|\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428239576 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [17 x z - y - 10, 9 z + 7 y + 2 z, -14 x + 13 x y - 4 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [4 x z - 3 y + 7, 13 x + 9 x - 17 y, 16 x z - 20 y z + 14 y] > Problem := [F,G]; 2 2 2 Problem := [[17 x z - y - 10, 9 z + 7 y + 2 z, -14 x + 13 x y - 4 y z], 2 [4 x z - 3 y + 7, 13 x + 9 x - 17 y, 16 x z - 20 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.54 memory used=47.0MB, alloc=32.3MB, time=0.86 memory used=66.2MB, alloc=56.3MB, time=1.17 memory used=106.9MB, alloc=60.3MB, time=1.79 memory used=146.3MB, alloc=84.3MB, time=2.42 memory used=208.5MB, alloc=92.3MB, time=3.41 memory used=269.8MB, alloc=116.3MB, time=4.37 memory used=352.3MB, alloc=116.3MB, time=5.70 memory used=434.7MB, alloc=396.3MB, time=7.09 memory used=538.6MB, alloc=396.3MB, time=8.84 memory used=649.6MB, alloc=420.3MB, time=10.49 memory used=773.9MB, alloc=444.3MB, time=12.36 memory used=912.5MB, alloc=468.3MB, time=14.72 memory used=1026.4MB, alloc=492.3MB, time=16.68 memory used=1129.1MB, alloc=492.3MB, time=18.44 memory used=1229.5MB, alloc=492.3MB, time=20.27 memory used=1330.9MB, alloc=492.3MB, time=22.11 memory used=1426.0MB, alloc=492.3MB, time=24.00 memory used=1514.0MB, alloc=492.3MB, time=25.77 memory used=1590.2MB, alloc=492.3MB, time=27.41 memory used=1669.5MB, alloc=492.3MB, time=29.10 memory used=1745.7MB, alloc=516.3MB, time=30.78 memory used=1805.6MB, alloc=516.3MB, time=31.96 memory used=1875.4MB, alloc=516.3MB, time=33.75 memory used=2080.4MB, alloc=540.3MB, time=37.75 memory used=2308.9MB, alloc=564.3MB, time=42.70 memory used=2509.9MB, alloc=588.3MB, time=46.78 memory used=2693.7MB, alloc=612.3MB, time=50.85 memory used=2883.7MB, alloc=636.3MB, time=55.33 memory used=3049.0MB, alloc=660.3MB, time=59.33 memory used=3180.5MB, alloc=660.3MB, time=62.60 memory used=3284.4MB, alloc=660.3MB, time=65.35 memory used=3406.5MB, alloc=684.3MB, time=68.25 memory used=3524.9MB, alloc=684.3MB, time=71.21 memory used=3615.5MB, alloc=684.3MB, time=74.01 memory used=3710.3MB, alloc=684.3MB, time=76.77 memory used=4056.5MB, alloc=708.3MB, time=84.49 memory used=4415.5MB, alloc=732.3MB, time=92.91 memory used=4797.5MB, alloc=756.3MB, time=101.30 memory used=5175.5MB, alloc=780.3MB, time=110.16 memory used=5573.0MB, alloc=804.3MB, time=119.38 memory used=5876.1MB, alloc=828.3MB, time=126.17 memory used=6183.8MB, alloc=852.3MB, time=133.10 memory used=6514.0MB, alloc=876.3MB, time=140.99 memory used=6803.4MB, alloc=900.3MB, time=148.21 memory used=7200.6MB, alloc=924.3MB, time=156.04 memory used=7564.7MB, alloc=948.3MB, time=163.57 memory used=7877.7MB, alloc=972.3MB, time=170.36 memory used=8220.8MB, alloc=996.3MB, time=177.88 memory used=8554.6MB, alloc=1020.3MB, time=185.89 memory used=8861.5MB, alloc=1044.3MB, time=193.46 memory used=9302.4MB, alloc=1068.3MB, time=204.20 memory used=9742.2MB, alloc=1092.3MB, time=214.67 memory used=10165.3MB, alloc=1116.3MB, time=225.12 memory used=10591.6MB, alloc=1140.3MB, time=235.65 |\^/| 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(); 1428239876 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-6 x - 11 x y + 8 z, -20 x - 17 x z - 6 y z, 6 x y - 19 x z + 17] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [9 y z + 15 z - 5 x, 2 x z + 5 x + 10, 4 x z + 13 z + 9 y] > Problem := [F,G]; Problem := [ 2 2 [-6 x - 11 x y + 8 z, -20 x - 17 x z - 6 y z, 6 x y - 19 x z + 17], 2 2 [9 y z + 15 z - 5 x, 2 x z + 5 x + 10, 4 x z + 13 z + 9 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.52 memory used=47.1MB, alloc=32.3MB, time=0.84 memory used=67.2MB, alloc=56.3MB, time=1.16 memory used=109.2MB, alloc=60.3MB, time=1.81 memory used=149.2MB, alloc=84.3MB, time=2.44 memory used=213.4MB, alloc=92.3MB, time=3.40 memory used=275.6MB, alloc=116.3MB, time=4.36 memory used=352.2MB, alloc=116.3MB, time=5.52 memory used=426.2MB, alloc=396.3MB, time=6.74 memory used=537.2MB, alloc=420.3MB, time=8.50 memory used=672.8MB, alloc=444.3MB, time=10.69 memory used=821.1MB, alloc=468.3MB, time=13.24 memory used=949.5MB, alloc=468.3MB, time=15.36 memory used=1063.8MB, alloc=492.3MB, time=17.45 memory used=1189.8MB, alloc=492.3MB, time=19.74 memory used=1299.1MB, alloc=492.3MB, time=21.76 memory used=1398.5MB, alloc=492.3MB, time=23.64 memory used=1490.8MB, alloc=492.3MB, time=25.52 memory used=1580.8MB, alloc=516.3MB, time=27.29 memory used=1653.3MB, alloc=516.3MB, time=28.89 memory used=1727.1MB, alloc=516.3MB, time=30.45 memory used=1792.6MB, alloc=516.3MB, time=31.92 memory used=1856.6MB, alloc=516.3MB, time=33.48 memory used=1910.3MB, alloc=516.3MB, time=34.76 memory used=1972.7MB, alloc=516.3MB, time=36.11 memory used=2029.9MB, alloc=516.3MB, time=37.53 memory used=2235.0MB, alloc=540.3MB, time=41.55 memory used=2461.7MB, alloc=564.3MB, time=46.25 memory used=2674.1MB, alloc=588.3MB, time=50.73 memory used=2845.6MB, alloc=612.3MB, time=54.31 memory used=3037.0MB, alloc=636.3MB, time=58.65 memory used=3229.2MB, alloc=660.3MB, time=63.22 memory used=3391.5MB, alloc=684.3MB, time=66.27 memory used=3522.9MB, alloc=708.3MB, time=69.98 memory used=3648.7MB, alloc=732.3MB, time=72.70 memory used=3772.7MB, alloc=732.3MB, time=76.26 memory used=3870.1MB, alloc=732.3MB, time=78.54 memory used=3953.5MB, alloc=732.3MB, time=80.47 memory used=4351.9MB, alloc=756.3MB, time=90.02 memory used=4779.6MB, alloc=780.3MB, time=99.18 memory used=5226.0MB, alloc=804.3MB, time=108.61 memory used=5671.5MB, alloc=828.3MB, time=119.19 memory used=6061.1MB, alloc=852.3MB, time=129.26 memory used=6465.0MB, alloc=876.3MB, time=139.61 memory used=6724.4MB, alloc=900.3MB, time=145.32 memory used=6981.4MB, alloc=924.3MB, time=152.41 memory used=7247.7MB, alloc=948.3MB, time=159.70 memory used=7545.8MB, alloc=972.3MB, time=167.70 memory used=7829.9MB, alloc=996.3MB, time=175.78 memory used=8063.1MB, alloc=1020.3MB, time=181.46 memory used=8707.1MB, alloc=1044.3MB, time=198.29 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428240176 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-5 x + z + 6 x, -7 x + 16 x y + 7 z, 12 x - 13 x + 12] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [6 x y - 14 y, -18 x + 2 x z - 2, 10 x z + 9 x - 10 z] > Problem := [F,G]; 2 2 2 2 Problem := [[-5 x + z + 6 x, -7 x + 16 x y + 7 z, 12 x - 13 x + 12], 2 [6 x y - 14 y, -18 x + 2 x z - 2, 10 x z + 9 x - 10 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=47.5MB, alloc=32.3MB, time=0.81 memory used=67.3MB, alloc=32.3MB, time=1.11 memory used=87.6MB, alloc=56.3MB, time=1.50 memory used=129.5MB, alloc=60.3MB, time=2.25 memory used=167.0MB, alloc=84.3MB, time=2.99 memory used=219.7MB, alloc=108.3MB, time=4.78 N1 := 1313 > GB := Basis(F, plex(op(vars))); 2 2 GB := [12 x - 13 x + 12, -2688 x y + 3072 y - 2891 x + 294, 192 y x + 84 z - 91 x + 84] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=292.8MB, alloc=116.3MB, time=6.10 memory used=373.7MB, alloc=140.3MB, time=7.68 N2 := 1143 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-5 x + z + 6 x, -7 x + 16 x y + 7 z, 12 x - 13 x + 12, 6 x y - 14 y, 2 -18 x + 2 x z - 2, 10 z x - 10 z + 9 x] > J:=[op(GB),op(G)]; 2 2 J := [12 x - 13 x + 12, -2688 x y + 3072 y - 2891 x + 294, 2 192 y x + 84 z - 91 x + 84, 6 x y - 14 y, -18 x + 2 x z - 2, 10 z x - 10 z + 9 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 12, 2, 2, 1, 2, 1, 1/3, 2/3, 11/17, 3/17, 5/17, 6, 12, 12, 11 2, 2, 2, 1, 1, 1/2, 1/2, --, 5/19, 4/19, 0, 0, 0] 19 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=412.8MB, alloc=140.3MB, time=9.12 |\^/| 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(); 1428240204 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [11 + 2 z, -17 x + 17 y z - 2 x, 16 x z + 20 y - 14 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-6 x + 12 y + 12 x, -15 x y + 7 x z + 2 z , 18 y + 9 z + 11] > Problem := [F,G]; 2 2 Problem := [[11 + 2 z, -17 x + 17 y z - 2 x, 16 x z + 20 y - 14 y z], 2 2 2 2 2 [-6 x + 12 y + 12 x, -15 x y + 7 x z + 2 z , 18 y + 9 z + 11]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.19 memory used=26.6MB, alloc=32.3MB, time=0.53 memory used=47.6MB, alloc=32.3MB, time=0.85 memory used=67.2MB, alloc=56.3MB, time=1.16 memory used=107.3MB, alloc=60.3MB, time=1.78 memory used=145.2MB, alloc=84.3MB, time=2.38 memory used=208.4MB, alloc=92.3MB, time=3.33 memory used=268.5MB, alloc=116.3MB, time=4.30 memory used=351.5MB, alloc=140.3MB, time=5.64 memory used=428.7MB, alloc=396.3MB, time=6.94 memory used=536.6MB, alloc=420.3MB, time=8.57 memory used=666.1MB, alloc=444.3MB, time=10.61 memory used=804.3MB, alloc=468.3MB, time=12.85 memory used=944.0MB, alloc=492.3MB, time=15.41 memory used=1060.5MB, alloc=492.3MB, time=17.42 memory used=1159.5MB, alloc=492.3MB, time=19.20 memory used=1261.3MB, alloc=492.3MB, time=20.91 memory used=1382.4MB, alloc=516.3MB, time=23.29 memory used=1498.8MB, alloc=516.3MB, time=25.73 memory used=1590.8MB, alloc=516.3MB, time=27.37 memory used=1703.9MB, alloc=516.3MB, time=29.83 memory used=1789.5MB, alloc=516.3MB, time=31.91 memory used=1857.5MB, alloc=516.3MB, time=33.39 memory used=1935.9MB, alloc=516.3MB, time=35.36 memory used=2009.3MB, alloc=516.3MB, time=37.35 memory used=2074.6MB, alloc=540.3MB, time=38.81 memory used=2137.2MB, alloc=540.3MB, time=40.34 memory used=2192.8MB, alloc=540.3MB, time=41.72 memory used=2417.7MB, alloc=564.3MB, time=46.56 memory used=2597.1MB, alloc=588.3MB, time=50.12 memory used=2802.5MB, alloc=612.3MB, time=54.19 memory used=3011.1MB, alloc=636.3MB, time=59.24 memory used=3221.5MB, alloc=660.3MB, time=64.91 memory used=3392.4MB, alloc=684.3MB, time=68.98 memory used=3566.0MB, alloc=684.3MB, time=72.59 memory used=3707.9MB, alloc=684.3MB, time=75.97 memory used=3863.9MB, alloc=684.3MB, time=80.20 memory used=3995.8MB, alloc=684.3MB, time=84.01 memory used=4119.9MB, alloc=708.3MB, time=87.54 memory used=4222.4MB, alloc=708.3MB, time=90.13 memory used=4337.0MB, alloc=708.3MB, time=94.06 memory used=4693.6MB, alloc=732.3MB, time=102.82 |\^/| 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(); 1428240504 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [9 x + 17 x y + 19 z , -12 x + 3 y - 10 y, 8 x y - 11] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-10 x z + 19 x + 20 y, 18 x y + 16 y z + 15 z , -18 x y + 10 y - 8 z] > Problem := [F,G]; 2 2 2 2 Problem := [[9 x + 17 x y + 19 z , -12 x + 3 y - 10 y, 8 x y - 11], 2 [-10 x z + 19 x + 20 y, 18 x y + 16 y z + 15 z , -18 x y + 10 y - 8 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.51 memory used=47.9MB, alloc=32.3MB, time=0.85 memory used=67.9MB, alloc=56.3MB, time=1.18 memory used=109.1MB, alloc=60.3MB, time=1.82 memory used=149.3MB, alloc=84.3MB, time=2.47 memory used=210.5MB, alloc=92.3MB, time=3.50 memory used=271.2MB, alloc=116.3MB, time=4.52 memory used=354.7MB, alloc=116.3MB, time=5.94 memory used=437.1MB, alloc=140.3MB, time=7.38 memory used=512.2MB, alloc=140.3MB, time=8.73 memory used=586.4MB, alloc=396.3MB, time=10.04 memory used=691.7MB, alloc=420.3MB, time=12.01 memory used=822.9MB, alloc=444.3MB, time=14.50 memory used=973.9MB, alloc=468.3MB, time=17.49 memory used=1141.9MB, alloc=492.3MB, time=20.89 memory used=1271.3MB, alloc=492.3MB, time=23.64 memory used=1407.7MB, alloc=516.3MB, time=26.71 memory used=1547.9MB, alloc=516.3MB, time=30.00 memory used=1680.9MB, alloc=540.3MB, time=33.13 memory used=1805.3MB, alloc=540.3MB, time=36.00 memory used=1907.8MB, alloc=540.3MB, time=38.18 memory used=2008.8MB, alloc=564.3MB, time=40.36 memory used=2096.8MB, alloc=564.3MB, time=42.44 memory used=2217.3MB, alloc=588.3MB, time=45.10 memory used=2343.7MB, alloc=612.3MB, time=47.91 memory used=2452.2MB, alloc=612.3MB, time=50.29 memory used=2569.1MB, alloc=636.3MB, time=52.88 memory used=2666.5MB, alloc=660.3MB, time=55.01 memory used=2773.0MB, alloc=660.3MB, time=57.30 memory used=2844.8MB, alloc=684.3MB, time=59.08 memory used=2929.0MB, alloc=684.3MB, time=61.07 memory used=3041.6MB, alloc=708.3MB, time=63.46 memory used=3144.0MB, alloc=708.3MB, time=65.61 memory used=3220.2MB, alloc=732.3MB, time=67.58 memory used=3289.8MB, alloc=732.3MB, time=69.38 memory used=3367.4MB, alloc=732.3MB, time=71.31 memory used=3451.9MB, alloc=756.3MB, time=73.42 memory used=3515.5MB, alloc=756.3MB, time=75.20 memory used=3830.1MB, alloc=780.3MB, time=81.66 memory used=4137.0MB, alloc=804.3MB, time=90.30 memory used=4412.9MB, alloc=828.3MB, time=101.05 |\^/| 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(); 1428240804 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [10 x y - 3 y - 12 x, -20 x + 16 x y - 12 z, -13 x y + 16 z - 11 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-20 x y - 16 y z + 18 z, -14 x z + 12 y, 4 y z - z ] > Problem := [F,G]; Problem := [ 2 2 2 [10 x y - 3 y - 12 x, -20 x + 16 x y - 12 z, -13 x y + 16 z - 11 y], 2 [-20 x y - 16 y z + 18 z, -14 x z + 12 y, 4 y z - z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=47.3MB, alloc=32.3MB, time=0.79 memory used=66.6MB, alloc=56.3MB, time=1.09 memory used=105.4MB, alloc=60.3MB, time=1.68 memory used=142.7MB, alloc=84.3MB, time=2.27 memory used=201.2MB, alloc=92.3MB, time=3.20 memory used=258.4MB, alloc=116.3MB, time=4.11 memory used=334.4MB, alloc=116.3MB, time=5.31 memory used=409.8MB, alloc=140.3MB, time=6.55 memory used=505.4MB, alloc=140.3MB, time=8.21 memory used=584.0MB, alloc=420.3MB, time=9.61 memory used=705.2MB, alloc=444.3MB, time=11.81 memory used=851.9MB, alloc=468.3MB, time=14.74 memory used=1021.8MB, alloc=492.3MB, time=18.36 memory used=1210.0MB, alloc=492.3MB, time=22.31 memory used=1397.4MB, alloc=516.3MB, time=26.88 memory used=1593.2MB, alloc=540.3MB, time=31.50 memory used=1772.3MB, alloc=564.3MB, time=36.10 memory used=1944.7MB, alloc=588.3MB, time=40.40 memory used=2082.6MB, alloc=612.3MB, time=43.82 memory used=2212.0MB, alloc=636.3MB, time=46.58 memory used=2327.4MB, alloc=636.3MB, time=49.05 memory used=2437.0MB, alloc=660.3MB, time=51.56 memory used=2557.3MB, alloc=684.3MB, time=54.21 memory used=2683.0MB, alloc=708.3MB, time=57.04 memory used=2803.9MB, alloc=732.3MB, time=59.78 memory used=2924.7MB, alloc=732.3MB, time=62.66 memory used=3026.8MB, alloc=756.3MB, time=65.07 memory used=3134.1MB, alloc=780.3MB, time=67.66 memory used=3236.5MB, alloc=804.3MB, time=70.10 memory used=3333.1MB, alloc=804.3MB, time=72.52 memory used=3422.5MB, alloc=828.3MB, time=74.84 memory used=3515.5MB, alloc=828.3MB, time=77.29 memory used=3595.4MB, alloc=852.3MB, time=79.43 memory used=3684.7MB, alloc=876.3MB, time=81.77 memory used=3765.4MB, alloc=876.3MB, time=84.02 memory used=4107.7MB, alloc=900.3MB, time=91.44 |\^/| 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(); 1428241104 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-4 x y - x + 4, 19 x z - 20 x + 19 y, 3 x + 11 y z - 13 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-16 y + 19 x + 6, -3 x y + 16 z - 2, -17 x + 13 x y - 9 z] > Problem := [F,G]; 2 Problem := [[-4 x y - x + 4, 19 x z - 20 x + 19 y, 3 x + 11 y z - 13 y], 2 2 [-16 y + 19 x + 6, -3 x y + 16 z - 2, -17 x + 13 x 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=32.3MB, alloc=40.3MB, time=0.60 memory used=60.1MB, alloc=40.3MB, time=1.02 memory used=85.5MB, alloc=64.3MB, time=1.43 memory used=132.3MB, alloc=76.3MB, time=2.20 memory used=178.6MB, alloc=100.3MB, time=2.97 memory used=247.7MB, alloc=100.3MB, time=4.09 memory used=316.1MB, alloc=124.3MB, time=5.19 memory used=406.3MB, alloc=124.3MB, time=6.65 memory used=491.2MB, alloc=404.3MB, time=8.10 memory used=603.8MB, alloc=428.3MB, time=10.00 memory used=732.1MB, alloc=452.3MB, time=12.43 memory used=869.9MB, alloc=476.3MB, time=14.97 memory used=1024.2MB, alloc=500.3MB, time=17.85 memory used=1186.9MB, alloc=524.3MB, time=21.06 memory used=1360.9MB, alloc=548.3MB, time=24.44 memory used=1533.8MB, alloc=572.3MB, time=28.05 memory used=1713.1MB, alloc=596.3MB, time=34.08 memory used=1898.5MB, alloc=620.3MB, time=40.79 memory used=2096.1MB, alloc=644.3MB, time=48.17 memory used=2308.0MB, alloc=668.3MB, time=56.30 memory used=2531.8MB, alloc=692.3MB, time=65.61 memory used=2770.6MB, alloc=716.3MB, time=76.02 |\^/| 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(); 1428241404 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-8 x z - 16 y - 9 z, -9 x y + 19 y + 14 x, 8 x y + 9 y - 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [3 x + 7 x y + 11 z , -14 x z - 20 y z, -19 x y + 7 x z - 2 y z] > Problem := [F,G]; 2 2 2 2 Problem := [[-8 x z - 16 y - 9 z, -9 x y + 19 y + 14 x, 8 x y + 9 y - 6 z ], 2 2 [3 x + 7 x y + 11 z , -14 x z - 20 y z, -19 x y + 7 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.79 memory used=68.3MB, alloc=32.3MB, time=1.09 memory used=86.9MB, alloc=56.3MB, time=1.37 memory used=126.3MB, alloc=60.3MB, time=1.96 memory used=163.2MB, alloc=84.3MB, time=2.50 memory used=209.6MB, alloc=84.3MB, time=3.18 memory used=268.3MB, alloc=92.3MB, time=4.05 memory used=327.1MB, alloc=116.3MB, time=4.92 memory used=408.6MB, alloc=140.3MB, time=6.11 memory used=476.9MB, alloc=396.3MB, time=7.07 memory used=585.2MB, alloc=420.3MB, time=8.58 memory used=721.2MB, alloc=444.3MB, time=10.47 memory used=869.4MB, alloc=468.3MB, time=12.50 memory used=1017.2MB, alloc=492.3MB, time=14.82 memory used=1155.1MB, alloc=516.3MB, time=17.00 memory used=1281.2MB, alloc=516.3MB, time=19.06 memory used=1389.7MB, alloc=516.3MB, time=20.72 memory used=1493.9MB, alloc=540.3MB, time=22.47 memory used=1603.9MB, alloc=540.3MB, time=24.60 memory used=1768.2MB, alloc=564.3MB, time=26.86 memory used=1876.3MB, alloc=588.3MB, time=29.09 memory used=1997.4MB, alloc=588.3MB, time=31.54 memory used=2123.7MB, alloc=612.3MB, time=34.11 memory used=2252.6MB, alloc=636.3MB, time=36.77 memory used=2375.5MB, alloc=660.3MB, time=39.35 memory used=2496.4MB, alloc=660.3MB, time=41.88 memory used=2618.0MB, alloc=684.3MB, time=44.41 memory used=2734.2MB, alloc=708.3MB, time=46.90 memory used=2835.6MB, alloc=708.3MB, time=49.10 memory used=2936.8MB, alloc=732.3MB, time=51.31 memory used=3036.6MB, alloc=732.3MB, time=53.52 memory used=3128.6MB, alloc=756.3MB, time=55.54 memory used=3226.9MB, alloc=756.3MB, time=57.62 memory used=3297.6MB, alloc=780.3MB, time=59.33 memory used=3386.7MB, alloc=780.3MB, time=61.24 memory used=3481.7MB, alloc=780.3MB, time=63.07 memory used=3613.2MB, alloc=780.3MB, time=64.97 memory used=3738.9MB, alloc=780.3MB, time=67.11 memory used=3861.1MB, alloc=804.3MB, time=69.32 memory used=4256.4MB, alloc=828.3MB, time=76.02 memory used=4558.3MB, alloc=852.3MB, time=82.01 memory used=4913.9MB, alloc=876.3MB, time=91.02 |\^/| 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(); 1428241704 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-14 x z - 4 z + 11, -3 - 19 x, 9 x y - 4 y - 18 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-16 x y + 20 y - 5, 11 x - 19 y z + 15 z , -15 x z + 14 y z - 4 z] > Problem := [F,G]; 2 Problem := [[-14 x z - 4 z + 11, -3 - 19 x, 9 x y - 4 y - 18 x], 2 2 [-16 x y + 20 y - 5, 11 x - 19 y z + 15 z , -15 x z + 14 y z - 4 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=47.2MB, alloc=32.3MB, time=0.78 memory used=66.8MB, alloc=56.3MB, time=1.08 memory used=109.0MB, alloc=60.3MB, time=1.77 memory used=148.7MB, alloc=84.3MB, time=2.47 memory used=208.7MB, alloc=84.3MB, time=3.51 memory used=264.6MB, alloc=108.3MB, time=4.47 memory used=337.4MB, alloc=140.3MB, time=5.77 memory used=425.7MB, alloc=164.3MB, time=7.83 memory used=521.5MB, alloc=188.3MB, time=10.78 memory used=629.1MB, alloc=212.3MB, time=14.80 memory used=759.4MB, alloc=212.3MB, time=19.70 memory used=889.8MB, alloc=236.3MB, time=24.76 memory used=1044.2MB, alloc=236.3MB, time=30.67 N1 := 4531 > GB := Basis(F, plex(op(vars))); 2 GB := [19 x + 3, 76 y + 27 y - 54, 34 z - 209] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1176.4MB, alloc=236.3MB, time=33.58 memory used=1348.0MB, alloc=516.3MB, time=36.76 memory used=1529.2MB, alloc=540.3MB, time=42.21 memory used=1703.7MB, alloc=564.3MB, time=49.32 memory used=1902.1MB, alloc=588.3MB, time=57.61 N2 := 4403 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [-14 x z - 4 z + 11, -3 - 19 x, -4 y + 9 y x - 18 x, -16 x y + 20 y - 5, 2 2 15 z - 19 z y + 11 x , -15 x z + 14 y z - 4 z] > J:=[op(GB),op(G)]; 2 J := [19 x + 3, 76 y + 27 y - 54, 34 z - 209, -16 x y + 20 y - 5, 2 2 15 z - 19 z y + 11 x , -15 x z + 14 y z - 4 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 11, 2, 2, 2, 2, 1, 2/3, 1/2, 7/17, 6/17, 7/17, 6, 11, 10, 2, 2, 2, 2, 2/3, 2/3, 1/2, 1/4, 3/8, 3/8, 2, 1, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=2054.6MB, alloc=588.3MB, time=63.47 |\^/| 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(); 1428241911 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-19 y z - 12 x + 3 y, 12 x y + 6 z - 15 z, -11 y + 11] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [5 x y + 3 y - 19 z , -7 y z + 11 x + 13, -2 y + 15 z - 10 z] > Problem := [F,G]; 2 2 Problem := [[-19 y z - 12 x + 3 y, 12 x y + 6 z - 15 z, -11 y + 11], 2 2 2 2 [5 x y + 3 y - 19 z , -7 y z + 11 x + 13, -2 y + 15 z - 10 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=47.1MB, alloc=32.3MB, time=0.82 memory used=66.4MB, alloc=56.3MB, time=1.13 memory used=106.4MB, alloc=60.3MB, time=1.74 memory used=144.1MB, alloc=84.3MB, time=2.31 memory used=202.1MB, alloc=92.3MB, time=3.22 memory used=260.2MB, alloc=116.3MB, time=4.16 memory used=342.0MB, alloc=116.3MB, time=5.43 memory used=420.9MB, alloc=396.3MB, time=6.65 memory used=527.6MB, alloc=396.3MB, time=8.35 memory used=629.1MB, alloc=420.3MB, time=10.19 memory used=754.5MB, alloc=444.3MB, time=12.48 memory used=899.7MB, alloc=468.3MB, time=14.80 memory used=1050.1MB, alloc=468.3MB, time=17.36 memory used=1205.8MB, alloc=492.3MB, time=20.37 memory used=1327.7MB, alloc=516.3MB, time=22.61 memory used=1491.9MB, alloc=540.3MB, time=25.72 memory used=1631.1MB, alloc=540.3MB, time=28.65 memory used=1783.5MB, alloc=564.3MB, time=32.13 memory used=1909.2MB, alloc=564.3MB, time=34.98 memory used=1993.7MB, alloc=564.3MB, time=36.68 memory used=2107.1MB, alloc=564.3MB, time=39.25 memory used=2214.9MB, alloc=564.3MB, time=41.83 memory used=2284.3MB, alloc=564.3MB, time=43.24 memory used=2369.9MB, alloc=564.3MB, time=45.33 memory used=2439.6MB, alloc=564.3MB, time=46.96 memory used=2511.5MB, alloc=588.3MB, time=48.56 memory used=2593.4MB, alloc=588.3MB, time=50.89 memory used=2672.7MB, alloc=588.3MB, time=53.39 memory used=2734.9MB, alloc=588.3MB, time=55.49 memory used=2804.7MB, alloc=588.3MB, time=57.48 memory used=2886.6MB, alloc=588.3MB, time=60.01 memory used=3155.0MB, alloc=612.3MB, time=67.39 memory used=3415.9MB, alloc=636.3MB, time=74.18 memory used=3656.2MB, alloc=660.3MB, time=80.70 memory used=3834.9MB, alloc=684.3MB, time=84.14 memory used=4004.5MB, alloc=708.3MB, time=88.11 memory used=4191.7MB, alloc=708.3MB, time=92.67 memory used=4374.9MB, alloc=732.3MB, time=97.53 memory used=4526.7MB, alloc=732.3MB, time=101.34 memory used=4679.1MB, alloc=732.3MB, time=105.45 memory used=4804.1MB, alloc=732.3MB, time=108.49 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428242212 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [x - 9 x z - 13 z , -11 + 3 x, -13 x - 3 x y - 18 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-5 y z + y + 9 z, -7 x - x z + 10, 8 x y - 16 y z + x] > Problem := [F,G]; 2 2 2 Problem := [[x - 9 x z - 13 z , -11 + 3 x, -13 x - 3 x y - 18 y], 2 [-5 y z + y + 9 z, -7 x - x z + 10, 8 x y - 16 y z + x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.2MB, alloc=32.3MB, time=0.79 memory used=66.5MB, alloc=56.3MB, time=1.09 memory used=106.2MB, alloc=60.3MB, time=1.69 memory used=144.9MB, alloc=60.3MB, time=2.29 memory used=182.2MB, alloc=84.3MB, time=2.89 memory used=240.7MB, alloc=84.3MB, time=3.80 memory used=300.1MB, alloc=116.3MB, time=4.83 memory used=382.1MB, alloc=140.3MB, time=6.33 memory used=477.3MB, alloc=164.3MB, time=8.07 memory used=588.5MB, alloc=188.3MB, time=10.02 memory used=714.4MB, alloc=212.3MB, time=12.32 memory used=850.4MB, alloc=492.3MB, time=14.86 memory used=1004.7MB, alloc=516.3MB, time=17.72 memory used=1168.9MB, alloc=540.3MB, time=20.77 memory used=1342.9MB, alloc=564.3MB, time=24.01 memory used=1521.9MB, alloc=588.3MB, time=28.15 memory used=1690.3MB, alloc=612.3MB, time=33.73 memory used=1867.4MB, alloc=636.3MB, time=40.08 memory used=2057.2MB, alloc=660.3MB, time=47.07 memory used=2261.4MB, alloc=684.3MB, time=54.65 memory used=2480.4MB, alloc=708.3MB, time=63.05 memory used=2714.8MB, alloc=732.3MB, time=72.14 memory used=2963.9MB, alloc=756.3MB, time=82.04 memory used=3225.9MB, alloc=780.3MB, time=93.20 |\^/| 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(); 1428242511 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [6 x y + 2 y z, 14 z + 15 y - 5, 12 x y - 5 x z - 3 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [11 z + 3 y + 17 z, 5 x + 12 z, -5 x y - 19 x - 11 y] > Problem := [F,G]; 2 Problem := [[6 x y + 2 y z, 14 z + 15 y - 5, 12 x y - 5 x z - 3 y], 2 2 [11 z + 3 y + 17 z, 5 x + 12 z, -5 x y - 19 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.4MB, alloc=32.3MB, time=0.80 memory used=66.9MB, alloc=56.3MB, time=1.12 memory used=107.2MB, alloc=60.3MB, time=1.74 memory used=145.0MB, alloc=84.3MB, time=2.32 memory used=204.4MB, alloc=92.3MB, time=3.27 memory used=259.1MB, alloc=116.3MB, time=4.16 memory used=336.2MB, alloc=140.3MB, time=5.48 memory used=436.7MB, alloc=140.3MB, time=7.24 memory used=526.8MB, alloc=164.3MB, time=8.80 memory used=616.0MB, alloc=420.3MB, time=10.39 memory used=741.7MB, alloc=444.3MB, time=12.72 memory used=890.3MB, alloc=468.3MB, time=15.50 memory used=1060.7MB, alloc=492.3MB, time=18.97 memory used=1252.8MB, alloc=516.3MB, time=23.21 memory used=1467.6MB, alloc=540.3MB, time=28.30 memory used=1702.5MB, alloc=564.3MB, time=34.20 memory used=1953.8MB, alloc=588.3MB, time=40.46 memory used=2228.1MB, alloc=612.3MB, time=47.64 memory used=2510.8MB, alloc=636.3MB, time=53.72 memory used=2784.0MB, alloc=660.3MB, time=59.15 memory used=3051.5MB, alloc=684.3MB, time=64.59 memory used=3315.9MB, alloc=708.3MB, time=70.03 memory used=3575.2MB, alloc=732.3MB, time=75.47 memory used=3834.8MB, alloc=756.3MB, time=81.08 memory used=4096.6MB, alloc=780.3MB, time=86.67 memory used=4360.5MB, alloc=804.3MB, time=92.27 memory used=4635.7MB, alloc=828.3MB, time=97.90 memory used=4906.9MB, alloc=852.3MB, time=103.48 |\^/| 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(); 1428242812 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [20 y z - 17 x - 15, -15 x z + 13 x - 2 y, x + 13 x y + 6 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-17 x + 14 y, 10 y + 10 y z + 15, -9 z + 7 y - 5] > Problem := [F,G]; 2 Problem := [[20 y z - 17 x - 15, -15 x z + 13 x - 2 y, x + 13 x y + 6 y], 2 2 2 [-17 x + 14 y, 10 y + 10 y z + 15, -9 z + 7 y - 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=46.6MB, alloc=32.3MB, time=0.80 memory used=66.1MB, alloc=56.3MB, time=1.11 memory used=106.1MB, alloc=60.3MB, time=1.71 memory used=143.4MB, alloc=84.3MB, time=2.30 memory used=203.8MB, alloc=92.3MB, time=3.23 memory used=264.7MB, alloc=116.3MB, time=4.17 memory used=347.8MB, alloc=116.3MB, time=5.44 memory used=428.2MB, alloc=140.3MB, time=6.75 memory used=504.3MB, alloc=140.3MB, time=7.96 memory used=575.7MB, alloc=396.3MB, time=9.12 memory used=678.6MB, alloc=420.3MB, time=10.85 memory used=803.4MB, alloc=444.3MB, time=12.84 memory used=940.6MB, alloc=468.3MB, time=15.05 memory used=1098.2MB, alloc=492.3MB, time=18.00 memory used=1260.9MB, alloc=516.3MB, time=21.14 memory used=1431.0MB, alloc=540.3MB, time=24.45 memory used=1603.6MB, alloc=564.3MB, time=27.86 memory used=1795.5MB, alloc=588.3MB, time=33.32 memory used=1979.3MB, alloc=612.3MB, time=39.92 memory used=2174.7MB, alloc=636.3MB, time=47.34 memory used=2376.8MB, alloc=660.3MB, time=55.75 memory used=2598.3MB, alloc=684.3MB, time=65.50 memory used=2843.8MB, alloc=708.3MB, time=76.20 memory used=3113.1MB, alloc=732.3MB, time=88.25 |\^/| 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(); 1428243112 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [16 y - 12 y z, 16 x - 15 y , 5 x - 11 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [15 x y + 16 y z - 8, -9 x z + x + 17 z, -14 x z - 20 y + 13 x] > Problem := [F,G]; 2 2 2 2 2 Problem := [[16 y - 12 y z, 16 x - 15 y , 5 x - 11 z ], 2 [15 x y + 16 y z - 8, -9 x z + x + 17 z, -14 x z - 20 y + 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.50 memory used=47.7MB, alloc=32.3MB, time=0.81 memory used=66.4MB, alloc=56.3MB, time=1.14 memory used=105.7MB, alloc=60.3MB, time=1.77 memory used=143.7MB, alloc=84.3MB, time=2.39 memory used=203.5MB, alloc=92.3MB, time=3.35 memory used=261.6MB, alloc=116.3MB, time=4.27 memory used=343.0MB, alloc=116.3MB, time=5.55 memory used=423.0MB, alloc=140.3MB, time=6.82 memory used=501.6MB, alloc=140.3MB, time=8.06 memory used=569.9MB, alloc=396.3MB, time=9.17 memory used=672.7MB, alloc=420.3MB, time=10.80 memory used=799.1MB, alloc=444.3MB, time=12.86 memory used=943.8MB, alloc=468.3MB, time=15.33 memory used=1090.7MB, alloc=492.3MB, time=17.85 memory used=1228.2MB, alloc=492.3MB, time=20.08 memory used=1333.6MB, alloc=516.3MB, time=21.94 memory used=1458.4MB, alloc=540.3MB, time=24.43 memory used=1581.5MB, alloc=564.3MB, time=26.90 memory used=1688.2MB, alloc=588.3MB, time=29.17 memory used=1834.6MB, alloc=612.3MB, time=32.24 memory used=2002.0MB, alloc=636.3MB, time=35.76 memory used=2157.9MB, alloc=660.3MB, time=39.07 memory used=2310.0MB, alloc=684.3MB, time=42.32 memory used=2451.9MB, alloc=708.3MB, time=45.33 memory used=2579.5MB, alloc=732.3MB, time=48.12 memory used=2708.5MB, alloc=756.3MB, time=50.97 memory used=2846.4MB, alloc=780.3MB, time=54.03 memory used=2969.4MB, alloc=804.3MB, time=56.83 memory used=3089.1MB, alloc=828.3MB, time=59.59 memory used=3202.9MB, alloc=852.3MB, time=62.24 memory used=3300.0MB, alloc=852.3MB, time=64.55 memory used=3411.9MB, alloc=876.3MB, time=67.23 memory used=3521.8MB, alloc=900.3MB, time=69.89 memory used=3624.0MB, alloc=900.3MB, time=72.49 memory used=4009.6MB, alloc=924.3MB, time=80.64 memory used=4387.8MB, alloc=948.3MB, time=88.79 memory used=4764.2MB, alloc=972.3MB, time=97.09 |\^/| 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(); 1428243412 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [x + 9 x y - 11 y, -4 x + 15 y + 3 y z, 5 x z + 12 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [16 x + 9 y + 1, -12 x z + 16 y - 6 y z, 10 x - 12 x y - 18 z ] > Problem := [F,G]; 2 2 2 Problem := [[x + 9 x y - 11 y, -4 x + 15 y + 3 y z, 5 x z + 12 z], 2 2 2 2 [16 x + 9 y + 1, -12 x z + 16 y - 6 y z, 10 x - 12 x y - 18 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=32.3MB, time=0.81 memory used=67.5MB, alloc=56.3MB, time=1.13 memory used=107.8MB, alloc=60.3MB, time=1.74 memory used=146.9MB, alloc=84.3MB, time=2.34 memory used=209.6MB, alloc=92.3MB, time=3.31 memory used=269.6MB, alloc=92.3MB, time=4.23 memory used=328.6MB, alloc=116.3MB, time=5.15 memory used=413.6MB, alloc=396.3MB, time=6.68 memory used=514.1MB, alloc=420.3MB, time=8.45 memory used=629.7MB, alloc=444.3MB, time=10.52 memory used=758.3MB, alloc=468.3MB, time=12.86 memory used=900.9MB, alloc=492.3MB, time=15.46 memory used=1057.6MB, alloc=516.3MB, time=18.42 memory used=1221.4MB, alloc=540.3MB, time=22.07 memory used=1377.2MB, alloc=564.3MB, time=27.23 memory used=1541.5MB, alloc=588.3MB, time=33.22 memory used=1718.8MB, alloc=612.3MB, time=39.94 memory used=1910.5MB, alloc=636.3MB, time=47.27 memory used=2111.6MB, alloc=660.3MB, time=55.80 memory used=2335.5MB, alloc=684.3MB, time=65.30 memory used=2583.3MB, alloc=708.3MB, time=76.20 memory used=2855.0MB, alloc=732.3MB, time=87.60 memory used=3150.6MB, alloc=732.3MB, time=100.08 |\^/| 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(); 1428243712 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-19 y z + 12 z - 2, -16 y z - 10 z - 1, -14 x z + 4 x + 20] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [8 x + 5 x z + 1, 17 x - 13 x z + 18 z , 8 y z + 2 z + 11 y] > Problem := [F,G]; 2 2 Problem := [[-19 y z + 12 z - 2, -16 y z - 10 z - 1, -14 x z + 4 x + 20], 2 2 2 2 [8 x + 5 x z + 1, 17 x - 13 x z + 18 z , 8 y z + 2 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=32.2MB, alloc=44.3MB, time=0.61 memory used=59.0MB, alloc=68.3MB, time=1.02 memory used=106.4MB, alloc=68.3MB, time=1.76 memory used=153.0MB, alloc=92.3MB, time=2.48 memory used=199.2MB, alloc=92.3MB, time=3.21 memory used=267.3MB, alloc=100.3MB, time=4.30 memory used=335.2MB, alloc=124.3MB, time=5.38 memory used=423.3MB, alloc=124.3MB, time=6.81 memory used=512.2MB, alloc=404.3MB, time=8.37 memory used=625.2MB, alloc=404.3MB, time=10.30 memory used=735.9MB, alloc=428.3MB, time=12.34 memory used=870.1MB, alloc=452.3MB, time=14.84 memory used=1025.7MB, alloc=476.3MB, time=17.75 memory used=1198.8MB, alloc=500.3MB, time=20.96 memory used=1394.8MB, alloc=524.3MB, time=25.26 memory used=1574.8MB, alloc=548.3MB, time=29.12 memory used=1722.7MB, alloc=548.3MB, time=32.59 memory used=1915.2MB, alloc=572.3MB, time=37.45 memory used=2053.1MB, alloc=572.3MB, time=40.73 memory used=2187.9MB, alloc=572.3MB, time=44.25 memory used=2316.4MB, alloc=572.3MB, time=47.42 memory used=2435.5MB, alloc=572.3MB, time=50.57 memory used=2549.7MB, alloc=572.3MB, time=53.64 memory used=2662.8MB, alloc=572.3MB, time=56.71 memory used=2779.1MB, alloc=572.3MB, time=60.03 memory used=2875.7MB, alloc=572.3MB, time=62.36 memory used=2997.3MB, alloc=596.3MB, time=65.81 memory used=3081.9MB, alloc=596.3MB, time=68.09 memory used=3178.7MB, alloc=596.3MB, time=71.03 memory used=3279.7MB, alloc=596.3MB, time=74.03 memory used=3360.0MB, alloc=596.3MB, time=76.16 memory used=3456.6MB, alloc=596.3MB, time=79.18 memory used=3529.1MB, alloc=596.3MB, time=81.15 memory used=3614.4MB, alloc=596.3MB, time=84.08 memory used=3692.3MB, alloc=596.3MB, time=86.68 memory used=3972.0MB, alloc=620.3MB, time=94.52 memory used=4278.2MB, alloc=644.3MB, time=103.15 memory used=4551.9MB, alloc=668.3MB, time=110.94 |\^/| 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(); 1428244012 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [19 x y + 12 z - 18 y, -14 y z - 7 z - 18, 15 x y + 18 y - 3 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-11 x y + x z - 9 z , 6 x - 15 y z - 18 y, -9 z - 8 z - 6] > Problem := [F,G]; 2 2 2 Problem := [[19 x y + 12 z - 18 y, -14 y z - 7 z - 18, 15 x y + 18 y - 3 x], 2 2 2 [-11 x y + x z - 9 z , 6 x - 15 y z - 18 y, -9 z - 8 z - 6]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.7MB, alloc=32.3MB, time=0.49 memory used=45.9MB, alloc=56.3MB, time=0.81 memory used=87.4MB, alloc=60.3MB, time=1.43 memory used=126.3MB, alloc=60.3MB, time=2.02 memory used=164.3MB, alloc=84.3MB, time=2.59 memory used=228.8MB, alloc=92.3MB, time=3.58 memory used=292.2MB, alloc=92.3MB, time=4.52 memory used=354.5MB, alloc=116.3MB, time=5.49 memory used=431.6MB, alloc=372.3MB, time=6.74 memory used=516.2MB, alloc=372.3MB, time=8.10 memory used=599.1MB, alloc=396.3MB, time=9.46 memory used=706.6MB, alloc=420.3MB, time=11.26 memory used=836.8MB, alloc=444.3MB, time=13.44 memory used=986.7MB, alloc=468.3MB, time=16.02 memory used=1131.2MB, alloc=492.3MB, time=18.54 memory used=1260.2MB, alloc=492.3MB, time=20.90 memory used=1379.0MB, alloc=492.3MB, time=22.94 memory used=1467.3MB, alloc=516.3MB, time=24.51 memory used=1567.9MB, alloc=516.3MB, time=26.51 memory used=1668.2MB, alloc=516.3MB, time=28.47 memory used=1748.0MB, alloc=516.3MB, time=29.86 memory used=1830.2MB, alloc=516.3MB, time=31.72 memory used=1903.8MB, alloc=516.3MB, time=33.04 memory used=1984.1MB, alloc=516.3MB, time=34.83 memory used=2041.6MB, alloc=516.3MB, time=35.96 memory used=2115.5MB, alloc=516.3MB, time=37.85 memory used=2166.2MB, alloc=516.3MB, time=38.97 memory used=2239.3MB, alloc=540.3MB, time=40.78 memory used=2283.4MB, alloc=540.3MB, time=41.95 memory used=2512.5MB, alloc=564.3MB, time=46.71 memory used=2718.6MB, alloc=588.3MB, time=51.16 memory used=2926.5MB, alloc=612.3MB, time=55.55 memory used=3106.2MB, alloc=636.3MB, time=59.54 memory used=3316.2MB, alloc=660.3MB, time=64.55 memory used=3486.1MB, alloc=660.3MB, time=68.57 memory used=3632.2MB, alloc=660.3MB, time=72.17 memory used=3793.9MB, alloc=684.3MB, time=76.12 memory used=3933.1MB, alloc=684.3MB, time=79.77 memory used=4068.6MB, alloc=684.3MB, time=83.26 memory used=4181.4MB, alloc=684.3MB, time=86.52 memory used=4296.0MB, alloc=684.3MB, time=89.94 memory used=4414.0MB, alloc=684.3MB, time=93.08 memory used=4519.6MB, alloc=684.3MB, time=96.17 memory used=4869.2MB, alloc=708.3MB, time=105.31 |\^/| 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(); 1428244312 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [4 x + 9 z + 11 x, -12 x z + 14 x + 15, 12 z + 3 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [19 y z + 5 z - 15, -y + 13 z + 1, 12 x - x z + 7] > Problem := [F,G]; 2 2 2 Problem := [[4 x + 9 z + 11 x, -12 x z + 14 x + 15, 12 z + 3 y], 2 2 [19 y z + 5 z - 15, -y + 13 z + 1, 12 x - x z + 7]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.49 memory used=46.6MB, alloc=32.3MB, time=0.80 memory used=65.6MB, alloc=56.3MB, time=1.09 memory used=104.9MB, alloc=60.3MB, time=1.68 memory used=143.0MB, alloc=60.3MB, time=2.24 memory used=180.1MB, alloc=84.3MB, time=2.81 memory used=237.8MB, alloc=84.3MB, time=3.69 memory used=294.8MB, alloc=84.3MB, time=4.59 memory used=351.4MB, alloc=116.3MB, time=5.52 memory used=426.6MB, alloc=116.3MB, time=6.71 memory used=507.8MB, alloc=140.3MB, time=7.94 memory used=582.6MB, alloc=140.3MB, time=9.20 memory used=648.5MB, alloc=420.3MB, time=10.31 memory used=770.5MB, alloc=444.3MB, time=12.32 memory used=914.3MB, alloc=444.3MB, time=14.85 memory used=1059.1MB, alloc=468.3MB, time=17.37 memory used=1207.5MB, alloc=492.3MB, time=20.00 memory used=1356.0MB, alloc=492.3MB, time=22.72 memory used=1482.0MB, alloc=516.3MB, time=24.93 memory used=1629.6MB, alloc=516.3MB, time=27.80 memory used=1764.2MB, alloc=540.3MB, time=30.40 memory used=1855.8MB, alloc=540.3MB, time=32.25 memory used=1969.2MB, alloc=540.3MB, time=34.82 memory used=2081.5MB, alloc=540.3MB, time=37.39 memory used=2164.7MB, alloc=540.3MB, time=39.07 memory used=2241.8MB, alloc=540.3MB, time=40.80 memory used=2334.4MB, alloc=564.3MB, time=42.84 memory used=2385.9MB, alloc=564.3MB, time=43.99 memory used=2464.7MB, alloc=564.3MB, time=45.94 memory used=2527.3MB, alloc=564.3MB, time=47.45 memory used=2601.4MB, alloc=564.3MB, time=49.37 memory used=2669.6MB, alloc=564.3MB, time=51.12 memory used=2726.2MB, alloc=564.3MB, time=52.71 memory used=2957.7MB, alloc=588.3MB, time=57.15 memory used=3205.1MB, alloc=612.3MB, time=62.13 memory used=3431.8MB, alloc=636.3MB, time=66.58 memory used=3664.3MB, alloc=660.3MB, time=71.41 memory used=3932.4MB, alloc=684.3MB, time=76.67 memory used=4208.2MB, alloc=708.3MB, time=82.14 memory used=4498.2MB, alloc=732.3MB, time=87.76 memory used=4785.2MB, alloc=756.3MB, time=93.64 memory used=5077.1MB, alloc=780.3MB, time=99.57 |\^/| 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(); 1428244612 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [9 x + 18 x - 14 y, -9 y + 11 z + 3, 19 x y - 12 x + 3 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-y - 17 x + 19, 14 y z + 17 z + 9, -12 x - 2 x y + 18 x] > Problem := [F,G]; 2 2 2 Problem := [[9 x + 18 x - 14 y, -9 y + 11 z + 3, 19 x y - 12 x + 3 z], 2 2 2 [-y - 17 x + 19, 14 y z + 17 z + 9, -12 x - 2 x y + 18 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.2MB, alloc=32.3MB, time=0.80 memory used=66.8MB, alloc=56.3MB, time=1.11 memory used=106.2MB, alloc=60.3MB, time=1.72 memory used=144.3MB, alloc=84.3MB, time=2.33 memory used=206.1MB, alloc=92.3MB, time=3.33 memory used=265.7MB, alloc=92.3MB, time=4.29 memory used=325.0MB, alloc=116.3MB, time=5.25 memory used=407.2MB, alloc=116.3MB, time=6.55 memory used=488.7MB, alloc=140.3MB, time=7.86 memory used=589.7MB, alloc=420.3MB, time=9.76 memory used=705.3MB, alloc=444.3MB, time=11.94 memory used=834.6MB, alloc=468.3MB, time=14.31 memory used=979.1MB, alloc=492.3MB, time=17.00 memory used=1134.2MB, alloc=516.3MB, time=19.93 memory used=1297.3MB, alloc=540.3MB, time=23.05 memory used=1466.8MB, alloc=564.3MB, time=26.32 memory used=1625.2MB, alloc=588.3MB, time=31.37 memory used=1791.2MB, alloc=612.3MB, time=37.15 memory used=1971.1MB, alloc=636.3MB, time=43.71 memory used=2165.7MB, alloc=660.3MB, time=51.05 memory used=2376.0MB, alloc=684.3MB, time=59.31 memory used=2602.7MB, alloc=708.3MB, time=68.39 memory used=2844.6MB, alloc=732.3MB, time=78.43 memory used=3102.1MB, alloc=756.3MB, 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(); 1428244912 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-6 x + 5 y + 8 z , 18 x - 6 z, 18 y z - 19 z + 18] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-2 x + 15 x z - 2 z , 18 y + 19 x + 10 z, 18 x - 18 y z - 3 y] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-6 x + 5 y + 8 z , 18 x - 6 z, 18 y z - 19 z + 18], 2 2 2 2 [-2 x + 15 x z - 2 z , 18 y + 19 x + 10 z, 18 x - 18 y z - 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.1MB, alloc=32.3MB, time=0.82 memory used=67.0MB, alloc=60.3MB, time=1.14 memory used=108.3MB, alloc=60.3MB, time=1.73 memory used=148.1MB, alloc=84.3MB, time=2.32 memory used=211.2MB, alloc=92.3MB, time=3.26 memory used=276.0MB, alloc=92.3MB, time=4.20 memory used=337.0MB, alloc=116.3MB, time=5.14 memory used=401.1MB, alloc=372.3MB, time=6.12 memory used=481.7MB, alloc=396.3MB, time=7.32 memory used=586.6MB, alloc=420.3MB, time=8.94 memory used=715.5MB, alloc=420.3MB, time=10.89 memory used=840.1MB, alloc=444.3MB, time=12.87 memory used=972.3MB, alloc=444.3MB, time=14.75 memory used=1096.5MB, alloc=468.3MB, time=16.84 memory used=1228.2MB, alloc=492.3MB, time=19.01 memory used=1343.1MB, alloc=492.3MB, time=20.78 memory used=1447.3MB, alloc=492.3MB, time=22.53 memory used=1556.5MB, alloc=492.3MB, time=24.43 memory used=1649.7MB, alloc=492.3MB, time=26.04 memory used=1742.3MB, alloc=492.3MB, time=27.71 memory used=1822.3MB, alloc=516.3MB, time=29.19 memory used=1894.4MB, alloc=516.3MB, time=30.50 memory used=1963.8MB, alloc=516.3MB, time=32.00 memory used=2035.4MB, alloc=516.3MB, time=33.39 memory used=2098.2MB, alloc=516.3MB, time=34.65 memory used=2164.1MB, alloc=516.3MB, time=35.99 memory used=2222.0MB, alloc=516.3MB, time=37.19 memory used=2280.5MB, alloc=516.3MB, time=38.35 memory used=2334.3MB, alloc=516.3MB, time=39.47 memory used=2536.3MB, alloc=540.3MB, time=43.15 memory used=2747.1MB, alloc=564.3MB, time=47.18 memory used=2919.7MB, alloc=588.3MB, time=49.95 memory used=3124.4MB, alloc=612.3MB, time=53.96 memory used=3285.2MB, alloc=636.3MB, time=56.34 memory used=3446.3MB, alloc=660.3MB, time=59.79 memory used=3590.6MB, alloc=684.3MB, time=62.93 memory used=3727.4MB, alloc=708.3MB, time=65.47 memory used=3859.8MB, alloc=708.3MB, time=67.83 memory used=3990.6MB, alloc=708.3MB, time=71.05 memory used=4086.6MB, alloc=708.3MB, time=73.06 memory used=4200.0MB, alloc=708.3MB, time=76.16 memory used=4581.3MB, alloc=732.3MB, time=82.88 memory used=4969.8MB, alloc=756.3MB, time=90.28 memory used=5334.3MB, alloc=780.3MB, time=96.45 |\^/| 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(); 1428245212 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [18 x - 4 y z - 19 x, 17 x y + 4 y - 12 z , 10 x - 8 x y - 3 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [7 x + 8 z - 12 x, 16 y + 11 z, y z - 6 z - 7 y] > Problem := [F,G]; 2 2 2 2 Problem := [[18 x - 4 y z - 19 x, 17 x y + 4 y - 12 z , 10 x - 8 x y - 3 z], 2 2 2 [7 x + 8 z - 12 x, 16 y + 11 z, y z - 6 z - 7 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.50 memory used=47.1MB, alloc=32.3MB, time=0.81 memory used=66.9MB, alloc=56.3MB, time=1.12 memory used=107.2MB, alloc=60.3MB, time=1.71 memory used=146.2MB, alloc=84.3MB, time=2.31 memory used=204.8MB, alloc=92.3MB, time=3.21 memory used=267.3MB, alloc=116.3MB, time=4.11 memory used=343.3MB, alloc=116.3MB, time=5.23 memory used=412.5MB, alloc=396.3MB, time=6.29 memory used=519.4MB, alloc=420.3MB, time=7.92 memory used=652.4MB, alloc=444.3MB, time=9.89 memory used=787.6MB, alloc=468.3MB, time=12.01 memory used=915.3MB, alloc=468.3MB, time=14.10 memory used=1038.8MB, alloc=492.3MB, time=16.12 memory used=1165.0MB, alloc=492.3MB, time=18.35 memory used=1269.6MB, alloc=492.3MB, time=20.21 memory used=1375.0MB, alloc=516.3MB, time=22.13 memory used=1469.0MB, alloc=516.3MB, time=23.90 memory used=1554.6MB, alloc=516.3MB, time=25.58 memory used=1637.4MB, alloc=516.3MB, time=27.14 memory used=1713.6MB, alloc=516.3MB, time=28.67 memory used=1777.6MB, alloc=516.3MB, time=30.04 memory used=1840.0MB, alloc=540.3MB, time=31.27 memory used=1911.9MB, alloc=540.3MB, time=32.79 memory used=1976.4MB, alloc=540.3MB, time=34.25 memory used=2032.6MB, alloc=540.3MB, time=35.56 memory used=2083.3MB, alloc=540.3MB, time=36.62 memory used=2303.0MB, alloc=564.3MB, time=40.86 memory used=2537.6MB, alloc=588.3MB, time=45.51 memory used=2758.4MB, alloc=612.3MB, time=50.34 memory used=2963.4MB, alloc=636.3MB, time=54.81 memory used=3125.2MB, alloc=660.3MB, time=58.69 memory used=3277.3MB, alloc=684.3MB, time=61.61 memory used=3448.4MB, alloc=708.3MB, time=65.98 memory used=3591.1MB, alloc=732.3MB, time=68.56 memory used=3732.5MB, alloc=732.3MB, time=72.42 memory used=3842.3MB, alloc=732.3MB, time=74.97 memory used=3974.7MB, alloc=732.3MB, time=78.60 memory used=4066.0MB, alloc=756.3MB, time=81.21 memory used=4482.7MB, alloc=780.3MB, time=91.15 memory used=4902.8MB, alloc=804.3MB, time=100.07 |\^/| 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(); 1428245512 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-3 y z - 8 y + 10 z, -14 + 3 x - 16 y, 16 x - 8 x z - 4 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [-20 x z - 19 y z - 14 z, -x z + 3 y - 9, 15 x y - 3 y z - 8 x] > Problem := [F,G]; 2 Problem := [[-3 y z - 8 y + 10 z, -14 + 3 x - 16 y, 16 x - 8 x z - 4 y z], [-20 x z - 19 y z - 14 z, -x z + 3 y - 9, 15 x y - 3 y z - 8 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.78 memory used=67.1MB, alloc=56.3MB, time=1.07 memory used=105.9MB, alloc=60.3MB, time=1.65 memory used=143.0MB, alloc=84.3MB, time=2.20 memory used=200.5MB, alloc=84.3MB, time=3.05 memory used=254.8MB, alloc=116.3MB, time=3.92 memory used=331.0MB, alloc=116.3MB, time=5.10 memory used=406.6MB, alloc=140.3MB, time=6.33 memory used=505.5MB, alloc=140.3MB, time=7.95 memory used=599.3MB, alloc=420.3MB, time=9.58 memory used=718.8MB, alloc=444.3MB, time=11.65 memory used=862.2MB, alloc=468.3MB, time=14.27 memory used=1022.8MB, alloc=492.3MB, time=17.32 memory used=1202.9MB, alloc=516.3MB, time=20.86 memory used=1383.3MB, alloc=540.3MB, time=24.56 memory used=1539.8MB, alloc=564.3MB, time=27.68 memory used=1660.1MB, alloc=588.3MB, time=30.09 memory used=1817.6MB, alloc=612.3MB, time=33.20 memory used=1970.7MB, alloc=636.3MB, time=36.27 memory used=2119.9MB, alloc=660.3MB, time=39.33 memory used=2268.0MB, alloc=684.3MB, time=42.33 memory used=2401.1MB, alloc=708.3MB, time=45.13 memory used=2535.7MB, alloc=732.3MB, time=48.13 memory used=2667.7MB, alloc=756.3MB, time=51.04 memory used=2785.8MB, alloc=780.3MB, time=53.69 memory used=2902.0MB, alloc=804.3MB, time=56.33 memory used=3019.4MB, alloc=828.3MB, time=58.95 memory used=3134.0MB, alloc=852.3MB, time=61.54 memory used=3237.0MB, alloc=852.3MB, time=63.91 memory used=3342.4MB, alloc=876.3MB, time=66.34 memory used=3451.0MB, alloc=900.3MB, time=68.87 memory used=3542.7MB, alloc=900.3MB, time=71.19 memory used=3632.8MB, alloc=924.3MB, time=73.56 memory used=3727.2MB, alloc=924.3MB, time=75.99 memory used=3815.5MB, alloc=948.3MB, time=78.26 memory used=3883.4MB, alloc=948.3MB, time=80.17 memory used=3960.2MB, alloc=972.3MB, time=82.25 memory used=4046.4MB, alloc=972.3MB, time=84.51 memory used=4121.0MB, alloc=996.3MB, time=86.59 memory used=4200.5MB, alloc=996.3MB, time=88.81 |\^/| 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(); 1428245812 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-15 y - 5 y z + 2 x, 19 x - 4 x z - 11 y, 4 x - 11 y - 19 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-8 + 18 x - 8 z, 4 x - 16 y z - 3 x, 15 x z - 15 y - 10 y z] > Problem := [F,G]; 2 2 2 2 Problem := [[-15 y - 5 y z + 2 x, 19 x - 4 x z - 11 y, 4 x - 11 y - 19 x], 2 2 [-8 + 18 x - 8 z, 4 x - 16 y z - 3 x, 15 x z - 15 y - 10 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.51 memory used=46.6MB, alloc=32.3MB, time=0.81 memory used=65.9MB, alloc=56.3MB, time=1.11 memory used=105.2MB, alloc=60.3MB, time=1.71 memory used=142.6MB, alloc=84.3MB, time=2.30 memory used=202.3MB, alloc=92.3MB, time=3.23 memory used=260.7MB, alloc=116.3MB, time=4.17 memory used=341.0MB, alloc=116.3MB, time=5.44 memory used=413.7MB, alloc=396.3MB, time=6.66 memory used=521.9MB, alloc=420.3MB, time=8.33 memory used=649.6MB, alloc=444.3MB, time=10.43 memory used=792.7MB, alloc=468.3MB, time=12.75 memory used=933.3MB, alloc=492.3MB, time=15.29 memory used=1062.8MB, alloc=492.3MB, time=17.63 memory used=1184.1MB, alloc=492.3MB, time=19.85 memory used=1291.5MB, alloc=516.3MB, time=21.80 memory used=1405.3MB, alloc=516.3MB, time=24.12 memory used=1511.6MB, alloc=516.3MB, time=26.27 memory used=1596.5MB, alloc=516.3MB, time=28.05 memory used=1677.5MB, alloc=516.3MB, time=29.78 memory used=1744.6MB, alloc=516.3MB, time=31.12 memory used=1810.6MB, alloc=516.3MB, time=32.70 memory used=1878.6MB, alloc=516.3MB, time=34.25 memory used=1944.9MB, alloc=540.3MB, time=35.85 memory used=2169.4MB, alloc=564.3MB, time=40.33 memory used=2396.5MB, alloc=588.3MB, time=44.83 memory used=2600.9MB, alloc=612.3MB, time=49.11 memory used=2794.4MB, alloc=636.3MB, time=53.37 memory used=2962.8MB, alloc=660.3MB, time=57.01 memory used=3119.8MB, alloc=684.3MB, time=60.64 memory used=3248.1MB, alloc=684.3MB, time=63.54 memory used=3377.1MB, alloc=684.3MB, time=66.67 memory used=3528.6MB, alloc=708.3MB, time=70.30 memory used=3683.5MB, alloc=732.3MB, time=73.97 memory used=3761.5MB, alloc=756.3MB, time=76.30 memory used=3918.4MB, alloc=780.3MB, time=80.08 memory used=4039.5MB, alloc=780.3MB, time=83.31 memory used=4376.7MB, alloc=804.3MB, time=90.52 |\^/| 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(); 1428246112 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [11 x y - 5 y z - 15 x, -5 y z - 3 x - 9, -14 - 17 x + 2 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [10 x - y + 10 z, -17 x - z + 8 y, 2 y - 20 x + 20 z] > Problem := [F,G]; Problem := [[11 x y - 5 y z - 15 x, -5 y z - 3 x - 9, -14 - 17 x + 2 z], 2 2 2 [10 x - y + 10 z, -17 x - z + 8 y, 2 y - 20 x + 20 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.7MB, alloc=32.3MB, time=0.50 memory used=45.6MB, alloc=56.3MB, time=0.81 memory used=86.3MB, alloc=60.3MB, time=1.43 memory used=124.8MB, alloc=84.3MB, time=2.02 memory used=171.1MB, alloc=84.3MB, time=2.71 memory used=229.4MB, alloc=116.3MB, time=3.63 memory used=310.0MB, alloc=116.3MB, time=4.88 memory used=388.9MB, alloc=140.3MB, time=6.14 memory used=489.9MB, alloc=140.3MB, time=7.80 memory used=576.8MB, alloc=164.3MB, time=9.37 memory used=666.5MB, alloc=420.3MB, time=10.95 memory used=783.8MB, alloc=444.3MB, time=13.00 memory used=927.5MB, alloc=468.3MB, time=15.39 memory used=1092.9MB, alloc=492.3MB, time=18.44 memory used=1288.0MB, alloc=516.3MB, time=21.58 memory used=1505.9MB, alloc=540.3MB, time=25.44 memory used=1733.6MB, alloc=564.3MB, time=29.55 memory used=1992.2MB, alloc=588.3MB, time=34.88 memory used=2274.9MB, alloc=612.3MB, time=40.74 memory used=2574.2MB, alloc=636.3MB, time=47.44 memory used=2818.8MB, alloc=660.3MB, time=53.15 memory used=3076.4MB, alloc=684.3MB, time=59.27 memory used=3307.9MB, alloc=708.3MB, time=65.16 memory used=3527.4MB, alloc=732.3MB, time=70.98 memory used=3724.0MB, alloc=756.3MB, time=76.05 memory used=3914.6MB, alloc=780.3MB, time=80.99 memory used=4104.2MB, alloc=780.3MB, time=86.40 memory used=4257.3MB, alloc=780.3MB, time=90.52 memory used=4410.2MB, alloc=780.3MB, time=94.81 memory used=4565.5MB, alloc=780.3MB, time=99.62 memory used=4691.9MB, alloc=780.3MB, time=103.83 |\^/| 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(); 1428246412 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [3 x - 7 x + 2 y, 12 y - 15 z - 14 x, 19 x z - 3 x - 7] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-19 x - x y - 15 x z, 11 x z + 20 y + 20 x, -8 y z - 18] > Problem := [F,G]; 2 2 2 Problem := [[3 x - 7 x + 2 y, 12 y - 15 z - 14 x, 19 x z - 3 x - 7], 2 2 [-19 x - x y - 15 x z, 11 x z + 20 y + 20 x, -8 y z - 18]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.5MB, alloc=32.3MB, time=0.80 memory used=66.9MB, alloc=56.3MB, time=1.10 memory used=109.2MB, alloc=60.3MB, time=1.71 memory used=149.5MB, alloc=84.3MB, time=2.31 memory used=212.4MB, alloc=92.3MB, time=3.27 memory used=272.9MB, alloc=116.3MB, time=4.19 memory used=348.4MB, alloc=116.3MB, time=5.34 memory used=425.2MB, alloc=396.3MB, time=6.58 memory used=534.8MB, alloc=420.3MB, time=8.19 memory used=660.8MB, alloc=444.3MB, time=10.25 memory used=798.1MB, alloc=468.3MB, time=12.49 memory used=919.8MB, alloc=468.3MB, time=14.53 memory used=1048.6MB, alloc=492.3MB, time=16.74 memory used=1148.5MB, alloc=492.3MB, time=18.50 memory used=1263.2MB, alloc=492.3MB, time=20.62 memory used=1345.7MB, alloc=492.3MB, time=22.22 memory used=1441.3MB, alloc=516.3MB, time=24.03 memory used=1515.1MB, alloc=516.3MB, time=25.50 memory used=1578.3MB, alloc=516.3MB, time=26.81 memory used=1666.3MB, alloc=516.3MB, time=28.71 memory used=1739.0MB, alloc=516.3MB, time=30.28 memory used=1806.0MB, alloc=516.3MB, time=31.78 memory used=1860.7MB, alloc=516.3MB, time=33.01 memory used=1907.9MB, alloc=516.3MB, time=34.16 memory used=2111.4MB, alloc=540.3MB, time=37.90 memory used=2331.6MB, alloc=564.3MB, time=42.52 memory used=2555.7MB, alloc=588.3MB, time=47.04 memory used=2751.4MB, alloc=612.3MB, time=51.18 memory used=2945.9MB, alloc=636.3MB, time=55.54 memory used=3095.7MB, alloc=660.3MB, time=58.73 memory used=3267.8MB, alloc=684.3MB, time=62.48 memory used=3411.5MB, alloc=708.3MB, time=65.67 memory used=3532.7MB, alloc=708.3MB, time=68.45 memory used=3666.5MB, alloc=732.3MB, time=71.79 memory used=3802.8MB, alloc=756.3MB, time=75.11 memory used=3936.4MB, alloc=756.3MB, time=78.43 memory used=4068.9MB, alloc=780.3MB, time=81.71 memory used=4426.6MB, alloc=804.3MB, time=88.96 memory used=4776.1MB, alloc=828.3MB, time=96.35 memory used=5121.1MB, alloc=852.3MB, time=103.72 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428246712 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-7 x + x + 3, 5 x y - 10 x z + 11, -2 x y + 3 y z + 11] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-19 x y + 10 z - 12 y, -5 x z - 7 y + 11 z, 2 y + 6 y - 5] > Problem := [F,G]; 2 Problem := [[-7 x + x + 3, 5 x y - 10 x z + 11, -2 x y + 3 y z + 11], 2 2 [-19 x y + 10 z - 12 y, -5 x z - 7 y + 11 z, 2 y + 6 y - 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=27.0MB, alloc=32.3MB, time=0.52 memory used=47.8MB, alloc=32.3MB, time=0.83 memory used=66.9MB, alloc=56.3MB, time=1.14 memory used=105.5MB, alloc=60.3MB, time=1.76 memory used=143.4MB, alloc=84.3MB, time=2.35 memory used=204.2MB, alloc=92.3MB, time=3.33 memory used=263.1MB, alloc=92.3MB, time=4.27 memory used=321.0MB, alloc=116.3MB, time=5.23 memory used=401.3MB, alloc=116.3MB, time=6.55 memory used=484.8MB, alloc=140.3MB, time=8.09 memory used=581.6MB, alloc=420.3MB, time=9.86 memory used=699.4MB, alloc=444.3MB, time=11.90 memory used=831.8MB, alloc=468.3MB, time=14.23 memory used=980.8MB, alloc=492.3MB, time=16.83 memory used=1141.4MB, alloc=516.3MB, time=19.73 memory used=1315.2MB, alloc=540.3MB, time=22.93 memory used=1503.1MB, alloc=564.3MB, time=26.40 memory used=1706.9MB, alloc=588.3MB, time=30.13 memory used=1915.1MB, alloc=612.3MB, time=35.09 memory used=2104.5MB, alloc=636.3MB, time=41.64 memory used=2303.0MB, alloc=660.3MB, time=48.98 memory used=2514.5MB, alloc=684.3MB, time=57.11 memory used=2740.7MB, alloc=708.3MB, time=66.05 memory used=2982.6MB, alloc=732.3MB, time=75.96 memory used=3239.8MB, alloc=756.3MB, time=86.69 memory used=3505.8MB, alloc=780.3MB, time=98.63 |\^/| 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(); 1428247012 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [-x y + 7 y - 4 z, -19 x z + 8 y z + 15, 9 x z - 19 y z + 15] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-12 y + 2 x, 17 x y - 6 y + 20 y z, 4 x y + 16 x z - 18 z] > Problem := [F,G]; Problem := [[-x y + 7 y - 4 z, -19 x z + 8 y z + 15, 9 x z - 19 y z + 15], 2 2 [-12 y + 2 x, 17 x y - 6 y + 20 y z, 4 x y + 16 x z - 18 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=45.1MB, alloc=56.3MB, time=0.79 memory used=84.8MB, alloc=60.3MB, time=1.45 memory used=124.9MB, alloc=84.3MB, time=2.10 memory used=170.4MB, alloc=84.3MB, time=2.82 memory used=230.3MB, alloc=92.3MB, time=3.83 memory used=288.0MB, alloc=116.3MB, time=4.78 memory used=368.6MB, alloc=140.3MB, time=6.07 memory used=456.2MB, alloc=396.3MB, time=7.54 memory used=564.7MB, alloc=420.3MB, time=9.15 memory used=693.0MB, alloc=444.3MB, time=11.14 memory used=842.7MB, alloc=468.3MB, time=13.64 memory used=990.0MB, alloc=492.3MB, time=16.24 memory used=1092.6MB, alloc=492.3MB, time=18.21 memory used=1213.7MB, alloc=492.3MB, time=20.33 memory used=1319.2MB, alloc=492.3MB, time=22.21 memory used=1432.7MB, alloc=516.3MB, time=24.52 memory used=1522.4MB, alloc=516.3MB, time=26.27 memory used=1614.9MB, alloc=516.3MB, time=28.35 memory used=1692.7MB, alloc=516.3MB, time=29.80 memory used=1775.4MB, alloc=540.3MB, time=31.54 memory used=1854.3MB, alloc=540.3MB, time=33.19 memory used=1915.1MB, alloc=540.3MB, time=34.57 memory used=1966.9MB, alloc=540.3MB, time=35.87 memory used=2022.7MB, alloc=540.3MB, time=37.24 memory used=2084.2MB, alloc=540.3MB, time=38.79 memory used=2296.5MB, alloc=564.3MB, time=42.99 memory used=2506.7MB, alloc=588.3MB, time=47.59 memory used=2722.7MB, alloc=612.3MB, time=52.38 memory used=2936.2MB, alloc=636.3MB, time=57.22 memory used=3158.3MB, alloc=660.3MB, time=61.97 memory used=3392.4MB, alloc=684.3MB, time=67.13 memory used=3608.3MB, alloc=708.3MB, time=71.92 memory used=3844.3MB, alloc=732.3MB, time=77.38 memory used=4039.0MB, alloc=756.3MB, time=81.87 memory used=4266.0MB, alloc=780.3MB, time=86.94 memory used=4475.2MB, alloc=804.3MB, time=91.66 memory used=4673.9MB, alloc=828.3MB, time=96.19 memory used=4856.3MB, alloc=852.3MB, time=100.46 |\^/| 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(); 1428247312 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-12 y + 7 y z - 2 z, -15 x + 2 x y - 19 z, 7 x + 14 x y + 8 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-4 x z - 2 x + 6, -19 x - 6 x z - 20 y , 6 x - 20 y z - 18 z] > Problem := [F,G]; 2 2 2 Problem := [[-12 y + 7 y z - 2 z, -15 x + 2 x y - 19 z, 7 x + 14 x y + 8 x], 2 2 2 [-4 x z - 2 x + 6, -19 x - 6 x z - 20 y , 6 x - 20 y z - 18 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.0MB, alloc=56.3MB, time=0.83 memory used=87.3MB, alloc=60.3MB, time=1.41 memory used=127.2MB, alloc=84.3MB, time=2.01 memory used=169.1MB, alloc=84.3MB, time=2.64 memory used=230.8MB, alloc=92.3MB, time=3.60 memory used=291.4MB, alloc=116.3MB, time=4.53 memory used=370.4MB, alloc=140.3MB, time=5.79 memory used=441.3MB, alloc=396.3MB, time=6.95 memory used=550.0MB, alloc=420.3MB, time=8.67 memory used=684.5MB, alloc=444.3MB, time=10.82 memory used=827.6MB, alloc=468.3MB, time=13.32 memory used=963.9MB, alloc=492.3MB, time=15.63 memory used=1068.6MB, alloc=492.3MB, time=17.44 memory used=1186.8MB, alloc=492.3MB, time=19.58 memory used=1274.4MB, alloc=492.3MB, time=21.16 memory used=1366.7MB, alloc=492.3MB, time=22.86 memory used=1443.7MB, alloc=492.3MB, time=24.38 memory used=1524.3MB, alloc=492.3MB, time=26.01 memory used=1600.6MB, alloc=492.3MB, time=27.83 memory used=1660.0MB, alloc=492.3MB, time=29.10 memory used=1725.2MB, alloc=492.3MB, time=30.63 memory used=1794.9MB, alloc=492.3MB, time=32.23 memory used=1854.6MB, alloc=516.3MB, time=33.71 memory used=2063.4MB, alloc=540.3MB, time=37.68 memory used=2281.6MB, alloc=564.3MB, time=41.93 memory used=2496.7MB, alloc=588.3MB, time=46.44 memory used=2684.3MB, alloc=612.3MB, time=50.60 memory used=2858.4MB, alloc=636.3MB, time=54.28 memory used=3022.0MB, alloc=660.3MB, time=58.22 memory used=3172.5MB, alloc=660.3MB, time=61.65 memory used=3301.7MB, alloc=660.3MB, time=64.44 memory used=3413.9MB, alloc=660.3MB, time=67.12 memory used=3503.9MB, alloc=660.3MB, time=69.33 memory used=3608.3MB, alloc=684.3MB, time=72.15 memory used=3952.1MB, alloc=708.3MB, time=79.79 memory used=4305.5MB, alloc=732.3MB, time=87.31 memory used=4621.0MB, alloc=756.3MB, time=94.44 memory used=4918.7MB, alloc=780.3MB, time=101.22 memory used=5218.8MB, alloc=804.3MB, time=108.05 |\^/| 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(); 1428247612 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-14 x y - z - 9, 14 x z - 7 y + 19 z, 6 x - 17 z + 15 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-8 x + 16 x z + 6 z, 3 z + 7 x + z, -x z + 20 y + 16 x] > Problem := [F,G]; 2 2 2 2 Problem := [[-14 x y - z - 9, 14 x z - 7 y + 19 z, 6 x - 17 z + 15 y], 2 2 2 [-8 x + 16 x z + 6 z, 3 z + 7 x + z, -x z + 20 y + 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=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=56.3MB, time=0.84 memory used=87.2MB, alloc=60.3MB, time=1.43 memory used=129.2MB, alloc=92.3MB, time=2.07 memory used=197.0MB, alloc=92.3MB, time=3.02 memory used=262.9MB, alloc=116.3MB, time=3.98 memory used=328.5MB, alloc=372.3MB, time=4.96 memory used=415.9MB, alloc=396.3MB, time=6.20 memory used=523.0MB, alloc=420.3MB, time=7.89 memory used=659.1MB, alloc=444.3MB, time=9.82 memory used=780.0MB, alloc=444.3MB, time=11.39 memory used=893.2MB, alloc=468.3MB, time=13.09 memory used=1005.1MB, alloc=468.3MB, time=14.72 memory used=1122.8MB, alloc=468.3MB, time=16.44 memory used=1223.4MB, alloc=492.3MB, time=18.06 memory used=1329.7MB, alloc=492.3MB, time=19.78 memory used=1433.2MB, alloc=492.3MB, time=21.35 memory used=1503.2MB, alloc=492.3MB, time=22.57 memory used=1578.2MB, alloc=492.3MB, time=23.86 memory used=1653.2MB, alloc=492.3MB, time=25.24 memory used=1724.2MB, alloc=492.3MB, time=26.56 memory used=1776.4MB, alloc=492.3MB, time=27.57 memory used=1859.4MB, alloc=492.3MB, time=28.89 memory used=1908.4MB, alloc=492.3MB, time=29.84 memory used=1962.5MB, alloc=492.3MB, time=30.81 memory used=2155.9MB, alloc=516.3MB, time=33.92 memory used=2357.9MB, alloc=540.3MB, time=37.45 memory used=2540.8MB, alloc=564.3MB, time=40.86 memory used=2713.0MB, alloc=588.3MB, time=44.13 memory used=2889.4MB, alloc=612.3MB, time=47.51 memory used=3035.5MB, alloc=636.3MB, time=50.59 memory used=3167.0MB, alloc=636.3MB, time=53.30 memory used=3318.4MB, alloc=660.3MB, time=56.66 memory used=3436.2MB, alloc=660.3MB, time=59.27 memory used=3548.1MB, alloc=660.3MB, time=61.76 memory used=3647.6MB, alloc=660.3MB, time=64.09 memory used=3737.9MB, alloc=660.3MB, time=66.30 memory used=4078.8MB, alloc=684.3MB, time=71.97 memory used=4428.1MB, alloc=708.3MB, time=78.20 memory used=4786.2MB, alloc=732.3MB, time=85.08 memory used=5151.3MB, alloc=756.3MB, time=91.39 memory used=5512.3MB, alloc=780.3MB, time=99.60 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428247912 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [2 y - 16 y z - 8 x, 5 x z - 9 z - 14 z, 16 y z - 3 x - 13] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [19 x + 20 z, 10 x z + 10 x - 17, 6 x + 8 z + 13] > Problem := [F,G]; 2 2 Problem := [[2 y - 16 y z - 8 x, 5 x z - 9 z - 14 z, 16 y z - 3 x - 13], 2 2 [19 x + 20 z, 10 x z + 10 x - 17, 6 x + 8 z + 13]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.49 memory used=45.2MB, alloc=32.3MB, time=0.77 memory used=64.0MB, alloc=56.3MB, time=1.08 memory used=102.6MB, alloc=60.3MB, time=1.67 memory used=139.3MB, alloc=84.3MB, time=2.25 memory used=199.2MB, alloc=92.3MB, time=3.21 memory used=257.1MB, alloc=116.3MB, time=4.13 memory used=335.8MB, alloc=116.3MB, time=5.44 memory used=408.9MB, alloc=140.3MB, time=6.68 memory used=501.8MB, alloc=140.3MB, time=8.20 memory used=584.7MB, alloc=420.3MB, time=9.68 memory used=705.3MB, alloc=444.3MB, time=11.81 memory used=844.8MB, alloc=444.3MB, time=14.15 memory used=978.5MB, alloc=468.3MB, time=16.50 memory used=1136.3MB, alloc=492.3MB, time=19.63 memory used=1297.1MB, alloc=516.3MB, time=22.65 memory used=1469.1MB, alloc=540.3MB, time=25.85 memory used=1659.6MB, alloc=564.3MB, time=29.34 memory used=1851.5MB, alloc=588.3MB, time=33.15 memory used=2051.4MB, alloc=612.3MB, time=37.09 memory used=2261.1MB, alloc=636.3MB, time=41.30 memory used=2478.1MB, alloc=660.3MB, time=45.59 memory used=2690.6MB, alloc=684.3MB, time=50.64 memory used=2888.2MB, alloc=708.3MB, time=57.33 memory used=3091.6MB, alloc=732.3MB, time=64.86 memory used=3306.2MB, alloc=756.3MB, time=73.03 memory used=3533.1MB, alloc=780.3MB, time=81.86 memory used=3773.8MB, alloc=804.3MB, time=91.57 |\^/| 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(); 1428248212 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [11 x z + 11 y - 9 y z, 11 x z + 3 y - 8 z, -13 x - 4 x y - y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [15 x z - y , -15 x z + 10 z - 17 y, -14 y z + 7 y] > Problem := [F,G]; Problem := [ 2 2 2 [11 x z + 11 y - 9 y z, 11 x z + 3 y - 8 z, -13 x - 4 x y - y z], 2 2 [15 x z - y , -15 x z + 10 z - 17 y, -14 y z + 7 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=47.1MB, alloc=32.3MB, time=0.80 memory used=66.7MB, alloc=56.3MB, time=1.10 memory used=105.9MB, alloc=60.3MB, time=1.68 memory used=142.3MB, alloc=84.3MB, time=2.22 memory used=206.2MB, alloc=92.3MB, time=3.18 memory used=267.3MB, alloc=116.3MB, time=4.10 memory used=350.5MB, alloc=116.3MB, time=5.36 memory used=430.9MB, alloc=140.3MB, time=6.64 memory used=494.0MB, alloc=140.3MB, time=7.61 memory used=562.1MB, alloc=396.3MB, time=8.78 memory used=661.5MB, alloc=420.3MB, time=10.39 memory used=778.6MB, alloc=444.3MB, time=12.24 memory used=913.0MB, alloc=468.3MB, time=14.34 memory used=1026.2MB, alloc=492.3MB, time=16.26 memory used=1134.6MB, alloc=492.3MB, time=18.13 memory used=1235.4MB, alloc=492.3MB, time=19.87 memory used=1316.1MB, alloc=516.3MB, time=21.32 memory used=1400.2MB, alloc=516.3MB, time=22.64 memory used=1493.9MB, alloc=516.3MB, time=24.61 memory used=1557.2MB, alloc=516.3MB, time=25.94 memory used=1640.1MB, alloc=516.3MB, time=27.72 memory used=1705.8MB, alloc=516.3MB, time=28.97 memory used=1776.4MB, alloc=516.3MB, time=30.65 memory used=1817.6MB, alloc=516.3MB, time=31.65 memory used=1863.2MB, alloc=540.3MB, time=32.62 memory used=2086.5MB, alloc=564.3MB, time=37.10 memory used=2310.9MB, alloc=588.3MB, time=41.62 memory used=2509.9MB, alloc=612.3MB, time=45.69 memory used=2702.0MB, alloc=636.3MB, time=49.55 memory used=2887.7MB, alloc=660.3MB, time=53.89 memory used=3057.8MB, alloc=684.3MB, time=57.85 memory used=3201.2MB, alloc=708.3MB, time=60.63 memory used=3360.2MB, alloc=708.3MB, time=64.89 memory used=3508.1MB, alloc=708.3MB, time=68.96 memory used=3619.0MB, alloc=708.3MB, time=71.84 memory used=3739.6MB, alloc=708.3MB, time=75.19 memory used=4103.5MB, alloc=732.3MB, time=84.19 memory used=4486.0MB, alloc=756.3MB, time=93.39 |\^/| 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(); 1428248512 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [7 x - 9 x y + 9, 15 y z - 14 x + 4 z, 20 x + 5 z - 2 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [14 x - 6 y z - 8 y, 12 z + 2 x + 12 z, -13 x y + 9 z - 10 z] > Problem := [F,G]; 2 2 2 Problem := [[7 x - 9 x y + 9, 15 y z - 14 x + 4 z, 20 x + 5 z - 2 y], 2 2 2 [14 x - 6 y z - 8 y, 12 z + 2 x + 12 z, -13 x y + 9 z - 10 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=48.5MB, alloc=32.3MB, time=0.83 memory used=68.9MB, alloc=56.3MB, time=1.15 memory used=110.4MB, alloc=60.3MB, time=1.79 memory used=150.7MB, alloc=84.3MB, time=2.40 memory used=211.6MB, alloc=92.3MB, time=3.35 memory used=271.5MB, alloc=116.3MB, time=4.30 memory used=355.3MB, alloc=116.3MB, time=5.61 memory used=437.1MB, alloc=396.3MB, time=6.97 memory used=545.1MB, alloc=396.3MB, time=8.72 memory used=650.3MB, alloc=420.3MB, time=10.50 memory used=775.8MB, alloc=444.3MB, time=12.69 memory used=926.2MB, alloc=468.3MB, time=15.38 memory used=1068.3MB, alloc=492.3MB, time=17.90 memory used=1214.6MB, alloc=492.3MB, time=20.72 memory used=1340.5MB, alloc=516.3MB, time=23.00 memory used=1458.9MB, alloc=516.3MB, time=25.38 memory used=1571.1MB, alloc=516.3MB, time=27.51 memory used=1675.9MB, alloc=540.3MB, time=29.55 memory used=1759.4MB, alloc=540.3MB, time=31.07 memory used=1853.8MB, alloc=540.3MB, time=33.11 memory used=1934.2MB, alloc=540.3MB, time=35.11 memory used=2020.1MB, alloc=540.3MB, time=37.09 memory used=2109.1MB, alloc=540.3MB, time=39.45 memory used=2174.7MB, alloc=540.3MB, time=40.81 memory used=2231.9MB, alloc=540.3MB, time=42.10 memory used=2297.8MB, alloc=540.3MB, time=44.00 memory used=2363.8MB, alloc=540.3MB, time=45.89 memory used=2403.7MB, alloc=540.3MB, time=46.95 memory used=2625.3MB, alloc=564.3MB, time=51.31 memory used=2852.4MB, alloc=588.3MB, time=56.47 memory used=3032.4MB, alloc=612.3MB, time=60.51 memory used=3234.1MB, alloc=636.3MB, time=64.94 memory used=3438.1MB, alloc=660.3MB, time=70.39 memory used=3601.8MB, alloc=684.3MB, time=74.75 memory used=3762.7MB, alloc=684.3MB, time=78.85 memory used=3898.7MB, alloc=684.3MB, time=82.49 memory used=4044.9MB, alloc=684.3MB, time=86.90 memory used=4171.9MB, alloc=684.3MB, time=90.06 memory used=4279.6MB, alloc=684.3MB, time=93.19 memory used=4404.6MB, alloc=684.3MB, time=97.22 memory used=4758.4MB, alloc=708.3MB, time=106.10 |\^/| 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(); 1428248812 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [17 x z + 14 y z - 12 z , -6 x + 14 y z + 4 z , -7 x y - 15 y z - 13] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-17 x + 11 y + 6 y z, -16 x y + 12 x + 17 y, -15 x y - 3 x + 17 y] > Problem := [F,G]; Problem := [ 2 2 2 [17 x z + 14 y z - 12 z , -6 x + 14 y z + 4 z , -7 x y - 15 y z - 13], 2 2 [-17 x + 11 y + 6 y z, -16 x y + 12 x + 17 y, -15 x y - 3 x + 17 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.47 memory used=47.4MB, alloc=32.3MB, time=0.77 memory used=67.0MB, alloc=56.3MB, time=1.07 memory used=106.3MB, alloc=60.3MB, time=1.67 memory used=144.6MB, alloc=84.3MB, time=2.25 memory used=204.8MB, alloc=92.3MB, time=3.19 memory used=263.4MB, alloc=116.3MB, time=4.13 memory used=342.9MB, alloc=116.3MB, time=5.36 memory used=421.1MB, alloc=140.3MB, time=6.60 memory used=496.7MB, alloc=140.3MB, time=7.79 memory used=571.1MB, alloc=420.3MB, time=9.01 memory used=695.3MB, alloc=444.3MB, time=11.05 memory used=850.0MB, alloc=476.3MB, time=13.67 memory used=982.7MB, alloc=476.3MB, time=15.95 memory used=1115.8MB, alloc=500.3MB, time=18.29 memory used=1229.9MB, alloc=500.3MB, time=20.32 memory used=1351.4MB, alloc=500.3MB, time=22.57 memory used=1451.8MB, alloc=524.3MB, time=24.45 memory used=1542.0MB, alloc=524.3MB, time=26.21 memory used=1643.1MB, alloc=524.3MB, time=28.24 memory used=1720.7MB, alloc=524.3MB, time=29.78 memory used=1792.6MB, alloc=524.3MB, time=31.31 memory used=1869.5MB, alloc=524.3MB, time=32.92 memory used=1918.1MB, alloc=548.3MB, time=34.02 memory used=1981.1MB, alloc=548.3MB, time=35.38 memory used=2036.0MB, alloc=548.3MB, time=36.65 memory used=2073.9MB, alloc=548.3MB, time=37.62 memory used=2297.4MB, alloc=572.3MB, time=41.86 memory used=2520.2MB, alloc=596.3MB, time=46.40 memory used=2741.8MB, alloc=620.3MB, time=50.89 memory used=2963.4MB, alloc=644.3MB, time=55.63 memory used=3193.7MB, alloc=668.3MB, time=60.44 memory used=3425.3MB, alloc=692.3MB, time=65.47 memory used=3661.1MB, alloc=716.3MB, time=70.55 memory used=3889.6MB, alloc=740.3MB, time=75.55 memory used=4109.2MB, alloc=764.3MB, time=80.43 memory used=4333.0MB, alloc=788.3MB, time=85.45 memory used=4558.0MB, alloc=812.3MB, time=90.56 memory used=4820.5MB, alloc=836.3MB, time=96.62 memory used=5084.0MB, alloc=860.3MB, time=102.57 |\^/| 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(); 1428249112 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-14 x + 17 y + 10 z, 11 x - 6 y + 3 z, 4 x - 18 x y + 18 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-7 y - 20 z + 17 z, 8 y + 5 z, 6 x z - 19 y z + 12] > Problem := [F,G]; 2 2 Problem := [[-14 x + 17 y + 10 z, 11 x - 6 y + 3 z, 4 x - 18 x y + 18 z], 2 2 2 [-7 y - 20 z + 17 z, 8 y + 5 z, 6 x z - 19 y z + 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=46.5MB, alloc=56.3MB, time=0.81 memory used=87.6MB, alloc=60.3MB, time=1.44 memory used=126.4MB, alloc=84.3MB, time=2.04 memory used=167.6MB, alloc=84.3MB, time=2.68 memory used=232.2MB, alloc=116.3MB, time=3.63 memory used=304.0MB, alloc=372.3MB, time=4.68 memory used=390.1MB, alloc=396.3MB, time=5.99 memory used=497.0MB, alloc=420.3MB, time=7.67 memory used=626.5MB, alloc=444.3MB, time=9.71 memory used=772.2MB, alloc=468.3MB, time=12.09 memory used=885.3MB, alloc=468.3MB, time=13.96 memory used=1011.2MB, alloc=492.3MB, time=16.07 memory used=1115.8MB, alloc=492.3MB, time=17.90 memory used=1204.8MB, alloc=492.3MB, time=19.46 memory used=1291.8MB, alloc=516.3MB, time=21.14 memory used=1374.9MB, alloc=516.3MB, time=22.69 memory used=1464.2MB, alloc=516.3MB, time=24.54 memory used=1531.3MB, alloc=516.3MB, time=25.90 memory used=1606.0MB, alloc=516.3MB, time=27.55 memory used=1663.7MB, alloc=516.3MB, time=28.66 memory used=1718.5MB, alloc=516.3MB, time=29.77 memory used=1762.0MB, alloc=540.3MB, time=30.59 memory used=1988.5MB, alloc=564.3MB, time=34.98 memory used=2185.5MB, alloc=588.3MB, time=38.63 memory used=2365.0MB, alloc=612.3MB, time=42.04 memory used=2539.9MB, alloc=636.3MB, time=45.48 memory used=2682.7MB, alloc=660.3MB, time=48.37 memory used=2876.3MB, alloc=684.3MB, time=53.11 memory used=3019.4MB, alloc=708.3MB, time=55.72 memory used=3164.9MB, alloc=708.3MB, time=59.26 memory used=3297.2MB, alloc=708.3MB, time=62.54 memory used=3396.6MB, alloc=708.3MB, time=64.81 memory used=3485.1MB, alloc=708.3MB, time=67.07 memory used=3853.6MB, alloc=732.3MB, time=74.97 memory used=4240.6MB, alloc=756.3MB, time=82.58 memory used=4618.1MB, alloc=780.3MB, time=90.76 memory used=5005.1MB, alloc=804.3MB, time=100.09 |\^/| 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(); 1428249412 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [8 + 18 x - 15 y, 2 y - 5 y + 16, 13 x + 18 x y + 4] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [3 y z + 18 z + 15, -14 x + 7 x y + 5 y, 6 x z - 17 z + 3 x] > Problem := [F,G]; 2 2 Problem := [[8 + 18 x - 15 y, 2 y - 5 y + 16, 13 x + 18 x y + 4], 2 2 2 [3 y z + 18 z + 15, -14 x + 7 x y + 5 y, 6 x z - 17 z + 3 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.8MB, alloc=32.3MB, time=0.81 memory used=68.2MB, alloc=56.3MB, time=1.13 memory used=109.4MB, alloc=60.3MB, time=1.77 memory used=149.5MB, alloc=84.3MB, time=2.42 memory used=214.0MB, alloc=92.3MB, time=3.56 memory used=270.9MB, alloc=116.3MB, time=4.56 memory used=351.0MB, alloc=140.3MB, time=5.93 memory used=442.3MB, alloc=164.3MB, time=8.25 memory used=541.9MB, alloc=188.3MB, time=11.59 memory used=657.4MB, alloc=188.3MB, time=15.92 memory used=773.0MB, alloc=212.3MB, time=20.28 N1 := 3405 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=917.6MB, alloc=468.3MB, time=23.50 N2 := 1103 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Input concluded false after GB computation" > > H:=[op(F),op(G)]; 2 2 2 H := [-15 y + 18 x + 8, 2 y - 5 y + 16, 18 y x + 13 x + 4, 3 y z + 18 z + 15, 2 2 -14 x + 7 x y + 5 y, -17 z + 6 z x + 3 x] > J:=[op(GB),op(G)]; 2 2 2 J := [1, 3 y z + 18 z + 15, -14 x + 7 x y + 5 y, -17 z + 6 z x + 3 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 11, 11, 2, 2, 2, 2, 2/3, 5/6, 1/3, 7/18, 7/18, 2/9, 4, 6, 6, 2, 2, 1, 2, 1/2, 1/2, 1/2, 2/5, 3/10, 2/5, 5, 5, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=955.7MB, alloc=468.3MB, time=24.78 |\^/| 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(); 1428249482 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-9 x z + 20 y + 11 z, x + 20 x z - 8 y, -20 y z - 8 z - 5 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [7 y z + 5 x, 3 x z + 12 z + 11 z, 8 x y + 2 y + 20 z] > Problem := [F,G]; 2 2 Problem := [[-9 x z + 20 y + 11 z, x + 20 x z - 8 y, -20 y z - 8 z - 5 y], 2 2 [7 y z + 5 x, 3 x z + 12 z + 11 z, 8 x y + 2 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=26.3MB, alloc=32.3MB, time=0.48 memory used=46.2MB, alloc=32.3MB, time=0.77 memory used=63.7MB, alloc=56.3MB, time=1.05 memory used=102.2MB, alloc=60.3MB, time=1.63 memory used=139.5MB, alloc=84.3MB, time=2.22 memory used=198.4MB, alloc=92.3MB, time=3.15 memory used=255.3MB, alloc=116.3MB, time=4.04 memory used=333.8MB, alloc=140.3MB, time=5.28 memory used=420.4MB, alloc=396.3MB, time=6.71 memory used=520.7MB, alloc=420.3MB, time=8.34 memory used=645.1MB, alloc=444.3MB, time=10.42 memory used=794.2MB, alloc=468.3MB, time=12.85 memory used=959.8MB, alloc=492.3MB, time=15.66 memory used=1124.5MB, alloc=516.3MB, time=18.52 memory used=1268.9MB, alloc=516.3MB, time=21.08 memory used=1387.8MB, alloc=540.3MB, time=23.23 memory used=1499.5MB, alloc=540.3MB, time=25.30 memory used=1607.3MB, alloc=540.3MB, time=27.31 memory used=1716.7MB, alloc=540.3MB, time=29.51 memory used=1810.2MB, alloc=540.3MB, time=31.58 memory used=1908.3MB, alloc=564.3MB, time=34.08 memory used=2009.0MB, alloc=564.3MB, time=36.49 memory used=2079.4MB, alloc=564.3MB, time=38.05 memory used=2150.3MB, alloc=564.3MB, time=39.68 memory used=2219.1MB, alloc=564.3MB, time=41.60 memory used=2290.5MB, alloc=564.3MB, time=43.30 memory used=2376.2MB, alloc=564.3MB, time=45.58 memory used=2435.3MB, alloc=564.3MB, time=47.30 memory used=2676.5MB, alloc=588.3MB, time=52.25 memory used=2917.9MB, alloc=612.3MB, time=57.91 memory used=3140.7MB, alloc=636.3MB, time=62.64 memory used=3370.5MB, alloc=660.3MB, time=68.95 memory used=3540.9MB, alloc=684.3MB, time=72.63 memory used=3723.6MB, alloc=708.3MB, time=77.19 memory used=3902.5MB, alloc=732.3MB, time=82.08 memory used=4076.1MB, alloc=756.3MB, time=86.60 memory used=4234.7MB, alloc=756.3MB, time=90.95 memory used=4350.0MB, alloc=756.3MB, time=94.02 memory used=4746.0MB, alloc=780.3MB, time=103.08 |\^/| 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(); 1428249782 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [4 x y - 19 y z + 18 y, -x z + 15 y z - 8 z , -9 x y + 13 x z + 13 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-4 y z - 9 z - 7 y, 7 + 18 x + 6 y, 13 x y - 3 y - 7] > Problem := [F,G]; Problem := [ 2 [4 x y - 19 y z + 18 y, -x z + 15 y z - 8 z , -9 x y + 13 x z + 13 y z], 2 [-4 y z - 9 z - 7 y, 7 + 18 x + 6 y, 13 x y - 3 y - 7]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.47 memory used=47.0MB, alloc=32.3MB, time=0.77 memory used=66.6MB, alloc=56.3MB, time=1.07 memory used=106.0MB, alloc=60.3MB, time=1.67 memory used=143.8MB, alloc=84.3MB, time=2.24 memory used=201.7MB, alloc=92.3MB, time=3.13 memory used=255.3MB, alloc=116.3MB, time=3.95 memory used=334.0MB, alloc=116.3MB, time=5.24 memory used=411.7MB, alloc=140.3MB, time=6.57 memory used=502.0MB, alloc=140.3MB, time=8.12 memory used=594.6MB, alloc=420.3MB, time=9.87 memory used=715.5MB, alloc=444.3MB, time=12.05 memory used=856.8MB, alloc=468.3MB, time=14.71 memory used=1022.0MB, alloc=492.3MB, time=18.10 memory used=1189.2MB, alloc=516.3MB, time=21.37 memory used=1347.9MB, alloc=540.3MB, time=24.45 memory used=1497.7MB, alloc=564.3MB, time=27.37 memory used=1672.7MB, alloc=588.3MB, time=30.81 memory used=1837.8MB, alloc=612.3MB, time=34.08 memory used=1997.1MB, alloc=636.3MB, time=37.22 memory used=2165.5MB, alloc=660.3MB, time=40.51 memory used=2309.4MB, alloc=684.3MB, time=43.47 memory used=2464.1MB, alloc=708.3MB, time=46.66 memory used=2591.3MB, alloc=732.3MB, time=49.38 memory used=2738.0MB, alloc=756.3MB, time=52.48 memory used=2864.6MB, alloc=780.3MB, time=55.22 memory used=2985.6MB, alloc=804.3MB, time=57.88 memory used=3104.3MB, alloc=828.3MB, time=60.56 memory used=3203.1MB, alloc=852.3MB, time=62.91 memory used=3307.7MB, alloc=876.3MB, time=65.35 memory used=3669.1MB, alloc=900.3MB, time=72.86 memory used=4007.7MB, alloc=924.3MB, time=82.72 memory used=4303.6MB, alloc=948.3MB, time=94.15 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428250082 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-5 y - 11 y + 5, 16 x z - 12 y + 15 z , -2 x - 15 x z - 5 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-16 y + 14 y z + 4 x, -19 x z + 15 z - 11 y, 16 + 10 y - 4 z] > Problem := [F,G]; 2 2 2 2 Problem := [[-5 y - 11 y + 5, 16 x z - 12 y + 15 z , -2 x - 15 x z - 5 y z], 2 2 [-16 y + 14 y z + 4 x, -19 x z + 15 z - 11 y, 16 + 10 y - 4 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=46.9MB, alloc=32.3MB, time=0.80 memory used=66.2MB, alloc=56.3MB, time=1.10 memory used=106.4MB, alloc=60.3MB, time=1.71 memory used=143.8MB, alloc=84.3MB, time=2.31 memory used=206.2MB, alloc=92.3MB, time=3.28 memory used=266.8MB, alloc=116.3MB, time=4.22 memory used=349.6MB, alloc=116.3MB, time=5.53 memory used=426.4MB, alloc=396.3MB, time=6.79 memory used=532.2MB, alloc=396.3MB, time=8.48 memory used=637.4MB, alloc=420.3MB, time=10.22 memory used=765.8MB, alloc=444.3MB, time=12.51 memory used=908.2MB, alloc=468.3MB, time=14.95 memory used=1060.7MB, alloc=492.3MB, time=17.62 memory used=1207.0MB, alloc=516.3MB, time=20.33 memory used=1321.9MB, alloc=516.3MB, time=22.10 memory used=1443.1MB, alloc=516.3MB, time=24.57 memory used=1540.0MB, alloc=540.3MB, time=26.30 memory used=1622.4MB, alloc=540.3MB, time=27.89 memory used=1717.6MB, alloc=540.3MB, time=29.89 memory used=1812.8MB, alloc=540.3MB, time=31.90 memory used=1912.0MB, alloc=540.3MB, time=34.08 memory used=1986.3MB, alloc=540.3MB, time=35.49 memory used=2063.0MB, alloc=540.3MB, time=37.05 memory used=2122.1MB, alloc=540.3MB, time=38.38 memory used=2179.3MB, alloc=564.3MB, time=39.43 memory used=2249.9MB, alloc=564.3MB, time=41.35 memory used=2314.9MB, alloc=564.3MB, time=43.04 memory used=2542.3MB, alloc=588.3MB, time=47.30 memory used=2784.2MB, alloc=612.3MB, time=52.53 memory used=2962.9MB, alloc=636.3MB, time=56.19 memory used=3149.2MB, alloc=660.3MB, time=60.19 memory used=3308.7MB, alloc=660.3MB, time=63.94 memory used=3461.8MB, alloc=660.3MB, time=67.36 memory used=3646.6MB, alloc=684.3MB, time=72.02 memory used=3812.1MB, alloc=684.3MB, time=76.34 memory used=3989.3MB, alloc=708.3MB, time=81.15 memory used=4113.6MB, alloc=708.3MB, time=84.23 memory