MB, alloc=131.8MB, time=155.31 memory used=9423.2MB, alloc=131.8MB, time=155.38 memory used=9431.0MB, alloc=131.8MB, time=155.46 memory used=9438.8MB, alloc=131.8MB, time=155.52 memory used=9446.6MB, alloc=131.8MB, time=155.59 memory used=9454.4MB, alloc=131.8MB, time=155.67 memory used=9462.2MB, alloc=131.8MB, time=155.75 memory used=9469.9MB, alloc=131.8MB, time=155.83 memory used=9477.7MB, alloc=131.8MB, time=155.90 memory used=9485.4MB, alloc=131.8MB, time=155.96 memory used=9493.2MB, alloc=131.8MB, time=156.02 memory used=9500.9MB, alloc=131.8MB, time=156.08 memory used=9508.6MB, alloc=131.8MB, time=156.14 memory used=9516.3MB, alloc=131.8MB, time=156.21 memory used=9524.0MB, alloc=131.8MB, time=156.27 memory used=9531.7MB, alloc=131.8MB, time=156.34 memory used=9539.4MB, alloc=131.8MB, time=156.40 memory used=9547.2MB, alloc=131.8MB, time=156.47 memory used=9557.2MB, alloc=131.8MB, time=156.53 memory used=9565.2MB, alloc=131.8MB, time=156.59 memory used=9575.1MB, alloc=131.8MB, time=156.65 memory used=9585.2MB, alloc=131.8MB, time=156.72 memory used=9595.3MB, alloc=131.8MB, time=156.78 memory used=9605.4MB, alloc=131.8MB, time=156.85 memory used=9615.5MB, alloc=131.8MB, time=156.92 memory used=9625.5MB, alloc=131.8MB, time=156.97 memory used=9635.5MB, alloc=131.8MB, time=157.04 memory used=9645.5MB, alloc=131.8MB, time=157.15 memory used=9655.5MB, alloc=131.8MB, time=157.21 memory used=9665.4MB, alloc=131.8MB, time=157.27 memory used=9675.3MB, alloc=131.8MB, time=157.35 memory used=9685.2MB, alloc=131.8MB, time=157.43 memory used=9695.0MB, alloc=131.8MB, time=157.51 memory used=9704.8MB, alloc=131.8MB, time=157.58 memory used=9714.6MB, alloc=131.8MB, time=157.66 memory used=9724.4MB, alloc=131.8MB, time=157.73 memory used=9734.1MB, alloc=131.8MB, time=157.79 memory used=9743.7MB, alloc=131.8MB, time=157.87 memory used=9753.4MB, alloc=131.8MB, time=157.92 memory used=9763.0MB, alloc=131.8MB, time=157.99 memory used=9772.6MB, alloc=131.8MB, time=158.07 memory used=9782.3MB, alloc=131.8MB, time=158.13 memory used=9794.0MB, alloc=131.8MB, time=158.21 memory used=9805.8MB, alloc=131.8MB, time=158.28 memory used=9817.5MB, alloc=131.8MB, time=158.35 memory used=9829.2MB, alloc=131.8MB, time=158.42 memory used=9840.8MB, alloc=131.8MB, time=158.48 memory used=9852.4MB, alloc=131.8MB, time=158.57 memory used=9863.9MB, alloc=131.8MB, time=158.64 memory used=9875.3MB, alloc=131.8MB, time=158.71 memory used=9886.6MB, alloc=131.8MB, time=158.79 memory used=9897.9MB, alloc=131.8MB, time=158.86 memory used=9909.1MB, alloc=131.8MB, time=158.95 memory used=9920.2MB, alloc=131.8MB, time=159.01 memory used=9931.3MB, alloc=131.8MB, time=159.08 memory used=9942.5MB, alloc=131.8MB, time=159.14 memory used=9955.3MB, alloc=131.8MB, time=159.22 memory used=9968.3MB, alloc=131.8MB, time=159.28 memory used=9981.1MB, alloc=131.8MB, time=159.36 memory used=9993.8MB, alloc=131.8MB, time=159.43 memory used=10006.4MB, alloc=131.8MB, time=159.49 memory used=10018.9MB, alloc=131.8MB, time=159.56 memory used=10031.2MB, alloc=131.8MB, time=159.63 memory used=10043.7MB, alloc=131.8MB, time=159.71 memory used=10057.5MB, alloc=131.8MB, time=159.78 memory used=10071.4MB, alloc=131.8MB, time=159.84 memory used=10085.1MB, alloc=131.8MB, time=159.92 memory used=10098.6MB, alloc=131.8MB, time=160.01 memory used=10112.1MB, alloc=131.8MB, time=160.08 memory used=10125.5MB, alloc=131.8MB, time=160.14 memory used=10140.0MB, alloc=131.8MB, time=160.22 memory used=10154.5MB, alloc=131.8MB, time=160.29 memory used=10168.7MB, alloc=131.8MB, time=160.39 memory used=10183.0MB, alloc=131.8MB, time=160.47 memory used=10197.9MB, alloc=131.8MB, time=160.55 memory used=10212.9MB, alloc=131.8MB, time=160.62 memory used=10229.1MB, alloc=131.8MB, time=160.69 memory used=10244.8MB, alloc=131.8MB, time=160.75 memory used=10260.4MB, alloc=131.8MB, time=160.82 memory used=10276.4MB, alloc=131.8MB, time=160.90 memory used=10293.0MB, alloc=131.8MB, time=160.97 memory used=10310.5MB, alloc=131.8MB, time=161.04 memory used=10328.3MB, alloc=131.8MB, time=161.12 memory used=10346.1MB, alloc=131.8MB, time=161.20 memory used=10364.2MB, alloc=131.8MB, time=161.28 memory used=10383.1MB, alloc=131.8MB, time=161.35 memory used=10431.4MB, alloc=131.8MB, time=161.84 memory used=10548.0MB, alloc=131.8MB, time=162.83 memory used=10620.9MB, alloc=387.8MB, time=163.88 memory used=10710.5MB, alloc=387.8MB, time=165.04 memory used=10805.3MB, alloc=387.8MB, time=171.46 memory used=10851.5MB, alloc=387.8MB, time=171.63 memory used=10889.3MB, alloc=387.8MB, time=171.78 memory used=10938.4MB, alloc=387.8MB, time=171.92 memory used=10980.1MB, alloc=387.8MB, time=172.05 memory used=11013.2MB, alloc=387.8MB, time=172.17 memory used=11049.8MB, alloc=387.8MB, time=172.28 memory used=11089.7MB, alloc=387.8MB, time=172.40 memory used=11133.9MB, alloc=387.8MB, time=172.52 memory used=11182.7MB, alloc=387.8MB, time=172.65 memory used=11243.9MB, alloc=387.8MB, time=172.78 memory used=11397.1MB, alloc=387.8MB, time=173.46 memory used=11445.8MB, alloc=387.8MB, time=173.80 memory used=11563.7MB, alloc=387.8MB, time=174.64 memory used=11636.7MB, alloc=387.8MB, time=174.82 memory used=11741.4MB, alloc=387.8MB, time=176.29 memory used=11785.5MB, alloc=387.8MB, time=176.46 memory used=11829.1MB, alloc=387.8MB, time=176.62 memory used=11879.9MB, alloc=387.8MB, time=176.78 memory used=11911.0MB, alloc=387.8MB, time=176.91 memory used=11943.9MB, alloc=387.8MB, time=177.05 memory used=11979.5MB, alloc=387.8MB, time=177.18 memory used=12018.4MB, alloc=387.8MB, time=177.31 memory used=12061.9MB, alloc=387.8MB, time=177.46 memory used=12109.7MB, alloc=387.8MB, time=177.61 memory used=12161.5MB, alloc=387.8MB, time=177.76 memory used=12209.9MB, alloc=387.8MB, time=177.91 memory used=12242.9MB, alloc=387.8MB, time=178.02 memory used=12272.2MB, alloc=387.8MB, time=178.13 memory used=12301.5MB, alloc=387.8MB, time=178.23 memory used=12332.3MB, alloc=387.8MB, time=178.34 memory used=12365.3MB, alloc=387.8MB, time=178.45 memory used=12399.1MB, alloc=387.8MB, time=178.56 memory used=12434.5MB, alloc=387.8MB, time=178.66 memory used=12472.0MB, alloc=387.8MB, time=178.78 memory used=12511.9MB, alloc=387.8MB, time=178.90 memory used=12554.5MB, alloc=387.8MB, time=179.02 memory used=12599.9MB, alloc=387.8MB, time=179.12 memory used=12673.9MB, alloc=387.8MB, time=192.37 memory used=12744.7MB, alloc=387.8MB, time=193.54 memory used=12788.6MB, alloc=387.8MB, time=193.69 memory used=12826.0MB, alloc=387.8MB, time=193.83 memory used=12872.1MB, alloc=387.8MB, time=193.98 memory used=12922.2MB, alloc=387.8MB, time=194.13 memory used=12953.1MB, alloc=387.8MB, time=194.24 memory used=12985.0MB, alloc=387.8MB, time=194.36 memory used=13019.8MB, alloc=387.8MB, time=194.47 memory used=13057.3MB, alloc=387.8MB, time=194.59 memory used=13097.4MB, alloc=387.8MB, time=194.70 memory used=13141.3MB, alloc=387.8MB, time=194.82 memory used=13189.0MB, alloc=387.8MB, time=194.95 memory used=13239.9MB, alloc=387.8MB, time=195.07 memory used=13301.9MB, alloc=387.8MB, time=195.21 memory used=13459.6MB, alloc=387.8MB, time=195.49 memory used=13637.2MB, alloc=387.8MB, time=196.11 memory used=13681.1MB, alloc=387.8MB, time=196.25 memory used=13719.2MB, alloc=387.8MB, time=196.39 memory used=13796.7MB, alloc=387.8MB, time=202.72 memory used=13850.1MB, alloc=387.8MB, time=202.92 memory used=13885.9MB, alloc=387.8MB, time=203.05 memory used=13931.6MB, alloc=387.8MB, time=203.20 memory used=13977.7MB, alloc=387.8MB, time=203.32 memory used=14009.3MB, alloc=387.8MB, time=203.43 memory used=14043.5MB, alloc=387.8MB, time=203.56 memory used=14081.1MB, alloc=387.8MB, time=203.68 memory used=14123.0MB, alloc=387.8MB, time=203.80 memory used=14169.0MB, alloc=387.8MB, time=203.92 memory used=14218.2MB, alloc=387.8MB, time=204.04 memory used=14411.3MB, alloc=387.8MB, time=204.80 memory used=14492.7MB, alloc=387.8MB, time=205.50 memory used=14546.3MB, alloc=387.8MB, time=205.96 memory used=14592.6MB, alloc=387.8MB, time=206.15 memory used=14636.0MB, alloc=387.8MB, time=206.31 memory used=14683.1MB, alloc=387.8MB, time=206.47 memory used=14714.3MB, alloc=387.8MB, time=206.60 memory used=14748.6MB, alloc=387.8MB, time=206.75 memory used=14787.1MB, alloc=387.8MB, time=206.89 memory used=14830.2MB, alloc=387.8MB, time=207.03 memory used=14878.4MB, alloc=387.8MB, time=207.18 memory used=14927.0MB, alloc=387.8MB, time=207.32 memory used=14956.8MB, alloc=387.8MB, time=207.45 memory used=14988.1MB, alloc=387.8MB, time=207.56 memory used=15049.1MB, alloc=387.8MB, time=221.65 memory used=15106.2MB, alloc=387.8MB, time=235.48 memory used=15174.9MB, alloc=387.8MB, time=235.93 memory used=15219.2MB, alloc=387.8MB, time=236.11 memory used=15255.4MB, alloc=387.8MB, time=236.26 memory used=15288.0MB, alloc=387.8MB, time=236.40 memory used=15324.9MB, alloc=387.8MB, time=236.55 memory used=15366.8MB, alloc=387.8MB, time=236.70 memory used=15413.8MB, alloc=387.8MB, time=236.85 memory used=15464.0MB, alloc=387.8MB, time=236.99 memory used=15494.3MB, alloc=411.8MB, time=237.12 memory used=15534.8MB, alloc=411.8MB, time=237.26 memory used=15578.4MB, alloc=411.8MB, time=237.40 memory used=15623.7MB, alloc=411.8MB, time=237.54 memory used=15672.6MB, alloc=411.8MB, time=237.67 memory used=15725.1MB, alloc=411.8MB, time=237.82 memory used=15779.1MB, alloc=411.8MB, time=237.96 memory used=15836.7MB, alloc=411.8MB, time=238.10 memory used=15897.8MB, alloc=411.8MB, time=238.25 memory used=15962.6MB, alloc=411.8MB, time=238.41 memory used=16030.7MB, alloc=411.8MB, time=238.56 memory used=16102.2MB, alloc=411.8MB, time=238.71 memory used=16193.6MB, alloc=411.8MB, time=238.88 memory used=16333.9MB, alloc=411.8MB, time=239.16 memory used=16486.4MB, alloc=411.8MB, time=239.44 memory used=16653.1MB, alloc=411.8MB, time=239.73 memory used=16837.4MB, alloc=411.8MB, time=240.03 memory used=17048.0MB, alloc=411.8MB, time=240.34 memory used=17262.3MB, alloc=411.8MB, time=241.86 memory used=17314.3MB, alloc=411.8MB, time=242.03 memory used=17380.2MB, alloc=411.8MB, time=242.21 memory used=17425.0MB, alloc=411.8MB, time=242.35 memory used=17476.5MB, alloc=411.8MB, time=242.50 memory used=17536.7MB, alloc=411.8MB, time=242.65 memory used=17623.5MB, alloc=411.8MB, time=242.97 memory used=17683.7MB, alloc=411.8MB, time=243.17 memory used=17759.1MB, alloc=411.8MB, time=249.39 |\^/| 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(); 1428286433 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 F := [-10 y z + 13 y z - 13 x y - 12 x z, 20 x y - 14 z + 17 y z - 14, 3 2 2 -20 x y + 9 x y - 16 x y z + y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 2 3 G := [15 x z + 4 x y - 9 x z - 8 y z, 18 y - 4 y z - 19 z - 8 x, 2 2 -2 x y z + 12 x y - 12 x z + 3 y ] > Problem := [F,G]; 3 2 Problem := [[-10 y z + 13 y z - 13 x y - 12 x z, 2 2 4 3 2 2 20 x y - 14 z + 17 y z - 14, -20 x y + 9 x y - 16 x y z + y z], [ 3 3 2 4 2 3 15 x z + 4 x y - 9 x z - 8 y z, 18 y - 4 y z - 19 z - 8 x, 2 2 -2 x y z + 12 x y - 12 x z + 3 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.52 memory used=46.3MB, alloc=56.3MB, time=0.83 memory used=85.2MB, alloc=60.3MB, time=1.37 memory used=129.2MB, alloc=68.3MB, time=1.97 memory used=170.8MB, alloc=68.3MB, time=2.55 memory used=214.0MB, alloc=92.3MB, time=3.07 memory used=267.3MB, alloc=92.3MB, time=3.39 memory used=329.5MB, alloc=92.3MB, time=3.99 memory used=418.8MB, alloc=94.0MB, time=5.35 memory used=483.4MB, alloc=94.0MB, time=6.17 memory used=523.1MB, alloc=94.0MB, time=6.38 memory used=569.1MB, alloc=94.0MB, time=6.75 memory used=600.7MB, alloc=94.0MB, time=6.85 memory used=651.7MB, alloc=94.0MB, time=7.25 memory used=713.1MB, alloc=94.0MB, time=7.78 memory used=744.3MB, alloc=94.0MB, time=7.89 memory used=794.9MB, alloc=94.0MB, time=8.29 memory used=861.7MB, alloc=94.0MB, time=9.07 memory used=901.9MB, alloc=94.0MB, time=9.41 memory used=964.5MB, alloc=94.0MB, time=10.17 memory used=1027.3MB, alloc=118.0MB, time=11.09 memory used=1096.7MB, alloc=118.0MB, time=12.08 memory used=1149.7MB, alloc=374.0MB, time=12.82 memory used=1234.5MB, alloc=398.0MB, time=13.93 memory used=1352.8MB, alloc=398.0MB, time=15.34 memory used=1442.1MB, alloc=398.0MB, time=16.22 memory used=1518.3MB, alloc=398.0MB, time=16.68 memory used=1593.2MB, alloc=398.0MB, time=17.22 memory used=1677.0MB, alloc=398.0MB, time=18.11 memory used=1773.6MB, alloc=422.0MB, time=22.05 memory used=1859.1MB, alloc=446.0MB, time=30.84 memory used=1930.1MB, alloc=470.0MB, time=45.04 memory used=1988.7MB, alloc=494.0MB, time=55.62 memory used=2084.4MB, alloc=494.0MB, time=77.83 memory used=2285.8MB, alloc=518.0MB, time=119.46 memory used=2383.9MB, alloc=542.0MB, time=120.18 memory used=2524.9MB, alloc=542.0MB, time=124.04 memory used=2750.1MB, alloc=542.0MB, time=124.79 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428286733 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 F := [-16 x z - 4 y z + 6 x + 6 x z, -9 x y - 3 y z + 8 x z - 13 y , 3 3 3 10 x y - 16 x y - 4 y z + 20] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 2 2 3 G := [9 x y + 5 x y z + 15 y + 20 y z , 14 x z + 13 x y z + 8 y z - z , 4 2 -13 x - 17 x z + 10 x z + 13 x] > Problem := [F,G]; 3 2 2 Problem := [[-16 x z - 4 y z + 6 x + 6 x z, 2 2 2 2 3 3 3 -9 x y - 3 y z + 8 x z - 13 y , 10 x y - 16 x y - 4 y z + 20], [ 3 2 3 2 3 2 2 3 9 x y + 5 x y z + 15 y + 20 y z , 14 x z + 13 x y z + 8 y z - z , 4 2 -13 x - 17 x z + 10 x z + 13 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=27.0MB, alloc=32.3MB, time=0.51 memory used=46.0MB, alloc=56.3MB, time=0.79 memory used=86.3MB, alloc=60.3MB, time=1.37 memory used=126.7MB, alloc=60.3MB, time=1.92 memory used=160.1MB, alloc=60.3MB, time=2.34 memory used=202.9MB, alloc=68.3MB, time=2.89 memory used=244.0MB, alloc=68.3MB, time=3.31 memory used=285.8MB, alloc=68.3MB, time=3.78 memory used=326.0MB, alloc=92.3MB, time=4.35 memory used=391.0MB, alloc=92.3MB, time=5.18 memory used=439.1MB, alloc=92.3MB, time=5.53 memory used=488.1MB, alloc=92.3MB, time=5.89 memory used=542.1MB, alloc=92.3MB, time=6.37 memory used=615.9MB, alloc=92.3MB, time=8.42 memory used=662.1MB, alloc=92.3MB, time=8.74 memory used=703.3MB, alloc=92.3MB, time=9.03 memory used=764.8MB, alloc=92.3MB, time=9.63 memory used=837.8MB, alloc=92.3MB, time=10.55 memory used=895.7MB, alloc=116.3MB, time=11.43 memory used=976.9MB, alloc=116.3MB, time=12.73 memory used=1041.3MB, alloc=396.3MB, time=13.77 memory used=1155.9MB, alloc=396.3MB, time=15.22 memory used=1272.9MB, alloc=420.3MB, time=16.64 memory used=1417.6MB, alloc=420.3MB, time=18.45 memory used=1546.5MB, alloc=444.3MB, time=19.95 memory used=1679.2MB, alloc=444.3MB, time=21.63 memory used=1799.1MB, alloc=444.3MB, time=23.05 memory used=1916.0MB, alloc=468.3MB, time=24.62 memory used=2034.1MB, alloc=468.3MB, time=26.29 memory used=2136.4MB, alloc=468.3MB, time=27.89 memory used=2250.7MB, alloc=468.3MB, time=29.33 memory used=2354.5MB, alloc=468.3MB, time=30.13 memory used=2461.4MB, alloc=468.3MB, time=30.93 memory used=2565.5MB, alloc=468.3MB, time=31.76 memory used=2656.1MB, alloc=468.3MB, time=32.29 memory used=2768.3MB, alloc=468.3MB, time=33.14 memory used=2867.3MB, alloc=468.3MB, time=33.77 memory used=2960.5MB, alloc=468.3MB, time=34.31 memory used=3044.3MB, alloc=468.3MB, time=34.77 memory used=3146.5MB, alloc=468.3MB, time=35.47 memory used=3232.5MB, alloc=468.3MB, time=35.90 memory used=3315.4MB, alloc=468.3MB, time=36.39 memory used=3393.7MB, alloc=468.3MB, time=36.79 memory used=3483.9MB, alloc=492.3MB, time=37.31 memory used=3568.8MB, alloc=492.3MB, time=37.64 memory used=3675.6MB, alloc=492.3MB, time=38.12 memory used=3762.1MB, alloc=492.3MB, time=38.45 memory used=3870.8MB, alloc=492.3MB, time=39.01 memory used=3971.4MB, alloc=492.3MB, time=39.56 memory used=4060.1MB, alloc=492.3MB, time=39.91 memory used=4154.7MB, alloc=492.3MB, time=40.26 memory used=4257.9MB, alloc=492.3MB, time=40.74 memory used=4348.6MB, alloc=492.3MB, time=41.07 memory used=4448.3MB, alloc=492.3MB, time=41.60 memory used=4559.2MB, alloc=492.3MB, time=42.32 memory used=4647.7MB, alloc=492.3MB, time=42.70 memory used=4741.4MB, alloc=492.3MB, time=43.04 memory used=4844.3MB, alloc=492.3MB, time=43.52 memory used=4935.2MB, alloc=492.3MB, time=43.85 memory used=5034.1MB, alloc=492.3MB, time=44.37 memory used=5141.4MB, alloc=492.3MB, time=44.86 memory used=5233.2MB, alloc=492.3MB, time=45.28 memory used=5409.0MB, alloc=492.3MB, time=47.24 memory used=5580.0MB, alloc=492.3MB, time=48.90 memory used=5756.8MB, alloc=492.3MB, time=51.08 memory used=5842.5MB, alloc=492.3MB, time=51.42 memory used=5936.9MB, alloc=492.3MB, time=51.76 memory used=6008.9MB, alloc=492.3MB, time=52.05 memory used=6186.2MB, alloc=492.3MB, time=53.37 memory used=6399.3MB, alloc=492.3MB, time=55.62 memory used=6491.0MB, alloc=492.3MB, time=56.00 memory used=6696.1MB, alloc=492.3MB, time=57.58 memory used=6901.2MB, alloc=492.3MB, time=59.84 memory used=7019.9MB, alloc=492.3MB, time=60.59 memory used=7132.7MB, alloc=492.3MB, time=61.46 memory used=7245.4MB, alloc=492.3MB, time=62.35 memory used=7348.5MB, alloc=492.3MB, time=62.88 memory used=7463.9MB, alloc=492.3MB, time=63.74 memory used=7564.1MB, alloc=492.3MB, time=64.41 memory used=7679.8MB, alloc=492.3MB, time=65.20 memory used=7786.7MB, alloc=492.3MB, time=65.82 memory used=7892.2MB, alloc=492.3MB, time=66.41 memory used=7982.1MB, alloc=492.3MB, time=66.87 memory used=8083.2MB, alloc=492.3MB, time=67.42 memory used=8237.1MB, alloc=492.3MB, time=68.78 memory used=8340.0MB, alloc=492.3MB, time=70.02 memory used=8482.1MB, alloc=516.3MB, time=71.31 memory used=8628.9MB, alloc=516.3MB, time=72.63 memory used=8775.5MB, alloc=516.3MB, time=73.76 memory used=8911.9MB, alloc=516.3MB, time=74.77 memory used=9047.9MB, alloc=516.3MB, time=75.83 memory used=9192.1MB, alloc=516.3MB, time=77.08 memory used=9323.2MB, alloc=516.3MB, time=77.91 memory used=9437.0MB, alloc=516.3MB, time=78.49 memory used=9545.4MB, alloc=516.3MB, time=79.00 memory used=9660.2MB, alloc=516.3MB, time=79.54 memory used=9768.2MB, alloc=516.3MB, time=80.74 memory used=9935.5MB, alloc=516.3MB, time=82.05 memory used=10036.0MB, alloc=516.3MB, time=83.13 memory used=10161.4MB, alloc=516.3MB, time=84.27 memory used=10270.4MB, alloc=516.3MB, time=85.67 memory used=10331.0MB, alloc=516.3MB, time=86.82 memory used=10393.5MB, alloc=516.3MB, time=87.98 memory used=10454.5MB, alloc=516.3MB, time=89.31 memory used=10503.6MB, alloc=516.3MB, time=90.30 memory used=10573.7MB, alloc=516.3MB, time=91.69 memory used=10623.4MB, alloc=516.3MB, time=92.80 memory used=10678.5MB, alloc=516.3MB, time=93.79 memory used=10729.4MB, alloc=516.3MB, time=94.69 memory used=10778.6MB, alloc=516.3MB, time=95.59 memory used=10822.3MB, alloc=516.3MB, time=96.29 memory used=10877.8MB, alloc=516.3MB, time=97.57 memory used=10925.6MB, alloc=540.3MB, time=98.62 memory used=11145.4MB, alloc=564.3MB, time=101.69 memory used=11339.1MB, alloc=564.3MB, time=104.73 memory used=11542.2MB, alloc=588.3MB, time=106.82 memory used=11684.1MB, alloc=588.3MB, time=107.90 memory used=11846.2MB, alloc=588.3MB, time=109.24 memory used=11988.1MB, alloc=588.3MB, time=110.31 memory used=12187.6MB, alloc=588.3MB, time=112.47 memory used=12312.2MB, alloc=588.3MB, time=113.10 memory used=12449.5MB, alloc=588.3MB, time=115.22 memory used=12568.3MB, alloc=588.3MB, time=115.82 memory used=12702.6MB, alloc=588.3MB, time=117.00 memory used=12872.4MB, alloc=588.3MB, time=118.18 memory used=13003.0MB, alloc=588.3MB, time=119.11 memory used=13203.3MB, alloc=588.3MB, time=121.11 memory used=13371.7MB, alloc=588.3MB, time=123.42 memory used=13520.2MB, alloc=588.3MB, time=125.66 memory used=13643.7MB, alloc=588.3MB, time=126.27 memory used=13753.4MB, alloc=588.3MB, time=126.83 memory used=13923.3MB, alloc=588.3MB, time=127.93 memory used=14039.7MB, alloc=588.3MB, time=128.52 memory used=14315.5MB, alloc=588.3MB, time=131.11 memory used=14596.6MB, alloc=588.3MB, time=134.48 memory used=14898.5MB, alloc=588.3MB, time=141.75 memory used=15191.5MB, alloc=612.3MB, time=143.64 memory used=15504.1MB, alloc=612.3MB, time=148.43 memory used=15764.0MB, alloc=612.3MB, time=154.25 memory used=15934.0MB, alloc=612.3MB, time=155.62 memory used=16089.1MB, alloc=612.3MB, time=156.77 memory used=16290.3MB, alloc=612.3MB, time=158.94 memory used=16424.1MB, alloc=612.3MB, time=159.60 memory used=16566.3MB, alloc=612.3MB, time=161.73 memory used=16692.0MB, alloc=612.3MB, time=162.37 memory used=16860.0MB, alloc=612.3MB, time=163.23 memory used=17009.9MB, alloc=612.3MB, time=164.24 memory used=17165.5MB, alloc=612.3MB, time=165.38 memory used=17329.3MB, alloc=612.3MB, time=166.57 memory used=17588.9MB, alloc=612.3MB, time=169.30 memory used=17780.0MB, alloc=612.3MB, time=170.86 memory used=17930.5MB, alloc=612.3MB, time=172.26 memory used=18155.0MB, alloc=612.3MB, time=175.11 memory used=18309.6MB, alloc=612.3MB, time=177.74 memory used=18435.8MB, alloc=612.3MB, time=178.42 memory used=18552.0MB, alloc=612.3MB, time=179.04 memory used=18788.2MB, alloc=612.3MB, time=180.26 memory used=18949.4MB, alloc=612.3MB, time=181.40 memory used=19143.3MB, alloc=612.3MB, time=182.21 memory used=19432.9MB, alloc=612.3MB, time=184.00 memory used=19615.2MB, alloc=612.3MB, time=184.76 memory used=19891.7MB, alloc=612.3MB, time=185.61 memory used=20078.9MB, alloc=612.3MB, time=186.38 memory used=20326.8MB, alloc=612.3MB, time=187.17 memory used=20527.9MB, alloc=612.3MB, time=189.41 |\^/| 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(); 1428287033 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 3 3 F := [8 x - 13 x y + 2 y z + 17 y , 15 x y - 10 x z - 8 x , 2 4 2 6 x y z + 9 z + 5 x z + 1] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [13 x y z - 20 x y - 20 y z + 7 y z, 3 2 3 2 3 2 2 14 x y - 15 x y z - 20 y z + 12 z , 20 x z - 13 y z + 19 x - 13 x] > Problem := [F,G]; 3 2 2 2 3 3 3 Problem := [[8 x - 13 x y + 2 y z + 17 y , 15 x y - 10 x z - 8 x , 2 4 2 2 2 2 6 x y z + 9 z + 5 x z + 1], [13 x y z - 20 x y - 20 y z + 7 y z, 3 2 3 2 3 2 2 14 x y - 15 x y z - 20 y z + 12 z , 20 x z - 13 y z + 19 x - 13 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=25.2MB, alloc=32.3MB, time=0.49 memory used=46.2MB, alloc=36.3MB, time=0.75 memory used=65.5MB, alloc=60.3MB, time=1.05 memory used=111.2MB, alloc=68.3MB, time=1.61 memory used=158.5MB, alloc=68.3MB, time=2.14 memory used=203.6MB, alloc=68.3MB, time=2.68 memory used=232.8MB, alloc=68.3MB, time=2.85 memory used=260.4MB, alloc=68.3MB, time=2.97 memory used=281.2MB, alloc=68.3MB, time=3.05 memory used=310.7MB, alloc=68.3MB, time=3.40 memory used=330.3MB, alloc=68.3MB, time=3.47 memory used=358.4MB, alloc=68.3MB, time=3.61 memory used=379.7MB, alloc=68.3MB, time=3.69 memory used=405.8MB, alloc=68.3MB, time=3.82 memory used=435.8MB, alloc=68.3MB, time=4.20 memory used=457.1MB, alloc=68.3MB, time=4.29 memory used=479.2MB, alloc=68.3MB, time=4.39 memory used=503.8MB, alloc=68.3MB, time=4.48 memory used=532.4MB, alloc=68.3MB, time=4.60 memory used=553.1MB, alloc=68.3MB, time=4.68 memory used=582.1MB, alloc=68.3MB, time=5.05 memory used=601.7MB, alloc=68.3MB, time=5.12 memory used=639.7MB, alloc=68.3MB, time=5.61 memory used=662.5MB, alloc=68.3MB, time=5.70 memory used=685.4MB, alloc=68.3MB, time=5.84 memory used=738.1MB, alloc=68.3MB, time=7.26 memory used=759.9MB, alloc=68.3MB, time=7.35 memory used=777.1MB, alloc=68.3MB, time=7.41 memory used=796.3MB, alloc=68.3MB, time=7.48 memory used=819.5MB, alloc=68.3MB, time=7.56 memory used=846.7MB, alloc=68.3MB, time=7.78 memory used=894.1MB, alloc=92.3MB, time=8.32 memory used=957.8MB, alloc=92.3MB, time=9.17 memory used=1026.5MB, alloc=92.3MB, time=9.99 memory used=1096.5MB, alloc=92.3MB, time=10.78 memory used=1154.2MB, alloc=92.3MB, time=11.26 memory used=1191.8MB, alloc=92.3MB, time=11.47 memory used=1239.0MB, alloc=92.3MB, time=11.83 memory used=1265.7MB, alloc=116.3MB, time=11.98 memory used=1314.6MB, alloc=116.3MB, time=12.13 memory used=1353.8MB, alloc=116.3MB, time=12.27 memory used=1402.2MB, alloc=116.3MB, time=12.40 memory used=1450.7MB, alloc=116.3MB, time=12.53 memory used=1506.4MB, alloc=116.3MB, time=12.85 memory used=1555.7MB, alloc=116.3MB, time=13.00 memory used=1594.3MB, alloc=116.3MB, time=13.15 memory used=1641.7MB, alloc=116.3MB, time=13.28 memory used=1690.8MB, alloc=116.3MB, time=13.41 memory used=1755.8MB, alloc=116.3MB, time=14.93 memory used=1798.4MB, alloc=116.3MB, time=15.07 memory used=1851.1MB, alloc=116.3MB, time=15.20 memory used=1890.0MB, alloc=116.3MB, time=15.31 memory used=1928.1MB, alloc=116.3MB, time=15.41 memory used=1974.4MB, alloc=116.3MB, time=15.52 memory used=2032.1MB, alloc=116.3MB, time=15.86 memory used=2080.5MB, alloc=116.3MB, time=16.02 memory used=2119.6MB, alloc=116.3MB, time=16.14 memory used=2167.9MB, alloc=116.3MB, time=16.27 memory used=2215.8MB, alloc=116.3MB, time=16.39 memory used=2271.4MB, alloc=116.3MB, time=16.71 memory used=2320.4MB, alloc=116.3MB, time=16.86 memory used=2358.7MB, alloc=116.3MB, time=16.99 memory used=2406.6MB, alloc=116.3MB, time=17.14 memory used=2456.0MB, alloc=116.3MB, time=17.27 memory used=2522.1MB, alloc=116.3MB, time=18.90 memory used=2564.8MB, alloc=116.3MB, time=19.04 memory used=2617.1MB, alloc=116.3MB, time=19.19 memory used=2655.7MB, alloc=116.3MB, time=19.30 memory used=2694.4MB, alloc=116.3MB, time=19.40 memory used=2750.6MB, alloc=116.3MB, time=19.70 memory used=2818.1MB, alloc=116.3MB, time=20.26 memory used=2884.0MB, alloc=116.3MB, time=23.46 memory used=2936.0MB, alloc=116.3MB, time=23.65 memory used=2971.9MB, alloc=116.3MB, time=23.82 memory used=3011.3MB, alloc=116.3MB, time=23.98 memory used=3055.5MB, alloc=116.3MB, time=24.13 memory used=3103.5MB, alloc=116.3MB, time=24.29 memory used=3155.0MB, alloc=116.3MB, time=24.46 memory used=3206.0MB, alloc=116.3MB, time=24.62 memory used=3238.6MB, alloc=140.3MB, time=24.77 memory used=3279.4MB, alloc=140.3MB, time=24.94 memory used=3321.8MB, alloc=140.3MB, time=25.10 memory used=3365.8MB, alloc=140.3MB, time=25.28 memory used=3411.5MB, alloc=140.3MB, time=25.45 memory used=3463.2MB, alloc=140.3MB, time=25.61 memory used=3516.8MB, alloc=140.3MB, time=25.77 memory used=3572.1MB, alloc=140.3MB, time=25.93 memory used=3628.8MB, alloc=140.3MB, time=26.09 memory used=3687.0MB, alloc=140.3MB, time=26.25 memory used=3746.6MB, alloc=140.3MB, time=26.43 memory used=3808.2MB, alloc=140.3MB, time=26.59 memory used=3876.2MB, alloc=140.3MB, time=26.78 memory used=3946.1MB, alloc=140.3MB, time=26.96 memory used=4017.5MB, alloc=140.3MB, time=27.13 memory used=4090.2MB, alloc=140.3MB, time=27.32 memory used=4151.3MB, alloc=140.3MB, time=27.48 memory used=4189.4MB, alloc=164.3MB, time=27.62 memory used=4234.9MB, alloc=164.3MB, time=27.75 memory used=4282.0MB, alloc=164.3MB, time=27.89 memory used=4330.3MB, alloc=164.3MB, time=28.02 memory used=4379.1MB, alloc=164.3MB, time=28.16 memory used=4428.8MB, alloc=164.3MB, time=28.30 memory used=4484.9MB, alloc=164.3MB, time=28.45 memory used=4541.9MB, alloc=164.3MB, time=28.59 memory used=4599.2MB, alloc=164.3MB, time=28.74 memory used=4656.9MB, alloc=164.3MB, time=28.88 memory used=4715.0MB, alloc=164.3MB, time=29.03 memory used=4773.3MB, alloc=164.3MB, time=29.17 memory used=4832.0MB, alloc=164.3MB, time=29.31 memory used=4891.6MB, alloc=164.3MB, time=29.45 memory used=4957.5MB, alloc=164.3MB, time=29.60 memory used=5024.2MB, alloc=164.3MB, time=29.75 memory used=5091.1MB, alloc=164.3MB, time=29.90 memory used=5158.1MB, alloc=164.3MB, time=30.05 memory used=5225.3MB, alloc=164.3MB, time=30.20 memory used=5293.6MB, alloc=164.3MB, time=30.34 memory used=5367.3MB, alloc=164.3MB, time=30.51 memory used=5442.0MB, alloc=164.3MB, time=30.67 memory used=5516.6MB, alloc=164.3MB, time=30.83 memory used=5591.9MB, alloc=164.3MB, time=30.99 memory used=5672.8MB, alloc=164.3MB, time=31.14 memory used=5754.1MB, alloc=164.3MB, time=31.30 memory used=5835.1MB, alloc=164.3MB, time=31.46 memory used=5922.8MB, alloc=164.3MB, time=31.62 memory used=6009.8MB, alloc=164.3MB, time=31.78 memory used=6097.1MB, alloc=164.3MB, time=31.93 memory used=6188.6MB, alloc=164.3MB, time=32.10 memory used=6280.9MB, alloc=164.3MB, time=32.26 memory used=6377.0MB, alloc=164.3MB, time=32.43 memory used=6467.3MB, alloc=179.8MB, time=32.60 memory used=6499.0MB, alloc=179.8MB, time=32.71 memory used=6513.4MB, alloc=179.8MB, time=32.80 memory used=6521.6MB, alloc=179.8MB, time=32.88 memory used=6527.1MB, alloc=179.8MB, time=32.96 memory used=6532.7MB, alloc=179.8MB, time=33.04 memory used=6538.4MB, alloc=179.8MB, time=33.12 memory used=6544.1MB, alloc=179.8MB, time=33.19 memory used=6549.9MB, alloc=179.8MB, time=33.26 memory used=6551.3MB, alloc=179.8MB, time=33.33 memory used=6555.7MB, alloc=179.8MB, time=33.40 memory used=6556.7MB, alloc=179.8MB, time=33.50 memory used=6561.8MB, alloc=179.8MB, time=33.57 memory used=6562.7MB, alloc=179.8MB, time=33.65 memory used=6563.2MB, alloc=179.8MB, time=33.73 memory used=6568.0MB, alloc=179.8MB, time=33.79 memory used=6568.9MB, alloc=179.8MB, time=33.86 memory used=6569.5MB, alloc=179.8MB, time=33.93 memory used=6574.3MB, alloc=179.8MB, time=34.00 memory used=6575.2MB, alloc=179.8MB, time=34.07 memory used=6575.8MB, alloc=179.8MB, time=34.14 memory used=6580.6MB, alloc=179.8MB, time=34.20 memory used=6581.5MB, alloc=179.8MB, time=34.28 memory used=6582.0MB, alloc=179.8MB, time=34.35 memory used=6586.8MB, alloc=179.8MB, time=34.42 memory used=6587.8MB, alloc=179.8MB, time=34.49 memory used=6588.3MB, alloc=179.8MB, time=34.55 memory used=6593.1MB, alloc=179.8MB, time=34.62 memory used=6594.1MB, alloc=179.8MB, time=34.70 memory used=6594.6MB, alloc=179.8MB, time=34.76 memory used=6599.4MB, alloc=179.8MB, time=34.84 memory used=6600.3MB, alloc=179.8MB, time=34.91 memory used=6605.6MB, alloc=179.8MB, time=34.98 memory used=6606.6MB, alloc=179.8MB, time=35.05 memory used=6611.8MB, alloc=179.8MB, time=35.12 memory used=6612.8MB, alloc=179.8MB, time=35.21 memory used=6618.0MB, alloc=179.8MB, time=35.28 memory used=6619.1MB, alloc=179.8MB, time=35.35 memory used=6624.2MB, alloc=179.8MB, time=35.42 memory used=6625.3MB, alloc=179.8MB, time=35.49 memory used=6630.4MB, alloc=179.8MB, time=35.56 memory used=6631.5MB, alloc=179.8MB, time=35.63 memory used=6636.6MB, alloc=179.8MB, time=35.72 memory used=6637.7MB, alloc=179.8MB, time=35.79 memory used=6642.8MB, alloc=179.8MB, time=35.86 memory used=6643.9MB, alloc=179.8MB, time=35.93 memory used=6648.9MB, alloc=179.8MB, time=36.00 memory used=6650.1MB, alloc=179.8MB, time=36.08 memory used=6655.1MB, alloc=179.8MB, time=36.15 memory used=6656.2MB, alloc=179.8MB, time=36.22 memory used=6661.2MB, alloc=179.8MB, time=36.30 memory used=6662.4MB, alloc=179.8MB, time=36.37 memory used=6667.3MB, alloc=179.8MB, time=36.44 memory used=6668.5MB, alloc=179.8MB, time=36.50 memory used=6673.4MB, alloc=179.8MB, time=36.57 memory used=6674.7MB, alloc=179.8MB, time=36.64 memory used=6680.5MB, alloc=179.8MB, time=36.71 memory used=6685.6MB, alloc=179.8MB, time=36.79 memory used=6687.1MB, alloc=179.8MB, time=36.91 memory used=6691.7MB, alloc=179.8MB, time=36.98 memory used=6693.2MB, alloc=179.8MB, time=37.06 memory used=6697.7MB, alloc=179.8MB, time=37.14 memory used=6699.2MB, alloc=179.8MB, time=37.21 memory used=6703.8MB, alloc=179.8MB, time=37.28 memory used=6705.3MB, alloc=179.8MB, time=37.35 memory used=6709.8MB, alloc=179.8MB, time=37.42 memory used=6711.3MB, alloc=179.8MB, time=37.49 memory used=6715.8MB, alloc=179.8MB, time=37.60 memory used=6717.3MB, alloc=179.8MB, time=37.67 memory used=6721.9MB, alloc=179.8MB, time=37.74 memory used=6723.4MB, alloc=179.8MB, time=37.81 memory used=6727.9MB, alloc=179.8MB, time=37.88 memory used=6729.4MB, alloc=179.8MB, time=37.96 memory used=6733.8MB, alloc=179.8MB, time=38.04 memory used=6735.3MB, alloc=179.8MB, time=38.11 memory used=6739.8MB, alloc=179.8MB, time=38.17 memory used=6741.3MB, alloc=179.8MB, time=38.25 memory used=6745.8MB, alloc=179.8MB, time=38.31 memory used=6747.3MB, alloc=179.8MB, time=38.39 memory used=6751.8MB, alloc=179.8MB, time=38.47 memory used=6757.7MB, alloc=179.8MB, time=38.56 memory used=6763.6MB, alloc=179.8MB, time=38.64 memory used=6769.5MB, alloc=179.8MB, time=38.72 memory used=6775.4MB, alloc=179.8MB, time=38.79 memory used=6781.3MB, alloc=179.8MB, time=38.87 memory used=6787.2MB, alloc=179.8MB, time=38.97 memory used=6793.1MB, alloc=179.8MB, time=39.05 memory used=6798.9MB, alloc=179.8MB, time=39.13 memory used=6804.7MB, alloc=179.8MB, time=39.21 memory used=6810.5MB, alloc=179.8MB, time=39.29 memory used=6816.4MB, alloc=179.8MB, time=39.36 memory used=6822.1MB, alloc=179.8MB, time=39.44 memory used=6827.9MB, alloc=179.8MB, time=39.52 memory used=6833.7MB, alloc=179.8MB, time=39.60 memory used=6839.4MB, alloc=179.8MB, time=39.68 memory used=6845.2MB, alloc=179.8MB, time=39.75 memory used=6850.9MB, alloc=179.8MB, time=39.82 memory used=6856.6MB, alloc=179.8MB, time=39.90 memory used=6862.3MB, alloc=179.8MB, time=39.98 memory used=6868.0MB, alloc=179.8MB, time=40.05 memory used=6873.7MB, alloc=179.8MB, time=40.11 memory used=6879.3MB, alloc=179.8MB, time=40.19 memory used=6885.0MB, alloc=179.8MB, time=40.26 memory used=6890.6MB, alloc=179.8MB, time=40.33 memory used=6896.2MB, alloc=179.8MB, time=40.40 memory used=6901.8MB, alloc=179.8MB, time=40.48 memory used=6907.4MB, alloc=179.8MB, time=40.55 memory used=6912.9MB, alloc=179.8MB, time=40.64 memory used=6918.5MB, alloc=179.8MB, time=40.70 memory used=6924.0MB, alloc=179.8MB, time=40.79 memory used=6929.6MB, alloc=179.8MB, time=40.86 memory used=6935.1MB, alloc=179.8MB, time=40.94 memory used=6940.6MB, alloc=179.8MB, time=41.00 memory used=6946.1MB, alloc=179.8MB, time=41.08 memory used=6951.5MB, alloc=179.8MB, time=41.15 memory used=6957.0MB, alloc=179.8MB, time=41.23 memory used=6962.4MB, alloc=179.8MB, time=41.31 memory used=6967.8MB, alloc=179.8MB, time=41.38 memory used=6973.3MB, alloc=179.8MB, time=41.46 memory used=6978.7MB, alloc=179.8MB, time=41.53 memory used=6984.0MB, alloc=179.8MB, time=41.61 memory used=6989.4MB, alloc=179.8MB, time=41.68 memory used=6994.7MB, alloc=179.8MB, time=41.75 memory used=7000.1MB, alloc=179.8MB, time=41.83 memory used=7005.4MB, alloc=179.8MB, time=41.91 memory used=7010.7MB, alloc=179.8MB, time=42.00 memory used=7016.0MB, alloc=179.8MB, time=42.07 memory used=7021.3MB, alloc=179.8MB, time=42.14 memory used=7026.5MB, alloc=179.8MB, time=42.21 memory used=7031.8MB, alloc=179.8MB, time=42.29 memory used=7037.0MB, alloc=179.8MB, time=42.36 memory used=7042.2MB, alloc=179.8MB, time=42.44 memory used=7047.4MB, alloc=179.8MB, time=42.51 memory used=7052.6MB, alloc=179.8MB, time=42.58 memory used=7057.7MB, alloc=179.8MB, time=42.65 memory used=7062.9MB, alloc=179.8MB, time=42.73 memory used=7068.0MB, alloc=179.8MB, time=42.79 memory used=7073.1MB, alloc=179.8MB, time=42.86 memory used=7078.2MB, alloc=179.8MB, time=42.93 memory used=7083.3MB, alloc=179.8MB, time=43.01 memory used=7088.4MB, alloc=179.8MB, time=43.08 memory used=7093.4MB, alloc=179.8MB, time=43.16 memory used=7098.5MB, alloc=179.8MB, time=43.23 memory used=7103.5MB, alloc=179.8MB, time=43.30 memory used=7108.5MB, alloc=179.8MB, time=43.38 memory used=7113.5MB, alloc=179.8MB, time=43.45 memory used=7118.5MB, alloc=179.8MB, time=43.52 memory used=7123.4MB, alloc=179.8MB, time=43.59 memory used=7128.3MB, alloc=179.8MB, time=43.67 memory used=7134.4MB, alloc=179.8MB, time=43.74 memory used=7139.8MB, alloc=179.8MB, time=43.82 memory used=7147.9MB, alloc=179.8MB, time=43.90 memory used=7153.9MB, alloc=179.8MB, time=43.98 memory used=7159.3MB, alloc=179.8MB, time=44.06 memory used=7167.2MB, alloc=179.8MB, time=44.12 memory used=7173.1MB, alloc=179.8MB, time=44.20 memory used=7181.5MB, alloc=179.8MB, time=44.28 memory used=7187.5MB, alloc=179.8MB, time=44.35 memory used=7195.7MB, alloc=179.8MB, time=44.43 memory used=7201.7MB, alloc=179.8MB, time=44.51 memory used=7209.7MB, alloc=179.8MB, time=44.58 memory used=7216.0MB, alloc=179.8MB, time=44.65 memory used=7223.5MB, alloc=179.8MB, time=44.73 memory used=7229.8MB, alloc=179.8MB, time=44.80 memory used=7237.2MB, alloc=179.8MB, time=44.87 memory used=7243.4MB, alloc=179.8MB, time=44.94 memory used=7250.7MB, alloc=179.8MB, time=45.02 memory used=7259.6MB, alloc=179.8MB, time=45.10 memory used=7268.5MB, alloc=179.8MB, time=45.18 memory used=7277.3MB, alloc=179.8MB, time=45.26 memory used=7285.9MB, alloc=179.8MB, time=45.34 memory used=7294.6MB, alloc=179.8MB, time=45.42 memory used=7303.1MB, alloc=179.8MB, time=45.50 memory used=7311.6MB, alloc=179.8MB, time=45.58 memory used=7320.0MB, alloc=179.8MB, time=45.66 memory used=7328.3MB, alloc=179.8MB, time=45.75 memory used=7336.5MB, alloc=179.8MB, time=45.82 memory used=7344.7MB, alloc=179.8MB, time=45.90 memory used=7352.8MB, alloc=179.8MB, time=45.97 memory used=7360.8MB, alloc=179.8MB, time=46.05 memory used=7368.7MB, alloc=179.8MB, time=46.13 memory used=7377.7MB, alloc=179.8MB, time=46.21 memory used=7386.1MB, alloc=179.8MB, time=46.29 memory used=7395.9MB, alloc=179.8MB, time=46.38 memory used=7404.8MB, alloc=179.8MB, time=46.46 memory used=7414.7MB, alloc=179.8MB, time=46.54 memory used=7423.8MB, alloc=179.8MB, time=46.61 memory used=7433.0MB, alloc=179.8MB, time=46.68 memory used=7443.7MB, alloc=179.8MB, time=46.76 memory used=7454.2MB, alloc=179.8MB, time=46.83 memory used=7464.5MB, alloc=179.8MB, time=46.91 memory used=7474.7MB, alloc=179.8MB, time=46.98 memory used=7484.7MB, alloc=179.8MB, time=47.07 memory used=7495.7MB, alloc=179.8MB, time=47.15 memory used=7507.2MB, alloc=179.8MB, time=47.22 memory used=7518.4MB, alloc=179.8MB, time=47.30 memory used=7529.9MB, alloc=179.8MB, time=47.38 memory used=7541.6MB, alloc=179.8MB, time=47.46 memory used=7553.7MB, alloc=179.8MB, time=47.54 memory used=7565.5MB, alloc=179.8MB, time=47.62 memory used=7701.1MB, alloc=179.8MB, time=118.83 |\^/| 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(); 1428287333 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 F := [-3 x y + 16 x y z + 12 x z + 14 z , 3 2 2 3 2 2 2 14 y z - 4 x z + 3 y z + 13 x y, -20 x y - 9 y z - 18 x z + 19 y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-2 x y - 8 x z - 6 y z - 19, x y + 13 y + 4 z, 2 3 19 x y z - 12 x z + 7 x y z - 6 x y] > Problem := [F,G]; 2 2 2 2 3 Problem := [[-3 x y + 16 x y z + 12 x z + 14 z , 3 2 2 3 2 2 2 14 y z - 4 x z + 3 y z + 13 x y, -20 x y - 9 y z - 18 x z + 19 y], [ 2 2 -2 x y - 8 x z - 6 y z - 19, x y + 13 y + 4 z, 2 3 19 x y z - 12 x z + 7 x y z - 6 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=23.7MB, alloc=32.3MB, time=0.43 memory used=43.0MB, alloc=56.3MB, time=0.71 memory used=85.7MB, alloc=61.0MB, time=1.13 memory used=129.5MB, alloc=69.0MB, time=1.53 memory used=177.2MB, alloc=72.6MB, time=2.08 memory used=226.8MB, alloc=72.6MB, time=2.58 memory used=270.9MB, alloc=72.6MB, time=3.21 memory used=317.6MB, alloc=72.6MB, time=3.64 memory used=356.8MB, alloc=72.6MB, time=3.88 memory used=399.6MB, alloc=72.6MB, time=4.29 memory used=436.8MB, alloc=72.6MB, time=4.52 memory used=465.0MB, alloc=72.6MB, time=4.62 memory used=496.1MB, alloc=72.6MB, time=5.00 memory used=518.6MB, alloc=72.6MB, time=5.08 memory used=561.9MB, alloc=72.6MB, time=5.39 memory used=595.1MB, alloc=72.6MB, time=5.49 memory used=620.5MB, alloc=72.6MB, time=6.45 memory used=656.3MB, alloc=72.6MB, time=6.72 memory used=675.7MB, alloc=72.6MB, time=6.80 memory used=699.5MB, alloc=72.6MB, time=6.89 memory used=745.3MB, alloc=72.6MB, time=7.48 memory used=773.6MB, alloc=72.6MB, time=7.67 memory used=795.9MB, alloc=72.6MB, time=7.83 memory used=817.7MB, alloc=72.6MB, time=7.91 memory used=843.1MB, alloc=72.6MB, time=8.17 memory used=872.3MB, alloc=72.6MB, time=8.36 memory used=894.7MB, alloc=72.6MB, time=8.44 memory used=917.4MB, alloc=72.6MB, time=8.57 memory used=947.7MB, alloc=72.6MB, time=9.21 memory used=967.4MB, alloc=72.6MB, time=9.30 memory used=987.0MB, alloc=72.6MB, time=9.37 memory used=1029.7MB, alloc=96.6MB, time=9.98 memory used=1092.9MB, alloc=96.6MB, time=10.76 memory used=1149.1MB, alloc=96.6MB, time=11.46 memory used=1215.0MB, alloc=376.6MB, time=12.49 memory used=1269.4MB, alloc=376.6MB, time=17.47 memory used=1307.1MB, alloc=376.6MB, time=20.00 memory used=1344.9MB, alloc=400.6MB, time=20.53 memory used=1410.8MB, alloc=424.6MB, time=27.45 memory used=1480.6MB, alloc=424.6MB, time=29.84 memory used=1546.1MB, alloc=424.6MB, time=30.10 memory used=1609.6MB, alloc=424.6MB, time=30.35 memory used=1674.8MB, alloc=424.6MB, time=30.61 memory used=1742.9MB, alloc=424.6MB, time=30.87 memory used=1814.1MB, alloc=424.6MB, time=31.11 memory used=1888.6MB, alloc=424.6MB, time=31.35 memory used=1963.6MB, alloc=424.6MB, time=40.22 memory used=2043.7MB, alloc=424.6MB, time=45.96 memory used=2115.6MB, alloc=424.6MB, time=46.16 memory used=2189.2MB, alloc=424.6MB, time=46.36 memory used=2264.9MB, alloc=424.6MB, time=46.55 memory used=2339.0MB, alloc=424.6MB, time=46.75 memory used=2414.9MB, alloc=424.6MB, time=46.97 memory used=2492.2MB, alloc=424.6MB, time=47.17 memory used=2570.6MB, alloc=424.6MB, time=47.39 memory used=2649.7MB, alloc=424.6MB, time=47.61 memory used=2729.3MB, alloc=424.6MB, time=47.81 memory used=2809.1MB, alloc=424.6MB, time=48.02 memory used=2891.2MB, alloc=424.6MB, time=48.25 memory used=2972.3MB, alloc=424.6MB, time=48.44 memory used=3054.5MB, alloc=424.6MB, time=48.66 memory used=3139.1MB, alloc=424.6MB, time=48.88 memory used=3224.4MB, alloc=424.6MB, time=49.09 memory used=3310.8MB, alloc=424.6MB, time=49.31 memory used=3397.4MB, alloc=424.6MB, time=49.52 memory used=3486.4MB, alloc=424.6MB, time=49.74 memory used=3577.8MB, alloc=424.6MB, time=49.96 memory used=3735.3MB, alloc=424.6MB, time=50.91 memory used=3937.8MB, alloc=424.6MB, time=54.27 memory used=4020.2MB, alloc=424.6MB, time=54.53 memory used=4106.7MB, alloc=424.6MB, time=54.77 memory used=4196.4MB, alloc=424.6MB, time=55.01 memory used=4291.6MB, alloc=424.6MB, time=55.27 memory used=4393.0MB, alloc=424.6MB, time=55.54 memory used=4492.2MB, alloc=424.6MB, time=55.95 memory used=4619.5MB, alloc=424.6MB, time=72.59 memory used=4677.0MB, alloc=424.6MB, time=92.92 |\^/| 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(); 1428287633 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 2 3 2 3 F := [7 x + 15 x y - 18 y - y , -13 x y z - x + 2 x y - 5 z , 3 2 2 2 -10 x z - 10 x y - 5 z - 6 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 2 2 2 G := [14 x y z + 5 y z - 16 x z + 9 y , -17 x y z + 14 x y + 2 x y + 2 x , 3 4 2 19 x y + 16 y + 16 x - 5 x y] > Problem := [F,G]; 4 3 3 2 2 3 2 3 Problem := [[7 x + 15 x y - 18 y - y , -13 x y z - x + 2 x y - 5 z , 3 2 2 2 2 3 2 3 -10 x z - 10 x y - 5 z - 6 x], [14 x y z + 5 y z - 16 x z + 9 y , 2 2 2 2 3 4 2 -17 x y z + 14 x y + 2 x y + 2 x , 19 x y + 16 y + 16 x - 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=0.17 memory used=24.2MB, alloc=32.3MB, time=0.45 memory used=43.1MB, alloc=56.3MB, time=0.72 memory used=82.2MB, alloc=60.3MB, time=1.20 memory used=123.8MB, alloc=61.7MB, time=1.40 memory used=165.6MB, alloc=61.7MB, time=1.79 memory used=211.9MB, alloc=69.7MB, time=2.37 memory used=251.7MB, alloc=69.7MB, time=2.76 memory used=299.8MB, alloc=69.7MB, time=3.34 memory used=331.6MB, alloc=69.7MB, time=3.53 memory used=349.4MB, alloc=69.7MB, time=3.60 memory used=373.5MB, alloc=69.7MB, time=3.68 memory used=416.0MB, alloc=69.7MB, time=3.99 memory used=456.5MB, alloc=69.7MB, time=4.39 memory used=494.3MB, alloc=69.7MB, time=4.72 memory used=512.4MB, alloc=93.7MB, time=4.81 memory used=550.6MB, alloc=93.7MB, time=4.93 memory used=598.4MB, alloc=93.7MB, time=5.24 memory used=683.0MB, alloc=93.7MB, time=6.31 memory used=721.4MB, alloc=93.7MB, time=6.43 memory used=750.6MB, alloc=93.7MB, time=6.54 memory used=784.2MB, alloc=93.7MB, time=6.64 memory used=824.6MB, alloc=93.7MB, time=6.76 memory used=862.3MB, alloc=93.7MB, time=6.86 memory used=887.7MB, alloc=93.7MB, time=6.94 memory used=914.3MB, alloc=93.7MB, time=7.03 memory used=942.9MB, alloc=93.7MB, time=7.13 memory used=973.5MB, alloc=93.7MB, time=7.22 memory used=1006.7MB, alloc=93.7MB, time=7.31 memory used=1042.9MB, alloc=93.7MB, time=7.40 memory used=1081.6MB, alloc=93.7MB, time=7.50 memory used=1122.6MB, alloc=93.7MB, time=7.60 memory used=1167.2MB, alloc=93.7MB, time=7.69 memory used=1186.0MB, alloc=107.8MB, time=7.77 memory used=1196.1MB, alloc=107.8MB, time=7.90 memory used=1206.6MB, alloc=107.8MB, time=7.97 memory used=1217.2MB, alloc=107.8MB, time=8.04 memory used=1228.1MB, alloc=107.8MB, time=8.14 memory used=1239.3MB, alloc=107.8MB, time=8.21 memory used=1250.9MB, alloc=107.8MB, time=8.28 memory used=1263.0MB, alloc=107.8MB, time=8.37 memory used=1275.5MB, alloc=107.8MB, time=8.46 memory used=1335.5MB, alloc=107.8MB, time=9.06 memory used=1370.0MB, alloc=107.8MB, time=9.18 memory used=1401.2MB, alloc=107.8MB, time=9.29 memory used=1438.6MB, alloc=107.8MB, time=9.41 memory used=1482.5MB, alloc=107.8MB, time=9.54 memory used=1510.0MB, alloc=107.8MB, time=9.64 memory used=1535.3MB, alloc=107.8MB, time=9.73 memory used=1562.9MB, alloc=107.8MB, time=9.83 memory used=1592.9MB, alloc=107.8MB, time=9.92 memory used=1624.7MB, alloc=107.8MB, time=10.02 memory used=1658.3MB, alloc=107.8MB, time=10.12 memory used=1694.8MB, alloc=107.8MB, time=10.21 memory used=1734.1MB, alloc=107.8MB, time=10.31 memory used=1775.4MB, alloc=107.8MB, time=10.40 memory used=1819.0MB, alloc=107.8MB, time=10.50 memory used=1838.9MB, alloc=107.8MB, time=10.58 memory used=1848.8MB, alloc=107.8MB, time=10.65 memory used=1859.0MB, alloc=107.8MB, time=10.74 memory used=1869.8MB, alloc=107.8MB, time=10.82 memory used=1880.6MB, alloc=107.8MB, time=10.90 memory used=1891.6MB, alloc=107.8MB, time=10.97 memory used=1902.9MB, alloc=107.8MB, time=11.04 memory used=1914.6MB, alloc=107.8MB, time=11.12 memory used=1926.6MB, alloc=107.8MB, time=11.19 memory used=1938.5MB, alloc=107.8MB, time=11.30 memory used=1951.2MB, alloc=107.8MB, time=11.38 memory used=1980.1MB, alloc=107.8MB, time=13.30 memory used=2026.9MB, alloc=107.8MB, time=13.93 memory used=2066.6MB, alloc=107.8MB, time=14.06 memory used=2093.1MB, alloc=107.8MB, time=14.16 memory used=2123.4MB, alloc=107.8MB, time=14.26 memory used=2158.5MB, alloc=107.8MB, time=14.38 memory used=2196.9MB, alloc=107.8MB, time=14.49 memory used=2239.7MB, alloc=107.8MB, time=14.61 memory used=2266.4MB, alloc=107.8MB, time=14.70 memory used=2289.9MB, alloc=107.8MB, time=14.79 memory used=2314.3MB, alloc=107.8MB, time=14.87 memory used=2339.4MB, alloc=107.8MB, time=14.97 memory used=2366.8MB, alloc=107.8MB, time=15.06 memory used=2394.9MB, alloc=107.8MB, time=15.15 memory used=2423.6MB, alloc=107.8MB, time=15.23 memory used=2454.7MB, alloc=107.8MB, time=15.32 memory used=2486.5MB, alloc=107.8MB, time=15.41 memory used=2520.6MB, alloc=107.8MB, time=15.50 memory used=2555.3MB, alloc=107.8MB, time=15.60 memory used=2592.5MB, alloc=107.8MB, time=15.69 memory used=2630.1MB, alloc=107.8MB, time=15.79 memory used=2670.0MB, alloc=107.8MB, time=15.88 memory used=2710.5MB, alloc=107.8MB, time=15.97 memory used=2752.7MB, alloc=107.8MB, time=16.07 memory used=2791.9MB, alloc=107.8MB, time=16.16 memory used=2800.1MB, alloc=107.8MB, time=16.22 memory used=2808.1MB, alloc=107.8MB, time=16.28 memory used=2816.3MB, alloc=107.8MB, time=16.36 memory used=2824.6MB, alloc=107.8MB, time=16.43 memory used=2832.7MB, alloc=107.8MB, time=16.51 memory used=2840.9MB, alloc=107.8MB, time=16.60 memory used=2849.4MB, alloc=107.8MB, time=16.66 memory used=2857.7MB, alloc=107.8MB, time=16.72 memory used=2867.4MB, alloc=107.8MB, time=16.80 memory used=2876.1MB, alloc=107.8MB, time=16.86 memory used=2885.7MB, alloc=107.8MB, time=16.92 memory used=2895.8MB, alloc=107.8MB, time=16.98 memory used=2905.9MB, alloc=107.8MB, time=17.05 memory used=2916.0MB, alloc=107.8MB, time=17.11 memory used=2926.0MB, alloc=107.8MB, time=17.21 memory used=2936.0MB, alloc=107.8MB, time=17.26 memory used=2946.0MB, alloc=107.8MB, time=17.37 memory used=2955.9MB, alloc=107.8MB, time=17.45 memory used=2965.8MB, alloc=107.8MB, time=17.52 memory used=2975.6MB, alloc=107.8MB, time=17.59 memory used=2985.5MB, alloc=107.8MB, time=17.65 memory used=2995.6MB, alloc=107.8MB, time=17.71 memory used=3006.9MB, alloc=107.8MB, time=17.80 memory used=3017.1MB, alloc=107.8MB, time=17.90 memory used=3028.1MB, alloc=107.8MB, time=17.97 memory used=3039.6MB, alloc=107.8MB, time=18.05 memory used=3051.0MB, alloc=107.8MB, time=18.12 memory used=3062.3MB, alloc=107.8MB, time=18.19 memory used=3073.5MB, alloc=107.8MB, time=18.26 memory used=3084.8MB, alloc=107.8MB, time=18.34 memory used=3096.2MB, alloc=107.8MB, time=18.41 memory used=3108.7MB, alloc=107.8MB, time=18.49 memory used=3121.3MB, alloc=107.8MB, time=18.56 memory used=3133.8MB, alloc=107.8MB, time=18.64 memory used=3146.3MB, alloc=107.8MB, time=18.73 memory used=3157.4MB, alloc=107.8MB, time=18.81 memory used=3170.7MB, alloc=107.8MB, time=18.90 memory used=3184.3MB, alloc=107.8MB, time=18.99 memory used=3197.8MB, alloc=107.8MB, time=19.07 memory used=3211.0MB, alloc=107.8MB, time=19.15 memory used=3224.6MB, alloc=107.8MB, time=19.24 memory used=3238.5MB, alloc=107.8MB, time=19.32 memory used=3252.6MB, alloc=107.8MB, time=19.41 memory used=3266.9MB, alloc=107.8MB, time=19.48 memory used=3281.7MB, alloc=107.8MB, time=19.55 memory used=3296.5MB, alloc=107.8MB, time=19.61 memory used=3311.9MB, alloc=107.8MB, time=19.70 memory used=3327.8MB, alloc=107.8MB, time=19.78 memory used=3343.9MB, alloc=107.8MB, time=19.85 memory used=3360.4MB, alloc=107.8MB, time=19.93 memory used=3377.5MB, alloc=107.8MB, time=20.00 memory used=3422.0MB, alloc=107.8MB, time=20.43 memory used=3460.9MB, alloc=107.8MB, time=20.56 memory used=3491.2MB, alloc=107.8MB, time=20.66 memory used=3531.7MB, alloc=107.8MB, time=20.76 memory used=3561.4MB, alloc=107.8MB, time=20.85 memory used=3588.9MB, alloc=107.8MB, time=20.93 memory used=3620.4MB, alloc=107.8MB, time=21.01 memory used=3656.9MB, alloc=107.8MB, time=21.12 memory used=3728.1MB, alloc=107.8MB, time=21.78 memory used=3797.8MB, alloc=107.8MB, time=22.61 memory used=3856.0MB, alloc=107.8MB, time=23.33 memory used=3905.7MB, alloc=387.8MB, time=23.89 memory used=3978.5MB, alloc=387.8MB, time=24.47 memory used=4064.0MB, alloc=387.8MB, time=25.34 memory used=4162.2MB, alloc=411.8MB, time=26.37 memory used=4277.3MB, alloc=435.8MB, time=27.78 memory used=4393.0MB, alloc=459.8MB, time=29.20 memory used=4497.1MB, alloc=459.8MB, time=30.54 memory used=4625.7MB, alloc=459.8MB, time=31.65 memory used=4710.9MB, alloc=459.8MB, time=32.13 memory used=4779.9MB, alloc=459.8MB, time=32.40 memory used=4854.9MB, alloc=459.8MB, time=32.76 memory used=4940.7MB, alloc=459.8MB, time=33.19 memory used=5015.7MB, alloc=459.8MB, time=33.53 memory used=5091.4MB, alloc=459.8MB, time=33.92 memory used=5185.9MB, alloc=459.8MB, time=34.58 memory used=5255.0MB, alloc=459.8MB, time=34.90 memory used=5318.9MB, alloc=459.8MB, time=35.19 memory used=5375.2MB, alloc=459.8MB, time=35.48 memory used=5442.1MB, alloc=459.8MB, time=35.75 memory used=5522.2MB, alloc=459.8MB, time=36.05 memory used=5620.6MB, alloc=459.8MB, time=36.69 memory used=5687.3MB, alloc=459.8MB, time=37.01 memory used=5754.7MB, alloc=459.8MB, time=37.31 memory used=5810.4MB, alloc=459.8MB, time=37.61 memory used=5876.2MB, alloc=459.8MB, time=37.89 memory used=5955.0MB, alloc=459.8MB, time=38.17 memory used=6076.2MB, alloc=483.8MB, time=69.31 memory used=6182.6MB, alloc=483.8MB, time=100.38 memory used=6265.8MB, alloc=483.8MB, time=100.72 memory used=6342.3MB, alloc=483.8MB, time=101.03 memory used=6437.7MB, alloc=483.8MB, time=101.38 memory used=6515.1MB, alloc=483.8MB, time=101.68 memory used=6575.7MB, alloc=483.8MB, time=101.95 memory used=6641.5MB, alloc=483.8MB, time=102.24 memory used=6713.7MB, alloc=483.8MB, time=102.52 memory used=6789.4MB, alloc=483.8MB, time=102.80 memory used=6870.7MB, alloc=483.8MB, time=103.08 memory used=6958.0MB, alloc=483.8MB, time=103.36 memory used=7053.7MB, alloc=483.8MB, time=103.66 memory used=7155.5MB, alloc=483.8MB, time=103.95 memory used=7381.1MB, alloc=483.8MB, time=104.56 memory used=7529.6MB, alloc=483.8MB, time=104.93 memory used=7688.8MB, alloc=483.8MB, time=105.32 memory used=7861.4MB, alloc=483.8MB, time=105.71 memory used=8048.4MB, alloc=483.8MB, time=106.10 memory used=8249.0MB, alloc=483.8MB, time=106.52 memory used=8469.7MB, alloc=483.8MB, time=106.94 memory used=8715.7MB, alloc=483.8MB, time=107.37 memory used=8951.1MB, alloc=483.8MB, time=108.23 memory used=9038.6MB, alloc=483.8MB, time=108.58 memory used=9108.8MB, alloc=483.8MB, time=108.87 memory used=9196.1MB, alloc=483.8MB, time=109.18 memory used=9306.2MB, alloc=483.8MB, time=109.70 memory used=9400.1MB, alloc=483.8MB, time=110.07 memory used=9484.5MB, alloc=483.8MB, time=110.39 memory used=9558.7MB, alloc=483.8MB, time=110.70 memory used=9650.0MB, alloc=483.8MB, time=111.01 memory used=9775.8MB, alloc=483.8MB, time=123.35 memory used=9905.6MB, alloc=483.8MB, time=175.28 memory used=9993.4MB, alloc=483.8MB, time=175.65 memory used=10065.7MB, alloc=483.8MB, time=175.98 memory used=10155.4MB, alloc=483.8MB, time=176.32 memory used=10246.5MB, alloc=483.8MB, time=176.63 memory used=10306.3MB, alloc=483.8MB, time=176.90 memory used=10368.8MB, alloc=483.8MB, time=177.17 memory used=10436.6MB, alloc=483.8MB, time=177.44 memory used=10510.3MB, alloc=483.8MB, time=177.71 memory used=10590.0MB, alloc=483.8MB, time=177.98 memory used=10675.7MB, alloc=483.8MB, time=178.26 memory used=10767.5MB, alloc=483.8MB, time=178.55 memory used=10865.1MB, alloc=483.8MB, time=178.83 memory used=10968.6MB, alloc=483.8MB, time=179.12 memory used=11163.7MB, alloc=483.8MB, time=179.55 memory used=11308.7MB, alloc=483.8MB, time=179.93 memory used=11464.5MB, alloc=483.8MB, time=180.33 memory used=11631.7MB, alloc=483.8MB, time=180.72 memory used=11812.2MB, alloc=483.8MB, time=181.13 memory used=12006.6MB, alloc=483.8MB, time=181.54 memory used=12217.4MB, alloc=483.8MB, time=181.98 memory used=12447.6MB, alloc=483.8MB, time=182.42 memory used=12685.4MB, alloc=483.8MB, time=182.84 memory used=12934.8MB, alloc=483.8MB, time=183.97 memory used=13068.5MB, alloc=483.8MB, time=187.60 memory used=13190.2MB, alloc=483.8MB, time=196.43 memory used=13261.5MB, alloc=483.8MB, time=196.74 memory used=13355.2MB, alloc=483.8MB, time=197.06 memory used=13421.7MB, alloc=483.8MB, time=197.34 memory used=13484.5MB, alloc=483.8MB, time=197.61 memory used=13555.3MB, alloc=483.8MB, time=197.88 memory used=13633.7MB, alloc=483.8MB, time=198.18 memory used=13720.9MB, alloc=483.8MB, time=198.47 memory used=13816.7MB, alloc=483.8MB, time=198.76 memory used=14032.2MB, alloc=483.8MB, time=199.21 memory used=14193.8MB, alloc=483.8MB, time=199.59 memory used=14385.1MB, alloc=483.8MB, time=199.99 memory used=14551.6MB, alloc=483.8MB, time=201.32 memory used=14668.4MB, alloc=483.8MB, time=202.47 memory used=14763.4MB, alloc=483.8MB, time=203.79 memory used=14883.6MB, alloc=483.8MB, time=204.81 memory used=14981.2MB, alloc=483.8MB, time=205.63 memory used=15059.4MB, alloc=507.8MB, time=206.04 memory used=15143.7MB, alloc=507.8MB, time=206.43 memory used=15241.3MB, alloc=507.8MB, time=206.82 memory used=15312.9MB, alloc=507.8MB, time=207.18 memory used=15399.1MB, alloc=507.8MB, time=207.52 memory used=15508.2MB, alloc=507.8MB, time=208.17 memory used=15592.7MB, alloc=507.8MB, time=208.57 memory used=15690.2MB, alloc=507.8MB, time=208.95 memory used=15762.2MB, alloc=507.8MB, time=209.29 memory used=15849.7MB, alloc=507.8MB, time=209.62 memory used=15964.0MB, alloc=507.8MB, time=211.78 memory used=16051.5MB, alloc=507.8MB, time=212.14 memory used=16138.8MB, alloc=507.8MB, time=212.49 memory used=16280.7MB, alloc=507.8MB, time=213.06 memory used=16373.0MB, alloc=507.8MB, time=213.45 memory used=16479.7MB, alloc=507.8MB, time=214.44 memory used=16564.1MB, alloc=507.8MB, time=214.78 memory used=16681.9MB, alloc=507.8MB, time=215.56 memory used=16774.6MB, alloc=507.8MB, time=215.99 memory used=16852.8MB, alloc=507.8MB, time=216.38 memory used=16950.6MB, alloc=507.8MB, time=216.79 memory used=17044.8MB, alloc=507.8MB, time=217.18 memory used=17113.5MB, alloc=507.8MB, time=217.52 memory used=17222.8MB, alloc=507.8MB, time=218.23 memory used=17316.8MB, alloc=507.8MB, time=218.67 memory used=17395.0MB, alloc=507.8MB, time=219.08 memory used=17492.6MB, alloc=507.8MB, time=219.49 memory used=17587.9MB, alloc=507.8MB, time=219.87 memory used=17656.1MB, alloc=507.8MB, time=220.19 |\^/| 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(); 1428287933 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 4 2 2 3 3 F := [13 x y - 14 y z + 13 y z - 13 z , 6 y - 20 y z - 8 y + 2 z , 3 3 3 2 14 x z - x z - 4 y z + 11 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 G := [-12 x - 20 x y z - 6 x z, -10 x z + 13 x y z - 2 z + 14 z, 2 2 2 2 2 6 x y z + 8 x z + 7 x y z - 5 y z] > Problem := [F,G]; 2 2 2 2 2 3 Problem := [[13 x y - 14 y z + 13 y z - 13 z , 4 2 2 3 3 3 3 3 2 6 y - 20 y z - 8 y + 2 z , 14 x z - x z - 4 y z + 11 y z], [ 4 2 2 2 2 -12 x - 20 x y z - 6 x z, -10 x z + 13 x y z - 2 z + 14 z, 2 2 2 2 2 6 x y z + 8 x z + 7 x y z - 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=46.7MB, alloc=56.3MB, time=0.81 memory used=88.0MB, alloc=60.3MB, time=1.41 memory used=128.4MB, alloc=68.3MB, time=2.02 memory used=167.8MB, alloc=92.3MB, time=2.49 memory used=238.0MB, alloc=92.3MB, time=3.40 memory used=309.8MB, alloc=92.3MB, time=4.25 memory used=372.6MB, alloc=92.3MB, time=5.08 memory used=437.7MB, alloc=116.3MB, time=6.01 memory used=507.9MB, alloc=116.3MB, time=7.07 memory used=560.6MB, alloc=396.3MB, time=7.80 memory used=677.7MB, alloc=420.3MB, time=9.36 memory used=810.3MB, alloc=420.3MB, time=11.29 memory used=923.8MB, alloc=444.3MB, time=12.96 memory used=1033.8MB, alloc=444.3MB, time=14.55 memory used=1154.8MB, alloc=468.3MB, time=16.00 memory used=1282.1MB, alloc=468.3MB, time=16.86 memory used=1422.1MB, alloc=468.3MB, time=18.61 memory used=1531.3MB, alloc=468.3MB, time=19.99 memory used=1652.9MB, alloc=468.3MB, time=21.35 memory used=1742.8MB, alloc=468.3MB, time=22.77 memory used=1807.0MB, alloc=468.3MB, time=23.78 memory used=1880.2MB, alloc=468.3MB, time=25.03 memory used=1982.1MB, alloc=468.3MB, time=26.24 memory used=2076.0MB, alloc=468.3MB, time=26.77 memory used=2171.1MB, alloc=468.3MB, time=27.32 memory used=2272.0MB, alloc=468.3MB, time=28.07 memory used=2366.8MB, alloc=468.3MB, time=28.61 memory used=2480.9MB, alloc=468.3MB, time=30.67 memory used=2547.6MB, alloc=468.3MB, time=31.03 memory used=2653.0MB, alloc=468.3MB, time=31.67 memory used=2722.0MB, alloc=468.3MB, time=32.08 memory used=2802.0MB, alloc=492.3MB, time=32.48 memory used=2879.1MB, alloc=492.3MB, time=32.88 memory used=2996.3MB, alloc=492.3MB, time=33.62 memory used=3097.7MB, alloc=492.3MB, time=34.09 memory used=3174.4MB, alloc=492.3MB, time=34.50 memory used=3323.9MB, alloc=492.3MB, time=40.69 memory used=3416.3MB, alloc=492.3MB, time=41.12 memory used=3499.7MB, alloc=492.3MB, time=41.52 memory used=3604.8MB, alloc=492.3MB, time=41.92 memory used=3673.7MB, alloc=492.3MB, time=42.26 memory used=3811.3MB, alloc=492.3MB, time=43.63 memory used=3894.2MB, alloc=492.3MB, time=44.74 memory used=4032.5MB, alloc=492.3MB, time=48.17 memory used=4113.8MB, alloc=492.3MB, time=48.59 memory used=4202.5MB, alloc=492.3MB, time=49.00 memory used=4302.9MB, alloc=492.3MB, time=49.99 memory used=4377.6MB, alloc=492.3MB, time=51.22 memory used=4431.9MB, alloc=492.3MB, time=52.27 memory used=4494.7MB, alloc=492.3MB, time=53.32 memory used=4623.7MB, alloc=492.3MB, time=54.22 memory used=4725.4MB, alloc=492.3MB, time=55.64 memory used=4783.6MB, alloc=492.3MB, time=56.69 memory used=4865.9MB, alloc=492.3MB, time=57.82 memory used=4918.8MB, alloc=492.3MB, time=58.65 memory used=4978.0MB, alloc=492.3MB, time=59.92 memory used=5015.8MB, alloc=492.3MB, time=60.83 memory used=5203.5MB, alloc=516.3MB, time=63.96 memory used=5373.3MB, alloc=540.3MB, time=66.71 memory used=5558.7MB, alloc=564.3MB, time=70.01 memory used=5702.2MB, alloc=588.3MB, time=72.70 memory used=5870.2MB, alloc=612.3MB, time=76.02 memory used=6009.8MB, alloc=612.3MB, time=78.73 memory used=6131.6MB, alloc=612.3MB, time=81.12 memory used=6257.1MB, alloc=612.3MB, time=83.58 memory used=6386.6MB, alloc=612.3MB, time=85.84 memory used=6526.9MB, alloc=612.3MB, time=87.92 memory used=6657.1MB, alloc=612.3MB, time=90.40 memory used=6747.7MB, alloc=636.3MB, time=92.33 memory used=6890.9MB, alloc=636.3MB, time=94.81 memory used=7003.4MB, alloc=636.3MB, time=97.08 memory used=7091.8MB, alloc=636.3MB, time=99.14 memory used=7223.1MB, alloc=636.3MB, time=101.27 memory used=7326.8MB, alloc=636.3MB, time=103.15 memory used=7652.7MB, alloc=660.3MB, time=107.30 memory used=7808.6MB, alloc=660.3MB, time=108.46 memory used=8029.5MB, alloc=660.3MB, time=110.95 memory used=8186.0MB, alloc=660.3MB, time=112.00 memory used=8356.5MB, alloc=660.3MB, time=116.27 memory used=8499.9MB, alloc=660.3MB, time=117.28 memory used=8638.0MB, alloc=660.3MB, time=118.21 memory used=8927.9MB, alloc=660.3MB, time=119.97 memory used=9254.7MB, alloc=684.3MB, time=124.37 memory used=9648.1MB, alloc=708.3MB, time=130.39 memory used=9936.5MB, alloc=732.3MB, time=133.94 memory used=10119.5MB, alloc=732.3MB, time=135.31 memory used=10355.8MB, alloc=732.3MB, time=138.49 memory used=10526.9MB, alloc=732.3MB, time=139.67 memory used=10757.9MB, alloc=732.3MB, time=141.37 memory used=10941.2MB, alloc=732.3MB, time=142.71 memory used=11089.8MB, alloc=732.3MB, time=143.86 memory used=11242.3MB, alloc=732.3MB, time=144.99 memory used=11448.6MB, alloc=732.3MB, time=146.55 memory used=11615.7MB, alloc=732.3MB, time=147.89 memory used=11810.2MB, alloc=732.3MB, time=149.18 memory used=11943.2MB, alloc=732.3MB, time=150.34 memory used=12103.5MB, alloc=732.3MB, time=151.48 memory used=12412.4MB, alloc=732.3MB, time=160.05 memory used=12583.7MB, alloc=732.3MB, time=161.33 memory used=12741.2MB, alloc=732.3MB, time=162.52 memory used=13027.9MB, alloc=732.3MB, time=163.91 memory used=13152.6MB, alloc=732.3MB, time=165.01 memory used=13498.4MB, alloc=732.3MB, time=167.40 memory used=13691.5MB, alloc=732.3MB, time=168.79 memory used=13974.1MB, alloc=732.3MB, time=171.95 memory used=14216.1MB, alloc=732.3MB, time=174.13 memory used=14449.3MB, alloc=732.3MB, time=177.19 memory used=14701.5MB, alloc=732.3MB, time=180.35 |\^/| 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(); 1428288233 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 2 2 F := [-11 x z - x y - 18 x - 9 y , -20 x z + 14 y z + 11 x y + 5, 2 2 2 6 x y z - 15 x z - 8 y z + 8 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 3 2 G := [19 y z + 9 x z + 18 x y - 4 y, -20 x y z + 10 x + 7 z - 18 z , 3 -20 z - 20 x z - 15 y z + 10 y] > Problem := [F,G]; 3 2 2 2 3 2 2 2 Problem := [[-11 x z - x y - 18 x - 9 y , -20 x z + 14 y z + 11 x y + 5, 2 2 2 2 2 2 6 x y z - 15 x z - 8 y z + 8 y z], [19 y z + 9 x z + 18 x y - 4 y, 2 3 3 2 3 -20 x y z + 10 x + 7 z - 18 z , -20 z - 20 x 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=4.3MB, alloc=32.3MB, time=0.18 memory used=24.8MB, alloc=32.3MB, time=0.48 memory used=44.1MB, alloc=56.3MB, time=0.79 memory used=88.7MB, alloc=60.3MB, time=1.32 memory used=131.6MB, alloc=60.3MB, time=1.76 memory used=174.2MB, alloc=60.3MB, time=2.27 memory used=218.0MB, alloc=68.3MB, time=2.90 memory used=263.1MB, alloc=92.3MB, time=3.50 memory used=326.6MB, alloc=92.3MB, time=4.18 memory used=389.8MB, alloc=95.2MB, time=4.98 memory used=420.7MB, alloc=95.2MB, time=5.09 memory used=477.4MB, alloc=95.2MB, time=5.51 memory used=509.6MB, alloc=95.2MB, time=5.63 memory used=539.4MB, alloc=95.2MB, time=5.76 memory used=574.8MB, alloc=95.2MB, time=5.87 memory used=617.0MB, alloc=95.2MB, time=6.00 memory used=644.7MB, alloc=95.2MB, time=6.11 memory used=669.7MB, alloc=95.2MB, time=6.22 memory used=695.8MB, alloc=95.2MB, time=6.31 memory used=724.2MB, alloc=95.2MB, time=6.41 memory used=755.6MB, alloc=95.2MB, time=6.52 memory used=789.8MB, alloc=95.2MB, time=6.63 memory used=828.2MB, alloc=95.2MB, time=6.73 memory used=875.8MB, alloc=95.2MB, time=7.13 memory used=923.0MB, alloc=95.2MB, time=7.29 memory used=949.8MB, alloc=95.2MB, time=7.41 memory used=981.9MB, alloc=95.2MB, time=7.52 memory used=1019.7MB, alloc=95.2MB, time=7.65 memory used=1059.7MB, alloc=95.2MB, time=7.77 memory used=1083.0MB, alloc=95.2MB, time=7.87 memory used=1107.6MB, alloc=95.2MB, time=7.96 memory used=1134.6MB, alloc=95.2MB, time=8.06 memory used=1164.2MB, alloc=95.2MB, time=8.16 memory used=1196.8MB, alloc=95.2MB, time=8.26 memory used=1232.7MB, alloc=95.2MB, time=8.36 memory used=1272.8MB, alloc=95.2MB, time=8.46 memory used=1325.6MB, alloc=103.0MB, time=17.41 memory used=1332.5MB, alloc=107.8MB, time=25.54 memory used=1340.6MB, alloc=107.8MB, time=25.62 memory used=1357.5MB, alloc=107.8MB, time=29.43 memory used=1384.0MB, alloc=107.8MB, time=31.53 memory used=1399.3MB, alloc=107.8MB, time=31.62 memory used=1407.7MB, alloc=107.8MB, time=33.62 memory used=1428.3MB, alloc=107.8MB, time=33.75 memory used=1436.8MB, alloc=107.8MB, time=33.81 memory used=1445.0MB, alloc=107.8MB, time=33.87 memory used=1453.1MB, alloc=107.8MB, time=33.93 memory used=1461.1MB, alloc=107.8MB, time=33.99 memory used=1469.0MB, alloc=107.8MB, time=34.05 memory used=1476.9MB, alloc=107.8MB, time=34.11 memory used=1485.7MB, alloc=107.8MB, time=34.18 memory used=1494.5MB, alloc=107.8MB, time=34.25 memory used=1503.1MB, alloc=107.8MB, time=34.31 memory used=1511.5MB, alloc=107.8MB, time=34.38 memory used=1521.0MB, alloc=107.8MB, time=34.45 memory used=1530.2MB, alloc=107.8MB, time=34.52 memory used=1539.2MB, alloc=107.8MB, time=34.58 memory used=1549.1MB, alloc=107.8MB, time=34.65 memory used=1558.6MB, alloc=107.8MB, time=34.72 memory used=1568.0MB, alloc=107.8MB, time=34.79 memory used=1577.8MB, alloc=107.8MB, time=34.88 memory used=1587.5MB, alloc=107.8MB, time=34.95 memory used=1597.4MB, alloc=107.8MB, time=35.02 memory used=1607.7MB, alloc=107.8MB, time=35.09 memory used=1618.2MB, alloc=107.8MB, time=35.17 memory used=1628.9MB, alloc=107.8MB, time=35.23 memory used=1640.0MB, alloc=107.8MB, time=35.29 memory used=1651.4MB, alloc=107.8MB, time=35.36 memory used=1666.3MB, alloc=107.8MB, time=35.59 memory used=1741.3MB, alloc=107.8MB, time=37.50 memory used=1779.1MB, alloc=107.8MB, time=37.63 memory used=1808.0MB, alloc=107.8MB, time=37.74 memory used=1877.5MB, alloc=107.8MB, time=38.49 memory used=1939.4MB, alloc=363.8MB, time=39.30 memory used=2006.7MB, alloc=387.8MB, time=40.17 memory used=2077.8MB, alloc=387.8MB, time=41.69 memory used=2129.7MB, alloc=387.8MB, time=42.19 memory used=2177.4MB, alloc=387.8MB, time=42.39 memory used=2222.5MB, alloc=387.8MB, time=42.57 memory used=2270.8MB, alloc=387.8MB, time=42.73 memory used=2303.1MB, alloc=387.8MB, time=42.89 memory used=2339.5MB, alloc=387.8MB, time=43.04 memory used=2380.3MB, alloc=387.8MB, time=43.19 memory used=2425.3MB, alloc=387.8MB, time=43.33 memory used=2476.5MB, alloc=387.8MB, time=43.49 memory used=2521.9MB, alloc=387.8MB, time=43.62 memory used=2553.1MB, alloc=387.8MB, time=43.74 memory used=2588.2MB, alloc=387.8MB, time=43.85 memory used=2647.0MB, alloc=387.8MB, time=44.39 memory used=2689.1MB, alloc=387.8MB, time=44.57 memory used=2743.0MB, alloc=387.8MB, time=44.76 memory used=2775.7MB, alloc=387.8MB, time=44.91 memory used=2810.8MB, alloc=387.8MB, time=45.06 memory used=2849.7MB, alloc=387.8MB, time=45.22 memory used=2894.5MB, alloc=387.8MB, time=45.37 memory used=2944.3MB, alloc=387.8MB, time=45.53 memory used=2994.1MB, alloc=387.8MB, time=45.69 memory used=3026.7MB, alloc=387.8MB, time=45.80 memory used=3060.3MB, alloc=387.8MB, time=45.93 memory used=3144.1MB, alloc=387.8MB, time=64.41 memory used=3339.1MB, alloc=387.8MB, time=68.89 memory used=3530.9MB, alloc=387.8MB, time=72.83 memory used=3572.0MB, alloc=387.8MB, time=72.98 memory used=3637.1MB, alloc=387.8MB, time=73.41 memory used=3712.1MB, alloc=387.8MB, time=74.40 memory used=3754.7MB, alloc=387.8MB, time=74.59 memory used=3800.2MB, alloc=387.8MB, time=74.76 memory used=3849.1MB, alloc=387.8MB, time=75.08 memory used=3889.7MB, alloc=387.8MB, time=75.25 memory used=3934.2MB, alloc=387.8MB, time=75.41 memory used=3980.3MB, alloc=387.8MB, time=77.94 memory used=4046.6MB, alloc=387.8MB, time=78.45 memory used=4137.6MB, alloc=387.8MB, time=79.58 memory used=4199.1MB, alloc=387.8MB, time=79.97 memory used=4257.9MB, alloc=387.8MB, time=81.60 memory used=4298.2MB, alloc=387.8MB, time=81.78 memory used=4341.2MB, alloc=387.8MB, time=82.04 memory used=4385.0MB, alloc=387.8MB, time=82.32 memory used=4432.9MB, alloc=387.8MB, time=82.60 memory used=4480.1MB, alloc=387.8MB, time=82.77 memory used=4518.3MB, alloc=387.8MB, time=82.91 memory used=4607.8MB, alloc=411.8MB, time=84.14 memory used=4704.1MB, alloc=411.8MB, time=85.40 memory used=4765.0MB, alloc=411.8MB, time=85.66 memory used=4889.7MB, alloc=411.8MB, time=87.14 memory used=4993.0MB, alloc=411.8MB, time=88.50 memory used=5105.8MB, alloc=435.8MB, time=89.88 memory used=5209.6MB, alloc=435.8MB, time=90.84 memory used=5293.8MB, alloc=435.8MB, time=92.34 memory used=5347.9MB, alloc=435.8MB, time=92.61 memory used=5415.1MB, alloc=435.8MB, time=92.89 memory used=5476.4MB, alloc=459.8MB, time=93.16 memory used=5532.8MB, alloc=459.8MB, time=93.43 memory used=5595.9MB, alloc=459.8MB, time=93.68 memory used=5663.4MB, alloc=459.8MB, time=93.95 memory used=5738.5MB, alloc=459.8MB, time=94.22 memory used=5821.4MB, alloc=459.8MB, time=94.49 memory used=5912.0MB, alloc=459.8MB, time=94.80 memory used=6009.5MB, alloc=459.8MB, time=95.07 memory used=6064.4MB, alloc=459.8MB, time=95.29 memory used=6113.1MB, alloc=459.8MB, time=95.53 memory used=6167.5MB, alloc=459.8MB, time=95.75 memory used=6222.1MB, alloc=459.8MB, time=95.97 memory used=6277.1MB, alloc=459.8MB, time=96.19 memory used=6336.8MB, alloc=459.8MB, time=96.41 memory used=6396.6MB, alloc=459.8MB, time=96.63 memory used=6460.8MB, alloc=459.8MB, time=96.86 memory used=6529.2MB, alloc=459.8MB, time=97.09 memory used=6597.6MB, alloc=459.8MB, time=97.31 memory used=6669.2MB, alloc=459.8MB, time=97.54 memory used=6743.9MB, alloc=459.8MB, time=97.77 memory used=6824.8MB, alloc=459.8MB, time=98.01 memory used=6907.9MB, alloc=459.8MB, time=98.24 memory used=6995.5MB, alloc=459.8MB, time=98.49 memory used=7089.2MB, alloc=459.8MB, time=98.72 memory used=7334.9MB, alloc=459.8MB, time=100.71 memory used=7415.9MB, alloc=459.8MB, time=101.05 memory used=7498.6MB, alloc=459.8MB, time=101.37 memory used=7576.3MB, alloc=459.8MB, time=101.67 memory used=7632.5MB, alloc=459.8MB, time=101.94 memory used=7696.5MB, alloc=459.8MB, time=102.21 memory used=7764.7MB, alloc=459.8MB, time=102.47 memory used=7840.4MB, alloc=459.8MB, time=102.75 memory used=7923.8MB, alloc=459.8MB, time=103.04 memory used=8014.9MB, alloc=459.8MB, time=103.32 memory used=8107.5MB, alloc=459.8MB, time=103.60 memory used=8160.1MB, alloc=459.8MB, time=103.83 memory used=8211.8MB, alloc=459.8MB, time=104.04 memory used=8266.2MB, alloc=459.8MB, time=104.23 memory used=8320.9MB, alloc=459.8MB, time=104.44 memory used=8376.4MB, alloc=459.8MB, time=104.64 memory used=8435.6MB, alloc=459.8MB, time=104.86 memory used=8495.8MB, alloc=459.8MB, time=105.07 memory used=8559.5MB, alloc=459.8MB, time=105.28 memory used=8627.9MB, alloc=459.8MB, time=105.50 memory used=8696.2MB, alloc=459.8MB, time=105.71 memory used=8767.7MB, alloc=459.8MB, time=105.94 memory used=8842.5MB, alloc=459.8MB, time=106.17 memory used=8922.8MB, alloc=459.8MB, time=106.38 memory used=9005.5MB, alloc=459.8MB, time=106.60 memory used=9092.8MB, alloc=459.8MB, time=106.82 memory used=9186.1MB, alloc=459.8MB, time=107.04 memory used=9431.0MB, alloc=459.8MB, time=120.00 memory used=9529.7MB, alloc=459.8MB, time=179.69 memory used=9629.9MB, alloc=459.8MB, time=194.19 memory used=9701.0MB, alloc=459.8MB, time=194.47 memory used=9777.0MB, alloc=459.8MB, time=194.73 memory used=9864.3MB, alloc=459.8MB, time=194.99 memory used=9918.8MB, alloc=459.8MB, time=195.20 memory used=9977.2MB, alloc=459.8MB, time=195.41 memory used=10041.0MB, alloc=459.8MB, time=195.62 memory used=10111.7MB, alloc=459.8MB, time=195.84 memory used=10189.2MB, alloc=459.8MB, time=196.06 memory used=10273.3MB, alloc=459.8MB, time=196.30 memory used=10363.5MB, alloc=459.8MB, time=196.53 memory used=10583.0MB, alloc=459.8MB, time=196.92 memory used=10736.1MB, alloc=459.8MB, time=197.24 memory used=10909.4MB, alloc=459.8MB, time=197.57 memory used=11113.0MB, alloc=459.8MB, time=197.92 memory used=11259.2MB, alloc=459.8MB, time=198.89 memory used=11342.3MB, alloc=459.8MB, time=199.18 memory used=11405.2MB, alloc=459.8MB, time=199.43 memory used=11485.4MB, alloc=459.8MB, time=199.69 memory used=11568.9MB, alloc=459.8MB, time=200.60 memory used=11668.9MB, alloc=459.8MB, time=206.36 memory used=11754.1MB, alloc=459.8MB, time=206.63 memory used=11814.7MB, alloc=459.8MB, time=206.86 memory used=11888.9MB, alloc=459.8MB, time=207.08 memory used=11992.6MB, alloc=459.8MB, time=207.47 memory used=12159.2MB, alloc=459.8MB, time=226.57 memory used=12255.9MB, alloc=459.8MB, time=228.58 memory used=12325.3MB, alloc=459.8MB, time=228.84 memory used=12396.4MB, alloc=459.8MB, time=229.11 memory used=12483.2MB, alloc=459.8MB, time=229.38 memory used=12547.6MB, alloc=459.8MB, time=229.60 memory used=12602.1MB, alloc=459.8MB, time=229.80 memory used=12661.1MB, alloc=459.8MB, time=230.02 memory used=12725.1MB, alloc=459.8MB, time=230.23 memory used=12794.1MB, alloc=459.8MB, time=230.46 memory used=12867.8MB, alloc=459.8MB, time=230.68 memory used=12946.3MB, alloc=459.8MB, time=230.90 memory used=13029.3MB, alloc=459.8MB, time=231.12 memory used=13119.3MB, alloc=459.8MB, time=231.34 memory used=13337.4MB, alloc=459.8MB, time=231.75 memory used=13486.6MB, alloc=459.8MB, time=232.06 memory used=13648.8MB, alloc=459.8MB, time=232.40 memory used=13827.6MB, alloc=459.8MB, time=232.74 memory used=14024.7MB, alloc=459.8MB, time=233.09 memory used=14254.4MB, alloc=459.8MB, time=233.46 memory used=14372.5MB, alloc=459.8MB, time=234.48 memory used=14452.5MB, alloc=459.8MB, time=234.75 memory used=14517.4MB, alloc=459.8MB, time=234.97 memory used=14582.0MB, alloc=459.8MB, time=235.19 memory used=14658.5MB, alloc=459.8MB, time=235.41 memory used=14830.9MB, alloc=459.8MB, time=236.10 |\^/| 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(); 1428288533 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 2 F := [-6 x z + 9 x z - 8 z + 2 x y, 3 y z - 7 x y + x + 19 y, 2 2 2 2 12 x y - 13 y z - 5 y z - 17 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 2 G := [13 x z - 9 z - 3 z + 15, -20 x + 17 y z - 6 x z - 19 y z, 2 2 2 4 2 -11 x y z - 13 x z + 6 y + x y ] > Problem := [F,G]; 2 2 2 3 2 2 2 Problem := [[-6 x z + 9 x z - 8 z + 2 x y, 3 y z - 7 x y + x + 19 y, 2 2 2 2 3 3 12 x y - 13 y z - 5 y z - 17 z ], [13 x z - 9 z - 3 z + 15, 4 2 2 2 2 4 2 -20 x + 17 y z - 6 x z - 19 y z, -11 x y z - 13 x z + 6 y + 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=24.8MB, alloc=32.3MB, time=0.45 memory used=45.0MB, alloc=56.3MB, time=0.73 memory used=89.4MB, alloc=60.3MB, time=1.12 memory used=130.4MB, alloc=60.3MB, time=1.46 memory used=177.5MB, alloc=60.3MB, time=1.99 memory used=220.2MB, alloc=60.8MB, time=2.40 memory used=251.9MB, alloc=60.8MB, time=3.75 memory used=275.8MB, alloc=60.8MB, time=3.86 memory used=307.8MB, alloc=61.6MB, time=4.04 memory used=336.2MB, alloc=61.6MB, time=5.04 memory used=362.2MB, alloc=61.6MB, time=5.88 memory used=395.1MB, alloc=61.6MB, time=6.12 memory used=417.4MB, alloc=61.6MB, time=6.19 memory used=442.3MB, alloc=61.6MB, time=6.26 memory used=476.6MB, alloc=61.6MB, time=6.49 memory used=497.6MB, alloc=61.6MB, time=6.56 memory used=525.4MB, alloc=61.6MB, time=7.50 memory used=556.1MB, alloc=61.6MB, time=9.11 memory used=582.7MB, alloc=61.6MB, time=9.27 memory used=623.5MB, alloc=85.6MB, time=13.72 memory used=673.3MB, alloc=85.6MB, time=19.11 memory used=711.3MB, alloc=85.6MB, time=19.21 memory used=772.6MB, alloc=85.6MB, time=20.24 memory used=838.4MB, alloc=93.6MB, time=20.90 memory used=906.4MB, alloc=93.6MB, time=21.77 memory used=977.4MB, alloc=93.6MB, time=22.90 memory used=1023.6MB, alloc=93.6MB, time=23.04 memory used=1051.4MB, alloc=93.6MB, time=23.14 memory used=1082.9MB, alloc=93.6MB, time=23.26 memory used=1118.3MB, alloc=93.6MB, time=23.38 memory used=1161.1MB, alloc=93.6MB, time=23.51 memory used=1188.3MB, alloc=93.6MB, time=23.61 memory used=1222.4MB, alloc=93.6MB, time=24.13 memory used=1273.3MB, alloc=93.6MB, time=24.30 memory used=1304.8MB, alloc=93.6MB, time=24.42 memory used=1334.9MB, alloc=93.6MB, time=24.54 memory used=1370.2MB, alloc=93.6MB, time=24.66 memory used=1410.7MB, alloc=93.6MB, time=24.79 memory used=1442.6MB, alloc=93.6MB, time=24.89 memory used=1468.8MB, alloc=93.6MB, time=25.01 memory used=1511.3MB, alloc=93.6MB, time=26.82 memory used=1548.7MB, alloc=93.6MB, time=26.92 memory used=1599.7MB, alloc=93.6MB, time=27.46 memory used=1638.4MB, alloc=93.6MB, time=27.60 memory used=1666.6MB, alloc=93.6MB, time=27.72 memory used=1699.8MB, alloc=93.6MB, time=27.85 memory used=1736.9MB, alloc=93.6MB, time=27.96 memory used=1776.0MB, alloc=93.6MB, time=28.08 memory used=1800.9MB, alloc=93.6MB, time=28.18 memory used=1841.9MB, alloc=93.6MB, time=28.68 memory used=1889.0MB, alloc=93.6MB, time=28.83 memory used=1916.8MB, alloc=93.6MB, time=28.95 memory used=1947.5MB, alloc=93.6MB, time=29.06 memory used=1982.8MB, alloc=93.6MB, time=29.19 memory used=2023.8MB, alloc=93.6MB, time=29.32 memory used=2052.8MB, alloc=93.6MB, time=29.42 memory used=2080.5MB, alloc=93.6MB, time=29.54 memory used=2123.1MB, alloc=93.6MB, time=31.33 memory used=2160.4MB, alloc=93.6MB, time=31.44 memory used=2212.3MB, alloc=93.6MB, time=32.86 memory used=2251.8MB, alloc=93.6MB, time=32.99 memory used=2277.4MB, alloc=93.6MB, time=33.10 memory used=2304.5MB, alloc=93.6MB, time=33.23 memory used=2334.9MB, alloc=93.6MB, time=33.36 memory used=2367.8MB, alloc=93.6MB, time=33.48 memory used=2404.1MB, alloc=93.6MB, time=33.60 memory used=2442.6MB, alloc=93.6MB, time=33.73 memory used=2485.3MB, alloc=93.6MB, time=33.87 memory used=2511.8MB, alloc=93.6MB, time=33.97 memory used=2534.4MB, alloc=93.6MB, time=34.06 memory used=2558.0MB, alloc=93.6MB, time=34.17 memory used=2582.3MB, alloc=93.6MB, time=34.27 memory used=2608.3MB, alloc=93.6MB, time=34.39 memory used=2636.7MB, alloc=93.6MB, time=34.49 memory used=2666.5MB, alloc=93.6MB, time=34.61 memory used=2698.5MB, alloc=93.6MB, time=34.72 memory used=2733.2MB, alloc=93.6MB, time=34.83 memory used=2784.3MB, alloc=93.6MB, time=36.11 memory used=2825.9MB, alloc=93.6MB, time=36.25 memory used=2852.5MB, alloc=93.6MB, time=36.36 memory used=2880.2MB, alloc=93.6MB, time=36.48 memory used=2910.6MB, alloc=93.6MB, time=36.62 memory used=2943.5MB, alloc=93.6MB, time=36.74 memory used=2979.9MB, alloc=93.6MB, time=36.86 memory used=3019.7MB, alloc=93.6MB, time=37.00 memory used=3062.2MB, alloc=93.6MB, time=37.12 memory used=3088.8MB, alloc=93.6MB, time=37.22 memory used=3111.3MB, alloc=93.6MB, time=37.33 memory used=3135.0MB, alloc=93.6MB, time=37.43 memory used=3159.3MB, alloc=93.6MB, time=37.53 memory used=3184.0MB, alloc=93.6MB, time=37.64 memory used=3210.0MB, alloc=93.6MB, time=37.73 memory used=3239.2MB, alloc=93.6MB, time=37.84 memory used=3270.8MB, alloc=93.6MB, time=37.95 memory used=3304.9MB, alloc=93.6MB, time=38.05 memory used=3352.8MB, alloc=93.6MB, time=40.62 memory used=3382.2MB, alloc=93.6MB, time=40.70 memory used=3406.0MB, alloc=93.6MB, time=40.78 memory used=3458.1MB, alloc=93.6MB, time=41.78 memory used=3502.2MB, alloc=93.6MB, time=57.82 memory used=3543.8MB, alloc=117.6MB, time=81.33 memory used=3604.2MB, alloc=117.6MB, time=114.14 memory used=3658.4MB, alloc=117.6MB, time=115.49 memory used=3707.5MB, alloc=117.6MB, time=115.64 memory used=3764.6MB, alloc=117.6MB, time=115.79 memory used=3801.6MB, alloc=117.6MB, time=115.90 memory used=3839.8MB, alloc=117.6MB, time=116.02 memory used=3881.3MB, alloc=117.6MB, time=116.16 memory used=3927.5MB, alloc=117.6MB, time=116.29 memory used=3978.1MB, alloc=117.6MB, time=116.42 memory used=4033.5MB, alloc=117.6MB, time=116.56 memory used=4094.1MB, alloc=117.6MB, time=116.71 memory used=4130.6MB, alloc=117.6MB, time=116.81 memory used=4164.7MB, alloc=117.6MB, time=116.90 memory used=4200.8MB, alloc=117.6MB, time=117.00 memory used=4238.7MB, alloc=117.6MB, time=117.09 memory used=4304.2MB, alloc=117.6MB, time=117.55 memory used=4391.4MB, alloc=118.8MB, time=123.09 memory used=4445.3MB, alloc=118.8MB, time=123.25 memory used=4485.5MB, alloc=118.8MB, time=123.40 memory used=4560.4MB, alloc=118.8MB, time=123.89 memory used=4633.5MB, alloc=118.8MB, time=124.62 memory used=4683.1MB, alloc=118.8MB, time=124.79 memory used=4726.3MB, alloc=118.8MB, time=124.93 memory used=4763.3MB, alloc=118.8MB, time=125.07 memory used=4806.7MB, alloc=118.8MB, time=125.20 memory used=4856.6MB, alloc=118.8MB, time=125.33 memory used=4912.8MB, alloc=118.8MB, time=125.47 memory used=4952.9MB, alloc=118.8MB, time=125.58 memory used=4986.4MB, alloc=118.8MB, time=125.68 memory used=5022.0MB, alloc=118.8MB, time=125.77 memory used=5061.2MB, alloc=118.8MB, time=125.88 memory used=5112.2MB, alloc=118.8MB, time=126.11 memory used=5159.9MB, alloc=118.8MB, time=126.34 memory used=5218.2MB, alloc=118.8MB, time=126.87 memory used=5269.5MB, alloc=118.8MB, time=127.05 memory used=5311.9MB, alloc=118.8MB, time=127.20 memory used=5349.7MB, alloc=118.8MB, time=127.34 memory used=5393.7MB, alloc=118.8MB, time=127.48 memory used=5443.9MB, alloc=118.8MB, time=127.63 memory used=5501.7MB, alloc=118.8MB, time=127.79 memory used=5538.8MB, alloc=118.8MB, time=127.90 memory used=5573.2MB, alloc=118.8MB, time=128.01 memory used=5610.2MB, alloc=118.8MB, time=128.12 memory used=5650.2MB, alloc=118.8MB, time=128.22 memory used=5702.5MB, alloc=118.8MB, time=128.47 memory used=5749.2MB, alloc=118.8MB, time=128.68 memory used=5815.8MB, alloc=118.8MB, time=139.34 memory used=5870.7MB, alloc=118.8MB, time=167.31 memory used=6189.3MB, alloc=118.8MB, time=171.64 memory used=6247.8MB, alloc=118.8MB, time=172.02 memory used=6285.9MB, alloc=118.8MB, time=172.17 memory used=6331.9MB, alloc=118.8MB, time=172.32 memory used=6387.5MB, alloc=118.8MB, time=172.49 memory used=6421.5MB, alloc=118.8MB, time=172.61 memory used=6454.7MB, alloc=118.8MB, time=172.73 memory used=6490.5MB, alloc=118.8MB, time=172.84 memory used=6529.3MB, alloc=118.8MB, time=172.96 memory used=6571.2MB, alloc=118.8MB, time=173.08 memory used=6616.0MB, alloc=118.8MB, time=173.20 memory used=6663.8MB, alloc=118.8MB, time=173.33 memory used=6716.2MB, alloc=118.8MB, time=173.46 memory used=6771.2MB, alloc=118.8MB, time=173.59 memory used=6818.9MB, alloc=131.8MB, time=173.73 memory used=6827.5MB, alloc=131.8MB, time=173.79 memory used=6836.4MB, alloc=131.8MB, time=173.86 memory used=6845.3MB, alloc=131.8MB, time=173.94 memory used=6854.2MB, alloc=131.8MB, time=174.02 memory used=6863.1MB, alloc=131.8MB, time=174.10 memory used=6872.0MB, alloc=131.8MB, time=174.17 memory used=6880.8MB, alloc=131.8MB, time=174.23 memory used=6889.8MB, alloc=131.8MB, time=174.31 memory used=6900.2MB, alloc=131.8MB, time=174.39 memory used=6910.7MB, alloc=131.8MB, time=174.46 memory used=6921.2MB, alloc=131.8MB, time=174.54 memory used=6931.6MB, alloc=131.8MB, time=174.61 memory used=6942.0MB, alloc=131.8MB, time=174.68 memory used=6952.3MB, alloc=131.8MB, time=174.75 memory used=6962.5MB, alloc=131.8MB, time=174.83 memory used=6972.7MB, alloc=131.8MB, time=174.89 memory used=6983.1MB, alloc=131.8MB, time=174.97 memory used=6994.5MB, alloc=131.8MB, time=175.06 memory used=7006.1MB, alloc=131.8MB, time=175.15 memory used=7017.6MB, alloc=131.8MB, time=175.22 memory used=7029.0MB, alloc=131.8MB, time=175.29 memory used=7040.3MB, alloc=131.8MB, time=175.39 memory used=7053.1MB, alloc=131.8MB, time=175.47 memory used=7065.7MB, alloc=131.8MB, time=175.54 memory used=7078.1MB, alloc=131.8MB, time=175.61 memory used=7090.6MB, alloc=131.8MB, time=175.69 memory used=7103.9MB, alloc=131.8MB, time=175.77 memory used=7117.1MB, alloc=131.8MB, time=175.84 memory used=7129.2MB, alloc=131.8MB, time=175.92 memory used=7142.8MB, alloc=131.8MB, time=176.01 memory used=7156.6MB, alloc=131.8MB, time=176.11 memory used=7171.4MB, alloc=131.8MB, time=176.20 memory used=7185.8MB, alloc=131.8MB, time=176.28 memory used=7200.7MB, alloc=131.8MB, time=176.38 memory used=7216.2MB, alloc=131.8MB, time=176.48 memory used=7232.1MB, alloc=131.8MB, time=176.56 memory used=7248.4MB, alloc=131.8MB, time=176.64 memory used=7265.3MB, alloc=131.8MB, time=176.72 memory used=7282.4MB, alloc=131.8MB, time=176.81 memory used=7301.0MB, alloc=131.8MB, time=176.88 memory used=7362.8MB, alloc=131.8MB, time=177.79 memory used=7410.5MB, alloc=131.8MB, time=177.96 memory used=7460.9MB, alloc=131.8MB, time=178.14 memory used=7494.1MB, alloc=131.8MB, time=178.27 memory used=7530.8MB, alloc=131.8MB, time=178.41 memory used=7571.7MB, alloc=131.8MB, time=178.57 memory used=7617.5MB, alloc=131.8MB, time=178.72 memory used=7668.0MB, alloc=131.8MB, time=178.87 memory used=7722.9MB, alloc=131.8MB, time=179.03 memory used=7771.4MB, alloc=131.8MB, time=179.18 memory used=7800.8MB, alloc=131.8MB, time=179.28 memory used=7832.2MB, alloc=131.8MB, time=179.39 memory used=7864.2MB, alloc=131.8MB, time=179.48 memory used=7898.0MB, alloc=131.8MB, time=179.59 memory used=7934.7MB, alloc=131.8MB, time=179.71 memory used=7973.3MB, alloc=131.8MB, time=179.83 memory used=8014.0MB, alloc=131.8MB, time=179.94 memory used=8056.1MB, alloc=131.8MB, time=180.05 memory used=8101.2MB, alloc=131.8MB, time=180.17 memory used=8148.8MB, alloc=131.8MB, time=180.28 memory used=8200.4MB, alloc=131.8MB, time=180.40 memory used=8261.9MB, alloc=131.8MB, time=180.67 memory used=8309.2MB, alloc=131.8MB, time=180.80 memory used=8368.4MB, alloc=131.8MB, time=181.65 memory used=8415.9MB, alloc=131.8MB, time=181.82 memory used=8466.4MB, alloc=131.8MB, time=181.98 memory used=8499.7MB, alloc=131.8MB, time=182.13 memory used=8536.5MB, alloc=131.8MB, time=182.28 memory used=8577.3MB, alloc=131.8MB, time=182.43 memory used=8623.1MB, alloc=131.8MB, time=182.57 memory used=8673.6MB, alloc=131.8MB, time=182.71 memory used=8728.6MB, alloc=131.8MB, time=182.88 memory used=8776.9MB, alloc=131.8MB, time=183.01 memory used=8806.3MB, alloc=131.8MB, time=183.11 memory used=8837.8MB, alloc=131.8MB, time=183.23 memory used=8869.8MB, alloc=131.8MB, time=183.34 memory used=8903.5MB, alloc=131.8MB, time=183.45 memory used=8940.2MB, alloc=131.8MB, time=183.57 memory used=8978.9MB, alloc=131.8MB, time=183.68 memory used=9019.6MB, alloc=131.8MB, time=183.79 memory used=9061.6MB, alloc=131.8MB, time=183.90 memory used=9106.8MB, alloc=131.8MB, time=184.01 memory used=9154.6MB, alloc=131.8MB, time=184.12 memory used=9207.0MB, alloc=131.8MB, time=184.23 memory used=9272.7MB, alloc=131.8MB, time=195.26 memory used=9328.4MB, alloc=131.8MB, time=223.52 memory used=9516.9MB, alloc=131.8MB, time=227.18 memory used=9656.0MB, alloc=131.8MB, time=228.07 memory used=9712.7MB, alloc=131.8MB, time=228.41 memory used=9750.4MB, alloc=131.8MB, time=228.54 memory used=9795.3MB, alloc=131.8MB, time=228.71 memory used=9850.8MB, alloc=131.8MB, time=228.86 memory used=9885.4MB, alloc=131.8MB, time=228.98 memory used=9918.2MB, alloc=131.8MB, time=229.09 memory used=9953.9MB, alloc=131.8MB, time=229.21 memory used=9992.6MB, alloc=131.8MB, time=229.32 memory used=10034.5MB, alloc=131.8MB, time=229.43 memory used=10079.3MB, alloc=131.8MB, time=229.55 memory used=10127.1MB, alloc=131.8MB, time=229.67 memory used=10177.6MB, alloc=131.8MB, time=229.79 memory used=10232.5MB, alloc=131.8MB, time=229.93 memory used=10284.0MB, alloc=131.8MB, time=230.05 memory used=10293.2MB, alloc=131.8MB, time=230.12 memory used=10302.1MB, alloc=131.8MB, time=230.20 memory used=10311.0MB, alloc=131.8MB, time=230.27 memory used=10319.9MB, alloc=131.8MB, time=230.35 memory used=10328.8MB, alloc=131.8MB, time=230.42 memory used=10337.7MB, alloc=131.8MB, time=230.49 memory used=10346.6MB, alloc=131.8MB, time=230.56 memory used=10355.6MB, alloc=131.8MB, time=230.62 memory used=10366.0MB, alloc=131.8MB, time=230.70 memory used=10376.5MB, alloc=131.8MB, time=230.78 memory used=10387.0MB, alloc=131.8MB, time=230.86 memory used=10397.4MB, alloc=131.8MB, time=230.93 memory used=10407.7MB, alloc=131.8MB, time=231.02 memory used=10418.1MB, alloc=131.8MB, time=231.10 memory used=10428.3MB, alloc=131.8MB, time=231.18 memory used=10438.5MB, alloc=131.8MB, time=231.26 memory used=10448.8MB, alloc=131.8MB, time=231.35 memory used=10460.3MB, alloc=131.8MB, time=231.43 memory used=10471.9MB, alloc=131.8MB, time=231.53 memory used=10483.5MB, alloc=131.8MB, time=231.60 memory used=10494.9MB, alloc=131.8MB, time=231.66 memory used=10506.1MB, alloc=131.8MB, time=231.75 memory used=10517.6MB, alloc=131.8MB, time=231.84 memory used=10530.0MB, alloc=131.8MB, time=231.93 memory used=10542.5MB, alloc=131.8MB, time=232.01 memory used=10554.7MB, alloc=131.8MB, time=232.09 memory used=10568.3MB, alloc=131.8MB, time=232.17 memory used=10581.6MB, alloc=131.8MB, time=232.25 memory used=10594.8MB, alloc=131.8MB, time=232.33 memory used=10608.7MB, alloc=131.8MB, time=232.42 memory used=10622.5MB, alloc=131.8MB, time=232.49 memory used=10637.3MB, alloc=131.8MB, time=232.56 memory used=10651.8MB, alloc=131.8MB, time=232.65 memory used=10666.6MB, alloc=131.8MB, time=232.74 memory used=10682.2MB, alloc=131.8MB, time=232.82 memory used=10698.1MB, alloc=131.8MB, time=232.90 memory used=10714.4MB, alloc=131.8MB, time=232.98 memory used=10731.2MB, alloc=131.8MB, time=233.06 memory used=10749.0MB, alloc=131.8MB, time=233.15 memory used=10766.9MB, alloc=131.8MB, time=233.26 memory used=10832.4MB, alloc=131.8MB, time=235.20 memory used=10872.5MB, alloc=131.8MB, time=235.37 memory used=10922.1MB, alloc=131.8MB, time=235.55 memory used=10974.0MB, alloc=131.8MB, time=235.72 memory used=11005.6MB, alloc=131.8MB, time=235.86 memory used=11036.9MB, alloc=131.8MB, time=236.01 memory used=11072.3MB, alloc=131.8MB, time=236.14 memory used=11109.2MB, alloc=131.8MB, time=236.28 memory used=11147.8MB, alloc=131.8MB, time=236.42 memory used=11187.8MB, alloc=131.8MB, time=236.57 memory used=11229.6MB, alloc=131.8MB, time=236.72 memory used=11276.3MB, alloc=131.8MB, time=236.86 memory used=11324.9MB, alloc=131.8MB, time=237.00 memory used=11374.9MB, alloc=131.8MB, time=237.16 memory used=11430.8MB, alloc=131.8MB, time=237.31 memory used=11474.0MB, alloc=155.8MB, time=237.45 memory used=11513.0MB, alloc=155.8MB, time=237.58 memory used=11550.8MB, alloc=155.8MB, time=237.70 memory used=11590.0MB, alloc=155.8MB, time=237.82 memory used=11634.4MB, alloc=155.8MB, time=237.95 memory used=11679.6MB, alloc=155.8MB, time=238.08 memory used=11725.2MB, alloc=155.8MB, time=238.21 memory used=11771.2MB, alloc=155.8MB, time=238.34 memory used=11818.0MB, alloc=155.8MB, time=238.47 memory used=11869.2MB, alloc=155.8MB, time=238.61 memory used=11921.2MB, alloc=155.8MB, time=238.74 memory used=11973.4MB, alloc=155.8MB, time=238.88 memory used=12030.9MB, alloc=155.8MB, time=239.01 memory used=12088.3MB, alloc=155.8MB, time=239.15 memory used=12146.2MB, alloc=155.8MB, time=239.29 memory used=12207.9MB, alloc=155.8MB, time=239.44 memory used=12269.9MB, alloc=155.8MB, time=239.59 memory used=12336.4MB, alloc=155.8MB, time=239.74 memory used=12407.1MB, alloc=155.8MB, time=239.88 memory used=12477.0MB, alloc=155.8MB, time=240.03 memory used=12550.1MB, alloc=155.8MB, time=240.18 memory used=12626.1MB, alloc=155.8MB, time=240.33 memory used=12678.0MB, alloc=155.8MB, time=240.45 memory used=12684.2MB, alloc=155.8MB, time=240.52 memory used=12688.7MB, alloc=155.8MB, time=240.59 memory used=12695.7MB, alloc=155.8MB, time=240.67 memory used=12700.6MB, alloc=155.8MB, time=240.73 memory used=12705.1MB, alloc=155.8MB, time=240.79 memory used=12712.3MB, alloc=155.8MB, time=240.86 memory used=12717.1MB, alloc=155.8MB, time=240.93 memory used=12721.6MB, alloc=155.8MB, time=241.00 memory used=12728.7MB, alloc=155.8MB, time=241.08 memory used=12733.5MB, alloc=155.8MB, time=241.17 memory used=12740.8MB, alloc=155.8MB, time=241.24 memory used=12745.7MB, alloc=155.8MB, time=241.34 memory used=12752.9MB, alloc=155.8MB, time=241.40 memory used=12757.9MB, alloc=155.8MB, time=241.48 memory used=12764.8MB, alloc=155.8MB, time=241.57 memory used=12769.8MB, alloc=155.8MB, time=241.65 memory used=12776.6MB, alloc=155.8MB, time=241.73 memory used=12784.4MB, alloc=155.8MB, time=241.82 memory used=12792.1MB, alloc=155.8MB, time=241.90 memory used=12799.8MB, alloc=155.8MB, time=241.96 memory used=12807.4MB, alloc=155.8MB, time=242.04 memory used=12815.0MB, alloc=155.8MB, time=242.12 memory used=12822.5MB, alloc=155.8MB, time=242.22 memory used=12830.0MB, alloc=155.8MB, time=242.31 memory used=12837.4MB, alloc=155.8MB, time=242.41 memory used=12844.7MB, alloc=155.8MB, time=242.49 memory used=12852.0MB, alloc=155.8MB, time=242.58 memory used=12859.2MB, alloc=155.8MB, time=242.65 memory used=12866.4MB, alloc=155.8MB, time=242.73 memory used=12873.5MB, alloc=155.8MB, time=242.79 memory used=12880.5MB, alloc=155.8MB, time=242.87 memory used=12887.5MB, alloc=155.8MB, time=242.93 memory used=12894.4MB, alloc=155.8MB, time=243.01 memory used=12902.0MB, alloc=155.8MB, time=243.09 memory used=12909.2MB, alloc=155.8MB, time=243.16 memory used=12918.1MB, alloc=155.8MB, time=243.24 memory used=12925.7MB, alloc=155.8MB, time=243.31 memory used=12934.6MB, alloc=155.8MB, time=243.38 memory used=12944.2MB, alloc=155.8MB, time=243.48 memory used=12953.7MB, alloc=155.8MB, time=243.56 memory used=12963.1MB, alloc=155.8MB, time=243.64 memory used=12972.3MB, alloc=155.8MB, time=243.71 memory used=12981.3MB, alloc=155.8MB, time=243.78 memory used=12990.1MB, alloc=155.8MB, time=243.84 memory used=12999.6MB, alloc=155.8MB, time=243.92 memory used=13010.2MB, alloc=155.8MB, time=243.99 memory used=13019.7MB, alloc=155.8MB, time=244.06 memory used=13029.3MB, alloc=155.8MB, time=244.12 memory used=13039.8MB, alloc=155.8MB, time=244.21 memory used=13050.0MB, alloc=155.8MB, time=244.29 memory used=13060.7MB, alloc=155.8MB, time=244.36 memory used=13071.8MB, alloc=155.8MB, time=244.42 memory used=13083.1MB, alloc=155.8MB, time=244.49 memory used=13094.9MB, alloc=155.8MB, time=244.57 memory used=13107.1MB, alloc=155.8MB, time=244.65 memory used=13191.7MB, alloc=155.8MB, time=245.16 |\^/| 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(); 1428288833 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 F := [6 x y z + 12 y z + 16 z, -2 y + 10 y z - 15 y z - 16 y , 3 2 2 14 y z + 16 x y - 4 x z - 10] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 G := [-15 x z + 18 x y z - 13 x y - 8 y z , 12 x z - 20 y z + 19 x y - 7 y, 2 4 -19 x y z - y - 7 z - 14] > Problem := [F,G]; 4 3 2 2 Problem := [[6 x y z + 12 y z + 16 z, -2 y + 10 y z - 15 y z - 16 y , 3 2 2 3 2 2 2 14 y z + 16 x y - 4 x z - 10], [-15 x z + 18 x y z - 13 x y - 8 y z , 2 2 2 4 12 x z - 20 y z + 19 x y - 7 y, -19 x y z - y - 7 z - 14]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.7MB, alloc=32.3MB, time=0.49 memory used=45.4MB, alloc=56.3MB, time=0.79 memory used=88.7MB, alloc=60.3MB, time=1.31 memory used=120.1MB, alloc=60.3MB, time=1.60 memory used=142.1MB, alloc=60.3MB, time=1.65 memory used=184.7MB, alloc=60.3MB, time=2.11 memory used=226.0MB, alloc=60.3MB, time=2.73 memory used=268.8MB, alloc=68.3MB, time=3.36 memory used=311.4MB, alloc=92.3MB, time=3.98 memory used=377.4MB, alloc=92.3MB, time=4.92 memory used=440.9MB, alloc=116.3MB, time=5.88 memory used=559.7MB, alloc=116.3MB, time=7.83 memory used=659.5MB, alloc=116.3MB, time=9.87 memory used=703.1MB, alloc=116.3MB, time=10.03 memory used=764.2MB, alloc=116.3MB, time=23.75 memory used=817.8MB, alloc=116.3MB, time=24.59 memory used=868.2MB, alloc=116.3MB, time=24.73 memory used=904.4MB, alloc=116.3MB, time=29.61 memory used=941.1MB, alloc=140.3MB, time=39.26 memory used=996.5MB, alloc=140.3MB, time=64.14 memory used=1039.0MB, alloc=164.3MB, time=87.40 memory used=1081.5MB, alloc=188.3MB, time=122.91 memory used=1141.5MB, alloc=212.3MB, time=177.07 memory used=1203.0MB, alloc=236.3MB, time=209.87 |\^/| 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(); 1428289133 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 2 F := [9 x + 19 z - 7 y - 9, 12 x y + 20 x y z + 10 y z + 3 x z, 4 3 2 17 y - 17 y z + 15 x z - 20 x y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 4 3 2 G := [-6 x y + 5 z + 10 x - 18 z, 7 x z + 3 y - 13 x - 5 y , 2 4 2 2 18 x y z - 6 y + 14 x z + 5 z ] > Problem := [F,G]; 4 2 3 2 2 2 Problem := [[9 x + 19 z - 7 y - 9, 12 x y + 20 x y z + 10 y z + 3 x z, 4 3 2 2 2 3 17 y - 17 y z + 15 x z - 20 x y z], [-6 x y + 5 z + 10 x - 18 z, 3 4 3 2 2 4 2 2 7 x z + 3 y - 13 x - 5 y , 18 x y z - 6 y + 14 x z + 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.17 memory used=32.3MB, alloc=38.3MB, time=0.44 memory used=45.3MB, alloc=38.3MB, time=0.48 memory used=58.2MB, alloc=38.3MB, time=0.51 memory used=80.5MB, alloc=38.3MB, time=0.96 memory used=99.0MB, alloc=38.3MB, time=1.03 memory used=114.0MB, alloc=62.3MB, time=1.09 memory used=138.6MB, alloc=62.3MB, time=1.17 memory used=169.2MB, alloc=62.3MB, time=1.24 memory used=205.0MB, alloc=62.3MB, time=1.33 memory used=225.9MB, alloc=62.3MB, time=1.39 memory used=247.7MB, alloc=62.3MB, time=1.45 memory used=270.3MB, alloc=62.3MB, time=1.52 memory used=295.6MB, alloc=62.3MB, time=1.58 memory used=322.3MB, alloc=62.3MB, time=1.65 memory used=350.0MB, alloc=62.3MB, time=1.72 memory used=379.4MB, alloc=62.3MB, time=1.78 memory used=411.1MB, alloc=62.3MB, time=1.85 memory used=444.9MB, alloc=62.3MB, time=1.93 memory used=481.4MB, alloc=62.3MB, time=2.00 memory used=505.7MB, alloc=62.3MB, time=2.06 memory used=522.7MB, alloc=62.3MB, time=2.10 memory used=540.7MB, alloc=62.3MB, time=2.15 memory used=559.4MB, alloc=62.3MB, time=2.19 memory used=578.2MB, alloc=62.3MB, time=2.24 memory used=597.9MB, alloc=62.3MB, time=2.28 memory used=619.2MB, alloc=62.3MB, time=2.33 memory used=641.3MB, alloc=62.3MB, time=2.38 memory used=663.4MB, alloc=62.3MB, time=2.43 memory used=685.4MB, alloc=62.3MB, time=2.48 memory used=708.3MB, alloc=62.3MB, time=2.53 memory used=732.3MB, alloc=62.3MB, time=2.58 memory used=757.0MB, alloc=62.3MB, time=2.63 memory used=782.6MB, alloc=62.3MB, time=2.68 memory used=808.9MB, alloc=62.3MB, time=2.73 memory used=836.7MB, alloc=62.3MB, time=2.78 memory used=866.1MB, alloc=62.3MB, time=2.83 memory used=896.5MB, alloc=62.3MB, time=2.89 memory used=928.1MB, alloc=62.3MB, time=2.94 memory used=960.7MB, alloc=62.3MB, time=3.00 memory used=1003.5MB, alloc=62.3MB, time=3.39 memory used=1038.1MB, alloc=62.3MB, time=3.49 memory used=1064.3MB, alloc=62.3MB, time=3.57 memory used=1096.5MB, alloc=62.3MB, time=3.65 memory used=1127.7MB, alloc=62.3MB, time=3.73 memory used=1147.0MB, alloc=62.3MB, time=3.79 memory used=1167.9MB, alloc=62.3MB, time=3.85 memory used=1190.1MB, alloc=62.3MB, time=3.91 memory used=1214.2MB, alloc=62.3MB, time=3.97 memory used=1240.4MB, alloc=62.3MB, time=4.04 memory used=1268.2MB, alloc=62.3MB, time=4.11 memory used=1297.5MB, alloc=62.3MB, time=4.17 memory used=1329.2MB, alloc=62.3MB, time=4.24 memory used=1362.5MB, alloc=62.3MB, time=4.31 memory used=1399.6MB, alloc=62.3MB, time=4.38 memory used=1422.4MB, alloc=62.3MB, time=4.44 memory used=1440.6MB, alloc=62.3MB, time=4.48 memory used=1459.2MB, alloc=62.3MB, time=4.53 memory used=1478.0MB, alloc=62.3MB, time=4.58 memory used=1496.8MB, alloc=62.3MB, time=4.63 memory used=1516.5MB, alloc=62.3MB, time=4.67 memory used=1537.8MB, alloc=62.3MB, time=4.72 memory used=1559.9MB, alloc=62.3MB, time=4.77 memory used=1582.0MB, alloc=62.3MB, time=4.82 memory used=1604.0MB, alloc=62.3MB, time=4.87 memory used=1626.9MB, alloc=62.3MB, time=4.92 memory used=1650.9MB, alloc=62.3MB, time=4.97 memory used=1675.6MB, alloc=62.3MB, time=5.02 memory used=1701.2MB, alloc=62.3MB, time=5.07 memory used=1727.3MB, alloc=62.3MB, time=5.12 memory used=1755.1MB, alloc=62.3MB, time=5.18 memory used=1783.4MB, alloc=62.3MB, time=5.23 memory used=1813.1MB, alloc=62.3MB, time=5.28 memory used=1844.0MB, alloc=62.3MB, time=5.34 memory used=1877.0MB, alloc=62.3MB, time=5.39 memory used=1922.6MB, alloc=62.3MB, time=7.62 memory used=1979.1MB, alloc=62.3MB, time=31.95 memory used=2016.4MB, alloc=62.3MB, time=56.27 memory used=2041.0MB, alloc=86.3MB, time=82.30 memory used=2083.6MB, alloc=86.3MB, time=110.34 memory used=2132.7MB, alloc=86.3MB, time=156.22 memory used=2223.6MB, alloc=86.3MB, time=159.68 memory used=2322.3MB, alloc=86.3MB, time=160.47 memory used=2419.2MB, alloc=86.3MB, time=161.23 memory used=2515.3MB, alloc=86.3MB, time=161.95 memory used=2613.4MB, alloc=86.3MB, time=162.62 memory used=2654.9MB, alloc=86.3MB, time=162.74 memory used=2700.2MB, alloc=86.3MB, time=162.86 memory used=2731.6MB, alloc=86.3MB, time=162.97 memory used=2768.7MB, alloc=86.3MB, time=163.08 memory used=2810.1MB, alloc=86.3MB, time=163.19 memory used=2855.3MB, alloc=86.3MB, time=163.31 memory used=2904.0MB, alloc=86.3MB, time=163.44 memory used=2955.2MB, alloc=86.3MB, time=163.57 memory used=2985.2MB, alloc=86.3MB, time=163.65 memory used=3011.6MB, alloc=86.3MB, time=163.72 memory used=3038.9MB, alloc=86.3MB, time=163.81 memory used=3067.2MB, alloc=86.3MB, time=163.89 memory used=3096.2MB, alloc=86.3MB, time=163.97 memory used=3125.9MB, alloc=86.3MB, time=164.05 memory used=3156.4MB, alloc=86.3MB, time=164.14 memory used=3187.6MB, alloc=86.3MB, time=164.22 memory used=3219.5MB, alloc=86.3MB, time=164.30 memory used=3252.2MB, alloc=86.3MB, time=164.39 memory used=3285.5MB, alloc=86.3MB, time=164.48 memory used=3319.8MB, alloc=86.3MB, time=164.56 memory used=3358.6MB, alloc=86.3MB, time=164.65 memory used=3398.5MB, alloc=86.3MB, time=164.74 memory used=3439.3MB, alloc=86.3MB, time=164.84 memory used=3480.8MB, alloc=86.3MB, time=164.94 memory used=3523.1MB, alloc=86.3MB, time=165.04 memory used=3566.3MB, alloc=86.3MB, time=165.13 memory used=3610.0MB, alloc=86.3MB, time=165.23 memory used=3654.6MB, alloc=86.3MB, time=165.33 memory used=3700.1MB, alloc=86.3MB, time=165.41 memory used=3746.2MB, alloc=86.3MB, time=165.51 memory used=3793.1MB, alloc=86.3MB, time=165.61 memory used=3840.7MB, alloc=86.3MB, time=165.72 memory used=3889.0MB, alloc=86.3MB, time=165.81 memory used=3914.4MB, alloc=107.8MB, time=165.90 memory used=3922.4MB, alloc=107.8MB, 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used=4395.2MB, alloc=107.8MB, time=169.38 memory used=4401.3MB, alloc=107.8MB, time=169.42 memory used=4407.3MB, alloc=107.8MB, time=169.46 memory used=4413.4MB, alloc=107.8MB, time=169.50 memory used=4419.4MB, alloc=107.8MB, time=169.61 memory used=4425.5MB, alloc=107.8MB, time=169.66 memory used=4431.6MB, alloc=107.8MB, time=169.70 memory used=4437.7MB, alloc=107.8MB, time=169.74 memory used=4443.7MB, alloc=107.8MB, time=169.80 memory used=4449.8MB, alloc=107.8MB, time=169.85 memory used=4455.9MB, alloc=107.8MB, time=169.89 memory used=4462.0MB, alloc=107.8MB, time=169.93 memory used=4468.2MB, alloc=107.8MB, time=170.00 memory used=4474.3MB, alloc=107.8MB, time=170.04 memory used=4480.4MB, alloc=107.8MB, time=170.08 memory used=4486.5MB, alloc=107.8MB, time=170.11 memory used=4492.7MB, alloc=107.8MB, time=170.16 memory used=4498.8MB, alloc=107.8MB, time=170.20 memory used=4505.0MB, alloc=107.8MB, time=170.24 memory used=4511.1MB, alloc=107.8MB, time=170.28 memory used=4517.3MB, 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alloc=107.8MB, time=172.99 memory used=4911.1MB, alloc=107.8MB, time=173.03 memory used=4917.6MB, alloc=107.8MB, time=173.08 memory used=4924.2MB, alloc=107.8MB, time=173.12 memory used=4930.7MB, alloc=107.8MB, time=173.17 memory used=4937.3MB, alloc=107.8MB, time=173.22 memory used=4943.8MB, alloc=107.8MB, time=173.26 memory used=4950.4MB, alloc=107.8MB, time=173.30 memory used=4956.9MB, alloc=107.8MB, time=173.35 memory used=4963.5MB, alloc=107.8MB, time=173.39 memory used=4970.0MB, alloc=107.8MB, time=173.44 memory used=4976.6MB, alloc=107.8MB, time=173.47 memory used=4983.2MB, alloc=107.8MB, time=173.53 memory used=4989.8MB, alloc=107.8MB, time=173.58 memory used=4996.4MB, alloc=107.8MB, time=173.63 memory used=5003.0MB, alloc=107.8MB, time=173.68 memory used=5009.6MB, alloc=107.8MB, time=173.73 memory used=5016.2MB, alloc=107.8MB, time=173.76 memory used=5022.8MB, alloc=107.8MB, time=173.80 memory used=5029.4MB, alloc=107.8MB, time=173.85 memory used=5036.0MB, alloc=107.8MB, 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used=5176.1MB, alloc=107.8MB, time=174.85 memory used=5182.9MB, alloc=107.8MB, time=174.89 memory used=5189.6MB, alloc=107.8MB, time=174.92 memory used=5196.3MB, alloc=107.8MB, time=174.97 memory used=5203.0MB, alloc=107.8MB, time=175.01 memory used=5209.8MB, alloc=107.8MB, time=175.05 memory used=5216.5MB, alloc=107.8MB, time=175.10 memory used=5223.7MB, alloc=107.8MB, time=175.14 memory used=5230.6MB, alloc=107.8MB, time=175.18 memory used=5243.5MB, alloc=107.8MB, time=175.23 memory used=5250.7MB, alloc=107.8MB, time=175.28 memory used=5257.7MB, alloc=107.8MB, time=175.34 memory used=5270.6MB, alloc=107.8MB, time=175.38 memory used=5277.8MB, alloc=107.8MB, time=175.42 memory used=5284.8MB, alloc=107.8MB, time=175.46 memory used=5297.8MB, alloc=107.8MB, time=175.51 memory used=5305.0MB, alloc=107.8MB, time=175.55 memory used=5318.2MB, alloc=107.8MB, time=175.61 memory used=5325.4MB, alloc=107.8MB, time=175.66 memory used=5338.6MB, alloc=107.8MB, time=175.70 memory used=5345.9MB, alloc=107.8MB, time=175.74 memory used=5359.1MB, alloc=107.8MB, time=175.79 memory used=5366.4MB, alloc=107.8MB, time=175.83 memory used=5379.6MB, alloc=107.8MB, time=175.88 memory used=5387.1MB, alloc=107.8MB, time=175.93 memory used=5400.2MB, alloc=107.8MB, time=175.98 memory used=5407.6MB, alloc=107.8MB, time=176.02 memory used=5420.8MB, alloc=107.8MB, time=176.07 memory used=5428.2MB, alloc=107.8MB, time=176.10 memory used=5441.4MB, alloc=107.8MB, time=176.15 memory used=5448.9MB, alloc=107.8MB, time=176.19 memory used=5462.1MB, alloc=107.8MB, time=176.24 memory used=5475.9MB, alloc=107.8MB, time=176.28 memory used=5489.7MB, alloc=107.8MB, time=176.35 memory used=5503.5MB, alloc=107.8MB, time=176.40 memory used=5517.4MB, alloc=107.8MB, time=176.45 memory used=5531.2MB, alloc=107.8MB, time=176.50 memory used=5545.1MB, alloc=107.8MB, time=176.55 memory used=5558.9MB, alloc=107.8MB, time=176.60 memory used=5572.8MB, alloc=107.8MB, time=176.65 memory used=5586.7MB, alloc=107.8MB, 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time=187.99 memory used=7987.3MB, alloc=107.8MB, time=188.03 memory used=8000.8MB, alloc=107.8MB, time=188.08 memory used=8008.6MB, alloc=107.8MB, time=188.12 memory used=8022.0MB, alloc=107.8MB, time=188.17 memory used=8030.0MB, alloc=107.8MB, time=188.22 memory used=8043.2MB, alloc=107.8MB, time=188.28 memory used=8051.2MB, alloc=107.8MB, time=188.32 memory used=8064.4MB, alloc=107.8MB, time=188.37 memory used=8072.4MB, alloc=107.8MB, time=188.41 memory used=8085.6MB, alloc=107.8MB, time=188.46 memory used=8099.7MB, alloc=107.8MB, time=188.51 memory used=8113.8MB, alloc=107.8MB, time=188.55 memory used=8127.9MB, alloc=107.8MB, time=188.61 memory used=8141.9MB, alloc=107.8MB, time=188.66 memory used=8156.0MB, alloc=107.8MB, time=188.71 memory used=8170.0MB, alloc=107.8MB, time=188.76 memory used=8184.0MB, alloc=107.8MB, time=188.81 memory used=8198.0MB, alloc=107.8MB, time=188.86 memory used=8212.0MB, alloc=107.8MB, time=188.91 memory used=8226.0MB, alloc=107.8MB, time=188.96 memory used=8240.0MB, alloc=107.8MB, time=189.01 memory used=8253.9MB, alloc=107.8MB, time=189.06 memory used=8267.9MB, alloc=107.8MB, time=189.10 memory used=8281.8MB, alloc=107.8MB, time=189.16 memory used=8295.8MB, alloc=107.8MB, time=189.21 memory used=8309.7MB, alloc=107.8MB, time=189.26 memory used=8323.6MB, alloc=107.8MB, time=189.31 memory used=8337.4MB, alloc=107.8MB, time=189.36 memory used=8351.3MB, alloc=107.8MB, time=189.41 memory used=8365.2MB, alloc=107.8MB, time=189.45 memory used=8379.0MB, alloc=107.8MB, time=189.51 memory used=8392.8MB, alloc=107.8MB, time=189.55 memory used=8406.6MB, alloc=107.8MB, time=189.59 memory used=8420.4MB, alloc=107.8MB, time=189.64 memory used=8434.2MB, alloc=107.8MB, time=189.69 memory used=8448.0MB, alloc=107.8MB, time=189.73 memory used=8461.7MB, alloc=107.8MB, time=189.78 memory used=8475.4MB, alloc=107.8MB, time=189.83 memory used=8489.2MB, alloc=107.8MB, time=189.89 memory used=8502.9MB, alloc=107.8MB, time=189.93 memory used=8516.6MB, alloc=107.8MB, time=189.98 memory used=8530.2MB, alloc=107.8MB, time=190.02 memory used=8543.9MB, alloc=107.8MB, time=190.07 memory used=8557.5MB, alloc=107.8MB, time=190.12 memory used=8571.2MB, alloc=107.8MB, time=190.17 memory used=8584.8MB, alloc=107.8MB, time=190.24 memory used=8598.4MB, alloc=107.8MB, time=190.28 memory used=8611.9MB, alloc=107.8MB, time=190.35 memory used=8625.5MB, alloc=107.8MB, time=190.39 memory used=8639.0MB, alloc=107.8MB, time=190.44 memory used=8652.6MB, alloc=107.8MB, time=190.49 memory used=8666.1MB, alloc=107.8MB, time=190.55 memory used=8679.6MB, alloc=107.8MB, time=190.60 memory used=8693.0MB, alloc=107.8MB, time=190.66 memory used=8706.5MB, alloc=107.8MB, time=190.71 memory used=8719.9MB, alloc=107.8MB, time=190.77 memory used=8733.3MB, alloc=107.8MB, time=190.81 memory used=8746.7MB, alloc=107.8MB, time=190.88 memory used=8760.1MB, alloc=107.8MB, time=190.93 memory used=8773.5MB, alloc=107.8MB, time=190.97 memory used=8786.8MB, alloc=107.8MB, time=191.05 memory used=8800.2MB, alloc=107.8MB, time=191.10 memory used=8813.5MB, alloc=107.8MB, time=191.16 memory used=8826.8MB, alloc=107.8MB, time=191.21 memory used=8840.0MB, alloc=107.8MB, time=191.26 memory used=8853.3MB, alloc=107.8MB, time=191.31 memory used=8866.5MB, alloc=107.8MB, time=191.36 memory used=8879.8MB, alloc=107.8MB, time=191.41 memory used=8892.9MB, alloc=107.8MB, time=191.46 memory used=8906.1MB, alloc=107.8MB, time=191.51 memory used=8919.3MB, alloc=107.8MB, time=191.56 memory used=8932.4MB, alloc=107.8MB, time=191.60 memory used=8945.5MB, alloc=107.8MB, time=191.65 memory used=8958.6MB, alloc=107.8MB, time=191.71 memory used=8971.7MB, alloc=107.8MB, time=191.76 memory used=8984.7MB, alloc=107.8MB, time=191.81 memory used=8997.8MB, alloc=107.8MB, time=191.86 memory used=9010.8MB, alloc=107.8MB, time=191.95 memory used=9023.8MB, alloc=107.8MB, time=192.01 memory used=9036.8MB, alloc=107.8MB, time=192.06 memory used=9049.7MB, alloc=107.8MB, time=192.11 memory used=9062.7MB, alloc=107.8MB, time=192.16 memory used=9075.6MB, alloc=107.8MB, time=192.21 memory used=9088.5MB, alloc=107.8MB, time=192.26 memory used=9101.3MB, alloc=107.8MB, time=192.31 memory used=9114.2MB, alloc=107.8MB, time=192.36 memory used=9127.0MB, alloc=107.8MB, time=192.43 memory used=9139.8MB, alloc=107.8MB, time=192.48 memory used=9152.6MB, alloc=107.8MB, time=192.52 memory used=9165.3MB, alloc=107.8MB, time=192.59 memory used=9178.7MB, alloc=107.8MB, time=192.64 memory used=9191.8MB, alloc=107.8MB, time=192.70 memory used=9209.7MB, alloc=107.8MB, time=192.75 memory used=9223.1MB, alloc=107.8MB, time=192.80 memory used=9241.3MB, alloc=107.8MB, time=192.85 memory used=9254.7MB, alloc=107.8MB, time=192.91 memory used=9272.8MB, alloc=107.8MB, time=192.97 memory used=9286.3MB, alloc=107.8MB, time=193.02 memory used=9304.0MB, alloc=107.8MB, time=193.06 memory used=9317.6MB, alloc=107.8MB, time=193.12 memory used=9335.1MB, alloc=107.8MB, time=193.17 memory used=9353.7MB, alloc=107.8MB, time=193.22 memory used=9372.3MB, alloc=107.8MB, time=193.27 memory used=9390.8MB, alloc=107.8MB, time=193.33 memory used=9409.2MB, alloc=107.8MB, time=193.43 memory used=9427.6MB, alloc=107.8MB, time=193.48 memory used=9445.9MB, alloc=107.8MB, time=193.54 memory used=9464.1MB, alloc=107.8MB, time=193.60 memory used=9482.3MB, alloc=107.8MB, time=193.65 memory used=9500.5MB, alloc=107.8MB, time=193.70 memory used=9518.6MB, alloc=107.8MB, time=193.75 memory used=9536.6MB, alloc=107.8MB, time=193.81 memory used=9554.5MB, alloc=107.8MB, time=193.86 memory used=9572.4MB, alloc=107.8MB, time=193.91 memory used=9590.3MB, alloc=107.8MB, time=193.97 memory used=9608.0MB, alloc=107.8MB, time=194.02 memory used=9625.7MB, alloc=107.8MB, time=194.07 memory used=9643.4MB, alloc=107.8MB, time=194.12 memory used=9661.0MB, alloc=107.8MB, time=194.17 memory used=9678.5MB, alloc=107.8MB, time=194.24 memory used=9695.3MB, alloc=107.8MB, time=194.30 memory used=9711.1MB, alloc=107.8MB, time=194.35 memory used=9728.4MB, alloc=107.8MB, time=194.41 memory used=9745.0MB, alloc=107.8MB, time=194.46 memory used=9760.7MB, alloc=107.8MB, time=194.51 memory used=9772.0MB, alloc=107.8MB, time=194.58 memory used=9782.7MB, alloc=107.8MB, time=194.64 memory used=9793.0MB, alloc=107.8MB, time=194.69 memory used=9804.1MB, alloc=107.8MB, time=194.73 memory used=9815.3MB, alloc=107.8MB, time=194.78 memory used=9826.5MB, alloc=107.8MB, time=194.82 memory used=9837.8MB, alloc=107.8MB, time=194.87 memory used=9849.0MB, alloc=107.8MB, time=194.91 memory used=9860.1MB, alloc=107.8MB, time=194.98 memory used=9871.3MB, alloc=107.8MB, time=195.03 memory used=9882.4MB, alloc=107.8MB, time=195.07 memory used=9893.5MB, alloc=107.8MB, time=195.11 memory used=9904.5MB, alloc=107.8MB, time=195.16 memory used=9915.5MB, alloc=107.8MB, time=195.20 memory used=9926.5MB, alloc=107.8MB, time=195.26 memory used=9937.5MB, alloc=107.8MB, time=195.30 memory used=9948.4MB, alloc=107.8MB, time=195.36 memory used=9959.3MB, alloc=107.8MB, time=195.40 memory used=9970.1MB, alloc=107.8MB, time=195.46 memory used=9980.9MB, alloc=107.8MB, time=195.50 memory used=9992.5MB, alloc=107.8MB, time=195.60 memory used=10003.6MB, alloc=107.8MB, time=195.65 memory used=10018.5MB, alloc=107.8MB, time=195.69 memory used=10030.0MB, alloc=107.8MB, time=195.76 memory used=10045.2MB, alloc=107.8MB, time=195.81 memory used=10056.6MB, alloc=107.8MB, time=195.87 memory used=10071.6MB, alloc=107.8MB, time=195.92 memory used=10083.2MB, alloc=107.8MB, time=195.97 memory used=10097.8MB, alloc=107.8MB, time=196.04 memory used=10109.3MB, alloc=107.8MB, time=196.09 memory used=10123.7MB, alloc=107.8MB, time=196.15 memory used=10139.2MB, alloc=107.8MB, time=196.19 memory used=10154.6MB, alloc=107.8MB, time=196.25 memory used=10170.0MB, alloc=107.8MB, time=196.30 memory used=10185.2MB, alloc=107.8MB, time=196.35 memory used=10200.4MB, alloc=107.8MB, time=196.40 memory used=10215.5MB, alloc=107.8MB, time=196.45 memory used=10230.5MB, alloc=107.8MB, time=196.49 memory used=10245.4MB, alloc=107.8MB, time=196.54 memory used=10260.2MB, alloc=107.8MB, time=196.60 memory used=10275.0MB, alloc=107.8MB, time=196.64 memory used=10289.7MB, alloc=107.8MB, time=196.68 memory used=10304.3MB, alloc=107.8MB, time=196.74 memory used=10318.8MB, alloc=107.8MB, time=196.78 memory used=10333.2MB, alloc=107.8MB, time=196.83 memory used=10347.6MB, alloc=107.8MB, time=196.88 memory used=10361.8MB, alloc=107.8MB, time=196.92 memory used=10376.0MB, alloc=107.8MB, time=196.98 memory used=10390.1MB, alloc=107.8MB, time=197.02 memory used=10404.1MB, alloc=107.8MB, time=197.07 memory used=10418.0MB, alloc=107.8MB, time=197.12 memory used=10431.8MB, alloc=107.8MB, time=197.22 memory used=10446.4MB, alloc=107.8MB, time=197.28 memory used=10457.2MB, alloc=107.8MB, time=197.32 memory used=10472.9MB, alloc=107.8MB, time=197.37 memory used=10487.4MB, alloc=107.8MB, time=197.42 memory used=10504.2MB, alloc=107.8MB, time=197.50 memory used=10521.9MB, alloc=107.8MB, time=197.56 memory used=10539.4MB, alloc=107.8MB, time=197.61 memory used=10556.7MB, alloc=107.8MB, time=197.67 memory used=10573.9MB, alloc=107.8MB, time=197.72 memory used=10590.9MB, alloc=107.8MB, time=197.76 memory used=10607.7MB, alloc=107.8MB, time=197.81 memory used=10624.4MB, alloc=107.8MB, time=197.86 memory used=10640.9MB, alloc=107.8MB, time=197.91 memory used=10657.3MB, alloc=107.8MB, time=197.98 memory used=10673.4MB, alloc=107.8MB, time=198.03 memory used=10690.3MB, alloc=107.8MB, time=198.08 memory used=10706.5MB, alloc=107.8MB, time=198.13 memory used=10724.8MB, alloc=107.8MB, time=198.18 memory used=10741.5MB, alloc=107.8MB, time=198.24 memory used=10759.3MB, alloc=107.8MB, time=198.31 memory used=10778.0MB, alloc=107.8MB, time=198.36 memory used=10796.5MB, alloc=107.8MB, time=198.41 memory used=10814.7MB, alloc=107.8MB, time=198.45 memory used=10832.6MB, alloc=107.8MB, time=198.51 memory used=10851.1MB, alloc=107.8MB, time=198.56 memory used=10871.0MB, alloc=107.8MB, time=198.62 memory used=10889.3MB, alloc=107.8MB, time=198.67 memory used=10908.0MB, alloc=107.8MB, time=198.72 memory used=10927.5MB, alloc=107.8MB, time=198.77 memory used=10946.7MB, alloc=107.8MB, time=198.82 memory used=10966.3MB, alloc=107.8MB, time=198.87 memory used=10986.6MB, alloc=107.8MB, time=198.93 memory used=11007.3MB, alloc=107.8MB, time=198.98 memory used=11027.3MB, alloc=107.8MB, time=199.03 memory used=11047.9MB, alloc=107.8MB, time=199.09 memory used=11069.1MB, alloc=107.8MB, time=199.13 memory used=11090.3MB, alloc=107.8MB, time=199.19 memory used=11112.1MB, alloc=107.8MB, time=199.25 memory used=11134.5MB, alloc=107.8MB, time=199.31 memory used=11166.1MB, alloc=107.8MB, time=199.82 memory used=11220.5MB, alloc=107.8MB, time=199.98 memory used=11270.8MB, alloc=107.8MB, time=200.11 memory used=11313.5MB, alloc=107.8MB, time=200.22 memory used=11349.1MB, alloc=107.8MB, time=200.34 memory used=11388.2MB, alloc=107.8MB, time=200.44 memory used=11432.4MB, alloc=107.8MB, time=200.56 memory used=11482.2MB, alloc=107.8MB, time=200.67 memory used=11537.4MB, alloc=107.8MB, time=200.79 memory used=11588.6MB, alloc=107.8MB, time=200.90 memory used=11618.3MB, alloc=107.8MB, time=200.98 memory used=11649.9MB, alloc=107.8MB, time=201.06 memory used=11681.8MB, alloc=107.8MB, time=201.13 memory used=11717.1MB, alloc=107.8MB, time=201.21 memory used=11752.4MB, alloc=107.8MB, time=201.29 memory used=11790.8MB, alloc=107.8MB, time=201.37 memory used=11829.9MB, alloc=107.8MB, time=201.45 memory used=11871.2MB, alloc=107.8MB, time=201.53 memory used=11914.7MB, alloc=107.8MB, time=201.62 memory used=11961.6MB, alloc=107.8MB, time=201.70 memory used=12011.1MB, alloc=107.8MB, time=201.79 memory used=12063.6MB, alloc=107.8MB, time=201.89 memory used=12124.3MB, alloc=107.8MB, time=202.32 memory used=12170.4MB, alloc=107.8MB, time=202.45 memory used=12218.8MB, alloc=107.8MB, time=202.57 memory used=12253.1MB, alloc=107.8MB, time=202.68 memory used=12291.5MB, alloc=107.8MB, time=202.78 memory used=12334.8MB, alloc=107.8MB, time=202.89 memory used=12384.0MB, alloc=107.8MB, time=203.02 memory used=12438.8MB, alloc=107.8MB, time=203.14 memory used=12495.3MB, alloc=107.8MB, time=203.27 memory used=12526.1MB, alloc=107.8MB, time=203.35 memory used=12556.9MB, alloc=107.8MB, time=203.43 memory used=12588.8MB, alloc=107.8MB, time=203.51 memory used=12624.1MB, alloc=107.8MB, time=203.59 memory used=12659.4MB, alloc=107.8MB, time=203.67 memory used=12697.8MB, alloc=107.8MB, time=203.76 memory used=12737.0MB, alloc=107.8MB, time=203.83 memory used=12778.2MB, alloc=107.8MB, time=203.92 memory used=12821.7MB, alloc=107.8MB, time=204.01 memory used=12867.6MB, alloc=107.8MB, time=204.10 memory used=12917.1MB, alloc=107.8MB, time=204.18 memory used=12970.2MB, alloc=107.8MB, time=204.26 memory used=13054.3MB, alloc=107.8MB, time=221.43 |\^/| 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(); 1428289433 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 2 3 F := [-8 x z + 10 x y - 10 x y z + 20 y z , 2 x y + 15 x y + 19, 3 4 2 3 -20 x z - z + 7 x z + 14 y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 2 2 G := [-18 x z - 5 x y - 7 x y - 9 x y, 18 x z - 7 x y - 5 x z + 16 y z, 3 3 2 -16 x y + 17 x z + 18 x - 18 x] > Problem := [F,G]; 3 3 2 2 2 2 2 3 Problem := [[-8 x z + 10 x y - 10 x y z + 20 y z , 2 x y + 15 x y + 19, 3 4 2 3 3 2 2 2 -20 x z - z + 7 x z + 14 y ], [-18 x z - 5 x y - 7 x y - 9 x y, 3 2 2 2 3 3 2 18 x z - 7 x y - 5 x z + 16 y z, -16 x y + 17 x z + 18 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=4.4MB, alloc=32.3MB, time=0.18 memory used=25.2MB, alloc=32.3MB, time=0.49 memory used=44.9MB, alloc=60.3MB, time=0.77 memory used=83.1MB, alloc=60.3MB, time=1.27 memory used=126.0MB, alloc=60.3MB, time=1.74 memory used=168.0MB, alloc=60.3MB, time=2.15 memory used=210.7MB, alloc=68.3MB, time=2.63 memory used=252.9MB, alloc=68.3MB, time=3.22 memory used=295.1MB, alloc=92.3MB, time=3.76 memory used=360.6MB, alloc=92.3MB, time=4.62 memory used=415.0MB, alloc=92.3MB, time=5.13 memory used=481.0MB, alloc=92.3MB, time=6.05 memory used=545.9MB, alloc=116.3MB, time=6.99 memory used=606.1MB, alloc=372.3MB, time=7.75 memory used=691.6MB, alloc=372.3MB, time=8.60 memory used=780.4MB, alloc=396.3MB, time=9.78 memory used=908.6MB, alloc=396.3MB, time=11.10 memory used=1023.0MB, alloc=420.3MB, time=12.54 memory used=1146.2MB, alloc=420.3MB, time=14.11 memory used=1222.8MB, alloc=420.3MB, time=14.62 memory used=1305.0MB, alloc=420.3MB, time=15.21 memory used=1381.1MB, alloc=420.3MB, time=15.72 memory used=1507.3MB, alloc=444.3MB, time=17.34 memory used=1664.2MB, alloc=444.3MB, time=18.67 memory used=1763.5MB, alloc=444.3MB, time=19.41 memory used=1855.8MB, alloc=444.3MB, time=20.03 memory used=1976.9MB, alloc=444.3MB, time=21.55 memory used=2072.2MB, alloc=468.3MB, time=22.72 memory used=2223.1MB, alloc=468.3MB, time=24.08 memory used=2334.0MB, alloc=468.3MB, time=25.41 memory used=2430.6MB, alloc=468.3MB, time=26.60 memory used=2534.8MB, alloc=468.3MB, time=27.92 memory used=2636.6MB, alloc=468.3MB, time=29.18 memory used=2723.2MB, alloc=468.3MB, time=30.34 memory used=2806.7MB, alloc=468.3MB, time=31.39 memory used=2893.8MB, alloc=468.3MB, time=32.57 memory used=2975.3MB, alloc=468.3MB, time=33.76 memory used=3045.5MB, alloc=468.3MB, time=34.75 memory used=3128.3MB, alloc=492.3MB, time=35.85 memory used=3199.5MB, alloc=492.3MB, time=37.02 memory used=3268.6MB, alloc=492.3MB, time=38.18 memory used=3322.5MB, alloc=492.3MB, time=39.09 memory used=3365.5MB, alloc=492.3MB, time=39.82 memory used=3430.6MB, alloc=492.3MB, time=40.99 memory used=3476.7MB, alloc=492.3MB, time=41.92 memory used=3544.0MB, alloc=492.3MB, time=42.95 memory used=3633.3MB, alloc=492.3MB, time=43.84 memory used=3734.6MB, alloc=492.3MB, time=44.67 memory used=3852.1MB, alloc=492.3MB, time=45.49 memory used=3931.7MB, alloc=492.3MB, time=46.39 memory used=4025.8MB, alloc=492.3MB, time=47.34 memory used=4073.8MB, alloc=492.3MB, time=48.37 memory used=4151.8MB, alloc=492.3MB, time=49.28 memory used=4194.2MB, alloc=492.3MB, time=50.13 memory used=4371.8MB, alloc=492.3MB, time=52.00 memory used=4519.0MB, alloc=492.3MB, time=53.33 memory used=4718.6MB, alloc=516.3MB, time=55.92 memory used=4935.8MB, alloc=540.3MB, time=58.85 memory used=5086.0MB, alloc=540.3MB, time=61.30 memory used=5264.5MB, alloc=540.3MB, time=63.03 memory used=5470.6MB, alloc=564.3MB, time=65.55 memory used=5639.4MB, alloc=564.3MB, time=67.88 memory used=5801.0MB, alloc=564.3MB, time=69.31 memory used=5969.6MB, alloc=564.3MB, time=70.97 memory used=6107.1MB, alloc=564.3MB, time=71.93 memory used=6237.4MB, alloc=564.3MB, time=73.09 memory used=6461.8MB, alloc=564.3MB, time=75.42 memory used=6650.6MB, alloc=588.3MB, time=77.22 memory used=6867.5MB, alloc=588.3MB, time=79.53 memory used=7006.4MB, alloc=588.3MB, time=81.88 memory used=7128.6MB, alloc=588.3MB, time=82.64 memory used=7285.6MB, alloc=588.3MB, time=84.00 memory used=7450.5MB, alloc=588.3MB, time=84.82 memory used=7595.2MB, alloc=588.3MB, time=86.08 memory used=7740.1MB, alloc=588.3MB, time=87.54 memory used=7944.5MB, alloc=588.3MB, time=89.93 memory used=8139.9MB, alloc=588.3MB, time=92.66 memory used=8322.2MB, alloc=588.3MB, time=94.97 memory used=8470.5MB, alloc=588.3MB, time=96.17 memory used=8628.6MB, alloc=588.3MB, time=99.00 memory used=8746.7MB, alloc=588.3MB, time=99.81 memory used=8932.6MB, alloc=588.3MB, time=101.99 memory used=9082.3MB, alloc=612.3MB, time=104.78 memory used=9204.2MB, alloc=612.3MB, time=107.47 memory used=9296.2MB, alloc=612.3MB, time=109.24 memory used=9379.5MB, alloc=612.3MB, time=111.00 memory used=9557.8MB, alloc=612.3MB, time=112.71 memory used=9760.8MB, alloc=612.3MB, time=115.28 memory used=9870.1MB, alloc=612.3MB, time=117.13 memory used=9998.5MB, alloc=636.3MB, time=119.03 memory used=10139.6MB, alloc=636.3MB, time=121.65 memory used=10348.3MB, alloc=636.3MB, time=124.05 memory used=10510.8MB, alloc=636.3MB, time=126.70 memory used=10643.4MB, alloc=636.3MB, time=127.53 memory used=10811.8MB, alloc=636.3MB, time=129.58 memory used=10989.3MB, alloc=636.3MB, time=132.13 memory used=11089.9MB, alloc=660.3MB, time=134.42 memory used=11411.3MB, alloc=684.3MB, time=139.09 memory used=11637.6MB, alloc=684.3MB, time=141.24 memory used=11833.7MB, alloc=684.3MB, time=142.89 memory used=12007.7MB, alloc=684.3MB, time=144.66 memory used=12189.5MB, alloc=684.3MB, time=146.06 memory used=12490.0MB, alloc=684.3MB, time=152.95 memory used=12652.7MB, alloc=684.3MB, time=153.99 memory used=12785.1MB, alloc=684.3MB, time=154.94 memory used=12941.8MB, alloc=684.3MB, time=155.87 memory used=13163.7MB, alloc=684.3MB, time=157.37 memory used=13440.8MB, alloc=684.3MB, time=159.68 memory used=13602.6MB, alloc=684.3MB, time=160.80 memory used=13739.4MB, alloc=684.3MB, time=161.86 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428289733 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 F := [-y - 3 x z - 2 y z - 20 x, 7 x z + 11 x y z + 18 x z + x, 3 2 2 3 6 x y - 17 y z - 18 z + 13 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 3 G := [-10 x y - 20 x y z - 2 z - 12 y, 5 x y z - 14 y z - 13 y + 7 x z, 4 2 2 10 x + 6 x y z - 11 y ] > Problem := [F,G]; 4 2 2 3 2 Problem := [[-y - 3 x z - 2 y z - 20 x, 7 x z + 11 x y z + 18 x z + x, 3 2 2 3 2 2 3 6 x y - 17 y z - 18 z + 13 x], [-10 x y - 20 x y z - 2 z - 12 y, 2 2 2 3 4 2 2 5 x y z - 14 y z - 13 y + 7 x z, 10 x + 6 x y z - 11 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.5MB, time=0.45 memory used=49.7MB, alloc=35.4MB, time=0.93 memory used=62.2MB, alloc=35.4MB, time=0.97 memory used=76.4MB, alloc=35.4MB, time=1.00 memory used=86.3MB, alloc=35.4MB, time=1.03 memory used=97.1MB, alloc=35.4MB, time=1.07 memory used=109.1MB, alloc=35.4MB, time=1.10 memory used=122.3MB, alloc=35.4MB, time=1.13 memory used=137.2MB, alloc=35.4MB, time=1.17 memory used=149.3MB, alloc=35.4MB, time=1.20 memory used=158.3MB, alloc=35.4MB, time=1.23 memory used=167.9MB, alloc=35.4MB, time=1.26 memory used=178.0MB, alloc=35.4MB, time=1.28 memory used=189.0MB, alloc=35.4MB, time=1.31 memory used=210.6MB, alloc=35.4MB, time=1.53 memory used=231.2MB, alloc=39.4MB, time=1.83 memory used=253.1MB, alloc=39.4MB, time=2.11 memory used=277.1MB, alloc=63.4MB, time=2.39 memory used=319.9MB, alloc=63.4MB, time=2.97 memory used=345.1MB, alloc=63.4MB, time=3.04 memory used=366.1MB, alloc=63.4MB, time=3.10 memory used=391.3MB, alloc=63.4MB, time=3.16 memory used=417.5MB, alloc=63.4MB, time=3.21 memory used=435.2MB, alloc=63.4MB, time=3.26 memory used=454.9MB, alloc=63.4MB, time=3.31 memory used=482.9MB, alloc=63.4MB, time=3.42 memory used=511.6MB, alloc=63.4MB, time=3.51 memory used=533.5MB, alloc=63.4MB, time=3.57 memory used=561.4MB, alloc=63.4MB, time=3.64 memory used=579.4MB, alloc=63.4MB, time=3.69 memory used=598.8MB, alloc=63.4MB, time=3.75 memory used=632.6MB, alloc=63.4MB, time=3.90 memory used=655.4MB, alloc=63.4MB, time=3.97 memory used=680.1MB, alloc=63.4MB, time=4.04 memory used=704.9MB, alloc=63.4MB, time=4.10 memory used=723.0MB, alloc=63.4MB, time=4.15 memory used=744.1MB, alloc=63.4MB, time=4.21 memory used=794.8MB, alloc=63.4MB, time=13.39 memory used=849.2MB, alloc=63.4MB, time=14.02 memory used=874.2MB, alloc=63.4MB, time=14.10 memory used=900.8MB, alloc=63.4MB, time=14.17 memory used=921.1MB, alloc=63.4MB, time=14.23 memory used=939.7MB, alloc=63.4MB, time=14.29 memory used=959.8MB, alloc=63.4MB, time=14.35 memory used=982.5MB, alloc=63.4MB, time=14.42 memory used=1007.6MB, alloc=63.4MB, time=14.48 memory used=1035.2MB, alloc=63.4MB, time=14.55 memory used=1062.9MB, alloc=63.4MB, time=14.61 memory used=1079.6MB, alloc=63.4MB, time=14.65 memory used=1095.5MB, alloc=63.4MB, time=14.70 memory used=1111.5MB, alloc=63.4MB, time=14.75 memory used=1128.0MB, alloc=63.4MB, time=14.80 memory used=1145.9MB, alloc=63.4MB, time=14.85 memory used=1164.0MB, alloc=63.4MB, time=14.90 memory used=1182.5MB, alloc=63.4MB, time=14.95 memory used=1202.0MB, alloc=63.4MB, time=14.99 memory used=1222.0MB, alloc=63.4MB, time=15.05 memory used=1242.9MB, alloc=63.4MB, time=15.10 memory used=1264.3MB, alloc=63.4MB, time=15.16 memory used=1286.6MB, alloc=63.4MB, time=15.21 memory used=1310.3MB, alloc=63.4MB, time=15.26 memory used=1335.2MB, alloc=63.4MB, time=15.31 memory used=1361.0MB, alloc=63.4MB, time=15.37 memory used=1387.5MB, alloc=63.4MB, time=15.42 memory used=1414.0MB, alloc=63.4MB, time=15.47 memory used=1451.4MB, alloc=75.3MB, time=15.55 memory used=1466.0MB, alloc=81.9MB, time=15.61 memory used=1477.7MB, alloc=81.9MB, time=15.67 memory used=1489.8MB, alloc=81.9MB, time=15.71 memory used=1501.8MB, alloc=81.9MB, time=15.76 memory used=1514.4MB, alloc=81.9MB, time=15.81 memory used=1527.3MB, alloc=81.9MB, time=15.86 memory used=1540.0MB, alloc=81.9MB, time=15.91 memory used=1553.8MB, alloc=81.9MB, time=15.96 memory used=1568.1MB, alloc=81.9MB, time=16.01 memory used=1610.3MB, alloc=81.9MB, time=16.35 memory used=1632.3MB, alloc=81.9MB, time=16.42 memory used=1655.8MB, alloc=81.9MB, time=16.60 memory used=1686.9MB, alloc=81.9MB, time=16.79 memory used=1727.2MB, alloc=81.9MB, time=17.21 memory used=1765.4MB, alloc=81.9MB, time=18.49 memory used=1804.9MB, alloc=105.9MB, time=35.39 memory used=1852.6MB, alloc=105.9MB, time=59.92 memory used=1894.7MB, alloc=105.9MB, time=79.85 memory used=1962.7MB, alloc=105.9MB, time=80.96 memory used=2003.8MB, alloc=105.9MB, time=81.09 memory used=2040.2MB, alloc=105.9MB, time=81.20 memory used=2070.7MB, alloc=105.9MB, time=81.31 memory used=2104.9MB, alloc=105.9MB, time=81.40 memory used=2142.6MB, alloc=105.9MB, time=81.50 memory used=2185.0MB, alloc=105.9MB, time=81.61 memory used=2230.5MB, alloc=105.9MB, time=81.73 memory used=2269.7MB, alloc=105.9MB, time=81.83 memory