used=4248.9MB, alloc=708.3MB, time=87.89 memory used=4375.4MB, alloc=708.3MB, time=91.33 |\^/| 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(); 1428250383 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [7 x y + 13 y z - 10 y, x - 10 x y - 15 y, -x + 9 z + 18] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [10 x y + 8 y z + 12, -10 x y - 10 y - 17 x, -15 y + 18 z + 16] > Problem := [F,G]; 2 2 Problem := [[7 x y + 13 y z - 10 y, x - 10 x y - 15 y, -x + 9 z + 18], 2 2 [10 x y + 8 y z + 12, -10 x y - 10 y - 17 x, -15 y + 18 z + 16]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.47 memory used=47.0MB, alloc=32.3MB, time=0.77 memory used=65.9MB, alloc=56.3MB, time=1.05 memory used=106.0MB, alloc=60.3MB, time=1.64 memory used=145.8MB, alloc=60.3MB, time=2.22 memory used=183.3MB, alloc=84.3MB, time=2.80 memory used=241.7MB, alloc=84.3MB, time=3.69 memory used=302.6MB, alloc=116.3MB, time=4.73 memory used=381.6MB, alloc=140.3MB, time=6.15 memory used=474.1MB, alloc=164.3MB, time=7.79 memory used=581.8MB, alloc=188.3MB, time=9.73 memory used=703.1MB, alloc=212.3MB, time=11.95 memory used=828.3MB, alloc=492.3MB, time=14.28 memory used=973.9MB, alloc=516.3MB, time=16.95 memory used=1128.0MB, alloc=540.3MB, time=19.85 memory used=1284.5MB, alloc=564.3MB, time=24.35 memory used=1443.1MB, alloc=588.3MB, time=29.76 memory used=1615.2MB, alloc=612.3MB, time=35.98 memory used=1802.1MB, alloc=636.3MB, time=42.88 memory used=2004.7MB, alloc=660.3MB, time=50.53 memory used=2223.4MB, alloc=684.3MB, time=59.08 memory used=2456.8MB, alloc=708.3MB, time=68.56 memory used=2705.8MB, alloc=732.3MB, time=79.26 memory used=2978.6MB, alloc=756.3MB, time=90.87 |\^/| 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(); 1428250682 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-11 y z - 16 z, 18 x y - 7, -14 x + 5 x y - 5 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [4 x + 20 x + 5 y, 6 x z + 10 y z - 11, 17 x z - 12 y z + 8 y] > Problem := [F,G]; 2 2 Problem := [[-11 y z - 16 z, 18 x y - 7, -14 x + 5 x y - 5 y ], 2 [4 x + 20 x + 5 y, 6 x z + 10 y z - 11, 17 x z - 12 y z + 8 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.47 memory used=46.7MB, alloc=32.3MB, time=0.76 memory used=66.7MB, alloc=56.3MB, time=1.07 memory used=107.5MB, alloc=60.3MB, time=1.68 memory used=146.3MB, alloc=60.3MB, time=2.25 memory used=184.3MB, alloc=84.3MB, time=2.88 memory used=236.6MB, alloc=84.3MB, time=3.81 memory used=291.5MB, alloc=116.3MB, time=4.83 memory used=364.8MB, alloc=140.3MB, time=6.15 memory used=455.0MB, alloc=164.3MB, time=8.02 memory used=554.6MB, alloc=188.3MB, time=11.08 memory used=663.1MB, alloc=212.3MB, time=15.32 memory used=795.7MB, alloc=212.3MB, time=20.46 memory used=928.5MB, alloc=236.3MB, time=25.66 N1 := 3769 > GB := Basis(F, plex(op(vars))); 4 2 3 GB := [648 x - 90 x + 35, 36 x - 5 x + 5 y, z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1032.8MB, alloc=236.3MB, time=27.55 memory used=1216.0MB, alloc=516.3MB, time=31.26 memory used=1393.1MB, alloc=540.3MB, time=38.27 N2 := 2695 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-11 y z - 16 z, 18 y x - 7, -14 x + 5 x y - 5 y , 4 x + 5 y + 20 x, 10 z y + 6 z x - 11, -12 z y + 17 z x + 8 y] > J:=[op(GB),op(G)]; 4 2 3 2 J := [648 x - 90 x + 35, 36 x + 5 y - 5 x, z, 4 x + 5 y + 20 x, 10 z y + 6 z x - 11, -12 z y + 17 z x + 8 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 12, 2, 2, 2, 1, 5/6, 1, 1/2, 7/16, 1/2, 3/8, 6, 12, 14, 4, 4, 1, 1, 5/6, 2/3, 1/2, 1/2, 5/16, 5/16, 2, -2, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1459.3MB, alloc=540.3MB, time=40.82 |\^/| 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(); 1428250805 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [14 x + 14 x + 2 y, -13 x + 15 y z + 7 z , -4 z + 19 x + 6 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [14 x y + 6 y + 16 z , -7 y + 5 y z - 18 z , -5 x + 18 x z - 2 z] > Problem := [F,G]; 2 2 2 2 Problem := [[14 x + 14 x + 2 y, -13 x + 15 y z + 7 z , -4 z + 19 x + 6 y], 2 2 2 2 2 [14 x y + 6 y + 16 z , -7 y + 5 y z - 18 z , -5 x + 18 x z - 2 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.5MB, alloc=32.3MB, time=0.82 memory used=66.9MB, alloc=56.3MB, time=1.12 memory used=107.8MB, alloc=60.3MB, time=1.75 memory used=146.7MB, alloc=84.3MB, time=2.34 memory used=206.8MB, alloc=92.3MB, time=3.25 memory used=270.5MB, alloc=116.3MB, time=4.17 memory used=352.5MB, alloc=116.3MB, time=5.41 memory used=428.6MB, alloc=396.3MB, time=6.63 memory used=534.7MB, alloc=420.3MB, time=8.36 memory used=665.4MB, alloc=444.3MB, time=10.45 memory used=815.3MB, alloc=468.3MB, time=12.97 memory used=969.0MB, alloc=468.3MB, time=15.57 memory used=1104.9MB, alloc=492.3MB, time=17.86 memory used=1226.8MB, alloc=492.3MB, time=20.02 memory used=1332.1MB, alloc=516.3MB, time=21.96 memory used=1440.0MB, alloc=516.3MB, time=23.84 memory used=1552.1MB, alloc=516.3MB, time=25.89 memory used=1662.1MB, alloc=516.3MB, time=27.90 memory used=1746.7MB, alloc=540.3MB, time=29.34 memory used=1844.6MB, alloc=540.3MB, time=31.19 memory used=1920.6MB, alloc=540.3MB, time=32.52 memory used=2006.1MB, alloc=540.3MB, time=34.35 memory used=2069.9MB, alloc=540.3MB, time=35.46 memory used=2136.4MB, alloc=540.3MB, time=36.87 memory used=2187.7MB, alloc=540.3MB, time=37.92 memory used=2254.2MB, alloc=540.3MB, time=39.43 memory used=2299.2MB, alloc=540.3MB, time=40.57 memory used=2515.6MB, alloc=564.3MB, time=44.87 memory used=2744.7MB, alloc=588.3MB, time=49.24 memory used=2930.3MB, alloc=612.3MB, time=52.68 memory used=3142.4MB, alloc=636.3MB, time=56.77 memory used=3314.6MB, alloc=660.3MB, time=60.53 memory used=3476.3MB, alloc=684.3MB, time=63.86 memory used=3631.3MB, alloc=684.3MB, time=67.00 memory used=3765.5MB, alloc=684.3MB, time=70.05 memory used=3911.7MB, alloc=708.3MB, time=73.24 memory used=4045.3MB, alloc=708.3MB, time=76.00 memory used=4169.7MB, alloc=708.3MB, time=78.58 memory used=4292.6MB, alloc=708.3MB, time=81.35 memory used=4407.4MB, alloc=708.3MB, time=83.86 memory used=4779.7MB, alloc=732.3MB, time=91.29 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428251105 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [8 y z + 14 y + 5 z, -7 x + 20 y z + 15 z, 5 x z - 9 y + 18 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [12 x - 20 y z - 20 z , 17 x y - 5 x z + 17 y z, 4 x z + 15 z + 14 x] > Problem := [F,G]; 2 2 Problem := [[8 y z + 14 y + 5 z, -7 x + 20 y z + 15 z, 5 x z - 9 y + 18 y], 2 2 2 [12 x - 20 y z - 20 z , 17 x y - 5 x z + 17 y z, 4 x z + 15 z + 14 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=46.5MB, alloc=32.3MB, time=0.78 memory used=65.7MB, alloc=56.3MB, time=1.08 memory used=105.5MB, alloc=60.3MB, time=1.67 memory used=143.5MB, alloc=84.3MB, time=2.25 memory used=204.8MB, alloc=92.3MB, time=3.18 memory used=264.3MB, alloc=116.3MB, time=4.13 memory used=345.9MB, alloc=116.3MB, time=5.40 memory used=425.9MB, alloc=140.3MB, time=6.74 memory used=503.1MB, alloc=140.3MB, time=8.01 memory used=574.0MB, alloc=420.3MB, time=9.15 memory used=700.7MB, alloc=444.3MB, time=11.20 memory used=849.9MB, alloc=468.3MB, time=13.70 memory used=1001.7MB, alloc=492.3MB, time=16.49 memory used=1151.1MB, alloc=492.3MB, time=19.32 memory used=1285.2MB, alloc=516.3MB, time=21.89 memory used=1430.3MB, alloc=516.3MB, time=25.01 memory used=1562.6MB, alloc=516.3MB, time=27.84 memory used=1689.4MB, alloc=540.3MB, time=30.56 memory used=1793.7MB, alloc=540.3MB, time=32.65 memory used=1898.3MB, alloc=540.3MB, time=34.85 memory used=2008.6MB, alloc=540.3MB, time=37.48 memory used=2106.2MB, alloc=540.3MB, time=39.83 memory used=2210.0MB, alloc=540.3MB, time=42.66 memory used=2277.8MB, alloc=564.3MB, time=44.20 memory used=2364.2MB, alloc=564.3MB, time=46.35 memory used=2422.4MB, alloc=564.3MB, time=47.79 memory used=2471.5MB, alloc=564.3MB, time=48.87 memory used=2532.2MB, alloc=564.3MB, time=50.62 memory used=2586.0MB, alloc=564.3MB, time=52.25 memory used=2827.0MB, alloc=588.3MB, time=58.35 memory used=3077.2MB, alloc=612.3MB, time=63.73 memory used=3310.0MB, alloc=636.3MB, time=68.76 memory used=3551.6MB, alloc=660.3MB, time=75.15 memory used=3736.3MB, alloc=684.3MB, time=80.07 memory used=3945.0MB, alloc=708.3MB, time=84.92 memory used=4115.6MB, alloc=732.3MB, time=89.19 memory used=4251.4MB, alloc=756.3MB, time=91.51 memory used=4403.6MB, alloc=780.3MB, time=96.15 memory used=4528.3MB, alloc=780.3MB, time=98.55 memory used=4652.8MB, alloc=780.3MB, time=101.71 |\^/| 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(); 1428251405 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [8 y z + 16 x - 13 z, 15 y z + 13 z + 7 y, 16 x y + 10 x z - 6 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-20 x + x y + 7 z , -13 x z + 4 z + 19 z, -5 x y - 19 x z + 15 z] > Problem := [F,G]; 2 Problem := [[8 y z + 16 x - 13 z, 15 y z + 13 z + 7 y, 16 x y + 10 x z - 6 x], 2 2 2 [-20 x + x y + 7 z , -13 x z + 4 z + 19 z, -5 x y - 19 x z + 15 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.47 memory used=46.5MB, alloc=32.3MB, time=0.77 memory used=65.0MB, alloc=56.3MB, time=1.05 memory used=104.2MB, alloc=60.3MB, time=1.64 memory used=141.3MB, alloc=84.3MB, time=2.19 memory used=198.6MB, alloc=92.3MB, time=3.07 memory used=252.9MB, alloc=116.3MB, time=3.93 memory used=328.7MB, alloc=116.3MB, time=5.12 memory used=403.8MB, alloc=140.3MB, time=6.35 memory used=501.0MB, alloc=164.3MB, time=7.93 memory used=587.9MB, alloc=420.3MB, time=9.39 memory used=709.8MB, alloc=444.3MB, time=11.52 memory used=850.1MB, alloc=468.3MB, time=14.01 memory used=1011.9MB, alloc=492.3MB, time=17.07 memory used=1196.3MB, alloc=516.3MB, time=21.12 memory used=1400.3MB, alloc=540.3MB, time=25.47 memory used=1623.7MB, alloc=564.3MB, time=30.69 memory used=1867.6MB, alloc=588.3MB, time=36.55 memory used=2130.9MB, alloc=612.3MB, time=43.31 memory used=2411.7MB, alloc=636.3MB, time=50.32 memory used=2709.1MB, alloc=660.3MB, time=58.28 memory used=3023.9MB, alloc=684.3MB, time=66.84 memory used=3329.6MB, alloc=708.3MB, time=74.39 memory used=3651.2MB, alloc=732.3MB, time=82.97 memory used=3994.8MB, alloc=756.3MB, time=94.36 memory used=4259.1MB, alloc=780.3MB, time=101.22 |\^/| 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(); 1428251705 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-11 x y - z - 17 y, 18 y + 12 x - 18, 13 y - 13 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-6 x - 20 x y + 7, -6 x y - 6 y + 13 x, 6 x y + 16 x z - 5 y] > Problem := [F,G]; 2 2 2 2 Problem := [[-11 x y - z - 17 y, 18 y + 12 x - 18, 13 y - 13 z ], 2 2 [-6 x - 20 x y + 7, -6 x y - 6 y + 13 x, 6 x y + 16 x z - 5 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=46.9MB, alloc=32.3MB, time=0.81 memory used=67.1MB, alloc=32.3MB, time=1.10 memory used=87.1MB, alloc=32.3MB, time=1.41 memory used=106.0MB, alloc=56.3MB, time=1.72 memory used=145.4MB, alloc=60.3MB, time=2.36 memory used=184.4MB, alloc=84.3MB, time=3.03 memory used=246.3MB, alloc=116.3MB, time=4.21 memory used=324.9MB, alloc=116.3MB, time=5.69 memory used=395.9MB, alloc=140.3MB, time=6.98 memory used=484.8MB, alloc=164.3MB, time=8.59 memory used=588.2MB, alloc=188.3MB, time=10.56 memory used=701.3MB, alloc=212.3MB, time=13.86 memory used=823.7MB, alloc=236.3MB, time=17.95 memory used=958.5MB, alloc=260.3MB, time=23.02 memory used=1110.3MB, alloc=284.3MB, time=29.48 memory used=1286.1MB, alloc=284.3MB, time=36.77 memory used=1461.8MB, alloc=308.3MB, time=43.89 memory used=1661.6MB, alloc=308.3MB, time=52.24 memory used=1861.3MB, alloc=308.3MB, time=60.38 memory used=2061.0MB, alloc=332.3MB, time=68.51 N1 := 7145 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [726 x + 1159 x - 1644 x - 2592, -726 x - 37 x + 201 y + 1689, 2 3 z + 2 x - 3] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2289.7MB, alloc=332.3MB, time=76.72 memory used=2379.9MB, alloc=588.3MB, time=78.63 memory used=2642.1MB, alloc=612.3MB, time=84.84 memory used=2880.1MB, alloc=636.3MB, time=94.85 N2 := 3435 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [-11 x y - z - 17 y, 18 y + 12 x - 18, 13 y - 13 z , -6 x - 20 x y + 7, 2 -6 x y - 6 y + 13 x, 16 z x + 6 y x - 5 y] > J:=[op(GB),op(G)]; 3 2 2 J := [726 x + 1159 x - 1644 x - 2592, -726 x - 37 x + 201 y + 1689, 2 2 2 3 z + 2 x - 3, -6 x - 20 x y + 7, -6 x y - 6 y + 13 x, 16 z x + 6 y x - 5 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 12, 2, 2, 2, 2, 5/6, 1, 1/2, 8/17, 9/17, 3/17, 6, 12, 13, 3, 3, 2, 2, 1, 2/3, 1/3, 3/5, 3/10, 1/10, 2, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=2968.5MB, alloc=636.3MB, time=98.33 |\^/| 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(); 1428251998 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [5 x y - 5 z - 4 z, -6 x y - 4 x z - 5 z, -18 x + y - 15 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-14 x y + 17 z - 3 z, 3 x - 8 x z + 4 z , 11 x - 9 x - 17 y] > Problem := [F,G]; 2 2 2 Problem := [[5 x y - 5 z - 4 z, -6 x y - 4 x z - 5 z, -18 x + y - 15 x], 2 2 2 2 [-14 x y + 17 z - 3 z, 3 x - 8 x z + 4 z , 11 x - 9 x - 17 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=46.4MB, alloc=32.3MB, time=0.78 memory used=65.3MB, alloc=56.3MB, time=1.08 memory used=105.1MB, alloc=60.3MB, time=1.69 memory used=143.1MB, alloc=84.3MB, time=2.29 memory used=201.8MB, alloc=92.3MB, time=3.24 memory used=259.3MB, alloc=116.3MB, time=4.17 memory used=338.4MB, alloc=116.3MB, time=5.46 memory used=414.4MB, alloc=140.3MB, time=6.72 memory used=506.7MB, alloc=164.3MB, time=8.30 memory used=589.4MB, alloc=420.3MB, time=9.78 memory used=714.7MB, alloc=444.3MB, time=12.18 memory used=859.2MB, alloc=468.3MB, time=15.12 memory used=1028.1MB, alloc=492.3MB, time=18.83 memory used=1212.8MB, alloc=516.3MB, time=22.54 memory used=1415.1MB, alloc=540.3MB, time=26.77 memory used=1649.3MB, alloc=564.3MB, time=33.25 memory used=1898.3MB, alloc=588.3MB, time=39.93 memory used=2170.0MB, alloc=612.3MB, time=47.23 memory used=2454.8MB, alloc=636.3MB, time=54.46 memory used=2763.1MB, alloc=660.3MB, time=63.49 memory used=3055.4MB, alloc=684.3MB, time=69.03 memory used=3344.8MB, alloc=708.3MB, time=74.82 memory used=3629.6MB, alloc=732.3MB, time=80.64 memory used=3913.4MB, alloc=756.3MB, time=86.52 memory used=4202.5MB, alloc=780.3MB, time=92.42 memory used=4490.1MB, alloc=804.3MB, time=98.37 memory used=4780.2MB, alloc=828.3MB, time=104.51 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428252298 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-2 y + 11 y z - 9 z, 14 + 15 x - 17 z, 17 x z - 16 x + 17 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [3 y z - 11 z - 19, -16 x z - 17 y + 9 y, 15 x - 7 x y - 16 y z] > Problem := [F,G]; 2 Problem := [[-2 y + 11 y z - 9 z, 14 + 15 x - 17 z, 17 x z - 16 x + 17 y], 2 2 [3 y z - 11 z - 19, -16 x z - 17 y + 9 y, 15 x - 7 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=46.0MB, alloc=56.3MB, time=0.80 memory used=87.8MB, alloc=60.3MB, time=1.42 memory used=128.3MB, alloc=60.3MB, time=2.02 memory used=167.3MB, alloc=84.3MB, time=2.62 memory used=228.8MB, alloc=116.3MB, time=3.58 memory used=307.9MB, alloc=372.3MB, time=4.81 memory used=392.6MB, alloc=396.3MB, time=6.14 memory used=500.9MB, alloc=420.3MB, time=7.88 memory used=631.3MB, alloc=444.3MB, time=10.00 memory used=775.5MB, alloc=468.3MB, time=12.41 memory used=898.5MB, alloc=468.3MB, time=14.51 memory used=1028.4MB, alloc=492.3MB, time=16.82 memory used=1145.6MB, alloc=492.3MB, time=18.88 memory used=1263.3MB, alloc=516.3MB, time=21.02 memory used=1365.6MB, alloc=516.3MB, time=23.04 memory used=1462.9MB, alloc=516.3MB, time=24.86 memory used=1538.3MB, alloc=516.3MB, time=26.33 memory used=1628.8MB, alloc=516.3MB, time=28.21 memory used=1682.3MB, alloc=516.3MB, time=29.46 memory used=1750.3MB, alloc=540.3MB, time=30.95 memory used=1823.5MB, alloc=540.3MB, time=32.67 memory used=1871.3MB, alloc=540.3MB, time=33.81 memory used=1919.0MB, alloc=540.3MB, time=34.80 memory used=1994.3MB, alloc=540.3MB, time=36.86 memory used=2042.7MB, alloc=540.3MB, time=38.13 memory used=2265.5MB, alloc=564.3MB, time=42.70 memory used=2492.8MB, alloc=588.3MB, time=47.37 memory used=2680.4MB, alloc=612.3MB, time=51.32 memory used=2893.6MB, alloc=636.3MB, time=55.65 memory used=3110.1MB, alloc=660.3MB, time=60.76 memory used=3266.0MB, alloc=684.3MB, time=64.04 memory used=3461.7MB, alloc=684.3MB, time=69.18 memory used=3646.0MB, alloc=708.3MB, time=73.65 memory used=3788.6MB, alloc=708.3MB, time=77.43 memory used=3920.1MB, alloc=708.3MB, time=80.82 memory used=3997.1MB, alloc=708.3MB, time=82.90 memory used=4122.5MB, alloc=708.3MB, time=86.53 memory used=4494.0MB, alloc=732.3MB, time=95.50 |\^/| 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(); 1428252598 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-16 x - 5 x y - 18 x z, -19 y + 2 y z + 7 z , 6 x y - 10 x z - 1] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [8 x y + 5 y - 18 x, -16 x z + 15 z + 10 y, -12 x - 5 x y + 2 y z] > Problem := [F,G]; Problem := [ 2 2 2 [-16 x - 5 x y - 18 x z, -19 y + 2 y z + 7 z , 6 x y - 10 x z - 1], 2 2 2 [8 x y + 5 y - 18 x, -16 x z + 15 z + 10 y, -12 x - 5 x y + 2 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.9MB, alloc=32.3MB, time=0.82 memory used=67.9MB, alloc=56.3MB, time=1.15 memory used=108.6MB, alloc=60.3MB, time=1.76 memory used=148.8MB, alloc=84.3MB, time=2.39 memory used=212.5MB, alloc=92.3MB, time=3.39 memory used=275.3MB, alloc=116.3MB, time=4.34 memory used=355.6MB, alloc=116.3MB, time=5.60 memory used=434.6MB, alloc=396.3MB, time=6.91 memory used=541.8MB, alloc=420.3MB, time=8.63 memory used=674.2MB, alloc=444.3MB, time=10.78 memory used=815.5MB, alloc=468.3MB, time=13.15 memory used=939.3MB, alloc=468.3MB, time=15.28 memory used=1065.2MB, alloc=492.3MB, time=17.50 memory used=1189.1MB, alloc=492.3MB, time=19.75 memory used=1297.3MB, alloc=516.3MB, time=21.67 memory used=1404.8MB, alloc=516.3MB, time=23.83 memory used=1488.8MB, alloc=516.3MB, time=25.44 memory used=1587.7MB, alloc=516.3MB, time=27.62 memory used=1671.5MB, alloc=516.3MB, time=29.41 memory used=1739.6MB, alloc=516.3MB, time=30.75 memory used=1802.8MB, alloc=516.3MB, time=32.17 memory used=1863.4MB, alloc=516.3MB, time=33.74 memory used=1930.2MB, alloc=516.3MB, time=35.40 memory used=1974.3MB, alloc=516.3MB, time=36.43 memory used=2033.1MB, alloc=516.3MB, time=38.02 memory used=2239.7MB, alloc=540.3MB, time=42.12 memory used=2461.4MB, alloc=564.3MB, time=47.13 memory used=2659.7MB, alloc=588.3MB, time=51.39 memory used=2856.6MB, alloc=612.3MB, time=55.76 memory used=3044.4MB, alloc=636.3MB, time=60.34 memory used=3221.4MB, alloc=660.3MB, time=64.75 memory used=3393.6MB, alloc=684.3MB, time=69.04 memory used=3549.2MB, alloc=684.3MB, time=73.03 memory used=3693.9MB, alloc=684.3MB, time=76.95 memory used=3819.0MB, alloc=684.3MB, time=80.36 memory used=3945.0MB, alloc=684.3MB, time=83.73 memory used=4049.2MB, alloc=684.3MB, time=86.60 memory used=4394.3MB, alloc=708.3MB, time=95.40 memory used=4760.1MB, alloc=732.3MB, time=104.30 |\^/| 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(); 1428252898 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-10 x z - 18 y - 14 z, -13 x + 14 y z - 19 z , -13 x + 16 x + 16 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-3 y z + 18 x + 19 y, 8 x y - 10 x z + 12 y z, -9 x y + 4 y + 15 y z] > Problem := [F,G]; Problem := [ 2 2 2 2 [-10 x z - 18 y - 14 z, -13 x + 14 y z - 19 z , -13 x + 16 x + 16 y], 2 [-3 y z + 18 x + 19 y, 8 x y - 10 x z + 12 y z, -9 x y + 4 y + 15 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=46.9MB, alloc=32.3MB, time=0.80 memory used=66.1MB, alloc=56.3MB, time=1.09 memory used=104.8MB, alloc=60.3MB, time=1.68 memory used=144.1MB, alloc=84.3MB, time=2.25 memory used=207.3MB, alloc=92.3MB, time=3.23 memory used=267.6MB, alloc=116.3MB, time=4.17 memory used=350.0MB, alloc=140.3MB, time=5.49 memory used=423.3MB, alloc=396.3MB, time=6.72 memory used=524.2MB, alloc=420.3MB, time=8.30 memory used=653.6MB, alloc=444.3MB, time=10.30 memory used=793.4MB, alloc=468.3MB, time=12.44 memory used=908.4MB, alloc=468.3MB, time=14.20 memory used=1033.7MB, alloc=492.3MB, time=16.35 memory used=1144.4MB, alloc=492.3MB, time=18.27 memory used=1236.7MB, alloc=492.3MB, time=20.00 memory used=1326.1MB, alloc=492.3MB, time=21.64 memory used=1414.2MB, alloc=492.3MB, time=23.45 memory used=1498.5MB, alloc=516.3MB, time=25.07 memory used=1573.8MB, alloc=516.3MB, time=26.45 memory used=1651.2MB, alloc=516.3MB, time=28.12 memory used=1722.9MB, alloc=516.3MB, time=29.73 memory used=1788.2MB, alloc=516.3MB, time=31.01 memory used=1861.5MB, alloc=516.3MB, time=32.67 memory used=1905.9MB, alloc=516.3MB, time=33.72 memory used=1961.8MB, alloc=516.3MB, time=35.12 memory used=2164.9MB, alloc=540.3MB, time=38.87 memory used=2375.1MB, alloc=564.3MB, time=42.99 memory used=2567.2MB, alloc=588.3MB, time=46.89 memory used=2754.5MB, alloc=612.3MB, time=50.94 memory used=2914.6MB, alloc=636.3MB, time=53.96 memory used=3079.0MB, alloc=660.3MB, time=57.06 memory used=3264.9MB, alloc=684.3MB, time=61.22 memory used=3396.9MB, alloc=684.3MB, time=64.31 memory used=3534.9MB, alloc=684.3MB, time=67.45 memory used=3672.0MB, alloc=708.3MB, time=70.92 memory used=3801.3MB, alloc=708.3MB, time=74.36 memory used=3884.0MB, alloc=708.3MB, time=76.48 memory used=3989.9MB, alloc=708.3MB, time=79.22 memory used=4360.8MB, alloc=732.3MB, time=86.89 memory used=4749.3MB, alloc=756.3MB, time=95.42 |\^/| 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(); 1428253198 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-2 x y - 6 y z - 10 y, -13 y - 14 y - 13 z, 15 x - 14 y z + 19 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-18 x - 17 y - 15 z, -10 x y - 14 y - 3 z, 6 x z + 2 y + 4 z] > Problem := [F,G]; Problem := [ 2 2 [-2 x y - 6 y z - 10 y, -13 y - 14 y - 13 z, 15 x - 14 y z + 19 z], 2 [-18 x - 17 y - 15 z, -10 x y - 14 y - 3 z, 6 x z + 2 y + 4 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=45.6MB, alloc=32.3MB, time=0.76 memory used=64.9MB, alloc=56.3MB, time=1.06 memory used=105.1MB, alloc=60.3MB, time=1.69 memory used=142.0MB, alloc=84.3MB, time=2.25 memory used=200.4MB, alloc=92.3MB, time=3.15 memory used=258.6MB, alloc=116.3MB, time=4.07 memory used=337.4MB, alloc=116.3MB, time=5.29 memory used=414.6MB, alloc=140.3MB, time=6.55 memory used=512.7MB, alloc=164.3MB, time=8.17 memory used=596.1MB, alloc=420.3MB, time=9.57 memory used=720.5MB, alloc=444.3MB, time=11.59 memory used=872.6MB, alloc=468.3MB, time=14.14 memory used=1044.9MB, alloc=492.3MB, time=17.09 memory used=1236.7MB, alloc=516.3MB, time=20.36 memory used=1450.3MB, alloc=540.3MB, time=24.40 memory used=1688.7MB, alloc=564.3MB, time=29.11 memory used=1946.2MB, alloc=588.3MB, time=34.75 memory used=2226.1MB, alloc=612.3MB, time=41.57 memory used=2483.7MB, alloc=636.3MB, time=47.87 memory used=2732.0MB, alloc=660.3MB, time=54.16 memory used=2976.4MB, alloc=684.3MB, time=60.75 memory used=3179.3MB, alloc=708.3MB, time=65.71 memory used=3384.3MB, alloc=732.3MB, time=71.23 memory used=3568.3MB, alloc=756.3MB, time=76.54 memory used=3738.0MB, alloc=756.3MB, time=81.57 memory used=3869.3MB, alloc=756.3MB, time=85.20 memory used=4021.7MB, alloc=756.3MB, time=89.82 memory used=4139.4MB, alloc=756.3MB, time=93.28 memory used=4552.1MB, alloc=780.3MB, time=104.49 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428253498 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [5 x - 5 y z - x, 15 x y + y + 18 z , 10 x z + 5 z + 18 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [3 x y - 3 z + 7, y - 18 y - 6, -3 x - y + 10 z] > Problem := [F,G]; 2 2 2 2 Problem := [[5 x - 5 y z - x, 15 x y + y + 18 z , 10 x z + 5 z + 18 y], 2 2 [3 x y - 3 z + 7, y - 18 y - 6, -3 x - y + 10 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.50 memory used=47.5MB, alloc=32.3MB, time=0.80 memory used=66.8MB, alloc=56.3MB, time=1.11 memory used=106.0MB, alloc=60.3MB, time=1.70 memory used=145.5MB, alloc=84.3MB, time=2.31 memory used=207.0MB, alloc=92.3MB, time=3.31 memory used=267.2MB, alloc=92.3MB, time=4.30 memory used=327.8MB, alloc=116.3MB, time=5.28 memory used=410.2MB, alloc=116.3MB, time=6.67 memory used=492.9MB, alloc=140.3MB, time=8.06 memory used=575.2MB, alloc=396.3MB, time=9.48 memory used=679.8MB, alloc=420.3MB, time=11.26 memory used=807.9MB, alloc=444.3MB, time=13.45 memory used=959.6MB, alloc=468.3MB, time=16.06 memory used=1092.8MB, alloc=492.3MB, time=18.46 memory used=1238.2MB, alloc=516.3MB, time=21.21 memory used=1364.9MB, alloc=516.3MB, time=23.65 memory used=1454.0MB, alloc=516.3MB, time=25.47 memory used=1565.8MB, alloc=516.3MB, time=27.74 memory used=1664.3MB, alloc=516.3MB, time=29.78 memory used=1769.9MB, alloc=516.3MB, time=32.05 memory used=1859.5MB, alloc=516.3MB, time=34.08 memory used=1938.7MB, alloc=516.3MB, time=35.96 memory used=2013.3MB, alloc=516.3MB, time=37.75 memory used=2101.2MB, alloc=516.3MB, time=39.95 memory used=2153.2MB, alloc=516.3MB, time=41.16 memory used=2213.6MB, alloc=516.3MB, time=42.81 memory used=2265.1MB, alloc=540.3MB, time=44.19 memory used=2494.9MB, alloc=564.3MB, time=52.57 memory used=2741.1MB, alloc=588.3MB, time=61.84 memory used=2945.3MB, alloc=612.3MB, time=69.70 memory used=3163.0MB, alloc=636.3MB, time=78.22 memory used=3352.2MB, alloc=660.3MB, time=85.30 memory used=3564.3MB, alloc=684.3MB, time=94.34 memory used=3757.8MB, alloc=684.3MB, time=102.82 memory used=3911.5MB, alloc=684.3MB, time=109.34 memory used=4053.1MB, alloc=684.3MB, time=115.36 |\^/| 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(); 1428253798 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-9 x y - 2 x z + 10 z, 17 x + 3 y - 13 z, x + 18 y z - 11 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-17 x z + 16 y z - y, -17 x - x z + 16 y z, -4 y z - 20 x - 13] > Problem := [F,G]; 2 2 Problem := [[-9 x y - 2 x z + 10 z, 17 x + 3 y - 13 z, x + 18 y z - 11 z], 2 [-17 x z + 16 y z - y, -17 x - x z + 16 y z, -4 y z - 20 x - 13]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.89 memory used=47.1MB, alloc=32.3MB, time=1.41 memory used=65.9MB, alloc=56.3MB, time=1.93 memory used=107.1MB, alloc=60.3MB, time=2.99 memory used=147.1MB, alloc=60.3MB, time=4.02 memory used=186.5MB, alloc=84.3MB, time=5.07 memory used=224.4MB, alloc=84.3MB, time=6.08 memory used=283.1MB, alloc=92.3MB, time=7.68 memory used=341.9MB, alloc=116.3MB, time=9.28 memory used=422.6MB, alloc=116.3MB, time=11.36 memory used=491.3MB, alloc=396.3MB, time=13.16 memory used=597.3MB, alloc=420.3MB, time=16.06 memory used=727.2MB, alloc=420.3MB, time=19.72 memory used=857.3MB, alloc=444.3MB, time=23.43 memory used=1001.2MB, alloc=468.3MB, time=27.77 memory used=1145.9MB, alloc=492.3MB, time=32.25 memory used=1275.2MB, alloc=492.3MB, time=36.29 memory used=1411.9MB, alloc=516.3MB, time=40.84 memory used=1517.4MB, alloc=516.3MB, time=44.23 memory used=1633.3MB, alloc=516.3MB, time=48.26 memory used=1733.0MB, alloc=516.3MB, time=51.63 memory used=1834.0MB, alloc=516.3MB, time=55.30 memory used=1923.8MB, alloc=540.3MB, time=58.72 memory used=2003.3MB, alloc=540.3MB, time=61.75 memory used=2068.2MB, alloc=540.3MB, time=64.34 memory used=2144.1MB, alloc=540.3MB, time=67.23 memory used=2213.5MB, alloc=540.3MB, time=69.92 memory used=2281.7MB, alloc=540.3MB, time=72.67 memory used=2338.3MB, alloc=540.3MB, time=75.23 memory used=2554.6MB, alloc=564.3MB, time=82.28 memory used=2755.2MB, alloc=588.3MB, time=88.67 memory used=2963.7MB, alloc=612.3MB, time=95.29 memory used=3179.7MB, alloc=636.3MB, time=102.53 memory used=3349.4MB, alloc=660.3MB, time=108.43 |\^/| 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(); 1428254098 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [6 y - 16 y z + 5 x, -2 x y + 6 y z + 9, -14 z + 13 y + 6 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [-18 y z - 2 x + 4 y, 14 x y - 18 x z - 5, 17 - 18 x - 17 y] > Problem := [F,G]; 2 2 Problem := [[6 y - 16 y z + 5 x, -2 x y + 6 y z + 9, -14 z + 13 y + 6 z], [-18 y z - 2 x + 4 y, 14 x y - 18 x z - 5, 17 - 18 x - 17 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.88 memory used=47.1MB, alloc=32.3MB, time=1.40 memory used=65.8MB, alloc=56.3MB, time=1.90 memory used=104.3MB, alloc=60.3MB, time=2.93 memory used=142.1MB, alloc=84.3MB, time=3.97 memory used=202.6MB, alloc=92.3MB, time=5.63 memory used=261.6MB, alloc=92.3MB, time=7.22 memory used=318.7MB, alloc=116.3MB, time=8.76 memory used=402.1MB, alloc=140.3MB, time=11.03 memory used=484.2MB, alloc=140.3MB, time=13.36 memory used=546.2MB, alloc=396.3MB, time=15.19 memory used=651.7MB, alloc=420.3MB, time=18.29 memory used=778.9MB, alloc=444.3MB, time=21.95 memory used=931.4MB, alloc=468.3MB, time=26.82 memory used=1070.5MB, alloc=492.3MB, time=31.10 memory used=1201.4MB, alloc=492.3MB, time=35.26 memory used=1323.6MB, alloc=492.3MB, time=39.36 memory used=1439.9MB, alloc=492.3MB, time=43.31 memory used=1546.9MB, alloc=516.3MB, time=46.96 memory used=1653.9MB, alloc=516.3MB, time=50.96 memory used=1751.3MB, alloc=516.3MB, time=54.42 memory used=1839.4MB, alloc=516.3MB, time=57.51 memory used=1916.2MB, alloc=516.3MB, time=60.36 memory used=1973.0MB, alloc=516.3MB, time=62.52 memory used=2028.9MB, alloc=516.3MB, time=64.59 memory used=2109.9MB, alloc=516.3MB, time=67.75 memory used=2167.1MB, alloc=540.3MB, time=70.27 memory used=2225.2MB, alloc=540.3MB, time=72.62 memory used=2270.3MB, alloc=540.3MB, time=74.53 memory used=2498.6MB, alloc=564.3MB, time=82.30 memory used=2701.2MB, alloc=588.3MB, time=88.98 memory used=2857.9MB, alloc=612.3MB, time=94.44 memory used=3062.5MB, alloc=636.3MB, time=102.39 |\^/| 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(); 1428254398 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [12 x z + 6 y + 19 x, -19 x z + 10 z + 9 y, -20 y - 12 y z - 16 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-15 y z + 15 x - 12 z, -11 x - 18 y z - 17 x, -10 x y - 8 y + 1] > Problem := [F,G]; Problem := [ 2 2 2 2 [12 x z + 6 y + 19 x, -19 x z + 10 z + 9 y, -20 y - 12 y z - 16 z ], 2 2 [-15 y z + 15 x - 12 z, -11 x - 18 y z - 17 x, -10 x y - 8 y + 1]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.0MB, alloc=32.3MB, time=0.88 memory used=46.5MB, alloc=32.3MB, time=1.41 memory used=66.3MB, alloc=56.3MB, time=1.93 memory used=106.6MB, alloc=60.3MB, time=2.97 memory used=144.4MB, alloc=84.3MB, time=3.99 memory used=208.8MB, alloc=92.3MB, time=5.65 memory used=273.1MB, alloc=116.3MB, time=7.29 memory used=352.8MB, alloc=116.3MB, time=9.46 memory used=421.3MB, alloc=372.3MB, time=11.32 memory used=507.3MB, alloc=396.3MB, time=13.50 memory used=614.0MB, alloc=396.3MB, time=16.24 memory used=721.8MB, alloc=420.3MB, time=19.11 memory used=850.6MB, alloc=444.3MB, time=22.61 memory used=984.6MB, alloc=468.3MB, time=26.37 memory used=1101.0MB, alloc=468.3MB, time=29.48 memory used=1231.1MB, alloc=492.3MB, time=33.35 memory used=1342.5MB, alloc=492.3MB, time=36.66 memory used=1446.1MB, alloc=516.3MB, time=39.81 memory used=1547.1MB, alloc=516.3MB, time=42.90 memory used=1631.8MB, alloc=516.3MB, time=45.32 memory used=1723.2MB, alloc=516.3MB, time=48.30 memory used=1789.9MB, alloc=516.3MB, time=50.68 memory used=1873.2MB, alloc=516.3MB, time=53.61 memory used=1935.9MB, alloc=516.3MB, time=55.87 memory used=2000.5MB, alloc=516.3MB, time=58.32 memory used=2062.0MB, alloc=516.3MB, time=60.63 memory used=2127.0MB, alloc=516.3MB, time=63.25 memory used=2177.5MB, alloc=516.3MB, time=65.06 memory used=2382.2MB, alloc=540.3MB, time=70.97 memory used=2596.2MB, alloc=564.3MB, time=77.53 memory used=2795.5MB, alloc=588.3MB, time=83.17 memory used=2977.8MB, alloc=612.3MB, time=88.57 memory used=3149.0MB, alloc=636.3MB, time=94.76 memory used=3315.0MB, alloc=660.3MB, time=100.96 |\^/| 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(); 1428254698 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-11 y z - z, -10 y z - 6 y - 16, -2 x - 9 y - 18 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [20 y z + 9 z + 8, -15 x - 13 x z + 20 y , 19 z + 2 x + 4 y] > Problem := [F,G]; 2 2 Problem := [[-11 y z - z, -10 y z - 6 y - 16, -2 x - 9 y - 18 z], 2 2 2 2 [20 y z + 9 z + 8, -15 x - 13 x z + 20 y , 19 z + 2 x + 4 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.85 memory used=47.6MB, alloc=32.3MB, time=1.40 memory used=67.2MB, alloc=56.3MB, time=1.93 memory used=107.1MB, alloc=60.3MB, time=2.98 memory used=146.4MB, alloc=84.3MB, time=3.99 memory used=207.0MB, alloc=92.3MB, time=5.59 memory used=265.2MB, alloc=116.3MB, time=7.16 memory used=346.3MB, alloc=116.3MB, time=9.32 memory used=428.7MB, alloc=396.3MB, time=11.55 memory used=534.6MB, alloc=420.3MB, time=14.37 memory used=665.5MB, alloc=420.3MB, time=17.85 memory used=793.3MB, alloc=444.3MB, time=21.47 memory used=943.2MB, alloc=468.3MB, time=25.54 memory used=1062.7MB, alloc=492.3MB, time=28.80 memory used=1198.6MB, alloc=492.3MB, time=32.70 memory used=1312.5MB, alloc=492.3MB, time=36.05 memory used=1431.2MB, alloc=516.3MB, time=39.26 memory used=1534.0MB, alloc=516.3MB, time=42.41 memory used=1638.9MB, alloc=540.3MB, time=45.11 memory used=1758.6MB, alloc=540.3MB, time=48.95 memory used=1877.3MB, alloc=540.3MB, time=53.07 memory used=1960.9MB, alloc=540.3MB, time=55.69 memory used=2059.6MB, alloc=540.3MB, time=59.10 memory used=2159.7MB, alloc=564.3MB, time=62.61 memory used=2247.9MB, alloc=564.3MB, time=65.52 memory used=2336.6MB, alloc=564.3MB, time=68.97 memory used=2385.3MB, alloc=564.3MB, time=70.84 memory used=2440.8MB, alloc=564.3MB, time=72.61 memory used=2499.4MB, alloc=564.3MB, time=75.01 memory used=2720.7MB, alloc=588.3MB, time=81.56 memory used=2915.9MB, alloc=612.3MB, time=87.76 memory used=3081.8MB, alloc=636.3MB, time=92.53 memory used=3275.4MB, alloc=660.3MB, time=98.36 memory used=3425.6MB, alloc=684.3MB, time=103.56 memory used=3597.0MB, alloc=708.3MB, time=109.84 |\^/| 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(); 1428254998 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-14 y - 20 x + 19 z, 17 x z - 20 x - 16 z, -19 z - 4 z + 7] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [5 x z + 16 y - 6, 3 x z + 13 y z - 10 x, -11 x - 2 x y - 13 x z] > Problem := [F,G]; 2 2 Problem := [[-14 y - 20 x + 19 z, 17 x z - 20 x - 16 z, -19 z - 4 z + 7], 2 2 [5 x z + 16 y - 6, 3 x z + 13 y z - 10 x, -11 x - 2 x y - 13 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.86 memory used=46.8MB, alloc=32.3MB, time=1.40 memory used=66.8MB, alloc=56.3MB, time=1.94 memory used=108.2MB, alloc=60.3MB, time=3.02 memory used=146.1MB, alloc=84.3MB, time=4.04 memory used=209.0MB, alloc=92.3MB, time=5.65 memory used=270.6MB, alloc=116.3MB, time=7.22 memory used=339.5MB, alloc=116.3MB, time=8.94 memory used=401.8MB, alloc=396.3MB, time=10.57 memory used=509.4MB, alloc=420.3MB, time=13.47 memory used=637.7MB, alloc=444.3MB, time=17.06 memory used=765.8MB, alloc=468.3MB, time=20.58 memory used=885.0MB, alloc=468.3MB, time=23.96 memory used=998.6MB, alloc=492.3MB, time=27.25 memory used=1115.7MB, alloc=492.3MB, time=30.77 memory used=1213.9MB, alloc=492.3MB, time=33.78 memory used=1296.3MB, alloc=492.3MB, time=36.42 memory used=1372.0MB, alloc=492.3MB, time=38.98 memory used=1436.8MB, alloc=492.3MB, time=41.06 memory used=1520.1MB, alloc=516.3MB, time=43.89 memory used=1588.5MB, alloc=516.3MB, time=46.24 memory used=1639.9MB, alloc=516.3MB, time=48.14 memory used=1697.7MB, alloc=516.3MB, time=50.17 memory used=1746.0MB, alloc=516.3MB, time=52.14 memory used=1940.9MB, alloc=540.3MB, time=57.92 memory used=2162.7MB, alloc=564.3MB, time=64.53 memory used=2345.2MB, alloc=588.3MB, time=69.94 memory used=2522.4MB, alloc=612.3MB, time=75.83 memory used=2692.0MB, alloc=636.3MB, time=81.84 memory used=2859.6MB, alloc=660.3MB, time=88.13 memory used=3007.2MB, alloc=684.3MB, time=93.22 memory used=3147.5MB, alloc=684.3MB, time=98.27 memory used=3282.8MB, alloc=684.3MB, time=103.81 memory used=3378.9MB, alloc=684.3MB, time=107.62 memory used=3478.6MB, alloc=684.3MB, time=111.42 |\^/| 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(); 1428255298 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [13 x y - 2 x z + 8 y z, -10 y z - 11 z + 12 x, 13 x y - 7 x z + 11] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [5 x y - 14 y z - 16 z, 14 y + 8 y z - 20 y, 14 x y + 7 y + 18 y z] > Problem := [F,G]; Problem := [ 2 [13 x y - 2 x z + 8 y z, -10 y z - 11 z + 12 x, 13 x y - 7 x z + 11], 2 2 [5 x y - 14 y z - 16 z, 14 y + 8 y z - 20 y, 14 x y + 7 y + 18 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.86 memory used=46.2MB, alloc=32.3MB, time=1.36 memory used=65.3MB, alloc=56.3MB, time=1.89 memory used=105.5MB, alloc=60.3MB, time=2.95 memory used=144.5MB, alloc=84.3MB, time=4.01 memory used=202.6MB, alloc=92.3MB, time=5.61 memory used=261.1MB, alloc=116.3MB, time=7.27 memory used=342.2MB, alloc=140.3MB, time=9.57 memory used=419.7MB, alloc=396.3MB, time=11.70 memory used=523.0MB, alloc=420.3MB, time=14.63 memory used=651.2MB, alloc=444.3MB, time=18.51 memory used=798.5MB, alloc=468.3MB, time=23.07 memory used=968.9MB, alloc=492.3MB, time=28.58 memory used=1117.1MB, alloc=516.3MB, time=33.72 memory used=1266.5MB, alloc=516.3MB, time=38.96 memory used=1393.6MB, alloc=540.3MB, time=43.30 memory used=1524.3MB, alloc=540.3MB, time=47.91 memory used=1646.4MB, alloc=540.3MB, time=52.50 memory used=1768.3MB, alloc=564.3MB, time=57.07 memory used=1874.1MB, alloc=564.3MB, time=61.38 memory used=1981.3MB, alloc=564.3MB, time=65.79 memory used=2075.7MB, alloc=564.3MB, time=69.42 memory used=2163.3MB, alloc=564.3MB, time=72.93 memory used=2234.8MB, alloc=564.3MB, time=75.44 memory used=2313.4MB, alloc=564.3MB, time=79.12 memory used=2377.3MB, alloc=588.3MB, time=81.67 memory used=2450.9MB, alloc=588.3MB, time=85.10 memory used=2496.7MB, alloc=588.3MB, time=87.39 memory used=2745.0MB, alloc=612.3MB, time=96.10 memory used=3010.5MB, alloc=636.3MB, time=106.03 |\^/| 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(); 1428255598 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-5 x z + 15 z - 14 x, -6 x - 17 x y - 2 x z, -17 x - 9 y z - 7] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [12 x z + 5 x + 16 z, -15 x - 12 y z - 17 x, 14 y z + 16 z - 20 y] > Problem := [F,G]; Problem := [ 2 2 2 [-5 x z + 15 z - 14 x, -6 x - 17 x y - 2 x z, -17 x - 9 y z - 7], 2 2 [12 x z + 5 x + 16 z, -15 x - 12 y z - 17 x, 14 y z + 16 z - 20 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.86 memory used=45.7MB, alloc=32.3MB, time=1.36 memory used=64.8MB, alloc=56.3MB, time=1.87 memory used=104.0MB, alloc=60.3MB, time=2.84 memory used=141.6MB, alloc=84.3MB, time=3.85 memory used=201.0MB, alloc=92.3MB, time=5.45 memory used=260.5MB, alloc=92.3MB, time=7.00 memory used=319.2MB, alloc=116.3MB, time=8.58 memory used=399.8MB, alloc=116.3MB, time=10.69 memory used=479.3MB, alloc=140.3MB, time=12.78 memory used=562.9MB, alloc=396.3MB, time=15.13 memory used=660.6MB, alloc=420.3MB, time=17.84 memory used=790.3MB, alloc=444.3MB, time=21.27 memory used=940.8MB, alloc=468.3MB, time=25.66 memory used=1087.4MB, alloc=492.3MB, time=29.76 memory used=1218.6MB, alloc=492.3MB, time=33.30 memory used=1361.3MB, alloc=516.3MB, time=37.03 memory used=1499.7MB, alloc=516.3MB, time=41.01 memory used=1622.2MB, alloc=540.3MB, time=44.46 memory used=1725.8MB, alloc=540.3MB, time=47.23 memory used=1849.0MB, alloc=540.3MB, time=51.02 memory used=1938.5MB, alloc=540.3MB, time=53.84 memory used=2031.9MB, alloc=540.3MB, time=56.75 memory used=2122.2MB, alloc=540.3MB, time=59.79 memory used=2205.4MB, alloc=540.3MB, time=61.99 memory used=2303.5MB, alloc=540.3MB, time=65.43 memory used=2376.1MB, alloc=564.3MB, time=67.60 memory used=2458.1MB, alloc=564.3MB, time=70.87 memory used=2519.8MB, alloc=564.3MB, time=72.88 memory used=2600.7MB, alloc=564.3MB, time=76.19 memory used=2659.5MB, alloc=564.3MB, time=78.19 memory used=2735.7MB, alloc=564.3MB, time=81.34 memory used=2976.3MB, alloc=588.3MB, time=88.56 memory used=3233.0MB, alloc=612.3MB, time=97.44 memory used=3460.3MB, alloc=636.3MB, time=104.93 memory used=3671.8MB, alloc=660.3MB, time=112.73 |\^/| 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(); 1428255898 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-6 x + 14 x z + 10 z, 12 x - 16 z - 13 y, -6 x + 11 z + 12] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [13 + 17 x, 18 z + 8 x, -4 x y - 19 y + 15 y z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-6 x + 14 x z + 10 z, 12 x - 16 z - 13 y, -6 x + 11 z + 12], 2 2 [13 + 17 x, 18 z + 8 x, -4 x y - 19 y + 15 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=47.1MB, alloc=32.3MB, time=1.38 memory used=66.5MB, alloc=56.3MB, time=1.90 memory used=105.7MB, alloc=60.3MB, time=2.92 memory used=144.7MB, alloc=84.3MB, time=3.94 memory used=205.5MB, alloc=92.3MB, time=5.56 memory used=263.3MB, alloc=116.3MB, time=7.15 memory used=343.4MB, alloc=116.3MB, time=9.33 memory used=421.7MB, alloc=140.3MB, time=11.50 memory used=502.1MB, alloc=164.3MB, time=13.77 memory used=596.8MB, alloc=444.3MB, time=16.86 memory used=735.3MB, alloc=468.3MB, time=21.16 memory used=885.5MB, alloc=492.3MB, time=25.82 memory used=1045.3MB, alloc=516.3MB, time=30.85 memory used=1215.6MB, alloc=540.3MB, time=36.27 memory used=1394.1MB, alloc=564.3MB, time=42.12 memory used=1566.2MB, alloc=588.3MB, time=49.99 memory used=1737.5MB, alloc=612.3MB, time=59.14 memory used=1919.7MB, alloc=636.3MB, time=69.35 memory used=2115.6MB, alloc=660.3MB, time=80.75 memory used=2325.2MB, alloc=684.3MB, time=93.62 memory used=2549.7MB, alloc=708.3MB, time=108.24 |\^/| 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(); 1428256198 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [18 z + 10 y - 2, 10 y + 7 z - 1, 4 x - 13 y z + 7 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [14 x z - 6 y z + 10 x, 1, 16 x z - 10 y + 10 z] > Problem := [F,G]; 2 2 2 2 Problem := [[18 z + 10 y - 2, 10 y + 7 z - 1, 4 x - 13 y z + 7 y], 2 [14 x z - 6 y z + 10 x, 1, 16 x z - 10 y + 10 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.89 memory used=47.2MB, alloc=32.3MB, time=1.42 memory used=66.1MB, alloc=56.3MB, time=1.95 memory used=108.2MB, alloc=68.3MB, time=3.00 memory used=151.3MB, alloc=92.3MB, time=4.02 memory used=215.9MB, alloc=92.3MB, time=5.63 memory used=284.3MB, alloc=372.3MB, time=7.25 memory used=375.2MB, alloc=372.3MB, time=9.41 memory used=463.3MB, alloc=396.3MB, time=11.53 memory used=575.3MB, alloc=420.3MB, time=14.34 memory used=700.8MB, alloc=444.3MB, time=17.48 memory used=824.3MB, alloc=468.3MB, time=20.72 memory used=936.8MB, alloc=468.3MB, time=23.62 memory used=1037.7MB, alloc=468.3MB, time=25.96 memory used=1152.4MB, alloc=492.3MB, time=29.15 memory used=1256.3MB, alloc=492.3MB, time=31.96 memory used=1345.6MB, alloc=492.3MB, time=34.47 memory used=1433.9MB, alloc=516.3MB, time=36.39 memory used=1514.6MB, alloc=516.3MB, time=38.88 memory used=1583.1MB, alloc=516.3MB, time=40.61 memory used=1655.1MB, alloc=516.3MB, time=43.02 memory used=1725.8MB, alloc=516.3MB, time=45.26 memory used=1782.5MB, alloc=516.3MB, time=46.98 memory used=1836.1MB, alloc=516.3MB, time=48.49 memory used=1896.3MB, alloc=516.3MB, time=50.70 memory used=2109.1MB, alloc=540.3MB, time=56.39 memory used=2304.3MB, alloc=564.3MB, time=61.48 memory used=2494.8MB, alloc=588.3MB, time=66.61 memory used=2679.9MB, alloc=612.3MB, time=72.41 memory used=2852.7MB, alloc=636.3MB, time=77.98 memory used=3018.8MB, alloc=636.3MB, time=83.02 memory used=3133.0MB, alloc=636.3MB, time=86.46 memory used=3281.2MB, alloc=636.3MB, time=91.54 memory used=3413.8MB, alloc=660.3MB, time=95.78 memory used=3539.8MB, alloc=660.3MB, time=100.54 memory used=3635.5MB, alloc=660.3MB, time=103.92 memory used=3743.2MB, alloc=660.3MB, time=108.36 |\^/| 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(); 1428256498 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-8 x y + 15 x z + 12 y, -9 x y + 18 y + 9 y z, -17 x - 18 x y + 18 x z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-12 x y + 7 y - 4 z, 9 y z + 9 x - 17, -8 x - 16 x y - 12 y ] > Problem := [F,G]; Problem := [ 2 2 [-8 x y + 15 x z + 12 y, -9 x y + 18 y + 9 y z, -17 x - 18 x y + 18 x z], 2 2 2 [-12 x y + 7 y - 4 z, 9 y z + 9 x - 17, -8 x - 16 x y - 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=0.30 memory used=26.6MB, alloc=32.3MB, time=0.86 memory used=46.1MB, alloc=56.3MB, time=1.38 memory used=85.9MB, alloc=60.3MB, time=2.42 memory used=123.8MB, alloc=84.3MB, time=3.44 memory used=180.1MB, alloc=84.3MB, time=4.92 memory used=239.7MB, alloc=116.3MB, time=6.58 memory used=319.7MB, alloc=116.3MB, time=8.83 memory used=400.7MB, alloc=140.3MB, time=11.22 memory used=492.0MB, alloc=396.3MB, time=14.04 memory used=594.2MB, alloc=420.3MB, time=17.09 memory used=720.1MB, alloc=444.3MB, time=20.86 memory used=867.6MB, alloc=468.3MB, time=25.39 memory used=1037.9MB, alloc=492.3MB, time=30.75 memory used=1187.3MB, alloc=516.3MB, time=35.41 memory used=1324.0MB, alloc=516.3MB, time=39.67 memory used=1451.5MB, alloc=540.3MB, time=44.01 memory used=1590.3MB, alloc=564.3MB, time=48.96 memory used=1693.6MB, alloc=588.3MB, time=52.61 memory used=1820.9MB, alloc=588.3MB, time=57.06 memory used=1944.7MB, alloc=612.3MB, time=61.44 memory used=2069.0MB, alloc=636.3MB, time=65.93 memory used=2183.8MB, alloc=660.3MB, time=70.17 memory used=2294.5MB, alloc=684.3MB, time=74.29 memory used=2412.4MB, alloc=684.3MB, time=78.67 memory used=2516.0MB, alloc=708.3MB, time=82.65 memory used=2612.6MB, alloc=732.3MB, time=86.42 memory used=2696.5MB, alloc=732.3MB, time=89.77 memory used=2794.0MB, alloc=756.3MB, time=93.62 memory used=2891.2MB, alloc=756.3MB, time=97.45 memory used=2976.0MB, alloc=780.3MB, time=100.94 memory used=3061.3MB, alloc=780.3MB, time=104.46 memory used=3140.0MB, alloc=804.3MB, time=107.78 memory used=3216.9MB, alloc=804.3MB, time=111.16 |\^/| 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(); 1428256798 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-11 x + 16 y z - 3 x, 5 x z + 4 y z - 12 z, -20 y z - 5 z + 2 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-20 y - 3 y - 5, 14 y + 18 y - 18 z, -4 x y - 6 y - 18] > Problem := [F,G]; Problem := [ 2 2 [-11 x + 16 y z - 3 x, 5 x z + 4 y z - 12 z, -20 y z - 5 z + 2 z], 2 2 2 [-20 y - 3 y - 5, 14 y + 18 y - 18 z, -4 x y - 6 y - 18]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=25.9MB, alloc=32.3MB, time=0.83 memory used=46.7MB, alloc=32.3MB, time=1.35 memory used=66.5MB, alloc=32.3MB, time=1.84 memory used=85.3MB, alloc=56.3MB, time=2.34 memory used=123.2MB, alloc=60.3MB, time=3.37 memory used=159.9MB, alloc=60.3MB, time=4.34 memory used=195.0MB, alloc=84.3MB, time=5.31 memory used=250.7MB, alloc=84.3MB, time=6.83 memory used=307.6MB, alloc=108.3MB, time=8.56 memory used=382.8MB, alloc=140.3MB, time=10.96 memory used=473.7MB, alloc=164.3MB, time=13.76 memory used=578.1MB, alloc=188.3MB, time=17.03 memory used=692.4MB, alloc=212.3MB, time=21.69 memory used=810.3MB, alloc=236.3MB, time=27.62 memory used=941.0MB, alloc=260.3MB, time=35.06 memory used=1087.4MB, alloc=284.3MB, time=44.04 memory used=1257.7MB, alloc=308.3MB, time=54.40 memory used=1452.0MB, alloc=308.3MB, time=66.12 memory used=1646.3MB, alloc=308.3MB, time=77.85 memory used=1840.7MB, alloc=332.3MB, time=89.61 N1 := 6581 > GB := Basis(F, plex(op(vars))); 4 3 2 GB := [6105 x - 24130 x + 23589 x + 8352 x, 3 2 2 55 x + 44 x y - 117 x + 12 x y - 36 x, 3 2 -6105 x + 9478 x + 3039 x + 7056 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2061.6MB, alloc=332.3MB, time=102.26 N2 := 489 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-11 x + 16 y z - 3 x, 5 x z + 4 y z - 12 z, -20 y z - 5 z + 2 z, 2 2 2 -20 y - 3 y - 5, 14 y + 18 y - 18 z, -4 x y - 6 y - 18] > J:=[op(GB),op(G)]; 4 3 2 J := [6105 x - 24130 x + 23589 x + 8352 x, 3 2 2 55 x + 44 x y - 117 x + 12 x y - 36 x, 3 2 2 2 -6105 x + 9478 x + 3039 x + 7056 z, -20 y - 3 y - 5, 14 y + 18 y - 18 z, 2 -4 x y - 6 y - 18] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 12, 2, 2, 2, 2, 1/2, 1, 2/3, 2/9, 1/2, 4/9, 6, 10, 16, 4, 13 4, 2, 1, 2/3, 2/3, 1/3, --, 4/11, 1/11, 3, -4, -2] 22 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=2140.4MB, alloc=332.3MB, time=104.73 |\^/| 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(); 1428257075 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [13 x y + 11 y + 16, 7 x y - 5 z - 10, 12 y + 8 z - 4 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [17 y - 10 x + 4 z, 20 x - 15 z + 5, 8 x z + 18 y] > Problem := [F,G]; 2 2 2 Problem := [[13 x y + 11 y + 16, 7 x y - 5 z - 10, 12 y + 8 z - 4 z], 2 2 [17 y - 10 x + 4 z, 20 x - 15 z + 5, 8 x z + 18 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.89 memory used=47.5MB, alloc=32.3MB, time=1.42 memory used=65.9MB, alloc=56.3MB, time=1.93 memory used=107.4MB, alloc=60.3MB, time=3.02 memory used=147.4MB, alloc=60.3MB, time=4.08 memory used=185.6MB, alloc=84.3MB, time=5.12 memory used=238.5MB, alloc=84.3MB, time=6.59 memory used=300.4MB, alloc=116.3MB, time=8.26 memory used=375.4MB, alloc=372.3MB, time=10.33 memory used=463.3MB, alloc=396.3MB, time=12.53 memory used=571.6MB, alloc=420.3MB, time=15.56 memory used=702.6MB, alloc=444.3MB, time=19.39 memory used=839.4MB, alloc=468.3MB, time=23.39 memory used=974.5MB, alloc=492.3MB, time=27.42 memory used=1086.6MB, alloc=492.3MB, time=31.13 memory used=1202.5MB, alloc=492.3MB, time=34.95 memory used=1311.0MB, alloc=492.3MB, time=38.46 memory used=1413.3MB, alloc=492.3MB, time=41.83 memory used=1490.8MB, alloc=516.3MB, time=44.55 memory used=1580.1MB, alloc=516.3MB, time=47.78 memory used=1651.4MB, alloc=516.3MB, time=50.36 memory used=1716.7MB, alloc=516.3MB, time=53.02 memory used=1779.5MB, alloc=516.3MB, time=55.50 memory used=1852.0MB, alloc=516.3MB, time=58.31 memory used=1913.1MB, alloc=516.3MB, time=60.67 memory used=1976.6MB, alloc=516.3MB, time=63.44 memory used=2180.0MB, alloc=540.3MB, time=70.63 memory used=2407.1MB, alloc=564.3MB, time=78.42 memory used=2614.5MB, alloc=588.3MB, time=86.22 memory used=2818.4MB, alloc=612.3MB, time=93.67 memory used=3000.5MB, alloc=636.3MB, time=100.56 memory used=3162.0MB, alloc=660.3MB, time=106.95 |\^/| 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(); 1428257375 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-15 x - 8 y z - 4 x, -3 x - 13 x z + 4 z , -4 y z - 17 z + 7 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-y - 13 z + 15 z, -11 x + 10 y - 16 z, -12 y + 14 y - 6 z] > Problem := [F,G]; Problem := [ 2 2 2 2 [-15 x - 8 y z - 4 x, -3 x - 13 x z + 4 z , -4 y z - 17 z + 7 z], 2 2 2 2 2 [-y - 13 z + 15 z, -11 x + 10 y - 16 z, -12 y + 14 y - 6 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.84 memory used=47.0MB, alloc=32.3MB, time=1.36 memory used=66.3MB, alloc=56.3MB, time=1.87 memory used=103.6MB, alloc=60.3MB, time=2.84 memory used=139.7MB, alloc=84.3MB, time=3.80 memory used=198.2MB, alloc=92.3MB, time=5.41 memory used=255.4MB, alloc=116.3MB, time=6.95 memory used=333.4MB, alloc=116.3MB, time=9.07 memory used=411.1MB, alloc=140.3MB, time=11.22 memory used=507.5MB, alloc=140.3MB, time=14.05 memory used=592.9MB, alloc=420.3MB, time=16.66 memory used=716.3MB, alloc=444.3MB, time=20.38 memory used=863.3MB, alloc=468.3MB, time=24.84 memory used=1033.3MB, alloc=492.3MB, time=30.27 memory used=1166.7MB, alloc=492.3MB, time=34.44 memory used=1334.0MB, alloc=516.3MB, time=40.19 memory used=1484.9MB, alloc=516.3MB, time=45.26 memory used=1629.8MB, alloc=540.3MB, time=50.34 memory used=1769.6MB, alloc=540.3MB, time=55.49 memory used=1907.6MB, alloc=540.3MB, time=60.94 memory used=2026.3MB, alloc=540.3MB, time=65.26 memory used=2141.0MB, alloc=564.3MB, time=69.37 memory used=2248.3MB, alloc=564.3MB, time=73.37 memory used=2336.0MB, alloc=564.3MB, time=76.68 memory used=2422.5MB, alloc=564.3MB, time=79.95 memory used=2527.6MB, alloc=564.3MB, time=84.47 memory used=2635.8MB, alloc=588.3MB, time=89.36 memory used=2719.2MB, alloc=588.3MB, time=92.79 memory used=2790.2MB, alloc=588.3MB, time=95.79 memory used=2861.4MB, alloc=588.3MB, time=98.82 memory used=2934.7MB, alloc=588.3MB, time=101.89 |\^/| 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(); 1428257675 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-5 y z + 16 z + 19, -3 x - 12 y - 2, 20 x z + 4 y + 16 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-14 x y - 17 x z - 9 z, -18 x y + 14 y z + 4 z, 15 y z - 7 z - 8 y] > Problem := [F,G]; 2 2 2 2 Problem := [[-5 y z + 16 z + 19, -3 x - 12 y - 2, 20 x z + 4 y + 16 z], 2 [-14 x y - 17 x z - 9 z, -18 x y + 14 y z + 4 z, 15 y z - 7 z - 8 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.88 memory used=47.3MB, alloc=32.3MB, time=1.41 memory used=66.8MB, alloc=56.3MB, time=1.94 memory used=106.5MB, alloc=60.3MB, time=2.99 memory used=144.3MB, alloc=84.3MB, time=4.01 memory used=207.3MB, alloc=92.3MB, time=5.69 memory used=267.4MB, alloc=116.3MB, time=7.37 memory used=352.7MB, alloc=116.3MB, time=9.71 memory used=434.0MB, alloc=396.3MB, time=12.01 memory used=542.1MB, alloc=420.3MB, time=15.03 memory used=672.1MB, alloc=444.3MB, time=18.72 memory used=814.0MB, alloc=468.3MB, time=22.57 memory used=958.0MB, alloc=492.3MB, time=27.05 memory used=1113.4MB, alloc=492.3MB, time=31.91 memory used=1243.6MB, alloc=516.3MB, time=35.99 memory used=1389.1MB, alloc=516.3MB, time=40.93 memory used=1533.9MB, alloc=516.3MB, time=46.05 memory used=1645.2MB, alloc=540.3MB, time=49.80 memory used=1745.1MB, alloc=540.3MB, time=53.19 memory used=1834.7MB, alloc=540.3MB, time=56.35 memory used=1942.7MB, alloc=540.3MB, time=60.21 memory used=2030.1MB, alloc=540.3MB, time=63.52 memory used=2110.6MB, alloc=540.3MB, time=66.54 memory used=2185.2MB, alloc=540.3MB, time=69.24 memory used=2278.5MB, alloc=540.3MB, time=73.07 memory used=2354.5MB, alloc=540.3MB, time=76.33 memory used=2425.3MB, alloc=540.3MB, time=79.38 memory used=2484.1MB, alloc=540.3MB, time=81.93 memory used=2542.3MB, alloc=540.3MB, time=84.81 memory used=2596.4MB, alloc=540.3MB, time=86.98 memory used=2661.1MB, alloc=540.3MB, time=89.87 memory used=2895.2MB, alloc=564.3MB, time=98.16 |\^/| 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(); 1428257975 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-3 x y - 6 y - 10 x, 3 y + 16 y z - 17 x, 2 y - 15 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-9 x y + 18 y + 3 z, -18 y z - 15 y + 13 z, y - 11 x - 19] > Problem := [F,G]; 2 2 2 Problem := [[-3 x y - 6 y - 10 x, 3 y + 16 y z - 17 x, 2 y - 15 x], 2 2 [-9 x y + 18 y + 3 z, -18 y z - 15 y + 13 z, y - 11 x - 19]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.85 memory used=47.4MB, alloc=32.3MB, time=1.38 memory used=66.8MB, alloc=56.3MB, time=1.90 memory used=106.6MB, alloc=60.3MB, time=2.92 memory used=144.1MB, alloc=84.3MB, time=3.91 memory used=203.2MB, alloc=84.3MB, time=5.46 memory used=260.9MB, alloc=84.3MB, time=7.00 memory used=321.8MB, alloc=116.3MB, time=8.88 memory used=403.5MB, alloc=140.3MB, time=11.36 memory used=495.8MB, alloc=164.3MB, time=14.22 memory used=592.0MB, alloc=444.3MB, time=17.25 memory used=722.0MB, alloc=468.3MB, time=21.14 memory used=862.4MB, alloc=492.3MB, time=25.46 memory used=1018.7MB, alloc=516.3MB, time=30.30 memory used=1182.1MB, alloc=540.3MB, time=36.45 memory used=1339.1MB, alloc=564.3MB, time=44.77 memory used=1508.2MB, alloc=588.3MB, time=54.28 memory used=1692.9MB, alloc=612.3MB, time=65.00 memory used=1893.7MB, alloc=636.3MB, time=76.91 memory used=2109.6MB, alloc=660.3MB, time=90.34 memory used=2340.5MB, alloc=684.3MB, time=105.32 |\^/| 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(); 1428258275 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [14 x - 14 x y - 10 x, -16 x y + 17 y - 8, 5 x y - 12 x z + 12 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-6 y + 20 y - 14 z, 11 y z - 10 x, 5 x - 6 x - 17 z] > Problem := [F,G]; Problem := [ 2 2 [14 x - 14 x y - 10 x, -16 x y + 17 y - 8, 5 x y - 12 x z + 12 x], 2 2 [-6 y + 20 y - 14 z, 11 y z - 10 x, 5 x - 6 x - 17 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.8MB, alloc=40.3MB, time=0.99 memory used=58.8MB, alloc=40.3MB, time=1.68 memory used=84.5MB, alloc=68.3MB, time=2.38 memory used=131.0MB, alloc=68.3MB, time=3.61 memory used=177.2MB, alloc=92.3MB, time=4.85 memory used=246.2MB, alloc=100.3MB, time=6.75 memory used=311.9MB, alloc=124.3MB, time=8.63 memory used=399.9MB, alloc=124.3MB, time=11.08 memory used=485.1MB, alloc=404.3MB, time=13.57 memory used=592.5MB, alloc=428.3MB, time=16.98 memory used=709.3MB, alloc=452.3MB, time=20.61 memory used=840.1MB, alloc=476.3MB, time=24.68 memory used=982.4MB, alloc=500.3MB, time=29.14 memory used=1135.8MB, alloc=524.3MB, time=34.02 memory used=1297.2MB, alloc=548.3MB, time=39.46 memory used=1451.6MB, alloc=572.3MB, time=47.27 memory used=1614.6MB, alloc=596.3MB, time=56.30 memory used=1791.4MB, alloc=620.3MB, time=66.59 memory used=1983.2MB, alloc=644.3MB, time=78.19 memory used=2190.3MB, alloc=668.3MB, time=90.80 memory used=2409.2MB, alloc=692.3MB, time=104.93 |\^/| 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(); 1428258575 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-20 y - 15 z + 5, -15 x - 12 x y - 17 y, 10 x + 5 y + 17 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [14 x y + 15 x z - 6 z, -5 y - 18 z + 18, 12 x - 20 x z + 15 x] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-20 y - 15 z + 5, -15 x - 12 x y - 17 y, 10 x + 5 y + 17 x], 2 2 [14 x y + 15 x z - 6 z, -5 y - 18 z + 18, 12 x - 20 x z + 15 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=47.3MB, alloc=32.3MB, time=1.38 memory used=67.3MB, alloc=56.3MB, time=1.91 memory used=107.5MB, alloc=60.3MB, time=2.92 memory used=145.7MB, alloc=84.3MB, time=3.91 memory used=207.0MB, alloc=92.3MB, time=5.51 memory used=266.4MB, alloc=116.3MB, time=7.09 memory used=348.4MB, alloc=116.3MB, time=9.28 memory used=425.7MB, alloc=396.3MB, time=11.34 memory used=529.2MB, alloc=420.3MB, time=14.26 memory used=655.1MB, alloc=444.3MB, time=17.86 memory used=802.8MB, alloc=468.3MB, time=22.10 memory used=970.9MB, alloc=492.3MB, time=27.29 memory used=1141.6MB, alloc=516.3MB, time=32.91 memory used=1323.1MB, alloc=540.3MB, time=38.83 memory used=1512.8MB, alloc=564.3MB, time=45.06 memory used=1711.6MB, alloc=588.3MB, time=51.57 memory used=1908.7MB, alloc=612.3MB, time=58.07 memory used=2092.7MB, alloc=636.3MB, time=64.37 memory used=2302.4MB, alloc=660.3MB, time=74.56 memory used=2506.4MB, alloc=684.3MB, time=86.15 memory used=2720.7MB, alloc=708.3MB, time=98.91 |\^/| 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(); 1428258875 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-10 x z + 5 x + 20, -14 y - 17 z - 20 y, -16 x z - 18 y z - 4 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-12 x y + 6 y z - 18 y, 2 z - 20 y + 17 z, 13 x z - 8 z - 19 z] > Problem := [F,G]; Problem := [ 2 2 2 [-10 x z + 5 x + 20, -14 y - 17 z - 20 y, -16 x z - 18 y z - 4 z ], 2 2 [-12 x y + 6 y z - 18 y, 2 z - 20 y + 17 z, 13 x z - 8 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=4.2MB, alloc=32.3MB, time=0.30 memory used=26.0MB, alloc=32.3MB, time=0.82 memory used=46.1MB, alloc=32.3MB, time=1.30 memory used=64.7MB, alloc=56.3MB, time=1.79 memory used=103.5MB, alloc=60.3MB, time=2.80 memory used=139.8MB, alloc=84.3MB, time=3.78 memory used=197.7MB, alloc=92.3MB, time=5.36 memory used=254.4MB, alloc=116.3MB, time=6.93 memory used=333.0MB, alloc=140.3MB, time=9.13 memory used=431.7MB, alloc=140.3MB, time=11.90 memory used=524.0MB, alloc=164.3MB, time=14.69 memory used=617.6MB, alloc=444.3MB, time=17.40 memory used=750.8MB, alloc=468.3MB, time=21.44 memory used=912.6MB, alloc=492.3MB, time=26.49 memory used=1098.5MB, alloc=516.3MB, time=32.30 memory used=1309.5MB, alloc=540.3MB, time=39.14 memory used=1537.8MB, alloc=564.3MB, time=47.43 memory used=1791.7MB, alloc=588.3MB, time=56.72 memory used=2066.1MB, alloc=612.3MB, time=67.06 memory used=2363.4MB, alloc=636.3MB, time=79.70 memory used=2684.6MB, alloc=660.3MB, time=93.08 memory used=3008.3MB, alloc=684.3MB, time=106.03 |\^/| 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(); 1428259175 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [3 x z + 13 y z - 9 x, 4 y z - 5 z + 1, -7 z - 15 z + 1] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-12 x + 9 y z + 11, 16 z - 17 x - 3, -10 x y - 19 x z + 4 y] > Problem := [F,G]; 2 2 Problem := [[3 x z + 13 y z - 9 x, 4 y z - 5 z + 1, -7 z - 15 z + 1], 2 2 [-12 x + 9 y z + 11, 16 z - 17 x - 3, -10 x y - 19 x z + 4 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.0MB, alloc=32.3MB, time=0.87 memory used=46.3MB, alloc=32.3MB, time=1.40 memory used=64.9MB, alloc=56.3MB, time=1.90 memory used=105.4MB, alloc=60.3MB, time=2.96 memory used=144.1MB, alloc=84.3MB, time=3.99 memory used=206.0MB, alloc=92.3MB, time=5.62 memory used=265.9MB, alloc=116.3MB, time=7.23 memory used=348.0MB, alloc=116.3MB, time=9.39 memory used=428.5MB, alloc=140.3MB, time=11.70 memory used=500.2MB, alloc=140.3MB, time=13.65 memory used=577.6MB, alloc=396.3MB, time=15.76 memory used=682.0MB, alloc=420.3MB, time=18.59 memory used=811.3MB, alloc=444.3MB, time=22.26 memory used=956.1MB, alloc=468.3MB, time=26.41 memory used=1101.3MB, alloc=468.3MB, time=30.44 memory used=1226.4MB, alloc=492.3MB, time=34.03 memory used=1354.8MB, alloc=492.3MB, time=37.96 memory used=1471.3MB, alloc=516.3MB, time=41.36 memory used=1574.8MB, alloc=516.3MB, time=44.47 memory used=1684.9MB, alloc=516.3MB, time=48.12 memory used=1783.1MB, alloc=516.3MB, time=51.59 memory used=1861.2MB, alloc=540.3MB, time=53.70 memory used=1957.8MB, alloc=540.3MB, time=57.27 memory used=2046.9MB, alloc=540.3MB, time=60.17 memory used=2129.7MB, alloc=540.3MB, time=63.59 memory used=2214.2MB, alloc=540.3MB, time=66.94 memory used=2272.4MB, alloc=540.3MB, time=69.29 memory used=2321.1MB, alloc=540.3MB, time=71.05 memory used=2396.3MB, alloc=540.3MB, time=74.34 memory used=2444.1MB, alloc=540.3MB, time=76.14 memory used=2478.6MB, alloc=540.3MB, time=77.68 memory used=2701.0MB, alloc=564.3MB, time=84.63 memory used=2955.8MB, alloc=588.3MB, time=91.68 memory used=3145.0MB, alloc=612.3MB, time=97.60 memory used=3355.0MB, alloc=636.3MB, time=104.95 memory used=3554.4MB, alloc=660.3MB, time=111.75 memory used=3744.2MB, alloc=684.3MB, time=119.00 |\^/| 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(); 1428259475 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-18 x z - 20 y - 6 z, 15 y - 13 x + 15 z, 8 x - 16 y + 18] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [19 x y + 18 x z - 8 y z, 10 x z + 4 y - 15 y, 5 y z - 5 x - 19 y] > Problem := [F,G]; 2 2 2 Problem := [[-18 x z - 20 y - 6 z, 15 y - 13 x + 15 z, 8 x - 16 y + 18], 2 [19 x y + 18 x z - 8 y z, 10 x z + 4 y - 15 y, 5 y z - 5 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=4.3MB, alloc=32.3MB, time=0.32 memory used=26.7MB, alloc=32.3MB, time=0.89 memory used=47.5MB, alloc=32.3MB, time=1.42 memory used=66.7MB, alloc=56.3MB, time=1.94 memory used=106.5MB, alloc=60.3MB, time=2.98 memory used=145.2MB, alloc=60.3MB, time=3.99 memory used=182.9MB, alloc=84.3MB, time=5.01 memory used=229.0MB, alloc=84.3MB, time=6.23 memory used=290.1MB, alloc=92.3MB, time=7.84 memory used=349.3MB, alloc=116.3MB, time=9.45 memory used=429.9MB, alloc=140.3MB, time=11.59 memory used=505.9MB, alloc=396.3MB, time=13.76 memory used=612.5MB, alloc=420.3MB, time=16.66 memory used=740.3MB, alloc=444.3MB, time=20.22 memory used=873.8MB, alloc=468.3MB, time=23.81 memory used=998.7MB, alloc=468.3MB, time=27.20 memory used=1120.2MB, alloc=492.3MB, time=30.64 memory used=1225.8MB, alloc=492.3MB, time=33.71 memory used=1320.0MB, alloc=492.3MB, time=36.47 memory used=1408.8MB, alloc=492.3MB, time=39.11 memory used=1490.9MB, alloc=492.3MB, time=41.77 memory used=1561.7MB, alloc=492.3MB, time=44.18 memory used=1638.2MB, alloc=492.3MB, time=46.92 memory used=1711.7MB, alloc=492.3MB, time=49.63 memory used=1777.7MB, alloc=492.3MB, time=52.08 memory used=1835.9MB, alloc=492.3MB, time=54.21 memory used=1875.3MB, alloc=492.3MB, time=55.96 memory used=2051.6MB, alloc=516.3MB, time=61.85 memory used=2251.5MB, alloc=540.3MB, time=68.52 memory used=2456.2MB, alloc=564.3MB, time=75.26 memory used=2650.2MB, alloc=588.3MB, time=82.32 memory used=2831.5MB, alloc=612.3MB, time=88.78 memory used=2990.5MB, alloc=636.3MB, time=94.66 memory used=3132.8MB, alloc=660.3MB, time=100.18 memory used=3232.6MB, alloc=660.3MB, time=104.71 memory used=3353.6MB, alloc=660.3MB, time=109.15 memory used=3482.8MB, alloc=660.3MB, time=114.53 |\^/| 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(); 1428259775 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-18 x z + 4 y - 12 z, 4 x - 2 y - 13 z, 12 x z + 19 z - 13 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-20 x y + 12 y + 18 y z, 10 y z + x + 17, 10 x + 18 y - 2] > Problem := [F,G]; 2 2 Problem := [[-18 x z + 4 y - 12 z, 4 x - 2 y - 13 z, 12 x z + 19 z - 13 x], 2 2 2 [-20 x y + 12 y + 18 y z, 10 y z + x + 17, 10 x + 18 y - 2]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.87 memory used=46.9MB, alloc=32.3MB, time=1.38 memory used=65.7MB, alloc=56.3MB, time=1.90 memory used=105.6MB, alloc=60.3MB, time=2.95 memory used=144.0MB, alloc=60.3MB, time=3.95 memory used=182.2MB, alloc=84.3MB, time=4.95 memory used=230.8MB, alloc=84.3MB, time=6.22 memory used=288.3MB, alloc=116.3MB, time=7.84 memory used=369.1MB, alloc=140.3MB, time=9.94 memory used=451.1MB, alloc=140.3MB, time=12.10 memory used=530.7MB, alloc=396.3MB, time=14.25 memory used=631.4MB, alloc=420.3MB, time=17.01 memory used=760.4MB, alloc=444.3MB, time=20.46 memory used=912.8MB, alloc=468.3MB, time=24.48 memory used=1057.5MB, alloc=492.3MB, time=28.68 memory used=1194.0MB, alloc=492.3MB, time=32.68 memory used=1318.0MB, alloc=492.3MB, time=36.30 memory used=1449.3MB, alloc=516.3MB, time=40.23 memory used=1564.0MB, alloc=516.3MB, time=43.58 memory used=1660.7MB, alloc=516.3MB, time=46.75 memory used=1768.4MB, alloc=516.3MB, time=50.27 memory used=1858.1MB, alloc=516.3MB, time=53.30 memory used=1926.2MB, alloc=540.3MB, time=55.70 memory used=1995.5MB, alloc=540.3MB, time=58.11 memory used=2074.4MB, alloc=540.3MB, time=60.90 memory used=2144.1MB, alloc=540.3MB, time=63.27 memory used=2219.4MB, alloc=540.3MB, time=66.08 memory used=2269.6MB, alloc=540.3MB, time=67.99 memory used=2320.7MB, alloc=540.3MB, time=70.00 memory used=2539.2MB, alloc=564.3MB, time=76.82 memory used=2768.0MB, alloc=588.3MB, time=84.58 memory used=2993.3MB, alloc=612.3MB, time=92.39 memory used=3216.6MB, alloc=636.3MB, time=100.28 memory used=3460.3MB, alloc=660.3MB, time=108.62 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428260075 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [9 x y - 15 y - 12, 20 x y + 2 x z + 14 z, -2 y + 10 x - 4 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-14 x + 7 y - 9 z , 15 x y - 20 y z - 2 x, 2 y - 19 y] > Problem := [F,G]; 2 Problem := [[9 x y - 15 y - 12, 20 x y + 2 x z + 14 z, -2 y + 10 x - 4 y], 2 2 2 2 [-14 x + 7 y - 9 z , 15 x y - 20 y z - 2 x, 2 y - 19 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.84 memory used=47.5MB, alloc=32.3MB, time=1.36 memory used=67.9MB, alloc=32.3MB, time=1.89 memory used=86.6MB, alloc=56.3MB, time=2.42 memory used=126.6MB, alloc=60.3MB, time=3.48 memory used=164.9MB, alloc=84.3MB, time=4.54 memory used=213.4MB, alloc=84.3MB, time=5.84 memory used=272.5MB, alloc=116.3MB, time=7.48 memory used=356.8MB, alloc=140.3MB, time=9.90 memory used=452.3MB, alloc=164.3MB, time=12.81 memory used=547.1MB, alloc=420.3MB, time=15.81 memory used=655.9MB, alloc=444.3MB, time=19.15 memory used=786.5MB, alloc=468.3MB, time=23.00 memory used=932.6MB, alloc=492.3MB, time=27.42 memory used=1093.8MB, alloc=516.3MB, time=32.31 memory used=1265.3MB, alloc=540.3MB, time=37.70 memory used=1447.3MB, alloc=564.3MB, time=43.54 memory used=1635.1MB, alloc=588.3MB, time=50.47 memory used=1811.9MB, alloc=612.3MB, time=59.91 memory used=1999.5MB, alloc=636.3MB, time=70.45 memory used=2200.5MB, alloc=660.3MB, time=82.24 memory used=2416.7MB, alloc=684.3MB, time=95.24 memory used=2648.5MB, alloc=708.3MB, time=109.33 |\^/| 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(); 1428260375 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [x y - 12 y - 16 y z, 14 x z - 12 y + 17 z , -2 x z - 18 y - 12] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [4 x y + 3 y z + 14 z , -4 y - 10 y + 19, 12 y + 17 z - 17] > Problem := [F,G]; 2 2 2 Problem := [[x y - 12 y - 16 y z, 14 x z - 12 y + 17 z , -2 x z - 18 y - 12], 2 2 2 2 [4 x y + 3 y z + 14 z , -4 y - 10 y + 19, 12 y + 17 z - 17]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.88 memory used=48.2MB, alloc=32.3MB, time=1.42 memory used=67.7MB, alloc=56.3MB, time=1.96 memory used=106.5MB, alloc=60.3MB, time=3.01 memory used=142.9MB, alloc=84.3MB, time=4.01 memory used=200.8MB, alloc=92.3MB, time=5.58 memory used=258.4MB, alloc=116.3MB, time=7.16 memory used=340.2MB, alloc=116.3MB, time=9.37 memory used=419.8MB, alloc=140.3MB, time=11.60 memory used=507.7MB, alloc=140.3MB, time=14.10 memory used=600.7MB, alloc=420.3MB, time=16.86 memory used=726.7MB, alloc=420.3MB, time=20.43 memory used=850.1MB, alloc=444.3MB, time=24.02 memory used=994.9MB, alloc=468.3MB, time=28.25 memory used=1157.0MB, alloc=492.3MB, time=33.18 memory used=1320.5MB, alloc=516.3MB, time=37.85 memory used=1473.6MB, alloc=516.3MB, time=42.60 memory used=1606.7MB, alloc=540.3MB, time=46.68 memory used=1727.8MB, alloc=540.3MB, time=50.28 memory used=1864.7MB, alloc=540.3MB, time=54.94 memory used=1989.8MB, alloc=564.3MB, time=59.01 memory used=2121.7MB, alloc=564.3MB, time=63.86 memory used=2244.9MB, alloc=564.3MB, time=68.26 memory used=2329.0MB, alloc=564.3MB, time=70.95 memory used=2423.7MB, alloc=564.3MB, time=74.49 memory used=2517.3MB, alloc=564.3MB, time=78.02 memory used=2612.6MB, alloc=564.3MB, time=81.36 memory used=2687.6MB, alloc=564.3MB, time=84.16 memory used=2777.1MB, alloc=564.3MB, time=87.72 memory used=2860.4MB, alloc=564.3MB, time=91.16 memory used=2925.5MB, alloc=588.3MB, time=93.38 memory used=3005.3MB, alloc=588.3MB, time=96.94 memory used=3057.0MB, alloc=588.3MB, time=99.12 memory used=3124.6MB, alloc=588.3MB, time=102.16 memory used=3382.2MB, alloc=612.3MB, time=111.01 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428260675 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-6 y - 16 x - 10, 3 - 4 x + 7 z, -17 y z - 13 z + z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-15 x + 13 x y - 10 x z, -8 x - 15 x y - 15 x z, -11 x - 2 x y - 15 x] > Problem := [F,G]; 2 2 Problem := [[-6 y - 16 x - 10, 3 - 4 x + 7 z, -17 y z - 13 z + z], 2 2 2 [-15 x + 13 x y - 10 x z, -8 x - 15 x y - 15 x z, -11 x - 2 x 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=31.7MB, alloc=40.3MB, time=0.95 memory used=59.3MB, alloc=40.3MB, time=1.61 memory used=85.9MB, alloc=40.3MB, time=2.26 memory used=110.3MB, alloc=64.3MB, time=2.89 memory used=154.0MB, alloc=68.3MB, time=4.01 memory used=194.0MB, alloc=92.3MB, time=5.04 memory used=245.6MB, alloc=92.3MB, time=6.35 memory used=306.6MB, alloc=124.3MB, time=7.96 memory used=387.8MB, alloc=124.3MB, time=10.03 memory used=465.4MB, alloc=148.3MB, time=12.07 memory used=558.8MB, alloc=428.3MB, time=14.74 memory used=674.6MB, alloc=452.3MB, time=18.38 memory used=800.5MB, alloc=476.3MB, time=22.33 memory used=937.6MB, alloc=500.3MB, time=26.62 memory used=1083.5MB, alloc=524.3MB, time=31.26 memory used=1239.9MB, alloc=548.3MB, time=36.21 memory used=1403.4MB, alloc=572.3MB, time=41.49 memory used=1565.2MB, alloc=596.3MB, time=48.95 memory used=1724.7MB, alloc=620.3MB, time=57.58 memory used=1895.6MB, alloc=644.3MB, time=67.28 memory used=2080.1MB, alloc=668.3MB, time=78.15 memory used=2279.6MB, alloc=692.3MB, time=90.25 |\^/| 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(); 1428260975 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-17 z - 9 z - 19, 7 y z - 4 y - 8 z, 4 x y - 9 y + 9 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [10 y - 4 y, -17 y z + 11 x + 18, -3 x + 2 x z + 16 y] > Problem := [F,G]; 2 2 Problem := [[-17 z - 9 z - 19, 7 y z - 4 y - 8 z, 4 x y - 9 y + 9 y], 2 2 [10 y - 4 y, -17 y z + 11 x + 18, -3 x + 2 x z + 16 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=47.0MB, alloc=32.3MB, time=1.39 memory used=65.7MB, alloc=56.3MB, time=1.90 memory used=105.4MB, alloc=60.3MB, time=2.96 memory used=142.2MB, alloc=84.3MB, time=3.93 memory used=200.9MB, alloc=92.3MB, time=5.57 memory used=258.9MB, alloc=116.3MB, time=7.23 memory used=339.6MB, alloc=116.3MB, time=9.52 memory used=418.5MB, alloc=140.3MB, time=11.88 memory used=502.3MB, alloc=140.3MB, time=14.28 memory used=582.6MB, alloc=420.3MB, time=16.75 memory used=700.9MB, alloc=444.3MB, time=20.57 memory used=829.7MB, alloc=468.3MB, time=24.69 memory used=973.9MB, alloc=492.3MB, time=29.30 memory used=1128.2MB, alloc=516.3MB, time=36.26 memory used=1283.0MB, alloc=540.3MB, time=44.88 memory used=1446.6MB, alloc=564.3MB, time=55.20 memory used=1634.3MB, alloc=588.3MB, time=66.93 memory used=1845.9MB, alloc=612.3MB, time=80.04 N1 := 5505 > GB := Basis(F, plex(op(vars))); 2 GB := [7760 x + 5928 x + 6885, -9 - 4 x + 9 y, 1940 x + 1173 + 1632 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2084.9MB, alloc=612.3MB, time=93.99 memory used=2304.7MB, alloc=612.3MB, time=100.99 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428261275 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-2 x z - 14 z + 4, 10 y - 8 y z - 8 z , -15 y + 8 x - 7 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-19 x - 7 x z - 17 z, 20 x y + 12 z - 14 z, 3 x z + 13 y - 13 y z] > Problem := [F,G]; 2 2 2 2 Problem := [[-2 x z - 14 z + 4, 10 y - 8 y z - 8 z , -15 y + 8 x - 7 z], 2 2 2 [-19 x - 7 x z - 17 z, 20 x y + 12 z - 14 z, 3 x z + 13 y - 13 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.31 memory used=26.6MB, alloc=32.3MB, time=0.89 memory used=47.7MB, alloc=32.3MB, time=1.43 memory used=67.0MB, alloc=56.3MB, time=1.95 memory used=109.8MB, alloc=68.3MB, time=3.00 memory used=152.0MB, alloc=92.3MB, time=4.02 memory used=215.4MB, alloc=92.3MB, time=5.63 memory used=279.4MB, alloc=116.3MB, time=7.22 memory used=345.1MB, alloc=116.3MB, time=8.85 memory used=402.6MB, alloc=372.3MB, time=10.31 memory used=487.1MB, alloc=396.3MB, time=12.48 memory used=594.5MB, alloc=420.3MB, time=15.34 memory used=723.7MB, alloc=444.3MB, time=18.80 memory used=870.3MB, alloc=468.3MB, time=22.89 memory used=984.6MB, alloc=468.3MB, time=26.02 memory used=1112.0MB, alloc=492.3MB, time=29.61 memory used=1219.5MB, alloc=492.3MB, time=32.48 memory used=1333.0MB, alloc=492.3MB, time=35.94 memory used=1430.0MB, alloc=492.3MB, time=38.67 memory used=1533.8MB, alloc=492.3MB, time=41.81 memory used=1621.9MB, alloc=492.3MB, time=44.50 memory used=1722.2MB, alloc=516.3MB, time=47.88 memory used=1794.7MB, alloc=516.3MB, time=50.19 memory used=1865.0MB, alloc=516.3MB, time=52.71 memory used=1934.8MB, alloc=516.3MB, time=54.91 memory used=1993.5MB, alloc=516.3MB, time=56.86 memory used=2064.2MB, alloc=516.3MB, time=59.50 memory used=2123.1MB, alloc=516.3MB, time=61.80 memory used=2189.7MB, alloc=516.3MB, time=64.40 memory used=2393.4MB, alloc=540.3MB, time=70.94 memory used=2609.4MB, alloc=564.3MB, time=77.90 memory used=2814.6MB, alloc=588.3MB, time=84.36 memory used=3035.7MB, alloc=612.3MB, time=91.88 memory used=3212.2MB, alloc=636.3MB, time=97.28 memory used=3393.5MB, alloc=660.3MB, time=103.65 |\^/| 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(); 1428261575 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [7 x - 9 x y, 3 x y - 12 x z - 5, 14 x + 16 z + 15] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [20 y z + 19 x + 17 z, -10 x + 19 x y, 18 x - 5 y + 12] > Problem := [F,G]; 2 2 Problem := [[7 x - 9 x y, 3 x y - 12 x z - 5, 14 x + 16 z + 15], 2 2 [20 y z + 19 x + 17 z, -10 x + 19 x y, 18 x - 5 y + 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.86 memory used=47.7MB, alloc=32.3MB, time=1.40 memory used=67.5MB, alloc=56.3MB, time=1.94 memory used=108.9MB, alloc=60.3MB, time=3.01 memory used=163.5MB, alloc=92.3MB, time=4.54 memory used=231.8MB, alloc=100.3MB, time=6.61 memory used=293.8MB, alloc=124.3MB, time=8.48 memory used=374.9MB, alloc=148.3MB, time=10.91 memory used=471.5MB, alloc=172.3MB, time=14.72 memory used=574.5MB, alloc=196.3MB, time=20.14 memory used=691.8MB, alloc=220.3MB, time=27.19 memory used=833.2MB, alloc=220.3MB, time=35.59 N1 := 3685 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [126 x + 28 x + 135 x - 60, 9 y - 7 x, 14 x + 16 z + 15] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=982.8MB, alloc=220.3MB, time=41.91 N2 := 605 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [7 x - 9 x y, -12 z x + 3 y x - 5, 14 x + 16 z + 15, 2 2 20 z y + 17 z + 19 x, -10 x + 19 x y, 18 x - 5 y + 12] > J:=[op(GB),op(G)]; 3 2 2 J := [126 x + 28 x + 135 x - 60, 9 y - 7 x, 14 x + 16 z + 15, 2 2 20 z y + 17 z + 19 x, -10 x + 19 x y, 18 x - 5 y + 12] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 12, 2, 2, 1, 1, 1, 5/6, 1/2, 9/16, 5/16, 1/4, 6, 12, 12, 3, 3, 1, 1, 1, 2/3, 1/3, 9/17, 4/17, 3/17, 2, 0, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1002.9MB, alloc=220.3MB, time=42.86 |\^/| 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(); 1428261703 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-16 x y + 18 z - 10, 15 x y - 4 z + 14 y, 6 x + 17 x y + 16 x z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [x y + y - 5, 16 x + 5 y - 13 z, 17 y z - 11 x - 3 y] > Problem := [F,G]; Problem := [ 2 2 [-16 x y + 18 z - 10, 15 x y - 4 z + 14 y, 6 x + 17 x y + 16 x z], 2 [x y + y - 5, 16 x + 5 y - 13 z, 17 y z - 11 x - 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=46.3MB, alloc=56.3MB, time=1.39 memory used=87.4MB, alloc=60.3MB, time=2.49 memory used=127.1MB, alloc=60.3MB, time=3.54 memory used=166.1MB, alloc=84.3MB, time=4.57 memory used=227.0MB, alloc=92.3MB, time=6.27 memory used=285.6MB, alloc=116.3MB, time=7.88 memory used=365.3MB, alloc=140.3MB, time=10.06 memory used=449.1MB, alloc=396.3MB, time=12.43 memory used=551.2MB, alloc=420.3MB, time=15.35 memory used=679.5MB, alloc=444.3MB, time=18.94 memory used=827.2MB, alloc=468.3MB, time=23.32 memory used=982.9MB, alloc=492.3MB, time=28.05 memory used=1118.9MB, alloc=492.3MB, time=32.24 memory used=1268.5MB, alloc=516.3MB, time=37.05 memory used=1403.8MB, alloc=516.3MB, time=41.50 memory used=1523.4MB, alloc=516.3MB, time=45.55 memory used=1629.4MB, alloc=540.3MB, time=49.12 memory used=1744.3MB, alloc=540.3MB, time=53.10 memory used=1835.4MB, alloc=540.3MB, time=56.27 memory used=1938.8MB, alloc=540.3MB, time=59.85 memory used=2027.5MB, alloc=540.3MB, time=63.04 memory used=2107.1MB, alloc=540.3MB, time=65.86 memory used=2188.5MB, alloc=564.3MB, time=68.85 memory used=2260.7MB, alloc=564.3MB, time=71.75 memory used=2330.2MB, alloc=564.3MB, time=74.50 memory used=2411.0MB, alloc=588.3MB, time=77.66 memory used=2471.7MB, alloc=588.3MB, time=80.19 memory used=2530.5MB, alloc=588.3MB, time=82.65 memory used=2593.6MB, alloc=588.3MB, time=85.34 memory used=2827.8MB, alloc=612.3MB, time=93.29 memory used=3058.2MB, alloc=636.3MB, time=101.29 memory used=3293.0MB, alloc=660.3MB, time=109.58 |\^/| 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(); 1428262003 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [18 x - 10 x + 16, -7 x y + 6 y - 15 x, 9 y + 4 y z - 3 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-8 x - 14 x z + 13 x, -6 x - z - 5 y, 6 x z - 15 z + 16 x] > Problem := [F,G]; 2 2 2 Problem := [[18 x - 10 x + 16, -7 x y + 6 y - 15 x, 9 y + 4 y z - 3 x], 2 2 2 2 [-8 x - 14 x z + 13 x, -6 x - z - 5 y, 6 x z - 15 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=26.7MB, alloc=32.3MB, time=0.89 memory used=47.6MB, alloc=32.3MB, time=1.44 memory used=66.8MB, alloc=56.3MB, time=1.98 memory used=106.7MB, alloc=60.3MB, time=3.02 memory used=143.6MB, alloc=84.3MB, time=4.01 memory used=203.6MB, alloc=92.3MB, time=5.59 memory used=262.3MB, alloc=92.3MB, time=7.13 memory used=322.7MB, alloc=116.3MB, time=8.70 memory used=404.0MB, alloc=116.3MB, time=10.88 memory used=483.2MB, alloc=140.3MB, time=13.05 memory used=551.8MB, alloc=396.3MB, time=14.80 memory used=659.0MB, alloc=420.3MB, time=17.97 memory used=778.1MB, alloc=444.3MB, time=21.71 memory used=916.6MB, alloc=468.3MB, time=25.84 memory used=1070.7MB, alloc=492.3MB, time=30.41 memory used=1232.4MB, alloc=516.3MB, time=35.49 memory used=1404.8MB, alloc=540.3MB, time=40.98 memory used=1593.4MB, alloc=564.3MB, time=46.95 memory used=1787.8MB, alloc=588.3MB, time=53.31 memory used=1986.5MB, alloc=612.3MB, time=60.19 memory used=2168.2MB, alloc=636.3MB, time=69.48 memory used=2356.5MB, alloc=660.3MB, time=79.75 memory used=2555.6MB, alloc=684.3MB, time=91.08 memory used=2768.5MB, alloc=708.3MB, time=103.52 |\^/| 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(); 1428262303 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [2 y + 14 y z + 9 z , y - 16 z, 9 x + 6 x z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-2 y z + 4 z - 1, 13 y - 10 y z + 2 x, -2 x + 5 y + 2 z ] > Problem := [F,G]; 2 2 2 Problem := [[2 y + 14 y z + 9 z , y - 16 z, 9 x + 6 x z], 2 2 2 2 2 [-2 y z + 4 z - 1, 13 y - 10 y z + 2 x, -2 x + 5 y + 2 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=27.0MB, alloc=32.3MB, time=0.89 memory used=47.9MB, alloc=56.3MB, time=1.45 memory used=89.2MB, alloc=60.3MB, time=2.53 memory used=127.8MB, alloc=84.3MB, time=3.56 memory used=179.2MB, alloc=84.3MB, time=4.93 memory used=240.6MB, alloc=116.3MB, time=6.56 memory used=324.3MB, alloc=140.3MB, time=8.79 memory used=419.4MB, alloc=140.3MB, time=11.44 memory used=496.4MB, alloc=420.3MB, time=13.59 memory used=623.4MB, alloc=444.3MB, time=17.09 memory used=774.1MB, alloc=468.3MB, time=21.22 memory used=923.2MB, alloc=492.3MB, time=25.34 memory used=1100.4MB, alloc=516.3MB, time=30.63 memory used=1238.5MB, alloc=540.3MB, time=35.01 memory used=1365.2MB, alloc=540.3MB, time=39.30 memory used=1481.8MB, alloc=540.3MB, time=43.18 memory used=1591.7MB, alloc=540.3MB, time=46.75 memory used=1702.0MB, alloc=564.3MB, time=50.48 memory used=1806.2MB, alloc=564.3MB, time=54.19 memory used=1891.3MB, alloc=564.3MB, time=57.09 memory used=1980.4MB, alloc=564.3MB, time=60.13 memory used=2060.8MB, alloc=588.3MB, time=63.10 memory used=2133.0MB, alloc=588.3MB, time=65.63 memory used=2195.3MB, alloc=588.3MB, time=68.14 memory used=2251.2MB, alloc=588.3MB, time=70.48 memory used=2326.8MB, alloc=588.3MB, time=73.67 memory used=2393.3MB, alloc=588.3MB, time=76.64 memory used=2636.1MB, alloc=612.3MB, time=84.47 memory used=2903.4MB, alloc=636.3MB, time=93.78 memory used=3122.2MB, alloc=660.3MB, time=100.87 memory used=3320.3MB, alloc=684.3MB, time=107.56 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428262603 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [12 