used=2296.4MB, alloc=105.9MB, time=81.91 memory used=2322.9MB, alloc=105.9MB, time=81.99 memory used=2349.0MB, alloc=105.9MB, time=82.07 memory used=2376.3MB, alloc=105.9MB, time=82.14 memory used=2406.3MB, alloc=105.9MB, time=82.23 memory used=2437.0MB, alloc=105.9MB, time=82.31 memory used=2468.2MB, alloc=105.9MB, time=82.39 memory used=2499.9MB, alloc=105.9MB, time=82.47 memory used=2534.5MB, alloc=105.9MB, time=82.55 memory used=2569.6MB, alloc=105.9MB, time=82.62 memory used=2605.2MB, alloc=105.9MB, time=82.71 memory used=2641.5MB, alloc=105.9MB, time=82.79 memory used=2680.2MB, alloc=105.9MB, time=82.86 memory used=2719.5MB, alloc=105.9MB, time=82.95 memory used=2761.7MB, alloc=105.9MB, time=83.03 memory used=2804.2MB, alloc=105.9MB, time=83.12 memory used=2847.3MB, alloc=105.9MB, time=83.21 memory used=2892.6MB, alloc=105.9MB, time=83.30 memory used=2938.8MB, alloc=105.9MB, time=83.39 memory used=2987.2MB, alloc=107.8MB, time=83.48 memory used=3002.1MB, alloc=107.8MB, time=83.53 memory used=3015.0MB, alloc=107.8MB, time=83.59 memory used=3026.6MB, alloc=107.8MB, time=83.64 memory used=3038.3MB, alloc=107.8MB, time=83.69 memory used=3048.2MB, alloc=107.8MB, time=83.74 memory used=3057.7MB, alloc=107.8MB, time=83.81 memory used=3067.3MB, alloc=107.8MB, time=83.86 memory used=3077.0MB, alloc=107.8MB, time=83.92 memory used=3086.9MB, alloc=107.8MB, time=83.97 memory used=3096.8MB, alloc=107.8MB, time=84.02 memory used=3106.7MB, alloc=107.8MB, time=84.08 memory used=3116.6MB, alloc=107.8MB, time=84.13 memory used=3126.7MB, alloc=107.8MB, time=84.18 memory used=3138.8MB, alloc=107.8MB, time=84.23 memory used=3149.1MB, alloc=107.8MB, time=84.30 memory used=3161.0MB, alloc=107.8MB, time=84.37 memory used=3173.2MB, alloc=107.8MB, time=84.43 memory used=3185.5MB, alloc=107.8MB, time=84.48 memory used=3197.7MB, alloc=107.8MB, time=84.53 memory used=3209.9MB, alloc=107.8MB, time=84.59 memory used=3222.1MB, alloc=107.8MB, time=84.64 memory used=3234.2MB, alloc=107.8MB, time=84.70 memory used=3246.3MB, alloc=107.8MB, time=84.74 memory used=3258.3MB, alloc=107.8MB, time=84.80 memory used=3270.4MB, alloc=107.8MB, time=84.86 memory used=3282.3MB, alloc=107.8MB, time=84.90 memory used=3294.3MB, alloc=107.8MB, time=84.95 memory used=3306.2MB, alloc=107.8MB, time=85.01 memory used=3318.0MB, alloc=107.8MB, time=85.06 memory used=3330.2MB, alloc=107.8MB, time=85.12 memory used=3344.0MB, alloc=107.8MB, time=85.17 memory used=3358.1MB, alloc=107.8MB, time=85.24 memory used=3372.1MB, alloc=107.8MB, time=85.29 memory used=3386.0MB, alloc=107.8MB, time=85.36 memory used=3399.8MB, alloc=107.8MB, time=85.42 memory used=3413.6MB, alloc=107.8MB, time=85.48 memory used=3427.3MB, alloc=107.8MB, time=85.55 memory used=3440.9MB, alloc=107.8MB, time=85.61 memory used=3454.4MB, alloc=107.8MB, time=85.68 memory used=3468.1MB, alloc=107.8MB, time=85.74 memory used=3483.3MB, alloc=107.8MB, time=85.79 memory used=3498.8MB, alloc=107.8MB, time=85.85 memory used=3514.0MB, alloc=107.8MB, time=85.91 memory used=3529.2MB, alloc=107.8MB, time=85.96 memory used=3544.2MB, alloc=107.8MB, time=86.02 memory used=3559.0MB, alloc=107.8MB, time=86.07 memory used=3574.1MB, alloc=107.8MB, time=86.12 memory used=3590.4MB, alloc=107.8MB, time=86.18 memory used=3606.8MB, alloc=107.8MB, time=86.24 memory used=3623.0MB, alloc=107.8MB, time=86.30 memory used=3639.0MB, alloc=107.8MB, time=86.40 memory used=3655.2MB, alloc=107.8MB, time=86.48 memory used=3672.4MB, alloc=107.8MB, time=86.57 memory used=3689.5MB, alloc=107.8MB, time=86.62 memory used=3706.7MB, alloc=107.8MB, time=86.68 memory used=3724.8MB, alloc=107.8MB, time=86.73 memory used=3742.7MB, alloc=107.8MB, time=86.81 memory used=3760.7MB, alloc=107.8MB, time=86.86 memory used=3779.0MB, alloc=107.8MB, time=86.93 memory used=3797.7MB, alloc=107.8MB, time=87.00 memory used=3816.8MB, alloc=107.8MB, time=87.06 memory used=3836.6MB, alloc=107.8MB, time=87.12 memory used=3857.4MB, alloc=107.8MB, time=87.17 memory used=3878.5MB, alloc=107.8MB, time=87.23 memory used=3899.8MB, alloc=107.8MB, time=87.29 memory used=3921.4MB, alloc=107.8MB, time=87.37 memory used=3944.1MB, alloc=107.8MB, time=87.43 memory used=4000.3MB, alloc=107.8MB, time=87.86 memory used=4090.9MB, alloc=107.8MB, time=88.73 memory used=4152.8MB, alloc=107.8MB, time=90.83 memory used=4203.6MB, alloc=107.8MB, time=91.14 memory used=4253.0MB, alloc=107.8MB, time=91.44 memory used=4321.9MB, alloc=107.8MB, time=92.12 memory used=4390.3MB, alloc=363.8MB, time=92.88 memory used=4456.4MB, alloc=387.8MB, time=93.76 memory used=4543.5MB, alloc=387.8MB, time=94.83 memory used=4594.5MB, alloc=387.8MB, time=95.23 memory used=4650.4MB, alloc=387.8MB, time=95.74 memory used=4707.9MB, alloc=387.8MB, time=96.01 memory used=4748.1MB, alloc=387.8MB, time=96.19 memory used=4792.5MB, alloc=387.8MB, time=96.35 memory used=4824.9MB, alloc=387.8MB, time=96.50 memory used=4860.4MB, alloc=387.8MB, time=96.62 memory used=4901.8MB, alloc=387.8MB, time=96.77 memory used=4966.3MB, alloc=387.8MB, time=97.13 memory used=5003.9MB, alloc=387.8MB, time=97.29 memory used=5050.8MB, alloc=387.8MB, time=97.45 memory used=5084.8MB, alloc=387.8MB, time=97.59 memory used=5119.6MB, alloc=387.8MB, time=97.72 memory used=5160.0MB, alloc=387.8MB, time=97.86 memory used=5234.6MB, alloc=387.8MB, time=109.62 memory used=5322.6MB, alloc=387.8MB, time=113.92 memory used=5361.8MB, alloc=387.8MB, time=114.09 memory used=5405.9MB, alloc=387.8MB, time=114.26 memory used=5437.8MB, alloc=387.8MB, time=114.41 memory used=5474.0MB, alloc=387.8MB, time=114.56 memory used=5514.8MB, alloc=387.8MB, time=114.71 memory used=5560.3MB, alloc=387.8MB, time=114.88 memory used=5609.4MB, alloc=387.8MB, time=115.04 memory used=5651.1MB, alloc=387.8MB, time=115.18 memory used=5679.5MB, alloc=387.8MB, time=115.30 memory used=5708.8MB, alloc=387.8MB, time=115.42 memory used=5739.5MB, alloc=387.8MB, time=115.54 memory used=5770.7MB, alloc=387.8MB, time=115.67 memory used=5802.6MB, alloc=387.8MB, time=115.82 memory used=5836.6MB, alloc=387.8MB, time=115.95 memory used=5871.3MB, alloc=387.8MB, time=116.08 memory used=5908.3MB, alloc=387.8MB, time=116.20 memory used=5946.0MB, alloc=387.8MB, time=116.33 memory used=5985.6MB, alloc=387.8MB, time=116.46 memory used=6027.6MB, alloc=387.8MB, time=116.59 memory used=6070.2MB, alloc=387.8MB, time=116.72 memory used=6114.6MB, alloc=387.8MB, time=116.88 memory used=6161.0MB, alloc=387.8MB, time=117.02 memory used=6213.3MB, alloc=387.8MB, time=117.15 memory used=6285.7MB, alloc=387.8MB, time=117.32 memory used=6461.5MB, alloc=387.8MB, time=117.80 memory used=6626.6MB, alloc=387.8MB, time=118.09 memory used=6827.8MB, alloc=387.8MB, time=118.85 memory used=6891.2MB, alloc=387.8MB, time=119.39 memory used=6936.7MB, alloc=387.8MB, time=119.58 memory used=6978.1MB, alloc=387.8MB, time=119.74 memory used=7022.3MB, alloc=387.8MB, time=119.91 memory used=7055.0MB, alloc=387.8MB, time=120.06 memory used=7090.5MB, alloc=387.8MB, time=120.19 memory used=7146.4MB, alloc=387.8MB, time=120.98 memory used=7196.8MB, alloc=387.8MB, time=121.19 memory used=7233.2MB, alloc=387.8MB, time=121.36 memory used=7277.2MB, alloc=387.8MB, time=121.52 memory used=7326.7MB, alloc=387.8MB, 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used=8353.2MB, alloc=411.8MB, time=124.99 memory used=8414.8MB, alloc=411.8MB, time=125.15 memory used=8481.0MB, alloc=411.8MB, time=125.30 memory used=8550.8MB, alloc=411.8MB, time=125.46 memory used=8724.9MB, alloc=411.8MB, time=126.45 memory used=8815.5MB, alloc=411.8MB, time=131.78 memory used=8875.7MB, alloc=411.8MB, time=131.98 memory used=8927.0MB, alloc=411.8MB, time=132.16 memory used=8989.4MB, alloc=411.8MB, time=132.38 memory used=9058.5MB, alloc=411.8MB, time=132.57 memory used=9106.9MB, alloc=411.8MB, time=132.70 memory used=9150.7MB, alloc=411.8MB, time=132.84 memory used=9198.6MB, alloc=411.8MB, time=132.98 memory used=9249.5MB, alloc=411.8MB, time=133.11 memory used=9304.3MB, alloc=411.8MB, time=133.26 memory used=9363.3MB, alloc=411.8MB, time=133.39 memory used=9427.6MB, alloc=411.8MB, time=133.56 memory used=9496.6MB, alloc=411.8MB, time=133.70 memory used=9599.5MB, alloc=411.8MB, time=133.90 memory used=9770.1MB, alloc=411.8MB, time=134.19 memory used=9907.8MB, alloc=411.8MB, time=135.12 memory used=9981.1MB, alloc=411.8MB, time=135.75 memory used=10053.3MB, alloc=411.8MB, time=135.96 memory used=10204.2MB, alloc=411.8MB, time=137.40 memory used=10313.9MB, alloc=411.8MB, time=137.60 memory used=10521.0MB, alloc=411.8MB, time=137.98 memory used=10695.7MB, alloc=411.8MB, time=140.08 memory used=10879.3MB, alloc=411.8MB, time=146.06 memory used=10933.2MB, alloc=411.8MB, time=146.26 memory used=10991.9MB, alloc=411.8MB, time=146.44 memory used=11041.2MB, alloc=411.8MB, time=146.59 memory used=11089.6MB, alloc=411.8MB, time=146.75 memory used=11155.5MB, alloc=411.8MB, time=147.28 memory used=11226.7MB, alloc=411.8MB, time=147.85 memory used=11295.5MB, alloc=411.8MB, time=148.06 memory used=11457.1MB, alloc=411.8MB, time=151.23 memory used=11512.0MB, alloc=411.8MB, time=151.42 memory used=11566.8MB, alloc=411.8MB, time=151.61 memory used=11626.2MB, alloc=411.8MB, time=151.78 memory used=11668.3MB, alloc=411.8MB, time=151.92 memory used=11717.9MB, alloc=411.8MB, time=152.07 memory used=11830.9MB, alloc=411.8MB, time=152.97 memory used=11974.5MB, alloc=411.8MB, time=154.77 memory used=12085.4MB, alloc=411.8MB, time=155.54 memory used=12180.3MB, alloc=411.8MB, time=156.09 memory used=12287.6MB, alloc=435.8MB, time=156.67 memory used=12423.8MB, alloc=435.8MB, time=157.56 memory used=12564.5MB, alloc=435.8MB, time=158.49 memory used=12701.9MB, alloc=435.8MB, time=159.59 memory used=12844.6MB, alloc=435.8MB, time=160.78 memory used=12986.2MB, alloc=435.8MB, time=162.08 memory used=13126.3MB, alloc=435.8MB, time=163.70 memory used=13272.2MB, alloc=435.8MB, time=165.32 memory used=13411.0MB, alloc=435.8MB, time=167.23 memory used=13555.1MB, alloc=435.8MB, time=169.08 memory used=13694.8MB, alloc=435.8MB, time=171.27 memory used=13840.2MB, alloc=435.8MB, time=173.37 memory used=13981.7MB, alloc=435.8MB, time=175.76 memory used=14126.5MB, alloc=435.8MB, time=177.93 memory used=14328.5MB, alloc=435.8MB, time=181.93 memory used=14436.7MB, alloc=435.8MB, time=183.26 memory used=14581.5MB, alloc=435.8MB, time=184.45 memory used=14719.4MB, alloc=435.8MB, time=185.56 memory used=14859.1MB, alloc=435.8MB, time=186.50 memory used=14997.5MB, alloc=435.8MB, time=187.58 memory used=15136.4MB, alloc=435.8MB, time=188.72 memory used=15271.0MB, alloc=435.8MB, time=190.01 memory used=15413.5MB, alloc=435.8MB, time=191.35 memory used=15550.1MB, alloc=435.8MB, time=192.89 memory used=15685.6MB, alloc=435.8MB, time=194.46 memory used=15828.5MB, alloc=435.8MB, time=196.44 memory used=15968.4MB, alloc=435.8MB, time=198.40 memory used=16106.6MB, alloc=435.8MB, time=200.41 memory used=16243.9MB, alloc=435.8MB, time=202.72 memory used=16386.5MB, alloc=435.8MB, time=204.96 memory used=16530.4MB, alloc=435.8MB, time=207.17 memory used=16659.2MB, alloc=435.8MB, time=211.21 memory used=16725.9MB, alloc=435.8MB, time=211.42 memory used=16810.8MB, alloc=435.8MB, time=212.36 memory used=16985.0MB, alloc=435.8MB, time=215.81 memory used=17048.3MB, alloc=435.8MB, time=216.03 memory used=17117.8MB, alloc=435.8MB, time=216.24 memory used=17170.0MB, alloc=435.8MB, time=216.42 memory used=17236.9MB, alloc=435.8MB, time=216.60 memory used=17408.6MB, alloc=435.8MB, time=219.45 memory used=17473.6MB, alloc=435.8MB, time=219.67 memory used=17538.0MB, alloc=435.8MB, time=219.87 memory used=17591.9MB, alloc=435.8MB, time=220.04 memory used=17656.1MB, alloc=435.8MB, time=220.22 memory used=17744.1MB, alloc=435.8MB, time=220.64 memory used=17826.7MB, alloc=435.8MB, time=221.49 memory used=17907.2MB, alloc=435.8MB, time=221.74 memory used=18077.8MB, alloc=435.8MB, time=223.93 memory used=18195.1MB, alloc=435.8MB, time=224.77 memory used=18335.9MB, alloc=435.8MB, time=225.46 memory used=18510.4MB, alloc=435.8MB, time=227.73 memory used=18648.7MB, alloc=435.8MB, time=228.44 memory used=18776.9MB, alloc=435.8MB, time=229.09 |\^/| 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(); 1428290033 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 2 3 F := [-7 y z + 2 y z + 4 x y, 19 x y + 11 x y z + 12 x y z + x , 4 2 3 2 -6 x + 8 x y z - y z - 7 x y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 3 4 G := [20 x y z - z - 9 x y + x, -19 x y + 13 z + 13 x y z + 3 y, 4 2 2 3 20 x + 9 x z - 4 x y + 5 x y] > Problem := [F,G]; 3 3 2 3 2 2 3 Problem := [[-7 y z + 2 y z + 4 x y, 19 x y + 11 x y z + 12 x y z + x , 4 2 3 2 2 4 2 -6 x + 8 x y z - y z - 7 x y ], [20 x y z - z - 9 x y + x, 3 4 4 2 2 3 -19 x y + 13 z + 13 x y z + 3 y, 20 x + 9 x z - 4 x y + 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=0.18 memory used=32.1MB, alloc=36.3MB, time=0.54 memory used=56.1MB, alloc=37.0MB, time=0.72 memory used=67.1MB, alloc=37.0MB, time=0.75 memory used=84.9MB, alloc=37.0MB, time=0.83 memory used=97.4MB, alloc=37.0MB, time=0.87 memory used=129.6MB, alloc=37.0MB, time=1.54 memory used=159.9MB, alloc=37.0MB, time=1.80 memory used=174.2MB, alloc=37.0MB, time=1.84 memory used=187.9MB, alloc=37.0MB, time=1.88 memory used=197.1MB, alloc=37.0MB, time=1.92 memory used=207.4MB, alloc=37.0MB, time=1.96 memory used=218.8MB, alloc=37.0MB, time=1.99 memory used=231.3MB, alloc=37.0MB, time=2.03 memory used=245.5MB, alloc=37.0MB, time=2.07 memory used=257.7MB, alloc=61.0MB, time=2.11 memory used=278.9MB, alloc=61.0MB, time=2.17 memory used=302.3MB, alloc=61.0MB, time=2.22 memory used=328.2MB, alloc=61.0MB, time=2.28 memory used=357.3MB, alloc=61.0MB, time=2.34 memory used=389.7MB, alloc=61.0MB, time=2.39 memory used=424.8MB, alloc=61.0MB, time=2.46 memory used=457.2MB, alloc=83.8MB, time=2.54 memory used=470.4MB, alloc=83.8MB, time=2.58 memory used=483.6MB, alloc=83.8MB, time=2.62 memory used=497.8MB, alloc=83.8MB, time=2.66 memory used=511.8MB, alloc=83.8MB, time=2.71 memory used=526.5MB, alloc=83.8MB, time=2.75 memory used=542.2MB, alloc=83.8MB, time=2.81 memory used=558.4MB, alloc=83.8MB, time=2.85 memory used=575.6MB, alloc=83.8MB, time=2.90 memory used=593.9MB, alloc=83.8MB, time=2.95 memory used=663.8MB, alloc=83.8MB, time=3.68 memory used=710.8MB, alloc=83.8MB, time=4.48 memory used=739.0MB, alloc=83.8MB, time=4.57 memory used=758.4MB, alloc=83.8MB, time=4.65 memory used=779.6MB, alloc=83.8MB, time=4.74 memory used=805.3MB, alloc=83.8MB, time=4.83 memory used=833.3MB, alloc=83.8MB, time=4.92 memory used=850.4MB, alloc=107.8MB, time=5.01 memory used=879.5MB, alloc=107.8MB, time=5.12 memory used=910.1MB, alloc=107.8MB, time=5.24 memory used=943.1MB, alloc=107.8MB, time=5.36 memory used=980.0MB, alloc=107.8MB, time=5.48 memory used=1019.4MB, alloc=107.8MB, time=5.60 memory used=1064.4MB, alloc=107.8MB, time=5.72 memory used=1111.0MB, alloc=107.8MB, time=5.83 memory used=1161.7MB, alloc=107.8MB, time=5.96 memory used=1190.4MB, alloc=107.8MB, time=6.04 memory used=1216.9MB, alloc=107.8MB, time=6.12 memory used=1243.4MB, alloc=107.8MB, time=6.19 memory used=1270.1MB, alloc=107.8MB, time=6.27 memory used=1296.9MB, alloc=107.8MB, time=6.35 memory used=1324.6MB, alloc=107.8MB, time=6.43 memory used=1355.3MB, alloc=107.8MB, time=6.52 memory used=1386.7MB, alloc=107.8MB, time=6.60 memory used=1418.2MB, alloc=107.8MB, time=6.68 memory used=1450.6MB, alloc=107.8MB, time=6.76 memory used=1485.2MB, alloc=107.8MB, time=6.84 memory used=1520.5MB, alloc=107.8MB, time=6.93 memory used=1557.0MB, alloc=107.8MB, time=7.02 memory used=1595.5MB, alloc=107.8MB, time=7.11 memory used=1636.5MB, alloc=107.8MB, time=7.19 memory used=1678.9MB, alloc=107.8MB, time=7.28 memory used=1723.4MB, alloc=107.8MB, time=7.37 memory used=1771.2MB, alloc=107.8MB, time=7.46 memory used=1821.5MB, alloc=107.8MB, time=7.55 memory used=1863.0MB, alloc=107.8MB, time=7.64 memory used=1932.4MB, alloc=107.8MB, time=8.54 memory used=1968.8MB, alloc=107.8MB, time=8.68 memory used=2015.3MB, alloc=107.8MB, time=8.84 memory used=2049.9MB, alloc=107.8MB, time=8.95 memory used=2078.2MB, alloc=107.8MB, time=9.06 memory used=2109.2MB, alloc=107.8MB, time=9.16 memory used=2142.6MB, alloc=107.8MB, time=9.28 memory used=2179.8MB, alloc=107.8MB, time=9.39 memory used=2219.3MB, alloc=107.8MB, time=9.50 memory used=2261.3MB, alloc=107.8MB, time=9.62 memory used=2307.1MB, alloc=107.8MB, time=9.73 memory used=2354.3MB, alloc=107.8MB, time=9.86 memory used=2382.5MB, alloc=107.8MB, time=9.95 memory used=2405.7MB, alloc=107.8MB, time=10.03 memory used=2431.1MB, alloc=107.8MB, time=10.11 memory used=2457.7MB, alloc=107.8MB, time=10.19 memory used=2484.4MB, alloc=107.8MB, time=10.27 memory used=2511.3MB, alloc=107.8MB, time=10.36 memory used=2539.3MB, alloc=107.8MB, time=10.44 memory used=2569.8MB, alloc=107.8MB, time=10.53 memory used=2601.2MB, alloc=107.8MB, time=10.61 memory used=2632.6MB, alloc=107.8MB, time=10.69 memory used=2665.3MB, alloc=107.8MB, time=10.78 memory used=2699.3MB, alloc=107.8MB, time=10.86 memory used=2735.4MB, alloc=107.8MB, time=10.95 memory used=2773.4MB, alloc=107.8MB, time=11.04 memory used=2812.7MB, alloc=107.8MB, time=11.13 memory used=2853.3MB, alloc=107.8MB, time=11.21 memory used=2897.7MB, alloc=107.8MB, time=11.30 memory used=2944.2MB, alloc=107.8MB, time=11.40 memory used=2992.2MB, alloc=107.8MB, time=11.48 memory used=3044.7MB, alloc=107.8MB, time=11.58 memory used=3055.5MB, alloc=107.8MB, time=11.64 memory used=3135.9MB, alloc=107.8MB, time=33.43 memory used=3182.0MB, alloc=107.8MB, time=67.66 memory used=3226.9MB, alloc=107.8MB, time=112.81 memory used=3271.5MB, alloc=131.8MB, time=159.64 memory used=3314.6MB, alloc=131.8MB, time=210.64 |\^/| 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(); 1428290333 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 3 2 F := [10 x z + x y z + 16 y - 17 y , -3 y - 4 z + 11 z - 13 z, 2 2 2 2 -17 x y + 6 x z + 12 y z + 16 y z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 2 G := [-y z + 14 x y + 14 x - 5 z, -14 y z - 7 y + y z - 18 x , 3 2 2 3 3 -9 x z - 14 x z - 19 x y - 4 x ] > Problem := [F,G]; 2 2 2 3 2 3 3 2 Problem := [[10 x z + x y z + 16 y - 17 y , -3 y - 4 z + 11 z - 13 z, 2 2 2 2 3 2 -17 x y + 6 x z + 12 y z + 16 y z ], [-y z + 14 x y + 14 x - 5 z, 2 2 3 2 2 3 2 2 3 3 -14 y z - 7 y + y z - 18 x , -9 x z - 14 x z - 19 x 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=33.7MB, alloc=44.3MB, time=0.53 memory used=66.6MB, alloc=44.3MB, time=0.91 memory used=102.0MB, alloc=44.3MB, time=1.52 memory used=116.3MB, alloc=44.3MB, time=1.57 memory used=133.0MB, alloc=44.3MB, time=1.62 memory used=151.2MB, alloc=44.3MB, time=1.67 memory used=162.4MB, alloc=44.3MB, time=1.70 memory used=175.2MB, alloc=44.3MB, time=1.75 memory used=190.1MB, alloc=44.3MB, time=1.79 memory used=219.8MB, alloc=44.3MB, time=2.26 memory used=234.2MB, alloc=44.3MB, time=2.30 memory used=251.7MB, alloc=44.3MB, time=2.35 memory used=263.3MB, alloc=44.3MB, time=2.39 memory used=276.6MB, alloc=44.3MB, time=2.43 memory used=291.9MB, alloc=44.3MB, time=2.47 memory used=308.6MB, alloc=44.3MB, time=2.51 memory used=323.5MB, alloc=44.3MB, time=2.55 memory used=338.5MB, alloc=44.3MB, time=2.59 memory used=349.6MB, alloc=44.3MB, time=2.62 memory used=361.3MB, alloc=44.3MB, time=2.66 memory used=374.2MB, alloc=44.3MB, time=2.69 memory used=388.6MB, alloc=44.3MB, time=2.73 memory used=411.5MB, alloc=44.3MB, time=2.87 memory used=431.2MB, alloc=44.3MB, time=2.94 memory used=446.8MB, alloc=44.3MB, time=2.99 memory used=466.6MB, alloc=68.3MB, time=5.59 memory used=749.8MB, alloc=71.0MB, time=14.82 memory used=946.4MB, alloc=79.0MB, time=17.69 memory used=1032.2MB, alloc=79.2MB, time=21.82 memory used=1204.1MB, alloc=79.2MB, time=23.58 memory used=1231.2MB, alloc=107.1MB, time=23.93 memory used=1284.8MB, alloc=103.2MB, time=24.16 memory used=1336.7MB, alloc=103.2MB, time=24.39 memory used=1385.4MB, alloc=103.2MB, time=24.53 memory used=1431.0MB, alloc=103.2MB, time=24.71 memory used=1481.5MB, alloc=103.2MB, time=24.89 memory used=1534.5MB, alloc=103.2MB, time=25.01 memory used=1568.0MB, alloc=103.2MB, time=25.13 memory used=1606.6MB, alloc=103.2MB, time=25.24 memory used=1650.9MB, alloc=103.2MB, time=25.35 memory used=1701.0MB, alloc=103.2MB, time=25.47 memory used=1751.1MB, alloc=103.2MB, time=25.58 memory used=1781.4MB, alloc=103.2MB, time=25.66 memory used=1815.4MB, alloc=103.2MB, time=25.74 memory used=1858.4MB, alloc=103.2MB, time=26.05 memory used=1911.9MB, alloc=103.2MB, time=26.43 memory used=1943.6MB, alloc=103.2MB, time=26.54 memory used=1974.7MB, alloc=103.2MB, time=26.66 memory used=2006.8MB, alloc=103.2MB, time=26.75 memory used=2039.0MB, alloc=103.2MB, time=26.86 memory used=2072.4MB, alloc=103.2MB, time=26.96 memory used=2108.8MB, alloc=103.2MB, time=27.07 memory used=2146.1MB, alloc=103.2MB, time=27.17 memory used=2184.2MB, alloc=103.2MB, time=27.27 memory used=2223.4MB, alloc=103.2MB, time=27.39 memory used=2265.6MB, alloc=103.2MB, time=27.50 memory used=2308.7MB, alloc=103.2MB, time=27.62 memory used=2352.7MB, alloc=103.2MB, time=27.74 memory used=2399.8MB, alloc=103.2MB, time=27.85 memory used=2447.6MB, alloc=103.2MB, time=27.96 memory used=2496.4MB, alloc=103.2MB, time=28.08 memory used=2536.4MB, alloc=103.2MB, time=28.18 memory used=2563.8MB, alloc=103.2MB, time=28.25 memory used=2588.7MB, alloc=103.2MB, time=28.33 memory used=2612.6MB, alloc=103.2MB, time=28.40 memory used=2637.5MB, alloc=103.2MB, time=28.47 memory used=2662.8MB, alloc=103.2MB, time=28.55 memory used=2688.2MB, alloc=103.2MB, time=28.62 memory used=2713.8MB, alloc=103.2MB, time=28.70 memory used=2739.5MB, alloc=103.2MB, time=28.80 memory used=2767.9MB, alloc=103.2MB, time=28.88 memory used=2796.4MB, alloc=103.2MB, time=28.96 memory used=2825.1MB, alloc=103.2MB, time=29.04 memory used=2853.8MB, alloc=103.2MB, time=29.12 memory used=2882.7MB, alloc=103.2MB, time=29.19 memory used=2911.6MB, alloc=103.2MB, time=29.28 memory used=2940.6MB, alloc=103.2MB, time=29.36 memory used=2969.8MB, alloc=103.2MB, time=29.44 memory used=3001.7MB, alloc=103.2MB, time=29.53 memory used=3033.6MB, alloc=103.2MB, time=29.60 memory used=3065.7MB, alloc=103.2MB, time=29.68 memory used=3097.7MB, alloc=103.2MB, time=29.76 memory used=3129.8MB, alloc=103.2MB, time=29.84 memory used=3162.0MB, alloc=103.2MB, time=29.92 memory used=3196.9MB, alloc=103.2MB, time=30.00 memory used=3231.8MB, alloc=103.2MB, time=30.09 memory used=3266.7MB, alloc=103.2MB, time=30.16 memory used=3301.5MB, alloc=103.2MB, time=30.24 memory used=3336.3MB, alloc=103.2MB, time=30.32 memory used=3373.8MB, alloc=103.2MB, time=30.40 memory used=3411.3MB, alloc=103.2MB, time=30.49 memory used=3448.6MB, alloc=103.2MB, time=30.58 memory used=3486.0MB, alloc=103.2MB, time=30.66 memory used=3525.8MB, alloc=103.2MB, time=30.75 memory used=3565.5MB, alloc=103.2MB, time=30.83 memory used=3605.0MB, alloc=103.2MB, time=30.91 memory used=3644.2MB, alloc=103.2MB, time=30.99 memory used=3685.9MB, alloc=103.2MB, time=31.08 memory used=3727.4MB, alloc=103.2MB, time=31.17 memory used=3771.2MB, alloc=103.2MB, time=31.26 memory used=3814.6MB, alloc=103.2MB, time=31.34 memory used=3857.7MB, alloc=103.2MB, time=31.43 memory used=3902.8MB, alloc=103.2MB, time=31.52 memory used=3947.3MB, alloc=103.2MB, time=31.60 memory used=3993.9MB, alloc=103.2MB, time=31.68 memory used=4042.2MB, alloc=103.2MB, time=31.77 memory used=4089.8MB, alloc=103.2MB, time=31.86 memory used=4138.9MB, alloc=103.2MB, time=31.94 memory used=4195.0MB, alloc=105.9MB, time=32.04 memory used=4211.4MB, alloc=115.8MB, time=32.10 memory used=4223.8MB, alloc=115.8MB, time=32.16 memory used=4234.6MB, alloc=115.8MB, time=32.21 memory used=4244.1MB, alloc=115.8MB, time=32.26 memory used=4252.0MB, alloc=115.8MB, time=32.30 memory used=4260.3MB, alloc=115.8MB, time=32.35 memory used=4268.8MB, alloc=115.8MB, time=32.41 memory used=4277.2MB, alloc=115.8MB, time=32.47 memory used=4285.5MB, alloc=115.8MB, time=32.53 memory used=4293.9MB, alloc=115.8MB, time=32.64 memory used=4302.1MB, alloc=115.8MB, time=32.72 memory used=4310.4MB, alloc=115.8MB, time=32.77 memory used=4318.6MB, alloc=115.8MB, time=32.82 memory used=4326.7MB, alloc=115.8MB, time=32.86 memory used=4334.8MB, alloc=115.8MB, time=32.93 memory used=4342.8MB, alloc=115.8MB, time=32.98 memory used=4350.9MB, alloc=115.8MB, time=33.02 memory used=4358.9MB, alloc=115.8MB, time=33.07 memory used=4368.7MB, alloc=115.8MB, time=33.11 memory used=4378.6MB, alloc=115.8MB, time=33.16 memory used=4388.3MB, alloc=115.8MB, time=33.22 memory used=4398.0MB, alloc=115.8MB, time=33.27 memory used=4407.6MB, alloc=115.8MB, time=33.33 memory used=4417.2MB, alloc=115.8MB, time=33.38 memory used=4426.6MB, alloc=115.8MB, time=33.43 memory used=4436.0MB, alloc=115.8MB, time=33.49 memory used=4445.3MB, alloc=115.8MB, time=33.55 memory used=4454.6MB, alloc=115.8MB, time=33.60 memory used=4463.7MB, alloc=115.8MB, time=33.66 memory used=4472.8MB, alloc=115.8MB, time=33.72 memory used=4481.8MB, alloc=115.8MB, time=33.78 memory used=4492.5MB, alloc=115.8MB, time=33.84 memory used=4503.1MB, alloc=115.8MB, time=33.91 memory used=4513.5MB, alloc=115.8MB, time=33.97 memory used=4523.9MB, alloc=115.8MB, time=34.02 memory used=4534.1MB, alloc=115.8MB, time=34.08 memory used=4544.2MB, alloc=115.8MB, time=34.14 memory used=4554.2MB, alloc=115.8MB, time=34.19 memory used=4564.0MB, alloc=115.8MB, time=34.25 memory used=4573.8MB, alloc=115.8MB, time=34.31 memory used=4585.0MB, alloc=115.8MB, time=34.37 memory used=4596.0MB, alloc=115.8MB, time=34.41 memory used=4606.8MB, alloc=115.8MB, time=34.47 memory used=4617.5MB, alloc=115.8MB, time=34.52 memory used=4628.0MB, alloc=115.8MB, time=34.57 memory used=4638.4MB, alloc=115.8MB, time=34.62 memory used=4649.9MB, alloc=115.8MB, time=34.73 memory used=4661.2MB, alloc=115.8MB, time=34.77 memory used=4672.2MB, alloc=115.8MB, time=34.82 memory used=4683.1MB, alloc=115.8MB, time=34.87 memory used=4695.0MB, alloc=115.8MB, time=34.92 memory used=4706.7MB, alloc=115.8MB, time=34.98 memory used=4719.1MB, alloc=115.8MB, time=35.03 memory used=4731.2MB, alloc=115.8MB, time=35.09 memory used=4743.9MB, alloc=115.8MB, time=35.15 memory used=4756.2MB, alloc=115.8MB, time=35.22 memory used=4769.0MB, alloc=115.8MB, time=35.30 memory used=4782.2MB, alloc=115.8MB, time=35.36 memory used=4795.5MB, alloc=115.8MB, time=35.42 memory used=4808.8MB, alloc=115.8MB, time=35.47 memory used=4822.6MB, alloc=115.8MB, time=35.53 memory used=4836.5MB, alloc=115.8MB, time=35.59 memory used=4850.9MB, alloc=115.8MB, time=35.65 memory used=4866.0MB, alloc=115.8MB, time=35.70 memory used=4939.6MB, alloc=115.8MB, time=36.41 memory used=4990.2MB, alloc=115.8MB, time=36.65 memory used=5033.4MB, alloc=115.8MB, time=36.77 memory used=5099.6MB, alloc=115.8MB, time=37.42 memory used=5166.9MB, alloc=115.8MB, time=39.51 memory used=5232.6MB, alloc=115.8MB, time=41.69 memory used=5268.0MB, alloc=115.8MB, time=41.79 memory used=5321.3MB, alloc=115.8MB, time=41.98 memory used=5396.2MB, alloc=115.8MB, time=45.96 memory used=5435.1MB, alloc=115.8MB, time=46.07 memory used=5484.6MB, alloc=115.8MB, time=46.28 memory used=5526.6MB, alloc=115.8MB, time=46.41 memory used=5576.1MB, alloc=115.8MB, time=46.61 memory used=5619.9MB, alloc=115.8MB, time=46.74 memory used=5671.7MB, alloc=115.8MB, time=48.61 memory used=5741.3MB, alloc=115.8MB, time=59.38 memory used=5795.7MB, alloc=115.8MB, time=59.56 memory used=5827.3MB, alloc=115.8MB, time=59.66 memory used=5869.2MB, alloc=115.8MB, time=59.77 memory used=5899.4MB, alloc=115.8MB, time=59.84 memory used=5940.9MB, alloc=115.8MB, time=60.07 memory used=5971.0MB, alloc=115.8MB, time=60.22 memory used=6020.2MB, alloc=115.8MB, time=60.32 memory used=6078.1MB, alloc=115.8MB, time=62.20 memory used=6151.8MB, alloc=115.8MB, time=67.97 memory used=6191.6MB, alloc=115.8MB, time=68.09 memory used=6228.1MB, alloc=115.8MB, time=68.19 memory used=6276.3MB, alloc=115.8MB, time=68.54 memory used=6345.6MB, alloc=115.8MB, time=69.23 memory used=6417.6MB, alloc=115.8MB, time=70.05 memory used=6482.4MB, alloc=139.8MB, time=71.93 memory used=6530.0MB, alloc=139.8MB, time=72.09 memory used=6590.6MB, alloc=139.8MB, time=72.25 memory used=6638.7MB, alloc=139.8MB, time=72.40 memory used=6676.8MB, alloc=139.8MB, time=72.53 memory used=6719.1MB, alloc=139.8MB, time=72.67 memory used=6766.4MB, alloc=139.8MB, time=72.81 memory used=6819.2MB, alloc=139.8MB, time=72.94 memory used=6880.0MB, alloc=139.8MB, time=73.08 memory used=6923.7MB, alloc=139.8MB, time=76.12 memory used=6982.3MB, alloc=139.8MB, time=77.38 memory used=7022.3MB, alloc=139.8MB, time=77.53 memory used=7058.2MB, alloc=139.8MB, time=77.66 memory used=7096.8MB, alloc=139.8MB, time=77.80 memory used=7137.7MB, alloc=139.8MB, time=77.95 memory used=7181.8MB, alloc=139.8MB, time=78.10 memory used=7229.0MB, alloc=139.8MB, time=78.25 memory used=7279.4MB, alloc=139.8MB, time=78.38 memory used=7331.2MB, alloc=139.8MB, time=78.54 memory used=7386.0MB, alloc=139.8MB, time=78.67 memory used=7445.6MB, alloc=139.8MB, time=78.82 memory used=7499.0MB, alloc=139.8MB, time=78.94 memory used=7532.4MB, alloc=139.8MB, time=79.05 memory used=7564.4MB, alloc=139.8MB, time=79.16 memory used=7597.3MB, alloc=139.8MB, time=79.27 memory used=7630.5MB, alloc=139.8MB, time=79.37 memory used=7663.8MB, alloc=139.8MB, time=79.47 memory used=7698.9MB, alloc=139.8MB, time=79.58 memory used=7734.2MB, alloc=139.8MB, time=79.70 memory used=7771.2MB, alloc=139.8MB, time=79.80 memory used=7809.9MB, alloc=139.8MB, time=79.91 memory used=7848.5MB, alloc=139.8MB, time=80.02 memory used=7888.8MB, alloc=139.8MB, time=80.13 memory used=7930.5MB, alloc=139.8MB, time=80.24 memory used=7973.7MB, alloc=139.8MB, time=80.36 memory used=8018.1MB, alloc=139.8MB, time=80.48 memory used=8063.6MB, alloc=139.8MB, time=80.60 memory used=8110.0MB, alloc=139.8MB, time=80.72 memory used=8157.2MB, alloc=139.8MB, time=80.83 memory used=8206.4MB, alloc=139.8MB, time=80.95 memory used=8257.2MB, alloc=139.8MB, time=81.06 memory used=8310.5MB, alloc=139.8MB, time=81.18 memory used=8365.6MB, alloc=139.8MB, time=81.29 memory used=8422.6MB, alloc=139.8MB, time=81.41 memory used=8482.0MB, alloc=139.8MB, time=81.53 memory used=8526.0MB, alloc=139.8MB, time=81.64 memory used=8536.6MB, alloc=139.8MB, time=81.71 memory used=8546.7MB, alloc=139.8MB, time=81.78 memory used=8557.5MB, alloc=139.8MB, time=81.85 memory used=8568.3MB, alloc=139.8MB, time=81.93 memory used=8579.2MB, alloc=139.8MB, time=82.04 memory used=8590.9MB, alloc=139.8MB, time=82.12 memory used=8602.7MB, alloc=139.8MB, time=82.19 memory used=8663.6MB, alloc=139.8MB, time=82.66 memory used=8715.7MB, alloc=139.8MB, time=82.82 memory used=8758.6MB, alloc=139.8MB, time=82.96 memory used=8811.2MB, alloc=139.8MB, time=83.09 memory used=8859.7MB, alloc=163.8MB, time=106.15 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428290633 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 3 3 2 F := [17 x y z + 15 z + 3 x z - 15 z , -15 x z - 2 x y z + 16 x y z + 15 z, 3 2 -16 x z + 6 y z - 12 x + 2 y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 2 2 G := [11 y z - 20 x y + 18 y z - 11 z , -8 x y z - y z - 14 x z - 12 x , 2 2 19 x y z + 6 x z + 14 x y - 11 x z] > Problem := [F,G]; 2 4 2 3 Problem := [[17 x y z + 15 z + 3 x z - 15 z , 3 2 3 2 -15 x z - 2 x y z + 16 x y z + 15 z, -16 x z + 6 y z - 12 x + 2 y], [ 3 2 2 2 2 3 2 2 11 y z - 20 x y + 18 y z - 11 z , -8 x y z - y z - 14 x z - 12 x , 2 2 19 x y z + 6 x z + 14 x y - 11 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.6MB, alloc=32.3MB, time=0.49 memory used=45.4MB, alloc=32.3MB, time=0.78 memory used=64.6MB, alloc=56.3MB, time=1.06 memory used=105.4MB, alloc=60.3MB, time=1.66 memory used=143.6MB, alloc=60.3MB, time=2.05 memory used=166.5MB, alloc=60.3MB, time=2.15 memory used=192.3MB, alloc=60.3MB, time=2.61 memory used=218.6MB, alloc=60.3MB, time=2.83 memory used=240.5MB, alloc=60.3MB, time=2.92 memory used=276.6MB, alloc=78.2MB, time=3.07 memory used=300.7MB, alloc=78.2MB, time=3.14 memory used=333.8MB, alloc=78.2MB, time=3.45 memory used=372.9MB, alloc=78.2MB, time=4.00 memory used=408.1MB, alloc=102.2MB, time=4.50 memory used=443.1MB, alloc=102.2MB, time=5.01 memory used=503.9MB, alloc=102.2MB, time=5.79 memory used=559.8MB, alloc=102.2MB, time=6.49 memory used=615.0MB, alloc=102.2MB, time=7.01 memory used=680.0MB, alloc=102.2MB, time=7.79 memory used=743.0MB, alloc=126.2MB, time=8.71 memory used=824.3MB, alloc=382.2MB, time=9.92 memory used=912.5MB, alloc=382.2MB, time=11.13 memory used=959.7MB, alloc=382.2MB, time=11.50 memory used=1000.8MB, alloc=382.2MB, time=11.80 memory used=1040.3MB, alloc=382.2MB, time=12.06 memory used=1091.6MB, alloc=406.2MB, time=24.87 memory used=1154.6MB, alloc=406.2MB, time=31.45 memory used=1206.0MB, alloc=406.2MB, time=31.63 memory used=1258.1MB, alloc=406.2MB, time=31.79 memory used=1329.3MB, alloc=406.2MB, time=32.36 memory used=1379.6MB, alloc=406.2MB, time=32.56 memory used=1442.2MB, alloc=406.2MB, time=33.06 memory used=1494.3MB, alloc=406.2MB, time=33.25 memory used=1561.4MB, alloc=406.2MB, time=38.67 memory used=1624.6MB, alloc=406.2MB, time=59.25 memory used=1693.6MB, alloc=406.2MB, time=70.21 memory used=1747.3MB, alloc=406.2MB, time=70.41 memory used=1791.8MB, alloc=406.2MB, time=70.56 memory used=1851.2MB, alloc=406.2MB, time=70.72 memory used=1942.5MB, alloc=406.2MB, time=72.34 memory used=1988.2MB, alloc=406.2MB, time=72.53 memory used=2034.3MB, alloc=406.2MB, time=72.70 memory used=2088.6MB, alloc=406.2MB, time=72.88 memory used=2151.8MB, alloc=406.2MB, time=73.10 memory used=2194.4MB, alloc=406.2MB, time=73.26 memory used=2232.2MB, alloc=406.2MB, time=73.40 memory used=2272.4MB, alloc=406.2MB, time=73.54 memory used=2316.3MB, alloc=406.2MB, time=73.70 memory used=2364.9MB, alloc=406.2MB, time=73.86 memory used=2420.4MB, alloc=406.2MB, time=74.01 memory used=2485.4MB, alloc=406.2MB, time=74.37 memory used=2553.6MB, alloc=406.2MB, time=74.62 memory used=2611.9MB, alloc=406.2MB, time=76.06 memory used=2666.1MB, alloc=406.2MB, time=76.27 memory used=2709.9MB, alloc=406.2MB, time=76.46 memory used=2762.8MB, alloc=406.2MB, time=76.65 memory used=2824.8MB, alloc=406.2MB, time=76.86 memory used=2876.9MB, alloc=406.2MB, time=77.04 memory used=2913.8MB, alloc=406.2MB, time=77.20 memory used=2954.1MB, alloc=406.2MB, time=77.35 memory used=2998.4MB, alloc=406.2MB, time=77.50 memory used=3047.9MB, alloc=406.2MB, time=77.66 memory used=3102.7MB, alloc=406.2MB, time=77.82 |\^/| 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(); 1428290933 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 2 2 F := [18 x + 3 y - 20 y - 6 y, -18 x + 16 x y + 20 y z + 20 x, 4 2 -2 z + 11 y z - 9 x y + 14 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 3 4 2 G := [-2 x y + 5 y z - 19 y z + 11 y, -2 x z - 18 y z - 3 z + 17 x z, 3 4 2 2 -5 x y - 14 z + 10 x y + 17 y z ] > Problem := [F,G]; 3 3 2 4 2 2 Problem := [[18 x + 3 y - 20 y - 6 y, -18 x + 16 x y + 20 y z + 20 x, 4 2 3 2 2 3 -2 z + 11 y z - 9 x y + 14 y z], [-2 x y + 5 y z - 19 y z + 11 y, 3 3 4 2 3 4 2 2 -2 x z - 18 y z - 3 z + 17 x z, -5 x y - 14 z + 10 x y + 17 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.50 memory used=47.5MB, alloc=32.3MB, time=0.79 memory used=66.9MB, alloc=56.3MB, time=1.07 memory used=112.3MB, alloc=68.3MB, time=1.60 memory used=196.4MB, alloc=68.4MB, time=3.07 memory used=263.0MB, alloc=68.4MB, time=3.74 memory used=295.6MB, alloc=68.4MB, time=3.85 memory used=319.5MB, alloc=68.4MB, time=3.93 memory used=364.3MB, alloc=68.4MB, time=4.15 memory used=390.7MB, alloc=68.4MB, time=4.24 memory used=416.5MB, alloc=68.4MB, time=4.35 memory used=451.5MB, alloc=92.4MB, time=7.48 memory used=490.9MB, alloc=92.4MB, time=7.67 memory used=524.7MB, alloc=92.4MB, time=7.78 memory used=561.4MB, alloc=92.4MB, time=7.89 memory used=601.6MB, alloc=92.4MB, time=8.02 memory used=644.9MB, alloc=92.4MB, time=8.13 memory used=691.5MB, alloc=92.4MB, time=8.26 memory used=741.2MB, alloc=92.4MB, time=8.37 memory used=793.8MB, alloc=92.4MB, time=8.50 memory used=827.6MB, alloc=92.4MB, time=8.59 memory used=856.7MB, alloc=92.4MB, time=8.69 memory used=886.7MB, alloc=92.4MB, time=8.79 memory used=917.3MB, alloc=92.4MB, time=8.88 memory used=948.6MB, alloc=92.4MB, time=8.99 memory used=980.3MB, alloc=92.4MB, time=9.09 memory used=1013.7MB, alloc=92.4MB, time=9.19 memory used=1047.3MB, alloc=92.4MB, time=9.30 memory used=1082.5MB, alloc=92.4MB, time=9.39 memory used=1119.2MB, alloc=92.4MB, time=9.49 memory used=1156.1MB, alloc=92.4MB, time=9.61 memory used=1194.5MB, alloc=92.4MB, time=9.71 memory used=1234.4MB, alloc=92.4MB, time=9.81 memory used=1275.5MB, alloc=92.4MB, time=9.92 memory used=1317.9MB, alloc=92.4MB, time=10.02 memory used=1361.6MB, alloc=92.4MB, time=10.13 memory used=1406.2MB, alloc=92.4MB, time=10.23 memory used=1451.8MB, alloc=92.4MB, time=10.33 memory used=1499.5MB, alloc=92.4MB, time=10.44 memory used=1549.1MB, alloc=92.4MB, time=10.56 memory used=1600.1MB, alloc=92.4MB, time=10.66 memory used=1651.6MB, alloc=92.4MB, time=10.77 memory used=1685.2MB, alloc=92.4MB, time=10.86 memory used=1714.1MB, alloc=92.4MB, time=10.93 memory used=1741.9MB, alloc=92.4MB, time=11.01 memory used=1770.1MB, alloc=92.4MB, time=11.09 memory used=1798.9MB, alloc=92.4MB, time=11.17 memory used=1828.6MB, alloc=92.4MB, time=11.25 memory used=1858.9MB, alloc=92.4MB, time=11.33 memory used=1889.4MB, alloc=92.4MB, time=11.41 memory used=1921.4MB, alloc=92.4MB, time=11.49 memory used=1953.8MB, alloc=92.4MB, time=11.57 memory used=1986.5MB, alloc=92.4MB, time=11.64 memory used=2020.4MB, alloc=92.4MB, time=11.73 memory used=2063.7MB, alloc=92.4MB, time=11.92 memory used=2149.7MB, alloc=92.4MB, time=12.62 memory used=2201.1MB, alloc=92.4MB, time=12.78 memory used=2236.4MB, alloc=92.4MB, time=12.92 memory used=2276.9MB, alloc=92.4MB, time=13.05 memory used=2323.6MB, alloc=92.4MB, time=13.19 memory used=2376.8MB, alloc=92.4MB, time=13.33 memory used=2412.4MB, alloc=92.4MB, time=13.43 memory used=2443.7MB, alloc=92.4MB, time=13.53 memory used=2477.3MB, alloc=92.4MB, time=13.64 memory used=2513.5MB, alloc=92.4MB, time=13.74 memory used=2552.4MB, alloc=92.4MB, time=13.85 memory used=2594.4MB, alloc=92.4MB, time=13.96 memory used=2638.6MB, alloc=92.4MB, time=14.06 memory used=2725.8MB, alloc=92.4MB, time=14.79 memory used=2871.4MB, alloc=92.4MB, time=16.83 memory used=2956.8MB, alloc=92.6MB, time=17.68 memory used=2992.2MB, alloc=92.6MB, time=17.80 memory used=3026.8MB, alloc=92.6MB, time=17.90 memory used=3060.4MB, alloc=92.6MB, time=17.99 memory used=3123.4MB, alloc=92.6MB, time=18.39 memory used=3160.0MB, alloc=92.6MB, time=18.51 memory used=3193.9MB, alloc=92.6MB, time=18.60 memory used=3228.7MB, alloc=92.6MB, time=18.68 memory used=3284.4MB, alloc=92.6MB, time=20.26 memory used=3327.5MB, alloc=92.6MB, time=20.40 memory used=3357.9MB, alloc=92.6MB, time=20.53 memory used=3389.8MB, alloc=92.6MB, time=20.64 memory used=3427.0MB, alloc=92.6MB, time=20.76 memory used=3468.1MB, alloc=92.6MB, time=20.89 memory used=3514.9MB, alloc=92.6MB, time=21.02 memory used=3548.3MB, alloc=92.6MB, time=21.13 memory used=3573.1MB, alloc=92.6MB, time=21.21 memory used=3598.5MB, alloc=92.6MB, time=21.30 memory used=3624.7MB, alloc=92.6MB, time=21.39 memory used=3651.9MB, alloc=92.6MB, time=21.48 memory used=3681.9MB, alloc=92.6MB, time=21.57 memory used=3712.9MB, alloc=92.6MB, time=21.67 memory used=3744.7MB, alloc=92.6MB, time=21.77 memory used=3777.3MB, alloc=92.6MB, time=21.87 memory used=3810.7MB, alloc=92.6MB, time=21.96 memory used=3845.0MB, alloc=92.6MB, time=22.06 memory used=3882.5MB, alloc=92.6MB, time=22.16 memory used=3921.0MB, alloc=92.6MB, time=22.28 memory used=3960.2MB, alloc=92.6MB, time=22.38 memory used=4000.1MB, alloc=92.6MB, time=22.48 memory used=4043.8MB, alloc=92.6MB, time=22.59 memory used=4088.2MB, alloc=92.6MB, time=22.69 memory used=4133.4MB, alloc=92.6MB, time=22.80 memory used=4179.2MB, alloc=92.6MB, time=22.91 memory used=4199.3MB, alloc=107.8MB, time=23.00 memory used=4206.7MB, alloc=107.8MB, time=23.06 memory used=4213.0MB, alloc=107.8MB, time=23.12 memory used=4219.5MB, alloc=107.8MB, time=23.18 memory used=4226.1MB, alloc=107.8MB, time=23.25 memory used=4232.6MB, alloc=107.8MB, time=23.31 memory used=4239.2MB, alloc=107.8MB, time=23.40 memory used=4245.8MB, alloc=107.8MB, time=23.47 memory used=4252.4MB, alloc=107.8MB, time=23.52 memory used=4259.0MB, alloc=107.8MB, time=23.59 memory used=4265.6MB, alloc=107.8MB, time=23.66 memory used=4272.3MB, alloc=107.8MB, time=23.73 memory used=4278.9MB, alloc=107.8MB, time=23.80 memory used=4285.5MB, alloc=107.8MB, time=23.88 memory used=4292.2MB, alloc=107.8MB, time=23.94 memory used=4298.9MB, alloc=107.8MB, time=23.99 memory used=4305.5MB, alloc=107.8MB, time=24.09 memory used=4312.2MB, alloc=107.8MB, time=24.14 memory used=4318.9MB, alloc=107.8MB, time=24.21 memory used=4325.6MB, alloc=107.8MB, time=24.28 memory used=4332.3MB, alloc=107.8MB, time=24.35 memory used=4339.0MB, alloc=107.8MB, time=24.42 memory used=4345.7MB, alloc=107.8MB, time=24.48 memory used=4352.5MB, alloc=107.8MB, time=24.53 memory used=4359.2MB, alloc=107.8MB, time=24.58 memory used=4365.9MB, alloc=107.8MB, time=24.63 memory used=4372.7MB, alloc=107.8MB, time=24.70 memory used=4379.5MB, alloc=107.8MB, time=24.75 memory used=4386.2MB, alloc=107.8MB, time=24.83 memory used=4393.0MB, alloc=107.8MB, time=24.90 memory used=4399.8MB, alloc=107.8MB, time=24.98 memory used=4406.6MB, alloc=107.8MB, time=25.06 memory used=4413.4MB, alloc=107.8MB, time=25.11 memory used=4420.2MB, alloc=107.8MB, time=25.18 memory used=4427.0MB, alloc=107.8MB, time=25.27 memory used=4433.8MB, alloc=107.8MB, time=25.36 memory used=4440.6MB, alloc=107.8MB, time=25.45 memory used=4447.4MB, alloc=107.8MB, time=25.50 memory used=4454.3MB, alloc=107.8MB, time=25.59 memory used=4461.1MB, alloc=107.8MB, time=25.67 memory used=4468.0MB, alloc=107.8MB, time=25.72 memory used=4474.8MB, alloc=107.8MB, time=25.78 memory used=4481.7MB, alloc=107.8MB, time=25.86 memory used=4488.5MB, alloc=107.8MB, time=25.91 memory used=4495.4MB, alloc=107.8MB, time=25.99 memory used=4502.3MB, alloc=107.8MB, time=26.05 memory used=4509.1MB, alloc=107.8MB, time=26.12 memory used=4516.0MB, alloc=107.8MB, time=26.18 memory used=4522.9MB, alloc=107.8MB, time=26.27 memory used=4530.0MB, alloc=107.8MB, time=26.35 memory used=4537.0MB, alloc=107.8MB, time=26.41 memory used=4547.0MB, alloc=107.8MB, time=26.47 memory used=4554.2MB, alloc=107.8MB, time=26.56 memory used=4564.3MB, alloc=107.8MB, time=26.63 memory used=4571.6MB, alloc=107.8MB, time=26.67 memory used=4581.6MB, alloc=107.8MB, time=26.76 memory used=4588.9MB, alloc=107.8MB, time=26.82 memory used=4598.9MB, alloc=107.8MB, time=26.91 memory used=4609.3MB, alloc=107.8MB, time=26.99 memory used=4619.7MB, alloc=107.8MB, time=27.07 memory used=4630.1MB, alloc=107.8MB, time=27.15 memory used=4640.5MB, alloc=107.8MB, time=27.22 memory used=4651.0MB, alloc=107.8MB, time=27.29 memory used=4661.4MB, alloc=107.8MB, time=27.38 memory used=4671.8MB, alloc=107.8MB, time=27.46 memory used=4682.3MB, alloc=107.8MB, time=27.52 memory used=4692.7MB, alloc=107.8MB, time=27.58 memory used=4703.1MB, alloc=107.8MB, time=27.66 memory used=4713.6MB, alloc=107.8MB, time=27.71 memory used=4724.0MB, alloc=107.8MB, time=27.77 memory used=4734.5MB, alloc=107.8MB, time=27.85 memory used=4744.9MB, alloc=107.8MB, time=27.92 memory used=4755.3MB, alloc=107.8MB, time=27.98 memory used=4765.8MB, alloc=107.8MB, time=28.04 memory used=4776.2MB, alloc=107.8MB, time=28.11 memory used=4786.7MB, alloc=107.8MB, time=28.18 memory used=4797.1MB, alloc=107.8MB, time=28.26 memory used=4807.6MB, alloc=107.8MB, time=28.32 memory used=4818.0MB, alloc=107.8MB, time=28.41 memory used=4828.5MB, alloc=107.8MB, time=28.48 memory used=4838.9MB, alloc=107.8MB, time=28.55 memory used=4849.3MB, alloc=107.8MB, time=28.64 memory used=4859.7MB, alloc=107.8MB, time=28.71 memory used=4870.2MB, alloc=107.8MB, time=28.78 memory used=4880.6MB, alloc=107.8MB, time=28.86 memory used=4891.0MB, alloc=107.8MB, time=28.93 memory used=4901.4MB, alloc=107.8MB, time=29.01 memory used=4911.8MB, alloc=107.8MB, time=29.07 memory used=4922.2MB, alloc=107.8MB, time=29.13 memory used=4932.6MB, alloc=107.8MB, time=29.22 memory used=4943.0MB, alloc=107.8MB, time=29.30 memory used=4953.4MB, alloc=107.8MB, time=29.37 memory used=4963.7MB, alloc=107.8MB, time=29.45 memory used=4974.1MB, alloc=107.8MB, time=29.54 memory used=4984.4MB, alloc=107.8MB, time=29.63 memory used=4994.8MB, alloc=107.8MB, time=29.73 memory used=5005.1MB, alloc=107.8MB, time=29.80 memory used=5015.5MB, alloc=107.8MB, time=29.86 memory used=5026.1MB, alloc=107.8MB, time=29.93 memory used=5036.5MB, alloc=107.8MB, time=30.01 memory used=5049.8MB, alloc=107.8MB, time=30.08 memory used=5060.5MB, alloc=107.8MB, time=30.16 memory used=5073.7MB, alloc=107.8MB, time=30.21 memory used=5087.4MB, alloc=107.8MB, time=30.32 memory used=5101.0MB, alloc=107.8MB, time=30.40 memory used=5114.6MB, alloc=107.8MB, time=30.47 memory used=5128.2MB, alloc=107.8MB, time=30.56 memory used=5141.8MB, alloc=107.8MB, time=30.65 memory used=5155.3MB, alloc=107.8MB, time=30.72 memory used=5168.8MB, alloc=107.8MB, time=30.81 memory used=5182.2MB, alloc=107.8MB, time=30.88 memory used=5195.6MB, alloc=107.8MB, time=30.97 memory used=5209.0MB, alloc=107.8MB, time=31.05 memory used=5222.4MB, alloc=107.8MB, time=31.11 memory used=5235.7MB, alloc=107.8MB, time=31.17 memory used=5249.0MB, alloc=107.8MB, time=31.26 memory used=5262.2MB, alloc=107.8MB, time=31.33 memory used=5275.4MB, alloc=107.8MB, time=31.38 memory used=5288.6MB, alloc=107.8MB, time=31.45 memory used=5301.7MB, alloc=107.8MB, time=31.55 memory used=5314.8MB, alloc=107.8MB, time=31.62 memory used=5327.9MB, alloc=107.8MB, time=31.69 memory used=5340.9MB, alloc=107.8MB, time=31.77 memory used=5354.1MB, alloc=107.8MB, time=31.87 memory used=5370.0MB, alloc=107.8MB, time=31.95 memory used=5383.3MB, alloc=107.8MB, time=32.01 memory used=5398.8MB, alloc=107.8MB, time=32.08 memory used=5414.7MB, alloc=107.8MB, time=32.15 memory used=5430.6MB, alloc=107.8MB, time=32.23 memory used=5446.3MB, alloc=107.8MB, time=32.30 memory used=5462.0MB, alloc=107.8MB, time=32.39 memory used=5477.6MB, alloc=107.8MB, time=32.46 memory used=5493.1MB, alloc=107.8MB, time=32.52 memory used=5508.5MB, alloc=107.8MB, time=32.58 memory used=5523.8MB, alloc=107.8MB, time=32.64 memory used=5539.1MB, alloc=107.8MB, time=32.73 memory used=5554.2MB, alloc=107.8MB, time=32.79 memory used=5569.6MB, alloc=107.8MB, time=32.85 memory used=5587.1MB, alloc=107.8MB, time=32.92 memory used=5604.9MB, alloc=107.8MB, time=32.99 memory used=5622.5MB, alloc=107.8MB, time=33.07 memory used=5640.0MB, alloc=107.8MB, time=33.16 memory used=5657.3MB, alloc=107.8MB, time=33.23 memory used=5674.4MB, alloc=107.8MB, time=33.30 memory used=5691.4MB, alloc=107.8MB, time=33.40 memory used=5708.2MB, alloc=107.8MB, time=33.49 memory used=5725.2MB, alloc=107.8MB, time=33.57 memory used=5742.1MB, alloc=107.8MB, time=33.64 memory used=5754.9MB, alloc=107.8MB, time=33.70 memory used=5766.4MB, alloc=107.8MB, time=33.78 memory used=5777.0MB, alloc=107.8MB, time=33.85 memory used=5787.5MB, alloc=107.8MB, time=33.93 memory used=5798.0MB, alloc=107.8MB, time=34.02 memory used=5808.7MB, alloc=107.8MB, time=34.10 memory used=5821.2MB, alloc=107.8MB, time=34.20 memory used=5833.8MB, alloc=107.8MB, time=34.26 memory used=5846.4MB, alloc=107.8MB, time=34.33 memory used=5858.8MB, alloc=107.8MB, time=34.39 memory used=5871.0MB, alloc=107.8MB, time=34.45 memory used=5883.1MB, alloc=107.8MB, time=34.53 memory 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memory used=6193.1MB, alloc=107.8MB, time=36.18 memory used=6449.7MB, alloc=363.8MB, time=40.85 memory used=6496.5MB, alloc=363.8MB, time=41.35 memory used=6538.0MB, alloc=363.8MB, time=41.49 memory used=6566.2MB, alloc=363.8MB, time=41.63 memory used=6598.3MB, alloc=363.8MB, time=41.76 memory used=6634.3MB, alloc=363.8MB, time=41.89 memory used=6675.3MB, alloc=363.8MB, time=42.01 memory used=6720.1MB, alloc=363.8MB, time=42.14 memory used=6751.1MB, alloc=363.8MB, time=42.23 memory used=6776.1MB, alloc=363.8MB, time=42.33 memory used=6801.4MB, alloc=363.8MB, time=42.42 memory used=6827.4MB, alloc=363.8MB, time=42.52 memory used=6854.1MB, alloc=363.8MB, time=42.62 memory used=6881.8MB, alloc=363.8MB, time=42.71 memory used=6912.4MB, alloc=363.8MB, time=42.81 memory used=6943.9MB, alloc=363.8MB, time=42.91 memory used=6976.2MB, alloc=363.8MB, time=43.02 memory used=7009.2MB, alloc=363.8MB, time=43.12 memory used=7042.9MB, alloc=363.8MB, time=43.22 memory used=7077.5MB, alloc=363.8MB, time=43.32 memory used=7115.3MB, alloc=363.8MB, time=43.43 memory used=7154.0MB, alloc=363.8MB, time=43.54 memory used=7193.4MB, alloc=363.8MB, time=43.65 memory used=7233.6MB, alloc=363.8MB, time=43.76 memory used=7277.4MB, alloc=363.8MB, time=43.86 memory used=7321.9MB, alloc=363.8MB, time=43.98 memory used=7367.0MB, alloc=363.8MB, time=44.09 memory used=7519.9MB, alloc=363.8MB, time=44.55 memory used=7666.1MB, alloc=363.8MB, time=44.84 memory used=7821.2MB, alloc=363.8MB, time=45.13 memory used=7989.6MB, alloc=363.8MB, time=45.45 memory used=8174.0MB, alloc=363.8MB, time=45.78 memory used=8372.7MB, alloc=363.8MB, time=46.13 memory used=8588.9MB, alloc=363.8MB, time=46.49 memory used=8824.8MB, alloc=363.8MB, time=46.85 memory used=9026.0MB, alloc=363.8MB, time=47.18 memory used=9216.2MB, alloc=363.8MB, time=47.49 memory used=9377.7MB, alloc=363.8MB, time=48.04 memory used=9453.4MB, alloc=363.8MB, time=48.99 memory used=9518.7MB, alloc=363.8MB, time=49.98 memory used=9581.9MB, alloc=387.8MB, time=50.81 memory used=9668.9MB, alloc=387.8MB, time=52.25 memory used=9754.6MB, alloc=387.8MB, time=53.34 memory used=9834.7MB, alloc=387.8MB, time=54.98 memory used=9924.2MB, alloc=411.8MB, time=56.05 memory used=9991.0MB, alloc=411.8MB, time=56.50 memory used=10054.4MB, alloc=411.8MB, time=56.88 memory used=10114.7MB, alloc=411.8MB, time=57.18 memory used=10175.5MB, alloc=411.8MB, time=57.47 memory used=10239.8MB, alloc=411.8MB, time=57.74 memory used=10303.8MB, alloc=411.8MB, time=58.08 memory used=10357.9MB, alloc=411.8MB, time=58.28 memory used=10405.4MB, alloc=411.8MB, time=58.45 memory used=10459.4MB, alloc=411.8MB, time=58.61 memory used=10500.1MB, alloc=411.8MB, time=58.74 memory used=10575.2MB, alloc=411.8MB, time=59.16 memory used=10622.6MB, alloc=411.8MB, time=59.34 memory used=10679.2MB, alloc=411.8MB, time=59.51 memory used=10720.8MB, alloc=411.8MB, time=59.65 memory used=10779.1MB, alloc=411.8MB, time=60.02 memory used=10853.3MB, alloc=411.8MB, time=60.52 memory used=10911.1MB, alloc=411.8MB, time=60.81 memory used=10972.4MB, alloc=411.8MB, time=61.08 memory used=11029.7MB, alloc=411.8MB, time=61.27 memory used=11073.5MB, alloc=411.8MB, time=61.43 memory used=11139.3MB, alloc=411.8MB, time=61.78 memory used=11187.6MB, alloc=411.8MB, time=61.95 memory used=11261.0MB, alloc=411.8MB, time=62.35 memory used=11309.2MB, alloc=411.8MB, time=62.52 memory used=11388.5MB, alloc=411.8MB, time=65.53 memory used=11459.7MB, alloc=435.8MB, time=65.81 memory used=11519.7MB, alloc=435.8MB, time=66.06 memory used=11574.6MB, alloc=435.8MB, time=66.31 memory used=11636.4MB, alloc=435.8MB, time=66.55 memory used=11704.8MB, alloc=435.8MB, time=66.79 memory used=11778.4MB, alloc=435.8MB, time=67.03 memory used=11857.0MB, alloc=435.8MB, time=67.30 memory used=11930.9MB, alloc=435.8MB, time=67.52 memory used=11978.9MB, alloc=435.8MB, time=67.73 memory used=12023.5MB, alloc=459.8MB, time=67.95 memory used=12079.6MB, alloc=459.8MB, time=68.17 memory used=12140.9MB, alloc=459.8MB, time=68.40 memory used=12204.3MB, alloc=459.8MB, time=68.62 memory used=12269.3MB, alloc=459.8MB, time=68.87 memory used=12335.9MB, alloc=459.8MB, time=69.10 memory used=12404.7MB, alloc=459.8MB, time=69.32 memory used=12480.6MB, alloc=459.8MB, time=69.55 memory used=12558.7MB, alloc=459.8MB, time=69.81 memory used=12638.4MB, alloc=459.8MB, time=70.06 memory used=12719.5MB, alloc=459.8MB, time=70.30 memory used=12803.0MB, alloc=459.8MB, time=70.56 memory used=12893.6MB, alloc=459.8MB, time=70.82 memory used=12986.5MB, alloc=459.8MB, time=71.06 memory used=13080.6MB, alloc=459.8MB, time=71.32 memory used=13177.4MB, alloc=459.8MB, time=71.57 memory used=13276.2MB, alloc=459.8MB, time=71.82 memory used=13358.2MB, alloc=459.8MB, time=72.03 memory used=13414.5MB, alloc=459.8MB, time=72.21 memory used=13465.6MB, alloc=459.8MB, time=72.38 memory used=13513.3MB, alloc=459.8MB, time=72.55 memory used=13562.1MB, alloc=459.8MB, time=72.71 memory used=13611.4MB, alloc=459.8MB, time=72.87 memory used=13667.4MB, alloc=459.8MB, time=73.05 memory used=13718.2MB, alloc=459.8MB, time=73.22 memory used=13774.3MB, alloc=459.8MB, time=73.40 memory used=13831.9MB, alloc=459.8MB, time=73.58 memory used=13889.5MB, alloc=459.8MB, time=73.75 memory used=13947.2MB, alloc=459.8MB, time=73.93 memory used=14005.0MB, alloc=459.8MB, time=74.11 memory used=14062.7MB, alloc=459.8MB, time=74.29 memory used=14121.7MB, alloc=459.8MB, time=74.47 memory used=14186.6MB, alloc=459.8MB, time=74.65 memory used=14252.5MB, alloc=459.8MB, time=74.83 memory used=14318.2MB, alloc=459.8MB, time=75.01 memory used=14383.7MB, alloc=459.8MB, time=75.19 memory used=14449.1MB, alloc=459.8MB, time=75.37 memory used=14515.6MB, alloc=459.8MB, time=75.55 memory used=14587.5MB, alloc=459.8MB, time=75.73 memory used=14660.1MB, alloc=459.8MB, time=75.91 memory used=14732.2MB, alloc=459.8MB, time=76.09 memory used=14804.0MB, alloc=459.8MB, time=76.28 memory used=14877.0MB, alloc=459.8MB, time=76.46 memory used=14953.8MB, alloc=459.8MB, time=76.64 memory used=15031.5MB, alloc=459.8MB, time=76.84 memory used=15109.9MB, alloc=459.8MB, time=77.04 memory used=15192.1MB, alloc=459.8MB, time=77.24 memory used=15274.6MB, alloc=459.8MB, time=77.43 memory used=15363.0MB, alloc=459.8MB, time=77.63 memory used=15450.1MB, alloc=459.8MB, time=77.83 memory used=15542.2MB, alloc=459.8MB, time=78.03 memory used=15633.8MB, alloc=459.8MB, time=78.22 memory used=15728.3MB, alloc=459.8MB, time=78.41 memory used=15824.9MB, alloc=459.8MB, time=78.62 memory used=15925.8MB, alloc=459.8MB, time=78.82 memory used=16096.5MB, alloc=459.8MB, time=79.11 memory used=16274.7MB, alloc=459.8MB, time=79.43 memory used=16514.1MB, alloc=459.8MB, time=82.92 memory used=16591.1MB, alloc=459.8MB, time=83.23 memory used=16662.5MB, alloc=459.8MB, time=83.50 memory used=16747.0MB, alloc=459.8MB, time=83.80 memory used=16840.4MB, alloc=459.8MB, time=84.11 memory used=16942.2MB, alloc=459.8MB, time=84.42 memory used=17021.1MB, alloc=459.8MB, time=84.68 memory used=17076.4MB, alloc=459.8MB, time=84.91 memory used=17134.5MB, alloc=459.8MB, time=85.14 memory used=17196.2MB, alloc=459.8MB, time=85.38 memory used=17259.6MB, alloc=459.8MB, time=85.61 memory used=17324.6MB, alloc=459.8MB, time=85.84 memory used=17391.1MB, alloc=459.8MB, time=86.07 memory used=17459.4MB, alloc=459.8MB, time=86.31 memory used=17535.8MB, alloc=459.8MB, time=86.56 memory used=17613.9MB, alloc=459.8MB, time=86.79 memory used=17693.6MB, alloc=459.8MB, time=87.03 memory used=17774.7MB, alloc=459.8MB, time=87.27 memory used=17858.1MB, alloc=459.8MB, time=87.50 memory used=17948.8MB, alloc=459.8MB, time=87.77 memory used=18041.6MB, alloc=459.8MB, time=88.02 memory used=18135.8MB, alloc=459.8MB, time=88.26 memory used=18232.1MB, alloc=459.8MB, time=88.52 memory used=18331.5MB, alloc=459.8MB, time=88.78 memory used=18410.0MB, alloc=459.8MB, time=88.99 memory used=18464.7MB, alloc=459.8MB, time=89.16 memory used=18513.5MB, alloc=459.8MB, time=89.33 memory used=18560.6MB, alloc=459.8MB, time=89.49 memory used=18608.3MB, alloc=459.8MB, time=89.66 memory used=18657.2MB, alloc=459.8MB, time=89.85 memory used=18706.3MB, alloc=459.8MB, time=90.02 memory used=18756.7MB, alloc=459.8MB, time=90.19 memory used=18813.1MB, alloc=459.8MB, time=90.36 memory used=18870.7MB, alloc=459.8MB, time=90.53 memory used=18928.3MB, alloc=459.8MB, time=90.71 memory used=18986.0MB, alloc=459.8MB, time=90.96 memory used=19043.7MB, alloc=459.8MB, time=91.13 memory used=19101.5MB, alloc=459.8MB, time=91.30 memory used=19159.2MB, alloc=459.8MB, time=91.48 memory used=19218.2MB, alloc=459.8MB, time=91.65 memory used=19283.0MB, alloc=459.8MB, time=91.82 memory used=19348.8MB, alloc=459.8MB, time=92.00 memory used=19414.4MB, alloc=459.8MB, time=92.18 memory used=19479.8MB, alloc=459.8MB, time=92.36 memory used=19545.1MB, alloc=459.8MB, time=92.54 memory used=19611.4MB, alloc=459.8MB, time=92.72 memory used=19683.0MB, alloc=459.8MB, time=92.90 memory used=19755.4MB, alloc=459.8MB, time=93.09 memory used=19827.3MB, alloc=459.8MB, time=93.28 memory used=19898.8MB, alloc=459.8MB, time=93.47 memory used=19971.7MB, alloc=459.8MB, time=93.65 memory used=20047.9MB, alloc=459.8MB, time=93.84 memory used=20125.2MB, alloc=459.8MB, time=94.02 memory used=20203.4MB, alloc=459.8MB, time=94.21 memory used=20284.8MB, alloc=459.8MB, time=94.41 memory used=20366.8MB, alloc=459.8MB, time=94.60 memory used=20454.5MB, alloc=459.8MB, time=94.79 memory used=20540.8MB, alloc=459.8MB, time=95.00 memory used=20632.2MB, alloc=459.8MB, time=95.19 memory used=20723.8MB, alloc=459.8MB, time=95.39 memory used=20821.4MB, alloc=459.8MB, time=95.61 memory used=20918.2MB, alloc=459.8MB, time=95.81 memory used=21019.2MB, alloc=459.8MB, time=96.01 memory used=21248.4MB, alloc=459.8MB, time=96.38 memory used=21410.0MB, alloc=459.8MB, time=96.67 memory used=21581.3MB, alloc=459.8MB, time=162.63 |\^/| 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(); 1428291233 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 2 F := [-18 x z + 16 x y z - 12 y + 7 x , -6 x y z + 6 y z + 9 x z + 9 y , 2 2 -17 y z + 13 x + 2 y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 3 3 2 G := [14 x z - 6 y z - 7 z + 12, -12 x z + 4 y z + 19 z - 18 z , 2 2 2 3 2 -7 x y z + 17 y z - 10 x + 9 x ] > Problem := [F,G]; 3 3 2 Problem := [[-18 x z + 16 x y z - 12 y + 7 x , 2 3 2 2 2 -6 x y z + 6 y z + 9 x z + 9 y , -17 y z + 13 x + 2 y], [ 3 2 2 2 3 3 3 2 14 x z - 6 y z - 7 z + 12, -12 x z + 4 y z + 19 z - 18 z , 2 2 2 3 2 -7 x y z + 17 y z - 10 x + 9 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.51 memory used=44.4MB, alloc=56.3MB, time=0.79 memory used=84.8MB, alloc=60.3MB, time=1.32 memory used=127.8MB, alloc=68.3MB, time=1.93 memory used=170.6MB, alloc=68.3MB, time=2.53 memory used=210.7MB, alloc=92.3MB, time=2.96 memory used=262.8MB, alloc=92.3MB, time=3.35 memory used=307.7MB, alloc=92.3MB, time=3.68 memory used=366.4MB, alloc=92.3MB, time=4.23 memory used=412.7MB, alloc=92.3MB, time=4.47 memory used=447.6MB, alloc=92.3MB, time=4.58 memory used=505.9MB, alloc=92.3MB, time=11.16 memory used=559.2MB, alloc=92.3MB, time=11.36 memory used=595.5MB, alloc=92.3MB, time=11.47 memory used=625.8MB, alloc=92.3MB, time=11.58 memory used=662.7MB, alloc=92.3MB, time=11.69 memory used=703.4MB, alloc=92.3MB, time=11.80 memory used=728.7MB, alloc=92.3MB, time=11.87 memory used=756.9MB, alloc=92.3MB, time=11.95 memory used=797.0MB, alloc=92.3MB, time=12.16 memory used=884.1MB, alloc=92.3MB, time=13.25 memory used=943.9MB, alloc=92.3MB, time=13.79 memory used=985.8MB, alloc=92.3MB, time=13.98 memory used=1021.6MB, alloc=92.3MB, time=14.10 memory used=1076.4MB, alloc=92.3MB, time=20.30 memory used=1132.3MB, alloc=92.3MB, time=21.07 memory used=1170.4MB, alloc=92.3MB, time=21.20 memory used=1197.9MB, alloc=92.3MB, time=21.31 memory used=1231.3MB, alloc=92.3MB, time=21.41 memory used=1271.5MB, alloc=92.3MB, time=21.52 memory used=1301.3MB, alloc=92.3MB, time=21.61 memory used=1327.4MB, alloc=92.3MB, time=21.69 memory used=1356.9MB, alloc=92.3MB, time=21.78 memory used=1395.6MB, alloc=92.3MB, time=22.01 memory used=1438.1MB, alloc=96.3MB, time=22.19 memory used=1488.9MB, alloc=96.3MB, time=22.54 memory used=1560.7MB, alloc=96.3MB, time=23.28 memory used=1622.7MB, alloc=96.3MB, time=23.93 memory used=1664.1MB, alloc=96.3MB, time=24.19 memory used=1699.8MB, alloc=96.3MB, time=24.30 memory used=1725.0MB, alloc=96.3MB, time=24.40 memory used=1765.7MB, alloc=96.3MB, time=25.21 memory used=1795.1MB, alloc=96.3MB, time=25.31 memory used=1850.0MB, alloc=96.3MB, time=25.78 memory used=1878.6MB, alloc=96.3MB, time=25.88 memory used=1913.9MB, alloc=96.3MB, time=26.09 memory used=1958.3MB, alloc=96.3MB, time=26.33 memory used=1987.3MB, alloc=96.3MB, time=26.44 memory used=2022.5MB, alloc=96.3MB, time=26.56 memory used=2054.7MB, alloc=96.3MB, time=26.76 memory used=2105.6MB, alloc=96.3MB, time=34.88 memory used=2161.0MB, alloc=96.3MB, time=35.73 memory used=2190.6MB, alloc=96.3MB, time=35.84 memory used=2222.0MB, alloc=96.3MB, time=35.95 memory used=2245.7MB, alloc=96.3MB, time=36.04 memory used=2273.1MB, alloc=96.3MB, time=36.14 memory used=2304.5MB, alloc=96.3MB, time=36.24 memory used=2340.6MB, alloc=96.3MB, time=36.35 memory used=2371.3MB, alloc=96.3MB, time=36.45 memory used=2392.5MB, alloc=96.3MB, time=36.53 memory used=2414.9MB, alloc=96.3MB, time=36.62 memory used=2438.8MB, alloc=96.3MB, time=36.72 memory used=2464.2MB, alloc=96.3MB, time=36.81 memory used=2491.6MB, alloc=96.3MB, time=36.90 memory used=2521.6MB, alloc=96.3MB, time=36.99 memory used=2584.0MB, alloc=96.3MB, time=37.49 memory used=2654.8MB, alloc=96.3MB, time=38.20 memory used=2702.9MB, alloc=96.3MB, time=38.70 memory used=2730.1MB, alloc=96.3MB, time=38.82 memory used=2763.7MB, alloc=96.3MB, time=38.95 memory used=2790.5MB, alloc=96.3MB, time=39.09 memory used=2849.4MB, alloc=96.3MB, time=41.50 memory used=2878.2MB, alloc=120.3MB, time=41.65 memory used=2924.5MB, alloc=120.3MB, time=41.81 memory used=2977.2MB, alloc=120.3MB, time=41.96 memory used=3013.3MB, alloc=120.3MB, time=42.10 memory used=3054.7MB, alloc=120.3MB, time=42.23 memory used=3113.8MB, alloc=120.3MB, time=42.57 memory used=3173.3MB, alloc=120.3MB, time=43.14 memory used=3220.1MB, alloc=120.3MB, time=43.31 memory used=3267.6MB, alloc=120.3MB, time=43.47 memory used=3310.0MB, alloc=120.3MB, time=43.61 memory used=3346.9MB, alloc=120.3MB, time=43.73 memory used=3389.1MB, alloc=120.3MB, time=43.86 memory used=3438.0MB, alloc=120.3MB, time=43.99 memory used=3501.3MB, alloc=131.8MB, time=44.15 memory used=3512.3MB, alloc=131.8MB, time=44.23 memory used=3523.5MB, alloc=131.8MB, time=44.31 memory used=3535.5MB, alloc=131.8MB, time=44.40 memory used=3548.0MB, alloc=131.8MB, time=44.48 memory used=3626.4MB, alloc=131.8MB, time=46.97 memory used=3670.3MB, alloc=131.8MB, time=47.12 memory used=3715.2MB, alloc=131.8MB, time=47.27 memory used=3768.6MB, alloc=131.8MB, time=47.44 memory used=3801.2MB, alloc=131.8MB, time=47.56 memory used=3836.4MB, alloc=131.8MB, time=47.68 memory used=3874.8MB, alloc=131.8MB, time=47.80 memory used=3917.6MB, alloc=131.8MB, time=47.93 memory used=3963.6MB, alloc=131.8MB, time=48.06 memory used=4015.2MB, alloc=131.8MB, time=48.20 memory used=4071.1MB, alloc=131.8MB, time=48.34 memory used=4108.9MB, alloc=131.8MB, time=48.45 memory used=4117.7MB, alloc=131.8MB, time=48.54 memory used=4126.7MB, alloc=131.8MB, time=48.62 memory used=4135.7MB, alloc=131.8MB, time=48.70 memory used=4144.9MB, alloc=131.8MB, time=48.78 memory used=4155.0MB, alloc=131.8MB, time=48.86 memory used=4165.4MB, alloc=131.8MB, time=48.94 memory used=4175.6MB, alloc=131.8MB, time=49.02 memory used=4185.8MB, alloc=131.8MB, time=49.10 memory used=4196.0MB, alloc=131.8MB, time=49.19 memory used=4207.4MB, alloc=131.8MB, time=49.27 memory used=4218.8MB, alloc=131.8MB, time=49.35 memory used=4228.9MB, alloc=131.8MB, time=49.43 memory used=4239.9MB, alloc=131.8MB, time=49.54 memory used=4250.7MB, alloc=131.8MB, time=49.63 memory used=4261.5MB, alloc=131.8MB, time=49.71 memory used=4273.4MB, alloc=131.8MB, time=49.78 memory used=4286.1MB, alloc=131.8MB, time=49.87 memory used=4297.9MB, alloc=131.8MB, time=49.97 memory used=4311.2MB, alloc=131.8MB, time=50.06 memory used=4324.4MB, alloc=131.8MB, time=50.14 memory used=4338.3MB, alloc=131.8MB, time=50.23 memory used=4352.9MB, alloc=131.8MB, time=50.33 memory used=4367.1MB, alloc=131.8MB, time=50.42 memory used=4382.2MB, alloc=131.8MB, time=50.53 memory used=4398.0MB, alloc=131.8MB, time=50.61 memory used=4414.3MB, alloc=131.8MB, time=50.71 memory used=4466.0MB, alloc=131.8MB, time=51.33 memory used=4517.5MB, alloc=131.8MB, time=51.51 memory used=4563.6MB, alloc=131.8MB, time=51.65 memory used=4640.7MB, alloc=131.8MB, time=66.14 memory used=4724.6MB, alloc=131.8MB, time=104.32 memory used=5518.8MB, alloc=155.8MB, time=111.45 memory used=5533.5MB, alloc=411.8MB, time=112.21 memory used=6057.6MB, alloc=411.8MB, time=118.95 memory used=6142.0MB, alloc=411.8MB, time=120.92 memory used=6759.3MB, alloc=411.8MB, time=129.10 memory used=6961.0MB, alloc=435.8MB, time=135.95 memory used=7573.0MB, alloc=459.8MB, time=140.95 memory used=7695.4MB, alloc=463.7MB, time=143.88 memory used=7699.2MB, alloc=467.6MB, time=143.98 memory used=7703.1MB, alloc=471.4MB, time=144.08 memory used=7707.0MB, alloc=475.3MB, time=144.17 memory used=7710.9MB, alloc=463.7MB, time=144.34 memory used=7816.6MB, alloc=459.8MB, time=145.14 memory used=7906.8MB, alloc=459.8MB, time=145.41 memory used=7986.0MB, alloc=459.8MB, time=145.62 memory used=8148.5MB, alloc=459.8MB, time=146.04 memory used=8246.0MB, alloc=459.8MB, time=152.30 memory used=8318.5MB, alloc=459.8MB, time=152.54 memory used=8385.0MB, alloc=459.8MB, time=152.79 memory used=8455.5MB, alloc=459.8MB, time=153.05 memory used=8528.8MB, alloc=459.8MB, time=153.30 memory used=8604.3MB, alloc=459.8MB, time=153.56 memory used=8684.9MB, alloc=459.8MB, time=153.82 memory used=8767.7MB, alloc=459.8MB, time=154.08 memory used=8852.7MB, alloc=459.8MB, time=154.34 memory used=8942.9MB, alloc=459.8MB, time=154.61 memory used=9035.2MB, alloc=459.8MB, time=154.88 memory used=9129.6MB, alloc=459.8MB, time=155.14 memory used=9229.4MB, alloc=459.8MB, time=155.39 memory used=9331.2MB, alloc=459.8MB, time=155.63 memory used=9438.4MB, alloc=459.8MB, time=155.91 memory used=9547.6MB, alloc=459.8MB, time=156.16 memory used=9662.2MB, alloc=459.8MB, time=156.41 memory used=9778.8MB, alloc=459.8MB, time=156.69 memory used=9859.0MB, alloc=459.8MB, time=156.89 memory used=9921.8MB, alloc=459.8MB, time=157.07 memory used=9982.8MB, alloc=459.8MB, time=157.24 memory used=10043.3MB, alloc=459.8MB, time=157.41 memory used=10105.2MB, alloc=459.8MB, time=157.59 memory used=10167.5MB, alloc=459.8MB, time=157.77 memory used=10230.1MB, alloc=459.8MB, time=157.95 memory used=10293.0MB, alloc=459.8MB, time=158.13 memory used=10356.4MB, alloc=459.8MB, time=158.30 memory used=10423.9MB, alloc=459.8MB, time=158.48 memory used=10491.7MB, alloc=459.8MB, time=158.66 memory used=10559.7MB, alloc=459.8MB, time=158.84 memory used=10628.1MB, alloc=459.8MB, time=159.02 memory used=10696.7MB, alloc=459.8MB, time=159.20 memory used=10769.6MB, alloc=459.8MB, time=159.38 memory used=10842.7MB, alloc=459.8MB, time=159.56 memory used=10916.0MB, alloc=459.8MB, time=159.75 memory used=10989.4MB, alloc=459.8MB, time=159.93 memory used=11063.1MB, alloc=459.8MB, time=160.11 memory used=11141.0MB, alloc=459.8MB, time=160.31 memory used=11219.0MB, alloc=459.8MB, time=160.49 memory used=11297.1MB, alloc=459.8MB, time=160.66 memory used=11375.3MB, alloc=459.8MB, time=160.85 memory used=11457.6MB, alloc=459.8MB, time=161.04 memory used=11539.9MB, alloc=459.8MB, time=161.23 memory used=11622.3MB, alloc=459.8MB, time=161.42 memory used=11708.7MB, alloc=459.8MB, time=161.61 memory used=11795.0MB, alloc=459.8MB, time=161.80 memory used=11881.2MB, alloc=459.8MB, time=161.99 memory used=11971.3MB, alloc=459.8MB, time=162.19 memory used=12061.2MB, alloc=459.8MB, time=162.37 memory used=12150.8MB, alloc=459.8MB, time=162.58 memory used=12244.2MB, alloc=459.8MB, time=162.78 memory used=12337.3MB, alloc=459.8MB, time=162.97 memory used=12433.8MB, alloc=459.8MB, time=163.17 memory used=12530.0MB, alloc=459.8MB, time=163.37 memory used=12629.4MB, alloc=459.8MB, time=163.57 memory used=12728.3MB, alloc=459.8MB, time=163.78 memory used=12830.3MB, alloc=459.8MB, time=163.98 memory used=12935.2MB, alloc=459.8MB, time=164.18 memory used=13039.2MB, alloc=459.8MB, time=164.40 memory used=13145.9MB, alloc=459.8MB, time=164.61 memory used=13255.1MB, alloc=459.8MB, time=164.82 memory used=13366.5MB, alloc=459.8MB, time=165.02 memory used=13479.9MB, alloc=459.8MB, time=165.23 memory used=13595.0MB, alloc=459.8MB, time=165.44 memory used=13712.0MB, alloc=459.8MB, time=165.65 memory used=13904.6MB, alloc=459.8MB, time=166.09 memory used=14038.9MB, alloc=459.8MB, time=166.38 memory used=14177.6MB, alloc=459.8MB, time=166.65 memory used=14320.2MB, alloc=459.8MB, time=166.94 memory used=14465.4MB, alloc=459.8MB, time=167.21 memory used=14614.1MB, alloc=459.8MB, time=167.49 memory used=14766.5MB, alloc=459.8MB, time=167.77 memory used=14923.3MB, alloc=459.8MB, time=168.06 memory used=15086.1MB, alloc=459.8MB, time=168.36 memory used=15258.9MB, alloc=459.8MB, time=168.65 memory used=15433.7MB, alloc=459.8MB, time=169.15 |\^/| 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(); 1428291533 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 4 2 3 F := [-7 x z + 11 y z + 10 x + 20 y , 12 x z + 5 z + 17 x y + y , 3 3 2 2 18 y z - 5 x + 2 x y + 4 y z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 2 2 G := [14 x z - 9 y - 6 z, -6 x - 18 x + 14 x z - 11 z , 2 2 2 2 y z + 11 x y + 18 y z + 15 y] > Problem := [F,G]; 3 3 2 2 2 2 4 2 3 Problem := [[-7 x z + 11 y z + 10 x + 20 y , 12 x z + 5 z + 17 x y + y , 3 3 2 2 2 2 3 18 y z - 5 x + 2 x y + 4 y z ], [14 x z - 9 y - 6 z, 4 2 2 2 2 2 2 -6 x - 18 x + 14 x z - 11 z , y z + 11 x y + 18 y z + 15 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.7MB, alloc=32.3MB, time=0.48 memory used=46.7MB, alloc=32.3MB, time=0.67 memory used=67.8MB, alloc=36.3MB, time=0.95 memory used=89.4MB, alloc=36.3MB, time=1.20 memory used=111.3MB, alloc=60.3MB, time=1.71 memory used=159.6MB, alloc=68.6MB, time=2.35 memory used=196.3MB, alloc=71.7MB, time=2.47 memory used=229.5MB, alloc=71.7MB, time=2.57 memory used=251.9MB, alloc=71.7MB, time=2.66 memory used=269.9MB, alloc=71.7MB, time=2.74 memory used=289.4MB, alloc=71.7MB, time=2.82 memory used=311.1MB, alloc=71.7MB, time=2.90 memory used=333.8MB, alloc=71.7MB, time=2.98 memory used=358.7MB, alloc=71.7MB, time=3.06 memory used=384.5MB, alloc=71.7MB, time=3.14 memory used=412.6MB, alloc=71.7MB, time=3.23 memory used=443.1MB, alloc=71.7MB, time=3.32 memory used=469.6MB, alloc=71.7MB, time=3.40 memory used=485.3MB, alloc=71.7MB, time=3.47 memory used=500.9MB, alloc=71.7MB, time=3.54 memory used=517.7MB, alloc=71.7MB, time=3.60 memory used=534.7MB, alloc=71.7MB, time=3.67 memory used=551.9MB, alloc=71.7MB, time=3.73 memory used=570.6MB, alloc=71.7MB, time=3.81 memory used=589.4MB, alloc=71.7MB, time=3.89 memory used=609.6MB, alloc=71.7MB, time=3.97 memory used=629.8MB, alloc=71.7MB, time=4.04 memory used=651.4MB, alloc=71.7MB, time=4.11 memory used=672.7MB, alloc=71.7MB, time=4.19 memory used=695.3MB, alloc=71.7MB, time=4.25 memory used=719.0MB, alloc=71.7MB, time=4.32 memory used=743.5MB, alloc=71.7MB, time=4.39 memory used=768.7MB, alloc=71.7MB, time=4.47 memory used=795.6MB, alloc=71.7MB, time=4.55 memory used=823.7MB, alloc=71.7MB, time=4.63 memory used=853.2MB, alloc=71.7MB, time=4.71 memory used=883.4MB, alloc=71.7MB, time=4.78 memory used=899.9MB, alloc=71.7MB, time=4.84 memory used=927.3MB, alloc=71.7MB, time=5.13 memory used=964.5MB, alloc=72.2MB, time=5.26 memory used=998.3MB, alloc=72.2MB, time=5.37 memory used=1021.3MB, alloc=72.2MB, time=5.46 memory used=1039.9MB, alloc=72.2MB, time=5.53 memory used=1059.4MB, alloc=72.2MB, time=5.62 memory used=1081.1MB, alloc=72.2MB, time=5.71 memory used=1103.8MB, alloc=72.2MB, time=5.78 memory used=1128.7MB, alloc=72.2MB, time=5.87 memory used=1154.5MB, alloc=72.2MB, time=5.95 memory used=1182.6MB, alloc=72.2MB, time=6.04 memory used=1213.0MB, alloc=72.2MB, time=6.13 memory used=1239.6MB, alloc=72.2MB, time=6.21 memory used=1255.3MB, alloc=72.2MB, time=6.28 memory used=1270.9MB, alloc=72.2MB, time=6.35 memory used=1287.6MB, alloc=72.2MB, time=6.42 memory used=1304.7MB, alloc=72.2MB, time=6.49 memory used=1321.8MB, alloc=72.2MB, time=6.57 memory used=1340.6MB, alloc=72.2MB, time=6.64 memory used=1359.3MB, alloc=72.2MB, time=6.71 memory used=1379.6MB, alloc=72.2MB, time=6.78 memory used=1399.8MB, alloc=72.2MB, time=6.85 memory used=1421.3MB, alloc=72.2MB, time=6.92 memory used=1442.7MB, alloc=72.2MB, time=7.00 memory used=1465.2MB, alloc=72.2MB, time=7.07 memory used=1488.9MB, alloc=72.2MB, time=7.14 memory used=1513.4MB, alloc=72.2MB, time=7.22 memory used=1538.6MB, alloc=72.2MB, time=7.29 memory used=1565.6MB, alloc=72.2MB, time=7.37 memory used=1593.6MB, alloc=72.2MB, time=7.45 memory used=1623.2MB, alloc=72.2MB, time=7.52 memory used=1653.3MB, alloc=72.2MB, time=7.60 memory used=1669.8MB, alloc=72.2MB, time=7.66 memory used=1698.8MB, alloc=72.2MB, time=10.94 memory used=1742.5MB, alloc=96.2MB, time=22.75 memory used=1799.7MB, alloc=96.2MB, time=45.54 memory used=1886.1MB, alloc=96.2MB, time=46.16 memory used=1924.6MB, alloc=96.2MB, time=46.28 memory used=1967.3MB, alloc=96.2MB, time=46.39 memory used=2018.9MB, alloc=96.2MB, time=46.53 memory used=2049.4MB, alloc=96.2MB, time=46.64 memory used=2081.1MB, alloc=96.2MB, time=46.74 memory used=2115.1MB, alloc=96.2MB, time=46.85 memory used=2151.8MB, alloc=96.2MB, time=46.95 memory used=2191.1MB, alloc=96.2MB, time=47.05 memory used=2233.0MB, alloc=96.2MB, time=47.16 memory used=2278.7MB, alloc=96.2MB, time=47.28 memory used=2326.8MB, alloc=96.2MB, time=47.38 memory used=2378.6MB, alloc=96.2MB, time=47.50 memory used=2412.1MB, alloc=96.2MB, time=47.60 memory used=2440.0MB, alloc=96.2MB, time=47.68 memory used=2468.8MB, alloc=96.2MB, time=47.76 memory used=2497.5MB, alloc=96.2MB, time=47.84 memory used=2527.5MB, alloc=96.2MB, time=47.91 memory used=2558.7MB, alloc=96.2MB, time=47.99 memory used=2590.8MB, alloc=96.2MB, time=48.07 memory used=2624.0MB, alloc=96.2MB, time=48.15 memory used=2659.0MB, alloc=96.2MB, time=48.23 memory used=2695.9MB, alloc=96.2MB, time=48.31 memory used=2734.1MB, alloc=96.2MB, time=48.39 memory used=2773.3MB, alloc=96.2MB, time=48.47 memory used=2815.0MB, alloc=96.2MB, time=48.56 memory used=2858.1MB, alloc=96.2MB, time=48.64 memory used=2902.9MB, alloc=96.2MB, time=48.73 memory used=2951.3MB, alloc=96.2MB, time=48.82 memory used=3016.3MB, alloc=100.8MB, time=49.35 memory used=3078.4MB, alloc=100.8MB, time=49.53 memory used=3123.3MB, alloc=100.8MB, time=49.66 memory used=3156.2MB, alloc=100.8MB, time=49.77 memory used=3192.5MB, alloc=100.8MB, time=49.89 memory used=3232.8MB, alloc=100.8MB, time=50.02 memory used=3277.0MB, alloc=100.8MB, time=50.15 memory used=3325.3MB, alloc=100.8MB, time=50.29 memory used=3379.5MB, alloc=100.8MB, time=50.42 memory used=3413.0MB, alloc=100.8MB, time=50.52 memory used=3440.7MB, alloc=100.8MB, time=50.63 memory used=3470.9MB, alloc=100.8MB, time=50.73 memory used=3501.4MB, alloc=100.8MB, time=50.82 memory used=3534.0MB, alloc=100.8MB, time=50.92 memory used=3568.7MB, alloc=100.8MB, time=51.03 memory used=3605.2MB, alloc=100.8MB, time=51.15 memory used=3643.4MB, alloc=100.8MB, time=51.25 memory used=3682.9MB, alloc=100.8MB, time=51.36 memory used=3723.6MB, alloc=100.8MB, time=51.48 memory used=3766.6MB, alloc=100.8MB, time=51.58 memory used=3812.9MB, alloc=100.8MB, time=51.69 memory used=3863.0MB, alloc=100.8MB, time=51.79 memory used=3916.7MB, alloc=100.8MB, time=51.90 memory used=3947.1MB, alloc=100.8MB, time=51.97 memory used=4003.0MB, alloc=100.8MB, time=52.49 memory used=4064.3MB, alloc=100.8MB, time=52.66 memory used=4104.7MB, alloc=100.8MB, time=52.80 memory used=4140.1MB, alloc=100.8MB, time=52.92 memory used=4178.9MB, alloc=100.8MB, time=53.05 memory used=4221.8MB, alloc=100.8MB, time=53.18 memory used=4268.8MB, alloc=100.8MB, time=53.31 memory used=4319.9MB, alloc=100.8MB, time=53.45 memory used=4370.3MB, alloc=100.8MB, time=53.57 memory used=4398.1MB, alloc=100.8MB, time=53.69 memory used=4428.3MB, alloc=100.8MB, time=53.78 memory used=4458.8MB, alloc=100.8MB, time=53.89 memory used=4491.5MB, alloc=100.8MB, time=54.00 memory used=4526.2MB, alloc=100.8MB, time=54.11 memory used=4560.9MB, alloc=100.8MB, time=54.21 memory used=4597.4MB, alloc=100.8MB, time=54.32 memory used=4637.2MB, alloc=100.8MB, time=54.44 memory used=4678.4MB, alloc=100.8MB, time=54.54 memory used=4722.2MB, alloc=100.8MB, time=54.65 memory used=4767.9MB, alloc=100.8MB, time=54.75 memory used=4816.0MB, alloc=100.8MB, time=54.86 memory used=4868.2MB, alloc=100.8MB, time=54.97 memory used=4909.5MB, alloc=100.8MB, time=55.06 memory used=4952.1MB, alloc=100.8MB, time=59.75 memory used=5024.4MB, alloc=100.8MB, time=91.63 memory used=5092.4MB, alloc=100.8MB, time=96.80 memory used=5161.7MB, alloc=100.8MB, time=97.18 memory used=5199.1MB, alloc=100.8MB, time=97.31 memory used=5245.7MB, alloc=100.8MB, time=97.43 memory used=5290.3MB, alloc=100.8MB, time=97.55 memory used=5320.7MB, alloc=100.8MB, time=97.65 memory used=5352.8MB, alloc=100.8MB, time=97.75 memory used=5387.6MB, alloc=100.8MB, time=97.86 memory used=5425.0MB, alloc=100.8MB, time=97.97 memory used=5465.1MB, alloc=100.8MB, time=98.07 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time=100.08 memory used=6364.3MB, alloc=100.8MB, time=100.86 memory used=6444.3MB, alloc=100.8MB, time=105.60 memory used=6482.1MB, alloc=100.8MB, time=105.73 memory used=6528.9MB, alloc=100.8MB, time=105.85 memory used=6560.0MB, alloc=100.8MB, time=105.94 memory used=6595.7MB, alloc=100.8MB, time=106.05 memory used=6636.4MB, alloc=100.8MB, time=106.16 memory used=6683.5MB, alloc=100.8MB, time=106.27 memory used=6728.0MB, alloc=100.8MB, time=106.37 memory used=6756.8MB, alloc=100.8MB, time=106.44 memory used=6788.9MB, alloc=100.8MB, time=106.52 memory used=6859.8MB, alloc=100.8MB, time=106.92 memory used=6928.0MB, alloc=100.8MB, time=107.78 memory used=6989.6MB, alloc=356.8MB, time=108.65 memory used=7038.9MB, alloc=356.8MB, time=108.92 memory used=7067.0MB, alloc=356.8MB, time=109.02 memory used=7111.1MB, alloc=356.8MB, time=109.20 memory used=7146.4MB, alloc=356.8MB, time=109.32 memory used=7175.9MB, alloc=356.8MB, time=109.43 memory used=7222.9MB, alloc=356.8MB, time=109.62 memory used=7256.5MB, alloc=356.8MB, time=109.75 memory used=7288.1MB, alloc=356.8MB, time=109.84 memory used=7338.7MB, alloc=356.8MB, time=112.53 memory used=7387.8MB, alloc=356.8MB, time=112.70 memory used=7430.0MB, alloc=356.8MB, time=112.85 memory used=7463.1MB, alloc=380.8MB, time=113.00 memory used=7499.9MB, alloc=380.8MB, time=113.16 memory used=7539.2MB, alloc=380.8MB, time=113.31 memory used=7582.7MB, alloc=380.8MB, time=113.48 memory used=7629.3MB, alloc=380.8MB, time=113.62 memory used=7678.9MB, alloc=380.8MB, time=113.80 memory used=7731.5MB, alloc=380.8MB, time=113.95 memory used=7787.2MB, alloc=380.8MB, time=114.13 memory used=7845.4MB, alloc=380.8MB, time=114.30 memory used=7880.8MB, alloc=380.8MB, time=114.43 memory used=7909.0MB, alloc=380.8MB, time=114.54 memory used=7937.6MB, alloc=404.8MB, time=114.67 memory used=7981.0MB, alloc=404.8MB, time=114.82 memory used=8029.2MB, alloc=404.8MB, time=114.99 memory used=8078.8MB, alloc=404.8MB, time=115.17 memory used=8129.6MB, alloc=404.8MB, time=115.33 memory used=8181.8MB, alloc=404.8MB, time=115.49 memory used=8235.2MB, alloc=404.8MB, time=115.66 memory used=8289.9MB, alloc=404.8MB, time=115.81 memory used=8345.7MB, alloc=404.8MB, time=115.98 memory used=8402.8MB, alloc=404.8MB, time=116.16 memory used=8461.0MB, alloc=404.8MB, time=116.33 memory used=8520.4MB, alloc=404.8MB, time=116.51 memory used=8581.6MB, alloc=404.8MB, time=116.67 memory used=8650.2MB, alloc=404.8MB, time=116.85 memory used=8720.8MB, alloc=404.8MB, time=117.01 memory used=8792.6MB, alloc=404.8MB, time=117.18 memory used=8865.7MB, alloc=404.8MB, time=117.35 memory used=8940.0MB, alloc=404.8MB, time=117.53 memory used=9015.4MB, alloc=404.8MB, time=117.71 memory used=9092.0MB, alloc=404.8MB, time=117.89 memory used=9169.7MB, alloc=404.8MB, time=118.08 memory used=9212.5MB, alloc=428.8MB, time=118.21 memory used=9257.4MB, alloc=428.8MB, time=118.35 memory used=9302.6MB, alloc=428.8MB, time=118.50 memory used=9354.5MB, alloc=428.8MB, 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memory used=12200.3MB, alloc=428.8MB, time=124.43 memory used=12292.2MB, alloc=428.8MB, time=124.59 memory used=12390.7MB, alloc=428.8MB, time=124.75 memory used=12490.2MB, alloc=428.8MB, time=124.91 memory used=12589.2MB, alloc=428.8MB, time=125.07 memory used=12687.7MB, alloc=428.8MB, time=125.23 memory used=12915.6MB, alloc=428.8MB, time=125.71 memory used=13036.2MB, alloc=428.8MB, time=125.94 memory used=13160.3MB, alloc=428.8MB, time=126.17 memory used=13290.7MB, alloc=428.8MB, time=126.41 memory used=13421.0MB, alloc=428.8MB, time=126.64 memory used=13552.1MB, alloc=428.8MB, time=126.87 memory used=13686.7MB, alloc=428.8MB, time=127.10 memory used=13825.9MB, alloc=428.8MB, time=127.34 memory used=13967.1MB, alloc=428.8MB, time=127.57 memory used=14115.6MB, alloc=428.8MB, time=127.82 memory used=14264.9MB, alloc=428.8MB, time=128.06 memory used=14420.1MB, alloc=428.8MB, time=128.31 memory used=14578.7MB, alloc=428.8MB, time=128.55 memory used=14743.7MB, alloc=428.8MB, time=128.80 memory used=14914.5MB, alloc=428.8MB, time=129.05 memory used=15092.2MB, alloc=428.8MB, time=129.30 memory used=15295.9MB, alloc=428.8MB, time=132.46 memory used=15375.1MB, alloc=428.8MB, time=132.71 memory used=15451.4MB, alloc=428.8MB, time=132.95 memory used=15539.2MB, alloc=428.8MB, time=133.21 memory used=15637.7MB, alloc=428.8MB, time=133.46 memory used=15734.0MB, alloc=428.8MB, time=133.68 memory used=15789.2MB, alloc=428.8MB, time=133.87 memory used=15846.6MB, alloc=428.8MB, time=134.06 memory used=15907.1MB, alloc=428.8MB, time=134.24 memory used=15969.8MB, alloc=428.8MB, time=134.45 memory used=16035.2MB, alloc=428.8MB, time=134.65 memory used=16108.2MB, alloc=428.8MB, time=134.86 memory used=16184.0MB, alloc=428.8MB, time=135.05 memory used=16262.0MB, alloc=428.8MB, time=135.25 memory used=16342.3MB, alloc=428.8MB, time=135.47 memory used=16424.7MB, alloc=428.8MB, time=135.66 memory used=16509.3MB, alloc=428.8MB, time=135.86 memory used=16596.6MB, alloc=428.8MB, time=136.08 memory used=16692.5MB, alloc=428.8MB, time=136.28 memory used=16791.2MB, alloc=428.8MB, time=136.49 memory used=16892.0MB, alloc=428.8MB, time=136.69 memory used=16994.9MB, alloc=428.8MB, time=136.89 memory used=17072.1MB, alloc=428.8MB, time=137.06 memory used=17118.4MB, alloc=428.8MB, time=137.19 memory used=17170.4MB, alloc=428.8MB, time=137.31 memory used=17223.6MB, alloc=428.8MB, time=137.45 memory used=17277.3MB, alloc=428.8MB, time=137.59 memory used=17331.3MB, alloc=428.8MB, time=137.73 memory used=17385.8MB, alloc=428.8MB, time=137.86 memory used=17440.6MB, alloc=428.8MB, time=137.98 memory used=17495.8MB, alloc=428.8MB, time=138.11 memory used=17551.4MB, alloc=428.8MB, time=138.24 memory used=17607.3MB, alloc=428.8MB, time=138.37 memory used=17663.5MB, alloc=428.8MB, time=138.50 memory used=17720.1MB, alloc=428.8MB, time=138.63 memory used=17777.0MB, alloc=428.8MB, time=138.76 memory used=17834.2MB, alloc=428.8MB, time=138.89 memory used=17891.6MB, alloc=428.8MB, time=139.02 memory used=17949.5MB, alloc=428.8MB, time=139.16 memory used=18008.7MB, alloc=428.8MB, time=139.30 memory used=18075.5MB, alloc=428.8MB, time=139.44 memory used=18135.9MB, alloc=428.8MB, time=139.57 memory used=18202.9MB, alloc=428.8MB, time=139.71 memory used=18271.8MB, alloc=428.8MB, time=139.85 memory used=18341.0MB, alloc=428.8MB, time=139.99 memory used=18410.5MB, alloc=428.8MB, time=140.12 memory used=18480.2MB, alloc=428.8MB, time=140.27 memory used=18550.1MB, alloc=428.8MB, time=140.41 memory used=18620.3MB, alloc=428.8MB, time=140.54 memory used=18690.6MB, alloc=428.8MB, time=140.68 memory used=18761.2MB, alloc=428.8MB, time=140.83 memory used=18833.3MB, alloc=428.8MB, time=140.97 memory used=18912.9MB, alloc=428.8MB, time=141.12 memory used=18994.0MB, alloc=428.8MB, time=141.27 memory used=19075.3MB, alloc=428.8MB, time=141.42 memory used=19156.6MB, alloc=428.8MB, time=141.57 memory used=19237.9MB, alloc=428.8MB, time=141.72 memory used=19319.4MB, alloc=428.8MB, time=141.87 memory used=19400.8MB, alloc=428.8MB, time=142.02 memory used=19482.3MB, alloc=428.8MB, time=142.18 memory used=19565.3MB, alloc=428.8MB, time=142.33 memory used=19655.3MB, alloc=428.8MB, time=142.48 memory used=19746.7MB, alloc=428.8MB, time=142.64 memory used=19837.9MB, alloc=428.8MB, time=142.80 memory used=19928.9MB, alloc=428.8MB, time=142.95 memory used=20019.8MB, alloc=428.8MB, time=143.11 memory used=20111.9MB, alloc=428.8MB, time=143.26 memory used=20210.6MB, alloc=428.8MB, time=143.43 memory used=20310.4MB, alloc=428.8MB, time=143.59 memory used=20409.7MB, alloc=428.8MB, time=143.74 memory used=20508.5MB, alloc=428.8MB, time=143.90 memory used=20608.7MB, alloc=428.8MB, time=144.06 memory used=20784.2MB, alloc=428.8MB, time=144.34 memory used=20904.7MB, alloc=428.8MB, time=144.56 memory used=21028.6MB, alloc=428.8MB, time=144.79 memory used=21159.0MB, alloc=428.8MB, time=145.02 memory used=21289.3MB, alloc=428.8MB, time=145.25 memory used=21420.4MB, alloc=428.8MB, time=145.48 memory used=21555.0MB, alloc=428.8MB, time=145.71 memory used=21694.2MB, alloc=428.8MB, time=145.94 memory used=21835.4MB, alloc=428.8MB, time=146.18 memory used=21983.9MB, alloc=428.8MB, time=146.42 memory used=22133.2MB, alloc=428.8MB, time=146.67 memory used=22288.4MB, alloc=428.8MB, time=146.91 memory used=22447.0MB, alloc=428.8MB, time=147.17 memory used=22612.0MB, alloc=428.8MB, time=147.41 memory used=22782.8MB, alloc=428.8MB, time=147.66 memory used=22960.5MB, alloc=428.8MB, 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(); 1428291833 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 F := [-6 x z + 4 x z + 15 x - 7 x y, -10 x z + 19 x z - z - 4 y z, 2 2 -18 x y z + x y z + 15 y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 2 3 2 G := [-18 x z - 2 y - y z + 19 x y, -x + 15 y z - 20 y z - 16 z, 2 2 3 17 x y + 2 x - 20 y z - 16] > Problem := [F,G]; 3 2 2 2 2 3 Problem := [[-6 x z + 4 x z + 15 x - 7 x y, -10 x z + 19 x z - z - 4 y z, 2 2 3 4 3 2 -18 x y z + x y z + 15 y ], [-18 x z - 2 y - y z + 19 x y, 3 2 2 2 3 -x + 15 y z - 20 y z - 16 z, 17 x y + 2 x - 20 y z - 16]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=46.8MB, alloc=60.3MB, time=0.81 memory used=86.5MB, alloc=60.3MB, time=1.36 memory used=130.6MB, alloc=68.3MB, time=1.93 memory used=171.9MB, alloc=92.3MB, time=2.51 memory used=236.9MB, alloc=92.3MB, time=3.12 memory used=308.5MB, alloc=92.3MB, time=3.88 memory used=373.4MB, alloc=92.3MB, time=4.81 memory used=436.7MB, alloc=116.3MB, time=5.74 memory used=511.4MB, alloc=116.3MB, time=6.88 memory used=572.3MB, alloc=396.3MB, time=7.86 memory used=681.7MB, alloc=396.3MB, time=9.31 memory used=791.2MB, alloc=420.3MB, time=10.95 memory used=923.1MB, alloc=444.3MB, time=12.87 memory used=1072.9MB, alloc=468.3MB, time=15.10 memory used=1197.2MB, alloc=468.3MB, time=16.97 memory used=1319.8MB, alloc=492.3MB, time=18.77 memory used=1427.0MB, alloc=492.3MB, time=20.37 memory used=1537.7MB, alloc=492.3MB, time=21.79 memory used=1645.3MB, alloc=492.3MB, time=23.25 memory used=1734.5MB, alloc=492.3MB, time=24.50 memory used=1825.8MB, alloc=492.3MB, time=26.12 memory used=1906.9MB, alloc=492.3MB, time=27.62 memory used=1975.4MB, alloc=516.3MB, time=28.88 memory used=2050.2MB, alloc=516.3MB, time=30.34 memory used=2119.3MB, alloc=516.3MB, time=31.76 memory used=2182.7MB, alloc=516.3MB, time=32.87 memory used=2259.4MB, alloc=516.3MB, time=34.25 memory used=2314.2MB, alloc=516.3MB, time=35.42 memory used=2374.2MB, alloc=516.3MB, time=36.64 memory used=2423.8MB, alloc=516.3MB, time=37.87 memory used=2630.0MB, alloc=540.3MB, time=41.62 memory used=2844.1MB, alloc=564.3MB, time=45.75 memory used=3057.8MB, alloc=588.3MB, time=48.43 memory used=3228.2MB, alloc=612.3MB, time=51.07 memory used=3408.8MB, alloc=612.3MB, time=53.66 memory used=3577.4MB, alloc=612.3MB, time=56.81 memory used=3731.2MB, alloc=636.3MB, time=60.05 memory used=3879.2MB, alloc=636.3MB, time=63.15 memory used=4052.8MB, alloc=636.3MB, time=67.07 memory used=4199.9MB, alloc=660.3MB, time=70.13 memory used=4346.8MB, alloc=660.3MB, time=72.64 memory used=4448.5MB, alloc=660.3MB, time=74.77 memory used=4542.3MB, alloc=660.3MB, time=76.80 memory used=4693.0MB, alloc=660.3MB, time=79.21 memory used=4773.9MB, alloc=660.3MB, time=81.08 memory used=4873.3MB, alloc=660.3MB, time=83.95 memory used=5198.4MB, alloc=684.3MB, time=91.21 memory used=5541.0MB, alloc=708.3MB, time=99.20 memory used=5909.9MB, alloc=732.3MB, time=106.85 memory used=6298.9MB, alloc=756.3MB, time=114.37 memory used=6632.5MB, alloc=780.3MB, time=121.35 |\^/| 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(); 1428292133 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 3 2 2 F := [-16 x y z - 10 y z - 3 y z - z, 10 x y + 4 x z - 11 x z - 18 x z , 2 x y + 14 x z - 14 x + 9 y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 4 3 2 G := [2 x y - 4 x y z - 15 x z + 20 y , -8 y + 19 x y z + 16 z - 15 z , 4 2 4 3 -4 x + 13 x y z + 5 y - 9 z ] > Problem := [F,G]; 2 2 2 3 Problem := [[-16 x y z - 10 y z - 3 y z - z, 3 3 2 2 10 x y + 4 x z - 11 x z - 18 x z , 2 x y + 14 x z - 14 x + 9 y], [ 3 2 2 3 4 3 2 2 x y - 4 x y z - 15 x z + 20 y , -8 y + 19 x y z + 16 z - 15 z , 4 2 4 3 -4 x + 13 x y z + 5 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=0.17 memory used=27.1MB, alloc=32.3MB, time=0.51 memory used=46.0MB, alloc=56.3MB, time=0.80 memory used=87.1MB, alloc=60.3MB, time=1.41 memory used=128.0MB, alloc=84.3MB, time=1.99 memory used=168.2MB, alloc=84.3MB, time=2.52 memory used=238.1MB, alloc=92.3MB, time=3.24 memory used=288.0MB, alloc=92.3MB, time=3.62 memory used=355.2MB, alloc=92.3MB, time=4.53 memory used=418.4MB, alloc=116.3MB, time=5.39 memory used=502.5MB, alloc=116.3MB, time=6.21 memory used=572.2MB, alloc=116.3MB, time=6.75 memory used=649.1MB, alloc=116.3MB, time=7.50 memory used=718.6MB, alloc=372.3MB, time=8.58 memory used=803.7MB, alloc=396.3MB, time=9.82 memory used=911.0MB, alloc=420.3MB, time=11.39 memory used=1041.9MB, alloc=444.3MB, time=13.15 memory used=1166.4MB, alloc=444.3MB, time=14.88 memory used=1286.6MB, alloc=468.3MB, time=16.38 memory used=1393.6MB, alloc=468.3MB, time=17.96 memory used=1528.2MB, alloc=468.3MB, time=19.28 memory used=1608.9MB, alloc=468.3MB, time=19.63 memory used=1699.7MB, alloc=468.3MB, time=20.14 memory used=1800.5MB, alloc=468.3MB, time=23.49 memory used=1875.5MB, alloc=468.3MB, time=23.83 memory used=1951.9MB, alloc=468.3MB, time=24.14 memory used=2048.2MB, alloc=468.3MB, time=24.64 memory used=2136.7MB, alloc=468.3MB, time=25.15 memory used=2231.5MB, alloc=468.3MB, time=28.57 memory used=2317.2MB, alloc=468.3MB, time=28.93 memory used=2397.5MB, alloc=468.3MB, time=29.24 memory used=2483.9MB, alloc=468.3MB, time=29.70 memory used=2579.1MB, alloc=468.3MB, time=30.17 memory used=2654.3MB, alloc=468.3MB, time=30.50 memory used=2758.4MB, alloc=468.3MB, time=33.82 memory used=2833.2MB, alloc=468.3MB, time=34.13 memory used=2914.6MB, alloc=468.3MB, time=34.58 memory used=3070.1MB, alloc=468.3MB, time=36.37 memory used=3178.2MB, alloc=468.3MB, time=37.71 memory used=3317.8MB, alloc=492.3MB, time=43.93 memory used=3410.7MB, alloc=492.3MB, time=44.34 memory used=3507.9MB, alloc=492.3MB, time=44.69 memory used=3641.6MB, alloc=492.3MB, time=45.66 memory used=3766.7MB, alloc=492.3MB, time=47.06 memory used=3874.6MB, alloc=492.3MB, time=47.61 memory used=3975.4MB, alloc=492.3MB, time=48.18 memory used=4088.2MB, alloc=492.3MB, time=51.53 memory used=4173.0MB, alloc=492.3MB, time=51.94 memory used=4279.9MB, alloc=492.3MB, time=52.54 memory used=4363.9MB, alloc=492.3MB, time=52.93 memory used=4478.4MB, alloc=492.3MB, time=53.71 memory used=4576.0MB, alloc=492.3MB, time=54.24 memory used=4694.6MB, alloc=492.3MB, time=57.74 memory used=4777.9MB, alloc=492.3MB, time=58.11 memory used=4879.6MB, alloc=492.3MB, time=58.65 memory used=4975.3MB, alloc=492.3MB, time=59.17 memory used=5083.2MB, alloc=492.3MB, time=59.75 memory used=5198.1MB, alloc=492.3MB, time=63.24 memory used=5283.1MB, alloc=492.3MB, time=63.61 memory used=5434.4MB, alloc=492.3MB, time=65.08 memory used=5563.6MB, alloc=492.3MB, time=66.59 memory used=5719.3MB, alloc=492.3MB, time=72.38 memory used=5796.9MB, alloc=492.3MB, time=72.76 memory used=5879.2MB, alloc=492.3MB, time=73.14 memory used=5983.7MB, alloc=492.3MB, time=74.33 memory used=6073.5MB, alloc=516.3MB, time=75.82 memory used=6144.4MB, alloc=516.3MB, time=76.96 memory used=6200.7MB, alloc=516.3MB, time=77.79 memory used=6282.3MB, alloc=516.3MB, time=79.36 memory used=6350.1MB, alloc=516.3MB, time=80.53 memory used=6422.1MB, alloc=516.3MB, time=81.75 memory used=6480.3MB, alloc=516.3MB, time=82.96 memory used=6531.2MB, alloc=516.3MB, time=83.93 memory used=6595.9MB, alloc=516.3MB, time=85.08 memory used=6640.9MB, alloc=516.3MB, time=86.17 memory used=6842.0MB, alloc=540.3MB, time=89.38 memory used=7059.3MB, alloc=564.3MB, time=92.16 memory used=7218.9MB, alloc=564.3MB, time=93.48 memory used=7327.8MB, alloc=564.3MB, time=94.15 memory used=7463.3MB, alloc=564.3MB, time=95.04 memory used=7598.2MB, alloc=564.3MB, time=100.01 memory used=7711.7MB, alloc=564.3MB, time=100.66 memory used=7842.5MB, alloc=564.3MB, time=101.66 memory used=7952.3MB, alloc=564.3MB, time=102.33 memory used=8088.3MB, alloc=564.3MB, time=103.21 memory used=8223.2MB, alloc=564.3MB, time=108.21 memory used=8335.9MB, alloc=564.3MB, time=108.88 memory used=8460.1MB, alloc=564.3MB, time=109.73 memory used=8569.7MB, alloc=564.3MB, time=110.41 memory used=8706.3MB, alloc=564.3MB, time=111.31 memory used=8844.0MB, alloc=564.3MB, time=116.26 memory used=8956.2MB, alloc=564.3MB, time=116.92 memory used=9168.3MB, alloc=564.3MB, time=119.80 memory used=9382.0MB, alloc=588.3MB, time=128.90 memory used=9505.1MB, alloc=588.3MB, time=129.62 memory used=9628.0MB, alloc=588.3MB, time=130.28 memory used=9858.8MB, alloc=588.3MB, time=133.20 memory used=10024.5MB, alloc=588.3MB, time=136.02 memory used=10248.5MB, alloc=612.3MB, time=137.91 memory used=10438.5MB, alloc=612.3MB, time=141.05 memory used=10667.7MB, alloc=612.3MB, time=148.13 memory used=10920.3MB, alloc=612.3MB, time=150.49 memory used=11080.0MB, alloc=612.3MB, time=151.53 memory used=11277.8MB, alloc=612.3MB, time=155.96 memory used=11439.7MB, alloc=612.3MB, time=157.01 memory used=11602.9MB, alloc=612.3MB, time=158.14 memory used=11807.4MB, alloc=612.3MB, time=162.74 memory used=11964.4MB, alloc=612.3MB, time=163.80 memory used=12127.1MB, alloc=612.3MB, time=164.91 memory used=12324.3MB, alloc=612.3MB, time=169.31 memory used=12557.1MB, alloc=612.3MB, time=172.20 memory used=12788.0MB, alloc=612.3MB, time=178.93 memory used=12913.0MB, alloc=612.3MB, time=179.72 memory used=13059.1MB, alloc=612.3MB, time=181.92 memory used=13281.7MB, alloc=612.3MB, time=184.84 memory used=13482.2MB, alloc=612.3MB, time=187.49 memory used=13624.8MB, alloc=612.3MB, time=189.93 memory used=13780.9MB, alloc=636.3MB, time=193.05 memory used=13896.8MB, alloc=636.3MB, 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(); 1428292433 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 4 2 F := [9 x z - 4 x z - 4 y z + 6 z, -18 x z + 15 y z - 7 z + 8 z , 3 4 13 x y - 14 y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 2 2 G := [-7 y z - 14 x y z + 16 y - 8 y, -10 y z + 17 y z + 5 x z - 13 y , 3 2 2 -18 x y + 16 x y z - 16 x z + 10 x y] > Problem := [F,G]; 3 2 2 3 3 4 2 Problem := [[9 x z - 4 x z - 4 y z + 6 z, -18 x z + 15 y z - 7 z + 8 z , 3 4 2 2 3 13 x y - 14 y ], [-7 y z - 14 x y z + 16 y - 8 y, 2 2 3 2 2 -10 y z + 17 y z + 5 x z - 13 y , 3 2 2 -18 x y + 16 x y z - 16 x 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=26.9MB, alloc=32.3MB, time=0.52 memory used=46.5MB, alloc=56.3MB, time=0.85 memory used=88.9MB, alloc=60.3MB, time=1.47 memory used=128.6MB, alloc=60.3MB, time=2.07 memory used=165.2MB, alloc=84.3MB, time=2.60 memory used=228.3MB, alloc=92.3MB, time=3.56 memory used=293.1MB, alloc=92.3MB, time=4.51 memory used=356.0MB, alloc=116.3MB, time=5.49 memory used=428.0MB, alloc=116.3MB, time=6.14 memory used=492.8MB, alloc=116.3MB, time=6.70 memory used=557.7MB, alloc=372.3MB, time=7.53 memory used=644.6MB, alloc=396.3MB, time=8.84 memory used=755.5MB, alloc=396.3MB, time=10.44 memory used=865.0MB, alloc=420.3MB, time=12.08 memory used=1001.7MB, alloc=420.3MB, time=13.62 memory used=1126.4MB, alloc=420.3MB, time=15.26 memory used=1244.0MB, alloc=420.3MB, time=16.62 memory used=1380.2MB, alloc=444.3MB, time=18.56 memory used=1505.4MB, alloc=444.3MB, time=20.43 memory used=1652.7MB, alloc=468.3MB, time=22.22 memory used=1775.3MB, alloc=468.3MB, time=23.28 memory used=1868.9MB, alloc=468.3MB, time=24.19 memory used=2032.8MB, alloc=468.3MB, time=25.82 memory used=2220.5MB, alloc=468.3MB, time=27.77 memory used=2337.7MB, alloc=468.3MB, time=28.73 memory used=2425.9MB, alloc=468.3MB, time=29.55 memory used=2557.1MB, alloc=468.3MB, time=31.26 memory used=2687.6MB, alloc=468.3MB, time=33.05 memory used=2804.2MB, alloc=492.3MB, time=34.47 memory used=2916.8MB, alloc=492.3MB, time=35.81 memory used=3037.0MB, alloc=492.3MB, time=37.45 memory used=3186.1MB, alloc=492.3MB, time=38.66 memory used=3285.0MB, alloc=492.3MB, time=39.30 memory used=3392.3MB, alloc=492.3MB, time=40.19 memory used=3518.5MB, alloc=492.3MB, time=41.88 memory used=3615.4MB, alloc=492.3MB, time=43.78 memory used=3698.6MB, alloc=492.3MB, time=45.35 memory used=3780.7MB, alloc=492.3MB, time=46.88 memory used=3860.1MB, alloc=516.3MB, time=48.40 memory used=3941.8MB, alloc=516.3MB, time=50.10 memory used=4015.6MB, alloc=516.3MB, time=51.60 memory used=4072.2MB, alloc=516.3MB, time=52.61 memory used=4150.5MB, alloc=516.3MB, time=53.71 memory used=4255.2MB, alloc=516.3MB, time=54.87 memory used=4346.2MB, alloc=516.3MB, time=56.21 memory used=4410.1MB, alloc=516.3MB, time=57.39 memory used=4489.8MB, alloc=516.3MB, time=58.53 memory used=4534.8MB, alloc=516.3MB, time=59.41 memory used=4584.1MB, alloc=516.3MB, time=60.23 memory used=4785.3MB, alloc=540.3MB, time=64.08 memory used=5001.7MB, alloc=564.3MB, time=68.12 memory used=5197.9MB, alloc=588.3MB, time=71.42 memory used=5396.2MB, alloc=612.3MB, time=75.56 memory used=5589.0MB, alloc=636.3MB, time=79.59 memory used=5795.2MB, alloc=660.3MB, time=83.10 memory used=5976.8MB, alloc=660.3MB, time=86.34 memory used=6155.3MB, alloc=660.3MB, time=89.77 memory used=6351.6MB, alloc=684.3MB, time=93.51 memory used=6565.8MB, alloc=684.3MB, time=95.81 memory used=6764.6MB, alloc=684.3MB, time=97.46 memory used=6938.4MB, alloc=684.3MB, time=100.32 memory used=7133.8MB, alloc=684.3MB, time=102.88 memory used=7361.8MB, alloc=684.3MB, time=105.64 memory used=7539.4MB, alloc=684.3MB, time=108.17 memory used=7704.9MB, alloc=684.3MB, time=109.31 memory used=7896.8MB, alloc=684.3MB, time=113.05 memory used=8042.5MB, alloc=684.3MB, time=113.92 memory used=8224.3MB, alloc=684.3MB, time=116.23 memory used=8457.3MB, alloc=684.3MB, time=119.92 memory used=8610.9MB, alloc=684.3MB, time=120.87 memory used=8858.5MB, alloc=708.3MB, time=124.13 memory used=9074.5MB, alloc=708.3MB, time=126.99 memory used=9217.1MB, alloc=708.3MB, time=130.79 memory used=9316.3MB, alloc=708.3MB, time=133.15 memory used=9430.6MB, alloc=708.3MB, time=135.69 memory used=9689.8MB, alloc=732.3MB, time=140.11 memory used=10008.4MB, alloc=732.3MB, time=144.51 memory used=10387.1MB, alloc=756.3MB, time=151.56 memory used=10819.8MB, alloc=780.3MB, time=159.59 memory used=11123.3MB, alloc=804.3MB, time=163.51 memory used=11369.1MB, alloc=828.3MB, time=166.32 memory used=11611.4MB, alloc=828.3MB, time=168.09 memory used=11856.3MB, alloc=828.3MB, time=171.19 memory used=12097.8MB, alloc=828.3MB, time=173.31 memory used=12355.4MB, alloc=828.3MB, time=177.71 memory used=12597.9MB, alloc=828.3MB, time=183.65 memory used=12824.1MB, alloc=828.3MB, time=185.32 |\^/| 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(); 1428292733 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 2 2 2 3 2 F := [-13 x y - y + 6 x + 10, -11 x y - 14 x z + 18 z + 2 y , 2 2 2 -8 x y + 19 x y - 12 x - 12 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-2 x y - 11 y z - 4 y z + 2 y, 2 x y z - 11 x y z + 9 x z + 16 x z, 2 2 2 -19 x y z + x y z - 13 x y z - 4 y z ] > Problem := [F,G]; 3 4 3 2 2 2 3 2 Problem := [[-13 x y - y + 6 x + 10, -11 x y - 14 x z + 18 z + 2 y , 2 2 2 2 2 -8 x y + 19 x y - 12 x - 12 x], [-2 x y - 11 y z - 4 y z + 2 y, 2 2 2 x y z - 11 x y z + 9 x z + 16 x z, 2 2 2 -19 x y z + x y z - 13 x y z - 4 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.49 memory used=46.1MB, alloc=32.3MB, time=0.79 memory used=65.2MB, alloc=56.3MB, time=1.08 memory used=105.2MB, alloc=60.3MB, time=1.69 memory used=144.2MB, alloc=60.3MB, time=2.26 memory used=179.8MB, alloc=84.3MB, time=2.82 memory used=222.5MB, alloc=84.3MB, time=3.51 memory used=280.9MB, alloc=92.3MB, time=4.46 memory used=337.9MB, alloc=116.3MB, time=5.39 memory used=418.8MB, alloc=116.3MB, time=6.75 memory used=497.8MB, alloc=140.3MB, time=8.05 memory used=574.9MB, alloc=140.3MB, time=9.31 memory used=666.2MB, alloc=420.3MB, time=10.90 memory used=788.6MB, alloc=444.3MB, time=13.02 memory used=940.8MB, alloc=468.3MB, time=15.71 memory used=1098.6MB, alloc=492.3MB, time=18.70 memory used=1251.7MB, alloc=492.3MB, time=21.93 memory used=1377.3MB, alloc=516.3MB, time=24.09 memory used=1503.1MB, alloc=516.3MB, time=26.28 memory used=1620.4MB, alloc=516.3MB, time=28.48 memory used=1756.5MB, alloc=540.3MB, time=31.34 memory used=1878.1MB, alloc=540.3MB, time=33.91 memory used=1971.7MB, alloc=540.3MB, time=35.83 memory used=2055.7MB, alloc=540.3MB, time=37.46 memory used=2160.3MB, alloc=540.3MB, time=39.78 memory used=2253.9MB, alloc=540.3MB, time=41.58 memory used=2343.6MB, alloc=540.3MB, time=43.41 memory used=2414.6MB, alloc=540.3MB, time=44.93 memory used=2501.3MB, alloc=540.3MB, time=46.95 memory used=2588.1MB, alloc=540.3MB, time=49.05 memory used=2677.5MB, alloc=540.3MB, time=51.31 memory used=2757.8MB, alloc=540.3MB, time=53.35 memory used=2808.6MB, alloc=540.3MB, time=54.48 memory used=2903.6MB, alloc=540.3MB, time=57.20 memory used=2984.4MB, alloc=540.3MB, time=59.37 memory used=3036.7MB, alloc=564.3MB, time=60.74 memory used=3110.8MB, alloc=564.3MB, time=62.98 memory used=3359.8MB, alloc=588.3MB, time=69.66 memory used=3607.3MB, alloc=612.3MB, time=75.43 memory used=3815.3MB, alloc=636.3MB, time=79.85 memory used=4077.4MB, alloc=660.3MB, time=83.56 memory used=4281.0MB, alloc=660.3MB, time=85.79 memory used=4528.2MB, alloc=660.3MB, time=88.48 memory used=4709.1MB, alloc=660.3MB, time=90.11 memory used=4887.0MB, alloc=660.3MB, time=91.67 memory used=5110.7MB, alloc=660.3MB, time=94.80 memory used=5373.5MB, alloc=660.3MB, time=98.80 memory used=5576.7MB, alloc=660.3MB, time=102.34 memory used=5751.6MB, alloc=684.3MB, time=106.75 memory used=5957.5MB, alloc=684.3MB, time=111.04 memory used=6098.5MB, alloc=684.3MB, time=114.25 memory used=6261.0MB, alloc=708.3MB, time=117.31 memory used=6382.7MB, alloc=708.3MB, time=120.47 memory used=6528.0MB, alloc=708.3MB, time=124.73 memory used=6687.3MB, alloc=708.3MB, time=129.38 memory used=6825.9MB, alloc=708.3MB, time=133.43 memory used=6941.4MB, alloc=732.3MB, time=136.46 memory used=7053.6MB, alloc=732.3MB, time=139.17 memory used=7287.5MB, alloc=732.3MB, time=141.51 memory used=7462.9MB, alloc=732.3MB, time=143.98 memory used=7537.8MB, alloc=732.3MB, time=146.14 memory used=7930.5MB, alloc=756.3MB, time=154.00 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428293033 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [8 x - 14 y + 15 z + 1, 10 x y z - 12 x - 11 y + 20 x, 2 -16 x y - 17 x y z + 8 x y + 12] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 2 2 3 2 G := [-13 x y + 8 x z - 19 x y z - 4 z , -10 x z + 7 y - y z + 8 z, 4 3 4 12 y + 15 y z - 16 z - 15 x] > Problem := [F,G]; 3 2 2 Problem := [[8 x - 14 y + 15 z + 1, 10 x y z - 12 x - 11 y + 20 x, 2 3 3 2 4 -16 x y - 17 x y z + 8 x y + 12], [-13 x y + 8 x z - 19 x y z - 4 z , 2 2 3 2 4 3 4 -10 x z + 7 y - y z + 8 z, 12 y + 15 y z - 16 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=25.4MB, alloc=32.3MB, time=0.50 memory used=45.2MB, alloc=32.3MB, time=0.80 memory used=62.9MB, alloc=60.3MB, time=1.08 memory used=108.7MB, alloc=68.3MB, time=1.70 memory used=155.4MB, alloc=92.3MB, time=2.31 memory used=224.1MB, alloc=92.3MB, time=3.29 memory used=289.6MB, alloc=348.3MB, time=4.22 memory used=357.2MB, alloc=372.3MB, time=5.14 memory used=442.9MB, alloc=372.3MB, time=6.06 memory used=496.8MB, alloc=372.3MB, time=6.34 memory used=593.1MB, alloc=372.3MB, time=7.24 memory used=692.2MB, alloc=372.3MB, time=8.32 memory used=740.5MB, alloc=372.3MB, time=8.67 memory used=821.8MB, alloc=372.3MB, time=9.39 memory used=908.9MB, alloc=396.3MB, time=10.75 memory used=1020.0MB, alloc=420.3MB, time=12.51 memory used=1145.4MB, alloc=420.3MB, time=13.80 memory used=1288.5MB, alloc=420.3MB, time=15.29 memory used=1370.6MB, alloc=420.3MB, time=15.93 memory used=1444.7MB, alloc=420.3MB, time=16.35 memory used=1567.6MB, alloc=420.3MB, time=17.55 memory used=1681.3MB, alloc=444.3MB, time=19.29 memory used=1798.4MB, alloc=444.3MB, time=20.81 memory used=1924.8MB, alloc=444.3MB, time=22.17 memory used=2059.9MB, alloc=444.3MB, time=24.07 memory used=2162.3MB, alloc=444.3MB, time=25.70 memory used=2271.0MB, alloc=468.3MB, time=27.11 memory used=2372.2MB, alloc=468.3MB, time=27.66 memory used=2464.8MB, alloc=468.3MB, time=28.17 memory used=2572.6MB, alloc=468.3MB, time=28.83 memory used=2658.2MB, alloc=468.3MB, time=29.25 memory used=2754.1MB, alloc=468.3MB, time=29.69 memory used=2860.2MB, alloc=468.3MB, time=31.73 memory used=2935.9MB, alloc=468.3MB, time=32.06 memory used=3013.5MB, alloc=468.3MB, time=32.36 memory used=3082.0MB, alloc=468.3MB, time=32.63 memory used=3182.4MB, alloc=468.3MB, time=33.12 memory used=3275.0MB, alloc=468.3MB, time=33.87 memory used=3354.9MB, alloc=468.3MB, time=34.19 memory used=3478.0MB, alloc=468.3MB, time=35.41 memory used=3619.8MB, alloc=468.3MB, time=36.60 memory used=3741.1MB, alloc=468.3MB, time=37.66 memory used=3835.8MB, alloc=468.3MB, time=38.46 memory used=3912.1MB, alloc=468.3MB, time=38.79 memory used=4055.8MB, alloc=468.3MB, time=39.92 memory used=4149.5MB, alloc=468.3MB, time=41.40 memory used=4264.8MB, alloc=468.3MB, time=42.37 memory used=4352.7MB, alloc=468.3MB, time=42.87 memory used=4451.2MB, alloc=468.3MB, time=44.07 memory used=4526.0MB, alloc=468.3MB, time=44.45 memory used=4596.3MB, alloc=468.3MB, time=44.77 memory used=4683.4MB, alloc=468.3MB, time=45.32 memory used=4769.4MB, alloc=468.3MB, time=45.90 memory used=4895.2MB, alloc=468.3MB, time=46.89 memory used=5004.6MB, alloc=492.3MB, time=48.09 memory used=5106.7MB, alloc=492.3MB, time=48.54 memory used=5206.7MB, alloc=492.3MB, time=49.58 memory used=5295.3MB, alloc=492.3MB, time=49.98 memory used=5385.6MB, alloc=492.3MB, time=50.34 memory used=5465.0MB, alloc=492.3MB, time=50.69 memory used=5592.6MB, alloc=492.3MB, time=51.84 memory used=5677.9MB, alloc=492.3MB, time=52.23 memory used=5785.2MB, alloc=492.3MB, time=53.35 memory used=5882.4MB, alloc=492.3MB, time=53.76 memory used=5953.7MB, alloc=492.3MB, time=54.11 memory used=6102.3MB, alloc=492.3MB, time=55.29 memory used=6177.6MB, alloc=492.3MB, time=56.43 memory used=6265.7MB, alloc=492.3MB, time=57.76 memory used=6371.7MB, alloc=492.3MB, time=58.77 memory used=6466.4MB, alloc=492.3MB, time=59.76 memory used=6543.4MB, alloc=492.3MB, time=61.09 memory used=6607.5MB, alloc=492.3MB, time=62.33 memory used=6660.7MB, alloc=492.3MB, time=63.30 memory used=6714.8MB, alloc=492.3MB, time=64.28 memory used=6766.3MB, alloc=492.3MB, time=65.11 memory used=6821.3MB, alloc=492.3MB, time=66.19 memory used=6873.3MB, alloc=492.3MB, time=67.13 memory used=7059.2MB, alloc=516.3MB, time=69.60 memory used=7256.9MB, alloc=540.3MB, time=72.69 memory used=7483.1MB, alloc=564.3MB, time=75.93 memory used=7688.2MB, alloc=588.3MB, time=78.33 memory used=7865.0MB, alloc=612.3MB, time=81.39 memory used=7997.6MB, alloc=612.3MB, time=83.83 memory used=8157.7MB, alloc=612.3MB, time=86.25 memory used=8290.2MB, alloc=636.3MB, time=88.29 memory used=8442.9MB, alloc=636.3MB, time=91.09 memory used=8570.2MB, alloc=636.3MB, time=93.12 memory used=8690.6MB, alloc=660.3MB, time=95.13 memory used=8837.0MB, alloc=660.3MB, time=97.81 memory used=8964.6MB, alloc=660.3MB, time=99.99 memory used=9105.6MB, alloc=660.3MB, time=102.18 memory used=9329.4MB, alloc=660.3MB, time=104.35 memory used=9523.4MB, alloc=660.3MB, time=105.66 memory used=9705.0MB, alloc=660.3MB, time=109.08 memory used=9880.5MB, alloc=660.3MB, time=110.36 memory used=10029.7MB, alloc=660.3MB, time=111.38 memory used=10205.5MB, alloc=660.3MB, time=112.65 memory used=10352.8MB, alloc=660.3MB, time=113.63 memory used=10554.7MB, alloc=660.3MB, time=120.14 memory used=10696.4MB, alloc=660.3MB, time=121.10 memory used=10894.0MB, alloc=660.3MB, time=124.63 memory used=11087.5MB, alloc=660.3MB, time=126.94 memory used=11197.6MB, alloc=660.3MB, time=128.89 memory used=11316.3MB, alloc=660.3MB, time=130.81 memory used=11432.5MB, alloc=684.3MB, time=132.79 memory used=11748.0MB, alloc=684.3MB, time=142.26 memory used=11908.4MB, alloc=684.3MB, time=143.26 memory used=12239.3MB, alloc=708.3MB, time=146.56 memory used=12530.8MB, alloc=708.3MB, time=149.27 memory used=12774.4MB, alloc=708.3MB, time=151.77 memory used=12971.5MB, alloc=708.3MB, time=154.18 memory used=13162.1MB, alloc=708.3MB, time=155.50 memory used=13327.2MB, alloc=708.3MB, time=156.59 memory used=13526.2MB, alloc=708.3MB, time=158.05 memory used=13737.7MB, alloc=708.3MB, time=162.97 memory used=13904.0MB, alloc=708.3MB, time=164.05 memory used=14094.5MB, alloc=708.3MB, time=165.92 memory used=14268.7MB, alloc=708.3MB, time=167.12 memory used=14410.8MB, alloc=732.3MB, time=168.23 memory used=14609.2MB, alloc=732.3MB, time=169.38 memory used=14788.5MB, alloc=732.3MB, time=170.46 memory used=14927.6MB, alloc=732.3MB, time=171.43 memory used=15082.5MB, alloc=732.3MB, time=172.44 memory used=15258.1MB, alloc=732.3MB, time=173.45 memory used=15462.0MB, alloc=732.3MB, time=174.46 memory used=15697.2MB, alloc=732.3MB, time=176.57 memory used=15852.5MB, alloc=732.3MB, time=177.71 memory used=16046.2MB, alloc=732.3MB, time=178.86 memory used=16237.8MB, alloc=732.3MB, time=179.92 memory used=16372.4MB, alloc=732.3MB, time=180.90 memory used=16524.0MB, alloc=732.3MB, time=181.88 memory used=16696.5MB, alloc=732.3MB, time=182.90 memory used=16895.1MB, alloc=732.3MB, time=183.89 memory used=17135.4MB, alloc=732.3MB, time=205.58 memory used=17321.0MB, alloc=732.3MB, time=206.70 memory used=17472.2MB, alloc=732.3MB, time=207.71 memory used=17666.6MB, alloc=732.3MB, time=208.77 memory used=17875.8MB, alloc=732.3MB, time=209.92 memory used=18163.0MB, alloc=732.3MB, time=211.40 |\^/| 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(); 1428293333 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 3 F := [11 z + 3 x + 20 x y + 13 z, -17 x y + 11 x y z + 2 x y + 13 z , 3 2 4 -8 x z - 19 x y z - 10 z - 19 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 3 2 G := [-3 x y - 19 x y - 20 y z + 7 x z, -x z - x z - 13 x + 15 z, 2 -x z - 15 x y z + 20 z + 5] > Problem := [F,G]; 4 2 Problem := [[11 z + 3 x + 20 x y + 13 z, 2 2 2 2 3 -17 x y + 11 x y z + 2 x y + 13 z , 3 2 4 -8 x z - 19 x y z - 10 z - 19 x z], [ 3 2 2 2 2 2 2 3 2 -3 x y - 19 x y - 20 y z + 7 x z, -x z - x z - 13 x + 15 z, 2 -x z - 15 x y z + 20 z + 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.18 memory used=25.8MB, alloc=32.3MB, time=0.50 memory used=45.0MB, alloc=56.3MB, time=0.77 memory used=84.8MB, alloc=62.5MB, time=1.05 memory used=129.2MB, alloc=62.5MB, time=1.68 memory used=169.7MB, alloc=62.5MB, time=2.23 memory used=214.1MB, alloc=70.5MB, time=2.84 memory used=257.0MB, alloc=70.5MB, time=3.26 memory used=286.7MB, alloc=94.5MB, time=3.39 memory used=339.5MB, alloc=94.5MB, time=3.87 memory used=396.0MB, alloc=94.5MB, time=4.05 memory used=431.1MB, alloc=94.5MB, time=4.17 memory used=465.3MB, alloc=94.5MB, time=4.30 memory used=506.0MB, alloc=94.5MB, time=4.41 memory used=552.8MB, alloc=94.5MB, time=4.53 memory used=583.5MB, alloc=94.5MB, time=4.64 memory used=613.2MB, alloc=94.5MB, time=4.75 memory used=645.8MB, alloc=94.5MB, time=4.85 memory used=690.7MB, alloc=94.5MB, time=5.16 memory used=747.6MB, alloc=94.5MB, time=5.34 memory used=782.6MB, alloc=94.5MB, time=5.46 memory used=816.0MB, alloc=94.5MB, time=5.58 memory used=855.7MB, alloc=94.5MB, time=5.72 memory used=901.6MB, alloc=94.5MB, time=5.85 memory used=932.8MB, alloc=94.5MB, time=5.96 memory used=961.5MB, alloc=94.5MB, time=6.07 memory used=992.7MB, alloc=94.5MB, time=6.17 memory used=1028.3MB, alloc=94.5MB, time=6.27 memory used=1094.8MB, alloc=95.4MB, time=8.55 memory used=1128.9MB, alloc=95.4MB, time=8.67 memory used=1171.3MB, alloc=95.4MB, time=8.79 memory used=1199.8MB, alloc=95.4MB, time=8.88 memory used=1232.3MB, alloc=95.4MB, time=8.98 memory used=1271.3MB, alloc=95.4MB, time=9.09 memory used=1339.3MB, alloc=95.4MB, time=9.84 memory used=1404.2MB, alloc=95.4MB, time=11.50 memory used=1438.8MB, alloc=95.4MB, time=11.63 memory used=1475.6MB, alloc=95.4MB, time=11.74 memory used=1503.9MB, alloc=95.4MB, time=11.83 memory used=1539.1MB, alloc=95.4MB, time=11.92 memory used=1598.8MB, alloc=95.4MB, time=12.34 memory used=1658.5MB, alloc=96.7MB, time=12.89 memory used=1703.6MB, alloc=96.7MB, time=13.68 memory used=1756.2MB, alloc=96.7MB, time=13.87 memory used=1803.0MB, alloc=96.7MB, time=14.01 memory used=1832.3MB, alloc=96.7MB, time=14.12 memory used=1861.8MB, alloc=96.7MB, time=14.24 memory used=1894.7MB, alloc=96.7MB, time=14.36 memory used=1930.8MB, alloc=96.7MB, time=14.47 memory used=1969.5MB, alloc=96.7MB, time=14.59 memory used=2012.0MB, alloc=96.7MB, time=14.72 memory used=2058.1MB, alloc=96.7MB, time=14.85 memory used=2086.4MB, alloc=96.7MB, time=14.96 memory used=2111.8MB, alloc=96.7MB, time=15.06 memory used=2138.6MB, alloc=96.7MB, time=15.15 memory used=2167.6MB, alloc=96.7MB, time=15.24 memory used=2198.2MB, alloc=96.7MB, time=15.34 memory used=2231.7MB, alloc=96.7MB, time=15.44 memory used=2286.3MB, alloc=96.7MB, time=16.30 memory used=2337.8MB, alloc=96.7MB, time=16.47 memory used=2377.5MB, alloc=96.7MB, time=16.61 memory used=2405.6MB, alloc=96.7MB, time=16.72 memory used=2435.4MB, alloc=96.7MB, time=16.84 memory used=2468.4MB, alloc=96.7MB, time=16.96 memory used=2504.6MB, alloc=96.7MB, time=17.07 memory used=2543.6MB, alloc=96.7MB, time=17.20 memory used=2586.1MB, alloc=96.7MB, time=17.32 memory used=2628.8MB, alloc=96.7MB, time=17.44 memory used=2654.4MB, alloc=96.7MB, time=17.54 memory used=2680.2MB, alloc=96.7MB, time=17.65 memory used=2706.8MB, alloc=96.7MB, time=17.74 memory used=2735.4MB, alloc=96.7MB, time=17.85 memory used=2766.2MB, alloc=96.7MB, time=17.94 memory used=2799.8MB, alloc=96.7MB, time=18.05 memory used=2841.3MB, alloc=96.7MB, time=18.67 memory used=2873.4MB, alloc=96.7MB, time=18.75 memory used=2920.8MB, alloc=96.7MB, time=19.04 memory used=2976.6MB, alloc=96.7MB, time=19.43 memory used=3018.2MB, alloc=96.7MB, time=19.62 memory used=3066.1MB, alloc=96.7MB, time=19.79 memory used=3115.8MB, alloc=96.7MB, time=20.61 memory used=3169.5MB, alloc=96.7MB, time=21.02 memory used=3244.9MB, alloc=96.7MB, time=22.98 memory used=3277.4MB, alloc=96.7MB, time=23.09 memory used=3312.5MB, alloc=96.7MB, time=23.20 memory used=3369.3MB, alloc=96.7MB, time=23.91 memory used=3432.1MB, alloc=96.7MB, time=24.78 memory used=3492.5MB, alloc=120.7MB, time=25.70 memory used=3562.6MB, alloc=120.7MB, time=26.72 memory used=3630.7MB, alloc=376.7MB, time=27.72 memory used=3706.2MB, alloc=376.7MB, time=28.43 memory used=3760.5MB, alloc=376.7MB, time=28.87 memory used=3832.1MB, alloc=376.7MB, time=29.64 memory used=3882.0MB, alloc=376.7MB, time=29.96 memory used=3925.6MB, alloc=376.7MB, time=30.18 memory used=3970.1MB, alloc=376.7MB, time=30.41 memory used=4030.7MB, alloc=400.7MB, time=31.22 memory used=4083.9MB, alloc=400.7MB, time=31.44 memory used=4140.8MB, alloc=400.7MB, time=31.66 memory used=4209.7MB, alloc=400.7MB, time=31.88 memory used=4249.6MB, alloc=400.7MB, time=32.05 memory used=4291.9MB, alloc=400.7MB, time=32.23 memory used=4337.7MB, alloc=400.7MB, time=32.40 memory used=4387.5MB, alloc=400.7MB, time=32.59 memory used=4441.4MB, alloc=400.7MB, time=32.78 memory used=4499.3MB, alloc=400.7MB, time=32.97 memory used=4561.3MB, alloc=400.7MB, time=33.15 memory used=4628.5MB, alloc=400.7MB, time=33.36 memory used=4684.0MB, alloc=400.7MB, time=33.52 memory used=4721.7MB, alloc=400.7MB, time=33.67 memory used=4759.6MB, alloc=400.7MB, time=33.81 memory used=4798.4MB, alloc=400.7MB, time=33.95 memory used=4838.9MB, alloc=400.7MB, time=34.09 memory used=4882.7MB, alloc=400.7MB, time=34.23 memory used=4928.3MB, alloc=400.7MB, time=34.38 memory used=4975.0MB, alloc=400.7MB, time=34.52 memory used=5024.2MB, alloc=400.7MB, time=34.65 memory used=5077.2MB, alloc=400.7MB, time=34.79 memory used=5132.8MB, alloc=400.7MB, time=34.93 memory used=5192.6MB, alloc=400.7MB, time=35.07 memory used=5273.8MB, alloc=400.7MB, time=36.01 memory used=5333.1MB, alloc=400.7MB, time=36.26 memory used=5387.9MB, alloc=400.7MB, time=36.47 memory used=5457.4MB, alloc=400.7MB, time=36.70 memory used=5501.6MB, alloc=400.7MB, time=36.88 memory used=5544.8MB, alloc=400.7MB, time=37.05 memory used=5590.5MB, alloc=400.7MB, time=37.22 memory used=5640.2MB, alloc=400.7MB, time=37.40 memory used=5694.0MB, alloc=400.7MB, time=37.57 memory used=5752.1MB, alloc=400.7MB, time=37.74 memory used=5815.8MB, alloc=400.7MB, time=37.92 memory used=5883.2MB, alloc=400.7MB, time=38.10 memory used=5939.6MB, alloc=400.7MB, time=38.27 memory used=5976.9MB, alloc=400.7MB, time=38.41 memory used=6014.5MB, alloc=400.7MB, time=38.55 memory used=6054.9MB, alloc=400.7MB, time=38.70 memory used=6095.7MB, alloc=400.7MB, time=38.84 memory used=6139.6MB, alloc=400.7MB, time=38.98 memory used=6185.3MB, alloc=400.7MB, time=39.12 memory used=6232.5MB, alloc=400.7MB, time=39.27 memory used=6283.4MB, alloc=400.7MB, time=39.41 memory used=6336.3MB, alloc=400.7MB, time=39.56 memory used=6393.1MB, alloc=400.7MB, time=39.71 memory used=6454.1MB, alloc=400.7MB, time=39.86 memory used=6548.4MB, alloc=400.7MB, time=45.76 memory used=6617.1MB, alloc=400.7MB, time=46.10 memory used=6672.9MB, alloc=400.7MB, time=46.29 memory used=6719.6MB, alloc=400.7MB, time=46.47 memory used=6775.0MB, alloc=400.7MB, time=46.66 memory used=6840.2MB, alloc=400.7MB, time=46.84 memory used=6893.9MB, alloc=400.7MB, time=47.00 memory used=6933.9MB, alloc=400.7MB, time=47.17 memory used=6976.9MB, alloc=400.7MB, time=47.32 memory used=7022.8MB, alloc=400.7MB, time=47.48 memory used=7072.5MB, alloc=400.7MB, time=47.63 memory used=7125.7MB, alloc=400.7MB, time=47.78 memory used=7183.7MB, alloc=400.7MB, time=47.93 memory used=7244.9MB, alloc=400.7MB, time=48.09 memory used=7369.7MB, alloc=400.7MB, time=48.58 memory used=7428.0MB, alloc=400.7MB, time=49.02 memory used=7513.5MB, alloc=400.7MB, time=49.70 memory used=7595.4MB, alloc=400.7MB, time=49.93 memory used=7665.7MB, alloc=400.7MB, time=50.86 memory used=7762.1MB, alloc=400.7MB, time=51.44 memory used=7808.0MB, alloc=400.7MB, time=51.64 memory used=7866.0MB, alloc=400.7MB, time=51.84 memory used=7927.8MB, alloc=400.7MB, time=52.03 memory used=7969.3MB, alloc=400.7MB, time=52.19 memory used=8015.4MB, alloc=400.7MB, time=52.36 memory used=8068.3MB, alloc=400.7MB, time=52.53 memory used=8156.0MB, alloc=400.7MB, time=53.73 memory used=8206.0MB, alloc=400.7MB, time=53.95 memory used=8256.3MB, alloc=400.7MB, time=54.16 memory used=8315.9MB, alloc=400.7MB, time=54.36 memory used=8384.8MB, alloc=400.7MB, time=54.58 memory used=8426.9MB, alloc=400.7MB, time=54.75 memory used=8466.5MB, alloc=400.7MB, time=54.93 memory used=8507.0MB, alloc=400.7MB, time=55.11 memory used=8551.2MB, alloc=400.7MB, time=55.28 memory used=8597.0MB, alloc=400.7MB, time=55.47 memory used=8647.0MB, alloc=400.7MB, time=55.64 memory used=8698.4MB, alloc=400.7MB, time=55.83 memory used=8754.0MB, alloc=400.7MB, time=56.02 memory used=8811.0MB, alloc=400.7MB, time=56.21 memory used=8871.5MB, alloc=400.7MB, time=56.39 memory used=8936.4MB, alloc=400.7MB, time=56.59 memory used=9000.9MB, alloc=400.7MB, time=56.77 memory used=9051.4MB, alloc=400.7MB, time=56.93 memory used=9087.3MB, alloc=400.7MB, time=57.06 memory used=9123.2MB, alloc=400.7MB, time=57.21 memory used=9160.0MB, alloc=400.7MB, time=57.35 memory used=9196.8MB, alloc=400.7MB, time=57.49 memory used=9236.5MB, alloc=400.7MB, time=57.65 memory used=9276.0MB, alloc=400.7MB, time=57.79 memory used=9315.9MB, alloc=400.7MB, time=57.94 memory used=9357.6MB, alloc=400.7MB, time=58.08 memory used=9401.4MB, alloc=400.7MB, time=58.22 memory used=9445.7MB, alloc=400.7MB, time=58.36 memory used=9491.7MB, alloc=400.7MB, time=58.51 memory used=9539.3MB, alloc=400.7MB, time=58.65 memory used=9590.1MB, alloc=400.7MB, time=58.80 memory used=9642.5MB, alloc=400.7MB, time=58.95 memory used=9697.6MB, alloc=400.7MB, time=59.11 memory used=9755.0MB, alloc=400.7MB, time=59.26 memory used=9816.5MB, alloc=400.7MB, time=59.42 memory used=9882.0MB, alloc=400.7MB, time=59.56 memory used=9988.2MB, alloc=400.7MB, time=82.44 memory used=10044.8MB, alloc=400.7MB, time=82.67 memory used=10104.2MB, alloc=400.7MB, time=82.87 memory used=10146.4MB, alloc=400.7MB, time=83.04 memory used=10195.5MB, alloc=400.7MB, time=83.21 memory used=10250.7MB, alloc=400.7MB, time=83.39 memory used=10313.2MB, alloc=400.7MB, time=83.57 memory used=10381.0MB, alloc=400.7MB, time=83.75 memory used=10420.5MB, alloc=400.7MB, time=83.90 memory used=10459.0MB, alloc=400.7MB, time=84.05 memory used=10499.5MB, alloc=400.7MB, time=84.20 memory used=10542.5MB, alloc=400.7MB, time=84.35 memory used=10586.2MB, alloc=400.7MB, time=84.50 memory used=10632.3MB, alloc=400.7MB, time=84.65 memory used=10681.9MB, alloc=400.7MB, time=84.80 memory used=10734.0MB, alloc=400.7MB, time=84.96 memory used=10788.1MB, alloc=400.7MB, time=85.12 memory used=10844.3MB, alloc=400.7MB, time=85.28 memory used=10903.5MB, alloc=400.7MB, time=85.44 memory used=10966.9MB, alloc=400.7MB, time=85.60 memory used=11033.1MB, alloc=400.7MB, time=85.78 memory used=11234.8MB, alloc=400.7MB, time=86.22 memory used=11392.8MB, alloc=400.7MB, time=86.51 memory used=11560.0MB, alloc=424.7MB, time=91.58 memory used=11694.0MB, alloc=424.7MB, time=129.89 memory used=11774.5MB, alloc=424.7MB, time=134.64 memory used=11843.4MB, alloc=424.7MB, time=134.89 memory used=11912.4MB, alloc=424.7MB, time=135.12 memory used=11963.0MB, alloc=424.7MB, time=135.35 memory used=12012.5MB, alloc=424.7MB, time=135.57 memory used=12063.9MB, alloc=424.7MB, time=135.79 memory used=12120.2MB, alloc=424.7MB, time=136.02 memory used=12179.7MB, alloc=424.7MB, time=136.24 memory used=12242.3MB, alloc=424.7MB, time=136.47 memory used=12308.0MB, alloc=424.7MB, time=136.68 memory used=12380.3MB, alloc=424.7MB, time=136.91 memory used=12455.8MB, alloc=424.7MB, time=137.13 memory used=12534.2MB, alloc=424.7MB, time=137.36 memory used=12597.4MB, alloc=424.7MB, time=137.57 memory used=12644.3MB, alloc=448.7MB, time=137.76 memory used=12698.9MB, alloc=448.7MB, time=137.95 memory used=12752.8MB, alloc=448.7MB, time=138.14 memory used=12810.3MB, alloc=448.7MB, time=138.33 memory used=12869.0MB, alloc=448.7MB, time=138.51 memory used=12928.8MB, alloc=448.7MB, time=138.71 memory used=12989.8MB, alloc=448.7MB, time=138.90 memory used=13051.9MB, alloc=448.7MB, time=139.10 memory used=13115.1MB, alloc=448.7MB, time=139.29 memory used=13179.3MB, alloc=448.7MB, time=139.48 memory used=13244.7MB, alloc=448.7MB, time=139.68 memory used=13311.1MB, alloc=448.7MB, time=139.88 memory used=13383.5MB, alloc=448.7MB, time=140.08 memory used=13457.3MB, alloc=448.7MB, time=140.27 memory used=13532.1MB, alloc=448.7MB, time=140.47 memory used=13608.1MB, alloc=448.7MB, time=140.67 memory used=13685.2MB, alloc=448.7MB, time=140.87 memory used=13763.3MB, alloc=448.7MB, time=141.07 memory used=13842.4MB, alloc=448.7MB, time=141.27 memory used=13922.6MB, alloc=448.7MB, time=141.48 memory used=14009.5MB, alloc=448.7MB, time=141.68 memory used=14097.5MB, alloc=448.7MB, time=141.89 memory used=14186.6MB, alloc=448.7MB, time=142.10 memory used=14276.7MB, alloc=448.7MB, time=142.32 memory used=14367.5MB, alloc=448.7MB, time=142.53 memory used=14459.5MB, alloc=448.7MB, time=142.74 memory used=14552.6MB, alloc=448.7MB, time=142.96 memory used=14652.8MB, alloc=448.7MB, time=143.17 memory used=14753.9MB, alloc=448.7MB, time=143.38 memory used=14928.4MB, alloc=448.7MB, time=143.69 memory used=15056.1MB, alloc=448.7MB, time=143.98 memory used=15180.4MB, alloc=448.7MB, time=144.26 memory used=15312.8MB, alloc=448.7MB, time=144.55 memory used=15446.3MB, alloc=448.7MB, time=144.84 memory used=15580.8MB, alloc=448.7MB, time=145.13 memory used=15716.5MB, alloc=448.7MB, time=145.43 memory used=15859.9MB, alloc=448.7MB, time=145.74 memory used=16004.3MB, alloc=448.7MB, time=146.03 memory used=16149.6MB, alloc=448.7MB, time=146.33 memory used=16302.7MB, alloc=448.7MB, time=146.63 memory used=16456.5MB, alloc=448.7MB, time=146.93 memory used=16611.5MB, alloc=448.7MB, time=147.24 memory used=16773.4MB, alloc=448.7MB, time=147.56 memory used=16936.0MB, alloc=448.7MB, time=147.89 memory used=17106.2MB, alloc=448.7MB, time=148.21 memory used=17276.7MB, alloc=448.7MB, time=148.52 memory used=17454.4MB, alloc=448.7MB, time=148.85 memory used=17632.2MB, alloc=448.7MB, time=149.19 memory used=17817.1MB, alloc=448.7MB, time=149.51 memory used=18001.7MB, alloc=448.7MB, time=149.84 memory used=18193.0MB, alloc=448.7MB, time=150.18 memory used=18390.9MB, alloc=448.7MB, time=150.52 memory used=18594.8MB, alloc=448.7MB, time=150.87 memory used=18797.4MB, alloc=448.7MB, time=151.21 memory used=19005.6MB, alloc=448.7MB, time=151.55 memory used=19218.9MB, alloc=448.7MB, time=151.90 memory used=19436.8MB, alloc=448.7MB, time=152.26 memory used=19659.3MB, alloc=448.7MB, time=152.61 memory used=19891.0MB, alloc=448.7MB, time=152.96 memory used=20123.4MB, alloc=448.7MB, time=153.33 memory used=20346.7MB, alloc=448.7MB, time=153.68 memory used=20573.2MB, alloc=448.7MB, time=154.02 memory used=20751.3MB, alloc=448.7MB, time=154.33 memory used=20921.3MB, alloc=448.7MB, time=154.62 memory used=21094.0MB, alloc=448.7MB, time=154.94 memory used=21273.1MB, alloc=448.7MB, time=155.25 memory used=21452.4MB, alloc=448.7MB, time=155.56 memory used=21636.0MB, alloc=448.7MB, time=155.86 memory used=21826.8MB, alloc=448.7MB, time=156.19 memory used=22022.5MB, alloc=448.7MB, time=156.50 memory used=22220.9MB, alloc=448.7MB, time=156.81 memory used=22425.3MB, alloc=448.7MB, time=157.13 memory used=22638.7MB, alloc=448.7MB, time=157.46 memory used=22863.6MB, alloc=448.7MB, time=157.78 memory used=23167.4MB, alloc=448.7MB, time=162.46 memory used=23311.8MB, alloc=448.7MB, time=199.44 memory used=23400.7MB, alloc=448.7MB, time=202.11 memory used=23484.4MB, alloc=448.7MB, time=202.40 memory used=23547.4MB, alloc=448.7MB, time=202.65 memory used=23614.0MB, alloc=448.7MB, time=202.90 memory used=23689.4MB, alloc=448.7MB, time=203.15 memory used=23771.8MB, alloc=448.7MB, time=203.41 memory used=23861.1MB, alloc=448.7MB, time=203.67 memory used=23955.1MB, alloc=448.7MB, time=203.93 memory used=24014.6MB, alloc=448.7MB, time=204.13 memory used=24067.4MB, alloc=448.7MB, time=204.33 memory used=24120.8MB, alloc=448.7MB, time=204.52 memory used=24173.5MB, alloc=448.7MB, time=204.71 memory used=24227.9MB, alloc=448.7MB, time=204.91 memory used=24288.2MB, alloc=448.7MB, time=205.11 memory used=24350.4MB, alloc=448.7MB, time=205.32 memory used=24414.2MB, alloc=448.7MB, time=205.51 memory used=24479.6MB, alloc=448.7MB, time=205.71 memory used=24546.5MB, alloc=448.7MB, time=205.91 memory used=24615.0MB, alloc=448.7MB, time=206.12 memory used=24685.0MB, alloc=448.7MB, time=206.32 memory used=24756.4MB, alloc=448.7MB, time=206.52 memory used=24829.4MB, alloc=448.7MB, time=206.73 memory used=24903.7MB, alloc=448.7MB, time=206.94 memory used=24979.5MB, alloc=448.7MB, time=207.14 memory used=25056.7MB, alloc=448.7MB, time=207.36 memory used=25141.9MB, alloc=448.7MB, time=207.57 memory used=25228.6MB, alloc=448.7MB, time=207.78 memory used=25316.8MB, alloc=448.7MB, time=207.98 memory used=25406.6MB, alloc=448.7MB, time=208.20 memory used=25497.9MB, alloc=448.7MB, time=208.42 memory used=25590.7MB, alloc=448.7MB, time=208.63 memory used=25684.9MB, alloc=448.7MB, time=208.85 memory used=25862.8MB, alloc=448.7MB, time=209.20 memory used=25984.2MB, alloc=448.7MB, time=209.49 memory used=26114.6MB, alloc=448.7MB, time=209.78 memory used=26247.7MB, alloc=448.7MB, time=210.09 memory used=26382.9MB, alloc=448.7MB, time=210.40 memory used=26520.3MB, alloc=448.7MB, time=210.70 memory used=26659.6MB, alloc=448.7MB, time=210.99 memory used=26801.3MB, alloc=448.7MB, time=211.30 memory used=26952.5MB, alloc=448.7MB, time=211.61 memory used=27106.1MB, alloc=448.7MB, time=211.93 memory used=27261.8MB, alloc=448.7MB, time=212.24 memory used=27419.4MB, alloc=448.7MB, time=212.55 memory used=27587.6MB, alloc=448.7MB, time=212.87 memory used=27757.8MB, alloc=448.7MB, time=213.19 memory used=27929.7MB, alloc=448.7MB, time=213.52 memory used=28103.4MB, alloc=448.7MB, time=213.85 memory used=28279.4MB, alloc=448.7MB, time=214.17 memory used=28464.9MB, alloc=448.7MB, time=214.50 memory used=28652.8MB, alloc=448.7MB, time=214.85 memory used=28842.2MB, alloc=448.7MB, time=215.19 memory used=29042.5MB, alloc=448.7MB, time=215.53 memory used=29244.3MB, alloc=448.7MB, time=215.88 memory used=29447.5MB, alloc=448.7MB, time=216.23 memory used=29661.7MB, alloc=448.7MB, time=216.59 memory used=29877.0MB, alloc=448.7MB, time=216.94 memory used=30093.4MB, alloc=448.7MB, time=217.30 memory used=30320.5MB, alloc=448.7MB, time=217.65 memory used=30548.3MB, alloc=448.7MB, time=218.02 memory used=30786.8MB, alloc=448.7MB, time=218.39 memory used=31012.2MB, alloc=448.7MB, time=218.74 memory used=31197.6MB, alloc=448.7MB, time=219.06 memory used=31358.8MB, alloc=448.7MB, time=219.36 memory