x y + 14 y - 9 y z, -16 x + 20 x z + 4 y , -8 y - 12 z - 20] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-15 x y - 3 x z - 16 x, 10 x + 4 x + 18 z, -12 x y + 5 z - 4] > Problem := [F,G]; Problem := [ 2 2 2 2 [12 x y + 14 y - 9 y z, -16 x + 20 x z + 4 y , -8 y - 12 z - 20], 2 2 [-15 x y - 3 x z - 16 x, 10 x + 4 x + 18 z, -12 x y + 5 z - 4]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.84 memory used=46.7MB, alloc=32.3MB, time=1.36 memory used=65.8MB, alloc=56.3MB, time=1.87 memory used=105.0MB, alloc=60.3MB, time=2.86 memory used=140.6MB, alloc=84.3MB, time=3.81 memory used=198.6MB, alloc=92.3MB, time=5.38 memory used=257.9MB, alloc=116.3MB, time=6.90 memory used=340.7MB, alloc=116.3MB, time=9.05 memory used=418.0MB, alloc=140.3MB, time=11.19 memory used=500.3MB, alloc=140.3MB, time=13.48 memory used=578.0MB, alloc=420.3MB, time=15.70 memory used=700.2MB, alloc=444.3MB, time=19.21 memory used=842.0MB, alloc=468.3MB, time=23.24 memory used=999.1MB, alloc=492.3MB, time=27.93 memory used=1147.8MB, alloc=516.3MB, time=32.49 memory used=1274.7MB, alloc=516.3MB, time=36.22 memory used=1388.2MB, alloc=540.3MB, time=39.45 memory used=1490.7MB, alloc=540.3MB, time=42.54 memory used=1582.9MB, alloc=540.3MB, time=45.16 memory used=1675.9MB, alloc=540.3MB, time=48.32 memory used=1748.5MB, alloc=540.3MB, time=50.66 memory used=1820.6MB, alloc=564.3MB, time=53.36 memory used=1895.2MB, alloc=564.3MB, time=56.41 memory used=1956.3MB, alloc=564.3MB, time=58.62 memory used=2026.8MB, alloc=564.3MB, time=61.26 memory used=2103.3MB, alloc=564.3MB, time=64.50 memory used=2155.4MB, alloc=564.3MB, time=66.53 memory used=2403.6MB, alloc=588.3MB, time=74.40 memory used=2617.7MB, alloc=612.3MB, time=81.96 memory used=2823.9MB, alloc=636.3MB, time=88.88 memory used=3022.8MB, alloc=660.3MB, time=96.61 memory used=3201.7MB, alloc=684.3MB, time=103.69 |\^/| 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(); 1428262903 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [15 x + 16 y + 9 y z, 18 y z + 12 y, 7 x - 2 z - 3 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-5 z + 11 z, 9 x - z + 16 z, 4 x - 2 z + 20] > Problem := [F,G]; 2 2 2 2 Problem := [[15 x + 16 y + 9 y z, 18 y z + 12 y, 7 x - 2 z - 3 x], 2 2 2 2 2 [-5 z + 11 z, 9 x - z + 16 z, 4 x - 2 z + 20]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.87 memory used=48.1MB, alloc=32.3MB, time=1.42 memory used=68.3MB, alloc=32.3MB, time=1.93 memory used=87.4MB, alloc=56.3MB, time=2.45 memory used=126.3MB, alloc=60.3MB, time=3.44 memory used=164.4MB, alloc=60.3MB, time=4.41 memory used=201.4MB, alloc=84.3MB, time=5.41 memory used=260.1MB, alloc=92.3MB, time=6.97 memory used=316.1MB, alloc=92.3MB, time=8.45 memory used=373.8MB, alloc=116.3MB, time=10.13 memory used=453.8MB, alloc=140.3MB, time=12.57 memory used=553.2MB, alloc=164.3MB, time=15.54 memory used=668.8MB, alloc=188.3MB, time=18.99 memory used=795.7MB, alloc=212.3MB, time=22.84 memory used=929.7MB, alloc=236.3MB, time=27.12 memory used=1059.5MB, alloc=260.3MB, time=32.52 memory used=1191.3MB, alloc=284.3MB, time=38.86 memory used=1333.1MB, alloc=308.3MB, time=46.39 memory used=1483.4MB, alloc=332.3MB, time=55.68 memory used=1657.7MB, alloc=356.3MB, time=66.46 memory used=1856.0MB, alloc=380.3MB, time=78.61 memory used=2078.2MB, alloc=404.3MB, time=92.13 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428263203 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [10 x y + 14 y + 8 z, 17 - x + 7 z, 9 y - 17 y z + 6 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-15 x - 20 x y + 4 x, -15 x y + 5 z, 3 y z + 10 x - 20 z] > Problem := [F,G]; 2 2 Problem := [[10 x y + 14 y + 8 z, 17 - x + 7 z, 9 y - 17 y z + 6 z], 2 [-15 x - 20 x y + 4 x, -15 x y + 5 z, 3 y z + 10 x - 20 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.86 memory used=47.0MB, alloc=32.3MB, time=1.39 memory used=65.2MB, alloc=56.3MB, time=1.89 memory used=104.7MB, alloc=60.3MB, time=2.95 memory used=142.9MB, alloc=60.3MB, time=3.96 memory used=180.1MB, alloc=84.3MB, time=4.96 memory used=235.7MB, alloc=84.3MB, time=6.45 memory used=290.9MB, alloc=116.3MB, time=8.02 memory used=367.5MB, alloc=116.3MB, time=10.11 memory used=444.8MB, alloc=140.3MB, time=12.39 memory used=542.3MB, alloc=396.3MB, time=15.30 memory used=642.6MB, alloc=420.3MB, time=18.35 memory used=766.0MB, alloc=444.3MB, time=22.09 memory used=913.9MB, alloc=468.3MB, time=26.76 memory used=1079.0MB, alloc=492.3MB, time=32.44 memory used=1264.1MB, alloc=516.3MB, time=38.91 memory used=1464.0MB, alloc=540.3MB, time=45.87 memory used=1656.9MB, alloc=564.3MB, time=52.83 memory used=1809.5MB, alloc=588.3MB, time=57.82 memory used=1928.2MB, alloc=588.3MB, time=61.78 memory used=2061.3MB, alloc=612.3MB, time=66.27 memory used=2170.3MB, alloc=636.3MB, time=70.14 memory used=2312.0MB, alloc=660.3MB, time=75.01 memory used=2452.1MB, alloc=684.3MB, time=80.02 memory used=2582.3MB, alloc=708.3MB, time=84.74 memory used=2711.7MB, alloc=732.3MB, time=89.44 memory used=2835.2MB, alloc=756.3MB, time=94.08 memory used=2945.7MB, alloc=780.3MB, time=98.37 memory used=3039.2MB, alloc=780.3MB, time=102.06 memory used=3143.7MB, alloc=804.3MB, time=106.21 |\^/| 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(); 1428263504 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-15 x - 11 y + 19 x, -3 y z - 3 x + 3 z, -7 x z + 7 z + 12 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [4 x z - 2 y - z, 19 x - 16 y - 6 z, -18 x z - 7 y - 4] > Problem := [F,G]; 2 2 2 Problem := [[-15 x - 11 y + 19 x, -3 y z - 3 x + 3 z, -7 x z + 7 z + 12 y], 2 [4 x z - 2 y - z, 19 x - 16 y - 6 z, -18 x z - 7 y - 4]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.32 memory used=26.7MB, alloc=32.3MB, time=0.91 memory used=47.3MB, alloc=32.3MB, time=1.44 memory used=65.3MB, alloc=56.3MB, time=1.95 memory used=104.6MB, alloc=60.3MB, time=3.01 memory used=143.8MB, alloc=84.3MB, time=4.05 memory used=206.7MB, alloc=92.3MB, time=5.77 memory used=266.7MB, alloc=116.3MB, time=7.45 memory used=350.1MB, alloc=116.3MB, time=9.77 memory used=431.6MB, alloc=140.3MB, time=12.12 memory used=509.4MB, alloc=140.3MB, time=14.38 memory used=572.9MB, alloc=420.3MB, time=16.24 memory used=701.6MB, alloc=444.3MB, time=20.00 memory used=830.4MB, alloc=468.3MB, time=23.49 memory used=986.5MB, alloc=492.3MB, time=28.38 memory used=1109.7MB, alloc=492.3MB, time=32.24 memory used=1220.0MB, alloc=492.3MB, time=35.60 memory used=1344.2MB, alloc=516.3MB, time=40.05 memory used=1431.9MB, alloc=516.3MB, time=43.07 memory used=1540.8MB, alloc=516.3MB, time=47.01 memory used=1636.7MB, alloc=516.3MB, time=50.45 memory used=1725.7MB, alloc=516.3MB, time=53.86 memory used=1810.7MB, alloc=516.3MB, time=57.34 memory used=1871.3MB, alloc=516.3MB, time=59.65 memory used=1937.3MB, alloc=516.3MB, time=62.53 memory used=1985.3MB, alloc=516.3MB, time=64.58 memory used=2182.8MB, alloc=540.3MB, time=71.84 memory used=2409.0MB, alloc=564.3MB, time=80.61 memory used=2656.5MB, alloc=588.3MB, time=90.29 memory used=2902.0MB, alloc=612.3MB, time=100.15 memory used=3092.8MB, alloc=636.3MB, time=107.77 memory used=3335.1MB, alloc=660.3MB, time=118.38 |\^/| 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(); 1428263803 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [-15 x + 9 y + y, -3 y + z, -19 x + 9 y - 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [16 x + 19 x z + 10 z, -5 x z - 2 y - 14 y z, -5 y + 20 z] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[-15 x + 9 y + y, -3 y + z, -19 x + 9 y - 6 z ], 2 2 [16 x + 19 x z + 10 z, -5 x z - 2 y - 14 y z, -5 y + 20 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.85 memory used=47.2MB, alloc=32.3MB, time=1.37 memory used=65.9MB, alloc=56.3MB, time=1.88 memory used=104.9MB, alloc=60.3MB, time=2.92 memory used=142.1MB, alloc=84.3MB, time=3.94 memory used=201.3MB, alloc=92.3MB, time=5.55 memory used=259.2MB, alloc=116.3MB, time=7.13 memory used=339.1MB, alloc=116.3MB, time=9.37 memory used=417.7MB, alloc=396.3MB, time=11.55 memory used=521.7MB, alloc=420.3MB, time=14.41 memory used=652.1MB, alloc=444.3MB, time=17.93 memory used=800.8MB, alloc=468.3MB, time=22.23 memory used=960.3MB, alloc=492.3MB, time=26.81 memory used=1098.9MB, alloc=516.3MB, time=30.83 memory used=1230.2MB, alloc=516.3MB, time=34.71 memory used=1375.9MB, alloc=540.3MB, time=39.45 memory used=1499.1MB, alloc=540.3MB, time=43.56 memory used=1629.3MB, alloc=540.3MB, time=47.93 memory used=1714.3MB, alloc=540.3MB, time=50.81 memory used=1806.8MB, alloc=564.3MB, time=54.00 memory used=1897.0MB, alloc=564.3MB, time=57.42 memory used=1984.7MB, alloc=564.3MB, time=60.42 memory used=2069.2MB, alloc=564.3MB, time=63.60 memory used=2160.1MB, alloc=564.3MB, time=67.23 memory used=2224.9MB, alloc=564.3MB, time=69.81 memory used=2293.6MB, alloc=564.3MB, time=72.62 memory used=2357.3MB, alloc=564.3MB, time=75.25 memory used=2417.6MB, alloc=564.3MB, time=77.72 memory used=2640.7MB, alloc=588.3MB, time=85.07 memory used=2865.8MB, alloc=612.3MB, time=93.00 memory used=3079.5MB, alloc=636.3MB, time=99.76 memory used=3332.0MB, alloc=660.3MB, time=107.79 memory used=3580.7MB, alloc=684.3MB, time=116.74 |\^/| 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(); 1428264104 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-12 x y - 6 x z - 4 z , -19 x y - 13 x z - 10 x, 8 x z - 17 y z + 20] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [x z - 12 z - 9 y, -6 x y + 9 y - 3 y z, 17 y z + 15 z - 17 z] > Problem := [F,G]; Problem := [ 2 [-12 x y - 6 x z - 4 z , -19 x y - 13 x z - 10 x, 8 x z - 17 y z + 20], 2 2 2 [x z - 12 z - 9 y, -6 x y + 9 y - 3 y z, 17 y z + 15 z - 17 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=25.8MB, alloc=32.3MB, time=0.83 memory used=45.9MB, alloc=32.3MB, time=1.32 memory used=63.5MB, alloc=56.3MB, time=1.78 memory used=101.8MB, alloc=60.3MB, time=2.74 memory used=136.0MB, alloc=84.3MB, time=3.66 memory used=190.6MB, alloc=116.3MB, time=5.16 memory used=266.2MB, alloc=116.3MB, time=7.21 memory used=339.2MB, alloc=140.3MB, time=9.26 memory used=425.8MB, alloc=164.3MB, time=11.54 memory used=520.3MB, alloc=164.3MB, time=14.17 memory used=610.8MB, alloc=444.3MB, time=16.77 memory used=743.0MB, alloc=468.3MB, time=20.64 memory used=901.6MB, alloc=492.3MB, time=25.35 memory used=1083.6MB, alloc=516.3MB, time=31.06 memory used=1284.0MB, alloc=540.3MB, time=37.63 memory used=1505.9MB, alloc=564.3MB, time=45.32 memory used=1745.6MB, alloc=588.3MB, time=54.45 memory used=2007.1MB, alloc=612.3MB, time=64.79 memory used=2285.7MB, alloc=636.3MB, time=75.71 memory used=2583.4MB, alloc=660.3MB, time=87.91 memory used=2898.8MB, alloc=684.3MB, time=100.41 |\^/| 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(); 1428264404 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [2 y z + 11 y, -6 x + 4 y + 12, -8 x + 4 y - 18 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-9 x - 9 x - 12 y, -4 x y + x z + 9 x, -9 x y - 10 z + x] > Problem := [F,G]; 2 2 2 Problem := [[2 y z + 11 y, -6 x + 4 y + 12, -8 x + 4 y - 18 y], 2 2 [-9 x - 9 x - 12 y, -4 x y + x z + 9 x, -9 x y - 10 z + x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.84 memory used=46.7MB, alloc=32.3MB, time=1.32 memory used=66.7MB, alloc=32.3MB, time=1.85 memory used=85.5MB, alloc=56.3MB, time=2.37 memory used=124.8MB, alloc=60.3MB, time=3.41 memory used=163.1MB, alloc=60.3MB, time=4.40 memory used=199.5MB, alloc=84.3MB, time=5.38 memory used=259.2MB, alloc=116.3MB, time=7.13 memory used=338.0MB, alloc=140.3MB, time=9.58 memory used=431.5MB, alloc=164.3MB, time=12.50 memory used=539.2MB, alloc=188.3MB, time=15.90 memory used=657.5MB, alloc=212.3MB, time=20.18 memory used=775.9MB, alloc=236.3MB, time=26.02 memory used=908.0MB, alloc=260.3MB, time=33.00 memory used=1054.3MB, alloc=284.3MB, time=41.53 memory used=1217.4MB, alloc=308.3MB, time=51.58 memory used=1404.5MB, alloc=308.3MB, time=63.06 memory used=1591.5MB, alloc=332.3MB, time=74.65 memory used=1802.5MB, alloc=332.3MB, time=87.56 memory used=2013.5MB, alloc=356.3MB, time=100.47 |\^/| 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(); 1428264704 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-8 x y - 10 x - 7 y, 10 y + 18 z - 17 y, -18 z - 5 x + 13] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-13 z + 8 x - 12 z, -15 y - 3 z + 2 y, -19 x - 8 y z + 13 z] > Problem := [F,G]; 2 2 2 Problem := [[-8 x y - 10 x - 7 y, 10 y + 18 z - 17 y, -18 z - 5 x + 13], 2 2 2 2 [-13 z + 8 x - 12 z, -15 y - 3 z + 2 y, -19 x - 8 y z + 13 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.88 memory used=48.1MB, alloc=32.3MB, time=1.42 memory used=68.6MB, alloc=56.3MB, time=1.96 memory used=109.5MB, alloc=60.3MB, time=2.99 memory used=149.6MB, alloc=84.3MB, time=4.00 memory used=209.7MB, alloc=92.3MB, time=5.55 memory used=270.4MB, alloc=116.3MB, time=7.11 memory used=354.7MB, alloc=116.3MB, time=9.25 memory used=433.9MB, alloc=372.3MB, time=11.37 memory used=513.0MB, alloc=396.3MB, time=13.47 memory used=615.7MB, alloc=420.3MB, time=16.12 memory used=737.9MB, alloc=444.3MB, time=19.38 memory used=879.6MB, alloc=444.3MB, time=23.16 memory used=1020.4MB, alloc=468.3MB, time=27.04 memory used=1165.9MB, alloc=492.3MB, time=31.15 memory used=1307.2MB, alloc=492.3MB, time=35.21 memory used=1438.1MB, alloc=516.3MB, time=39.04 memory used=1562.4MB, alloc=516.3MB, time=42.59 memory used=1702.7MB, alloc=516.3MB, time=47.01 memory used=1833.1MB, alloc=516.3MB, time=51.21 memory used=1945.0MB, alloc=540.3MB, time=54.83 memory used=2035.9MB, alloc=540.3MB, time=57.77 memory used=2135.5MB, alloc=540.3MB, time=60.90 memory used=2247.1MB, alloc=540.3MB, time=64.45 memory used=2342.5MB, alloc=540.3MB, time=67.44 memory used=2453.5MB, alloc=540.3MB, time=71.26 memory used=2541.6MB, alloc=564.3MB, time=74.35 memory used=2617.2MB, alloc=564.3MB, time=76.93 memory used=2687.7MB, alloc=564.3MB, time=79.33 memory used=2761.6MB, alloc=564.3MB, time=81.82 memory used=2826.7MB, alloc=564.3MB, time=83.98 memory used=2891.3MB, alloc=564.3MB, time=86.25 memory used=2943.8MB, alloc=564.3MB, time=88.31 memory used=3009.2MB, alloc=564.3MB, time=90.88 memory used=3241.2MB, alloc=588.3MB, time=98.55 memory used=3491.4MB, alloc=612.3MB, time=106.09 |\^/| 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(); 1428265004 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-14 x + 7 y - 18, -10 z - 10 z + 15, x - 17 y z - 16 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [11 x z + z - z, -4 x - 11 y z + 19, 16 x y - 17 y + 14 y z] > Problem := [F,G]; 2 2 2 2 Problem := [[-14 x + 7 y - 18, -10 z - 10 z + 15, x - 17 y z - 16 z ], 2 2 2 [11 x z + z - z, -4 x - 11 y z + 19, 16 x y - 17 y + 14 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=47.3MB, alloc=32.3MB, time=1.39 memory used=66.6MB, alloc=56.3MB, time=1.92 memory used=105.5MB, alloc=60.3MB, time=2.95 memory used=143.3MB, alloc=84.3MB, time=3.98 memory used=202.2MB, alloc=92.3MB, time=5.63 memory used=258.6MB, alloc=116.3MB, time=7.21 memory used=336.9MB, alloc=140.3MB, time=9.29 memory used=421.7MB, alloc=396.3MB, time=11.70 memory used=525.9MB, alloc=420.3MB, time=14.54 memory used=652.3MB, alloc=444.3MB, time=18.17 memory used=802.0MB, alloc=468.3MB, time=22.54 memory used=947.7MB, alloc=492.3MB, time=26.70 memory used=1078.6MB, alloc=492.3MB, time=30.81 memory used=1222.8MB, alloc=516.3MB, time=35.52 memory used=1352.2MB, alloc=540.3MB, time=39.91 memory used=1469.1MB, alloc=540.3MB, time=43.97 memory used=1587.3MB, alloc=540.3MB, time=48.11 memory used=1694.7MB, alloc=540.3MB, time=52.14 memory used=1795.5MB, alloc=540.3MB, time=56.07 memory used=1889.7MB, alloc=540.3MB, time=59.82 memory used=1969.7MB, alloc=564.3MB, time=63.15 memory used=2042.9MB, alloc=564.3MB, time=66.13 memory used=2126.6MB, alloc=564.3MB, time=69.70 memory used=2198.1MB, alloc=564.3MB, time=72.81 memory used=2262.1MB, alloc=564.3MB, time=75.53 memory used=2320.9MB, alloc=564.3MB, time=78.34 memory used=2558.4MB, alloc=588.3MB, time=87.28 memory used=2799.3MB, alloc=612.3MB, time=96.12 memory used=3021.2MB, alloc=636.3MB, time=104.50 memory used=3245.4MB, alloc=660.3MB, time=113.45 |\^/| 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(); 1428265304 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-2 x - 12 y - 3, 5 x - 11 x z - 14 z, -9 x y - 10 z + 19] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [11 + 9 x, 8 x y - 11 z + 17, 10 x + z + 3 y] > Problem := [F,G]; 2 2 2 Problem := [[-2 x - 12 y - 3, 5 x - 11 x z - 14 z, -9 x y - 10 z + 19], 2 2 2 [11 + 9 x, 8 x y - 11 z + 17, 10 x + z + 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.89 memory used=47.9MB, alloc=32.3MB, time=1.44 memory used=67.3MB, alloc=56.3MB, time=1.97 memory used=107.6MB, alloc=60.3MB, time=3.02 memory used=147.8MB, alloc=84.3MB, time=4.06 memory used=210.0MB, alloc=92.3MB, time=5.68 memory used=270.7MB, alloc=116.3MB, time=7.30 memory used=353.1MB, alloc=116.3MB, time=9.49 memory used=434.4MB, alloc=140.3MB, time=11.72 memory used=522.1MB, alloc=140.3MB, time=14.09 memory used=605.9MB, alloc=420.3MB, time=16.46 memory used=727.6MB, alloc=444.3MB, time=20.28 memory used=864.6MB, alloc=468.3MB, time=24.62 memory used=1018.1MB, alloc=492.3MB, time=29.50 memory used=1186.3MB, alloc=516.3MB, time=34.75 memory used=1369.9MB, alloc=540.3MB, time=40.54 memory used=1565.3MB, alloc=564.3MB, time=46.75 memory used=1765.1MB, alloc=588.3MB, time=53.36 memory used=1960.2MB, alloc=612.3MB, time=61.84 memory used=2143.8MB, alloc=636.3MB, time=71.69 memory used=2338.3MB, alloc=660.3MB, time=82.39 memory used=2543.7MB, alloc=684.3MB, time=94.24 memory used=2761.1MB, alloc=708.3MB, time=107.29 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428265604 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [11 x y + 10 y + 4, 3 x + 14 y z - 5 x, 10 x - 17 y z - 11 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-11 y + z - 19 y, -11 x y + 4 y z - 13 z , -17 x y + z - 13 x] > Problem := [F,G]; 2 2 2 Problem := [[11 x y + 10 y + 4, 3 x + 14 y z - 5 x, 10 x - 17 y z - 11 y], 2 2 2 2 [-11 y + z - 19 y, -11 x y + 4 y z - 13 z , -17 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=48.3MB, alloc=32.3MB, time=1.44 memory used=68.4MB, alloc=56.3MB, time=1.98 memory used=110.0MB, alloc=60.3MB, time=3.06 memory used=148.2MB, alloc=84.3MB, time=4.04 memory used=210.3MB, alloc=92.3MB, time=5.63 memory used=274.8MB, alloc=116.3MB, time=7.23 memory used=343.9MB, alloc=116.3MB, time=8.90 memory used=418.5MB, alloc=372.3MB, time=10.84 memory used=506.9MB, alloc=396.3MB, time=12.92 memory used=617.7MB, alloc=420.3MB, time=15.65 memory used=748.5MB, alloc=444.3MB, time=18.99 memory used=878.0MB, alloc=444.3MB, time=22.26 memory used=1013.3MB, alloc=468.3MB, time=25.45 memory used=1109.1MB, alloc=468.3MB, time=26.70 memory used=1214.9MB, alloc=468.3MB, time=29.29 memory used=1332.5MB, alloc=492.3MB, time=32.65 memory used=1424.5MB, alloc=492.3MB, time=35.05 memory used=1547.5MB, alloc=492.3MB, time=39.01 memory used=1642.2MB, alloc=492.3MB, time=41.74 memory used=1728.8MB, alloc=516.3MB, time=44.75 memory used=1797.5MB, alloc=516.3MB, time=46.71 memory used=1888.7MB, alloc=516.3MB, time=49.64 memory used=1952.9MB, alloc=516.3MB, time=51.55 memory used=2018.3MB, alloc=516.3MB, time=53.46 memory used=2089.2MB, alloc=516.3MB, time=56.04 memory used=2131.1MB, alloc=516.3MB, time=57.46 memory used=2192.9MB, alloc=516.3MB, time=59.19 memory used=2262.8MB, alloc=516.3MB, time=61.89 memory used=2338.2MB, alloc=516.3MB, time=64.73 memory used=2377.6MB, alloc=516.3MB, time=66.31 memory used=2585.3MB, alloc=540.3MB, time=71.91 memory used=2817.8MB, alloc=596.3MB, time=78.67 memory used=3013.0MB, alloc=620.3MB, time=84.52 memory used=3188.4MB, alloc=644.3MB, time=89.92 memory used=3345.1MB, alloc=644.3MB, time=95.05 memory used=3484.5MB, alloc=644.3MB, time=99.91 memory used=3629.3MB, alloc=668.3MB, time=104.93 |\^/| 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(); 1428265904 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-6 x y - 7 x z + 6 y , 18 x y - 7 y z - 19 z , -2 x z + 6 y z + 8 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-9 x y + 5 y + 8 z, -14 y + 5 z - 7 x, -11 x z + 18 y - 14 z ] > Problem := [F,G]; Problem := [ 2 2 [-6 x y - 7 x z + 6 y , 18 x y - 7 y z - 19 z , -2 x z + 6 y z + 8 z], 2 2 2 2 2 [-9 x y + 5 y + 8 z, -14 y + 5 z - 7 x, -11 x z + 18 y - 14 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.85 memory used=48.0MB, alloc=32.3MB, time=1.40 memory used=68.0MB, alloc=56.3MB, time=1.94 memory used=108.4MB, alloc=60.3MB, time=2.99 memory used=146.6MB, alloc=84.3MB, time=3.99 memory used=207.3MB, alloc=92.3MB, time=5.54 memory used=263.3MB, alloc=116.3MB, time=7.03 memory used=343.8MB, alloc=116.3MB, time=9.21 memory used=425.3MB, alloc=140.3MB, time=11.39 memory used=492.3MB, alloc=140.3MB, time=13.19 memory used=562.7MB, alloc=396.3MB, time=15.15 memory used=667.8MB, alloc=420.3MB, time=17.88 memory used=795.5MB, alloc=444.3MB, time=20.88 memory used=936.1MB, alloc=468.3MB, time=24.56 memory used=1078.0MB, alloc=492.3MB, time=28.71 memory used=1201.8MB, alloc=492.3MB, time=32.39 memory used=1328.2MB, alloc=516.3MB, time=36.37 memory used=1437.3MB, alloc=516.3MB, time=39.78 memory used=1539.0MB, alloc=516.3MB, time=43.01 memory used=1630.3MB, alloc=516.3MB, time=45.59 memory used=1709.2MB, alloc=516.3MB, time=48.22 memory used=1771.9MB, alloc=540.3MB, time=50.14 memory used=1842.2MB, alloc=540.3MB, time=52.33 memory used=1916.5MB, alloc=540.3MB, time=54.75 memory used=1985.2MB, alloc=540.3MB, time=56.74 memory used=2054.9MB, alloc=540.3MB, time=59.09 memory used=2117.9MB, alloc=540.3MB, time=61.52 memory used=2165.1MB, alloc=540.3MB, time=63.39 memory used=2215.6MB, alloc=564.3MB, time=65.48 memory used=2419.5MB, alloc=588.3MB, time=71.38 memory used=2664.9MB, alloc=612.3MB, time=79.48 memory used=2899.8MB, alloc=636.3MB, time=87.89 memory used=3076.9MB, alloc=660.3MB, time=93.60 memory used=3240.6MB, alloc=684.3MB, time=98.81 memory used=3405.3MB, alloc=684.3MB, time=105.05 |\^/| 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(); 1428266204 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [15 x z + y, -13 x - 2 y z - 19 y, 7 x y + 5 x z - 17 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-7 x - 11 x y + 5 x, 10 y z + 17 x + 4 y, 10 x - 12 y + 6 x] > Problem := [F,G]; 2 2 Problem := [[15 x z + y, -13 x - 2 y z - 19 y, 7 x y + 5 x z - 17 z ], 2 2 2 [-7 x - 11 x y + 5 x, 10 y z + 17 x + 4 y, 10 x - 12 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=0.32 memory used=26.5MB, alloc=32.3MB, time=0.90 memory used=46.9MB, alloc=32.3MB, time=1.43 memory used=66.3MB, alloc=56.3MB, time=1.96 memory used=106.0MB, alloc=60.3MB, time=3.02 memory used=144.1MB, alloc=84.3MB, time=4.05 memory used=206.0MB, alloc=92.3MB, time=5.75 memory used=267.4MB, alloc=116.3MB, time=7.42 memory used=351.2MB, alloc=140.3MB, time=9.74 memory used=437.6MB, alloc=396.3MB, time=12.16 memory used=542.8MB, alloc=420.3MB, time=15.06 memory used=671.9MB, alloc=420.3MB, time=18.64 memory used=796.8MB, alloc=444.3MB, time=22.26 memory used=926.1MB, alloc=468.3MB, time=25.88 memory used=1109.9MB, alloc=492.3MB, time=31.05 memory used=1261.0MB, alloc=516.3MB, time=35.91 memory used=1422.6MB, alloc=540.3MB, time=41.08 memory used=1579.7MB, alloc=564.3MB, time=45.76 memory used=1749.4MB, alloc=588.3MB, time=50.79 memory used=1944.6MB, alloc=612.3MB, time=55.77 memory used=2141.7MB, alloc=612.3MB, time=60.44 memory used=2315.6MB, alloc=636.3MB, time=65.19 memory used=2478.2MB, alloc=660.3MB, time=70.01 memory used=2632.5MB, alloc=660.3MB, time=74.39 memory used=2794.9MB, alloc=684.3MB, time=79.31 memory used=2954.0MB, alloc=708.3MB, time=84.31 memory used=3077.6MB, alloc=708.3MB, time=88.52 memory used=3203.8MB, alloc=732.3MB, time=92.81 memory used=3327.0MB, alloc=756.3MB, time=97.31 memory used=3445.3MB, alloc=756.3MB, time=101.50 memory used=3622.6MB, alloc=780.3MB, time=110.23 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428266504 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [12 z + x + 5, 3 x z - 14 y - 16 x, -15 x y + 11 y - 9 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [5 x + 12 y z + 17 x, 13 x - 15 y z + 3, 12 y - 12 z + 6 z] > Problem := [F,G]; 2 2 2 Problem := [[12 z + x + 5, 3 x z - 14 y - 16 x, -15 x y + 11 y - 9 x], 2 2 2 2 [5 x + 12 y z + 17 x, 13 x - 15 y z + 3, 12 y - 12 z + 6 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.88 memory used=46.8MB, alloc=32.3MB, time=1.39 memory used=66.2MB, alloc=56.3MB, time=1.92 memory used=106.9MB, alloc=60.3MB, time=2.96 memory used=146.6MB, alloc=84.3MB, time=4.01 memory used=211.5MB, alloc=92.3MB, time=5.62 memory used=271.2MB, alloc=92.3MB, time=7.18 memory used=330.5MB, alloc=116.3MB, time=8.73 memory used=413.3MB, alloc=116.3MB, time=10.96 memory used=472.9MB, alloc=140.3MB, time=12.31 memory used=534.5MB, alloc=396.3MB, time=13.92 memory used=643.2MB, alloc=420.3MB, time=16.77 memory used=774.2MB, alloc=444.3MB, time=20.30 memory used=907.9MB, alloc=468.3MB, time=23.45 memory used=1038.2MB, alloc=468.3MB, time=26.15 memory used=1146.7MB, alloc=492.3MB, time=28.64 memory used=1254.2MB, alloc=492.3MB, time=31.48 memory used=1355.3MB, alloc=492.3MB, time=34.28 memory used=1454.3MB, alloc=516.3MB, time=36.66 memory used=1537.7MB, alloc=516.3MB, time=39.03 memory used=1621.4MB, alloc=516.3MB, time=41.73 memory used=1689.4MB, alloc=516.3MB, time=43.61 memory used=1766.5MB, alloc=516.3MB, time=45.85 memory used=1823.9MB, alloc=516.3MB, time=47.43 memory used=1878.0MB, alloc=516.3MB, time=49.18 memory used=1943.2MB, alloc=516.3MB, time=51.68 memory used=2003.3MB, alloc=516.3MB, time=53.54 memory used=2058.2MB, alloc=516.3MB, time=55.25 memory used=2271.4MB, alloc=540.3MB, time=60.00 memory used=2489.9MB, alloc=564.3MB, time=66.03 memory used=2685.5MB, alloc=588.3MB, time=71.17 memory used=2848.9MB, alloc=612.3MB, time=75.15 memory used=3025.8MB, alloc=636.3MB, time=79.76 memory used=3207.6MB, alloc=660.3MB, time=84.28 memory used=3366.5MB, alloc=684.3MB, time=88.69 memory used=3496.2MB, alloc=684.3MB, time=93.06 memory used=3639.8MB, alloc=684.3MB, time=96.47 memory used=3760.6MB, alloc=684.3MB, time=100.34 memory used=3882.1MB, alloc=684.3MB, time=104.06 memory used=3995.1MB, alloc=708.3MB, time=107.19 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428266804 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-9 x - 2 x z + 10 y z, 19 x y - 3 z + 20 x, -11 y z + 12 x - 11] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [-9 x - 13 x y + 5 z , 10 x + 7 y + 2 z, -12 x + 11 z - 19 y] > Problem := [F,G]; Problem := [ 2 2 [-9 x - 2 x z + 10 y z, 19 x y - 3 z + 20 x, -11 y z + 12 x - 11], 2 2 2 2 2 2 [-9 x - 13 x y + 5 z , 10 x + 7 y + 2 z, -12 x + 11 z - 19 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.5MB, alloc=32.3MB, time=0.32 memory used=26.7MB, alloc=32.3MB, time=0.91 memory used=47.2MB, alloc=32.3MB, time=1.44 memory used=66.8MB, alloc=56.3MB, time=1.98 memory used=109.8MB, alloc=68.3MB, time=3.09 memory used=151.1MB, alloc=92.3MB, time=4.15 memory used=214.9MB, alloc=92.3MB, time=5.81 memory used=281.4MB, alloc=116.3MB, time=7.45 memory used=357.9MB, alloc=116.3MB, time=9.42 memory used=418.5MB, alloc=372.3MB, time=10.97 memory used=505.1MB, alloc=396.3MB, time=13.25 memory used=613.0MB, alloc=420.3MB, time=16.17 memory used=741.6MB, alloc=444.3MB, time=19.44 memory used=862.7MB, alloc=468.3MB, time=22.66 memory used=978.9MB, alloc=468.3MB, time=25.51 memory used=1082.9MB, alloc=468.3MB, time=28.27 memory used=1175.2MB, alloc=492.3MB, time=30.76 memory used=1277.6MB, alloc=492.3MB, time=33.68 memory used=1381.0MB, alloc=492.3MB, time=36.79 memory used=1462.1MB, alloc=492.3MB, time=39.05 memory used=1525.0MB, alloc=492.3MB, time=40.58 memory used=1601.5MB, alloc=492.3MB, time=42.98 memory used=1662.2MB, alloc=516.3MB, time=44.82 memory used=1720.0MB, alloc=516.3MB, time=46.79 memory used=1770.9MB, alloc=516.3MB, time=48.44 memory used=1826.7MB, alloc=516.3MB, time=50.43 memory used=1871.7MB, alloc=516.3MB, time=52.18 memory used=1914.3MB, alloc=516.3MB, time=54.04 memory used=2116.4MB, alloc=540.3MB, time=59.21 memory used=2293.0MB, alloc=564.3MB, time=64.18 memory used=2469.3MB, alloc=588.3MB, time=69.22 memory used=2626.4MB, alloc=612.3MB, time=74.15 memory used=2781.4MB, alloc=612.3MB, time=79.18 memory used=2930.2MB, alloc=636.3MB, time=83.95 memory used=3074.6MB, alloc=636.3MB, time=88.83 memory used=3192.0MB, alloc=636.3MB, time=92.57 memory used=3292.4MB, alloc=636.3MB, time=95.94 memory used=3397.6MB, alloc=636.3MB, time=99.23 memory used=3497.3MB, alloc=636.3MB, time=102.68 memory used=3581.8MB, alloc=636.3MB, time=105.68 memory used=3883.0MB, alloc=660.3MB, time=115.75 |\^/| 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(); 1428267104 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [16 x y - 16 z - 3, -8 y - z + 20, -18 x + y z - 14 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [18 y z - 12 z + 1, -16 x + 6 y z - 8 x, -17 x - 2 y + 11 y z] > Problem := [F,G]; 2 2 2 Problem := [[16 x y - 16 z - 3, -8 y - z + 20, -18 x + y z - 14 x], 2 2 2 2 [18 y z - 12 z + 1, -16 x + 6 y z - 8 x, -17 x - 2 y + 11 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.32 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=47.7MB, alloc=32.3MB, time=1.42 memory used=67.8MB, alloc=32.3MB, time=1.94 memory used=87.1MB, alloc=56.3MB, time=2.47 memory used=128.0MB, alloc=60.3MB, time=3.55 memory used=168.6MB, alloc=92.3MB, time=4.64 memory used=231.3MB, alloc=92.3MB, time=6.21 memory used=295.0MB, alloc=116.3MB, time=7.88 memory used=354.7MB, alloc=372.3MB, time=9.35 memory used=441.1MB, alloc=396.3MB, time=11.64 memory used=554.5MB, alloc=420.3MB, time=14.54 memory used=686.3MB, alloc=444.3MB, time=18.06 memory used=808.0MB, alloc=444.3MB, time=21.16 memory used=917.8MB, alloc=444.3MB, time=23.97 memory used=1038.1MB, alloc=468.3MB, time=27.21 memory used=1132.5MB, alloc=468.3MB, time=29.72 memory used=1233.2MB, alloc=468.3MB, time=32.35 memory used=1324.7MB, alloc=468.3MB, time=35.00 memory used=1408.0MB, alloc=468.3MB, time=37.10 memory used=1484.5MB, alloc=492.3MB, time=39.25 memory used=1560.7MB, alloc=492.3MB, time=41.47 memory used=1643.3MB, alloc=492.3MB, time=44.06 memory used=1719.7MB, alloc=492.3MB, time=46.41 memory used=1786.4MB, alloc=492.3MB, time=48.52 memory used=1855.3MB, alloc=492.3MB, time=50.88 memory used=1914.8MB, alloc=492.3MB, time=52.87 memory used=1975.5MB, alloc=492.3MB, time=54.82 memory used=2032.0MB, alloc=492.3MB, time=56.82 memory used=2088.9MB, alloc=492.3MB, time=58.77 memory used=2145.0MB, alloc=492.3MB, time=60.95 memory used=2325.7MB, alloc=516.3MB, time=65.52 memory used=2509.8MB, alloc=540.3MB, time=70.54 memory used=2688.7MB, alloc=564.3MB, time=75.34 memory used=2874.6MB, alloc=588.3MB, time=81.03 memory used=3038.2MB, alloc=612.3MB, time=85.32 memory used=3208.6MB, alloc=636.3MB, time=91.18 memory used=3358.5MB, alloc=660.3MB, time=96.11 memory used=3469.2MB, alloc=660.3MB, time=99.54 memory used=3589.2MB, alloc=684.3MB, time=102.91 memory used=3705.8MB, alloc=684.3MB, time=107.50 memory used=3796.0MB, alloc=684.3MB, time=110.61 memory used=3885.1MB, alloc=684.3MB, time=114.41 |\^/| 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(); 1428267404 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [7 z - 12 y + z, -18 x y + 9 y z + 8 z, -14 x y + 9 y z - 16 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [10 x y + 6 x + 4, -17 y z - 14 x + 5 y, -4 y z + 4 z - 5] > Problem := [F,G]; 2 Problem := [[7 z - 12 y + z, -18 x y + 9 y z + 8 z, -14 x y + 9 y z - 16 y], 2 [10 x y + 6 x + 4, -17 y z - 14 x + 5 y, -4 y z + 4 z - 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=47.5MB, alloc=32.3MB, time=1.41 memory used=66.7MB, alloc=56.3MB, time=1.93 memory used=104.2MB, alloc=60.3MB, time=2.92 memory used=141.1MB, alloc=84.3MB, time=3.92 memory used=199.5MB, alloc=92.3MB, time=5.53 memory used=257.8MB, alloc=116.3MB, time=7.14 memory used=337.4MB, alloc=116.3MB, time=9.35 memory used=416.7MB, alloc=140.3MB, time=11.60 memory used=508.7MB, alloc=164.3MB, time=14.32 memory used=599.5MB, alloc=420.3MB, time=17.02 memory used=717.7MB, alloc=444.3MB, time=20.67 memory used=858.5MB, alloc=468.3MB, time=24.72 memory used=1021.4MB, alloc=492.3MB, time=29.77 memory used=1211.5MB, alloc=516.3MB, time=35.75 memory used=1422.4MB, alloc=540.3MB, time=42.69 memory used=1689.0MB, alloc=596.3MB, time=51.68 memory used=1978.6MB, alloc=620.3MB, time=62.19 memory used=2284.0MB, alloc=644.3MB, time=72.99 memory used=2615.4MB, alloc=668.3MB, time=85.79 memory used=2934.1MB, alloc=692.3MB, time=98.95 memory used=3213.5MB, alloc=716.3MB, time=110.48 |\^/| 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(); 1428267704 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-2 y + 19 y + 4, 18 x - 10 y - 4 z , 13 x y - 14 y - 19] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-15 z - 11 z - 17, 13 y z - y - 10, 14 x - x y + 8 x z] > Problem := [F,G]; 2 2 2 2 Problem := [[-2 y + 19 y + 4, 18 x - 10 y - 4 z , 13 x y - 14 y - 19], 2 2 [-15 z - 11 z - 17, 13 y z - y - 10, 14 x - x y + 8 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=47.2MB, alloc=32.3MB, time=1.40 memory used=66.2MB, alloc=56.3MB, time=1.92 memory used=107.3MB, alloc=60.3MB, time=3.03 memory used=147.1MB, alloc=84.3MB, time=4.09 memory used=207.1MB, alloc=92.3MB, time=5.72 memory used=266.3MB, alloc=116.3MB, time=7.37 memory used=349.0MB, alloc=116.3MB, time=9.68 memory used=431.2MB, alloc=140.3MB, time=12.04 memory used=508.8MB, alloc=140.3MB, time=14.23 memory used=573.5MB, alloc=396.3MB, time=16.19 memory used=677.1MB, alloc=420.3MB, time=19.23 memory used=802.6MB, alloc=444.3MB, time=22.97 memory used=953.0MB, alloc=468.3MB, time=27.14 memory used=1125.3MB, alloc=492.3MB, time=32.54 memory used=1304.0MB, alloc=516.3MB, time=37.99 memory used=1487.5MB, alloc=540.3MB, time=43.99 memory used=1670.2MB, alloc=564.3MB, time=49.99 memory used=1861.9MB, alloc=588.3MB, time=56.41 memory used=2049.3MB, alloc=612.3MB, time=62.38 memory used=2261.8MB, alloc=636.3MB, time=72.85 memory used=2470.5MB, alloc=660.3MB, time=84.82 memory used=2692.4MB, alloc=684.3MB, time=97.93 memory used=2929.1MB, alloc=708.3MB, time=112.26 |\^/| 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(); 1428268004 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-20 x y + 9 z - 16, 2 y + 20 x, -x + 16 x z - 7 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [10 x z - 2 y + 9 y z, -20 x y - 13 x - 9 y, -11 x z + 11 y z - 19 y] > Problem := [F,G]; 2 2 2 Problem := [[-20 x y + 9 z - 16, 2 y + 20 x, -x + 16 x z - 7 y z], 2 [10 x z - 2 y + 9 y z, -20 x y - 13 x - 9 y, -11 x z + 11 y z - 19 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.88 memory used=47.3MB, alloc=32.3MB, time=1.41 memory used=65.7MB, alloc=56.3MB, time=1.92 memory used=104.9MB, alloc=60.3MB, time=2.96 memory used=143.1MB, alloc=84.3MB, time=4.00 memory used=205.1MB, alloc=92.3MB, time=5.68 memory used=265.4MB, alloc=116.3MB, time=7.28 memory used=348.1MB, alloc=140.3MB, time=9.48 memory used=419.9MB, alloc=396.3MB, time=11.43 memory used=524.4MB, alloc=420.3MB, time=14.28 memory used=656.5MB, alloc=444.3MB, time=17.86 memory used=807.4MB, alloc=468.3MB, time=22.25 memory used=943.0MB, alloc=492.3MB, time=26.04 memory used=1084.2MB, alloc=492.3MB, time=30.30 memory used=1198.9MB, alloc=492.3MB, time=33.81 memory used=1311.5MB, alloc=516.3MB, time=37.34 memory used=1408.4MB, alloc=516.3MB, time=40.49 memory used=1501.6MB, alloc=516.3MB, time=43.38 memory used=1584.8MB, alloc=516.3MB, time=45.99 memory used=1673.5MB, alloc=516.3MB, time=49.02 memory used=1746.0MB, alloc=516.3MB, time=51.43 memory used=1816.4MB, alloc=540.3MB, time=53.95 memory used=1872.9MB, alloc=540.3MB, time=55.96 memory used=1928.7MB, alloc=540.3MB, time=58.04 memory used=1967.5MB, alloc=540.3MB, time=59.72 memory used=2033.1MB, alloc=540.3MB, time=62.14 memory used=2079.3MB, alloc=540.3MB, time=64.08 memory used=2294.9MB, alloc=564.3MB, time=70.70 memory used=2486.1MB, alloc=588.3MB, time=76.51 memory used=2679.9MB, alloc=612.3MB, time=82.02 memory used=2926.6MB, alloc=636.3MB, time=89.74 memory used=3134.0MB, alloc=660.3MB, time=96.54 memory used=3325.9MB, alloc=684.3MB, time=103.28 memory used=3571.2MB, alloc=708.3MB, time=109.62 memory used=3853.7MB, alloc=732.3MB, time=117.46 memory used=4096.3MB, alloc=756.3MB, time=124.33 |\^/| 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(); 1428268304 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [14 x + 18 x y - 6 y z, 8 x - 5 y z + 15, 4 x y + 15 y + 11 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [12 x y + 13 y - 6 y, -16 y + 3 y z + 15 y, x + 16 y - 8 z] > Problem := [F,G]; 2 2 2 2 Problem := [[14 x + 18 x y - 6 y z, 8 x - 5 y z + 15, 4 x y + 15 y + 11 z ], 2 2 2 [12 x y + 13 y - 6 y, -16 y + 3 y z + 15 y, x + 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=4.2MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=47.0MB, alloc=32.3MB, time=1.39 memory used=65.2MB, alloc=56.3MB, time=1.90 memory used=104.8MB, alloc=60.3MB, time=2.94 memory used=143.4MB, alloc=84.3MB, time=3.97 memory used=204.9MB, alloc=92.3MB, time=5.59 memory used=264.3MB, alloc=116.3MB, time=7.20 memory used=343.4MB, alloc=140.3MB, time=9.44 memory used=428.4MB, alloc=396.3MB, time=11.84 memory used=535.9MB, alloc=420.3MB, time=14.69 memory used=669.5MB, alloc=444.3MB, time=18.29 memory used=822.8MB, alloc=468.3MB, time=22.70 memory used=959.4MB, alloc=492.3MB, time=26.66 memory used=1082.6MB, alloc=492.3MB, time=30.32 memory used=1191.1MB, alloc=492.3MB, time=33.50 memory used=1291.6MB, alloc=516.3MB, time=36.53 memory used=1408.4MB, alloc=516.3MB, time=40.39 memory used=1515.9MB, alloc=516.3MB, time=44.09 memory used=1604.7MB, alloc=516.3MB, time=47.22 memory used=1681.6MB, alloc=516.3MB, time=49.99 memory used=1756.2MB, alloc=516.3MB, time=52.75 memory used=1829.2MB, alloc=516.3MB, time=55.43 memory used=1887.7MB, alloc=516.3MB, time=57.59 memory used=1945.0MB, alloc=540.3MB, time=59.89 memory used=2176.5MB, alloc=564.3MB, time=67.48 memory used=2397.1MB, alloc=588.3MB, time=75.11 memory used=2599.1MB, alloc=612.3MB, time=81.62 memory used=2792.0MB, alloc=636.3MB, time=88.29 memory used=2955.7MB, alloc=660.3MB, time=93.89 memory used=3094.9MB, alloc=660.3MB, time=99.03 memory used=3244.4MB, alloc=684.3MB, time=104.50 memory used=3379.0MB, alloc=684.3MB, time=109.47 |\^/| 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(); 1428268604 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-13 y + 2 z - 2 z, -8 y - 5 y z - 12, 13 y - 18 z - 7 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-15 x y + 14 y z - 18 x, -5 x + 3 x z + 18 z, -y z - 15 x + 4 z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-13 y + 2 z - 2 z, -8 y - 5 y z - 12, 13 y - 18 z - 7 z], 2 [-15 x y + 14 y z - 18 x, -5 x + 3 x z + 18 z, -y z - 15 x + 4 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.85 memory used=47.0MB, alloc=32.3MB, time=1.37 memory used=66.0MB, alloc=56.3MB, time=1.89 memory used=105.6MB, alloc=60.3MB, time=2.91 memory used=144.1MB, alloc=60.3MB, time=3.93 memory used=180.2MB, alloc=84.3MB, time=4.93 memory used=223.7MB, alloc=84.3MB, time=6.08 memory used=280.3MB, alloc=116.3MB, time=7.67 memory used=364.9MB, alloc=116.3MB, time=9.85 memory used=443.4MB, alloc=140.3MB, time=12.11 memory used=515.9MB, alloc=396.3MB, time=14.06 memory used=620.8MB, alloc=420.3MB, time=16.91 memory used=747.5MB, alloc=444.3MB, time=20.51 memory used=896.0MB, alloc=468.3MB, time=24.81 memory used=1063.2MB, alloc=492.3MB, time=29.66 memory used=1216.0MB, alloc=492.3MB, time=34.31 memory used=1351.1MB, alloc=516.3MB, time=38.46 memory used=1460.1MB, alloc=516.3MB, time=41.86 memory used=1581.8MB, alloc=516.3MB, time=45.69 memory used=1672.8MB, alloc=516.3MB, time=48.41 memory used=1777.9MB, alloc=540.3MB, time=51.77 memory used=1880.4MB, alloc=540.3MB, time=55.16 memory used=1951.6MB, alloc=540.3MB, time=57.50 memory used=2038.3MB, alloc=540.3MB, time=60.44 memory used=2117.5MB, alloc=540.3MB, time=63.12 memory used=2190.1MB, alloc=540.3MB, time=65.62 memory used=2273.1MB, alloc=540.3MB, time=68.51 memory used=2339.7MB, alloc=540.3MB, time=70.88 memory used=2407.3MB, alloc=564.3MB, time=73.19 memory used=2466.1MB, alloc=564.3MB, time=75.27 memory used=2524.7MB, alloc=564.3MB, time=77.48 memory used=2576.7MB, alloc=564.3MB, time=79.44 memory used=2808.5MB, alloc=588.3MB, time=86.48 memory used=3037.6MB, alloc=612.3MB, time=93.90 memory used=3272.4MB, alloc=636.3MB, time=102.21 |\^/| 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(); 1428268904 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [12 y z + 2 z - 18 y, 13 x y - 3 y z + 13 z , -7 y z + 4 z + 15 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-10 x - 7 y - 16 z, 20 z + 13 x + 2, 6 z ] > Problem := [F,G]; Problem := [ 2 2 2 [12 y z + 2 z - 18 y, 13 x y - 3 y z + 13 z , -7 y z + 4 z + 15 y], 2 2 2 [-10 x - 7 y - 16 z, 20 z + 13 x + 2, 6 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.90 memory used=48.3MB, alloc=32.3MB, time=1.46 memory used=67.3MB, alloc=56.3MB, time=1.98 memory used=106.8MB, alloc=60.3MB, time=3.02 memory used=143.0MB, alloc=84.3MB, time=3.99 memory used=202.2MB, alloc=92.3MB, time=5.59 memory used=262.4MB, alloc=92.3MB, time=7.17 memory used=321.9MB, alloc=116.3MB, time=8.79 memory used=404.3MB, alloc=116.3MB, time=11.08 memory used=483.2MB, alloc=140.3MB, time=13.30 memory used=573.6MB, alloc=396.3MB, time=15.96 memory used=675.4MB, alloc=420.3MB, time=18.98 memory used=798.2MB, alloc=444.3MB, time=22.57 memory used=942.1MB, alloc=468.3MB, time=26.95 memory used=1102.8MB, alloc=492.3MB, time=31.66 memory used=1288.1MB, alloc=516.3MB, time=38.00 memory used=1439.0MB, alloc=516.3MB, time=42.66 memory used=1596.2MB, alloc=540.3MB, time=48.26 memory used=1738.5MB, alloc=540.3MB, time=53.23 memory used=1886.4MB, alloc=540.3MB, time=58.58 memory used=2015.7MB, alloc=540.3MB, time=63.50 memory used=2156.7MB, alloc=564.3MB, time=69.41 memory used=2277.7MB, alloc=564.3MB, time=74.12 memory used=2405.5MB, alloc=564.3MB, time=79.11 memory used=2513.9MB, alloc=564.3MB, time=83.60 memory used=2628.0MB, alloc=564.3MB, time=88.76 memory used=2731.1MB, alloc=564.3MB, time=93.18 memory used=2858.5MB, alloc=564.3MB, time=99.21 memory used=2959.7MB, alloc=564.3MB, time=103.68 memory used=3040.9MB, alloc=564.3MB, time=106.89 memory used=3141.8MB, alloc=564.3MB, time=111.42 memory used=3235.1MB, alloc=588.3MB, time=115.78 memory used=3333.5MB, alloc=588.3MB, time=120.74 memory used=3408.2MB, alloc=588.3MB, time=124.21 memory used=3497.5MB, alloc=588.3MB, time=128.70 memory used=3587.5MB, alloc=588.3MB, time=133.06 memory used=3649.9MB, alloc=588.3MB, time=136.06 |\^/| 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(); 1428269204 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-8 y - 13 z - 5 z, -14 y z + 17 x + 16, -15 x + 9 x z + 16 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-11 x - 4 x z + 10 z, -12 x z + 20 z - 16 z, 6 x z - 7 x - 11 z] > Problem := [F,G]; 2 2 2 2 Problem := [[-8 y - 13 z - 5 z, -14 y z + 17 x + 16, -15 x + 9 x z + 16 z ], 2 2 [-11 x - 4 x z + 10 z, -12 x z + 20 z - 16 z, 6 x z - 7 x - 11 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.85 memory used=46.3MB, alloc=56.3MB, time=1.40 memory used=86.6MB, alloc=60.3MB, time=2.46 memory used=126.3MB, alloc=84.3MB, time=3.51 memory used=168.9MB, alloc=84.3MB, time=4.61 memory used=229.9MB, alloc=116.3MB, time=6.24 memory used=312.8MB, alloc=116.3MB, time=8.41 memory used=393.0MB, alloc=140.3MB, time=10.58 memory used=471.1MB, alloc=396.3MB, time=12.86 memory used=571.9MB, alloc=420.3MB, time=15.62 memory used=690.6MB, alloc=444.3MB, time=18.98 memory used=827.9MB, alloc=468.3MB, time=22.92 memory used=989.3MB, alloc=468.3MB, time=27.61 memory used=1150.2MB, alloc=492.3MB, time=32.20 memory used=1310.4MB, alloc=516.3MB, time=37.34 memory used=1451.4MB, alloc=516.3MB, time=41.54 memory used=1590.6MB, alloc=516.3MB, time=45.95 memory used=1736.8MB, alloc=540.3MB, time=50.95 memory used=1877.6MB, alloc=540.3MB, time=55.78 memory used=1998.9MB, alloc=564.3MB, time=59.91 memory used=2115.4MB, alloc=564.3MB, time=63.65 memory used=2226.5MB, alloc=564.3MB, time=67.70 memory used=2339.7MB, alloc=588.3MB, time=72.00 memory used=2563.8MB, alloc=612.3MB, time=79.65 memory used=2750.4MB, alloc=636.3MB, time=85.80 memory used=2938.2MB, alloc=660.3MB, time=92.06 memory used=3123.0MB, alloc=684.3MB, time=98.43 memory used=3299.5MB, alloc=708.3MB, time=104.57 memory used=3490.9MB, alloc=732.3MB, time=111.38 memory used=3664.7MB, alloc=756.3MB, time=117.69 memory used=3818.0MB, alloc=780.3MB, time=123.42 memory used=3920.6MB, alloc=804.3MB, time=128.05 |\^/| 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(); 1428269504 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-10 x + 19 x z - 18 y z, -9 y z - 15 y - 6, -7 y z + 3 z + 12 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-13 y z - 13 z - 7, -16 y + 3 z - 11 x, 16 - 3 x - 10 z] > Problem := [F,G]; Problem := [ 2 2 [-10 x + 19 x z - 18 y z, -9 y z - 15 y - 6, -7 y z + 3 z + 12 y], 2 2 2 [-13 y z - 13 z - 7, -16 y + 3 z - 11 x, 16 - 3 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=4.2MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.87 memory used=46.8MB, alloc=56.3MB, time=1.41 memory used=87.2MB, alloc=60.3MB, time=2.47 memory used=126.8MB, alloc=84.3MB, time=3.51 memory used=163.9MB, alloc=84.3MB, time=4.44 memory used=226.2MB, alloc=92.3MB, time=6.10 memory used=287.4MB, alloc=116.3MB, time=7.69 memory used=360.7MB, alloc=116.3MB, time=9.50 memory used=434.3MB, alloc=396.3MB, time=11.47 memory used=541.6MB, alloc=420.3MB, time=14.16 memory used=666.2MB, alloc=444.3MB, time=17.61 memory used=816.4MB, alloc=468.3MB, time=21.69 memory used=931.2MB, alloc=468.3MB, time=24.68 memory used=1054.6MB, alloc=492.3MB, time=28.40 memory used=1184.9MB, alloc=492.3MB, time=32.12 memory used=1301.5MB, alloc=516.3MB, time=35.43 memory used=1403.4MB, alloc=516.3MB, time=38.60 memory used=1492.6MB, alloc=516.3MB, time=41.24 memory used=1591.5MB, alloc=516.3MB, time=43.50 memory used=1680.1MB, alloc=516.3MB, time=46.46 memory used=1775.4MB, alloc=516.3MB, time=49.88 memory used=1854.8MB, alloc=516.3MB, time=52.49 memory used=1933.2MB, alloc=540.3MB, time=55.16 memory used=2005.2MB, alloc=540.3MB, time=57.64 memory used=2055.5MB, alloc=540.3MB, time=59.42 memory used=2121.4MB, alloc=540.3MB, time=61.89 memory used=2172.3MB, alloc=540.3MB, time=63.66 memory used=2226.7MB, alloc=540.3MB, time=65.90 memory used=2447.9MB, alloc=564.3MB, time=72.45 memory used=2683.1MB, alloc=588.3MB, time=80.32 memory used=2887.6MB, alloc=612.3MB, time=87.76 memory used=3107.0MB, alloc=636.3MB, time=95.63 memory used=3291.0MB, alloc=660.3MB, time=102.07 memory used=3452.4MB, alloc=684.3MB, time=108.03 memory used=3615.2MB, alloc=684.3MB, time=114.23 memory used=3754.2MB, alloc=684.3MB, time=120.10 memory used=3892.7MB, alloc=708.3MB, time=125.86 |\^/| 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(); 1428269804 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [16 y - 4 y z + 7, -19 y + 14 y + 2 z, -x z - 7 x + 13] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-11 x y + 3 x z + 12 x, -12 x y - 11 y + 15 z , -5 x z - 9 y z - 18 y] > Problem := [F,G]; 2 2 Problem := [[16 y - 4 y z + 7, -19 y + 14 y + 2 z, -x z - 7 x + 13], 2 2 [-11 x y + 3 x z + 12 x, -12 x y - 11 y + 15 z , -5 x z - 9 y z - 18 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.88 memory used=46.5MB, alloc=32.3MB, time=1.41 memory used=65.0MB, alloc=56.3MB, time=1.93 memory used=104.9MB, alloc=60.3MB, time=3.00 memory used=141.5MB, alloc=84.3MB, time=4.02 memory used=201.4MB, alloc=92.3MB, time=5.75 memory used=260.7MB, alloc=92.3MB, time=7.44 memory used=319.3MB, alloc=116.3MB, time=9.12 memory used=399.8MB, alloc=116.3MB, time=11.54 memory used=480.2MB, alloc=140.3MB, time=14.05 memory used=583.2MB, alloc=140.3MB, time=17.26 memory used=683.9MB, alloc=164.3MB, time=20.46 memory used=780.6MB, alloc=420.3MB, time=23.66 memory used=900.8MB, alloc=444.3MB, time=27.47 memory used=1041.3MB, alloc=468.3MB, time=32.01 memory used=1202.2MB, alloc=492.3MB, time=37.60 memory used=1396.1MB, alloc=516.3MB, time=44.51 memory used=1607.8MB, alloc=540.3MB, time=52.39 memory used=1848.1MB, alloc=564.3MB, time=60.84 memory used=2107.2MB, alloc=588.3MB, time=71.75 memory used=2391.8MB, alloc=612.3MB, time=83.93 memory used=2698.1MB, alloc=636.3MB, time=97.42 memory used=3032.0MB, alloc=660.3MB, time=111.54 |\^/| 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(); 1428270104 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [12 x z + 18 x + 17 y, -15 x y - 8 y - 15 z , -2 x - 10 y - 6 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-18 z + 3 y + 7, -16 y z - 5 z - 16 x, 5 y + 12 z + 11] > Problem := [F,G]; 2 2 2 Problem := [[12 x z + 18 x + 17 y, -15 x y - 8 y - 15 z , -2 x - 10 y - 6 z], 2 2 2 2 [-18 z + 3 y + 7, -16 y z - 5 z - 16 x, 5 y + 12 z + 11]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.88 memory used=45.9MB, alloc=56.3MB, time=1.40 memory used=85.8MB, alloc=60.3MB, time=2.45 memory used=124.8MB, alloc=84.3MB, time=3.49 memory used=167.8MB, alloc=84.3MB, time=4.67 memory used=228.1MB, alloc=92.3MB, time=6.31 memory used=288.2MB, alloc=116.3MB, time=7.94 memory used=370.9MB, alloc=116.3MB, time=10.19 memory used=447.4MB, alloc=140.3MB, time=12.32 memory used=525.9MB, alloc=140.3MB, time=14.54 memory used=594.6MB, alloc=420.3MB, time=16.52 memory used=723.0MB, alloc=444.3MB, time=20.07 memory used=870.8MB, alloc=468.3MB, time=24.40 memory used=1015.8MB, alloc=492.3MB, time=28.68 memory used=1146.3MB, alloc=492.3MB, time=32.80 memory used=1266.4MB, alloc=492.3MB, time=36.56 memory used=1382.1MB, alloc=516.3MB, time=40.50 memory used=1468.7MB, alloc=516.3MB, time=43.46 memory used=1568.0MB, alloc=516.3MB, time=46.70 memory used=1671.9MB, alloc=516.3MB, time=50.52 memory used=1760.3MB, alloc=516.3MB, time=53.91 memory used=1842.0MB, alloc=516.3MB, time=57.01 memory used=1912.7MB, alloc=516.3MB, time=59.61 memory used=1978.3MB, alloc=516.3MB, time=62.25 memory used=2037.8MB, alloc=516.3MB, time=64.75 memory used=2099.4MB, alloc=516.3MB, time=67.62 memory used=2298.4MB, alloc=540.3MB, time=74.85 memory used=2519.5MB, alloc=564.3MB, time=83.31 memory used=2738.6MB, alloc=588.3MB, time=91.49 memory used=2951.0MB, alloc=612.3MB, time=99.86 memory used=3147.8MB, alloc=636.3MB, time=107.31 memory used=3318.3MB, alloc=660.3MB, time=114.13 memory used=3499.4MB, alloc=684.3MB, time=121.50 memory used=3653.3MB, alloc=684.3MB, time=127.87 |\^/| 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(); 1428270404 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [3 x y + 16 x - 9 y, -15 x y - 6 y + 9, -19 y z + 11 z - 5 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-3 y z + 16 x + 18 z, -x y - 9 z + 2 y, -2 x y - 9 y z] > Problem := [F,G]; 2 2 Problem := [[3 x y + 16 x - 9 y, -15 x y - 6 y + 9, -19 y z + 11 z - 5 y], 2 [-3 y z + 16 x + 18 z, -x y - 9 z + 2 y, -2 x y - 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.32 memory used=26.3MB, alloc=32.3MB, time=0.92 memory used=47.4MB, alloc=32.3MB, time=1.49 memory used=67.9MB, alloc=32.3MB, time=2.06 memory used=86.9MB, alloc=56.3MB, time=2.62 memory used=126.2MB, alloc=60.3MB, time=3.72 memory used=163.2MB, alloc=84.3MB, time=4.79 memory used=219.4MB, alloc=84.3MB, time=6.56 memory used=275.9MB, alloc=116.3MB, time=8.32 memory used=356.0MB, alloc=116.3MB, time=10.55 memory used=434.3MB, alloc=140.3MB, time=13.01 memory used=535.5MB, alloc=140.3MB, time=16.15 memory used=625.3MB, alloc=164.3MB, time=18.94 memory used=724.9MB, alloc=420.3MB, time=22.26 memory used=845.1MB, alloc=444.3MB, time=26.22 memory used=986.8MB, alloc=468.3MB, time=30.65 memory used=1146.1MB, alloc=492.3MB, time=35.85 memory used=1313.6MB, alloc=516.3MB, time=41.21 memory used=1488.8MB, alloc=540.3MB, time=46.91 memory used=1673.4MB, alloc=564.3MB, time=53.05 memory used=1868.6MB, alloc=588.3MB, time=59.56 memory used=2071.4MB, alloc=612.3MB, time=66.48 memory used=2280.0MB, alloc=636.3MB, time=73.52 memory used=2496.3MB, alloc=660.3MB, time=80.89 memory used=2717.5MB, alloc=684.3MB, time=88.52 memory used=2945.2MB, alloc=708.3MB, time=96.47 memory used=3178.6MB, alloc=732.3MB, time=104.67 memory used=3416.8MB, alloc=756.3MB, time=113.15 |\^/| 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(); 1428270704 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [9 x z + 16 y - 12 x, x z + 6 z - 14 z, -12 x + 6 y - z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [9 x z - 8 y + 11 y, 8 - 3 y + 5 z, 16 y + 17 y - 1] > Problem := [F,G]; 2 2 2 Problem := [[9 x z + 16 y - 12 x, x z + 6 z - 14 z, -12 x + 6 y - z], 2 2 [9 x z - 8 y + 11 y, 8 - 3 y + 5 z, 16 y + 17 y - 1]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=47.2MB, alloc=32.3MB, time=1.40 memory used=64.2MB, alloc=56.3MB, time=1.86 memory used=102.0MB, alloc=60.3MB, time=2.88 memory used=138.7MB, alloc=84.3MB, time=3.89 memory used=198.6MB, alloc=92.3MB, time=5.60 memory used=256.6MB, alloc=116.3MB, time=7.24 memory used=335.6MB, alloc=116.3MB, time=9.48 memory used=414.7MB, alloc=140.3MB, time=11.81 memory used=514.1MB, alloc=140.3MB, time=14.62 memory used=601.2MB, alloc=420.3MB, time=17.44 memory used=721.6MB, alloc=444.3MB, time=21.12 memory used=864.0MB, alloc=468.3MB, time=25.68 memory used=1031.0MB, alloc=492.3MB, time=31.34 memory used=1204.8MB, alloc=516.3MB, time=37.21 memory used=1368.0MB, alloc=540.3MB, time=42.55 memory used=1525.1MB, alloc=540.3MB, time=48.14 memory used=1664.0MB, alloc=564.3MB, time=53.29 memory used=1800.7MB, alloc=564.3MB, time=58.46 memory used=1925.3MB, alloc=564.3MB, time=63.62 memory used=2042.6MB, alloc=564.3MB, time=67.87 memory used=2162.3MB, alloc=564.3MB, time=72.77 memory used=2257.3MB, alloc=564.3MB, time=76.72 memory used=2346.0MB, alloc=564.3MB, time=80.42 memory used=2436.3MB, alloc=564.3MB, time=84.69 memory used=2506.9MB, alloc=588.3MB, time=88.20 memory used=2579.5MB, alloc=588.3MB, time=91.68 memory used=2645.6MB, alloc=588.3MB, time=94.87 memory used=2907.1MB, alloc=612.3MB, time=105.81 memory used=3186.7MB, alloc=636.3MB, time=118.14 |\^/| 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(); 1428271004 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-20 x - 11 x + 7, 8 y z + 14 z + 6, 6 x + x z - 12 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [18 x + 17 z , -20 x + 2 y z + 18 x, -18 x - 6 z + 3 y] > Problem := [F,G]; 2 2 2 2 Problem := [[-20 x - 11 x + 7, 8 y z + 14 z + 6, 6 x + x z - 12 y ], 2 2 2 2 2 [18 x + 17 z , -20 x + 2 y z + 18 x, -18 x - 6 z + 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.89 memory used=47.1MB, alloc=56.3MB, time=1.45 memory used=88.8MB, alloc=60.3MB, time=2.52 memory used=132.6MB, alloc=92.3MB, time=3.59 memory used=202.9MB, alloc=92.3MB, time=5.15 memory used=268.3MB, alloc=92.3MB, time=6.73 memory used=333.7MB, alloc=116.3MB, time=8.33 memory used=399.8MB, alloc=116.3MB, time=9.98 memory used=462.1MB, alloc=396.3MB, time=11.55 memory used=569.2MB, alloc=420.3MB, time=14.53 memory used=707.0MB, alloc=444.3MB, time=18.01 memory used=855.9MB, alloc=444.3MB, time=21.17 memory used=994.4MB, alloc=468.3MB, time=24.14 memory used=1106.7MB, alloc=468.3MB, time=27.02 memory used=1213.3MB, alloc=492.3MB, time=29.89 memory used=1302.8MB, alloc=492.3MB, time=32.12 memory used=1405.5MB, alloc=492.3MB, time=34.91 memory used=1474.4MB, alloc=492.3MB, time=36.67 memory used=1551.2MB, alloc=492.3MB, time=39.11 memory used=1633.5MB, alloc=492.3MB, time=41.58 memory used=1700.5MB, alloc=492.3MB, time=43.53 memory used=1762.0MB, alloc=492.3MB, time=45.60 memory used=1818.5MB, alloc=492.3MB, time=47.43 memory used=1890.1MB, alloc=516.3MB, time=49.81 memory used=1940.3MB, alloc=516.3MB, time=51.44 memory used=2004.2MB, alloc=516.3MB, time=53.80 memory used=2048.8MB, alloc=516.3MB, time=55.41 memory used=2269.0MB, alloc=540.3MB, time=61.27 memory used=2478.0MB, alloc=564.3MB, time=67.75 memory used=2667.8MB, alloc=588.3MB, time=73.04 memory used=2849.6MB, alloc=612.3MB, time=79.12 memory used=3024.8MB, alloc=636.3MB, time=84.81 memory used=3173.9MB, alloc=660.3MB, time=89.95 memory used=3293.2MB, alloc=660.3MB, time=94.48 memory used=3429.8MB, alloc=660.3MB, time=99.06 memory used=3556.5MB, alloc=660.3MB, time=103.86 memory used=3656.9MB, alloc=660.3MB, time=107.86 memory used=3766.8MB, alloc=684.3MB, time=112.31 memory used=3847.5MB, alloc=684.3MB, time=116.06 memory used=4208.8MB, alloc=708.3MB, time=127.09 memory used=4576.4MB, alloc=732.3MB, time=139.01 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428271304 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-3 y + 5 z + 12, 11 x y + 14 x z - 20 y, -17 x z + y z + 8 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [9 x z - 17 y z - z, -12 x + 8 x y - 9 z, 9 y z - 10 x + 14] > Problem := [F,G]; 2 Problem := [[-3 y + 5 z + 12, 11 x y + 14 x z - 20 y, -17 x z + y z + 8 z], 2 [9 x z - 17 y z - z, -12 x + 8 x y - 9 z, 9 y z - 10 x + 14]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=47.2MB, alloc=32.3MB, time=1.36 memory used=66.8MB, alloc=56.3MB, time=1.89 memory used=105.1MB, alloc=60.3MB, time=2.91 memory used=142.6MB, alloc=60.3MB, time=3.89 memory used=178.9MB, alloc=84.3MB, time=4.86 memory used=235.2MB, alloc=84.3MB, time=6.36 memory used=288.0MB, alloc=116.3MB, time=7.84 memory used=362.2MB, alloc=116.3MB, time=9.85 memory used=435.1MB, alloc=140.3MB, time=11.90 memory used=532.0MB, alloc=140.3MB, time=14.65 memory used=627.5MB, alloc=164.3MB, time=17.54 memory used=731.1MB, alloc=420.3MB, time=20.67 memory used=848.3MB, alloc=444.3MB, time=24.25 memory used=986.9MB, alloc=468.3MB, time=28.45 memory used=1147.0MB, alloc=492.3MB, time=33.44 memory used=1321.0MB, alloc=516.3MB, time=39.15 memory used=1492.3MB, alloc=540.3MB, time=44.74 memory used=1671.6MB, alloc=564.3MB, time=50.71 memory used=1858.2MB, alloc=588.3MB, time=57.03 memory used=2052.7MB, alloc=612.3MB, time=63.55 memory used=2262.8MB, alloc=636.3MB, time=70.38 memory used=2473.7MB, alloc=660.3MB, time=77.58 memory used=2687.2MB, alloc=684.3MB, time=84.92 memory used=2905.5MB, alloc=708.3MB, time=92.60 memory used=3129.3MB, alloc=732.3MB, time=100.38 memory used=3357.4MB, alloc=756.3MB, time=108.32 memory used=3590.2MB, alloc=780.3MB, time=116.46 memory used=3820.4MB, alloc=804.3MB, time=124.95 |\^/| 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(); 1428271604 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [x + 18 y + 13, -5 x z + 18 z - 11, -4 x z - 18 z - 14 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-2 x z + 8 x + 7, -17 x + 9 x y - 18 y , 19 x y + 15 y - 10 z ] > Problem := [F,G]; 2 2 Problem := [[x + 18 y + 13, -5 x z + 18 z - 11, -4 x z - 18 z - 14 y], 2 2 2 2 [-2 x z + 8 x + 7, -17 x + 9 x y - 18 y , 19 x y + 15 y - 10 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.88 memory used=47.7MB, alloc=32.3MB, time=1.43 memory used=67.6MB, alloc=56.3MB, time=1.98 memory used=109.3MB, alloc=60.3MB, time=3.08 memory used=149.1MB, alloc=84.3MB, time=4.12 memory used=210.0MB, alloc=92.3MB, time=5.74 memory used=270.6MB, alloc=116.3MB, time=7.38 memory used=354.3MB, alloc=116.3MB, time=9.66 memory used=437.0MB, alloc=140.3MB, time=11.98 memory used=515.6MB, alloc=140.3MB, time=14.17 memory used=590.1MB, alloc=396.3MB, time=16.37 memory used=693.9MB, alloc=420.3MB, time=19.35 memory used=819.9MB, alloc=444.3MB, time=23.13 memory used=969.1MB, alloc=468.3MB, time=27.79 memory used=1114.4MB, alloc=492.3MB, time=32.09 memory used=1272.3MB, alloc=516.3MB, time=37.19 memory used=1437.2MB, alloc=540.3MB, time=42.37 memory used=1650.2MB, alloc=564.3MB, time=48.97 memory used=1857.6MB, alloc=588.3MB, time=55.64 memory used=2058.9MB, alloc=612.3MB, time=62.16 memory used=2267.7MB, alloc=636.3MB, time=68.93 memory used=2438.5MB, alloc=660.3MB, time=74.58 memory used=2614.2MB, alloc=684.3MB, time=80.46 memory used=2779.7MB, alloc=708.3MB, time=86.14 memory used=2950.7MB, alloc=732.3MB, time=91.91 memory used=3101.0MB, alloc=756.3MB, time=97.06 memory used=3243.8MB, alloc=780.3MB, time=102.09 memory used=3393.7MB, alloc=804.3MB, time=107.40 memory used=3534.3MB, alloc=828.3MB, time=112.48 memory used=3672.4MB, alloc=852.3MB, time=117.53 |\^/| 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(); 1428271904 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [-16 x y + 2 x z + 17 y, 5 x y - 3 y z + 15 z, 17 x y - 14 x + 10 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-3 x z + 6 y - 15, 3 y + 3 y z - 17 x, 6 x y + 19 x - y] > Problem := [F,G]; Problem := [ [-16 x y + 2 x z + 17 y, 5 x y - 3 y z + 15 z, 17 x y - 14 x + 10 y], 2 [-3 x z + 6 y - 15, 3 y + 3 y z - 17 x, 6 x y + 19 x - y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=47.1MB, alloc=32.3MB, time=1.38 memory used=66.3MB, alloc=56.3MB, time=1.90 memory used=106.3MB, alloc=60.3MB, time=2.94 memory used=144.4MB, alloc=84.3MB, time=3.93 memory used=203.3MB, alloc=92.3MB, time=5.53 memory used=261.1MB, alloc=92.3MB, time=7.09 memory used=318.2MB, alloc=116.3MB, time=8.67 memory used=398.2MB, alloc=116.3MB, time=10.87 memory used=475.8MB, alloc=140.3MB, time=13.17 memory used=577.2MB, alloc=164.3MB, time=16.12 memory used=665.2MB, alloc=164.3MB, time=18.83 memory used=760.6MB, alloc=444.3MB, time=21.93 memory used=891.6MB, alloc=468.3MB, time=25.94 memory used=1033.2MB, alloc=492.3MB, time=30.35 memory used=1188.8MB, alloc=516.3MB, time=35.31 memory used=1358.4MB, alloc=540.3MB, time=40.77 memory used=1539.2MB, alloc=564.3MB, time=46.57 memory used=1729.9MB, alloc=588.3MB, time=52.90 memory used=1930.2MB, alloc=612.3MB, time=59.51 memory used=2140.5MB, alloc=636.3MB, time=66.44 memory used=2363.7MB, alloc=660.3MB, time=73.84 memory used=2573.9MB, alloc=684.3MB, time=84.79 memory used=2786.3MB, alloc=708.3MB, time=97.04 memory used=3010.6MB, alloc=732.3MB, time=110.51 memory used=3248.9MB, alloc=756.3MB, time=125.20 |\^/| 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(); 1428272204 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [16 x + 8 x - 17 y, x y - x z - 17 y z, 10 x z + 10 y + 8 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-20 y z - 5 x + 2 z, -11 x + 14 x z + 8 y z, -15 x - 16 x y - 7 y] > Problem := [F,G]; 2 2 Problem := [[16 x + 8 x - 17 y, x y - x z - 17 y z, 10 x z + 10 y + 8 z], 2 2 [-20 y z - 5 x + 2 z, -11 x + 14 x z + 8 y z, -15 x - 16 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=4.2MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=46.8MB, alloc=32.3MB, time=1.40 memory used=66.3MB, alloc=56.3MB, time=1.92 memory used=107.4MB, alloc=60.3MB, time=3.02 memory used=146.5MB, alloc=60.3MB, time=4.03 memory used=184.5MB, alloc=84.3MB, time=5.06 memory used=230.2MB, alloc=84.3MB, time=6.30 memory used=289.1MB, alloc=116.3MB, time=7.91 memory used=371.7MB, alloc=116.3MB, time=10.13 memory used=446.9MB, alloc=140.3MB, time=12.26 memory used=524.2MB, alloc=396.3MB, time=14.53 memory used=628.0MB, alloc=420.3MB, time=17.62 memory used=752.1MB, alloc=444.3MB, time=21.28 memory used=900.6MB, alloc=468.3MB, time=25.82 memory used=1065.4MB, alloc=492.3MB, time=30.98 memory used=1218.9MB, alloc=516.3MB, time=36.21 memory used=1363.5MB, alloc=516.3MB, time=40.95 memory used=1479.1MB, alloc=540.3MB, time=44.63 memory used=1604.9MB, alloc=564.3MB, time=48.94 memory used=1718.1MB, alloc=564.3MB, time=52.88 memory used=1842.7MB, alloc=588.3MB, time=57.27 memory used=1967.4MB, alloc=588.3MB, time=61.64 memory used=2079.4MB, alloc=612.3MB, time=65.50 memory used=2194.8MB, alloc=612.3MB, time=69.51 memory used=2317.9MB, alloc=636.3MB, time=73.92 memory used=2432.2MB, alloc=660.3MB, time=78.07 memory used=2538.9MB, alloc=660.3MB, time=82.02 memory used=2644.6MB, alloc=684.3MB, time=85.96 memory used=2745.3MB, alloc=684.3MB, time=89.76 memory used=2841.1MB, alloc=708.3MB, time=93.45 memory used=2944.8MB, alloc=708.3MB, time=97.36 memory used=3036.7MB, alloc=732.3MB, time=100.91 memory used=3099.8MB, alloc=732.3MB, time=103.60 memory used=3191.4MB, alloc=756.3MB, time=107.19 memory used=3282.1MB, alloc=756.3MB, time=110.68 memory used=3388.7MB, alloc=756.3MB, time=114.07 memory used=3482.6MB, alloc=780.3MB, time=117.33 memory used=3567.2MB, alloc=780.3MB, time=120.69 memory used=3655.9MB, alloc=780.3MB, time=124.33 memory used=3738.7MB, alloc=804.3MB, time=127.82 memory used=3810.7MB, alloc=804.3MB, time=130.90 memory used=3886.1MB, alloc=804.3MB, time=134.14 memory used=3962.7MB, alloc=828.3MB, time=137.53 |\^/| 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(); 1428272504 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-2 x + 9 x z + 7 z, -11 x z - 18 y z + 14 z, 17 x y - x + 19 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [14 x - 19 z + 16 y, 4 y z + 11 x + 7 z, 15 y z + 14 z - 12 x] > Problem := [F,G]; 2 Problem := [[-2 x + 9 x z + 7 z, -11 x z - 18 y z + 14 z, 17 x y - x + 19 y], 2 2 2 [14 x - 19 z + 16 y, 4 y z + 11 x + 7 z, 15 y z + 14 z - 12 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.84 memory used=47.5MB, alloc=32.3MB, time=1.40 memory used=67.4MB, alloc=56.3MB, time=1.95 memory used=108.4MB, alloc=60.3MB, time=3.03 memory used=147.5MB, alloc=60.3MB, time=4.07 memory used=183.0MB, alloc=84.3MB, time=5.05 memory used=229.4MB, alloc=84.3MB, time=6.30 memory used=286.5MB, alloc=116.3MB, time=7.90 memory used=366.3MB, alloc=116.3MB, time=10.09 memory used=447.8MB, alloc=140.3MB, time=12.33 memory used=534.7MB, alloc=396.3MB, time=14.85 memory used=638.0MB, alloc=420.3MB, time=17.94 memory used=767.3MB, alloc=444.3MB, time=21.66 memory used=918.2MB, alloc=468.3MB, time=26.25 memory used=1086.4MB, alloc=492.3MB, time=31.54 memory used=1246.2MB, alloc=516.3MB, time=36.74 memory used=1385.8MB, alloc=516.3MB, time=41.25 memory used=1527.9MB, alloc=540.3MB, time=45.84 memory used=1651.0MB, alloc=540.3MB, time=49.88 memory used=1753.1MB, alloc=540.3MB, time=53.22 memory used=1864.3MB, alloc=564.3MB, time=57.16 memory used=1968.4MB, alloc=588.3MB, time=60.91 memory used=2062.2MB, alloc=588.3MB, time=64.34 memory used=2199.6MB, alloc=612.3MB, time=69.05 memory used=2322.5MB, alloc=636.3MB, time=73.43 memory used=2448.4MB, alloc=660.3MB, time=77.95 memory used=2563.7MB, alloc=660.3MB, time=82.14 memory used=2668.5MB, alloc=684.3MB, time=86.07 memory used=2789.4MB, alloc=708.3MB, time=90.61 memory used=2910.4MB, alloc=732.3MB, time=95.14 memory used=3031.6MB, alloc=732.3MB, time=99.75 memory used=3133.1MB, alloc=756.3MB, time=103.81 memory used=3240.0MB, alloc=780.3MB, time=107.97 memory used=3336.3MB, alloc=780.3MB, time=111.79 memory used=3428.4MB, alloc=804.3MB, time=115.52 memory used=3508.5MB, alloc=804.3MB, time=118.94 memory used=3599.0MB, alloc=828.3MB, time=122.89 |\^/| 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(); 1428272804 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [18 x z + 16 y z - 4 z , -4 x y + 20 x z + 10 y , -17 x z - 7 y z + 5 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [8 x y + 9 y - 18 z, -13 x + 9 y z - 5, 9 x - 17 y - 13 z] > Problem := [F,G]; Problem := [ 2 2 2 [18 x z + 16 y z - 4 z , -4 x y + 20 x z + 10 y , -17 x z - 7 y z + 5 z ], 2 2 2 [8 x y + 9 y - 18 z, -13 x + 9 y z - 5, 9 x - 17 y - 13 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.85 memory used=46.2MB, alloc=32.3MB, time=1.35 memory used=64.9MB, alloc=56.3MB, time=1.87 memory used=103.7MB, alloc=60.3MB, time=2.88 memory used=139.8MB, alloc=84.3MB, time=3.86 memory used=197.9MB, alloc=116.3MB, time=5.43 memory used=277.2MB, alloc=116.3MB, time=7.54 memory used=350.5MB, alloc=140.3MB, time=9.57 memory used=447.0MB, alloc=140.3MB, time=12.24 memory used=537.5MB, alloc=164.3MB, time=14.76 memory used=613.2MB, alloc=420.3MB, time=16.78 memory used=733.9MB, alloc=444.3MB, time=19.93 memory used=874.2MB, alloc=468.3MB, time=23.78 memory used=1037.5MB, alloc=492.3MB, time=28.53 memory used=1209.8MB, alloc=516.3MB, time=33.64 memory used=1413.3MB, alloc=540.3MB, time=39.75 memory used=1632.7MB, alloc=564.3MB, time=46.74 memory used=1872.7MB, alloc=588.3MB, time=54.47 memory used=2123.1MB, alloc=612.3MB, time=62.90 memory used=2372.5MB, alloc=636.3MB, time=70.71 memory used=2647.5MB, alloc=660.3MB, time=79.90 memory used=2888.6MB, alloc=684.3MB, time=87.96 memory used=3111.2MB, alloc=708.3MB, time=95.08 memory used=3291.3MB, alloc=732.3MB, time=101.31 memory used=3489.7MB, alloc=756.3MB, time=107.82 memory used=3705.5MB, alloc=780.3MB, time=116.81 memory used=3858.9MB, alloc=804.3MB, time=123.05 memory used=4033.9MB, alloc=828.3MB, time=129.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428273104 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-10 y z - 9 y - 8 z, 9 x y + 17 x z - 10 z , -3 x - 11 x z + 11 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [11 x + 10 x z + 15 x, -4 x - 17 x z + 15 z, -14 y - 20 y z - 12 z ] > Problem := [F,G]; Problem := [ 2 2 [-10 y z - 9 y - 8 z, 9 x y + 17 x z - 10 z , -3 x - 11 x z + 11 z], 2 2 2 2 [11 x + 10 x z + 15 x, -4 x - 17 x z + 15 z, -14 y - 20 y z - 12 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=25.9MB, alloc=32.3MB, time=0.83 memory used=46.0MB, alloc=56.3MB, time=1.38 memory used=85.0MB, alloc=60.3MB, time=2.40 memory used=123.2MB, alloc=84.3MB, time=3.42 memory used=178.3MB, alloc=84.3MB, time=4.91 memory used=237.8MB, alloc=116.3MB, time=6.57 memory used=319.3MB, alloc=116.3MB, time=8.86 memory used=399.7MB, alloc=140.3MB, time=11.27 memory used=502.3MB, alloc=164.3MB, time=14.31 memory used=597.9MB, alloc=164.3MB, time=17.19 memory used=697.2MB, alloc=444.3MB, time=20.12 memory used=833.7MB, alloc=468.3MB, time=24.39 memory used=998.4MB, alloc=492.3MB, time=29.82 memory used=1191.3MB, alloc=516.3MB, time=36.12 memory used=1407.4MB, alloc=540.3MB, time=43.66 memory used=1646.8MB, alloc=564.3MB, time=52.42 memory used=1905.0MB, alloc=588.3MB, time=61.87 memory used=2186.7MB, alloc=612.3MB, time=72.57 memory used=2484.3MB, alloc=636.3MB, time=84.37 memory used=2807.8MB, alloc=660.3MB, time=96.86 memory used=3124.8MB, alloc=684.3MB, time=110.10 |\^/| 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(); 1428273405 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [16 x + 9 x z - 2, 20 - x - 3 y, 17 x - 3 y - 11 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [15 y z + 14 x + 9 y, 10 x + 20 y z - 8 y, -11 y + 3 y + 19] > Problem := [F,G]; 2 2 2 2 Problem := [[16 x + 9 x z - 2, 20 - x - 3 y, 17 x - 3 y - 11 z ], 2 2 [15 y z + 14 x + 9 y, 10 x + 20 y z - 8 y, -11 y + 3 y + 19]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.29 memory used=26.7MB, alloc=32.3MB, time=0.86 memory used=47.7MB, alloc=32.3MB, time=1.39 memory used=68.1MB, alloc=32.3MB, time=1.91 memory used=86.7MB, alloc=56.3MB, time=2.43 memory used=126.9MB, alloc=84.3MB, time=3.52 memory used=188.3MB, alloc=92.3MB, time=5.24 memory used=249.4MB, alloc=92.3MB, time=6.97 memory used=309.8MB, alloc=116.3MB, time=8.66 memory used=394.1MB, alloc=116.3MB, time=10.99 memory used=476.3MB, alloc=140.3MB, time=13.43 memory used=551.3MB, alloc=396.3MB, time=15.54 memory used=658.1MB, alloc=420.3MB, time=18.55 memory used=787.0MB, alloc=444.3MB, time=22.25 memory used=939.3MB, alloc=468.3MB, time=26.46 memory used=1077.2MB, alloc=492.3MB, time=30.47 memory used=1239.7MB, alloc=516.3MB, time=35.47 memory used=1393.9MB, alloc=540.3MB, time=40.48 memory used=1518.7MB, alloc=564.3MB, time=44.57 memory used=1692.4MB, alloc=588.3MB, time=50.36 memory used=1860.3MB, alloc=612.3MB, time=56.00 memory used=2045.8MB, alloc=636.3MB, time=61.84 memory used=2200.5MB, alloc=660.3MB, time=66.88 memory used=2330.6MB, alloc=684.3MB, time=71.38 memory used=2466.9MB, alloc=708.3MB, time=76.04 memory used=2594.8MB, alloc=732.3MB, time=80.59 memory used=2743.1MB, alloc=756.3MB, time=85.83 memory used=2869.3MB, alloc=780.3MB, time=90.43 memory used=2999.1MB, alloc=780.3MB, time=95.07 memory used=3123.3MB, alloc=804.3MB, time=99.55 memory used=3238.4MB, alloc=828.3MB, time=103.88 memory used=3365.9MB, alloc=828.3MB, time=108.37 memory used=3481.1MB, alloc=852.3MB, time=112.81 memory used=3593.2MB, alloc=876.3MB, time=117.15 |\^/| 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(); 1428273705 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-2 y + 10 z - 1, -19 y z - 19 y - 19, -x y + 20 y z + 7 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [18 x z + 6 x + 7, y - 17 y z, -5 x z - 7 z + 20] > Problem := [F,G]; 2 2 2 Problem := [[-2 y + 10 z - 1, -19 y z - 19 y - 19, -x y + 20 y z + 7 z ], 2 [18 x z + 6 x + 7, y - 17 y z, -5 x z - 7 z + 20]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=46.9MB, alloc=32.3MB, time=1.37 memory used=65.0MB, alloc=56.3MB, time=1.86 memory used=102.3MB, alloc=60.3MB, time=2.86 memory used=139.6MB, alloc=84.3MB, time=3.88 memory used=198.5MB, alloc=92.3MB, time=5.47 memory used=256.4MB, alloc=116.3MB, time=7.10 memory used=336.3MB, alloc=116.3MB, time=9.30 memory used=414.0MB, alloc=140.3MB, time=11.49 memory used=514.5MB, alloc=140.3MB, time=14.34 memory used=610.3MB, alloc=164.3MB, time=17.06 memory used=705.9MB, alloc=164.3MB, time=19.84 memory used=799.0MB, alloc=444.3MB, time=22.96 memory used=941.8MB, alloc=468.3MB, time=27.80 memory used=1103.6MB, alloc=492.3MB, time=33.10 memory used=1291.5MB, alloc=516.3MB, time=40.05 memory used=1506.7MB, alloc=540.3MB, time=48.14 memory used=1743.6MB, alloc=564.3MB, time=57.22 memory used=2002.1MB, alloc=588.3MB, time=68.14 memory used=2287.2MB, alloc=612.3MB, time=80.31 memory used=2595.2MB, alloc=636.3MB, time=94.64 memory used=2927.9MB, alloc=660.3MB, time=110.44 |\^/| 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(); 1428274005 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-15 x y + 19 y + 2 y, -6 x - 20 x z + 20 z, 16 x - 3 x z + 11 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [2 z + 6 y + 11 z, 11 y z + 7 x + 20 z, -12 y z - 15 z - 11 y] > Problem := [F,G]; Problem := [ 2 2 2 2 [-15 x y + 19 y + 2 y, -6 x - 20 x z + 20 z, 16 x - 3 x z + 11 z ], 2 2 [2 z + 6 y + 11 z, 11 y z + 7 x + 20 z, -12 y z - 15 z - 11 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.85 memory used=48.1MB, alloc=32.3MB, time=1.40 memory used=68.3MB, alloc=56.3MB, time=1.95 memory used=107.4MB, alloc=60.3MB, time=2.95 memory used=143.4MB, alloc=84.3MB, time=3.90 memory used=200.5MB, alloc=84.3MB, time=5.42 memory used=257.3MB, alloc=92.3MB, time=6.98 memory used=313.6MB, alloc=116.3MB, time=8.55 memory used=389.6MB, alloc=116.3MB, time=10.67 memory used=463.1MB, alloc=140.3MB, time=12.73 memory used=559.0MB, alloc=164.3MB, time=15.51 memory used=655.2MB, alloc=164.3MB, time=18.46 memory used=734.9MB, alloc=420.3MB, time=20.75 memory used=853.7MB, alloc=444.3MB, time=24.38 memory used=999.0MB, alloc=468.3MB, time=28.87 memory used=1168.2MB, alloc=492.3MB, time=34.29 memory used=1359.3MB, alloc=516.3MB, time=40.98 memory used=1575.1MB, alloc=540.3MB, time=48.23 memory used=1814.9MB, alloc=564.3MB, time=56.75 memory used=2072.2MB, alloc=588.3MB, time=66.61 memory used=2352.4MB, alloc=612.3MB, time=77.14 memory used=2648.3MB, alloc=636.3MB, time=88.61 memory used=2968.5MB, alloc=660.3MB, time=101.26 memory used=3287.7MB, alloc=684.3MB, time=114.14 memory used=3596.1MB, alloc=708.3MB, time=127.44 |\^/| 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(); 1428274305 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [x + 3 x y + 9 x z, 5 y - 15 z + 15, -16 x - 19 x y - 20 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [-8 x y - 7 x z - 14 z, -11 x y + 14 y - 6 z, 12 x y - 9 y - 7] > Problem := [F,G]; 2 2 2 Problem := [[x + 3 x y + 9 x z, 5 y - 15 z + 15, -16 x - 19 x y - 20 y], [-8 x y - 7 x z - 14 z, -11 x y + 14 y - 6 z, 12 x y - 9 y - 7]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.85 memory used=46.9MB, alloc=32.3MB, time=1.36 memory used=66.2MB, alloc=56.3MB, time=1.88 memory used=105.2MB, alloc=60.3MB, time=2.87 memory used=143.1MB, alloc=84.3MB, time=3.88 memory used=203.1MB, alloc=92.3MB, time=5.49 memory used=259.8MB, alloc=92.3MB, time=6.99 memory used=316.7MB, alloc=116.3MB, time=8.60 memory used=396.3MB, alloc=140.3MB, time=11.05 memory used=490.9MB, alloc=164.3MB, time=13.92 memory used=590.6MB, alloc=444.3MB, time=17.00 memory used=715.7MB, alloc=468.3MB, time=20.81 memory used=851.2MB, alloc=492.3MB, time=25.83 memory used=986.2MB, alloc=516.3MB, time=32.62 memory used=1133.0MB, alloc=540.3MB, time=40.53 memory used=1289.2MB, alloc=564.3MB, time=50.19 memory used=1466.7MB, alloc=588.3MB, time=61.33 memory used=1668.3MB, alloc=612.3MB, time=73.86 memory used=1893.7MB, alloc=612.3MB, time=87.91 memory used=2119.1MB, alloc=636.3MB, time=101.99 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428274605 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [14 y z - 5 z - 5 x, -13 y + 6 y z + 18 y, -2 x y + 2 x z - 8 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-4 x z + 5 z - 5 z, 9 x z + 11 y, -8 x z + 12 y + 20 z] > Problem := [F,G]; Problem := [ 2 2 2 [14 y z - 5 z - 5 x, -13 y + 6 y z + 18 y, -2 x y + 2 x z - 8 z ], 2 2 [-4 x z + 5 z - 5 z, 9 x z + 11 y, -8 x z + 12 y + 20 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.83 memory used=46.1MB, alloc=32.3MB, time=1.33 memory used=64.4MB, alloc=56.3MB, time=1.83 memory used=103.0MB, alloc=60.3MB, time=2.83 memory used=140.2MB, alloc=84.3MB, time=3.81 memory used=197.0MB, alloc=92.3MB, time=5.36 memory used=252.6MB, alloc=116.3MB, time=6.89 memory used=332.5MB, alloc=116.3MB, time=9.09 memory used=410.5MB, alloc=140.3MB, time=11.36 memory used=501.6MB, alloc=140.3MB, time=13.99 memory used=594.0MB, alloc=420.3MB, time=16.67 memory used=716.4MB, alloc=444.3MB, time=20.54 memory used=860.4MB, alloc=468.3MB, time=25.22 memory used=1023.6MB, alloc=492.3MB, time=30.50 memory used=1203.4MB, alloc=516.3MB, time=36.68 memory used=1383.8MB, alloc=540.3MB, time=42.92 memory used=1546.7MB, alloc=564.3MB, time=48.79 memory used=1709.3MB, alloc=588.3MB, time=55.07 memory used=1838.6MB, alloc=588.3MB, time=59.89 memory used=1949.6MB, alloc=612.3MB, time=63.41 memory used=2076.6MB, alloc=612.3MB, time=68.60 memory used=2197.5MB, alloc=612.3MB, time=73.59 memory used=2313.8MB, alloc=612.3MB, time=78.41 memory used=2403.2MB, alloc=612.3MB, time=81.62 memory used=2504.7MB, alloc=612.3MB, time=86.16 memory used=2597.4MB, alloc=612.3MB, time=90.43 memory used=2675.8MB, alloc=636.3MB, time=93.75 memory used=2762.8MB, alloc=636.3MB, time=97.88 memory used=2822.6MB, alloc=636.3MB, time=100.34 memory used=2913.7MB, alloc=636.3MB, time=104.74 memory used=2967.3MB, alloc=636.3MB, time=107.02 memory used=3221.9MB, alloc=660.3MB, time=115.86 |\^/| 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(); 1428274905 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [8 x - 10 y, 13 y - 16 y z - 11 z, 15 x - 10] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-9 y z + 6 z + 19 x, -12 x - 6 z - 8, -10 x y + 3 z + 8] > Problem := [F,G]; 2 2 2 Problem := [[8 x - 10 y, 13 y - 16 y z - 11 z, 15 x - 10], 2 2 2 2 [-9 y z + 6 z + 19 x, -12 x - 6 z - 8, -10 x y + 3 z + 8]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.87 memory used=47.9MB, alloc=32.3MB, time=1.42 memory used=67.6MB, alloc=56.3MB, time=1.94 memory used=106.8MB, alloc=60.3MB, time=2.95 memory used=146.8MB, alloc=60.3MB, time=3.94 memory used=184.9MB, alloc=84.3MB, time=4.98 memory used=219.4MB, alloc=84.3MB, time=5.87 memory used=283.6MB, alloc=116.3MB, time=7.53 memory used=366.2MB, alloc=372.3MB, time=9.73 memory used=448.0MB, alloc=396.3MB, time=11.99 memory used=559.9MB, alloc=396.3MB, time=14.91 memory used=670.0MB, alloc=420.3MB, time=17.77 memory used=798.2MB, alloc=444.3MB, time=21.49 memory used=940.3MB, alloc=444.3MB, time=25.10 memory used=1081.5MB, alloc=468.3MB, time=28.93 memory used=1205.1MB, alloc=492.3MB, time=32.14 memory used=1329.5MB, alloc=492.3MB, time=35.80 memory used=1454.9MB, alloc=516.3MB, time=39.61 memory used=1543.3MB, alloc=516.3MB, time=42.21 memory used=1647.4MB, alloc=516.3MB, time=45.48 memory used=1765.0MB, alloc=540.3MB, time=49.21 memory used=1898.6MB, alloc=540.3MB, time=53.50 memory used=2047.6MB, alloc=564.3MB, time=58.35 memory used=2195.1MB, alloc=588.3MB, time=63.57 memory used=2322.9MB, alloc=612.3MB, time=68.14 memory used=2448.8MB, alloc=612.3MB, time=72.70 memory used=2577.4MB, alloc=636.3MB, time=77.20 memory used=2721.7MB, alloc=660.3MB, time=83.69 memory used=2967.3MB, alloc=684.3MB, time=97.67 memory used=3221.7MB, alloc=708.3MB, time=112.98 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428275205 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-15 x + 12 y + 12 z, -8 + 20 x - 17 y, -5 x - 9] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [2 z + 3 x + 7 y, 16 x - 17 y + 6 y z, 6 x y - 5 y + 7 y z] > Problem := [F,G]; 2 Problem := [[-15 x + 12 y + 12 z, -8 + 20 x - 17 y, -5 x - 9], 2 2 2 2 [2 z + 3 x + 7 y, 16 x - 17 y + 6 y z, 6 x y - 5 y + 7 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.86 memory used=46.6MB, alloc=56.3MB, time=1.40 memory used=86.1MB, alloc=60.3MB, time=2.41 memory used=125.2MB, alloc=84.3MB, time=3.43 memory used=171.1MB, alloc=84.3MB, time=4.64 memory used=231.0MB, alloc=116.3MB, time=6.28 memory used=311.5MB, alloc=396.3MB, time=8.36 memory used=420.2MB, alloc=420.3MB, time=11.24 memory used=552.6MB, alloc=444.3MB, time=15.14 memory used=688.9MB, alloc=468.3MB, time=19.38 memory used=838.6MB, alloc=492.3MB, time=24.08 memory used=1001.2MB, alloc=516.3MB, time=29.20 memory used=1190.8MB, alloc=540.3MB, time=34.57 memory used=1383.6MB, alloc=564.3MB, time=40.57 memory used=1590.6MB, alloc=588.3MB, time=46.52 memory used=1791.0MB, alloc=612.3MB, time=55.02 memory used=1977.7MB, alloc=636.3MB, time=65.20 memory used=2173.5MB, alloc=660.3MB, time=76.39 memory used=2382.6MB, alloc=684.3MB, time=88.64 memory used=2606.7MB, alloc=708.3MB, time=102.07 memory used=2846.5MB, alloc=732.3MB, time=116.80 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428275505 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-15 y - 8 z - 4 x, -3 x + 12 y + 15, -6 x y - 10 x z + 17 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [17 x y + 19 y z - 4 z , 2 x - 14 y - 3, 11 x z - 20 x + 16 z] > Problem := [F,G]; 2 2 2 2 Problem := [[-15 y - 8 z - 4 x, -3 x + 12 y + 15, -6 x y - 10 x z + 17 z], 2 2 [17 x y + 19 y z - 4 z , 2 x - 14 y - 3, 11 x z - 20 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=4.3MB, alloc=32.3MB, time=0.30 memory used=55.8MB, alloc=68.3MB, time=1.64 memory used=105.4MB, alloc=68.3MB, time=2.90 memory used=152.6MB, alloc=68.3MB, time=4.13 memory used=198.8MB, alloc=100.3MB, time=5.33 memory used=267.1MB, alloc=100.3MB, time=7.07 memory used=333.5MB, alloc=124.3MB, time=8.84 memory used=414.0MB, alloc=380.3MB, time=11.01 memory used=504.9MB, alloc=404.3MB, time=13.48 memory used=621.6MB, alloc=428.3MB, time=16.77 memory used=760.0MB, alloc=452.3MB, time=20.87 memory used=919.5MB, alloc=476.3MB, time=25.61 memory used=1088.3MB, alloc=500.3MB, time=30.88 memory used=1221.5MB, alloc=500.3MB, time=35.08 memory used=1360.1MB, alloc=500.3MB, time=39.45 memory used=1490.0MB, alloc=524.3MB, time=43.53 memory used=1628.1MB, alloc=524.3MB, time=48.04 memory used=1731.7MB, alloc=548.3MB, time=51.20 memory used=1848.7MB, alloc=548.3MB, time=55.17 memory used=1946.4MB, alloc=572.3MB, time=58.62 memory used=2086.8MB, alloc=596.3MB, time=63.16 memory used=2234.8MB, alloc=596.3MB, time=67.81 memory used=2370.0MB, alloc=620.3MB, time=72.53 memory used=2499.4MB, alloc=644.3MB, time=77.17 memory used=2619.9MB, alloc=644.3MB, time=81.59 memory used=2732.3MB, alloc=668.3MB, time=85.76 memory used=2834.0MB, alloc=692.3MB, time=89.61 memory used=2943.6MB, alloc=692.3MB, time=93.69 memory used=3047.4MB, alloc=716.3MB, time=97.62 memory used=3146.2MB, alloc=716.3MB, time=101.32 memory used=3249.9MB, alloc=740.3MB, time=105.25 memory used=3349.8MB, alloc=740.3MB, time=109.01 memory used=3447.2MB, alloc=764.3MB, time=112.82 memory used=3541.7MB, alloc=764.3MB, time=116.60 memory used=3644.9MB, alloc=788.3MB, time=120.83 |\^/| 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(); 1428275805 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-8 y z - 19 z , -19 x y + 8 x + 11 z, -17 x + 17 z - 15 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-18 x z - 7 y + 7 z, -11 x - 8 y z + 5 z , 3 x + 20 x z + 2 x] > Problem := [F,G]; 2 2 2 Problem := [[-8 y z - 19 z , -19 x y + 8 x + 11 z, -17 x + 17 z - 15 z], 2 2 2 [-18 x z - 7 y + 7 z, -11 x - 8 y z + 5 z , 3 x + 20 x z + 2 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=46.8MB, alloc=32.3MB, time=1.35 memory used=66.4MB, alloc=56.3MB, time=1.87 memory used=105.0MB, alloc=60.3MB, time=2.87 memory used=140.9MB, alloc=84.3MB, time=3.84 memory used=199.2MB, alloc=92.3MB, time=5.42 memory used=256.2MB, alloc=116.3MB, time=6.94 memory used=333.9MB, alloc=116.3MB, time=9.08 memory used=409.3MB, alloc=140.3MB, time=11.20 memory used=504.3MB, alloc=164.3MB, time=13.82 memory used=598.4MB, alloc=420.3MB, time=16.50 memory used=714.3MB, alloc=444.3MB, time=19.78 memory used=860.6MB, alloc=468.3MB, time=23.92 memory used=1029.9MB, alloc=492.3MB, time=28.96 memory used=1218.6MB, alloc=516.3MB, time=34.70 memory used=1429.6MB, alloc=540.3MB, time=41.66 memory used=1666.1MB, alloc=564.3MB, time=49.65 memory used=1922.3MB, alloc=588.3MB, time=58.60 memory used=2201.4MB, alloc=612.3MB, time=68.58 memory used=2486.9MB, alloc=636.3MB, time=78.63 memory used=2798.9MB, alloc=660.3MB, time=90.77 memory used=3065.9MB, alloc=684.3MB, time=101.30 memory used=3366.7MB, alloc=708.3MB, time=114.24 |\^/| 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(); 1428276105 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-14 x y + 11 x z - 7 y z, 13 x y - 13 y z + 15 x, -6 x z + 7 z - 13] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [18 x y - 11 y - 6 x, -20 x - 5 x y + 5 y, -6 y + 10 z + 7 y] > Problem := [F,G]; Problem := [ 2 [-14 x y + 11 x z - 7 y z, 13 x y - 13 y z + 15 x, -6 x z + 7 z - 13], 2 2 2 2 [18 x y - 11 y - 6 x, -20 x - 5 x y + 5 y, -6 y + 10 z + 7 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=54.4MB, alloc=68.3MB, time=1.60 memory used=102.6MB, alloc=68.3MB, time=2.85 memory used=148.7MB, alloc=68.3MB, time=4.04 memory used=194.7MB, alloc=92.3MB, time=5.25 memory used=236.9MB, alloc=92.3MB, time=6.35 memory used=307.1MB, alloc=124.3MB, time=8.18 memory used=389.1MB, alloc=380.3MB, time=10.38 memory used=477.1MB, alloc=404.3MB, time=12.84 memory used=588.8MB, alloc=404.3MB, time=15.98 memory used=702.7MB, alloc=428.3MB, time=19.30 memory used=839.7MB, alloc=452.3MB, time=23.11 memory used=991.3MB, alloc=476.3MB, time=27.41 memory used=1163.2MB, alloc=500.3MB, time=32.79 memory used=1308.8MB, alloc=500.3MB, time=37.41 memory used=1448.6MB, alloc=524.3MB, time=41.93 memory used=1567.4MB, alloc=524.3MB, time=45.58 memory used=1696.3MB, alloc=524.3MB, time=50.01 memory used=1797.5MB, alloc=524.3MB, time=53.28 memory used=1918.2MB, alloc=548.3MB, time=57.13 memory used=2039.5MB, alloc=572.3MB, time=61.03 memory used=2159.4MB, alloc=572.3MB, time=64.92 memory used=2266.6MB, alloc=596.3MB, time=68.61 memory used=2369.4MB, alloc=596.3MB, time=72.06 memory used=2448.9MB, alloc=620.3MB, time=75.01 memory used=2580.9MB, alloc=620.3MB, time=79.09 memory used=2708.2MB, alloc=644.3MB, time=83.60 memory used=2821.8MB, alloc=668.3MB, time=87.73 memory used=2937.1MB, alloc=668.3MB, time=91.87 memory used=3039.8MB, alloc=692.3MB, time=95.67 memory used=3131.4MB, alloc=716.3MB, time=99.24 memory used=3212.9MB, alloc=716.3MB, time=102.55 memory used=3323.5MB, alloc=740.3MB, time=106.47 memory used=3422.8MB, alloc=740.3MB, time=110.26 memory used=3489.7MB, alloc=764.3MB, time=113.09 memory used=3583.1MB, alloc=764.3MB, time=116.79 memory used=3660.3MB, alloc=788.3MB, time=120.05 memory used=3741.8MB, alloc=788.3MB, time=123.43 memory used=3816.7MB, alloc=812.3MB, time=126.71 |\^/| 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(); 1428276405 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [16 x + 9 x z - 12 z , -20 x + 3 x y + 4 z , 15 x - 8 x y + 12 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [20 x - 15 x - 12 z, 15 x z - 19 y - 18, 6 x z - 19 y z + 20 y] > Problem := [F,G]; Problem := [ 2 2 2 2 2 [16 x + 9 x z - 12 z , -20 x + 3 x y + 4 z , 15 x - 8 x y + 12 z], 2 [20 x - 15 x - 12 z, 15 x z - 19 y - 18, 6 x z - 19 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=4.2MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.87 memory used=46.9MB, alloc=56.3MB, time=1.41 memory used=88.8MB, alloc=60.3MB, time=2.48 memory used=129.3MB, alloc=84.3MB, time=3.53 memory used=171.6MB, alloc=84.3MB, time=4.64 memory used=234.5MB, alloc=116.3MB, time=6.30 memory used=308.4MB, alloc=372.3MB, time=8.17 memory used=391.3MB, alloc=396.3MB, time=10.30 memory used=501.0MB, alloc=420.3MB, time=13.17 memory used=634.2MB, alloc=444.3MB, time=16.75 memory used=778.4MB, alloc=468.3MB, time=20.80 memory used=930.3MB, alloc=492.3MB, time=25.20 memory used=1059.3MB, alloc=492.3MB, time=28.94 memory used=1176.6MB, alloc=492.3MB, time=32.46 memory used=1304.3MB, alloc=516.3MB, time=36.44 memory used=1406.8MB, alloc=516.3MB, time=39.52 memory used=1499.4MB, alloc=516.3MB, time=42.55 memory used=1597.4MB, alloc=516.3MB, time=45.87 memory used=1686.6MB, alloc=516.3MB, time=49.05 memory used=1761.3MB, alloc=516.3MB, time=51.49 memory used=1842.9MB, alloc=516.3MB, time=54.45 memory used=1910.6MB, alloc=516.3MB, time=56.95 memory used=1983.9MB, alloc=540.3MB, time=59.66 memory used=2048.4MB, alloc=540.3MB, time=62.26 memory used=2111.3MB, alloc=540.3MB, time=64.90 memory used=2334.5MB, alloc=564.3MB, time=72.33 memory used=2561.9MB, alloc=588.3MB, time=79.65 memory used=2755.1MB, alloc=612.3MB, time=86.63 memory used=2940.2MB, alloc=636.3MB, time=92.98 memory used=3136.1MB, alloc=660.3MB, time=99.97 memory used=3325.3MB, alloc=684.3MB, time=106.47 memory used=3479.2MB, alloc=708.3MB, time=112.28 memory used=3624.1MB, alloc=708.3MB, time=117.61 memory used=3752.0MB, alloc=708.3MB, time=122.82 memory used=3887.2MB, alloc=708.3MB, time=128.53 memory used=4021.0MB, alloc=708.3MB, time=134.31 memory used=4137.3MB, alloc=708.3MB, time=139.87 |\^/| 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(); 1428276705 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [10 y + 6 z + 16 y, 17 x z + 2 y - 6 z, -13 x z + 17 y z - 4 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [20 x + 6 x z - 10 x, 16 x y + 10 x + 2, 19 x - 16 x - 8 z] > Problem := [F,G]; 2 2 2 Problem := [[10 y + 6 z + 16 y, 17 x z + 2 y - 6 z, -13 x z + 17 y z - 4 z], 2 2 [20 x + 6 x z - 10 x, 16 x y + 10 x + 2, 19 x - 16 x - 8 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.83 memory used=47.4MB, alloc=32.3MB, time=1.36 memory used=67.7MB, alloc=32.3MB, time=1.89 memory used=84.0MB, alloc=56.3MB, time=2.35 memory used=121.0MB, alloc=60.3MB, time=3.35 memory used=158.2MB, alloc=84.3MB, time=4.35 memory used=211.2MB, alloc=84.3MB, time=5.80 memory used=268.6MB, alloc=92.3MB, time=7.40 memory used=324.9MB, alloc=116.3MB, time=8.97 memory used=403.1MB, alloc=116.3MB, time=11.12 memory used=479.3MB, alloc=140.3MB, time=13.26 memory used=567.0MB, alloc=164.3MB, time=15.95 memory used=652.6MB, alloc=444.3MB, time=18.72 memory used=783.7MB, alloc=468.3MB, time=22.86 memory used=929.1MB, alloc=492.3MB, time=27.33 memory used=1084.1MB, alloc=516.3MB, time=32.23 memory used=1251.4MB, alloc=540.3MB, time=37.52 memory used=1424.2MB, alloc=564.3MB, time=43.19 memory used=1601.9MB, alloc=588.3MB, time=49.17 memory used=1784.8MB, alloc=612.3MB, time=55.50 memory used=1954.8MB, alloc=636.3MB, time=64.18 memory used=2131.5MB, alloc=660.3MB, time=73.89 memory used=2320.4MB, alloc=684.3MB, time=84.59 memory used=2522.5MB, alloc=708.3MB, time=96.26 memory used=2739.0MB, alloc=732.3MB, time=109.21 memory used=2970.3MB, alloc=756.3MB, time=123.12 memory used=3217.0MB, alloc=780.3MB, time=138.18 |\^/| 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(); 1428277005 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-9 y z + 12 x + 14 z, -10 x z + 4 z , x z + 20 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-3 x y + x z + 3, 12 x y + 5 x z - 15 y z, 14 x z - 5 y + x] > Problem := [F,G]; 2 Problem := [[-9 y z + 12 x + 14 z, -10 x z + 4 z , x z + 20 x], 2 [-3 x y + x z + 3, 12 x y + 5 x z - 15 y z, 14 x z - 5 y + x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.86 memory used=46.9MB, alloc=32.3MB, time=1.39 memory used=66.5MB, alloc=56.3MB, time=1.92 memory used=106.1MB, alloc=60.3MB, time=2.96 memory used=142.2MB, alloc=84.3MB, time=3.93 memory used=202.3MB, alloc=92.3MB, time=5.50 memory used=261.5MB, alloc=116.3MB, time=7.10 memory used=344.3MB, alloc=116.3MB, time=9.29 memory used=424.4MB, alloc=140.3MB, time=11.54 memory used=506.4MB, alloc=140.3MB, time=13.91 memory used=599.3MB, alloc=420.3MB, time=16.77 memory used=719.9MB, alloc=444.3MB, time=20.37 memory used=859.6MB, alloc=468.3MB, time=24.62 memory used=1019.6MB, alloc=492.3MB, time=29.54 memory used=1185.0MB, alloc=516.3MB, time=34.81 memory used=1328.3MB, alloc=540.3MB, time=39.67 memory used=1458.1MB, alloc=564.3MB, time=44.00 memory used=1572.8MB, alloc=564.3MB, time=48.00 memory used=1677.7MB, alloc=564.3MB, time=51.85 memory used=1784.3MB, alloc=564.3MB, time=55.76 memory used=1876.1MB, alloc=564.3MB, time=59.29 memory used=1937.1MB, alloc=564.3MB, time=61.52 memory used=2023.4MB, alloc=564.3MB, time=65.06 memory used=2092.9MB, alloc=564.3MB, time=68.00 memory used=2157.2MB, alloc=564.3MB, time=70.83 memory used=2389.4MB, alloc=588.3MB, time=79.72 memory used=2638.2MB, alloc=612.3MB, time=88.81 memory used=2870.0MB, alloc=636.3MB, time=97.18 memory used=3144.0MB, alloc=660.3MB, time=109.08 memory used=3358.6MB, alloc=684.3MB, time=118.10 memory used=3573.1MB, alloc=708.3MB, time=127.38 memory used=3757.8MB, alloc=732.3MB, time=135.42 memory used=3921.6MB, alloc=756.3MB, time=142.64 |\^/| 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(); 1428277305 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-2 y + 6 x + 6 z, -3 x z + 10 y z - 12 y, -14 x z - 3 y + 10 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [12 z - 8 z - 5, -8 y z + 2 z - 11 z, 17 y z - 17 z - 15 y] > Problem := [F,G]; 2 Problem := [[-2 y + 6 x + 6 z, -3 x z + 10 y z - 12 y, -14 x z - 3 y + 10 z], 2 2 2 [12 z - 8 z - 5, -8 y z + 2 z - 11 z, 17 y z - 17 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=4.3MB, alloc=32.3MB, time=0.30 memory used=25.6MB, alloc=32.3MB, time=0.82 memory used=45.9MB, alloc=32.3MB, time=1.32 memory used=64.7MB, alloc=56.3MB, time=1.81 memory used=101.8MB, alloc=60.3MB, time=2.77 memory used=138.0MB, alloc=84.3MB, time=3.72 memory used=196.3MB, alloc=92.3MB, time=5.27 memory used=253.0MB, alloc=116.3MB, time=6.79 memory used=332.5MB, alloc=116.3MB, time=8.92 memory used=409.2MB, alloc=140.3MB, time=11.03 memory used=498.9MB, alloc=164.3MB, time=13.48 memory used=576.8MB, alloc=420.3MB, time=15.75 memory used=696.0MB, alloc=444.3MB, time=19.19 memory used=837.5MB, alloc=468.3MB, time=23.40 memory used=1004.1MB, alloc=492.3MB, time=28.62 memory used=1193.0MB, alloc=516.3MB, time=34.57 memory used=1401.8MB, alloc=540.3MB, time=41.72 memory used=1631.3MB, alloc=564.3MB, time=49.94 memory used=1879.1MB, alloc=588.3MB, time=58.98 memory used=2147.5MB, alloc=612.3MB, time=68.55 memory used=2431.2MB, alloc=636.3MB, time=79.40 memory used=2718.0MB, alloc=660.3MB, time=89.63 memory used=3010.1MB, alloc=684.3MB, time=101.31 memory used=3282.0MB, alloc=708.3MB, time=110.96 memory used=3544.4MB, alloc=732.3MB, time=122.10 |\^/| 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(); 1428277605 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [2 x + 11 x z + 16, 7 x y + 6 z + 8, 4 x y + 2 y - 8 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-15 x y - 4 y - 7 y, -x - 9 y + 6, x y - 2 y z + 7] > Problem := [F,G]; 2 2 2 2 Problem := [[2 x + 11 x z + 16, 7 x y + 6 z + 8, 4 x y + 2 y - 8 z ], 2 2 2 [-15 x y - 4 y - 7 y, -x - 9 y + 6, x y - 2 y z + 7]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.84 memory used=48.1MB, alloc=32.3MB, time=1.38 memory used=67.9MB, alloc=56.3MB, time=1.90 memory used=109.2MB, alloc=60.3MB, time=2.94 memory used=148.2MB, alloc=84.3MB, time=3.95 memory used=208.4MB, alloc=92.3MB, time=5.51 memory used=269.0MB, alloc=116.3MB, time=7.08 memory used=351.0MB, alloc=116.3MB, time=9.14 memory used=429.0MB, alloc=396.3MB, time=11.24 memory used=535.0MB, alloc=420.3MB, time=14.10 memory used=666.1MB, alloc=444.3MB, time=17.54 memory used=820.6MB, alloc=468.3MB, time=21.84 memory used=965.8MB, alloc=492.3MB, time=26.01 memory used=1094.1MB, alloc=492.3MB, time=29.61 memory used=1212.2MB, alloc=492.3MB, time=33.06 memory used=1319.7MB, alloc=516.3MB, time=36.17 memory used=1418.9MB, alloc=516.3MB, time=39.14 memory used=1507.7MB, alloc=516.3MB, time=41.92 memory used=1623.3MB, alloc=540.3MB, time=46.00 memory used=1717.8MB, alloc=564.3MB, time=49.40 memory used=1824.6MB, alloc=564.3MB, time=53.16 memory used=1954.4MB, alloc=588.3MB, time=57.70 memory used=2074.6MB, alloc=612.3MB, time=62.00 memory used=2201.4MB, alloc=636.3MB, time=66.52 memory used=2304.4MB, alloc=636.3MB, time=70.36 memory used=2416.6MB, alloc=660.3MB, time=74.44 memory used=2519.8MB, alloc=684.3MB, time=78.25 memory used=2617.5MB, alloc=684.3MB, time=81.89 memory used=2704.3MB, alloc=708.3MB, time=85.22 memory used=2799.6MB, alloc=708.3MB, time=88.83 memory used=2873.0MB, alloc=732.3MB, time=91.86 memory used=2968.8MB, alloc=732.3MB, time=95.65 memory used=3267.2MB, alloc=756.3MB, time=105.66 memory used=3569.0MB, alloc=780.3MB, time=115.89 |\^/| 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(); 1428277905 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-18 x y - 3 x z + 6 y z, -19 x + 14 z, -8 x y + 3 y - 2] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [17 x - 6 x - 3, 6 x y + 7 x z - 11 y, 3 z + 6 z] > Problem := [F,G]; 2 2 Problem := [[-18 x y - 3 x z + 6 y z, -19 x + 14 z, -8 x y + 3 y - 2], 2 2 [17 x - 6 x - 3, 6 x y + 7 x z - 11 y, 3 z + 6 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.86 memory used=46.3MB, alloc=32.3MB, time=1.36 memory used=64.8MB, alloc=56.3MB, time=1.85 memory used=103.6MB, alloc=60.3MB, time=2.88 memory used=141.4MB, alloc=60.3MB, time=3.89 memory used=178.5MB, alloc=84.3MB, time=4.91 memory used=230.3MB, alloc=84.3MB, time=6.40 memory used=286.8MB, alloc=116.3MB, time=8.21 memory used=360.0MB, alloc=140.3MB, time=10.50 memory used=450.2MB, alloc=164.3MB, time=13.31 memory used=554.5MB, alloc=188.3MB, time=16.61 memory used=673.0MB, alloc=212.3MB, time=20.37 memory used=799.9MB, alloc=236.3MB, time=25.58 memory used=927.9MB, alloc=260.3MB, time=31.94 memory used=1068.3MB, alloc=284.3MB, time=39.40 memory used=1220.7MB, alloc=308.3MB, time=48.46 memory used=1391.6MB, alloc=332.3MB, time=59.06 memory used=1586.4MB, alloc=356.3MB, time=71.08 memory used=1805.2MB, alloc=356.3MB, time=84.54 memory used=2024.0MB, alloc=356.3MB, time=98.02 memory used=2242.7MB, alloc=380.3MB, time=111.50 |\^/| 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(); 1428278205 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-16 x - 16 z + 13, -19 x y - 10 x z - 11 y z, -5 x + 8 y + 5] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-17 y + 20 x - 11, -15 x + 10 x y - 5 y , -11 x z - 2 x - 6 z] > Problem := [F,G]; 2 2 Problem := [[-16 x - 16 z + 13, -19 x y - 10 x z - 11 y z, -5 x + 8 y + 5], 2 2 2 [-17 y + 20 x - 11, -15 x + 10 x y - 5 y , -11 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.85 memory used=47.9MB, alloc=32.3MB, time=1.38 memory used=68.1MB, alloc=56.3MB, time=1.93 memory used=109.2MB, alloc=60.3MB, time=3.00 memory used=149.4MB, alloc=84.3MB, time=4.10 memory used=211.9MB, alloc=92.3MB, time=6.01 memory used=269.3MB, alloc=116.3MB, time=7.71 memory used=345.0MB, alloc=140.3MB, time=10.09 memory used=432.4MB, alloc=164.3MB, time=14.37 memory used=533.2MB, alloc=164.3MB, time=20.16 N1 := 2593 > GB := Basis(F, plex(op(vars))); GB := 4 3 2 2 2 [176 x - 48 x - 319 x + 96 x + 143, -5 x + 8 y + 5, 16 x + 16 z - 13] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=639.6MB, alloc=164.3MB, time=24.51 N2 := 423 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-16 x - 16 z + 13, -19 x y - 10 x z - 11 y z, -5 x + 8 y + 5, 2 2 2 -17 y + 20 x - 11, -15 x + 10 x y - 5 y , -11 x z - 2 x - 6 z] > J:=[op(GB),op(G)]; 4 3 2 2 2 J := [176 x - 48 x - 319 x + 96 x + 143, -5 x + 8 y + 5, 16 x + 16 z - 13, 2 2 2 -17 y + 20 x - 11, -15 x + 10 x y - 5 y , -11 x z - 2 x - 6 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 12, 2, 2, 2, 1, 1, 2/3, 1/2, 1/2, 1/3, 5/18, 6, 11, 14, 11 4, 4, 2, 1, 1, 1/2, 1/3, --, 1/5, 3/20, 2, -2, -2] 20 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=658.3MB, alloc=164.3MB, time=25.19 |\^/| 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(); 1428278269 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [15 x y + 17 y z + 1, 5 y - 19 y - 12, 4 y - 20 y z - 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [5 y - z - 10, 16 - 9 x - 16 z, -2 x y + 13 z + 7] > Problem := [F,G]; 2 2 2 Problem := [[15 x y + 17 y z + 1, 5 y - 19 y - 12, 4 y - 20 y z - 2 z ], 2 [5 y - z - 10, 16 - 9 x - 16 z, -2 x y + 13 z + 7]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.1MB, alloc=40.3MB, time=1.01 memory used=58.0MB, alloc=40.3MB, time=1.68 memory used=83.0MB, alloc=64.3MB, time=2.38 memory used=129.9MB, alloc=68.3MB, time=3.65 memory used=174.6MB, alloc=92.3MB, time=4.84 memory used=241.5MB, alloc=100.3MB, time=6.63 memory used=304.7MB, alloc=124.3MB, time=8.43 memory used=392.2MB, alloc=124.3MB, time=10.90 memory used=478.7MB, alloc=148.3MB, time=13.53 memory used=567.8MB, alloc=148.3MB, time=16.15 memory used=647.2MB, alloc=428.3MB, time=18.55 memory used=781.3MB, alloc=428.3MB, time=22.56 memory used=912.8MB, alloc=452.3MB, time=26.72 memory used=1065.7MB, alloc=476.3MB, time=31.65 memory used=1240.1MB, alloc=500.3MB, time=37.21 memory used=1405.1MB, alloc=524.3MB, time=42.52 memory used=1551.0MB, alloc=524.3MB, time=47.01 memory used=1675.9MB, alloc=548.3MB, time=50.72 memory used=1800.5MB, alloc=548.3MB, time=54.52 memory used=1968.1MB, alloc=572.3MB, time=58.82 memory used=2188.9MB, alloc=572.3MB, time=63.27 memory used=2353.4MB, alloc=596.3MB, time=67.56 memory used=2479.3MB, alloc=596.3MB, time=71.50 memory used=2591.7MB, alloc=620.3MB, time=75.20 memory used=2701.7MB, alloc=620.3MB, time=78.77 memory used=2812.6MB, alloc=644.3MB, time=82.43 memory used=2921.8MB, alloc=668.3MB, time=86.12 memory used=3025.4MB, alloc=668.3MB, time=89.37 memory used=3154.4MB, alloc=692.3MB, time=93.22 memory used=3270.4MB, alloc=692.3MB, time=96.69 memory used=3317.7MB, alloc=692.3MB, time=98.78 memory used=3443.4MB, alloc=716.3MB, time=102.75 memory used=3533.2MB, alloc=716.3MB, time=105.68 memory used=3649.4MB, alloc=740.3MB, time=109.43 memory used=3770.1MB, alloc=740.3MB, time=113.44 memory used=3883.5MB, alloc=764.3MB, time=117.10 memory used=4000.1MB, alloc=764.3MB, time=120.85 memory used=4097.9MB, alloc=764.3MB, time=124.37 memory used=4462.9MB, alloc=788.3MB, time=134.86 |\^/| 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(); 1428278569 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [10 x - 19 x z - 19 y , -17 y + 13 z + 14 z, -20 x - 9 x - 15] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [9 x z - 5 z - 1, x - 7 y z + 18 z , 16 y - 6 y - 17 z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[10 x - 19 x z - 19 y , -17 y + 13 z + 14 z, -20 x - 9 x - 15], 2 2 2 [9 x z - 5 z - 1, x - 7 y z + 18 z , 16 y - 6 y - 17 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.6MB, alloc=32.3MB, time=0.89 memory used=45.9MB, alloc=56.3MB, time=1.43 memory used=85.2MB, alloc=60.3MB, time=2.46 memory used=123.6MB, alloc=84.3MB, time=3.50 memory used=162.2MB, alloc=84.3MB, time=4.51 memory used=227.1MB, alloc=92.3MB, time=6.13 memory used=288.1MB, alloc=116.3MB, time=7.76 memory used=372.2MB, alloc=116.3MB, time=10.02 memory used=452.0MB, alloc=396.3MB, time=12.34 memory used=556.0MB, alloc=420.3MB, time=15.18 memory used=683.2MB, alloc=420.3MB, time=18.68 memory used=815.2MB, alloc=444.3MB, time=22.17 memory used=951.4MB, alloc=468.3MB, time=25.66 memory used=1084.4MB, alloc=468.3MB, time=29.23 memory used=1209.6MB, alloc=492.3MB, time=32.29 memory used=1325.4MB, alloc=492.3MB, time=35.60 memory used=1431.1MB, alloc=492.3MB, time=38.65 memory used=1517.5MB, alloc=492.3MB, time=41.07 memory used=1623.8MB, alloc=516.3MB, time=44.63 memory used=1726.7MB, alloc=516.3MB, time=48.05 memory used=1816.7MB, alloc=516.3MB, time=50.88 memory used=1904.9MB, alloc=516.3MB, time=53.54 memory used=2002.2MB, alloc=516.3MB, time=56.76 memory used=2078.8MB, alloc=516.3MB, time=59.42 memory used=2176.8MB, alloc=516.3MB, time=63.26 memory used=2245.8MB, alloc=516.3MB, time=65.98 memory used=2303.8MB, alloc=516.3MB, time=68.09 memory used=2367.9MB, alloc=540.3MB, time=70.77 memory used=2414.2MB, alloc=540.3MB, time=72.37 memory used=2480.6MB, alloc=540.3MB, time=75.04 memory used=2532.1MB, alloc=540.3MB, time=76.89 memory used=2767.8MB, alloc=564.3MB, time=84.21 memory used=2984.7MB, alloc=588.3MB, time=91.17 memory used=3209.0MB, alloc=612.3MB, time=98.69 memory used=3409.0MB, alloc=636.3MB, time=105.98 memory used=3613.5MB, alloc=660.3MB, time=114.08 memory used=3793.9MB, alloc=684.3MB, time=120.07 memory used=3970.0MB, alloc=684.3MB, time=126.28 memory used=4138.3MB, alloc=684.3MB, time=132.31 memory used=4287.2MB, alloc=684.3MB, time=137.40 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428278869 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [11 y z + 10 y - 17, -15 x y + 8 z + 4 y, -7 x y + 18 y z + 12 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-6 x y - 14 y z - 6 z , 13 x y - 11 y z - y, -y - 19 x - 12] > Problem := [F,G]; 2 Problem := [[11 y z + 10 y - 17, -15 x y + 8 z + 4 y, -7 x y + 18 y z + 12 z], 2 2 [-6 x y - 14 y z - 6 z , 13 x y - 11 y z - y, -y - 19 x - 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=46.8MB, alloc=32.3MB, time=1.38 memory used=65.5MB, alloc=56.3MB, time=1.89 memory used=103.6MB, alloc=60.3MB, time=2.90 memory used=140.8MB, alloc=84.3MB, time=3.89 memory used=198.6MB, alloc=84.3MB, time=5.42 memory used=256.2MB, alloc=92.3MB, time=7.00 memory used=312.3MB, alloc=116.3MB, time=8.55 memory used=389.6MB, alloc=140.3MB, time=10.68 memory used=487.5MB, alloc=140.3MB, time=13.39 memory used=581.0MB, alloc=420.3MB, time=16.08 memory used=705.9MB, alloc=444.3MB, time=19.50 memory used=846.8MB, alloc=444.3MB, time=23.48 memory used=994.7MB, alloc=468.3MB, time=27.72 memory used=1163.6MB, alloc=492.3MB, time=33.08 memory used=1317.9MB, alloc=516.3MB, time=37.85 memory used=1476.7MB, alloc=540.3MB, time=43.10 memory used=1608.0MB, alloc=540.3MB, time=47.84 memory used=1752.3MB, alloc=540.3MB, time=52.88 memory used=1901.3MB, alloc=540.3MB, time=58.61 memory used=2016.6MB, alloc=540.3MB, time=62.69 memory used=2162.8MB, alloc=564.3MB, time=68.66 memory used=2285.5MB, alloc=564.3MB, time=73.98 memory used=2409.9MB, alloc=564.3MB, time=79.66 memory used=2530.4MB, alloc=564.3MB, time=85.07 memory used=2627.1MB, alloc=588.3MB, time=89.09 memory used=2744.4MB, alloc=588.3MB, time=94.43 memory used=2832.2MB, alloc=588.3MB, time=98.37 memory used=2912.1MB, alloc=588.3MB, time=101.98 memory used=3012.9MB, alloc=588.3MB, time=106.69 memory used=3079.1MB, alloc=588.3MB, time=109.55 memory used=3149.7MB, alloc=588.3MB, time=113.11 memory used=3406.9MB, alloc=612.3MB, time=122.97 memory used=3685.8MB, alloc=636.3MB, time=134.83 |\^/| 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(); 1428279169 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-20 x - y - 14 x, -5 x + 10 y z - 16, -15 x y + 16 x + 6 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [9 x y - 11 y - 5 y z, -16 x + 9 x - 8 z, -17 y + 2 z + 12 z] > Problem := [F,G]; 2 2 2 Problem := [[-20 x - y - 14 x, -5 x + 10 y z - 16, -15 x y + 16 x + 6 z], 2 2 2 2 [9 x y - 11 y - 5 y z, -16 x + 9 x - 8 z, -17 y + 2 z + 12 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.83 memory used=46.8MB, alloc=32.3MB, time=1.35 memory used=65.2MB, alloc=56.3MB, time=1.86 memory used=104.2MB, alloc=60.3MB, time=2.90 memory used=142.4MB, alloc=84.3MB, time=3.92 memory used=202.0MB, alloc=92.3MB, time=5.55 memory used=257.4MB, alloc=116.3MB, time=7.06 memory used=337.2MB, alloc=116.3MB, time=9.23 memory used=409.3MB, alloc=396.3MB, time=11.19 memory used=511.4MB, alloc=420.3MB, time=14.14 memory used=643.5MB, alloc=444.3MB, time=17.76 memory used=797.9MB, alloc=468.3MB, time=22.12 memory used=943.5MB, alloc=492.3MB, time=26.59 memory used=1083.2MB, alloc=492.3MB, time=30.83 memory used=1207.0MB, alloc=492.3MB, time=34.95 memory used=1323.8MB, alloc=516.3MB, time=38.95 memory used=1437.5MB, alloc=516.3MB, time=42.58 memory used=1512.8MB, alloc=516.3MB, time=45.24 memory used=1617.5MB, alloc=516.3MB, time=49.08 memory used=1710.9MB, alloc=516.3MB, time=52.38 memory used=1798.5MB, alloc=540.3MB, time=55.72 memory used=1864.2MB, alloc=540.3MB, time=58.37 memory used=1929.7MB, alloc=540.3MB, time=61.01 memory used=2008.6MB, alloc=540.3MB, time=64.18 memory used=2072.8MB, alloc=540.3MB, time=66.86 memory used=2137.8MB, alloc=540.3MB, time=69.61 memory used=2196.3MB, alloc=540.3MB, time=72.21 memory used=2231.7MB, alloc=540.3MB, time=73.85 memory used=2452.7MB, alloc=564.3MB, time=81.84 memory used=2673.0MB, alloc=588.3MB, time=89.75 memory used=2882.6MB, alloc=612.3MB, time=97.58 memory used=3096.4MB, alloc=636.3MB, time=105.23 memory used=3266.4MB, alloc=660.3MB, time=111.63 memory used=3452.5MB, alloc=684.3MB, time=119.12 memory used=3592.6MB, alloc=708.3MB, time=125.02 memory used=3741.8MB, alloc=708.3MB, time=130.59 memory used=3901.7MB, alloc=732.3MB, time=136.91 memory used=4044.5MB, alloc=756.3MB, time=142.75 |\^/| 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(); 1428279469 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [19 x z - 18 y, -11 x + 11 y z + 18 z, 4 x z - 2 y z - 16 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-18 x y + 2 x - 7 y, 2 x y - 14 x z - 12 y z, -7 z + z - 4] > Problem := [F,G]; 2 Problem := [[19 x z - 18 y, -11 x + 11 y z + 18 z, 4 x z - 2 y z - 16 z], 2 [-18 x y + 2 x - 7 y, 2 x y - 14 x z - 12 y z, -7 z + z - 4]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.85 memory used=47.2MB, alloc=32.3MB, time=1.40 memory used=66.6MB, alloc=56.3MB, time=1.92 memory used=106.4MB, alloc=60.3MB, time=2.97 memory used=144.6MB, alloc=84.3MB, time=4.01 memory used=202.9MB, alloc=92.3MB, time=5.61 memory used=258.7MB, alloc=116.3MB, time=7.14 memory used=337.2MB, alloc=116.3MB, time=9.28 memory used=414.9MB, alloc=140.3MB, time=11.48 memory used=501.0MB, alloc=140.3MB, time=13.96 memory used=592.2MB, alloc=420.3MB, time=16.73 memory used=713.3MB, alloc=444.3MB, time=20.30 memory used=856.8MB, alloc=468.3MB, time=24.79 memory used=1016.6MB, alloc=492.3MB, time=29.91 memory used=1181.6MB, alloc=516.3MB, time=35.28 memory used=1359.1MB, alloc=540.3MB, time=41.16 memory used=1547.5MB, alloc=564.3MB, time=47.70 memory used=1729.1MB, alloc=588.3MB, time=57.08 memory used=1916.6MB, alloc=612.3MB, time=67.55 memory used=2109.2MB, alloc=636.3MB, time=79.78 memory used=2323.1MB, alloc=660.3MB, time=93.50 memory used=2560.9MB, alloc=684.3MB, time=108.69 memory used=2822.7MB, alloc=708.3MB, time=125.29 memory used=3108.5MB, alloc=732.3MB, time=143.38 |\^/| 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(); 1428279769 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-15 y z - 13 x, -16 y z + 13 y + 2, -13 z + 13 z - 2] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [11 x z - 8 y - 5, -2 y - 13 z - 10, 19 x y - 16 x + 7 y] > Problem := [F,G]; 2 Problem := [[-15 y z - 13 x, -16 y z + 13 y + 2, -13 z + 13 z - 2], 2 2 [11 x z - 8 y - 5, -2 y - 13 z - 10, 19 x y - 16 x + 7 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=46.8MB, alloc=32.3MB, time=1.38 memory used=66.4MB, alloc=56.3MB, time=1.92 memory used=105.6MB, alloc=60.3MB, time=2.97 memory used=143.8MB, alloc=84.3MB, time=4.01 memory used=205.0MB, alloc=92.3MB, time=5.71 memory used=265.4MB, alloc=116.3MB, time=7.39 memory used=348.9MB, alloc=116.3MB, time=9.60 memory used=427.2MB, alloc=396.3MB, time=11.73 memory used=533.1MB, alloc=420.3MB, time=14.61 memory used=657.5MB, alloc=444.3MB, time=18.05 memory used=804.4MB, alloc=468.3MB, time=22.58 memory used=970.5MB, alloc=492.3MB, time=27.68 memory used=1103.1MB, alloc=492.3MB, time=31.57 memory used=1245.2MB, alloc=516.3MB, time=35.90 memory used=1370.1MB, alloc=516.3MB, time=39.58 memory used=1493.2MB, alloc=516.3MB, time=43.66 memory used=1633.7MB, alloc=540.3MB, time=48.81 memory used=1741.5MB, alloc=540.3MB, time=52.01 memory used=1847.7MB, alloc=540.3MB, time=55.72 memory used=1947.3MB, alloc=540.3MB, time=59.25 memory used=2047.6MB, alloc=540.3MB, time=63.12 memory used=2146.7MB, alloc=540.3MB, time=66.83 memory used=2238.7MB, alloc=540.3MB, time=70.59 memory used=2326.6MB, alloc=564.3MB, time=74.24 memory used=2398.9MB, alloc=564.3MB, time=77.30 memory used=2480.0MB, alloc=564.3MB, time=80.79 memory used=2554.5MB, alloc=564.3MB, time=83.80 memory used=2615.6MB, alloc=564.3MB, time=86.49 memory used=2678.8MB, alloc=564.3MB, time=89.02 memory used=2722.4MB, alloc=564.3MB, time=91.14 memory used=2953.9MB, alloc=588.3MB, time=99.43 memory used=3200.3MB, alloc=612.3MB, time=108.08 memory used=3431.1MB, alloc=636.3MB, time=116.26 memory used=3665.5MB, alloc=660.3MB, time=124.64 memory used=3905.2MB, alloc=684.3MB, time=133.30 memory used=4149.7MB, alloc=708.3MB, time=142.23 memory used=4396.0MB, alloc=732.3MB, time=151.58 |\^/| 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(); 1428280069 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-5 x y + 2 y + 9 y z, -19 y - 19 x - 14 z, -17 x - y - 14 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [14 y - 15 z + 19 x, 7 y + 19 y z - 17 z, -16 x - 9 y - 7 z] > Problem := [F,G]; 2 2 2 2 Problem := [[-5 x y + 2 y + 9 y z, -19 y - 19 x - 14 z, -17 x - y - 14 y], 2 2 2 [14 y - 15 z + 19 x, 7 y + 19 y z - 17 z, -16 x - 9 y - 7 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=46.8MB, alloc=32.3MB, time=1.38 memory used=65.3MB, alloc=56.3MB, time=1.90 memory used=104.6MB, alloc=60.3MB, time=2.93 memory used=141.6MB, alloc=84.3MB, time=3.94 memory used=202.5MB, alloc=92.3MB, time=5.57 memory used=261.6MB, alloc=116.3MB, time=7.15 memory used=342.4MB, alloc=140.3MB, time=9.37 memory used=434.6MB, alloc=396.3MB, time=12.07 memory used=539.5MB, alloc=420.3MB, time=14.92 memory used=661.4MB, alloc=444.3MB, time=18.40 memory used=807.9MB, alloc=468.3MB, time=22.53 memory used=951.1MB, alloc=492.3MB, time=26.78 memory used=1094.2MB, alloc=492.3MB, time=31.20 memory used=1226.4MB, alloc=516.3MB, time=35.62 memory used=1350.5MB, alloc=516.3MB, time=39.85 memory used=1463.3MB, alloc=516.3MB, time=43.55 memory used=1585.6MB, alloc=540.3MB, time=47.76 memory used=1703.2MB, alloc=540.3MB, time=52.24 memory used=1791.9MB, alloc=540.3MB, time=55.37 memory used=1887.8MB, alloc=540.3MB, time=58.86 memory used=1996.7MB, alloc=540.3MB, time=63.05 memory used=2078.5MB, alloc=540.3MB, time=66.10 memory used=2163.5MB, alloc=564.3MB, time=69.38 memory used=2230.8MB, alloc=564.3MB, time=72.16 memory used=2294.4MB, alloc=564.3MB, time=74.50 memory used=2349.7MB, alloc=564.3MB, time=77.01 memory used=2402.2MB, alloc=564.3MB, time=79.52 memory used=2640.4MB, alloc=588.3MB, time=87.61 memory used=2898.1MB, alloc=612.3MB, time=96.87 memory used=3104.5MB, alloc=636.3MB, time=104.05 memory used=3305.0MB, alloc=660.3MB, time=111.16 memory used=3537.8MB, alloc=684.3MB, time=120.64 memory used=3714.8MB, alloc=708.3MB, time=126.99 memory used=3855.0MB, alloc=732.3MB, time=131.91 memory used=4007.2MB, alloc=756.3MB, time=137.26 memory used=4123.3MB, alloc=756.3MB, time=141.89 memory used=4261.3MB, alloc=780.3MB, time=147.49 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428280369 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-x - 16 x y - 10 y z, 4 x z + 12 y + 13 y z, 9 x z + 3 y + 20 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [8 x - 6 x y + 9 z , 7 x - 3 z - 17 x, -16 y z - 18 x - 7 z] > Problem := [F,G]; Problem := [ 2 2 2 [-x - 16 x y - 10 y z, 4 x z + 12 y + 13 y z, 9 x z + 3 y + 20 z], 2 2 2 2 [8 x - 6 x y + 9 z , 7 x - 3 z - 17 x, -16 y z - 18 x - 7 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=46.6MB, alloc=32.3MB, time=1.39 memory used=64.5MB, alloc=56.3MB, time=1.88 memory used=106.0MB, alloc=60.3MB, time=2.92 memory used=145.1MB, alloc=84.3MB, time=3.98 memory used=238.1MB, alloc=124.3MB, time=6.47 memory used=326.9MB, alloc=380.3MB, time=8.84 memory used=416.1MB, alloc=404.3MB, time=11.25 memory used=536.7MB, alloc=428.3MB, time=14.14 memory used=672.1MB, alloc=452.3MB, time=17.87 memory used=802.2MB, alloc=452.3MB, time=21.30 memory used=934.7MB, alloc=476.3MB, time=25.09 memory used=1063.9MB, alloc=476.3MB, time=28.70 memory used=1179.5MB, alloc=476.3MB, time=31.98 memory used=1293.4MB, alloc=500.3MB, time=35.12 memory used=1420.7MB, alloc=500.3MB, time=39.10 memory used=1526.8MB, alloc=500.3MB, time=42.05 memory used=1615.8MB, alloc=500.3MB, time=44.64 memory used=1729.2MB, alloc=524.3MB, time=48.37 memory used=1818.9MB, alloc=524.3MB, time=51.38 memory used=1895.1MB, alloc=524.3MB, time=53.93 memory used=1967.0MB, alloc=524.3MB, time=56.37 memory used=2027.8MB, alloc=524.3MB, time=58.46 memory used=2094.6MB, alloc=524.3MB, time=60.77 memory used=2153.0MB, alloc=524.3MB, time=62.69 memory used=2210.7MB, alloc=524.3MB, time=64.77 memory used=2258.6MB, alloc=524.3MB, time=66.70 memory used=2459.7MB, alloc=548.3MB, time=73.09 memory used=2673.1MB, alloc=572.3MB, time=79.58 memory used=2851.3MB, alloc=596.3MB, time=84.81 memory used=3049.8MB, alloc=620.3MB, time=91.00 memory used=3234.3MB, alloc=644.3MB, time=97.17 memory used=3426.1MB, alloc=668.3MB, time=103.53 memory used=3589.4MB, alloc=692.3MB, time=109.32 memory used=3738.9MB, alloc=692.3MB, time=114.11 memory used=3898.6MB, alloc=716.3MB, time=119.97 memory used=4017.7MB, alloc=716.3MB, time=123.61 memory used=4131.1MB, alloc=740.3MB, time=126.73 memory used=4259.4MB, alloc=764.3MB, time=130.66 memory used=4681.8MB, alloc=788.3MB, time=144.42 |\^/| 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(); 1428280669 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [4 + 18 y - 7 z, 4 x - 13 x y + 12 z, -13 z - 8 y - 11 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-13 x z - x - 7 y, -14 y + 13 z - 12, -15 y z + 2 y + 20 z] > Problem := [F,G]; 2 2 Problem := [[4 + 18 y - 7 z, 4 x - 13 x y + 12 z, -13 z - 8 y - 11 z], 2 [-13 x z - x - 7 y, -14 y + 13 z - 12, -15 y z + 2 y + 20 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.86 memory used=46.2MB, alloc=32.3MB, time=1.37 memory used=65.6MB, alloc=56.3MB, time=1.90 memory used=104.4MB, alloc=60.3MB, time=2.90 memory used=142.2MB, alloc=84.3MB, time=3.91 memory used=203.3MB, alloc=92.3MB, time=5.57 memory used=262.5MB, alloc=92.3MB, time=7.17 memory used=321.4MB, alloc=116.3MB, time=8.81 memory used=402.9MB, alloc=116.3MB, time=11.08 memory used=483.5MB, alloc=140.3MB, time=13.37 memory used=563.5MB, alloc=396.3MB, time=15.75 memory used=666.9MB, alloc=420.3MB, time=18.70 memory used=790.8MB, alloc=444.3MB, time=22.26 memory used=935.5MB, alloc=468.3MB, time=26.47 memory used=1097.8MB, alloc=492.3MB, time=31.34 memory used=1244.3MB, alloc=516.3MB, time=36.11 memory used=1383.3MB, alloc=516.3MB, time=40.65 memory used=1500.6MB, alloc=516.3MB, time=44.77 memory used=1627.5MB, alloc=516.3MB, time=49.09 memory used=1748.8MB, alloc=516.3MB, time=53.36 memory used=1861.9MB, alloc=540.3MB, time=57.73 memory used=1965.0MB, alloc=540.3MB, time=61.58 memory used=2061.8MB, alloc=540.3MB, time=65.29 memory used=2155.4MB, alloc=540.3MB, time=68.99 memory used=2251.0MB, alloc=540.3MB, time=72.88 memory used=2348.1MB, alloc=540.3MB, time=77.05 memory used=2428.4MB, alloc=540.3MB, time=80.67 memory used=2505.6MB, alloc=540.3MB, time=84.17 memory used=2574.3MB, alloc=540.3MB, time=87.09 memory used=2648.5MB, alloc=540.3MB, time=90.51 memory used=2697.6MB, alloc=540.3MB, time=92.78 memory used=2917.3MB, alloc=564.3MB, time=101.27 memory used=3158.3MB, alloc=588.3MB, time=111.21 memory used=3396.2MB, alloc=612.3MB, time=120.65 memory used=3637.4MB, alloc=636.3MB, time=130.29 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428280969 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [14 z + 2 y + 14, x y - 11 y - 1, -16 x y - 16 y - 6 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [x - 3 y z + 4, 12 x + 18 y z + 20 z , 11 x + 18 x z - 10 y] > Problem := [F,G]; 2 2 Problem := [[14 z + 2 y + 14, x y - 11 y - 1, -16 x y - 16 y - 6 x], 2 2 2 2 [x - 3 y z + 4, 12 x + 18 y z + 20 z , 11 x + 18 x z - 10 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.9MB, alloc=40.3MB, time=1.03 memory used=59.3MB, alloc=44.3MB, time=1.74 memory used=85.8MB, alloc=68.3MB, time=2.46 memory used=133.8MB, alloc=68.3MB, time=3.71 memory used=178.6MB, alloc=68.3MB, time=4.92 memory used=224.5MB, alloc=100.3MB, time=6.20 memory used=292.8MB, alloc=124.3MB, time=8.01 memory used=373.8MB, alloc=124.3MB, time=10.21 memory used=448.1MB, alloc=404.3MB, time=12.26 memory used=561.9MB, alloc=404.3MB, time=15.36 memory used=677.1MB, alloc=428.3MB, time=18.63 memory used=814.6MB, alloc=452.3MB, time=22.76 memory used=950.7MB, alloc=476.3MB, time=26.90 memory used=1111.2MB, alloc=476.3MB, time=31.96 memory used=1246.3MB, alloc=500.3MB, time=35.99 memory used=1381.1MB, alloc=500.3MB, time=40.13 memory used=1494.2MB, alloc=500.3MB, time=43.70 memory used=1604.8MB, alloc=524.3MB, time=47.16 memory used=1710.4MB, alloc=524.3MB, time=50.58 memory used=1819.5MB, alloc=524.3MB, time=54.18 memory used=1909.5MB, alloc=524.3MB, time=57.19 memory used=2014.0MB, alloc=524.3MB, time=60.84 memory used=2100.4MB, alloc=524.3MB, time=63.87 memory used=2180.0MB, alloc=548.3MB, time=66.72 memory used=2255.2MB, alloc=548.3MB, time=69.27 memory used=2337.4MB, alloc=548.3MB, time=72.31 memory used=2418.2MB, alloc=572.3MB, time=75.37 memory used=2500.3MB, alloc=572.3MB, time=78.45 memory used=2579.4MB, alloc=596.3MB, time=81.51 memory used=2664.4MB, alloc=596.3MB, time=84.72 memory used=2754.5MB, alloc=596.3MB, time=87.98 memory used=2850.1MB, alloc=620.3MB, time=91.46 memory used=2935.1MB, alloc=620.3MB, time=94.72 memory used=3174.7MB, alloc=644.3MB, time=102.67 memory used=3425.2MB, alloc=668.3MB, time=111.14 memory used=3671.4MB, alloc=692.3MB, time=122.35 memory used=3897.7MB, alloc=716.3MB, time=135.05 |\^/| 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(); 1428281269 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-7 x y + 5 y - 15, -11 x + 4 y z - 14 y, 7 y z + 12 y + 20 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [8 x z + 18 x + 15 y, -3 x - 16 x y + 9 z , 11 x + 10 y z] > Problem := [F,G]; 2 Problem := [[-7 x y + 5 y - 15, -11 x + 4 y z - 14 y, 7 y z + 12 y + 20 z], 2 2 2 [8 x z + 18 x + 15 y, -3 x - 16 x y + 9 z , 11 x + 10 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.29 memory used=26.5MB, alloc=32.3MB, time=0.84 memory used=47.8MB, alloc=32.3MB, time=1.36 memory used=67.4MB, alloc=56.3MB, time=1.88 memory used=107.3MB, alloc=60.3MB, time=2.90 memory used=145.6MB, alloc=84.3MB, time=3.89 memory used=205.9MB, alloc=92.3MB, time=5.48 memory used=264.6MB, alloc=116.3MB, time=7.00 memory used=345.2MB, alloc=116.3MB, time=9.10 memory used=422.7MB, alloc=140.3MB, time=11.21 memory used=488.6MB, alloc=140.3MB, time=12.83 memory used=557.4MB, alloc=396.3MB, time=14.78 memory used=665.8MB, alloc=420.3MB, time=17.49 memory used=796.2MB, alloc=444.3MB, time=20.82 memory used=941.0MB, alloc=468.3MB, time=25.06 memory used=1059.1MB, alloc=492.3MB, time=28.35 memory used=1177.7MB, alloc=492.3MB, time=32.00 memory used=1284.0MB, alloc=492.3MB, time=35.17 memory used=1380.9MB, alloc=492.3MB, time=38.05 memory used=1476.8MB, alloc=516.3MB, time=41.06 memory used=1571.0MB, alloc=516.3MB, time=44.21 memory used=1654.9MB, alloc=516.3MB, time=46.97 memory used=1738.4MB, alloc=516.3MB, time=49.92 memory used=1825.4MB, alloc=516.3MB, time=53.01 memory used=1899.5MB, alloc=516.3MB, time=55.83 memory used=1974.7MB, alloc=516.3MB, time=58.65 memory used=2039.9MB, alloc=516.3MB, time=61.05 memory used=2087.1MB, alloc=516.3MB, time=63.05 memory used=2288.2MB, alloc=540.3MB, time=69.47 memory used=2512.6MB, alloc=564.3MB, time=76.79 memory used=2718.9MB, alloc=588.3MB, time=83.60 memory used=2891.5MB, alloc=612.3MB, time=89.79 memory used=3078.0MB, alloc=636.3MB, time=95.80 memory used=3250.8MB, alloc=660.3MB, time=102.24 memory used=3409.0MB, alloc=684.3MB, time=107.83 memory used=3571.9MB, alloc=684.3MB, time=114.22 memory used=3702.7MB, alloc=684.3MB, time=119.44 memory used=3814.1MB, alloc=684.3MB, time=123.94 memory used=3902.5MB, alloc=684.3MB, time=127.92 memory used=3999.9MB, alloc=684.3MB, time=132.01 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428281570 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [13 x + 19 y - 13 y, -19 - 15 x - 3 z, -13 y z - y + 17] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [4 y + 20 y z + 16 z , 18 x + 11 x y - 12 y , -7 x - 2 x + 15 z] > Problem := [F,G]; 2 2 Problem := [[13 x + 19 y - 13 y, -19 - 15 x - 3 z, -13 y z - y + 17], 2 2 2 2 2 [4 y + 20 y z + 16 z , 18 x + 11 x y - 12 y , -7 x - 2 x + 15 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.87 memory used=47.0MB, alloc=32.3MB, time=1.38 memory used=66.7MB, alloc=56.3MB, time=1.90 memory used=107.3MB, alloc=60.3MB, time=2.93 memory used=145.3MB, alloc=84.3MB, time=3.91 memory used=203.6MB, alloc=92.3MB, time=5.47 memory used=261.3MB, alloc=116.3MB, time=7.08 memory used=341.9MB, alloc=116.3MB, time=9.35 memory used=419.7MB, alloc=140.3MB, time=11.57 memory used=516.1MB, alloc=140.3MB, time=14.34 memory used=614.6MB, alloc=164.3MB, time=17.26 memory used=702.4MB, alloc=188.3MB, time=19.90 memory used=778.8MB, alloc=444.3MB, time=22.19 memory used=912.1MB, alloc=468.3MB, time=26.40 memory used=1052.4MB, alloc=492.3MB, time=30.81 memory used=1203.7MB, alloc=516.3MB, time=35.73 memory used=1365.4MB, alloc=540.3MB, time=41.06 memory used=1530.2MB, alloc=564.3MB, time=47.35 memory used=1685.9MB, alloc=588.3MB, time=55.48 memory used=1851.1MB, alloc=612.3MB, time=64.59 memory used=2029.2MB, alloc=636.3MB, time=74.91 memory used=2221.0MB, alloc=660.3MB, time=86.33 memory used=2422.2MB, alloc=684.3MB, time=99.55 memory used=2647.4MB, alloc=708.3MB, time=114.21 memory used=2896.6MB, alloc=732.3MB, time=130.45 |\^/| 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(); 1428281870 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-16 x + 16 x z - 13, -3 x - 8 x y - 14 x, -16 x - 11 y z - 18 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-14 x - 5 x y - 10, 12 x + 10 y + 6 z, -3 x y - 9 y + 15 z] > Problem := [F,G]; Problem := [ 2 2 2 [-16 x + 16 x z - 13, -3 x - 8 x y - 14 x, -16 x - 11 y z - 18 x], 2 2 [-14 x - 5 x y - 10, 12 x + 10 y + 6 z, -3 x y - 9 y + 15 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=47.1MB, alloc=32.3MB, time=1.41 memory used=66.2MB, alloc=56.3MB, time=1.92 memory used=105.7MB, alloc=60.3MB, time=2.97 memory used=144.6MB, alloc=84.3MB, time=3.97 memory used=207.6MB, alloc=92.3MB, time=5.68 memory used=268.5MB, alloc=116.3MB, time=7.33 memory used=352.5MB, alloc=116.3MB, time=9.58 memory used=433.4MB, alloc=396.3MB, time=11.85 memory used=537.3MB, alloc=420.3MB, time=14.76 memory used=664.4MB, alloc=444.3MB, time=18.55 memory used=799.7MB, alloc=468.3MB, time=22.82 memory used=947.8MB, alloc=492.3MB, time=27.53 memory used=1108.3MB, alloc=516.3MB, time=32.66 memory used=1279.0MB, alloc=540.3MB, time=38.27 memory used=1455.0MB, alloc=564.3MB, time=46.34 memory used=1627.3MB, alloc=588.3MB, time=55.75 memory used=1811.6MB, alloc=612.3MB, time=66.35 memory used=2007.7MB, alloc=636.3MB, time=78.35 memory used=2215.6MB, alloc=660.3MB, time=91.89 memory used=2447.5MB, alloc=684.3MB, time=106.94 memory used=2703.4MB, alloc=708.3MB, time=123.50 |\^/| 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(); 1428282170 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [20 x y - 11 z, -9 x + 18 y + 18 y z, -19 y - 10 x - 13] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [11 z + 2 x - 9 y, 6 x y - 20 y - 10 z , -17 y - 9 y z + 20] > Problem := [F,G]; 2 2 2 Problem := [[20 x y - 11 z, -9 x + 18 y + 18 y z, -19 y - 10 x - 13], 2 2 2 2 [11 z + 2 x - 9 y, 6 x y - 20 y - 10 z , -17 y - 9 y z + 20]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.85 memory used=47.6MB, alloc=32.3MB, time=1.39 memory used=65.8MB, alloc=56.3MB, time=1.89 memory used=105.1MB, alloc=60.3MB, time=2.92 memory used=142.6MB, alloc=84.3MB, time=3.92 memory used=206.5MB, alloc=92.3MB, time=5.54 memory used=270.8MB, alloc=116.3MB, time=7.12 memory used=347.9MB, alloc=116.3MB, time=9.12 memory used=421.6MB, alloc=396.3MB, time=11.03 memory used=529.9MB, alloc=420.3MB, time=13.74 memory used=664.5MB, alloc=444.3MB, time=17.00 memory used=814.3MB, alloc=468.3MB, time=21.08 memory used=970.6MB, alloc=492.3MB, time=25.30 memory used=1112.9MB, alloc=492.3MB, time=29.14 memory used=1234.7MB, alloc=516.3MB, time=32.13 memory used=1355.1MB, alloc=516.3MB, time=35.17 memory used=1451.6MB, alloc=516.3MB, time=37.87 memory used=1555.4MB, alloc=516.3MB, time=40.88 memory used=1648.2MB, alloc=540.3MB, time=43.39 memory used=1723.3MB, alloc=540.3MB, time=45.73 memory used=1798.6MB, alloc=540.3MB, time=48.10 memory used=1881.4MB, alloc=540.3MB, time=50.82 memory used=1939.1MB, alloc=540.3MB, time=52.62 memory used=2005.7MB, alloc=540.3MB, time=55.03 memory used=2049.7MB, alloc=540.3MB, time=56.61 memory used=2097.4MB, alloc=540.3MB, time=58.04 memory used=2167.6MB, alloc=540.3MB, time=60.69 memory used=2212.4MB, alloc=540.3MB, time=62.41 memory used=2448.5MB, alloc=564.3MB, time=68.37 memory used=2667.9MB, alloc=588.3MB, time=74.94 memory used=2853.7MB, alloc=612.3MB, time=80.03 memory used=3023.2MB, alloc=636.3MB, time=84.95 memory used=3201.8MB, alloc=636.3MB, time=89.85 memory used=3376.7MB, alloc=660.3MB, time=95.55 memory used=3537.5MB, alloc=660.3MB, time=100.46 memory used=3700.8MB, alloc=684.3MB, time=105.61 memory used=3845.4MB, alloc=684.3MB, time=110.74 memory used=3968.8MB, alloc=684.3MB, time=115.09 memory used=4101.4MB, alloc=684.3MB, time=120.04 memory used=4213.1MB, alloc=684.3MB, time=124.46 memory used=4316.4MB, alloc=684.3MB, time=129.09 memory used=4661.8MB, alloc=708.3MB, time=140.12 |\^/| 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(); 1428282470 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [12 y + 13 z - 9, -3 x + 17 x y + 16 y, -2 x + 11 x + 11 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [18 z - 11 x + 17 z, -12 x - 5 y z - 14 y, 4 x + 9 x y] > Problem := [F,G]; 2 2 2 Problem := [[12 y + 13 z - 9, -3 x + 17 x y + 16 y, -2 x + 11 x + 11 y], 2 2 2 [18 z - 11 x + 17 z, -12 x - 5 y z - 14 y, 4 x + 9 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.87 memory used=47.5MB, alloc=32.3MB, time=1.41 memory used=67.1MB, alloc=56.3MB, time=1.94 memory used=107.9MB, alloc=60.3MB, time=3.00 memory used=147.4MB, alloc=84.3MB, time=4.04 memory used=208.9MB, alloc=92.3MB, time=5.65 memory used=271.8MB, alloc=116.3MB, time=7.42 memory used=352.3MB, alloc=140.3MB, time=9.82 memory used=448.9MB, alloc=164.3MB, time=12.78 memory used=564.2MB, alloc=188.3MB, time=16.18 memory used=688.6MB, alloc=468.3MB, time=19.95 memory used=831.0MB, alloc=492.3MB, time=24.18 memory used=979.7MB, alloc=516.3MB, time=30.17 memory used=1124.3MB, alloc=540.3MB, time=37.49 memory used=1281.2MB, alloc=564.3MB, time=45.76 memory used=1453.0MB, alloc=588.3MB, time=55.06 memory used=1635.4MB, alloc=612.3MB, time=66.30 memory used=1839.6MB, alloc=636.3MB, time=78.98 memory used=2067.8MB, alloc=660.3MB, time=93.42 memory used=2319.8MB, alloc=660.3MB, time=108.92 memory used=2572.0MB, alloc=684.3MB, time=124.62 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428282770 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [2 x y - 4 x + 16, -16 y z - 6 x, 6 x z - 10 y z - 11 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-20 y - 8 z + 6 x, -10 x z - 16 y - 7 x, -16 y - 15 x + 1] > Problem := [F,G]; Problem := [[2 x y - 4 x + 16, -16 y z - 6 x, 6 x z - 10 y z - 11 z], 2 2 2 2 [-20 y - 8 z + 6 x, -10 x z - 16 y - 7 x, -16 y - 15 x + 1]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.85 memory used=47.4MB, alloc=32.3MB, time=1.37 memory used=67.5MB, alloc=56.3MB, time=1.90 memory used=108.0MB, alloc=60.3MB, time=2.90 memory used=147.0MB, alloc=84.3MB, time=3.93 memory used=208.1MB, alloc=92.3MB, time=5.52 memory used=268.0MB, alloc=116.3MB, time=7.07 memory used=349.4MB, alloc=116.3MB, time=9.17 memory used=428.1MB, alloc=140.3MB, time=11.29 memory used=509.7MB, alloc=140.3MB, time=13.63 memory used=602.8MB, alloc=164.3MB, time=16.56 memory used=708.5MB, alloc=188.3MB, time=19.84 memory used=805.0MB, alloc=468.3MB, time=22.94 memory used=944.7MB, alloc=492.3MB, time=28.34 memory used=1084.5MB, alloc=516.3MB, time=35.29 memory used=1227.9MB, alloc=540.3MB, time=44.07 memory used=1394.6MB, alloc=564.3MB, time=54.27 memory used=1585.3MB, alloc=588.3MB, time=65.82 memory used=1800.1MB, alloc=588.3MB, time=78.73 memory used=2015.0MB, alloc=612.3MB, time=91.63 N1 := 5905 > GB := Basis(F, plex(op(vars))); 2 GB := [6 x - 31 x + 80, -6 x + 11 + 10 y, 240 - 33 x + 208 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2262.6MB, alloc=612.3MB, time=99.43 memory used=2545.0MB, alloc=636.3MB, time=108.67 |\^/| 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(); 1428283070 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [4 x - 20 x z + 10 y, 11 z + 19 x - 5 y, -19 y z - 15 z - 15 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [12 x - 8 x y + 15 x z, 15 x + 5 y + 6 z , 7 x z + 9 y z - 1] > Problem := [F,G]; 2 2 2 Problem := [[4 x - 20 x z + 10 y, 11 z + 19 x - 5 y, -19 y z - 15 z - 15 y], 2 2 2 2 [12 x - 8 x y + 15 x z, 15 x + 5 y + 6 z , 7 x z + 9 y z - 1]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.88 memory used=47.0MB, alloc=32.3MB, time=1.42 memory used=67.2MB, alloc=60.3MB, time=1.96 memory used=108.3MB, alloc=60.3MB, time=2.99 memory used=142.7MB, alloc=84.3MB, time=3.87 memory used=205.6MB, alloc=92.3MB, time=5.51 memory used=267.6MB, alloc=116.3MB, time=7.15 memory used=345.1MB, alloc=140.3MB, time=9.24 memory used=409.2MB, alloc=396.3MB, time=10.98 memory used=514.4MB, alloc=420.3MB, time=13.62 memory used=645.5MB, alloc=444.3MB, time=16.95 memory used=773.1MB, alloc=468.3MB, time=20.28 memory used=885.6MB, alloc=468.3MB, time=23.35 memory used=993.4MB, alloc=492.3MB, time=26.20 memory used=1090.6MB, alloc=492.3MB, time=29.05 memory used=1182.2MB, alloc=492.3MB, time=31.74 memory used=1268.2MB, alloc=492.3MB, time=34.28 memory used=1355.0MB, alloc=492.3MB, time=37.09 memory used=1441.0MB, alloc=492.3MB, time=38.94 memory used=1501.0MB, alloc=492.3MB, time=40.03 memory used=1571.8MB, alloc=492.3MB, time=41.51 memory used=1634.4MB, alloc=516.3MB, time=42.66 memory used=1700.4MB, alloc=516.3MB, time=44.16 memory used=1752.8MB, alloc=516.3MB, time=45.20 memory used=1816.7MB, alloc=516.3MB, time=46.74 memory used=1860.9MB, alloc=516.3MB, time=47.76 memory used=2061.7MB, alloc=540.3MB, time=51.64 memory used=2248.8MB, alloc=564.3MB, time=55.05 memory used=2431.8MB, alloc=588.3MB, time=58.60 memory used=2592.8MB, alloc=612.3MB, time=61.75 memory used=2737.6MB, alloc=636.3MB, time=64.58 memory used=2893.4MB, alloc=660.3MB, time=67.87 memory used=3021.5MB, alloc=660.3MB, time=70.68 memory used=3170.0MB, alloc=660.3MB, time=74.10 memory used=3271.8MB, alloc=660.3MB, time=76.52 memory used=3382.6MB, alloc=660.3MB, time=79.14 memory used=3480.3MB, alloc=684.3MB, time=81.64 memory used=3823.9MB, alloc=708.3MB, time=88.42 memory used=4179.0MB, alloc=732.3MB, time=96.19 memory used=4559.6MB, alloc=756.3MB, time=103.90 memory used=4921.4MB, alloc=780.3MB, time=112.19 memory used=5266.5MB, alloc=804.3MB, time=119.46 memory used=5587.1MB, alloc=828.3MB, time=127.44 memory used=5865.0MB, alloc=852.3MB, time=134.49 memory used=6078.5MB, alloc=876.3MB, time=139.46 memory used=6319.2MB, alloc=900.3MB, time=146.39 |\^/| 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(); 1428283370 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [3 x z - 2 y + 16 x, -2 x - 8 x z + 6 z, -5 x + 8 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-20 x + 6 z - 3, x + 19 x z - 16 y z, 6 x y + 11 x - y] > Problem := [F,G]; 2 2 Problem := [[3 x z - 2 y + 16 x, -2 x - 8 x z + 6 z, -5 x + 8 z], 2 2 [-20 x + 6 z - 3, x + 19 x z - 16 y z, 6 x y + 11 x - y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.0MB, alloc=32.3MB, time=0.81 memory used=66.0MB, alloc=56.3MB, time=1.12 memory used=105.7MB, alloc=60.3MB, time=1.71 memory used=144.0MB, alloc=84.3MB, time=2.28 memory used=204.5MB, alloc=92.3MB, time=3.23 memory used=264.0MB, alloc=116.3MB, time=4.19 memory used=344.6MB, alloc=116.3MB, time=5.47 memory used=423.5MB, alloc=140.3MB, time=6.80 memory used=495.4MB, alloc=140.3MB, time=8.00 memory used=567.6MB, alloc=420.3MB, time=9.29 memory used=695.0MB, alloc=444.3MB, time=11.68 memory used=826.3MB, alloc=468.3MB, time=14.12 memory used=993.1MB, alloc=492.3MB, time=16.81 memory used=1164.3MB, alloc=516.3MB, time=19.83 memory used=1339.0MB, alloc=540.3MB, time=23.16 memory used=1524.5MB, alloc=564.3MB, time=26.64 memory used=1719.5MB, alloc=588.3MB, time=30.34 memory used=1926.1MB, alloc=612.3MB, time=34.29 memory used=2134.5MB, alloc=636.3MB, time=39.54 memory used=2324.8MB, alloc=660.3MB, time=46.05 memory used=2523.5MB, alloc=684.3MB, time=53.37 memory used=2735.1MB, alloc=708.3MB, time=61.53 memory used=2960.9MB, alloc=732.3MB, time=70.47 memory used=3201.5MB, alloc=756.3MB, time=79.90 memory used=3456.5MB, alloc=780.3MB, time=90.23 memory used=3725.3MB, alloc=804.3MB, time=101.50 memory used=4008.1MB, alloc=828.3MB, time=113.68 memory used=4314.9MB, alloc=852.3MB, time=126.91 |\^/| 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(); 1428283670 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [13 x + 16 x z + 7 z , 17 x + y z + 2 x, 4 x + 3 y z - 20] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [20 y - 3 x + 9 z, 3 x y - 6 z + 2 y, 20 x + 13 z - 11 z] > Problem := [F,G]; 2 2 2 2 Problem := [[13 x + 16 x z + 7 z , 17 x + y z + 2 x, 4 x + 3 y z - 20], 2 2 2 2 [20 y - 3 x + 9 z, 3 x y - 6 z + 2 y, 20 x + 13 z - 11 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.49 memory used=46.7MB, alloc=32.3MB, time=0.79 memory used=65.6MB, alloc=56.3MB, time=1.08 memory used=108.2MB, alloc=68.3MB, time=1.72 memory used=149.3MB, alloc=68.3MB, time=2.29 memory used=190.5MB, alloc=92.3MB, time=2.87 memory used=254.8MB, alloc=92.3MB, time=3.81 memory used=315.7MB, alloc=116.3MB, time=4.73 memory used=394.8MB, alloc=372.3MB, time=5.93 memory used=487.5MB, alloc=396.3MB, time=7.22 memory used=602.6MB, alloc=396.3MB, time=8.83 memory used=714.2MB, alloc=420.3MB, time=10.54 memory used=847.7MB, alloc=420.3MB, time=12.30 memory used=982.4MB, alloc=444.3MB, time=14.35 memory used=1105.2MB, alloc=444.3MB, time=16.13 memory used=1225.7MB, alloc=468.3MB, time=18.05 memory used=1337.0MB, alloc=468.3MB, time=19.86 memory used=1439.7MB, alloc=468.3MB, time=21.48 memory used=1534.1MB, alloc=492.3MB, time=22.96 memory used=1627.2MB, alloc=492.3MB, time=24.50 memory used=1715.2MB, alloc=492.3MB, time=26.04 memory used=1810.6MB, alloc=492.3MB, time=27.53 memory used=1881.2MB, alloc=492.3MB, time=28.79 memory used=1959.4MB, alloc=492.3MB, time=30.12 memory used=2029.0MB, alloc=492.3MB, time=31.35 memory used=2094.7MB, alloc=492.3MB, time=32.50 memory used=2173.8MB, alloc=516.3MB, time=33.97 memory used=2242.7MB, alloc=516.3MB, time=35.25 memory used=2298.7MB, alloc=516.3MB, time=36.39 memory used=2357.7MB, alloc=516.3MB, time=37.51 memory used=2418.4MB, alloc=516.3MB, time=38.73 memory used=2480.8MB, alloc=516.3MB, time=40.04 memory used=2549.3MB, alloc=516.3MB, time=41.56 memory used=2598.4MB, alloc=516.3MB, time=42.54 memory used=2677.5MB, alloc=516.3MB, time=44.46 memory used=2869.3MB, alloc=540.3MB, time=48.42 memory used=3094.2MB, alloc=564.3MB, time=52.19 memory used=3299.2MB, alloc=588.3MB, time=55.75 memory used=3490.2MB, alloc=612.3MB, time=58.95 memory used=3658.8MB, alloc=636.3MB, time=62.31 memory used=3833.2MB, alloc=636.3MB, time=65.53 memory used=4002.6MB, alloc=660.3MB, time=68.44 memory used=4147.1MB, alloc=660.3MB, time=71.02 memory used=4317.5MB, alloc=660.3MB, time=75.12 memory used=4447.2MB, alloc=684.3MB, time=77.36 memory used=4582.1MB, alloc=684.3MB, time=80.39 memory used=4701.2MB, alloc=684.3MB, time=83.14 memory used=4808.9MB, alloc=684.3MB, time=85.27 memory used=4905.6MB, alloc=684.3MB, time=87.87 memory used=5017.9MB, alloc=684.3MB, time=91.05 memory used=5374.2MB, alloc=708.3MB, time=97.42 memory used=5740.9MB, alloc=732.3MB, time=104.28 memory used=6119.7MB, alloc=756.3MB, time=111.96 memory used=6455.7MB, alloc=780.3MB, time=118.22 memory used=6821.3MB, alloc=804.3MB, time=125.60 memory used=7179.7MB, alloc=828.3MB, time=133.24 memory used=7494.1MB, alloc=852.3MB, time=139.74 |\^/| 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(); 1428283970 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-2 z - 14 x - 10 z, -5 x z + 18 y z - 20 z , 4 x y - 4 y + 10 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-11 x z - 18 z - 20, 19 x + 15 x z - y z, 12 y - 1] > Problem := [F,G]; 2 2 Problem := [[-2 z - 14 x - 10 z, -5 x z + 18 y z - 20 z , 4 x y - 4 y + 10 z], 2 2 [-11 x z - 18 z - 20, 19 x + 15 x z - y z, 12 y - 1]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=74.5MB, alloc=68.3MB, time=1.20 memory used=118.7MB, alloc=68.3MB, time=1.87 memory used=162.5MB, alloc=92.3MB, time=2.55 memory used=215.6MB, alloc=92.3MB, time=3.39 memory used=281.5MB, alloc=100.3MB, time=4.42 memory used=345.0MB, alloc=124.3MB, time=5.44 memory used=430.5MB, alloc=148.3MB, time=6.82 memory used=522.9MB, alloc=404.3MB, time=8.36 memory used=626.6MB, alloc=428.3MB, time=10.05 memory used=752.1MB, alloc=428.3MB, time=12.18 memory used=879.4MB, alloc=452.3MB, time=14.37 memory used=1029.3MB, alloc=476.3MB, time=17.08 memory used=1199.3MB, alloc=500.3MB, time=20.25 memory used=1379.9MB, alloc=524.3MB, time=23.57 memory used=1546.9MB, alloc=548.3MB, time=26.63 memory used=1691.5MB, alloc=548.3MB, time=29.27 memory used=1824.0MB, alloc=572.3MB, time=31.85 memory used=1958.7MB, alloc=572.3MB, time=34.62 memory used=2084.2MB, alloc=572.3MB, time=37.10 memory used=2198.0MB, alloc=596.3MB, time=39.65 memory used=2312.8MB, alloc=596.3MB, time=42.02 memory used=2425.1MB, alloc=620.3MB, time=44.41 memory used=2531.3MB, alloc=644.3MB, time=46.72 memory used=2634.1MB, alloc=644.3MB, time=48.95 memory used=2714.5MB, alloc=668.3MB, time=50.86 memory used=2836.5MB, alloc=692.3MB, time=53.40 memory used=2967.5MB, alloc=716.3MB, time=56.15 memory used=3076.4MB, alloc=716.3MB, time=58.57 memory used=3176.7MB, alloc=740.3MB, time=60.81 memory used=3292.3MB, alloc=764.3MB, time=63.37 memory used=3405.8MB, alloc=764.3MB, time=65.96 memory used=3497.4MB, alloc=788.3MB, time=68.26 memory used=3836.7MB, alloc=812.3MB, time=75.08 memory used=4171.5MB, alloc=836.3MB, time=81.90 memory used=4501.4MB, alloc=860.3MB, time=88.68 memory used=4826.2MB, alloc=884.3MB, time=95.56 memory used=5145.7MB, alloc=908.3MB, time=102.39 memory used=5461.7MB, alloc=932.3MB, time=109.18 memory used=5771.3MB, alloc=956.3MB, time=115.81 memory used=6084.7MB, alloc=980.3MB, time=122.45 memory used=6390.6MB, alloc=1004.3MB, time=129.07 memory used=6698.0MB, alloc=1028.3MB, time=135.84 |\^/| 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(); 1428284270 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-18 x - y + y z, 7 x + 8 z - 11, 11 x z - 16 y + 6] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-3 x z - 11 y z + 10 x, 15 x - 6 x y + 13 y , -17 x - 9 y - 12 y z] > Problem := [F,G]; 2 2 2 2 Problem := [[-18 x - y + y z, 7 x + 8 z - 11, 11 x z - 16 y + 6], 2 2 2 2 [-3 x z - 11 y z + 10 x, 15 x - 6 x y + 13 y , -17 x - 9 y - 12 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=48.2MB, alloc=32.3MB, time=0.82 memory used=68.2MB, alloc=56.3MB, time=1.13 memory used=108.3MB, alloc=60.3MB, time=1.72 memory used=148.1MB, alloc=84.3MB, time=2.30 memory used=211.0MB, alloc=92.3MB, time=3.25 memory used=276.2MB, alloc=116.3MB, time=4.21 memory used=349.4MB, alloc=116.3MB, time=5.31 memory used=418.0MB, alloc=372.3MB, time=6.39 memory used=501.7MB, alloc=396.3MB, time=7.67 memory used=607.5MB, alloc=420.3MB, time=9.29 memory used=739.0MB, alloc=444.3MB, time=11.30 memory used=857.0MB, alloc=468.3MB, time=13.10 memory used=974.2MB, alloc=468.3MB, time=14.76 memory used=1084.7MB, alloc=492.3MB, time=16.60 memory used=1194.6MB, alloc=492.3MB, time=18.53 memory used=1293.6MB, alloc=492.3MB, time=20.11 memory used=1378.1MB, alloc=492.3MB, time=21.41 memory used=1468.8MB, alloc=516.3MB, time=23.07 memory used=1553.6MB, alloc=516.3MB, time=24.63 memory used=1623.1MB, alloc=516.3MB, time=25.92 memory used=1694.8MB, alloc=516.3MB, time=27.41 memory used=1770.4MB, alloc=516.3MB, time=28.84 memory used=1819.0MB, alloc=516.3MB, time=29.95 memory used=1879.7MB, alloc=516.3MB, time=31.18 memory used=1946.1MB, alloc=516.3MB, time=32.55 memory used=2012.8MB, alloc=516.3MB, time=33.99 memory used=2063.8MB, alloc=516.3MB, time=35.04 memory used=2275.7MB, alloc=540.3MB, time=38.80 memory used=2501.6MB, alloc=564.3MB, time=43.17 memory used=2685.2MB, alloc=588.3MB, time=46.51 memory used=2876.4MB, alloc=612.3MB, time=50.56 memory used=3051.2MB, alloc=636.3MB, time=53.95 memory used=3235.8MB, alloc=660.3MB, time=57.68 memory used=3410.7MB, alloc=684.3MB, time=62.12 memory used=3547.3MB, alloc=684.3MB, time=65.03 memory used=3671.2MB, alloc=684.3MB, time=67.56 memory used=3794.3MB, alloc=708.3MB, time=70.16 memory used=3932.6MB, alloc=708.3MB, time=73.70 memory used=4043.8MB, alloc=708.3MB, time=76.64 memory used=4146.1MB, alloc=708.3MB, time=79.22 memory used=4516.6MB, alloc=732.3MB, time=86.12 memory used=4904.8MB, alloc=756.3MB, time=93.71 memory used=5307.6MB, alloc=780.3MB, time=101.38 memory used=5693.2MB, alloc=804.3MB, time=109.36 memory used=6030.3MB, alloc=828.3MB, time=116.88 memory used=6347.4MB, alloc=852.3MB, time=124.02 |\^/| 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(); 1428284570 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-8 x z - 5 z - 5 z, 3 x z - 19 y - 9 z, 14 z - 19 z - 9] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [13 x y - 19 x z + 9 y, -17 x z + 13 z , 13 x + 10 x z] > Problem := [F,G]; 2 2 2 Problem := [[-8 x z - 5 z - 5 z, 3 x z - 19 y - 9 z, 14 z - 19 z - 9], 2 2 [13 x y - 19 x z + 9 y, -17 x z + 13 z , 13 x + 10 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.47 memory used=46.0MB, alloc=32.3MB, time=0.76 memory used=64.2MB, alloc=56.3MB, time=1.04 memory used=103.2MB, alloc=60.3MB, time=1.62 memory used=141.0MB, alloc=84.3MB, time=2.19 memory used=197.6MB, alloc=92.3MB, time=3.05 memory used=255.0MB, alloc=116.3MB, time=3.92 memory used=335.9MB, alloc=116.3MB, time=5.12 memory used=413.6MB, alloc=140.3MB, time=6.33 memory used=511.4MB, alloc=164.3MB, time=7.82 memory used=597.1MB, alloc=420.3MB, time=9.29 memory used=715.9MB, alloc=444.3MB, time=11.43 memory used=841.8MB, alloc=468.3MB, time=13.69 memory used=979.4MB, alloc=492.3MB, time=16.14 memory used=1128.4MB, alloc=516.3MB, time=18.81 memory used=1285.0MB, alloc=540.3MB, time=21.68 memory used=1450.2MB, alloc=564.3MB, time=24.76 memory used=1622.4MB, alloc=588.3MB, time=27.96 memory used=1801.5MB, alloc=612.3MB, time=31.25 memory used=1987.0MB, alloc=636.3MB, time=34.77 memory used=2175.9MB, alloc=660.3MB, time=38.36 memory used=2369.5MB, alloc=684.3MB, time=42.14 memory used=2567.3MB, alloc=708.3MB, time=46.12 memory used=2755.5MB, alloc=732.3MB, time=51.67 memory used=2937.2MB, alloc=756.3MB, time=57.92 memory used=3126.9MB, alloc=780.3MB, time=64.80 memory used=3327.2MB, alloc=804.3MB, time=72.35 memory used=3539.5MB, alloc=828.3MB, time=80.50 memory used=3764.3MB, alloc=852.3MB, time=89.36 memory used=4002.7MB, alloc=876.3MB, time=98.94 memory used=4255.1MB, alloc=900.3MB, time=109.32 |\^/| 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(); 1428284870 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [x z - y - 5 z, 5 x z - 3 y z + 3 y, -17 x y - 16 y + 15 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-19 x y + 4 y z + 18 z, 9 x y - 10 x + 5, x y - 11 z - 13 x] > Problem := [F,G]; 2 2 Problem := [[x z - y - 5 z, 5 x z - 3 y z + 3 y, -17 x y - 16 y + 15 z ], 2 [-19 x y + 4 y z + 18 z, 9 x y - 10 x + 5, x y - 11 z - 13 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.80 memory used=66.9MB, alloc=56.3MB, time=1.10 memory used=105.9MB, alloc=60.3MB, time=1.67 memory used=142.7MB, alloc=84.3MB, time=2.23 memory used=203.0MB, alloc=92.3MB, time=3.20 memory used=262.0MB, alloc=116.3MB, time=4.16 memory used=343.0MB, alloc=116.3MB, time=5.44 memory used=422.2MB, alloc=140.3MB, time=6.76 memory used=515.3MB, alloc=140.3MB, time=8.29 memory used=592.6MB, alloc=420.3MB, time=9.62 memory used=716.9MB, alloc=444.3MB, time=11.79 memory used=862.5MB, alloc=468.3MB, time=14.24 memory used=1028.4MB, alloc=492.3MB, time=17.31 memory used=1197.8MB, alloc=516.3MB, time=20.75 memory used=1350.5MB, alloc=516.3MB, time=23.91 memory used=1514.3MB, alloc=540.3MB, time=27.41 memory used=1643.0MB, alloc=540.3MB, time=30.06 memory used=1763.6MB, alloc=564.3MB, time=32.53 memory used=1877.4MB, alloc=564.3MB, time=34.85 memory used=1977.8MB, alloc=564.3MB, time=36.82 memory used=2097.8MB, alloc=564.3MB, time=39.74 memory used=2195.5MB, alloc=564.3MB, time=42.52 memory used=2277.2MB, alloc=564.3MB, time=44.68 memory used=2373.9MB, alloc=564.3MB, time=47.18 memory used=2434.8MB, alloc=564.3MB, time=48.63 memory used=2515.5MB, alloc=564.3MB, time=50.75 memory used=2579.3MB, alloc=564.3MB, time=52.36 memory used=2628.2MB, alloc=564.3MB, time=53.90 memory used=2876.9MB, alloc=588.3MB, time=60.44 memory used=3139.4MB, alloc=612.3MB, time=67.13 memory used=3373.8MB, alloc=636.3MB, time=72.85 memory used=3570.5MB, alloc=660.3MB, time=77.71 memory used=3787.6MB, alloc=684.3MB, time=83.30 memory used=3994.0MB, alloc=708.3MB, time=88.63 memory used=4206.6MB, alloc=732.3MB, time=94.86 memory used=4388.5MB, alloc=732.3MB, time=100.22 memory used=4575.1MB, alloc=732.3MB, time=106.13 memory used=4754.1MB, alloc=756.3MB, time=112.13 memory used=4900.8MB, alloc=756.3MB, time=116.58 memory used=5019.1MB, alloc=756.3MB, time=120.74 memory used=5426.0MB, alloc=780.3MB, time=131.89 |\^/| 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(); 1428285170 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [16 x - 20 x y - 10 y , 9 x - 12 y + 15 z, -16 x z + 18 z + 10 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-7 y z - 4 z - 2, -9 x - 18 x y + 16 x, -18 x + 2 x y - 14 y z] > Problem := [F,G]; Problem := [ 2 2 2 2 2 [16 x - 20 x y - 10 y , 9 x - 12 y + 15 z, -16 x z + 18 z + 10 y], 2 2 [-7 y z - 4 z - 2, -9 x - 18 x y + 16 x, -18 x + 2 x y - 14 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=47.1MB, alloc=32.3MB, time=0.82 memory used=67.5MB, alloc=56.3MB, time=1.14 memory used=109.4MB, alloc=60.3MB, time=1.76 memory used=150.0MB, alloc=84.3MB, time=2.38 memory used=212.8MB, alloc=92.3MB, time=3.35 memory used=273.2MB, alloc=116.3MB, time=4.35 memory used=346.5MB, alloc=116.3MB, time=5.48 memory used=418.8MB, alloc=396.3MB, time=6.70 memory used=526.1MB, alloc=396.3MB, time=8.51 memory used=636.0MB, alloc=420.3MB, time=10.33 memory used=768.3MB, alloc=444.3MB, time=12.62 memory used=914.8MB, alloc=468.3MB, time=15.25 memory used=1052.9MB, alloc=492.3MB, time=17.73 memory used=1188.2MB, alloc=492.3MB, time=20.31 memory used=1304.4MB, alloc=492.3MB, time=22.52 memory used=1424.5MB, alloc=492.3MB, time=24.91 memory used=1518.0MB, alloc=516.3MB, time=26.80 memory used=1600.2MB, alloc=516.3MB, time=28.35 memory used=1689.2MB, alloc=516.3MB, time=30.11 memory used=1764.5MB, alloc=516.3MB, time=31.59 memory used=1831.8MB, alloc=516.3MB, time=32.86 memory used=1904.3MB, alloc=516.3MB, time=34.44 memory used=1966.6MB, alloc=516.3MB, time=35.82 memory used=2030.5MB, alloc=540.3MB, time=37.26 memory used=2101.1MB, alloc=540.3MB, time=38.82 memory used=2172.5MB, alloc=540.3MB, time=40.41 memory used=2237.0MB, alloc=564.3MB, time=41.96 memory used=2300.3MB, alloc=564.3MB, time=43.54 memory used=2367.0MB, alloc=588.3MB, time=45.17 memory used=2407.1MB, alloc=588.3MB, time=46.39 memory used=2639.2MB, alloc=612.3MB, time=51.02 memory used=2875.8MB, alloc=636.3MB, time=55.74 memory used=3117.0MB, alloc=660.3MB, time=60.65 memory used=3363.1MB, alloc=684.3MB, time=65.73 memory used=3614.1MB, alloc=708.3MB, time=70.87 memory used=3871.7MB, alloc=732.3MB, time=76.33 memory used=4141.6MB, alloc=756.3MB, time=81.81 memory used=4360.9MB, alloc=780.3MB, time=86.53 memory used=4628.1MB, alloc=804.3MB, time=91.74 memory used=4871.7MB, alloc=828.3MB, time=97.05 memory used=5165.1MB, alloc=852.3MB, time=103.46 memory used=5458.6MB, alloc=876.3MB, time=109.79 memory used=5753.5MB, alloc=900.3MB, time=116.28 memory used=6056.8MB, alloc=924.3MB, time=122.81 memory used=6320.8MB, alloc=948.3MB, time=132.02 |\^/| 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(); 1428285470 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [17 x + 9 y + 1, 9 x z + 3 y z - x, -8 y z - 13 z - 15 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [14 x - 9 y - 14 z, -17 x y + 15 y - 2 z , -6 x + 10 y + 17] > Problem := [F,G]; 2 2 Problem := [[17 x + 9 y + 1, 9 x z + 3 y z - x, -8 y z - 13 z - 15 y], 2 2 2 2 2 2 [14 x - 9 y - 14 z, -17 x y + 15 y - 2 z , -6 x + 10 y + 17]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=46.7MB, alloc=32.3MB, time=0.80 memory used=66.3MB, alloc=60.3MB, time=1.09 memory used=109.5MB, alloc=68.3MB, time=1.71 memory used=151.0MB, alloc=92.3MB, time=2.31 memory used=216.5MB, alloc=92.3MB, time=3.24 memory used=280.5MB, alloc=116.3MB, time=4.19 memory used=345.9MB, alloc=116.3MB, time=5.14 memory used=415.1MB, alloc=396.3MB, time=6.20 memory used=526.4MB, alloc=420.3MB, time=7.78 memory used=651.9MB, alloc=444.3MB, time=9.62 memory used=789.8MB, alloc=468.3MB, time=11.73 memory used=909.4MB, alloc=468.3MB, time=13.65 memory used=1015.7MB, alloc=492.3MB, time=15.24 memory used=1130.5MB, alloc=492.3MB, time=17.26 memory used=1221.4MB, alloc=492.3MB, time=18.70 memory used=1307.0MB, alloc=492.3MB, time=20.15 memory used=1387.6MB, alloc=492.3MB, time=21.58 memory used=1472.6MB, alloc=492.3MB, time=23.03 memory used=1562.9MB, alloc=492.3MB, time=24.75 memory used=1631.2MB, alloc=492.3MB, time=26.04 memory used=1704.8MB, alloc=516.3MB, time=27.43 memory used=1761.4MB, alloc=516.3MB, time=28.44 memory used=1823.0MB, alloc=516.3MB, time=29.77 memory used=1880.0MB, alloc=516.3MB, time=30.96 memory used=1929.1MB, alloc=516.3MB, time=32.02 memory used=2132.9MB, alloc=540.3MB, time=35.74 memory used=2313.3MB, alloc=564.3MB, time=39.04 memory used=2513.4MB, alloc=588.3MB, time=42.75 memory used=2682.4MB, alloc=612.3MB, time=46.04 memory used=2835.5MB, alloc=636.3MB, time=49.22 memory used=2976.8MB, alloc=660.3MB, time=51.80 memory used=3093.9MB, alloc=660.3MB, time=54.37 memory used=3214.4MB, alloc=660.3MB, time=56.73 memory used=3343.0MB, alloc=660.3MB, time=59.44 memory used=3436.3MB, alloc=660.3MB, time=61.56 memory used=3541.8MB, alloc=684.3MB, time=64.01 memory used=3626.6MB, alloc=684.3MB, time=66.25 memory used=3975.8MB, alloc=708.3MB, time=72.60 memory used=4332.7MB, alloc=732.3MB, time=79.39 memory used=4691.7MB, alloc=756.3MB, time=86.29 memory used=5007.0MB, alloc=780.3MB, time=92.89 memory used=5322.3MB, alloc=804.3MB, time=99.73 memory used=5645.4MB, alloc=828.3MB, time=106.68 memory used=5961.9MB, alloc=852.3MB, time=113.81 memory used=6296.7MB, alloc=876.3MB, time=120.82 memory used=6622.3MB, alloc=900.3MB, time=128.10 |\^/| 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(); 1428285770 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-4 x z - 4 z - 20 y, 20 x + 7 y - 14 z, 3 y - 12 y z + 5 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [18 y z - 15 x - 5, 5 x y - 11 y - 6, 19 x z + 16 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-4 x z - 4 z - 20 y, 20 x + 7 y - 14 z, 3 y - 12 y z + 5 z], 2 2 [18 y z - 15 x - 5, 5 x y - 11 y - 6, 19 x z + 16 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=32.3MB, time=0.81 memory used=67.6MB, alloc=56.3MB, time=1.11 memory used=108.8MB, alloc=60.3MB, time=1.71 memory used=146.6MB, alloc=84.3MB, time=2.29 memory used=207.3MB, alloc=92.3MB, time=3.22 memory used=269.0MB, alloc=116.3MB, time=4.15 memory used=350.4MB, alloc=116.3MB, time=5.40 memory used=423.7MB, alloc=396.3MB, time=6.60 memory used=528.7MB, alloc=396.3MB, time=8.25 memory used=632.4MB, alloc=420.3MB, time=9.89 memory used=756.3MB, alloc=444.3MB, time=11.93 memory used=899.4MB, alloc=468.3MB, time=14.53 memory used=1021.3MB, alloc=492.3MB, time=16.75 memory used=1146.4MB, alloc=492.3MB, time=19.05 memory used=1249.9MB, alloc=516.3MB, time=20.77 memory used=1368.1MB, alloc=516.3MB, time=23.22 memory used=1465.9MB, alloc=516.3MB, time=25.18 memory used=1546.9MB, alloc=516.3MB, time=26.63 memory used=1614.2MB, alloc=516.3MB, time=28.07 memory used=1690.9MB, alloc=516.3MB, time=29.67 memory used=1749.1MB, alloc=516.3MB, time=30.75 memory used=1818.6MB, alloc=516.3MB, time=32.32 memory used=1867.8MB, alloc=516.3MB, time=33.40 memory used=1915.1MB, alloc=540.3MB, time=34.60 memory used=2144.5MB, alloc=564.3MB, time=39.05 memory used=2382.6MB, alloc=588.3MB, time=43.67 memory used=2587.9MB, alloc=612.3MB, time=48.01 memory used=2799.8MB, alloc=636.3MB, time=52.48 memory used=2955.3MB, alloc=660.3MB, time=55.85 memory used=3136.7MB, alloc=660.3MB, time=60.19 memory used=3292.5MB, alloc=684.3MB, time=63.71 memory used=3435.6MB, alloc=684.3MB, time=67.78 memory used=3555.8MB, alloc=684.3MB, time=71.12 memory used=3667.5MB, alloc=684.3MB, time=74.28 memory used=3783.0MB, alloc=684.3MB, time=77.66 memory used=4127.7MB, alloc=708.3MB, time=86.17 memory used=4492.3MB, alloc=732.3MB, time=94.86 memory used=4868.0MB, alloc=756.3MB, time=104.39 memory used=5266.7MB, alloc=780.3MB, time=114.35 memory used=5621.5MB, alloc=804.3MB, time=123.01 memory used=5962.0MB, alloc=828.3MB, time=131.66 |\^/| 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(); 1428286070 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-18 x z - 5 x, -12 x - 9 x z - 6 y z, 5 x + 2 y - 2] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-8 y z + 2, -2 x , 16 x y + 5 y z - 13 x] > Problem := [F,G]; 2 2 Problem := [[-18 x z - 5 x, -12 x - 9 x z - 6 y z, 5 x + 2 y - 2], 2 [-8 y z + 2, -2 x , 16 x y + 5 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=46.4MB, alloc=32.3MB, time=0.78 memory used=65.3MB, alloc=56.3MB, time=1.06 memory used=104.7MB, alloc=60.3MB, time=1.66 memory used=142.6MB, alloc=84.3MB, time=2.24 memory used=201.2MB, alloc=92.3MB, time=3.15 memory used=257.1MB, alloc=116.3MB, time=4.04 memory used=336.7MB, alloc=140.3MB, time=5.46 memory used=429.5MB, alloc=164.3MB, time=7.10 memory used=538.1MB, alloc=188.3MB, time=9.03 memory used=643.3MB, alloc=468.3MB, time=10.95 memory used=781.5MB, alloc=492.3MB, time=13.52 memory used=929.2MB, alloc=516.3MB, time=17.36 memory used=1074.9MB, alloc=540.3MB, time=22.56 memory used=1232.9MB, alloc=564.3MB, time=28.08 memory used=1404.5MB, alloc=588.3MB, time=34.69 memory used=1588.9MB, alloc=612.3MB, time=42.47 memory used=1797.3MB, alloc=636.3MB, time=51.15 memory used=2029.7MB, alloc=660.3MB, time=60.47 memory used=2286.0MB, alloc=660.3MB, time=71.25 memory used=2542.2MB, alloc=660.3MB, time=81.88 memory used=2798.2MB, alloc=684.3MB, time=92.32 memory used=3078.3MB, alloc=684.3MB, time=103.58 memory used=3358.3MB, alloc=708.3MB, time=115.15 memory used=3662.4MB, alloc=732.3MB, time=127.57 |\^/| 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(); 1428286370 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-6 z - 9 x + 17 y, -2 x y - 11 y + 9 y z, 3 y z - z - 4 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-10 x z + 20 y z + 20, -11 x y - 5 y z + y, 13 x y + 13 y - 11 z ] > Problem := [F,G]; 2 2 2 Problem := [[-6 z - 9 x + 17 y, -2 x y - 11 y + 9 y z, 3 y z - z - 4 z], 2 2 [-10 x z + 20 y z + 20, -11 x y - 5 y z + y, 13 x y + 13 y - 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=46.6MB, alloc=32.3MB, time=0.76 memory used=64.9MB, alloc=56.3MB, time=1.05 memory used=103.0MB, alloc=60.3MB, time=1.61 memory used=138.8MB, alloc=84.3MB, time=2.16 memory used=195.7MB, alloc=92.3MB, time=3.08 memory used=250.0MB, alloc=116.3MB, time=3.96 memory used=323.4MB, alloc=140.3MB, time=5.12 memory used=415.5MB, alloc=140.3MB, time=6.55 memory used=507.5MB, alloc=164.3MB, time=8.02 memory used=603.1MB, alloc=444.3MB, time=9.62 memory used=740.3MB, alloc=468.3MB, time=11.96 memory used=902.4MB, alloc=492.3MB, time=14.87 memory used=1084.8MB, alloc=516.3MB, time=18.17 memory used=1283.3MB, alloc=540.3MB, time=22.45 memory used=1504.1MB, alloc=564.3MB, time=27.28 memory used=1738.4MB, alloc=588.3MB, time=32.57 memory used=1995.1MB, alloc=612.3MB, time=38.42 memory used=2264.6MB, alloc=636.3MB, time=44.57 memory used=2551.7MB, alloc=660.3MB, time=51.42 memory used=2825.2MB, alloc=684.3MB, time=56.25 memory used=3139.8MB, alloc=708.3MB, time=63.63 memory used=3425.6MB, alloc=732.3MB, time=70.64 memory used=3676.6MB, alloc=756.3MB, time=77.00 memory used=3938.2MB, alloc=780.3MB, time=84.05 memory used=4173.1MB, alloc=804.3MB, time=89.95 memory used=4398.0MB, alloc=828.3MB, time=96.57 memory used=4595.0MB, alloc=852.3MB, time=102.14 memory used=4781.5MB, alloc=876.3MB, time=107.45 memory used=4952.9MB, alloc=876.3MB, time=112.46 memory used=5125.2MB, alloc=876.3MB, time=117.69 memory used=5264.8MB, alloc=876.3MB, time=121.88 memory used=5409.6MB, alloc=876.3MB, time=126.86 memory used=5567.4MB, alloc=900.3MB, time=132.28 memory used=5651.0MB, alloc=900.3MB, time=135.00 |\^/| 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(); 1428286670 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [14 x - y + 17, -7 x + 7 z - 20, -17 y z - 17] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [11 y - 5 y + 17, 7 y z - 19 z + 18 y, -4 x z + 4 y - 19] > Problem := [F,G]; 2 2 2 2 Problem := [[14 x - y + 17, -7 x + 7 z - 20, -17 y z - 17], 2 2 [11 y - 5 y + 17, 7 y z - 19 z + 18 y, -4 x z + 4 y - 19]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.50 memory used=47.6MB, alloc=32.3MB, time=0.81 memory used=67.7MB, alloc=56.3MB, time=1.13 memory used=108.4MB, alloc=60.3MB, time=1.76 memory used=145.9MB, alloc=84.3MB, time=2.34 memory used=207.0MB, alloc=92.3MB, time=3.30 memory used=265.7MB, alloc=92.3MB, time=4.25 memory used=323.6MB, alloc=116.3MB, time=5.21 memory used=406.5MB, alloc=116.3MB, time=6.57 memory used=487.5MB, alloc=140.3MB, time=7.95 memory used=572.7MB, alloc=396.3MB, time=9.38 memory used=677.5MB, alloc=420.3MB, time=11.24 memory used=804.9MB, alloc=420.3MB, time=13.43 memory used=930.4MB, alloc=444.3MB, time=15.67 memory used=1076.6MB, alloc=468.3MB, time=18.19 memory used=1240.8MB, alloc=492.3MB, time=21.18 memory used=1414.6MB, alloc=516.3MB, time=24.24 memory used=1594.7MB, alloc=540.3MB, time=27.54 memory used=1784.1MB, alloc=564.3MB, time=31.06 memory used=1968.3MB, alloc=588.3MB, time=34.58 memory used=2162.3MB, alloc=612.3MB, time=38.26 memory used=2319.5MB, alloc=636.3MB, time=41.37 memory used=2503.7MB, alloc=660.3MB, time=44.98 memory used=2679.8MB, alloc=684.3MB, time=48.53 memory used=2825.3MB, alloc=708.3MB, time=51.53 memory used=2990.6MB, alloc=732.3MB, time=55.77 memory used=3226.7MB, alloc=756.3MB, time=64.11 memory used=3466.3MB, alloc=780.3MB, time=73.11 memory used=3715.7MB, alloc=804.3MB, time=82.94 memory used=3977.2MB, alloc=828.3MB, time=93.71 memory used=4251.2MB, alloc=852.3MB, time=105.04 memory used=4538.9MB, alloc=876.3MB, time=117.26 memory used=4841.0MB, alloc=900.3MB, time=130.18 |\^/| 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(); 1428286970 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-13 y z + 20 z - 17, -17 z + 12 x - z, 4 x z - 13 x + 15 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [13 x y - 8 y + 16 x, -19 x y + 7 y z, 11 x - 5 x + 3 y] > Problem := [F,G]; 2 Problem := [[-13 y z + 20 z - 17, -17 z + 12 x - z, 4 x z - 13 x + 15 y], 2 2 [13 x y - 8 y + 16 x, -19 x y + 7 y z, 11 x - 5 x + 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.5MB, alloc=32.3MB, time=0.79 memory used=67.3MB, alloc=56.3MB, time=1.09 memory used=107.3MB, alloc=60.3MB, time=1.68 memory used=144.2MB, alloc=84.3MB, time=2.23 memory used=201.8MB, alloc=92.3MB, time=3.11 memory used=259.2MB, alloc=92.3MB, time=3.98 memory used=315.9MB, alloc=116.3MB, time=4.87 memory used=392.4MB, alloc=116.3MB, time=6.08 memory used=469.1MB, alloc=140.3MB, time=7.36 memory used=566.5MB, alloc=164.3MB, time=9.17 memory used=676.8MB, alloc=188.3MB, time=11.20 memory used=787.8MB, alloc=468.3MB, time=13.24 memory used=927.1MB, alloc=492.3MB, time=15.79 memory used=1076.3MB, alloc=516.3MB, time=18.56 memory used=1235.6MB, alloc=540.3MB, time=21.56 memory