used=31525.3MB, alloc=448.7MB, time=219.65 memory used=31693.7MB, alloc=448.7MB, time=219.95 memory used=31862.1MB, alloc=448.7MB, time=220.25 memory used=32030.3MB, alloc=448.7MB, time=220.55 memory used=32208.2MB, alloc=448.7MB, time=220.87 memory used=32385.7MB, alloc=448.7MB, time=221.18 memory used=32562.8MB, alloc=448.7MB, time=221.49 memory used=32740.5MB, alloc=448.7MB, time=221.80 memory used=32925.1MB, alloc=448.7MB, time=222.12 memory used=33110.2MB, alloc=448.7MB, time=222.44 memory used=33304.1MB, alloc=448.7MB, time=222.76 memory used=33497.0MB, alloc=448.7MB, time=223.07 memory used=33689.5MB, alloc=448.7MB, time=223.39 memory used=33888.8MB, alloc=448.7MB, time=223.71 memory used=34087.5MB, alloc=448.7MB, time=224.04 memory used=34293.8MB, alloc=448.7MB, time=224.37 memory used=34499.3MB, alloc=448.7MB, time=224.70 memory used=34710.3MB, alloc=448.7MB, time=225.05 memory used=34928.7MB, alloc=448.7MB, time=225.38 memory used=35145.4MB, alloc=448.7MB, time=225.71 memory used=35365.9MB, alloc=448.7MB, time=226.04 memory used=35592.8MB, alloc=448.7MB, time=226.40 memory used=35824.2MB, alloc=448.7MB, time=226.74 memory used=36056.7MB, alloc=448.7MB, time=227.08 memory used=36280.4MB, alloc=448.7MB, time=227.42 memory used=36504.0MB, alloc=448.7MB, time=227.75 memory used=36704.3MB, alloc=448.7MB, time=228.07 memory used=36890.5MB, alloc=448.7MB, time=228.37 memory used=37081.2MB, alloc=448.7MB, time=228.69 memory used=37274.4MB, alloc=448.7MB, time=229.00 memory used=37474.9MB, alloc=448.7MB, time=229.33 memory used=37675.7MB, alloc=448.7MB, time=229.65 memory used=37884.4MB, alloc=448.7MB, time=229.96 memory used=38095.4MB, alloc=448.7MB, time=230.29 memory used=38312.1MB, alloc=448.7MB, time=230.62 memory used=38536.6MB, alloc=448.7MB, time=230.94 memory used=38768.4MB, alloc=448.7MB, time=231.28 memory used=39011.0MB, alloc=448.7MB, time=231.61 memory used=39155.8MB, alloc=448.7MB, time=233.00 memory used=39253.6MB, alloc=448.7MB, time=233.48 |\^/| 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(); 1428293633 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 2 2 F := [-15 x z - 13 y z - 17 y z - 10 y z, -14 y z + 7 x z - 4, 2 2 2 2 2 -11 x y - 15 x y z + 7 x z + y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-19 x y + 2 x y z + 20 y z + 3 x, 2 2 2 2 2 -12 x z - 11 x y z - 3 x y z - 11 x y, 4 2 2 2 2 5 x + 12 y z + 18 x z - 14 y z ] > Problem := [F,G]; 2 2 3 2 2 2 2 2 2 Problem := [[-15 x z - 13 y z - 17 y z - 10 y z, -14 y z + 7 x z - 4, 2 2 2 2 2 -11 x y - 15 x y z + 7 x z + y z], [ 3 2 2 2 -19 x y + 2 x y z + 20 y z + 3 x, 2 2 2 2 2 -12 x z - 11 x y z - 3 x y z - 11 x y, 4 2 2 2 2 5 x + 12 y z + 18 x z - 14 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.1MB, alloc=32.3MB, time=0.82 memory used=65.6MB, alloc=56.3MB, time=1.11 memory used=105.9MB, alloc=60.3MB, time=1.69 memory used=144.3MB, alloc=60.3MB, time=2.25 memory used=184.4MB, alloc=84.3MB, time=2.88 memory used=219.7MB, alloc=84.3MB, time=3.38 memory used=284.3MB, alloc=92.3MB, time=4.36 memory used=349.9MB, alloc=116.3MB, time=5.20 memory used=419.9MB, alloc=116.3MB, time=5.79 memory used=471.9MB, alloc=116.3MB, time=6.20 memory used=551.6MB, alloc=116.3MB, time=6.95 memory used=640.4MB, alloc=373.7MB, time=8.34 memory used=749.6MB, alloc=373.7MB, time=9.84 memory used=832.5MB, alloc=373.7MB, time=10.82 memory used=923.2MB, alloc=373.7MB, time=12.03 memory used=988.4MB, alloc=397.7MB, time=12.65 memory used=1057.2MB, alloc=397.7MB, time=13.02 memory used=1130.1MB, alloc=397.7MB, time=14.04 memory used=1208.7MB, alloc=397.7MB, time=14.61 memory used=1324.2MB, alloc=397.7MB, time=15.73 memory used=1384.9MB, alloc=397.7MB, time=16.14 memory used=1454.3MB, alloc=397.7MB, time=16.53 memory used=1557.9MB, alloc=397.7MB, time=17.54 memory used=1662.4MB, alloc=397.7MB, time=19.15 memory used=1721.2MB, alloc=397.7MB, time=19.53 memory used=1816.0MB, alloc=397.7MB, time=20.37 memory used=1918.2MB, alloc=421.7MB, time=21.99 memory used=2043.5MB, alloc=445.7MB, time=24.04 memory used=2167.3MB, alloc=445.7MB, time=25.97 memory used=2260.1MB, alloc=469.7MB, time=27.31 memory used=2344.8MB, alloc=469.7MB, time=28.40 memory used=2471.9MB, alloc=493.7MB, time=30.74 memory used=2572.1MB, alloc=493.7MB, time=32.51 memory used=2670.7MB, alloc=493.7MB, time=34.05 memory used=2756.9MB, alloc=517.7MB, time=35.28 memory used=2872.3MB, alloc=517.7MB, time=37.20 memory used=2976.0MB, alloc=517.7MB, time=38.87 memory used=3079.7MB, alloc=517.7MB, time=40.21 memory used=3147.6MB, alloc=517.7MB, time=41.43 memory used=3220.4MB, alloc=517.7MB, time=42.55 memory used=3296.8MB, alloc=517.7MB, time=43.75 memory used=3390.5MB, alloc=541.7MB, time=45.19 memory used=3453.1MB, alloc=541.7MB, time=46.33 memory used=3518.0MB, alloc=541.7MB, time=47.42 memory used=3589.9MB, alloc=541.7MB, time=48.62 memory used=3722.1MB, alloc=541.7MB, time=49.50 memory used=3838.0MB, alloc=541.7MB, time=50.38 memory used=3955.7MB, alloc=541.7MB, time=51.10 memory used=4089.3MB, alloc=541.7MB, time=57.69 memory used=4203.6MB, alloc=541.7MB, time=58.28 memory used=4314.0MB, alloc=541.7MB, time=59.02 memory used=4451.4MB, alloc=541.7MB, time=61.26 memory used=4575.5MB, alloc=541.7MB, time=62.22 memory used=4681.1MB, alloc=541.7MB, time=62.79 memory used=4775.6MB, alloc=541.7MB, time=63.34 memory used=4906.4MB, alloc=541.7MB, time=64.16 memory used=5013.0MB, alloc=541.7MB, time=64.73 memory used=5107.4MB, alloc=541.7MB, time=65.25 memory used=5246.9MB, alloc=541.7MB, time=80.56 memory used=5403.8MB, alloc=541.7MB, time=82.66 memory used=5509.9MB, alloc=541.7MB, time=83.21 memory used=5600.9MB, alloc=541.7MB, time=83.72 memory used=5725.4MB, alloc=541.7MB, time=84.50 memory used=5855.1MB, alloc=541.7MB, time=86.21 memory used=5990.9MB, alloc=541.7MB, time=87.40 memory used=6102.2MB, alloc=541.7MB, time=88.11 memory used=6213.0MB, alloc=541.7MB, time=88.68 memory used=6344.9MB, alloc=541.7MB, time=91.66 memory used=6423.2MB, alloc=541.7MB, time=92.80 memory used=6484.3MB, alloc=541.7MB, time=94.08 memory used=6535.0MB, alloc=541.7MB, time=94.95 memory used=6777.1MB, alloc=565.7MB, time=98.45 memory used=7008.8MB, alloc=565.7MB, time=101.23 memory used=7149.7MB, alloc=565.7MB, time=105.11 memory used=7279.9MB, alloc=565.7MB, time=105.98 memory used=7454.4MB, alloc=565.7MB, time=107.45 memory used=7712.3MB, alloc=565.7MB, time=110.57 memory used=7916.7MB, alloc=589.7MB, time=113.79 memory used=8117.0MB, alloc=613.7MB, time=116.94 memory used=8272.5MB, alloc=637.7MB, time=119.48 memory used=8493.0MB, alloc=637.7MB, time=122.64 memory used=8657.9MB, alloc=637.7MB, time=123.58 memory used=8906.7MB, alloc=637.7MB, time=129.60 memory used=9093.8MB, alloc=637.7MB, time=132.80 memory used=9265.2MB, alloc=637.7MB, time=135.81 memory used=9392.2MB, alloc=661.7MB, time=138.21 memory used=9624.6MB, alloc=661.7MB, time=140.65 memory used=9796.9MB, alloc=661.7MB, time=141.97 memory used=10078.4MB, alloc=661.7MB, time=152.73 memory used=10265.0MB, alloc=661.7MB, time=156.12 memory used=10427.8MB, alloc=661.7MB, time=157.17 memory used=10593.2MB, alloc=661.7MB, time=158.57 memory used=10751.1MB, alloc=661.7MB, time=159.47 memory used=10891.7MB, alloc=661.7MB, time=160.51 memory used=11085.3MB, alloc=661.7MB, time=162.02 memory used=11231.6MB, alloc=661.7MB, time=162.96 memory used=11389.4MB, alloc=661.7MB, time=163.84 memory used=11544.3MB, alloc=661.7MB, time=164.95 memory used=11729.7MB, alloc=661.7MB, time=166.13 memory used=12115.1MB, alloc=661.7MB, time=195.85 memory used=12264.4MB, alloc=661.7MB, time=196.76 memory used=12405.8MB, alloc=661.7MB, time=197.57 memory used=12607.2MB, alloc=661.7MB, time=200.41 memory used=12772.6MB, alloc=661.7MB, time=202.70 memory used=12946.5MB, alloc=685.7MB, time=208.79 memory used=13103.0MB, alloc=685.7MB, time=210.80 memory used=13338.2MB, alloc=685.7MB, time=213.48 memory used=13488.3MB, alloc=685.7MB, time=214.50 memory used=13663.2MB, alloc=685.7MB, time=215.48 |\^/| 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(); 1428293933 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 F := [-4 x - 15 x y + 12 y z - 17 z, 15 y z + 20 x y + 12 x y z + 13 x, 3 2 2 18 x z + 6 y z - 15 x ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 4 2 2 G := [-13 x - 3 y + 19 z - 14 y , -20 x y - 15 x z + 2 y , 3 3 3 3 x z + 4 x z + 17 z + 8 x z] > Problem := [F,G]; 4 Problem := [[-4 x - 15 x y + 12 y z - 17 z, 2 2 2 3 2 2 15 y z + 20 x y + 12 x y z + 13 x, 18 x z + 6 y z - 15 x ], [ 4 4 4 2 2 -13 x - 3 y + 19 z - 14 y , -20 x y - 15 x z + 2 y , 3 3 3 3 x z + 4 x z + 17 z + 8 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.19 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=47.1MB, alloc=32.3MB, time=0.82 memory used=65.0MB, alloc=56.3MB, time=1.08 memory used=104.1MB, alloc=60.3MB, time=1.66 memory used=143.5MB, alloc=60.3MB, time=2.21 memory used=182.9MB, alloc=84.3MB, time=2.77 memory used=225.0MB, alloc=84.3MB, time=3.42 memory used=286.5MB, alloc=92.3MB, time=4.36 memory used=350.0MB, alloc=116.3MB, time=5.27 memory used=423.4MB, alloc=116.3MB, time=6.24 memory used=487.4MB, alloc=372.3MB, time=7.20 memory used=571.3MB, alloc=396.3MB, time=8.44 memory used=683.9MB, alloc=420.3MB, time=10.04 memory used=814.7MB, alloc=420.3MB, time=11.62 memory used=939.7MB, alloc=444.3MB, time=13.44 memory used=1071.7MB, alloc=444.3MB, time=15.38 memory used=1179.3MB, alloc=444.3MB, time=16.15 memory used=1301.3MB, alloc=468.3MB, time=17.61 memory used=1425.7MB, alloc=468.3MB, time=19.68 memory used=1524.9MB, alloc=468.3MB, time=21.29 memory used=1621.6MB, alloc=492.3MB, time=22.99 memory used=1716.4MB, alloc=492.3MB, time=24.65 memory used=1804.8MB, alloc=492.3MB, time=26.18 memory used=1887.7MB, alloc=492.3MB, time=27.78 memory used=1966.8MB, alloc=492.3MB, time=29.29 memory used=2040.4MB, alloc=492.3MB, time=30.65 memory used=2107.5MB, alloc=492.3MB, time=31.95 memory used=2177.1MB, alloc=492.3MB, time=33.37 memory used=2226.3MB, alloc=492.3MB, time=34.33 memory used=2311.9MB, alloc=492.3MB, time=35.57 memory used=2397.2MB, alloc=492.3MB, time=36.55 memory used=2467.7MB, alloc=492.3MB, time=37.70 memory used=2550.3MB, alloc=492.3MB, time=38.83 memory used=2612.9MB, alloc=516.3MB, time=40.21 memory used=2696.3MB, alloc=516.3MB, time=41.33 memory used=2771.7MB, alloc=516.3MB, time=42.93 memory used=2832.4MB, alloc=516.3MB, time=44.26 memory used=2882.7MB, alloc=516.3MB, time=45.31 memory used=2950.7MB, alloc=516.3MB, time=46.53 memory used=2994.8MB, alloc=516.3MB, time=47.62 memory used=3207.5MB, alloc=540.3MB, time=51.26 memory used=3415.4MB, alloc=564.3MB, time=54.41 memory used=3634.3MB, alloc=588.3MB, time=57.76 memory used=3874.4MB, alloc=588.3MB, time=61.18 memory used=4022.4MB, alloc=588.3MB, time=62.20 memory used=4157.6MB, alloc=588.3MB, time=63.01 memory used=4343.6MB, alloc=588.3MB, time=65.00 memory used=4473.5MB, alloc=588.3MB, time=65.81 memory used=4667.0MB, alloc=588.3MB, time=68.59 memory used=4851.1MB, alloc=612.3MB, time=71.78 memory used=5011.4MB, alloc=612.3MB, time=74.39 memory used=5203.7MB, alloc=612.3MB, time=76.62 memory used=5330.2MB, alloc=612.3MB, time=77.37 memory used=5468.5MB, alloc=612.3MB, time=78.81 memory used=5599.2MB, alloc=612.3MB, time=79.60 memory used=5706.6MB, alloc=612.3MB, time=80.27 memory used=5917.1MB, alloc=636.3MB, time=82.66 memory used=6080.7MB, alloc=636.3MB, time=85.31 memory used=6273.6MB, alloc=636.3MB, time=88.15 memory used=6439.5MB, alloc=636.3MB, time=90.81 memory used=6558.8MB, alloc=636.3MB, time=93.40 memory used=6701.4MB, alloc=660.3MB, time=96.25 memory used=6845.0MB, alloc=660.3MB, time=99.18 memory used=7010.1MB, alloc=660.3MB, time=102.89 memory used=7156.7MB, alloc=660.3MB, time=103.88 memory used=7312.6MB, alloc=660.3MB, time=104.81 memory used=7433.7MB, alloc=660.3MB, time=105.62 memory used=7626.3MB, alloc=660.3MB, time=107.48 memory used=7803.3MB, alloc=660.3MB, time=109.30 memory used=7991.4MB, alloc=660.3MB, time=111.34 memory used=8161.2MB, alloc=684.3MB, time=114.08 memory used=8299.6MB, alloc=684.3MB, time=116.40 memory used=8430.5MB, alloc=684.3MB, time=118.71 memory used=8603.0MB, alloc=684.3MB, time=120.86 memory used=8711.1MB, alloc=684.3MB, time=122.72 memory used=9082.2MB, alloc=708.3MB, time=128.81 memory used=9432.0MB, alloc=732.3MB, time=136.62 memory used=9820.0MB, alloc=756.3MB, time=143.48 memory used=10231.4MB, alloc=780.3MB, time=150.71 memory used=10517.5MB, alloc=804.3MB, time=155.68 memory used=10865.9MB, alloc=828.3MB, time=162.28 |\^/| 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(); 1428294233 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 4 3 3 F := [5 y + 4 x y - x y z - 14 x , -9 x + 20 x y + 11 y z + 10, 3 3 2 11 x z - 19 y z + 19 x z - 5 y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 4 2 2 2 G := [3 x z - 4 x y + 10 x z - 20 y , -4 z + 11 x z - 8 y z + 10 z , 3 2 2 -11 x z - 5 y z - 18 y + 5 y] > Problem := [F,G]; 4 2 2 4 3 3 Problem := [[5 y + 4 x y - x y z - 14 x , -9 x + 20 x y + 11 y z + 10, 3 3 2 3 3 2 2 11 x z - 19 y z + 19 x z - 5 y], [3 x z - 4 x y + 10 x z - 20 y , 4 2 2 2 3 2 2 -4 z + 11 x z - 8 y z + 10 z , -11 x z - 5 y z - 18 y + 5 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.2MB, alloc=32.3MB, time=0.49 memory used=47.5MB, alloc=32.3MB, time=0.73 memory used=70.1MB, alloc=34.9MB, time=1.08 memory used=79.9MB, alloc=34.9MB, time=1.12 memory used=92.3MB, alloc=34.9MB, time=1.16 memory used=102.2MB, alloc=58.9MB, time=1.20 memory used=126.7MB, alloc=58.9MB, time=1.26 memory used=156.7MB, alloc=58.9MB, time=1.31 memory used=188.9MB, alloc=58.9MB, time=1.45 memory used=234.5MB, alloc=70.9MB, time=2.06 memory used=278.8MB, alloc=70.9MB, time=2.64 memory used=322.8MB, alloc=94.9MB, time=3.23 memory used=390.3MB, alloc=94.9MB, time=3.85 memory used=424.6MB, alloc=94.9MB, time=3.96 memory used=457.6MB, alloc=94.9MB, time=4.08 memory used=497.2MB, alloc=94.9MB, time=4.20 memory used=537.8MB, alloc=94.9MB, time=4.32 memory used=564.8MB, alloc=94.9MB, time=4.42 memory used=591.5MB, alloc=94.9MB, time=4.51 memory used=620.2MB, alloc=94.9MB, time=4.60 memory used=652.2MB, alloc=94.9MB, time=4.70 memory used=686.7MB, alloc=94.9MB, time=4.80 memory used=724.4MB, alloc=94.9MB, time=4.89 memory used=765.0MB, alloc=94.9MB, time=5.00 memory used=803.3MB, alloc=94.9MB, time=5.09 memory used=831.1MB, alloc=94.9MB, time=5.17 memory used=858.2MB, alloc=94.9MB, time=5.24 memory used=908.9MB, alloc=94.9MB, time=5.82 memory used=954.8MB, alloc=94.9MB, time=5.95 memory used=986.2MB, alloc=94.9MB, time=6.06 memory used=1023.8MB, alloc=94.9MB, time=6.17 memory used=1066.5MB, alloc=94.9MB, time=6.28 memory used=1098.1MB, alloc=94.9MB, time=6.37 memory used=1125.1MB, alloc=94.9MB, time=6.47 memory used=1153.5MB, alloc=94.9MB, time=6.56 memory used=1184.2MB, alloc=94.9MB, time=6.65 memory used=1218.6MB, alloc=94.9MB, time=6.75 memory used=1255.1MB, alloc=94.9MB, time=6.85 memory used=1295.7MB, alloc=94.9MB, time=6.94 memory used=1339.3MB, alloc=94.9MB, time=7.04 memory used=1368.0MB, alloc=94.9MB, time=7.12 memory used=1395.9MB, alloc=94.9MB, time=7.19 memory used=1439.6MB, alloc=94.9MB, time=8.38 memory used=1521.0MB, alloc=94.9MB, time=18.36 memory used=1558.0MB, alloc=94.9MB, time=18.49 memory used=1597.8MB, alloc=94.9MB, time=18.61 memory used=1625.3MB, alloc=94.9MB, time=18.71 memory used=1656.4MB, alloc=94.9MB, time=18.80 memory used=1691.8MB, alloc=94.9MB, time=18.90 memory used=1732.0MB, alloc=94.9MB, time=19.00 memory used=1773.3MB, alloc=94.9MB, time=19.11 memory used=1803.1MB, alloc=94.9MB, time=19.19 memory used=1828.3MB, alloc=94.9MB, time=19.27 memory used=1854.8MB, alloc=94.9MB, time=19.34 memory used=1882.9MB, alloc=94.9MB, time=19.42 memory used=1912.3MB, alloc=94.9MB, time=19.50 memory used=1943.0MB, alloc=94.9MB, time=19.58 memory used=1975.7MB, alloc=94.9MB, time=19.66 memory used=2010.6MB, alloc=94.9MB, time=19.75 memory used=2047.2MB, alloc=94.9MB, time=19.83 memory used=2085.8MB, alloc=94.9MB, time=19.90 memory used=2127.1MB, alloc=94.9MB, time=19.98 memory used=2159.2MB, alloc=107.8MB, time=20.07 memory used=2182.6MB, alloc=107.8MB, time=20.13 memory used=2199.7MB, alloc=107.8MB, time=20.22 memory used=2211.0MB, alloc=107.8MB, time=20.27 memory used=2223.3MB, alloc=107.8MB, time=20.33 memory used=2270.5MB, alloc=107.8MB, time=20.65 memory used=2314.1MB, alloc=107.8MB, time=20.98 memory used=2355.6MB, alloc=107.8MB, time=21.20 memory used=2437.8MB, alloc=107.8MB, time=23.16 memory used=2496.2MB, alloc=107.8MB, time=25.23 memory used=2534.2MB, alloc=107.8MB, time=25.36 memory used=2561.9MB, alloc=107.8MB, time=25.46 memory used=2594.9MB, alloc=107.8MB, time=25.57 memory used=2634.3MB, alloc=107.8MB, time=25.67 memory used=2668.1MB, alloc=107.8MB, time=25.77 memory used=2693.0MB, alloc=107.8MB, time=25.85 memory used=2719.8MB, alloc=107.8MB, time=25.93 memory used=2749.6MB, alloc=107.8MB, time=26.01 memory used=2783.6MB, alloc=107.8MB, time=26.10 memory used=2825.5MB, alloc=107.8MB, time=26.37 memory used=2858.1MB, alloc=107.8MB, time=26.55 memory used=2929.3MB, alloc=107.8MB, time=27.36 memory used=2984.4MB, alloc=363.8MB, time=28.23 memory used=3047.5MB, alloc=363.8MB, time=37.53 memory used=3093.9MB, alloc=363.8MB, time=37.70 memory used=3137.9MB, alloc=363.8MB, time=37.85 memory used=3171.6MB, alloc=363.8MB, time=37.98 memory used=3196.1MB, alloc=363.8MB, time=38.10 memory used=3222.6MB, alloc=363.8MB, time=38.21 memory used=3250.8MB, alloc=363.8MB, time=38.33 memory used=3317.4MB, alloc=363.8MB, time=38.94 memory used=3392.3MB, alloc=387.8MB, time=48.63 memory used=3468.2MB, alloc=387.8MB, time=49.25 memory used=3530.0MB, alloc=387.8MB, time=49.45 memory used=3570.1MB, alloc=387.8MB, time=49.61 memory used=3624.4MB, alloc=387.8MB, time=49.89 memory used=3722.8MB, alloc=387.8MB, time=50.74 memory used=3805.8MB, alloc=387.8MB, time=51.53 memory used=3879.1MB, alloc=387.8MB, time=52.11 memory used=3967.8MB, alloc=387.8MB, time=53.35 memory used=4053.8MB, alloc=411.8MB, time=54.52 memory used=4145.8MB, alloc=411.8MB, time=55.35 memory used=4197.0MB, alloc=411.8MB, time=55.52 memory used=4281.3MB, alloc=411.8MB, time=56.19 memory used=4332.2MB, alloc=411.8MB, time=56.39 memory used=4396.0MB, alloc=411.8MB, time=56.67 memory used=4457.6MB, alloc=411.8MB, time=57.42 memory used=4547.2MB, alloc=411.8MB, time=74.10 memory used=4599.5MB, alloc=411.8MB, time=74.31 memory used=4642.7MB, alloc=411.8MB, time=74.48 memory used=4685.7MB, alloc=411.8MB, time=74.65 memory used=4735.9MB, alloc=411.8MB, time=74.82 memory used=4793.0MB, alloc=411.8MB, time=75.01 memory used=4847.8MB, alloc=435.8MB, time=75.21 memory used=4895.1MB, alloc=435.8MB, time=75.37 memory used=4946.2MB, alloc=435.8MB, time=75.54 memory used=4999.9MB, alloc=435.8MB, time=75.74 memory used=5057.8MB, alloc=435.8MB, time=75.91 memory used=5119.7MB, alloc=435.8MB, time=76.08 memory used=5185.6MB, alloc=435.8MB, time=76.28 memory used=5257.6MB, alloc=435.8MB, time=76.46 memory used=5333.3MB, alloc=435.8MB, time=76.64 memory used=5414.9MB, alloc=435.8MB, time=76.83 memory used=5642.3MB, alloc=435.8MB, time=77.35 memory used=5796.5MB, alloc=435.8MB, time=77.65 memory used=5966.5MB, alloc=435.8MB, time=77.95 memory used=6158.9MB, alloc=435.8MB, time=78.28 memory used=6386.5MB, alloc=435.8MB, time=79.08 memory used=6461.6MB, alloc=435.8MB, time=79.28 memory used=6514.3MB, alloc=435.8MB, time=79.44 memory used=6581.4MB, alloc=435.8MB, time=79.62 memory used=6739.2MB, alloc=435.8MB, time=82.74 memory used=6803.9MB, alloc=435.8MB, time=82.96 memory used=6864.7MB, alloc=435.8MB, time=83.14 memory used=7036.0MB, alloc=435.8MB, time=85.13 memory used=7172.9MB, alloc=435.8MB, time=86.85 memory used=7308.7MB, alloc=435.8MB, time=90.23 memory used=7444.8MB, alloc=435.8MB, time=94.69 memory used=7581.1MB, alloc=435.8MB, time=100.20 memory used=7718.3MB, alloc=435.8MB, time=106.98 memory used=7857.9MB, alloc=435.8MB, time=115.16 memory used=8015.5MB, alloc=435.8MB, time=123.40 memory used=8124.0MB, alloc=435.8MB, time=125.13 memory used=8220.6MB, alloc=435.8MB, time=125.86 memory used=8320.5MB, alloc=459.8MB, time=127.28 memory used=8452.0MB, alloc=459.8MB, time=128.40 memory used=8540.7MB, alloc=459.8MB, time=130.52 memory used=8609.4MB, alloc=459.8MB, time=130.81 memory used=8678.9MB, alloc=459.8MB, time=131.07 memory used=8751.4MB, alloc=459.8MB, time=131.34 memory used=8806.0MB, alloc=459.8MB, time=131.60 memory used=8868.2MB, alloc=459.8MB, time=131.85 memory used=8942.6MB, alloc=459.8MB, time=132.08 memory used=9060.6MB, alloc=459.8MB, time=154.89 memory used=9135.6MB, alloc=459.8MB, time=155.19 memory used=9193.9MB, alloc=459.8MB, time=155.45 memory used=9259.1MB, alloc=459.8MB, time=155.72 memory used=9337.4MB, alloc=459.8MB, time=156.01 memory used=9410.0MB, alloc=459.8MB, time=156.26 memory used=9458.5MB, alloc=459.8MB, time=156.48 memory used=9510.0MB, alloc=459.8MB, time=156.71 memory used=9566.4MB, alloc=459.8MB, time=156.94 memory used=9626.3MB, alloc=459.8MB, time=157.20 memory used=9691.0MB, alloc=459.8MB, time=157.42 memory used=9760.5MB, alloc=459.8MB, time=157.67 memory used=9834.3MB, alloc=459.8MB, time=157.91 memory used=9913.8MB, alloc=459.8MB, time=158.15 memory used=9998.0MB, alloc=459.8MB, time=158.39 memory used=10193.1MB, alloc=459.8MB, time=158.79 memory used=10355.5MB, alloc=459.8MB, time=159.15 memory used=10527.1MB, alloc=459.8MB, time=160.22 memory used=10614.8MB, alloc=459.8MB, time=160.59 memory used=10708.4MB, alloc=459.8MB, time=164.60 memory used=10808.6MB, alloc=459.8MB, time=184.76 memory used=10881.2MB, alloc=459.8MB, time=185.08 memory used=10938.2MB, alloc=459.8MB, time=185.36 memory used=11005.6MB, alloc=459.8MB, time=185.64 memory used=11085.3MB, alloc=459.8MB, time=185.94 memory used=11153.2MB, alloc=459.8MB, time=186.23 memory used=11202.2MB, alloc=459.8MB, time=186.46 memory used=11255.0MB, alloc=459.8MB, time=186.72 memory used=11311.2MB, alloc=459.8MB, time=186.99 memory used=11370.8MB, alloc=459.8MB, time=187.23 memory used=11435.3MB, alloc=459.8MB, time=187.54 memory used=11502.9MB, alloc=459.8MB, time=187.79 memory used=11575.0MB, alloc=459.8MB, time=188.04 memory used=11652.8MB, alloc=459.8MB, time=188.30 memory used=11736.3MB, alloc=459.8MB, time=188.57 memory used=11952.1MB, alloc=459.8MB, time=189.00 memory used=12111.0MB, alloc=459.8MB, time=189.37 memory used=12306.5MB, alloc=459.8MB, time=190.17 memory used=12393.4MB, alloc=459.8MB, time=191.01 memory used=12459.0MB, alloc=459.8MB, time=191.28 memory used=12524.1MB, alloc=459.8MB, time=191.54 |\^/| 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(); 1428294533 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 3 F := [4 x y - 19 y z + 14 y + 5 z , 19 x y - 10 x y z + 9 z - 8 x, 2 4 2 2 -5 x y z - 6 y - 19 x z + 9 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 G := [-12 y z - 16 x - 18 x - 18, 2 x y + 6 y z - 11 x y + 18 y, 3 x y - 8 x y - 7 x z - 11] > Problem := [F,G]; 3 2 2 2 3 2 3 Problem := [[4 x y - 19 y z + 14 y + 5 z , 19 x y - 10 x y z + 9 z - 8 x, 2 4 2 2 2 2 -5 x y z - 6 y - 19 x z + 9 y z], [-12 y z - 16 x - 18 x - 18, 3 2 2 2 3 2 x y + 6 y z - 11 x y + 18 y, x y - 8 x y - 7 x 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=0.18 memory used=29.3MB, alloc=34.3MB, time=0.44 memory used=43.1MB, alloc=34.3MB, time=0.48 memory used=54.1MB, alloc=34.3MB, time=0.51 memory used=71.7MB, alloc=34.3MB, time=0.61 memory used=86.6MB, alloc=34.3MB, time=0.72 memory used=101.1MB, alloc=34.3MB, time=0.82 memory used=126.1MB, alloc=38.3MB, time=1.18 memory used=145.0MB, alloc=38.3MB, time=1.24 memory used=158.2MB, alloc=38.3MB, time=1.28 memory used=167.3MB, alloc=38.3MB, time=1.31 memory used=178.0MB, alloc=38.3MB, time=1.35 memory used=189.6MB, alloc=38.3MB, time=1.38 memory used=202.6MB, alloc=38.3MB, time=1.42 memory used=217.0MB, alloc=38.3MB, time=1.46 memory used=228.9MB, alloc=62.3MB, time=1.50 memory used=250.7MB, alloc=62.3MB, time=1.55 memory used=275.6MB, alloc=62.3MB, time=1.61 memory used=304.3MB, alloc=62.3MB, time=1.67 memory used=346.7MB, alloc=63.5MB, time=1.87 memory used=375.2MB, alloc=63.5MB, time=1.94 memory used=407.4MB, alloc=63.5MB, time=2.01 memory used=436.8MB, alloc=63.5MB, time=2.08 memory used=460.0MB, alloc=63.5MB, time=2.13 memory used=486.8MB, alloc=63.5MB, time=2.19 memory used=518.3MB, alloc=63.5MB, time=2.25 memory used=579.6MB, alloc=64.0MB, time=9.71 memory used=614.5MB, alloc=64.0MB, time=9.81 memory used=644.8MB, alloc=64.0MB, time=9.89 memory used=669.6MB, alloc=64.0MB, time=9.96 memory used=698.6MB, alloc=64.0MB, time=10.03 memory used=732.8MB, alloc=64.0MB, time=10.11 memory used=763.9MB, alloc=64.0MB, time=10.18 memory used=785.1MB, alloc=64.0MB, time=10.23 memory used=808.1MB, alloc=64.0MB, time=10.29 memory used=832.1MB, alloc=64.0MB, time=10.34 memory used=858.4MB, alloc=64.0MB, time=10.40 memory used=885.5MB, alloc=64.0MB, time=10.46 memory used=915.0MB, alloc=64.0MB, time=10.53 memory used=947.2MB, alloc=64.0MB, time=10.58 memory used=997.8MB, alloc=81.8MB, time=10.74 memory used=1027.3MB, alloc=81.8MB, time=10.98 memory used=1056.0MB, alloc=81.8MB, time=11.06 memory used=1097.1MB, alloc=81.8MB, time=11.39 memory used=1122.8MB, alloc=81.8MB, time=11.46 memory used=1156.5MB, alloc=81.8MB, time=11.54 memory used=1183.1MB, alloc=81.8MB, time=11.61 memory used=1206.4MB, alloc=81.8MB, time=11.67 memory used=1233.5MB, alloc=81.8MB, time=11.74 memory used=1268.1MB, alloc=81.8MB, time=11.87 memory used=1309.8MB, alloc=81.8MB, time=12.09 memory used=1336.0MB, alloc=81.8MB, time=12.17 memory used=1370.0MB, alloc=81.8MB, time=12.26 memory used=1395.2MB, alloc=81.8MB, time=12.34 memory used=1418.8MB, alloc=81.8MB, time=12.39 memory used=1445.8MB, alloc=81.8MB, time=12.46 memory used=1484.3MB, alloc=81.8MB, time=13.88 memory used=1544.9MB, alloc=81.8MB, time=20.01 memory used=1575.0MB, alloc=81.8MB, time=20.08 memory used=1602.7MB, alloc=81.8MB, time=20.15 memory used=1627.3MB, alloc=81.8MB, time=20.22 memory used=1656.8MB, alloc=81.8MB, time=20.30 memory used=1691.1MB, alloc=81.8MB, time=20.36 memory used=1719.8MB, alloc=81.8MB, time=20.42 memory used=1740.1MB, alloc=81.8MB, time=20.48 memory used=1762.1MB, alloc=81.8MB, time=20.54 memory used=1786.0MB, alloc=81.8MB, time=20.59 memory used=1811.4MB, alloc=81.8MB, time=20.65 memory used=1837.6MB, alloc=81.8MB, time=20.71 memory used=1866.4MB, alloc=81.8MB, time=20.76 memory used=1897.2MB, alloc=81.8MB, time=20.82 memory used=1944.7MB, alloc=81.8MB, time=20.90 memory used=1982.3MB, alloc=81.8MB, time=21.33 memory used=2033.1MB, alloc=81.8MB, time=24.98 memory used=2063.7MB, alloc=81.8MB, time=25.06 memory used=2085.6MB, alloc=81.8MB, time=25.12 memory used=2111.3MB, alloc=81.8MB, time=25.20 memory used=2141.8MB, alloc=81.8MB, time=25.29 memory used=2172.2MB, alloc=81.8MB, time=25.36 memory used=2191.2MB, alloc=81.8MB, time=25.41 memory used=2212.0MB, alloc=81.8MB, time=25.47 memory used=2234.4MB, alloc=81.8MB, time=25.52 memory used=2259.1MB, alloc=81.8MB, time=25.57 memory used=2286.9MB, alloc=81.8MB, time=25.63 memory used=2323.4MB, alloc=81.8MB, time=25.78 memory used=2352.1MB, alloc=81.8MB, time=26.03 memory used=2379.2MB, alloc=81.8MB, time=26.11 memory used=2407.0MB, alloc=81.8MB, time=26.20 memory used=2450.0MB, alloc=81.8MB, time=26.56 memory used=2488.3MB, alloc=81.8MB, time=26.72 memory used=2530.5MB, alloc=81.8MB, time=30.20 memory used=2572.7MB, alloc=81.8MB, time=31.00 memory used=2602.1MB, alloc=81.8MB, time=31.08 memory used=2626.3MB, alloc=81.8MB, time=31.15 memory used=2664.0MB, alloc=81.8MB, time=31.31 memory used=2702.3MB, alloc=81.8MB, time=31.46 memory used=2743.1MB, alloc=81.8MB, time=33.94 memory used=2788.2MB, alloc=81.8MB, time=35.79 memory used=2815.9MB, alloc=81.8MB, time=35.86 memory used=2840.9MB, alloc=81.8MB, time=35.94 memory used=2873.1MB, alloc=81.8MB, time=36.08 memory used=2914.6MB, alloc=81.8MB, time=36.40 memory used=2951.9MB, alloc=81.8MB, time=36.82 memory used=2993.7MB, alloc=81.8MB, time=37.25 memory used=3029.7MB, alloc=81.8MB, time=37.50 memory used=3062.7MB, alloc=81.8MB, time=37.60 memory used=3081.7MB, alloc=81.8MB, time=37.68 memory used=3103.5MB, alloc=81.8MB, time=37.76 memory used=3128.5MB, alloc=81.8MB, time=37.84 memory used=3156.7MB, alloc=81.8MB, time=37.92 memory used=3180.8MB, alloc=81.8MB, time=37.99 memory used=3197.7MB, alloc=81.8MB, time=38.06 memory used=3215.3MB, alloc=81.8MB, time=38.14 memory used=3234.3MB, alloc=81.8MB, time=38.20 memory used=3254.5MB, alloc=81.8MB, time=38.27 memory used=3276.0MB, alloc=81.8MB, time=38.34 memory used=3299.5MB, alloc=81.8MB, time=38.41 memory used=3324.9MB, alloc=81.8MB, time=38.49 memory used=3363.6MB, alloc=81.8MB, time=38.78 memory used=3395.9MB, alloc=81.8MB, time=38.88 memory used=3414.8MB, alloc=81.8MB, time=38.96 memory used=3436.8MB, alloc=81.8MB, time=39.05 memory used=3461.8MB, alloc=81.8MB, time=39.12 memory used=3490.4MB, alloc=81.8MB, time=39.20 memory used=3514.1MB, alloc=81.8MB, time=39.28 memory used=3531.2MB, alloc=81.8MB, time=39.35 memory used=3548.8MB, alloc=81.8MB, time=39.43 memory used=3567.8MB, alloc=81.8MB, time=39.49 memory used=3588.3MB, alloc=81.8MB, time=39.56 memory used=3610.3MB, alloc=81.8MB, time=39.63 memory used=3634.2MB, alloc=81.8MB, time=39.71 memory used=3660.2MB, alloc=81.8MB, time=39.80 memory used=3707.7MB, alloc=81.8MB, time=47.32 memory used=3752.9MB, alloc=81.8MB, time=48.10 memory used=3775.3MB, alloc=81.8MB, time=48.18 memory used=3801.9MB, alloc=81.8MB, time=48.27 memory used=3826.5MB, alloc=81.8MB, time=48.35 memory used=3844.4MB, alloc=81.8MB, time=48.42 memory used=3864.3MB, alloc=81.8MB, time=48.48 memory used=3886.3MB, alloc=81.8MB, time=48.55 memory used=3910.2MB, alloc=81.8MB, time=48.62 memory used=3935.5MB, alloc=81.8MB, time=48.69 memory used=3963.7MB, alloc=81.8MB, time=48.76 memory used=3994.0MB, alloc=81.8MB, time=48.84 memory used=4016.0MB, alloc=81.8MB, time=48.91 memory used=4031.6MB, alloc=81.8MB, time=48.96 memory used=4048.6MB, alloc=81.8MB, time=49.02 memory used=4065.7MB, alloc=81.8MB, time=49.08 memory used=4083.0MB, alloc=81.8MB, time=49.13 memory used=4101.4MB, alloc=81.8MB, time=49.20 memory used=4121.0MB, alloc=81.8MB, time=49.27 memory used=4140.5MB, alloc=81.8MB, time=49.33 memory used=4161.1MB, alloc=81.8MB, time=49.39 memory used=4182.6MB, alloc=81.8MB, time=49.45 memory used=4205.0MB, alloc=81.8MB, time=49.51 memory used=4228.2MB, alloc=81.8MB, time=49.57 memory used=4251.8MB, alloc=81.8MB, time=49.62 memory used=4276.5MB, alloc=81.8MB, time=49.68 memory used=4302.7MB, alloc=81.8MB, time=49.75 memory used=4330.4MB, alloc=81.8MB, time=49.82 memory used=4359.7MB, alloc=81.8MB, time=49.90 memory used=4393.1MB, alloc=81.9MB, time=49.97 memory used=4430.9MB, alloc=81.9MB, time=50.26 memory used=4457.7MB, alloc=81.9MB, time=50.34 memory used=4505.5MB, alloc=81.9MB, time=57.13 memory used=4536.7MB, alloc=81.9MB, time=57.25 memory used=4559.7MB, alloc=81.9MB, time=57.33 memory used=4588.7MB, alloc=81.9MB, time=57.41 memory used=4607.1MB, alloc=81.9MB, time=57.49 memory used=4625.5MB, alloc=81.9MB, time=57.56 memory used=4645.6MB, alloc=81.9MB, time=57.63 memory used=4666.9MB, alloc=81.9MB, time=57.70 memory used=4690.2MB, alloc=81.9MB, time=57.77 memory used=4715.5MB, alloc=81.9MB, time=57.84 memory used=4742.9MB, alloc=81.9MB, time=57.90 memory used=4771.5MB, alloc=81.9MB, time=57.98 memory used=4796.8MB, alloc=81.9MB, time=58.05 memory used=4812.5MB, alloc=81.9MB, time=58.11 memory used=4828.2MB, alloc=81.9MB, time=58.17 memory used=4844.2MB, alloc=81.9MB, time=58.22 memory used=4861.2MB, alloc=81.9MB, time=58.27 memory used=4878.5MB, alloc=81.9MB, time=58.32 memory used=4896.9MB, alloc=81.9MB, time=58.38 memory used=4915.5MB, alloc=81.9MB, time=58.44 memory used=4935.3MB, alloc=81.9MB, time=58.50 memory used=4955.0MB, alloc=81.9MB, time=58.56 memory used=4975.9MB, alloc=81.9MB, time=58.61 memory used=4997.9MB, alloc=81.9MB, time=58.67 memory used=5019.9MB, alloc=81.9MB, time=58.74 memory used=5043.4MB, alloc=81.9MB, time=58.79 memory used=5068.0MB, alloc=81.9MB, time=58.85 memory used=5091.8MB, alloc=81.9MB, time=58.91 memory used=5117.3MB, alloc=81.9MB, time=58.97 memory used=5143.9MB, alloc=81.9MB, time=59.02 memory used=5172.1MB, alloc=81.9MB, time=59.08 memory used=5201.5MB, alloc=81.9MB, time=59.15 memory used=5220.8MB, alloc=81.9MB, time=59.20 memory used=5232.5MB, alloc=81.9MB, time=59.25 memory used=5244.9MB, alloc=81.9MB, time=59.31 memory used=5282.0MB, alloc=81.9MB, time=59.63 memory used=5320.9MB, alloc=81.9MB, time=59.99 memory used=5366.3MB, alloc=105.9MB, time=62.04 memory used=5393.8MB, alloc=105.9MB, time=63.19 memory used=5460.5MB, alloc=105.9MB, time=64.40 memory used=5516.4MB, alloc=105.9MB, time=64.75 memory used=5581.3MB, alloc=105.9MB, time=70.75 memory used=5620.5MB, alloc=105.9MB, time=70.87 memory used=5654.7MB, alloc=105.9MB, time=70.98 memory used=5697.3MB, alloc=105.9MB, time=71.09 memory used=5737.1MB, alloc=105.9MB, time=71.19 memory used=5765.0MB, alloc=105.9MB, time=71.27 memory used=5795.6MB, alloc=105.9MB, time=71.35 memory used=5829.7MB, alloc=105.9MB, time=71.44 memory used=5866.0MB, alloc=105.9MB, time=71.52 memory used=5907.3MB, alloc=105.9MB, time=71.60 memory used=5958.5MB, alloc=105.9MB, time=71.70 memory used=6041.0MB, alloc=107.3MB, time=72.49 memory used=6097.6MB, alloc=107.3MB, time=73.71 memory used=6132.0MB, alloc=107.3MB, time=73.81 memory used=6189.2MB, alloc=107.3MB, time=75.20 memory used=6223.2MB, alloc=107.3MB, time=75.30 memory used=6292.2MB, alloc=107.3MB, time=76.07 memory used=6369.1MB, alloc=107.3MB, time=77.73 memory used=6400.8MB, alloc=107.3MB, time=77.84 memory used=6457.1MB, alloc=107.3MB, time=81.39 memory used=6496.7MB, alloc=107.3MB, time=81.53 memory used=6524.0MB, alloc=107.3MB, time=81.64 memory used=6556.0MB, alloc=107.3MB, time=81.74 memory used=6593.6MB, alloc=107.3MB, time=81.85 memory used=6633.8MB, alloc=107.3MB, time=81.95 memory used=6658.3MB, alloc=107.3MB, time=82.03 memory used=6685.1MB, alloc=107.3MB, time=82.14 memory used=6715.4MB, alloc=107.3MB, time=82.23 memory used=6778.1MB, alloc=107.3MB, time=89.52 memory used=6815.0MB, alloc=107.3MB, time=89.66 memory used=6855.0MB, alloc=107.3MB, time=89.79 memory used=6881.8MB, alloc=107.3MB, time=89.90 memory used=6912.5MB, alloc=107.3MB, time=90.00 memory used=6947.1MB, alloc=107.3MB, time=90.10 memory used=6986.2MB, alloc=107.3MB, time=90.21 memory used=7027.1MB, alloc=107.3MB, time=90.34 memory used=7050.6MB, alloc=107.3MB, time=90.42 memory used=7076.2MB, alloc=107.3MB, time=90.51 memory used=7103.1MB, alloc=107.3MB, time=90.59 memory used=7131.1MB, alloc=107.3MB, time=90.68 memory used=7162.2MB, alloc=107.3MB, time=90.77 memory used=7195.8MB, alloc=107.3MB, time=90.85 memory used=7248.4MB, alloc=107.3MB, time=91.26 memory used=7288.0MB, alloc=107.3MB, time=91.41 memory used=7323.2MB, alloc=107.3MB, time=91.53 memory used=7357.3MB, alloc=107.3MB, time=91.63 memory used=7384.8MB, alloc=107.3MB, time=91.73 memory used=7416.3MB, alloc=107.3MB, time=91.83 memory used=7464.2MB, alloc=107.3MB, time=92.09 memory used=7497.7MB, alloc=107.3MB, time=92.22 memory used=7537.0MB, alloc=107.3MB, time=92.35 memory used=7565.8MB, alloc=107.3MB, time=92.45 memory used=7594.6MB, alloc=107.3MB, time=92.56 memory used=7628.3MB, alloc=107.3MB, time=92.66 memory used=7684.4MB, alloc=107.3MB, time=99.09 memory used=7739.4MB, alloc=107.3MB, time=100.45 memory used=7775.4MB, alloc=107.3MB, time=100.57 memory used=7802.9MB, alloc=107.3MB, time=100.66 memory used=7836.4MB, alloc=107.3MB, time=100.77 memory used=7876.9MB, alloc=107.3MB, time=100.87 memory used=7906.6MB, alloc=107.3MB, time=100.96 memory used=7930.8MB, alloc=107.3MB, time=101.04 memory used=7957.8MB, alloc=107.3MB, time=101.13 memory used=7986.5MB, alloc=107.3MB, time=101.22 memory used=8016.8MB, alloc=107.3MB, time=101.30 memory used=8051.3MB, alloc=107.3MB, time=101.39 memory used=8089.3MB, alloc=107.3MB, time=101.47 memory used=8125.3MB, alloc=107.8MB, time=101.56 memory used=8166.2MB, alloc=107.8MB, time=101.91 memory used=8198.3MB, alloc=107.8MB, time=102.03 memory used=8244.3MB, alloc=107.8MB, time=102.39 memory used=8277.4MB, alloc=107.8MB, time=102.51 memory used=8314.2MB, alloc=107.8MB, time=102.62 memory used=8340.4MB, alloc=107.8MB, time=102.73 memory used=8371.1MB, alloc=107.8MB, time=102.82 memory used=8416.0MB, alloc=107.8MB, time=103.08 memory used=8452.9MB, alloc=107.8MB, time=103.22 memory used=8489.4MB, alloc=107.8MB, time=103.35 memory used=8521.8MB, alloc=107.8MB, time=103.45 memory used=8549.1MB, alloc=107.8MB, time=103.55 memory used=8581.2MB, alloc=107.8MB, time=103.66 memory used=8636.7MB, alloc=107.8MB, time=109.99 memory used=8689.3MB, alloc=107.8MB, time=111.37 memory used=8724.8MB, alloc=107.8MB, time=111.48 memory used=8752.3MB, alloc=107.8MB, time=111.59 memory used=8785.9MB, alloc=107.8MB, time=111.69 memory used=8825.6MB, alloc=107.8MB, time=111.81 memory used=8855.4MB, alloc=107.8MB, time=111.90 memory used=8879.6MB, alloc=107.8MB, time=111.98 memory used=8905.9MB, alloc=107.8MB, time=112.08 memory used=8934.5MB, alloc=107.8MB, time=112.17 memory used=8964.8MB, alloc=107.8MB, time=112.26 memory used=8997.8MB, alloc=107.8MB, time=112.36 memory used=9035.1MB, alloc=107.8MB, time=112.44 memory used=9074.4MB, alloc=107.8MB, time=112.54 memory used=9120.0MB, alloc=107.8MB, time=112.81 memory used=9188.4MB, alloc=107.8MB, time=113.66 memory used=9262.8MB, alloc=363.8MB, time=115.34 memory used=9318.2MB, alloc=363.8MB, time=122.17 memory used=9348.3MB, alloc=363.8MB, time=122.29 memory used=9374.6MB, alloc=387.8MB, time=122.41 memory used=9417.8MB, alloc=387.8MB, time=122.55 memory used=9473.6MB, alloc=387.8MB, time=122.69 memory used=9511.5MB, alloc=387.8MB, time=122.80 memory used=9548.0MB, alloc=387.8MB, time=122.91 memory used=9589.1MB, alloc=387.8MB, time=123.02 memory used=9633.4MB, alloc=387.8MB, time=123.13 memory used=9683.9MB, alloc=387.8MB, time=123.25 memory used=9785.1MB, alloc=387.8MB, time=123.91 memory used=9896.0MB, alloc=387.8MB, time=124.77 memory used=9984.3MB, alloc=387.8MB, time=125.37 memory used=10045.2MB, alloc=387.8MB, time=127.26 memory used=10107.3MB, alloc=387.8MB, time=130.01 memory used=10148.3MB, alloc=387.8MB, time=130.16 memory used=10193.0MB, alloc=387.8MB, time=130.42 memory used=10253.0MB, alloc=387.8MB, time=130.72 memory used=10325.5MB, alloc=387.8MB, time=135.22 memory used=10372.3MB, alloc=387.8MB, time=135.40 memory used=10410.1MB, alloc=387.8MB, time=135.54 memory used=10467.5MB, alloc=387.8MB, time=135.90 memory used=10544.1MB, alloc=387.8MB, time=136.76 memory used=10632.2MB, alloc=411.8MB, time=137.77 memory used=10744.9MB, alloc=411.8MB, time=139.09 memory used=10841.9MB, alloc=435.8MB, time=140.17 memory used=10928.6MB, alloc=435.8MB, time=140.69 memory used=10986.4MB, alloc=435.8MB, time=140.94 memory used=11055.1MB, alloc=435.8MB, time=141.19 memory used=11100.8MB, alloc=435.8MB, time=141.40 memory used=11154.6MB, alloc=435.8MB, time=141.61 memory used=11231.0MB, alloc=435.8MB, time=142.01 memory used=11297.5MB, alloc=435.8MB, time=142.31 memory used=11366.1MB, alloc=435.8MB, time=142.57 memory used=11415.6MB, alloc=435.8MB, time=142.78 memory used=11467.4MB, alloc=435.8MB, time=143.01 memory used=11528.6MB, alloc=435.8MB, time=143.22 memory used=11633.7MB, alloc=435.8MB, time=151.47 memory used=11695.3MB, alloc=435.8MB, time=151.72 memory used=11747.5MB, alloc=435.8MB, time=151.95 memory used=11812.3MB, alloc=435.8MB, time=152.18 memory used=11878.2MB, alloc=435.8MB, time=152.40 memory used=11921.7MB, alloc=435.8MB, time=152.59 memory used=11968.9MB, alloc=435.8MB, time=152.77 memory used=12021.2MB, alloc=435.8MB, time=152.95 memory used=12079.2MB, alloc=435.8MB, time=153.15 memory used=12141.9MB, alloc=435.8MB, time=153.34 memory used=12212.2MB, alloc=435.8MB, time=153.54 memory used=12324.1MB, alloc=435.8MB, time=154.00 memory used=12380.9MB, alloc=435.8MB, time=154.26 memory used=12444.7MB, alloc=435.8MB, time=154.50 memory used=12492.2MB, alloc=435.8MB, time=154.72 memory used=12547.8MB, alloc=435.8MB, time=154.94 memory used=12634.3MB, alloc=435.8MB, time=155.42 memory used=12693.9MB, alloc=435.8MB, time=155.69 memory used=12763.9MB, alloc=435.8MB, time=155.94 memory used=12809.1MB, alloc=435.8MB, time=156.14 memory used=12861.8MB, alloc=435.8MB, time=156.34 memory used=12937.7MB, alloc=435.8MB, time=157.58 memory used=13034.2MB, alloc=435.8MB, time=165.06 memory used=13093.4MB, alloc=435.8MB, time=165.31 memory used=13147.1MB, alloc=435.8MB, time=165.53 memory used=13214.1MB, alloc=435.8MB, time=165.77 memory used=13275.8MB, alloc=435.8MB, time=165.99 memory used=13319.3MB, alloc=435.8MB, time=166.18 memory used=13366.8MB, alloc=435.8MB, time=166.37 memory used=13418.9MB, alloc=435.8MB, time=166.59 memory used=13476.7MB, alloc=435.8MB, time=166.79 memory used=13539.2MB, alloc=435.8MB, time=166.98 memory used=13610.0MB, alloc=435.8MB, time=167.17 memory used=13708.2MB, alloc=435.8MB, time=167.53 memory used=13778.7MB, alloc=435.8MB, time=167.91 memory used=13847.6MB, alloc=435.8MB, time=168.22 memory used=13957.6MB, alloc=435.8MB, time=171.02 memory used=14020.6MB, alloc=435.8MB, time=171.29 memory used=14072.0MB, alloc=435.8MB, time=171.52 memory used=14126.0MB, alloc=435.8MB, time=171.76 memory used=14189.7MB, alloc=435.8MB, time=171.99 memory used=14263.6MB, alloc=435.8MB, time=172.22 memory used=14306.6MB, alloc=435.8MB, time=172.40 memory used=14349.3MB, alloc=435.8MB, time=172.58 memory used=14395.8MB, alloc=435.8MB, time=172.77 memory used=14444.7MB, alloc=435.8MB, time=172.98 memory used=14497.3MB, alloc=435.8MB, time=173.16 memory used=14553.4MB, alloc=435.8MB, time=173.34 memory used=14614.1MB, alloc=435.8MB, time=173.54 memory used=14678.8MB, alloc=435.8MB, time=173.74 memory used=14748.2MB, alloc=435.8MB, time=173.94 memory used=14828.4MB, alloc=435.8MB, time=174.13 memory used=14979.0MB, alloc=435.8MB, time=174.60 memory used=15074.6MB, alloc=435.8MB, time=175.00 memory used=15140.7MB, alloc=435.8MB, time=175.24 memory used=15190.1MB, alloc=435.8MB, time=175.46 memory used=15276.9MB, alloc=435.8MB, time=189.04 memory used=15357.8MB, alloc=435.8MB, time=191.54 memory used=15419.7MB, alloc=435.8MB, time=191.78 memory used=15468.6MB, alloc=435.8MB, time=192.00 memory used=15526.3MB, alloc=435.8MB, time=192.22 memory used=15594.3MB, alloc=435.8MB, time=192.44 memory used=15657.7MB, alloc=435.8MB, time=192.66 memory used=15699.2MB, alloc=435.8MB, time=192.84 memory used=15743.2MB, alloc=435.8MB, time=193.02 memory used=15789.9MB, alloc=435.8MB, time=193.22 memory used=15840.5MB, alloc=435.8MB, time=193.41 memory used=15893.4MB, alloc=435.8MB, time=193.61 memory used=15949.8MB, alloc=435.8MB, time=193.81 memory used=16011.2MB, alloc=435.8MB, time=194.00 memory used=16076.8MB, alloc=435.8MB, time=194.19 memory used=16146.0MB, alloc=435.8MB, time=194.39 memory used=16222.9MB, alloc=435.8MB, time=194.59 memory used=16376.3MB, alloc=435.8MB, time=194.91 memory used=16495.6MB, alloc=435.8MB, time=195.32 memory used=16572.9MB, alloc=435.8MB, time=196.74 memory used=16651.5MB, alloc=459.8MB, time=197.08 memory used=16716.6MB, alloc=459.8MB, time=197.39 memory used=16794.3MB, alloc=459.8MB, time=197.70 memory used=16888.6MB, alloc=459.8MB, time=198.01 memory used=16954.3MB, alloc=459.8MB, time=198.26 memory used=17007.7MB, alloc=459.8MB, time=198.49 memory used=17065.2MB, alloc=459.8MB, time=198.74 memory used=17128.8MB, alloc=459.8MB, time=199.00 memory used=17194.8MB, alloc=459.8MB, time=199.25 memory used=17267.0MB, alloc=459.8MB, time=199.51 memory used=17341.5MB, alloc=459.8MB, time=199.78 memory used=17422.2MB, alloc=459.8MB, time=200.04 memory used=17505.3MB, alloc=459.8MB, time=200.30 memory used=17593.6MB, alloc=459.8MB, time=200.56 memory used=17688.5MB, alloc=459.8MB, time=200.82 memory used=17757.3MB, alloc=459.8MB, time=201.04 memory used=17805.4MB, alloc=459.8MB, time=201.23 memory used=17853.2MB, alloc=459.8MB, time=201.45 memory used=17904.3MB, alloc=459.8MB, time=201.66 memory used=17956.1MB, alloc=459.8MB, time=201.86 memory used=18008.4MB, alloc=459.8MB, time=202.06 memory used=18064.0MB, alloc=459.8MB, time=202.25 memory used=18120.0MB, alloc=459.8MB, time=202.44 memory used=18180.3MB, alloc=459.8MB, time=202.64 memory used=18240.0MB, alloc=459.8MB, time=202.85 memory used=18303.7MB, alloc=459.8MB, time=203.05 memory used=18367.2MB, alloc=459.8MB, time=203.25 memory used=18432.7MB, alloc=459.8MB, time=203.45 memory used=18501.8MB, alloc=459.8MB, time=203.68 memory used=18573.5MB, alloc=459.8MB, time=203.90 memory used=18647.0MB, alloc=459.8MB, time=204.11 memory used=18723.1MB, alloc=459.8MB, time=204.32 memory used=18804.1MB, alloc=459.8MB, time=204.53 memory used=18888.2MB, alloc=459.8MB, time=204.74 memory used=18976.7MB, alloc=459.8MB, time=204.94 memory used=19086.3MB, alloc=459.8MB, time=206.46 memory used=19176.0MB, alloc=459.8MB, time=206.81 memory used=19245.7MB, alloc=459.8MB, time=207.10 memory used=19329.5MB, alloc=459.8MB, time=207.41 memory used=19420.5MB, alloc=459.8MB, time=207.71 memory used=19474.7MB, alloc=459.8MB, time=207.97 memory used=19530.5MB, alloc=459.8MB, time=208.20 memory used=19588.7MB, alloc=459.8MB, time=208.45 memory used=19653.0MB, alloc=459.8MB, time=208.69 memory used=19719.7MB, alloc=459.8MB, time=208.94 memory used=19792.5MB, alloc=459.8MB, time=209.18 memory used=19867.6MB, alloc=459.8MB, time=209.45 memory used=19948.9MB, alloc=459.8MB, time=209.71 memory used=20036.5MB, alloc=459.8MB, time=209.97 memory used=20125.7MB, alloc=459.8MB, time=210.24 memory used=20221.0MB, alloc=459.8MB, time=210.50 memory used=20275.3MB, alloc=459.8MB, time=210.70 memory used=20323.4MB, alloc=459.8MB, time=210.91 memory used=20371.4MB, alloc=459.8MB, time=211.10 memory used=20422.3MB, alloc=459.8MB, time=211.29 memory used=20474.0MB, alloc=459.8MB, time=211.49 memory used=20526.7MB, alloc=459.8MB, time=211.70 memory used=20581.9MB, alloc=459.8MB, time=211.91 memory used=20637.8MB, alloc=459.8MB, time=212.10 memory used=20697.9MB, alloc=459.8MB, time=212.31 memory used=20757.6MB, alloc=459.8MB, time=212.51 memory used=20821.0MB, alloc=459.8MB, time=212.72 memory used=20884.8MB, alloc=459.8MB, time=212.95 memory used=20950.8MB, alloc=459.8MB, time=213.14 memory used=21019.3MB, alloc=459.8MB, time=213.35 memory used=21090.6MB, alloc=459.8MB, time=213.56 memory used=21164.1MB, alloc=459.8MB, time=213.77 memory used=21240.9MB, alloc=459.8MB, time=213.97 memory used=21322.3MB, alloc=459.8MB, time=214.18 memory used=21406.7MB, alloc=459.8MB, time=214.39 memory used=21497.0MB, alloc=459.8MB, time=214.61 memory used=21609.8MB, alloc=459.8MB, time=233.40 |\^/| 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(); 1428294833 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 3 F := [-16 x y z + 18 x y + 11 y z + 20 z, -11 x y + 20 y z + 20 z + 11 y, 4 2 -4 z + 5 x y z - 19 y z + 8 x] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 3 3 G := [7 x z - 4 z + 13 x + 9 y, -5 x z - y z - 18 x y, 2 3 2 -x y z - 17 x z - 12 x + 20] > Problem := [F,G]; 2 2 2 Problem := [[-16 x y z + 18 x y + 11 y z + 20 z, 2 2 2 3 4 2 -11 x y + 20 y z + 20 z + 11 y, -4 z + 5 x y z - 19 y z + 8 x], [ 3 4 3 3 3 7 x z - 4 z + 13 x + 9 y, -5 x z - y z - 18 x y, 2 3 2 -x y z - 17 x z - 12 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=0.18 memory used=25.0MB, alloc=32.3MB, time=0.45 memory used=49.9MB, alloc=32.3MB, time=0.90 memory used=61.3MB, alloc=32.3MB, time=0.94 memory used=72.2MB, alloc=32.3MB, time=0.98 memory used=88.0MB, alloc=32.3MB, time=1.13 memory used=100.7MB, alloc=32.3MB, time=1.19 memory used=112.8MB, alloc=32.3MB, time=1.23 memory used=126.4MB, alloc=32.3MB, time=1.27 memory used=146.1MB, alloc=41.6MB, time=1.36 memory used=158.5MB, alloc=41.6MB, time=1.40 memory used=170.2MB, alloc=41.6MB, time=1.43 memory used=183.0MB, alloc=41.6MB, time=1.46 memory used=200.1MB, alloc=41.6MB, time=1.51 memory used=213.9MB, alloc=41.6MB, time=1.54 memory used=225.4MB, alloc=41.6MB, time=1.58 memory used=238.0MB, alloc=41.6MB, time=1.61 memory used=249.1MB, alloc=41.6MB, time=1.64 memory used=270.9MB, alloc=41.6MB, time=1.88 memory used=294.0MB, alloc=65.6MB, time=2.20 memory used=346.2MB, alloc=73.6MB, time=2.78 memory used=377.1MB, alloc=73.6MB, time=2.96 memory used=416.6MB, alloc=73.6MB, time=6.71 memory used=449.7MB, alloc=73.6MB, time=6.87 memory used=476.2MB, alloc=73.6MB, time=6.96 memory used=501.2MB, alloc=73.6MB, time=7.04 memory used=520.5MB, alloc=73.6MB, time=7.10 memory used=542.2MB, alloc=73.6MB, time=7.18 memory used=566.9MB, alloc=73.6MB, time=7.25 memory used=594.3MB, alloc=73.6MB, time=7.32 memory used=623.8MB, alloc=73.6MB, time=7.39 memory used=648.9MB, alloc=73.6MB, time=7.46 memory used=666.5MB, alloc=73.6MB, time=7.52 memory used=684.7MB, alloc=73.6MB, time=7.57 memory used=703.9MB, alloc=73.6MB, time=7.63 memory used=723.8MB, alloc=73.6MB, time=7.69 memory used=745.0MB, alloc=73.6MB, time=7.74 memory used=767.1MB, alloc=73.6MB, time=7.80 memory used=789.9MB, alloc=73.6MB, time=7.86 memory used=814.2MB, alloc=73.6MB, time=7.92 memory used=841.7MB, alloc=73.6MB, time=7.98 memory used=870.0MB, alloc=81.9MB, time=8.05 memory used=911.0MB, alloc=81.9MB, time=8.36 memory used=939.3MB, alloc=81.9MB, time=8.52 memory used=971.0MB, alloc=81.9MB, time=11.05 memory used=1005.9MB, alloc=81.9MB, time=12.50 memory used=1034.7MB, alloc=81.9MB, time=12.64 memory used=1059.9MB, alloc=81.9MB, time=12.72 memory used=1080.2MB, alloc=81.9MB, time=12.81 memory used=1105.0MB, alloc=81.9MB, time=12.89 memory used=1134.0MB, alloc=81.9MB, time=12.97 memory used=1157.7MB, alloc=81.9MB, time=13.05 memory used=1175.0MB, alloc=81.9MB, time=13.11 memory used=1193.0MB, alloc=81.9MB, time=13.17 memory used=1211.8MB, alloc=81.9MB, time=13.24 memory used=1232.5MB, alloc=81.9MB, time=13.30 memory used=1253.8MB, alloc=81.9MB, time=13.38 memory used=1277.1MB, alloc=81.9MB, time=13.45 memory used=1300.9MB, alloc=81.9MB, time=13.53 memory used=1326.6MB, alloc=81.9MB, time=13.60 memory used=1352.9MB, alloc=81.9MB, time=13.67 memory used=1380.8MB, alloc=81.9MB, time=13.74 memory used=1410.6MB, alloc=81.9MB, time=13.82 memory used=1441.8MB, alloc=83.8MB, time=13.90 memory used=1449.3MB, alloc=83.8MB, time=13.94 memory used=1456.6MB, alloc=83.8MB, time=13.99 memory used=1464.1MB, alloc=83.8MB, time=14.05 memory used=1471.6MB, alloc=83.8MB, time=14.09 memory used=1479.1MB, alloc=83.8MB, time=14.22 memory used=1486.5MB, alloc=83.8MB, time=14.27 memory used=1494.1MB, alloc=83.8MB, time=14.34 memory used=1502.8MB, alloc=83.8MB, time=14.42 memory used=1511.7MB, alloc=83.8MB, time=14.47 memory used=1520.5MB, alloc=83.8MB, time=14.52 memory used=1529.2MB, alloc=83.8MB, time=14.56 memory used=1537.9MB, alloc=83.8MB, time=14.61 memory used=1546.6MB, alloc=83.8MB, time=14.65 memory used=1555.4MB, alloc=83.8MB, time=14.69 memory used=1565.1MB, alloc=83.8MB, time=14.75 memory used=1574.9MB, alloc=83.8MB, time=14.80 memory used=1584.7MB, alloc=83.8MB, time=14.85 memory used=1594.3MB, alloc=83.8MB, time=14.89 memory used=1604.0MB, alloc=83.8MB, time=14.95 memory used=1614.4MB, alloc=83.8MB, time=14.99 memory used=1624.9MB, alloc=83.8MB, time=15.04 memory used=1635.5MB, alloc=83.8MB, time=15.09 memory used=1646.7MB, alloc=83.8MB, time=15.13 memory used=1657.8MB, alloc=83.8MB, time=15.19 memory used=1669.9MB, alloc=83.8MB, time=15.24 memory used=1681.6MB, alloc=83.8MB, time=15.30 memory used=1694.1MB, alloc=83.8MB, time=15.34 memory used=1706.4MB, alloc=83.8MB, time=15.41 memory used=1719.6MB, alloc=83.8MB, time=15.45 memory used=1733.3MB, alloc=83.8MB, time=15.50 memory used=1747.1MB, alloc=83.8MB, time=15.55 memory used=1761.6MB, alloc=83.8MB, time=15.60 memory used=1776.9MB, alloc=83.8MB, time=15.66 memory used=1815.6MB, alloc=83.8MB, time=16.27 memory used=1839.1MB, alloc=83.8MB, time=16.35 memory used=1862.6MB, alloc=83.8MB, time=16.44 memory used=1889.5MB, alloc=83.8MB, time=16.68 memory used=1917.5MB, alloc=83.8MB, time=16.76 memory used=1937.9MB, alloc=83.8MB, time=16.82 memory used=1950.3MB, alloc=83.8MB, time=16.88 memory used=1964.0MB, alloc=83.8MB, time=16.93 memory used=1992.3MB, alloc=83.8MB, time=17.00 memory used=2015.5MB, alloc=83.8MB, time=17.07 memory used=2034.5MB, alloc=83.8MB, time=17.14 memory used=2048.0MB, alloc=83.8MB, time=17.20 memory used=2076.8MB, alloc=83.8MB, time=17.28 memory used=2099.7MB, alloc=83.8MB, time=17.34 memory used=2120.9MB, alloc=83.8MB, time=17.84 memory used=2135.7MB, alloc=83.8MB, time=17.89 memory used=2151.1MB, alloc=83.8MB, time=17.95 memory used=2167.1MB, alloc=83.8MB, time=18.01 memory used=2183.8MB, alloc=83.8MB, time=18.06 memory used=2201.1MB, alloc=83.8MB, time=18.12 memory used=2219.8MB, alloc=83.8MB, time=18.17 memory used=2248.4MB, alloc=83.8MB, time=18.24 memory used=2278.4MB, alloc=83.8MB, time=18.32 memory used=2310.0MB, alloc=83.8MB, time=18.38 memory used=2343.0MB, alloc=83.8MB, time=18.45 memory used=2365.3MB, alloc=83.8MB, time=18.51 memory used=2375.0MB, alloc=83.8MB, time=18.56 memory used=2384.9MB, alloc=83.8MB, time=18.61 memory used=2394.9MB, alloc=83.8MB, time=18.65 memory used=2405.0MB, alloc=83.8MB, time=18.71 memory used=2415.2MB, alloc=83.8MB, time=18.75 memory used=2425.6MB, alloc=83.8MB, time=18.83 memory used=2436.0MB, alloc=83.8MB, time=18.87 memory used=2449.3MB, alloc=83.8MB, time=18.94 memory used=2463.9MB, alloc=83.8MB, time=19.00 memory used=2479.1MB, alloc=83.8MB, time=19.05 memory used=2495.0MB, alloc=83.8MB, time=19.11 memory used=2511.6MB, alloc=83.8MB, time=19.19 memory used=2528.8MB, alloc=83.8MB, time=19.25 memory used=2547.9MB, alloc=83.8MB, time=19.31 memory used=2576.3MB, alloc=83.8MB, time=19.38 memory used=2606.2MB, alloc=83.8MB, time=19.44 memory used=2637.5MB, alloc=83.8MB, time=19.51 memory used=2670.4MB, alloc=83.8MB, time=19.58 memory used=2690.1MB, alloc=83.8MB, time=19.66 memory used=2699.8MB, alloc=83.8MB, time=19.80 memory used=2709.5MB, alloc=83.8MB, time=19.85 memory used=2719.5MB, alloc=83.8MB, time=19.92 memory used=2729.5MB, alloc=83.8MB, time=19.99 memory used=2739.6MB, alloc=83.8MB, time=20.03 memory used=2749.9MB, alloc=83.8MB, time=20.10 memory used=2760.2MB, alloc=83.8MB, time=20.15 memory used=2814.5MB, alloc=83.8MB, time=24.66 memory used=2845.5MB, alloc=83.8MB, time=24.79 memory used=2874.3MB, alloc=83.8MB, time=24.88 memory used=2895.3MB, alloc=83.8MB, time=24.95 memory used=2915.3MB, alloc=83.8MB, time=25.02 memory used=2937.4MB, alloc=83.8MB, time=25.08 memory used=2962.5MB, alloc=83.8MB, time=25.16 memory used=2990.3MB, alloc=83.8MB, time=25.25 memory used=3020.9MB, alloc=83.8MB, time=25.33 memory used=3042.2MB, alloc=83.8MB, time=25.39 memory used=3059.0MB, alloc=83.8MB, time=25.46 memory used=3076.5MB, alloc=83.8MB, time=25.52 memory used=3095.7MB, alloc=83.8MB, time=25.58 memory used=3115.5MB, alloc=83.8MB, time=25.64 memory used=3136.6MB, alloc=83.8MB, time=25.69 memory used=3158.4MB, alloc=83.8MB, time=25.76 memory used=3181.0MB, alloc=83.8MB, time=25.81 memory used=3205.0MB, alloc=83.8MB, time=25.87 memory used=3231.6MB, alloc=83.8MB, time=25.93 memory used=3262.9MB, alloc=83.8MB, time=26.00 memory used=3365.3MB, alloc=83.8MB, time=27.20 memory used=3388.0MB, alloc=83.8MB, time=27.28 memory used=3412.2MB, alloc=83.8MB, time=27.35 memory used=3495.1MB, alloc=107.8MB, time=29.58 memory used=3534.0MB, alloc=131.8MB, time=64.39 memory used=3582.9MB, alloc=155.8MB, time=90.56 memory used=3671.2MB, alloc=155.8MB, time=171.38 memory used=4859.8MB, alloc=155.8MB, time=177.81 memory used=5716.1MB, alloc=411.8MB, time=183.75 memory used=5754.7MB, alloc=411.8MB, time=186.16 memory used=5854.0MB, alloc=411.8MB, time=190.19 |\^/| 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(); 1428295133 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 2 F := [-5 x z - 5 z - 8 y + 18 z, 14 y - 18 y z - 2 x z + 7 x, 2 2 2 2 2 17 y z + 12 x y - 11 x z + 18 x ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 G := [19 x - 6 x y z - 19 y - 16 z, -5 x z - 17 x + 13 y + 6 z, 2 2 2 4 2 2 x y - 19 x y z + 14 y - 17 x z] > Problem := [F,G]; 3 3 2 4 2 Problem := [[-5 x z - 5 z - 8 y + 18 z, 14 y - 18 y z - 2 x z + 7 x, 2 2 2 2 2 4 2 17 y z + 12 x y - 11 x z + 18 x ], [19 x - 6 x y z - 19 y - 16 z, 3 2 2 2 2 2 4 2 -5 x z - 17 x + 13 y + 6 z, 2 x y - 19 x y z + 14 y - 17 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.18 memory used=25.9MB, alloc=32.4MB, time=0.42 memory used=43.4MB, alloc=32.4MB, time=0.59 memory used=61.7MB, alloc=32.5MB, time=0.72 memory used=73.4MB, alloc=32.5MB, time=0.75 memory used=85.3MB, alloc=32.5MB, time=0.79 memory used=106.7MB, alloc=32.5MB, time=0.98 memory used=126.2MB, alloc=32.5MB, time=1.24 memory used=147.3MB, alloc=56.5MB, time=2.29 memory used=187.5MB, alloc=65.2MB, time=2.43 memory used=210.1MB, alloc=65.2MB, time=2.53 memory used=232.5MB, alloc=65.2MB, time=2.62 memory used=259.0MB, alloc=65.2MB, time=2.72 memory used=288.5MB, alloc=65.2MB, time=2.81 memory used=320.6MB, alloc=65.2MB, time=2.90 memory used=342.6MB, alloc=65.2MB, time=2.98 memory used=357.7MB, alloc=65.2MB, time=3.04 memory used=373.9MB, alloc=65.2MB, time=3.12 memory used=390.8MB, alloc=65.2MB, time=3.18 memory used=408.2MB, alloc=65.2MB, time=3.25 memory used=426.1MB, alloc=65.2MB, time=3.32 memory used=444.5MB, alloc=65.2MB, time=3.39 memory used=463.7MB, alloc=65.2MB, time=3.46 memory used=486.3MB, alloc=65.2MB, time=3.54 memory used=506.8MB, alloc=65.2MB, time=3.61 memory used=530.3MB, alloc=65.2MB, time=3.69 memory used=555.0MB, alloc=65.2MB, time=3.77 memory used=580.3MB, alloc=65.2MB, time=3.85 memory used=606.1MB, alloc=65.2MB, time=3.92 memory used=632.4MB, alloc=65.2MB, time=4.00 memory used=659.2MB, alloc=65.2MB, time=4.07 memory used=686.4MB, alloc=65.2MB, time=4.14 memory used=714.2MB, alloc=65.2MB, time=4.22 memory used=742.2MB, alloc=65.2MB, time=4.31 memory used=771.2MB, alloc=65.2MB, time=4.40 memory used=795.1MB, alloc=65.2MB, time=4.46 memory used=809.4MB, alloc=65.2MB, time=4.51 memory used=823.8MB, alloc=65.2MB, time=4.57 memory used=838.5MB, alloc=65.2MB, time=4.63 memory used=853.2MB, alloc=65.2MB, time=4.68 memory used=868.0MB, alloc=65.2MB, time=4.74 memory used=882.9MB, alloc=65.2MB, time=4.78 memory used=897.9MB, alloc=65.2MB, time=4.83 memory used=913.0MB, alloc=65.2MB, time=4.89 memory used=928.1MB, alloc=89.2MB, time=4.98 memory used=957.4MB, alloc=89.2MB, time=5.07 memory used=988.3MB, alloc=89.2MB, time=5.14 memory used=1019.5MB, alloc=89.2MB, time=5.22 memory used=1050.9MB, alloc=89.2MB, time=5.30 memory used=1082.5MB, alloc=89.2MB, time=5.39 memory used=1114.3MB, alloc=89.2MB, time=5.47 memory used=1146.3MB, alloc=89.2MB, time=5.55 memory used=1178.5MB, alloc=89.2MB, time=5.62 memory used=1211.8MB, alloc=89.2MB, time=5.71 memory used=1248.8MB, alloc=89.2MB, time=5.80 memory used=1286.8MB, alloc=89.2MB, time=5.89 memory used=1325.0MB, alloc=89.2MB, time=5.98 memory used=1363.2MB, alloc=89.2MB, time=6.06 memory used=1401.5MB, alloc=89.2MB, time=6.14 memory used=1440.7MB, alloc=89.2MB, time=6.24 memory used=1483.6MB, alloc=89.2MB, time=6.33 memory used=1527.4MB, alloc=89.2MB, time=6.43 memory used=1571.0MB, alloc=89.2MB, time=6.52 memory used=1614.6MB, alloc=89.2MB, time=6.61 memory used=1659.1MB, alloc=89.2MB, time=6.70 memory used=1706.5MB, alloc=89.2MB, time=6.80 memory used=1754.7MB, alloc=89.2MB, time=6.89 memory used=1803.6MB, alloc=89.2MB, time=7.00 memory used=1855.1MB, alloc=89.2MB, time=7.10 memory used=1907.0MB, alloc=89.2MB, time=7.20 memory used=1962.9MB, alloc=89.8MB, time=7.30 memory used=1975.8MB, alloc=107.8MB, time=7.36 memory used=1983.3MB, alloc=107.8MB, time=7.41 memory used=1988.9MB, alloc=107.8MB, time=7.45 memory used=1994.0MB, alloc=107.8MB, time=7.50 memory used=1999.2MB, alloc=107.8MB, time=7.55 memory used=2006.9MB, alloc=107.8MB, time=7.64 memory used=2012.9MB, alloc=107.8MB, time=7.70 memory used=2018.4MB, alloc=107.8MB, time=7.76 memory used=2026.0MB, alloc=107.8MB, time=7.81 memory used=2032.0MB, alloc=107.8MB, time=7.86 memory used=2037.4MB, alloc=107.8MB, time=7.89 memory used=2044.9MB, alloc=107.8MB, time=7.93 memory used=2050.9MB, alloc=107.8MB, time=7.97 memory used=2059.0MB, alloc=107.8MB, time=8.02 memory used=2065.0MB, alloc=107.8MB, time=8.06 memory used=2073.0MB, alloc=107.8MB, time=8.13 memory used=2079.1MB, alloc=107.8MB, time=8.17 memory used=2086.8MB, alloc=107.8MB, time=8.21 memory used=2093.3MB, alloc=107.8MB, time=8.26 memory used=2100.6MB, alloc=107.8MB, time=8.34 memory used=2107.1MB, alloc=107.8MB, time=8.38 memory used=2114.2MB, alloc=107.8MB, time=8.44 memory used=2120.7MB, alloc=107.8MB, time=8.48 memory used=2127.8MB, alloc=107.8MB, time=8.53 memory used=2134.2MB, alloc=107.8MB, time=8.56 memory used=2141.3MB, alloc=107.8MB, time=8.60 memory used=2150.2MB, alloc=107.8MB, time=8.65 memory used=2159.0MB, alloc=107.8MB, time=8.73 memory used=2167.8MB, alloc=107.8MB, time=8.77 memory used=2176.6MB, alloc=107.8MB, time=8.83 memory used=2185.3MB, alloc=107.8MB, time=8.88 memory used=2193.9MB, alloc=107.8MB, time=8.93 memory used=2202.5MB, alloc=107.8MB, time=8.97 memory used=2211.1MB, alloc=107.8MB, time=9.05 memory used=2219.5MB, alloc=107.8MB, time=9.10 memory used=2228.0MB, alloc=107.8MB, time=9.17 memory used=2236.3MB, alloc=107.8MB, time=9.24 memory used=2244.6MB, alloc=107.8MB, time=9.28 memory used=2252.9MB, alloc=107.8MB, time=9.33 memory used=2261.1MB, alloc=107.8MB, time=9.38 memory used=2270.6MB, alloc=107.8MB, time=9.44 memory used=2279.4MB, alloc=107.8MB, time=9.51 memory used=2289.3MB, alloc=107.8MB, time=9.57 memory used=2298.6MB, alloc=107.8MB, time=9.62 memory used=2309.0MB, alloc=107.8MB, time=9.66 memory used=2318.4MB, alloc=107.8MB, time=9.71 memory used=2328.3MB, alloc=107.8MB, time=9.76 memory used=2338.0MB, alloc=107.8MB, time=9.81 memory used=2348.6MB, alloc=107.8MB, time=9.86 memory used=2358.3MB, alloc=107.8MB, time=9.91 memory used=2369.3MB, alloc=107.8MB, time=9.96 memory used=2380.1MB, alloc=107.8MB, time=10.01 memory used=2390.8MB, alloc=107.8MB, time=10.05 memory used=2401.4MB, alloc=107.8MB, time=10.10 memory used=2413.2MB, alloc=107.8MB, time=10.14 memory used=2425.3MB, alloc=107.8MB, time=10.19 memory used=2437.0MB, alloc=107.8MB, time=10.24 memory used=2449.8MB, alloc=107.8MB, time=10.29 memory used=2462.5MB, alloc=107.8MB, time=10.34 memory used=2508.7MB, alloc=107.8MB, time=11.66 memory used=2560.1MB, alloc=107.8MB, time=11.81 memory used=2600.4MB, alloc=107.8MB, time=11.93 memory used=2649.5MB, alloc=107.8MB, time=12.08 memory used=2695.1MB, alloc=107.8MB, time=12.21 memory used=2726.6MB, alloc=107.8MB, time=12.32 memory used=2758.2MB, alloc=107.8MB, time=12.43 memory used=2794.2MB, alloc=107.8MB, time=12.55 memory used=2832.4MB, alloc=107.8MB, time=12.67 memory used=2872.2MB, alloc=107.8MB, time=12.79 memory used=2913.8MB, alloc=107.8MB, time=12.91 memory used=2957.3MB, alloc=107.8MB, time=13.04 memory used=3005.8MB, alloc=107.8MB, time=13.15 memory used=3056.4MB, alloc=107.8MB, time=13.27 memory used=3108.4MB, alloc=107.8MB, time=13.39 memory used=3150.2MB, alloc=107.8MB, time=13.49 memory used=3173.9MB, alloc=107.8MB, time=13.57 memory used=3198.4MB, alloc=107.8MB, time=13.64 memory used=3223.3MB, alloc=107.8MB, time=13.72 memory used=3249.0MB, alloc=107.8MB, time=13.80 memory used=3278.7MB, alloc=107.8MB, time=13.88 memory used=3309.4MB, alloc=107.8MB, time=13.97 memory used=3340.3MB, alloc=107.8MB, time=14.05 memory used=3371.4MB, alloc=107.8MB, time=14.14 memory used=3402.9MB, alloc=107.8MB, time=14.22 memory used=3434.5MB, alloc=107.8MB, time=14.30 memory used=3466.3MB, alloc=107.8MB, time=14.38 memory used=3498.3MB, alloc=107.8MB, time=14.47 memory used=3530.5MB, alloc=107.8MB, time=14.55 memory used=3563.9MB, alloc=107.8MB, time=14.63 memory used=3600.8MB, alloc=107.8MB, time=14.72 memory used=3638.8MB, alloc=107.8MB, time=14.80 memory used=3677.0MB, alloc=107.8MB, time=14.89 memory used=3715.2MB, alloc=107.8MB, time=14.97 memory used=3753.5MB, alloc=107.8MB, time=15.07 memory used=3792.7MB, alloc=107.8MB, time=15.16 memory used=3835.6MB, alloc=107.8MB, time=15.24 memory used=3879.4MB, alloc=107.8MB, time=15.34 memory used=3923.0MB, alloc=107.8MB, time=15.43 memory used=3966.6MB, alloc=107.8MB, time=15.53 memory used=4011.2MB, alloc=107.8MB, time=15.62 memory used=4058.5MB, alloc=107.8MB, time=15.71 memory used=4106.7MB, alloc=107.8MB, time=15.81 memory used=4155.7MB, alloc=107.8MB, time=15.91 memory used=4207.1MB, alloc=107.8MB, time=16.00 memory used=4259.1MB, alloc=107.8MB, time=16.10 memory used=4327.3MB, alloc=107.8MB, time=16.22 memory used=4335.1MB, alloc=107.8MB, time=16.26 memory used=4340.7MB, alloc=107.8MB, time=16.30 memory used=4345.8MB, alloc=107.8MB, time=16.34 memory used=4351.0MB, alloc=107.8MB, time=16.38 memory used=4358.7MB, alloc=107.8MB, time=16.42 memory used=4364.7MB, alloc=107.8MB, time=16.47 memory used=4370.2MB, alloc=107.8MB, time=16.51 memory used=4377.8MB, alloc=107.8MB, time=16.56 memory used=4383.8MB, alloc=107.8MB, time=16.60 memory used=4389.2MB, alloc=107.8MB, time=16.64 memory used=4396.7MB, alloc=107.8MB, time=16.74 memory used=4402.7MB, alloc=107.8MB, time=16.78 memory used=4410.8MB, alloc=107.8MB, time=16.82 memory used=4416.8MB, alloc=107.8MB, time=16.86 