used=1407.6MB, alloc=564.3MB, time=24.82 memory used=1582.3MB, alloc=588.3MB, time=29.04 memory used=1745.0MB, alloc=612.3MB, time=34.40 memory used=1916.7MB, alloc=636.3MB, time=40.53 memory used=2101.4MB, alloc=660.3MB, time=47.39 memory used=2300.5MB, alloc=684.3MB, time=55.14 memory used=2514.6MB, alloc=708.3MB, time=63.46 memory used=2744.3MB, alloc=732.3MB, time=72.41 memory used=2986.5MB, alloc=756.3MB, time=82.37 memory used=3246.4MB, alloc=780.3MB, time=93.41 memory used=3530.1MB, alloc=804.3MB, time=105.39 memory used=3837.9MB, alloc=828.3MB, time=118.32 memory used=4169.6MB, alloc=852.3MB, time=132.17 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428287270 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-4 x z + 9 z + 2 z, -7 y + 6 z + 6, 3 x y - 15 y + 17 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-16 x z - 4, -11 x - 7 x - 6 y, 13 x + 20 x y + 20 y z] > Problem := [F,G]; 2 2 2 Problem := [[-4 x z + 9 z + 2 z, -7 y + 6 z + 6, 3 x y - 15 y + 17 z], 2 2 [-16 x z - 4, -11 x - 7 x - 6 y, 13 x + 20 x y + 20 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.50 memory used=47.5MB, alloc=32.3MB, time=0.79 memory used=67.0MB, alloc=56.3MB, time=1.09 memory used=106.6MB, alloc=60.3MB, time=1.68 memory used=143.9MB, alloc=84.3MB, time=2.25 memory used=201.8MB, alloc=92.3MB, time=3.12 memory used=258.9MB, alloc=92.3MB, time=3.99 memory used=314.2MB, alloc=116.3MB, time=4.85 memory used=389.7MB, alloc=116.3MB, time=6.01 memory used=468.6MB, alloc=140.3MB, time=7.20 memory used=560.3MB, alloc=396.3MB, time=8.67 memory used=658.7MB, alloc=420.3MB, time=10.24 memory used=780.1MB, alloc=444.3MB, time=12.36 memory used=924.9MB, alloc=468.3MB, time=14.92 memory used=1091.9MB, alloc=492.3MB, time=17.88 memory used=1250.5MB, alloc=516.3MB, time=20.88 memory used=1401.0MB, alloc=516.3MB, time=23.81 memory used=1547.8MB, alloc=540.3MB, time=26.85 memory used=1678.4MB, alloc=540.3MB, time=29.66 memory used=1797.8MB, alloc=540.3MB, time=32.25 memory used=1917.5MB, alloc=540.3MB, time=35.09 memory used=2024.1MB, alloc=564.3MB, time=37.39 memory used=2136.6MB, alloc=564.3MB, time=40.11 memory used=2231.6MB, alloc=564.3MB, time=42.35 memory used=2318.3MB, alloc=564.3MB, time=44.50 memory used=2403.5MB, alloc=564.3MB, time=46.59 memory used=2479.2MB, alloc=588.3MB, time=48.42 memory used=2557.1MB, alloc=588.3MB, time=50.45 memory used=2621.8MB, alloc=588.3MB, time=52.05 memory used=2872.2MB, alloc=612.3MB, time=57.35 memory used=3111.6MB, alloc=636.3MB, time=62.08 memory used=3359.5MB, alloc=660.3MB, time=67.15 memory used=3630.7MB, alloc=684.3MB, time=72.26 memory used=3885.7MB, alloc=708.3MB, time=77.37 memory used=4137.3MB, alloc=732.3MB, time=82.51 memory used=4387.9MB, alloc=756.3MB, time=87.70 memory used=4638.4MB, alloc=780.3MB, time=92.97 memory used=4891.7MB, alloc=804.3MB, time=98.69 memory used=5146.0MB, alloc=828.3MB, time=104.57 memory used=5404.9MB, alloc=852.3MB, time=110.28 memory used=5660.9MB, alloc=876.3MB, time=115.83 memory used=5923.3MB, alloc=900.3MB, time=121.45 memory used=6187.0MB, alloc=924.3MB, time=127.17 memory used=6447.9MB, alloc=948.3MB, time=132.97 |\^/| 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(); 1428287570 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-20 x y + 4 y + 14 y, 2 x z - 9 y z + 9 z , 7 x z - 3 y + 9 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [9 y - 11 y z - 20 y, 8 x z - 13 x + 2 z, 7 x y - 6 z - 3] > Problem := [F,G]; 2 2 2 2 Problem := [[-20 x y + 4 y + 14 y, 2 x z - 9 y z + 9 z , 7 x z - 3 y + 9 z ], 2 [9 y - 11 y z - 20 y, 8 x z - 13 x + 2 z, 7 x y - 6 z - 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=46.8MB, alloc=32.3MB, time=0.75 memory used=66.5MB, alloc=56.3MB, time=1.05 memory used=105.0MB, alloc=60.3MB, time=1.60 memory used=140.4MB, alloc=84.3MB, time=2.10 memory used=195.4MB, alloc=84.3MB, time=2.90 memory used=250.2MB, alloc=108.3MB, time=3.73 memory used=325.3MB, alloc=116.3MB, time=4.87 memory used=397.3MB, alloc=140.3MB, time=6.07 memory used=488.5MB, alloc=164.3MB, time=7.60 memory used=584.2MB, alloc=420.3MB, time=9.21 memory used=698.7MB, alloc=444.3MB, time=11.25 memory used=835.9MB, alloc=468.3MB, time=13.68 memory used=994.3MB, alloc=492.3MB, time=16.53 memory used=1174.3MB, alloc=516.3MB, time=19.89 memory used=1381.3MB, alloc=540.3MB, time=24.19 memory used=1610.1MB, alloc=564.3MB, time=29.34 memory used=1861.0MB, alloc=588.3MB, time=35.13 memory used=2128.2MB, alloc=612.3MB, time=41.68 memory used=2419.7MB, alloc=636.3MB, time=49.74 memory used=2731.6MB, alloc=660.3MB, time=58.68 memory used=3059.6MB, alloc=684.3MB, time=67.84 memory used=3401.1MB, alloc=708.3MB, time=76.88 memory used=3758.7MB, alloc=732.3MB, time=86.96 memory used=4050.0MB, alloc=756.3MB, time=95.31 memory used=4317.6MB, alloc=780.3MB, time=102.60 memory used=4577.7MB, alloc=804.3MB, time=110.84 memory used=4835.9MB, alloc=828.3MB, time=119.41 memory used=5015.1MB, alloc=852.3MB, time=123.84 memory used=5192.2MB, alloc=876.3MB, time=128.12 |\^/| 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(); 1428287870 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-11 x y + 2 y + 4 y z, 7 x y + 11 x z - 2 y z, -15 x - 17 y - 16 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [18 y z + 2 y - 18 z, -19 x + 3 y + 14 y, -13 x z - 18 z ] > Problem := [F,G]; Problem := [ 2 2 [-11 x y + 2 y + 4 y z, 7 x y + 11 x z - 2 y z, -15 x - 17 y - 16 z], 2 2 2 [18 y z + 2 y - 18 z, -19 x + 3 y + 14 y, -13 x z - 18 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=47.2MB, alloc=32.3MB, time=0.80 memory used=66.6MB, alloc=56.3MB, time=1.11 memory used=105.0MB, alloc=60.3MB, time=1.69 memory used=140.2MB, alloc=84.3MB, time=2.24 memory used=198.9MB, alloc=92.3MB, time=3.12 memory used=254.8MB, alloc=116.3MB, time=3.98 memory used=334.2MB, alloc=116.3MB, time=5.17 memory used=410.8MB, alloc=140.3MB, time=6.38 memory used=500.6MB, alloc=164.3MB, time=7.84 memory used=585.8MB, alloc=420.3MB, time=9.27 memory used=696.7MB, alloc=444.3MB, time=11.16 memory used=832.3MB, alloc=468.3MB, time=13.42 memory used=993.8MB, alloc=492.3MB, time=16.30 memory used=1173.6MB, alloc=516.3MB, time=19.67 memory used=1379.7MB, alloc=540.3MB, time=23.96 memory used=1608.9MB, alloc=564.3MB, time=28.54 memory used=1854.6MB, alloc=588.3MB, time=33.72 memory used=2115.9MB, alloc=612.3MB, time=39.40 memory used=2399.5MB, alloc=636.3MB, time=46.05 memory used=2679.9MB, alloc=660.3MB, time=52.93 memory used=2943.8MB, alloc=684.3MB, time=58.67 memory used=3181.6MB, alloc=708.3MB, time=63.63 memory used=3439.8MB, alloc=732.3MB, time=68.92 memory used=3689.5MB, alloc=756.3MB, time=74.22 memory used=3931.7MB, alloc=780.3MB, time=79.37 memory used=4201.8MB, alloc=804.3MB, time=85.22 memory used=4473.0MB, alloc=828.3MB, time=91.22 memory used=4712.4MB, alloc=852.3MB, time=96.46 memory used=4961.6MB, alloc=876.3MB, time=102.00 memory used=5266.0MB, alloc=900.3MB, time=108.86 memory used=5565.1MB, alloc=924.3MB, time=115.50 memory used=5858.9MB, alloc=948.3MB, time=122.21 memory used=6154.1MB, alloc=972.3MB, time=129.19 memory used=6407.1MB, alloc=996.3MB, time=138.93 |\^/| 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(); 1428288170 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [18 x + 13 x z + x, 14 x z + 5 x + 4 z, -4 x - 13 x y - 12 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-13 x + 15 x z - 15 y z, -9 x y + 13 x z - 12, 17 x - 19 z] > Problem := [F,G]; 2 2 Problem := [[18 x + 13 x z + x, 14 x z + 5 x + 4 z, -4 x - 13 x y - 12 y z], 2 [-13 x + 15 x z - 15 y z, -9 x y + 13 x z - 12, 17 x - 19 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=46.5MB, alloc=56.3MB, time=0.81 memory used=87.0MB, alloc=60.3MB, time=1.44 memory used=126.5MB, alloc=84.3MB, time=2.05 memory used=172.6MB, alloc=84.3MB, time=2.78 memory used=230.9MB, alloc=116.3MB, time=3.73 memory used=312.0MB, alloc=140.3MB, time=5.01 memory used=396.0MB, alloc=140.3MB, time=6.27 memory used=473.9MB, alloc=420.3MB, time=7.52 memory used=605.5MB, alloc=444.3MB, time=9.53 memory used=757.6MB, alloc=468.3MB, time=12.10 memory used=927.2MB, alloc=492.3MB, time=15.05 memory used=1084.6MB, alloc=516.3MB, time=18.00 memory used=1210.8MB, alloc=516.3MB, time=20.46 memory used=1345.2MB, alloc=516.3MB, time=23.10 memory used=1465.4MB, alloc=540.3MB, time=25.55 memory used=1582.9MB, alloc=540.3MB, time=27.96 memory used=1685.4MB, alloc=540.3MB, time=30.16 memory used=1784.2MB, alloc=540.3MB, time=32.65 memory used=1874.2MB, alloc=540.3MB, time=34.67 memory used=1959.2MB, alloc=540.3MB, time=36.54 memory used=2036.4MB, alloc=564.3MB, time=38.33 memory used=2111.1MB, alloc=564.3MB, time=40.21 memory used=2177.8MB, alloc=564.3MB, time=42.00 memory used=2236.5MB, alloc=564.3MB, time=43.44 memory used=2464.8MB, alloc=588.3MB, time=48.15 memory used=2710.9MB, alloc=612.3MB, time=53.01 memory used=2931.1MB, alloc=636.3MB, time=57.59 memory used=3179.6MB, alloc=660.3MB, time=62.80 memory used=3428.8MB, alloc=684.3MB, time=67.91 memory used=3681.2MB, alloc=708.3MB, time=73.23 memory used=3938.2MB, alloc=732.3MB, time=78.74 memory used=4199.5MB, alloc=756.3MB, time=84.35 memory used=4468.2MB, alloc=780.3MB, time=90.14 memory used=4741.8MB, alloc=804.3MB, time=96.25 memory used=5021.2MB, alloc=828.3MB, time=102.34 memory used=5307.0MB, alloc=852.3MB, time=108.31 memory used=5611.3MB, alloc=876.3MB, time=114.75 memory used=5920.7MB, alloc=900.3MB, time=121.14 memory used=6253.2MB, alloc=924.3MB, time=127.75 memory used=6565.0MB, alloc=948.3MB, time=134.44 memory used=6871.7MB, alloc=972.3MB, time=141.24 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428288470 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-14 x y + 2 z - 4, 15 x + 14 x y - 5 y, -15 x - 2 x y - 17 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [6 x y + 13 y - 18 z , -4 x z - 10 x + 12 y, -7 y z + 5 x + 3 z] > Problem := [F,G]; 2 2 2 Problem := [[-14 x y + 2 z - 4, 15 x + 14 x y - 5 y, -15 x - 2 x y - 17 y ], 2 2 [6 x y + 13 y - 18 z , -4 x z - 10 x + 12 y, -7 y z + 5 x + 3 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.4MB, alloc=32.3MB, time=0.82 memory used=67.6MB, alloc=56.3MB, time=1.14 memory used=109.5MB, alloc=60.3MB, time=1.78 memory used=148.9MB, alloc=84.3MB, time=2.39 memory used=211.4MB, alloc=92.3MB, time=3.39 memory used=271.5MB, alloc=116.3MB, time=4.36 memory used=352.5MB, alloc=116.3MB, time=5.70 memory used=430.6MB, alloc=396.3MB, time=7.11 memory used=539.1MB, alloc=420.3MB, time=8.98 memory used=671.4MB, alloc=444.3MB, time=11.35 memory used=824.1MB, alloc=468.3MB, time=14.10 memory used=979.5MB, alloc=468.3MB, time=16.85 memory used=1098.1MB, alloc=492.3MB, time=19.08 memory used=1220.0MB, alloc=492.3MB, time=21.29 memory used=1342.2MB, alloc=492.3MB, time=23.60 memory used=1458.1MB, alloc=516.3MB, time=26.13 memory used=1554.3MB, alloc=516.3MB, time=28.05 memory used=1650.7MB, alloc=516.3MB, time=30.10 memory used=1719.1MB, alloc=516.3MB, time=31.43 memory used=1814.0MB, alloc=540.3MB, time=33.45 memory used=1915.3MB, alloc=540.3MB, time=35.59 memory used=2002.7MB, alloc=564.3MB, time=37.53 memory used=2099.6MB, alloc=564.3MB, time=39.61 memory used=2211.8MB, alloc=588.3MB, time=42.00 memory used=2307.0MB, alloc=612.3MB, time=44.13 memory used=2391.9MB, alloc=612.3MB, time=46.11 memory used=2489.7MB, alloc=636.3MB, time=48.33 memory used=2580.2MB, alloc=660.3MB, time=50.42 memory used=2655.3MB, alloc=660.3MB, time=52.27 memory used=2728.7MB, alloc=660.3MB, time=54.07 memory used=2803.9MB, alloc=684.3MB, time=55.89 memory used=2882.8MB, alloc=684.3MB, time=57.83 memory used=3153.8MB, alloc=708.3MB, time=63.21 memory used=3429.1MB, alloc=732.3MB, time=68.77 memory used=3705.4MB, alloc=756.3MB, time=74.40 memory used=3982.7MB, alloc=780.3MB, time=80.13 memory used=4255.9MB, alloc=804.3MB, time=85.86 memory used=4526.1MB, alloc=828.3MB, time=94.40 memory used=4776.3MB, alloc=852.3MB, time=104.53 memory used=5035.4MB, alloc=876.3MB, time=115.11 memory used=5306.7MB, alloc=900.3MB, time=126.64 memory used=5590.5MB, alloc=924.3MB, time=139.14 |\^/| 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(); 1428288770 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [13 z + 15 x, -x - 19 y + 15 z, -12 x z - 19 y z + 8 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-18 z - 7 x + 15 z, 11 y z - 6 z - 15 y, 2 x - 5 z + 19] > Problem := [F,G]; 2 Problem := [[13 z + 15 x, -x - 19 y + 15 z, -12 x z - 19 y z + 8 z], 2 2 2 [-18 z - 7 x + 15 z, 11 y z - 6 z - 15 y, 2 x - 5 z + 19]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.81 memory used=67.3MB, alloc=56.3MB, time=1.10 memory used=106.3MB, alloc=60.3MB, time=1.70 memory used=144.1MB, alloc=84.3MB, time=2.28 memory used=204.8MB, alloc=92.3MB, time=3.20 memory used=264.5MB, alloc=116.3MB, time=4.17 memory used=347.2MB, alloc=116.3MB, time=5.46 memory used=426.3MB, alloc=140.3MB, time=6.75 memory used=511.5MB, alloc=164.3MB, time=8.19 memory used=586.9MB, alloc=420.3MB, time=9.48 memory used=709.9MB, alloc=444.3MB, time=11.62 memory used=855.2MB, alloc=468.3MB, time=14.30 memory used=1022.6MB, alloc=492.3MB, time=17.45 memory used=1208.6MB, alloc=516.3MB, time=21.18 memory used=1417.2MB, alloc=540.3MB, time=25.43 memory used=1643.3MB, alloc=564.3MB, time=30.11 memory used=1884.7MB, alloc=588.3MB, time=34.59 memory used=2131.2MB, alloc=612.3MB, time=39.14 memory used=2379.6MB, alloc=636.3MB, time=43.73 memory used=2626.6MB, alloc=660.3MB, time=48.28 memory used=2870.7MB, alloc=684.3MB, time=52.90 memory used=3115.6MB, alloc=708.3MB, time=57.53 memory used=3361.4MB, alloc=732.3MB, time=62.24 memory used=3605.4MB, alloc=756.3MB, time=66.87 memory used=3850.0MB, alloc=780.3MB, time=71.61 memory used=4097.0MB, alloc=804.3MB, time=76.34 memory used=4329.9MB, alloc=828.3MB, time=81.21 memory used=4533.0MB, alloc=852.3MB, time=87.68 memory used=4733.3MB, alloc=876.3MB, time=94.72 memory used=4940.3MB, alloc=900.3MB, time=102.45 memory used=5157.0MB, alloc=924.3MB, time=110.61 memory used=5383.8MB, alloc=948.3MB, time=119.40 |\^/| 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(); 1428289070 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [x z - 15 y - 9 z , -14 y z + 8, 18 x z - 6 y - 20 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-13 x - 4 y z - 7 z, -x y - 16 x z + 13 y z, -19 x z - 18 y - 13 z ] > Problem := [F,G]; 2 2 2 Problem := [[x z - 15 y - 9 z , -14 y z + 8, 18 x z - 6 y - 20 x], 2 2 2 [-13 x - 4 y z - 7 z, -x y - 16 x z + 13 y z, -19 x z - 18 y - 13 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.8MB, alloc=32.3MB, time=0.48 memory used=47.1MB, alloc=32.3MB, time=0.76 memory used=66.4MB, alloc=60.3MB, time=1.06 memory used=106.7MB, alloc=60.3MB, time=1.64 memory used=147.3MB, alloc=60.3MB, time=2.20 memory used=186.1MB, alloc=84.3MB, time=2.76 memory used=221.7MB, alloc=84.3MB, time=3.26 memory used=283.0MB, alloc=92.3MB, time=4.13 memory used=342.6MB, alloc=116.3MB, time=5.00 memory used=422.2MB, alloc=140.3MB, time=6.19 memory used=487.2MB, alloc=396.3MB, time=7.16 memory used=592.7MB, alloc=420.3MB, time=8.75 memory used=726.7MB, alloc=444.3MB, time=10.69 memory used=860.6MB, alloc=468.3MB, time=12.65 memory used=986.2MB, alloc=468.3MB, time=14.63 memory used=1109.4MB, alloc=492.3MB, time=16.58 memory used=1216.6MB, alloc=492.3MB, time=18.29 memory used=1335.5MB, alloc=492.3MB, time=20.32 memory used=1416.1MB, alloc=492.3MB, time=21.56 memory used=1501.7MB, alloc=492.3MB, time=23.09 memory used=1585.8MB, alloc=492.3MB, time=24.63 memory used=1664.3MB, alloc=492.3MB, time=26.22 memory used=1755.0MB, alloc=516.3MB, time=28.06 memory used=1822.3MB, alloc=516.3MB, time=29.33 memory used=1893.4MB, alloc=516.3MB, time=30.79 memory used=1962.9MB, alloc=516.3MB, time=32.36 memory used=2030.7MB, alloc=516.3MB, time=33.86 memory used=2083.9MB, alloc=516.3MB, time=35.00 memory used=2293.6MB, alloc=540.3MB, time=38.63 memory used=2496.8MB, alloc=564.3MB, time=42.20 memory used=2688.5MB, alloc=588.3MB, time=45.75 memory used=2870.8MB, alloc=612.3MB, time=48.95 memory used=3044.4MB, alloc=636.3MB, time=52.54 memory used=3187.9MB, alloc=636.3MB, time=55.35 memory used=3328.2MB, alloc=660.3MB, time=58.21 memory used=3483.4MB, alloc=660.3MB, time=61.98 memory used=3636.5MB, alloc=660.3MB, time=65.69 memory used=3758.1MB, alloc=684.3MB, time=68.74 memory used=3846.7MB, alloc=684.3MB, time=70.75 memory used=3932.5MB, alloc=684.3MB, time=73.02 memory used=4026.1MB, alloc=684.3MB, time=75.42 memory used=4376.7MB, alloc=708.3MB, time=82.26 memory used=4741.9MB, alloc=732.3MB, time=89.40 memory used=5132.3MB, alloc=756.3MB, time=97.14 memory used=5520.2MB, alloc=780.3MB, time=105.93 memory used=5872.1MB, alloc=804.3MB, time=112.74 memory used=6189.0MB, alloc=828.3MB, time=119.24 |\^/| 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(); 1428289370 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [11 x + 18 x y - 4 x z, 11 x - 17 y + 12 y z, 20 x y - 3 x z - 7 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [5 y z + 18 z - 8 y, 10 x + 16 x y - x z, 2 x + 5 z - 5 x] > Problem := [F,G]; Problem := [ 2 2 2 [11 x + 18 x y - 4 x z, 11 x - 17 y + 12 y z, 20 x y - 3 x z - 7 y z], 2 2 2 2 [5 y z + 18 z - 8 y, 10 x + 16 x y - x z, 2 x + 5 z - 5 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=46.8MB, alloc=32.3MB, time=0.83 memory used=64.9MB, alloc=56.3MB, time=1.15 memory used=104.4MB, alloc=60.3MB, time=1.80 memory used=144.5MB, alloc=84.3MB, time=2.37 memory used=211.8MB, alloc=116.3MB, time=3.27 memory used=292.2MB, alloc=372.3MB, time=4.47 memory used=379.8MB, alloc=396.3MB, time=5.72 memory used=481.7MB, alloc=420.3MB, time=7.40 memory used=613.8MB, alloc=444.3MB, time=9.37 memory used=760.0MB, alloc=468.3MB, time=11.64 memory used=892.5MB, alloc=492.3MB, time=13.95 memory used=1040.1MB, alloc=516.3MB, time=16.50 memory used=1172.2MB, alloc=516.3MB, time=18.88 memory used=1277.7MB, alloc=540.3MB, time=20.67 memory used=1409.3MB, alloc=540.3MB, time=23.07 memory used=1531.9MB, alloc=540.3MB, time=25.73 memory used=1624.9MB, alloc=564.3MB, time=27.14 memory used=1719.3MB, alloc=564.3MB, time=28.62 memory used=1802.7MB, alloc=588.3MB, time=29.87 memory used=1897.1MB, alloc=588.3MB, time=31.32 memory used=1980.1MB, alloc=588.3MB, time=32.96 memory used=2047.9MB, alloc=588.3MB, time=34.20 memory used=2112.3MB, alloc=612.3MB, time=35.25 memory used=2189.1MB, alloc=612.3MB, time=37.11 memory used=2239.1MB, alloc=612.3MB, time=38.12 memory used=2296.0MB, alloc=612.3MB, time=39.41 memory used=2545.5MB, alloc=636.3MB, time=43.41 memory used=2776.7MB, alloc=660.3MB, time=47.61 memory used=2980.4MB, alloc=684.3MB, time=50.72 memory used=3187.2MB, alloc=708.3MB, time=54.75 memory used=3398.1MB, alloc=732.3MB, time=58.51 memory used=3584.8MB, alloc=732.3MB, time=62.85 memory used=3773.8MB, alloc=756.3MB, time=67.19 memory used=3962.8MB, alloc=756.3MB, time=71.85 memory used=4103.7MB, alloc=780.3MB, time=74.71 memory used=4253.4MB, alloc=780.3MB, time=77.64 memory used=4410.2MB, alloc=804.3MB, time=81.40 memory used=4526.2MB, alloc=804.3MB, time=84.36 memory used=4644.0MB, alloc=804.3MB, time=87.26 memory used=5105.8MB, alloc=828.3MB, time=97.35 memory used=5565.8MB, alloc=852.3MB, time=106.26 memory used=5932.5MB, alloc=876.3MB, time=114.77 memory used=6375.8MB, alloc=900.3MB, time=123.99 memory used=6770.1MB, alloc=924.3MB, time=133.32 |\^/| 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(); 1428289670 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [16 y - 2 y + 17 z, 3 x y + 9 x z + 18 y z, -20 x z + 3 y z - 15 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-10 y - 19 y z + 13 x, 15 x y - 16 x + 12 y, -17 x z - y z + 17 z ] > Problem := [F,G]; Problem := [ 2 2 [16 y - 2 y + 17 z, 3 x y + 9 x z + 18 y z, -20 x z + 3 y z - 15 z ], 2 2 [-10 y - 19 y z + 13 x, 15 x y - 16 x + 12 y, -17 x z - y z + 17 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.5MB, alloc=32.3MB, time=0.79 memory used=67.0MB, alloc=56.3MB, time=1.09 memory used=106.3MB, alloc=60.3MB, time=1.68 memory used=142.8MB, alloc=84.3MB, time=2.23 memory used=199.3MB, alloc=92.3MB, time=3.13 memory used=255.0MB, alloc=116.3MB, time=3.99 memory used=332.0MB, alloc=116.3MB, time=5.18 memory used=408.0MB, alloc=140.3MB, time=6.36 memory used=503.9MB, alloc=164.3MB, time=7.95 memory used=605.4MB, alloc=420.3MB, time=9.66 memory used=718.9MB, alloc=444.3MB, time=11.61 memory used=850.5MB, alloc=468.3MB, time=13.74 memory used=1009.7MB, alloc=492.3MB, time=16.45 memory used=1181.4MB, alloc=516.3MB, time=19.42 memory used=1388.2MB, alloc=540.3MB, time=23.12 memory used=1610.9MB, alloc=564.3MB, time=27.10 memory used=1853.4MB, alloc=588.3MB, time=31.60 memory used=2118.0MB, alloc=612.3MB, time=36.62 memory used=2404.0MB, alloc=636.3MB, time=42.39 memory used=2711.0MB, alloc=660.3MB, time=48.84 memory used=3014.0MB, alloc=684.3MB, time=55.34 memory used=3293.0MB, alloc=708.3MB, time=62.13 memory used=3565.3MB, alloc=732.3MB, time=68.89 memory used=3825.4MB, alloc=756.3MB, time=75.95 memory used=4074.3MB, alloc=780.3MB, time=82.73 memory used=4267.8MB, alloc=804.3MB, time=88.26 memory used=4463.8MB, alloc=828.3MB, time=94.05 memory used=4651.1MB, alloc=852.3MB, time=99.00 memory used=4818.4MB, alloc=876.3MB, time=104.07 memory used=4954.5MB, alloc=900.3MB, time=107.40 memory used=5089.7MB, alloc=924.3MB, time=110.91 memory used=5211.8MB, alloc=948.3MB, time=114.14 memory used=5332.1MB, alloc=948.3MB, time=117.30 memory used=5420.3MB, alloc=972.3MB, time=120.15 memory used=5914.0MB, alloc=996.3MB, time=130.84 |\^/| 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(); 1428289970 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-14 x y - 17 z + 7, -19 x + 19 y + 4 z, -17 x + 2 x z + 9 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-14 x y + 5 y + 20 x, 19 x z - 10 y + 20, -13 y + 19] > Problem := [F,G]; 2 2 2 Problem := [[-14 x y - 17 z + 7, -19 x + 19 y + 4 z, -17 x + 2 x z + 9 y], 2 2 2 [-14 x y + 5 y + 20 x, 19 x z - 10 y + 20, -13 y + 19]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=32.3MB, time=0.83 memory used=67.8MB, alloc=56.3MB, time=1.14 memory used=108.9MB, alloc=60.3MB, time=1.79 memory used=148.0MB, alloc=84.3MB, time=2.41 memory used=209.5MB, alloc=92.3MB, time=3.41 memory used=272.3MB, alloc=116.3MB, time=4.43 memory used=345.0MB, alloc=116.3MB, time=5.58 memory used=409.5MB, alloc=372.3MB, time=6.63 memory used=492.8MB, alloc=396.3MB, time=8.00 memory used=601.3MB, alloc=420.3MB, time=9.81 memory used=732.0MB, alloc=444.3MB, time=12.06 memory used=867.2MB, alloc=468.3MB, time=14.35 memory used=995.8MB, alloc=468.3MB, time=16.60 memory used=1103.7MB, alloc=492.3MB, time=18.49 memory used=1218.3MB, alloc=492.3MB, time=20.70 memory used=1344.1MB, alloc=516.3MB, time=23.12 memory used=1467.0MB, alloc=540.3MB, time=25.66 memory used=1613.5MB, alloc=564.3MB, time=28.57 memory used=1748.1MB, alloc=588.3MB, time=31.32 memory used=1872.3MB, alloc=612.3MB, time=33.92 memory used=2008.7MB, alloc=636.3MB, time=36.77 memory used=2134.9MB, alloc=660.3MB, time=39.42 memory used=2251.3MB, alloc=684.3MB, time=41.86 memory used=2338.2MB, alloc=684.3MB, time=43.82 memory used=2465.2MB, alloc=708.3MB, time=46.52 memory used=2575.4MB, alloc=732.3MB, time=48.96 memory used=2692.7MB, alloc=732.3MB, time=51.59 memory used=2800.8MB, alloc=756.3MB, time=54.02 memory used=2905.2MB, alloc=780.3MB, time=56.38 memory used=2996.8MB, alloc=780.3MB, time=58.52 memory used=3097.6MB, alloc=804.3MB, time=60.81 memory used=3185.1MB, alloc=804.3MB, time=62.86 memory used=3282.4MB, alloc=828.3MB, time=65.06 memory used=3369.1MB, alloc=828.3MB, time=67.09 memory used=3456.2MB, alloc=852.3MB, time=69.24 memory used=3807.6MB, alloc=876.3MB, time=76.31 memory used=4148.4MB, alloc=900.3MB, time=83.43 memory used=4505.7MB, alloc=924.3MB, time=92.00 memory used=4813.3MB, alloc=948.3MB, time=103.73 memory used=5125.1MB, alloc=972.3MB, time=116.21 memory used=5446.7MB, alloc=996.3MB, time=129.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428290270 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-19 x + 2 y + 6 y, 3 y + 13 y z - 8 z , -15 x y - 14 x z + 11 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-4 x z + 9 y + 20 z, -5 x z + 17 y + 4 x, -x + 9 x y + 16 x z] > Problem := [F,G]; Problem := [ 2 2 2 2 2 [-19 x + 2 y + 6 y, 3 y + 13 y z - 8 z , -15 x y - 14 x z + 11 y ], 2 2 [-4 x z + 9 y + 20 z, -5 x z + 17 y + 4 x, -x + 9 x y + 16 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.49 memory used=47.3MB, alloc=32.3MB, time=0.78 memory used=66.0MB, alloc=56.3MB, time=1.07 memory used=104.8MB, alloc=60.3MB, time=1.64 memory used=143.5MB, alloc=84.3MB, time=2.21 memory used=204.8MB, alloc=92.3MB, time=3.14 memory used=263.7MB, alloc=116.3MB, time=4.06 memory used=344.1MB, alloc=116.3MB, time=5.31 memory used=423.4MB, alloc=140.3MB, time=6.59 memory used=494.9MB, alloc=140.3MB, time=7.70 memory used=571.0MB, alloc=396.3MB, time=8.91 memory used=675.5MB, alloc=420.3MB, time=10.71 memory used=803.1MB, alloc=444.3MB, time=12.94 memory used=950.8MB, alloc=468.3MB, time=15.55 memory used=1097.5MB, alloc=492.3MB, time=18.15 memory used=1241.5MB, alloc=492.3MB, time=20.70 memory used=1380.2MB, alloc=516.3MB, time=23.32 memory used=1491.6MB, alloc=516.3MB, time=25.40 memory used=1598.3MB, alloc=516.3MB, time=27.48 memory used=1681.8MB, alloc=540.3MB, time=29.17 memory used=1786.4MB, alloc=540.3MB, time=31.27 memory used=1895.2MB, alloc=564.3MB, time=33.43 memory used=1989.2MB, alloc=564.3MB, time=35.37 memory used=2087.9MB, alloc=588.3MB, time=37.41 memory used=2184.6MB, alloc=588.3MB, time=39.46 memory used=2284.1MB, alloc=612.3MB, time=41.58 memory used=2382.6MB, alloc=636.3MB, time=43.74 memory used=2483.5MB, alloc=636.3MB, time=45.90 memory used=2558.3MB, alloc=660.3MB, time=47.66 memory used=2638.5MB, alloc=660.3MB, time=49.59 memory used=2713.6MB, alloc=684.3MB, time=51.47 memory used=2796.8MB, alloc=684.3MB, time=53.49 memory used=2877.3MB, alloc=708.3MB, time=55.47 memory used=2952.7MB, alloc=708.3MB, time=57.32 memory used=3029.3MB, alloc=732.3MB, time=59.25 memory used=3332.3MB, alloc=756.3MB, time=65.26 memory used=3635.1MB, alloc=780.3MB, time=71.33 memory used=3938.6MB, alloc=804.3MB, time=77.57 memory used=4247.5MB, alloc=828.3MB, time=83.78 memory used=4514.0MB, alloc=852.3MB, time=89.41 memory used=4827.1MB, alloc=876.3MB, time=96.11 memory used=5147.1MB, alloc=900.3MB, time=102.70 memory used=5462.8MB, alloc=924.3MB, time=109.42 memory used=5781.1MB, alloc=948.3MB, time=116.20 memory used=6076.7MB, alloc=972.3MB, time=126.01 memory used=6351.2MB, alloc=996.3MB, time=136.98 |\^/| 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(); 1428290570 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [19 x + 10 x + 15 y, 18 x + 11 x y - 4 z , 5 x y + 15 y - 2 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [14 y + y + 10, x y + 15 x + 10, -14 x + 12 x z - 10 x] > Problem := [F,G]; Problem := [ 2 2 2 2 [19 x + 10 x + 15 y, 18 x + 11 x y - 4 z , 5 x y + 15 y - 2 y z], 2 2 [14 y + y + 10, x y + 15 x + 10, -14 x + 12 x z - 10 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.47 memory used=47.1MB, alloc=32.3MB, time=0.76 memory used=66.4MB, alloc=56.3MB, time=1.06 memory used=107.2MB, alloc=60.3MB, time=1.68 memory used=145.3MB, alloc=84.3MB, time=2.26 memory used=204.5MB, alloc=84.3MB, time=3.17 memory used=263.3MB, alloc=116.3MB, time=4.20 memory used=341.0MB, alloc=140.3MB, time=5.61 memory used=434.8MB, alloc=164.3MB, time=7.25 memory used=543.3MB, alloc=188.3MB, time=9.24 memory used=654.9MB, alloc=468.3MB, time=11.50 memory used=779.2MB, alloc=492.3MB, time=15.34 memory used=914.6MB, alloc=516.3MB, time=19.93 memory used=1061.8MB, alloc=540.3MB, time=25.61 memory used=1228.6MB, alloc=564.3MB, time=32.26 memory used=1419.4MB, alloc=564.3MB, time=39.81 memory used=1610.2MB, alloc=588.3MB, time=47.32 memory used=1824.9MB, alloc=588.3MB, time=55.74 memory used=2039.4MB, alloc=612.3MB, time=64.16 memory used=2278.0MB, alloc=636.3MB, time=73.70 N1 := 7165 > GB := Basis(F, plex(op(vars))); 6 5 4 3 2 GB := [102885 x + 112271 x + 34675 x + 2150 x , 19 x + 15 y + 10 x, 4 3 2 2 3 2 2 361 x + 285 x + 38 x z + 50 x + 20 x z, 209 x - 160 x + 60 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 679 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [19 x + 15 y + 10 x, -4 z + 11 y x + 18 x , 5 x y + 15 y - 2 y z, 2 2 14 y + y + 10, y x + 15 x + 10, -14 x + 12 x z - 10 x] > J:=[op(GB),op(G)]; 6 5 4 3 2 J := [102885 x + 112271 x + 34675 x + 2150 x , 19 x + 15 y + 10 x, 4 3 2 2 3 2 2 361 x + 285 x + 38 x z + 50 x + 20 x z, 209 x + 60 z - 160 x , 2 2 14 y + y + 10, y x + 15 x + 10, -14 x + 12 x z - 10 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 12, 2, 2, 2, 2, 5/6, 5/6, 1/2, 5/9, 4/9, 1/6, 7, 12, 21, 6, 6, 2, 2, 6/7, 3/7, 3/7, 3/4, 1/6, 1/6, 1, -9, -4] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=2440.2MB, alloc=636.3MB, time=77.62 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428290754 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-10 - 11 x - 3 y, 11 x - 7 x y + 20 x, 5 x y - 9 y + 3 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [19 x y + 8 x z + 3 y , -7 y z + 14 z + 20 z, 8 x y + 4 x z + 11 x] > Problem := [F,G]; 2 2 Problem := [[-10 - 11 x - 3 y, 11 x - 7 x y + 20 x, 5 x y - 9 y + 3 x], 2 2 [19 x y + 8 x z + 3 y , -7 y z + 14 z + 20 z, 8 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.48 memory used=46.3MB, alloc=32.3MB, time=0.75 memory used=65.5MB, alloc=32.3MB, time=1.02 memory used=83.8MB, alloc=56.3MB, time=1.29 memory used=121.1MB, alloc=60.3MB, time=1.85 memory used=157.2MB, alloc=60.3MB, time=2.38 memory used=192.2MB, alloc=84.3MB, time=2.91 memory used=247.9MB, alloc=84.3MB, time=3.73 memory used=300.6MB, alloc=108.3MB, time=4.55 memory used=375.4MB, alloc=140.3MB, time=5.80 memory used=470.7MB, alloc=164.3MB, time=7.53 memory used=576.9MB, alloc=188.3MB, time=9.40 memory used=688.9MB, alloc=468.3MB, time=11.43 memory used=819.3MB, alloc=492.3MB, time=13.83 memory used=958.2MB, alloc=516.3MB, time=17.04 memory used=1094.3MB, alloc=540.3MB, time=21.49 memory used=1242.4MB, alloc=564.3MB, time=26.65 memory used=1405.4MB, alloc=588.3MB, time=32.49 memory used=1582.2MB, alloc=612.3MB, time=39.25 memory used=1775.3MB, alloc=636.3MB, time=47.29 memory used=1992.4MB, alloc=660.3MB, time=56.15 memory used=2233.3MB, alloc=684.3MB, time=65.89 memory used=2498.3MB, alloc=684.3MB, time=76.61 memory used=2763.2MB, alloc=708.3MB, time=87.34 memory used=3052.0MB, alloc=708.3MB, time=99.27 memory used=3340.9MB, alloc=708.3MB, time=111.17 memory used=3629.6MB, alloc=732.3MB, time=123.00 |\^/| 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(); 1428291054 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [x z - 15 x + 11 y, -17 x + 3 y + 3, 15 x z - 3 y - 14 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [9 x - 7 x y + 19 x z, 13 x + 10 x y + 14 z , -18 x z - 5 x + 6 z] > Problem := [F,G]; 2 2 2 Problem := [[x z - 15 x + 11 y, -17 x + 3 y + 3, 15 x z - 3 y - 14 z ], 2 2 2 [9 x - 7 x y + 19 x z, 13 x + 10 x y + 14 z , -18 x z - 5 x + 6 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=47.1MB, alloc=32.3MB, time=0.81 memory used=66.8MB, alloc=56.3MB, time=1.12 memory used=107.8MB, alloc=60.3MB, time=1.74 memory used=146.4MB, alloc=84.3MB, time=2.34 memory used=208.3MB, alloc=92.3MB, time=3.32 memory used=268.3MB, alloc=116.3MB, time=4.30 memory used=349.8MB, alloc=140.3MB, time=5.58 memory used=426.5MB, alloc=396.3MB, time=6.62 memory used=534.5MB, alloc=420.3MB, time=8.25 memory used=663.7MB, alloc=444.3MB, time=10.31 memory used=818.4MB, alloc=468.3MB, time=12.73 memory used=955.8MB, alloc=492.3MB, time=14.93 memory used=1084.2MB, alloc=492.3MB, time=17.03 memory used=1207.0MB, alloc=516.3MB, time=19.17 memory used=1326.3MB, alloc=516.3MB, time=21.29 memory used=1448.4MB, alloc=516.3MB, time=23.56 memory used=1556.0MB, alloc=516.3MB, time=25.65 memory used=1653.2MB, alloc=516.3MB, time=27.50 memory used=1753.6MB, alloc=516.3MB, time=29.55 memory used=1834.8MB, alloc=540.3MB, time=31.18 memory used=1922.1MB, alloc=540.3MB, time=32.91 memory used=1999.2MB, alloc=540.3MB, time=34.54 memory used=2078.1MB, alloc=540.3MB, time=36.14 memory used=2156.1MB, alloc=540.3MB, time=37.79 memory used=2221.1MB, alloc=540.3MB, time=39.19 memory used=2289.5MB, alloc=540.3MB, time=40.87 memory used=2340.3MB, alloc=540.3MB, time=42.31 memory used=2567.2MB, alloc=564.3MB, time=46.85 memory used=2811.8MB, alloc=588.3MB, time=52.26 memory used=3018.4MB, alloc=612.3MB, time=56.67 memory used=3242.0MB, alloc=636.3MB, time=62.15 memory used=3440.8MB, alloc=660.3MB, time=66.80 memory used=3637.0MB, alloc=684.3MB, time=71.31 memory used=3813.5MB, alloc=708.3MB, time=75.57 memory used=3978.4MB, alloc=708.3MB, time=79.66 memory used=4121.6MB, alloc=708.3MB, time=82.92 memory used=4290.7MB, alloc=732.3MB, time=87.11 memory used=4432.0MB, alloc=732.3MB, time=90.62 memory used=4555.0MB, alloc=732.3MB, time=94.28 memory used=4665.3MB, alloc=732.3MB, time=97.70 memory used=4797.9MB, alloc=732.3MB, time=101.47 memory used=5184.7MB, alloc=756.3MB, time=109.66 memory used=5522.5MB, alloc=780.3MB, time=117.15 memory used=5850.3MB, alloc=804.3MB, time=124.29 memory used=6185.5MB, alloc=828.3MB, time=131.50 |\^/| 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(); 1428291354 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-17 z + 2 y - 1, -11 x y + z - 9, 18 y - 20 y z - 20 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-10 x y + 12 y z + 8, -10 x - 10 y, 3 x + 14 x - 16 z] > Problem := [F,G]; 2 2 Problem := [[-17 z + 2 y - 1, -11 x y + z - 9, 18 y - 20 y z - 20 z], 2 [-10 x y + 12 y z + 8, -10 x - 10 y, 3 x + 14 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=32.3MB, time=0.80 memory used=65.4MB, alloc=56.3MB, time=1.08 memory used=106.2MB, alloc=60.3MB, time=1.69 memory used=144.8MB, alloc=84.3MB, time=2.27 memory used=205.8MB, alloc=92.3MB, time=3.24 memory used=266.4MB, alloc=116.3MB, time=4.19 memory used=347.5MB, alloc=116.3MB, time=5.51 memory used=427.3MB, alloc=140.3MB, time=6.84 memory used=513.9MB, alloc=140.3MB, time=8.24 memory used=580.9MB, alloc=420.3MB, time=9.37 memory used=706.5MB, alloc=444.3MB, time=11.61 memory used=857.0MB, alloc=468.3MB, time=14.18 memory used=1019.3MB, alloc=492.3MB, time=17.29 memory used=1170.2MB, alloc=516.3MB, time=20.06 memory used=1313.4MB, alloc=516.3MB, time=22.83 memory used=1454.9MB, alloc=516.3MB, time=25.64 memory used=1574.7MB, alloc=540.3MB, time=28.14 memory used=1692.5MB, alloc=540.3MB, time=30.76 memory used=1790.5MB, alloc=540.3MB, time=32.82 memory used=1893.3MB, alloc=540.3MB, time=35.05 memory used=1987.0MB, alloc=540.3MB, time=37.16 memory used=2083.9MB, alloc=540.3MB, time=39.42 memory used=2180.8MB, alloc=540.3MB, time=41.85 memory used=2253.3MB, alloc=564.3MB, time=43.65 memory used=2328.4MB, alloc=564.3MB, time=45.71 memory used=2384.5MB, alloc=564.3MB, time=47.18 memory used=2437.9MB, alloc=564.3MB, time=48.60 memory used=2497.8MB, alloc=564.3MB, time=50.22 memory used=2740.4MB, alloc=588.3MB, time=55.42 memory used=2984.6MB, alloc=612.3MB, time=61.33 memory used=3210.8MB, alloc=636.3MB, time=66.74 memory used=3424.8MB, alloc=660.3MB, time=71.64 memory used=3603.8MB, alloc=684.3MB, time=75.39 memory used=3801.0MB, alloc=708.3MB, time=79.78 memory used=3981.2MB, alloc=732.3MB, time=83.72 memory used=4242.0MB, alloc=756.3MB, time=88.96 memory used=4459.2MB, alloc=780.3MB, time=93.67 memory used=4682.3MB, alloc=804.3MB, time=98.51 memory used=4857.3MB, alloc=828.3MB, time=102.54 memory used=5053.0MB, alloc=852.3MB, time=107.02 memory used=5251.3MB, alloc=876.3MB, time=111.67 memory used=5440.0MB, alloc=900.3MB, time=116.03 memory used=5617.4MB, alloc=924.3MB, time=120.44 memory used=5784.6MB, alloc=948.3MB, time=124.53 memory used=6180.2MB, alloc=972.3MB, time=133.02 |\^/| 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(); 1428291654 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [3 x y - 7 z - 5 z, 12 x + 16 x y - 2 z, 6 y - 3 z + 13 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [2 y - 10 y z + 8 y, -7 x - 18 x y + 12, -18 x z - 12 y z - 17 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[3 x y - 7 z - 5 z, 12 x + 16 x y - 2 z, 6 y - 3 z + 13 x], 2 2 2 [2 y - 10 y z + 8 y, -7 x - 18 x y + 12, -18 x z - 12 y z - 17 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=47.1MB, alloc=32.3MB, time=0.76 memory used=66.3MB, alloc=56.3MB, time=1.05 memory used=106.1MB, alloc=60.3MB, time=1.63 memory used=142.6MB, alloc=84.3MB, time=2.18 memory used=199.9MB, alloc=92.3MB, time=3.08 memory used=256.3MB, alloc=116.3MB, time=3.99 memory used=334.7MB, alloc=116.3MB, time=5.22 memory used=412.6MB, alloc=140.3MB, time=6.49 memory used=511.4MB, alloc=164.3MB, time=8.07 memory used=612.3MB, alloc=420.3MB, time=9.86 memory used=731.8MB, alloc=444.3MB, time=11.92 memory used=871.2MB, alloc=468.3MB, time=14.45 memory used=1030.0MB, alloc=492.3MB, time=17.32 memory used=1208.0MB, alloc=516.3MB, time=21.00 memory used=1411.8MB, alloc=540.3MB, time=25.12 memory used=1634.1MB, alloc=564.3MB, time=29.51 memory used=1882.0MB, alloc=588.3MB, time=34.74 memory used=2146.4MB, alloc=612.3MB, time=40.61 memory used=2429.6MB, alloc=636.3MB, time=46.39 memory used=2730.3MB, alloc=660.3MB, time=52.94 memory used=3012.2MB, alloc=684.3MB, time=59.48 memory used=3282.2MB, alloc=708.3MB, time=66.03 memory used=3573.6MB, alloc=732.3MB, time=74.14 memory used=3788.1MB, alloc=756.3MB, time=79.59 memory used=4026.8MB, alloc=780.3MB, time=86.09 memory used=4254.6MB, alloc=804.3MB, time=92.73 memory used=4420.4MB, alloc=804.3MB, time=97.50 memory used=4597.8MB, alloc=804.3MB, time=102.43 memory used=4802.6MB, alloc=828.3MB, time=109.31 |\^/| 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(); 1428291954 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-3 x + 6 x y - 7 y , -10 y - 18 z + y, -20 y z + 10 x + 14 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [-5 x y - 17 x + 2 z, -4 y z - 8 y - 18, x z + 8 x + 17 y] > Problem := [F,G]; 2 2 2 2 Problem := [[-3 x + 6 x y - 7 y , -10 y - 18 z + y, -20 y z + 10 x + 14 y], [-5 x y - 17 x + 2 z, -4 y z - 8 y - 18, x z + 8 x + 17 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=32.3MB, time=0.80 memory used=66.4MB, alloc=56.3MB, time=1.09 memory used=105.8MB, alloc=60.3MB, time=1.68 memory used=144.4MB, alloc=60.3MB, time=2.26 memory used=181.9MB, alloc=84.3MB, time=2.84 memory used=229.4MB, alloc=84.3MB, time=3.57 memory used=288.2MB, alloc=116.3MB, time=4.52 memory used=369.5MB, alloc=116.3MB, time=5.85 memory used=442.6MB, alloc=140.3MB, time=7.07 memory used=530.2MB, alloc=396.3MB, time=8.59 memory used=637.1MB, alloc=420.3MB, time=10.37 memory used=764.8MB, alloc=444.3MB, time=12.61 memory used=917.7MB, alloc=468.3MB, time=15.46 memory used=1073.5MB, alloc=492.3MB, time=18.37 memory used=1218.5MB, alloc=492.3MB, time=21.24 memory used=1361.8MB, alloc=516.3MB, time=24.11 memory used=1482.0MB, alloc=516.3MB, time=26.46 memory used=1604.1MB, alloc=516.3MB, time=29.12 memory used=1722.2MB, alloc=516.3MB, time=31.66 memory used=1828.4MB, alloc=516.3MB, time=34.08 memory used=1920.1MB, alloc=540.3MB, time=36.16 memory used=2006.4MB, alloc=540.3MB, time=38.05 memory used=2088.7MB, alloc=540.3MB, time=39.92 memory used=2166.2MB, alloc=540.3MB, time=41.79 memory used=2237.4MB, alloc=540.3MB, time=43.50 memory used=2309.8MB, alloc=540.3MB, time=45.34 memory used=2369.7MB, alloc=540.3MB, time=46.91 memory used=2428.7MB, alloc=540.3MB, time=48.44 memory used=2490.1MB, alloc=540.3MB, time=50.14 memory used=2710.1MB, alloc=564.3MB, time=54.77 memory used=2949.9MB, alloc=588.3MB, time=60.00 memory used=3174.5MB, alloc=612.3MB, time=65.02 memory used=3367.9MB, alloc=636.3MB, time=68.95 memory used=3562.9MB, alloc=660.3MB, time=73.12 memory used=3773.4MB, alloc=684.3MB, time=77.46 memory used=4015.1MB, alloc=708.3MB, time=82.51 memory used=4221.9MB, alloc=732.3MB, time=86.84 memory used=4434.1MB, alloc=756.3MB, time=91.01 memory used=4638.5MB, alloc=780.3MB, time=94.85 memory used=4859.1MB, alloc=804.3MB, time=99.07 memory used=5052.9MB, alloc=828.3MB, time=103.38 memory used=5248.0MB, alloc=852.3MB, time=107.86 memory used=5419.1MB, alloc=876.3MB, time=112.00 |\^/| 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(); 1428292254 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [4 - 14 x - 2 z, 20 x z - 14 z - z, 16 x + 9 x z - 14 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-8 y + 5 y z + 4 y, x y + 17 x z + 19 z, 6 x y - 5 x z + 9 y z] > Problem := [F,G]; 2 2 2 Problem := [[4 - 14 x - 2 z, 20 x z - 14 z - z, 16 x + 9 x z - 14 y ], 2 [-8 y + 5 y z + 4 y, x y + 17 x z + 19 z, 6 x y - 5 x z + 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.47 memory used=46.2MB, alloc=32.3MB, time=0.76 memory used=65.2MB, alloc=56.3MB, time=1.05 memory used=102.9MB, alloc=60.3MB, time=1.60 memory used=138.4MB, alloc=84.3MB, time=2.16 memory used=196.2MB, alloc=92.3MB, time=3.10 memory used=254.3MB, alloc=116.3MB, time=4.06 memory used=332.2MB, alloc=140.3MB, time=5.30 memory used=432.1MB, alloc=164.3MB, time=7.03 memory used=521.4MB, alloc=164.3MB, time=8.60 memory used=605.9MB, alloc=444.3MB, time=10.14 memory used=749.6MB, alloc=468.3MB, time=12.70 memory used=909.8MB, alloc=492.3MB, time=15.48 memory used=1086.1MB, alloc=516.3MB, time=18.51 memory used=1286.2MB, alloc=540.3MB, time=22.35 memory used=1516.3MB, alloc=564.3MB, time=27.11 memory used=1758.8MB, alloc=588.3MB, time=32.03 memory used=2035.0MB, alloc=612.3MB, time=37.94 memory used=2326.3MB, alloc=636.3MB, time=44.72 memory used=2640.2MB, alloc=660.3MB, time=52.27 memory used=2918.7MB, alloc=684.3MB, time=59.58 memory used=3173.2MB, alloc=708.3MB, time=66.07 memory used=3421.9MB, alloc=732.3MB, time=72.25 memory used=3626.3MB, alloc=756.3MB, time=77.04 memory used=3837.2MB, alloc=780.3MB, time=82.85 memory used=4002.4MB, alloc=804.3MB, time=87.31 memory used=4145.9MB, alloc=804.3MB, time=91.41 memory used=4308.3MB, alloc=804.3MB, time=95.93 memory used=4445.6MB, alloc=804.3MB, time=100.03 memory used=4564.4MB, alloc=804.3MB, time=103.94 memory used=4685.4MB, alloc=804.3MB, time=108.01 memory used=5144.8MB, alloc=828.3MB, time=120.83 memory used=5613.1MB, alloc=852.3MB, time=134.85 memory used=6095.6MB, alloc=876.3MB, time=149.01 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428292554 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [20 y - 18 z - 3, -18 x - 8 x z + 17 y, 8 y - 11 z - 18 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [16 y z + 15 y + 16, 17 x - 19 x z - 15, 14 y z - 8 x + 12 y] > Problem := [F,G]; 2 2 2 2 Problem := [[20 y - 18 z - 3, -18 x - 8 x z + 17 y, 8 y - 11 z - 18 x], 2 [16 y z + 15 y + 16, 17 x - 19 x z - 15, 14 y z - 8 x + 12 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.80 memory used=68.2MB, alloc=60.3MB, time=1.13 memory used=110.1MB, alloc=60.3MB, time=1.74 memory used=150.5MB, alloc=60.3MB, time=2.34 memory used=186.9MB, alloc=84.3MB, time=2.91 memory used=225.8MB, alloc=84.3MB, time=3.53 memory used=288.4MB, alloc=116.3MB, time=4.49 memory used=366.5MB, alloc=372.3MB, time=5.65 memory used=449.2MB, alloc=396.3MB, time=6.93 memory used=554.4MB, alloc=396.3MB, time=8.64 memory used=657.0MB, alloc=420.3MB, time=10.34 memory used=784.5MB, alloc=444.3MB, time=12.43 memory used=931.9MB, alloc=468.3MB, time=14.88 memory used=1082.4MB, alloc=492.3MB, time=17.57 memory used=1228.5MB, alloc=492.3MB, time=20.43 memory used=1327.1MB, alloc=516.3MB, time=22.03 memory used=1442.5MB, alloc=516.3MB, time=24.25 memory used=1550.5MB, alloc=516.3MB, time=26.34 memory used=1623.0MB, alloc=516.3MB, time=27.53 memory used=1717.6MB, alloc=516.3MB, time=29.52 memory used=1785.9MB, alloc=540.3MB, time=30.75 memory used=1872.7MB, alloc=540.3MB, time=32.59 memory used=1935.4MB, alloc=540.3MB, time=33.85 memory used=1991.9MB, alloc=540.3MB, time=34.91 memory used=2049.7MB, alloc=540.3MB, time=36.08 memory used=2109.8MB, alloc=540.3MB, time=37.69 memory used=2159.0MB, alloc=540.3MB, time=38.86 memory used=2362.4MB, alloc=564.3MB, time=42.55 memory used=2567.5MB, alloc=588.3MB, time=46.33 memory used=2811.3MB, alloc=612.3MB, time=52.17 memory used=3011.6MB, alloc=636.3MB, time=56.87 memory used=3186.6MB, alloc=660.3MB, time=60.85 memory used=3321.1MB, alloc=684.3MB, time=63.96 memory used=3465.2MB, alloc=684.3MB, time=67.57 memory used=3589.2MB, alloc=684.3MB, time=70.68 memory used=3719.0MB, alloc=684.3MB, time=74.24 memory used=3803.5MB, alloc=684.3MB, time=76.43 memory used=3928.6MB, alloc=684.3MB, time=80.26 memory used=4047.7MB, alloc=684.3MB, time=83.86 memory used=4401.0MB, alloc=708.3MB, time=92.50 memory used=4770.9MB, alloc=732.3MB, time=101.87 memory used=5164.4MB, alloc=756.3MB, time=111.35 memory used=5570.1MB, alloc=780.3MB, time=122.74 memory used=5978.9MB, alloc=804.3MB, time=133.81 memory used=6427.7MB, alloc=828.3MB, time=147.07 |\^/| 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(); 1428292854 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [6 y + 19 z + 18 z, 11 x y + 4 y z + 2, 9 y z - 14 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [10 y + 20 z - 7, 5 z - 19 x + 12, 18 y z - 3 x + 4 y] > Problem := [F,G]; 2 2 2 Problem := [[6 y + 19 z + 18 z, 11 x y + 4 y z + 2, 9 y z - 14 z ], 2 2 2 [10 y + 20 z - 7, 5 z - 19 x + 12, 18 y z - 3 x + 4 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=46.6MB, alloc=32.3MB, time=0.78 memory used=65.3MB, alloc=56.3MB, time=1.07 memory used=104.3MB, alloc=60.3MB, time=1.66 memory used=142.3MB, alloc=84.3MB, time=2.23 memory used=201.8MB, alloc=92.3MB, time=3.17 memory used=259.8MB, alloc=116.3MB, time=4.07 memory used=337.8MB, alloc=116.3MB, time=5.27 memory used=412.6MB, alloc=140.3MB, time=6.48 memory used=497.6MB, alloc=164.3MB, time=7.88 memory used=577.0MB, alloc=420.3MB, time=9.22 memory used=696.2MB, alloc=444.3MB, time=11.27 memory used=844.0MB, alloc=468.3MB, time=13.79 memory used=1014.6MB, alloc=492.3MB, time=16.88 memory used=1207.3MB, alloc=516.3MB, time=20.53 memory used=1418.7MB, alloc=540.3MB, time=24.56 memory used=1652.6MB, alloc=564.3MB, time=29.38 memory used=1907.5MB, alloc=588.3MB, time=34.77 memory used=2179.9MB, alloc=612.3MB, time=40.57 memory used=2461.7MB, alloc=636.3MB, time=46.91 memory used=2732.6MB, alloc=660.3MB, time=52.68 memory used=2933.2MB, alloc=684.3MB, time=56.81 memory used=3160.5MB, alloc=708.3MB, time=61.57 memory used=3378.2MB, alloc=732.3MB, time=66.42 memory used=3617.3MB, alloc=756.3MB, time=72.74 memory used=3847.8MB, alloc=780.3MB, time=78.88 memory used=4018.3MB, alloc=780.3MB, time=83.57 memory used=4221.1MB, alloc=780.3MB, time=88.74 memory used=4392.6MB, alloc=780.3MB, time=94.16 memory used=4543.0MB, alloc=804.3MB, time=98.30 memory used=4721.2MB, alloc=804.3MB, time=104.01 memory used=4836.5MB, alloc=804.3MB, time=107.69 memory used=4965.4MB, alloc=804.3MB, time=111.98 memory used=5094.4MB, alloc=804.3MB, time=116.18 memory used=5541.6MB, alloc=828.3MB, time=129.24 memory used=6010.8MB, alloc=852.3MB, time=142.67 |\^/| 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(); 1428293154 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-17 x - 18 x y + 10 x, -3 x y - 5 y + 7 z, 6 y z + 14 x + 15 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [19 z + 19 x + 15 y, -11 y + 17 z + 7 y, 20 y z + 10 x - 6] > Problem := [F,G]; 2 2 Problem := [[-17 x - 18 x y + 10 x, -3 x y - 5 y + 7 z, 6 y z + 14 x + 15 y], 2 2 2 [19 z + 19 x + 15 y, -11 y + 17 z + 7 y, 20 y z + 10 x - 6]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=46.9MB, alloc=32.3MB, time=0.79 memory used=66.4MB, alloc=56.3MB, time=1.08 memory used=106.2MB, alloc=60.3MB, time=1.67 memory used=145.6MB, alloc=84.3MB, time=2.27 memory used=209.2MB, alloc=92.3MB, time=3.23 memory used=269.2MB, alloc=116.3MB, time=4.18 memory used=347.4MB, alloc=116.3MB, time=5.35 memory used=421.0MB, alloc=396.3MB, time=6.47 memory used=526.9MB, alloc=396.3MB, time=8.10 memory used=629.4MB, alloc=420.3MB, time=9.64 memory used=754.4MB, alloc=444.3MB, time=11.64 memory used=890.9MB, alloc=468.3MB, time=13.80 memory used=1013.7MB, alloc=492.3MB, time=15.77 memory used=1125.8MB, alloc=492.3MB, time=17.63 memory used=1241.2MB, alloc=492.3MB, time=19.80 memory used=1337.0MB, alloc=492.3MB, time=21.56 memory used=1440.7MB, alloc=492.3MB, time=23.43 memory used=1511.4MB, alloc=516.3MB, time=24.67 memory used=1586.0MB, alloc=516.3MB, time=26.18 memory used=1661.1MB, alloc=516.3MB, time=27.67 memory used=1745.4MB, alloc=516.3MB, time=29.37 memory used=1795.3MB, alloc=516.3MB, time=30.37 memory used=1845.7MB, alloc=516.3MB, time=31.31 memory used=1905.2MB, alloc=516.3MB, time=32.79 memory used=2113.9MB, alloc=540.3MB, time=36.71 memory used=2315.8MB, alloc=564.3MB, time=40.58 memory used=2497.9MB, alloc=588.3MB, time=43.68 memory used=2687.5MB, alloc=612.3MB, time=47.38 memory used=2853.0MB, alloc=636.3MB, time=51.02 memory used=3007.8MB, alloc=660.3MB, time=54.69 memory used=3171.9MB, alloc=660.3MB, time=58.72 memory used=3314.3MB, alloc=660.3MB, time=62.03 memory used=3431.1MB, alloc=660.3MB, time=64.91 memory used=3546.6MB, alloc=660.3MB, time=67.68 memory used=3658.1MB, alloc=684.3MB, time=70.43 memory used=4014.1MB, alloc=708.3MB, time=77.21 memory used=4370.2MB, alloc=732.3MB, time=85.38 memory used=4753.5MB, alloc=756.3MB, time=92.79 memory used=5085.5MB, alloc=780.3MB, time=99.98 memory used=5458.4MB, alloc=804.3MB, time=107.45 memory used=5815.9MB, alloc=828.3MB, time=114.67 memory used=6153.8MB, alloc=852.3MB, time=122.91 memory used=6419.4MB, alloc=876.3MB, time=128.49 memory used=6693.2MB, alloc=900.3MB, time=134.80 memory used=6945.1MB, alloc=924.3MB, time=140.78 memory used=7174.7MB, alloc=948.3MB, time=146.68 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428293454 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-15 x y - 6 x - 2 z, -6 y z - 10 x - 3, -8 x z - 15 y z - 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-18 + 12 x + 2 y, -4 x z + 2 y - z, -7 x z + 17 y + 5] > Problem := [F,G]; 2 Problem := [[-15 x y - 6 x - 2 z, -6 y z - 10 x - 3, -8 x z - 15 y z - 2 z ], 2 [-18 + 12 x + 2 y, -4 x z + 2 y - z, -7 x z + 17 y + 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.47 memory used=47.5MB, alloc=32.3MB, time=0.77 memory used=66.9MB, alloc=56.3MB, time=1.06 memory used=105.8MB, alloc=60.3MB, time=1.63 memory used=140.7MB, alloc=84.3MB, time=2.17 memory used=197.3MB, alloc=84.3MB, time=3.02 memory used=253.4MB, alloc=108.3MB, time=3.90 memory used=330.9MB, alloc=116.3MB, time=5.14 memory used=406.5MB, alloc=140.3MB, time=6.36 memory used=504.6MB, alloc=164.3MB, time=7.98 memory used=617.6MB, alloc=420.3MB, time=9.85 memory used=729.2MB, alloc=444.3MB, time=11.68 memory used=866.8MB, alloc=468.3MB, time=14.22 memory used=1026.4MB, alloc=492.3MB, time=17.20 memory used=1213.7MB, alloc=516.3MB, time=20.92 memory used=1421.7MB, alloc=540.3MB, time=25.22 memory used=1654.1MB, alloc=564.3MB, time=31.03 memory used=1908.2MB, alloc=588.3MB, time=37.40 memory used=2179.3MB, alloc=612.3MB, time=44.20 memory used=2467.8MB, alloc=636.3MB, time=51.34 memory used=2773.1MB, alloc=660.3MB, time=58.95 memory used=3080.0MB, alloc=684.3MB, time=66.56 memory used=3373.6MB, alloc=708.3MB, time=74.29 memory used=3659.5MB, alloc=732.3MB, time=80.98 memory used=3915.6MB, alloc=756.3MB, time=86.67 memory used=4183.6MB, alloc=780.3MB, time=92.54 memory used=4457.4MB, alloc=804.3MB, time=98.55 memory used=4702.1MB, alloc=828.3MB, time=104.07 memory used=4948.3MB, alloc=852.3MB, time=109.64 memory used=5189.7MB, alloc=876.3MB, time=115.11 memory used=5419.4MB, alloc=900.3MB, time=120.40 memory used=5757.6MB, alloc=924.3MB, time=128.05 memory used=6091.6MB, alloc=948.3MB, time=135.38 memory used=6425.8MB, alloc=972.3MB, time=142.80 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428293754 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [16 x - 18 y - 4 z, 11 x - 2 x y - 6 z, 13 y - 18 x + 18 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-10 x y + 5 z - 15, 8 x y - 17 y - 14 y, -11 x - 7 z - 17] > Problem := [F,G]; 2 2 Problem := [[16 x - 18 y - 4 z, 11 x - 2 x y - 6 z, 13 y - 18 x + 18 y], 2 2 [-10 x y + 5 z - 15, 8 x y - 17 y - 14 y, -11 x - 7 z - 17]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.2MB, alloc=32.3MB, time=0.77 memory used=67.0MB, alloc=56.3MB, time=1.08 memory used=105.8MB, alloc=60.3MB, time=1.65 memory used=142.0MB, alloc=84.3MB, time=2.19 memory used=200.3MB, alloc=92.3MB, time=3.09 memory used=256.8MB, alloc=116.3MB, time=3.98 memory used=333.8MB, alloc=116.3MB, time=5.20 memory used=411.5MB, alloc=140.3MB, time=6.60 memory used=503.1MB, alloc=164.3MB, time=8.31 memory used=609.3MB, alloc=444.3MB, time=10.30 memory used=729.4MB, alloc=468.3MB, time=12.53 memory used=860.7MB, alloc=492.3MB, time=15.08 memory used=996.1MB, alloc=516.3MB, time=19.27 memory used=1139.8MB, alloc=540.3MB, time=24.19 memory used=1297.6MB, alloc=564.3MB, time=29.81 memory used=1464.4MB, alloc=588.3MB, time=36.77 memory used=1654.4MB, alloc=612.3MB, time=44.66 memory used=1868.3MB, alloc=636.3MB, time=53.64 memory used=2106.2MB, alloc=636.3MB, time=63.40 memory used=2344.0MB, alloc=660.3MB, time=73.22 memory used=2605.8MB, alloc=660.3MB, time=83.98 memory used=2867.6MB, alloc=660.3MB, time=94.63 memory used=3129.3MB, alloc=684.3MB, time=105.18 memory used=3415.2MB, alloc=708.3MB, time=116.93 N1 := 9127 > GB := Basis(F, plex(op(vars))); 4 3 2 GB := [1573 x - 6540 x + 3222 x - 1458 x, 3 2 3146 x + 29391 x - 77472 x + 87399 y, 3 2 -3146 x - 29391 x - 216 x + 19422 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3730.1MB, alloc=708.3MB, time=125.21 N2 := 2291 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [16 x - 18 y - 4 z, -2 y x + 11 x - 6 z, 13 y - 18 x + 18 y, 2 2 -10 x y + 5 z - 15, 8 x y - 17 y - 14 y, -11 x - 7 z - 17] > J:=[op(GB),op(G)]; 4 3 2 J := [1573 x - 6540 x + 3222 x - 1458 x, 3 2 3146 x + 29391 x + 87399 y - 77472 x, 3 2 -3146 x - 29391 x - 216 x + 19422 z, -10 x y + 5 z - 15, 2 2 8 x y - 17 y - 14 y, -11 x - 7 z - 17] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 11, 2, 2, 2, 1, 1, 5/6, 2/3, 7/18, 4/9, 2/9, 6, 12, 16, 13 4, 4, 2, 1, 1, 1/2, 1/2, --, 5/21, 1/7, 3, -5, -2] 21 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=3927.0MB, alloc=708.3MB, time=132.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428294037 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-10 x - 6 x y - 18 y , 9 x - 5 y + 17, -16 x y - 5 x z + 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [18 y - 11 y + 20, 13 x z + y z - 8 z, 12 x y - x z - 18 x] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-10 x - 6 x y - 18 y , 9 x - 5 y + 17, -16 x y - 5 x z + 6 z ], 2 [18 y - 11 y + 20, 13 x z + y z - 8 z, 12 x y - 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=46.8MB, alloc=32.3MB, time=0.79 memory used=65.4MB, alloc=56.3MB, time=1.07 memory used=105.0MB, alloc=60.3MB, time=1.67 memory used=143.2MB, alloc=60.3MB, time=2.22 memory used=180.5MB, alloc=84.3MB, time=2.79 memory used=237.4MB, alloc=84.3MB, time=3.65 memory used=296.4MB, alloc=116.3MB, time=4.68 memory used=373.4MB, alloc=140.3MB, time=6.04 memory used=463.2MB, alloc=164.3MB, time=8.13 memory used=556.5MB, alloc=188.3MB, time=11.58 memory used=670.5MB, alloc=212.3MB, time=15.88 N1 := 2825 > GB := Basis(F, plex(op(vars))); 4 2 3 GB := [10831 x + 31671 x + 23409, -10831 x - 15453 x + 2295 y, 2 2 1696 x - 75 x z + 90 z + 2448] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 267 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [-10 x - 6 x y - 18 y , -5 y + 9 x + 17, -16 x y - 5 x z + 6 z , 2 18 y - 11 y + 20, 13 x z + y z - 8 z, 12 x y - x z - 18 x] > J:=[op(GB),op(G)]; 4 2 3 J := [10831 x + 31671 x + 23409, -10831 x - 15453 x + 2295 y, 2 2 2 90 z - 75 z x + 1696 x + 2448, 18 y - 11 y + 20, 13 x z + y z - 8 z, 12 x y - x z - 18 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 12, 2, 2, 2, 2, 5/6, 1, 1/2, 1/2, 4/9, 1/3, 6, 12, 15, 4, 10 4, 2, 2, 5/6, 2/3, 1/2, --, 5/19, 6/19, 2, -3, -2] 19 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=797.4MB, alloc=212.3MB, time=18.25 |\^/| 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(); 1428294077 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-19 z + 13 z - 3, -8 x + 15 y + 16, -16 x y - x - y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [5 x - 6 y + 7, 3 y z - 7 y, 16 x - 2 x z + 10 z ] > Problem := [F,G]; 2 2 2 Problem := [[-19 z + 13 z - 3, -8 x + 15 y + 16, -16 x y - x - y], 2 2 2 [5 x - 6 y + 7, 3 y z - 7 y, 16 x - 2 x z + 10 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.79 memory used=70.1MB, alloc=32.3MB, time=1.16 memory used=90.9MB, alloc=56.3MB, time=1.55 N1 := 367 > GB := Basis(F, plex(op(vars))); 4 3 2 GB := [2048 x + 256 x - 4103 x - 512 x - 16, 3 2 2 -2048 x - 128 x + 4111 x + 15 y + 256, 19 z - 13 z + 3] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=131.0MB, alloc=60.3MB, time=2.21 memory used=173.9MB, alloc=60.3MB, time=2.97 N2 := 377 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-19 z + 13 z - 3, -8 x + 15 y + 16, -16 x y - x - y, 5 x - 6 y + 7, 2 2 3 y z - 7 y, 16 x - 2 x z + 10 z ] > J:=[op(GB),op(G)]; 4 3 2 J := [2048 x + 256 x - 4103 x - 512 x - 16, 3 2 2 2 -2048 x - 128 x + 4111 x + 15 y + 256, 19 z - 13 z + 3, 5 x - 6 y + 7, 2 2 3 y z - 7 y, 16 x - 2 x z + 10 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 11, 12, 2, 2, 2, 2, 2/3, 2/3, 1/2, 6/17, 6/17, 5/17, 6, 10, 10 15, 4, 4, 1, 2, 2/3, 1/2, 1/2, --, 4/21, 5/21, 1, -3, -2] 21 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=181.6MB, alloc=60.3MB, time=3.19 |\^/| 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(); 1428294083 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-4 x - 11 y - 11, 19 z + 6 x - 13 y, 7 x z + 8 y + 17 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [16 y - 5 y - 9 z, x y + 12 y z - 15, -7 y - 7 z - 14] > Problem := [F,G]; 2 2 2 Problem := [[-4 x - 11 y - 11, 19 z + 6 x - 13 y, 7 x z + 8 y + 17 z], 2 2 2 [16 y - 5 y - 9 z, x y + 12 y z - 15, -7 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=47.1MB, alloc=32.3MB, time=0.82 memory used=66.1MB, alloc=56.3MB, time=1.12 memory used=106.6MB, alloc=60.3MB, time=1.73 memory used=145.8MB, alloc=84.3MB, time=2.32 memory used=210.0MB, alloc=92.3MB, time=3.27 memory used=273.2MB, alloc=116.3MB, time=4.24 memory used=346.3MB, alloc=116.3MB, time=5.35 memory used=428.1MB, alloc=396.3MB, time=6.66 memory used=537.6MB, alloc=396.3MB, time=8.29 memory used=646.1MB, alloc=420.3MB, time=9.96 memory used=775.2MB, alloc=444.3MB, time=11.99 memory used=917.5MB, alloc=468.3MB, time=14.32 memory used=1041.9MB, alloc=492.3MB, time=16.42 memory used=1152.9MB, alloc=492.3MB, time=18.28 memory used=1252.0MB, alloc=492.3MB, time=19.93 memory used=1364.5MB, alloc=492.3MB, time=21.92 memory used=1431.2MB, alloc=492.3MB, time=23.02 memory used=1523.6MB, alloc=516.3MB, time=24.65 memory used=1608.7MB, alloc=516.3MB, time=26.26 memory used=1697.6MB, alloc=516.3MB, time=27.92 memory used=1768.2MB, alloc=516.3MB, time=29.43 memory used=1838.4MB, alloc=516.3MB, time=30.86 memory used=1895.9MB, alloc=516.3MB, time=32.08 memory used=1967.4MB, alloc=516.3MB, time=33.64 memory used=2017.7MB, alloc=516.3MB, time=34.71 memory used=2065.3MB, alloc=516.3MB, time=35.65 memory used=2268.1MB, alloc=540.3MB, time=39.45 memory used=2462.0MB, alloc=564.3MB, time=42.76 memory used=2687.3MB, alloc=588.3MB, time=47.28 memory used=2877.5MB, alloc=612.3MB, time=50.77 memory used=3052.6MB, alloc=636.3MB, time=54.57 memory used=3195.6MB, alloc=636.3MB, time=57.38 memory used=3357.6MB, alloc=660.3MB, time=60.99 memory used=3512.4MB, alloc=660.3MB, time=64.53 memory used=3670.6MB, alloc=660.3MB, time=68.07 memory used=3795.4MB, alloc=660.3MB, time=71.01 memory used=3910.1MB, alloc=684.3MB, time=73.73 memory used=4035.4MB, alloc=684.3MB, time=77.10 memory used=4389.2MB, alloc=708.3MB, time=84.44 memory used=4762.1MB, alloc=732.3MB, time=91.67 memory used=5126.4MB, alloc=756.3MB, time=98.84 memory used=5437.0MB, alloc=780.3MB, time=105.31 memory used=5808.5MB, alloc=804.3MB, time=112.61 memory used=6152.2MB, alloc=828.3MB, time=119.80 memory used=6416.7MB, alloc=852.3MB, time=125.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428294383 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-16 x y + 3 x z - 15 y , 14 x z - 11 x + 3 y, -10 y z + 5 y - 15] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-16 x z + 14 y z - 6 z, 10 x z - 10 y - 8, 4 x z + 11 y + 16 z] > Problem := [F,G]; 2 Problem := [[-16 x y + 3 x z - 15 y , 14 x z - 11 x + 3 y, -10 y z + 5 y - 15], 2 [-16 x z + 14 y z - 6 z, 10 x z - 10 y - 8, 4 x z + 11 y + 16 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=67.0MB, alloc=56.3MB, time=1.08 memory used=106.1MB, alloc=60.3MB, time=1.67 memory used=142.2MB, alloc=84.3MB, time=2.20 memory used=199.8MB, alloc=92.3MB, time=3.09 memory used=256.8MB, alloc=116.3MB, time=3.98 memory used=336.7MB, alloc=116.3MB, time=5.20 memory used=415.2MB, alloc=140.3MB, time=6.46 memory used=515.0MB, alloc=164.3MB, time=8.16 memory used=613.4MB, alloc=420.3MB, time=9.88 memory used=732.1MB, alloc=444.3MB, time=11.93 memory used=867.8MB, alloc=468.3MB, time=14.30 memory used=1036.3MB, alloc=492.3MB, time=17.34 memory used=1223.5MB, alloc=516.3MB, time=20.91 memory used=1431.3MB, alloc=540.3MB, time=24.95 memory used=1664.3MB, alloc=564.3MB, time=29.72 memory used=1917.4MB, alloc=588.3MB, time=35.34 memory used=2195.1MB, alloc=612.3MB, time=41.98 memory used=2493.4MB, alloc=636.3MB, time=49.57 memory used=2810.8MB, alloc=660.3MB, time=58.48 memory used=3143.3MB, alloc=684.3MB, time=68.59 memory used=3489.9MB, alloc=708.3MB, time=78.72 memory used=3817.2MB, alloc=732.3MB, time=88.16 memory used=4071.0MB, alloc=756.3MB, time=95.41 memory used=4317.8MB, alloc=780.3MB, time=102.22 memory used=4563.6MB, alloc=804.3MB, time=109.22 memory used=4772.5MB, alloc=828.3MB, time=114.74 memory used=4992.5MB, alloc=852.3MB, time=119.73 memory used=5144.7MB, alloc=876.3MB, time=123.50 memory used=5347.0MB, alloc=900.3MB, time=128.16 |\^/| 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(); 1428294683 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [14 x y + 5 y z + 4 y, -9 x - 4 x y - z , -9 x - 10 x z + 13 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [-11 x z + 7 y - 2 z, 8 x y - 8 x - 3, 14 y z - 4 x + 2] > Problem := [F,G]; Problem := [ 2 2 2 [14 x y + 5 y z + 4 y, -9 x - 4 x y - z , -9 x - 10 x z + 13 y z], [-11 x z + 7 y - 2 z, 8 x y - 8 x - 3, 14 y z - 4 x + 2]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=47.0MB, alloc=32.3MB, time=0.78 memory used=66.2MB, alloc=56.3MB, time=1.08 memory used=105.6MB, alloc=60.3MB, time=1.68 memory used=143.8MB, alloc=84.3MB, time=2.26 memory used=204.1MB, alloc=92.3MB, time=3.22 memory used=263.4MB, alloc=116.3MB, time=4.17 memory used=343.2MB, alloc=116.3MB, time=5.42 memory used=422.9MB, alloc=140.3MB, time=6.64 memory used=504.2MB, alloc=164.3MB, time=8.00 memory used=572.2MB, alloc=420.3MB, time=9.11 memory used=700.2MB, alloc=444.3MB, time=11.25 memory used=853.8MB, alloc=468.3MB, time=13.88 memory used=1028.8MB, alloc=492.3MB, time=17.07 memory used=1225.0MB, alloc=516.3MB, time=20.90 memory used=1443.3MB, alloc=540.3MB, time=25.07 memory used=1683.2MB, alloc=564.3MB, time=29.91 memory used=1942.4MB, alloc=588.3MB, time=35.78 memory used=2222.0MB, alloc=612.3MB, time=42.43 memory used=2480.9MB, alloc=636.3MB, time=47.96 memory used=2741.6MB, alloc=660.3MB, time=54.18 memory used=2954.4MB, alloc=684.3MB, time=59.04 memory used=3143.0MB, alloc=708.3MB, time=63.28 memory used=3308.6MB, alloc=732.3MB, time=67.14 memory used=3502.2MB, alloc=732.3MB, time=72.45 memory used=3682.2MB, alloc=756.3MB, time=77.14 memory used=3826.6MB, alloc=756.3MB, time=80.43 memory used=3942.7MB, alloc=756.3MB, time=83.63 memory used=4063.1MB, alloc=780.3MB, time=86.45 memory used=4203.0MB, alloc=780.3MB, time=89.96 memory used=4390.7MB, alloc=804.3MB, time=94.34 memory used=4551.7MB, alloc=828.3MB, time=98.40 memory used=4942.7MB, alloc=852.3MB, time=106.63 memory used=5334.4MB, alloc=876.3MB, time=114.99 memory used=5723.9MB, alloc=900.3MB, time=123.28 memory used=6111.1MB, alloc=924.3MB, time=132.90 |\^/| 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(); 1428294983 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [15 x z - 11 y z + 20 y, -16 x - 13 x z + 13 y, 10 x y + 5 y - 5 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [7 y z - 18 z - 6, -13 x - 20 x y + 7 x z, 10 y - 11 y z + 7 z ] > Problem := [F,G]; Problem := [ 2 2 [15 x z - 11 y z + 20 y, -16 x - 13 x z + 13 y, 10 x y + 5 y - 5 z], 2 2 2 2 [7 y z - 18 z - 6, -13 x - 20 x y + 7 x z, 10 y - 11 y z + 7 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=45.2MB, alloc=56.3MB, time=0.78 memory used=86.0MB, alloc=60.3MB, time=1.38 memory used=126.1MB, alloc=84.3MB, time=1.98 memory used=171.5MB, alloc=84.3MB, time=2.67 memory used=233.3MB, alloc=116.3MB, time=3.65 memory used=317.1MB, alloc=116.3MB, time=4.97 memory used=388.0MB, alloc=140.3MB, time=6.04 memory used=458.1MB, alloc=396.3MB, time=7.18 memory used=566.7MB, alloc=420.3MB, time=8.88 memory used=700.4MB, alloc=444.3MB, time=10.99 memory used=834.1MB, alloc=468.3MB, time=13.22 memory used=942.2MB, alloc=468.3MB, time=14.99 memory used=1067.9MB, alloc=492.3MB, time=17.21 memory used=1172.1MB, alloc=492.3MB, time=19.13 memory used=1282.5MB, alloc=492.3MB, time=21.26 memory used=1357.6MB, alloc=492.3MB, time=22.73 memory used=1446.8MB, alloc=492.3MB, time=24.47 memory used=1532.3MB, alloc=516.3MB, time=26.19 memory used=1611.6MB, alloc=516.3MB, time=27.85 memory used=1679.3MB, alloc=516.3MB, time=29.45 memory used=1745.4MB, alloc=516.3MB, time=30.89 memory used=1801.0MB, alloc=516.3MB, time=32.08 memory used=1850.6MB, alloc=516.3MB, time=33.33 memory used=1906.0MB, alloc=516.3MB, time=34.77 memory used=2105.6MB, alloc=540.3MB, time=38.42 memory used=2311.8MB, alloc=564.3MB, time=42.59 memory used=2505.1MB, alloc=588.3MB, time=46.58 memory used=2690.3MB, alloc=612.3MB, time=50.63 memory used=2857.5MB, alloc=636.3MB, time=54.34 memory used=3006.5MB, alloc=660.3MB, time=57.67 memory used=3158.8MB, alloc=660.3MB, time=61.05 memory used=3284.5MB, alloc=660.3MB, time=64.17 memory used=3422.0MB, alloc=684.3MB, time=67.67 memory used=3550.5MB, alloc=684.3MB, time=71.07 memory used=3663.0MB, alloc=684.3MB, time=74.09 memory used=4011.3MB, alloc=708.3MB, time=81.54 memory used=4361.8MB, alloc=732.3MB, time=89.94 memory used=4730.3MB, alloc=756.3MB, time=98.50 memory used=5122.9MB, alloc=780.3MB, time=108.53 memory used=5530.2MB, alloc=804.3MB, time=119.31 memory used=5865.9MB, alloc=828.3MB, time=127.71 |\^/| 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(); 1428295283 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [2 x y + 20 y z + 2, -16 x z - 11 z - 12 y, -14 x + 6 x y + 19 x z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [17 y z + 5 z + 3 z, -7 x - 6 y z + 8 x, -16 x y + 7 z - 4 x] > Problem := [F,G]; Problem := [ 2 2 [2 x y + 20 y z + 2, -16 x z - 11 z - 12 y, -14 x + 6 x y + 19 x z], 2 2 2 [17 y z + 5 z + 3 z, -7 x - 6 y z + 8 x, -16 x y + 7 z - 4 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.3MB, alloc=32.3MB, time=0.79 memory used=65.0MB, alloc=56.3MB, time=1.05 memory used=102.8MB, alloc=60.3MB, time=1.62 memory used=139.5MB, alloc=84.3MB, time=2.17 memory used=197.7MB, alloc=92.3MB, time=3.06 memory used=254.2MB, alloc=116.3MB, time=3.96 memory used=332.6MB, alloc=116.3MB, time=5.19 memory used=405.9MB, alloc=140.3MB, time=6.36 memory used=501.9MB, alloc=164.3MB, time=7.99 memory used=591.8MB, alloc=420.3MB, time=9.54 memory used=708.5MB, alloc=444.3MB, time=11.59 memory used=848.8MB, alloc=468.3MB, time=14.09 memory used=1014.8MB, alloc=492.3MB, time=17.16 memory used=1202.9MB, alloc=516.3MB, time=20.82 memory used=1413.6MB, alloc=540.3MB, time=24.95 memory used=1643.9MB, alloc=564.3MB, time=30.02 memory used=1894.5MB, alloc=588.3MB, time=35.68 memory used=2162.9MB, alloc=612.3MB, time=41.91 memory used=2453.2MB, alloc=636.3MB, time=48.89 memory used=2756.5MB, alloc=660.3MB, time=55.78 memory used=3061.3MB, alloc=684.3MB, time=63.07 memory used=3326.3MB, alloc=708.3MB, time=69.54 memory used=3594.8MB, alloc=732.3MB, time=76.21 memory used=3860.6MB, alloc=756.3MB, time=83.44 memory used=4078.2MB, alloc=780.3MB, time=89.02 memory used=4284.7MB, alloc=804.3MB, time=94.24 memory used=4502.7MB, alloc=828.3MB, time=100.36 memory used=4703.8MB, alloc=852.3MB, time=106.21 memory used=4895.0MB, alloc=852.3MB, time=111.91 memory used=5079.1MB, alloc=852.3MB, time=117.71 memory used=5222.7MB, alloc=852.3MB, time=121.28 memory used=5390.0MB, alloc=852.3MB, time=127.01 memory used=5558.9MB, alloc=876.3MB, time=133.07 memory used=5723.4MB, alloc=876.3MB, time=138.58 |\^/| 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(); 1428295583 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-14 z + 9 x - 6 z, -7 y + 4 z + 9, -9 x y - 7 y - 11] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [11 x - 5 y + 3, -7 x - x y - z , 20 y z + 20 x - 19 z] > Problem := [F,G]; 2 2 2 2 Problem := [[-14 z + 9 x - 6 z, -7 y + 4 z + 9, -9 x y - 7 y - 11], 2 2 2 [11 x - 5 y + 3, -7 x - x y - z , 20 y z + 20 x - 19 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=47.1MB, alloc=32.3MB, time=0.81 memory used=66.2MB, alloc=56.3MB, time=1.12 memory used=107.0MB, alloc=60.3MB, time=1.74 memory used=147.0MB, alloc=84.3MB, time=2.37 memory used=210.7MB, alloc=92.3MB, time=3.37 memory used=272.6MB, alloc=92.3MB, time=4.34 memory used=333.0MB, alloc=116.3MB, time=5.32 memory used=414.2MB, alloc=140.3MB, time=6.65 memory used=499.0MB, alloc=140.3MB, time=8.06 memory used=571.0MB, alloc=396.3MB, time=9.27 memory used=672.4MB, alloc=420.3MB, time=10.99 memory used=799.5MB, alloc=444.3MB, time=13.12 memory used=949.8MB, alloc=444.3MB, time=15.74 memory used=1098.8MB, alloc=468.3MB, time=18.41 memory used=1263.7MB, alloc=492.3MB, time=21.54 memory used=1418.5MB, alloc=516.3MB, time=24.52 memory used=1576.5MB, alloc=516.3MB, time=27.61 memory used=1714.3MB, alloc=540.3MB, time=30.23 memory used=1842.9MB, alloc=540.3MB, time=32.86 memory used=1955.5MB, alloc=564.3MB, time=35.16 memory used=2061.0MB, alloc=564.3MB, time=37.21 memory used=2168.3MB, alloc=588.3MB, time=39.32 memory used=2268.8MB, alloc=588.3MB, time=41.56 memory used=2420.0MB, alloc=612.3MB, time=44.86 memory used=2563.7MB, alloc=636.3MB, time=47.97 memory used=2723.1MB, alloc=660.3MB, time=51.09 memory used=2874.8MB, alloc=684.3MB, time=54.02 memory used=2999.6MB, alloc=708.3MB, time=56.70 memory used=3127.3MB, alloc=708.3MB, time=59.38 memory used=3226.0MB, alloc=732.3MB, time=61.65 memory used=3310.8MB, alloc=732.3MB, time=63.65 memory used=3425.4MB, alloc=756.3MB, time=66.16 memory used=3530.7MB, alloc=780.3MB, time=68.58 memory used=3641.8MB, alloc=804.3MB, time=71.21 memory used=3755.4MB, alloc=804.3MB, time=73.83 memory used=3858.7MB, alloc=828.3MB, time=76.23 memory used=3967.3MB, alloc=828.3MB, time=78.64 memory used=4333.1MB, alloc=852.3MB, time=86.07 memory used=4688.1MB, alloc=876.3MB, time=93.53 memory used=5044.0MB, alloc=900.3MB, time=101.08 memory used=5369.9MB, alloc=924.3MB, time=112.27 memory used=5676.8MB, alloc=948.3MB, time=124.29 memory used=5990.5MB, alloc=972.3MB, time=137.15 memory used=6312.0MB, alloc=996.3MB, time=150.64 |\^/| 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(); 1428295884 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-10 x + 19 x z - 18 z , 10 x z - 19 z - 3, -17 y z - 15 z + 11 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [3 x z - 2 x - 9 y, 12 x + 12 x - 16, -7 x - 2 x y + 3 x z] > Problem := [F,G]; Problem := [ 2 2 2 [-10 x + 19 x z - 18 z , 10 x z - 19 z - 3, -17 y z - 15 z + 11 y], 2 2 [3 x z - 2 x - 9 y, 12 x + 12 x - 16, -7 x - 2 x y + 3 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=46.1MB, alloc=32.3MB, time=0.80 memory used=64.9MB, alloc=56.3MB, time=1.10 memory used=106.2MB, alloc=60.3MB, time=1.72 memory used=145.7MB, alloc=84.3MB, time=2.32 memory used=207.2MB, alloc=92.3MB, time=3.28 memory used=268.9MB, alloc=116.3MB, time=4.27 memory used=347.9MB, alloc=140.3MB, time=5.54 memory used=427.9MB, alloc=396.3MB, time=6.87 memory used=534.4MB, alloc=420.3MB, time=8.65 memory used=666.6MB, alloc=444.3MB, time=10.97 memory used=819.0MB, alloc=468.3MB, time=13.72 memory used=989.3MB, alloc=492.3MB, time=17.02 memory used=1133.1MB, alloc=516.3MB, time=19.91 memory used=1268.4MB, alloc=516.3MB, time=22.75 memory used=1391.4MB, alloc=516.3MB, time=25.38 memory used=1507.2MB, alloc=516.3MB, time=27.83 memory used=1632.0MB, alloc=540.3MB, time=30.74 memory used=1761.9MB, alloc=540.3MB, time=33.70 memory used=1857.0MB, alloc=540.3MB, time=35.72 memory used=1962.3MB, alloc=564.3MB, time=37.95 memory used=2039.3MB, alloc=564.3MB, time=39.62 memory used=2112.4MB, alloc=564.3MB, time=41.26 memory used=2191.7MB, alloc=588.3MB, time=43.17 memory used=2317.1MB, alloc=588.3MB, time=45.91 memory used=2428.6MB, alloc=612.3MB, time=48.33 memory used=2540.6MB, alloc=636.3MB, time=50.79 memory used=2658.8MB, alloc=636.3MB, time=53.37 memory used=2747.8MB, alloc=660.3MB, time=55.45 memory used=2837.1MB, alloc=660.3MB, time=57.70 memory used=3100.3MB, alloc=684.3MB, time=63.11 memory used=3357.4MB, alloc=708.3MB, time=71.05 memory used=3598.2MB, alloc=732.3MB, time=80.26 memory used=3848.0MB, alloc=756.3MB, time=90.15 memory used=4109.4MB, alloc=780.3MB, time=100.84 memory used=4374.0MB, alloc=804.3MB, time=112.76 memory used=4661.8MB, alloc=828.3MB, time=125.75 memory used=4973.5MB, alloc=852.3MB, time=139.91 |\^/| 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(); 1428296184 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-17 x y + x z - 20 z , -19 x y + 6 y - 2 y z, 13 x - 10 x z + 3 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-19 x z - 16 z + 17 z, -16 x z - 20 y - 11, -12 x - 9 x y - 3 y] > Problem := [F,G]; Problem := [ 2 2 2 2 [-17 x y + x z - 20 z , -19 x y + 6 y - 2 y z, 13 x - 10 x z + 3 z ], 2 2 [-19 x z - 16 z + 17 z, -16 x z - 20 y - 11, -12 x - 9 x y - 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.47 memory used=46.8MB, alloc=32.3MB, time=0.76 memory used=66.6MB, alloc=56.3MB, time=1.06 memory used=105.6MB, alloc=60.3MB, time=1.64 memory used=142.2MB, alloc=84.3MB, time=2.20 memory used=200.0MB, alloc=92.3MB, time=3.08 memory used=255.8MB, alloc=116.3MB, time=3.94 memory used=331.7MB, alloc=116.3MB, time=5.11 memory used=405.3MB, alloc=140.3MB, time=6.30 memory used=490.8MB, alloc=164.3MB, time=7.72 memory used=575.6MB, alloc=420.3MB, time=9.20 memory used=698.0MB, alloc=444.3MB, time=11.30 memory used=839.4MB, alloc=468.3MB, time=13.81 memory used=1008.8MB, alloc=492.3MB, time=16.68 memory used=1198.1MB, alloc=516.3MB, time=20.23 memory used=1408.5MB, alloc=540.3MB, time=24.22 memory used=1641.2MB, alloc=564.3MB, time=29.10 memory used=1892.1MB, alloc=588.3MB, time=34.54 memory used=2163.6MB, alloc=612.3MB, time=40.71 memory used=2451.5MB, alloc=636.3MB, time=46.98 memory used=2740.8MB, alloc=660.3MB, time=53.42 memory used=2999.5MB, alloc=684.3MB, time=58.81 memory used=3230.2MB, alloc=708.3MB, time=64.41 memory used=3467.5MB, alloc=732.3MB, time=69.67 memory used=3794.3MB, alloc=756.3MB, time=76.66 memory used=4123.2MB, alloc=780.3MB, time=83.75 memory used=4405.4MB, alloc=804.3MB, time=89.97 memory used=4722.7MB, alloc=828.3MB, time=98.74 memory used=4997.8MB, alloc=852.3MB, time=109.44 memory used=5277.6MB, alloc=876.3MB, time=120.79 memory used=5565.3MB, alloc=900.3MB, time=132.91 |\^/| 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(); 1428296484 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [5 x y + x z + 11 y, -x - 9 x z - 7 y z, -20 x z + 16 z - 13 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [3 x y + 19, 6 x - 12 y + 2 y z, 12 x - 6 x z + 19 y ] > Problem := [F,G]; 2 2 Problem := [[5 x y + x z + 11 y, -x - 9 x z - 7 y z, -20 x z + 16 z - 13 z], 2 2 2 2 [3 x y + 19, 6 x - 12 y + 2 y z, 12 x - 6 x z + 19 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.4MB, alloc=32.3MB, time=0.79 memory used=67.3MB, alloc=56.3MB, time=1.10 memory used=106.5MB, alloc=60.3MB, time=1.70 memory used=144.5MB, alloc=84.3MB, time=2.26 memory used=206.0MB, alloc=92.3MB, time=3.21 memory used=267.6MB, alloc=116.3MB, time=4.16 memory used=348.8MB, alloc=116.3MB, time=5.42 memory used=427.7MB, alloc=396.3MB, time=6.69 memory used=530.3MB, alloc=420.3MB, time=8.34 memory used=654.1MB, alloc=444.3MB, time=10.39 memory used=795.0MB, alloc=468.3MB, time=12.62 memory used=909.7MB, alloc=492.3MB, time=14.37 memory used=1018.7MB, alloc=492.3MB, time=16.05 memory used=1141.5MB, alloc=492.3MB, time=18.20 memory used=1246.0MB, alloc=516.3MB, time=19.86 memory used=1342.4MB, alloc=516.3MB, time=21.61 memory used=1424.4MB, alloc=516.3MB, time=23.10 memory used=1505.8MB, alloc=516.3MB, time=24.66 memory used=1570.6MB, alloc=516.3MB, time=25.84 memory used=1640.2MB, alloc=516.3MB, time=27.27 memory used=1703.1MB, alloc=516.3MB, time=28.63 memory used=1762.6MB, alloc=516.3MB, time=29.89 memory used=1813.5MB, alloc=516.3MB, time=31.09 memory used=2023.0MB, alloc=540.3MB, time=34.60 memory used=2246.0MB, alloc=564.3MB, time=38.50 memory used=2446.5MB, alloc=588.3MB, time=42.45 memory used=2635.1MB, alloc=612.3MB, time=46.19 memory used=2818.2MB, alloc=636.3MB, time=50.06 memory used=2955.7MB, alloc=660.3MB, time=52.92 memory used=3107.5MB, alloc=684.3MB, time=56.37 memory used=3214.1MB, alloc=684.3MB, time=59.03 memory used=3329.7MB, alloc=684.3MB, time=61.88 memory used=3431.8MB, alloc=684.3MB, time=64.48 memory used=3497.0MB, alloc=684.3MB, time=66.29 memory used=3836.0MB, alloc=708.3MB, time=73.76 memory used=4192.0MB, alloc=732.3MB, time=81.36 memory used=4565.4MB, alloc=756.3MB, time=89.58 memory used=4920.1MB, alloc=780.3MB, time=97.83 memory used=5203.2MB, alloc=804.3MB, time=104.76 memory used=5489.8MB, alloc=828.3MB, time=111.29 memory used=5813.4MB, alloc=852.3MB, time=119.23 memory used=6154.2MB, alloc=876.3MB, time=127.55 memory used=6481.2MB, alloc=900.3MB, time=135.39 |\^/| 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(); 1428296784 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-5 x y + 18 y z - 19 z , 14 z + 15 y + 6, -20 y z - 6 z - 14 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-12 z - 7 z - 9, 6 x - y + 17 z, -18 x - 5 y z - 16 z ] > Problem := [F,G]; 2 2 2 Problem := [[-5 x y + 18 y z - 19 z , 14 z + 15 y + 6, -20 y z - 6 z - 14 z], 2 2 2 2 [-12 z - 7 z - 9, 6 x - y + 17 z, -18 x - 5 y z - 16 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.79 memory used=67.0MB, alloc=56.3MB, time=1.07 memory used=104.7MB, alloc=60.3MB, time=1.63 memory used=140.0MB, alloc=84.3MB, time=2.15 memory used=196.3MB, alloc=84.3MB, time=2.98 memory used=250.6MB, alloc=116.3MB, time=3.85 memory used=325.5MB, alloc=116.3MB, time=4.96 memory used=398.2MB, alloc=140.3MB, time=6.13 memory used=492.2MB, alloc=164.3MB, time=7.66 memory used=587.2MB, alloc=420.3MB, time=9.22 memory used=703.5MB, alloc=444.3MB, time=11.27 memory used=845.9MB, alloc=468.3MB, time=13.86 memory used=1011.4MB, alloc=468.3MB, time=16.92 memory used=1180.3MB, alloc=492.3MB, time=20.08 memory used=1367.4MB, alloc=516.3MB, time=24.01 memory used=1574.5MB, alloc=540.3MB, time=28.49 memory used=1801.9MB, alloc=564.3MB, time=33.56 memory used=2050.1MB, alloc=588.3MB, time=39.26 memory used=2316.8MB, alloc=612.3MB, time=45.76 memory used=2597.9MB, alloc=636.3MB, time=52.45 memory used=2904.7MB, alloc=660.3MB, time=60.31 memory used=3231.9MB, alloc=684.3MB, time=69.62 memory used=3580.1MB, alloc=708.3MB, time=79.59 memory used=3944.7MB, alloc=732.3MB, time=90.34 memory used=4315.0MB, alloc=756.3MB, time=100.84 memory used=4707.0MB, alloc=780.3MB, time=113.39 |\^/| 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(); 1428297084 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [18 x - 4 y - 19 y, -20 x - 15 x z - 18 z, -18 + 20 y + 5 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [5 x z + 18 z + 20, -6 x + 20 x z - 2 y, 14 x y + 15 x - 17 z] > Problem := [F,G]; 2 2 2 Problem := [[18 x - 4 y - 19 y, -20 x - 15 x z - 18 z, -18 + 20 y + 5 z], 2 [5 x z + 18 z + 20, -6 x + 20 x z - 2 y, 14 x y + 15 x - 17 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=46.6MB, alloc=32.3MB, time=0.78 memory used=65.2MB, alloc=56.3MB, time=1.07 memory used=105.8MB, alloc=60.3MB, time=1.66 memory used=144.6MB, alloc=60.3MB, time=2.24 memory used=181.9MB, alloc=84.3MB, time=2.82 memory used=232.5MB, alloc=84.3MB, time=3.59 memory used=291.1MB, alloc=92.3MB, time=4.53 memory used=349.6MB, alloc=116.3MB, time=5.46 memory used=431.4MB, alloc=116.3MB, time=6.81 memory used=510.6MB, alloc=140.3MB, time=8.21 memory used=613.0MB, alloc=140.3MB, time=10.08 memory used=712.7MB, alloc=164.3MB, time=11.85 memory used=783.8MB, alloc=164.3MB, time=13.10 memory used=858.1MB, alloc=444.3MB, time=14.54 memory used=992.8MB, alloc=468.3MB, time=16.96 memory used=1136.5MB, alloc=492.3MB, time=19.57 memory used=1294.3MB, alloc=516.3MB, time=22.44 memory used=1462.2MB, alloc=540.3MB, time=25.60 memory used=1640.6MB, alloc=564.3MB, time=28.98 memory used=1829.1MB, alloc=588.3MB, time=32.52 memory used=2026.1MB, alloc=612.3MB, time=36.30 memory used=2232.9MB, alloc=636.3MB, time=40.37 memory used=2452.4MB, alloc=660.3MB, time=44.63 memory used=2676.0MB, alloc=684.3MB, time=49.06 memory used=2905.4MB, alloc=708.3MB, time=53.66 memory used=3133.4MB, alloc=732.3MB, time=60.32 memory used=3346.0MB, alloc=756.3MB, time=68.15 memory used=3567.9MB, alloc=780.3MB, time=76.81 memory used=3802.5MB, alloc=804.3MB, time=86.19 memory used=4050.3MB, alloc=828.3MB, time=96.38 memory used=4312.4MB, alloc=852.3MB, time=107.12 memory used=4589.1MB, alloc=876.3MB, time=118.61 memory used=4881.2MB, alloc=900.3MB, time=130.91 |\^/| 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(); 1428297384 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [17 y - 7 z - 2 y, 9 x - z - 20 z, -15 y + 15 y + 5 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-x + 9 y - 10 z, -18 x z + y - 18, 2 x y - 18 x z + 6 y ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[17 y - 7 z - 2 y, 9 x - z - 20 z, -15 y + 15 y + 5 z], 2 [-x + 9 y - 10 z, -18 x z + y - 18, 2 x y - 18 x z + 6 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=46.4MB, alloc=32.3MB, time=0.78 memory used=65.3MB, alloc=56.3MB, time=1.07 memory used=105.2MB, alloc=60.3MB, time=1.68 memory used=143.2MB, alloc=84.3MB, time=2.24 memory used=202.8MB, alloc=92.3MB, time=3.17 memory used=261.9MB, alloc=116.3MB, time=4.14 memory used=344.7MB, alloc=116.3MB, time=5.49 memory used=426.8MB, alloc=140.3MB, time=6.89 memory used=508.1MB, alloc=140.3MB, time=8.29 memory used=587.7MB, alloc=396.3MB, time=9.71 memory used=692.9MB, alloc=420.3MB, time=11.61 memory used=819.8MB, alloc=444.3MB, time=13.88 memory used=966.9MB, alloc=468.3MB, time=16.37 memory used=1110.2MB, alloc=492.3MB, time=19.06 memory used=1247.8MB, alloc=492.3MB, time=21.61 memory used=1395.5MB, alloc=516.3MB, time=24.64 memory used=1531.4MB, alloc=516.3MB, time=27.32 memory used=1640.0MB, alloc=540.3MB, time=29.46 memory used=1736.3MB, alloc=540.3MB, time=31.53 memory used=1840.3MB, alloc=540.3MB, time=33.70 memory used=1937.8MB, alloc=540.3MB, time=35.90 memory used=2038.6MB, alloc=540.3MB, time=38.18 memory used=2110.4MB, alloc=564.3MB, time=39.85 memory used=2189.8MB, alloc=564.3MB, time=41.56 memory used=2278.8MB, alloc=564.3MB, time=43.79 memory used=2369.4MB, alloc=564.3MB, time=46.40 memory used=2452.7MB, alloc=564.3MB, time=48.78 memory used=2509.9MB, alloc=564.3MB, time=50.28 memory used=2584.8MB, alloc=564.3MB, time=52.50 memory used=2822.4MB, alloc=588.3MB, time=58.13 memory used=3062.1MB, alloc=612.3MB, time=63.93 memory used=3279.6MB, alloc=636.3MB, time=69.30 memory used=3490.9MB, alloc=660.3MB, time=74.57 memory used=3697.8MB, alloc=684.3MB, time=80.09 memory used=3877.9MB, alloc=708.3MB, time=84.64 memory used=4063.4MB, alloc=708.3MB, time=89.69 memory used=4208.3MB, alloc=732.3MB, time=93.31 memory used=4338.2MB, alloc=732.3MB, time=96.27 memory used=4502.8MB, alloc=732.3MB, time=101.12 memory used=4643.7MB, alloc=732.3MB, time=105.17 memory used=4727.2MB, alloc=732.3MB, time=107.50 memory used=4839.8MB, alloc=732.3MB, time=110.94 memory used=5226.9MB, alloc=756.3MB, time=120.69 memory used=5629.8MB, alloc=780.3MB, time=131.63 memory used=6058.3MB, alloc=804.3MB, time=143.31 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428440460 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-11 x y - 6 y - 2 z , -2 x z - 13 y + 8, 16 x y - 20 z - 5 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [7 x + 10 x y + 19 y, 18 x - 4 y + z, 12 x z - 18 y z - 1] > Problem := [F,G]; 2 2 2 2 Problem := [[-11 x y - 6 y - 2 z , -2 x z - 13 y + 8, 16 x y - 20 z - 5 z], 2 2 2 [7 x + 10 x y + 19 y, 18 x - 4 y + z, 12 x z - 18 y z - 1]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.38 memory used=47.5MB, alloc=32.3MB, time=0.57 memory used=67.1MB, alloc=56.3MB, time=0.76 memory used=108.2MB, alloc=60.3MB, time=1.13 memory used=141.7MB, alloc=84.3MB, time=1.43 memory used=203.9MB, alloc=92.3MB, time=1.99 memory used=267.8MB, alloc=372.3MB, time=2.56 memory used=359.7MB, alloc=396.3MB, time=3.33 memory used=472.7MB, alloc=420.3MB, time=4.33 memory used=604.4MB, alloc=444.3MB, time=5.53 memory used=724.7MB, alloc=444.3MB, time=6.67 memory used=835.8MB, alloc=468.3MB, time=7.77 memory used=929.7MB, alloc=468.3MB, time=8.67 memory used=1015.1MB, alloc=468.3MB, time=9.59 memory used=1107.7MB, alloc=468.3MB, time=10.61 memory used=1189.8MB, alloc=492.3MB, time=11.43 memory used=1272.6MB, alloc=492.3MB, time=12.30 memory used=1342.9MB, alloc=492.3MB, time=13.16 memory used=1407.3MB, alloc=492.3MB, time=13.93 memory used=1471.1MB, alloc=492.3MB, time=14.63 memory used=1524.2MB, alloc=492.3MB, time=15.26 memory used=1568.2MB, alloc=492.3MB, time=15.86 memory used=1610.6MB, alloc=492.3MB, time=16.47 memory used=1654.0MB, alloc=492.3MB, time=17.10 memory used=1835.7MB, alloc=516.3MB, time=18.97 memory used=2012.2MB, alloc=540.3MB, time=20.84 memory used=2181.5MB, alloc=564.3MB, time=22.70 memory used=2346.3MB, alloc=588.3MB, time=24.49 memory used=2498.6MB, alloc=612.3MB, time=26.33 memory used=2644.6MB, alloc=636.3MB, time=27.97 memory used=2779.8MB, alloc=636.3MB, time=29.77 memory used=2891.3MB, alloc=636.3MB, time=31.21 memory used=2991.0MB, alloc=636.3MB, time=32.66 memory used=3079.2MB, alloc=636.3MB, time=34.06 memory used=3384.7MB, alloc=660.3MB, time=37.41 memory used=3709.0MB, alloc=684.3MB, time=40.93 memory used=4051.8MB, alloc=708.3MB, time=44.99 memory used=4414.2MB, alloc=732.3MB, time=49.11 memory used=4733.4MB, alloc=756.3MB, time=52.69 memory used=5024.8MB, alloc=780.3MB, time=57.72 memory used=5309.2MB, alloc=804.3MB, time=63.23 memory used=5579.2MB, alloc=828.3MB, time=68.29 memory used=5795.3MB, alloc=852.3MB, time=72.00 memory used=6049.5MB, alloc=876.3MB, time=77.47 memory used=6255.1MB, alloc=900.3MB, time=82.40 memory used=6774.7MB, alloc=924.3MB, time=90.58 memory used=7319.3MB, alloc=948.3MB, time=101.42 memory used=7885.8MB, alloc=972.3MB, time=112.68 memory used=8437.3MB, alloc=996.3MB, time=125.89 memory used=9006.8MB, alloc=1020.3MB, time=140.59 memory used=9583.7MB, alloc=1044.3MB, time=156.74 memory used=10136.0MB, alloc=1068.3MB, time=169.94 memory used=10725.5MB, alloc=1092.3MB, time=184.95 memory used=11245.5MB, alloc=1116.3MB, time=198.78 memory used=11712.1MB, alloc=1140.3MB, time=213.12 memory used=12180.3MB, alloc=1164.3MB, time=225.38 memory used=12549.3MB, alloc=1188.3MB, time=235.53 memory used=12934.5MB, alloc=1212.3MB, time=247.23 memory used=13378.9MB, alloc=1236.3MB, time=258.51 memory used=13707.7MB, alloc=1260.3MB, time=267.98 memory used=14021.8MB, alloc=1284.3MB, time=277.71 memory used=14352.5MB, alloc=1308.3MB, time=288.92 memory used=14641.3MB, alloc=1332.3MB, time=297.68 memory used=14906.6MB, alloc=1356.3MB, time=306.57 memory used=15161.9MB, alloc=1380.3MB, time=315.82 memory used=15368.7MB, alloc=1404.3MB, time=324.87 memory used=15575.6MB, alloc=1428.3MB, time=333.83 memory used=15786.9MB, alloc=1452.3MB, time=342.56 memory used=15968.7MB, alloc=1476.3MB, time=351.30 memory used=16127.6MB, alloc=1500.3MB, time=359.89 memory used=16245.4MB, alloc=1524.3MB, time=366.97 memory used=16387.6MB, alloc=1548.3MB, time=374.16 memory used=16516.9MB, alloc=1572.3MB, time=381.22 memory used=16583.1MB, alloc=1596.3MB, time=387.66 memory used=16671.6MB, alloc=1620.3MB, time=394.25 memory used=16712.7MB, alloc=1644.3MB, time=399.93 memory used=16733.4MB, alloc=1668.3MB, time=405.58 memory used=16827.4MB, alloc=1668.3MB, time=412.51 memory used=16864.7MB, alloc=1668.3MB, time=418.20 memory used=16883.8MB, alloc=1668.3MB, time=423.49 memory used=16933.5MB, alloc=1668.3MB, time=429.51 memory used=16992.2MB, alloc=1668.3MB, time=436.20 memory used=17062.8MB, alloc=1692.3MB, time=443.42 memory used=17120.1MB, alloc=1692.3MB, time=450.02 memory used=17169.6MB, alloc=1692.3MB, time=456.22 memory used=17201.2MB, alloc=1692.3MB, time=462.10 memory used=17264.4MB, alloc=1692.3MB, time=468.27 memory used=17319.4MB, alloc=1692.3MB, time=474.69 memory used=17352.1MB, alloc=1692.3MB, time=480.51 memory used=17377.8MB, alloc=1692.3MB, time=486.77 memory used=17409.1MB, alloc=1692.3MB, time=492.71 memory used=17465.7MB, alloc=1692.3MB, time=499.07 memory used=17474.8MB, alloc=1948.3MB, time=510.67 memory used=18596.3MB, alloc=1972.3MB, time=540.79 memory used=19635.2MB, alloc=1996.3MB, time=567.97 memory used=20533.3MB, alloc=2020.3MB, time=595.44 memory used=21371.6MB, alloc=2044.3MB, time=622.53 memory used=22168.3MB, alloc=2068.3MB, time=649.79 memory used=22941.1MB, alloc=2092.3MB, time=679.47 memory used=23733.1MB, alloc=2116.3MB, time=705.24 memory used=24496.3MB, alloc=2140.3MB, time=729.32 memory used=25195.1MB, alloc=2164.3MB, time=753.19 memory used=25906.1MB, alloc=2188.3MB, time=776.85 memory used=26615.3MB, alloc=2212.3MB, time=800.71 memory used=27317.5MB, alloc=2236.3MB, time=828.08 memory used=27967.4MB, alloc=2260.3MB, time=855.57 memory used=28546.7MB, alloc=2284.3MB, time=880.64 memory used=29180.9MB, alloc=2308.3MB, time=906.02 memory used=29792.9MB, alloc=2332.3MB, time=931.29 memory used=30328.3MB, alloc=2356.3MB, time=956.34 memory used=30860.2MB, alloc=2380.3MB, time=982.33 memory used=31420.7MB, alloc=2404.3MB, time=1008.42 memory used=31845.4MB, alloc=2428.3MB, time=1038.14 |\^/| 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(); 1428441661 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-16 x y + y z + 5 x, -14 z - 3 x - 7 y, 4 x z + 13 x + 7] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [11 x z - 7 y - 19 z, -19 x y + 10 y + 5 y, -15 x y - 2 y - 14 z] > Problem := [F,G]; 2 Problem := [[-16 x y + y z + 5 x, -14 z - 3 x - 7 y, 4 x z + 13 x + 7], 2 2 2 [11 x z - 7 y - 19 z, -19 x y + 10 y + 5 y, -15 x y - 2 y - 14 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.24 memory used=26.4MB, alloc=32.3MB, time=0.61 memory used=47.3MB, alloc=32.3MB, time=0.94 memory used=66.3MB, alloc=56.3MB, time=1.25 memory used=106.1MB, alloc=60.3MB, time=1.88 memory used=144.2MB, alloc=84.3MB, time=2.48 memory used=204.8MB, alloc=92.3MB, time=3.45 memory used=264.3MB, alloc=92.3MB, time=4.42 memory used=320.0MB, alloc=116.3MB, time=5.37 memory used=396.6MB, alloc=372.3MB, time=6.60 memory used=480.0MB, alloc=396.3MB, time=7.96 memory used=586.9MB, alloc=420.3MB, time=9.70 memory used=718.7MB, alloc=444.3MB, time=11.91 memory used=852.1MB, alloc=468.3MB, time=14.16 memory used=980.8MB, alloc=468.3MB, time=16.32 memory used=1096.9MB, alloc=492.3MB, time=18.12 memory used=1216.9MB, alloc=492.3MB, time=20.30 memory used=1313.9MB, alloc=492.3MB, time=21.96 memory used=1414.6MB, alloc=492.3MB, time=23.98 memory used=1511.1MB, alloc=492.3MB, time=26.00 memory used=1599.7MB, alloc=492.3MB, time=27.87 memory used=1678.0MB, alloc=516.3MB, time=29.55 memory used=1748.9MB, alloc=516.3MB, time=31.29 memory used=1820.7MB, alloc=516.3MB, time=32.98 memory used=1875.1MB, alloc=516.3MB, time=34.41 memory used=1927.7MB, alloc=516.3MB, time=35.61 memory used=1985.4MB, alloc=516.3MB, time=37.19 memory used=2193.6MB, alloc=540.3MB, time=41.16 memory used=2404.3MB, alloc=564.3MB, time=45.30 memory used=2576.0MB, alloc=588.3MB, time=48.98 memory used=2764.0MB, alloc=612.3MB, time=52.67 memory used=2924.0MB, alloc=636.3MB, time=56.09 memory used=3085.5MB, alloc=636.3MB, time=59.58 memory used=3226.1MB, alloc=660.3MB, time=62.82 memory used=3359.5MB, alloc=660.3MB, time=65.72 memory used=3504.2MB, alloc=660.3MB, time=69.27 memory used=3605.9MB, alloc=684.3MB, time=71.69 memory used=3726.4MB, alloc=684.3MB, time=74.80 memory used=3824.1MB, alloc=684.3MB, time=77.41 memory used=4175.1MB, alloc=708.3MB, time=84.58 memory used=4541.5MB, alloc=732.3MB, time=91.66 memory used=4899.7MB, alloc=756.3MB, time=97.57 memory used=5175.4MB, alloc=780.3MB, time=99.62 memory used=5495.0MB, alloc=804.3MB, time=101.50 memory used=5911.6MB, alloc=828.3MB, time=103.45 memory used=6373.7MB, alloc=852.3MB, time=105.43 memory used=6964.4MB, alloc=852.3MB, time=107.51 memory used=7646.7MB, alloc=852.3MB, time=109.74 memory used=8420.2MB, alloc=852.3MB, time=111.92 memory used=8856.2MB, alloc=867.8MB, time=113.65 memory used=9094.8MB, alloc=867.8MB, time=115.09 memory used=9340.2MB, alloc=867.8MB, time=116.54 memory used=9592.4MB, alloc=867.8MB, time=118.03 memory used=9851.3MB, alloc=867.8MB, time=119.60 memory used=10116.9MB, alloc=867.8MB, time=121.04 memory used=10389.3MB, alloc=867.8MB, time=122.45 memory used=10668.3MB, alloc=867.8MB, time=123.91 memory used=10954.1MB, alloc=867.8MB, time=125.36 memory used=11246.6MB, alloc=867.8MB, time=126.77 memory used=11545.9MB, alloc=867.8MB, time=128.31 memory used=11851.8MB, alloc=867.8MB, time=129.84 memory used=12164.6MB, alloc=867.8MB, time=131.50 memory used=12484.0MB, alloc=867.8MB, time=133.01 memory used=12810.2MB, alloc=867.8MB, time=134.55 memory used=13143.1MB, alloc=867.8MB, time=136.03 memory used=13479.4MB, alloc=867.8MB, time=137.51 memory used=13812.2MB, alloc=867.8MB, time=138.98 memory used=14151.4MB, alloc=867.8MB, time=140.44 memory used=14496.7MB, alloc=867.8MB, time=141.99 memory used=14848.2MB, alloc=867.8MB, time=143.61 memory used=15205.9MB, alloc=867.8MB, time=145.21 memory used=15570.0MB, alloc=867.8MB, time=146.77 memory used=15940.2MB, alloc=867.8MB, time=148.35 memory used=16316.5MB, alloc=867.8MB, time=149.84 memory used=16699.1MB, alloc=867.8MB, time=151.31 memory used=17088.1MB, alloc=867.8MB, time=152.81 memory used=17483.1MB, alloc=867.8MB, time=154.35 memory used=17884.4MB, alloc=867.8MB, time=155.82 memory used=18291.8MB, alloc=867.8MB, time=157.38 memory used=18705.7MB, alloc=867.8MB, time=158.92 memory used=19125.7MB, alloc=867.8MB, time=160.47 memory used=19551.8MB, alloc=867.8MB, time=162.01 memory used=19951.2MB, alloc=867.8MB, time=163.50 memory used=20240.7MB, alloc=867.8MB, time=164.88 memory used=20533.0MB, alloc=867.8MB, time=166.27 memory used=20828.2MB, alloc=867.8MB, time=167.65 memory used=21125.9MB, alloc=867.8MB, time=169.04 memory used=21426.4MB, alloc=867.8MB, time=170.52 memory used=21729.4MB, alloc=867.8MB, time=171.94 memory used=22035.2MB, alloc=867.8MB, time=173.43 memory used=22343.9MB, alloc=867.8MB, time=174.86 memory used=22655.1MB, alloc=867.8MB, time=176.29 memory used=22969.3MB, alloc=867.8MB, time=177.72 memory used=23286.0MB, alloc=867.8MB, time=179.15 memory used=23605.7MB, alloc=867.8MB, time=180.55 memory used=23927.8MB, alloc=867.8MB, time=182.00 memory used=24252.8MB, alloc=867.8MB, time=183.47 memory used=24580.6MB, alloc=867.8MB, time=184.97 memory used=24911.2MB, alloc=867.8MB, time=186.38 memory used=25244.5MB, alloc=867.8MB, time=187.91 memory used=25580.5MB, alloc=867.8MB, time=189.42 memory used=25919.0MB, alloc=867.8MB, time=190.91 memory used=26260.3MB, alloc=867.8MB, time=192.40 memory used=26604.4MB, alloc=867.8MB, time=193.89 memory used=26951.1MB, alloc=867.8MB, time=195.36 memory used=27300.8MB, alloc=867.8MB, time=196.90 memory used=27652.9MB, alloc=867.8MB, time=198.33 memory used=28008.0MB, alloc=867.8MB, time=199.76 memory used=28366.2MB, alloc=867.8MB, time=201.20 memory used=28728.4MB, alloc=867.8MB, time=202.67 memory used=29093.3MB, alloc=867.8MB, time=204.13 memory used=29460.8MB, alloc=867.8MB, time=205.63 memory used=29831.0MB, alloc=867.8MB, time=207.10 memory used=30204.0MB, alloc=867.8MB, time=208.54 memory used=30579.7MB, alloc=867.8MB, time=209.97 memory used=30958.6MB, alloc=867.8MB, time=211.42 memory used=31340.1MB, alloc=867.8MB, time=212.87 memory used=31724.2MB, alloc=867.8MB, time=214.30 memory used=32111.0MB, alloc=867.8MB, time=215.75 memory used=32500.6MB, alloc=867.8MB, time=217.17 memory used=32892.8MB, alloc=867.8MB, time=218.60 memory used=33288.2MB, alloc=867.8MB, time=220.02 memory used=33686.2MB, alloc=867.8MB, time=221.46 memory used=34086.9MB, alloc=867.8MB, time=222.87 memory used=34490.3MB, alloc=867.8MB, time=224.27 memory used=34896.3MB, alloc=867.8MB, time=225.66 memory used=35305.0MB, alloc=867.8MB, time=227.05 memory used=35716.9MB, alloc=867.8MB, time=228.43 memory used=36131.4MB, alloc=867.8MB, time=229.83 memory used=36548.6MB, alloc=867.8MB, time=231.20 memory used=36968.4MB, alloc=867.8MB, time=232.58 memory used=37391.0MB, alloc=867.8MB, time=233.95 memory used=37816.3MB, alloc=867.8MB, time=235.35 memory used=38244.7MB, alloc=867.8MB, time=236.81 memory used=38600.5MB, alloc=867.8MB, time=238.31 memory used=38916.3MB, alloc=867.8MB, time=239.79 memory used=39233.7MB, alloc=867.8MB, time=241.14 memory used=39552.7MB, alloc=867.8MB, time=242.50 memory used=39873.3MB, alloc=867.8MB, time=243.89 memory used=40194.9MB, alloc=867.8MB, time=245.26 memory used=40518.2MB, alloc=867.8MB, time=246.63 memory used=40843.1MB, alloc=867.8MB, time=247.98 memory used=41169.5MB, alloc=867.8MB, time=249.34 memory used=41497.3MB, alloc=867.8MB, time=250.68 memory used=41826.7MB, alloc=867.8MB, time=252.11 memory used=42157.2MB, alloc=867.8MB, time=253.48 memory used=42489.2MB, alloc=867.8MB, time=254.87 memory used=42823.0MB, alloc=867.8MB, time=256.33 memory used=43158.2MB, alloc=867.8MB, time=257.76 memory used=43494.5MB, alloc=867.8MB, time=259.22 memory used=43832.4MB, alloc=867.8MB, time=260.61 memory used=44171.8MB, alloc=867.8MB, time=262.01 memory used=44512.5MB, alloc=867.8MB, time=263.40 memory used=44855.2MB, alloc=867.8MB, time=264.85 memory used=45199.3MB, alloc=867.8MB, time=266.26 memory used=45544.6MB, alloc=867.8MB, time=267.67 memory used=45891.6MB, alloc=867.8MB, time=269.07 memory used=46240.0MB, alloc=867.8MB, time=270.45 memory used=46589.9MB, alloc=867.8MB, time=271.85 memory used=46940.9MB, alloc=867.8MB, time=273.22 memory used=47293.5MB, alloc=867.8MB, time=274.61 memory used=47647.6MB, alloc=867.8MB, time=276.03 memory used=48002.9MB, alloc=867.8MB, time=277.54 memory used=48360.4MB, alloc=867.8MB, time=278.93 memory used=48719.2MB, alloc=867.8MB, time=280.31 memory used=49079.0MB, alloc=867.8MB, time=281.71 memory used=49440.5MB, alloc=867.8MB, time=283.11 memory used=49803.3MB, alloc=867.8MB, time=284.50 memory used=50167.9MB, alloc=867.8MB, time=285.83 memory used=50536.4MB, alloc=867.8MB, time=287.17 memory used=50913.6MB, alloc=867.8MB, time=288.60 memory used=51292.1MB, alloc=867.8MB, time=289.97 memory used=51672.2MB, alloc=867.8MB, time=291.33 memory used=52054.2MB, alloc=867.8MB, time=292.87 memory used=52437.5MB, alloc=867.8MB, time=294.38 memory used=52822.2MB, alloc=867.8MB, time=295.91 memory used=53208.3MB, alloc=867.8MB, time=297.34 memory used=53596.4MB, alloc=867.8MB, time=298.76 memory used=53985.9MB, alloc=867.8MB, time=300.20 memory used=54376.7MB, alloc=867.8MB, time=301.64 memory used=54769.1MB, alloc=867.8MB, time=303.10 memory used=55163.4MB, alloc=867.8MB, time=304.64 memory used=55559.2MB, alloc=867.8MB, time=306.19 memory used=55956.2MB, alloc=867.8MB, time=307.70 memory used=56354.7MB, alloc=867.8MB, time=309.13 memory used=56755.1MB, alloc=867.8MB, time=310.68 memory used=57157.0MB, alloc=867.8MB, time=312.24 memory used=57560.2MB, alloc=867.8MB, time=313.79 memory used=57964.9MB, alloc=867.8MB, time=315.33 memory used=58371.7MB, alloc=867.8MB, time=316.87 memory used=58779.8MB, alloc=867.8MB, time=318.43 memory used=59189.2MB, alloc=867.8MB, time=320.02 memory used=59600.0MB, alloc=867.8MB, time=321.60 memory used=60012.8MB, alloc=867.8MB, time=323.06 memory used=60427.1MB, alloc=867.8MB, time=324.57 memory used=60842.6MB, alloc=867.8MB, time=326.09 memory used=61259.7MB, alloc=867.8MB, time=327.61 memory used=61678.9MB, alloc=867.8MB, time=329.10 memory used=62099.3MB, alloc=867.8MB, time=330.64 memory used=62521.1MB, alloc=867.8MB, time=332.20 memory used=62944.3MB, alloc=867.8MB, time=333.73 memory used=63369.5MB, alloc=867.8MB, time=335.16 memory used=63796.1MB, alloc=867.8MB, time=336.54 memory used=64215.0MB, alloc=867.8MB, time=337.93 memory used=64549.7MB, alloc=867.8MB, time=339.25 memory used=64881.0MB, alloc=867.8MB, time=340.57 memory used=65213.1MB, alloc=867.8MB, time=341.87 memory used=65545.9MB, alloc=867.8MB, time=343.17 memory used=65879.6MB, alloc=867.8MB, time=344.56 memory used=66214.7MB, alloc=867.8MB, time=345.92 memory used=66550.3MB, alloc=867.8MB, time=347.24 memory used=66886.8MB, alloc=867.8MB, time=348.58 memory used=67224.5MB, alloc=867.8MB, time=349.91 memory used=67562.5MB, alloc=867.8MB, time=351.25 memory used=67901.7MB, alloc=867.8MB, time=352.66 memory used=68242.1MB, alloc=867.8MB, time=354.09 memory used=68582.9MB, alloc=867.8MB, time=355.55 memory used=68924.7MB, alloc=867.8MB, time=357.00 memory used=69267.7MB, alloc=867.8MB, time=358.44 memory used=69611.3MB, alloc=867.8MB, time=359.89 memory used=69956.1MB, alloc=867.8MB, time=361.34 memory used=70301.9MB, alloc=867.8MB, time=362.76 memory used=70648.2MB, alloc=867.8MB, time=364.18 memory used=70995.7MB, alloc=867.8MB, time=365.64 memory used=71344.3MB, alloc=867.8MB, time=367.06 memory used=71693.3MB, alloc=867.8MB, time=368.46 memory used=72043.6MB, alloc=867.8MB, time=369.88 memory used=72394.9MB, alloc=867.8MB, time=371.28 memory used=72746.7MB, alloc=867.8MB, time=372.67 memory used=73099.7MB, alloc=867.8MB, time=374.06 memory used=73453.7MB, alloc=867.8MB, time=375.45 memory used=73808.3MB, alloc=867.8MB, time=376.87 memory used=74164.0MB, alloc=867.8MB, time=378.26 memory used=74520.8MB, alloc=867.8MB, time=379.66 memory used=74878.3MB, alloc=867.8MB, time=381.07 memory used=75236.7MB, alloc=867.8MB, time=382.46 memory used=75596.3MB, alloc=867.8MB, time=383.90 memory used=75956.5MB, alloc=867.8MB, time=385.33 memory used=76317.7MB, alloc=867.8MB, time=386.71 memory used=76680.2MB, alloc=867.8MB, time=388.06 memory used=77043.1MB, alloc=867.8MB, time=389.41 memory used=77406.9MB, alloc=867.8MB, time=390.74 memory used=77772.0MB, alloc=867.8MB, time=392.08 memory used=78137.9MB, alloc=867.8MB, time=393.41 memory used=78504.8MB, alloc=867.8MB, time=394.73 memory used=78872.4MB, alloc=867.8MB, time=396.07 memory used=79241.0MB, alloc=867.8MB, time=397.38 memory used=79610.2MB, alloc=867.8MB, time=398.69 memory used=79982.7MB, alloc=867.8MB, time=400.01 memory used=80368.3MB, alloc=867.8MB, time=401.33 memory used=80754.8MB, alloc=867.8MB, time=402.65 memory used=81142.8MB, alloc=867.8MB, time=403.97 memory used=81531.6MB, alloc=867.8MB, time=405.35 memory used=81921.0MB, alloc=867.8MB, time=406.69 memory used=82311.4MB, alloc=867.8MB, time=408.04 memory used=82702.6MB, alloc=867.8MB, time=409.38 memory used=83095.3MB, alloc=867.8MB, time=410.72 memory used=83488.9MB, alloc=867.8MB, time=412.09 memory used=83883.2MB, alloc=867.8MB, time=413.47 memory used=84278.6MB, alloc=867.8MB, time=414.85 memory used=84674.7MB, alloc=867.8MB, time=416.24 memory used=85072.3MB, alloc=867.8MB, time=417.60 memory used=85470.9MB, alloc=867.8MB, time=419.00 memory used=85870.1MB, alloc=867.8MB, time=420.40 memory used=86270.4MB, alloc=867.8MB, time=421.85 memory used=86671.4MB, alloc=867.8MB, time=423.33 memory used=87074.0MB, alloc=867.8MB, time=424.78 memory used=87477.5MB, alloc=867.8MB, time=426.20 memory used=87881.6MB, alloc=867.8MB, time=427.65 memory used=88286.8MB, alloc=867.8MB, time=429.08 memory used=88692.8MB, alloc=867.8MB, time=430.52 memory used=89100.3MB, alloc=867.8MB, time=431.96 memory used=89508.7MB, alloc=867.8MB, time=433.38 memory used=89917.8MB, alloc=867.8MB, time=434.80 memory used=90327.9MB, alloc=867.8MB, time=436.21 memory used=90738.8MB, alloc=867.8MB, time=437.65 memory used=91151.2MB, alloc=867.8MB, time=439.08 memory used=91564.6MB, alloc=867.8MB, time=440.52 memory used=91978.6MB, alloc=867.8MB, time=441.94 memory used=92393.6MB, alloc=867.8MB, time=443.35 memory used=92809.4MB, alloc=867.8MB, time=444.76 memory used=93226.8MB, alloc=867.8MB, time=446.17 memory used=93645.0MB, alloc=867.8MB, time=447.60 memory used=94064.0MB, alloc=867.8MB, time=449.06 memory used=94483.9MB, alloc=867.8MB, time=450.45 memory used=94904.7MB, alloc=867.8MB, time=451.94 memory used=95327.0MB, alloc=867.8MB, time=453.40 memory used=95750.2MB, alloc=867.8MB, time=454.80 memory used=96174.0MB, alloc=867.8MB, time=456.23 memory used=96598.9MB, alloc=867.8MB, time=457.72 memory used=97024.6MB, alloc=867.8MB, time=459.24 memory used=97421.5MB, alloc=867.8MB, time=460.72 memory used=97761.3MB, alloc=867.8MB, time=462.18 memory used=98102.1MB, alloc=867.8MB, time=463.67 memory used=98443.0MB, alloc=867.8MB, time=465.14 memory used=98784.8MB, alloc=867.8MB, time=466.63 memory used=99127.5MB, alloc=867.8MB, time=468.13 memory used=99470.4MB, alloc=867.8MB, time=469.63 memory used=99814.1MB, alloc=867.8MB, time=471.13 memory used=100158.7MB, alloc=867.8MB, time=472.71 memory used=100503.3MB, alloc=867.8MB, time=474.06 memory used=100849.0MB, alloc=867.8MB, time=475.41 memory used=101195.5MB, alloc=867.8MB, time=476.76 memory used=101542.0MB, alloc=867.8MB, time=478.12 memory used=101889.5MB, alloc=867.8MB, time=479.48 memory used=102237.9MB, alloc=867.8MB, time=480.89 memory used=102586.2MB, alloc=867.8MB, time=482.39 memory used=102935.6MB, alloc=867.8MB, time=483.83 memory used=103285.8MB, alloc=867.8MB, time=485.21 memory used=103636.0MB, alloc=867.8MB, time=486.57 memory used=103987.3MB, alloc=867.8MB, time=487.92 memory used=104339.4MB, alloc=867.8MB, time=489.25 memory used=104691.5MB, alloc=867.8MB, time=490.57 memory used=105044.6MB, alloc=867.8MB, time=491.95 memory used=105398.7MB, alloc=867.8MB, time=493.29 memory used=105752.7MB, alloc=867.8MB, time=494.63 memory used=106107.5MB, alloc=867.8MB, time=495.95 memory used=106463.3MB, alloc=867.8MB, time=497.31 memory used=106819.2MB, alloc=867.8MB, time=498.74 memory used=107175.9MB, alloc=867.8MB, time=500.15 memory used=107533.7MB, alloc=867.8MB, time=501.58 memory used=107891.4MB, alloc=867.8MB, time=502.99 memory used=108250.1MB, alloc=867.8MB, time=504.42 memory used=108609.6MB, alloc=867.8MB, time=505.81 memory used=108969.3MB, alloc=867.8MB, time=507.21 memory used=109329.8MB, alloc=867.8MB, time=508.60 memory used=109691.2MB, alloc=867.8MB, time=509.99 memory used=110052.7MB, alloc=867.8MB, time=511.40 memory used=110415.2MB, alloc=867.8MB, time=512.80 memory used=110778.1MB, alloc=867.8MB, time=514.21 memory used=111141.5MB, alloc=867.8MB, time=515.59 memory used=111505.5MB, alloc=867.8MB, time=517.00 memory used=111870.6MB, alloc=867.8MB, time=518.37 memory used=112235.8MB, alloc=867.8MB, time=519.82 memory used=112602.0MB, alloc=867.8MB, time=521.22 memory used=112969.0MB, alloc=867.8MB, time=522.62 memory used=113336.0MB, alloc=867.8MB, time=524.00 memory used=113704.1MB, alloc=867.8MB, time=525.44 memory used=114073.0MB, alloc=867.8MB, time=526.91 memory used=114441.9MB, alloc=867.8MB, time=528.39 memory used=114811.8MB, alloc=867.8MB, time=529.88 memory used=115182.6MB, alloc=867.8MB, time=531.41 memory used=115553.4MB, alloc=867.8MB, time=532.90 memory used=115925.2MB, alloc=867.8MB, time=534.45 memory used=116297.8MB, alloc=867.8MB, time=535.92 memory used=116670.7MB, alloc=867.8MB, time=537.38 memory used=117061.1MB, alloc=867.8MB, time=538.83 memory used=117453.0MB, alloc=867.8MB, time=540.32 memory used=117845.4MB, alloc=867.8MB, time=541.85 memory used=118238.2MB, alloc=867.8MB, time=543.37 memory used=118632.3MB, alloc=867.8MB, time=544.90 memory used=119027.0MB, alloc=867.8MB, time=546.43 memory used=119422.0MB, alloc=867.8MB, time=547.92 memory used=119817.7MB, alloc=867.8MB, time=549.43 memory used=120213.9MB, alloc=867.8MB, time=550.92 memory used=120611.4MB, alloc=867.8MB, time=552.42 memory used=121009.5MB, alloc=867.8MB, time=553.93 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memory used=242588.4MB, alloc=867.8MB, time=989.66 memory used=242944.4MB, alloc=867.8MB, time=991.05 memory used=243300.9MB, alloc=867.8MB, time=992.41 memory used=243657.1MB, alloc=867.8MB, time=993.79 memory used=244014.4MB, alloc=867.8MB, time=995.14 memory used=244371.5MB, alloc=867.8MB, time=996.54 memory used=244729.3MB, alloc=867.8MB, time=997.96 memory used=245086.8MB, alloc=867.8MB, time=999.36 memory used=245444.8MB, alloc=867.8MB, time=1000.81 memory used=245802.6MB, alloc=867.8MB, time=1002.22 memory used=246161.4MB, alloc=867.8MB, time=1003.68 memory used=246520.3MB, alloc=867.8MB, time=1005.13 memory used=246879.3MB, alloc=867.8MB, time=1006.55 memory used=247238.2MB, alloc=867.8MB, time=1007.94 memory used=247598.1MB, alloc=867.8MB, time=1009.28 memory used=247957.9MB, alloc=867.8MB, time=1010.66 memory used=248318.0MB, alloc=867.8MB, time=1012.00 memory used=248678.4MB, alloc=867.8MB, time=1013.34 memory used=249039.3MB, alloc=867.8MB, time=1014.69 memory used=249400.0MB, alloc=867.8MB, time=1016.05 memory used=249761.4MB, alloc=867.8MB, time=1017.37 memory used=250123.0MB, alloc=867.8MB, time=1018.69 memory used=250484.8MB, alloc=867.8MB, time=1020.00 memory used=250846.3MB, alloc=867.8MB, time=1021.42 memory used=251208.6MB, alloc=867.8MB, time=1022.83 memory used=251570.8MB, alloc=867.8MB, time=1024.25 memory used=251933.9MB, alloc=867.8MB, time=1025.68 memory used=252296.5MB, alloc=867.8MB, time=1027.19 memory used=252660.0MB, alloc=867.8MB, time=1028.68 memory used=253023.7MB, alloc=867.8MB, time=1030.04 memory used=253387.8MB, alloc=867.8MB, time=1031.35 memory used=253751.6MB, alloc=867.8MB, time=1032.76 memory used=254116.3MB, alloc=867.8MB, time=1034.13 memory used=254480.6MB, alloc=867.8MB, time=1035.51 memory used=254845.6MB, alloc=867.8MB, time=1036.89 memory used=255210.7MB, alloc=867.8MB, time=1038.24 memory used=255576.4MB, alloc=867.8MB, time=1039.60 memory used=255942.2MB, alloc=867.8MB, time=1040.95 memory used=256308.3MB, alloc=867.8MB, time=1042.31 memory used=256674.1MB, alloc=867.8MB, time=1043.73 memory used=257040.6MB, alloc=867.8MB, time=1045.13 memory used=257407.0MB, alloc=867.8MB, time=1046.55 memory used=257774.4MB, alloc=867.8MB, time=1047.96 memory used=258141.3MB, alloc=867.8MB, time=1049.31 memory used=258509.1MB, alloc=867.8MB, time=1050.66 memory used=258877.0MB, alloc=867.8MB, time=1052.00 memory used=259245.4MB, alloc=867.8MB, time=1053.32 memory used=259613.5MB, alloc=867.8MB, time=1054.73 memory used=259982.4MB, alloc=867.8MB, time=1056.15 memory used=260351.0MB, alloc=867.8MB, time=1057.55 memory used=260720.3MB, alloc=867.8MB, time=1058.97 memory used=261089.6MB, alloc=867.8MB, time=1060.35 memory used=261459.6MB, alloc=867.8MB, time=1061.70 memory used=261829.6MB, alloc=867.8MB, time=1063.03 memory used=262200.0MB, alloc=867.8MB, time=1064.39 memory used=262570.0MB, alloc=867.8MB, time=1065.76 memory used=262940.8MB, alloc=867.8MB, time=1067.12 memory used=263311.5MB, alloc=867.8MB, time=1068.46 memory used=263683.2MB, alloc=867.8MB, time=1069.84 memory used=264054.3MB, alloc=867.8MB, time=1071.32 memory used=264426.4MB, alloc=867.8MB, time=1072.73 memory used=264798.5MB, alloc=867.8MB, time=1074.09 memory used=265171.2MB, alloc=867.8MB, time=1075.51 memory used=265543.5MB, alloc=867.8MB, time=1076.83 memory used=265916.7MB, alloc=867.8MB, time=1078.16 memory used=266289.6MB, alloc=867.8MB, time=1079.49 memory used=266663.1MB, alloc=867.8MB, time=1080.94 memory used=267036.7MB, alloc=867.8MB, time=1082.28 memory used=267410.9MB, alloc=867.8MB, time=1083.60 memory used=267785.3MB, alloc=867.8MB, time=1085.05 memory used=268159.9MB, alloc=867.8MB, time=1086.61 memory used=268534.2MB, alloc=867.8MB, time=1087.94 memory used=268909.3MB, alloc=867.8MB, time=1089.34 memory used=269284.2MB, alloc=867.8MB, time=1090.82 memory used=269660.1MB, alloc=867.8MB, time=1092.14 memory used=270035.5MB, alloc=867.8MB, time=1093.46 memory used=270411.8MB, alloc=867.8MB, time=1094.80 memory used=270788.2MB, alloc=867.8MB, time=1096.11 memory used=271188.0MB, alloc=867.8MB, time=1097.50 memory used=271587.9MB, alloc=867.8MB, time=1098.87 memory used=271988.6MB, alloc=867.8MB, time=1100.23 memory used=272389.9MB, alloc=867.8MB, time=1101.59 memory used=272791.0MB, alloc=867.8MB, time=1102.97 memory used=273193.0MB, alloc=867.8MB, time=1104.32 memory used=273594.5MB, alloc=867.8MB, time=1105.67 memory used=273996.5MB, alloc=867.8MB, time=1107.02 memory used=274398.4MB, alloc=867.8MB, time=1108.42 memory used=274801.2MB, alloc=867.8MB, time=1109.78 memory used=275204.7MB, alloc=867.8MB, time=1111.15 memory used=275607.9MB, alloc=867.8MB, time=1112.57 memory used=276011.9MB, alloc=867.8MB, time=1114.03 memory used=276415.6MB, alloc=867.8MB, time=1115.46 memory used=276819.6MB, alloc=867.8MB, time=1116.93 memory used=277223.7MB, alloc=867.8MB, time=1118.36 memory used=277628.6MB, alloc=867.8MB, time=1119.73 memory used=278034.1MB, alloc=867.8MB, time=1121.21 memory used=278439.4MB, alloc=867.8MB, time=1122.68 memory used=278845.6MB, alloc=867.8MB, time=1124.15 memory used=279251.3MB, alloc=867.8MB, time=1125.68 memory used=279657.5MB, alloc=867.8MB, time=1127.16 memory used=280063.6MB, alloc=867.8MB, time=1128.75 memory used=280470.6MB, alloc=867.8MB, time=1130.30 memory used=280878.3MB, alloc=867.8MB, time=1131.87 memory used=281285.7MB, alloc=867.8MB, time=1133.42 memory used=281694.0MB, alloc=867.8MB, time=1134.98 memory used=282101.8MB, alloc=867.8MB, time=1136.54 memory used=282510.0MB, alloc=867.8MB, time=1138.13 memory used=282918.3MB, alloc=867.8MB, time=1139.70 memory used=283327.4MB, alloc=867.8MB, time=1141.25 memory used=283737.1MB, alloc=867.8MB, time=1142.82 memory used=284146.7MB, alloc=867.8MB, time=1144.26 memory used=284557.1MB, alloc=867.8MB, time=1145.69 memory used=284967.0MB, alloc=867.8MB, time=1147.14 memory used=285377.3MB, alloc=867.8MB, time=1148.64 memory used=285787.7MB, alloc=867.8MB, time=1150.06 memory used=286198.9MB, alloc=867.8MB, time=1151.50 memory used=286610.8MB, alloc=867.8MB, time=1152.97 memory used=287022.4MB, alloc=867.8MB, time=1154.37 memory used=287434.9MB, alloc=867.8MB, time=1155.82 memory used=287846.9MB, alloc=867.8MB, time=1157.35 memory used=288259.4MB, alloc=867.8MB, time=1158.86 memory used=288671.8MB, alloc=867.8MB, time=1160.37 memory used=289085.1MB, alloc=867.8MB, time=1161.81 memory used=289499.1MB, alloc=867.8MB, time=1163.26 memory used=289912.8MB, alloc=867.8MB, time=1164.68 memory used=290327.4MB, alloc=867.8MB, time=1166.06 memory used=290741.6MB, alloc=867.8MB, time=1167.48 memory used=291156.1MB, alloc=867.8MB, time=1168.90 memory used=291570.7MB, alloc=867.8MB, time=1170.33 memory used=291986.1MB, alloc=867.8MB, time=1171.81 memory used=292402.1MB, alloc=867.8MB, time=1173.27 memory used=292818.0MB, alloc=867.8MB, time=1174.82 memory used=293234.7MB, alloc=867.8MB, time=1176.31 memory used=293650.9MB, alloc=867.8MB, time=1177.76 memory used=294067.6MB, alloc=867.8MB, time=1179.27 memory used=294484.2MB, alloc=867.8MB, time=1180.73 memory used=294901.8MB, alloc=867.8MB, time=1182.15 memory used=295319.9MB, alloc=867.8MB, time=1183.51 memory used=295737.9MB, alloc=867.8MB, time=1184.89 memory used=296156.7MB, alloc=867.8MB, time=1186.26 memory used=296575.0MB, alloc=867.8MB, time=1187.65 memory used=296993.8MB, alloc=867.8MB, time=1189.02 memory used=297412.5MB, alloc=867.8MB, time=1190.41 memory used=297832.2MB, alloc=867.8MB, time=1191.78 memory used=298252.4MB, alloc=867.8MB, time=1193.22 memory used=298672.5MB, alloc=867.8MB, time=1194.61 memory used=299093.4MB, alloc=867.8MB, time=1195.97 memory used=299513.8MB, alloc=867.8MB, time=1197.29 memory used=299934.7MB, alloc=867.8MB, time=1198.66 memory used=300355.6MB, alloc=867.8MB, time=1199.97 memory used=300777.3MB, alloc=867.8MB, time=1201.32 memory used=301199.7MB, alloc=867.8MB, time=1202.72 memory used=301621.8MB, alloc=867.8MB, time=1204.08 memory used=302044.8MB, alloc=867.8MB, time=1205.49 memory used=302467.4MB, alloc=867.8MB, time=1206.95 memory used=302856.0MB, alloc=867.8MB, time=1208.34 memory used=303213.0MB, alloc=867.8MB, time=1209.79 memory used=303570.3MB, alloc=867.8MB, time=1211.16 memory used=303928.5MB, alloc=867.8MB, time=1212.53 memory used=304286.4MB, alloc=867.8MB, time=1213.98 memory used=304644.7MB, alloc=867.8MB, time=1215.38 memory used=305003.1MB, alloc=867.8MB, time=1216.76 memory used=305361.7MB, alloc=867.8MB, time=1218.13 memory used=305721.2MB, alloc=867.8MB, time=1219.57 memory used=306080.0MB, alloc=867.8MB, time=1220.97 memory used=306439.8MB, alloc=867.8MB, time=1222.30 memory used=306799.5MB, alloc=867.8MB, time=1223.63 memory used=307158.9MB, alloc=867.8MB, time=1224.94 memory used=307519.0MB, alloc=867.8MB, time=1226.30 memory used=307878.9MB, alloc=867.8MB, time=1227.61 memory used=308239.0MB, alloc=867.8MB, time=1228.91 memory used=308600.3MB, alloc=867.8MB, time=1230.20 memory used=308960.7MB, alloc=867.8MB, time=1231.51 memory used=309321.7MB, alloc=867.8MB, time=1232.82 memory used=309683.3MB, alloc=867.8MB, time=1234.16 memory used=310044.6MB, alloc=867.8MB, time=1235.66 memory used=310406.6MB, alloc=867.8MB, time=1237.14 memory used=310767.6MB, alloc=867.8MB, time=1238.64 memory used=311129.3MB, alloc=867.8MB, time=1240.10 memory used=311491.8MB, alloc=867.8MB, time=1241.59 memory used=311853.5MB, alloc=867.8MB, time=1243.02 memory used=312215.7MB, alloc=867.8MB, time=1244.46 memory used=312579.0MB, alloc=867.8MB, time=1245.91 memory used=312941.5MB, alloc=867.8MB, time=1247.32 memory used=313304.3MB, alloc=867.8MB, time=1248.84 memory used=313668.1MB, alloc=867.8MB, time=1250.27 memory used=314031.1MB, alloc=867.8MB, time=1251.63 memory used=314394.7MB, alloc=867.8MB, time=1252.98 memory used=314759.0MB, alloc=867.8MB, time=1254.30 memory used=315122.9MB, alloc=867.8MB, time=1255.71 memory used=315487.0MB, alloc=867.8MB, time=1257.07 memory used=315852.1MB, alloc=867.8MB, time=1258.40 memory used=316217.0MB, alloc=867.8MB, time=1259.88 memory used=316582.1MB, alloc=867.8MB, time=1261.28 memory used=316948.0MB, alloc=867.8MB, time=1262.59 memory used=317313.6MB, alloc=867.8MB, time=1264.02 memory used=317679.6MB, alloc=867.8MB, time=1265.40 memory used=318045.7MB, alloc=867.8MB, time=1266.88 memory used=318412.0MB, alloc=867.8MB, time=1268.32 memory used=318779.1MB, alloc=867.8MB, time=1269.76 memory used=319145.4MB, alloc=867.8MB, time=1271.24 memory used=319512.1MB, alloc=867.8MB, time=1272.66 memory used=319879.8MB, alloc=867.8MB, time=1274.04 memory used=320247.1MB, alloc=867.8MB, time=1275.49 memory used=320614.7MB, alloc=867.8MB, time=1276.88 memory used=320982.7MB, alloc=867.8MB, time=1278.26 memory used=321350.6MB, alloc=867.8MB, time=1279.64 memory used=321719.1MB, alloc=867.8MB, time=1281.15 memory used=322086.7MB, alloc=867.8MB, time=1282.54 memory used=322455.0MB, alloc=867.8MB, time=1283.94 memory used=322825.0MB, alloc=867.8MB, time=1285.37 memory used=323193.8MB, alloc=867.8MB, time=1286.78 memory used=323563.3MB, alloc=867.8MB, time=1288.20 memory used=323933.2MB, alloc=867.8MB, time=1289.59 memory used=324302.6MB, alloc=867.8MB, time=1290.97 memory used=324672.9MB, alloc=867.8MB, time=1292.37 memory used=325042.9MB, alloc=867.8MB, time=1293.74 memory used=325413.1MB, alloc=867.8MB, time=1295.15 memory used=325783.9MB, alloc=867.8MB, time=1296.48 memory used=326154.5MB, alloc=867.8MB, time=1297.82 memory used=326525.9MB, alloc=867.8MB, time=1299.17 memory used=326897.5MB, alloc=867.8MB, time=1300.52 memory used=327268.8MB, alloc=867.8MB, time=1301.86 memory used=327640.9MB, alloc=867.8MB, time=1303.23 memory used=328012.0MB, alloc=867.8MB, time=1304.65 memory used=328383.7MB, alloc=867.8MB, time=1306.13 memory used=328756.3MB, alloc=867.8MB, time=1307.61 memory used=329128.0MB, alloc=867.8MB, time=1309.13 memory used=329500.3MB, alloc=867.8MB, time=1310.61 |\^/| 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(); 1428442861 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-2 x z - 12 y + 2, -8 y - 13 y z + 14, -11 y + 10 y z - 5 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [16 y - 20 z - x, 13 x y + y z - 16, -10 y + 20 y z - 16 x] > Problem := [F,G]; 2 2 Problem := [[-2 x z - 12 y + 2, -8 y - 13 y z + 14, -11 y + 10 y z - 5 x], 2 2 2 [16 y - 20 z - x, 13 x y + y z - 16, -10 y + 20 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.54 memory used=46.7MB, alloc=32.3MB, time=0.87 memory used=65.8MB, alloc=56.3MB, time=1.16 memory used=106.1MB, alloc=60.3MB, time=1.80 memory used=145.2MB, alloc=60.3MB, time=2.42 memory used=182.9MB, alloc=84.3MB, time=3.04 memory used=227.1MB, alloc=84.3MB, time=3.75 memory used=286.3MB, alloc=116.3MB, time=4.73 memory used=368.1MB, alloc=116.3MB, time=6.10 memory used=445.5MB, alloc=140.3MB, time=7.42 memory used=521.9MB, alloc=396.3MB, time=8.73 memory used=626.9MB, alloc=420.3MB, time=10.64 memory used=751.7MB, alloc=420.3MB, time=12.92 memory used=875.7MB, alloc=444.3MB, time=15.23 memory used=1021.2MB, alloc=468.3MB, time=18.13 memory used=1180.6MB, alloc=492.3MB, time=21.46 memory used=1333.7MB, alloc=516.3MB, time=24.64 memory used=1437.0MB, alloc=516.3MB, time=26.64 memory used=1544.4MB, alloc=540.3MB, time=28.99 memory used=1619.3MB, alloc=540.3MB, time=30.40 memory used=1716.1MB, alloc=540.3MB, time=32.49 memory used=1795.1MB, alloc=540.3MB, time=34.22 memory used=1889.1MB, alloc=540.3MB, time=36.54 memory used=1972.9MB, alloc=540.3MB, time=38.64 memory used=2028.0MB, alloc=540.3MB, time=39.95 memory used=2077.8MB, alloc=540.3MB, time=40.99 memory used=2150.2MB, alloc=540.3MB, time=43.00 memory used=2380.3MB, alloc=564.3MB, time=47.77 memory used=2596.4MB, alloc=588.3MB, time=52.12 memory used=2806.5MB, alloc=612.3MB, time=56.65 memory used=2998.2MB, alloc=636.3MB, time=61.07 memory used=3185.6MB, alloc=660.3MB, time=66.24 memory used=3349.8MB, alloc=684.3MB, time=70.00 memory used=3506.9MB, alloc=684.3MB, time=74.21 memory used=3649.8MB, alloc=684.3MB, time=78.20 memory used=3778.4MB, alloc=708.3MB, time=81.69 memory used=3877.9MB, alloc=708.3MB, time=84.55 memory used=4250.2MB, alloc=732.3MB, time=94.02 memory used=4641.5MB, alloc=756.3MB, time=104.61 memory used=5054.6MB, alloc=780.3MB, time=115.81 memory used=5466.1MB, alloc=804.3MB, time=126.61 memory used=5816.9MB, alloc=828.3MB, time=136.91 memory used=6204.2MB, alloc=852.3MB, time=148.68 memory used=6511.5MB, alloc=876.3MB, time=157.38 memory used=6884.2MB, alloc=900.3MB, time=169.35 memory used=7105.7MB, alloc=924.3MB, time=176.78 memory used=7331.6MB, alloc=948.3MB, time=183.85 memory used=7540.2MB, alloc=972.3MB, time=190.14 memory used=7779.4MB, alloc=996.3MB, time=198.12 memory used=8405.3MB, alloc=1020.3MB, time=215.90 memory used=9036.1MB, alloc=1044.3MB, time=232.85 memory used=9682.3MB, alloc=1068.3MB, time=251.41 memory used=10335.1MB, alloc=1092.3MB, time=271.86 memory used=11002.6MB, alloc=1116.3MB, time=289.67 memory used=11680.6MB, alloc=1140.3MB, time=309.73 memory used=12366.7MB, alloc=1164.3MB, time=330.45 memory used=13039.9MB, alloc=1188.3MB, time=353.67 memory used=13656.5MB, alloc=1212.3MB, time=370.96 memory used=14136.6MB, alloc=1236.3MB, time=387.19 memory used=14621.4MB, alloc=1260.3MB, time=401.06 memory used=15257.9MB, alloc=1284.3MB, time=422.47 memory used=15825.7MB, alloc=1308.3MB, time=442.15 memory used=16276.5MB, alloc=1332.3MB, time=459.10 memory used=16647.1MB, alloc=1356.3MB, time=470.97 memory used=17001.3MB, alloc=1380.3MB, time=482.64 memory used=17262.8MB, alloc=1404.3MB, time=492.33 memory used=17533.9MB, alloc=1428.3MB, time=501.53 memory used=17884.6MB, alloc=1452.3MB, time=513.96 memory used=18197.8MB, alloc=1476.3MB, time=527.61 memory used=18462.4MB, alloc=1500.3MB, time=537.22 memory used=18772.3MB, alloc=1524.3MB, time=547.38 memory used=19037.5MB, alloc=1548.3MB, time=557.92 memory used=19277.0MB, alloc=1572.3MB, time=568.03 memory used=19500.1MB, alloc=1596.3MB, time=578.28 memory used=19704.0MB, alloc=1620.3MB, time=587.93 memory used=19938.3MB, alloc=1644.3MB, time=597.55 memory used=20180.9MB, alloc=1668.3MB, time=607.48 memory used=20282.6MB, alloc=1692.3MB, time=615.07 memory used=20638.6MB, alloc=1716.3MB, time=625.88 memory used=20946.1MB, alloc=1740.3MB, time=637.46 memory used=21187.1MB, alloc=1764.3MB, time=647.54 memory used=21426.0MB, alloc=1788.3MB, time=657.28 memory used=21625.1MB, alloc=1812.3MB, time=666.77 memory used=21881.1MB, alloc=1836.3MB, time=676.83 memory used=22174.8MB, alloc=1860.3MB, time=687.13 memory used=22328.9MB, alloc=1884.3MB, time=695.59 memory used=22545.1MB, alloc=1908.3MB, time=705.57 memory used=22866.7MB, alloc=1932.3MB, time=716.27 memory used=23060.0MB, alloc=1956.3MB, time=725.81 memory used=23328.1MB, alloc=1980.3MB, time=736.54 memory used=23557.2MB, alloc=2004.3MB, time=747.15 memory used=23714.8MB, alloc=2028.3MB, time=755.76 memory used=23917.3MB, alloc=2052.3MB, time=765.71 memory used=24096.8MB, alloc=2076.3MB, time=775.46 memory used=24285.8MB, alloc=2100.3MB, time=785.52 memory used=24474.9MB, alloc=2124.3MB, time=794.42 memory used=24729.3MB, alloc=2148.3MB, time=804.28 memory used=24874.0MB, alloc=2172.3MB, time=813.06 memory used=24952.3MB, alloc=2196.3MB, time=820.57 memory used=25119.8MB, alloc=2220.3MB, time=830.02 memory used=25267.1MB, alloc=2244.3MB, time=839.12 memory used=25450.1MB, alloc=2268.3MB, time=847.48 memory used=25617.0MB, alloc=2292.3MB, time=856.42 memory used=25763.5MB, alloc=2316.3MB, time=865.27 memory used=25994.0MB, alloc=2340.3MB, time=876.27 memory used=26144.6MB, alloc=2364.3MB, time=885.36 memory used=26258.4MB, alloc=2388.3MB, time=894.10 memory used=26406.8MB, alloc=2412.3MB, time=903.35 memory used=26563.0MB, alloc=2436.3MB, time=913.53 memory used=26577.0MB, alloc=2460.3MB, time=920.54 memory used=26742.3MB, alloc=2484.3MB, time=929.50 memory used=26845.0MB, alloc=2508.3MB, time=938.25 memory used=26962.9MB, alloc=2532.3MB, time=947.56 memory used=27107.6MB, alloc=2556.3MB, time=958.03 memory used=27246.5MB, alloc=2580.3MB, time=967.71 memory used=27506.9MB, alloc=2580.3MB, time=980.16 memory used=27610.8MB, alloc=2604.3MB, time=989.27 memory used=27706.8MB, alloc=2604.3MB, time=997.51 memory used=27812.6MB, alloc=2628.3MB, time=1007.28 memory used=27915.1MB, alloc=2628.3MB, time=1016.69 memory used=28018.7MB, alloc=2628.3MB, time=1026.39 memory used=28084.5MB, alloc=2652.3MB, time=1034.28 memory used=28151.4MB, alloc=2652.3MB, time=1042.01 memory used=28179.5MB, alloc=2652.3MB, time=1049.44 memory used=28282.5MB, alloc=2676.3MB, time=1058.79 memory used=28377.7MB, alloc=2676.3MB, time=1068.52 memory used=28443.1MB, alloc=2676.3MB, time=1077.79 memory used=28480.1MB, alloc=2932.3MB, time=1093.14 |\^/| 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(); 1428444061 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [2 x z - 7 y z - 7 y, -8 x y + 7 y z + 20 y, -6 x y + 6 y - 7] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [13 x - 8 x z - 9 y, 17 x y - 7 y + 17 z, 16 x y + 7 y - 1] > Problem := [F,G]; 2 Problem := [[2 x z - 7 y z - 7 y, -8 x y + 7 y z + 20 y, -6 x y + 6 y - 7], 2 [13 x - 8 x z - 9 y, 17 x y - 7 y + 17 z, 16 x y + 7 y - 1]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=46.8MB, alloc=32.3MB, time=0.81 memory used=66.0MB, alloc=56.3MB, time=1.11 memory used=104.7MB, alloc=60.3MB, time=1.73 memory used=141.9MB, alloc=84.3MB, time=2.31 memory used=201.2MB, alloc=92.3MB, time=3.28 memory used=259.1MB, alloc=92.3MB, time=4.22 memory used=317.3MB, alloc=116.3MB, time=5.24 memory used=397.5MB, alloc=116.3MB, time=6.60 memory used=477.3MB, alloc=140.3MB, time=8.02 memory used=578.5MB, alloc=164.3MB, time=9.91 memory used=658.1MB, alloc=164.3MB, time=11.33 memory used=736.3MB, alloc=444.3MB, time=12.72 memory used=864.7MB, alloc=468.3MB, time=15.03 memory used=1007.4MB, alloc=492.3MB, time=17.58 memory used=1162.6MB, alloc=516.3MB, time=20.37 memory used=1329.0MB, alloc=540.3MB, time=23.39 memory used=1508.1MB, alloc=564.3MB, time=26.59 memory used=1698.0MB, alloc=588.3MB, time=30.08 memory used=1895.5MB, alloc=612.3MB, time=33.63 memory used=2101.2MB, alloc=636.3MB, time=37.55 memory used=2312.6MB, alloc=660.3MB, time=42.04 memory used=2506.5MB, alloc=684.3MB, time=48.76 memory used=2708.3MB, alloc=708.3MB, time=56.22 memory used=2922.6MB, alloc=732.3MB, time=64.25 memory used=3151.7MB, alloc=756.3MB, time=73.15 memory used=3396.0MB, alloc=780.3MB, time=82.91 memory used=3655.9MB, alloc=804.3MB, time=93.43 memory used=3931.5MB, alloc=828.3MB, time=104.67 memory used=4223.4MB, alloc=852.3MB, time=116.72 memory used=4531.9MB, alloc=876.3MB, time=129.47 memory used=4857.2MB, alloc=900.3MB, time=143.18 memory used=5196.7MB, alloc=924.3MB, time=157.81 memory used=5552.6MB, alloc=948.3MB, time=173.44 memory used=5932.4MB, alloc=972.3MB, time=190.04 memory used=6336.2MB, alloc=996.3MB, time=207.73 memory used=6763.9MB, alloc=1020.3MB, time=226.49 memory used=7215.6MB, alloc=1044.3MB, time=246.10 memory used=7691.2MB, alloc=1068.3MB, time=266.68 memory used=8190.7MB, alloc=1092.3MB, time=288.59 memory used=8714.2MB, alloc=1092.3MB, time=311.29 memory used=9237.6MB, alloc=1092.3MB, time=334.08 memory used=9761.0MB, alloc=1092.3MB, time=356.78 memory used=10284.3MB, alloc=1116.3MB, time=379.29 memory used=10831.6MB, alloc=1116.3MB, time=402.83 memory used=11378.8MB, alloc=1116.3MB, time=426.44 memory used=11926.0MB, alloc=1116.3MB, time=450.12 memory used=12473.2MB, alloc=1140.3MB, time=474.04 memory used=13044.2MB, alloc=1140.3MB, time=498.91 memory used=13615.0MB, alloc=1140.3MB, time=523.45 memory used=14185.8MB, alloc=1164.3MB, time=547.92 memory used=14780.5MB, alloc=1164.3MB, time=573.52 memory used=15375.1MB, alloc=1164.3MB, time=599.28 memory used=15969.6MB, alloc=1188.3MB, time=624.78 memory used=16588.1MB, alloc=1188.3MB, time=651.31 memory used=17206.6MB, alloc=1188.3MB, time=677.67 memory used=17824.9MB, alloc=1212.3MB, time=704.17 memory used=18467.3MB, alloc=1212.3MB, time=731.74 memory used=19109.8MB, alloc=1236.3MB, time=759.16 memory used=19776.1MB, alloc=1236.3MB, time=787.54 memory used=20442.4MB, alloc=1260.3MB, time=815.82 memory used=21132.7MB, alloc=1284.3MB, time=845.28 memory used=21846.6MB, alloc=1308.3MB, time=875.80 N1 := 25279 > GB := Basis(F, plex(op(vars))); 4 3 2 GB := [3840 x - 14496 x + 34192 x - 71344 x + 57967, 3 2 960 x - 2064 x + 4648 x + 1911 y - 8918, -8 x + 7 z + 20] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=22599.3MB, alloc=1308.3MB, time=901.52 N2 := 3127 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [-7 z y + 2 z x - 7 y, -8 x y + 7 y z + 20 y, -6 x y + 6 y - 7, 2 -8 z x + 13 x - 9 y, 17 y x + 17 z - 7 y, 16 y x + 7 y - 1] > J:=[op(GB),op(G)]; 4 3 2 J := [3840 x - 14496 x + 34192 x - 71344 x + 57967, 3 2 960 x - 2064 x + 1911 y + 4648 x - 8918, -8 x + 7 z + 20, 2 -8 z x + 13 x - 9 y, 17 y x + 17 z - 7 y, 16 y x + 7 y - 1] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 16, 12, 2, 2, 2, 1, 1, 1, 2/3, 7/18, 2/3, 5/18, 6, 13, 14, 4, 4, 1, 1, 1, 2/3, 1/2, 6/11, 3/11, 3/22, 3, -2, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=22769.9MB, alloc=1308.3MB, time=908.50 |\^/| 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(); 1428445077 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [20 x y - 16 y z + 10, -10 x - 6 y + 2 z, 5 y z - 8 z + 11 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [19 z + 10 x + 4, 13 y + 5 y + 11 z, -6 x z + 9 y + z ] > Problem := [F,G]; 2 2 Problem := [[20 x y - 16 y z + 10, -10 x - 6 y + 2 z, 5 y z - 8 z + 11 z], 2 2 2 2 [19 z + 10 x + 4, 13 y + 5 y + 11 z, -6 x z + 9 y + z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=47.4MB, alloc=32.3MB, time=0.79 memory used=65.8MB, alloc=56.3MB, time=1.08 memory used=102.2MB, alloc=60.3MB, time=1.64 memory used=138.9MB, alloc=84.3MB, time=2.21 memory used=197.2MB, alloc=92.3MB, time=3.12 memory used=254.3MB, alloc=116.3MB, time=4.01 memory used=331.8MB, alloc=116.3MB, time=5.28 memory used=407.6MB, alloc=140.3MB, time=6.54 memory used=502.9MB, alloc=164.3MB, time=8.12 memory used=600.9MB, alloc=420.3MB, time=9.76 memory used=723.0MB, alloc=444.3MB, time=11.75 memory used=865.2MB, alloc=468.3MB, time=14.12 memory used=1031.0MB, alloc=492.3MB, time=16.98 memory used=1217.1MB, alloc=516.3MB, time=20.26 memory used=1427.3MB, alloc=540.3MB, time=24.41 memory used=1660.5MB, alloc=564.3MB, time=29.17 memory used=1908.8MB, alloc=588.3MB, time=34.21 memory used=2179.3MB, alloc=612.3MB, time=39.96 memory used=2462.6MB, alloc=636.3MB, time=46.21 memory used=2769.9MB, alloc=660.3MB, time=52.57 memory used=3065.1MB, alloc=684.3MB, time=59.16 memory used=3273.8MB, alloc=708.3MB, time=63.73 memory used=3509.9MB, alloc=732.3MB, time=68.74 memory used=3792.9MB, alloc=756.3MB, time=76.23 memory used=4038.5MB, alloc=780.3MB, time=82.26 memory used=4261.6MB, alloc=804.3MB, time=88.17 memory used=4405.2MB, alloc=828.3MB, time=90.93 memory used=4593.2MB, alloc=852.3MB, time=96.05 memory used=4788.0MB, alloc=852.3MB, time=101.47 memory used=4961.3MB, alloc=852.3MB, time=106.70 memory used=5089.5MB, alloc=876.3MB, time=109.75 memory used=5240.8MB, alloc=876.3MB, time=114.49 memory used=5356.9MB, alloc=876.3MB, time=117.75 memory used=5865.1MB, alloc=900.3MB, time=130.98 memory used=6404.9MB, alloc=924.3MB, time=145.51 memory used=6818.8MB, alloc=948.3MB, time=155.21 memory used=7259.9MB, alloc=972.3MB, time=166.28 memory used=7606.2MB, alloc=996.3MB, time=175.60 memory used=8066.5MB, alloc=1020.3MB, time=189.68 memory used=8699.9MB, alloc=1044.3MB, time=209.39 memory used=9356.7MB, alloc=1068.3MB, time=228.75 memory used=10024.8MB, alloc=1092.3MB, time=248.70 memory used=10698.6MB, alloc=1116.3MB, time=270.02 memory used=11391.9MB, alloc=1140.3MB, time=289.29 memory used=12085.5MB, alloc=1164.3MB, time=312.15 memory used=12799.5MB, alloc=1188.3MB, time=334.10 memory used=13531.8MB, alloc=1212.3MB, time=357.63 memory used=14269.3MB, alloc=1236.3MB, time=379.86 memory used=15019.8MB, alloc=1260.3MB, time=404.35 memory used=15762.1MB, alloc=1284.3MB, time=433.11 memory used=16473.3MB, alloc=1308.3MB, time=454.59 memory used=17268.3MB, alloc=1332.3MB, time=482.87 memory used=17899.1MB, alloc=1356.3MB, time=503.38 memory used=18651.3MB, alloc=1380.3MB, time=531.94 memory used=19240.6MB, alloc=1404.3MB, time=552.90 memory used=19872.5MB, alloc=1428.3MB, time=579.07 memory used=20370.7MB, alloc=1452.3MB, time=599.58 memory used=20899.8MB, alloc=1476.3MB, time=620.12 memory used=21326.1MB, alloc=1500.3MB, time=639.66 memory used=21749.5MB, alloc=1524.3MB, time=658.37 memory used=22038.8MB, alloc=1548.3MB, time=668.69 memory used=22476.7MB, alloc=1572.3MB, time=689.24 memory used=22837.5MB, alloc=1596.3MB, time=708.65 memory used=23137.1MB, alloc=1620.3MB, time=723.74 memory used=23448.9MB, alloc=1644.3MB, time=738.53 memory used=23858.2MB, alloc=1668.3MB, time=757.74 memory used=24212.8MB, alloc=1692.3MB, time=776.05 memory used=24418.0MB, alloc=1716.3MB, time=787.86 memory used=24777.1MB, alloc=1740.3MB, time=807.40 memory used=24886.5MB, alloc=1764.3MB, time=815.21 memory used=25138.7MB, alloc=1788.3MB, time=831.46 memory used=25291.3MB, alloc=1812.3MB, time=842.12 memory used=25368.5MB, alloc=1836.3MB, time=849.63 memory used=25485.9MB, alloc=1860.3MB, time=858.39 memory used=25561.4MB, alloc=1884.3MB, time=866.18 memory used=25769.9MB, alloc=1908.3MB, time=880.81 memory used=25931.3MB, alloc=1932.3MB, time=892.16 memory used=25981.5MB, alloc=1956.3MB, time=899.04 memory used=26057.1MB, alloc=1980.3MB, time=905.79 memory used=26167.3MB, alloc=2004.3MB, time=915.21 memory used=26375.8MB, alloc=2028.3MB, time=931.79 memory used=26480.7MB, alloc=2052.3MB, time=941.60 memory used=26578.9MB, alloc=2052.3MB, time=951.99 memory used=26615.3MB, alloc=2308.3MB, time=967.01 memory used=28017.9MB, alloc=2347.8MB, time=1024.26 memory used=29492.6MB, alloc=2371.8MB, time=1087.05 |\^/| 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(); 1428446277 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-13 x + x + 9 z, 11 x y + 19 x z - 4 y z, 14 x y + 5 y - 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 G := [19 y + 9 z - 3 z, 5 x - 20 x z - 10 z , -12 x + y + 12 z ] > Problem := [F,G]; 2 2 2 Problem := [[-13 x + x + 9 z, 11 x y + 19 x z - 4 y z, 14 x y + 5 y - 2 z ], 2 2 2 2 2 2 2 [19 y + 9 z - 3 z, 5 x - 20 x z - 10 z , -12 x + y + 12 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.52 memory used=47.3MB, alloc=56.3MB, time=0.86 memory used=88.9MB, alloc=60.3MB, time=1.46 memory used=130.6MB, alloc=92.3MB, time=2.08 memory used=193.5MB, alloc=92.3MB, time=3.00 memory used=264.9MB, alloc=116.3MB, time=3.87 memory used=336.2MB, alloc=372.3MB, time=4.92 memory used=422.1MB, alloc=396.3MB, time=6.19 memory used=530.5MB, alloc=420.3MB, time=7.69 memory used=662.2MB, alloc=444.3MB, time=9.59 memory used=802.8MB, alloc=468.3MB, time=11.61 memory used=930.0MB, alloc=468.3MB, time=13.48 memory used=1061.4MB, alloc=492.3MB, time=15.73 memory used=1182.4MB, alloc=492.3MB, time=17.48 memory used=1299.5MB, alloc=516.3MB, time=18.75 memory used=1398.1MB, alloc=516.3MB, time=20.50 memory used=1477.3MB, alloc=516.3MB, time=21.97 memory used=1567.1MB, alloc=540.3MB, time=23.36 memory used=1653.4MB, alloc=540.3MB, time=25.13 memory used=1735.0MB, alloc=540.3MB, time=26.63 memory used=1808.8MB, alloc=540.3MB, time=28.01 memory used=1854.4MB, alloc=540.3MB, time=28.89 memory used=1915.7MB, alloc=540.3MB, time=30.10 memory used=1968.1MB, alloc=540.3MB, time=31.26 memory used=2017.1MB, alloc=540.3MB, time=32.27 memory used=2244.3MB, alloc=564.3MB, time=36.20 memory used=2446.2MB, alloc=588.3MB, time=39.56 memory used=2653.2MB, alloc=612.3MB, time=43.68 memory used=2831.4MB, alloc=636.3MB, time=47.09 memory used=2991.6MB, alloc=660.3MB, time=50.49 memory used=3148.3MB, alloc=660.3MB, time=53.52 memory used=3294.1MB, alloc=684.3MB, time=56.51 memory used=3413.4MB, alloc=684.3MB, time=59.04 memory used=3544.2MB, alloc=684.3MB, time=62.02 memory used=3640.6MB, alloc=684.3MB, time=64.12 memory used=3749.0MB, alloc=684.3MB, time=66.93 memory used=4085.8MB, alloc=708.3MB, time=73.62 memory used=4449.3MB, alloc=732.3MB, time=80.64 memory used=4783.7MB, alloc=756.3MB, time=87.32 memory used=5197.6MB, alloc=780.3MB, time=94.96 memory used=5580.5MB, alloc=804.3MB, time=102.09 memory used=5908.0MB, alloc=828.3MB, time=109.12 memory used=6231.3MB, alloc=852.3MB, time=116.46 memory used=6522.0MB, alloc=876.3MB, time=123.33 memory used=6817.1MB, alloc=900.3MB, time=129.79 memory used=7084.2MB, alloc=924.3MB, time=136.45 memory used=7297.9MB, alloc=948.3MB, time=141.99 memory used=7472.6MB, alloc=972.3MB, time=147.19 memory used=7687.6MB, alloc=996.3MB, time=152.32 memory used=7906.5MB, alloc=1020.3MB, time=158.63 memory used=8527.0MB, alloc=1044.3MB, time=171.91 memory used=9134.6MB, alloc=1068.3MB, time=186.21 memory used=9769.0MB, alloc=1092.3MB, time=200.86 memory used=10427.1MB, alloc=1116.3MB, time=214.06 memory used=11044.1MB, alloc=1140.3MB, time=229.39 memory used=11691.6MB, alloc=1164.3MB, time=243.13 memory used=12360.9MB, alloc=1188.3MB, time=258.68 memory used=12926.2MB, alloc=1212.3MB, time=273.16 memory used=13603.3MB, alloc=1236.3MB, time=290.82 memory used=14210.5MB, alloc=1260.3MB, time=306.18 memory used=14794.7MB, alloc=1284.3MB, time=322.04 memory used=15241.4MB, alloc=1308.3MB, time=334.62 memory used=15755.5MB, alloc=1332.3MB, time=348.88 memory used=16151.8MB, alloc=1356.3MB, time=361.06 memory used=16557.5MB, alloc=1380.3MB, time=374.33 memory used=16851.9MB, alloc=1404.3MB, time=385.22 memory used=17259.4MB, alloc=1428.3MB, time=399.67 memory used=17493.0MB, alloc=1452.3MB, time=408.23 memory used=17789.0MB, alloc=1476.3MB, time=419.29 memory used=18072.7MB, alloc=1500.3MB, time=430.13 memory used=18406.1MB, alloc=1524.3MB, time=441.39 memory used=18665.2MB, alloc=1548.3MB, time=451.87 memory used=18988.8MB, alloc=1572.3MB, time=463.64 memory used=19157.1MB, alloc=1596.3MB, time=471.12 memory used=19445.1MB, alloc=1620.3MB, time=479.70 memory used=19653.6MB, alloc=1644.3MB, time=490.34 memory used=19879.0MB, alloc=1668.3MB, time=499.29 memory used=20072.4MB, alloc=1692.3MB, time=507.38 memory used=20256.1MB, alloc=1716.3MB, time=515.08 memory used=20481.9MB, alloc=1740.3MB, time=525.35 memory used=20706.5MB, alloc=1764.3MB, time=535.49 memory used=20846.2MB, alloc=1788.3MB, time=544.28 memory used=20967.9MB, alloc=1812.3MB, time=552.61 memory used=21030.8MB, alloc=2116.3MB, time=568.04 memory used=22251.3MB, alloc=2140.3MB, time=601.53 memory used=23483.1MB, alloc=2164.3MB, time=632.53 memory used=24661.5MB, alloc=2188.3MB, time=665.66 memory used=25891.9MB, alloc=2212.3MB, time=699.05 memory used=27094.2MB, alloc=2236.3MB, time=734.21 memory used=28292.9MB, alloc=2260.3MB, time=769.87 memory used=29443.9MB, alloc=2284.3MB, time=806.60 memory used=30590.2MB, alloc=2308.3MB, time=843.24 memory used=31692.1MB, alloc=2332.3MB, time=875.97 memory used=32701.4MB, alloc=2356.3MB, time=911.65 memory used=33698.9MB, alloc=2380.3MB, time=946.36 memory used=34358.7MB, alloc=2404.3MB, time=977.50 memory used=35118.9MB, alloc=2428.3MB, time=1012.06 |\^/| 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(); 1428447477 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-2 x z + 16 y + 2 y, 13 y - 13 z + 7 z, -20 x y + 12 y z - 19 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-19 x y - 6 x - z, -16 x - 12 x z + 2 y , -11 y z - 4 x - 2 y] > Problem := [F,G]; Problem := [ 2 2 2 [-2 x z + 16 y + 2 y, 13 y - 13 z + 7 z, -20 x y + 12 y z - 19 x], 2 2 [-19 x y - 6 x - z, -16 x - 12 x z + 2 y , -11 y z - 4 x - 2 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.19 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.0MB, alloc=56.3MB, time=0.82 memory used=89.7MB, alloc=60.3MB, time=1.45 memory used=131.8MB, alloc=68.3MB, time=2.08 memory used=172.3MB, alloc=92.3MB, time=2.68 memory used=236.3MB, alloc=92.3MB, time=3.59 memory used=295.7MB, alloc=116.3MB, time=4.49 memory used=374.9MB, alloc=116.3MB, time=5.71 memory used=441.9MB, alloc=396.3MB, time=6.74 memory used=549.0MB, alloc=396.3MB, time=8.39 memory used=656.8MB, alloc=420.3MB, time=10.03 memory used=787.2MB, alloc=444.3MB, time=12.14 memory used=934.4MB, alloc=468.3MB, time=14.66 memory used=1070.3MB, alloc=468.3MB, time=16.92 memory used=1198.1MB, alloc=492.3MB, time=19.15 memory used=1309.1MB, alloc=492.3MB, time=21.00 memory used=1402.2MB, alloc=492.3MB, time=22.56 memory used=1526.1MB, alloc=516.3MB, time=25.01 memory used=1631.3MB, alloc=516.3MB, time=27.04 memory used=1712.2MB, alloc=516.3MB, time=28.42 memory used=1796.4MB, alloc=516.3MB, time=30.19 memory used=1865.1MB, alloc=516.3MB, time=31.58 memory used=1930.8MB, alloc=540.3MB, time=32.58 memory used=2013.7MB, alloc=540.3MB, time=34.53 memory used=2092.6MB, alloc=540.3MB, time=36.36 memory used=2136.1MB, alloc=540.3MB, time=37.32 memory used=2186.0MB, alloc=540.3MB, time=38.43 memory used=2406.8MB, alloc=564.3MB, time=42.14 memory used=2606.8MB, alloc=588.3MB, time=45.78 memory used=2778.7MB, alloc=612.3MB, time=48.84 memory used=2937.6MB, alloc=636.3MB, time=51.81 memory used=3101.6MB, alloc=660.3MB, time=55.32 memory used=3244.4MB, alloc=660.3MB, time=58.09 memory used=3389.6MB, alloc=660.3MB, time=61.44 memory used=3548.7MB, alloc=684.3MB, time=64.90 memory used=3701.3MB, alloc=684.3MB, time=68.74 memory used=3815.1MB, alloc=684.3MB, time=71.44 memory used=3954.1MB, alloc=684.3MB, time=75.54 memory used=4312.6MB, alloc=708.3MB, time=83.08 memory used=4669.3MB, alloc=732.3MB, time=92.43 memory used=5062.0MB, alloc=756.3MB, time=101.50 memory used=5432.9MB, alloc=780.3MB, time=110.23 memory used=5836.8MB, alloc=804.3MB, time=120.90 memory used=6197.0MB, alloc=828.3MB, time=131.13 memory used=6526.5MB, alloc=852.3MB, time=139.79 memory used=6805.4MB, alloc=876.3MB, time=147.27 memory used=7106.5MB, alloc=900.3MB, time=155.52 memory used=7373.1MB, alloc=924.3MB, time=163.98 memory used=7603.2MB, alloc=948.3MB, time=170.84 memory used=7847.6MB, alloc=972.3MB, time=178.59 memory used=8026.8MB, alloc=996.3MB, time=184.93 memory used=8647.0MB, alloc=1020.3MB, time=202.58 memory used=9274.8MB, alloc=1044.3MB, time=219.31 memory used=9921.7MB, alloc=1068.3MB, time=235.69 memory used=10577.5MB, alloc=1092.3MB, time=254.91 memory used=11249.7MB, alloc=1116.3MB, time=273.80 memory used=11937.1MB, alloc=1140.3MB, time=292.82 memory used=12618.8MB, alloc=1164.3MB, time=313.70 memory used=13194.1MB, alloc=1188.3MB, time=329.87 memory used=13891.2MB, alloc=1212.3MB, time=351.59 memory used=14471.7MB, alloc=1236.3MB, time=368.45 memory used=15115.6MB, alloc=1260.3MB, time=388.58 memory used=15617.8MB, alloc=1284.3MB, time=404.50 memory used=16030.2MB, alloc=1308.3MB, time=417.43 memory used=16524.1MB, alloc=1332.3MB, time=433.66 memory used=16965.0MB, alloc=1356.3MB, time=449.25 memory used=17329.8MB, alloc=1380.3MB, time=462.13 memory used=17704.7MB, alloc=1404.3MB, time=476.04 memory used=18025.2MB, alloc=1428.3MB, time=488.18 memory used=18319.8MB, alloc=1452.3MB, time=498.99 memory used=18676.2MB, alloc=1476.3MB, time=512.29 memory used=18983.6MB, alloc=1500.3MB, time=524.11 memory used=19216.6MB, alloc=1524.3MB, time=534.37 memory used=19440.7MB, alloc=1548.3MB, time=544.96 memory used=19676.8MB, alloc=1572.3MB, time=555.34 memory used=19894.6MB, alloc=1596.3MB, time=564.80 memory used=20071.4MB, alloc=1620.3MB, time=574.61 memory used=20289.5MB, alloc=1644.3MB, time=585.90 memory used=20415.7MB, alloc=1668.3MB, time=594.63 memory used=20584.6MB, alloc=1692.3MB, time=604.78 memory used=20752.4MB, alloc=1716.3MB, time=615.42 memory used=20933.7MB, alloc=1740.3MB, time=625.66 memory used=21123.7MB, alloc=1764.3MB, time=636.41 memory used=21270.0MB, alloc=1788.3MB, time=644.65 memory used=21407.0MB, alloc=1812.3MB, time=653.77 memory used=21488.9MB, alloc=1812.3MB, time=661.95 memory used=21579.2MB, alloc=1812.3MB, time=669.37 memory used=21737.7MB, alloc=1812.3MB, time=679.57 memory used=21825.8MB, alloc=1812.3MB, time=686.79 memory used=21947.9MB, alloc=1836.3MB, time=696.14 memory used=22002.1MB, alloc=1836.3MB, time=703.52 memory used=22085.2MB, alloc=1836.3MB, time=710.73 memory used=22161.6MB, alloc=1836.3MB, time=718.95 memory used=22247.1MB, alloc=1836.3MB, time=726.50 memory used=22311.9MB, alloc=1836.3MB, time=733.28 memory used=22411.0MB, alloc=1836.3MB, time=742.27 memory used=22459.2MB, alloc=1836.3MB, time=749.64 memory used=22489.1MB, alloc=1836.3MB, time=756.47 memory used=22553.8MB, alloc=1836.3MB, time=764.51 memory used=22603.4MB, alloc=1836.3MB, time=772.31 memory used=22615.6MB, alloc=1836.3MB, time=778.62 memory used=22667.5MB, alloc=1836.3MB, time=786.35 memory used=22693.2MB, alloc=1836.3MB, time=793.39 memory used=22726.3MB, alloc=1836.3MB, time=800.39 memory used=22770.4MB, alloc=1836.3MB, time=807.74 memory used=22790.2MB, alloc=1836.3MB, time=814.27 memory used=22842.7MB, alloc=1836.3MB, time=821.82 memory used=22868.8MB, alloc=1836.3MB, time=828.27 memory used=22910.6MB, alloc=1836.3MB, time=835.34 memory used=22979.8MB, alloc=1836.3MB, time=843.20 memory used=23011.3MB, alloc=1836.3MB, time=850.62 memory used=23035.5MB, alloc=1836.3MB, time=857.39 memory used=23050.3MB, alloc=1836.3MB, time=863.98 memory used=23062.8MB, alloc=2092.3MB, time=878.43 memory used=24308.8MB, alloc=2116.3MB, time=912.27 memory used=25497.0MB, alloc=2140.3MB, time=944.50 memory used=26589.6MB, alloc=2164.3MB, time=975.84 memory used=27519.7MB, alloc=2188.3MB, time=1003.81 memory used=28402.3MB, alloc=2212.3MB, time=1030.68 memory used=29243.3MB, alloc=2236.3MB, time=1056.56 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428448678 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [18 x - 8 x y - 9 y z, 5 y z - 6 x + 18 z, 13 x y + 16 y + 3 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-3 x - 15 x z + 6, 7 x z + 3 y z + 5 z , 4 x + 5 y z - 20 z ] > Problem := [F,G]; 2 2 2 Problem := [[18 x - 8 x y - 9 y z, 5 y z - 6 x + 18 z, 13 x y + 16 y + 3 z ], 2 2 2 2 [-3 x - 15 x z + 6, 7 x z + 3 y z + 5 z , 4 x + 5 y z - 20 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.20 memory used=26.6MB, alloc=32.3MB, time=0.56 memory used=46.7MB, alloc=32.3MB, time=0.86 memory used=65.0MB, alloc=56.3MB, time=1.15 memory used=104.8MB, alloc=60.3MB, time=1.76 memory used=143.8MB, alloc=84.3MB, time=2.34 memory used=203.7MB, alloc=92.3MB, time=3.28 memory used=263.9MB, alloc=116.3MB, time=4.23 memory used=343.7MB, alloc=116.3MB, time=5.45 memory used=421.0MB, alloc=140.3MB, time=6.72 memory used=498.9MB, alloc=140.3MB, time=7.96 memory used=575.6MB, alloc=420.3MB, time=9.26 memory used=700.1MB, alloc=444.3MB, time=11.35 memory used=845.5MB, alloc=468.3MB, time=13.89 memory used=1000.5MB, alloc=492.3MB, time=16.61 memory used=1138.9MB, alloc=492.3MB, time=19.10 memory used=1264.8MB, alloc=516.3MB, time=21.51 memory used=1399.7MB, alloc=516.3MB, time=24.04 memory used=1511.7MB, alloc=516.3MB, time=26.37 memory used=1622.6MB, alloc=516.3MB, time=28.73 memory used=1724.0MB, alloc=540.3MB, time=30.96 memory used=1822.5MB, alloc=540.3MB, time=32.98 memory used=1926.1MB, alloc=540.3MB, time=35.17 memory used=2009.9MB, alloc=540.3MB, time=36.98 memory used=2075.9MB, alloc=540.3MB, time=38.43 memory used=2138.0MB, alloc=540.3MB, time=39.83 memory used=2202.4MB, alloc=540.3MB, time=41.39 memory used=2275.6MB, alloc=540.3MB, time=43.15 memory used=2323.1MB, alloc=540.3MB, time=44.37 memory used=2378.4MB, alloc=564.3MB, time=45.78 memory used=2613.5MB, alloc=588.3MB, time=50.86 memory used=2861.8MB, alloc=612.3MB, time=56.64 memory used=3087.3MB, alloc=636.3MB, time=61.89 memory used=3292.5MB, alloc=660.3MB, time=66.58 memory used=3485.0MB, alloc=684.3MB, time=71.34 memory used=3658.5MB, alloc=708.3MB, time=75.25 memory used=3851.1MB, alloc=732.3MB, time=80.10 memory used=3968.1MB, alloc=756.3MB, time=82.77 memory used=4115.1MB, alloc=756.3MB, time=86.55 memory used=4215.1MB, alloc=756.3MB, time=89.09 memory used=4337.1MB, alloc=756.3MB, time=91.75 memory used=4447.2MB, alloc=756.3MB, time=95.10 memory used=4848.9MB, alloc=780.3MB, time=104.14 memory used=5240.5MB, alloc=804.3MB, time=113.11 memory used=5670.9MB, alloc=828.3MB, time=122.31 memory used=6087.4MB, alloc=852.3MB, time=133.06 memory used=6442.5MB, alloc=876.3MB, time=141.47 memory used=6731.1MB, alloc=900.3MB, time=148.61 memory used=7004.0MB, alloc=924.3MB, time=155.55 memory used=7281.9MB, alloc=948.3MB, time=164.21 memory used=7483.6MB, alloc=972.3MB, time=171.05 memory used=7728.3MB, alloc=996.3MB, time=178.19 memory used=7976.5MB, alloc=1020.3MB, time=186.07 memory used=8198.3MB, alloc=1044.3MB, time=193.38 memory used=8837.6MB, alloc=1068.3MB, time=209.96 memory used=9491.2MB, alloc=1092.3MB, time=226.38 memory used=10154.3MB, alloc=1116.3MB, time=243.30 memory used=10842.8MB, alloc=1140.3MB, time=258.75 memory used=11497.7MB, alloc=1164.3MB, time=277.84 memory used=12042.1MB, alloc=1188.3MB, time=291.32 memory used=12719.5MB, alloc=1212.3MB, time=313.03 memory used=13356.1MB, alloc=1236.3MB, time=332.74 memory used=13972.6MB, alloc=1260.3MB, time=352.04 memory used=14503.2MB, alloc=1284.3MB, time=368.21 memory used=14908.3MB, alloc=1308.3MB, time=382.05 memory used=15330.7MB, alloc=1332.3MB, time=395.79 memory used=15794.1MB, alloc=1356.3MB, time=410.96 memory used=16263.0MB, alloc=1380.3MB, time=428.36 memory used=16560.6MB, alloc=1404.3MB, time=439.03 memory used=16978.5MB, alloc=1428.3MB, time=453.45 memory used=17240.5MB, alloc=1452.3MB, time=466.06 memory used=17441.5MB, alloc=1476.3MB, time=474.30 memory used=17627.7MB, alloc=1500.3MB, time=485.58 memory used=17747.9MB, alloc=1524.3MB, time=492.58 memory used=17892.8MB, alloc=1548.3MB, time=502.77 memory used=18076.7MB, alloc=1572.3MB, time=511.29 memory used=18176.5MB, alloc=1596.3MB, time=518.66 memory used=18338.1MB, alloc=1620.3MB, time=529.48 memory used=18466.2MB, alloc=1644.3MB, time=536.83 memory used=18551.0MB, alloc=1948.3MB, time=549.20 memory used=19698.2MB, alloc=1972.3MB, time=581.97 memory used=20794.7MB, alloc=1996.3MB, time=619.60 memory used=21904.5MB, alloc=2020.3MB, time=657.55 memory used=23013.7MB, alloc=2044.3MB, time=695.99 memory used=24110.6MB, alloc=2068.3MB, time=733.96 memory used=25168.6MB, alloc=2092.3MB, time=775.77 memory used=26258.4MB, alloc=2116.3MB, time=817.41 memory used=27332.3MB, alloc=2140.3MB, time=859.17 memory used=28391.7MB, alloc=2164.3MB, time=898.29 memory used=29488.6MB, alloc=2188.3MB, time=939.94 memory used=30484.8MB, alloc=2212.3MB, time=978.69 memory used=31244.9MB, alloc=2236.3MB, time=1013.47 memory used=32079.5MB, alloc=2260.3MB, time=1047.84 memory used=32746.1MB, alloc=2284.3MB, time=1077.48 memory used=33419.1MB, alloc=2308.3MB, time=1107.24 memory used=34114.9MB, alloc=2332.3MB, time=1139.07 |\^/| 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(); 1428449878 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-2 x - y - 9 z, -19 x z + 4 y - 2 y z, -19 x - 8 x - 3] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [16 x + 16 y + 18 z , -8 x z + 9 y - 10 z , -12 x z + 19 y + 13 x] > Problem := [F,G]; 2 2 2 Problem := [[-2 x - y - 9 z, -19 x z + 4 y - 2 y z, -19 x - 8 x - 3], 2 2 2 2 2 2 [16 x + 16 y + 18 z , -8 x z + 9 y - 10 z , -12 x z + 19 y + 13 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=46.9MB, alloc=32.3MB, time=0.82 memory used=65.6MB, alloc=56.3MB, time=1.12 memory used=107.4MB, alloc=60.3MB, time=1.75 memory used=147.8MB, alloc=84.3MB, time=2.37 memory used=213.9MB, alloc=92.3MB, time=3.32 memory used=278.7MB, alloc=116.3MB, time=4.29 memory used=346.0MB, alloc=116.3MB, time=5.26 memory used=412.6MB, alloc=372.3MB, time=6.25 memory used=502.7MB, alloc=396.3MB, time=7.50 memory used=610.0MB, alloc=420.3MB, time=9.18 memory used=742.0MB, alloc=444.3MB, time=11.20 memory used=853.4MB, alloc=468.3MB, time=12.97 memory used=976.4MB, alloc=468.3MB, time=15.08 memory used=1073.2MB, alloc=492.3MB, time=16.62 memory used=1193.1MB, alloc=492.3MB, time=18.71 memory used=1296.0MB, alloc=492.3MB, time=20.45 memory used=1387.8MB, alloc=516.3MB, time=21.74 memory used=1481.9MB, alloc=516.3MB, time=23.44 memory used=1547.6MB, alloc=516.3MB, time=24.56 memory used=1622.2MB, alloc=516.3MB, time=26.03 memory used=1687.7MB, alloc=516.3MB, time=27.19 memory used=1738.1MB, alloc=516.3MB, time=28.07 memory used=1788.9MB, alloc=516.3MB, time=28.93 memory used=1853.9MB, alloc=516.3MB, time=30.32 memory used=2054.9MB, alloc=540.3MB, time=33.35 memory used=2247.4MB, alloc=564.3MB, time=36.52 memory used=2418.4MB, alloc=588.3MB, time=39.29 memory used=2578.7MB, alloc=612.3MB, time=42.34 memory used=2728.7MB, alloc=636.3MB, time=45.15 memory used=2872.4MB, alloc=636.3MB, time=47.32 memory used=3022.0MB, alloc=660.3MB, time=49.45 memory used=3182.4MB, alloc=660.3MB, time=52.33 memory used=3328.2MB, alloc=684.3MB, time=55.73 memory used=3468.6MB, alloc=684.3MB, time=58.53 memory used=3553.5MB, alloc=684.3MB, time=60.84 memory used=3659.0MB, alloc=684.3MB, time=63.21 memory used=4024.1MB, alloc=708.3MB, time=69.44 memory used=4389.7MB, alloc=732.3MB, time=76.28 memory used=4769.9MB, alloc=756.3MB, time=82.34 memory used=5107.0MB, alloc=780.3MB, time=89.84 memory used=5395.2MB, alloc=804.3MB, time=95.38 memory used=5699.7MB, alloc=828.3MB, time=102.01 memory used=6003.4MB, alloc=852.3MB, time=108.59 memory used=6210.6MB, alloc=876.3MB, time=113.58 memory used=6418.7MB, alloc=900.3MB, time=118.59 memory used=6677.9MB, alloc=924.3MB, time=123.77 memory used=6882.2MB, alloc=948.3MB, time=128.60 memory used=7090.7MB, alloc=972.3MB, time=134.47 memory used=7669.3MB, alloc=996.3MB, time=146.89 memory used=8263.0MB, alloc=1020.3MB, time=159.39 memory used=8848.6MB, alloc=1044.3MB, time=173.12 memory used=9451.8MB, alloc=1068.3MB, time=186.88 memory used=10064.4MB, alloc=1092.3MB, time=201.01 memory used=10671.1MB, alloc=1116.3MB, time=215.17 memory used=11191.5MB, alloc=1140.3MB, time=228.45 memory used=11657.5MB, alloc=1164.3MB, time=240.57 memory used=12080.2MB, alloc=1188.3MB, time=253.04 memory used=12496.9MB, alloc=1212.3MB, time=265.30 memory used=12947.6MB, alloc=1236.3MB, time=277.90 memory used=13416.0MB, alloc=1260.3MB, time=290.73 memory used=13812.1MB, alloc=1284.3MB, time=306.63 memory used=14149.5MB, alloc=1308.3MB, time=323.89 memory used=14488.6MB, alloc=1332.3MB, time=341.97 memory used=14836.3MB, alloc=1356.3MB, time=360.52 memory used=15194.4MB, alloc=1380.3MB, time=379.82 memory used=15565.6MB, alloc=1404.3MB, time=399.57 memory used=15944.8MB, alloc=1428.3MB, time=420.82 memory used=16336.9MB, alloc=1452.3MB, time=443.09 memory used=16752.9MB, alloc=1476.3MB, time=466.66 memory used=17192.9MB, alloc=1500.3MB, time=490.93 memory used=17656.7MB, alloc=1524.3MB, time=516.41 memory used=18144.6MB, alloc=1548.3MB, time=542.98 memory used=18656.3MB, alloc=1572.3MB, time=570.68 memory used=19191.9MB, alloc=1596.3MB, time=599.57 memory used=19751.5MB, alloc=1620.3MB, time=629.94 memory used=20335.1MB, alloc=1644.3MB, time=661.36 memory used=20942.5MB, alloc=1668.3MB, time=693.20 memory used=21573.8MB, alloc=1692.3MB, time=725.86 memory used=22229.0MB, alloc=1716.3MB, time=759.49 memory used=22907.9MB, alloc=1740.3MB, time=794.14 memory used=23610.8MB, alloc=1764.3MB, time=830.64 memory used=24337.7MB, alloc=1788.3MB, time=868.00 memory used=25088.4MB, alloc=1812.3MB, time=906.65 memory used=25862.9MB, alloc=1836.3MB, time=945.37 memory used=26661.4MB, alloc=1860.3MB, time=985.15 memory used=27483.8MB, alloc=1884.3MB, time=1026.94 |\^/| 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(); 1428451078 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [14 + 14 x - 14 y, -19 x - 16 y z - 5 z, -4 x + 3 x z - 13 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-11 x y - 7 y + 13 y, 9 x z + 5 y z - 18 z , 16 x - 2 y z + 11] > Problem := [F,G]; 2 2 2 Problem := [[14 + 14 x - 14 y, -19 x - 16 y z - 5 z, -4 x + 3 x z - 13 z ], 2 2 2 [-11 x y - 7 y + 13 y, 9 x z + 5 y z - 18 z , 16 x - 2 y z + 11]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.4MB, alloc=32.3MB, time=0.78 memory used=67.2MB, alloc=56.3MB, time=1.08 memory used=105.7MB, alloc=60.3MB, time=1.65 memory used=143.3MB, alloc=84.3MB, time=2.23 memory used=201.3MB, alloc=92.3MB, time=3.14 memory used=254.3MB, alloc=116.3MB, time=3.95 memory used=331.5MB, alloc=116.3MB, time=5.20 memory used=407.9MB, alloc=140.3MB, time=6.51 memory used=502.9MB, alloc=164.3MB, time=8.20 memory used=598.6MB, alloc=420.3MB, time=9.99 memory used=720.4MB, alloc=444.3MB, time=12.34 memory used=863.0MB, alloc=468.3MB, time=15.04 memory used=1024.8MB, alloc=492.3MB, time=18.08 memory used=1195.4MB, alloc=516.3MB, time=21.37 memory used=1368.8MB, alloc=540.3MB, time=25.83 memory used=1527.3MB, alloc=564.3MB, time=31.90 memory used=1707.2MB, alloc=588.3MB, time=38.91 N1 := 4257 > GB := Basis(F, plex(op(vars))); 4 3 2 3 2 GB := [947 x + 555 x + 252 x , y - 1 - x, -15152 x + 11007 x + 15561 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1916.3MB, alloc=588.3MB, time=45.91 memory used=2179.4MB, alloc=588.3MB, time=50.70 memory used=2422.9MB, alloc=612.3MB, time=59.39 memory used=2656.5MB, alloc=636.3MB, time=69.46 N2 := 3975 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [14 + 14 x - 14 y, -19 x - 16 y z - 5 z, -4 x + 3 x z - 13 z , 2 2 2 -11 x y - 7 y + 13 y, 9 x z + 5 y z - 18 z , -2 z y + 16 x + 11] > J:=[op(GB),op(G)]; 4 3 2 3 2 J := [947 x + 555 x + 252 x , y - 1 - x, -15152 x + 11007 x + 15561 z, 2 2 2 -11 x y - 7 y + 13 y, 9 x z + 5 y z - 18 z , -2 z y + 16 x + 11] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 11, 2, 2, 2, 2, 1, 5/6, 2/3, 7/18, 7/18, 4/9, 6, 13, 14, 4, 4, 2, 2, 1, 2/3, 1/2, 1/2, 1/3, 5/18, 2, -3, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=2760.4MB, alloc=636.3MB, time=73.31 |\^/| 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(); 1428451172 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-5 + 8 x + 17 z, -20 x y - 17 y + 3 y z, 20 y - 14 x + 9 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-20 y z + 8 y + 16, 16 x - 3 y z + 19 z , -20 x y + 15 y z - x] > Problem := [F,G]; 2 2 Problem := [[-5 + 8 x + 17 z, -20 x y - 17 y + 3 y z, 20 y - 14 x + 9 y], 2 2 [-20 y z + 8 y + 16, 16 x - 3 y z + 19 z , -20 x y + 15 y z - x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.19 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=47.2MB, alloc=32.3MB, time=0.80 memory used=66.0MB, alloc=56.3MB, time=1.09 memory used=105.4MB, alloc=60.3MB, time=1.72 memory used=144.0MB, alloc=84.3MB, time=2.31 memory used=203.0MB, alloc=92.3MB, time=3.25 memory used=257.8MB, alloc=116.3MB, time=4.09 memory used=338.7MB, alloc=140.3MB, time=5.42 memory used=422.2MB, alloc=396.3MB, time=6.76 memory used=526.9MB, alloc=420.3MB, time=8.58 memory used=653.1MB, alloc=444.3MB, time=10.82 memory used=804.9MB, alloc=468.3MB, time=13.57 memory used=972.5MB, alloc=492.3MB, time=16.46 memory used=1144.9MB, alloc=516.3MB, time=19.87 memory used=1301.8MB, alloc=516.3MB, time=22.94 memory used=1442.1MB, alloc=540.3MB, time=25.98 memory used=1594.3MB, alloc=540.3MB, time=29.25 memory used=1732.8MB, alloc=564.3MB, time=32.29 memory used=1839.3MB, alloc=564.3MB, time=34.65 memory used=1961.4MB, alloc=564.3MB, time=37.63 memory used=2076.3MB, alloc=564.3MB, time=40.41 memory used=2172.9MB, alloc=564.3MB, time=42.75 memory used=2268.1MB, alloc=564.3MB, time=45.00 memory used=2342.7MB, alloc=564.3MB, time=46.83 memory used=2418.6MB, alloc=588.3MB, time=48.73 memory used=2488.8MB, alloc=588.3MB, time=50.50 memory used=2559.6MB, alloc=588.3MB, time=52.38 memory used=2610.2MB, alloc=588.3MB, time=53.81 memory used=2677.4MB, alloc=588.3MB, time=55.74 memory used=2933.7MB, alloc=612.3MB, time=61.50 memory used=3193.5MB, alloc=636.3MB, time=66.39 memory used=3437.0MB, alloc=660.3MB, time=71.27 memory used=3688.2MB, alloc=684.3MB, time=76.28 memory used=3950.6MB, alloc=708.3MB, time=81.41 memory used=4213.2MB, alloc=732.3MB, time=86.42 memory used=4507.6MB, alloc=756.3MB, time=91.89 memory used=4740.1MB, alloc=780.3MB, time=96.58 memory used=4999.3MB, alloc=804.3MB, time=101.97 memory used=5241.5MB, alloc=828.3MB, time=107.03 memory used=5492.8MB, alloc=852.3MB, time=112.36 memory used=5792.7MB, alloc=876.3MB, time=118.94 memory used=6098.7MB, alloc=900.3MB, time=125.43 memory used=6403.2MB, alloc=924.3MB, time=132.72 memory used=6654.1MB, alloc=948.3MB, time=142.57 memory used=6910.8MB, alloc=972.3MB, time=153.14 memory used=7177.7MB, alloc=996.3MB, time=164.44 memory used=7457.2MB, alloc=1020.3MB, time=176.50 memory used=7749.5MB, alloc=1044.3MB, time=189.16 memory used=8055.2MB, alloc=1068.3MB, time=202.49 memory used=8375.1MB, alloc=1092.3MB, time=216.64 memory used=8708.9MB, alloc=1116.3MB, time=231.53 memory used=9057.9MB, alloc=1140.3MB, time=247.41 memory used=9422.2MB, alloc=1164.3MB, time=263.77 memory used=9802.6MB, alloc=1188.3MB, time=280.86 memory used=10198.7MB, alloc=1212.3MB, time=298.52 memory used=10610.9MB, alloc=1236.3MB, time=316.87 memory used=11039.6MB, alloc=1260.3MB, time=336.00 memory used=11484.7MB, alloc=1284.3MB, time=356.01 memory used=11946.5MB, alloc=1308.3MB, time=376.81 memory used=12425.1MB, alloc=1332.3MB, time=398.51 memory used=12920.7MB, alloc=1356.3MB, time=421.14 memory used=13433.4MB, alloc=1380.3MB, time=444.49 memory used=13963.2MB, alloc=1404.3MB, time=468.73 memory used=14508.2MB, alloc=1428.3MB, time=494.30 memory used=15066.8MB, alloc=1452.3MB, time=521.03 memory used=15649.4MB, alloc=1476.3MB, time=548.93 memory used=16255.8MB, alloc=1500.3MB, time=577.82 memory used=16886.3MB, alloc=1524.3MB, time=607.72 memory used=17540.6MB, alloc=1548.3MB, time=638.96 memory used=18218.9MB, alloc=1572.3MB, time=671.00 memory used=18921.2MB, alloc=1596.3MB, time=704.36 memory used=19647.4MB, alloc=1620.3MB, time=739.06 memory used=20397.5MB, alloc=1644.3MB, time=774.25 memory used=21171.6MB, alloc=1668.3MB, time=810.63 memory used=21969.5MB, alloc=1692.3MB, time=847.97 memory used=22791.5MB, alloc=1716.3MB, time=886.33 memory used=23637.4MB, alloc=1740.3MB, time=926.39 memory used=24507.2MB, alloc=1764.3MB, time=967.75 memory used=25401.0MB, alloc=1788.3MB, time=1010.52 |\^/| 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(); 1428452372 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-x y + 17 x z + 9 y, 20 x y + 8 x z + 10 y , -17 x y - 13 z + 12 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-17 x y - 17 z - 7 x, 3 y z - 8 x + 10, 13 x z + 4 z] > Problem := [F,G]; Problem := [ 2 2 [-x y + 17 x z + 9 y, 20 x y + 8 x z + 10 y , -17 x y - 13 z + 12 y], 2 [-17 x y - 17 z - 7 x, 3 y z - 8 x + 10, 13 x z + 4 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.78 memory used=67.2MB, alloc=56.3MB, time=1.09 memory used=106.6MB, alloc=60.3MB, time=1.67 