memory used=4424.7MB, alloc=107.8MB, time=16.90 memory used=4430.9MB, alloc=107.8MB, time=16.94 memory used=4438.6MB, alloc=107.8MB, time=16.98 memory used=4444.8MB, alloc=107.8MB, time=17.05 memory used=4452.4MB, alloc=107.8MB, time=17.09 memory used=4458.9MB, alloc=107.8MB, time=17.13 memory used=4466.0MB, alloc=107.8MB, time=17.20 memory used=4472.5MB, alloc=107.8MB, time=17.24 memory used=4479.6MB, alloc=107.8MB, time=17.29 memory used=4486.1MB, alloc=107.8MB, time=17.32 memory used=4493.1MB, alloc=107.8MB, time=17.37 memory used=4502.0MB, alloc=107.8MB, time=17.41 memory used=4510.8MB, alloc=107.8MB, time=17.46 memory used=4519.6MB, alloc=107.8MB, time=17.52 memory used=4528.4MB, alloc=107.8MB, time=17.58 memory used=4537.1MB, alloc=107.8MB, time=17.63 memory used=4545.7MB, alloc=107.8MB, time=17.67 memory used=4554.3MB, alloc=107.8MB, time=17.72 memory used=4562.9MB, alloc=107.8MB, time=17.79 memory used=4571.3MB, alloc=107.8MB, time=17.83 memory used=4579.8MB, alloc=107.8MB, time=17.90 memory used=4588.1MB, alloc=107.8MB, time=17.94 memory used=4596.4MB, alloc=107.8MB, time=17.98 memory used=4604.7MB, alloc=107.8MB, time=18.05 memory used=4612.9MB, alloc=107.8MB, time=18.09 memory used=4622.4MB, alloc=107.8MB, time=18.14 memory used=4631.2MB, alloc=107.8MB, time=18.19 memory used=4641.1MB, alloc=107.8MB, time=18.23 memory used=4650.4MB, alloc=107.8MB, time=18.28 memory used=4660.8MB, alloc=107.8MB, time=18.32 memory used=4670.2MB, alloc=107.8MB, time=18.44 memory used=4680.1MB, alloc=107.8MB, time=18.48 memory used=4689.8MB, alloc=107.8MB, time=18.57 memory used=4700.4MB, alloc=107.8MB, time=18.61 memory used=4710.1MB, alloc=107.8MB, time=18.66 memory used=4721.1MB, alloc=107.8MB, time=18.71 memory used=4731.9MB, alloc=107.8MB, time=18.75 memory used=4742.6MB, alloc=107.8MB, time=18.84 memory used=4753.2MB, alloc=107.8MB, time=18.89 memory used=4765.0MB, alloc=107.8MB, time=18.93 memory used=4776.0MB, alloc=107.8MB, time=19.00 memory used=4788.5MB, alloc=107.8MB, time=19.05 memory used=4800.1MB, alloc=107.8MB, time=19.09 memory used=4811.9MB, alloc=107.8MB, time=19.14 memory used=4825.8MB, alloc=107.8MB, time=19.23 memory used=4913.7MB, alloc=107.8MB, time=50.67 memory used=4963.6MB, alloc=107.8MB, time=66.51 memory used=5039.5MB, alloc=107.8MB, time=67.04 memory used=5085.8MB, alloc=107.8MB, time=67.17 memory used=5119.9MB, alloc=107.8MB, time=67.28 memory used=5159.7MB, alloc=107.8MB, time=67.40 memory used=5206.9MB, alloc=107.8MB, time=67.52 memory used=5260.4MB, alloc=107.8MB, time=67.65 memory used=5290.1MB, alloc=107.8MB, time=67.74 memory used=5320.7MB, alloc=107.8MB, time=67.82 memory used=5351.9MB, alloc=107.8MB, time=67.91 memory used=5384.5MB, alloc=107.8MB, time=68.00 memory used=5420.5MB, alloc=107.8MB, time=68.09 memory used=5457.8MB, alloc=107.8MB, time=68.18 memory used=5496.2MB, alloc=107.8MB, time=68.26 memory used=5535.6MB, alloc=107.8MB, time=68.36 memory used=5579.0MB, alloc=107.8MB, time=68.45 memory used=5623.3MB, alloc=107.8MB, time=68.55 memory used=5668.8MB, alloc=107.8MB, time=68.64 memory used=5718.2MB, alloc=107.8MB, time=68.75 memory used=5768.6MB, alloc=107.8MB, time=68.85 memory used=5820.3MB, alloc=107.8MB, time=68.95 memory used=5859.1MB, alloc=107.8MB, time=69.05 memory used=5867.2MB, alloc=107.8MB, time=69.10 memory used=5876.2MB, alloc=107.8MB, time=69.15 memory used=5885.3MB, alloc=107.8MB, time=69.19 memory used=5894.5MB, alloc=107.8MB, time=69.23 memory used=5903.6MB, alloc=107.8MB, time=69.28 memory used=5912.8MB, alloc=107.8MB, time=69.33 memory used=5922.0MB, alloc=107.8MB, time=69.38 memory used=5931.2MB, alloc=107.8MB, time=69.43 memory used=5940.4MB, alloc=107.8MB, time=69.47 memory used=5949.7MB, alloc=107.8MB, time=69.52 memory used=5958.9MB, alloc=107.8MB, time=69.57 memory used=5968.2MB, alloc=107.8MB, time=69.61 memory used=5977.5MB, alloc=107.8MB, time=69.66 memory used=5986.8MB, alloc=107.8MB, time=69.71 memory used=5996.2MB, alloc=107.8MB, time=69.78 memory used=6005.5MB, alloc=107.8MB, time=69.84 memory used=6014.9MB, alloc=107.8MB, time=69.90 memory used=6024.3MB, alloc=107.8MB, time=69.95 memory used=6033.6MB, alloc=107.8MB, time=70.00 memory used=6043.1MB, alloc=107.8MB, time=70.04 memory used=6052.5MB, alloc=107.8MB, time=70.08 memory used=6061.9MB, alloc=107.8MB, time=70.15 memory used=6071.3MB, alloc=107.8MB, time=70.19 memory used=6080.8MB, alloc=107.8MB, time=70.24 memory used=6090.3MB, alloc=107.8MB, time=70.28 memory used=6099.7MB, alloc=107.8MB, time=70.33 memory used=6109.2MB, alloc=107.8MB, time=70.38 memory used=6118.7MB, alloc=107.8MB, time=70.42 memory used=6128.2MB, alloc=107.8MB, time=70.47 memory used=6137.7MB, alloc=107.8MB, time=70.52 memory used=6147.3MB, alloc=107.8MB, time=70.56 memory used=6156.8MB, alloc=107.8MB, time=70.61 memory used=6166.3MB, alloc=107.8MB, time=70.66 memory used=6175.9MB, alloc=107.8MB, time=70.70 memory used=6185.4MB, alloc=107.8MB, time=70.75 memory used=6195.0MB, alloc=107.8MB, time=70.79 memory used=6204.5MB, alloc=107.8MB, time=70.85 memory used=6214.1MB, alloc=107.8MB, time=70.89 memory used=6224.0MB, alloc=107.8MB, time=70.94 memory used=6233.7MB, alloc=107.8MB, time=70.99 memory used=6246.0MB, alloc=107.8MB, time=71.06 memory used=6256.0MB, alloc=107.8MB, time=71.11 memory used=6268.4MB, alloc=107.8MB, time=71.16 memory used=6278.5MB, alloc=107.8MB, time=71.20 memory used=6290.8MB, alloc=107.8MB, time=71.26 memory used=6303.6MB, alloc=107.8MB, time=71.31 memory used=6316.4MB, alloc=107.8MB, time=71.37 memory used=6329.2MB, alloc=107.8MB, time=71.43 memory used=6342.0MB, alloc=107.8MB, time=71.48 memory used=6354.8MB, alloc=107.8MB, time=71.53 memory used=6367.6MB, alloc=107.8MB, time=71.58 memory used=6380.3MB, alloc=107.8MB, time=71.63 memory used=6393.1MB, alloc=107.8MB, time=71.68 memory used=6405.9MB, alloc=107.8MB, time=71.73 memory used=6418.6MB, alloc=107.8MB, time=71.78 memory used=6431.4MB, alloc=107.8MB, time=71.83 memory used=6444.1MB, alloc=107.8MB, time=71.88 memory used=6456.9MB, alloc=107.8MB, time=71.96 memory used=6469.6MB, alloc=107.8MB, time=72.02 memory used=6482.3MB, alloc=107.8MB, time=72.07 memory used=6495.0MB, alloc=107.8MB, time=72.12 memory used=6507.7MB, alloc=107.8MB, time=72.17 memory used=6520.3MB, alloc=107.8MB, time=72.22 memory used=6532.9MB, alloc=107.8MB, time=72.28 memory used=6545.6MB, alloc=107.8MB, time=72.33 memory used=6558.2MB, alloc=107.8MB, time=72.38 memory used=6571.1MB, alloc=107.8MB, time=72.43 memory used=6586.4MB, alloc=107.8MB, time=72.49 memory used=6599.5MB, alloc=107.8MB, time=72.54 memory used=6614.6MB, alloc=107.8MB, time=72.64 memory used=6630.2MB, alloc=107.8MB, time=72.69 memory used=6645.7MB, alloc=107.8MB, time=72.75 memory used=6661.2MB, alloc=107.8MB, time=72.84 memory used=6676.7MB, alloc=107.8MB, time=72.90 memory used=6692.1MB, alloc=107.8MB, time=72.95 memory used=6707.4MB, alloc=107.8MB, time=73.01 memory used=6722.7MB, alloc=107.8MB, time=73.06 memory used=6737.9MB, alloc=107.8MB, time=73.13 memory used=6753.1MB, alloc=107.8MB, time=73.21 memory used=6768.2MB, alloc=107.8MB, time=73.26 memory used=6783.3MB, alloc=107.8MB, time=73.32 memory used=6798.7MB, alloc=107.8MB, time=73.39 memory used=6816.2MB, alloc=107.8MB, time=73.44 memory used=6831.6MB, alloc=107.8MB, time=73.49 memory used=6848.8MB, alloc=107.8MB, time=73.55 memory used=6866.4MB, alloc=107.8MB, time=73.60 memory used=6883.9MB, alloc=107.8MB, time=73.65 memory used=6901.3MB, alloc=107.8MB, time=73.70 memory used=6918.6MB, alloc=107.8MB, time=73.75 memory used=6935.7MB, alloc=107.8MB, time=73.83 memory used=6952.7MB, alloc=107.8MB, time=73.88 memory used=6970.1MB, alloc=107.8MB, time=73.93 memory used=6989.2MB, alloc=107.8MB, time=73.99 memory used=7008.6MB, alloc=107.8MB, time=74.05 memory used=7027.7MB, alloc=107.8MB, time=74.10 memory used=7046.7MB, alloc=107.8MB, time=74.15 memory used=7065.5MB, alloc=107.8MB, time=74.21 memory used=7084.1MB, alloc=107.8MB, time=74.28 memory used=7103.1MB, alloc=107.8MB, time=74.34 memory used=7123.3MB, alloc=107.8MB, time=74.40 memory used=7143.8MB, alloc=107.8MB, time=74.46 memory used=7163.9MB, alloc=107.8MB, time=74.51 memory used=7184.3MB, alloc=107.8MB, time=74.57 memory used=7203.7MB, alloc=107.8MB, time=74.62 memory used=7218.0MB, alloc=107.8MB, time=74.68 memory used=7231.0MB, alloc=107.8MB, time=74.75 memory used=7244.4MB, alloc=107.8MB, time=74.80 memory used=7258.0MB, alloc=107.8MB, time=74.86 memory used=7271.5MB, alloc=107.8MB, time=74.91 memory used=7285.3MB, alloc=107.8MB, time=74.98 memory used=7298.6MB, alloc=107.8MB, time=75.03 memory used=7312.8MB, alloc=107.8MB, time=75.08 memory used=7327.4MB, alloc=107.8MB, time=75.13 memory used=7341.8MB, alloc=107.8MB, time=75.18 memory used=7356.4MB, alloc=107.8MB, time=75.23 memory used=7371.5MB, alloc=107.8MB, time=75.28 memory used=7386.7MB, alloc=107.8MB, time=75.33 memory used=7402.2MB, alloc=107.8MB, time=75.38 memory used=7417.7MB, alloc=107.8MB, time=75.43 memory used=7433.8MB, alloc=107.8MB, time=75.48 memory used=7450.5MB, alloc=107.8MB, time=75.53 memory used=7467.4MB, alloc=107.8MB, time=75.60 memory used=7484.6MB, alloc=107.8MB, time=75.65 memory used=7502.4MB, alloc=107.8MB, time=75.70 memory used=7581.5MB, alloc=107.8MB, time=76.75 memory used=7631.5MB, alloc=107.8MB, time=76.88 memory used=7670.5MB, alloc=107.8MB, time=76.99 memory used=7715.0MB, alloc=107.8MB, time=77.09 memory used=7788.7MB, alloc=107.8MB, time=79.40 memory used=7831.8MB, alloc=107.8MB, time=79.52 memory used=7876.4MB, alloc=107.8MB, time=79.64 memory used=7922.6MB, alloc=107.8MB, time=79.75 memory used=7956.6MB, alloc=107.8MB, time=79.83 memory used=7995.3MB, alloc=107.8MB, time=79.92 memory used=8038.2MB, alloc=107.8MB, time=80.02 memory used=8086.4MB, alloc=107.8MB, time=80.12 memory used=8140.2MB, alloc=107.8MB, time=80.21 memory used=8169.4MB, alloc=107.8MB, time=80.29 memory used=8182.2MB, alloc=107.8MB, time=80.34 memory used=8195.4MB, alloc=107.8MB, time=80.39 memory used=8208.7MB, alloc=107.8MB, time=80.43 memory used=8222.7MB, alloc=107.8MB, time=80.49 memory used=8237.3MB, alloc=107.8MB, time=80.54 memory used=8252.4MB, alloc=107.8MB, time=80.59 memory used=8268.3MB, alloc=107.8MB, time=80.64 memory used=8314.5MB, alloc=107.8MB, time=81.25 memory used=8403.7MB, alloc=107.8MB, time=102.76 memory used=8477.1MB, alloc=107.8MB, time=106.12 memory used=8523.5MB, alloc=107.8MB, time=106.26 memory used=8557.0MB, alloc=107.8MB, time=106.36 memory used=8596.4MB, alloc=107.8MB, time=106.48 memory used=8643.6MB, alloc=107.8MB, time=106.59 memory used=8691.9MB, alloc=107.8MB, time=106.72 memory used=8719.6MB, alloc=107.8MB, time=106.79 memory used=8750.5MB, alloc=107.8MB, time=106.88 memory used=8782.7MB, alloc=107.8MB, time=106.97 memory used=8816.1MB, alloc=107.8MB, time=107.06 memory used=8852.9MB, alloc=107.8MB, time=107.15 memory used=8891.0MB, alloc=107.8MB, time=107.24 memory used=8930.4MB, alloc=107.8MB, time=107.34 memory used=8972.9MB, alloc=107.8MB, time=107.45 memory used=9016.6MB, alloc=107.8MB, time=107.55 memory used=9063.9MB, alloc=107.8MB, time=107.66 memory used=9112.4MB, alloc=107.8MB, time=107.76 memory used=9164.0MB, alloc=107.8MB, time=107.86 memory used=9202.9MB, alloc=107.8MB, time=107.95 memory used=9208.3MB, alloc=107.8MB, time=107.99 memory used=9213.4MB, alloc=107.8MB, time=108.04 memory used=9218.5MB, alloc=107.8MB, time=108.08 memory used=9223.6MB, alloc=107.8MB, time=108.12 memory used=9228.8MB, alloc=107.8MB, time=108.16 memory used=9234.0MB, alloc=107.8MB, time=108.21 memory used=9239.1MB, alloc=107.8MB, time=108.26 memory used=9244.3MB, alloc=107.8MB, time=108.32 memory used=9249.5MB, alloc=107.8MB, time=108.39 memory used=9254.6MB, alloc=107.8MB, time=108.43 memory used=9259.8MB, alloc=107.8MB, time=108.47 memory used=9265.0MB, alloc=107.8MB, time=108.52 memory used=9270.2MB, alloc=107.8MB, time=108.56 memory used=9275.4MB, alloc=107.8MB, time=108.61 memory used=9280.6MB, alloc=107.8MB, time=108.64 memory used=9285.8MB, alloc=107.8MB, time=108.68 memory used=9291.0MB, alloc=107.8MB, time=108.77 memory used=9296.2MB, alloc=107.8MB, time=108.81 memory used=9301.4MB, alloc=107.8MB, time=108.86 memory used=9306.7MB, alloc=107.8MB, time=108.92 memory used=9312.1MB, alloc=107.8MB, time=108.97 memory used=9317.5MB, alloc=107.8MB, time=109.01 memory used=9324.9MB, alloc=107.8MB, time=109.06 memory used=9330.5MB, alloc=107.8MB, time=109.10 memory used=9338.0MB, alloc=107.8MB, time=109.15 memory used=9343.6MB, alloc=107.8MB, time=109.20 memory used=9351.1MB, alloc=107.8MB, time=109.25 memory used=9356.8MB, alloc=107.8MB, time=109.29 memory used=9364.2MB, alloc=107.8MB, time=109.34 memory used=9369.9MB, alloc=107.8MB, time=109.40 memory used=9377.4MB, alloc=107.8MB, time=109.47 memory used=9385.3MB, alloc=107.8MB, time=109.51 memory used=9393.1MB, alloc=107.8MB, time=109.56 memory used=9401.0MB, alloc=107.8MB, time=109.61 memory used=9408.9MB, alloc=107.8MB, time=109.66 memory used=9416.8MB, alloc=107.8MB, time=109.72 memory used=9424.7MB, alloc=107.8MB, time=109.77 memory used=9432.5MB, alloc=107.8MB, time=109.82 memory used=9440.4MB, alloc=107.8MB, time=109.86 memory used=9448.3MB, alloc=107.8MB, time=109.91 memory used=9456.2MB, alloc=107.8MB, time=109.98 memory used=9464.1MB, alloc=107.8MB, time=110.03 memory used=9472.0MB, alloc=107.8MB, time=110.07 memory used=9479.8MB, alloc=107.8MB, time=110.11 memory used=9487.7MB, alloc=107.8MB, time=110.18 memory used=9495.6MB, alloc=107.8MB, time=110.25 memory used=9503.4MB, alloc=107.8MB, time=110.31 memory used=9511.3MB, alloc=107.8MB, time=110.37 memory used=9519.2MB, alloc=107.8MB, time=110.42 memory used=9527.0MB, alloc=107.8MB, time=110.47 memory used=9534.9MB, alloc=107.8MB, time=110.51 memory used=9542.7MB, alloc=107.8MB, time=110.57 memory used=9550.5MB, alloc=107.8MB, time=110.61 memory used=9558.4MB, alloc=107.8MB, time=110.67 memory used=9566.2MB, alloc=107.8MB, time=110.72 memory used=9574.0MB, alloc=107.8MB, time=110.78 memory used=9581.8MB, alloc=107.8MB, time=110.82 memory used=9589.6MB, alloc=107.8MB, time=110.86 memory used=9597.4MB, alloc=107.8MB, time=110.93 memory used=9605.2MB, alloc=107.8MB, time=110.97 memory used=9612.9MB, alloc=107.8MB, time=111.04 memory used=9620.7MB, alloc=107.8MB, time=111.09 memory used=9628.8MB, alloc=107.8MB, time=111.14 memory used=9636.7MB, alloc=107.8MB, time=111.19 memory used=9646.5MB, alloc=107.8MB, time=111.24 memory used=9654.6MB, alloc=107.8MB, time=111.28 memory used=9664.4MB, alloc=107.8MB, time=111.33 memory used=9672.6MB, alloc=107.8MB, time=111.38 memory used=9682.3MB, alloc=107.8MB, time=111.44 memory used=9692.5MB, alloc=107.8MB, time=111.49 memory used=9702.6MB, alloc=107.8MB, time=111.55 memory used=9712.8MB, alloc=107.8MB, time=111.60 memory used=9722.9MB, alloc=107.8MB, time=111.65 memory used=9732.9MB, alloc=107.8MB, time=111.70 memory used=9743.0MB, alloc=107.8MB, time=111.74 memory used=9753.0MB, alloc=107.8MB, time=111.79 memory used=9762.9MB, alloc=107.8MB, time=111.85 memory used=9772.9MB, alloc=107.8MB, time=111.90 memory used=9782.8MB, alloc=107.8MB, time=111.95 memory used=9792.6MB, alloc=107.8MB, time=112.00 memory used=9802.4MB, alloc=107.8MB, time=112.05 memory used=9812.2MB, alloc=107.8MB, time=112.10 memory used=9822.0MB, alloc=107.8MB, time=112.15 memory used=9832.0MB, alloc=107.8MB, time=112.21 memory used=9841.9MB, alloc=107.8MB, time=112.26 memory used=9853.3MB, alloc=107.8MB, time=112.31 memory used=9863.5MB, alloc=107.8MB, time=112.38 memory used=9874.8MB, alloc=107.8MB, time=112.43 memory used=9886.6MB, alloc=107.8MB, time=112.48 memory used=9898.3MB, alloc=107.8MB, time=112.53 memory used=9909.9MB, alloc=107.8MB, time=112.59 memory used=9921.5MB, alloc=107.8MB, time=112.63 memory used=9933.0MB, alloc=107.8MB, time=112.69 memory used=9944.5MB, alloc=107.8MB, time=112.74 memory used=9955.8MB, alloc=107.8MB, time=112.79 memory used=9967.5MB, alloc=107.8MB, time=112.85 memory used=9980.4MB, alloc=107.8MB, time=112.90 memory used=9993.6MB, alloc=107.8MB, time=112.95 memory used=10006.7MB, alloc=107.8MB, time=113.01 memory used=10019.7MB, alloc=107.8MB, time=113.06 memory used=10032.5MB, alloc=107.8MB, time=113.11 memory used=10045.1MB, alloc=107.8MB, time=113.16 memory used=10058.1MB, alloc=107.8MB, time=113.23 memory used=10072.0MB, alloc=107.8MB, time=113.28 memory used=10086.2MB, alloc=107.8MB, time=113.35 memory used=10100.1MB, alloc=107.8MB, time=113.41 memory used=10113.8MB, alloc=107.8MB, time=113.46 memory used=10127.7MB, alloc=107.8MB, time=113.51 memory used=10142.3MB, alloc=107.8MB, time=113.57 memory used=10157.1MB, alloc=107.8MB, time=113.63 memory used=10171.9MB, alloc=107.8MB, time=113.68 memory used=10187.3MB, alloc=107.8MB, time=113.73 memory used=10202.7MB, alloc=107.8MB, time=113.79 memory used=10218.1MB, alloc=107.8MB, time=113.84 memory used=10234.1MB, alloc=107.8MB, time=113.89 memory used=10246.6MB, alloc=107.8MB, time=113.94 memory used=10257.1MB, alloc=107.8MB, time=114.00 memory used=10267.5MB, alloc=107.8MB, time=114.05 memory used=10278.5MB, alloc=107.8MB, time=114.09 memory used=10289.5MB, alloc=107.8MB, time=114.14 memory used=10300.9MB, alloc=107.8MB, time=114.19 memory used=10312.3MB, alloc=107.8MB, time=114.23 memory used=10369.7MB, alloc=107.8MB, time=115.16 memory used=10455.9MB, alloc=107.8MB, time=115.89 memory used=10531.6MB, alloc=363.8MB, time=117.06 memory used=10611.5MB, alloc=363.8MB, time=120.01 memory used=10671.9MB, alloc=387.8MB, time=161.91 memory used=10728.6MB, alloc=387.8MB, time=204.79 |\^/| 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(); 1428295433 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 4 2 F := [-9 x - 16 y z + 18 x + 11 y, 18 x - 19 x y z - 3 y - 13 y z, 2 2 3 3 -11 x y + 3 x z - 13 y z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 G := [15 x z + 19 y + 16 z, 15 x y + 12 y z - 13 x - 19 y, 3 3 2 9 x y - 11 x z - 20 y z + 15 z] > Problem := [F,G]; 4 3 2 4 2 Problem := [[-9 x - 16 y z + 18 x + 11 y, 18 x - 19 x y z - 3 y - 13 y z, 2 2 3 3 -11 x y + 3 x z - 13 y z ], [15 x z + 19 y + 16 z, 3 3 3 3 3 2 15 x y + 12 y z - 13 x - 19 y, 9 x y - 11 x z - 20 y z + 15 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=46.8MB, alloc=32.3MB, time=0.80 memory used=66.5MB, alloc=56.3MB, time=1.11 memory used=109.6MB, alloc=60.3MB, time=1.69 memory used=152.2MB, alloc=60.3MB, time=2.14 memory used=198.2MB, alloc=68.3MB, time=2.73 memory used=243.6MB, alloc=92.3MB, time=3.30 memory used=313.2MB, alloc=92.3MB, time=4.20 memory used=378.7MB, alloc=348.3MB, time=5.01 memory used=442.4MB, alloc=372.3MB, time=5.63 memory used=519.1MB, alloc=372.3MB, time=6.26 memory used=575.8MB, alloc=372.3MB, time=6.52 memory used=642.0MB, alloc=372.3MB, time=9.55 memory used=684.9MB, alloc=372.3MB, time=9.71 memory used=734.1MB, alloc=372.3MB, time=9.85 memory used=770.9MB, alloc=372.3MB, time=9.98 memory used=816.6MB, alloc=372.3MB, time=10.17 memory used=892.3MB, alloc=372.3MB, time=10.73 memory used=981.6MB, alloc=372.3MB, time=13.94 memory used=1034.7MB, alloc=372.3MB, time=14.44 memory used=1072.8MB, alloc=372.3MB, time=14.59 memory used=1120.9MB, alloc=372.3MB, time=14.73 memory used=1153.4MB, alloc=372.3MB, time=14.84 memory used=1218.6MB, alloc=372.3MB, time=15.33 memory used=1326.2MB, alloc=372.3MB, time=16.00 memory used=1422.5MB, alloc=372.3MB, time=17.36 memory used=1522.4MB, alloc=396.3MB, time=18.15 memory used=1637.3MB, alloc=420.3MB, time=19.66 memory used=1768.2MB, alloc=420.3MB, time=21.04 memory used=1901.9MB, alloc=420.3MB, time=22.23 memory used=1973.0MB, alloc=420.3MB, time=22.68 memory used=2056.9MB, alloc=420.3MB, time=24.72 memory used=2119.6MB, alloc=420.3MB, time=24.97 memory used=2166.9MB, alloc=420.3MB, time=25.16 memory used=2229.8MB, alloc=420.3MB, time=25.37 memory used=2384.9MB, alloc=420.3MB, time=26.85 memory used=2506.6MB, alloc=444.3MB, time=28.14 memory used=2601.8MB, alloc=444.3MB, time=28.92 memory used=2674.6MB, alloc=444.3MB, time=29.24 memory used=2765.3MB, alloc=444.3MB, time=29.86 memory used=2834.2MB, alloc=444.3MB, time=30.15 memory used=2907.5MB, alloc=444.3MB, time=30.51 memory used=2977.3MB, alloc=444.3MB, time=30.83 memory used=3048.0MB, alloc=444.3MB, time=31.08 memory used=3125.6MB, alloc=444.3MB, time=31.82 memory used=3190.6MB, alloc=444.3MB, time=32.06 memory used=3268.6MB, alloc=444.3MB, time=32.44 memory used=3340.9MB, alloc=444.3MB, time=32.71 memory used=3415.6MB, alloc=444.3MB, time=33.14 memory used=3484.2MB, alloc=444.3MB, time=33.44 memory used=3560.9MB, alloc=444.3MB, time=34.54 memory used=3632.3MB, alloc=444.3MB, time=34.83 memory used=3695.1MB, alloc=444.3MB, time=35.06 memory used=3862.5MB, alloc=444.3MB, time=36.43 memory used=4003.3MB, alloc=444.3MB, time=37.81 memory used=4078.6MB, alloc=444.3MB, time=38.11 memory used=4133.0MB, alloc=444.3MB, time=38.38 memory used=4192.9MB, alloc=444.3MB, time=38.63 memory used=4265.3MB, alloc=444.3MB, time=38.89 memory used=4361.7MB, alloc=444.3MB, time=39.37 memory used=4427.1MB, alloc=444.3MB, time=39.67 memory used=4493.0MB, alloc=444.3MB, time=39.95 memory used=4549.4MB, alloc=444.3MB, time=40.21 memory used=4617.6MB, alloc=444.3MB, time=40.47 memory used=4706.4MB, alloc=444.3MB, time=42.09 memory used=4814.0MB, alloc=444.3MB, time=51.32 memory used=4877.4MB, alloc=444.3MB, time=51.62 memory used=4942.0MB, alloc=444.3MB, time=51.93 memory used=5021.6MB, alloc=444.3MB, time=52.22 memory used=5075.6MB, alloc=468.3MB, time=52.48 memory used=5140.5MB, alloc=468.3MB, time=52.74 memory used=5213.8MB, alloc=468.3MB, time=53.00 memory used=5296.1MB, alloc=468.3MB, time=53.26 memory used=5387.9MB, alloc=468.3MB, time=53.54 memory used=5496.4MB, alloc=468.3MB, time=53.82 memory used=5662.8MB, alloc=468.3MB, time=54.35 memory used=5873.6MB, alloc=468.3MB, time=56.37 memory used=6099.8MB, alloc=468.3MB, time=58.47 memory used=6303.6MB, alloc=468.3MB, time=60.99 memory used=6507.7MB, alloc=468.3MB, time=66.64 memory used=6718.2MB, alloc=468.3MB, time=74.96 memory used=6818.9MB, alloc=468.3MB, time=76.96 memory used=6924.3MB, alloc=468.3MB, time=78.15 memory used=7049.5MB, alloc=468.3MB, time=79.41 memory used=7149.7MB, alloc=468.3MB, time=80.88 memory used=7222.1MB, alloc=468.3MB, time=81.20 memory used=7352.7MB, alloc=468.3MB, time=82.47 memory used=7432.6MB, alloc=468.3MB, time=83.67 memory used=7513.9MB, alloc=492.3MB, time=84.81 memory used=7611.3MB, alloc=492.3MB, time=85.41 memory used=7706.1MB, alloc=492.3MB, time=85.91 memory used=7810.7MB, alloc=492.3MB, time=87.14 memory used=7888.6MB, alloc=492.3MB, time=87.58 memory used=7988.4MB, alloc=492.3MB, time=88.04 memory used=8065.0MB, alloc=492.3MB, time=88.45 memory used=8133.3MB, alloc=492.3MB, time=88.83 memory used=8206.9MB, alloc=492.3MB, time=89.20 memory used=8290.0MB, alloc=492.3MB, time=89.59 memory used=8380.9MB, alloc=492.3MB, time=89.98 memory used=8482.3MB, alloc=492.3MB, time=90.39 memory used=8593.6MB, alloc=492.3MB, time=90.80 memory used=8748.3MB, alloc=492.3MB, time=91.32 memory used=8892.8MB, alloc=492.3MB, time=91.82 memory used=9053.5MB, alloc=492.3MB, time=92.32 memory used=9333.5MB, alloc=492.3MB, time=93.92 memory used=9413.9MB, alloc=492.3MB, time=94.36 memory used=9520.2MB, alloc=492.3MB, time=94.82 memory used=9585.3MB, alloc=492.3MB, time=95.17 memory used=9654.5MB, alloc=492.3MB, time=95.57 memory used=9731.9MB, alloc=492.3MB, time=95.94 memory used=9816.6MB, alloc=492.3MB, time=96.36 memory used=9909.0MB, alloc=492.3MB, time=96.76 memory used=10010.8MB, alloc=492.3MB, time=97.18 memory used=10251.7MB, alloc=492.3MB, time=97.82 memory used=10394.0MB, alloc=492.3MB, time=98.32 memory used=10554.0MB, alloc=492.3MB, time=98.82 memory used=10830.3MB, alloc=492.3MB, time=107.53 memory used=10925.6MB, alloc=492.3MB, time=107.98 memory used=10994.6MB, alloc=492.3MB, time=108.35 memory used=11077.3MB, alloc=492.3MB, time=108.75 memory used=11175.5MB, alloc=492.3MB, time=109.14 memory used=11394.2MB, alloc=492.3MB, time=109.77 memory used=11552.7MB, alloc=492.3MB, time=110.28 memory used=11736.7MB, alloc=492.3MB, time=110.81 memory used=11958.0MB, alloc=492.3MB, time=111.38 memory used=12193.4MB, alloc=492.3MB, time=112.49 memory used=12302.4MB, alloc=492.3MB, time=113.58 memory used=12374.2MB, alloc=492.3MB, time=113.99 memory used=12461.6MB, alloc=492.3MB, time=114.41 memory used=12567.8MB, alloc=492.3MB, time=114.84 memory used=12629.9MB, alloc=492.3MB, time=115.22 memory used=12696.6MB, alloc=492.3MB, time=115.59 memory used=12767.9MB, alloc=492.3MB, time=115.96 memory used=12845.4MB, alloc=492.3MB, time=116.32 memory used=12928.8MB, alloc=492.3MB, time=116.70 memory used=13021.9MB, alloc=492.3MB, time=117.08 memory used=13120.8MB, alloc=492.3MB, time=117.47 memory used=13228.9MB, alloc=492.3MB, time=117.86 memory used=13384.6MB, alloc=492.3MB, time=118.35 memory used=13532.0MB, alloc=492.3MB, time=118.83 memory used=13641.4MB, alloc=492.3MB, time=120.11 memory used=13728.3MB, alloc=492.3MB, time=120.56 memory used=13806.6MB, alloc=492.3MB, time=120.99 memory used=13905.0MB, alloc=492.3MB, time=121.43 memory used=13991.1MB, alloc=516.3MB, time=121.86 memory used=14067.2MB, alloc=516.3MB, time=122.25 memory used=14151.3MB, alloc=516.3MB, time=122.66 memory used=14243.8MB, alloc=516.3MB, time=123.07 memory used=14346.3MB, alloc=516.3MB, time=123.46 memory used=14462.7MB, alloc=516.3MB, time=123.88 memory used=14589.5MB, alloc=516.3MB, time=124.31 memory used=14777.5MB, alloc=516.3MB, time=124.84 memory used=14923.1MB, alloc=516.3MB, time=125.31 memory used=15086.4MB, alloc=516.3MB, time=185.44 memory used=15206.6MB, alloc=516.3MB, time=186.10 memory used=15318.9MB, alloc=516.3MB, time=186.56 memory used=15396.0MB, alloc=516.3MB, time=186.94 memory used=15486.5MB, alloc=516.3MB, time=187.34 memory used=15590.3MB, alloc=516.3MB, time=187.76 memory used=15707.3MB, alloc=516.3MB, time=188.21 memory used=15947.9MB, alloc=516.3MB, time=188.84 memory used=16088.9MB, alloc=516.3MB, time=189.33 memory used=16244.5MB, alloc=516.3MB, time=189.83 memory used=16414.8MB, alloc=516.3MB, time=190.34 memory used=16599.7MB, alloc=516.3MB, time=190.86 memory used=16798.4MB, alloc=516.3MB, time=191.40 memory used=17014.3MB, alloc=516.3MB, time=191.95 memory used=17250.4MB, alloc=516.3MB, time=192.52 memory used=17421.4MB, alloc=516.3MB, time=193.01 memory used=17599.8MB, alloc=516.3MB, time=193.51 memory used=17788.5MB, alloc=516.3MB, time=194.02 memory used=17988.0MB, alloc=516.3MB, time=194.54 memory used=18203.6MB, alloc=516.3MB, time=195.07 memory used=18436.0MB, alloc=516.3MB, time=195.60 memory used=18641.8MB, alloc=516.3MB, time=196.10 memory used=18797.7MB, alloc=516.3MB, time=197.33 memory used=18941.6MB, alloc=516.3MB, time=198.60 memory used=19084.3MB, alloc=516.3MB, time=200.04 memory used=19190.7MB, alloc=516.3MB, time=203.06 memory used=19310.6MB, alloc=516.3MB, time=204.06 memory used=19560.9MB, alloc=516.3MB, time=205.40 memory used=19716.5MB, alloc=516.3MB, time=206.47 memory used=19837.8MB, alloc=516.3MB, time=207.55 memory used=19933.7MB, alloc=516.3MB, time=207.97 memory used=20044.6MB, alloc=516.3MB, time=208.99 memory used=20148.5MB, alloc=516.3MB, time=209.46 memory used=20231.9MB, alloc=516.3MB, time=209.84 memory used=20367.8MB, alloc=516.3MB, time=211.02 memory used=20474.2MB, alloc=516.3MB, time=211.51 memory used=20551.2MB, alloc=516.3MB, time=211.94 memory used=20648.8MB, alloc=516.3MB, time=212.37 memory used=20756.3MB, alloc=516.3MB, time=212.81 memory used=20865.0MB, alloc=516.3MB, time=213.51 memory used=20969.1MB, alloc=516.3MB, time=213.97 memory used=21049.0MB, alloc=516.3MB, time=214.41 memory used=21149.6MB, alloc=516.3MB, time=214.86 memory used=21250.5MB, alloc=516.3MB, time=215.27 memory used=21396.7MB, alloc=516.3MB, time=229.35 memory used=21489.9MB, alloc=516.3MB, time=229.82 memory used=21596.8MB, alloc=516.3MB, time=230.30 memory used=21683.2MB, alloc=516.3MB, time=230.72 memory used=21760.9MB, alloc=516.3MB, time=231.12 memory used=21848.7MB, alloc=516.3MB, time=231.51 memory used=21948.2MB, alloc=516.3MB, time=231.90 memory used=22060.1MB, alloc=516.3MB, time=232.30 memory used=22287.8MB, alloc=516.3MB, time=232.85 memory used=22526.2MB, alloc=516.3MB, time=234.28 memory used=22632.3MB, alloc=516.3MB, time=235.54 memory used=22715.9MB, alloc=516.3MB, time=237.06 memory used=22804.9MB, alloc=516.3MB, time=237.52 |\^/| 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(); 1428295733 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 F := [17 x y z - 17 x y + x y + 8, 15 x y + 2 y z + 8 z + 12 x, 2 2 3 2 6 x y z + 18 x y z + 15 x z - 16 y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [13 x y z + 12 x y z + 19 y z + 4 y , 2 2 2 3 2 3 4 2 13 x y + 15 x y z - 13 y - 8 y z , -18 x z - 11 z - 6 x y + 11 x z] > Problem := [F,G]; 2 2 2 3 2 2 Problem := [[17 x y z - 17 x y + x y + 8, 15 x y + 2 y z + 8 z + 12 x, 2 2 3 2 6 x y z + 18 x y z + 15 x z - 16 y ], [ 2 2 2 13 x y z + 12 x y z + 19 y z + 4 y , 2 2 2 3 2 3 4 2 13 x y + 15 x y z - 13 y - 8 y z , -18 x z - 11 z - 6 x y + 11 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.8MB, alloc=32.3MB, time=0.50 memory used=45.3MB, alloc=60.3MB, time=0.77 memory used=87.6MB, alloc=60.3MB, time=1.37 memory used=120.6MB, alloc=60.3MB, time=1.55 memory used=164.5MB, alloc=60.3MB, time=2.00 memory used=214.1MB, alloc=68.3MB, time=2.59 memory used=261.6MB, alloc=68.3MB, time=3.16 memory used=307.9MB, alloc=68.3MB, time=3.63 memory used=332.5MB, alloc=68.3MB, time=3.72 memory used=350.3MB, alloc=68.3MB, time=3.80 memory used=370.9MB, alloc=68.3MB, time=3.86 memory used=391.6MB, alloc=68.3MB, time=3.92 memory used=417.5MB, alloc=68.3MB, time=4.11 memory used=438.7MB, alloc=68.3MB, time=4.19 memory used=456.2MB, alloc=68.3MB, time=4.25 memory used=478.7MB, alloc=68.3MB, time=4.31 memory used=496.7MB, alloc=68.3MB, time=4.38 memory used=535.9MB, alloc=68.3MB, time=4.71 memory used=575.5MB, alloc=92.3MB, time=5.33 memory used=634.8MB, alloc=92.3MB, time=6.16 memory used=696.4MB, alloc=372.3MB, time=7.00 memory used=788.5MB, alloc=396.3MB, time=8.27 memory used=888.1MB, alloc=396.3MB, time=9.25 memory used=954.0MB, alloc=396.3MB, time=9.61 memory used=1034.4MB, alloc=396.3MB, time=11.38 memory used=1082.7MB, alloc=396.3MB, time=11.56 memory used=1137.7MB, alloc=396.3MB, time=11.73 memory used=1227.8MB, alloc=396.3MB, time=12.47 memory used=1364.8MB, alloc=396.3MB, time=13.94 memory used=1443.7MB, alloc=396.3MB, time=14.64 memory used=1574.7MB, alloc=396.3MB, time=16.05 memory used=1705.2MB, alloc=420.3MB, time=17.74 memory used=1814.0MB, alloc=420.3MB, time=19.25 memory used=1919.0MB, alloc=444.3MB, time=20.17 memory used=2018.0MB, alloc=444.3MB, time=20.89 memory used=2094.7MB, alloc=444.3MB, time=21.24 memory used=2205.2MB, alloc=444.3MB, time=24.61 memory used=2281.4MB, alloc=444.3MB, time=24.92 memory used=2352.4MB, alloc=444.3MB, time=25.19 memory used=2422.4MB, alloc=444.3MB, time=25.43 memory used=2484.9MB, alloc=444.3MB, time=25.65 memory used=2577.8MB, alloc=444.3MB, time=26.19 memory used=2717.5MB, alloc=444.3MB, time=27.69 memory used=2834.3MB, alloc=444.3MB, time=28.61 memory used=2955.9MB, alloc=444.3MB, time=29.83 memory used=3066.9MB, alloc=444.3MB, time=30.80 memory used=3139.0MB, alloc=444.3MB, time=31.11 memory used=3239.2MB, alloc=444.3MB, time=33.92 memory used=3302.1MB, alloc=444.3MB, time=34.21 memory used=3374.6MB, alloc=444.3MB, time=34.50 memory used=3425.2MB, alloc=444.3MB, time=34.78 memory used=3485.4MB, alloc=444.3MB, time=35.01 memory used=3558.1MB, alloc=444.3MB, time=35.26 memory used=3690.3MB, alloc=444.3MB, time=36.46 memory used=3813.4MB, alloc=444.3MB, time=37.64 memory used=3923.1MB, alloc=468.3MB, time=38.55 memory used=4042.0MB, alloc=468.3MB, time=40.02 memory used=4126.8MB, alloc=468.3MB, time=41.50 memory used=4198.0MB, alloc=468.3MB, time=42.61 memory used=4264.7MB, alloc=468.3MB, time=43.76 memory used=4339.3MB, alloc=492.3MB, time=45.16 memory used=4405.0MB, alloc=492.3MB, time=46.29 memory used=4493.9MB, alloc=492.3MB, time=47.38 memory used=4562.8MB, alloc=492.3MB, time=48.58 memory used=4630.5MB, alloc=492.3MB, time=49.52 memory used=4687.9MB, alloc=492.3MB, time=50.47 memory used=4740.5MB, alloc=492.3MB, time=51.39 memory used=4791.6MB, alloc=492.3MB, time=52.49 memory used=4824.3MB, alloc=492.3MB, time=53.17 memory used=4869.6MB, alloc=492.3MB, time=54.13 memory used=5035.3MB, alloc=516.3MB, time=56.51 memory used=5248.7MB, alloc=540.3MB, time=59.09 memory used=5414.4MB, alloc=540.3MB, time=60.85 memory used=5612.5MB, alloc=540.3MB, time=62.86 memory used=5797.1MB, alloc=564.3MB, time=65.79 memory used=5925.9MB, alloc=564.3MB, time=66.80 memory used=6046.6MB, alloc=564.3MB, time=67.55 memory used=6152.5MB, alloc=564.3MB, time=68.23 memory used=6304.0MB, alloc=564.3MB, time=74.36 memory used=6414.9MB, alloc=588.3MB, time=75.05 memory used=6520.9MB, alloc=588.3MB, time=75.70 memory used=6654.1MB, alloc=588.3MB, time=76.38 memory used=6916.5MB, alloc=588.3MB, time=77.38 memory used=7053.0MB, alloc=588.3MB, time=78.07 memory used=7207.2MB, alloc=588.3MB, time=78.76 memory used=7378.9MB, alloc=588.3MB, time=79.48 memory used=7571.6MB, alloc=588.3MB, time=80.22 memory used=7788.4MB, alloc=588.3MB, time=80.95 memory used=7956.9MB, alloc=588.3MB, time=81.62 memory used=8135.6MB, alloc=588.3MB, time=82.31 memory used=8292.1MB, alloc=588.3MB, time=83.21 memory used=8446.5MB, alloc=588.3MB, time=84.75 memory used=8564.8MB, alloc=588.3MB, time=85.38 memory used=8703.0MB, alloc=588.3MB, time=86.14 memory used=8824.2MB, alloc=588.3MB, time=86.92 memory used=8944.3MB, alloc=588.3MB, time=87.57 memory used=9087.2MB, alloc=588.3MB, time=88.36 memory used=9257.7MB, alloc=588.3MB, time=90.64 memory used=9444.5MB, alloc=588.3MB, time=92.57 memory used=9620.0MB, alloc=588.3MB, time=94.01 memory used=9780.2MB, alloc=588.3MB, time=96.62 memory used=9986.6MB, alloc=588.3MB, time=99.26 memory used=10108.6MB, alloc=612.3MB, time=101.82 memory used=10233.5MB, alloc=612.3MB, time=104.23 memory used=10355.9MB, alloc=636.3MB, time=106.73 memory used=10465.9MB, alloc=636.3MB, time=109.17 memory used=10544.3MB, alloc=636.3MB, time=110.83 memory used=10655.0MB, alloc=636.3MB, time=112.80 memory used=10782.3MB, alloc=636.3MB, time=114.41 memory used=10872.3MB, alloc=636.3MB, time=116.15 memory used=11018.0MB, alloc=660.3MB, time=118.16 memory used=11200.9MB, alloc=660.3MB, time=121.01 memory used=11372.8MB, alloc=660.3MB, time=123.15 memory used=11708.6MB, alloc=684.3MB, time=128.56 memory used=12035.4MB, alloc=708.3MB, time=133.86 memory used=12386.4MB, alloc=732.3MB, time=139.68 memory used=12737.1MB, alloc=756.3MB, time=145.13 memory used=13070.8MB, alloc=780.3MB, time=149.81 memory used=13307.1MB, alloc=804.3MB, time=152.39 memory used=13509.2MB, alloc=828.3MB, time=153.98 memory used=13738.1MB, alloc=852.3MB, time=155.86 memory used=13959.6MB, alloc=852.3MB, time=157.49 memory used=14248.1MB, alloc=852.3MB, time=175.80 memory used=14477.3MB, alloc=852.3MB, time=177.28 memory used=14669.5MB, alloc=852.3MB, time=178.63 memory used=14944.1MB, alloc=852.3MB, time=180.63 memory used=15152.3MB, alloc=852.3MB, time=182.14 memory used=15405.2MB, alloc=852.3MB, time=184.03 memory used=15686.4MB, alloc=852.3MB, time=202.18 memory used=15924.4MB, alloc=852.3MB, time=203.68 memory used=16107.9MB, alloc=852.3MB, time=205.00 memory used=16368.8MB, alloc=852.3MB, time=206.69 |\^/| 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(); 1428296033 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 2 2 F := [-2 z - 9 x y - 4 y z + 5 x z, -19 y z - 14 x y + 4 y z + 9 y , 2 -16 x y - 5 x y z - 11 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [-2 x y - 15 x y - 12 z + 16 z, 14 x y + 8 x - 20 y - 10, 2 2 3 5 x y + 20 x z + 17 z - 5 x y] > Problem := [F,G]; 4 2 2 Problem := [[-2 z - 9 x y - 4 y z + 5 x z, 3 2 2 2 2 -19 y z - 14 x y + 4 y z + 9 y , -16 x y - 5 x y z - 11 y z], [ 2 2 2 3 2 -2 x y - 15 x y - 12 z + 16 z, 14 x y + 8 x - 20 y - 10, 2 2 3 5 x y + 20 x z + 17 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=0.19 memory used=26.5MB, alloc=32.3MB, time=0.52 memory used=46.5MB, alloc=56.3MB, time=0.84 memory used=87.4MB, alloc=60.3MB, time=1.45 memory used=128.5MB, alloc=68.3MB, time=2.09 memory used=168.9MB, alloc=92.3MB, time=2.70 memory used=231.7MB, alloc=92.3MB, time=3.69 memory used=294.4MB, alloc=92.3MB, time=4.67 memory used=359.3MB, alloc=116.3MB, time=5.62 memory used=430.5MB, alloc=372.3MB, time=6.70 memory used=515.0MB, alloc=372.3MB, time=7.79 memory used=599.5MB, alloc=372.3MB, time=8.86 memory used=681.0MB, alloc=396.3MB, time=10.22 memory used=788.6MB, alloc=420.3MB, time=11.94 memory used=927.8MB, alloc=420.3MB, time=14.01 memory used=1063.3MB, alloc=444.3MB, time=15.97 memory used=1196.4MB, alloc=468.3MB, time=18.29 memory used=1330.5MB, alloc=492.3MB, time=20.68 memory used=1448.6MB, alloc=492.3MB, time=22.66 memory used=1597.5MB, alloc=492.3MB, time=24.45 memory used=1706.7MB, alloc=492.3MB, time=26.13 memory used=1840.7MB, alloc=492.3MB, time=28.96 memory used=1938.5MB, alloc=492.3MB, time=29.62 memory used=2106.4MB, alloc=492.3MB, time=30.24 memory used=2278.8MB, alloc=492.3MB, time=31.96 memory used=2389.0MB, alloc=492.3MB, time=32.73 memory used=2486.6MB, alloc=492.3MB, time=33.17 memory used=2717.7MB, alloc=492.3MB, time=39.80 memory used=2840.2MB, alloc=492.3MB, time=41.45 memory used=2958.0MB, alloc=492.3MB, time=42.61 memory used=3065.5MB, alloc=492.3MB, time=43.71 memory used=3174.9MB, alloc=492.3MB, time=44.40 memory used=3275.2MB, alloc=492.3MB, time=44.91 memory used=3353.5MB, alloc=492.3MB, time=45.28 memory used=3599.5MB, alloc=492.3MB, time=53.21 memory used=3714.9MB, alloc=516.3MB, time=55.04 memory used=3793.8MB, alloc=516.3MB, time=56.47 memory used=3889.8MB, alloc=516.3MB, time=58.42 memory used=4020.1MB, alloc=516.3MB, time=60.12 memory used=4130.7MB, alloc=516.3MB, time=61.00 memory used=4251.9MB, alloc=516.3MB, time=62.11 memory used=4360.4MB, alloc=516.3MB, time=63.64 memory used=4448.8MB, alloc=516.3MB, time=65.02 memory used=4535.7MB, alloc=516.3MB, time=66.72 memory used=4612.4MB, alloc=516.3MB, time=68.28 memory used=4748.6MB, alloc=516.3MB, time=69.47 memory used=4863.3MB, alloc=516.3MB, time=72.63 memory used=4975.1MB, alloc=516.3MB, time=74.34 memory used=5052.8MB, alloc=516.3MB, time=75.80 memory used=5113.4MB, alloc=516.3MB, time=77.08 memory used=5188.7MB, alloc=516.3MB, time=78.88 memory used=5274.0MB, alloc=540.3MB, time=81.16 memory used=5390.4MB, alloc=540.3MB, time=81.79 memory used=5482.8MB, alloc=540.3MB, time=82.40 memory used=5590.2MB, alloc=540.3MB, time=82.98 memory used=5723.2MB, alloc=540.3MB, time=84.63 memory used=5838.6MB, alloc=540.3MB, time=85.26 memory used=5938.9MB, alloc=540.3MB, time=85.83 memory used=6065.5MB, alloc=540.3MB, time=86.84 memory used=6190.9MB, alloc=540.3MB, time=88.57 memory used=6310.8MB, alloc=540.3MB, time=89.23 memory used=6409.1MB, alloc=540.3MB, time=89.83 memory used=6513.7MB, alloc=540.3MB, time=90.44 memory used=6661.8MB, alloc=540.3MB, time=92.30 memory used=6775.9MB, alloc=540.3MB, time=92.95 memory used=6875.4MB, alloc=540.3MB, time=93.54 memory used=7001.3MB, alloc=540.3MB, time=94.54 memory used=7125.2MB, alloc=540.3MB, time=98.68 memory used=7270.0MB, alloc=564.3MB, time=100.80 memory used=7379.0MB, alloc=564.3MB, time=101.47 memory used=7479.4MB, alloc=564.3MB, time=102.11 memory used=7578.2MB, alloc=564.3MB, time=102.78 memory used=7682.3MB, alloc=564.3MB, time=103.43 memory used=7790.5MB, alloc=564.3MB, time=104.09 memory used=7904.4MB, alloc=564.3MB, time=104.77 memory used=8023.6MB, alloc=564.3MB, time=105.44 memory used=8150.0MB, alloc=564.3MB, time=106.14 memory used=8282.5MB, alloc=564.3MB, time=106.80 memory used=8422.1MB, alloc=564.3MB, time=107.49 memory used=8566.0MB, alloc=564.3MB, time=108.15 memory used=8718.7MB, alloc=564.3MB, time=108.85 memory used=8871.3MB, alloc=564.3MB, time=109.52 memory used=8966.2MB, alloc=564.3MB, time=110.12 memory used=9059.1MB, alloc=564.3MB, time=110.71 memory used=9185.6MB, alloc=564.3MB, time=126.03 memory used=9320.2MB, alloc=564.3MB, time=126.74 memory used=9452.4MB, alloc=564.3MB, time=127.41 memory used=9591.4MB, alloc=564.3MB, time=128.09 memory used=9736.5MB, alloc=564.3MB, time=128.80 memory used=9887.4MB, alloc=564.3MB, time=129.48 memory used=10043.9MB, alloc=564.3MB, time=130.18 memory used=10203.0MB, alloc=564.3MB, time=130.91 memory used=10315.0MB, alloc=564.3MB, time=131.53 memory used=10411.9MB, alloc=564.3MB, time=132.12 memory used=10501.7MB, alloc=564.3MB, time=132.70 memory used=10586.9MB, alloc=564.3MB, time=133.28 memory used=10671.1MB, alloc=564.3MB, time=133.84 memory used=10757.1MB, alloc=564.3MB, time=134.39 memory used=10843.3MB, alloc=564.3MB, time=134.96 memory used=10933.1MB, alloc=564.3MB, time=135.52 memory used=11022.9MB, alloc=564.3MB, time=136.12 memory used=11116.2MB, alloc=564.3MB, time=136.67 memory used=11209.2MB, alloc=564.3MB, time=137.24 memory used=11305.5MB, alloc=564.3MB, time=137.82 memory used=11401.4MB, alloc=564.3MB, time=138.42 memory used=11500.6MB, alloc=564.3MB, time=139.02 memory used=11602.6MB, alloc=564.3MB, time=139.60 memory used=11703.9MB, alloc=564.3MB, time=140.18 memory used=11807.7MB, alloc=564.3MB, time=140.72 memory used=11914.2MB, alloc=564.3MB, time=141.31 memory used=12023.0MB, alloc=564.3MB, time=141.89 memory used=12133.7MB, alloc=564.3MB, time=142.45 memory used=12246.0MB, alloc=564.3MB, time=143.02 memory used=12359.8MB, alloc=564.3MB, time=143.61 memory used=12477.7MB, alloc=564.3MB, time=144.19 memory used=12596.1MB, alloc=564.3MB, time=144.82 memory used=12717.5MB, alloc=564.3MB, time=145.43 memory used=12842.5MB, alloc=564.3MB, time=146.04 memory used=12969.1MB, alloc=564.3MB, time=146.63 memory used=13098.8MB, alloc=564.3MB, time=147.21 memory used=13231.8MB, alloc=564.3MB, time=147.79 memory used=13367.6MB, alloc=564.3MB, time=148.41 memory used=13506.6MB, alloc=564.3MB, time=148.97 memory used=13651.5MB, alloc=564.3MB, time=149.57 memory used=13798.8MB, alloc=564.3MB, time=150.13 memory used=14053.9MB, alloc=564.3MB, time=152.40 memory used=14226.2MB, alloc=564.3MB, time=154.00 memory used=14283.2MB, alloc=564.3MB, time=155.22 memory used=14353.5MB, alloc=564.3MB, time=156.58 memory used=14466.7MB, alloc=564.3MB, time=157.99 memory used=14599.7MB, alloc=564.3MB, time=160.01 memory used=14691.4MB, alloc=564.3MB, time=160.83 memory used=14828.3MB, alloc=564.3MB, time=161.95 memory used=14953.7MB, alloc=564.3MB, time=162.64 memory used=15083.2MB, alloc=564.3MB, time=163.25 memory used=15193.8MB, alloc=564.3MB, time=163.81 memory used=15544.0MB, alloc=564.3MB, time=175.59 memory used=15606.5MB, alloc=564.3MB, time=178.18 memory used=15685.0MB, alloc=564.3MB, time=179.50 memory used=15739.0MB, alloc=564.3MB, time=180.51 memory used=15989.6MB, alloc=564.3MB, time=184.67 memory used=16179.4MB, alloc=564.3MB, time=186.71 memory used=16311.9MB, alloc=564.3MB, time=187.44 memory used=16465.3MB, alloc=564.3MB, time=191.01 memory used=16661.6MB, alloc=564.3MB, time=191.86 memory used=16953.4MB, alloc=564.3MB, time=195.06 memory used=17125.5MB, alloc=564.3MB, time=197.34 memory used=17291.9MB, alloc=564.3MB, time=198.44 |\^/| 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(); 1428296333 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 4 3 2 2 F := [-6 x y + 13 y + 13 x z + 18 z , -y + 15 y z + 16 x z + 6 y z, 2 2 3 2 -16 x z - 13 x + 3 x y z + 2 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 3 3 G := [3 x y - 20 y z - 4 x z + 10 x y , x y z - 8 x y z + 9 y z + 14 y z , 2 4 -13 x y z + 19 y + 8 x y z] > Problem := [F,G]; 2 3 2 4 3 2 2 Problem := [[-6 x y + 13 y + 13 x z + 18 z , -y + 15 y z + 16 x z + 6 y z, 2 2 3 2 -16 x z - 13 x + 3 x y z + 2 y z], [ 3 3 2 2 2 2 3 3 3 x y - 20 y z - 4 x z + 10 x y , x y z - 8 x y z + 9 y z + 14 y z , 2 4 -13 x y z + 19 y + 8 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=4.5MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=46.5MB, alloc=32.3MB, time=0.78 memory used=66.4MB, alloc=56.3MB, time=1.05 memory used=112.9MB, alloc=68.3MB, time=1.63 memory used=157.5MB, alloc=92.3MB, time=2.23 memory used=223.5MB, alloc=92.3MB, time=3.16 memory used=286.6MB, alloc=92.3MB, time=3.96 memory used=346.7MB, alloc=92.3MB, time=4.67 memory used=424.7MB, alloc=92.3MB, time=5.40 memory used=474.7MB, alloc=92.3MB, time=5.91 memory used=513.8MB, alloc=92.3MB, time=6.26 memory used=543.2MB, alloc=92.3MB, time=6.38 memory used=606.3MB, alloc=116.3MB, time=7.11 memory used=689.2MB, alloc=116.3MB, time=8.24 memory used=763.9MB, alloc=372.3MB, time=9.23 memory used=852.4MB, alloc=396.3MB, time=10.32 memory used=959.3MB, alloc=396.3MB, time=11.50 memory used=1057.9MB, alloc=396.3MB, time=12.61 memory used=1157.5MB, alloc=420.3MB, time=13.94 memory used=1286.6MB, alloc=420.3MB, time=15.67 memory used=1420.5MB, alloc=444.3MB, time=17.05 memory used=1568.1MB, alloc=468.3MB, time=18.64 memory used=1727.3MB, alloc=468.3MB, time=20.52 memory used=1833.0MB, alloc=492.3MB, time=21.80 memory used=1951.7MB, alloc=492.3MB, time=23.41 memory used=2087.7MB, alloc=492.3MB, time=25.40 memory used=2203.3MB, alloc=516.3MB, time=26.88 memory used=2366.5MB, alloc=516.3MB, time=29.49 memory used=2521.7MB, alloc=516.3MB, time=31.23 memory used=2640.5MB, alloc=516.3MB, time=33.47 memory used=2769.1MB, alloc=516.3MB, time=35.91 memory used=2880.5MB, alloc=516.3MB, time=36.50 memory used=3004.0MB, alloc=516.3MB, time=38.88 memory used=3126.4MB, alloc=516.3MB, time=41.20 memory used=3297.5MB, alloc=516.3MB, time=44.97 memory used=3475.7MB, alloc=516.3MB, time=46.24 memory used=3617.3MB, alloc=516.3MB, time=49.25 memory used=3770.5MB, alloc=540.3MB, time=50.68 memory used=3939.7MB, alloc=540.3MB, time=56.09 memory used=4074.5MB, alloc=540.3MB, time=57.22 memory used=4238.8MB, alloc=540.3MB, time=58.63 memory used=4392.7MB, alloc=564.3MB, time=61.60 memory used=4527.7MB, alloc=564.3MB, time=62.30 memory used=4767.5MB, alloc=564.3MB, time=63.12 memory used=4947.8MB, alloc=564.3MB, time=66.20 memory used=5079.1MB, alloc=564.3MB, time=66.93 memory used=5313.8MB, alloc=564.3MB, time=67.68 memory used=5476.6MB, alloc=564.3MB, time=70.18 memory used=5626.6MB, alloc=564.3MB, time=72.57 memory used=5755.9MB, alloc=564.3MB, time=73.29 memory used=6013.6MB, alloc=564.3MB, time=74.19 memory used=6157.6MB, alloc=564.3MB, time=76.62 memory used=6348.4MB, alloc=564.3MB, time=77.49 memory used=6585.0MB, alloc=564.3MB, time=78.92 memory used=6721.9MB, alloc=564.3MB, time=81.67 memory used=6836.8MB, alloc=564.3MB, time=82.79 memory used=7009.9MB, alloc=564.3MB, time=87.50 memory used=7129.7MB, alloc=564.3MB, time=88.51 memory used=7284.1MB, alloc=564.3MB, time=89.08 memory used=7575.3MB, alloc=564.3MB, time=89.93 memory used=7860.1MB, alloc=564.3MB, time=90.62 memory used=7991.4MB, alloc=564.3MB, time=91.88 memory used=8142.9MB, alloc=564.3MB, time=93.45 memory used=8243.9MB, alloc=564.3MB, time=95.53 memory used=8297.1MB, alloc=564.3MB, time=96.47 memory used=8359.9MB, alloc=564.3MB, time=97.47 memory used=8417.2MB, alloc=588.3MB, time=98.27 memory used=8484.8MB, alloc=588.3MB, time=99.38 memory used=8561.5MB, alloc=588.3MB, time=100.23 memory used=8649.5MB, alloc=588.3MB, time=102.02 memory used=8697.0MB, alloc=588.3MB, time=102.97 memory used=8966.8MB, alloc=612.3MB, time=106.72 memory used=9254.7MB, alloc=636.3MB, time=109.83 memory used=9534.5MB, alloc=660.3MB, time=113.89 memory used=9805.6MB, alloc=684.3MB, time=117.17 memory used=10058.0MB, alloc=708.3MB, time=120.66 memory used=10286.2MB, alloc=732.3MB, time=123.19 memory used=10493.1MB, alloc=732.3MB, time=126.38 memory used=10681.4MB, alloc=756.3MB, time=128.98 memory used=10915.6MB, alloc=756.3MB, time=132.68 memory used=11142.2MB, alloc=756.3MB, time=137.82 memory used=11367.8MB, alloc=756.3MB, time=141.16 memory used=11593.4MB, alloc=756.3MB, time=144.75 memory used=11810.4MB, alloc=756.3MB, time=148.05 memory used=12024.0MB, alloc=756.3MB, time=151.46 memory used=12327.6MB, alloc=756.3MB, time=156.35 memory used=12653.7MB, alloc=780.3MB, time=165.34 memory used=13011.1MB, alloc=780.3MB, time=167.91 memory used=13198.8MB, alloc=780.3MB, time=171.07 memory used=13404.3MB, alloc=804.3MB, time=174.01 memory used=13609.6MB, alloc=804.3MB, time=176.91 memory used=13771.5MB, alloc=804.3MB, time=179.93 memory used=13941.3MB, alloc=804.3MB, time=182.13 memory used=14063.6MB, alloc=804.3MB, time=184.62 memory used=14193.0MB, alloc=804.3MB, time=186.88 memory used=14330.0MB, alloc=828.3MB, time=189.05 memory used=14461.5MB, alloc=828.3MB, time=191.44 |\^/| 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(); 1428296633 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 2 F := [-5 y + 13 x z - 8 x z + 16 x, 19 x y - 19 x y + 2 z - 11 x, 2 2 3 -15 x z - 14 y - 13 x y - 18 y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 2 2 2 3 G := [-3 x z - 13 x y z - 6 y - y z, 11 x z - 4 x z + 10 x z + 5 y , 2 2 2 17 x y z - 5 x y z + 6 x z + 18 x] > Problem := [F,G]; 4 2 2 2 3 2 Problem := [[-5 y + 13 x z - 8 x z + 16 x, 19 x y - 19 x y + 2 z - 11 x, 2 2 3 3 2 4 -15 x z - 14 y - 13 x y - 18 y z], [-3 x z - 13 x y z - 6 y - y z, 3 2 2 2 3 2 2 2 11 x z - 4 x z + 10 x z + 5 y , 17 x y z - 5 x y z + 6 x 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=4.4MB, alloc=32.3MB, time=0.17 memory used=24.9MB, alloc=32.3MB, time=0.46 memory used=65.8MB, alloc=37.1MB, time=1.11 memory used=97.0MB, alloc=62.9MB, time=1.51 memory used=143.1MB, alloc=63.4MB, time=1.83 memory used=170.2MB, alloc=63.4MB, time=1.91 memory used=195.4MB, alloc=63.4MB, time=1.97 memory used=225.3MB, alloc=63.4MB, time=2.04 memory used=259.1MB, alloc=63.4MB, time=2.12 memory used=278.8MB, alloc=63.4MB, time=2.17 memory used=298.1MB, alloc=63.4MB, time=2.22 memory used=318.8MB, alloc=63.4MB, time=2.27 memory used=340.4MB, alloc=63.4MB, time=2.32 memory used=363.3MB, alloc=63.4MB, time=2.37 memory used=388.1MB, alloc=63.4MB, time=2.43 memory used=414.2MB, alloc=63.4MB, time=2.49 memory used=441.1MB, alloc=63.4MB, time=2.54 memory used=471.0MB, alloc=63.4MB, time=2.60 memory used=501.6MB, alloc=63.4MB, time=2.66 memory used=533.1MB, alloc=63.4MB, time=2.72 memory used=567.6MB, alloc=63.4MB, time=2.79 memory used=607.1MB, alloc=81.9MB, time=2.87 memory used=616.3MB, alloc=83.8MB, time=2.91 memory used=625.2MB, alloc=83.8MB, time=2.94 memory used=634.2MB, alloc=83.8MB, time=2.98 memory used=643.7MB, alloc=83.8MB, time=3.02 memory used=653.1MB, alloc=83.8MB, time=3.05 memory used=662.7MB, alloc=83.8MB, time=3.09 memory used=672.2MB, alloc=83.8MB, time=3.14 memory used=681.8MB, alloc=83.8MB, time=3.24 memory used=691.4MB, alloc=83.8MB, time=3.29 memory used=701.5MB, alloc=83.8MB, time=3.34 memory used=711.4MB, alloc=83.8MB, time=3.41 memory used=722.9MB, alloc=83.8MB, time=3.45 memory used=733.3MB, alloc=83.8MB, time=3.49 memory used=744.8MB, alloc=83.8MB, time=3.54 memory used=757.1MB, alloc=83.8MB, time=3.59 memory used=769.3MB, alloc=83.8MB, time=3.64 memory used=781.6MB, alloc=83.8MB, time=3.72 memory used=794.0MB, alloc=83.8MB, time=3.77 memory used=806.3MB, alloc=83.8MB, time=3.84 memory used=818.6MB, alloc=83.8MB, time=3.89 memory used=831.0MB, alloc=83.8MB, time=3.95 memory used=843.4MB, alloc=83.8MB, time=4.02 memory used=855.8MB, alloc=83.8MB, time=4.10 memory used=868.2MB, alloc=83.8MB, time=4.16 memory used=880.6MB, alloc=83.8MB, time=4.23 memory used=893.5MB, alloc=83.8MB, time=4.30 memory used=907.9MB, alloc=83.8MB, time=4.36 memory used=921.1MB, alloc=83.8MB, time=4.41 memory used=935.2MB, alloc=83.8MB, time=4.46 memory used=950.1MB, alloc=83.8MB, time=4.51 memory used=964.9MB, alloc=83.8MB, time=4.56 memory used=979.8MB, alloc=83.8MB, time=4.60 memory used=994.6MB, alloc=83.8MB, time=4.65 memory used=1009.3MB, alloc=83.8MB, time=4.70 memory used=1024.0MB, alloc=83.8MB, time=4.76 memory used=1039.2MB, alloc=83.8MB, time=4.81 memory used=1055.8MB, alloc=83.8MB, time=4.86 memory used=1071.3MB, alloc=83.8MB, time=4.90 memory used=1087.4MB, alloc=83.8MB, time=4.97 memory used=1104.2MB, alloc=83.8MB, time=5.02 memory used=1120.9MB, alloc=83.8MB, time=5.07 memory used=1137.6MB, alloc=83.8MB, time=5.12 memory used=1154.7MB, alloc=83.8MB, time=5.16 memory used=1172.9MB, alloc=83.8MB, time=5.21 memory used=1191.4MB, alloc=83.8MB, time=5.26 memory used=1209.8MB, alloc=83.8MB, time=5.33 memory used=1228.6MB, alloc=83.8MB, time=5.38 memory used=1248.2MB, alloc=83.8MB, time=5.45 memory used=1268.2MB, alloc=83.8MB, time=5.50 memory used=1287.8MB, alloc=83.8MB, time=5.56 memory used=1308.2MB, alloc=83.8MB, time=5.62 memory used=1327.8MB, alloc=83.8MB, time=5.68 memory used=1349.0MB, alloc=83.8MB, time=5.73 memory used=1371.3MB, alloc=83.8MB, time=5.79 memory used=1388.2MB, alloc=83.8MB, time=5.85 memory used=1403.1MB, alloc=83.8MB, time=5.90 memory used=1417.8MB, alloc=83.8MB, time=5.95 memory used=1433.2MB, alloc=83.8MB, time=6.01 memory used=1447.8MB, alloc=83.8MB, time=6.06 memory used=1463.6MB, alloc=83.8MB, time=6.10 memory used=1479.6MB, alloc=83.8MB, time=6.15 memory used=1554.2MB, alloc=83.8MB, time=7.93 memory used=1584.6MB, alloc=83.8MB, time=8.06 memory used=1614.3MB, alloc=83.8MB, time=8.15 memory used=1635.7MB, alloc=83.8MB, time=8.23 memory used=1660.2MB, alloc=83.8MB, time=8.31 memory used=1688.0MB, alloc=83.8MB, time=8.39 memory used=1718.7MB, alloc=83.8MB, time=8.48 memory used=1752.1MB, alloc=83.8MB, time=8.57 memory used=1776.1MB, alloc=83.8MB, time=8.65 memory used=1793.4MB, alloc=83.8MB, time=8.71 memory used=1812.3MB, alloc=83.8MB, time=8.78 memory used=1830.7MB, alloc=83.8MB, time=8.83 memory used=1849.5MB, alloc=83.8MB, time=8.90 memory used=1868.9MB, alloc=83.8MB, time=8.97 memory used=1888.8MB, alloc=83.8MB, time=9.03 memory used=1909.2MB, alloc=83.8MB, time=9.09 memory used=1930.1MB, alloc=83.8MB, time=9.16 memory used=1951.5MB, alloc=83.8MB, time=9.23 memory used=1973.7MB, alloc=83.8MB, time=9.29 memory used=1999.1MB, alloc=83.8MB, time=9.36 memory used=2025.3MB, alloc=83.8MB, time=9.43 memory used=2052.1MB, alloc=83.8MB, time=9.51 memory used=2079.5MB, alloc=83.8MB, time=9.57 memory used=2107.5MB, alloc=83.8MB, time=9.65 memory used=2136.1MB, alloc=83.8MB, time=9.71 memory used=2165.2MB, alloc=83.8MB, time=9.79 memory used=2194.8MB, alloc=83.8MB, time=9.87 memory used=2225.0MB, alloc=83.8MB, time=9.95 memory used=2255.7MB, alloc=83.8MB, time=10.02 memory used=2286.9MB, alloc=83.8MB, time=10.09 memory used=2318.6MB, alloc=83.8MB, time=10.17 memory used=2326.7MB, alloc=83.8MB, time=10.21 memory used=2332.2MB, alloc=83.8MB, time=10.25 memory used=2338.7MB, alloc=83.8MB, time=10.31 memory used=2342.5MB, alloc=83.8MB, time=10.35 memory used=2345.8MB, alloc=83.8MB, time=10.41 memory used=2349.1MB, alloc=83.8MB, time=10.47 memory used=2352.8MB, alloc=83.8MB, time=10.54 memory used=2356.7MB, alloc=83.8MB, time=10.58 memory 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alloc=155.8MB, time=46.11 memory used=9507.3MB, alloc=411.8MB, time=46.16 memory used=9663.7MB, alloc=411.8MB, time=46.65 memory used=9781.5MB, alloc=411.8MB, time=46.89 memory used=9900.8MB, alloc=411.8MB, time=47.16 memory used=10034.4MB, alloc=411.8MB, time=47.42 memory used=10159.1MB, alloc=411.8MB, time=47.69 memory used=10293.5MB, alloc=411.8MB, time=47.95 memory used=10432.9MB, alloc=411.8MB, time=48.24 memory used=10573.1MB, alloc=411.8MB, time=48.51 memory used=10714.0MB, alloc=411.8MB, time=48.78 memory used=10855.5MB, alloc=411.8MB, time=49.07 memory used=11000.6MB, alloc=411.8MB, time=49.35 memory used=11157.9MB, alloc=411.8MB, time=49.64 memory used=11318.7MB, alloc=411.8MB, time=49.94 memory used=11479.8MB, alloc=411.8MB, time=50.23 memory used=11641.1MB, alloc=411.8MB, time=50.53 memory used=11806.1MB, alloc=411.8MB, time=50.84 memory used=11982.1MB, alloc=411.8MB, time=51.14 memory used=12161.3MB, alloc=411.8MB, time=51.46 memory used=12340.1MB, alloc=411.8MB, time=51.79 memory used=12522.3MB, alloc=411.8MB, time=52.11 memory used=12714.2MB, alloc=411.8MB, time=52.44 memory used=12908.6MB, alloc=411.8MB, time=52.76 memory used=13102.0MB, alloc=411.8MB, time=53.09 memory used=13311.3MB, alloc=411.8MB, time=53.43 memory used=13518.6MB, alloc=411.8MB, time=53.77 memory used=13730.1MB, alloc=411.8MB, time=54.10 memory used=13947.8MB, alloc=411.8MB, time=54.45 memory used=14175.8MB, alloc=411.8MB, time=54.81 memory used=14408.8MB, alloc=411.8MB, time=55.16 memory used=14648.4MB, alloc=411.8MB, time=55.52 memory used=14892.8MB, alloc=411.8MB, time=55.89 memory used=15139.5MB, alloc=411.8MB, time=56.25 memory used=15320.5MB, alloc=411.8MB, time=56.55 memory used=15496.9MB, alloc=411.8MB, time=56.83 memory used=15676.2MB, alloc=411.8MB, time=57.11 memory used=15859.3MB, alloc=411.8MB, time=57.39 memory used=16047.8MB, alloc=411.8MB, time=57.68 memory used=16189.2MB, alloc=411.8MB, time=59.68 memory used=16253.7MB, alloc=411.8MB, time=59.91 memory used=16333.9MB, alloc=411.8MB, time=60.16 memory used=16403.9MB, alloc=411.8MB, time=60.37 memory used=16452.4MB, alloc=411.8MB, time=60.54 memory used=16502.1MB, alloc=411.8MB, time=60.72 memory used=16555.3MB, alloc=411.8MB, time=60.90 memory used=16617.9MB, alloc=411.8MB, time=61.09 memory used=16678.2MB, alloc=411.8MB, time=61.26 memory used=16747.3MB, alloc=411.8MB, time=61.46 memory used=16821.3MB, alloc=411.8MB, time=61.65 memory used=16898.5MB, alloc=411.8MB, time=61.84 memory used=16979.1MB, alloc=411.8MB, time=62.03 memory used=17062.9MB, alloc=411.8MB, time=62.24 memory used=17123.3MB, alloc=411.8MB, time=62.40 memory used=17167.9MB, alloc=411.8MB, time=62.53 memory used=17207.7MB, alloc=411.8MB, time=62.66 memory used=17242.8MB, alloc=411.8MB, time=62.77 memory used=17287.0MB, alloc=411.8MB, time=62.89 memory used=17323.6MB, alloc=411.8MB, time=63.00 memory used=17368.9MB, alloc=411.8MB, time=63.13 memory used=17407.0MB, alloc=411.8MB, time=63.25 memory used=17453.2MB, alloc=411.8MB, time=63.38 memory used=17502.1MB, alloc=411.8MB, time=63.51 memory used=17551.8MB, alloc=411.8MB, time=63.63 memory used=17602.1MB, alloc=411.8MB, time=63.76 memory used=17653.0MB, alloc=411.8MB, time=63.89 memory used=17704.6MB, alloc=411.8MB, time=64.02 memory used=17756.8MB, alloc=411.8MB, time=64.16 memory used=17809.7MB, alloc=411.8MB, time=64.28 memory used=17863.1MB, alloc=411.8MB, time=64.42 memory used=17917.2MB, alloc=411.8MB, time=64.54 memory used=17971.8MB, alloc=411.8MB, time=64.68 memory used=18027.0MB, alloc=411.8MB, time=64.81 memory used=18082.8MB, alloc=411.8MB, time=64.94 memory used=18139.1MB, alloc=411.8MB, time=65.07 memory used=18196.0MB, alloc=411.8MB, time=65.21 memory used=18253.4MB, alloc=411.8MB, time=65.34 memory used=18311.3MB, alloc=411.8MB, time=65.47 memory used=18369.8MB, alloc=411.8MB, time=65.61 memory used=18428.7MB, alloc=411.8MB, time=65.74 memory used=18488.2MB, alloc=411.8MB, time=65.88 memory used=18548.1MB, alloc=411.8MB, time=66.00 memory used=18608.5MB, alloc=411.8MB, time=66.14 memory used=18669.4MB, alloc=411.8MB, time=66.27 memory used=18730.7MB, alloc=411.8MB, time=66.40 memory used=18792.4MB, alloc=411.8MB, time=66.54 memory used=18854.7MB, alloc=411.8MB, time=66.68 memory used=18919.5MB, alloc=411.8MB, time=66.82 memory used=18983.9MB, alloc=411.8MB, time=66.96 memory used=19059.7MB, alloc=411.8MB, time=67.12 memory used=19127.3MB, alloc=411.8MB, time=67.26 memory used=19204.3MB, alloc=411.8MB, time=67.43 memory used=19285.3MB, alloc=411.8MB, time=67.59 memory used=19366.9MB, alloc=411.8MB, time=67.75 memory used=19451.2MB, alloc=411.8MB, time=67.91 memory used=19634.0MB, alloc=411.8MB, time=68.26 memory used=19755.0MB, alloc=411.8MB, time=68.51 memory used=19873.8MB, alloc=411.8MB, time=68.77 memory used=19996.2MB, alloc=411.8MB, time=69.02 memory used=20131.1MB, alloc=411.8MB, time=69.31 memory used=20269.6MB, alloc=411.8MB, time=69.58 memory used=20409.0MB, alloc=411.8MB, time=69.86 memory used=20549.2MB, alloc=411.8MB, time=70.13 memory used=20690.1MB, alloc=411.8MB, time=70.41 memory used=20831.6MB, alloc=411.8MB, time=70.69 memory used=20976.7MB, alloc=411.8MB, time=70.97 memory used=21134.0MB, alloc=411.8MB, time=71.28 memory used=21294.8MB, alloc=411.8MB, time=71.58 memory used=21455.9MB, alloc=411.8MB, time=71.87 memory used=21617.2MB, alloc=411.8MB, time=72.17 memory used=21782.2MB, alloc=411.8MB, time=72.47 memory used=21958.2MB, alloc=411.8MB, time=72.78 memory used=22137.4MB, alloc=411.8MB, time=73.10 memory used=22316.2MB, alloc=411.8MB, time=73.42 memory used=22498.4MB, alloc=411.8MB, time=73.73 memory used=22690.3MB, alloc=411.8MB, time=74.05 memory used=22884.7MB, alloc=411.8MB, time=74.37 memory used=23078.1MB, alloc=411.8MB, time=74.71 memory used=23287.4MB, alloc=411.8MB, time=75.05 memory used=23494.8MB, alloc=411.8MB, time=75.39 memory used=23706.2MB, alloc=411.8MB, time=75.73 memory used=23923.9MB, alloc=411.8MB, time=76.08 memory used=24151.9MB, alloc=411.8MB, time=76.45 memory used=24384.9MB, alloc=411.8MB, time=76.81 memory used=24624.5MB, alloc=411.8MB, time=77.17 memory used=24868.9MB, alloc=411.8MB, time=77.54 memory used=25115.6MB, alloc=411.8MB, time=77.90 memory used=25296.6MB, alloc=411.8MB, time=78.19 memory used=25473.0MB, alloc=411.8MB, time=78.47 memory used=25652.3MB, alloc=411.8MB, time=78.75 memory used=25835.4MB, alloc=411.8MB, time=79.04 memory used=26023.9MB, alloc=411.8MB, time=79.32 memory used=26147.4MB, alloc=411.8MB, time=81.37 memory used=26255.4MB, alloc=435.8MB, time=180.03 |\^/| 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(); 1428296933 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-16 x y + 11 x y z - 18 y z + 15 z, 4 3 3 2 4 2 -15 y + 16 y z - 4 y - 15 y z, -19 x + 20 x y z + 20 x y - 10] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 2 4 2 3 G := [10 x y + 7 y z - 15 z - 6 x z , 5 x - 16 x y z + 7 y z - 15 x z, 2 2 2 4 -18 x y + 13 x y z + 13 y - 2 x y z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-16 x y + 11 x y z - 18 y z + 15 z, 4 3 3 2 4 2 -15 y + 16 y z - 4 y - 15 y z, -19 x + 20 x y z + 20 x y - 10], [ 2 2 3 4 2 4 2 3 10 x y + 7 y z - 15 z - 6 x z , 5 x - 16 x y z + 7 y z - 15 x z, 2 2 2 4 -18 x y + 13 x y z + 13 y - 2 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=25.1MB, alloc=32.3MB, time=0.48 memory used=44.1MB, alloc=56.3MB, time=0.77 memory used=84.0MB, alloc=60.3MB, time=1.34 memory used=126.7MB, alloc=68.3MB, time=1.92 memory used=175.5MB, alloc=68.3MB, time=2.48 memory used=216.6MB, alloc=92.3MB, time=3.10 memory used=280.3MB, alloc=92.3MB, time=3.63 memory used=332.7MB, alloc=92.3MB, time=3.94 memory used=399.0MB, alloc=92.3MB, time=4.55 memory used=472.8MB, alloc=92.3MB, time=5.39 memory used=540.4MB, alloc=92.3MB, time=6.15 memory used=605.6MB, alloc=92.3MB, time=6.87 memory used=669.0MB, alloc=372.3MB, time=7.69 memory used=761.2MB, alloc=372.3MB, time=9.00 memory used=813.0MB, alloc=372.3MB, time=9.42 memory used=862.0MB, alloc=372.3MB, time=9.78 memory used=953.8MB, alloc=372.3MB, time=10.84 memory used=1065.4MB, alloc=372.3MB, time=12.21 memory used=1172.0MB, alloc=372.3MB, time=13.64 memory used=1251.2MB, alloc=372.3MB, time=14.50 memory used=1326.0MB, alloc=372.3MB, time=15.17 memory used=1415.6MB, alloc=396.3MB, time=16.41 memory used=1525.1MB, alloc=420.3MB, time=18.04 memory used=1624.8MB, alloc=420.3MB, time=18.81 memory used=1692.6MB, alloc=420.3MB, time=19.13 memory used=1751.6MB, alloc=420.3MB, time=19.34 memory used=1821.8MB, alloc=420.3MB, time=19.79 memory used=1901.1MB, alloc=420.3MB, time=20.27 memory used=1991.6MB, alloc=420.3MB, time=20.84 memory used=2073.2MB, alloc=420.3MB, time=22.49 memory used=2137.7MB, alloc=420.3MB, time=22.71 memory used=2193.3MB, alloc=420.3MB, time=22.90 memory used=2244.8MB, alloc=420.3MB, time=23.07 memory used=2307.3MB, alloc=420.3MB, time=23.25 memory used=2388.1MB, alloc=420.3MB, time=23.71 memory used=2447.7MB, alloc=420.3MB, time=23.90 memory used=2526.7MB, alloc=420.3MB, time=24.63 memory used=2590.6MB, alloc=420.3MB, time=24.83 memory used=2642.1MB, alloc=420.3MB, time=25.02 memory used=2775.9MB, alloc=420.3MB, time=27.01 memory used=2844.5MB, alloc=420.3MB, time=27.41 memory used=2907.2MB, alloc=420.3MB, time=27.92 memory used=3059.3MB, alloc=420.3MB, time=30.06 memory used=3144.3MB, alloc=420.3MB, time=30.69 memory used=3224.5MB, alloc=420.3MB, time=31.37 memory used=3313.9MB, alloc=420.3MB, time=32.12 memory used=3379.3MB, alloc=420.3MB, time=32.62 memory used=3444.9MB, alloc=420.3MB, time=33.05 memory used=3573.2MB, alloc=420.3MB, time=34.33 memory used=3676.9MB, alloc=420.3MB, time=35.37 memory used=3746.9MB, alloc=420.3MB, time=35.75 memory used=3799.6MB, alloc=420.3MB, time=36.00 memory used=3851.0MB, alloc=420.3MB, time=36.20 memory used=3911.7MB, alloc=420.3MB, time=36.51 memory used=3965.7MB, alloc=420.3MB, time=36.75 memory used=4018.3MB, alloc=420.3MB, time=36.96 memory used=4075.8MB, alloc=420.3MB, time=37.30 memory used=4128.9MB, alloc=420.3MB, time=37.50 memory used=4190.6MB, alloc=420.3MB, time=37.91 memory used=4254.9MB, alloc=420.3MB, time=38.22 memory used=4337.3MB, alloc=420.3MB, time=38.86 memory used=4391.7MB, alloc=420.3MB, time=39.10 memory used=4464.5MB, alloc=420.3MB, time=39.75 memory used=4518.4MB, alloc=420.3MB, time=40.01 memory