memory used=144.2MB, alloc=84.3MB, time=2.24 memory used=203.4MB, alloc=92.3MB, time=3.16 memory used=262.6MB, alloc=116.3MB, time=4.08 memory used=340.7MB, alloc=116.3MB, time=5.34 memory used=421.1MB, alloc=396.3MB, time=6.70 memory used=525.7MB, alloc=420.3MB, time=8.33 memory used=654.0MB, alloc=444.3MB, time=10.32 memory used=802.5MB, alloc=468.3MB, time=12.64 memory used=946.0MB, alloc=468.3MB, time=14.96 memory used=1071.6MB, alloc=492.3MB, time=17.05 memory used=1189.2MB, alloc=492.3MB, time=19.16 memory used=1307.9MB, alloc=492.3MB, time=21.21 memory used=1397.7MB, alloc=492.3MB, time=22.73 memory used=1510.9MB, alloc=516.3MB, time=24.98 memory used=1593.7MB, alloc=516.3MB, time=26.44 memory used=1687.4MB, alloc=516.3MB, time=28.20 memory used=1770.1MB, alloc=516.3MB, time=29.85 memory used=1846.4MB, alloc=516.3MB, time=31.39 memory used=1912.8MB, alloc=516.3MB, time=32.76 memory used=1983.1MB, alloc=516.3MB, time=34.27 memory used=2045.7MB, alloc=540.3MB, time=35.57 memory used=2098.5MB, alloc=540.3MB, time=36.75 memory used=2159.3MB, alloc=540.3MB, time=38.13 memory used=2216.4MB, alloc=540.3MB, time=39.49 memory used=2439.3MB, alloc=564.3MB, time=43.65 memory used=2653.3MB, alloc=588.3MB, time=47.48 memory used=2866.2MB, alloc=612.3MB, time=51.52 memory used=3055.7MB, alloc=636.3MB, time=55.20 memory used=3236.5MB, alloc=660.3MB, time=58.50 memory used=3397.5MB, alloc=684.3MB, time=61.61 memory used=3542.2MB, alloc=684.3MB, time=64.50 memory used=3685.1MB, alloc=708.3MB, time=67.57 memory used=3833.3MB, alloc=732.3MB, time=70.92 memory used=3991.2MB, alloc=756.3MB, time=74.34 memory used=4124.4MB, alloc=756.3MB, time=77.42 memory used=4269.2MB, alloc=780.3MB, time=80.80 memory used=4413.5MB, alloc=804.3MB, time=84.12 memory used=4603.9MB, alloc=828.3MB, time=88.31 memory used=4747.5MB, alloc=852.3MB, time=91.71 memory used=4899.8MB, alloc=876.3MB, time=95.29 memory used=5071.9MB, alloc=900.3MB, time=99.36 memory used=5501.0MB, alloc=924.3MB, time=108.09 memory used=5916.4MB, alloc=948.3MB, time=116.70 memory used=6321.7MB, alloc=972.3MB, time=125.37 memory used=6717.4MB, alloc=996.3MB, time=134.08 memory used=7108.5MB, alloc=1020.3MB, time=142.74 memory used=7500.9MB, alloc=1044.3MB, time=151.43 memory used=7892.5MB, alloc=1068.3MB, time=160.11 memory used=8267.6MB, alloc=1092.3MB, time=168.75 memory used=8646.5MB, alloc=1116.3MB, time=177.44 memory used=9014.1MB, alloc=1140.3MB, time=186.13 memory used=9376.8MB, alloc=1164.3MB, time=194.77 memory used=9737.8MB, alloc=1188.3MB, time=203.38 memory used=10094.4MB, alloc=1212.3MB, time=211.97 memory used=10466.9MB, alloc=1236.3MB, time=220.53 memory used=10851.1MB, alloc=1260.3MB, time=229.23 memory used=11238.3MB, alloc=1284.3MB, time=238.11 memory used=11617.2MB, alloc=1308.3MB, time=247.19 memory used=11928.0MB, alloc=1332.3MB, time=258.67 memory used=12206.0MB, alloc=1356.3MB, time=271.17 memory used=12487.6MB, alloc=1380.3MB, time=284.40 memory used=12777.3MB, alloc=1404.3MB, time=298.19 memory used=13077.8MB, alloc=1428.3MB, time=312.61 memory used=13389.8MB, alloc=1452.3MB, time=327.67 memory used=13714.8MB, alloc=1476.3MB, time=343.62 memory used=14053.4MB, alloc=1500.3MB, time=360.43 memory used=14405.4MB, alloc=1524.3MB, time=377.69 memory used=14771.1MB, alloc=1548.3MB, time=395.46 memory used=15150.8MB, alloc=1572.3MB, time=414.00 memory used=15543.8MB, alloc=1596.3MB, time=433.33 memory used=15953.9MB, alloc=1620.3MB, time=453.39 memory used=16380.8MB, alloc=1644.3MB, time=474.44 memory used=16826.1MB, alloc=1668.3MB, time=496.14 memory used=17286.6MB, alloc=1692.3MB, time=518.67 memory used=17762.0MB, alloc=1716.3MB, time=542.06 memory used=18251.9MB, alloc=1740.3MB, time=566.52 memory used=18757.5MB, alloc=1764.3MB, time=591.41 memory used=19277.9MB, alloc=1788.3MB, time=617.47 memory used=19813.6MB, alloc=1812.3MB, time=644.04 memory used=20364.0MB, alloc=1836.3MB, time=671.41 memory used=20930.3MB, alloc=1860.3MB, time=699.67 memory used=21511.3MB, alloc=1884.3MB, time=728.38 memory used=22107.2MB, alloc=1908.3MB, time=757.51 memory used=22718.0MB, alloc=1932.3MB, time=787.43 memory used=23344.1MB, alloc=1956.3MB, time=818.22 memory used=23985.4MB, alloc=1980.3MB, time=849.66 memory used=24641.7MB, alloc=2004.3MB, time=881.88 memory used=25313.1MB, alloc=2028.3MB, time=915.27 memory used=25999.5MB, alloc=2052.3MB, time=949.50 memory used=26701.2MB, alloc=2076.3MB, time=984.17 memory used=27418.0MB, alloc=2100.3MB, time=1020.37 memory used=28150.1MB, alloc=2124.3MB, time=1057.34 memory used=28897.2MB, alloc=2148.3MB, time=1094.07 |\^/| 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(); 1428453572 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [18 x y - 9 z - 5 z, -16 x y - 2 y - 3 y, 2 x y - 11 x z - 3 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [6 - 19 y - 5 z, 2 x z + 19 y + 7 y z, 19 - 14 y - 12 z] > Problem := [F,G]; 2 2 Problem := [[18 x y - 9 z - 5 z, -16 x y - 2 y - 3 y, 2 x y - 11 x z - 3 y], 2 [6 - 19 y - 5 z, 2 x z + 19 y + 7 y z, 19 - 14 y - 12 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.20 memory used=26.1MB, alloc=32.3MB, time=0.50 memory used=46.1MB, alloc=32.3MB, time=0.79 memory used=64.1MB, alloc=56.3MB, time=1.07 memory used=102.6MB, alloc=60.3MB, time=1.65 memory used=139.8MB, alloc=84.3MB, time=2.26 memory used=198.4MB, alloc=92.3MB, time=3.20 memory used=254.0MB, alloc=116.3MB, time=4.08 memory used=331.9MB, alloc=116.3MB, time=5.37 memory used=408.2MB, alloc=140.3MB, time=6.60 memory used=501.5MB, alloc=164.3MB, time=8.17 memory used=587.1MB, alloc=420.3MB, time=9.59 memory used=710.5MB, alloc=444.3MB, time=11.70 memory used=858.3MB, alloc=468.3MB, time=14.41 memory used=1027.5MB, alloc=492.3MB, time=17.63 memory used=1217.5MB, alloc=516.3MB, time=21.48 memory used=1429.8MB, alloc=540.3MB, time=26.20 memory used=1663.8MB, alloc=564.3MB, time=31.64 memory used=1919.8MB, alloc=588.3MB, time=37.73 memory used=2194.4MB, alloc=612.3MB, time=44.29 memory used=2486.7MB, alloc=636.3MB, time=51.66 memory used=2797.3MB, alloc=660.3MB, time=59.51 memory used=3087.7MB, alloc=684.3MB, time=65.15 memory used=3356.1MB, alloc=708.3MB, time=70.47 memory used=3635.2MB, alloc=732.3MB, time=76.14 memory used=3920.8MB, alloc=756.3MB, time=81.82 memory used=4209.8MB, alloc=780.3MB, time=87.66 memory used=4502.2MB, alloc=804.3MB, time=93.61 memory used=4795.9MB, alloc=828.3MB, time=99.48 memory used=5023.7MB, alloc=852.3MB, time=104.23 memory used=5272.5MB, alloc=876.3MB, time=109.60 memory used=5584.3MB, alloc=900.3MB, time=116.10 memory used=5896.7MB, alloc=924.3MB, time=122.51 memory used=6208.6MB, alloc=948.3MB, time=129.10 memory used=6517.7MB, alloc=972.3MB, time=135.84 memory used=6825.6MB, alloc=996.3MB, time=142.63 memory used=7134.3MB, alloc=1020.3MB, time=149.56 memory used=7446.7MB, alloc=1044.3MB, time=156.47 memory used=7724.6MB, alloc=1068.3MB, time=166.15 memory used=7981.7MB, alloc=1092.3MB, time=177.06 memory used=8249.1MB, alloc=1116.3MB, time=188.51 memory used=8528.7MB, alloc=1140.3MB, time=200.79 memory used=8820.2MB, alloc=1164.3MB, time=213.70 memory used=9125.3MB, alloc=1188.3MB, time=227.26 memory used=9444.3MB, alloc=1212.3MB, time=241.57 memory used=9777.3MB, alloc=1236.3MB, time=256.57 memory used=10124.7MB, alloc=1260.3MB, time=272.29 memory used=10487.0MB, alloc=1284.3MB, time=288.72 memory used=10864.2MB, alloc=1308.3MB, time=305.69 memory used=11256.0MB, alloc=1332.3MB, time=323.39 memory used=11663.0MB, alloc=1356.3MB, time=341.73 memory used=12085.2MB, alloc=1380.3MB, time=360.72 memory used=12523.3MB, alloc=1404.3MB, time=380.76 memory used=12977.5MB, alloc=1428.3MB, time=401.51 memory used=13447.4MB, alloc=1452.3MB, time=423.00 memory used=13933.6MB, alloc=1476.3MB, time=445.07 memory used=14436.0MB, alloc=1500.3MB, time=468.56 memory used=14953.7MB, alloc=1524.3MB, time=492.97 memory used=15487.9MB, alloc=1548.3MB, time=518.27 memory used=16038.2MB, alloc=1572.3MB, time=544.37 memory used=16604.9MB, alloc=1596.3MB, time=571.12 memory used=17187.6MB, alloc=1620.3MB, time=598.78 memory used=17786.5MB, alloc=1644.3MB, time=627.30 memory used=18401.7MB, alloc=1668.3MB, time=656.67 memory used=19033.8MB, alloc=1692.3MB, time=686.75 memory used=19682.4MB, alloc=1716.3MB, time=717.18 memory used=20347.4MB, alloc=1740.3MB, time=748.05 memory used=21029.0MB, alloc=1764.3MB, time=779.87 memory used=21727.1MB, alloc=1788.3MB, time=812.53 memory used=22442.2MB, alloc=1812.3MB, time=846.20 memory used=23168.0MB, alloc=1836.3MB, time=880.88 memory used=23914.9MB, alloc=1860.3MB, time=916.69 memory used=24685.7MB, alloc=1884.3MB, time=953.54 memory used=25480.4MB, alloc=1908.3MB, time=991.48 memory used=26299.1MB, alloc=1932.3MB, time=1030.56 memory used=27141.7MB, alloc=1956.3MB, time=1070.93 memory used=28008.2MB, alloc=1980.3MB, time=1112.24 |\^/| 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(); 1428454773 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-2 x z + 19 y - 7 z, 19 x z + y + 2 z, 14 x y + 4 x z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-5 y z - 12 z + 17 z, -4 y z - 19 z + 20 x, 20 x - 17 z + 19] > Problem := [F,G]; 2 2 Problem := [[-2 x z + 19 y - 7 z, 19 x z + y + 2 z, 14 x y + 4 x z], 2 2 2 [-5 y z - 12 z + 17 z, -4 y z - 19 z + 20 x, 20 x - 17 z + 19]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.23 memory used=26.2MB, alloc=32.3MB, time=0.54 memory used=45.9MB, alloc=32.3MB, time=0.82 memory used=64.6MB, alloc=56.3MB, time=1.10 memory used=103.9MB, alloc=60.3MB, time=1.70 memory used=140.2MB, alloc=84.3MB, time=2.25 memory used=196.4MB, alloc=92.3MB, time=3.12 memory used=252.8MB, alloc=116.3MB, time=4.00 memory used=330.8MB, alloc=116.3MB, time=5.25 memory used=407.0MB, alloc=140.3MB, time=6.52 memory used=503.7MB, alloc=140.3MB, time=8.07 memory used=596.0MB, alloc=420.3MB, time=9.62 memory used=714.5MB, alloc=444.3MB, time=11.71 memory used=858.2MB, alloc=468.3MB, time=14.16 memory used=1011.4MB, alloc=492.3MB, time=16.82 memory used=1171.3MB, alloc=516.3MB, time=19.70 memory used=1307.0MB, alloc=540.3MB, time=22.21 memory used=1447.5MB, alloc=540.3MB, time=24.86 memory used=1568.4MB, alloc=540.3MB, time=27.28 memory used=1676.1MB, alloc=540.3MB, time=29.38 memory used=1795.9MB, alloc=540.3MB, time=31.81 memory used=1904.7MB, alloc=540.3MB, time=34.06 memory used=1994.1MB, alloc=564.3MB, time=36.06 memory used=2084.7MB, alloc=564.3MB, time=38.21 memory used=2184.7MB, alloc=564.3MB, time=40.41 memory used=2243.3MB, alloc=564.3MB, time=41.69 memory used=2322.3MB, alloc=564.3MB, time=43.65 memory used=2400.5MB, alloc=564.3MB, time=45.49 memory used=2460.6MB, alloc=564.3MB, time=46.99 memory used=2537.3MB, alloc=564.3MB, time=48.96 memory used=2778.5MB, alloc=588.3MB, time=54.30 memory used=3031.8MB, alloc=612.3MB, time=59.74 memory used=3276.6MB, alloc=636.3MB, time=65.53 memory used=3472.2MB, alloc=660.3MB, time=70.08 memory used=3678.6MB, alloc=684.3MB, time=74.98 memory used=3899.8MB, alloc=708.3MB, time=80.89 memory used=4073.0MB, alloc=732.3MB, time=85.12 memory used=4255.5MB, alloc=756.3MB, time=90.26 memory used=4409.9MB, alloc=756.3MB, time=94.27 memory used=4539.6MB, alloc=756.3MB, time=98.00 memory used=4644.1MB, alloc=756.3MB, time=101.15 memory used=4758.2MB, alloc=780.3MB, time=104.74 memory used=5174.9MB, alloc=804.3MB, time=115.48 memory used=5611.3MB, alloc=828.3MB, time=126.74 memory used=6063.7MB, alloc=852.3MB, time=139.40 memory used=6532.1MB, alloc=876.3MB, time=152.51 memory used=6978.6MB, alloc=900.3MB, time=164.78 memory used=7406.6MB, alloc=924.3MB, time=176.18 memory used=7826.1MB, alloc=948.3MB, time=188.43 memory used=8214.4MB, alloc=972.3MB, time=200.10 memory used=8501.6MB, alloc=996.3MB, time=208.17 memory used=8827.5MB, alloc=1020.3MB, time=217.20 memory used=9105.5MB, alloc=1044.3MB, time=225.34 memory used=9721.0MB, alloc=1068.3MB, time=241.97 memory used=10273.0MB, alloc=1092.3MB, time=254.66 memory used=10839.2MB, alloc=1116.3MB, time=264.92 memory used=11334.5MB, alloc=1140.3MB, time=276.40 memory used=11797.1MB, alloc=1164.3MB, time=287.59 memory used=12229.7MB, alloc=1188.3MB, time=298.42 memory used=12648.4MB, alloc=1212.3MB, time=308.96 memory used=13058.2MB, alloc=1236.3MB, time=319.48 memory used=13485.0MB, alloc=1260.3MB, time=330.05 memory used=13896.8MB, alloc=1284.3MB, time=340.49 memory used=14319.6MB, alloc=1308.3MB, time=351.06 memory used=14765.9MB, alloc=1332.3MB, time=361.48 memory used=15158.1MB, alloc=1356.3MB, time=371.76 memory used=15527.1MB, alloc=1380.3MB, time=381.81 memory used=15878.9MB, alloc=1404.3MB, time=391.76 memory used=16217.3MB, alloc=1428.3MB, time=401.55 memory used=16560.8MB, alloc=1452.3MB, time=411.40 memory used=16886.4MB, alloc=1476.3MB, time=421.16 memory used=17224.1MB, alloc=1500.3MB, time=431.16 memory used=17550.7MB, alloc=1524.3MB, time=441.05 memory used=17873.9MB, alloc=1548.3MB, time=450.90 memory used=18239.6MB, alloc=1572.3MB, time=461.13 memory used=18636.8MB, alloc=1596.3MB, time=471.37 memory used=19065.5MB, alloc=1620.3MB, time=481.80 memory used=19505.5MB, alloc=1644.3MB, time=492.55 memory used=19814.0MB, alloc=1668.3MB, time=506.55 memory used=20091.6MB, alloc=1692.3MB, time=521.18 memory used=20375.4MB, alloc=1716.3MB, time=536.34 memory used=20668.7MB, alloc=1740.3MB, time=552.07 memory used=20973.0MB, alloc=1764.3MB, time=568.79 memory used=21289.7MB, alloc=1788.3MB, time=586.34 memory used=21619.7MB, alloc=1812.3MB, time=604.48 memory used=21963.8MB, alloc=1836.3MB, time=623.27 memory used=22322.4MB, alloc=1860.3MB, time=642.54 memory used=22696.2MB, alloc=1884.3MB, time=662.48 memory used=23085.4MB, alloc=1908.3MB, time=683.33 memory used=23489.5MB, alloc=1932.3MB, time=704.72 memory used=23908.6MB, alloc=1956.3MB, time=727.32 memory used=24343.4MB, alloc=1980.3MB, time=750.57 memory used=24793.0MB, alloc=2004.3MB, time=774.56 memory used=25258.9MB, alloc=2028.3MB, time=799.46 memory used=25739.8MB, alloc=2052.3MB, time=825.19 memory used=26236.1MB, alloc=2076.3MB, time=851.62 memory used=26747.8MB, alloc=2100.3MB, time=878.86 memory used=27275.5MB, alloc=2124.3MB, time=906.73 memory used=27818.7MB, alloc=2148.3MB, time=935.33 memory used=28377.4MB, alloc=2172.3MB, time=964.67 memory used=28951.8MB, alloc=2196.3MB, time=995.28 memory used=29541.6MB, alloc=2220.3MB, time=1026.56 memory used=30146.3MB, alloc=2244.3MB, time=1057.89 memory used=30765.2MB, alloc=2268.3MB, time=1090.02 memory used=31398.7MB, alloc=2292.3MB, time=1123.07 memory used=32046.1MB, alloc=2316.3MB, time=1156.80 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428455972 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [18 y z + 7 z + 11 z, 6 x z - 19 y + 2 z, 2 x + 15 x y - 8 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [7 x y + 4 x z + 16 z, 3 x - 3 y + 18, 17 x z - 5 y - 10] > Problem := [F,G]; 2 2 2 Problem := [[18 y z + 7 z + 11 z, 6 x z - 19 y + 2 z, 2 x + 15 x y - 8 x], 2 [7 x y + 4 x z + 16 z, 3 x - 3 y + 18, 17 x z - 5 y - 10]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.4MB, alloc=32.3MB, time=0.78 memory used=67.0MB, alloc=56.3MB, time=1.08 memory used=106.6MB, alloc=60.3MB, time=1.67 memory used=144.2MB, alloc=60.3MB, time=2.25 memory used=179.4MB, alloc=84.3MB, time=2.79 memory used=234.7MB, alloc=84.3MB, time=3.68 memory used=288.7MB, alloc=116.3MB, time=4.58 memory used=365.2MB, alloc=116.3MB, time=5.88 memory used=441.2MB, alloc=140.3MB, time=7.22 memory used=541.2MB, alloc=140.3MB, time=9.02 memory used=636.6MB, alloc=164.3MB, time=10.71 memory used=735.9MB, alloc=444.3MB, time=12.42 memory used=870.9MB, alloc=468.3MB, time=14.78 memory used=1014.1MB, alloc=492.3MB, time=17.28 memory used=1168.1MB, alloc=516.3MB, time=20.03 memory used=1332.3MB, alloc=540.3MB, time=22.98 memory used=1507.6MB, alloc=564.3MB, time=26.25 memory used=1693.4MB, alloc=588.3MB, time=29.71 memory used=1887.2MB, alloc=612.3MB, time=33.34 memory used=2089.5MB, alloc=636.3MB, time=37.25 memory used=2289.4MB, alloc=660.3MB, time=43.31 memory used=2483.6MB, alloc=684.3MB, time=50.35 memory used=2688.3MB, alloc=708.3MB, time=58.24 memory used=2906.0MB, alloc=732.3MB, time=66.51 memory used=3137.7MB, alloc=756.3MB, time=75.62 memory used=3384.4MB, alloc=780.3MB, time=85.31 memory used=3645.5MB, alloc=804.3MB, time=95.63 memory used=3922.4MB, alloc=828.3MB, time=107.10 memory used=4214.3MB, alloc=852.3MB, time=119.62 memory used=4517.8MB, alloc=876.3MB, time=133.44 memory used=4845.2MB, alloc=900.3MB, time=147.53 memory used=5196.7MB, alloc=924.3MB, time=162.60 memory used=5572.0MB, alloc=948.3MB, time=178.77 memory used=5971.3MB, alloc=972.3MB, time=196.63 memory used=6394.5MB, alloc=996.3MB, time=215.84 memory used=6841.7MB, alloc=1020.3MB, time=235.83 memory used=7312.7MB, alloc=1044.3MB, time=257.09 memory used=7807.7MB, alloc=1044.3MB, time=278.73 memory used=8302.7MB, alloc=1044.3MB, time=299.88 memory used=8797.7MB, alloc=1044.3MB, time=320.79 memory used=9292.6MB, alloc=1068.3MB, time=341.76 memory used=9811.5MB, alloc=1068.3MB, time=363.71 memory used=10330.4MB, alloc=1068.3MB, time=385.88 memory used=10849.2MB, alloc=1092.3MB, time=408.11 memory used=11392.0MB, alloc=1092.3MB, time=431.12 memory used=11934.7MB, alloc=1092.3MB, time=454.57 memory used=12477.2MB, alloc=1092.3MB, time=478.48 memory used=13019.7MB, alloc=1116.3MB, time=502.21 memory used=13586.0MB, alloc=1116.3MB, time=526.45 memory used=14152.3MB, alloc=1140.3MB, time=550.59 memory used=14742.5MB, alloc=1140.3MB, time=575.73 memory used=15332.6MB, alloc=1140.3MB, time=600.88 memory used=15922.7MB, alloc=1164.3MB, time=626.05 memory used=16536.9MB, alloc=1164.3MB, time=652.07 memory used=17151.1MB, alloc=1188.3MB, time=678.10 memory used=17789.2MB, alloc=1212.3MB, time=705.54 memory used=18451.3MB, alloc=1236.3MB, time=733.44 N1 := 23647 > GB := Basis(F, plex(op(vars))); 5 4 3 2 GB := [1354 x - 22069 x + 102669 x - 108664 x - 142256 x, 2 2 x + 15 x y - 8 x, 4 4 3 3 2 2 -96 x + 49875 y + 1592 x + 13500 y - 8128 x + 8250 y + 13184 x, 4 3 2 2 8124 x - 135122 x + 691024 x - 1685775 y - 1122080 x + 177450 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=19141.9MB, alloc=1236.3MB, time=761.49 memory used=19956.3MB, alloc=1236.3MB, time=777.29 memory used=20761.0MB, alloc=1260.3MB, time=806.47 memory used=21471.2MB, alloc=1284.3MB, time=839.73 memory used=22205.8MB, alloc=1308.3MB, time=874.00 N2 := 7985 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [18 y z + 7 z + 11 z, 6 z x - 19 y + 2 z, 2 x + 15 x y - 8 x, 2 4 z x + 7 y x + 16 z, 3 x - 3 y + 18, 17 z x - 5 y - 10] > J:=[op(GB),op(G)]; 5 4 3 2 J := [1354 x - 22069 x + 102669 x - 108664 x - 142256 x, 2 2 x + 15 x y - 8 x, 4 4 3 3 2 2 -96 x + 49875 y + 1592 x + 13500 y - 8128 x + 8250 y + 13184 x, 4 3 2 2 8124 x - 135122 x - 1685775 y + 691024 x + 177450 z - 1122080 x, 2 4 z x + 7 y x + 16 z, 3 x - 3 y + 18, 17 z x - 5 y - 10] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 12, 2, 2, 2, 2, 5/6, 1, 2/3, 4/9, 1/3, 4/9, 7, 16, 21, 5, 5, 4, 1, 1, 6/7, 3/7, 2/3, 4/15, 2/15, -1, -9, -3] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=22345.0MB, alloc=1308.3MB, time=879.77 |\^/| 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(); 1428457038 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [17 z + 6 y - 7 z, -9 x z - 17 y - 3 z, 17 x z + 4 z - 8] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [16 y - 10 y - 4 z, 15 y z - 4 z - 5, 13 x - 16 y z + 6] > Problem := [F,G]; 2 Problem := [[17 z + 6 y - 7 z, -9 x z - 17 y - 3 z, 17 x z + 4 z - 8], 2 2 [16 y - 10 y - 4 z, 15 y z - 4 z - 5, 13 x - 16 y z + 6]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=47.0MB, alloc=32.3MB, time=0.80 memory used=66.4MB, alloc=56.3MB, time=1.11 memory used=106.1MB, alloc=60.3MB, time=1.71 memory used=143.8MB, alloc=84.3MB, time=2.29 memory used=201.3MB, alloc=92.3MB, time=3.21 memory used=259.6MB, alloc=116.3MB, time=4.09 memory used=340.1MB, alloc=116.3MB, time=5.37 memory used=420.3MB, alloc=140.3MB, time=6.61 memory used=518.2MB, alloc=140.3MB, time=8.21 memory used=611.3MB, alloc=420.3MB, time=9.83 memory used=733.9MB, alloc=420.3MB, time=11.85 memory used=853.7MB, alloc=444.3MB, time=14.04 memory used=990.0MB, alloc=468.3MB, time=16.44 memory used=1149.8MB, alloc=492.3MB, time=19.39 memory used=1290.5MB, alloc=516.3MB, time=22.03 memory used=1438.4MB, alloc=540.3MB, time=24.75 memory used=1571.9MB, alloc=540.3MB, time=27.45 memory used=1696.4MB, alloc=540.3MB, time=29.91 memory used=1829.9MB, alloc=564.3MB, time=32.68 memory used=1944.8MB, alloc=564.3MB, time=35.13 memory used=2055.7MB, alloc=564.3MB, time=37.58 memory used=2168.0MB, alloc=564.3MB, time=40.22 memory used=2289.0MB, alloc=564.3MB, time=43.19 memory used=2397.1MB, alloc=564.3MB, time=45.83 memory used=2488.3MB, alloc=564.3MB, time=48.34 memory used=2571.6MB, alloc=564.3MB, time=50.51 memory used=2659.7MB, alloc=564.3MB, time=52.76 memory used=2718.3MB, alloc=564.3MB, time=54.39 memory used=2802.8MB, alloc=564.3MB, time=56.79 memory used=2878.6MB, alloc=564.3MB, time=59.12 memory used=3116.2MB, alloc=588.3MB, time=64.78 memory used=3378.4MB, alloc=612.3MB, time=71.98 memory used=3663.7MB, alloc=636.3MB, time=79.45 memory used=3968.2MB, alloc=660.3MB, time=88.34 memory used=4270.3MB, alloc=684.3MB, time=97.51 memory used=4547.3MB, alloc=708.3MB, time=106.06 memory used=4758.5MB, alloc=732.3MB, time=112.21 memory used=4957.7MB, alloc=756.3MB, time=117.53 memory used=5184.1MB, alloc=780.3MB, time=124.84 memory used=5369.0MB, alloc=780.3MB, time=129.93 memory used=5558.3MB, alloc=804.3MB, time=136.24 memory used=5707.7MB, alloc=804.3MB, time=141.69 memory used=5843.0MB, alloc=804.3MB, time=146.13 memory used=5988.9MB, alloc=804.3MB, time=150.59 memory used=6159.2MB, alloc=804.3MB, time=156.62 memory used=6612.8MB, alloc=828.3MB, time=170.40 memory used=7077.4MB, alloc=852.3MB, time=184.60 memory used=7553.1MB, alloc=876.3MB, time=199.93 memory used=8050.6MB, alloc=900.3MB, time=214.44 memory used=8561.9MB, alloc=924.3MB, time=229.52 memory used=9058.9MB, alloc=948.3MB, time=243.55 memory used=9539.1MB, alloc=972.3MB, time=258.49 memory used=9967.1MB, alloc=996.3MB, time=271.05 memory used=10327.2MB, alloc=1020.3MB, time=279.73 memory used=10727.1MB, alloc=1044.3MB, time=289.11 memory used=11190.8MB, alloc=1068.3MB, time=300.09 memory used=11637.5MB, alloc=1092.3MB, time=310.45 memory used=12070.5MB, alloc=1116.3MB, time=320.55 memory used=12493.3MB, alloc=1140.3MB, time=330.55 memory used=12920.8MB, alloc=1164.3MB, time=340.84 memory used=13346.4MB, alloc=1188.3MB, time=351.02 memory used=13749.3MB, alloc=1212.3MB, time=360.93 memory used=14131.6MB, alloc=1236.3MB, time=370.56 memory used=14504.2MB, alloc=1260.3MB, time=380.11 memory used=14897.2MB, alloc=1284.3MB, time=391.60 memory used=15212.6MB, alloc=1308.3MB, time=405.90 memory used=15526.6MB, alloc=1332.3MB, time=420.74 memory used=15847.4MB, alloc=1356.3MB, time=436.10 memory used=16177.9MB, alloc=1380.3MB, time=452.17 memory used=16520.2MB, alloc=1404.3MB, time=468.83 memory used=16874.9MB, alloc=1428.3MB, time=486.32 memory used=17242.6MB, alloc=1452.3MB, time=504.93 memory used=17623.6MB, alloc=1476.3MB, time=523.89 memory used=18018.3MB, alloc=1500.3MB, time=543.34 memory used=18427.0MB, alloc=1524.3MB, time=563.32 memory used=18850.3MB, alloc=1548.3MB, time=584.70 memory used=19288.8MB, alloc=1572.3MB, time=606.90 memory used=19742.5MB, alloc=1596.3MB, time=629.38 memory used=20210.9MB, alloc=1620.3MB, time=652.58 memory used=20695.3MB, alloc=1644.3MB, time=676.92 memory used=21195.1MB, alloc=1668.3MB, time=702.06 memory used=21709.9MB, alloc=1692.3MB, time=728.06 memory used=22239.7MB, alloc=1716.3MB, time=754.91 memory used=22785.5MB, alloc=1740.3MB, time=782.41 memory used=23347.0MB, alloc=1764.3MB, time=810.69 memory used=23924.1MB, alloc=1788.3MB, time=840.29 memory used=24517.0MB, alloc=1812.3MB, time=869.69 memory used=25125.8MB, alloc=1836.3MB, time=900.07 memory used=25750.6MB, alloc=1860.3MB, time=931.74 memory used=26390.4MB, alloc=1884.3MB, time=963.46 memory used=27046.4MB, alloc=1908.3MB, time=996.26 memory used=27718.3MB, alloc=1932.3MB, time=1029.61 |\^/| 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(); 1428458238 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [13 x y + 16 y + 8 y z, 7 x y + 18 z + 9 y, 13 x + 8 z + 8] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-10 y + 11 y - 15 z, 3 x + 2 y - 9 x, 2 y - 8 y z + 12] > Problem := [F,G]; 2 2 2 Problem := [[13 x y + 16 y + 8 y z, 7 x y + 18 z + 9 y, 13 x + 8 z + 8], 2 2 2 2 [-10 y + 11 y - 15 z, 3 x + 2 y - 9 x, 2 y - 8 y z + 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.19 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=32.3MB, time=0.81 memory used=65.6MB, alloc=56.3MB, time=1.09 memory used=105.9MB, alloc=60.3MB, time=1.69 memory used=144.7MB, alloc=84.3MB, time=2.29 memory used=205.9MB, alloc=92.3MB, time=3.26 memory used=266.0MB, alloc=116.3MB, time=4.16 memory used=345.6MB, alloc=116.3MB, time=5.38 memory used=422.8MB, alloc=140.3MB, time=6.64 memory used=494.1MB, alloc=140.3MB, time=7.72 memory used=575.6MB, alloc=396.3MB, time=9.10 memory used=676.5MB, alloc=420.3MB, time=10.76 memory used=805.6MB, alloc=444.3MB, time=12.86 memory used=957.1MB, alloc=468.3MB, time=15.31 memory used=1096.4MB, alloc=492.3MB, time=17.68 memory used=1247.6MB, alloc=492.3MB, time=20.50 memory used=1368.6MB, alloc=516.3MB, time=22.76 memory used=1507.8MB, alloc=516.3MB, time=25.36 memory used=1614.3MB, alloc=516.3MB, time=27.42 memory used=1728.6MB, alloc=516.3MB, time=29.62 memory used=1826.0MB, alloc=540.3MB, time=31.58 memory used=1928.7MB, alloc=540.3MB, time=33.64 memory used=2012.7MB, alloc=540.3MB, time=35.40 memory used=2087.6MB, alloc=540.3MB, time=36.95 memory used=2157.3MB, alloc=540.3MB, time=38.38 memory used=2230.3MB, alloc=540.3MB, time=39.92 memory used=2295.1MB, alloc=564.3MB, time=41.33 memory used=2355.2MB, alloc=564.3MB, time=42.74 memory used=2422.4MB, alloc=564.3MB, time=44.34 memory used=2482.1MB, alloc=588.3MB, time=45.78 memory used=2545.7MB, alloc=588.3MB, time=47.33 memory used=2771.7MB, alloc=612.3MB, time=51.86 memory used=3004.2MB, alloc=636.3MB, time=56.40 memory used=3243.7MB, alloc=660.3MB, time=61.20 memory used=3485.5MB, alloc=684.3MB, time=66.07 memory used=3727.3MB, alloc=708.3MB, time=71.07 memory used=3977.1MB, alloc=732.3MB, time=76.23 memory used=4227.0MB, alloc=756.3MB, time=81.50 memory used=4478.7MB, alloc=780.3MB, time=86.86 memory used=4732.8MB, alloc=804.3MB, time=92.31 memory used=4975.2MB, alloc=828.3MB, time=99.73 memory used=5197.4MB, alloc=852.3MB, time=108.43 memory used=5427.4MB, alloc=876.3MB, time=117.70 memory used=5669.0MB, alloc=900.3MB, time=127.83 memory used=5923.7MB, alloc=924.3MB, time=138.70 memory used=6191.6MB, alloc=948.3MB, time=150.22 memory used=6473.8MB, alloc=972.3MB, time=162.47 memory used=6770.9MB, alloc=996.3MB, time=175.63 memory used=7083.4MB, alloc=1020.3MB, time=189.41 memory used=7411.2MB, alloc=1044.3MB, time=204.18 memory used=7754.7MB, alloc=1068.3MB, time=219.69 memory used=8113.7MB, alloc=1092.3MB, time=235.76 memory used=8487.9MB, alloc=1116.3MB, time=252.54 memory used=8878.0MB, alloc=1140.3MB, time=270.08 memory used=9283.8MB, alloc=1164.3MB, time=288.43 memory used=9705.7MB, alloc=1188.3MB, time=307.30 memory used=10143.4MB, alloc=1212.3MB, time=327.01 memory used=10591.3MB, alloc=1236.3MB, time=347.91 memory used=11059.4MB, alloc=1260.3MB, time=370.01 memory used=11551.5MB, alloc=1284.3MB, time=393.02 memory used=12067.4MB, alloc=1308.3MB, time=417.18 memory used=12607.4MB, alloc=1332.3MB, time=442.39 memory used=13171.3MB, alloc=1356.3MB, time=468.71 memory used=13759.1MB, alloc=1380.3MB, time=495.98 memory used=14370.9MB, alloc=1404.3MB, time=524.17 memory used=15006.6MB, alloc=1428.3MB, time=553.61 memory used=15666.2MB, alloc=1452.3MB, time=584.68 memory used=16349.8MB, alloc=1476.3MB, time=616.40 memory used=17057.3MB, alloc=1500.3MB, time=649.28 memory used=17788.7MB, alloc=1524.3MB, time=683.11 memory used=18544.1MB, alloc=1548.3MB, time=717.90 memory used=19323.4MB, alloc=1572.3MB, time=753.69 memory used=20126.5MB, alloc=1596.3MB, time=790.39 memory used=20953.7MB, alloc=1596.3MB, time=828.09 memory used=21780.9MB, alloc=1596.3MB, time=866.18 memory used=22607.9MB, alloc=1596.3MB, time=903.96 memory used=23434.9MB, alloc=1620.3MB, time=941.70 memory used=24285.8MB, alloc=1620.3MB, time=980.51 memory used=25136.7MB, alloc=1620.3MB, time=1019.33 memory used=25987.4MB, alloc=1620.3MB, time=1058.33 |\^/| 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(); 1428459438 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [-5 y z + z - 11, -17 x y - 11 y z - 16 z, -3 x z + 10 y z - 19 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-14 x z + 17 y z - 5 y, 4 x y + 4 y z - 3 y, 9 x y - 20 y z - 7 z ] > Problem := [F,G]; Problem := [[-5 y z + z - 11, -17 x y - 11 y z - 16 z, -3 x z + 10 y z - 19 y], 2 [-14 x z + 17 y z - 5 y, 4 x y + 4 y z - 3 y, 9 x y - 20 y z - 7 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=46.1MB, alloc=32.3MB, time=0.77 memory used=63.9MB, alloc=56.3MB, time=1.04 memory used=100.9MB, alloc=60.3MB, time=1.61 memory used=137.1MB, alloc=84.3MB, time=2.17 memory used=195.2MB, alloc=92.3MB, time=3.11 memory used=251.9MB, alloc=116.3MB, time=4.04 memory used=328.5MB, alloc=116.3MB, time=5.24 memory used=403.1MB, alloc=140.3MB, time=6.40 memory used=497.3MB, alloc=164.3MB, time=7.92 memory used=594.6MB, alloc=420.3MB, time=9.61 memory used=717.1MB, alloc=444.3MB, time=11.83 memory used=862.1MB, alloc=468.3MB, time=14.57 memory used=1025.8MB, alloc=492.3MB, time=17.54 memory used=1216.9MB, alloc=516.3MB, time=21.69 memory used=1426.6MB, alloc=540.3MB, time=26.43 memory used=1654.8MB, alloc=564.3MB, time=31.56 memory used=1894.8MB, alloc=588.3MB, time=36.43 memory used=2155.1MB, alloc=612.3MB, time=41.85 memory used=2431.4MB, alloc=636.3MB, time=47.79 memory used=2739.4MB, alloc=660.3MB, time=56.07 memory used=3067.4MB, alloc=684.3MB, time=64.68 memory used=3399.7MB, alloc=708.3MB, time=74.71 memory used=3715.0MB, alloc=732.3MB, time=84.34 memory used=3981.0MB, alloc=756.3MB, time=91.88 memory used=4264.7MB, alloc=780.3MB, time=100.50 memory used=4549.0MB, alloc=804.3MB, time=109.27 memory used=4767.0MB, alloc=828.3MB, time=115.06 memory used=5013.8MB, alloc=852.3MB, time=123.47 memory used=5236.8MB, alloc=876.3MB, time=131.14 memory used=5502.6MB, alloc=876.3MB, time=141.74 memory used=5744.1MB, alloc=876.3MB, time=150.86 memory used=5964.5MB, alloc=876.3MB, time=159.67 memory used=6140.7MB, alloc=876.3MB, time=165.83 memory used=6344.2MB, alloc=876.3MB, time=173.69 memory used=6465.7MB, alloc=876.3MB, time=178.19 memory used=7000.3MB, alloc=900.3MB, time=197.98 memory used=7558.2MB, alloc=924.3MB, time=217.13 memory used=8113.1MB, alloc=948.3MB, time=235.96 memory used=8705.3MB, alloc=972.3MB, time=258.18 memory used=9309.1MB, alloc=996.3MB, time=280.20 memory used=9948.6MB, alloc=1020.3MB, time=305.18 memory used=10490.8MB, alloc=1300.3MB, time=323.84 memory used=11171.8MB, alloc=1324.3MB, time=351.88 memory used=11870.0MB, alloc=1348.3MB, time=380.46 memory used=12584.3MB, alloc=1372.3MB, time=410.36 memory used=13311.3MB, alloc=1396.3MB, time=440.46 memory used=14058.6MB, alloc=1420.3MB, time=470.68 memory used=14823.8MB, alloc=1444.3MB, time=503.97 memory used=15603.8MB, alloc=1468.3MB, time=537.00 memory used=16389.1MB, alloc=1492.3MB, time=569.66 memory used=17197.4MB, alloc=1516.3MB, time=603.22 memory used=18018.8MB, alloc=1540.3MB, time=636.56 memory used=18848.2MB, alloc=1564.3MB, time=670.71 memory used=19702.9MB, alloc=1588.3MB, time=708.25 memory used=20575.2MB, alloc=1612.3MB, time=747.25 memory used=21456.8MB, alloc=1636.3MB, time=786.94 memory used=22343.5MB, alloc=1660.3MB, time=822.82 memory used=23241.9MB, alloc=1684.3MB, time=858.46 memory used=24162.5MB, alloc=1708.3MB, time=898.38 memory used=25095.9MB, alloc=1732.3MB, time=939.62 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428460638 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-13 x - 12 x z - 9 z , -2 x + 12 x y - 8, 7 x + 5 z - 15] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-8 x y + x + 11, -20 x + 13 x z + 13 z, -11 x z + 15 y + 2 z] > Problem := [F,G]; 2 2 2 2 Problem := [[-13 x - 12 x z - 9 z , -2 x + 12 x y - 8, 7 x + 5 z - 15], 2 2 [-8 x y + x + 11, -20 x + 13 x z + 13 z, -11 x z + 15 y + 2 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.49 memory used=48.1MB, alloc=32.3MB, time=0.79 memory used=67.6MB, alloc=32.3MB, time=1.07 memory used=86.5MB, alloc=56.3MB, time=1.37 memory used=126.8MB, alloc=60.3MB, time=1.95 memory used=168.9MB, alloc=60.3MB, time=2.67 memory used=207.1MB, alloc=84.3MB, time=3.35 memory used=266.3MB, alloc=84.3MB, time=4.36 memory used=319.9MB, alloc=108.3MB, time=5.50 memory used=385.6MB, alloc=132.3MB, time=7.72 N1 := 1899 > GB := Basis(F, plex(op(vars))); 4 3 2 GB := [441 x - 420 x - 1565 x + 900 x + 2025, 3 2 2 1764 x - 1680 x - 8285 x + 12150 y + 3600, 7 x + 5 z - 15] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=475.6MB, alloc=132.3MB, time=9.89 memory used=575.9MB, alloc=140.3MB, time=11.61 memory used=671.1MB, alloc=164.3MB, time=13.49 memory used=772.2MB, alloc=188.3MB, time=17.09 N2 := 2217 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-13 x - 12 x z - 9 z , -2 x + 12 x y - 8, 7 x + 5 z - 15, 2 2 -8 x y + x + 11, -20 x + 13 x z + 13 z, -11 x z + 15 y + 2 z] > J:=[op(GB),op(G)]; 4 3 2 J := [441 x - 420 x - 1565 x + 900 x + 2025, 3 2 2 1764 x - 1680 x + 12150 y - 8285 x + 3600, 7 x + 5 z - 15, 2 2 -8 x y + x + 11, -20 x + 13 x z + 13 z, -11 x z + 15 y + 2 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 12, 2, 2, 2, 2, 1, 1/2, 2/3, 5/9, 1/6, 7/18, 6, 12, 15, 13 4, 4, 2, 1, 1, 1/2, 1/2, --, 3/22, 5/22, 1, -3, -2] 22 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=833.1MB, alloc=188.3MB, time=19.12 |\^/| 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(); 1428460677 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-2 x - 15 x y - 19 x z, -x - 11 x, 16 x y - 3 x z - 5 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [8 y + 16 z + x, -4 y + 17 y - 16, 4 y + 8 y z + 3 z ] > Problem := [F,G]; 2 2 Problem := [[-2 x - 15 x y - 19 x z, -x - 11 x, 16 x y - 3 x z - 5 y], 2 2 2 2 2 [8 y + 16 z + x, -4 y + 17 y - 16, 4 y + 8 y z + 3 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.5MB, alloc=32.3MB, time=0.77 memory used=66.0MB, alloc=56.3MB, time=1.06 memory used=103.8MB, alloc=60.3MB, time=1.66 memory used=140.1MB, alloc=84.3MB, time=2.22 memory used=199.6MB, alloc=92.3MB, time=3.16 memory used=256.9MB, alloc=116.3MB, time=4.06 memory used=335.9MB, alloc=116.3MB, time=5.31 memory used=412.5MB, alloc=140.3MB, time=6.56 memory used=509.5MB, alloc=164.3MB, time=8.15 memory used=595.1MB, alloc=444.3MB, time=9.60 memory used=735.5MB, alloc=468.3MB, time=12.02 memory used=885.8MB, alloc=492.3MB, time=14.54 memory used=1048.6MB, alloc=516.3MB, time=17.48 memory used=1218.6MB, alloc=540.3MB, time=20.60 memory used=1397.2MB, alloc=564.3MB, time=23.83 memory used=1584.5MB, alloc=588.3MB, time=27.26 memory used=1779.8MB, alloc=612.3MB, time=30.87 memory used=1974.6MB, alloc=636.3MB, time=35.70 memory used=2155.5MB, alloc=660.3MB, time=41.88 memory used=2344.5MB, alloc=684.3MB, time=48.89 memory used=2545.7MB, alloc=708.3MB, time=56.62 memory used=2760.8MB, alloc=732.3MB, time=65.03 memory used=2989.9MB, alloc=756.3MB, time=74.45 memory used=3233.6MB, alloc=780.3MB, time=84.15 memory used=3491.0MB, alloc=804.3MB, time=95.07 memory used=3762.5MB, alloc=828.3MB, time=107.12 memory used=4054.5MB, alloc=852.3MB, time=119.84 memory used=4370.4MB, alloc=876.3MB, time=133.74 memory used=4710.2MB, alloc=900.3MB, time=148.81 memory used=5074.0MB, alloc=924.3MB, time=165.14 memory used=5461.7MB, alloc=948.3MB, time=182.11 memory used=5873.4MB, alloc=972.3MB, time=200.05 memory used=6309.0MB, alloc=996.3MB, time=219.41 memory used=6768.5MB, alloc=996.3MB, time=239.41 memory used=7228.0MB, alloc=1020.3MB, time=260.38 memory used=7711.4MB, alloc=1020.3MB, time=280.97 memory used=8194.8MB, alloc=1020.3MB, time=301.89 memory used=8678.1MB, alloc=1020.3MB, time=324.07 memory used=9161.5MB, alloc=1044.3MB, time=344.76 memory used=9668.7MB, alloc=1044.3MB, time=366.77 memory used=10175.8MB, alloc=1044.3MB, time=388.99 memory used=10682.9MB, alloc=1068.3MB, time=410.59 memory used=11213.8MB, alloc=1068.3MB, time=433.47 memory used=11744.5MB, alloc=1068.3MB, time=455.96 memory used=12275.2MB, alloc=1092.3MB, time=479.24 memory used=12829.7MB, alloc=1092.3MB, time=503.15 memory used=13384.3MB, alloc=1116.3MB, time=527.20 memory used=13962.7MB, alloc=1116.3MB, time=552.12 memory used=14541.3MB, alloc=1140.3MB, time=576.61 memory used=15143.8MB, alloc=1164.3MB, time=602.61 memory used=15770.6MB, alloc=1188.3MB, time=628.96 N1 := 21787 > GB := Basis(F, plex(op(vars))); 2 GB := [x + 11 x, 1967 y + 33 x, 1967 x z - 1991 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=16435.7MB, alloc=1188.3MB, time=652.47 memory used=17227.8MB, alloc=1212.3MB, time=670.44 memory used=17917.9MB, alloc=1236.3MB, time=699.17 memory used=18588.3MB, alloc=1260.3MB, time=729.71 memory used=19282.6MB, alloc=1284.3MB, time=761.35 memory used=20000.7MB, alloc=1308.3MB, time=794.99 memory used=20742.9MB, alloc=1332.3MB, time=828.64 memory used=21509.5MB, alloc=1356.3MB, time=862.59 N2 := 12149 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-2 x - 15 x y - 19 x z, -x - 11 x, -3 z x + 16 y x - 5 y, 2 2 2 2 2 16 z + 8 y + x, -4 y + 17 y - 16, 4 y + 8 y z + 3 z ] > J:=[op(GB),op(G)]; 2 2 2 J := [x + 11 x, 1967 y + 33 x, 1967 x z - 1991 x, 16 z + 8 y + x, 2 2 2 -4 y + 17 y - 16, 4 y + 8 y z + 3 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 12, 2, 2, 2, 2, 2/3, 5/6, 2/3, 8/17, 8/17, 5/17, 6, 11, 11, 2, 2, 2, 2, 2/3, 2/3, 1/2, 2/5, 2/5, 4/15, 2, 1, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=21709.4MB, alloc=1356.3MB, time=870.85 |\^/| 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(); 1428461845 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-12 y - 6 y z + 19 z , 10 x z + 5 y - 9 x, -17 x + 17 y - 2 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [17 x - 20 z - 18 y, 10 y z - 5 x + 20 y, -11 x y + x z - 15 z ] > Problem := [F,G]; Problem := [ 2 2 2 2 2 [-12 y - 6 y z + 19 z , 10 x z + 5 y - 9 x, -17 x + 17 y - 2 y], 2 2 2 [17 x - 20 z - 18 y, 10 y z - 5 x + 20 y, -11 x y + x z - 15 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=47.3MB, alloc=60.3MB, time=0.84 memory used=89.5MB, alloc=60.3MB, time=1.44 memory used=129.6MB, alloc=84.3MB, time=2.04 memory used=170.2MB, alloc=84.3MB, time=2.65 memory used=233.0MB, alloc=92.3MB, time=3.58 memory used=296.3MB, alloc=116.3MB, time=4.54 memory used=363.3MB, alloc=116.3MB, time=5.46 memory used=435.3MB, alloc=372.3MB, time=6.56 memory used=523.7MB, alloc=396.3MB, time=7.84 memory used=631.1MB, alloc=396.3MB, time=9.43 memory used=740.0MB, alloc=420.3MB, time=11.14 memory used=873.3MB, alloc=420.3MB, time=13.10 memory used=1002.2MB, alloc=444.3MB, time=15.18 memory used=1133.7MB, alloc=468.3MB, time=17.27 memory used=1246.3MB, alloc=468.3MB, time=19.04 memory used=1358.4MB, alloc=468.3MB, time=20.86 memory used=1457.6MB, alloc=492.3MB, time=22.45 memory used=1558.2MB, alloc=492.3MB, time=24.19 memory used=1651.1MB, alloc=492.3MB, time=25.88 memory used=1727.8MB, alloc=492.3MB, time=27.26 memory used=1820.0MB, alloc=492.3MB, time=28.89 memory used=1896.1MB, alloc=516.3MB, time=30.30 memory used=2008.7MB, alloc=516.3MB, time=32.66 memory used=2069.4MB, alloc=516.3MB, time=33.83 memory used=2134.9MB, alloc=516.3MB, time=35.01 memory used=2210.3MB, alloc=516.3MB, time=36.69 memory used=2257.5MB, alloc=516.3MB, time=37.67 memory used=2306.9MB, alloc=540.3MB, time=38.62 memory used=2371.7MB, alloc=540.3MB, time=40.00 memory used=2416.5MB, alloc=540.3MB, time=41.04 memory used=2639.0MB, alloc=564.3MB, time=44.84 memory used=2838.1MB, alloc=588.3MB, time=48.24 memory used=3043.9MB, alloc=612.3MB, time=52.32 memory used=3203.9MB, alloc=636.3MB, time=55.35 memory used=3379.0MB, alloc=660.3MB, time=58.63 memory used=3527.5MB, alloc=660.3MB, time=61.61 memory used=3680.8MB, alloc=660.3MB, time=64.73 memory used=3812.6MB, alloc=684.3MB, time=67.19 memory used=3918.3MB, alloc=684.3MB, time=69.56 memory used=4049.4MB, alloc=684.3MB, time=72.60 memory used=4149.5MB, alloc=684.3MB, time=74.82 memory used=4227.5MB, alloc=684.3MB, time=77.13 memory used=4310.7MB, alloc=684.3MB, time=79.21 memory used=4642.0MB, alloc=708.3MB, time=85.71 memory used=5004.3MB, alloc=732.3MB, time=92.37 memory used=5383.9MB, alloc=756.3MB, time=99.55 memory used=5750.0MB, alloc=780.3MB, time=106.70 memory used=6133.5MB, alloc=804.3MB, time=114.94 memory used=6478.1MB, alloc=828.3MB, time=122.89 memory used=6781.6MB, alloc=852.3MB, time=129.37 memory used=7078.9MB, alloc=876.3MB, time=136.37 memory used=7364.0MB, alloc=900.3MB, time=142.87 memory used=7664.8MB, alloc=924.3MB, time=150.87 memory used=7907.9MB, alloc=948.3MB, time=156.84 memory used=8157.0MB, alloc=972.3MB, time=163.91 memory used=8367.6MB, alloc=996.3MB, time=170.04 memory used=8985.9MB, alloc=1020.3MB, time=183.66 memory used=9608.9MB, alloc=1044.3MB, time=197.72 memory used=10260.5MB, alloc=1068.3MB, time=211.79 memory used=10905.0MB, alloc=1092.3MB, time=226.35 memory used=11531.4MB, alloc=1116.3MB, time=239.26 memory used=12209.4MB, alloc=1140.3MB, time=255.30 memory used=12868.1MB, alloc=1164.3MB, time=269.08 memory used=13583.3MB, alloc=1188.3MB, time=287.71 memory used=14245.3MB, alloc=1212.3MB, time=305.15 memory used=14830.8MB, alloc=1236.3MB, time=320.22 memory used=15397.1MB, alloc=1260.3MB, time=334.02 memory used=16079.1MB, alloc=1284.3MB, time=348.90 memory used=16583.3MB, alloc=1308.3MB, time=361.01 memory used=17010.2MB, alloc=1332.3MB, time=372.45 memory used=17632.2MB, alloc=1356.3MB, time=386.73 memory used=18178.3MB, alloc=1380.3MB, time=401.56 memory used=18684.6MB, alloc=1404.3MB, time=416.03 memory used=19179.1MB, alloc=1428.3MB, time=430.27 memory used=19661.5MB, alloc=1452.3MB, time=444.41 memory used=20184.3MB, alloc=1476.3MB, time=458.51 memory used=20687.0MB, alloc=1500.3MB, time=472.51 memory used=21151.4MB, alloc=1524.3MB, time=486.57 memory used=21589.3MB, alloc=1548.3MB, time=500.26 memory used=22060.0MB, alloc=1572.3MB, time=514.24 memory used=22481.3MB, alloc=1596.3MB, time=527.90 memory used=22933.8MB, alloc=1620.3MB, time=541.73 memory used=23325.2MB, alloc=1644.3MB, time=555.07 memory used=23760.0MB, alloc=1668.3MB, time=568.75 memory used=24137.2MB, alloc=1692.3MB, time=582.17 memory used=24545.3MB, alloc=1716.3MB, time=595.93 memory used=24944.9MB, alloc=1740.3MB, time=609.68 memory used=25315.6MB, alloc=1764.3MB, time=623.21 memory used=25749.8MB, alloc=1788.3MB, time=637.20 memory used=26159.5MB, alloc=1812.3MB, time=650.36 memory used=26635.9MB, alloc=1836.3MB, time=663.97 memory used=27147.0MB, alloc=1860.3MB, time=678.35 memory used=27633.6MB, alloc=1884.3MB, time=692.03 memory used=28026.9MB, alloc=1908.3MB, time=705.11 memory used=28425.1MB, alloc=1932.3MB, time=718.16 memory used=28763.0MB, alloc=1956.3MB, time=731.14 memory used=29038.3MB, alloc=1980.3MB, time=743.14 memory used=29386.4MB, alloc=2004.3MB, time=756.44 memory used=29746.7MB, alloc=2028.3MB, time=769.88 memory used=30041.2MB, alloc=2052.3MB, time=782.47 memory used=30348.6MB, alloc=2076.3MB, time=795.48 memory used=30652.0MB, alloc=2100.3MB, time=808.32 memory used=30944.7MB, alloc=2124.3MB, time=821.07 memory used=31251.2MB, alloc=2148.3MB, time=833.65 memory used=31459.2MB, alloc=2172.3MB, time=845.67 memory used=31720.2MB, alloc=2196.3MB, time=858.07 memory used=31980.4MB, alloc=2220.3MB, time=869.99 memory used=32222.4MB, alloc=2244.3MB, time=882.14 memory used=32494.9MB, alloc=2268.3MB, time=894.95 memory used=32755.8MB, alloc=2292.3MB, time=907.70 memory used=32929.7MB, alloc=2316.3MB, time=919.91 memory used=33176.4MB, alloc=2340.3MB, time=932.39 memory used=33408.0MB, alloc=2364.3MB, time=944.80 memory used=33625.8MB, alloc=2388.3MB, time=956.89 memory used=33791.5MB, alloc=2412.3MB, time=968.10 memory used=34020.9MB, alloc=2436.3MB, time=982.13 memory used=34193.2MB, alloc=2460.3MB, time=992.98 memory used=34390.4MB, alloc=2484.3MB, time=1004.20 memory used=34564.3MB, alloc=2508.3MB, time=1015.21 memory used=34732.0MB, alloc=2532.3MB, time=1026.13 memory used=34914.0MB, alloc=2556.3MB, time=1037.72 memory used=35108.1MB, alloc=2580.3MB, time=1049.63 memory used=35255.9MB, alloc=2604.3MB, time=1060.47 memory used=35434.8MB, alloc=2628.3MB, time=1071.85 memory used=35582.1MB, alloc=2652.3MB, time=1082.76 memory used=35762.0MB, alloc=2676.3MB, time=1094.29 memory used=35932.2MB, alloc=2700.3MB, time=1105.70 memory used=36066.4MB, alloc=2724.3MB, time=1116.73 memory used=36131.2MB, alloc=2748.3MB, time=1126.01 memory used=36298.0MB, alloc=2772.3MB, time=1137.51 memory used=36470.4MB, alloc=2796.3MB, time=1149.11 memory used=36646.6MB, alloc=2820.3MB, time=1160.48 memory used=36793.9MB, alloc=2844.3MB, time=1171.87 memory used=36923.0MB, alloc=2868.3MB, time=1182.90 memory used=37026.6MB, alloc=2892.3MB, time=1192.93 |\^/| 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(); 1428463045 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-16 x + 19 y z - 17 y, 18 x + 18 x z + 18 z , 19 z - 5] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-18 y + 2 x + 13 y, -2 x z + 19 y + 11 z, -3 x + 16 z + 16] > Problem := [F,G]; 2 2 2 2 Problem := [[-16 x + 19 y z - 17 y, 18 x + 18 x z + 18 z , 19 z - 5], 2 2 2 2 [-18 y + 2 x + 13 y, -2 x z + 19 y + 11 z, -3 x + 16 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=47.2MB, alloc=56.3MB, time=0.81 memory used=88.5MB, alloc=60.3MB, time=1.42 memory used=129.7MB, alloc=60.3MB, time=2.00 memory used=171.0MB, alloc=84.3MB, time=2.58 memory used=236.1MB, alloc=92.3MB, time=3.52 memory used=298.2MB, alloc=92.3MB, time=4.42 memory used=359.8MB, alloc=116.3MB, time=5.27 memory used=435.2MB, alloc=372.3MB, time=6.35 memory used=520.0MB, alloc=396.3MB, time=7.60 memory used=628.0MB, alloc=396.3MB, time=9.13 memory used=733.9MB, alloc=420.3MB, time=10.67 memory used=862.7MB, alloc=444.3MB, time=12.46 memory used=1005.7MB, alloc=444.3MB, time=14.36 memory used=1150.0MB, alloc=468.3MB, time=16.59 memory used=1274.9MB, alloc=468.3MB, time=18.49 memory used=1397.8MB, alloc=492.3MB, time=20.33 memory used=1515.9MB, alloc=492.3MB, time=22.23 memory used=1663.1MB, alloc=516.3MB, time=25.03 memory used=1843.6MB, alloc=540.3MB, time=28.41 memory used=2020.0MB, alloc=564.3MB, time=31.70 memory used=2185.9MB, alloc=588.3MB, time=35.42 memory used=2375.3MB, alloc=612.3MB, time=41.68 memory used=2569.3MB, alloc=636.3MB, time=48.68 memory used=2763.5MB, alloc=660.3MB, time=56.74 memory used=2981.7MB, alloc=684.3MB, time=65.66 memory used=3223.8MB, alloc=708.3MB, time=75.75 memory used=3489.8MB, alloc=732.3MB, time=86.69 memory used=3779.9MB, alloc=756.3MB, time=98.63 memory used=4093.9MB, alloc=756.3MB, time=111.71 memory used=4407.8MB, alloc=780.3MB, time=124.64 memory used=4745.5MB, alloc=804.3MB, time=138.58 memory used=5107.2MB, alloc=828.3MB, time=153.40 N1 := 10001 > GB := Basis(F, plex(op(vars))); 4 2 3 2 3 GB := [361 x + 95 x + 25, -152 x + 136 x - 40 x + 97 y, -19 x + 5 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5324.3MB, alloc=828.3MB, time=160.31 memory used=5501.3MB, alloc=828.3MB, time=164.42 N2 := 2207 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-16 x + 19 y z - 17 y, 18 x + 18 x z + 18 z , 19 z - 5, 2 2 2 2 -18 y + 13 y + 2 x, -2 x z + 19 y + 11 z, -3 x + 16 z + 16] > J:=[op(GB),op(G)]; 4 2 3 2 3 J := [361 x + 95 x + 25, -152 x + 136 x - 40 x + 97 y, -19 x + 5 z, 2 2 2 2 -18 y + 13 y + 2 x, -2 x z + 19 y + 11 z, -3 x + 16 z + 16] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 12, 2, 2, 2, 2, 5/6, 1/2, 5/6, 6/17, 5/17, 7/17, 6, 12, 16, 4, 4, 2, 2, 1, 1/2, 1/2, 1/2, 2/9, 2/9, 1, -4, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=5653.7MB, alloc=828.3MB, time=170.47 |\^/| 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(); 1428463236 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [4 x z + 18 z + 2, 13 x y + 19 y z + 7 z , 5 y z - 10 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [11 x + 6 y - 11 y, 9 x y - 13 z - 12 z, 8 x + 18 x - 14 z] > Problem := [F,G]; 2 2 Problem := [[4 x z + 18 z + 2, 13 x y + 19 y z + 7 z , 5 y z - 10 z ], 2 2 2 2 [11 x + 6 y - 11 y, 9 x y - 13 z - 12 z, 8 x + 18 x - 14 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.19 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=46.6MB, alloc=32.3MB, time=0.79 memory used=65.9MB, alloc=56.3MB, time=1.08 memory used=106.2MB, alloc=60.3MB, time=1.70 memory used=145.2MB, alloc=60.3MB, time=2.28 memory used=182.5MB, alloc=84.3MB, time=2.86 memory used=235.2MB, alloc=84.3MB, time=3.69 memory used=289.5MB, alloc=116.3MB, time=4.60 memory used=365.8MB, alloc=140.3MB, time=5.85 memory used=464.3MB, alloc=140.3MB, time=7.47 memory used=554.1MB, alloc=420.3MB, time=9.05 memory used=678.6MB, alloc=444.3MB, time=11.24 memory used=824.2MB, alloc=468.3MB, time=13.95 memory used=992.0MB, alloc=492.3MB, time=17.17 memory used=1179.5MB, alloc=516.3MB, time=20.89 memory used=1365.0MB, alloc=540.3MB, time=24.61 memory used=1559.0MB, alloc=564.3MB, time=28.93 memory used=1742.7MB, alloc=588.3MB, time=33.51 memory used=1902.6MB, alloc=588.3MB, time=37.50 memory used=2036.4MB, alloc=588.3MB, time=40.36 memory used=2198.0MB, alloc=612.3MB, time=44.24 memory used=2330.1MB, alloc=612.3MB, time=47.44 memory used=2464.1MB, alloc=636.3MB, time=50.82 memory used=2570.5MB, alloc=636.3MB, time=53.41 memory used=2668.7MB, alloc=636.3MB, time=55.83 memory used=2761.8MB, alloc=660.3MB, time=57.86 memory used=2846.1MB, alloc=660.3MB, time=59.90 memory used=2915.3MB, alloc=684.3MB, time=61.59 memory used=2992.0MB, alloc=684.3MB, time=63.42 memory used=3070.0MB, alloc=708.3MB, time=65.32 memory used=3165.8MB, alloc=732.3MB, time=67.66 memory used=3507.2MB, alloc=756.3MB, time=74.25 memory used=3844.5MB, alloc=780.3MB, time=80.79 memory used=4171.1MB, alloc=804.3MB, time=87.37 memory used=4488.4MB, alloc=828.3MB, time=93.95 memory used=4801.7MB, alloc=852.3MB, time=100.42 memory used=5112.8MB, alloc=876.3MB, time=107.10 memory used=5419.6MB, alloc=900.3MB, time=113.55 memory used=5725.9MB, alloc=924.3MB, time=120.02 memory used=6033.2MB, alloc=948.3MB, time=126.50 memory used=6339.2MB, alloc=972.3MB, time=132.96 memory used=6640.5MB, alloc=996.3MB, time=139.45 memory used=6937.9MB, alloc=1020.3MB, time=146.02 memory used=7229.4MB, alloc=1044.3MB, time=152.56 memory used=7518.3MB, alloc=1068.3MB, time=159.16 memory used=7794.4MB, alloc=1092.3MB, time=166.03 memory used=8022.2MB, alloc=1116.3MB, time=175.13 memory used=8249.9MB, alloc=1140.3MB, time=184.82 memory used=8486.0MB, alloc=1164.3MB, time=195.23 memory used=8733.2MB, alloc=1188.3MB, time=206.17 memory used=8991.9MB, alloc=1212.3MB, time=217.95 memory used=9263.5MB, alloc=1236.3MB, time=230.42 memory used=9548.4MB, alloc=1260.3MB, time=243.58 memory used=9846.9MB, alloc=1284.3MB, time=257.48 memory used=10159.9MB, alloc=1308.3MB, time=272.19 memory used=10487.0MB, alloc=1332.3MB, time=287.05 memory used=10828.2MB, alloc=1356.3MB, time=302.37 memory used=11184.2MB, alloc=1380.3MB, time=318.32 memory used=11555.5MB, alloc=1404.3MB, time=335.04 memory used=11941.5MB, alloc=1428.3MB, time=352.40 memory used=12342.5MB, alloc=1452.3MB, time=370.50 memory used=12759.2MB, alloc=1476.3MB, time=389.21 memory used=13190.8MB, alloc=1500.3MB, time=408.86 memory used=13636.8MB, alloc=1524.3MB, time=429.22 memory used=14097.7MB, alloc=1548.3MB, time=450.45 memory used=14573.4MB, alloc=1572.3MB, time=472.30 memory used=15064.2MB, alloc=1596.3MB, time=494.89 memory used=15570.0MB, alloc=1620.3MB, time=518.12 memory used=16090.5MB, alloc=1644.3MB, time=542.19 memory used=16626.1MB, alloc=1668.3MB, time=567.08 memory used=17176.8MB, alloc=1692.3MB, time=592.29 memory used=17741.7MB, alloc=1716.3MB, time=618.20 memory used=18321.7MB, alloc=1740.3MB, time=645.01 memory used=18916.5MB, alloc=1764.3MB, time=672.43 memory used=19526.5MB, alloc=1788.3MB, time=700.53 memory used=20151.6MB, alloc=1812.3MB, time=729.32 memory used=20791.5MB, alloc=1836.3MB, time=759.01 memory used=21446.5MB, alloc=1860.3MB, time=789.45 memory used=22116.8MB, alloc=1884.3MB, time=820.95 memory used=22802.4MB, alloc=1908.3MB, time=853.40 memory used=23503.1MB, alloc=1932.3MB, time=886.56 memory used=24218.6MB, alloc=1956.3MB, time=920.58 memory used=24949.9MB, alloc=1980.3MB, time=955.32 memory used=25694.9MB, alloc=2004.3MB, time=991.03 |\^/| 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(); 1428464436 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-9 x + 16 y - 11, 20 z + 10 x - 17 z, 8 x + 5 y z - 17 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-14 x y - 6 x z + 14 y , -3 z - 7 x - 15 y, 7 y - 20 y] > Problem := [F,G]; 2 2 2 2 Problem := [[-9 x + 16 y - 11, 20 z + 10 x - 17 z, 8 x + 5 y z - 17 x], 2 2 2 [-14 x y - 6 x z + 14 y , -3 z - 7 x - 15 y, 7 y - 20 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.49 memory used=47.1MB, alloc=32.3MB, time=0.80 memory used=66.5MB, alloc=56.3MB, time=1.10 memory used=108.1MB, alloc=60.3MB, time=1.73 memory used=148.5MB, alloc=84.3MB, time=2.32 memory used=212.8MB, alloc=92.3MB, time=3.27 memory used=272.2MB, alloc=116.3MB, time=4.19 memory used=356.5MB, alloc=116.3MB, time=5.47 memory used=432.2MB, alloc=396.3MB, time=6.69 memory used=542.7MB, alloc=396.3MB, time=8.25 memory used=647.6MB, alloc=420.3MB, time=9.97 memory used=781.9MB, alloc=444.3MB, time=11.98 memory used=931.1MB, alloc=468.3MB, time=14.47 memory used=1073.8MB, alloc=492.3MB, time=16.73 memory used=1202.6MB, alloc=492.3MB, time=18.53 memory used=1330.0MB, alloc=492.3MB, time=20.56 memory used=1433.3MB, alloc=516.3MB, time=22.37 memory used=1535.5MB, alloc=516.3MB, time=24.21 memory used=1641.1MB, alloc=516.3MB, time=26.19 memory used=1755.5MB, alloc=540.3MB, time=28.44 memory used=1896.8MB, alloc=564.3MB, time=31.15 memory used=2036.6MB, alloc=588.3MB, time=33.77 memory used=2152.5MB, alloc=612.3MB, time=36.07 memory used=2283.1MB, alloc=612.3MB, time=38.68 memory used=2399.9MB, alloc=636.3MB, time=41.03 memory used=2517.1MB, alloc=660.3MB, time=43.51 memory used=2641.6MB, alloc=684.3MB, time=46.09 memory used=2756.5MB, alloc=708.3MB, time=48.49 memory used=2889.2MB, alloc=708.3MB, time=51.03 memory used=3006.6MB, alloc=732.3MB, time=53.45 memory used=3127.6MB, alloc=756.3MB, time=55.89 memory used=3228.9MB, alloc=756.3MB, time=58.10 memory used=3331.4MB, alloc=780.3MB, time=60.39 memory used=3430.5MB, alloc=780.3MB, time=62.71 memory used=3507.5MB, alloc=804.3MB, time=64.60 memory used=3622.1MB, alloc=828.3MB, time=68.48 memory used=3959.0MB, alloc=852.3MB, time=80.50 memory used=4293.2MB, alloc=876.3MB, time=93.29 memory used=4633.7MB, alloc=900.3MB, time=106.82 memory used=4983.0MB, alloc=924.3MB, time=121.06 memory used=5343.0MB, alloc=948.3MB, time=135.98 memory used=5715.9MB, alloc=972.3MB, time=151.67 memory used=6099.7MB, alloc=996.3MB, time=168.33 memory used=6498.6MB, alloc=1020.3MB, time=186.09 memory used=6921.5MB, alloc=1044.3MB, time=204.93 memory used=7368.3MB, alloc=1068.3MB, time=224.86 memory used=7839.0MB, alloc=1092.3MB, time=245.69 memory used=8333.6MB, alloc=1116.3MB, time=267.71 memory used=8852.2MB, alloc=1116.3MB, time=290.68 memory used=9370.7MB, alloc=1116.3MB, time=313.66 memory used=9889.2MB, alloc=1140.3MB, time=336.71 memory used=10431.7MB, alloc=1140.3MB, time=360.75 memory used=10974.1MB, alloc=1140.3MB, time=384.58 memory used=11516.4MB, alloc=1140.3MB, time=408.58 memory used=12058.7MB, alloc=1164.3MB, time=432.41 memory used=12624.8MB, alloc=1164.3MB, time=457.33 memory used=13190.8MB, alloc=1164.3MB, time=482.30 memory used=13756.7MB, alloc=1164.3MB, time=507.18 memory used=14322.6MB, alloc=1188.3MB, time=532.14 memory used=14912.5MB, alloc=1188.3MB, time=557.95 memory used=15502.1MB, alloc=1188.3MB, time=583.71 memory used=16091.6MB, alloc=1212.3MB, time=609.58 memory used=16705.0MB, alloc=1212.3MB, time=636.39 memory used=17318.4MB, alloc=1212.3MB, time=663.86 memory used=17931.7MB, alloc=1236.3MB, time=690.92 memory used=18568.9MB, alloc=1236.3MB, time=718.84 memory used=19206.1MB, alloc=1236.3MB, time=747.04 memory used=19843.2MB, alloc=1260.3MB, time=775.05 memory used=20504.5MB, alloc=1260.3MB, time=804.50 memory used=21165.7MB, alloc=1284.3MB, time=833.66 memory used=21850.8MB, alloc=1308.3MB, time=863.90 memory used=22559.8MB, alloc=1308.3MB, time=894.95 memory used=23268.3MB, alloc=1332.3MB, time=925.82 memory used=24000.8MB, alloc=1356.3MB, time=957.26 N1 := 26175 > GB := Basis(F, plex(op(vars))); 7 6 5 4 3 GB := [4194304 x - 34729984 x + 109107393 x - 152871296 x + 77041474 x 2 6 5 4 + 8545152 x - 3599299 x, -33554432 x + 206536704 x - 433968648 x 3 2 + 321938991 x - 19783608 x + 11237000 x y - 14886883 x, 2 2 6 5 4 -9 x + 16 y - 11, -71609352192 x + 705889234944 x - 2710476988273 x 3 2 + 4685262005936 x - 2993971584223 x - 175422375568 x + 163408454000 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=24792.8MB, alloc=1356.3MB, time=979.81 memory used=25756.8MB, alloc=1380.3MB, time=997.59 memory used=26648.2MB, alloc=1404.3MB, time=1028.14 |\^/| 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(); 1428465636 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-3 y + 7 x - 20 y, -2 y z + 9 x - 3 y, -9 y - 7 y z - 8] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-2 y z - 16 z - 14, -9 x y + 17 y - 13 y z, -3 x z - 11 y + 20 z ] > Problem := [F,G]; 2 2 Problem := [[-3 y + 7 x - 20 y, -2 y z + 9 x - 3 y, -9 y - 7 y z - 8], 2 2 2 2 [-2 y z - 16 z - 14, -9 x y + 17 y - 13 y z, -3 x z - 11 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=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.0MB, alloc=32.3MB, time=0.79 memory used=66.1MB, alloc=56.3MB, time=1.07 memory used=105.6MB, alloc=84.3MB, time=1.68 memory used=149.1MB, alloc=84.3MB, time=2.35 memory used=210.6MB, alloc=92.3MB, time=3.31 memory used=272.7MB, alloc=116.3MB, time=4.27 memory used=349.3MB, alloc=116.3MB, time=5.45 memory used=423.2MB, alloc=396.3MB, time=6.61 memory used=532.4MB, alloc=396.3MB, time=8.22 memory used=639.8MB, alloc=420.3MB, time=9.84 memory used=764.3MB, alloc=444.3MB, time=11.82 memory used=915.1MB, alloc=468.3MB, time=14.39 memory used=1061.4MB, alloc=492.3MB, time=16.98 memory used=1197.7MB, alloc=492.3MB, time=19.25 memory used=1321.4MB, alloc=492.3MB, time=21.64 memory used=1439.5MB, alloc=516.3MB, time=23.87 memory used=1549.7MB, alloc=516.3MB, time=25.87 memory used=1660.1MB, alloc=516.3MB, time=27.82 memory used=1756.5MB, alloc=540.3MB, time=29.59 memory used=1820.0MB, alloc=540.3MB, time=30.81 memory used=1912.5MB, alloc=540.3MB, time=32.64 memory used=1996.0MB, alloc=540.3MB, time=34.49 memory used=2059.9MB, alloc=540.3MB, time=35.67 memory used=2131.7MB, alloc=540.3MB, time=37.27 memory used=2187.0MB, alloc=540.3MB, time=38.37 memory used=2256.3MB, alloc=540.3MB, time=39.94 memory used=2303.6MB, alloc=540.3MB, time=41.08 memory used=2527.6MB, alloc=564.3MB, time=45.65 memory used=2751.6MB, alloc=588.3MB, time=50.40 memory used=2965.4MB, alloc=612.3MB, time=54.60 memory used=3144.3MB, alloc=636.3MB, time=58.27 memory used=3312.6MB, alloc=660.3MB, time=61.84 memory used=3483.1MB, alloc=660.3MB, time=65.49 memory used=3628.6MB, alloc=660.3MB, time=69.12 memory used=3819.1MB, alloc=684.3MB, time=73.90 memory used=4004.3MB, alloc=684.3MB, time=78.99 memory used=4114.3MB, alloc=684.3MB, time=81.97 memory used=4239.1MB, alloc=684.3MB, time=85.43 memory used=4355.7MB, alloc=684.3MB, time=88.80 memory used=4481.5MB, alloc=708.3MB, time=92.03 memory used=4582.4MB, alloc=708.3MB, time=95.08 memory used=4952.4MB, alloc=732.3MB, time=104.19 memory used=5337.3MB, alloc=756.3MB, time=113.65 memory used=5743.7MB, alloc=780.3MB, time=124.14 memory used=6171.9MB, alloc=804.3MB, time=133.97 memory used=6551.5MB, alloc=828.3MB, time=142.79 memory used=6890.2MB, alloc=852.3MB, time=150.56 memory used=7250.0MB, alloc=876.3MB, time=160.16 memory used=7607.9MB, alloc=900.3MB, time=169.27 memory used=7907.5MB, alloc=924.3MB, time=176.83 memory used=8178.4MB, alloc=948.3MB, time=183.17 memory used=8433.0MB, alloc=972.3MB, time=189.66 memory used=8692.6MB, alloc=996.3MB, time=196.00 memory used=8995.9MB, alloc=1020.3MB, time=202.82 memory used=9313.7MB, alloc=1044.3MB, time=210.47 memory used=9823.7MB, alloc=1068.3MB, time=222.21 memory used=10309.0MB, alloc=1092.3MB, time=233.46 memory used=10778.3MB, alloc=1116.3MB, time=244.50 memory used=11237.0MB, alloc=1140.3MB, time=255.19 memory used=11688.8MB, alloc=1164.3MB, time=266.31 memory used=12138.8MB, alloc=1188.3MB, time=277.11 memory used=12613.5MB, alloc=1212.3MB, time=288.07 memory used=13078.0MB, alloc=1236.3MB, time=299.02 memory used=13415.6MB, alloc=1260.3MB, time=313.36 memory used=13739.5MB, alloc=1284.3MB, time=328.25 memory used=14067.2MB, alloc=1308.3MB, time=343.76 memory used=14402.5MB, alloc=1332.3MB, time=360.09 memory used=14748.8MB, alloc=1356.3MB, time=377.19 memory used=15107.5MB, alloc=1380.3MB, time=394.85 memory used=15479.4MB, alloc=1404.3MB, time=413.83 memory used=15865.7MB, alloc=1428.3MB, time=433.26 memory used=16266.3MB, alloc=1452.3MB, time=453.34 memory used=16682.0MB, alloc=1476.3MB, time=474.39 memory used=17113.4MB, alloc=1500.3MB, time=495.98 memory used=17560.4MB, alloc=1524.3MB, time=518.43 memory used=18023.2MB, alloc=1548.3MB, time=541.59 memory used=18501.7MB, alloc=1572.3MB, time=565.11 memory used=18996.1MB, alloc=1596.3MB, time=589.07 memory used=19506.9MB, alloc=1620.3MB, time=613.80 memory used=20033.2MB, alloc=1644.3MB, time=639.91 memory used=20574.6MB, alloc=1668.3MB, time=667.05 memory used=21131.6MB, alloc=1692.3MB, time=694.76 memory used=21704.0MB, alloc=1716.3MB, time=723.07 memory used=22291.7MB, alloc=1740.3MB, time=752.00 memory used=22894.2MB, alloc=1764.3MB, time=781.76 memory used=23511.7MB, alloc=1788.3MB, time=812.26 memory used=24135.9MB, alloc=1812.3MB, time=844.61 memory used=24781.7MB, alloc=1836.3MB, time=877.82 memory used=25451.5MB, alloc=1860.3MB, time=912.34 memory used=26145.3MB, alloc=1884.3MB, time=949.37 memory used=26863.0MB, alloc=1908.3MB, time=985.26 memory used=27604.6MB, alloc=1932.3MB, time=1023.34 |\^/| 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(); 1428466836 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [15 x z - 6 y z + 4 z, 8 x - 2 x y + 16 x z, 3 x - 13 y z + 20 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [15 x y + 9 y - 18, 6 x z + 4 y - 2 z , -2 x - 15 x y - 4 z] > Problem := [F,G]; Problem := [ 2 2 [15 x z - 6 y z + 4 z, 8 x - 2 x y + 16 x z, 3 x - 13 y z + 20 z], 2 2 2 [15 x y + 9 y - 18, 6 x z + 4 y - 2 z , -2 x - 15 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.1MB, alloc=32.3MB, time=0.77 memory used=66.7MB, alloc=56.3MB, time=1.08 memory used=107.1MB, alloc=60.3MB, time=1.69 memory used=145.6MB, alloc=84.3MB, time=2.28 memory used=205.2MB, alloc=92.3MB, time=3.18 memory used=262.3MB, alloc=116.3MB, time=4.12 memory used=340.4MB, alloc=140.3MB, time=5.39 memory used=431.4MB, alloc=396.3MB, time=6.96 memory used=533.3MB, alloc=420.3MB, time=8.69 memory used=657.1MB, alloc=444.3MB, time=10.81 memory used=802.9MB, alloc=468.3MB, time=13.41 memory used=973.0MB, alloc=492.3MB, time=16.41 memory used=1126.0MB, alloc=516.3MB, time=19.25 memory used=1286.6MB, alloc=540.3MB, time=22.29 memory used=1430.1MB, alloc=540.3MB, time=25.02 memory used=1565.2MB, alloc=564.3MB, time=27.74 memory used=1692.3MB, alloc=564.3MB, time=30.34 memory used=1804.8MB, alloc=564.3MB, time=32.78 memory used=1935.5MB, alloc=564.3MB, time=35.85 memory used=2036.5MB, alloc=588.3MB, time=38.20 memory used=2135.7MB, alloc=588.3MB, time=40.46 memory used=2219.5MB, alloc=588.3MB, time=42.32 memory used=2307.9MB, alloc=612.3MB, time=44.25 memory used=2398.9MB, alloc=612.3MB, time=46.18 memory used=2490.2MB, alloc=636.3MB, time=48.09 memory used=2571.4MB, alloc=636.3MB, time=49.93 memory used=2622.0MB, alloc=660.3MB, time=51.24 memory used=2707.3MB, alloc=660.3MB, time=53.18 memory used=2786.2MB, alloc=684.3MB, time=55.05 memory used=3079.5MB, alloc=708.3MB, time=60.78 memory used=3370.3MB, alloc=732.3MB, time=66.50 memory used=3659.5MB, alloc=756.3MB, time=72.39 memory used=3950.4MB, alloc=780.3MB, time=78.01 memory used=4231.7MB, alloc=804.3MB, time=83.65 memory used=4538.8MB, alloc=828.3MB, time=89.85 memory used=4858.0MB, alloc=852.3MB, time=96.12 memory used=5162.7MB, alloc=876.3MB, time=102.52 memory used=5463.0MB, alloc=900.3MB, time=109.00 memory used=5777.8MB, alloc=924.3MB, time=115.31 memory used=6080.2MB, alloc=948.3MB, time=121.89 memory used=6378.4MB, alloc=972.3MB, time=128.33 memory used=6676.2MB, alloc=996.3MB, time=134.87 memory used=6973.1MB, alloc=1020.3MB, time=141.49 memory used=7250.1MB, alloc=1044.3MB, time=149.43 memory used=7489.1MB, alloc=1068.3MB, time=159.08 memory used=7735.3MB, alloc=1092.3MB, time=169.35 memory used=7991.9MB, alloc=1116.3MB, time=180.39 memory used=8259.8MB, alloc=1140.3MB, time=192.23 memory used=8540.7MB, alloc=1164.3MB, time=204.82 memory used=8835.1MB, alloc=1188.3MB, time=218.06 memory used=9143.8MB, alloc=1212.3MB, time=232.09 memory used=9467.3MB, alloc=1236.3MB, time=247.23 memory used=9805.9MB, alloc=1260.3MB, time=262.79 memory used=10159.6MB, alloc=1284.3MB, time=278.91 memory used=10527.9MB, alloc=1308.3MB, time=295.33 memory used=10911.7MB, alloc=1332.3MB, time=312.85 memory used=11310.9MB, alloc=1356.3MB, time=330.94 memory used=11725.6MB, alloc=1380.3MB, time=349.65 memory used=12155.9MB, alloc=1404.3MB, time=369.03 memory used=12602.4MB, alloc=1428.3MB, time=389.60 memory used=13064.5MB, alloc=1452.3MB, time=410.93 memory used=13542.5MB, alloc=1476.3MB, time=433.60 memory used=14035.5MB, alloc=1500.3MB, time=457.11 memory used=14544.4MB, alloc=1524.3MB, time=481.49 memory used=15069.3MB, alloc=1548.3MB, time=505.85 memory used=15610.1MB, alloc=1572.3MB, time=531.41 memory used=16166.9MB, alloc=1596.3MB, time=557.64 memory used=16739.8MB, alloc=1620.3MB, time=584.16 memory used=17328.4MB, alloc=1644.3MB, time=612.32 memory used=17933.1MB, alloc=1668.3MB, time=643.63 memory used=18553.6MB, alloc=1692.3MB, time=673.11 memory used=19189.6MB, alloc=1716.3MB, time=702.89 memory used=19841.9MB, alloc=1740.3MB, time=733.42 memory used=20509.9MB, alloc=1764.3MB, time=764.68 memory used=21194.1MB, alloc=1788.3MB, time=796.87 memory used=21894.1MB, alloc=1812.3MB, time=830.02 memory used=22610.3MB, alloc=1836.3MB, time=863.96 memory used=23342.7MB, alloc=1860.3MB, time=898.54 memory used=24088.6MB, alloc=1884.3MB, time=934.12 memory used=24848.1MB, alloc=1908.3MB, time=970.80 memory used=25631.5MB, alloc=1932.3MB, time=1008.95 |\^/| 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(); 1428468036 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [15 y z + 20 y + 10, -20 z - 5 x + 5, 19 x y + 3 x z + 17 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [5 x + 12 y - 3 z, 17 x + x - 8 z, -19 x y + 20 x - 3 y] > Problem := [F,G]; 2 Problem := [[15 y z + 20 y + 10, -20 z - 5 x + 5, 19 x y + 3 x z + 17 x], 2 2 [5 x + 12 y - 3 z, 17 x + x - 8 z, -19 x y + 20 x - 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=46.0MB, alloc=56.3MB, time=0.78 memory used=86.7MB, alloc=60.3MB, time=1.39 memory used=126.7MB, alloc=60.3MB, time=1.98 memory used=164.6MB, alloc=84.3MB, time=2.58 memory used=222.8MB, alloc=92.3MB, time=3.51 memory used=279.4MB, alloc=116.3MB, time=4.45 memory used=359.1MB, alloc=116.3MB, time=5.73 memory used=438.2MB, alloc=140.3MB, time=7.01 memory used=535.0MB, alloc=140.3MB, time=8.61 memory used=628.3MB, alloc=420.3MB, time=10.23 memory used=749.7MB, alloc=444.3MB, time=12.34 memory used=890.6MB, alloc=468.3MB, time=14.80 memory used=1052.4MB, alloc=492.3MB, time=17.60 memory used=1220.0MB, alloc=516.3MB, time=20.59 memory used=1417.4MB, alloc=540.3MB, time=24.16 memory used=1616.0MB, alloc=564.3MB, time=27.82 memory used=1815.6MB, alloc=588.3MB, time=31.55 memory used=2016.0MB, alloc=612.3MB, time=35.39 memory used=2211.7MB, alloc=636.3MB, time=39.31 memory used=2396.6MB, alloc=660.3MB, time=43.08 memory used=2568.0MB, alloc=684.3MB, time=46.61 memory used=2729.6MB, alloc=708.3MB, time=49.95 memory used=2979.1MB, alloc=732.3MB, time=54.78 memory used=3226.2MB, alloc=756.3MB, time=59.62 memory used=3464.3MB, alloc=780.3MB, time=64.44 memory used=3685.5MB, alloc=804.3MB, time=71.34 memory used=3897.4MB, alloc=828.3MB, time=79.11 memory used=4118.2MB, alloc=852.3MB, time=87.45 memory used=4351.0MB, alloc=876.3MB, time=96.60 memory used=4596.3MB, alloc=900.3MB, time=106.43 memory used=4854.9MB, alloc=924.3MB, time=116.87 memory used=5127.3MB, alloc=948.3MB, time=128.03 memory used=5414.3MB, alloc=972.3MB, time=139.82 memory used=5716.5MB, alloc=996.3MB, time=152.78 memory used=6033.8MB, alloc=1020.3MB, time=166.83 memory used=6366.6MB, alloc=1044.3MB, time=181.23 memory used=6715.2MB, alloc=1068.3MB, time=195.81 memory used=7078.6MB, alloc=1092.3MB, time=210.99 memory used=7457.6MB, alloc=1116.3MB, time=226.89 memory used=7852.3MB, alloc=1140.3MB, time=243.53 memory used=8262.5MB, alloc=1164.3MB, time=260.89 memory used=8688.7MB, alloc=1188.3MB, time=279.79 memory used=9129.3MB, alloc=1212.3MB, time=299.28 memory used=9584.1MB, alloc=1236.3MB, time=319.41 memory used=10061.2MB, alloc=1260.3MB, time=340.66 memory used=10562.2MB, alloc=1284.3MB, time=362.96 memory used=11087.1MB, alloc=1308.3MB, time=386.34 memory used=11636.1MB, alloc=1332.3MB, time=410.70 memory used=12208.9MB, alloc=1356.3MB, time=436.21 memory used=12805.7MB, alloc=1380.3MB, time=462.94 memory used=13426.5MB, alloc=1404.3MB, time=490.43 memory used=14071.1MB, alloc=1428.3MB, time=519.03 memory used=14739.7MB, alloc=1452.3MB, time=549.30 memory used=15432.2MB, alloc=1476.3MB, time=580.32 memory used=16148.7MB, alloc=1500.3MB, time=613.06 memory used=16889.1MB, alloc=1524.3MB, time=647.00 memory used=17653.5MB, alloc=1548.3MB, time=680.70 memory used=18441.7MB, alloc=1548.3MB, time=715.12 memory used=19230.0MB, alloc=1548.3MB, time=749.47 memory used=20018.1MB, alloc=1572.3MB, time=784.16 memory used=20830.3MB, alloc=1572.3MB, time=819.88 memory used=21642.5MB, alloc=1572.3MB, time=855.89 memory used=22454.6MB, alloc=1572.3MB, time=891.77 memory used=23266.7MB, alloc=1572.3MB, time=927.74 |\^/| 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(); 1428469236 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-6 y z + 18 z, 6 x z + 11 x, -x + 8 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-9 x - 2 y + 19 x, 2 x y - 20 z + 3, 4 y z - 2 x - 15 z] > Problem := [F,G]; 2 Problem := [[-6 y z + 18 z, 6 x z + 11 x, -x + 8 x], 2 2 2 [-9 x - 2 y + 19 x, 2 x y - 20 z + 3, 4 y z - 2 x - 15 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.79 memory used=68.1MB, alloc=32.3MB, time=1.10 memory used=87.9MB, alloc=56.3MB, time=1.41 memory used=127.6MB, alloc=60.3MB, time=2.02 memory used=165.4MB, alloc=84.3MB, time=2.65 memory used=224.7MB, alloc=108.3MB, time=3.73 memory used=304.2MB, alloc=140.3MB, time=5.15 memory used=399.0MB, alloc=164.3MB, time=6.84 memory used=504.1MB, alloc=188.3MB, time=9.12 memory used=612.7MB, alloc=212.3MB, time=12.38 memory used=730.8MB, alloc=236.3MB, time=16.70 memory used=867.7MB, alloc=260.3MB, time=22.02 memory used=1028.5MB, alloc=260.3MB, time=28.02 memory used=1189.2MB, alloc=260.3MB, time=34.10 memory used=1350.0MB, alloc=284.3MB, time=40.10 memory used=1534.9MB, alloc=308.3MB, time=46.99 N1 := 5847 > GB := Basis(F, plex(op(vars))); 2 GB := [x - 8 x, x y - 3 x, 6 x z + 11 x, y z - 3 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1652.1MB, alloc=308.3MB, time=49.47 memory used=1895.3MB, alloc=564.3MB, time=53.70 memory used=2121.9MB, alloc=588.3MB, time=58.85 memory used=2324.9MB, alloc=612.3MB, time=66.33 memory used=2540.0MB, alloc=636.3MB, time=74.82 memory used=2779.0MB, alloc=660.3MB, time=84.22 memory used=3042.3MB, alloc=684.3MB, time=94.51 N2 := 5847 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-6 y z + 18 z, 6 x z + 11 x, -x + 8 x, -9 x - 2 y + 19 x, 2 -20 z + 2 y x + 3, 4 y z - 2 x - 15 z] > J:=[op(GB),op(G)]; 2 2 2 J := [x - 8 x, x y - 3 x, 6 x z + 11 x, y z - 3 z, -9 x - 2 y + 19 x, 2 -20 z + 2 y x + 3, 4 y z - 2 x - 15 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 12, 2, 2, 2, 2, 5/6, 2/3, 2/3, 8/15, 4/15, 2/5, 7, 15, 10 14, 2, 2, 2, 2, 6/7, 5/7, 4/7, --, 5/17, 6/17, -2, -2, 0] 17 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=3133.4MB, alloc=684.3MB, time=97.77 |\^/| 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(); 1428469343 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-17 y z - 20 z - 17, 10 y z + 11 z + 17 z, -7 x y - 7 z - y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-11 z - 2 y - 19 z, -14 x - 16 y z - 6 z, 5 y z - x - 12] > Problem := [F,G]; 2 2 2 Problem := [[-17 y z - 20 z - 17, 10 y z + 11 z + 17 z, -7 x y - 7 z - y], 2 2 [-11 z - 2 y - 19 z, -14 x - 16 y z - 6 z, 5 y z - x - 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.47 memory used=47.0MB, alloc=32.3MB, time=0.76 memory used=65.7MB, alloc=56.3MB, time=1.06 memory used=103.8MB, alloc=60.3MB, time=1.65 memory used=141.4MB, alloc=84.3MB, time=2.23 memory used=200.4MB, alloc=92.3MB, time=3.16 memory used=258.8MB, alloc=92.3MB, time=4.04 memory used=314.7MB, alloc=116.3MB, time=4.96 memory used=390.2MB, alloc=140.3MB, time=6.12 memory used=478.9MB, alloc=140.3MB, time=7.56 memory used=570.6MB, alloc=420.3MB, time=9.09 memory used=693.3MB, alloc=444.3MB, time=11.17 memory used=844.6MB, alloc=468.3MB, time=13.66 memory used=1009.0MB, alloc=492.3MB, time=16.42 memory used=1146.1MB, alloc=492.3MB, time=18.73 memory used=1295.3MB, alloc=516.3MB, time=21.38 memory used=1436.4MB, alloc=516.3MB, time=24.19 memory used=1570.7MB, alloc=516.3MB, time=26.81 memory used=1717.4MB, alloc=540.3MB, time=29.87 memory used=1846.6MB, alloc=540.3MB, time=32.74 memory used=1941.3MB, alloc=540.3MB, time=34.79 memory used=2044.4MB, alloc=540.3MB, time=37.02 memory used=2153.0MB, alloc=564.3MB, time=39.55 memory used=2235.6MB, alloc=564.3MB, time=41.49 memory used=2317.0MB, alloc=564.3MB, time=43.50 memory used=2401.6MB, alloc=564.3MB, time=45.66 memory used=2465.5MB, alloc=564.3MB, time=47.43 memory used=2529.2MB, alloc=564.3MB, time=49.05 memory used=2594.5MB, alloc=564.3MB, time=50.89 memory used=2655.8MB, alloc=564.3MB, time=52.64 memory used=2894.0MB, alloc=588.3MB, time=58.72 memory used=3138.2MB, alloc=612.3MB, time=64.34 memory used=3359.3MB, alloc=636.3MB, time=69.73 memory used=3582.3MB, alloc=660.3MB, time=74.76 memory used=3804.6MB, alloc=684.3MB, time=80.46 memory used=4011.6MB, alloc=708.3MB, time=85.74 memory used=4184.2MB, alloc=732.3MB, time=89.44 memory used=4420.1MB, alloc=756.3MB, time=96.81 memory used=4575.0MB, alloc=780.3MB, time=101.11 memory used=4812.7MB, alloc=804.3MB, time=108.86 memory used=5013.7MB, alloc=804.3MB, time=114.92 memory used=5180.1MB, alloc=804.3MB, time=120.22 memory used=5313.6MB, alloc=804.3MB, time=124.71 memory used=5416.3MB, alloc=804.3MB, time=127.71 memory used=5540.1MB, alloc=804.3MB, time=132.06 memory used=5986.8MB, alloc=828.3MB, time=143.61 memory used=6447.1MB, alloc=852.3MB, time=156.55 memory used=6911.4MB, alloc=876.3MB, time=169.68 memory used=7415.4MB, alloc=900.3MB, time=183.87 memory used=7877.8MB, alloc=924.3MB, time=197.60 memory used=8336.3MB, alloc=948.3MB, time=211.90 memory used=8774.9MB, alloc=972.3MB, time=226.33 memory used=9164.8MB, alloc=996.3MB, time=238.39 memory used=9517.0MB, alloc=1020.3MB, time=250.61 memory used=9911.7MB, alloc=1044.3MB, time=264.41 memory used=10553.2MB, alloc=1068.3MB, time=285.61 memory used=11213.7MB, alloc=1092.3MB, time=308.64 memory used=11889.0MB, alloc=1116.3MB, time=332.96 memory used=12580.5MB, alloc=1140.3MB, time=356.24 memory used=13292.4MB, alloc=1164.3MB, time=382.20 memory used=14023.5MB, alloc=1188.3MB, time=408.97 memory used=14769.6MB, alloc=1212.3MB, time=436.07 memory used=15534.3MB, alloc=1236.3MB, time=465.50 memory used=16306.5MB, alloc=1260.3MB, time=494.23 memory used=17091.0MB, alloc=1284.3MB, time=525.21 memory used=17882.6MB, alloc=1308.3MB, time=555.78 memory used=18711.7MB, alloc=1332.3MB, time=590.37 memory used=19556.1MB, alloc=1356.3MB, time=624.56 memory used=20410.9MB, alloc=1380.3MB, time=659.75 memory used=21204.6MB, alloc=1404.3MB, time=692.34 memory used=21929.3MB, alloc=1428.3MB, time=722.98 memory used=22498.6MB, alloc=1452.3MB, time=746.86 memory used=23194.5MB, alloc=1476.3MB, time=779.12 memory used=23814.4MB, alloc=1500.3MB, time=805.12 memory used=24422.5MB, alloc=1524.3MB, time=832.04 memory used=24959.2MB, alloc=1548.3MB, time=856.48 memory used=25375.2MB, alloc=1572.3MB, time=875.96 memory used=25797.1MB, alloc=1596.3MB, time=897.06 memory used=26123.3MB, alloc=1620.3MB, time=913.86 memory used=26516.8MB, alloc=1644.3MB, time=933.20 memory used=26790.4MB, alloc=1668.3MB, time=948.25 memory used=27052.4MB, alloc=1692.3MB, time=962.60 memory used=27336.0MB, alloc=1716.3MB, time=978.07 memory used=27560.3MB, alloc=1740.3MB, time=991.02 memory used=27823.6MB, alloc=1764.3MB, time=1006.35 memory used=28082.7MB, alloc=1788.3MB, time=1021.03 memory used=28315.2MB, alloc=1812.3MB, time=1035.38 memory used=28542.0MB, alloc=1836.3MB, time=1049.81 memory used=28677.9MB, alloc=1860.3MB, time=1060.40 memory used=28869.5MB, alloc=1884.3MB, time=1073.26 |\^/| 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(); 1428470544 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [17 y z - 11 z - 14 x, 9 - 11 x + 10 y, 9 x - 2 x y - 12 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [15 x z + 2 y z - 7 x, -7 x y - 3 x z - 20 y z, 6 x y - z + 7 x] > Problem := [F,G]; 2 2 Problem := [[17 y z - 11 z - 14 x, 9 - 11 x + 10 y, 9 x - 2 x y - 12 y], 2 [15 x z + 2 y z - 7 x, -7 x y - 3 x z - 20 y z, 6 x y - z + 7 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=47.0MB, alloc=32.3MB, time=0.80 memory used=66.4MB, alloc=56.3MB, time=1.10 memory used=106.6MB, alloc=60.3MB, time=1.69 memory used=144.7MB, alloc=84.3MB, time=2.27 memory used=205.6MB, alloc=92.3MB, time=3.20 memory used=266.0MB, alloc=116.3MB, time=4.09 memory used=348.7MB, alloc=116.3MB, time=5.35 memory used=423.1MB, alloc=396.3MB, time=6.53 memory used=526.4MB, alloc=420.3MB, time=8.18 memory used=653.6MB, alloc=444.3MB, time=10.27 memory used=805.6MB, alloc=468.3MB, time=12.74 memory used=951.9MB, alloc=468.3MB, time=14.98 memory used=1100.5MB, alloc=492.3MB, time=17.64 memory used=1231.3MB, alloc=516.3MB, time=19.73 memory used=1385.5MB, alloc=516.3MB, time=22.63 memory used=1526.9MB, alloc=540.3MB, time=25.35 memory used=1656.7MB, alloc=540.3MB, time=27.84 memory used=1781.3MB, alloc=540.3MB, time=30.37 memory used=1888.0MB, alloc=540.3MB, time=32.72 memory used=1984.0MB, alloc=540.3MB, time=34.89 memory used=2076.8MB, alloc=564.3MB, time=36.89 memory used=2157.0MB, alloc=564.3MB, time=38.60 memory used=2231.7MB, alloc=564.3MB, time=40.29 memory used=2318.8MB, alloc=564.3MB, time=42.41 memory used=2407.7MB, alloc=564.3MB, time=44.18 memory used=2489.6MB, alloc=564.3MB, time=46.09 memory used=2573.6MB, alloc=588.3MB, time=48.37 memory used=2641.5MB, alloc=588.3MB, time=50.09 memory used=2690.0MB, alloc=588.3MB, time=51.42 memory used=2942.8MB, alloc=612.3MB, time=56.57 memory used=3195.3MB, alloc=636.3MB, time=61.42 memory used=3432.1MB, alloc=660.3MB, time=66.33 memory used=3680.9MB, alloc=684.3MB, time=71.27 memory used=3919.1MB, alloc=708.3MB, time=76.10 memory used=4166.8MB, alloc=732.3MB, time=81.08 memory used=4411.6MB, alloc=756.3MB, time=86.07 memory used=4654.7MB, alloc=780.3MB, time=91.10 memory used=4922.4MB, alloc=804.3MB, time=96.24 memory used=5171.9MB, alloc=828.3MB, time=100.90 memory used=5403.6MB, alloc=852.3MB, time=105.52 memory used=5630.6MB, alloc=876.3MB, time=110.24 memory used=5847.4MB, alloc=900.3MB, time=114.99 memory used=6069.6MB, alloc=924.3MB, time=119.85 memory used=6462.8MB, alloc=948.3MB, time=128.15 memory used=6847.3MB, alloc=972.3MB, time=136.17 memory used=7234.3MB, alloc=996.3MB, time=144.49 memory used=7604.1MB, alloc=1020.3MB, time=154.94 memory used=7916.1MB, alloc=1044.3MB, time=167.64 memory used=8231.2MB, alloc=1068.3MB, time=181.14 memory used=8555.0MB, alloc=1092.3MB, time=195.09 memory used=8890.0MB, alloc=1116.3MB, time=209.44 memory used=9238.1MB, alloc=1140.3MB, time=224.68 memory used=9600.4MB, alloc=1164.3MB, time=240.66 memory used=9977.3MB, alloc=1188.3MB, time=257.44 memory used=10368.7MB, alloc=1212.3MB, time=275.11 memory used=10774.9MB, alloc=1236.3MB, time=293.91 memory used=11195.7MB, alloc=1260.3MB, time=312.76 memory used=11631.4MB, alloc=1284.3MB, time=332.31 memory used=12082.5MB, alloc=1308.3MB, time=352.61 memory used=12549.3MB, alloc=1332.3MB, time=373.54 memory used=13032.1MB, alloc=1356.3MB, time=395.06 memory used=13531.2MB, alloc=1380.3MB, time=417.67 memory used=14046.6MB, alloc=1404.3MB, time=441.33 memory used=14577.9MB, alloc=1428.3MB, time=465.71 memory used=15126.1MB, alloc=1452.3MB, time=491.12 memory used=15691.7MB, alloc=1476.3MB, time=517.20 memory used=16274.5MB, alloc=1500.3MB, time=544.36 memory used=16874.5MB, alloc=1524.3MB, time=572.53 memory used=17485.7MB, alloc=1548.3MB, time=601.16 memory used=18117.2MB, alloc=1572.3MB, time=631.20 memory used=18772.6MB, alloc=1596.3MB, time=662.28 memory used=19452.0MB, alloc=1620.3MB, time=694.66 memory used=20155.4MB, alloc=1644.3MB, time=728.14 memory used=20882.6MB, alloc=1668.3MB, time=762.15 memory used=21633.8MB, alloc=1692.3MB, time=797.15 memory used=22409.0MB, alloc=1716.3MB, time=833.10 memory used=23208.1MB, alloc=1740.3MB, time=870.17 memory used=24031.1MB, alloc=1764.3MB, time=908.34 memory used=24878.1MB, alloc=1788.3MB, time=947.39 memory used=25749.0MB, alloc=1812.3MB, time=987.51 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428471744 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-16 x + 18 x y, 17 x + 17 z , -19 x + 6 x y - 5] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-5 x - 10 x z - 3 y z, 2 y + 5 z - 5 y, 4 y z - 12 z + 15 x] > Problem := [F,G]; 2 2 2 2 Problem := [[-16 x + 18 x y, 17 x + 17 z , -19 x + 6 x y - 5], 2 2 2 2 [-5 x - 10 x z - 3 y z, 2 y + 5 z - 5 y, 4 y z - 12 z + 15 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.49 memory used=48.2MB, alloc=32.3MB, time=0.79 memory used=69.3MB, alloc=56.3MB, time=1.09 memory used=111.4MB, alloc=60.3MB, time=1.70 memory used=151.4MB, alloc=84.3MB, time=2.28 memory used=215.0MB, alloc=92.3MB, time=3.21 memory used=273.6MB, alloc=116.3MB, time=4.15 memory used=334.6MB, alloc=116.3MB, time=5.02 memory