used=4587.5MB, alloc=420.3MB, time=40.69 memory used=4667.7MB, alloc=444.3MB, time=45.06 memory used=4736.9MB, alloc=444.3MB, time=45.34 memory used=4807.9MB, alloc=444.3MB, time=45.59 memory used=4866.0MB, alloc=444.3MB, time=45.81 memory used=4933.9MB, alloc=444.3MB, time=46.05 memory used=5010.7MB, alloc=444.3MB, time=46.29 memory used=5099.1MB, alloc=444.3MB, time=46.56 memory used=5269.3MB, alloc=444.3MB, time=47.12 memory used=5430.8MB, alloc=444.3MB, time=47.53 memory used=5629.3MB, alloc=444.3MB, time=47.93 memory used=5723.2MB, alloc=444.3MB, time=48.56 memory used=5790.4MB, alloc=444.3MB, time=48.79 memory used=5861.0MB, alloc=444.3MB, time=49.05 memory used=6001.9MB, alloc=444.3MB, time=50.65 memory used=6074.5MB, alloc=444.3MB, time=50.94 memory used=6144.3MB, alloc=444.3MB, time=51.20 memory used=6206.7MB, alloc=444.3MB, time=51.43 memory used=6281.6MB, alloc=444.3MB, time=51.67 memory used=6375.8MB, alloc=444.3MB, time=51.94 memory used=6524.7MB, alloc=444.3MB, time=52.29 memory used=6653.8MB, alloc=444.3MB, time=53.33 memory used=6768.9MB, alloc=444.3MB, time=54.22 memory used=6880.3MB, alloc=444.3MB, time=54.55 memory used=7026.6MB, alloc=444.3MB, time=56.39 memory used=7169.7MB, alloc=444.3MB, time=57.71 memory used=7290.6MB, alloc=444.3MB, time=58.78 memory used=7412.7MB, alloc=444.3MB, time=60.21 memory used=7509.1MB, alloc=444.3MB, time=61.65 memory used=7604.1MB, alloc=444.3MB, time=62.45 memory used=7665.4MB, alloc=444.3MB, time=62.71 memory used=7743.4MB, alloc=444.3MB, time=63.26 memory used=7807.1MB, alloc=444.3MB, time=63.54 memory used=7877.8MB, alloc=444.3MB, time=63.91 memory used=7968.1MB, alloc=444.3MB, time=64.58 memory used=8052.8MB, alloc=444.3MB, time=65.96 memory used=8120.2MB, alloc=444.3MB, time=66.28 memory used=8174.5MB, alloc=444.3MB, time=66.57 memory used=8237.9MB, alloc=444.3MB, time=66.85 memory used=8366.0MB, alloc=444.3MB, time=67.38 memory used=8457.0MB, alloc=444.3MB, time=70.21 memory used=8531.8MB, alloc=444.3MB, time=71.31 memory used=8605.6MB, alloc=444.3MB, time=71.61 memory used=8655.9MB, alloc=444.3MB, time=71.87 memory used=8713.7MB, alloc=444.3MB, time=72.14 memory used=8781.8MB, alloc=444.3MB, time=72.40 memory used=8864.8MB, alloc=444.3MB, time=72.68 memory used=9020.4MB, alloc=444.3MB, time=73.09 memory used=9115.2MB, alloc=444.3MB, time=73.66 memory used=9173.5MB, alloc=444.3MB, time=73.93 memory used=9260.4MB, alloc=444.3MB, time=75.16 memory used=9327.0MB, alloc=444.3MB, time=75.47 memory used=9387.4MB, alloc=444.3MB, time=75.75 memory used=9447.2MB, alloc=444.3MB, time=76.01 memory used=9522.6MB, alloc=444.3MB, time=76.30 memory used=9682.4MB, alloc=444.3MB, time=78.02 memory used=9797.6MB, alloc=468.3MB, time=79.45 memory used=9891.6MB, alloc=468.3MB, time=80.21 memory used=9966.8MB, alloc=468.3MB, time=80.49 memory used=10047.2MB, alloc=468.3MB, time=80.76 memory used=10143.4MB, alloc=468.3MB, time=83.09 memory used=10229.1MB, alloc=468.3MB, time=83.42 memory used=10291.6MB, alloc=468.3MB, time=83.72 memory used=10368.5MB, alloc=468.3MB, time=84.02 memory used=10465.8MB, alloc=468.3MB, time=84.31 memory used=10645.0MB, alloc=468.3MB, time=85.51 memory used=10734.4MB, alloc=468.3MB, time=85.94 memory used=10823.1MB, alloc=468.3MB, time=87.03 memory used=10898.5MB, alloc=468.3MB, time=87.35 memory used=11037.4MB, alloc=468.3MB, time=88.59 memory used=11151.9MB, alloc=468.3MB, time=89.71 memory used=11257.2MB, alloc=468.3MB, time=94.34 memory used=11330.1MB, alloc=468.3MB, time=94.69 memory used=11400.6MB, alloc=468.3MB, time=95.01 memory used=11486.6MB, alloc=468.3MB, time=95.34 memory used=11564.4MB, alloc=492.3MB, time=95.67 memory used=11631.7MB, alloc=492.3MB, time=95.96 memory used=11707.1MB, alloc=492.3MB, time=96.25 memory used=11789.1MB, alloc=492.3MB, time=96.55 memory used=11877.5MB, alloc=492.3MB, time=96.87 memory used=11972.5MB, alloc=492.3MB, time=97.17 memory used=12075.9MB, alloc=492.3MB, time=97.51 memory used=12188.4MB, alloc=492.3MB, time=97.82 memory used=12438.5MB, alloc=492.3MB, time=98.32 memory used=12574.9MB, alloc=492.3MB, time=98.70 memory used=12722.6MB, alloc=492.3MB, time=99.09 memory used=12883.8MB, alloc=492.3MB, time=99.48 memory used=13058.1MB, alloc=492.3MB, time=99.87 memory used=13246.6MB, alloc=492.3MB, time=100.27 memory used=13455.9MB, alloc=492.3MB, time=100.69 memory used=13733.0MB, alloc=492.3MB, time=102.05 memory used=13867.8MB, alloc=492.3MB, time=102.89 memory used=14007.1MB, alloc=492.3MB, time=103.33 memory used=14250.3MB, alloc=492.3MB, time=105.04 memory used=14460.8MB, alloc=492.3MB, time=105.48 memory used=14758.9MB, alloc=492.3MB, time=106.09 memory used=14995.2MB, alloc=492.3MB, time=111.16 memory used=15086.6MB, alloc=492.3MB, time=111.53 memory used=15184.9MB, alloc=492.3MB, time=111.88 memory used=15281.1MB, alloc=492.3MB, time=112.40 memory used=15369.2MB, alloc=492.3MB, time=112.73 memory used=15472.0MB, alloc=492.3MB, time=114.01 memory used=15557.8MB, alloc=492.3MB, time=115.57 memory used=15665.8MB, alloc=492.3MB, time=117.73 memory used=15762.5MB, alloc=492.3MB, time=118.83 memory used=15871.9MB, alloc=492.3MB, time=119.76 memory used=15989.4MB, alloc=492.3MB, time=120.98 memory used=16087.1MB, alloc=492.3MB, time=121.63 memory used=16171.4MB, alloc=492.3MB, time=122.71 memory used=16273.8MB, alloc=492.3MB, time=123.74 memory used=16345.8MB, alloc=492.3MB, time=124.95 memory used=16428.6MB, alloc=492.3MB, time=125.95 memory used=16482.1MB, alloc=492.3MB, time=126.95 memory used=16555.2MB, alloc=492.3MB, time=128.16 memory used=16617.3MB, alloc=492.3MB, time=129.23 memory used=16684.8MB, alloc=492.3MB, time=130.27 memory used=16747.1MB, alloc=492.3MB, time=131.42 memory used=16808.3MB, alloc=492.3MB, time=132.41 memory used=16867.1MB, alloc=492.3MB, time=133.29 memory used=16915.1MB, alloc=492.3MB, time=134.18 memory used=16973.6MB, alloc=516.3MB, time=134.89 memory used=17029.9MB, alloc=516.3MB, time=135.96 memory used=17071.2MB, alloc=516.3MB, time=136.67 memory used=17274.5MB, alloc=540.3MB, time=139.44 memory used=17443.0MB, alloc=564.3MB, time=142.19 memory used=17620.9MB, alloc=564.3MB, time=143.76 memory used=17783.2MB, alloc=564.3MB, time=144.98 memory used=17986.0MB, alloc=588.3MB, time=147.64 memory used=18156.4MB, alloc=588.3MB, time=149.69 memory used=18345.2MB, alloc=612.3MB, time=152.04 memory used=18564.0MB, alloc=636.3MB, time=154.25 memory used=18711.4MB, alloc=636.3MB, time=156.77 memory used=18870.8MB, alloc=660.3MB, time=159.33 memory used=19026.9MB, alloc=660.3MB, time=161.73 memory used=19222.5MB, alloc=660.3MB, time=163.92 memory used=19327.6MB, alloc=660.3MB, time=165.86 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428297233 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 F := [-6 x z + 10 x y z - 14 x z + 3 y z , 19 y z - 5 x y + 12 y z + 19 z , 3 3 2 2 12 x z + 2 x y + 18 x y z + 12 x y ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 G := [-2 x y - 3 y - 7 x - 13 z, -6 x y + 11 x y - 9 x y z + 3 y , 3 3 3 6 y z + 15 x y z + 16 y - 8 z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-6 x z + 10 x y z - 14 x z + 3 y z , 3 2 3 3 2 2 19 y z - 5 x y + 12 y z + 19 z , 12 x z + 2 x y + 18 x y z + 12 x y ], 3 2 3 2 3 [-2 x y - 3 y - 7 x - 13 z, -6 x y + 11 x y - 9 x y z + 3 y , 3 3 3 6 y z + 15 x y z + 16 y - 8 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.8MB, alloc=32.3MB, time=0.49 memory used=44.5MB, alloc=56.3MB, time=0.79 memory used=84.6MB, alloc=60.3MB, time=1.37 memory used=125.7MB, alloc=60.3MB, time=1.96 memory used=160.7MB, alloc=60.3MB, time=2.46 memory used=202.5MB, alloc=92.3MB, time=3.06 memory used=269.8MB, alloc=92.3MB, time=3.93 memory used=333.5MB, alloc=116.3MB, time=4.89 memory used=403.9MB, alloc=372.3MB, time=5.98 memory used=495.0MB, alloc=396.3MB, time=7.23 memory used=608.0MB, alloc=420.3MB, time=8.81 memory used=731.9MB, alloc=420.3MB, time=10.59 memory used=841.3MB, alloc=444.3MB, time=12.21 memory used=953.5MB, alloc=444.3MB, time=13.91 memory used=1055.1MB, alloc=444.3MB, time=15.11 memory used=1151.9MB, alloc=468.3MB, time=16.32 memory used=1248.8MB, alloc=468.3MB, time=17.85 memory used=1330.4MB, alloc=468.3MB, time=19.02 memory used=1419.3MB, alloc=468.3MB, time=20.46 memory used=1498.4MB, alloc=468.3MB, time=21.78 memory used=1569.8MB, alloc=468.3MB, time=23.08 memory used=1637.4MB, alloc=468.3MB, time=24.31 memory used=1708.7MB, alloc=468.3MB, time=25.61 memory used=1766.7MB, alloc=468.3MB, time=26.66 memory used=1830.5MB, alloc=492.3MB, time=27.90 memory used=1887.9MB, alloc=492.3MB, time=29.12 memory used=1932.5MB, alloc=492.3MB, time=29.97 memory used=1972.6MB, alloc=492.3MB, time=30.83 memory used=2020.5MB, alloc=492.3MB, time=31.94 memory used=2063.3MB, alloc=492.3MB, time=33.01 memory used=2246.9MB, alloc=516.3MB, time=35.98 memory used=2428.7MB, alloc=540.3MB, time=38.71 memory used=2613.9MB, alloc=564.3MB, time=42.05 memory used=2788.8MB, alloc=588.3MB, time=44.69 memory used=2938.0MB, alloc=588.3MB, time=47.05 memory used=3099.3MB, alloc=588.3MB, time=50.05 memory used=3233.4MB, alloc=612.3MB, time=52.00 memory used=3389.2MB, alloc=612.3MB, time=54.71 memory used=3535.6MB, alloc=636.3MB, time=57.61 memory used=3663.7MB, alloc=636.3MB, time=60.34 memory used=3785.2MB, alloc=636.3MB, time=62.58 memory used=3918.0MB, alloc=636.3MB, time=64.60 memory used=4025.3MB, alloc=636.3MB, time=66.69 memory used=4133.8MB, alloc=660.3MB, time=69.12 memory used=4249.0MB, alloc=660.3MB, time=72.13 memory used=4572.3MB, alloc=684.3MB, time=78.02 memory used=4921.8MB, alloc=708.3MB, time=83.23 memory used=5250.9MB, alloc=732.3MB, time=88.96 memory used=5577.7MB, alloc=756.3MB, time=94.45 memory used=5834.1MB, alloc=780.3MB, time=99.06 memory used=6069.0MB, alloc=804.3MB, time=103.98 memory used=6368.9MB, alloc=828.3MB, time=109.75 memory used=6594.0MB, alloc=852.3MB, time=114.06 memory used=6846.7MB, alloc=876.3MB, time=118.84 memory used=7068.8MB, alloc=900.3MB, time=123.98 memory used=7312.1MB, alloc=924.3MB, time=128.39 memory used=7534.8MB, alloc=948.3MB, time=132.75 memory used=7737.1MB, alloc=972.3MB, time=136.70 memory used=8301.4MB, alloc=996.3MB, time=146.23 memory used=8908.1MB, alloc=1020.3MB, time=157.64 |\^/| 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(); 1428297533 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 2 3 2 F := [-3 x y - 8 z + 12 x y + 14 x z, 16 x z + 12 y z + 15 x - 11 x z , 4 3 3 3 -2 x + 17 x z - 9 x y + 14 y z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 2 G := [10 x z - 6 x z + 12 x y z + x , 11 x y - 20 x y - 18 y - 15 z, 3 3 2 2 -12 y z + 6 x + 20 x y - 5 x ] > Problem := [F,G]; 2 2 3 Problem := [[-3 x y - 8 z + 12 x y + 14 x z, 3 2 2 3 2 4 3 3 3 16 x z + 12 y z + 15 x - 11 x z , -2 x + 17 x z - 9 x y + 14 y z ], 3 2 2 2 2 3 2 [10 x z - 6 x z + 12 x y z + x , 11 x y - 20 x y - 18 y - 15 z, 3 3 2 2 -12 y z + 6 x + 20 x y - 5 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=25.1MB, alloc=32.3MB, time=0.43 memory used=43.3MB, alloc=56.3MB, time=0.69 memory used=78.4MB, alloc=60.3MB, time=1.04 memory used=125.5MB, alloc=68.3MB, time=1.54 memory used=167.6MB, alloc=68.3MB, time=1.79 memory used=207.4MB, alloc=68.3MB, time=2.08 memory used=245.9MB, alloc=68.3MB, time=2.31 memory used=295.3MB, alloc=68.3MB, time=2.82 memory used=333.6MB, alloc=68.3MB, time=3.07 memory used=382.4MB, alloc=68.3MB, time=3.61 memory used=415.2MB, alloc=68.3MB, time=3.86 memory used=450.5MB, alloc=68.3MB, time=4.09 memory used=475.1MB, alloc=68.3MB, time=4.17 memory used=502.4MB, alloc=68.3MB, time=4.29 memory used=525.3MB, alloc=68.3MB, time=4.37 memory used=552.3MB, alloc=68.3MB, time=4.51 memory used=574.2MB, alloc=68.3MB, time=4.58 memory used=602.1MB, alloc=68.3MB, time=4.77 memory used=627.7MB, alloc=68.3MB, time=4.89 memory used=663.6MB, alloc=68.3MB, time=5.14 memory used=692.8MB, alloc=68.3MB, time=5.32 memory used=718.1MB, alloc=68.3MB, time=5.42 memory used=778.2MB, alloc=68.3MB, time=7.53 memory used=821.6MB, alloc=68.3MB, time=11.22 memory used=845.4MB, alloc=92.3MB, time=11.32 memory used=880.6MB, alloc=92.3MB, time=11.45 memory used=925.8MB, alloc=92.3MB, time=11.58 memory used=960.4MB, alloc=92.3MB, time=11.70 memory used=990.0MB, alloc=92.3MB, time=11.81 memory used=1021.6MB, alloc=92.3MB, time=11.91 memory used=1055.3MB, alloc=92.3MB, time=12.01 memory used=1092.7MB, alloc=92.3MB, time=12.12 memory used=1132.1MB, alloc=92.3MB, time=12.23 memory used=1173.5MB, alloc=92.3MB, time=12.35 memory used=1218.8MB, alloc=92.3MB, time=12.46 memory used=1266.0MB, alloc=92.3MB, time=12.58 memory used=1300.3MB, alloc=92.3MB, time=12.67 memory used=1326.3MB, alloc=92.3MB, time=12.75 memory used=1350.5MB, alloc=92.3MB, time=12.83 memory used=1375.9MB, alloc=92.3MB, time=12.90 memory used=1401.7MB, alloc=92.3MB, time=12.98 memory used=1427.9MB, alloc=92.3MB, time=13.07 memory used=1456.8MB, alloc=92.3MB, time=13.15 memory used=1486.1MB, alloc=92.3MB, time=13.23 memory used=1515.8MB, alloc=92.3MB, time=13.31 memory used=1545.8MB, alloc=92.3MB, time=13.39 memory used=1576.2MB, alloc=92.3MB, time=13.47 memory used=1607.0MB, alloc=92.3MB, time=13.56 memory used=1640.6MB, alloc=92.3MB, time=13.64 memory used=1674.5MB, alloc=92.3MB, time=13.73 memory used=1708.8MB, alloc=92.3MB, time=13.82 memory used=1743.4MB, alloc=92.3MB, time=13.90 memory used=1778.3MB, alloc=92.3MB, time=13.98 memory used=1816.1MB, alloc=92.3MB, time=14.08 memory used=1854.2MB, alloc=92.3MB, time=14.16 memory used=1892.4MB, alloc=92.3MB, time=14.25 memory used=1931.0MB, alloc=92.3MB, time=14.34 memory used=1972.5MB, alloc=92.3MB, time=14.44 memory used=2014.1MB, alloc=92.3MB, time=14.53 memory used=2055.9MB, alloc=92.3MB, time=14.62 memory used=2100.6MB, alloc=92.3MB, time=14.71 memory used=2145.3MB, alloc=92.3MB, time=14.81 memory used=2190.1MB, alloc=92.3MB, time=14.90 memory used=2237.7MB, alloc=92.3MB, time=14.99 memory used=2294.8MB, alloc=105.4MB, time=15.10 memory used=2306.6MB, alloc=107.8MB, time=15.16 memory used=2315.2MB, alloc=107.8MB, time=15.22 memory used=2324.3MB, alloc=107.8MB, time=15.27 memory used=2331.9MB, alloc=107.8MB, time=15.36 memory used=2339.9MB, alloc=107.8MB, time=15.41 memory used=2348.1MB, alloc=107.8MB, time=15.48 memory used=2356.2MB, alloc=107.8MB, time=15.54 memory used=2364.4MB, alloc=107.8MB, time=15.60 memory used=2372.5MB, alloc=107.8MB, time=15.67 memory used=2380.7MB, alloc=107.8MB, time=15.74 memory used=2388.8MB, alloc=107.8MB, time=15.79 memory used=2396.9MB, alloc=107.8MB, time=15.85 memory used=2405.0MB, alloc=107.8MB, time=15.90 memory used=2413.1MB, alloc=107.8MB, time=15.96 memory used=2421.2MB, alloc=107.8MB, time=16.01 memory used=2429.3MB, alloc=107.8MB, time=16.07 memory used=2437.4MB, alloc=107.8MB, time=16.12 memory used=2445.5MB, alloc=107.8MB, time=16.17 memory used=2453.5MB, alloc=107.8MB, time=16.22 memory used=2461.6MB, alloc=107.8MB, time=16.27 memory used=2469.6MB, alloc=107.8MB, time=16.33 memory used=2477.6MB, alloc=107.8MB, time=16.40 memory used=2485.6MB, alloc=107.8MB, time=16.47 memory used=2493.7MB, alloc=107.8MB, time=16.52 memory used=2501.6MB, alloc=107.8MB, time=16.57 memory used=2509.6MB, alloc=107.8MB, time=16.63 memory used=2517.6MB, alloc=107.8MB, time=16.68 memory used=2525.6MB, alloc=107.8MB, time=16.74 memory used=2533.5MB, alloc=107.8MB, time=16.81 memory used=2541.4MB, alloc=107.8MB, time=16.87 memory used=2549.4MB, alloc=107.8MB, time=16.94 memory used=2557.3MB, alloc=107.8MB, time=17.01 memory used=2565.2MB, alloc=107.8MB, time=17.07 memory used=2573.3MB, alloc=107.8MB, time=17.13 memory used=2581.3MB, alloc=107.8MB, time=17.20 memory used=2591.4MB, alloc=107.8MB, time=17.26 memory used=2599.5MB, alloc=107.8MB, time=17.31 memory used=2609.6MB, alloc=107.8MB, time=17.38 memory used=2620.0MB, alloc=107.8MB, time=17.45 memory used=2630.4MB, alloc=107.8MB, time=17.50 memory used=2640.7MB, alloc=107.8MB, time=17.56 memory used=2651.0MB, alloc=107.8MB, time=17.62 memory used=2661.3MB, alloc=107.8MB, time=17.69 memory used=2671.5MB, alloc=107.8MB, time=17.75 memory used=2681.7MB, alloc=107.8MB, time=17.81 memory used=2691.9MB, alloc=107.8MB, time=17.87 memory used=2702.1MB, alloc=107.8MB, time=17.95 memory used=2712.2MB, alloc=107.8MB, time=18.00 memory used=2722.2MB, alloc=107.8MB, time=18.05 memory used=2732.3MB, alloc=107.8MB, time=18.11 memory used=2742.3MB, alloc=107.8MB, time=18.18 memory used=2752.3MB, alloc=107.8MB, time=18.23 memory used=2762.2MB, alloc=107.8MB, time=18.29 memory used=2772.1MB, alloc=107.8MB, time=18.35 memory used=2782.0MB, alloc=107.8MB, time=18.42 memory used=2791.8MB, alloc=107.8MB, time=18.48 memory used=2801.6MB, alloc=107.8MB, time=18.55 memory used=2811.3MB, alloc=107.8MB, time=18.61 memory used=2821.3MB, alloc=107.8MB, time=18.66 memory used=2831.1MB, alloc=107.8MB, time=18.71 memory used=2842.7MB, alloc=107.8MB, time=18.78 memory used=2852.7MB, alloc=107.8MB, time=18.84 memory used=2864.1MB, alloc=107.8MB, time=18.91 memory used=2876.0MB, alloc=107.8MB, time=18.96 memory used=2887.7MB, alloc=107.8MB, time=19.07 memory used=2899.4MB, alloc=107.8MB, time=19.16 memory used=2911.0MB, alloc=107.8MB, time=19.24 memory used=2922.6MB, alloc=107.8MB, time=19.31 memory used=2934.0MB, alloc=107.8MB, time=19.37 memory used=2945.4MB, alloc=107.8MB, time=19.46 memory used=2956.8MB, alloc=107.8MB, time=19.52 memory used=2968.0MB, alloc=107.8MB, time=19.58 memory used=2979.1MB, alloc=107.8MB, time=19.63 memory used=2990.5MB, alloc=107.8MB, time=19.70 memory used=3003.4MB, alloc=107.8MB, time=19.77 memory used=3016.5MB, alloc=107.8MB, time=19.82 memory used=3029.4MB, alloc=107.8MB, time=19.92 memory used=3042.2MB, alloc=107.8MB, time=19.98 memory used=3054.9MB, alloc=107.8MB, time=20.04 memory used=3067.5MB, alloc=107.8MB, time=20.09 memory used=3079.9MB, alloc=107.8MB, time=20.16 memory used=3092.2MB, alloc=107.8MB, time=20.22 memory used=3104.7MB, alloc=107.8MB, time=20.30 memory used=3118.4MB, alloc=107.8MB, time=20.36 memory used=3132.2MB, alloc=107.8MB, time=20.42 memory used=3145.9MB, alloc=107.8MB, time=20.49 memory used=3159.4MB, alloc=107.8MB, time=20.55 memory used=3172.9MB, alloc=107.8MB, time=20.61 memory used=3187.5MB, alloc=107.8MB, time=20.68 memory used=3202.2MB, alloc=107.8MB, time=20.76 memory used=3216.5MB, alloc=107.8MB, time=20.83 memory used=3230.6MB, alloc=107.8MB, time=20.89 memory used=3244.8MB, alloc=107.8MB, time=20.96 memory used=3259.5MB, alloc=107.8MB, time=21.02 memory used=3274.3MB, alloc=107.8MB, time=21.09 memory used=3290.2MB, alloc=107.8MB, time=21.17 memory used=3305.7MB, alloc=107.8MB, time=21.23 memory used=3321.3MB, alloc=107.8MB, time=21.29 memory used=3337.1MB, alloc=107.8MB, time=21.36 memory used=3353.3MB, alloc=107.8MB, time=21.42 memory used=3369.8MB, alloc=107.8MB, time=21.48 memory used=3386.9MB, alloc=107.8MB, time=21.53 memory used=3404.5MB, alloc=107.8MB, time=21.60 memory used=3422.4MB, alloc=107.8MB, time=21.67 memory used=3440.8MB, alloc=107.8MB, time=21.73 memory used=3530.8MB, alloc=107.8MB, time=27.01 memory used=3569.1MB, alloc=107.8MB, time=27.13 memory used=3609.7MB, alloc=107.8MB, time=27.26 memory used=3652.1MB, alloc=107.8MB, time=27.38 memory used=3679.9MB, alloc=107.8MB, time=27.48 memory used=3709.6MB, alloc=107.8MB, time=27.59 memory used=3742.2MB, alloc=107.8MB, time=27.68 memory used=3776.7MB, alloc=107.8MB, time=27.79 memory used=3813.2MB, alloc=107.8MB, time=27.89 memory used=3853.3MB, alloc=107.8MB, time=28.00 memory used=3895.4MB, alloc=107.8MB, time=28.12 memory used=3941.4MB, alloc=107.8MB, time=28.24 memory used=3987.0MB, alloc=107.8MB, time=28.35 memory used=4014.9MB, alloc=107.8MB, time=28.43 memory used=4038.7MB, alloc=107.8MB, time=28.51 memory used=4063.5MB, alloc=107.8MB, time=28.59 memory used=4089.0MB, alloc=107.8MB, time=28.67 memory used=4114.9MB, alloc=107.8MB, time=28.75 memory used=4141.1MB, alloc=107.8MB, time=28.86 memory used=4167.8MB, alloc=107.8MB, time=28.96 memory used=4197.2MB, alloc=107.8MB, time=29.04 memory used=4227.0MB, alloc=107.8MB, time=29.15 memory used=4257.1MB, alloc=107.8MB, time=29.24 memory used=4287.6MB, alloc=107.8MB, time=29.32 memory used=4318.3MB, alloc=107.8MB, time=29.41 memory used=4349.5MB, alloc=107.8MB, time=29.51 memory used=4383.5MB, alloc=107.8MB, time=29.59 memory used=4417.8MB, alloc=107.8MB, time=29.67 memory used=4452.5MB, alloc=107.8MB, time=29.75 memory used=4487.4MB, alloc=107.8MB, time=29.84 memory used=4522.6MB, alloc=107.8MB, time=29.92 memory used=4560.7MB, alloc=107.8MB, time=30.01 memory used=4599.0MB, alloc=107.8MB, time=30.09 memory used=4637.5MB, alloc=107.8MB, time=30.18 memory used=4676.3MB, alloc=107.8MB, time=30.27 memory used=4718.0MB, alloc=107.8MB, time=30.36 memory used=4759.8MB, alloc=107.8MB, time=30.45 memory used=4801.7MB, alloc=107.8MB, time=30.54 memory used=4846.5MB, alloc=107.8MB, time=30.63 memory used=4891.4MB, alloc=107.8MB, time=30.72 memory used=4936.4MB, alloc=107.8MB, time=30.81 memory used=4985.1MB, alloc=107.8MB, time=30.90 memory used=5005.0MB, alloc=107.8MB, time=30.97 memory used=5015.8MB, alloc=107.8MB, time=31.03 memory used=5024.6MB, alloc=107.8MB, time=31.08 memory used=5032.0MB, alloc=107.8MB, time=31.13 memory used=5039.6MB, alloc=107.8MB, time=31.19 memory used=5047.7MB, alloc=107.8MB, time=31.24 memory used=5055.8MB, alloc=107.8MB, time=31.30 memory used=5064.0MB, alloc=107.8MB, time=31.35 memory used=5072.2MB, alloc=107.8MB, time=31.41 memory used=5080.3MB, alloc=107.8MB, time=31.47 memory used=5088.5MB, alloc=107.8MB, time=31.53 memory used=5096.6MB, alloc=107.8MB, time=31.58 memory used=5104.8MB, alloc=107.8MB, time=31.65 memory used=5112.9MB, alloc=107.8MB, time=31.71 memory used=5121.0MB, alloc=107.8MB, time=31.78 memory used=5129.1MB, alloc=107.8MB, time=31.84 memory used=5137.2MB, alloc=107.8MB, time=31.89 memory used=5145.3MB, alloc=107.8MB, time=31.94 memory used=5153.4MB, alloc=107.8MB, time=32.01 memory used=5161.5MB, alloc=107.8MB, time=32.06 memory used=5169.5MB, alloc=107.8MB, time=32.11 memory used=5177.6MB, alloc=107.8MB, time=32.16 memory used=5185.6MB, alloc=107.8MB, time=32.21 memory used=5193.7MB, alloc=107.8MB, time=32.26 memory used=5201.7MB, alloc=107.8MB, time=32.31 memory used=5209.7MB, alloc=107.8MB, time=32.36 memory used=5217.7MB, alloc=107.8MB, time=32.42 memory used=5225.7MB, alloc=107.8MB, time=32.47 memory used=5233.6MB, alloc=107.8MB, time=32.53 memory used=5241.6MB, alloc=107.8MB, time=32.60 memory used=5249.6MB, alloc=107.8MB, time=32.65 memory used=5257.5MB, alloc=107.8MB, time=32.70 memory used=5265.4MB, alloc=107.8MB, time=32.75 memory used=5273.3MB, alloc=107.8MB, time=32.83 memory used=5281.2MB, alloc=107.8MB, time=32.90 memory used=5289.4MB, alloc=107.8MB, time=32.97 memory used=5297.4MB, alloc=107.8MB, time=33.04 memory used=5307.4MB, alloc=107.8MB, time=33.10 memory used=5315.6MB, alloc=107.8MB, time=33.17 memory used=5325.7MB, alloc=107.8MB, time=33.23 memory used=5336.1MB, alloc=107.8MB, time=33.31 memory used=5346.5MB, alloc=107.8MB, time=33.37 memory used=5356.8MB, alloc=107.8MB, time=33.43 memory used=5367.1MB, alloc=107.8MB, time=33.54 memory used=5377.3MB, alloc=107.8MB, time=33.62 memory used=5387.6MB, alloc=107.8MB, time=33.72 memory used=5397.8MB, alloc=107.8MB, time=33.79 memory used=5408.0MB, alloc=107.8MB, time=33.84 memory used=5418.1MB, alloc=107.8MB, time=33.91 memory used=5428.2MB, alloc=107.8MB, time=33.99 memory used=5438.3MB, alloc=107.8MB, time=34.04 memory used=5448.3MB, alloc=107.8MB, time=34.10 memory used=5458.3MB, alloc=107.8MB, time=34.16 memory used=5468.3MB, alloc=107.8MB, time=34.23 memory used=5478.2MB, alloc=107.8MB, time=34.30 memory used=5488.1MB, alloc=107.8MB, time=34.35 memory used=5497.9MB, alloc=107.8MB, time=34.41 memory used=5507.8MB, alloc=107.8MB, time=34.49 memory used=5517.5MB, alloc=107.8MB, time=34.59 memory used=5527.3MB, alloc=107.8MB, time=34.65 memory used=5537.2MB, alloc=107.8MB, time=34.70 memory used=5549.0MB, alloc=107.8MB, time=34.76 memory used=5559.1MB, alloc=107.8MB, time=34.82 memory used=5570.6MB, alloc=107.8MB, time=34.88 memory used=5582.4MB, alloc=107.8MB, time=34.95 memory used=5594.2MB, alloc=107.8MB, time=35.01 memory used=5606.0MB, alloc=107.8MB, time=35.07 memory used=5617.6MB, alloc=107.8MB, time=35.13 memory used=5629.2MB, alloc=107.8MB, time=35.19 memory used=5640.7MB, alloc=107.8MB, time=35.24 memory used=5652.2MB, alloc=107.8MB, time=35.31 memory used=5663.5MB, alloc=107.8MB, time=35.36 memory used=5674.8MB, alloc=107.8MB, time=35.45 memory used=5686.0MB, alloc=107.8MB, time=35.51 memory used=5697.1MB, alloc=107.8MB, time=35.59 memory used=5708.5MB, alloc=107.8MB, time=35.65 memory used=5721.3MB, alloc=107.8MB, time=35.70 memory used=5734.3MB, alloc=107.8MB, time=35.76 memory used=5747.2MB, alloc=107.8MB, time=35.82 memory used=5760.0MB, alloc=107.8MB, time=35.89 memory used=5772.6MB, alloc=107.8MB, time=35.95 memory used=5785.1MB, alloc=107.8MB, time=36.02 memory used=5797.5MB, alloc=107.8MB, time=36.07 memory used=5809.7MB, alloc=107.8MB, time=36.14 memory used=5822.2MB, alloc=107.8MB, time=36.20 memory used=5835.8MB, alloc=107.8MB, time=36.27 memory used=5849.6MB, alloc=107.8MB, time=36.35 memory used=5863.2MB, alloc=107.8MB, time=36.42 memory used=5876.6MB, alloc=107.8MB, time=36.49 memory used=5890.1MB, alloc=107.8MB, time=36.56 memory used=5904.6MB, alloc=107.8MB, time=36.64 memory used=5917.8MB, alloc=107.8MB, time=36.71 memory used=5931.9MB, alloc=107.8MB, time=36.80 memory used=5944.9MB, alloc=107.8MB, time=36.88 memory used=5959.3MB, alloc=107.8MB, time=36.94 memory used=5974.4MB, alloc=107.8MB, time=37.00 memory used=5989.1MB, alloc=107.8MB, time=37.07 memory used=6003.9MB, alloc=107.8MB, time=37.14 memory used=6019.3MB, alloc=107.8MB, time=37.20 memory used=6035.3MB, alloc=107.8MB, time=37.27 memory used=6051.2MB, alloc=107.8MB, time=37.32 memory used=6067.7MB, alloc=107.8MB, time=37.38 memory used=6084.8MB, alloc=107.8MB, time=37.46 memory used=6102.2MB, alloc=107.8MB, time=37.54 memory used=6119.6MB, alloc=107.8MB, time=37.60 memory used=6137.4MB, alloc=107.8MB, time=37.67 memory used=6155.3MB, alloc=107.8MB, time=37.74 memory used=6253.3MB, alloc=107.8MB, time=38.58 memory used=6334.9MB, alloc=107.8MB, time=39.05 memory used=6409.9MB, alloc=107.8MB, time=39.76 memory used=6463.8MB, alloc=107.8MB, time=40.27 memory used=6535.3MB, alloc=107.8MB, time=44.33 memory used=6595.1MB, alloc=107.8MB, time=45.99 memory used=6627.6MB, alloc=107.8MB, time=46.12 memory used=6667.5MB, alloc=107.8MB, time=46.25 memory used=6706.5MB, alloc=107.8MB, time=46.36 memory used=6733.1MB, alloc=107.8MB, time=46.46 memory used=6761.3MB, alloc=107.8MB, time=46.57 memory used=6792.0MB, alloc=107.8MB, time=46.67 memory used=6824.4MB, alloc=107.8MB, time=46.79 memory used=6858.5MB, alloc=107.8MB, time=46.89 memory used=6894.3MB, alloc=107.8MB, time=47.00 memory used=6933.2MB, alloc=107.8MB, time=47.12 memory used=6974.0MB, alloc=107.8MB, time=47.23 memory used=7018.4MB, alloc=107.8MB, time=47.35 memory used=7058.0MB, alloc=107.8MB, time=47.46 memory used=7085.0MB, alloc=107.8MB, time=47.54 memory used=7108.5MB, alloc=107.8MB, time=47.62 memory used=7130.9MB, alloc=107.8MB, time=47.70 memory used=7153.9MB, alloc=107.8MB, time=47.78 memory used=7177.5MB, alloc=107.8MB, time=47.90 memory used=7203.4MB, alloc=107.8MB, time=48.00 memory used=7229.8MB, alloc=107.8MB, time=48.08 memory used=7256.5MB, alloc=107.8MB, time=48.16 memory used=7283.4MB, alloc=107.8MB, time=48.25 memory used=7310.7MB, alloc=107.8MB, time=48.33 memory used=7338.3MB, alloc=107.8MB, time=48.42 memory used=7366.1MB, alloc=107.8MB, time=48.50 memory used=7396.8MB, alloc=107.8MB, time=48.59 memory used=7427.7MB, alloc=107.8MB, time=48.67 memory used=7458.8MB, alloc=107.8MB, time=48.76 memory used=7490.2MB, alloc=107.8MB, time=48.84 memory used=7521.9MB, alloc=107.8MB, time=48.94 memory used=7554.0MB, alloc=107.8MB, time=49.03 memory used=7588.6MB, alloc=107.8MB, time=49.13 memory used=7623.5MB, alloc=107.8MB, time=49.22 memory used=7658.6MB, alloc=107.8MB, time=49.32 memory used=7694.0MB, alloc=107.8MB, time=49.41 memory used=7732.2MB, alloc=107.8MB, time=49.51 memory used=7770.5MB, alloc=107.8MB, time=49.60 memory used=7808.9MB, alloc=107.8MB, time=49.69 memory used=7847.6MB, alloc=107.8MB, time=49.79 memory used=7888.9MB, alloc=107.8MB, time=49.87 memory used=7930.3MB, alloc=107.8MB, time=49.97 memory used=7977.5MB, alloc=107.8MB, time=50.07 memory used=8030.7MB, alloc=107.8MB, time=50.18 memory used=8084.3MB, alloc=107.8MB, time=50.29 memory used=8116.5MB, alloc=107.8MB, time=50.37 memory used=8128.6MB, alloc=107.8MB, time=50.45 memory used=8138.3MB, alloc=107.8MB, time=50.53 memory used=8147.6MB, alloc=107.8MB, time=50.59 memory used=8155.0MB, alloc=107.8MB, time=50.66 memory used=8162.7MB, alloc=107.8MB, time=50.73 memory used=8170.8MB, alloc=107.8MB, time=50.80 memory used=8178.8MB, alloc=107.8MB, time=50.86 memory used=8186.8MB, alloc=107.8MB, time=50.92 memory used=8194.8MB, alloc=107.8MB, time=51.00 memory used=8202.7MB, alloc=107.8MB, time=51.06 memory used=8210.7MB, alloc=107.8MB, time=51.12 memory used=8218.7MB, alloc=107.8MB, time=51.18 memory used=8226.6MB, alloc=107.8MB, time=51.25 memory used=8234.6MB, alloc=107.8MB, time=51.34 memory used=8242.5MB, alloc=107.8MB, time=51.40 memory used=8250.4MB, alloc=107.8MB, time=51.48 memory used=8258.4MB, alloc=107.8MB, time=51.55 memory used=8266.3MB, alloc=107.8MB, time=51.62 memory used=8274.2MB, alloc=107.8MB, time=51.70 memory used=8282.1MB, alloc=107.8MB, time=51.76 memory used=8289.9MB, alloc=107.8MB, time=51.83 memory used=8297.8MB, alloc=107.8MB, time=51.90 memory used=8305.6MB, alloc=107.8MB, time=51.97 memory used=8313.5MB, alloc=107.8MB, time=52.03 memory used=8321.3MB, alloc=107.8MB, time=52.09 memory used=8329.1MB, alloc=107.8MB, time=52.16 memory used=8336.9MB, alloc=107.8MB, time=52.22 memory used=8344.7MB, alloc=107.8MB, time=52.29 memory used=8352.7MB, alloc=107.8MB, time=52.35 memory used=8360.7MB, alloc=107.8MB, time=52.41 memory used=8370.5MB, alloc=107.8MB, time=52.47 memory used=8378.7MB, alloc=107.8MB, time=52.53 memory used=8388.5MB, alloc=107.8MB, time=52.59 memory used=8398.8MB, alloc=107.8MB, time=52.65 memory used=8409.0MB, alloc=107.8MB, time=52.72 memory used=8419.2MB, alloc=107.8MB, time=52.78 memory used=8429.3MB, alloc=107.8MB, time=52.85 memory used=8439.4MB, alloc=107.8MB, time=52.91 memory used=8449.5MB, alloc=107.8MB, time=52.97 memory used=8459.6MB, alloc=107.8MB, time=53.04 memory used=8469.6MB, alloc=107.8MB, time=53.14 memory used=8479.6MB, alloc=107.8MB, time=53.20 memory used=8489.6MB, alloc=107.8MB, time=53.28 memory used=8499.5MB, alloc=107.8MB, time=53.34 memory used=8509.4MB, alloc=107.8MB, time=53.39 memory used=8519.3MB, alloc=107.8MB, time=53.45 memory used=8529.1MB, alloc=107.8MB, time=53.53 memory used=8538.9MB, alloc=107.8MB, time=53.60 memory used=8548.6MB, alloc=107.8MB, time=53.66 memory used=8558.3MB, alloc=107.8MB, time=53.73 memory used=8568.0MB, alloc=107.8MB, time=53.79 memory used=8577.7MB, alloc=107.8MB, time=53.87 memory used=8587.3MB, alloc=107.8MB, time=53.95 memory used=8597.2MB, alloc=107.8MB, time=54.02 memory used=8608.8MB, alloc=107.8MB, time=54.08 memory used=8618.7MB, alloc=107.8MB, time=54.14 memory used=8630.0MB, alloc=107.8MB, time=54.21 memory used=8641.8MB, alloc=107.8MB, time=54.28 memory used=8653.4MB, alloc=107.8MB, time=54.34 memory used=8665.0MB, alloc=107.8MB, time=54.42 memory used=8676.5MB, alloc=107.8MB, time=54.49 memory used=8687.9MB, alloc=107.8MB, time=54.55 memory used=8699.3MB, alloc=107.8MB, time=54.61 memory used=8710.6MB, alloc=107.8MB, time=54.67 memory used=8721.8MB, alloc=107.8MB, time=54.73 memory used=8733.0MB, alloc=107.8MB, time=54.81 memory used=8744.1MB, alloc=107.8MB, time=54.87 memory used=8755.4MB, alloc=107.8MB, time=54.99 memory used=8768.2MB, alloc=107.8MB, time=55.07 memory used=8779.5MB, alloc=107.8MB, time=55.14 memory used=8791.9MB, alloc=107.8MB, time=55.20 memory used=8804.6MB, alloc=107.8MB, time=55.26 memory used=8817.3MB, alloc=107.8MB, time=55.33 memory used=8829.8MB, alloc=107.8MB, time=55.43 memory used=8842.2MB, alloc=107.8MB, time=55.49 memory used=8854.4MB, alloc=107.8MB, time=55.56 memory used=8867.0MB, alloc=107.8MB, time=55.64 memory used=8880.7MB, alloc=107.8MB, time=55.71 memory used=8894.5MB, alloc=107.8MB, time=55.78 memory used=8908.1MB, alloc=107.8MB, time=55.85 memory used=8921.6MB, alloc=107.8MB, time=55.91 memory used=8934.9MB, alloc=107.8MB, time=55.97 memory used=8948.4MB, alloc=107.8MB, time=56.03 memory used=8962.7MB, alloc=107.8MB, time=56.10 memory used=8977.1MB, alloc=107.8MB, time=56.17 memory used=8991.2MB, alloc=107.8MB, time=56.23 memory used=9005.6MB, alloc=107.8MB, time=56.30 memory used=9020.4MB, alloc=107.8MB, time=56.37 memory used=9035.3MB, alloc=107.8MB, time=56.43 memory used=9050.4MB, alloc=107.8MB, time=56.49 memory used=9065.7MB, alloc=107.8MB, time=56.57 memory used=9081.4MB, alloc=107.8MB, time=56.63 memory used=9097.7MB, alloc=107.8MB, time=56.72 memory used=9114.3MB, alloc=107.8MB, time=56.78 memory used=9131.1MB, alloc=107.8MB, time=56.85 memory used=9148.3MB, alloc=107.8MB, time=56.93 memory used=9166.1MB, alloc=107.8MB, time=57.00 memory used=9184.5MB, alloc=107.8MB, time=57.07 memory used=9277.6MB, alloc=107.8MB, time=62.56 memory used=9315.7MB, alloc=107.8MB, time=62.69 memory used=9350.2MB, alloc=107.8MB, time=62.81 memory used=9393.0MB, alloc=107.8MB, time=62.93 memory used=9423.7MB, alloc=107.8MB, time=63.04 memory used=9449.9MB, alloc=107.8MB, time=63.15 memory used=9477.9MB, alloc=107.8MB, time=63.25 memory used=9507.6MB, alloc=107.8MB, time=63.36 memory used=9540.5MB, alloc=107.8MB, time=63.47 memory used=9575.0MB, alloc=107.8MB, time=63.58 memory used=9611.2MB, alloc=107.8MB, time=63.69 memory used=9650.8MB, alloc=107.8MB, time=63.80 memory used=9691.9MB, alloc=107.8MB, time=63.90 memory used=9733.9MB, alloc=107.8MB, time=64.02 memory used=9769.6MB, alloc=107.8MB, time=64.11 memory used=9794.2MB, alloc=107.8MB, time=64.19 memory used=9816.5MB, alloc=107.8MB, time=64.27 memory used=9839.1MB, alloc=107.8MB, time=64.35 memory used=9862.2MB, alloc=107.8MB, time=64.44 memory used=9885.6MB, alloc=107.8MB, time=64.51 memory used=9909.4MB, alloc=107.8MB, time=64.60 memory used=9933.6MB, alloc=107.8MB, time=64.70 memory used=9960.1MB, alloc=107.8MB, time=64.79 memory used=9987.1MB, alloc=107.8MB, time=64.88 memory used=10014.3MB, alloc=107.8MB, time=65.00 memory used=10041.9MB, alloc=107.8MB, time=65.08 memory used=10069.7MB, alloc=107.8MB, time=65.16 memory used=10097.8MB, alloc=107.8MB, time=65.25 memory used=10126.4MB, alloc=107.8MB, time=65.34 memory used=10157.3MB, alloc=107.8MB, time=65.43 memory used=10188.6MB, alloc=107.8MB, time=65.52 memory used=10220.3MB, alloc=107.8MB, time=65.60 memory used=10252.1MB, alloc=107.8MB, time=65.68 memory used=10284.2MB, alloc=107.8MB, time=65.77 memory used=10319.1MB, alloc=107.8MB, time=65.86 memory used=10354.2MB, alloc=107.8MB, time=65.95 memory used=10389.5MB, alloc=107.8MB, time=66.04 memory used=10425.0MB, alloc=107.8MB, time=66.13 memory used=10460.8MB, alloc=107.8MB, time=66.23 memory used=10499.0MB, alloc=107.8MB, time=66.32 memory used=10537.6MB, alloc=107.8MB, time=66.41 memory used=10576.3MB, alloc=107.8MB, time=66.50 memory used=10617.7MB, alloc=107.8MB, time=66.61 memory used=10660.2MB, alloc=107.8MB, time=66.71 memory used=10713.4MB, alloc=107.8MB, time=66.82 memory used=10765.2MB, alloc=107.8MB, time=66.93 memory used=10813.6MB, alloc=107.8MB, time=67.03 memory used=10830.8MB, alloc=107.8MB, time=67.09 memory used=10841.4MB, alloc=107.8MB, time=67.15 memory used=10850.3MB, alloc=107.8MB, time=67.21 memory used=10857.6MB, alloc=107.8MB, time=67.28 memory used=10865.2MB, alloc=107.8MB, time=67.34 memory used=10873.2MB, alloc=107.8MB, time=67.42 memory used=10881.2MB, alloc=107.8MB, time=67.48 memory used=10889.2MB, alloc=107.8MB, time=67.54 memory used=10897.2MB, alloc=107.8MB, time=67.60 memory used=10905.2MB, alloc=107.8MB, time=67.66 memory used=10913.2MB, alloc=107.8MB, time=67.71 memory used=10921.2MB, alloc=107.8MB, time=67.77 memory used=10929.2MB, alloc=107.8MB, time=67.82 memory used=10937.2MB, alloc=107.8MB, time=67.88 memory used=10945.1MB, alloc=107.8MB, time=67.94 memory used=10953.1MB, alloc=107.8MB, time=68.00 memory used=10961.0MB, alloc=107.8MB, time=68.07 memory used=10968.9MB, alloc=107.8MB, time=68.15 memory used=10976.8MB, alloc=107.8MB, time=68.22 memory used=10984.8MB, alloc=107.8MB, time=68.28 memory used=10992.7MB, alloc=107.8MB, time=68.35 memory used=11000.5MB, alloc=107.8MB, time=68.40 memory used=11008.4MB, alloc=107.8MB, time=68.47 memory used=11016.2MB, alloc=107.8MB, time=68.53 memory used=11024.1MB, alloc=107.8MB, time=68.58 memory used=11031.9MB, alloc=107.8MB, time=68.65 memory used=11039.7MB, alloc=107.8MB, time=68.71 memory used=11047.5MB, alloc=107.8MB, time=68.76 memory used=11055.3MB, alloc=107.8MB, time=68.81 memory used=11063.4MB, alloc=107.8MB, time=68.88 memory used=11071.4MB, alloc=107.8MB, time=68.95 memory used=11081.2MB, alloc=107.8MB, time=69.03 memory used=11089.3MB, alloc=107.8MB, time=69.10 memory used=11099.2MB, alloc=107.8MB, time=69.16 memory used=11107.4MB, alloc=107.8MB, time=69.23 memory used=11117.2MB, alloc=107.8MB, time=69.29 memory used=11127.4MB, alloc=107.8MB, time=69.35 memory 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alloc=107.8MB, time=70.65 memory used=11348.1MB, alloc=107.8MB, time=70.71 memory used=11359.8MB, alloc=107.8MB, time=70.78 memory used=11371.4MB, alloc=107.8MB, time=70.85 memory used=11382.9MB, alloc=107.8MB, time=70.93 memory used=11394.4MB, alloc=107.8MB, time=70.99 memory used=11405.8MB, alloc=107.8MB, time=71.05 memory used=11417.2MB, alloc=107.8MB, time=71.11 memory used=11428.4MB, alloc=107.8MB, time=71.17 memory used=11439.6MB, alloc=107.8MB, time=71.23 memory used=11450.7MB, alloc=107.8MB, time=71.28 memory used=11461.8MB, alloc=107.8MB, time=71.35 memory used=11473.1MB, alloc=107.8MB, time=71.41 memory used=11485.8MB, alloc=107.8MB, time=71.48 memory used=11498.8MB, alloc=107.8MB, time=71.57 memory used=11511.6MB, alloc=107.8MB, time=71.63 memory used=11524.3MB, alloc=107.8MB, time=71.69 memory used=11536.8MB, alloc=107.8MB, time=71.76 memory used=11549.3MB, alloc=107.8MB, time=71.83 memory used=11561.6MB, alloc=107.8MB, time=71.90 memory used=11573.8MB, alloc=107.8MB, 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memory used=45893.0MB, alloc=411.8MB, time=205.56 memory used=45958.3MB, alloc=411.8MB, time=205.74 memory used=46115.7MB, alloc=411.8MB, time=207.15 memory used=46177.7MB, alloc=411.8MB, time=207.39 memory used=46231.4MB, alloc=411.8MB, time=207.59 memory used=46296.6MB, alloc=411.8MB, time=207.82 memory used=46337.4MB, alloc=411.8MB, time=208.00 memory used=46380.0MB, alloc=411.8MB, time=208.18 memory used=46426.9MB, alloc=411.8MB, time=208.37 memory used=46478.1MB, alloc=411.8MB, time=208.55 memory used=46534.5MB, alloc=411.8MB, time=208.73 memory used=46595.8MB, alloc=411.8MB, time=208.93 memory used=46662.9MB, alloc=411.8MB, time=209.13 memory used=46714.3MB, alloc=411.8MB, time=209.29 memory used=46751.2MB, alloc=411.8MB, time=209.44 memory used=46789.5MB, alloc=411.8MB, time=209.58 memory used=46829.8MB, alloc=411.8MB, time=209.72 memory used=46872.1MB, alloc=411.8MB, time=209.87 memory used=46917.0MB, alloc=411.8MB, time=210.02 memory used=46964.3MB, alloc=411.8MB, time=210.18 memory used=47013.7MB, alloc=411.8MB, time=210.34 memory used=47067.2MB, alloc=411.8MB, time=210.49 memory used=47143.5MB, alloc=411.8MB, time=210.83 memory used=47197.5MB, alloc=411.8MB, time=211.03 memory used=47251.2MB, alloc=411.8MB, time=211.24 memory used=47296.8MB, alloc=411.8MB, time=211.41 memory used=47350.5MB, alloc=411.8MB, time=211.59 memory used=47413.8MB, alloc=411.8MB, time=211.77 memory used=47457.2MB, alloc=411.8MB, time=211.92 memory used=47545.6MB, alloc=411.8MB, time=212.78 memory used=47597.1MB, alloc=411.8MB, time=212.97 memory used=47689.3MB, alloc=411.8MB, time=219.96 memory used=47737.1MB, alloc=411.8MB, time=220.16 memory used=47794.8MB, alloc=411.8MB, time=220.38 memory used=47851.6MB, alloc=411.8MB, time=220.59 memory used=47890.9MB, alloc=411.8MB, time=220.78 memory used=47932.8MB, alloc=411.8MB, time=220.95 memory used=47978.4MB, alloc=411.8MB, time=221.13 memory used=48026.5MB, alloc=411.8MB, time=221.32 memory used=48079.0MB, alloc=411.8MB, time=221.50 memory used=48134.0MB, alloc=411.8MB, time=221.69 memory used=48193.5MB, alloc=411.8MB, time=221.89 memory used=48257.4MB, alloc=411.8MB, time=222.08 memory used=48319.2MB, alloc=411.8MB, time=222.27 memory used=48357.8MB, alloc=411.8MB, time=222.43 memory used=48392.4MB, alloc=411.8MB, time=222.57 memory used=48427.2MB, alloc=411.8MB, time=222.72 memory used=48463.2MB, alloc=411.8MB, time=222.87 memory used=48499.7MB, alloc=411.8MB, time=223.01 memory used=48539.1MB, alloc=411.8MB, time=223.16 memory used=48578.9MB, alloc=411.8MB, time=223.31 memory used=48619.1MB, alloc=411.8MB, time=223.46 memory used=48659.8MB, alloc=411.8MB, time=223.62 memory used=48703.3MB, alloc=411.8MB, time=223.78 memory used=48747.1MB, alloc=411.8MB, time=223.92 memory used=48791.3MB, alloc=411.8MB, time=224.07 memory used=48838.3MB, alloc=411.8MB, time=224.22 memory used=48885.7MB, alloc=411.8MB, time=224.38 memory used=48933.4MB, alloc=411.8MB, time=224.54 memory used=48983.6MB, alloc=411.8MB, time=224.69 memory used=49034.2MB, alloc=411.8MB, time=224.85 memory used=49087.4MB, alloc=411.8MB, time=225.01 memory used=49140.8MB, alloc=411.8MB, time=225.17 memory used=49196.8MB, alloc=411.8MB, time=225.33 memory used=49252.9MB, alloc=411.8MB, time=225.50 memory used=49311.1MB, alloc=411.8MB, time=225.67 memory used=49372.1MB, alloc=411.8MB, time=225.82 memory used=49447.0MB, alloc=411.8MB, time=225.99 memory used=49524.2MB, alloc=411.8MB, time=226.17 memory used=49605.0MB, alloc=411.8MB, time=226.36 memory used=49786.9MB, alloc=411.8MB, time=226.68 memory used=49933.8MB, alloc=411.8MB, time=226.97 memory used=50092.0MB, alloc=411.8MB, time=227.27 memory used=50263.1MB, alloc=411.8MB, time=227.57 memory used=50458.7MB, alloc=411.8MB, time=227.88 memory used=50547.9MB, alloc=411.8MB, time=229.30 memory used=50602.6MB, alloc=411.8MB, time=229.51 memory used=50658.5MB, alloc=411.8MB, time=229.71 memory used=50699.2MB, alloc=411.8MB, time=229.89 memory used=50744.5MB, alloc=411.8MB, time=230.08 memory used=50794.5MB, alloc=411.8MB, time=230.27 memory used=50850.4MB, alloc=411.8MB, time=230.45 memory used=50912.4MB, alloc=411.8MB, time=230.65 memory used=50975.2MB, alloc=411.8MB, time=230.85 memory used=51020.3MB, alloc=411.8MB, time=231.01 memory used=51057.5MB, alloc=411.8MB, time=231.14 memory used=51095.5MB, alloc=411.8MB, time=231.28 memory used=51135.7MB, alloc=411.8MB, time=231.43 memory used=51177.8MB, alloc=411.8MB, time=231.58 memory used=51221.8MB, alloc=411.8MB, time=231.73 memory used=51267.5MB, alloc=411.8MB, time=231.87 memory used=51314.9MB, alloc=411.8MB, time=232.01 memory used=51365.1MB, alloc=411.8MB, time=232.16 memory used=51416.7MB, alloc=411.8MB, time=232.33 memory used=51470.9MB, alloc=411.8MB, time=232.48 memory used=51528.7MB, alloc=411.8MB, time=232.63 memory used=51589.5MB, alloc=411.8MB, time=232.79 memory used=51672.9MB, alloc=411.8MB, time=232.97 memory used=51889.0MB, alloc=411.8MB, time=233.57 memory used=51948.3MB, alloc=411.8MB, time=233.80 memory used=52003.1MB, alloc=411.8MB, time=233.99 memory used=52047.8MB, alloc=411.8MB, time=234.18 memory used=52100.8MB, alloc=411.8MB, time=234.38 memory used=52162.1MB, alloc=411.8MB, time=234.55 memory used=52212.3MB, alloc=411.8MB, time=234.71 memory used=52252.1MB, alloc=411.8MB, time=234.84 memory used=52294.9MB, alloc=411.8MB, time=234.98 memory used=52342.3MB, alloc=411.8MB, time=235.12 memory used=52425.4MB, alloc=411.8MB, time=235.83 |\^/| 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(); 1428297833 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 3 3 2 2 F := [-3 x z - 4 x - 19 x z + 13 y , 11 y z - 18 x + 7 x y - 5 x , 3 3 2 2 y z + 12 y z - 2 x y - 17 x z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 2 G := [11 y z + 11 x z - 16 x - 6 y, 17 x z + 13 x y z - 18 x z - 17, 2 2 2 3 x y z - 16 y z + 8 z + x z] > Problem := [F,G]; 3 3 2 3 3 3 2 2 Problem := [[-3 x z - 4 x - 19 x z + 13 y , 11 y z - 18 x + 7 x y - 5 x , 3 3 2 2 3 2 2 y z + 12 y z - 2 x y - 17 x z ], [11 y z + 11 x z - 16 x - 6 y, 3 2 2 2 2 2 3 17 x z + 13 x y z - 18 x z - 17, x y z - 16 y z + 8 z + x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.46 memory used=45.8MB, alloc=32.3MB, time=0.66 memory used=65.7MB, alloc=32.3MB, time=0.89 memory used=85.0MB, alloc=56.3MB, time=1.34 memory used=129.8MB, alloc=60.4MB, time=2.05 memory used=174.0MB, alloc=60.6MB, time=3.15 memory used=222.6MB, alloc=60.6MB, time=5.46 memory used=263.2MB, alloc=60.6MB, time=5.78 memory used=309.3MB, alloc=60.6MB, time=6.45 memory used=349.4MB, alloc=60.6MB, time=6.75 memory used=388.6MB, alloc=60.6MB, time=7.34 memory used=430.7MB, alloc=68.6MB, time=7.82 memory used=477.5MB, alloc=68.6MB, time=8.51 memory used=524.3MB, alloc=68.6MB, time=8.93 memory used=577.3MB, alloc=76.6MB, time=9.45 memory used=613.9MB, alloc=76.6MB, time=10.03 memory used=663.9MB, alloc=100.6MB, time=12.07 memory used=739.5MB, alloc=100.6MB, time=12.61 memory used=803.5MB, alloc=100.6MB, time=13.32 memory used=870.3MB, alloc=100.6MB, time=14.14 memory used=935.6MB, alloc=124.6MB, time=15.01 memory used=1017.4MB, alloc=124.6MB, time=15.97 memory used=1064.5MB, alloc=380.6MB, time=16.60 memory used=1152.4MB, alloc=380.6MB, time=17.83 memory used=1189.2MB, alloc=380.6MB, time=18.00 memory used=1252.0MB, alloc=380.6MB, time=18.56 memory used=1298.8MB, alloc=380.6MB, time=18.75 memory used=1336.0MB, alloc=380.6MB, time=18.91 memory used=1380.0MB, alloc=380.6MB, time=19.07 memory used=1411.2MB, alloc=380.6MB, time=19.21 memory used=1472.2MB, alloc=380.6MB, time=19.54 memory used=1506.1MB, alloc=380.6MB, time=19.72 memory used=1549.8MB, alloc=380.6MB, time=19.88 memory used=1585.7MB, alloc=380.6MB, time=20.04 memory used=1641.3MB, alloc=404.6MB, time=27.04 memory used=1710.2MB, alloc=404.6MB, time=28.61 memory used=1764.4MB, alloc=404.6MB, time=28.82 memory used=1816.9MB, alloc=404.6MB, time=29.00 memory used=1882.2MB, alloc=404.6MB, time=29.19 memory used=1932.8MB, alloc=404.6MB, time=29.34 memory used=1975.8MB, alloc=404.6MB, time=29.49 memory used=2026.1MB, alloc=404.6MB, time=29.63 memory used=2097.0MB, alloc=404.6MB, time=30.28 memory used=2194.4MB, alloc=404.6MB, time=31.81 memory used=2260.5MB, alloc=404.6MB, time=32.23 memory used=2309.8MB, alloc=404.6MB, time=32.40 memory used=2405.1MB, alloc=404.6MB, time=33.17 memory used=2535.1MB, alloc=404.6MB, time=34.27 memory used=2663.7MB, alloc=404.6MB, time=36.03 memory used=2794.8MB, alloc=404.6MB, time=39.22 memory used=2927.2MB, alloc=404.6MB, time=43.81 memory used=3035.9MB, alloc=428.6MB, time=45.34 memory used=3146.4MB, alloc=428.6MB, time=46.38 memory used=3234.6MB, alloc=428.6MB, time=49.26 memory used=3288.3MB, alloc=428.6MB, time=49.49 memory used=3354.7MB, alloc=428.6MB, time=49.71 memory used=3428.1MB, alloc=428.6MB, time=50.15 memory used=3489.6MB, alloc=428.6MB, time=50.43 memory used=3555.0MB, alloc=428.6MB, time=50.78 memory used=3628.0MB, alloc=428.6MB, time=51.08 memory used=3690.3MB, alloc=428.6MB, time=51.32 memory used=3777.7MB, alloc=428.6MB, time=57.32 memory used=3838.6MB, alloc=428.6MB, time=57.55 memory used=3896.3MB, alloc=428.6MB, time=57.77 memory used=3967.9MB, alloc=428.6MB, time=57.99 memory used=4013.3MB, alloc=428.6MB, time=58.17 memory used=4066.2MB, alloc=428.6MB, time=58.35 memory used=4136.6MB, alloc=428.6MB, time=58.81 memory used=4273.4MB, alloc=428.6MB, time=60.18 memory used=4352.7MB, alloc=428.6MB, time=62.87 memory used=4414.2MB, alloc=428.6MB, time=63.12 memory used=4462.5MB, alloc=428.6MB, time=63.35 memory used=4520.1MB, alloc=428.6MB, time=63.58 memory used=4588.5MB, alloc=428.6MB, time=63.81 memory used=4646.2MB, alloc=428.6MB, time=64.03 memory used=4688.5MB, alloc=428.6MB, time=64.22 memory used=4734.9MB, alloc=428.6MB, time=64.41 memory used=4785.2MB, alloc=428.6MB, time=64.61 memory used=4839.7MB, alloc=428.6MB, time=64.81 memory used=4901.4MB, alloc=428.6MB, time=65.01 memory used=4972.1MB, alloc=428.6MB, time=65.47 memory used=5080.2MB, alloc=428.6MB, time=70.70 memory used=5146.3MB, alloc=428.6MB, time=71.52 memory used=5210.1MB, alloc=428.6MB, time=71.77 memory used=5255.2MB, alloc=428.6MB, time=71.99 memory used=5306.6MB, alloc=428.6MB, time=72.22 memory used=5365.8MB, alloc=428.6MB, time=72.46 memory used=5433.0MB, alloc=428.6MB, time=72.70 memory used=5497.9MB, alloc=452.6MB, time=72.94 memory used=5551.4MB, alloc=452.6MB, time=73.15 memory used=5608.1MB, alloc=452.6MB, time=73.36 memory used=5669.4MB, alloc=452.6MB, time=73.57 memory used=5736.1MB, alloc=452.6MB, time=73.79 memory used=5808.6MB, alloc=452.6MB, time=74.05 memory used=5887.8MB, alloc=452.6MB, time=74.27 memory used=5973.7MB, alloc=452.6MB, time=74.50 memory used=6162.9MB, alloc=452.6MB, time=75.50 memory used=6320.8MB, alloc=452.6MB, time=77.02 memory used=6401.2MB, alloc=452.6MB, time=77.53 memory used=6604.5MB, alloc=452.6MB, time=84.21 memory used=6674.1MB, alloc=452.6MB, time=84.49 memory used=6741.6MB, alloc=452.6MB, time=84.75 memory used=6807.4MB, alloc=452.6MB, time=84.96 memory used=6941.7MB, alloc=452.6MB, time=91.09 memory used=7011.0MB, alloc=452.6MB, time=91.37 memory used=7072.9MB, alloc=452.6MB, time=91.60 memory used=7154.0MB, alloc=452.6MB, time=91.87 memory used=7247.0MB, alloc=452.6MB, time=92.51 memory used=7383.8MB, alloc=452.6MB, time=93.06 memory used=7518.6MB, alloc=452.6MB, time=94.31 memory used=7585.9MB, alloc=452.6MB, time=94.55 memory used=7725.4MB, alloc=452.6MB, time=96.19 memory used=7846.3MB, alloc=476.6MB, time=98.61 memory used=8003.5MB, alloc=476.6MB, time=103.01 memory used=8152.2MB, alloc=476.6MB, time=104.84 memory used=8269.2MB, alloc=500.6MB, time=106.04 memory used=8386.6MB, alloc=500.6MB, time=107.30 memory used=8496.7MB, alloc=524.6MB, time=108.61 memory used=8629.3MB, alloc=524.6MB, time=110.96 memory used=8734.6MB, alloc=524.6MB, time=112.48 memory used=8853.8MB, alloc=524.6MB, time=114.55 memory used=8972.4MB, alloc=524.6MB, time=116.12 memory used=9097.5MB, alloc=548.6MB, time=117.29 memory used=9183.8MB, alloc=548.6MB, time=118.46 memory used=9339.1MB, alloc=572.6MB, time=119.60 memory used=9405.4MB, alloc=572.6MB, time=120.58 memory used=9530.0MB, alloc=572.6MB, time=121.54 memory used=9600.2MB, alloc=572.6MB, time=122.60 memory used=9680.6MB, alloc=572.6MB, time=124.03 memory used=9758.6MB, alloc=572.6MB, time=125.24 memory used=9816.1MB, alloc=572.6MB, time=126.30 memory used=9880.3MB, alloc=572.6MB, time=128.59 memory used=9941.9MB, alloc=572.6MB, time=129.57 memory used=9999.5MB, alloc=572.6MB, time=130.98 memory used=10052.8MB, alloc=572.6MB, time=131.86 memory used=10273.5MB, alloc=596.6MB, time=134.55 memory used=10521.9MB, alloc=620.6MB, time=138.48 memory used=10724.3MB, alloc=620.6MB, time=140.51 memory used=10860.3MB, alloc=620.6MB, time=141.20 memory used=11022.5MB, alloc=620.6MB, time=142.15 memory used=11158.2MB, alloc=620.6MB, time=142.84 memory used=11373.8MB, alloc=620.6MB, time=160.94 memory used=11501.1MB, alloc=620.6MB, time=161.56 memory used=11717.6MB, alloc=644.6MB, time=164.14 memory used=11971.7MB, alloc=668.6MB, time=166.83 memory used=12195.5MB, alloc=668.6MB, time=169.83 memory used=12321.7MB, alloc=692.6MB, time=171.84 memory used=12483.5MB, alloc=692.6MB, time=174.34 memory used=12647.3MB, alloc=716.6MB, time=177.07 memory used=12800.4MB, alloc=716.6MB, time=179.27 memory used=12946.8MB, alloc=716.6MB, time=181.57 memory used=13101.2MB, alloc=716.6MB, time=183.99 memory used=13240.5MB, alloc=716.6MB, time=186.11 memory used=13365.0MB, alloc=740.6MB, time=188.01 memory used=13450.2MB, alloc=740.6MB, time=189.50 memory used=13530.9MB, alloc=740.6MB, time=191.42 memory used=13625.5MB, alloc=740.6MB, time=193.34 memory used=13716.6MB, alloc=740.6MB, time=195.13 memory used=14114.5MB, alloc=764.6MB, time=200.38 memory used=14348.3MB, alloc=788.6MB, time=202.56 memory used=14567.7MB, alloc=812.6MB, time=208.52 memory used=14787.8MB, alloc=836.6MB, time=213.10 memory used=15024.5MB, alloc=836.6MB, time=215.97 memory used=15276.5MB, alloc=836.6MB, time=217.79 memory used=15518.8MB, alloc=836.6MB, time=219.53 memory used=15774.1MB, alloc=836.6MB, time=229.11 memory used=15971.6MB, alloc=836.6MB, time=230.34 memory used=16255.4MB, alloc=836.6MB, time=236.18 memory used=16463.8MB, alloc=836.6MB, time=237.61 memory used=16723.2MB, alloc=836.6MB, time=239.47 |\^/| 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(); 1428298134 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 3 2 F := [8 x y - 10 y + 17 x z - 13 y, 5 x y z - 15 x y + 17 x y - 13 x y z, 4 3 2 2 -2 x + 16 x y + 5 y z - 9 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 2 2 3 G := [-4 x y z + 15 y - 2 x z + 2 y z, -3 x z - 6 x z - 7 z + 15 y, 2 4 2 -11 x y z - 12 z + 6 x z - 3] > Problem := [F,G]; 2 2 4 2 Problem := [[8 x y - 10 y + 17 x z - 13 y, 2 3 2 4 3 2 2 5 x y z - 15 x y + 17 x y - 13 x y z, -2 x + 16 x y + 5 y z - 9 z ], 2 4 2 2 2 2 3 [-4 x y z + 15 y - 2 x z + 2 y z, -3 x z - 6 x z - 7 z + 15 y, 2 4 2 -11 x y z - 12 z + 6 x z - 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=25.5MB, alloc=32.3MB, time=0.48 memory used=44.7MB, alloc=60.3MB, time=0.74 memory used=81.9MB, alloc=60.3MB, time=1.23 memory used=126.2MB, alloc=68.3MB, time=1.83 memory used=170.0MB, alloc=68.3MB, time=2.21 memory used=196.0MB, alloc=68.3MB, time=2.30 memory used=226.5MB, alloc=68.3MB, time=2.45 memory used=252.0MB, alloc=68.3MB, time=2.54 memory used=285.2MB, alloc=68.3MB, time=3.25 memory used=307.5MB, alloc=68.3MB, time=3.33 memory used=341.7MB, alloc=68.3MB, time=3.57 memory used=400.9MB, alloc=68.3MB, time=5.42 memory used=428.7MB, alloc=68.3MB, time=5.52 memory used=450.3MB, alloc=68.3MB, time=5.60 memory used=476.9MB, alloc=68.3MB, time=5.68 memory used=499.1MB, alloc=68.3MB, time=5.75 memory used=516.6MB, alloc=68.3MB, time=5.82 memory used=535.9MB, alloc=68.3MB, time=5.89 memory used=557.2MB, alloc=68.3MB, time=5.96 memory used=580.1MB, alloc=68.3MB, time=6.04 memory used=605.3MB, alloc=68.3MB, time=6.12 memory used=628.0MB, alloc=68.3MB, time=6.18 memory used=665.9MB, alloc=68.3MB, time=6.51 memory used=710.8MB, alloc=68.3MB, time=6.90 memory used=760.0MB, alloc=68.3MB, time=7.26 memory used=809.0MB, alloc=68.3MB, time=7.77 memory used=857.6MB, alloc=68.3MB, time=8.58 memory used=897.6MB, alloc=68.3MB, time=8.96 memory used=939.3MB, alloc=92.3MB, time=9.43 memory used=1002.5MB, alloc=92.3MB, time=10.03 memory used=1051.4MB, alloc=92.3MB, time=10.49 memory used=1117.1MB, alloc=92.3MB, time=11.08 memory used=1164.0MB, alloc=92.3MB, time=11.56 memory used=1200.7MB, alloc=92.3MB, time=11.68 memory used=1231.6MB, alloc=92.3MB, time=11.79 memory used=1297.0MB, alloc=92.3MB, time=12.48 memory used=1371.4MB, alloc=92.3MB, time=16.01 memory used=1425.5MB, alloc=92.3MB, time=16.29 memory used=1459.3MB, alloc=92.3MB, time=16.42 memory used=1493.8MB, alloc=92.3MB, time=16.54 memory used=1519.2MB, alloc=92.3MB, time=16.65 memory used=1547.6MB, alloc=92.3MB, time=16.75 memory used=1579.0MB, alloc=92.3MB, time=16.87 memory used=1613.1MB, alloc=92.3MB, time=16.98 memory used=1651.1MB, alloc=92.3MB, time=17.09 memory used=1691.7MB, alloc=92.3MB, time=17.20 memory used=1714.6MB, alloc=92.3MB, time=17.28 memory used=1737.4MB, alloc=92.3MB, time=17.37 memory used=1760.6MB, alloc=92.3MB, time=17.46 memory used=1785.8MB, alloc=92.3MB, time=17.54 memory used=1811.2MB, alloc=92.3MB, time=17.62 memory used=1838.5MB, alloc=92.3MB, time=17.71 memory used=1866.8MB, alloc=92.3MB, time=17.79 memory used=1896.8MB, alloc=92.3MB, time=17.88 memory used=1928.2MB, alloc=92.3MB, time=17.96 memory used=1961.3MB, alloc=92.3MB, time=18.05 memory used=1995.1MB, alloc=92.3MB, time=18.14 memory used=2031.1MB, alloc=92.3MB, time=18.23 memory used=2071.3MB, alloc=92.3MB, time=18.32 memory used=2086.7MB, alloc=107.8MB, time=18.40 memory used=2136.1MB, alloc=107.8MB, time=18.70 memory used=2225.0MB, alloc=107.8MB, time=19.39 memory used=2297.7MB, alloc=107.8MB, time=20.18 memory used=2325.4MB, alloc=107.8MB, time=20.29 memory used=2373.3MB, alloc=107.8MB, time=20.57 memory used=2404.0MB, alloc=107.8MB, time=20.68 memory used=2429.0MB, alloc=107.8MB, time=20.77 memory used=2459.8MB, alloc=107.8MB, time=20.88 memory used=2495.0MB, alloc=107.8MB, time=20.99 memory used=2516.3MB, alloc=107.8MB, time=21.07 memory used=2538.7MB, alloc=107.8MB, time=21.15 memory used=2563.9MB, alloc=107.8MB, time=21.23 memory used=2592.0MB, alloc=107.8MB, time=21.32 memory used=2639.9MB, alloc=131.8MB, time=24.18 memory used=2723.4MB, alloc=131.8MB, time=25.16 memory used=2776.5MB, alloc=131.8MB, time=25.33 memory used=2813.5MB, alloc=131.8MB, time=25.46 memory used=2854.4MB, alloc=131.8MB, time=25.59 memory used=2901.3MB, alloc=131.8MB, time=25.72 memory used=2954.4MB, alloc=131.8MB, time=25.86 memory used=3011.7MB, alloc=131.8MB, time=26.01 memory used=3045.6MB, alloc=131.8MB, time=26.13 memory used=3077.7MB, alloc=131.8MB, time=26.23 memory used=3111.1MB, alloc=131.8MB, time=26.34 memory used=3147.4MB, alloc=131.8MB, time=26.45 memory used=3184.5MB, alloc=131.8MB, time=26.56 memory used=3224.6MB, alloc=131.8MB, time=26.68 memory used=3265.5MB, alloc=131.8MB, time=26.80 memory used=3309.3MB, alloc=131.8MB, time=26.91 memory used=3353.7MB, alloc=131.8MB, time=27.02 memory used=3401.1MB, alloc=131.8MB, time=27.14 memory used=3449.3MB, alloc=131.8MB, time=27.25 memory used=3499.9MB, alloc=131.8MB, time=27.38 memory used=3553.5MB, alloc=131.8MB, time=27.49 memory used=3609.6MB, alloc=131.8MB, time=27.61 memory used=3668.3MB, alloc=131.8MB, time=27.73 memory used=3710.3MB, alloc=131.8MB, time=27.85 memory used=3723.4MB, alloc=131.8MB, time=27.93 memory used=3733.2MB, alloc=131.8MB, time=28.02 memory used=3741.3MB, alloc=131.8MB, time=28.09 memory used=3749.9MB, alloc=131.8MB, time=28.19 memory used=3758.8MB, alloc=131.8MB, time=28.28 memory used=3767.7MB, alloc=131.8MB, time=28.35 memory used=3776.6MB, alloc=131.8MB, time=28.42 memory used=3785.5MB, alloc=131.8MB, time=28.50 memory used=3794.4MB, alloc=131.8MB, time=28.57 memory used=3803.3MB, alloc=131.8MB, time=28.65 memory used=3812.1MB, alloc=131.8MB, time=28.74 memory used=3820.9MB, alloc=131.8MB, time=28.82 memory used=3829.8MB, alloc=131.8MB, time=28.89 memory used=3838.6MB, alloc=131.8MB, time=28.96 memory used=3847.3MB, alloc=131.8MB, time=29.03 memory used=3856.1MB, alloc=131.8MB, time=29.10 memory used=3864.8MB, alloc=131.8MB, time=29.20 memory used=3873.5MB, alloc=131.8MB, time=29.29 memory used=3882.2MB, alloc=131.8MB, time=29.37 memory used=3890.9MB, alloc=131.8MB, time=29.46 memory used=3899.5MB, alloc=131.8MB, time=29.54 memory used=3908.4MB, alloc=131.8MB, time=29.62 memory used=3918.9MB, alloc=131.8MB, time=29.70 memory used=3927.9MB, alloc=131.8MB, time=29.77 memory used=3938.1MB, alloc=131.8MB, time=29.86 memory used=3948.7MB, alloc=131.8MB, time=29.95 memory used=3959.3MB, alloc=131.8MB, time=30.03 memory used=3969.8MB, alloc=131.8MB, time=30.11 memory used=3980.3MB, alloc=131.8MB, time=30.19 memory used=3990.7MB, alloc=131.8MB, time=30.26 memory used=4001.1MB, alloc=131.8MB, time=30.34 memory used=4011.4MB, alloc=131.8MB, time=30.42 memory used=4021.6MB, alloc=131.8MB, time=30.49 memory used=4031.8MB, alloc=131.8MB, time=30.56 memory used=4042.0MB, alloc=131.8MB, time=30.64 memory used=4052.3MB, alloc=131.8MB, time=30.71 memory used=4064.1MB, alloc=131.8MB, time=30.80 memory used=4076.0MB, alloc=131.8MB, time=30.88 memory used=4087.8MB, alloc=131.8MB, time=30.96 memory used=4099.6MB, alloc=131.8MB, time=31.03 memory used=4111.2MB, alloc=131.8MB, time=31.11 memory used=4122.8MB, alloc=131.8MB, time=31.19 memory used=4134.2MB, alloc=131.8MB, time=31.27 memory used=4145.5MB, alloc=131.8MB, time=31.34 memory used=4157.1MB, alloc=131.8MB, time=31.43 memory used=4169.8MB, alloc=131.8MB, time=31.51 memory used=4182.6MB, alloc=131.8MB, time=31.58 memory used=4195.3MB, alloc=131.8MB, time=31.67 memory used=4207.7MB, alloc=131.8MB, time=31.74 memory used=4220.4MB, alloc=131.8MB, time=31.82 memory used=4234.0MB, alloc=131.8MB, time=31.90 memory used=4247.6MB, alloc=131.8MB, time=31.98 memory used=4261.0MB, alloc=131.8MB, time=32.05 memory used=4274.5MB, alloc=131.8MB, time=32.13 memory used=4288.7MB, alloc=131.8MB, time=32.21 memory used=4302.9MB, alloc=131.8MB, time=32.28 memory used=4317.1MB, alloc=131.8MB, time=32.37 memory used=4331.7MB, alloc=131.8MB, time=32.45 memory used=4346.3MB, alloc=131.8MB, time=32.53 memory used=4361.9MB, alloc=131.8MB, time=32.61 memory used=4377.2MB, alloc=131.8MB, time=32.70 memory used=4392.9MB, alloc=131.8MB, time=32.77 memory used=4409.1MB, alloc=131.8MB, time=32.85 memory used=4425.7MB, alloc=131.8MB, time=32.94 memory used=4443.0MB, alloc=131.8MB, time=33.02 memory used=4460.7MB, alloc=131.8MB, time=33.10 memory used=4571.1MB, alloc=131.8MB, time=36.84 memory used=4618.6MB, alloc=131.8MB, time=37.00 memory used=4662.4MB, alloc=131.8MB, time=37.14 memory used=4700.6MB, alloc=131.8MB, time=37.29 memory used=4744.9MB, alloc=131.8MB, time=37.42 memory used=4795.0MB, alloc=131.8MB, time=37.56 memory used=4851.3MB, alloc=131.8MB, time=37.71 memory used=4897.0MB, alloc=131.8MB, time=37.85 memory used=4928.4MB, alloc=131.8MB, time=37.95 memory used=4961.3MB, alloc=131.8MB, time=38.06 memory used=4995.6MB, alloc=131.8MB, time=38.16 memory used=5030.9MB, alloc=131.8MB, time=38.27 memory used=5069.0MB, alloc=131.8MB, time=38.38 memory used=5107.8MB, alloc=131.8MB, time=38.50 memory used=5149.7MB, alloc=131.8MB, time=38.62 memory used=5192.3MB, alloc=131.8MB, time=38.74 memory used=5237.8MB, alloc=131.8MB, time=38.85 memory used=5284.1MB, alloc=131.8MB, time=38.97 memory used=5333.1MB, alloc=131.8MB, time=39.09 memory used=5383.0MB, alloc=131.8MB, time=39.20 memory used=5435.1MB, alloc=131.8MB, time=39.33 memory used=5489.9MB, alloc=131.8MB, time=39.45 memory used=5547.4MB, alloc=131.8MB, time=39.58 memory used=5590.6MB, alloc=131.8MB, time=39.70 memory used=5603.8MB, alloc=131.8MB, time=39.79 memory used=5614.1MB, alloc=131.8MB, time=39.88 memory used=5622.4MB, alloc=131.8MB, time=39.95 memory used=5631.2MB, alloc=131.8MB, time=40.03 memory used=5640.3MB, alloc=131.8MB, time=40.11 memory used=5649.5MB, alloc=131.8MB, time=40.22 memory used=5658.7MB, alloc=131.8MB, time=40.30 memory used=5667.8MB, alloc=131.8MB, time=40.40 memory used=5677.0MB, alloc=131.8MB, time=40.48 memory used=5686.1MB, alloc=131.8MB, time=40.57 memory used=5695.2MB, alloc=131.8MB, time=40.64 memory used=5704.3MB, alloc=131.8MB, time=40.74 memory used=5713.3MB, alloc=131.8MB, time=40.81 memory used=5722.4MB, alloc=131.8MB, time=40.89 memory used=5731.4MB, alloc=131.8MB, time=40.97 memory used=5740.4MB, alloc=131.8MB, time=41.05 memory used=5749.4MB, alloc=131.8MB, time=41.13 memory used=5758.4MB, alloc=131.8MB, time=41.20 memory used=5767.4MB, alloc=131.8MB, time=41.29 memory used=5776.3MB, alloc=131.8MB, time=41.36 memory used=5785.2MB, alloc=131.8MB, time=41.43 memory used=5794.1MB, alloc=131.8MB, time=41.51 memory used=5802.9MB, alloc=131.8MB, time=41.58 memory used=5811.8MB, alloc=131.8MB, time=41.67 memory used=5820.6MB, alloc=131.8MB, time=41.76 memory used=5829.6MB, alloc=131.8MB, time=41.84 memory used=5840.3MB, alloc=131.8MB, time=41.94 memory used=5849.4MB, alloc=131.8MB, time=42.02 memory used=5859.9MB, alloc=131.8MB, time=42.10 memory used=5870.7MB, alloc=131.8MB, time=42.17 memory used=5881.5MB, alloc=131.8MB, time=42.28 memory used=5892.2MB, alloc=131.8MB, time=42.37 memory used=5902.8MB, alloc=131.8MB, time=42.45 memory used=5913.4MB, alloc=131.8MB, time=42.53 memory used=5924.0MB, alloc=131.8MB, time=42.61 memory used=5934.5MB, alloc=131.8MB, time=42.69 memory used=5944.9MB, alloc=131.8MB, time=42.77 memory used=5955.3MB, alloc=131.8MB, time=42.87 memory used=5965.6MB, alloc=131.8MB, time=42.94 memory used=5976.2MB, alloc=131.8MB, time=43.02 memory used=5988.1MB, alloc=131.8MB, time=43.09 memory used=6000.2MB, alloc=131.8MB, time=43.17 memory used=6012.2MB, alloc=131.8MB, time=43.24 memory used=6024.2MB, alloc=131.8MB, time=43.33 memory used=6036.0MB, alloc=131.8MB, time=43.41 memory used=6047.7MB, alloc=131.8MB, time=43.49 memory used=6059.3MB, alloc=131.8MB, time=43.56 memory used=6070.8MB, alloc=131.8MB, time=43.63 memory used=6082.6MB, alloc=131.8MB, time=43.72 memory used=6095.5MB, alloc=131.8MB, time=43.80 memory used=6108.5MB, alloc=131.8MB, time=43.87 memory used=6121.3MB, alloc=131.8MB, time=43.95 memory used=6134.0MB, alloc=131.8MB, time=44.02 memory used=6146.9MB, alloc=131.8MB, time=44.10 memory used=6160.6MB, alloc=131.8MB, time=44.18 memory used=6174.4MB, alloc=131.8MB, time=44.27 memory used=6188.0MB, alloc=131.8MB, time=44.35 memory used=6201.7MB, alloc=131.8MB, time=44.43 memory used=6216.1MB, alloc=131.8MB, time=44.50 memory used=6230.4MB, alloc=131.8MB, time=44.59 memory used=6244.8MB, alloc=131.8MB, time=44.67 memory used=6259.7MB, alloc=131.8MB, time=44.75 memory used=6274.8MB, alloc=131.8MB, time=44.83 memory used=6290.1MB, alloc=131.8MB, time=44.91 memory used=6305.7MB, alloc=131.8MB, time=44.98 memory used=6321.6MB, alloc=131.8MB, time=45.06 memory used=6337.9MB, alloc=131.8MB, time=45.16 memory used=6354.7MB, alloc=131.8MB, time=45.25 memory used=6372.1MB, alloc=131.8MB, time=45.33 memory used=6390.0MB, alloc=131.8MB, time=45.41 memory used=6519.0MB, alloc=131.8MB, time=49.53 memory used=6568.3MB, alloc=131.8MB, time=49.71 memory used=6616.8MB, alloc=131.8MB, time=49.86 memory used=6652.8MB, alloc=131.8MB, time=50.00 memory used=6694.6MB, alloc=131.8MB, time=50.14 memory used=6740.8MB, alloc=131.8MB, time=50.29 memory used=6793.0MB, alloc=131.8MB, time=50.44 memory used=6845.0MB, alloc=131.8MB, time=50.58 memory used=6876.6MB, alloc=131.8MB, time=50.69 memory used=6908.5MB, alloc=131.8MB, time=50.79 memory used=6941.8MB, alloc=131.8MB, time=50.90 memory used=6976.0MB, alloc=131.8MB, time=51.01 memory used=7012.8MB, alloc=131.8MB, time=51.12 memory used=7050.6MB, alloc=131.8MB, time=51.24 memory used=7091.2MB, alloc=131.8MB, time=51.35 memory used=7132.6MB, alloc=131.8MB, time=51.46 memory used=7176.8MB, alloc=131.8MB, time=51.57 memory used=7221.7MB, alloc=131.8MB, time=51.68 memory used=7269.3MB, alloc=131.8MB, time=51.80 memory used=7319.7MB, alloc=131.8MB, time=51.92 memory used=7370.4MB, alloc=131.8MB, time=52.04 memory used=7423.7MB, alloc=131.8MB, time=52.16 memory used=7479.6MB, alloc=131.8MB, time=52.28 memory used=7532.2MB, alloc=131.8MB, time=52.40 memory used=7545.5MB, alloc=131.8MB, time=52.48 memory used=7555.2MB, alloc=131.8MB, time=52.56 memory used=7563.1MB, alloc=131.8MB, time=52.67 memory used=7571.6MB, alloc=131.8MB, time=52.74 memory used=7580.4MB, alloc=131.8MB, time=52.82 memory used=7589.3MB, alloc=131.8MB, time=52.89 memory used=7598.1MB, alloc=131.8MB, time=52.97 memory used=7606.9MB, alloc=131.8MB, time=53.05 memory used=7615.8MB, alloc=131.8MB, time=53.13 memory used=7624.6MB, alloc=131.8MB, time=53.21 memory used=7633.3MB, alloc=131.8MB, time=53.28 memory used=7642.1MB, alloc=131.8MB, time=53.36 memory used=7650.9MB, alloc=131.8MB, time=53.43 memory used=7659.6MB, alloc=131.8MB, time=53.50 memory used=7668.3MB, alloc=131.8MB, time=53.58 memory used=7677.0MB, alloc=131.8MB, time=53.66 memory used=7685.6MB, alloc=131.8MB, time=53.75 memory used=7694.3MB, alloc=131.8MB, time=53.83 memory used=7702.9MB, alloc=131.8MB, time=53.90 memory used=7711.5MB, alloc=131.8MB, time=53.97 memory used=7720.3MB, alloc=131.8MB, time=54.05 memory used=7729.0MB, alloc=131.8MB, time=54.13 memory used=7739.2MB, alloc=131.8MB, time=54.20 memory used=7748.1MB, alloc=131.8MB, time=54.34 memory used=7758.3MB, alloc=131.8MB, time=54.42 memory used=7768.8MB, alloc=131.8MB, time=54.50 memory used=7779.3MB, alloc=131.8MB, time=54.58 memory used=7789.7MB, alloc=131.8MB, time=54.66 memory used=7800.1MB, alloc=131.8MB, time=54.75 memory used=7810.4MB, alloc=131.8MB, time=54.82 memory used=7820.7MB, alloc=131.8MB, time=54.90 memory used=7830.9MB, alloc=131.8MB, time=54.97 memory used=7841.0MB, alloc=131.8MB, time=55.05 memory used=7851.1MB, alloc=131.8MB, time=55.12 memory used=7861.2MB, alloc=131.8MB, time=55.21 memory used=7871.5MB, alloc=131.8MB, time=55.28 memory used=7883.1MB, alloc=131.8MB, time=55.35 memory used=7894.9MB, alloc=131.8MB, time=55.43 memory used=7906.6MB, alloc=131.8MB, time=55.51 memory used=7918.2MB, alloc=131.8MB, time=55.60 memory used=7929.7MB, alloc=131.8MB, time=55.68 memory used=7941.1MB, alloc=131.8MB, time=55.75 memory used=7952.4MB, alloc=131.8MB, time=55.83 memory used=7963.9MB, alloc=131.8MB, time=55.90 memory used=7976.6MB, alloc=131.8MB, time=55.97 memory used=7989.5MB, alloc=131.8MB, time=56.05 memory used=8002.1MB, alloc=131.8MB, time=56.12 memory used=8014.6MB, alloc=131.8MB, time=56.20 memory used=8026.9MB, alloc=131.8MB, time=56.28 memory used=8039.4MB, alloc=131.8MB, time=56.38 memory used=8052.7MB, alloc=131.8MB, time=56.47 memory used=8066.1MB, alloc=131.8MB, time=56.56 memory used=8079.3MB, alloc=131.8MB, time=56.63 memory used=8092.7MB, alloc=131.8MB, time=56.71 memory used=8106.6MB, alloc=131.8MB, time=56.78 memory used=8120.5MB, alloc=131.8MB, time=56.86 memory used=8134.6MB, alloc=131.8MB, time=56.93 memory used=8149.2MB, alloc=131.8MB, time=57.01 memory used=8164.6MB, alloc=131.8MB, time=57.09 memory used=8179.7MB, alloc=131.8MB, time=57.17 memory used=8195.6MB, alloc=131.8MB, time=57.26 memory used=8211.3MB, alloc=131.8MB, time=57.33 memory used=8227.8MB, alloc=131.8MB, time=57.42 memory used=8244.8MB, alloc=131.8MB, time=57.50 memory used=8262.0MB, alloc=131.8MB, time=57.58 memory used=8289.7MB, alloc=131.8MB, time=57.82 memory used=8375.8MB, alloc=131.8MB, time=58.61 memory used=8434.3MB, alloc=387.8MB, time=59.47 memory used=8521.3MB, alloc=387.8MB, time=60.49 memory used=8609.6MB, alloc=411.8MB, time=61.56 memory used=8726.2MB, alloc=411.8MB, time=62.87 memory used=8831.3MB, alloc=435.8MB, time=64.39 memory used=8939.1MB, alloc=435.8MB, time=65.24 memory used=9022.0MB, alloc=435.8MB, time=66.16 memory used=9105.1MB, alloc=435.8MB, time=66.51 memory used=9178.5MB, alloc=435.8MB, time=67.18 memory used=9271.0MB, alloc=435.8MB, time=68.86 memory used=9334.3MB, alloc=435.8MB, time=69.09 memory used=9384.9MB, alloc=435.8MB, time=69.30 memory used=9448.5MB, alloc=435.8MB, time=69.52 memory used=9512.0MB, alloc=435.8MB, time=69.92 memory used=9601.2MB, alloc=435.8MB, time=70.27 memory used=9652.4MB, alloc=435.8MB, time=70.51 memory used=9718.9MB, alloc=435.8MB, time=70.75 memory used=9788.2MB, alloc=435.8MB, time=71.19 memory used=9871.9MB, alloc=435.8MB, time=71.52 memory used=9924.2MB, alloc=435.8MB, time=71.75 memory used=9992.4MB, alloc=435.8MB, time=71.98 memory used=10071.4MB, alloc=435.8MB, time=81.08 memory used=10182.8MB, alloc=435.8MB, time=106.86 memory used=10246.5MB, alloc=435.8MB, time=107.13 memory used=10308.1MB, alloc=435.8MB, time=107.37 memory used=10369.9MB, alloc=435.8MB, time=107.59 memory used=10414.1MB, alloc=435.8MB, time=107.80 memory used=10462.7MB, alloc=459.8MB, time=108.01 memory used=10533.6MB, alloc=459.8MB, time=108.26 memory used=10613.6MB, alloc=459.8MB, time=108.51 memory used=10703.2MB, alloc=459.8MB, time=108.76 memory used=10785.5MB, alloc=459.8MB, time=108.99 memory used=10838.6MB, alloc=459.8MB, time=109.18 memory used=10893.3MB, alloc=459.8MB, time=109.39 memory used=10952.2MB, alloc=459.8MB, time=109.59 memory used=11013.6MB, alloc=459.8MB, time=109.79 memory used=11079.5MB, alloc=459.8MB, time=110.01 memory used=11150.1MB, alloc=459.8MB, time=110.21 memory used=11225.2MB, alloc=459.8MB, time=110.41 memory used=11306.5MB, alloc=459.8MB, time=110.61 memory used=11399.3MB, alloc=459.8MB, time=110.82 memory used=11530.8MB, alloc=459.8MB, time=111.41 memory used=11601.8MB, alloc=459.8MB, time=111.67 memory used=11683.1MB, alloc=459.8MB, time=111.93 memory used=11796.4MB, alloc=459.8MB, time=112.55 memory used=11866.0MB, alloc=459.8MB, time=112.80 memory used=11948.1MB, alloc=459.8MB, time=113.06 memory used=12071.7MB, alloc=459.8MB, time=148.36 memory used=12181.7MB, alloc=459.8MB, time=149.37 memory used=12267.3MB, alloc=459.8MB, time=149.65 memory used=12331.6MB, alloc=459.8MB, time=149.91 memory used=12392.8MB, alloc=459.8MB, time=150.14 memory used=12463.2MB, alloc=459.8MB, time=150.40 memory used=12542.0MB, alloc=459.8MB, time=150.66 memory used=12629.2MB, alloc=459.8MB, time=150.92 memory used=12715.4MB, alloc=459.8MB, time=151.18 memory used=12767.5MB, alloc=459.8MB, time=151.38 memory used=12822.3MB, alloc=459.8MB, time=151.60 memory used=12879.2MB, alloc=459.8MB, time=151.80 memory used=12940.1MB, alloc=459.8MB, time=152.00 memory used=13004.3MB, alloc=459.8MB, time=152.20 memory used=13072.3MB, alloc=459.8MB, time=152.40 memory used=13144.6MB, alloc=459.8MB, time=152.61 memory used=13222.4MB, alloc=459.8MB, time=152.82 memory used=13306.1MB, alloc=459.8MB, time=153.04 memory used=13428.8MB, alloc=459.8MB, time=153.58 memory used=13503.1MB, alloc=459.8MB, time=153.82 memory used=13696.7MB, alloc=459.8MB, time=155.74 memory used=13891.8MB, alloc=459.8MB, time=157.81 memory used=14075.2MB, alloc=459.8MB, time=159.83 memory used=14249.6MB, alloc=459.8MB, time=161.24 memory used=14387.4MB, alloc=459.8MB, time=163.04 memory used=14507.5MB, alloc=483.8MB, time=216.14 |\^/| 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(); 1428298434 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 4 3 F := [5 x - 2 x y + 13 x y - 10 y , 7 y + 18 x z + 8 x + 14, 3 2 2 -18 x + 8 x y + 8 x z + 2 x y] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 G := [12 x y z - x - 19 x y + 6 z, -7 y z + 8 x y - 13 y + 12 z , 3 2 -10 x y - 16 x y z - 6 y z + 3 x z] > Problem := [F,G]; 4 3 2 2 4 3 Problem := [[5 x - 2 x y + 13 x y - 10 y , 7 y + 18 x z + 8 x + 14, 3 2 2 2 2 -18 x + 8 x y + 8 x z + 2 x y], [12 x y z - x - 19 x y + 6 z, 3 2 3 2 3 2 -7 y z + 8 x y - 13 y + 12 z , -10 x y - 16 x y z - 6 y z + 3 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=25.3MB, alloc=32.3MB, time=0.48 memory used=45.1MB, alloc=32.3MB, time=0.69 memory used=64.2MB, alloc=34.6MB, time=0.77 memory used=81.9MB, alloc=34.6MB, time=0.89 memory used=95.4MB, alloc=34.6MB, time=0.94 memory used=115.6MB, alloc=34.6MB, time=1.06 memory used=134.1MB, alloc=34.6MB, time=1.15 memory used=152.0MB, alloc=34.6MB, time=1.27 memory used=166.6MB, alloc=34.6MB, time=1.37 memory used=189.2MB, alloc=38.6MB, time=1.67 memory used=211.2MB, alloc=62.6MB, time=1.92 memory used=256.5MB, alloc=70.6MB, time=2.45 memory used=303.1MB, alloc=70.6MB, time=3.00 memory used=333.9MB, alloc=70.6MB, time=3.25 memory used=380.1MB, alloc=70.6MB, time=3.74 memory used=424.5MB, alloc=70.6MB, time=4.34 memory used=461.7MB, alloc=94.6MB, time=4.71 memory used=540.1MB, alloc=94.6MB, time=5.67 memory used=603.6MB, alloc=94.6MB, time=6.44 memory used=644.6MB, alloc=94.6MB, time=6.74 memory used=706.6MB, alloc=94.6MB, time=7.34 memory used=770.4MB, alloc=94.6MB, time=7.93 memory used=815.9MB, alloc=94.6MB, time=8.27 memory used=857.3MB, alloc=94.6MB, time=8.49 memory used=904.4MB, alloc=94.6MB, time=8.71 memory used=945.4MB, alloc=94.6MB, time=9.02 memory used=993.5MB, alloc=94.6MB, time=9.26 memory used=1035.3MB, alloc=94.6MB, time=9.55 memory used=1077.7MB, alloc=94.6MB, time=9.74 memory used=1126.6MB, alloc=94.6MB, time=10.18 memory used=1182.9MB, alloc=94.6MB, time=10.83 memory used=1241.5MB, alloc=118.6MB, time=11.47 memory used=1291.7MB, alloc=374.6MB, time=12.10 memory used=1381.0MB, alloc=398.6MB, time=13.35 memory used=1493.0MB, alloc=398.6MB, time=14.52 memory used=1607.2MB, alloc=398.6MB, time=15.92 memory used=1683.2MB, alloc=422.6MB, time=19.33 memory used=1766.3MB, alloc=446.6MB, time=21.29 memory used=1833.2MB, alloc=446.6MB, time=25.16 memory used=1943.7MB, alloc=446.6MB, time=25.55 memory used=2047.4MB, alloc=446.6MB, time=26.66 memory used=2138.9MB, alloc=446.6MB, time=27.10 memory used=2295.7MB, alloc=446.6MB, time=29.71 memory used=2367.4MB, alloc=446.6MB, time=30.01 memory used=2517.5MB, alloc=446.6MB, time=31.20 memory used=2632.3MB, alloc=446.6MB, time=32.04 memory used=2736.2MB, alloc=446.6MB, time=33.01 memory used=2868.6MB, alloc=446.6MB, time=34.32 memory used=3002.0MB, alloc=446.6MB, time=35.81 memory used=3106.9MB, alloc=446.6MB, time=36.49 memory used=3238.9MB, alloc=446.6MB, time=37.79 memory used=3329.8MB, alloc=470.6MB, time=38.85 memory used=3420.7MB, alloc=470.6MB, time=40.28 memory used=3545.4MB, alloc=470.6MB, time=41.15 memory used=3650.4MB, alloc=470.6MB, time=41.81 memory used=3754.9MB, alloc=470.6MB, time=42.37 memory used=3856.1MB, alloc=470.6MB, time=43.35 memory used=3958.5MB, alloc=470.6MB, time=43.89 memory used=4058.1MB, alloc=470.6MB, time=45.17 memory used=4135.6MB, alloc=470.6MB, time=46.18 memory used=4253.3MB, alloc=470.6MB, time=47.62 memory used=4365.5MB, alloc=470.6MB, time=48.69 memory used=4445.4MB, alloc=470.6MB, time=49.89 memory used=4500.1MB, alloc=494.6MB, time=50.82 memory used=4546.9MB, alloc=494.6MB, time=51.77 memory used=4601.9MB, alloc=494.6MB, time=52.70 memory used=4664.4MB, alloc=494.6MB, time=53.84 memory used=4713.5MB, alloc=494.6MB, time=54.71 memory used=4833.5MB, alloc=494.6MB, time=55.85 memory used=4923.2MB, alloc=494.6MB, time=56.84 memory used=4974.3MB, alloc=494.6MB, time=57.78 memory used=5022.7MB, alloc=494.6MB, time=58.81 memory used=5109.7MB, alloc=494.6MB, time=59.69 memory used=5302.8MB, alloc=518.6MB, time=62.38 memory used=5434.6MB, alloc=542.6MB, time=63.44 memory used=5588.0MB, alloc=542.6MB, time=65.00 memory used=5738.1MB, alloc=542.6MB, time=67.60 memory used=5843.8MB, alloc=542.6MB, time=68.13 memory used=6065.7MB, alloc=566.6MB, time=70.63 memory used=6204.2MB, alloc=566.6MB, time=71.40 memory used=6334.3MB, alloc=566.6MB, time=72.32 memory used=6522.5MB, alloc=566.6MB, time=74.02 memory used=6662.5MB, alloc=566.6MB, time=75.09 memory used=6868.9MB, alloc=566.6MB, time=76.89 memory used=7051.3MB, alloc=566.6MB, time=79.37 memory used=7274.7MB, alloc=590.6MB, time=82.04 memory used=7444.8MB, alloc=590.6MB, time=83.53 memory used=7598.4MB, alloc=590.6MB, time=85.60 memory used=7787.0MB, alloc=590.6MB, time=87.50 memory used=7934.9MB, alloc=590.6MB, time=88.68 memory used=8184.1MB, alloc=590.6MB, time=91.58 memory used=8382.5MB, alloc=590.6MB, time=94.18 memory used=8541.4MB, alloc=614.6MB, time=97.04 memory used=8775.2MB, alloc=614.6MB, time=99.61 memory used=8888.3MB, alloc=614.6MB, time=101.78 memory used=9010.2MB, alloc=614.6MB, time=104.08 memory used=9111.9MB, alloc=638.6MB, time=106.15 memory used=9261.8MB, alloc=638.6MB, time=108.22 memory used=9427.9MB, alloc=638.6MB, time=109.28 memory used=9602.2MB, alloc=638.6MB, time=112.33 memory used=9791.9MB, alloc=638.6MB, time=114.24 memory used=9914.9MB, alloc=638.6MB, time=116.83 memory used=10110.3MB, alloc=638.6MB, time=119.36 memory used=10301.9MB, alloc=638.6MB, time=124.59 memory used=10429.4MB, alloc=638.6MB, time=127.01 memory used=10573.1MB, alloc=662.6MB, time=127.97 memory used=10721.4MB, alloc=662.6MB, time=128.83 memory used=10885.5MB, alloc=662.6MB, time=129.94 memory used=11033.7MB, alloc=662.6MB, time=130.81 memory used=11209.6MB, alloc=662.6MB, time=132.55 memory used=11353.5MB, alloc=662.6MB, time=133.37 memory used=11471.5MB, alloc=662.6MB, time=135.20 memory used=11758.1MB, alloc=662.6MB, time=138.68 memory used=11896.4MB, alloc=662.6MB, time=139.64 memory used=12067.0MB, alloc=662.6MB, time=140.79 memory used=12230.0MB, alloc=662.6MB, time=141.93 memory used=12406.2MB, alloc=662.6MB, time=147.51 memory used=12549.5MB, alloc=662.6MB, time=148.51 memory used=12686.4MB, alloc=662.6MB, time=149.47 memory used=12938.8MB, alloc=662.6MB, time=150.66 memory used=13384.2MB, alloc=686.6MB, time=155.02 memory used=13590.2MB, alloc=686.6MB, time=156.78 memory used=13993.4MB, alloc=710.6MB, time=163.19 memory used=14350.1MB, alloc=734.6MB, time=168.34 memory used=14685.3MB, alloc=758.6MB, time=172.78 memory used=14943.4MB, alloc=782.6MB, time=174.92 memory used=15153.8MB, alloc=782.6MB, time=176.42 memory used=15369.9MB, alloc=782.6MB, time=183.72 memory used=15588.2MB, alloc=782.6MB, time=189.15 memory used=15792.6MB, alloc=782.6MB, time=190.43 memory used=15947.1MB, alloc=782.6MB, time=191.60 memory used=16136.4MB, alloc=782.6MB, time=192.78 memory used=16369.8MB, alloc=782.6MB, time=193.98 memory used=16485.7MB, alloc=782.6MB, time=195.11 memory used=16853.2MB, alloc=782.6MB, time=198.33 memory used=17071.0MB, alloc=782.6MB, time=199.83 memory used=17270.1MB, alloc=782.6MB, time=201.17 memory used=17499.2MB, alloc=782.6MB, time=203.71 memory used=17831.9MB, alloc=782.6MB, time=206.78 memory used=18172.4MB, alloc=806.6MB, time=212.19 |\^/| 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(); 1428298734 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 F := [-20 x z + 16 x y + 6 x z - 9 x, -8 x y + 9 x - 20 x y + 6 x, 2 2 2 -10 x z - 17 x z + 12 x y + 5] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 4 2 G := [17 x z + 11 y z - 10 y z + 15 x y, 17 x + 8 y - 4 y , 2 2 2 2 2 -6 x z + 5 x y z - 16 x - 16 z ] > Problem := [F,G]; 3 2 2 3 2 Problem := [[-20 x z + 16 x y + 6 x z - 9 x, -8 x y + 9 x - 20 x y + 6 x, 2 2 2 3 3 2 -10 x z - 17 x z + 12 x y + 5], [17 x z + 11 y z - 10 y z + 15 x y, 4 4 2 2 2 2 2 2 17 x + 8 y - 4 y , -6 x z + 5 x y z - 16 x - 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=0.52 memory used=46.7MB, alloc=56.3MB, time=0.83 memory used=88.8MB, alloc=60.3MB, time=1.44 memory used=133.5MB, alloc=68.3MB, time=2.04 memory used=174.7MB, alloc=92.3MB, time=2.65 memory used=242.3MB, alloc=92.3MB, time=3.56 memory used=313.2MB, alloc=372.3MB, time=4.49 memory used=407.1MB, alloc=372.3MB, time=5.77 memory used=499.9MB, alloc=396.3MB, time=6.99 memory used=616.6MB, alloc=396.3MB, time=8.47 memory used=721.2MB, alloc=396.3MB, time=9.63 memory used=781.4MB, alloc=396.3MB, time=10.13 memory used=834.2MB, alloc=396.3MB, time=10.39 memory used=889.9MB, alloc=396.3MB, time=10.85 memory used=944.5MB, alloc=396.3MB, time=11.28 memory used=1002.1MB, alloc=396.3MB, time=11.75 memory used=1057.4MB, alloc=396.3MB, time=11.96 memory used=1110.7MB, alloc=396.3MB, time=12.52 memory used=1163.3MB, alloc=396.3MB, time=12.79 memory used=1217.7MB, alloc=396.3MB, time=13.30 memory used=1269.8MB, alloc=396.3MB, time=13.54 memory used=1327.4MB, alloc=396.3MB, time=13.99 memory used=1400.0MB, alloc=396.3MB, time=14.62 memory used=1452.5MB, alloc=396.3MB, time=15.16 memory used=1529.6MB, alloc=396.3MB, time=16.20 memory used=1588.4MB, alloc=396.3MB, time=16.65 memory used=1637.2MB, alloc=396.3MB, time=17.01 memory used=1694.3MB, alloc=396.3MB, time=17.59 memory used=1748.8MB, alloc=396.3MB, time=17.80 memory used=1804.2MB, alloc=396.3MB, time=18.00 memory used=1898.6MB, alloc=420.3MB, time=19.24 memory used=2031.6MB, alloc=444.3MB, time=21.03 memory used=2172.0MB, alloc=444.3MB, time=22.92 memory used=2289.7MB, alloc=444.3MB, time=24.49 memory used=2390.5MB, alloc=444.3MB, time=25.93 memory used=2491.5MB, alloc=468.3MB, time=27.37 memory used=2587.6MB, alloc=468.3MB, time=29.02 memory used=2680.8MB, alloc=468.3MB, time=30.43 memory used=2800.1MB, alloc=468.3MB, time=31.55 memory used=2882.6MB, alloc=468.3MB, time=31.98 memory used=3018.5MB, alloc=468.3MB, time=33.28 memory used=3094.8MB, alloc=468.3MB, time=34.27 memory used=3196.5MB, alloc=492.3MB, time=35.82 memory used=3316.4MB, alloc=492.3MB, time=36.95 memory used=3404.0MB, alloc=492.3MB, time=38.04 memory used=3507.4MB, alloc=492.3MB, time=39.45 memory used=3579.4MB, alloc=492.3MB, time=40.80 memory used=3643.5MB, alloc=492.3MB, time=42.02 memory used=3703.5MB, alloc=492.3MB, time=43.21 memory used=3752.5MB, alloc=492.3MB, time=44.13 memory used=3811.1MB, alloc=492.3MB, time=45.39 memory used=3995.0MB, alloc=516.3MB, time=48.26 memory used=4116.6MB, alloc=540.3MB, time=49.39 memory used=4237.1MB, alloc=540.3MB, time=50.32 memory used=4398.6MB, alloc=540.3MB, time=51.80 memory used=4564.2MB, alloc=540.3MB, time=53.89 memory used=4771.8MB, alloc=540.3MB, time=55.89 memory used=5021.8MB, alloc=540.3MB, time=60.27 memory used=5263.6MB, alloc=540.3MB, time=62.83 memory used=5517.1MB, alloc=564.3MB, time=66.51 memory used=5787.2MB, alloc=564.3MB, time=70.98 memory used=5957.8MB, alloc=564.3MB, time=72.49 memory used=6090.6MB, alloc=564.3MB, time=73.72 memory used=6296.5MB, alloc=564.3MB, time=76.27 memory used=6556.8MB, alloc=588.3MB, time=79.06 memory used=6811.4MB, alloc=588.3MB, time=82.63 memory used=6972.3MB, alloc=612.3MB, time=85.36 memory used=7129.7MB, alloc=636.3MB, time=88.09 memory used=7268.5MB, alloc=636.3MB, time=90.54 memory used=7391.2MB, alloc=636.3MB, time=92.74 memory used=7535.6MB, alloc=636.3MB, time=94.85 memory used=7719.3MB, alloc=660.3MB, time=96.45 memory used=7931.4MB, alloc=660.3MB, time=98.46 memory used=8143.1MB, alloc=660.3MB, time=100.50 memory used=8382.1MB, alloc=660.3MB, time=103.06 memory used=8504.8MB, alloc=660.3MB, time=105.61 memory used=8603.4MB, alloc=684.3MB, time=107.56 memory used=8800.3MB, alloc=684.3MB, time=110.17 memory used=8939.5MB, alloc=684.3MB, time=112.09 memory used=9273.0MB, alloc=708.3MB, time=118.94 memory used=9663.4MB, alloc=732.3MB, time=124.38 memory used=10054.0MB, alloc=756.3MB, time=131.65 memory used=10445.2MB, alloc=780.3MB, time=138.84 memory used=10794.3MB, alloc=804.3MB, time=143.94 memory used=11172.3MB, alloc=828.3MB, time=151.46 memory used=11553.0MB, alloc=852.3MB, time=157.83 memory used=11923.6MB, alloc=876.3MB, time=162.74 memory used=12164.4MB, alloc=900.3MB, time=164.92 memory used=12418.4MB, alloc=924.3MB, time=167.55 memory used=12707.0MB, alloc=948.3MB, time=170.19 memory used=12994.7MB, alloc=948.3MB, time=172.80 memory used=13264.3MB, alloc=948.3MB, time=174.70 memory used=13546.5MB, alloc=948.3MB, time=177.39 memory used=13817.1MB, alloc=948.3MB, time=179.38 memory used=14091.4MB, alloc=948.3MB, time=181.92 memory used=14375.2MB, alloc=972.3MB, time=184.01 memory used=14650.8MB, alloc=972.3MB, time=187.34 memory used=14968.8MB, alloc=972.3MB, time=189.59 memory used=15456.0MB, alloc=972.3MB, time=195.97 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428299034 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 3 2 F := [-9 x y + 12 y - 4 y z + 18 z, 3 y z + 2 y z - 12 x z - 3 y, 4 2 16 y + 8 x z + x y + 8 x z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 G := [-17 x z - 3 y z + 9 x y - 16 y , 14 x y + 18 y + 14 y z - 18 z , 4 2 2 2 17 x - 13 y z - 20 y z + 6 z ] > Problem := [F,G]; 2 3 2 2 2 3 2 Problem := [[-9 x y + 12 y - 4 y z + 18 z, 3 y z + 2 y z - 12 x z - 3 y, 4 2 3 2 2 2 16 y + 8 x z + x y + 8 x z], [-17 x z - 3 y z + 9 x y - 16 y , 2 2 4 2 2 2 14 x y + 18 y + 14 y z - 18 z , 17 x - 13 y z - 20 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=4.4MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=45.3MB, alloc=56.3MB, time=0.80 memory used=85.0MB, alloc=63.1MB, time=1.03 memory used=120.2MB, alloc=63.2MB, time=1.15 memory used=154.5MB, alloc=63.2MB, time=1.74 memory used=189.8MB, alloc=63.5MB, time=1.86 memory used=225.9MB, alloc=63.5MB, time=2.23 memory used=260.5MB, alloc=63.5MB, time=2.66 memory used=303.5MB, alloc=63.5MB, time=3.41 memory used=345.1MB, alloc=63.5MB, time=3.81 memory used=383.6MB, alloc=63.5MB, time=4.31 memory used=427.4MB, alloc=71.5MB, time=4.83 memory used=459.2MB, alloc=71.5MB, time=5.24 memory used=487.8MB, alloc=71.5MB, time=5.35 memory used=504.9MB, alloc=71.5MB, time=5.42 memory used=525.2MB, alloc=71.5MB, time=5.50 memory used=548.8MB, alloc=71.5MB, time=5.58 memory used=572.9MB, alloc=95.5MB, time=5.68 memory used=601.5MB, alloc=95.5MB, time=5.78 memory used=634.0MB, alloc=95.5MB, time=5.89 memory used=670.9MB, alloc=95.5MB, time=6.00 memory used=713.9MB, alloc=95.5MB, time=6.10 memory used=757.7MB, alloc=95.5MB, time=6.21 memory used=798.1MB, alloc=95.5MB, time=6.51 memory used=838.9MB, alloc=95.5MB, time=6.64 memory used=881.5MB, alloc=95.5MB, time=6.77 memory used=918.8MB, alloc=95.5MB, time=6.87 memory used=949.6MB, alloc=95.5MB, time=6.98 memory used=985.0MB, alloc=95.5MB, time=7.10 memory used=1025.8MB, alloc=95.5MB, time=7.20 memory used=1072.9MB, alloc=95.5MB, time=7.32 memory used=1104.9MB, alloc=95.5MB, time=7.40 memory used=1161.3MB, alloc=95.5MB, time=10.96 memory used=1199.7MB, alloc=95.5MB, time=11.07 memory used=1238.2MB, alloc=95.5MB, time=11.17 memory used=1281.3MB, alloc=95.5MB, time=11.27 memory used=1310.2MB, alloc=95.5MB, time=11.34 memory used=1344.3MB, alloc=95.5MB, time=11.41 memory used=1388.4MB, alloc=95.5MB, time=11.62 memory used=1434.0MB, alloc=95.5MB, time=12.00 memory used=1492.9MB, alloc=95.5MB, time=12.36 memory used=1530.6MB, alloc=95.5MB, time=12.48 memory used=1576.3MB, alloc=95.5MB, time=12.60 memory used=1607.5MB, alloc=95.5MB, time=12.69 memory used=1641.5MB, alloc=95.5MB, time=12.79 memory used=1702.7MB, alloc=95.5MB, time=20.96 memory used=1753.9MB, alloc=95.5MB, time=21.63 memory used=1791.1MB, alloc=95.5MB, time=21.74 memory used=1826.5MB, alloc=95.5MB, time=21.83 memory used=1870.7MB, alloc=95.5MB, time=21.93 memory used=1907.0MB, alloc=95.5MB, time=22.03 memory used=1935.9MB, alloc=95.5MB, time=22.10 memory used=1967.5MB, alloc=95.5MB, time=22.18 memory used=2002.1MB, alloc=95.5MB, time=22.26 memory used=2041.1MB, alloc=95.5MB, time=22.34 memory used=2087.1MB, alloc=95.5MB, time=22.55 memory used=2133.8MB, alloc=95.5MB, time=22.96 memory used=2170.3MB, alloc=95.5MB, time=23.07 memory used=2232.2MB, alloc=95.5MB, time=23.90 memory used=2303.2MB, alloc=95.5MB, time=25.75 memory used=2342.7MB, alloc=95.5MB, time=25.86 memory used=2374.5MB, alloc=95.5MB, time=25.95 memory used=2414.9MB, alloc=95.5MB, time=26.07 memory used=2455.8MB, alloc=95.5MB, time=26.15 memory used=2483.4MB, alloc=95.5MB, time=26.23 memory used=2514.0MB, alloc=95.5MB, time=26.30 memory used=2548.6MB, alloc=95.5MB, time=26.38 memory used=2588.7MB, alloc=95.5MB, time=26.46 memory used=2680.3MB, alloc=95.5MB, time=27.18 memory used=2757.3MB, alloc=95.5MB, time=27.66 memory used=2836.6MB, alloc=95.5MB, time=28.35 memory used=2915.4MB, alloc=95.5MB, time=29.44 memory used=2993.2MB, alloc=95.5MB, time=31.23 memory used=3071.0MB, alloc=95.5MB, time=33.23 memory used=3149.6MB, alloc=95.5MB, time=35.37 memory used=3229.7MB, alloc=95.5MB, time=38.02 memory used=3311.5MB, alloc=95.5MB, time=40.73 memory used=3356.9MB, alloc=95.5MB, time=41.10 memory used=3417.2MB, alloc=95.5MB, time=41.70 memory used=3474.3MB, alloc=95.5MB, time=43.35 memory used=3510.7MB, alloc=95.5MB, time=43.46 memory used=3541.1MB, alloc=95.5MB, time=43.57 memory used=3579.7MB, alloc=95.5MB, time=43.67 memory used=3617.1MB, alloc=95.5MB, time=43.77 memory used=3642.6MB, alloc=95.5MB, time=43.84 memory used=3671.1MB, alloc=95.5MB, time=43.92 memory used=3702.1MB, alloc=95.5MB, time=44.00 memory used=3737.1MB, alloc=95.5MB, time=44.08 memory used=3781.7MB, alloc=95.5MB, time=44.22 memory used=3863.5MB, alloc=95.5MB, time=44.98 memory used=3929.2MB, alloc=95.5MB, time=45.83 memory used=3983.9MB, alloc=119.5MB, time=46.36 memory used=4047.7MB, alloc=119.5MB, time=48.22 memory used=4092.3MB, alloc=119.5MB, time=48.36 memory used=4139.8MB, alloc=119.5MB, time=48.50 memory used=4189.1MB, alloc=119.5MB, time=48.62 memory used=4224.0MB, alloc=119.5MB, time=48.74 memory used=4264.7MB, alloc=119.5MB, time=48.84 memory used=4331.5MB, alloc=119.5MB, time=49.24 memory used=4379.6MB, alloc=119.5MB, time=49.41 memory used=4424.5MB, alloc=119.5MB, time=49.55 memory used=4479.6MB, alloc=119.5MB, time=49.72 memory used=4512.8MB, alloc=119.5MB, time=49.84 memory used=4548.9MB, alloc=119.5MB, time=49.95 memory used=4589.6MB, alloc=119.5MB, time=50.08 memory used=4635.6MB, alloc=119.5MB, time=50.22 memory used=4687.8MB, alloc=119.5MB, time=50.35 memory used=4775.9MB, alloc=119.5MB, time=62.90 memory used=4822.9MB, alloc=119.5MB, time=63.06 memory used=4862.0MB, alloc=119.5MB, time=63.19 memory used=4902.6MB, alloc=119.5MB, time=63.32 memory used=4950.3MB, alloc=119.5MB, time=63.45 memory used=5005.7MB, alloc=119.5MB, time=63.58 memory used=5038.9MB, alloc=119.5MB, time=63.70 memory used=5071.6MB, alloc=119.5MB, time=63.81 memory used=5107.4MB, alloc=119.5MB, time=63.91 memory used=5144.9MB, alloc=119.5MB, time=64.01 memory used=5185.9MB, alloc=119.5MB, time=64.12 memory used=5229.2MB, alloc=119.5MB, time=64.22 memory used=5276.2MB, alloc=119.5MB, time=64.33 memory used=5326.2MB, alloc=119.5MB, time=64.45 memory used=5380.7MB, alloc=119.5MB, time=64.55 memory used=5401.3MB, alloc=131.8MB, time=64.65 memory used=5412.0MB, alloc=131.8MB, time=64.73 memory used=5422.8MB, alloc=131.8MB, time=64.80 memory used=5434.2MB, alloc=131.8MB, time=64.87 memory used=5446.0MB, alloc=131.8MB, time=64.94 memory used=5510.4MB, alloc=131.8MB, time=65.48 memory used=5552.9MB, alloc=131.8MB, time=65.61 memory used=5596.7MB, alloc=131.8MB, time=65.72 memory used=5681.6MB, alloc=387.8MB, time=66.58 memory used=5758.7MB, alloc=387.8MB, time=68.57 memory used=5800.9MB, alloc=387.8MB, time=68.72 memory used=5840.2MB, alloc=387.8MB, time=68.85 memory used=5890.0MB, alloc=387.8MB, time=68.99 memory used=5928.2MB, alloc=387.8MB, time=69.12 memory used=5960.6MB, alloc=387.8MB, time=69.23 memory used=5996.6MB, alloc=387.8MB, time=69.34 memory used=6036.4MB, alloc=387.8MB, time=69.45 memory used=6080.3MB, alloc=387.8MB, time=69.57 memory used=6131.3MB, alloc=387.8MB, time=69.69 memory used=6230.3MB, alloc=387.8MB, time=72.05 memory used=6274.8MB, alloc=387.8MB, time=72.22 memory used=6309.8MB, alloc=387.8MB, time=72.35 memory used=6354.8MB, alloc=387.8MB, time=72.50 memory used=6401.2MB, alloc=387.8MB, time=72.64 memory used=6431.6MB, alloc=387.8MB, time=72.75 memory used=6465.9MB, alloc=387.8MB, time=72.86 memory used=6503.4MB, alloc=387.8MB, time=72.97 memory used=6544.4MB, alloc=387.8MB, time=73.07 memory used=6591.5MB, alloc=387.8MB, time=73.19 memory used=6692.6MB, alloc=387.8MB, time=73.89 memory used=6772.2MB, alloc=387.8MB, time=75.80 memory used=6830.2MB, alloc=387.8MB, time=85.10 memory used=6881.2MB, alloc=387.8MB, time=86.00 memory used=6926.2MB, alloc=387.8MB, time=86.16 memory used=6976.2MB, alloc=387.8MB, time=87.66 memory used=7018.9MB, alloc=387.8MB, time=87.93 memory used=7054.9MB, alloc=387.8MB, time=88.06 memory used=7115.3MB, alloc=387.8MB, time=97.62 memory used=7163.7MB, alloc=387.8MB, time=98.10 memory used=7202.7MB, alloc=387.8MB, time=98.27 memory used=7237.0MB, alloc=387.8MB, time=98.40 memory used=7271.4MB, alloc=387.8MB, time=98.52 memory used=7315.1MB, alloc=387.8MB, time=98.65 memory used=7414.0MB, alloc=387.8MB, time=99.80 memory used=7466.9MB, alloc=387.8MB, time=100.33 memory used=7512.5MB, alloc=387.8MB, time=100.61 memory used=7583.7MB, alloc=387.8MB, time=101.23 memory used=7658.4MB, alloc=411.8MB, time=102.37 memory used=7760.0MB, alloc=411.8MB, time=103.39 memory used=7823.1MB, alloc=411.8MB, time=104.23 memory used=7888.0MB, alloc=411.8MB, time=104.99 memory used=7952.5MB, alloc=411.8MB, time=105.36 memory used=8018.6MB, alloc=411.8MB, time=107.97 memory used=8065.2MB, alloc=411.8MB, time=108.15 memory used=8168.7MB, alloc=435.8MB, time=109.41 memory used=8296.7MB, alloc=459.8MB, time=110.91 memory used=8415.0MB, alloc=459.8MB, time=112.13 memory used=8546.5MB, alloc=483.8MB, time=114.08 memory used=8687.8MB, alloc=483.8MB, time=116.74 memory used=8823.8MB, alloc=483.8MB, time=119.10 memory used=8974.0MB, alloc=483.8MB, time=122.33 memory used=9111.5MB, alloc=507.8MB, time=123.54 memory used=9234.1MB, alloc=507.8MB, time=125.16 memory used=9385.8MB, alloc=531.8MB, time=126.61 memory used=9483.6MB, alloc=531.8MB, time=127.02 memory used=9598.9MB, alloc=531.8MB, time=127.54 memory used=9695.9MB, alloc=531.8MB, time=127.96 memory used=9820.6MB, alloc=531.8MB, time=131.82 memory used=9917.6MB, alloc=531.8MB, time=132.20 memory used=10018.7MB, alloc=531.8MB, time=132.72 memory used=10138.3MB, alloc=531.8MB, time=133.39 memory used=10232.3MB, alloc=531.8MB, time=133.77 memory used=10349.2MB, alloc=531.8MB, time=134.36 memory used=10471.0MB, alloc=531.8MB, time=138.17 memory used=10576.4MB, alloc=531.8MB, time=138.57 memory used=10661.2MB, alloc=531.8MB, time=138.90 memory used=10793.8MB, alloc=531.8MB, time=139.99 memory used=10902.2MB, alloc=531.8MB, time=140.45 memory used=10984.4MB, alloc=531.8MB, time=140.84 memory used=11076.1MB, alloc=531.8MB, time=141.23 memory used=11185.5MB, alloc=531.8MB, time=141.64 memory used=11288.0MB, alloc=531.8MB, time=142.01 memory used=11359.0MB, alloc=531.8MB, time=142.34 memory used=11438.4MB, alloc=531.8MB, time=142.66 memory used=11528.9MB, alloc=531.8MB, time=143.00 memory used=11662.2MB, alloc=531.8MB, time=160.03 memory used=11758.5MB, alloc=531.8MB, time=160.42 memory used=11863.5MB, alloc=531.8MB, time=160.80 memory used=11940.9MB, alloc=531.8MB, time=161.11 memory used=12033.3MB, alloc=531.8MB, time=161.44 memory used=12145.0MB, alloc=531.8MB, time=161.80 memory used=12326.3MB, alloc=531.8MB, time=162.77 memory used=12462.4MB, alloc=531.8MB, time=163.53 memory used=12611.3MB, alloc=531.8MB, time=172.89 memory used=12710.6MB, alloc=531.8MB, time=173.28 memory used=12796.6MB, alloc=531.8MB, time=173.61 memory used=12889.9MB, alloc=531.8MB, time=173.94 memory used=13036.0MB, alloc=531.8MB, time=178.32 memory used=13134.9MB, alloc=531.8MB, time=178.71 memory used=13219.1MB, alloc=531.8MB, time=179.02 memory used=13349.1MB, alloc=531.8MB, time=179.62 memory used=13490.8MB, alloc=531.8MB, time=188.67 memory used=13593.1MB, alloc=531.8MB, time=189.05 memory used=13674.0MB, alloc=531.8MB, time=189.38 memory used=13769.7MB, alloc=531.8MB, time=189.70 memory used=13891.1MB, alloc=531.8MB, time=190.49 memory used=14013.2MB, alloc=531.8MB, time=191.17 memory used=14101.8MB, alloc=531.8MB, time=191.56 memory used=14230.8MB, alloc=531.8MB, time=192.30 memory used=14334.2MB, alloc=531.8MB, time=192.71 memory used=14419.1MB, alloc=531.8MB, time=193.08 memory used=14558.5MB, alloc=555.8MB, time=218.01 memory used=14715.6MB, alloc=555.8MB, time=253.39 memory used=14826.7MB, alloc=555.8MB, time=253.83 memory used=14945.0MB, alloc=555.8MB, time=254.25 memory used=15057.0MB, alloc=555.8MB, time=254.67 memory used=15143.9MB, alloc=555.8MB, time=255.03 memory used=15243.0MB, alloc=555.8MB, time=255.37 memory used=15353.1MB, alloc=555.8MB, time=255.74 memory used=15475.6MB, alloc=555.8MB, time=256.11 memory used=15613.5MB, alloc=555.8MB, time=256.49 memory used=15821.3MB, alloc=555.8MB, time=257.11 memory used=15976.3MB, alloc=555.8MB, time=257.57 memory used=16154.6MB, alloc=555.8MB, time=258.03 memory used=16378.4MB, alloc=555.8MB, time=260.30 memory used=16512.7MB, alloc=555.8MB, time=260.83 memory used=16609.4MB, alloc=555.8MB, time=261.25 memory used=16701.1MB, alloc=555.8MB, time=261.67 memory used=16803.8MB, alloc=555.8MB, time=262.08 memory used=16919.6MB, alloc=555.8MB, time=262.52 memory used=17049.2MB, alloc=555.8MB, time=262.94 memory used=17191.0MB, alloc=555.8MB, time=263.40 memory used=17267.5MB, alloc=555.8MB, time=263.73 memory used=17347.1MB, alloc=555.8MB, time=264.08 memory used=17431.1MB, alloc=555.8MB, time=264.43 memory used=17521.9MB, alloc=555.8MB, time=264.80 memory used=17618.2MB, alloc=555.8MB, time=265.15 memory used=17722.1MB, alloc=555.8MB, time=265.53 memory used=17833.8MB, alloc=555.8MB, time=265.90 memory used=17954.3MB, alloc=555.8MB, time=266.27 memory used=18106.5MB, alloc=555.8MB, time=268.33 memory used=18215.9MB, alloc=555.8MB, time=268.84 memory used=18345.6MB, alloc=555.8MB, time=269.35 memory used=18432.7MB, alloc=555.8MB, time=269.81 memory used=18531.5MB, alloc=555.8MB, time=270.25 memory used=18640.5MB, alloc=555.8MB, time=270.70 memory used=18763.2MB, alloc=555.8MB, time=271.15 memory used=18899.4MB, alloc=555.8MB, time=271.62 memory used=19012.2MB, alloc=555.8MB, time=272.01 memory used=19088.9MB, alloc=555.8MB, time=272.32 memory used=19172.8MB, alloc=555.8MB, time=272.65 memory used=19260.5MB, alloc=555.8MB, time=273.00 memory used=19354.3MB, alloc=555.8MB, time=273.36 |\^/| 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(); 1428299334 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 2 3 3 F := [9 x y - 7 z - 16 x z + 13, 8 x - 9 x y - y z + 17 z , 3 4 2 2 -2 x z + 13 y + 15 x + 12 z ] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 2 4 3 G := [10 y z + 7 x z + 13 x + 20 y , -5 x z - 15 x y + 2 y + 11 y , 3 2 2 4 -13 x y - 5 x z - 2 z - 15 z] > Problem := [F,G]; 2 3 4 2 2 3 3 Problem := [[9 x y - 7 z - 16 x z + 13, 8 x - 9 x y - y z + 17 z , 3 4 2 2 3 2 2 2 -2 x z + 13 y + 15 x + 12 z ], [10 y z + 7 x z + 13 x + 20 y , 3 2 2 4 3 3 2 2 4 -5 x z - 15 x y + 2 y + 11 y , -13 x y - 5 x z - 2 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=0.19 memory used=28.0MB, alloc=34.3MB, time=0.42 memory used=40.5MB, alloc=34.3MB, time=0.46 memory used=57.9MB, alloc=34.3MB, time=0.59 memory used=79.8MB, alloc=34.3MB, time=0.80 memory used=91.0MB, alloc=34.3MB, time=0.84 memory used=102.7MB, alloc=34.3MB, time=0.88 memory used=116.4MB, alloc=34.3MB, time=0.93 memory used=132.3MB, alloc=34.3MB, time=0.97 memory used=141.7MB, alloc=34.3MB, time=1.01 memory used=150.3MB, alloc=34.3MB, time=1.04 memory used=159.7MB, alloc=34.3MB, time=1.07 memory used=170.0MB, alloc=34.3MB, time=1.11 memory used=181.7MB, alloc=34.3MB, time=1.15 memory used=193.6MB, alloc=34.3MB, time=1.18 memory used=206.9MB, alloc=34.3MB, time=1.22 memory used=221.3MB, alloc=34.3MB, time=1.26 memory used=237.1MB, alloc=34.3MB, time=1.30 memory used=246.8MB, alloc=34.3MB, time=1.32 memory used=267.7MB, alloc=34.3MB, time=1.54 memory used=281.3MB, alloc=34.3MB, time=1.59 memory used=292.5MB, alloc=34.3MB, time=1.63 memory used=305.8MB, alloc=34.3MB, time=1.68 memory used=322.2MB, alloc=34.3MB, time=1.73 memory used=333.5MB, alloc=34.3MB, time=1.76 memory used=342.8MB, alloc=34.3MB, time=1.80 memory used=352.4MB, alloc=34.3MB, time=1.83 memory used=362.8MB, alloc=34.3MB, time=1.86 memory used=374.2MB, alloc=34.3MB, time=1.90 memory used=387.0MB, alloc=34.3MB, time=1.93 memory used=400.6MB, alloc=34.3MB, time=1.97 memory used=415.2MB, alloc=34.3MB, time=2.01 memory used=431.3MB, alloc=34.3MB, time=2.04 memory used=440.8MB, alloc=34.3MB, time=2.07 memory used=456.6MB, alloc=34.3MB, time=2.19 memory used=468.8MB, alloc=34.3MB, time=2.25 memory used=484.2MB, alloc=34.3MB, time=2.58 memory used=508.0MB, alloc=58.3MB, time=6.59 memory used=542.7MB, alloc=58.3MB, time=19.95 memory used=591.1MB, alloc=58.3MB, time=22.59 memory used=656.3MB, alloc=58.3MB, time=22.95 memory used=692.9MB, alloc=58.4MB, time=23.06 memory used=717.4MB, alloc=58.4MB, time=23.12 memory used=746.5MB, alloc=58.4MB, time=23.19 memory used=781.9MB, alloc=58.4MB, time=23.27 memory used=803.9MB, alloc=58.4MB, time=23.32 memory used=825.8MB, alloc=58.4MB, time=23.37 memory used=849.6MB, alloc=58.4MB, time=23.43 memory used=875.2MB, alloc=58.4MB, time=23.48 memory used=903.6MB, alloc=58.4MB, time=23.54 memory used=934.6MB, alloc=58.4MB, time=23.60 memory used=967.6MB, alloc=58.4MB, time=23.66 memory used=1004.4MB, alloc=58.4MB, time=23.72 memory used=1029.0MB, alloc=81.9MB, time=23.80 memory used=1042.2MB, alloc=81.9MB, time=23.84 memory used=1055.3MB, alloc=81.9MB, time=23.88 memory used=1069.0MB, alloc=81.9MB, time=23.92 memory used=1083.0MB, alloc=81.9MB, time=23.97 memory used=1097.7MB, alloc=81.9MB, time=24.01 memory used=1113.6MB, alloc=81.9MB, time=24.06 memory used=1130.6MB, alloc=81.9MB, time=24.11 memory used=1185.3MB, alloc=81.9MB, time=24.74 memory used=1216.2MB, alloc=81.9MB, time=24.82 memory used=1241.4MB, alloc=81.9MB, time=24.88 memory used=1276.7MB, alloc=81.9MB, time=25.09 memory used=1312.9MB, alloc=81.9MB, time=25.27 memory used=1343.6MB, alloc=81.9MB, time=25.34 memory used=1379.0MB, alloc=81.9MB, time=25.42 memory used=1408.9MB, alloc=81.9MB, time=25.48 memory used=1448.5MB, alloc=81.9MB, time=26.01 memory used=1496.2MB, alloc=81.9MB, time=30.86 memory used=1522.3MB, alloc=81.9MB, time=42.30 memory used=1552.8MB, alloc=81.9MB, time=54.50 memory used=1585.7MB, alloc=81.9MB, time=73.11 memory used=1627.9MB, alloc=81.9MB, time=93.61 memory used=1668.1MB, alloc=81.9MB, time=95.23 memory used=1701.3MB, alloc=81.9MB, time=95.42 memory used=1734.0MB, alloc=81.9MB, time=95.61 memory used=1759.8MB, alloc=81.9MB, time=95.69 memory used=1782.8MB, alloc=81.9MB, time=95.76 memory used=1804.7MB, alloc=81.9MB, time=95.83 memory used=1830.4MB, alloc=81.9MB, time=95.91 memory used=1860.0MB, alloc=81.9MB, time=95.99 memory used=1889.3MB, alloc=81.9MB, time=96.08 memory used=1906.9MB, alloc=81.9MB, time=96.14 memory used=1924.4MB, alloc=81.9MB, time=96.19 memory used=1942.7MB, alloc=81.9MB, time=96.25 memory used=1962.9MB, alloc=81.9MB, time=96.30 memory used=1983.6MB, alloc=81.9MB, time=96.37 memory used=2004.9MB, alloc=81.9MB, time=96.43 memory used=2028.1MB, alloc=81.9MB, time=96.48 memory used=2051.7MB, alloc=81.9MB, time=96.55 memory used=2077.3MB, alloc=81.9MB, time=96.62 memory used=2103.3MB, alloc=81.9MB, time=96.68 memory used=2131.2MB, alloc=81.9MB, time=96.75 memory used=2161.0MB, alloc=81.9MB, time=96.82 memory used=2191.0MB, alloc=81.9MB, time=96.89 memory used=2227.0MB, alloc=81.9MB, time=96.97 memory used=2240.0MB, alloc=81.9MB, time=97.02 memory used=2250.8MB, alloc=83.8MB, time=97.06 memory used=2262.0MB, alloc=83.8MB, time=97.11 memory used=2273.2MB, alloc=83.8MB, time=97.15 memory used=2285.9MB, alloc=83.8MB, time=97.21 memory used=2298.5MB, alloc=83.8MB, time=97.25 memory used=2311.1MB, alloc=83.8MB, time=97.30 memory used=2323.6MB, alloc=83.8MB, time=97.34 memory used=2336.1MB, alloc=83.8MB, time=97.39 memory used=2349.8MB, alloc=83.8MB, time=97.44 memory used=2363.5MB, alloc=83.8MB, time=97.49 memory used=2377.0MB, alloc=83.8MB, time=97.55 memory used=2391.9MB, alloc=83.8MB, time=97.60 memory used=2406.6MB, alloc=83.8MB, time=97.65 memory used=2421.2MB, alloc=83.8MB, time=97.70 memory used=2436.5MB, alloc=83.8MB, time=97.75 memory used=2451.9MB, alloc=83.8MB, time=97.83 memory used=2467.9MB, alloc=83.8MB, time=97.92 memory used=2484.8MB, alloc=83.8MB, time=97.97 memory used=2502.5MB, alloc=83.8MB, time=98.02 memory used=2520.6MB, alloc=83.8MB, time=98.07 memory used=2539.0MB, alloc=83.8MB, time=98.13 memory used=2558.5MB, alloc=83.8MB, time=98.18 memory used=2578.4MB, alloc=83.8MB, time=98.24 memory used=2599.3MB, alloc=83.8MB, time=98.30 memory used=2623.6MB, alloc=83.8MB, time=98.42 memory used=2654.2MB, alloc=83.8MB, time=98.68 memory used=2679.9MB, alloc=83.8MB, time=98.82 memory used=2708.6MB, alloc=83.8MB, time=98.90 memory used=2735.2MB, alloc=83.8MB, time=98.98 memory used=2774.0MB, alloc=83.8MB, time=99.25 memory used=2803.9MB, alloc=83.8MB, time=99.32 memory used=2837.2MB, alloc=83.8MB, time=99.40 memory used=2874.0MB, alloc=83.8MB, time=99.48 memory used=2914.3MB, alloc=83.8MB, time=99.55 memory used=2958.0MB, alloc=83.8MB, time=99.63 memory used=2983.2MB, alloc=83.8MB, time=99.67 memory used=3039.6MB, alloc=83.8MB, time=100.33 memory used=3085.8MB, alloc=83.8MB, time=100.86 memory used=3132.6MB, alloc=83.8MB, time=102.20 memory used=3160.1MB, alloc=83.8MB, time=102.30 memory used=3179.6MB, alloc=83.8MB, time=102.37 memory used=3202.0MB, alloc=83.8MB, time=102.45 memory used=3228.4MB, alloc=83.8MB, time=102.53 memory used=3259.3MB, alloc=83.8MB, time=102.61 memory used=3277.1MB, alloc=83.8MB, time=102.68 memory used=3294.4MB, alloc=83.8MB, time=102.75 memory used=3313.3MB, alloc=83.8MB, time=102.80 memory used=3332.6MB, alloc=83.8MB, time=102.86 memory used=3353.7MB, alloc=83.8MB, time=102.92 memory used=3376.4MB, alloc=83.8MB, time=102.99 memory used=3400.5MB, alloc=83.8MB, time=103.05 memory used=3425.3MB, alloc=83.8MB, time=103.12 memory used=3452.4MB, alloc=83.8MB, time=103.20 memory used=3481.1MB, alloc=83.8MB, time=103.27 memory used=3510.7MB, alloc=83.8MB, time=103.35 memory used=3545.4MB, alloc=83.8MB, time=103.43 memory used=3554.9MB, alloc=83.8MB, time=103.48 memory used=3565.4MB, alloc=83.8MB, time=103.56 memory used=3575.8MB, alloc=83.8MB, time=103.62 memory used=3586.5MB, alloc=83.8MB, time=103.67 memory used=3597.5MB, alloc=83.8MB, time=103.73 memory used=3609.3MB, alloc=83.8MB, time=103.78 memory used=3621.1MB, alloc=83.8MB, time=103.83 memory used=3633.5MB, alloc=83.8MB, time=103.89 memory used=3646.0MB, alloc=83.8MB, time=103.93 memory used=3659.2MB, alloc=83.8MB, time=103.99 memory used=3672.6MB, alloc=83.8MB, time=104.04 memory used=3686.5MB, alloc=83.8MB, time=104.10 memory used=3701.1MB, alloc=83.8MB, time=104.15 memory used=3757.5MB, alloc=83.8MB, time=106.57 memory used=3788.4MB, alloc=83.8MB, time=106.68 memory used=3811.7MB, alloc=107.8MB, time=106.78 memory used=3842.1MB, alloc=107.8MB, time=106.90 memory used=3873.7MB, alloc=107.8MB, time=107.01 memory used=3910.0MB, alloc=107.8MB, time=107.13 memory used=3949.6MB, alloc=107.8MB, time=107.26 memory used=3992.4MB, alloc=107.8MB, time=107.39 memory used=4038.8MB, alloc=107.8MB, time=107.53 memory used=4070.0MB, alloc=107.8MB, time=107.64 memory used=4095.0MB, alloc=107.8MB, time=107.73 memory used=4117.7MB, alloc=107.8MB, time=107.83 memory used=4140.9MB, alloc=107.8MB, time=107.93 memory used=4164.6MB, alloc=107.8MB, time=108.02 memory used=4188.9MB, alloc=107.8MB, time=108.11 memory used=4213.7MB, alloc=131.8MB, time=108.21 memory used=4255.4MB, alloc=131.8MB, time=108.34 memory used=4301.6MB, alloc=131.8MB, time=108.47 memory used=4349.4MB, alloc=131.8MB, time=108.62 memory used=4398.7MB, alloc=131.8MB, time=108.77 memory used=4449.4MB, alloc=131.8MB, time=108.91 memory used=4501.6MB, alloc=131.8MB, time=109.06 memory used=4556.0MB, alloc=131.8MB, time=109.22 memory used=4617.9MB, alloc=131.8MB, time=109.36 memory used=4682.4MB, alloc=131.8MB, time=109.53 memory used=4748.4MB, alloc=131.8MB, time=109.69 memory used=4816.1MB, alloc=131.8MB, time=109.85 memory used=4873.4MB, alloc=131.8MB, time=109.99 memory used=4905.2MB, alloc=131.8MB, time=110.08 memory used=4931.8MB, alloc=155.8MB, time=110.17 memory used=4971.4MB, alloc=155.8MB, time=110.28 memory used=5015.1MB, alloc=155.8MB, time=110.39 memory used=5060.4MB, alloc=155.8MB, time=110.50 memory used=5106.1MB, alloc=155.8MB, time=110.62 memory used=5152.3MB, alloc=155.8MB, time=110.74 memory used=5199.0MB, alloc=155.8MB, time=110.85 memory used=5246.1MB, alloc=155.8MB, time=110.97 memory used=5293.6MB, alloc=155.8MB, time=111.09 memory used=5341.6MB, alloc=155.8MB, time=111.20 memory used=5390.0MB, alloc=155.8MB, time=111.32 memory used=5439.9MB, alloc=155.8MB, time=111.44 memory used=5497.9MB, alloc=155.8MB, time=111.58 memory used=5557.4MB, alloc=155.8MB, time=111.72 memory used=5617.4MB, alloc=155.8MB, time=111.87 memory used=5677.9MB, alloc=155.8MB, time=112.00 memory used=5738.8MB, alloc=155.8MB, time=112.13 memory used=5800.1MB, alloc=155.8MB, time=112.27 memory used=5861.8MB, alloc=155.8MB, time=112.41 memory used=5923.9MB, alloc=155.8MB, time=112.55 memory used=5986.3MB, alloc=155.8MB, time=112.69 memory used=6049.0MB, alloc=155.8MB, time=112.83 memory used=6112.1MB, alloc=155.8MB, time=112.96 memory used=6176.8MB, alloc=155.8MB, time=113.10 memory used=6249.6MB, alloc=155.8MB, time=113.24 memory used=6324.0MB, alloc=155.8MB, time=113.39 memory used=6398.6MB, alloc=155.8MB, time=113.53 memory used=6473.5MB, alloc=155.8MB, time=113.67 memory used=6548.5MB, alloc=155.8MB, time=113.80 memory used=6623.6MB, alloc=155.8MB, time=113.94 memory used=6698.8MB, alloc=155.8MB, time=114.09 memory used=6776.0MB, alloc=155.8MB, time=114.24 memory used=6860.2MB, alloc=155.8MB, time=114.39 memory used=6946.1MB, alloc=155.8MB, time=114.54 memory used=7031.9MB, alloc=155.8MB, time=114.69 memory used=7121.6MB, alloc=155.8MB, time=114.86 memory used=7148.7MB, alloc=155.8MB, time=114.93 memory used=7171.0MB, alloc=155.8MB, time=115.01 memory used=7192.7MB, alloc=155.8MB, time=115.08 memory used=7204.3MB, alloc=155.8MB, time=115.13 memory used=7207.5MB, alloc=411.8MB, time=115.17 memory used=7340.6MB, alloc=411.8MB, time=115.60 memory used=7473.4MB, alloc=411.8MB, time=115.86 memory used=7610.7MB, alloc=411.8MB, time=116.12 memory used=7748.6MB, alloc=411.8MB, time=116.39 memory used=7892.6MB, alloc=411.8MB, time=116.65 memory used=8042.8MB, alloc=411.8MB, time=116.92 memory used=8201.5MB, alloc=411.8MB, time=117.20 memory used=8366.0MB, alloc=411.8MB, time=117.49 memory used=8534.4MB, alloc=411.8MB, time=117.78 memory used=8707.9MB, alloc=411.8MB, time=118.06 memory used=8889.0MB, alloc=411.8MB, time=118.35 memory used=9080.8MB, alloc=411.8MB, time=118.64 memory used=9284.1MB, alloc=411.8MB, time=118.94 memory used=9454.0MB, alloc=411.8MB, time=121.49 memory used=9518.7MB, alloc=411.8MB, time=121.72 memory used=9598.7MB, alloc=411.8MB, time=121.96 memory used=9685.9MB, alloc=411.8MB, time=122.19 memory used=9736.0MB, alloc=411.8MB, time=122.34 memory used=9787.0MB, alloc=411.8MB, time=122.50 memory used=9842.4MB, alloc=411.8MB, time=122.66 memory used=9900.6MB, alloc=411.8MB, time=122.82 memory used=9962.3MB, alloc=411.8MB, time=123.00 memory used=10031.8MB, alloc=411.8MB, time=123.18 memory used=10105.2MB, alloc=411.8MB, time=123.38 memory used=10181.4MB, alloc=411.8MB, time=123.56 memory used=10260.4MB, alloc=411.8MB, time=123.74 memory used=10342.3MB, alloc=411.8MB, time=123.93 memory used=10434.9MB, alloc=411.8MB, time=124.14 memory used=10510.3MB, alloc=411.8MB, time=124.32 memory used=10555.0MB, alloc=411.8MB, time=124.44 memory used=10599.1MB, alloc=411.8MB, time=124.55 memory used=10643.9MB, alloc=411.8MB, time=124.67 memory used=10689.1MB, alloc=411.8MB, time=124.80 memory used=10734.8MB, alloc=411.8MB, time=124.92 memory used=10781.0MB, alloc=411.8MB, time=125.03 memory used=10827.7MB, alloc=411.8MB, time=125.15 memory used=10874.8MB, alloc=411.8MB, time=125.27 memory used=10922.3MB, alloc=411.8MB, time=125.39 memory used=10970.3MB, alloc=411.8MB, time=125.50 memory used=11018.7MB, alloc=411.8MB, time=125.63 memory used=11068.6MB, alloc=411.8MB, time=125.75 memory used=11126.6MB, alloc=411.8MB, time=125.88 memory used=11186.1MB, alloc=411.8MB, time=126.01 memory used=11246.1MB, alloc=411.8MB, time=126.15 memory used=11306.6MB, alloc=411.8MB, time=126.28 memory used=11367.5MB, alloc=411.8MB, time=126.41 memory used=11428.8MB, alloc=411.8MB, time=126.54 memory used=11490.5MB, alloc=411.8MB, time=126.68 memory used=11552.6MB, alloc=411.8MB, time=126.81 memory used=11615.0MB, alloc=411.8MB, time=126.94 memory used=11677.7MB, alloc=411.8MB, time=127.07 memory used=11740.8MB, alloc=411.8MB, time=127.21 memory used=11805.5MB, alloc=411.8MB, time=127.34 memory used=11878.3MB, alloc=411.8MB, time=127.49 memory used=11952.7MB, alloc=411.8MB, time=127.64 memory used=12027.4MB, alloc=411.8MB, time=127.79 memory used=12102.2MB, alloc=411.8MB, time=127.93 memory used=12177.2MB, alloc=411.8MB, time=128.08 memory used=12252.3MB, alloc=411.8MB, time=128.23 memory used=12327.5MB, alloc=411.8MB, time=128.39 memory used=12404.7MB, alloc=411.8MB, time=128.55 memory used=12488.9MB, alloc=411.8MB, time=128.71 memory used=12574.8MB, alloc=411.8MB, time=128.86 memory used=12660.6MB, alloc=411.8MB, time=129.02 memory used=12750.3MB, alloc=411.8MB, time=129.18 memory used=12942.3MB, alloc=411.8MB, time=129.51 memory used=13070.3MB, alloc=411.8MB, time=129.76 memory used=13207.8MB, alloc=411.8MB, time=130.02 memory used=13345.8MB, alloc=411.8MB, time=130.28 memory used=13488.7MB, alloc=411.8MB, time=130.54 memory used=13641.3MB, alloc=411.8MB, time=130.82 memory used=13793.3MB, alloc=411.8MB, time=131.09 memory used=13956.4MB, alloc=411.8MB, time=131.37 memory used=14120.1MB, alloc=411.8MB, time=131.64 memory used=14292.1MB, alloc=411.8MB, time=131.93 memory used=14472.3MB, alloc=411.8MB, time=132.22 memory used=14660.3MB, alloc=411.8MB, time=132.52 memory used=14860.0MB, alloc=411.8MB, time=132.81 memory used=15080.2MB, alloc=411.8MB, time=189.22 memory used=15161.6MB, alloc=411.8MB, time=274.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428299634 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 4 3 2 F := [16 y z + 5 z + 6 x + 13 x, -18 z + 17 x - 6 x y - 14 z , 3 2 4 13 x z - 11 x y z + 4 y + 4 x y z] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [17 y z + 15 x y + 8 y z - 14 z, x y z + 7 y z + 9 x y z - 2 y, 2 2 2 2 2 2 2 -19 x y + 10 x y z + 15 x z + 2 y z ] > Problem := [F,G]; 2 3 2 4 3 2 Problem := [[16 y z + 5 z + 6 x + 13 x, -18 z + 17 x - 6 x y - 14 z , 3 2 4 3 2 13 x z - 11 x y z + 4 y + 4 x y z], [17 y z + 15 x y + 8 y z - 14 z, 2 2 2 x y z + 7 y z + 9 x y z - 2 y, 2 2 2 2 2 2 2 -19 x y + 10 x y z + 15 x z + 2 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.2MB, alloc=44.3MB, time=0.54 memory used=59.4MB, alloc=44.3MB, time=0.88 memory used=98.4MB, alloc=68.3MB, time=1.47 memory used=173.4MB, alloc=80.8MB, time=2.28 memory used=214.3MB, alloc=80.8MB, time=2.44 memory used=255.2MB, alloc=80.8MB, time=2.61 memory used=289.7MB, alloc=80.8MB, time=2.78 memory used=357.5MB, alloc=80.8MB, time=3.42 memory used=387.2MB, alloc=80.8MB, time=3.51 memory used=414.9MB, alloc=80.8MB, time=3.58 memory used=442.5MB, alloc=80.8MB, time=3.66 memory used=488.8MB, alloc=88.1MB, time=3.83 memory used=522.3MB, alloc=88.1MB, time=3.95 memory used=553.6MB, alloc=88.1MB, time=4.04 memory used=579.0MB, alloc=88.1MB, time=4.10 memory used=609.8MB, alloc=88.1MB, time=4.18 memory used=657.8MB, alloc=91.8MB, time=4.44 memory used=687.3MB, alloc=91.8MB, time=4.53 memory used=717.5MB, alloc=91.8MB, time=4.62 memory used=742.5MB, alloc=91.8MB, time=4.68 memory used=774.3MB, alloc=91.8MB, time=4.75 memory used=795.3MB, alloc=91.8MB, time=4.82 memory used=878.7MB, alloc=91.8MB, time=5.87 memory used=910.7MB, alloc=91.8MB, time=5.96 memory used=938.6MB, alloc=91.8MB, time=6.06 memory used=972.1MB, alloc=91.8MB, time=6.14 memory used=1008.4MB, alloc=91.8MB, time=6.24 memory used=1031.5MB, alloc=91.8MB, time=6.32 memory used=1056.2MB, alloc=91.8MB, time=6.40 memory used=1083.6MB, alloc=91.8MB, time=6.47 memory used=1119.7MB, alloc=91.8MB, time=6.60 memory used=1156.2MB, alloc=115.8MB, time=23.96 memory used=1190.4MB, alloc=139.8MB, time=57.49 memory used=1227.1MB, alloc=163.8MB, time=100.11 memory used=1279.2MB, alloc=187.8MB, time=120.68 memory used=1365.7MB, alloc=211.8MB, time=224.81 memory used=1502.1MB, alloc=235.8MB, time=225.27 |\^/| 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(); 1428299934 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 2 F := [-3 x - 11 z + 13 x + 8 x y, -5 x z + 2 x y z - 16 y z , 2 2 11 x y - 3 x z - 4] > G := [ randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=4, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 2 3 G := [6 x y z + 18 z + 17 x y z, -16 x y + 9 x y - 16 z + 5 y, 2 2 3 3 3 19 x y - 2 y z + 6 x - 11 y ] > Problem := [F,G]; 3 3 2 3 2 2 Problem := [[-3 x - 11 z + 13 x + 8 x y, -5 x z + 2 x y z - 16 y z , 2 2 2 4 11 x y - 3 x z - 4], [6 x y z + 18 z + 17 x y z, 2 2 2 3 2 2 3 3 3 -16 x y + 9 x y - 16 z + 5 y, 19 x y - 2 y z + 6 x - 11 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=27.6MB, alloc=32.3MB, time=0.50 memory used=47.6MB, alloc=56.3MB, time=0.80 memory used=89.3MB, alloc=60.3MB, time=1.38 memory used=130.1MB, alloc=60.3MB, time=1.95 memory used=171.4MB, alloc=60.3MB, time=2.44 memory used=208.4MB, alloc=60.3MB, time=2.79 memory used=250.4MB, alloc=84.3MB, time=3.41 memory used=322.2MB, alloc=92.3MB, time=4.28 memory used=366.9MB, alloc=92.3MB, time=4.53 memory used=427.2MB, alloc=92.3MB, time=5.28 memory used=490.1MB, alloc=116.3MB, time=6.13 memory used=555.0MB, alloc=116.3MB, time=6.95 memory used=618.8MB, alloc=372.3MB, time=7.83 memory used=708.6MB, alloc=396.3MB, time=8.97 memory used=827.6MB, alloc=396.3MB, time=10.38 memory used=932.6MB, alloc=420.3MB, time=11.57 memory used=1051.4MB, alloc=420.3MB, time=13.18 memory used=1140.5MB, alloc=420.3MB, time=13.92 memory used=1225.4MB, alloc=420.3MB, time=14.41 memory used=1312.1MB, alloc=420.3MB, time=16.70 memory used=1367.6MB, alloc=420.3MB, time=16.93 memory used=1428.1MB, alloc=420.3MB, time=17.15 memory used=1489.3MB, alloc=420.3MB, time=17.77 memory used=1545.1MB, alloc=420.3MB, time=18.03 memory used=1623.4MB, alloc=420.3MB, time=18.46 memory used=1701.3MB, alloc=420.3MB, time=18.72 memory used=1777.2MB, alloc=420.3MB, time=19.32 memory used=1837.1MB, alloc=420.3MB, time=19.55 memory used=1983.4MB, alloc=420.3MB, time=21.10 memory used=2122.8MB, alloc=444.3MB, time=22.39 memory used=2258.0MB, alloc=444.3MB, time=24.23 memory used=2376.5MB, alloc=444.3MB, time=25.77 memory used=2452.1MB, alloc=444.3MB, time=26.36 memory used=2521.4MB, alloc=444.3MB, time=26.80 memory used=2599.0MB, alloc=444.3MB, time=27.35 memory used=2676.1MB, alloc=468.3MB, time=27.90 memory used=2772.9MB, alloc=468.3MB, time=28.90 memory used=2853.7MB, alloc=468.3MB, time=29.27 memory used=2928.4MB, alloc=468.3MB, time=29.55 memory used=3013.2MB, alloc=468.3MB, time=29.99 memory used=3096.2MB, alloc=468.3MB, time=30.32 memory used=3178.8MB, alloc=468.3MB, time=30.86 memory used=3257.2MB, alloc=468.3MB, time=31.21 memory used=3339.7MB, alloc=468.3MB, time=31.63 memory used=3450.0MB, alloc=468.3MB, time=32.42 memory used=3531.8MB, alloc=468.3MB, time=32.76 memory used=3600.7MB, alloc=468.3MB, time=33.04 memory used=3691.8MB, alloc=468.3MB, time=33.32 memory used=3803.5MB, alloc=468.3MB, time=33.90 memory used=3877.1MB, alloc=468.3MB, time=34.24 memory used=3954.3MB, alloc=468.3MB, time=34.59 memory used=4051.3MB, alloc=468.3MB, time=34.91 memory used=4110.9MB, alloc=468.3MB, time=35.18 memory used=4175.4MB, alloc=468.3MB, time=35.44 memory used=4271.1MB, alloc=468.3MB, time=36.11 memory used=4350.0MB, alloc=468.3MB, time=36.46 memory used=4423.8MB, alloc=468.3MB, time=36.80 memory used=4516.4MB, alloc=468.3MB, time=37.14 memory used=4585.6MB, alloc=468.3MB, time=37.41 memory used=4647.8MB, alloc=468.3MB, time=37.67 memory used=4763.3MB, alloc=468.3MB, time=52.90 memory used=4857.3MB, alloc=468.3MB, time=53.51 memory used=4932.4MB, alloc=468.3MB, time=53.87 memory used=5021.8MB, alloc=468.3MB, time=54.21 memory used=5079.9MB, alloc=468.3MB, time=54.47 memory used=5144.1MB, alloc=468.3MB, time=54.75 memory used=5215.4MB, alloc=468.3MB, time=55.04 memory used=5293.5MB, alloc=468.3MB, time=55.34 memory used=5380.7MB, alloc=468.3MB, time=55.64 memory used=5474.4MB, alloc=468.3MB, time=55.95 memory used=5691.6MB, alloc=468.3MB, time=56.62 memory used=5835.5MB, alloc=468.3MB, time=57.04 memory used=5993.8MB, alloc=468.3MB, time=57.47 memory used=6169.5MB, alloc=468.3MB, time=57.92 memory used=6364.3MB, alloc=468.3MB, time=58.37 memory used=6584.8MB, alloc=468.3MB, time=58.85 memory used=6861.8MB, alloc=468.3MB, time=60.19 memory used=6947.4MB, alloc=468.3MB, time=60.55 memory used=7008.6MB, alloc=468.3MB, time=60.88 memory used=7080.6MB, alloc=468.3MB, time=61.20 memory used=7163.4MB, alloc=468.3MB, time=61.55 memory used=7259.6MB, alloc=468.3MB, time=61.90 memory used=7332.9MB, alloc=468.3MB, time=62.19 memory used=7387.0MB, alloc=468.3MB, time=62.46 memory used=7445.3MB, alloc=468.3MB, time=62.73 memory used=7508.2MB, alloc=468.3MB, time=63.01 memory used=7572.9MB, alloc=468.3MB, time=63.28 memory used=7642.7MB, alloc=468.3MB, time=63.56 memory used=7717.5MB, alloc=468.3MB, time=63.86 memory used=7796.4MB, alloc=468.3MB, time=64.18 memory used=7882.0MB, alloc=468.3MB, time=64.50 memory used=7973.9MB, alloc=468.3MB, time=64.80 memory used=8073.2MB, alloc=468.3MB, time=65.10 memory used=8272.3MB, alloc=468.3MB, time=67.00 memory used=8415.5MB, alloc=468.3MB, time=68.29 memory used=8549.5MB, alloc=468.3MB, time=69.15 memory used=8652.8MB, alloc=468.3MB, time=70.04 memory used=8753.6MB, alloc=468.3MB, time=70.66 memory used=8859.4MB, alloc=468.3MB, time=72.42 memory used=8949.4MB, alloc=468.3MB, time=72.82 memory used=9084.3MB, alloc=468.3MB, time=73.82 memory used=9222.7MB, alloc=468.3MB, time=75.17 memory used=9326.3MB, alloc=492.3MB, time=76.78 memory used=9407.7MB, alloc=492.3MB, time=78.09 memory used=9480.2MB, alloc=492.3MB, time=79.30 memory used=9555.6MB, alloc=492.3MB, time=80.51 memory used=9620.7MB, alloc=492.3MB, time=81.60 memory used=9681.9MB, alloc=492.3MB, time=82.70 memory used=9747.1MB, alloc=492.3MB, time=83.75 memory used=9804.6MB, alloc=492.3MB, time=84.87 memory used=9863.2MB, alloc=492.3MB, time=85.95 memory used=9916.1MB, alloc=492.3MB, time=86.85 memory used=9985.1MB, alloc=516.3MB, time=87.74 memory used=10061.9MB, alloc=516.3MB, time=88.81 memory used=10105.8MB, alloc=516.3MB, time=89.69 memory used=10151.5MB, alloc=516.3MB, time=90.60 memory used=10200.2MB, alloc=516.3MB, time=91.64 memory used=10408.6MB, alloc=540.3MB, time=94.89 memory used=10618.7MB, alloc=564.3MB, time=97.47 memory used=10803.8MB, alloc=564.3MB, time=99.55 memory used=10911.1MB, alloc=564.3MB, time=100.16 memory used=11168.3MB, alloc=564.3MB, time=102.69 memory used=11317.3MB, alloc=564.3MB, time=103.96 memory used=11448.7MB, alloc=564.3MB, time=104.86 memory used=11568.7MB, alloc=588.3MB, time=105.62 memory used=11677.7MB, alloc=588.3MB, time=106.28 memory used=11822.3MB, alloc=588.3MB, time=106.93 memory used=11932.7MB, alloc=588.3MB, time=107.51 memory used=12031.7MB, alloc=588.3MB, time=108.07 memory used=12144.3MB, alloc=588.3MB, time=108.63 memory used=12271.8MB, alloc=588.3MB, time=109.20 memory used=12427.3MB, alloc=588.3MB, time=110.19 memory used=12535.2MB, alloc=588.3MB, time=110.82 memory used=12678.6MB, alloc=588.3MB, time=111.47 memory used=12791.0MB, alloc=588.3MB, time=112.06 memory used=12889.7MB, alloc=588.3MB, time=112.62 memory used=13002.1MB, alloc=588.3MB, time=113.19 memory used=13129.3MB, alloc=588.3MB, time=113.76 memory used=13327.2MB, alloc=588.3MB, time=134.11 memory used=13448.5MB, alloc=588.3MB, time=134.85 memory used=13571.8MB, alloc=588.3MB, time=135.53 memory used=13672.0MB, alloc=588.3MB, time=136.16 memory used=13788.0MB, alloc=588.3MB, time=136.77 memory used=13918.9MB, alloc=588.3MB, time=137.37 memory used=14066.4MB, alloc=588.3MB, time=137.98 memory used=14307.7MB, alloc=588.3MB, time=138.78 memory used=14436.3MB, alloc=588.3MB, time=139.47 memory used=14571.4MB, alloc=588.3MB, time=140.12 memory used=14718.2MB, alloc=588.3MB, time=140.73 memory used=14872.4MB, alloc=588.3MB, time=141.38 memory used=15037.8MB, alloc=588.3MB, time=142.02 memory used=15214.2MB, alloc=588.3MB, time=142.71 memory used=15404.6MB, alloc=588.3MB, time=143.39 memory used=15607.7MB, alloc=588.3MB, time=144.07 memory used=15817.8MB, alloc=588.3MB, time=144.76 memory used=16002.7MB, alloc=588.3MB, time=145.42 memory used=16165.6MB, alloc=588.3MB, time=146.05 memory used=16339.2MB, alloc=588.3MB, time=146.69 memory used=16523.6MB, alloc=588.3MB, time=147.33 memory used=16739.4MB, alloc=588.3MB, time=148.58 memory used=16887.9MB, alloc=588.3MB, time=149.41 memory used=16999.7MB, alloc=588.3MB, time=150.10 memory used=17116.6MB, alloc=588.3MB, time=150.76 memory used=17255.4MB, alloc=588.3MB, time=151.45 memory used=17396.5MB, alloc=588.3MB, time=152.13 memory used=17485.4MB, alloc=588.3MB, time=152.72 memory used=17577.8MB, alloc=588.3MB, time=153.29 memory used=17677.6MB, alloc=588.3MB, time=153.85 memory used=17786.3MB, alloc=588.3MB, time=154.43 memory used=17900.5MB, alloc=588.3MB, time=155.01 memory used=18024.5MB, alloc=588.3MB, time=155.60 memory used=18155.5MB, alloc=588.3MB, time=156.19 memory used=18296.5MB, alloc=588.3MB, time=156.80 memory used=18447.3MB, alloc=588.3MB, time=157.43 memory used=18698.8MB, alloc=588.3MB, time=158.17 memory used=18825.6MB, alloc=588.3MB, time=158.76 memory used=18954.3MB, alloc=588.3MB, time=159.35 memory used=19089.3MB, alloc=588.3MB, time=160.00 memory used=19285.5MB, alloc=588.3MB, time=161.69 memory used=19404.7MB, alloc=588.3MB, time=162.29 memory used=19538.4MB, alloc=588.3MB, time=162.99 memory used=19674.4MB, alloc=588.3MB, time=163.66 memory used=19779.7MB, alloc=588.3MB, time=164.21 memory used=19921.4MB, alloc=588.3MB, time=165.08 memory used=20041.0MB, alloc=588.3MB, time=165.67 memory used=20279.6MB, alloc=588.3MB, time=167.53 memory used=20420.0MB, alloc=588.3MB, time=168.44 memory used=20583.7MB, alloc=588.3MB, time=170.87 memory used=20701.0MB, alloc=588.3MB, time=171.46 memory used=20948.0MB, alloc=588.3MB, time=174.68 memory used=21153.2MB, alloc=588.3MB, time=177.81 memory used=21334.2MB, alloc=588.3MB, time=179.24 memory used=21574.2MB, alloc=612.3MB, time=183.24 memory used=21710.2MB, alloc=612.3MB, time=183.98 memory used=21936.2MB, alloc=612.3MB, time=185.79 memory used=22108.1MB, alloc=636.3MB, time=188.65 memory used=22250.0MB, alloc=636.3MB, time=190.87 memory used=22400.0MB, alloc=636.3MB, time=193.45 memory used=22534.3MB, alloc=660.3MB, time=195.91 memory used=22668.2MB, alloc=660.3MB, time=197.95 memory used=22802.4MB, alloc=684.3MB, time=199.88 memory used=22924.7MB, alloc=684.3MB, time=202.58 memory used=23026.0MB, alloc=684.3MB, time=204.60 memory used=23382.9MB, alloc=708.3MB, time=209.59 memory used=23777.6MB, alloc=732.3MB, time=214.34 memory used=24147.2MB, alloc=756.3MB, time=219.74 memory used=24542.8MB, alloc=780.3MB, time=225.38 memory used=24883.8MB, alloc=804.3MB, time=230.36 memory used=25212.3MB, alloc=828.3MB, time=234.66 memory used=25572.5MB, alloc=852.3MB, time=239.70 memory used=25805.8MB, alloc=876.3MB, time=241.52 memory used=26022.7MB, alloc=900.3MB, time=243.41 memory used=26298.0MB, alloc=924.3MB, time=245.93 memory used=26533.4MB, alloc=948.3MB, time=247.62 memory used=26759.8MB, alloc=972.3MB, time=249.33 memory used=27063.7MB, alloc=972.3MB, time=250.96 memory used=27319.1MB, alloc=972.3MB, time=252.55 memory used=27531.5MB, alloc=972.3MB, time=254.03 memory used=27779.0MB, alloc=972.3MB, time=255.57 memory used=28224.0MB, alloc=987.8MB, time=257.81 memory used=28695.2MB, alloc=987.8MB, time=299.32 memory used=28977.8MB, alloc=987.8MB, time=300.75 memory used=29193.8MB, alloc=987.8MB, time=301.98 memory used=29472.2MB, alloc=987.8MB, time=303.22 memory used=29742.2MB, alloc=987.8MB, time=304.45 memory used=30093.9MB, alloc=987.8MB, time=308.01 memory used=30444.4MB, alloc=1243.8MB, time=311.42 memory used=31134.6MB, alloc=1267.8MB, time=317.57 memory used=31786.4MB, alloc=1291.8MB, time=324.05 memory used=32208.2MB, alloc=1315.8MB, time=327.83