used=412.9MB, alloc=140.3MB, time=6.26 memory used=484.7MB, alloc=140.3MB, time=7.35 memory used=562.7MB, alloc=396.3MB, time=8.65 memory used=668.7MB, alloc=420.3MB, time=10.34 memory used=795.6MB, alloc=444.3MB, time=12.39 memory used=944.2MB, alloc=468.3MB, time=14.81 memory used=1097.8MB, alloc=492.3MB, time=17.45 memory used=1230.4MB, alloc=516.3MB, time=19.84 memory used=1354.7MB, alloc=516.3MB, time=22.15 memory used=1464.6MB, alloc=516.3MB, time=24.16 memory used=1551.4MB, alloc=516.3MB, time=25.76 memory used=1657.3MB, alloc=516.3MB, time=27.88 memory used=1767.7MB, alloc=540.3MB, time=30.06 memory used=1862.4MB, alloc=540.3MB, time=32.05 memory used=1941.4MB, alloc=540.3MB, time=33.64 memory used=2008.8MB, alloc=540.3MB, time=35.09 memory used=2079.1MB, alloc=540.3MB, time=36.49 memory used=2165.9MB, alloc=564.3MB, time=38.39 memory used=2258.3MB, alloc=564.3MB, time=40.42 memory used=2341.3MB, alloc=588.3MB, time=42.24 memory used=2445.4MB, alloc=588.3MB, time=44.38 memory used=2540.6MB, alloc=612.3MB, time=46.38 memory used=2618.9MB, alloc=612.3MB, time=48.14 memory used=2706.9MB, alloc=612.3MB, time=50.16 memory used=2941.0MB, alloc=636.3MB, time=55.49 memory used=3158.2MB, alloc=660.3MB, time=62.98 memory used=3381.6MB, alloc=684.3MB, time=71.33 memory used=3608.2MB, alloc=708.3MB, time=80.75 memory used=3858.8MB, alloc=732.3MB, time=91.14 memory used=4133.2MB, alloc=756.3MB, time=102.46 memory used=4431.6MB, alloc=780.3MB, time=114.70 memory used=4754.1MB, alloc=804.3MB, time=127.92 memory used=5100.6MB, alloc=828.3MB, time=141.95 N1 := 8569 > GB := Basis(F, plex(op(vars))); 2 2 GB := [41 x + 15, 9 y - 8 x, 41 z - 15] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5498.8MB, alloc=828.3MB, time=153.40 memory used=5757.3MB, alloc=828.3MB, time=158.34 memory used=5978.7MB, alloc=828.3MB, time=162.71 memory used=6216.2MB, alloc=828.3MB, time=167.44 memory used=6426.8MB, alloc=828.3MB, time=171.84 memory used=6616.4MB, alloc=852.3MB, time=175.92 memory used=6823.4MB, alloc=876.3MB, time=180.38 memory used=7062.2MB, alloc=900.3MB, time=185.47 memory used=7320.2MB, alloc=924.3MB, time=191.12 memory used=7546.9MB, alloc=948.3MB, time=196.14 memory used=7787.0MB, alloc=972.3MB, time=201.55 memory used=8001.2MB, alloc=996.3MB, time=206.38 memory used=8201.9MB, alloc=1020.3MB, time=210.99 memory used=8720.3MB, alloc=1044.3MB, time=221.80 memory used=9214.3MB, alloc=1068.3MB, time=232.20 memory used=9673.8MB, alloc=1092.3MB, time=247.18 memory used=10073.0MB, alloc=1116.3MB, time=263.68 memory used=10475.1MB, alloc=1140.3MB, time=280.43 memory used=10883.9MB, alloc=1164.3MB, time=297.73 memory used=11303.0MB, alloc=1188.3MB, time=315.54 memory used=11730.4MB, alloc=1212.3MB, time=333.96 memory used=12168.0MB, alloc=1236.3MB, time=353.11 memory used=12617.1MB, alloc=1260.3MB, time=372.71 memory used=13077.9MB, alloc=1284.3MB, time=392.64 memory used=13551.3MB, alloc=1308.3MB, time=412.94 memory used=14038.2MB, alloc=1332.3MB, time=433.84 memory used=14538.9MB, alloc=1356.3MB, time=455.80 memory used=15054.4MB, alloc=1380.3MB, time=478.62 memory used=15580.4MB, alloc=1404.3MB, time=502.93 memory used=16123.2MB, alloc=1428.3MB, time=528.40 memory used=16690.0MB, alloc=1452.3MB, time=554.78 memory used=17280.7MB, alloc=1476.3MB, time=582.17 memory used=17895.4MB, alloc=1500.3MB, time=610.63 memory used=18534.0MB, alloc=1524.3MB, time=639.60 memory used=19196.5MB, alloc=1548.3MB, time=669.68 memory used=19883.0MB, alloc=1572.3MB, time=700.68 memory used=20593.4MB, alloc=1596.3MB, time=732.90 memory used=21327.7MB, alloc=1620.3MB, time=765.99 memory used=22086.0MB, alloc=1644.3MB, time=800.04 memory used=22868.2MB, alloc=1668.3MB, time=835.57 memory used=23674.4MB, alloc=1692.3MB, time=872.38 |\^/| 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(); 1428472944 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [5 y z - 17 y + 12, -6 x + 19 x y + 8 z , 2 y - 12 z - 2 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [6 x - 12 x z - 3 y, 4 x z - 20 y z - 8 z , 3 x - 18 x - 18 y] > Problem := [F,G]; 2 2 2 2 Problem := [[5 y z - 17 y + 12, -6 x + 19 x y + 8 z , 2 y - 12 z - 2 y], 2 2 2 [6 x - 12 x z - 3 y, 4 x z - 20 y z - 8 z , 3 x - 18 x - 18 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=47.9MB, alloc=32.3MB, time=0.78 memory used=67.4MB, alloc=56.3MB, time=1.08 memory used=106.4MB, alloc=60.3MB, time=1.65 memory used=142.3MB, alloc=84.3MB, time=2.19 memory used=201.6MB, alloc=92.3MB, time=3.10 memory used=260.1MB, alloc=116.3MB, time=4.02 memory used=340.9MB, alloc=116.3MB, time=5.28 memory used=418.8MB, alloc=140.3MB, time=6.52 memory used=514.6MB, alloc=140.3MB, time=8.08 memory used=601.2MB, alloc=420.3MB, time=9.62 memory used=723.1MB, alloc=444.3MB, time=11.75 memory used=863.7MB, alloc=468.3MB, time=14.17 memory used=1023.3MB, alloc=492.3MB, time=17.00 memory used=1180.1MB, alloc=516.3MB, time=19.77 memory used=1330.4MB, alloc=516.3MB, time=22.75 memory used=1471.2MB, alloc=540.3MB, time=25.51 memory used=1612.9MB, alloc=540.3MB, time=28.34 memory used=1727.5MB, alloc=540.3MB, time=30.62 memory used=1857.3MB, alloc=564.3MB, time=33.60 memory used=1938.1MB, alloc=564.3MB, time=35.31 memory used=2044.1MB, alloc=564.3MB, time=37.87 memory used=2134.9MB, alloc=564.3MB, time=39.94 memory used=2231.2MB, alloc=564.3MB, time=42.14 memory used=2308.3MB, alloc=564.3MB, time=44.07 memory used=2390.5MB, alloc=564.3MB, time=46.10 memory used=2448.9MB, alloc=564.3MB, time=47.37 memory used=2524.8MB, alloc=564.3MB, time=49.40 memory used=2765.0MB, alloc=588.3MB, time=54.86 memory used=3032.8MB, alloc=612.3MB, time=60.79 memory used=3231.4MB, alloc=636.3MB, time=65.41 memory used=3474.1MB, alloc=660.3MB, time=71.39 memory used=3712.7MB, alloc=684.3MB, time=77.39 memory used=3916.8MB, alloc=708.3MB, time=82.79 memory used=4083.7MB, alloc=732.3MB, time=86.90 memory used=4297.1MB, alloc=732.3MB, time=93.27 memory used=4433.1MB, alloc=756.3MB, time=97.33 memory used=4601.9MB, alloc=756.3MB, time=102.45 memory used=4731.1MB, alloc=756.3MB, time=106.29 memory used=4863.3MB, alloc=756.3MB, time=110.35 memory used=5256.8MB, alloc=780.3MB, time=120.36 memory used=5666.6MB, alloc=804.3MB, time=132.90 memory used=6095.9MB, alloc=828.3MB, time=144.43 memory used=6540.6MB, alloc=852.3MB, time=156.20 memory used=6930.6MB, alloc=876.3MB, time=165.24 memory used=7315.9MB, alloc=900.3MB, time=173.22 memory used=7671.1MB, alloc=924.3MB, time=180.88 memory used=8087.0MB, alloc=948.3MB, time=189.83 memory used=8504.8MB, alloc=972.3MB, time=198.79 memory used=8903.4MB, alloc=996.3MB, time=207.56 memory used=9277.3MB, alloc=1020.3MB, time=216.31 memory used=9654.6MB, alloc=1044.3MB, time=224.95 memory used=10011.5MB, alloc=1068.3MB, time=233.68 memory used=10352.5MB, alloc=1092.3MB, time=241.95 memory used=10684.7MB, alloc=1116.3MB, time=250.15 memory used=11051.2MB, alloc=1140.3MB, time=258.36 memory used=11417.0MB, alloc=1164.3MB, time=266.72 memory used=11777.1MB, alloc=1188.3MB, time=275.14 memory used=12111.6MB, alloc=1212.3MB, time=283.46 memory used=12459.6MB, alloc=1236.3MB, time=291.90 memory used=12784.3MB, alloc=1260.3MB, time=300.40 memory used=13119.4MB, alloc=1284.3MB, time=309.41 memory used=13497.8MB, alloc=1308.3MB, time=317.83 memory used=13854.2MB, alloc=1332.3MB, time=326.73 memory used=14193.2MB, alloc=1356.3MB, time=335.64 memory used=14511.0MB, alloc=1380.3MB, time=344.36 memory used=14853.3MB, alloc=1404.3MB, time=353.16 memory used=15213.4MB, alloc=1428.3MB, time=362.29 memory used=15555.8MB, alloc=1452.3MB, time=371.34 memory used=15877.0MB, alloc=1476.3MB, time=380.33 memory used=16200.4MB, alloc=1500.3MB, time=389.41 memory used=16517.0MB, alloc=1524.3MB, time=398.58 memory used=16834.0MB, alloc=1548.3MB, time=407.71 memory used=17150.5MB, alloc=1572.3MB, time=417.64 memory used=17463.7MB, alloc=1596.3MB, time=427.32 memory used=17815.3MB, alloc=1620.3MB, time=436.65 memory used=18127.8MB, alloc=1644.3MB, time=445.92 memory used=18436.8MB, alloc=1668.3MB, time=455.16 memory used=18742.7MB, alloc=1692.3MB, time=464.57 memory used=19048.1MB, alloc=1716.3MB, time=473.91 memory used=19377.5MB, alloc=1740.3MB, time=483.55 memory used=19705.6MB, alloc=1764.3MB, time=493.32 memory used=19969.1MB, alloc=1788.3MB, time=503.93 memory used=20201.3MB, alloc=1812.3MB, time=515.68 memory used=20426.7MB, alloc=1836.3MB, time=528.18 memory used=20664.4MB, alloc=1860.3MB, time=541.50 memory used=20915.1MB, alloc=1884.3MB, time=555.60 memory used=21179.5MB, alloc=1908.3MB, time=570.36 memory used=21458.2MB, alloc=1932.3MB, time=585.84 memory used=21751.1MB, alloc=1956.3MB, time=602.04 memory used=22058.5MB, alloc=1980.3MB, time=618.72 memory used=22380.3MB, alloc=2004.3MB, time=636.04 memory used=22716.9MB, alloc=2028.3MB, time=654.18 memory used=23068.7MB, alloc=2052.3MB, time=673.06 memory used=23435.8MB, alloc=2076.3MB, time=692.68 memory used=23818.1MB, alloc=2100.3MB, time=713.18 memory used=24216.0MB, alloc=2124.3MB, time=734.56 memory used=24629.2MB, alloc=2148.3MB, time=756.71 memory used=25058.1MB, alloc=2172.3MB, time=780.06 memory used=25502.0MB, alloc=2196.3MB, time=804.18 memory used=25961.4MB, alloc=2220.3MB, time=829.25 memory used=26436.3MB, alloc=2244.3MB, time=855.09 memory used=26926.8MB, alloc=2268.3MB, time=881.66 memory used=27433.0MB, alloc=2292.3MB, time=908.98 memory used=27954.8MB, alloc=2316.3MB, time=937.20 memory used=28492.3MB, alloc=2340.3MB, time=966.19 memory used=29045.1MB, alloc=2364.3MB, time=995.55 memory used=29613.3MB, alloc=2388.3MB, time=1025.61 |\^/| 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(); 1428474144 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-13 x y - 4 z - 4, -13 x - 17 x y + 19 y, 6 + 2 x - 17 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-13 + 16 y + 14 z, -19 x - 18 y - 12 z, 1 - 17 x - 15 z] > Problem := [F,G]; 2 2 Problem := [[-13 x y - 4 z - 4, -13 x - 17 x y + 19 y, 6 + 2 x - 17 z], 2 2 [-13 + 16 y + 14 z, -19 x - 18 y - 12 z, 1 - 17 x - 15 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=46.3MB, alloc=56.3MB, time=0.79 memory used=87.7MB, alloc=60.3MB, time=1.40 memory used=126.4MB, alloc=84.3MB, time=2.00 memory used=167.9MB, alloc=84.3MB, time=2.62 memory used=229.4MB, alloc=116.3MB, time=3.55 memory used=309.9MB, alloc=396.3MB, time=4.76 memory used=418.2MB, alloc=420.3MB, time=6.52 memory used=547.5MB, alloc=444.3MB, time=8.69 memory used=701.1MB, alloc=468.3MB, time=11.28 memory used=849.8MB, alloc=492.3MB, time=13.84 memory used=985.1MB, alloc=492.3MB, time=16.24 memory used=1125.3MB, alloc=516.3MB, time=18.77 memory used=1245.2MB, alloc=516.3MB, time=20.97 memory used=1352.1MB, alloc=516.3MB, time=23.01 memory used=1448.9MB, alloc=540.3MB, time=24.88 memory used=1542.0MB, alloc=540.3MB, time=26.71 memory used=1621.0MB, alloc=540.3MB, time=28.31 memory used=1695.9MB, alloc=540.3MB, time=29.94 memory used=1761.7MB, alloc=564.3MB, time=31.35 memory used=1856.3MB, alloc=564.3MB, time=33.45 memory used=1925.8MB, alloc=588.3MB, time=35.03 memory used=2033.3MB, alloc=588.3MB, time=37.33 memory used=2129.5MB, alloc=612.3MB, time=39.35 memory used=2240.6MB, alloc=636.3MB, time=41.73 memory used=2331.7MB, alloc=660.3MB, time=44.00 memory used=2581.2MB, alloc=684.3MB, time=52.27 memory used=2823.5MB, alloc=708.3MB, time=61.47 memory used=3071.1MB, alloc=732.3MB, time=71.80 memory used=3342.6MB, alloc=756.3MB, time=83.02 memory used=3638.1MB, alloc=780.3MB, time=95.23 memory used=3957.5MB, alloc=780.3MB, time=108.42 memory used=4277.0MB, alloc=804.3MB, time=121.58 memory used=4620.3MB, alloc=828.3MB, time=135.79 memory used=4987.8MB, alloc=828.3MB, time=150.94 N1 := 9725 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [48569 x - 1328 x - 20276 x + 24700, -2857 x + 96 x + 4199 y + 1300, 17 z - 6 - 2 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5377.0MB, alloc=828.3MB, time=163.55 N2 := 1297 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-13 x y - 4 z - 4, -13 x - 17 x y + 19 y, -17 z + 2 x + 6, 2 2 14 z + 16 y - 13, -19 x - 18 y - 12 z, 1 - 17 x - 15 z] > J:=[op(GB),op(G)]; 3 2 2 J := [48569 x - 1328 x - 20276 x + 24700, -2857 x + 96 x + 4199 y + 1300, 2 2 17 z - 6 - 2 x, 14 z + 16 y - 13, -19 x - 18 y - 12 z, 1 - 17 x - 15 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 9, 2, 2, 2, 2, 5/6, 2/3, 5/6, 1/3, 5/18, 5/18, 6, 12, 10, 3, 3, 2, 1, 5/6, 1/2, 2/3, 2/5, 3/20, 1/5, 2, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=5512.7MB, alloc=828.3MB, time=166.72 |\^/| 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(); 1428474346 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [16 x y + 9 y z + 12 x, 18 x - 19 x z + 8 y z, -5 x - 14 x y + 11 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [11 y - 20 z + 9, 9 y z + 10 z + z, 19 y - 19 y - 20] > Problem := [F,G]; Problem := [ 2 2 [16 x y + 9 y z + 12 x, 18 x - 19 x z + 8 y z, -5 x - 14 x y + 11 x], 2 2 2 2 [11 y - 20 z + 9, 9 y z + 10 z + z, 19 y - 19 y - 20]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=47.5MB, alloc=32.3MB, time=0.81 memory used=66.0MB, alloc=56.3MB, time=1.10 memory used=104.6MB, alloc=60.3MB, time=1.69 memory used=142.3MB, alloc=84.3MB, time=2.31 memory used=200.7MB, alloc=84.3MB, time=3.24 memory used=256.0MB, alloc=116.3MB, time=4.17 memory used=332.8MB, alloc=116.3MB, time=5.41 memory used=408.5MB, alloc=140.3MB, time=6.72 memory used=507.3MB, alloc=140.3MB, time=8.48 memory used=606.6MB, alloc=164.3MB, time=10.28 memory used=712.4MB, alloc=164.3MB, time=12.17 memory used=818.0MB, alloc=444.3MB, time=14.24 memory used=958.2MB, alloc=468.3MB, time=16.83 memory used=1119.2MB, alloc=468.3MB, time=20.07 memory used=1276.0MB, alloc=492.3MB, time=23.16 memory used=1453.0MB, alloc=516.3MB, time=26.79 memory used=1648.9MB, alloc=540.3MB, time=30.67 memory used=1873.4MB, alloc=564.3MB, time=34.72 memory used=2102.3MB, alloc=588.3MB, time=38.94 memory used=2318.8MB, alloc=612.3MB, time=43.06 memory used=2542.1MB, alloc=636.3MB, time=47.40 memory used=2767.8MB, alloc=660.3MB, time=51.74 memory used=2997.7MB, alloc=684.3MB, time=56.23 memory used=3231.4MB, alloc=708.3MB, time=60.90 memory used=3469.9MB, alloc=732.3MB, time=65.70 memory used=3718.2MB, alloc=756.3MB, time=70.57 memory used=3968.5MB, alloc=780.3MB, time=75.58 memory used=4215.3MB, alloc=804.3MB, time=80.72 memory used=4466.8MB, alloc=828.3MB, time=85.89 memory used=4720.9MB, alloc=852.3MB, time=91.32 memory used=4974.1MB, alloc=876.3MB, time=96.74 memory used=5228.3MB, alloc=900.3MB, time=102.15 memory used=5486.3MB, alloc=924.3MB, time=107.82 memory used=5745.7MB, alloc=948.3MB, time=113.56 memory used=6004.7MB, alloc=972.3MB, time=119.30 memory used=6265.0MB, alloc=996.3MB, time=125.15 memory used=6504.4MB, alloc=1020.3MB, time=132.40 memory used=6717.9MB, alloc=1044.3MB, time=140.87 memory used=6941.7MB, alloc=1068.3MB, time=150.23 memory used=7176.9MB, alloc=1092.3MB, time=160.37 memory used=7425.2MB, alloc=1116.3MB, time=171.09 memory used=7686.8MB, alloc=1140.3MB, time=182.47 memory used=7962.5MB, alloc=1164.3MB, time=194.65 memory used=8253.0MB, alloc=1188.3MB, time=207.49 memory used=8558.5MB, alloc=1212.3MB, time=221.16 memory used=8879.3MB, alloc=1236.3MB, time=235.37 memory used=9215.6MB, alloc=1260.3MB, time=250.58 memory used=9566.8MB, alloc=1284.3MB, time=266.14 memory used=9933.4MB, alloc=1308.3MB, time=282.61 memory used=10316.0MB, alloc=1332.3MB, time=299.66 memory used=10714.2MB, alloc=1356.3MB, time=317.32 memory used=11128.0MB, alloc=1380.3MB, time=335.83 memory used=11557.7MB, alloc=1404.3MB, time=355.16 memory used=12003.1MB, alloc=1428.3MB, time=376.20 memory used=12464.4MB, alloc=1452.3MB, time=397.47 memory used=12941.6MB, alloc=1476.3MB, time=419.51 memory used=13434.4MB, alloc=1500.3MB, time=442.45 memory used=13942.8MB, alloc=1524.3MB, time=466.04 memory used=14467.2MB, alloc=1548.3MB, time=490.57 memory used=15007.6MB, alloc=1572.3MB, time=515.49 memory used=15564.1MB, alloc=1596.3MB, time=541.15 memory used=16136.7MB, alloc=1620.3MB, time=567.82 memory used=16725.4MB, alloc=1644.3MB, time=595.48 memory used=17330.2MB, alloc=1668.3MB, time=624.31 memory used=17950.7MB, alloc=1692.3MB, time=653.25 memory used=18586.9MB, alloc=1716.3MB, time=682.37 memory used=19239.3MB, alloc=1740.3MB, time=713.24 memory used=19907.9MB, alloc=1764.3MB, time=745.37 memory used=20592.5MB, alloc=1788.3MB, time=777.04 memory used=21293.3MB, alloc=1812.3MB, time=810.46 memory used=22009.9MB, alloc=1836.3MB, time=845.06 memory used=22742.6MB, alloc=1860.3MB, time=879.98 memory used=23491.3MB, alloc=1884.3MB, time=914.30 memory used=24256.2MB, alloc=1908.3MB, time=949.47 memory used=25030.8MB, alloc=1932.3MB, time=987.39 |\^/| 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(); 1428475546 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [14 x z - 17 y z + 19 y, -17 + 12 x + 19 y, 17 x y + 16 x z + 11 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [x + 15 z - 2 x, 11 y - 2 y z + 10, -5 x - 18 x z - 8 y ] > Problem := [F,G]; Problem := [ [14 x z - 17 y z + 19 y, -17 + 12 x + 19 y, 17 x y + 16 x z + 11 y], 2 2 2 2 2 [x + 15 z - 2 x, 11 y - 2 y z + 10, -5 x - 18 x z - 8 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=32.3MB, time=0.83 memory used=66.9MB, alloc=56.3MB, time=1.15 memory used=107.6MB, alloc=60.3MB, time=1.75 memory used=147.7MB, alloc=84.3MB, time=2.36 memory used=210.8MB, alloc=92.3MB, time=3.29 memory used=273.0MB, alloc=116.3MB, time=4.27 memory used=352.6MB, alloc=116.3MB, time=5.45 memory used=428.3MB, alloc=396.3MB, time=6.71 memory used=534.1MB, alloc=420.3MB, time=8.45 memory used=665.5MB, alloc=444.3MB, time=10.64 memory used=787.9MB, alloc=444.3MB, time=12.53 memory used=931.9MB, alloc=468.3MB, time=14.83 memory used=1056.3MB, alloc=492.3MB, time=16.91 memory used=1170.5MB, alloc=492.3MB, time=18.83 memory used=1275.4MB, alloc=492.3MB, time=20.55 memory used=1376.6MB, alloc=492.3MB, time=22.16 memory used=1480.1MB, alloc=492.3MB, time=24.05 memory used=1579.6MB, alloc=492.3MB, time=25.84 memory used=1673.9MB, alloc=516.3MB, time=27.63 memory used=1750.5MB, alloc=516.3MB, time=29.14 memory used=1824.3MB, alloc=516.3MB, time=30.54 memory used=1904.5MB, alloc=516.3MB, time=32.21 memory used=1975.5MB, alloc=516.3MB, time=33.62 memory used=2039.1MB, alloc=516.3MB, time=34.94 memory used=2105.1MB, alloc=516.3MB, time=36.36 memory used=2168.3MB, alloc=516.3MB, time=37.84 memory used=2372.4MB, alloc=540.3MB, time=41.49 memory used=2589.7MB, alloc=564.3MB, time=45.10 memory used=2802.0MB, alloc=588.3MB, time=49.22 memory used=2965.4MB, alloc=612.3MB, time=52.31 memory used=3139.3MB, alloc=636.3MB, time=55.51 memory used=3301.8MB, alloc=660.3MB, time=58.86 memory used=3456.6MB, alloc=684.3MB, time=61.91 memory used=3575.0MB, alloc=684.3MB, time=64.41 memory used=3704.2MB, alloc=684.3MB, time=67.07 memory used=3815.3MB, alloc=684.3MB, time=69.41 memory used=3921.8MB, alloc=708.3MB, time=71.58 memory used=4039.4MB, alloc=708.3MB, time=74.60 memory used=4403.9MB, alloc=732.3MB, time=81.69 memory used=4733.4MB, alloc=756.3MB, time=88.77 memory used=5048.0MB, alloc=780.3MB, time=95.46 memory used=5375.4MB, alloc=804.3MB, time=102.35 memory used=5706.7MB, alloc=828.3MB, time=109.45 memory used=6040.3MB, alloc=852.3MB, time=116.58 memory used=6365.8MB, alloc=876.3MB, time=124.58 memory used=6648.9MB, alloc=900.3MB, time=136.21 memory used=6933.5MB, alloc=924.3MB, time=147.88 memory used=7222.5MB, alloc=948.3MB, time=160.15 memory used=7519.8MB, alloc=972.3MB, time=173.05 memory used=7827.1MB, alloc=996.3MB, time=186.79 memory used=8146.8MB, alloc=1020.3MB, time=201.41 memory used=8477.3MB, alloc=1044.3MB, time=216.73 memory used=8817.0MB, alloc=1068.3MB, time=233.09 memory used=9180.6MB, alloc=1092.3MB, time=250.28 memory used=9568.2MB, alloc=1116.3MB, time=268.63 memory used=9979.7MB, alloc=1140.3MB, time=287.91 memory used=10415.1MB, alloc=1164.3MB, time=308.28 memory used=10874.5MB, alloc=1188.3MB, time=329.63 memory used=11357.9MB, alloc=1212.3MB, time=352.26 memory used=11865.1MB, alloc=1236.3MB, time=375.61 memory used=12396.3MB, alloc=1260.3MB, time=400.12 memory used=12951.5MB, alloc=1284.3MB, time=425.73 memory used=13530.5MB, alloc=1308.3MB, time=452.35 memory used=14133.5MB, alloc=1332.3MB, time=479.98 memory used=14760.4MB, alloc=1356.3MB, time=508.77 memory used=15411.3MB, alloc=1380.3MB, time=538.85 memory used=16086.0MB, alloc=1404.3MB, time=569.87 memory used=16784.6MB, alloc=1428.3MB, time=601.91 memory used=17507.0MB, alloc=1452.3MB, time=634.82 memory used=18253.2MB, alloc=1476.3MB, time=668.37 memory used=19023.3MB, alloc=1500.3MB, time=702.78 memory used=19817.3MB, alloc=1500.3MB, time=738.28 memory used=20611.2MB, alloc=1524.3MB, time=773.56 memory used=21429.0MB, alloc=1548.3MB, time=809.87 memory used=22271.0MB, alloc=1548.3MB, time=847.23 memory used=23112.9MB, alloc=1572.3MB, time=884.50 |\^/| 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(); 1428476746 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-5 x - 13 y + 13 y z, -12 x y - 13 y z - 4 z, -20 y z - 19 y + 19] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-17 z + y - 3, 8 x y + 6 z - 4, -12 x z - 15 z + 2 x] > Problem := [F,G]; Problem := [ 2 2 [-5 x - 13 y + 13 y z, -12 x y - 13 y z - 4 z, -20 y z - 19 y + 19], 2 2 [-17 z + y - 3, 8 x y + 6 z - 4, -12 x z - 15 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=0.19 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=46.7MB, alloc=32.3MB, time=0.79 memory used=63.7MB, alloc=56.3MB, time=1.06 memory used=101.8MB, alloc=60.3MB, time=1.64 memory used=139.6MB, alloc=84.3MB, time=2.21 memory used=200.3MB, alloc=92.3MB, time=3.14 memory used=257.6MB, alloc=116.3MB, time=4.02 memory used=341.3MB, alloc=116.3MB, time=5.29 memory used=419.5MB, alloc=140.3MB, time=6.54 memory used=496.0MB, alloc=140.3MB, time=7.73 memory used=545.5MB, alloc=396.3MB, time=8.55 memory used=652.3MB, alloc=420.3MB, time=10.27 memory used=782.2MB, alloc=444.3MB, time=12.34 memory used=920.7MB, alloc=444.3MB, time=14.70 memory used=1066.8MB, alloc=468.3MB, time=17.44 memory used=1194.1MB, alloc=492.3MB, time=19.55 memory used=1320.7MB, alloc=492.3MB, time=21.82 memory used=1450.8MB, alloc=516.3MB, time=24.22 memory used=1557.4MB, alloc=516.3MB, time=26.11 memory used=1675.2MB, alloc=516.3MB, time=28.34 memory used=1763.8MB, alloc=516.3MB, time=30.03 memory used=1849.8MB, alloc=516.3MB, time=31.67 memory used=1965.3MB, alloc=540.3MB, time=34.03 memory used=2029.0MB, alloc=540.3MB, time=35.35 memory used=2111.5MB, alloc=540.3MB, time=36.85 memory used=2175.1MB, alloc=540.3MB, time=38.27 memory used=2241.9MB, alloc=540.3MB, time=39.74 memory used=2309.6MB, alloc=540.3MB, time=41.16 memory used=2370.5MB, alloc=540.3MB, time=42.49 memory used=2441.2MB, alloc=540.3MB, time=44.08 memory used=2492.4MB, alloc=540.3MB, time=45.27 memory used=2543.7MB, alloc=540.3MB, time=46.46 memory used=2595.2MB, alloc=540.3MB, time=47.64 memory used=2639.2MB, alloc=540.3MB, time=48.74 memory used=2857.5MB, alloc=564.3MB, time=52.98 memory used=3045.8MB, alloc=588.3MB, time=56.50 memory used=3260.1MB, alloc=612.3MB, time=60.73 memory used=3493.3MB, alloc=636.3MB, time=65.14 memory used=3715.5MB, alloc=660.3MB, time=69.67 memory used=3882.4MB, alloc=684.3MB, time=73.39 memory used=4045.0MB, alloc=708.3MB, time=77.13 memory used=4195.5MB, alloc=708.3MB, time=80.61 memory used=4369.4MB, alloc=708.3MB, time=84.61 memory used=4525.4MB, alloc=708.3MB, time=88.18 memory used=4638.8MB, alloc=732.3MB, time=90.91 memory used=4798.5MB, alloc=732.3MB, time=95.26 memory used=5019.7MB, alloc=732.3MB, time=101.55 memory used=5123.7MB, alloc=756.3MB, time=104.28 memory used=5330.0MB, alloc=756.3MB, time=110.83 memory used=5477.9MB, alloc=756.3MB, time=115.29 memory used=5557.9MB, alloc=756.3MB, time=117.66 memory used=5968.1MB, alloc=780.3MB, time=127.41 memory used=6392.9MB, alloc=804.3MB, time=137.40 memory used=6848.0MB, alloc=828.3MB, time=149.46 memory used=7240.6MB, alloc=852.3MB, time=159.71 memory used=7695.9MB, alloc=876.3MB, time=171.40 memory used=8066.6MB, alloc=900.3MB, time=181.23 memory used=8476.0MB, alloc=924.3MB, time=194.04 memory used=8801.6MB, alloc=948.3MB, time=201.69 memory used=9170.7MB, alloc=972.3MB, time=212.63 memory used=9544.4MB, alloc=996.3MB, time=223.55 memory used=9820.7MB, alloc=1020.3MB, time=230.91 memory used=10130.6MB, alloc=1044.3MB, time=240.05 memory used=10785.4MB, alloc=1068.3MB, time=258.20 memory used=11465.3MB, alloc=1092.3MB, time=279.28 memory used=12169.2MB, alloc=1116.3MB, time=299.44 memory used=12882.0MB, alloc=1140.3MB, time=319.49 memory used=13607.9MB, alloc=1164.3MB, time=340.94 memory used=14349.7MB, alloc=1188.3MB, time=366.04 memory used=15084.5MB, alloc=1212.3MB, time=389.92 memory used=15858.0MB, alloc=1236.3MB, time=416.94 memory used=16639.1MB, alloc=1260.3MB, time=444.80 memory used=17426.2MB, alloc=1284.3MB, time=472.54 memory used=18239.2MB, alloc=1308.3MB, time=500.18 memory used=19058.7MB, alloc=1332.3MB, time=528.41 memory used=19774.2MB, alloc=1356.3MB, time=551.19 memory used=20558.7MB, alloc=1380.3MB, time=579.07 memory used=21271.7MB, alloc=1404.3MB, time=604.20 memory used=21866.8MB, alloc=1428.3MB, time=626.13 memory used=22479.8MB, alloc=1452.3MB, time=647.08 memory used=23055.1MB, alloc=1476.3MB, time=667.36 memory used=23527.9MB, alloc=1500.3MB, time=684.17 memory used=24255.8MB, alloc=1524.3MB, time=709.85 memory used=24842.7MB, alloc=1548.3MB, time=731.26 memory used=25263.0MB, alloc=1572.3MB, time=746.19 memory used=25665.6MB, alloc=1596.3MB, time=760.78 memory used=25969.5MB, alloc=1620.3MB, time=773.32 memory used=26245.5MB, alloc=1644.3MB, time=785.04 memory used=26504.2MB, alloc=1668.3MB, time=795.99 memory used=26764.0MB, alloc=1692.3MB, time=807.74 memory used=27182.5MB, alloc=1716.3MB, time=819.59 memory used=27641.6MB, alloc=1740.3MB, time=834.62 memory used=28026.6MB, alloc=1764.3MB, time=848.51 memory used=28302.5MB, alloc=1788.3MB, time=860.69 memory used=28474.1MB, alloc=1812.3MB, time=870.26 memory used=28880.7MB, alloc=1836.3MB, time=884.61 memory used=29153.4MB, alloc=1860.3MB, time=896.79 memory used=29442.8MB, alloc=1884.3MB, time=908.90 memory used=29735.5MB, alloc=1908.3MB, time=921.45 memory used=29921.2MB, alloc=1932.3MB, time=931.80 memory used=30095.9MB, alloc=1956.3MB, time=942.17 memory used=30379.6MB, alloc=1980.3MB, time=954.05 memory used=30518.2MB, alloc=2004.3MB, time=962.83 memory used=30822.8MB, alloc=2028.3MB, time=975.96 memory used=30990.7MB, alloc=2052.3MB, time=985.77 memory used=31257.3MB, alloc=2076.3MB, time=997.98 memory used=31584.8MB, alloc=2100.3MB, time=1011.20 memory used=31731.6MB, alloc=2124.3MB, time=1021.29 memory used=31974.8MB, alloc=2148.3MB, time=1032.97 memory used=32262.4MB, alloc=2172.3MB, time=1046.14 |\^/| 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(); 1428477946 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-8 x y - 15 y - 9 x, -17 x z - 20 x + 6 z, -y - 2 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-17 z + x - 7, 2 x z - 12 y + 5 z , -18 - 13 y - 17 z] > Problem := [F,G]; 2 Problem := [[-8 x y - 15 y - 9 x, -17 x z - 20 x + 6 z, -y - 2 z], 2 2 2 [-17 z + x - 7, 2 x z - 12 y + 5 z , -18 - 13 y - 17 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.47 memory used=47.4MB, alloc=32.3MB, time=0.78 memory used=67.4MB, alloc=56.3MB, time=1.08 memory used=106.4MB, alloc=60.3MB, time=1.64 memory used=143.2MB, alloc=84.3MB, time=2.15 memory used=201.6MB, alloc=92.3MB, time=3.04 memory used=258.9MB, alloc=116.3MB, time=3.93 memory used=340.4MB, alloc=116.3MB, time=5.23 memory used=419.1MB, alloc=140.3MB, time=6.48 memory used=513.3MB, alloc=140.3MB, time=7.98 memory used=606.8MB, alloc=420.3MB, time=9.60 memory used=729.4MB, alloc=444.3MB, time=11.68 memory used=874.4MB, alloc=468.3MB, time=14.29 memory used=1040.5MB, alloc=492.3MB, time=17.36 memory used=1227.3MB, alloc=516.3MB, time=20.93 memory used=1413.8MB, alloc=540.3MB, time=24.58 memory used=1602.5MB, alloc=564.3MB, time=28.35 memory used=1753.2MB, alloc=588.3MB, time=31.29 memory used=1902.1MB, alloc=612.3MB, time=34.20 memory used=2075.0MB, alloc=636.3MB, time=37.50 memory used=2267.5MB, alloc=660.3MB, time=41.22 memory used=2440.0MB, alloc=684.3MB, time=44.60 memory used=2609.1MB, alloc=708.3MB, time=47.97 memory used=2775.5MB, alloc=732.3MB, time=51.24 memory used=2932.2MB, alloc=756.3MB, time=54.34 memory used=3093.1MB, alloc=780.3MB, time=57.53 memory used=3250.7MB, alloc=804.3MB, time=60.66 memory used=3382.1MB, alloc=828.3MB, time=63.40 memory used=3499.6MB, alloc=852.3MB, time=66.03 memory used=3662.6MB, alloc=876.3MB, time=71.39 memory used=3936.5MB, alloc=900.3MB, time=81.61 memory used=4294.5MB, alloc=924.3MB, time=95.23 memory used=4658.9MB, alloc=948.3MB, time=109.18 memory used=5027.9MB, alloc=972.3MB, time=123.67 memory used=5404.6MB, alloc=996.3MB, time=138.85 memory used=5791.2MB, alloc=1020.3MB, time=154.84 memory used=6181.1MB, alloc=1044.3MB, time=171.98 memory used=6589.6MB, alloc=1068.3MB, time=189.95 memory used=7022.0MB, alloc=1092.3MB, time=209.02 memory used=7478.5MB, alloc=1116.3MB, time=229.20 memory used=7958.8MB, alloc=1140.3MB, time=250.23 memory used=8463.1MB, alloc=1164.3MB, time=272.28 memory used=8991.3MB, alloc=1188.3MB, time=295.21 memory used=9543.5MB, alloc=1212.3MB, time=319.06 memory used=10119.5MB, alloc=1236.3MB, time=344.20 memory used=10719.5MB, alloc=1236.3MB, time=370.64 memory used=11319.5MB, alloc=1260.3MB, time=397.18 memory used=11943.4MB, alloc=1260.3MB, time=424.54 memory used=12567.2MB, alloc=1260.3MB, time=451.81 memory used=13190.9MB, alloc=1260.3MB, time=478.94 memory used=13814.8MB, alloc=1284.3MB, time=505.88 memory used=14462.5MB, alloc=1284.3MB, time=533.70 memory used=15110.1MB, alloc=1284.3MB, time=561.78 memory used=15757.7MB, alloc=1284.3MB, time=589.53 memory used=16405.3MB, alloc=1308.3MB, time=617.39 memory used=17076.9MB, alloc=1308.3MB, time=646.23 memory used=17748.4MB, alloc=1308.3MB, time=674.86 memory used=18419.8MB, alloc=1332.3MB, time=703.52 memory used=19115.2MB, alloc=1332.3MB, time=734.25 memory used=19810.5MB, alloc=1332.3MB, time=763.93 memory used=20505.7MB, alloc=1356.3MB, time=793.44 memory used=21224.9MB, alloc=1356.3MB, time=824.72 memory used=21944.0MB, alloc=1356.3MB, time=855.91 memory used=22663.3MB, alloc=1380.3MB, time=886.56 memory used=23406.4MB, alloc=1380.3MB, time=917.93 memory used=24149.5MB, alloc=1404.3MB, time=949.69 memory used=24916.5MB, alloc=1404.3MB, time=983.15 memory used=25683.4MB, alloc=1428.3MB, time=1016.14 |\^/| 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(); 1428479146 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [16 x - 4 y + 10, 15 x y + 15 x z + 2 y z, -16 x + 10 y - 13 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [x z + 15 z - 3 x, -x z - 14 y + 14 y, -16 x z + z - 20] > Problem := [F,G]; Problem := [ 2 2 2 2 [16 x - 4 y + 10, 15 x y + 15 x z + 2 y z, -16 x + 10 y - 13 y z], 2 2 2 [x z + 15 z - 3 x, -x z - 14 y + 14 y, -16 x z + z - 20]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=36.3MB, time=0.83 memory used=67.8MB, alloc=60.3MB, time=1.14 memory used=109.4MB, alloc=60.3MB, time=1.74 memory used=148.4MB, alloc=84.3MB, time=2.33 memory used=214.5MB, alloc=92.3MB, time=3.29 memory used=278.9MB, alloc=116.3MB, time=4.25 memory used=352.4MB, alloc=116.3MB, time=5.29 memory used=421.6MB, alloc=372.3MB, time=6.33 memory used=505.8MB, alloc=396.3MB, time=7.58 memory used=615.3MB, alloc=420.3MB, time=9.17 memory used=749.2MB, alloc=444.3MB, time=11.06 memory used=876.0MB, alloc=468.3MB, time=12.96 memory used=1012.7MB, alloc=468.3MB, time=15.08 memory used=1143.7MB, alloc=492.3MB, time=17.03 memory used=1252.9MB, alloc=492.3MB, time=18.76 memory used=1363.7MB, alloc=492.3MB, time=20.59 memory used=1467.5MB, alloc=516.3MB, time=22.04 memory used=1579.4MB, alloc=516.3MB, time=24.06 memory used=1657.9MB, alloc=516.3MB, time=25.23 memory used=1732.5MB, alloc=516.3MB, time=26.59 memory used=1809.0MB, alloc=516.3MB, time=27.94 memory used=1880.2MB, alloc=516.3MB, time=29.30 memory used=1939.6MB, alloc=516.3MB, time=30.51 memory used=2007.1MB, alloc=516.3MB, time=31.52 memory used=2071.2MB, alloc=516.3MB, time=32.82 memory used=2136.3MB, alloc=516.3MB, time=34.06 memory used=2187.9MB, alloc=516.3MB, time=35.14 memory used=2395.1MB, alloc=540.3MB, time=38.34 memory used=2608.8MB, alloc=564.3MB, time=41.53 memory used=2825.7MB, alloc=588.3MB, time=45.31 memory used=2994.4MB, alloc=612.3MB, time=47.96 memory used=3163.7MB, alloc=636.3MB, time=50.74 memory used=3329.7MB, alloc=636.3MB, time=53.71 memory used=3492.1MB, alloc=660.3MB, time=56.87 memory used=3641.2MB, alloc=660.3MB, time=59.90 memory used=3785.1MB, alloc=660.3MB, time=62.79 memory used=3925.5MB, alloc=684.3MB, time=65.31 memory used=4033.6MB, alloc=684.3MB, time=67.71 memory used=4127.4MB, alloc=684.3MB, time=69.79 memory used=4233.9MB, alloc=684.3MB, time=72.00 memory used=4333.0MB, alloc=684.3MB, time=74.27 memory used=4679.9MB, alloc=708.3MB, time=80.08 memory used=5047.0MB, alloc=732.3MB, time=85.36 memory used=5440.2MB, alloc=756.3MB, time=92.26 memory used=5836.8MB, alloc=780.3MB, time=99.46 memory used=6277.7MB, alloc=804.3MB, time=105.94 memory used=6692.3MB, alloc=828.3MB, time=113.56 memory used=7065.4MB, alloc=852.3MB, time=121.00 memory used=7410.6MB, alloc=876.3MB, time=128.54 memory used=7760.6MB, alloc=900.3MB, time=136.07 memory used=8136.2MB, alloc=924.3MB, time=143.68 memory used=8518.4MB, alloc=948.3MB, time=151.50 memory used=8886.4MB, alloc=972.3MB, time=159.63 memory used=9258.5MB, alloc=996.3MB, time=167.87 memory used=9656.0MB, alloc=1020.3MB, time=176.12 memory used=10135.0MB, alloc=1044.3MB, time=183.25 memory used=10624.2MB, alloc=1068.3MB, time=191.36 memory used=11141.3MB, alloc=1092.3MB, time=199.43 memory used=11679.2MB, alloc=1116.3MB, time=207.57 memory used=12213.8MB, alloc=1140.3MB, time=216.82 memory used=12753.5MB, alloc=1164.3MB, time=226.23 memory used=13309.7MB, alloc=1188.3MB, time=235.59 memory used=13876.6MB, alloc=1212.3MB, time=245.86 memory used=14419.1MB, alloc=1236.3MB, time=256.81 memory used=14953.1MB, alloc=1260.3MB, time=267.91 memory used=15464.8MB, alloc=1284.3MB, time=279.06 memory used=15996.5MB, alloc=1308.3MB, time=290.00 memory used=16513.0MB, alloc=1332.3MB, time=301.27 memory used=17038.3MB, alloc=1356.3MB, time=312.26 memory used=17555.2MB, alloc=1380.3MB, time=323.63 memory used=18024.0MB, alloc=1404.3MB, time=334.14 memory used=18511.4MB, alloc=1428.3MB, time=345.71 memory used=18989.9MB, alloc=1452.3MB, time=357.03 memory used=19473.2MB, alloc=1476.3MB, time=368.31 memory used=19962.4MB, alloc=1500.3MB, time=379.51 memory used=20445.2MB, alloc=1524.3MB, time=390.70 memory used=20893.1MB, alloc=1548.3MB, time=401.88 memory used=21331.8MB, alloc=1572.3MB, time=412.90 memory used=21799.8MB, alloc=1596.3MB, time=424.10 memory used=22288.3MB, alloc=1620.3MB, time=435.19 memory used=22648.3MB, alloc=1644.3MB, time=448.48 memory used=22947.6MB, alloc=1668.3MB, time=463.09 memory used=23256.2MB, alloc=1692.3MB, time=478.24 memory used=23577.7MB, alloc=1716.3MB, time=494.00 memory used=23913.2MB, alloc=1740.3MB, time=510.70 memory used=24263.7MB, alloc=1764.3MB, time=528.34 memory used=24629.4MB, alloc=1788.3MB, time=546.74 memory used=25010.3MB, alloc=1812.3MB, time=565.96 memory used=25407.1MB, alloc=1836.3MB, time=585.86 memory used=25819.0MB, alloc=1860.3MB, time=606.18 memory used=26247.0MB, alloc=1884.3MB, time=627.33 memory used=26690.8MB, alloc=1908.3MB, time=649.21 memory used=27150.5MB, alloc=1932.3MB, time=671.87 memory used=27626.4MB, alloc=1956.3MB, time=695.61 memory used=28118.5MB, alloc=1980.3MB, time=720.06 memory used=28629.3MB, alloc=2004.3MB, time=745.36 memory used=29153.5MB, alloc=2028.3MB, time=771.33 memory used=29690.8MB, alloc=2052.3MB, time=798.12 memory used=30241.7MB, alloc=2076.3MB, time=825.82 memory used=30806.7MB, alloc=2100.3MB, time=854.19 memory used=31385.7MB, alloc=2124.3MB, time=883.34 memory used=31979.1MB, alloc=2148.3MB, time=913.05 memory used=32586.6MB, alloc=2172.3MB, time=943.67 memory used=33208.6MB, alloc=2196.3MB, time=974.87 |\^/| 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(); 1428480346 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-18 x y + 2 y z + 9 z, 4 x - 15 y z - 11 x, -8 x - 10 x + 18 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [6 x + 2 y z + 12 x, -18 y + 4 y z + 6 y, -12 x y + 5 z + 12 z] > Problem := [F,G]; 2 2 Problem := [[-18 x y + 2 y z + 9 z, 4 x - 15 y z - 11 x, -8 x - 10 x + 18 z], 2 2 2 [6 x + 2 y z + 12 x, -18 y + 4 y z + 6 y, -12 x y + 5 z + 12 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.19 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=46.9MB, alloc=32.3MB, time=0.79 memory used=66.0MB, alloc=56.3MB, time=1.07 memory used=104.3MB, alloc=60.3MB, time=1.64 memory used=141.3MB, alloc=84.3MB, time=2.22 memory used=201.0MB, alloc=92.3MB, time=3.17 memory used=260.4MB, alloc=116.3MB, time=4.14 memory used=342.9MB, alloc=116.3MB, time=5.45 memory used=424.1MB, alloc=140.3MB, time=6.81 memory used=513.5MB, alloc=140.3MB, time=8.34 memory used=591.2MB, alloc=420.3MB, time=9.75 memory used=715.1MB, alloc=444.3MB, time=11.96 memory used=860.2MB, alloc=468.3MB, time=14.56 memory used=1016.6MB, alloc=492.3MB, time=17.56 memory used=1172.6MB, alloc=516.3MB, time=20.77 memory used=1312.9MB, alloc=516.3MB, time=23.58 memory used=1445.0MB, alloc=540.3MB, time=26.12 memory used=1563.7MB, alloc=540.3MB, time=28.64 memory used=1676.4MB, alloc=540.3MB, time=31.15 memory used=1786.3MB, alloc=540.3MB, time=33.59 memory used=1852.8MB, alloc=540.3MB, time=34.99 memory used=1936.8MB, alloc=540.3MB, time=36.80 memory used=2031.5MB, alloc=564.3MB, time=39.08 memory used=2110.3MB, alloc=564.3MB, time=40.98 memory used=2184.2MB, alloc=564.3MB, time=42.79 memory used=2255.3MB, alloc=564.3MB, time=44.66 memory used=2317.6MB, alloc=564.3MB, time=46.39 memory used=2564.5MB, alloc=588.3MB, time=51.71 memory used=2816.9MB, alloc=612.3MB, time=57.29 memory used=3047.2MB, alloc=636.3MB, time=63.01 memory used=3275.5MB, alloc=660.3MB, time=68.96 memory used=3486.4MB, alloc=684.3MB, time=74.12 memory used=3670.4MB, alloc=708.3MB, time=78.86 memory used=3843.1MB, alloc=708.3MB, time=83.25 memory used=4066.9MB, alloc=732.3MB, time=90.13 memory used=4213.8MB, alloc=732.3MB, time=93.85 memory used=4396.5MB, alloc=732.3MB, time=99.52 memory used=4546.5MB, alloc=732.3MB, time=103.79 memory used=4679.0MB, alloc=732.3MB, time=107.94 memory used=5072.0MB, alloc=756.3MB, time=119.30 memory used=5484.4MB, alloc=780.3MB, time=131.27 memory used=5916.5MB, alloc=804.3MB, time=144.41 memory used=6366.5MB, alloc=828.3MB, time=157.75 memory used=6788.4MB, alloc=852.3MB, time=170.56 memory used=7235.8MB, alloc=876.3MB, time=184.51 memory used=7652.8MB, alloc=900.3MB, time=197.94 memory used=8057.2MB, alloc=924.3MB, time=211.42 memory used=8397.3MB, alloc=948.3MB, time=221.71 memory used=8785.9MB, alloc=972.3MB, time=234.77 memory used=9115.4MB, alloc=996.3MB, time=245.94 memory used=9457.4MB, alloc=1020.3MB, time=258.15 memory used=9702.8MB, alloc=1044.3MB, time=266.90 memory used=10343.0MB, alloc=1068.3MB, time=287.11 memory used=10983.2MB, alloc=1092.3MB, time=308.59 memory used=11650.0MB, alloc=1116.3MB, time=330.96 memory used=12329.0MB, alloc=1140.3MB, time=351.03 memory used=12960.2MB, alloc=1164.3MB, time=366.95 memory used=13514.6MB, alloc=1188.3MB, time=380.52 memory used=14018.1MB, alloc=1212.3MB, time=393.59 memory used=14472.0MB, alloc=1236.3MB, time=406.14 memory used=14920.9MB, alloc=1260.3MB, time=418.29 memory used=15341.6MB, alloc=1284.3MB, time=430.27 memory used=15768.4MB, alloc=1308.3MB, time=442.09 memory used=16189.4MB, alloc=1332.3MB, time=453.85 memory used=16615.9MB, alloc=1356.3MB, time=465.78 memory used=17017.4MB, alloc=1380.3MB, time=477.34 memory used=17404.0MB, alloc=1404.3MB, time=488.85 memory used=17776.3MB, alloc=1428.3MB, time=500.16 memory used=18141.1MB, alloc=1452.3MB, time=511.69 memory used=18503.1MB, alloc=1476.3MB, time=522.99 memory used=18862.4MB, alloc=1500.3MB, time=534.35 memory used=19258.4MB, alloc=1524.3MB, time=546.37 memory used=19627.1MB, alloc=1548.3MB, time=557.99 memory used=19974.1MB, alloc=1572.3MB, time=569.22 memory used=20325.9MB, alloc=1596.3MB, time=580.41 memory used=20689.8MB, alloc=1620.3MB, time=592.06 memory used=21021.5MB, alloc=1644.3MB, time=603.25 memory used=21389.4MB, alloc=1668.3MB, time=615.08 memory used=21781.1MB, alloc=1692.3MB, time=627.05 memory used=22196.4MB, alloc=1716.3MB, time=639.21 memory used=22536.6MB, alloc=1740.3MB, time=654.71 memory used=22840.2MB, alloc=1764.3MB, time=671.29 memory used=23151.0MB, alloc=1788.3MB, time=688.47 memory used=23471.5MB, alloc=1812.3MB, time=706.41 memory used=23803.4MB, alloc=1836.3MB, time=725.14 memory used=24148.2MB, alloc=1860.3MB, time=744.68 memory used=24506.3MB, alloc=1884.3MB, time=765.04 memory used=24878.1MB, alloc=1908.3MB, time=785.79 memory used=25262.8MB, alloc=1932.3MB, time=807.07 memory used=25661.8MB, alloc=1956.3MB, time=829.06 memory used=26075.4MB, alloc=1980.3MB, time=851.73 memory used=26503.6MB, alloc=2004.3MB, time=875.07 memory used=26946.6MB, alloc=2028.3MB, time=899.64 memory used=27404.6MB, alloc=2052.3MB, time=925.23 memory used=27877.9MB, alloc=2076.3MB, time=951.37 memory used=28366.4MB, alloc=2100.3MB, time=978.50 memory used=28869.5MB, alloc=2124.3MB, time=1006.40 memory used=29388.0MB, alloc=2148.3MB, time=1035.01 memory used=29921.9MB, alloc=2172.3MB, time=1064.47 memory used=30471.2MB, alloc=2196.3MB, time=1094.75 memory used=31035.5MB, alloc=2220.3MB, time=1126.05 memory used=31615.6MB, alloc=2244.3MB, time=1158.36 |\^/| 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(); 1428481546 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-14 x + 6 x - 9 y, 11 y + 5 z + 5, 5 y z + z - 10 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [15 x y + 12 y + 6, -5 x y - 13 y + 11, -20 x + 20 y z + 8 z ] > Problem := [F,G]; 2 2 2 Problem := [[-14 x + 6 x - 9 y, 11 y + 5 z + 5, 5 y z + z - 10 y], 2 2 [15 x y + 12 y + 6, -5 x y - 13 y + 11, -20 x + 20 y z + 8 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.4MB, alloc=32.3MB, time=0.19 memory used=26.6MB, alloc=32.3MB, time=0.52 memory used=47.6MB, alloc=32.3MB, time=0.83 memory used=67.5MB, alloc=56.3MB, time=1.14 memory used=107.5MB, alloc=60.3MB, time=1.76 memory used=146.0MB, alloc=84.3MB, time=2.35 memory used=207.6MB, alloc=92.3MB, time=3.30 memory used=268.5MB, alloc=92.3MB, time=4.25 memory used=328.2MB, alloc=116.3MB, time=5.18 memory used=411.5MB, alloc=116.3MB, time=6.48 memory used=493.1MB, alloc=140.3MB, time=7.78 memory used=566.7MB, alloc=396.3MB, time=8.91 memory used=668.5MB, alloc=420.3MB, time=10.53 memory used=797.4MB, alloc=444.3MB, time=12.81 memory used=934.6MB, alloc=468.3MB, time=15.31 memory used=1082.5MB, alloc=492.3MB, time=18.04 memory used=1239.9MB, alloc=516.3MB, time=21.00 memory used=1408.0MB, alloc=540.3MB, time=24.21 memory used=1585.6MB, alloc=564.3MB, time=27.63 memory used=1769.2MB, alloc=588.3MB, time=31.24 memory used=1930.9MB, alloc=612.3MB, time=34.43 memory used=2118.0MB, alloc=636.3MB, time=39.96 memory used=2302.0MB, alloc=660.3MB, time=46.36 memory used=2496.7MB, alloc=684.3MB, time=53.44 memory used=2705.0MB, alloc=708.3MB, time=61.28 memory used=2928.5MB, alloc=732.3MB, time=69.95 memory used=3166.5MB, alloc=756.3MB, time=79.43 memory used=3420.0MB, alloc=780.3MB, time=89.61 memory used=3689.5MB, alloc=804.3MB, time=100.59 memory used=3973.2MB, alloc=828.3MB, time=112.55 memory used=4271.1MB, alloc=852.3MB, time=125.66 memory used=4593.0MB, alloc=876.3MB, time=139.90 memory used=4938.9MB, alloc=900.3MB, time=155.12 memory used=5308.7MB, alloc=924.3MB, time=171.26 memory used=5702.4MB, alloc=948.3MB, time=188.41 memory used=6120.1MB, alloc=972.3MB, time=206.46 memory used=6561.6MB, alloc=972.3MB, time=225.59 memory used=7003.2MB, alloc=996.3MB, time=244.66 memory used=7468.6MB, alloc=996.3MB, time=264.85 memory used=7934.1MB, alloc=996.3MB, time=285.16 memory used=8399.6MB, alloc=996.3MB, time=305.26 memory used=8865.0MB, alloc=1020.3MB, time=325.29 memory used=9354.4MB, alloc=1020.3MB, time=346.50 memory used=9843.5MB, alloc=1020.3MB, time=367.52 memory used=10332.6MB, alloc=1044.3MB, time=388.90 memory used=10845.5MB, alloc=1044.3MB, time=411.50 memory used=11358.3MB, alloc=1044.3MB, time=433.80 memory used=11871.0MB, alloc=1044.3MB, time=455.93 memory used=12383.5MB, alloc=1068.3MB, time=477.87 memory used=12920.0MB, alloc=1068.3MB, time=500.75 memory used=13456.5MB, alloc=1092.3MB, time=523.69 memory used=14016.9MB, alloc=1092.3MB, time=547.46 memory used=14577.2MB, alloc=1116.3MB, time=571.63 memory used=15161.7MB, alloc=1116.3MB, time=596.92 memory used=15746.0MB, alloc=1140.3MB, time=621.95 memory used=16354.4MB, alloc=1164.3MB, time=647.37 memory used=16987.3MB, alloc=1188.3MB, time=674.38 N1 := 22163 > GB := Basis(F, plex(op(vars))); 8 7 6 5 4 GB := [4648336 x - 7968576 x + 11914056 x - 10195416 x + 5645376 x 3 2 2 - 2031480 x + 4148010 x - 1640250 x + 164025, 14 x + 9 y - 6 x, 4 3 2 2156 x - 1848 x + 396 x + 405 z + 405] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 1397 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-14 x + 6 x - 9 y, 11 y + 5 z + 5, z + 5 z y - 10 y, 15 x y + 12 y + 6, 2 2 -5 x y - 13 y + 11, -20 x + 20 y z + 8 z ] > J:=[op(GB),op(G)]; 8 7 6 5 4 J := [4648336 x - 7968576 x + 11914056 x - 10195416 x + 5645376 x 3 2 2 - 2031480 x + 4148010 x - 1640250 x + 164025, 14 x + 9 y - 6 x, 4 3 2 2156 x - 1848 x + 396 x + 405 z + 405, 15 x y + 12 y + 6, 2 2 -5 x y - 13 y + 11, -20 x + 20 y z + 8 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 12, 2, 2, 2, 2, 2/3, 1, 1/2, 5/18, 1/2, 5/18, 6, 12, 20, 8, 8, 1, 2, 1, 2/3, 1/3, 8/13, 3/13, 3/26, 1, -8, -6] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=17263.1MB, alloc=1188.3MB, time=681.16 |\^/| 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(); 1428482311 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-16 y + 20 y z + 6, -3 x z - 10 y z + 10 z , -19 y + 5 z - 17 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-17 x + 10 z - 16 z, -16 + y - 17 z, x + x z - 6 z] > Problem := [F,G]; Problem := [ 2 2 2 2 [-16 y + 20 y z + 6, -3 x z - 10 y z + 10 z , -19 y + 5 z - 17 y], 2 2 2 [-17 x + 10 z - 16 z, -16 + y - 17 z, x + x z - 6 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.52 memory used=46.1MB, alloc=56.3MB, time=0.83 memory used=85.5MB, alloc=60.3MB, time=1.45 memory used=122.8MB, alloc=84.3MB, time=2.04 memory used=176.8MB, alloc=84.3MB, time=2.94 memory used=234.3MB, alloc=116.3MB, time=3.90 memory used=313.7MB, alloc=116.3MB, time=5.16 memory used=388.2MB, alloc=140.3MB, time=6.36 memory used=485.2MB, alloc=140.3MB, time=8.01 memory used=580.1MB, alloc=164.3MB, time=9.70 memory used=672.4MB, alloc=420.3MB, time=11.37 memory used=793.1MB, alloc=444.3MB, time=13.52 memory used=934.0MB, alloc=468.3MB, time=16.10 memory used=1100.0MB, alloc=492.3MB, time=19.21 memory used=1284.9MB, alloc=516.3MB, time=22.82 memory used=1490.7MB, alloc=540.3MB, time=27.50 memory used=1715.9MB, alloc=564.3MB, time=32.36 memory used=1963.3MB, alloc=588.3MB, time=37.74 memory used=2224.8MB, alloc=612.3MB, time=43.89 memory used=2508.5MB, alloc=636.3MB, time=50.77 memory used=2803.4MB, alloc=660.3MB, time=57.44 memory used=3118.2MB, alloc=684.3MB, time=65.78 memory used=3463.6MB, alloc=708.3MB, time=75.89 memory used=3801.1MB, alloc=732.3MB, time=84.87 memory used=4117.1MB, alloc=756.3MB, time=94.07 memory used=4436.3MB, alloc=780.3MB, time=102.89 memory used=4787.2MB, alloc=804.3MB, time=114.07 memory used=5086.0MB, alloc=828.3MB, time=122.94 memory used=5343.7MB, alloc=852.3MB, time=130.82 memory used=5611.4MB, alloc=876.3MB, time=138.85 memory used=5845.7MB, alloc=900.3MB, time=146.55 memory used=6078.9MB, alloc=900.3MB, time=154.06 memory used=6310.0MB, alloc=900.3MB, time=161.93 memory used=6526.2MB, alloc=900.3MB, time=169.53 memory used=6708.9MB, alloc=900.3MB, time=175.49 memory used=6944.4MB, alloc=900.3MB, time=184.32 memory used=7088.6MB, alloc=900.3MB, time=189.83 memory used=7243.7MB, alloc=900.3MB, time=195.27 memory used=7400.0MB, alloc=900.3MB, time=201.12 memory used=7933.6MB, alloc=924.3MB, time=219.30 memory used=8491.7MB, alloc=948.3MB, time=238.89 memory used=9071.0MB, alloc=972.3MB, time=258.77 memory used=9673.9MB, alloc=996.3MB, time=281.16 memory used=10280.7MB, alloc=1020.3MB, time=304.87 memory used=10896.2MB, alloc=1044.3MB, time=328.73 memory used=11533.7MB, alloc=1324.3MB, time=353.12 memory used=12195.8MB, alloc=1348.3MB, time=377.31 memory used=12863.3MB, alloc=1372.3MB, time=402.59 memory used=13552.9MB, alloc=1396.3MB, time=431.00 memory used=14255.9MB, alloc=1420.3MB, time=455.61 memory used=14979.6MB, alloc=1444.3MB, time=478.89 memory used=15713.9MB, alloc=1468.3MB, time=502.81 memory used=16358.2MB, alloc=1492.3MB, time=518.20 memory used=16958.2MB, alloc=1516.3MB, time=532.39 memory used=17529.2MB, alloc=1540.3MB, time=546.01 memory used=18012.7MB, alloc=1564.3MB, time=558.05 memory used=18463.5MB, alloc=1588.3MB, time=569.45 memory used=18873.6MB, alloc=1612.3MB, time=580.83 memory used=19268.4MB, alloc=1636.3MB, time=591.82 memory used=19637.7MB, alloc=1660.3MB, time=602.78 memory used=19982.1MB, alloc=1684.3MB, time=613.24 memory used=20313.0MB, alloc=1708.3MB, time=623.92 memory used=20638.2MB, alloc=1732.3MB, time=634.26 memory used=20953.6MB, alloc=1756.3MB, time=644.12 memory used=21261.4MB, alloc=1780.3MB, time=654.58 memory used=21559.5MB, alloc=1804.3MB, time=664.76 memory used=21851.9MB, alloc=1828.3MB, time=674.51 memory used=22142.6MB, alloc=1852.3MB, time=684.85 memory used=22428.3MB, alloc=1876.3MB, time=694.51 memory used=22709.6MB, alloc=1900.3MB, time=704.87 memory used=22991.0MB, alloc=1924.3MB, time=714.98 memory used=23268.7MB, alloc=1948.3MB, time=725.34 memory used=23565.9MB, alloc=1972.3MB, time=735.32 memory used=23842.6MB, alloc=1996.3MB, time=745.97 memory used=24117.1MB, alloc=2020.3MB, time=756.25 memory used=24393.8MB, alloc=2044.3MB, time=766.80 memory used=24701.7MB, alloc=2068.3MB, time=777.98 memory used=24998.5MB, alloc=2092.3MB, time=788.87 memory used=25302.9MB, alloc=2116.3MB, time=799.53 memory used=25581.4MB, alloc=2140.3MB, time=810.68 memory used=25860.3MB, alloc=2164.3MB, time=821.63 memory used=26136.5MB, alloc=2188.3MB, time=832.59 memory used=26413.4MB, alloc=2212.3MB, time=843.64 memory used=26689.2MB, alloc=2236.3MB, time=854.82 memory used=26985.3MB, alloc=2260.3MB, time=865.87 memory used=27262.1MB, alloc=2284.3MB, time=877.60 memory used=27536.8MB, alloc=2308.3MB, time=888.64 memory used=27813.5MB, alloc=2332.3MB, time=900.09 memory used=28105.0MB, alloc=2356.3MB, time=911.66 memory used=28376.3MB, alloc=2380.3MB, time=923.34 memory used=28670.8MB, alloc=2404.3MB, time=934.77 memory used=28956.2MB, alloc=2428.3MB, time=946.71 memory used=29224.9MB, alloc=2452.3MB, time=958.14 memory used=29500.7MB, alloc=2476.3MB, time=970.12 memory used=29775.8MB, alloc=2500.3MB, time=982.13 memory used=30068.2MB, alloc=2524.3MB, time=994.39 memory used=30357.2MB, alloc=2548.3MB, time=1006.46 memory used=30646.5MB, alloc=2572.3MB, time=1019.12 memory used=30941.1MB, alloc=2596.3MB, time=1031.40 memory used=31235.4MB, alloc=2620.3MB, time=1043.73 memory used=31516.6MB, alloc=2644.3MB, time=1056.24 memory used=31792.5MB, alloc=2668.3MB, time=1068.35 memory used=32091.4MB, alloc=2692.3MB, time=1081.33 memory used=32391.2MB, alloc=2716.3MB, time=1094.71 |\^/| 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(); 1428483511 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-3 x - 3 x z - 12 z , 11 y z + 13 x + 5 z, 5 x - 10 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-19 x z + 5 z , 6 x + 16 x z - 9 x, 7 x - 12 y - 13 z] > Problem := [F,G]; 2 2 2 2 Problem := [[-3 x - 3 x z - 12 z , 11 y z + 13 x + 5 z, 5 x - 10 y ], 2 2 2 [-19 x z + 5 z , 6 x + 16 x z - 9 x, 7 x - 12 y - 13 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=46.8MB, alloc=32.3MB, time=0.78 memory used=66.1MB, alloc=56.3MB, time=1.08 memory used=106.0MB, alloc=60.3MB, time=1.68 memory used=144.1MB, alloc=84.3MB, time=2.27 memory used=203.2MB, alloc=92.3MB, time=3.17 memory used=257.9MB, alloc=116.3MB, time=4.02 memory used=336.4MB, alloc=116.3MB, time=5.24 memory used=413.0MB, alloc=140.3MB, time=6.48 memory used=503.6MB, alloc=140.3MB, time=7.89 memory used=594.9MB, alloc=420.3MB, time=9.46 memory used=714.7MB, alloc=444.3MB, time=11.59 memory used=847.7MB, alloc=468.3MB, time=14.00 memory used=991.5MB, alloc=492.3MB, time=16.60 memory used=1149.5MB, alloc=516.3MB, time=19.46 memory used=1316.3MB, alloc=540.3MB, time=22.53 memory used=1491.6MB, alloc=564.3MB, time=25.86 memory used=1658.9MB, alloc=588.3MB, time=30.98 memory used=1831.0MB, alloc=612.3MB, time=36.82 memory used=2014.9MB, alloc=636.3MB, time=43.34 memory used=2212.7MB, alloc=660.3MB, time=50.56 memory used=2418.9MB, alloc=684.3MB, time=58.87 memory used=2646.6MB, alloc=708.3MB, time=68.16 memory used=2898.3MB, alloc=732.3MB, time=78.44 memory used=3173.8MB, alloc=756.3MB, time=89.60 memory used=3473.3MB, alloc=780.3MB, time=101.67 memory used=3796.8MB, alloc=804.3MB, time=114.77 memory used=4144.2MB, alloc=804.3MB, time=128.80 memory used=4491.6MB, alloc=804.3MB, time=142.73 memory used=4838.7MB, alloc=828.3MB, time=156.56 memory used=5209.8MB, alloc=828.3MB, time=171.36 memory used=5580.7MB, alloc=828.3MB, time=186.20 memory used=5951.5MB, alloc=852.3MB, time=201.12 memory used=6346.4MB, alloc=852.3MB, time=216.77 memory used=6741.1MB, alloc=876.3MB, time=232.83 memory used=7160.0MB, alloc=900.3MB, time=250.13 N1 := 13715 > GB := Basis(F, plex(op(vars))); 6 4 2 4 2 2 GB := [14641 x + 305646 x + 1617984 x , -121 x + 66 x y - 1272 x , 2 2 5 3 -x + 2 y , -14641 x - 148104 x - 89232 x y + 40560 x + 15600 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7391.8MB, alloc=900.3MB, time=257.12 memory used=7523.2MB, alloc=900.3MB, time=260.00 memory used=7652.1MB, alloc=900.3MB, time=262.83 memory used=7769.4MB, alloc=900.3MB, time=265.75 memory used=7958.3MB, alloc=900.3MB, time=270.00 memory used=8122.8MB, alloc=900.3MB, time=273.53 memory used=8280.7MB, alloc=900.3MB, time=277.36 memory used=8424.2MB, alloc=924.3MB, time=280.75 memory used=8573.3MB, alloc=948.3MB, time=284.30 memory used=8676.9MB, alloc=972.3MB, time=286.95 memory used=8884.9MB, alloc=996.3MB, time=294.22 memory used=9192.6MB, alloc=1020.3MB, time=306.21 memory used=9691.8MB, alloc=1044.3MB, time=326.24 memory used=10189.8MB, alloc=1068.3MB, time=347.13 memory used=10690.4MB, alloc=1092.3MB, time=369.06 memory used=11214.8MB, alloc=1116.3MB, time=392.10 memory used=11763.3MB, alloc=1140.3MB, time=416.05 memory used=12335.6MB, alloc=1164.3MB, time=440.96 memory used=12931.8MB, alloc=1188.3MB, time=466.98 memory used=13551.9MB, alloc=1212.3MB, time=494.39 memory used=14195.9MB, alloc=1212.3MB, time=523.88 memory used=14840.0MB, alloc=1236.3MB, time=552.88 memory used=15507.9MB, alloc=1236.3MB, time=582.99 memory used=16175.8MB, alloc=1260.3MB, time=611.83 memory used=16867.4MB, alloc=1260.3MB, time=641.15 memory used=17558.9MB, alloc=1284.3MB, time=670.55 memory used=18274.4MB, alloc=1308.3MB, time=701.02 memory used=19013.8MB, alloc=1332.3MB, time=732.18 memory used=19777.8MB, alloc=1356.3MB, time=763.59 N2 := 19189 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [-3 x - 3 x z - 12 z , 11 z y + 5 z + 13 x, 5 x - 10 y , -19 x z + 5 z , 2 2 6 x + 16 x z - 9 x, 7 x - 13 z - 12 y] > J:=[op(GB),op(G)]; 6 4 2 4 2 2 J := [14641 x + 305646 x + 1617984 x , -121 x + 66 x y - 1272 x , 2 2 5 3 -x + 2 y , -14641 x - 148104 x - 89232 x y + 40560 x + 15600 z, 2 2 2 -19 x z + 5 z , 6 x + 16 x z - 9 x, 7 x - 13 z - 12 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 12, 2, 2, 2, 2, 1, 1/2, 5/6, 9/16, 3/16, 1/2, 7, 15, 23, 16 6, 6, 2, 2, 1, 4/7, 4/7, --, 4/21, 5/21, -1, -11, -4] 21 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=19904.5MB, alloc=1356.3MB, time=768.13 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428484486 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [13 x y - 20 y z - 16, -3 x - 18 z - 12 y, 5 x z - 17 y + 16 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [-12 x y - x z + 3 z, 14 x y + 13 x z + 2 x, -8 x - 11 y - 17 z] > Problem := [F,G]; 2 2 2 Problem := [[13 x y - 20 y z - 16, -3 x - 18 z - 12 y, 5 x z - 17 y + 16 x], [-12 x y - x z + 3 z, 14 x y + 13 x z + 2 x, -8 x - 11 y - 17 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=46.8MB, alloc=56.3MB, time=0.81 memory used=87.6MB, alloc=60.3MB, time=1.42 memory used=126.4MB, alloc=84.3MB, time=2.01 memory used=168.8MB, alloc=84.3MB, time=2.66 memory used=231.6MB, alloc=116.3MB, time=3.60 memory used=316.0MB, alloc=372.3MB, time=4.88 memory used=400.0MB, alloc=396.3MB, time=6.14 memory used=506.2MB, alloc=420.3MB, time=7.81 memory used=633.3MB, alloc=444.3MB, time=9.85 memory used=775.2MB, alloc=468.3MB, time=12.10 memory used=912.9MB, alloc=492.3MB, time=14.41 memory used=1031.8MB, alloc=492.3MB, time=16.43 memory used=1137.2MB, alloc=492.3MB, time=18.19 memory used=1241.9MB, alloc=516.3MB, time=20.05 memory used=1342.6MB, alloc=516.3MB, time=21.95 memory used=1439.6MB, alloc=516.3MB, time=23.62 memory used=1525.9MB, alloc=516.3MB, time=25.43 memory used=1619.5MB, alloc=516.3MB, time=27.23 memory used=1682.4MB, alloc=516.3MB, time=28.42 memory used=1759.6MB, alloc=516.3MB, time=30.02 memory used=1820.6MB, alloc=540.3MB, time=31.15 memory used=1879.8MB, alloc=540.3MB, time=32.37 memory used=1938.1MB, alloc=540.3MB, time=33.76 memory used=1983.2MB, alloc=540.3MB, time=34.67 memory used=2210.3MB, alloc=564.3MB, time=38.82 memory used=2414.5MB, alloc=588.3MB, time=42.44 memory used=2626.8MB, alloc=612.3MB, time=46.75 memory used=2802.9MB, alloc=636.3MB, time=50.17 memory used=2974.8MB, alloc=660.3MB, time=53.63 memory used=3146.0MB, alloc=684.3MB, time=57.38 memory used=3294.0MB, alloc=684.3MB, time=60.73 memory used=3435.5MB, alloc=684.3MB, time=63.99 memory used=3560.3MB, alloc=684.3MB, time=66.99 memory used=3653.3MB, alloc=684.3MB, time=69.24 memory used=3769.8MB, alloc=684.3MB, time=72.60 memory used=4118.8MB, alloc=708.3MB, time=79.81 memory used=4486.5MB, alloc=732.3MB, time=87.72 memory used=4867.3MB, alloc=756.3MB, time=96.57 memory used=5247.1MB, alloc=780.3MB, time=105.08 memory used=5618.4MB, alloc=804.3MB, time=114.36 memory used=5926.6MB, alloc=828.3MB, time=121.36 memory used=6284.5MB, alloc=852.3MB, time=131.96 memory used=6643.8MB, alloc=876.3MB, time=142.21 memory used=6974.2MB, alloc=900.3MB, time=151.87 memory used=7250.7MB, alloc=924.3MB, time=160.29 memory used=7544.1MB, alloc=948.3MB, time=170.00 memory used=8100.0MB, alloc=972.3MB, time=185.63 memory used=8666.4MB, alloc=996.3MB, time=203.30 memory used=9248.3MB, alloc=1020.3MB, time=220.72 memory used=9847.2MB, alloc=1044.3MB, time=238.23 memory used=10460.2MB, alloc=1068.3MB, time=256.71 memory used=11083.5MB, alloc=1092.3MB, time=274.57 memory used=11719.8MB, alloc=1116.3MB, time=292.40 memory used=12355.0MB, alloc=1140.3MB, time=312.84 memory used=13010.8MB, alloc=1164.3MB, time=332.82 memory used=13542.8MB, alloc=1188.3MB, time=349.83 memory used=14130.9MB, alloc=1212.3MB, time=368.70 memory used=14628.2MB, alloc=1236.3MB, time=383.29 memory used=15153.8MB, alloc=1260.3MB, time=400.10 memory used=15644.6MB, alloc=1284.3MB, time=416.07 memory used=16361.8MB, alloc=1308.3MB, time=444.39 memory used=16780.1MB, alloc=1332.3MB, time=459.55 memory used=17240.0MB, alloc=1356.3MB, time=478.82 memory used=17602.7MB, alloc=1380.3MB, time=492.70 memory used=17932.2MB, alloc=1404.3MB, time=505.71 memory used=18160.4MB, alloc=1428.3MB, time=514.43 memory used=18270.8MB, alloc=1452.3MB, time=522.03 memory used=18472.7MB, alloc=1476.3MB, time=532.16 memory used=18722.0MB, alloc=1500.3MB, time=541.86 memory used=18955.9MB, alloc=1524.3MB, time=551.91 memory used=19256.4MB, alloc=1548.3MB, time=563.53 memory used=19479.6MB, alloc=1572.3MB, time=573.66 memory used=19707.2MB, alloc=1596.3MB, time=583.52 memory used=19994.3MB, alloc=1620.3MB, time=595.26 memory used=20233.0MB, alloc=1644.3MB, time=605.70 memory used=20494.0MB, alloc=1668.3MB, time=617.22 memory used=20708.1MB, alloc=1692.3MB, time=627.40 memory used=20915.5MB, alloc=1716.3MB, time=637.22 memory used=21167.9MB, alloc=1740.3MB, time=648.58 memory used=21336.8MB, alloc=1764.3MB, time=658.43 memory used=21570.8MB, alloc=1788.3MB, time=668.99 memory used=21740.2MB, alloc=1812.3MB, time=679.01 memory used=21896.9MB, alloc=1836.3MB, time=688.45 memory used=22016.8MB, alloc=1860.3MB, time=697.03 memory used=22222.5MB, alloc=1884.3MB, time=707.61 memory used=22397.1MB, alloc=1908.3MB, time=717.82 memory used=22594.7MB, alloc=1932.3MB, time=728.25 memory used=22669.7MB, alloc=1956.3MB, time=736.31 memory used=22780.0MB, alloc=1980.3MB, time=744.78 memory used=22900.9MB, alloc=2004.3MB, time=753.26 memory used=23109.1MB, alloc=2028.3MB, time=763.30 memory used=23276.4MB, alloc=2052.3MB, time=772.24 memory used=23465.2MB, alloc=2076.3MB, time=781.07 memory used=23644.4MB, alloc=2100.3MB, time=790.06 memory used=23867.9MB, alloc=2124.3MB, time=799.83 memory used=23927.2MB, alloc=2148.3MB, time=807.23 memory used=24144.0MB, alloc=2172.3MB, time=816.41 memory used=24234.4MB, alloc=2196.3MB, time=824.30 memory used=24259.5MB, alloc=2220.3MB, time=830.87 memory used=24278.3MB, alloc=2244.3MB, time=837.29 memory used=24316.3MB, alloc=2268.3MB, time=843.94 memory used=24449.8MB, alloc=2292.3MB, time=853.29 memory used=24573.0MB, alloc=2316.3MB, time=862.61 memory used=24682.3MB, alloc=2340.3MB, time=871.38 memory used=24795.4MB, alloc=2364.3MB, time=880.27 memory used=24808.0MB, alloc=2388.3MB, time=887.36 memory used=24891.3MB, alloc=2412.3MB, time=895.68 memory used=25026.6MB, alloc=2436.3MB, time=905.56 memory used=25094.9MB, alloc=2460.3MB, time=913.63 memory used=25233.7MB, alloc=2484.3MB, time=922.78 memory used=25307.7MB, alloc=2508.3MB, time=930.95 memory used=25400.7MB, alloc=2532.3MB, time=940.03 memory used=25501.2MB, alloc=2556.3MB, time=950.46 memory used=25536.9MB, alloc=2580.3MB, time=961.50 memory used=25571.9MB, alloc=2604.3MB, time=970.09 memory used=25590.8MB, alloc=2628.3MB, time=977.49 memory used=25707.6MB, alloc=2652.3MB, time=987.17 memory used=25808.6MB, alloc=2676.3MB, time=996.57 memory used=25855.8MB, alloc=2676.3MB, time=1005.04 memory used=25970.6MB, alloc=2700.3MB, time=1015.12 memory used=26050.8MB, alloc=2700.3MB, time=1024.19 memory used=26103.9MB, alloc=2700.3MB, time=1032.40 memory used=26246.3MB, alloc=2724.3MB, time=1042.86 |\^/| 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(); 1428485686 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [20 x z + 10 y z + 8 z , 13 z + 11 x, 14 x y + 4 z + 15] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [6 y + y + 17 z, -20 x + 13 y - 6 y z, -19 z - 11 x + 13] > Problem := [F,G]; 2 2 2 Problem := [[20 x z + 10 y z + 8 z , 13 z + 11 x, 14 x y + 4 z + 15], 2 2 2 2 [6 y + y + 17 z, -20 x + 13 y - 6 y z, -19 z - 11 x + 13]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=46.8MB, alloc=32.3MB, time=0.80 memory used=66.0MB, alloc=56.3MB, time=1.10 memory used=104.9MB, alloc=60.3MB, time=1.69 memory used=141.6MB, alloc=84.3MB, time=2.26 memory used=204.0MB, alloc=92.3MB, time=3.22 memory used=262.6MB, alloc=116.3MB, time=4.15 memory used=344.3MB, alloc=140.3MB, time=5.45 memory used=427.3MB, alloc=396.3MB, time=6.80 memory used=530.9MB, alloc=420.3MB, time=8.41 memory used=653.3MB, alloc=444.3MB, time=10.27 memory used=797.4MB, alloc=468.3MB, time=13.05 memory used=952.2MB, alloc=492.3MB, time=15.57 memory used=1088.1MB, alloc=492.3MB, time=17.96 memory used=1207.0MB, alloc=516.3MB, time=19.84 memory used=1318.0MB, alloc=516.3MB, time=21.73 memory used=1430.5MB, alloc=516.3MB, time=23.62 memory used=1529.6MB, alloc=516.3MB, time=25.38 memory used=1617.1MB, alloc=516.3MB, time=27.34 memory used=1707.9MB, alloc=540.3MB, time=29.31 memory used=1795.6MB, alloc=540.3MB, time=31.04 memory used=1876.8MB, alloc=540.3MB, time=33.36 memory used=1950.0MB, alloc=540.3MB, time=34.77 memory used=2013.5MB, alloc=540.3MB, time=36.07 memory used=2093.6MB, alloc=540.3MB, time=38.06 memory used=2164.7MB, alloc=540.3MB, time=39.65 memory used=2223.7MB, alloc=540.3MB, time=40.99 memory used=2282.8MB, alloc=564.3MB, time=43.03 memory used=2342.2MB, alloc=564.3MB, time=45.22 memory used=2575.8MB, alloc=588.3MB, time=50.39 memory used=2796.2MB, alloc=612.3MB, time=55.63 memory used=2994.0MB, alloc=636.3MB, time=60.40 memory used=3167.2MB, alloc=660.3MB, time=63.54 memory used=3388.2MB, alloc=684.3MB, time=67.61 memory used=3573.2MB, alloc=708.3MB, time=71.51 memory used=3749.3MB, alloc=708.3MB, time=75.20 memory used=3955.4MB, alloc=732.3MB, time=80.14 memory used=4121.8MB, alloc=732.3MB, time=83.65 memory used=4261.9MB, alloc=732.3MB, time=86.30 memory used=4422.1MB, alloc=756.3MB, time=90.00 memory used=4516.3MB, alloc=756.3MB, time=91.97 memory used=4627.4MB, alloc=756.3MB, time=94.71 memory used=4754.5MB, alloc=756.3MB, time=98.37 memory used=5164.8MB, alloc=780.3MB, time=106.85 memory used=5561.5MB, alloc=804.3MB, time=114.45 memory used=5985.1MB, alloc=828.3MB, time=122.79 memory used=6237.6MB, alloc=852.3MB, time=127.39 memory used=6576.6MB, alloc=876.3MB, time=133.90 memory used=6928.3MB, alloc=900.3MB, time=141.42 memory used=7201.2MB, alloc=924.3MB, time=147.64 memory used=7497.9MB, alloc=948.3MB, time=154.70 memory used=7677.2MB, alloc=972.3MB, time=158.71 memory used=7863.1MB, alloc=996.3MB, time=162.53 memory used=8111.0MB, alloc=1020.3MB, time=169.12 memory used=8743.5MB, alloc=1044.3MB, time=180.01 memory used=9352.7MB, alloc=1068.3MB, time=191.90 memory used=9947.0MB, alloc=1092.3MB, time=206.14 memory used=10571.1MB, alloc=1116.3MB, time=223.70 memory used=11213.4MB, alloc=1140.3MB, time=241.09 memory used=11844.3MB, alloc=1164.3MB, time=257.50 memory used=12440.5MB, alloc=1188.3MB, time=272.19 memory used=13031.1MB, alloc=1212.3MB, time=288.31 memory used=13545.5MB, alloc=1236.3MB, time=303.05 memory used=13986.9MB, alloc=1260.3MB, time=316.01 memory used=14484.8MB, alloc=1284.3MB, time=329.72 memory used=14909.6MB, alloc=1308.3MB, time=342.87 memory used=15339.1MB, alloc=1332.3MB, time=356.11 memory used=15733.5MB, alloc=1356.3MB, time=368.94 memory used=16100.2MB, alloc=1380.3MB, time=381.25 memory used=16474.0MB, alloc=1404.3MB, time=393.53 memory used=16726.5MB, alloc=1428.3MB, time=401.63 |\^/| 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(); 1428486378 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [9 x y - 7 y - 9, 11 x + 16 x y + 5 x z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [11 x z + 16 z + 17 y, -7 y - 10 y - 7] > Problem := [F,G]; 2 Problem := [[9 x y - 7 y - 9, 11 x + 16 x y + 5 x z], 2 2 [11 x z + 16 z + 17 y, -7 y - 10 y - 7]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.12 memory used=26.9MB, alloc=32.3MB, time=0.33 memory used=48.6MB, alloc=56.3MB, time=0.56 memory used=92.2MB, alloc=60.3MB, time=1.02 N1 := 577 > GB := Basis(F, plex(op(vars))); 2 GB := [9 y x - 7 y - 9, 99 x + 45 x z + 112 y + 144, 2 1008 y + 315 y z + 891 x + 1835 y + 405 z + 693] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=128.2MB, alloc=60.3MB, time=1.36 memory used=165.3MB, alloc=84.3MB, time=1.71 memory used=226.6MB, alloc=92.3MB, time=2.30 memory used=287.1MB, alloc=116.3MB, time=2.84 memory used=372.6MB, alloc=140.3MB, time=3.73 memory used=475.2MB, alloc=164.3MB, time=4.87 memory used=576.7MB, alloc=188.3MB, time=6.05 memory used=698.5MB, alloc=212.3MB, time=8.40 memory used=828.7MB, alloc=212.3MB, time=11.40 memory used=959.2MB, alloc=236.3MB, time=13.97 N2 := 3391 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [9 y x - 7 y - 9, 11 x + 16 x y + 5 x z, 16 z + 11 z x + 17 y, 2 -7 y - 10 y - 7] > J:=[op(GB),op(G)]; 2 J := [9 y x - 7 y - 9, 45 z x + 99 x + 112 y + 144, 2 2 315 z y + 1008 y + 405 z + 1835 y + 891 x + 693, 16 z + 11 z x + 17 y, 2 -7 y - 10 y - 7] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 2, 3/4, 1, 1/2, 5/12, 1/2, 1/4, 5, 12, 10, 2, 2, 2, 2, 4/5, 1, 3/5, 5/19, 9/19, 5/19, -3, -2, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=969.2MB, alloc=236.3MB, time=14.12 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428486392 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [20 x + 19 z + 15, -12 y z + 14 z + 16 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [-15 y z + 18 z, 8 x z - y + 18] > Problem := [F,G]; 2 2 Problem := [[20 x + 19 z + 15, -12 y z + 14 z + 16 x], [-15 y z + 18 z, 8 x z - y + 18]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=26.7MB, alloc=32.3MB, time=0.38 memory used=47.6MB, alloc=32.3MB, time=0.57 memory used=67.1MB, alloc=56.3MB, time=0.75 memory used=108.3MB, alloc=60.3MB, time=1.16 memory used=146.3MB, alloc=84.3MB, time=1.62 memory used=204.5MB, alloc=108.3MB, time=2.43 memory used=281.0MB, alloc=140.3MB, time=3.54 memory used=367.6MB, alloc=164.3MB, time=5.66 memory used=466.4MB, alloc=164.3MB, time=9.01 memory used=565.2MB, alloc=188.3MB, time=11.66 N1 := 2987 > GB := Basis(F, plex(op(vars))); GB := 4 2 2 2 [2800 x + 2280 y x + 4200 x + 1710 y + 2888 x + 1575, 20 x + 19 z + 15] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 361 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := 2 2 [20 x + 19 z + 15, -12 y z + 14 z + 16 x, -15 y z + 18 z, 8 z x - y + 18] > J:=[op(GB),op(G)]; 4 2 2 2 J := [2800 x + 2280 y x + 4200 x + 1710 y + 2888 x + 1575, 20 x + 19 z + 15, -15 y z + 18 z, 8 z x - y + 18] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 1, 2, 3/4, 3/4, 1, 3/11, 3/11, 6/11, 4, 9, 10, 4, 4, 1, 1, 3/4, 3/4, 3/4, 3/7, 2/7, 2/7, 1, -2, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=632.4MB, alloc=188.3MB, time=12.58 |\^/| 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(); 1428486405 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-10 z - 4 x - 12 y, 15 y + 16 x - 3] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [x z + 14 y + 8, -3 z + x - 15] > Problem := [F,G]; Problem := [ 2 2 2 2 [-10 z - 4 x - 12 y, 15 y + 16 x - 3], [x z + 14 y + 8, -3 z + x - 15]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.9MB, alloc=32.3MB, time=0.41 memory used=48.1MB, alloc=32.3MB, time=0.66 memory used=68.3MB, alloc=56.3MB, time=0.91 memory used=110.2MB, alloc=60.3MB, time=1.41 memory used=149.9MB, alloc=84.3MB, time=2.00 memory used=209.4MB, alloc=108.3MB, time=2.94 N1 := 1055 > GB := Basis(F, plex(op(vars))); 2 2 GB := [15 y + 16 x - 3, 5 z + 6 y + 2 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=284.2MB, alloc=108.3MB, time=4.06 memory used=366.2MB, alloc=116.3MB, time=5.12 memory used=443.9MB, alloc=140.3MB, time=6.40 N2 := 1055 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-10 z - 4 x - 12 y, 15 y + 16 x - 3, z x + 14 y + 8, -3 z + x - 15] > J:=[op(GB),op(G)]; 2 2 2 2 J := [15 y + 16 x - 3, 5 z + 6 y + 2 x, z x + 14 y + 8, -3 z + x - 15] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 1, 2, 2, 1, 3/4, 3/4, 1/3, 1/4, 1/4, 4, 10, 8, 2, 1, 2, 2, 1, 3/4, 3/4, 1/3, 1/4, 1/4, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=469.0MB, alloc=140.3MB, time=6.99 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428486413 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-11 z - 2 x + 16 y, -5 x y + 14 z - 12 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-2 z - 20 x, 7 x y - 7 x - 3 z] > Problem := [F,G]; 2 2 Problem := [[-11 z - 2 x + 16 y, -5 x y + 14 z - 12 z], 2 [-2 z - 20 x, 7 x y - 7 x - 3 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.7MB, alloc=32.3MB, time=0.39 memory used=46.7MB, alloc=56.3MB, time=0.61 memory used=87.2MB, alloc=60.3MB, time=1.15 memory used=126.1MB, alloc=84.3MB, time=1.62 memory used=172.5MB, alloc=84.3MB, time=2.26 memory used=233.3MB, alloc=92.3MB, time=3.06 memory used=292.3MB, alloc=116.3MB, time=3.82 memory used=374.5MB, alloc=140.3MB, time=4.85 memory used=462.7MB, alloc=396.3MB, time=6.05 memory used=563.4MB, alloc=420.3MB, time=7.66 memory used=682.4MB, alloc=444.3MB, time=9.41 memory used=813.4MB, alloc=468.3MB, time=11.49 memory used=959.0MB, alloc=492.3MB, time=13.97 memory used=1127.4MB, alloc=516.3MB, time=16.30 memory used=1312.9MB, alloc=540.3MB, time=18.69 memory used=1514.0MB, alloc=564.3MB, time=21.48 memory used=1706.9MB, alloc=588.3MB, time=24.89 memory used=1890.2MB, alloc=612.3MB, time=29.94 memory used=2072.5MB, alloc=636.3MB, time=35.78 memory used=2264.6MB, alloc=660.3MB, time=42.25 memory used=2469.6MB, alloc=684.3MB, time=49.64 memory used=2687.0MB, alloc=708.3MB, time=57.97 memory used=2919.9MB, alloc=732.3MB, time=67.06 memory used=3164.7MB, alloc=756.3MB, time=77.25 memory used=3431.6MB, alloc=780.3MB, time=88.51 memory used=3722.4MB, alloc=804.3MB, time=100.80 memory used=4037.3MB, alloc=828.3MB, time=114.79 memory used=4376.0MB, alloc=852.3MB, time=129.69 memory used=4738.7MB, alloc=876.3MB, time=146.29 memory used=5125.3MB, alloc=876.3MB, time=163.74 memory used=5511.8MB, alloc=900.3MB, time=181.07 memory used=5922.4MB, alloc=900.3MB, time=199.30 memory used=6332.9MB, alloc=900.3MB, time=217.39 memory used=6743.3MB, alloc=900.3MB, time=235.50 |\^/| 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(); 1428486713 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-4 x + 5 z, -8 y - 15 z - 18 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-2 y + 12 y + 12, 18 z - 3 y - 3] > Problem := [F,G]; Problem := 2 2 2 2 2 [[-4 x + 5 z, -8 y - 15 z - 18 y], [-2 y + 12 y + 12, 18 z - 3 y - 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.20 memory used=26.7MB, alloc=32.3MB, time=0.56 memory used=48.3MB, alloc=32.3MB, time=0.91 memory used=68.2MB, alloc=56.3MB, time=1.25 memory used=112.3MB, alloc=60.3MB, time=2.12 memory used=151.2MB, alloc=84.3MB, time=2.89 memory used=211.3MB, alloc=84.3MB, time=4.13 memory used=264.6MB, alloc=108.3MB, time=5.22 memory used=333.0MB, alloc=132.3MB, time=6.93 memory used=412.0MB, alloc=156.3MB, time=9.25 memory used=505.2MB, alloc=180.3MB, time=13.03 memory used=618.9MB, alloc=180.3MB, time=17.71 memory used=732.4MB, alloc=180.3MB, time=22.01 memory used=846.1MB, alloc=204.3MB, time=26.37 N1 := 4315 > GB := Basis(F, plex(op(vars))); 4 2 2 GB := [24 x + 20 y + 45 y, -4 x + 5 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=989.6MB, alloc=212.3MB, time=30.53 memory used=1153.5MB, alloc=236.3MB, time=35.17 N2 := 1707 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [-4 x + 5 z, -8 y - 15 z - 18 y, -2 y + 12 y + 12, 18 z - 3 y - 3] > J:=[op(GB),op(G)]; 4 2 2 2 2 J := [24 x + 20 y + 45 y, -4 x + 5 z, -2 y + 12 y + 12, 18 z - 3 y - 3] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 7, 8, 2, 2, 2, 2, 1/4, 3/4, 3/4, 1/11, 5/11, 3/11, 4, 7, 10, 4, 4, 2, 2, 1/2, 3/4, 1/2, 2/11, 5/11, 2/11, 0, -2, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1179.9MB, alloc=236.3MB, time=36.13 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428486755 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-6 y - 19 y z + 15 z , 2 x z + 18 y z + 5 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [5 x y + 2 x z + 4 z, -3 x z - 12 z + 8 y] > Problem := [F,G]; 2 2 Problem := [[-6 y - 19 y z + 15 z , 2 x z + 18 y z + 5 z], 2 [5 x y + 2 x z + 4 z, -3 x z - 12 z + 8 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.81 memory used=67.6MB, alloc=56.3MB, time=1.13 memory used=110.8MB, alloc=60.3MB, time=1.90 memory used=150.9MB, alloc=84.3MB, time=2.64 memory used=211.2MB, alloc=116.3MB, time=3.77 memory used=289.7MB, alloc=140.3MB, time=5.34 memory used=382.8MB, alloc=164.3MB, time=7.33 memory used=482.2MB, alloc=188.3MB, time=10.45 memory used=589.4MB, alloc=212.3MB, time=15.39 memory used=720.8MB, alloc=212.3MB, time=20.80 memory used=852.0MB, alloc=236.3MB, time=26.16 memory used=1007.5MB, alloc=236.3MB, time=32.39 N1 := 4579 > GB := Basis(F, plex(op(vars))); 2 3 2 GB := [2 x y + 18 y + 5 y , 2 x z + 18 y z + 5 z, 2 2 38 x z - 108 y + 270 z + 95 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1124.1MB, alloc=236.3MB, time=34.85 memory used=1300.3MB, alloc=516.3MB, time=38.09 memory used=1495.4MB, alloc=540.3MB, time=41.94 memory used=1701.4MB, alloc=564.3MB, time=46.19 memory used=1913.5MB, alloc=588.3MB, time=51.56 memory used=2105.2MB, alloc=612.3MB, time=58.24 memory used=2300.5MB, alloc=636.3MB, time=66.58 memory used=2508.1MB, alloc=660.3MB, time=76.44 memory used=2739.6MB, alloc=684.3MB, time=87.20 Execution Stopped: Unhandled signal caught (UNKNOWN: 1)GC Thread signalAbort 0x108c75000 Execution Stopped: Unhandled signal caught (UNKNOWN: 1) memory used=2995.2MB, alloc=708.3MB, time=99.97 memory used=3274.6MB, alloc=732.3MB, time=113.58 memory used=3578.1MB, alloc=756.3MB, time=127.99 memory used=3905.5MB, alloc=780.3MB, time=143.37 memory used=4256.8MB, alloc=804.3MB, time=158.35 N2 := 9309 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-6 y - 19 y z + 15 z , 2 x z + 18 y z + 5 z, 2 z x + 5 y x + 4 z, 2 -3 x z - 12 z + 8 y] > J:=[op(GB),op(G)]; 2 3 2 J := [2 x y + 18 y + 5 y , 2 x z + 18 y z + 5 z, 2 2 2 270 z + 38 z x - 108 y + 95 z, 2 z x + 5 y x + 4 z, -3 x z - 12 z + 8 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 1, 2, 2, 3/4, 1, 1, 1/3, 5/12, 3/4, 5, 14, 11, 3, 1, 3, 2, 1, 1, 4/5, 3/8, 7/16, 5/8, -3, -3, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=4524.0MB, alloc=804.3MB, time=168.51 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428487000 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-13 x z - 3 y - 7 x, 19 y - 20 z + 17] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [14 x y - 11 y + 4 z, 11 x + 5 y z + 16 x] > Problem := [F,G]; 2 2 Problem := [[-13 x z - 3 y - 7 x, 19 y - 20 z + 17], 2 [14 x y - 11 y + 4 z, 11 x + 5 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=46.5MB, alloc=56.3MB, time=0.79 memory used=88.7MB, alloc=60.3MB, time=1.42 memory used=130.1MB, alloc=68.3MB, time=2.09 memory used=170.8MB, alloc=92.3MB, time=2.70 memory used=233.8MB, alloc=92.3MB, time=3.64 memory used=296.5MB, alloc=116.3MB, time=4.82 memory used=373.5MB, alloc=140.3MB, time=6.18 memory used=467.2MB, alloc=164.3MB, time=7.83 memory used=569.8MB, alloc=188.3MB, time=9.68 memory used=669.6MB, alloc=468.3MB, time=11.51 memory used=808.4MB, alloc=492.3MB, time=14.50 memory used=949.2MB, alloc=516.3MB, time=19.46 memory used=1101.4MB, alloc=540.3MB, time=24.62 memory used=1262.2MB, alloc=564.3MB, time=30.97 memory used=1444.9MB, alloc=588.3MB, time=38.55 memory used=1651.6MB, alloc=588.3MB, time=47.22 memory used=1858.2MB, alloc=612.3MB, time=56.03 memory used=2088.8MB, alloc=612.3MB, time=65.77 memory used=2319.2MB, alloc=612.3MB, time=74.92 memory used=2549.6MB, alloc=636.3MB, time=84.29 N1 := 7879 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [247 y x + 60 y + 361 x, -19 y + 20 z - 17] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2807.6MB, alloc=636.3MB, time=93.96 N2 := 1791 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-13 x z - 3 y - 7 x, 19 y - 20 z + 17, 14 y x + 4 z - 11 y, 2 5 z y + 11 x + 16 x] > J:=[op(GB),op(G)]; 2 2 2 J := [247 y x + 60 y + 361 x, -19 y + 20 z - 17, 14 y x + 4 z - 11 y, 2 5 z y + 11 x + 16 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 2, 2, 1, 3/4, 1, 1, 5/12, 5/12, 1/3, 4, 10, 9, 3, 2, 2, 1, 3/4, 1, 3/4, 5/12, 1/2, 1/4, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=3099.5MB, alloc=636.3MB, time=101.84 |\^/| 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(); 1428487150 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-15 x + 2 y z, -4 x z - y - 8 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [14 x + 3 y - 13 y, 5 y z + 20 x + 3 z] > Problem := [F,G]; 2 2 Problem := [[-15 x + 2 y z, -4 x z - y - 8 x], 2 2 [14 x + 3 y - 13 y, 5 y z + 20 x + 3 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.51 memory used=46.4MB, alloc=32.3MB, time=0.80 memory used=65.8MB, alloc=56.3MB, time=1.10 memory used=106.4MB, alloc=60.3MB, time=1.70 memory used=148.0MB, alloc=84.3MB, time=2.48 memory used=207.0MB, alloc=92.3MB, time=3.64 memory used=262.1MB, alloc=116.3MB, time=4.71 memory used=336.3MB, alloc=140.3MB, time=6.06 memory used=427.9MB, alloc=164.3MB, time=8.62 memory used=526.9MB, alloc=188.3MB, time=12.45 memory used=645.2MB, alloc=188.3MB, time=17.45 N1 := 3241 > GB := Basis(F, plex(op(vars))); 3 3 2 2 GB := [y + 30 x + 8 y x, 4 z x + y + 8 x, -15 x + 2 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=768.6MB, alloc=188.3MB, time=21.59 memory used=859.3MB, alloc=444.3MB, time=23.06 memory used=992.0MB, alloc=468.3MB, time=25.40 memory used=1144.7MB, alloc=492.3MB, time=28.67 memory used=1297.4MB, alloc=516.3MB, time=34.72 memory used=1463.3MB, alloc=540.3MB, time=41.92 N2 := 3241 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 2 2 2 -15 x + 2 y z, -4 x z - y - 8 x, 3 y + 14 x - 13 y, 5 z y + 3 z + 20 x] > J:=[op(GB),op(G)]; 3 3 2 2 2 2 J := [y + 30 x + 8 y x, 4 z x + y + 8 x, -15 x + 2 y z, 3 y + 14 x - 13 y, 5 z y + 3 z + 20 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 2, 2, 1, 1, 1, 3/4, 5/11, 5/11, 4/11, 5, 13, 11, 3, 3, 3, 1, 1, 1, 3/5, 1/2, 1/2, 2/7, -2, -3, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1494.5MB, alloc=540.3MB, time=43.18 |\^/| 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(); 1428487200 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-6 x y - 16 y + 15 z, 14 x + 18 x z + 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-11 x - 4 x z - 4 y , 7 x y - 3 y z + 8 z] > Problem := [F,G]; 2 2 2 Problem := [[-6 x y - 16 y + 15 z, 14 x + 18 x z + 2 z ], 2 2 [-11 x - 4 x z - 4 y , 7 x y - 3 y z + 8 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.7MB, alloc=40.3MB, time=0.61 memory used=58.8MB, alloc=44.3MB, time=1.04 memory used=84.1MB, alloc=68.3MB, time=1.44 memory used=132.0MB, alloc=76.3MB, time=2.21 memory used=182.3MB, alloc=100.3MB, time=2.95 memory used=255.6MB, alloc=100.3MB, time=4.05 memory used=327.8MB, alloc=124.3MB, time=5.22 memory used=409.3MB, alloc=124.3MB, time=6.53 memory used=499.3MB, alloc=404.3MB, time=8.21 memory used=601.9MB, alloc=428.3MB, time=10.02 memory used=720.2MB, alloc=452.3MB, time=12.09 memory used=855.7MB, alloc=476.3MB, time=14.46 memory used=1008.2MB, alloc=500.3MB, time=17.13 memory used=1178.1MB, alloc=524.3MB, time=20.02 memory used=1350.8MB, alloc=548.3MB, time=23.15 memory used=1519.6MB, alloc=572.3MB, time=28.17 memory used=1691.6MB, alloc=596.3MB, time=34.04 memory used=1874.7MB, alloc=620.3MB, time=41.07 memory used=2071.7MB, alloc=644.3MB, time=48.31 memory used=2279.0MB, alloc=668.3MB, time=56.74 memory used=2504.5MB, alloc=692.3MB, time=66.72 memory used=2753.9MB, alloc=716.3MB, time=77.11 memory used=3027.2MB, alloc=740.3MB, time=88.52 memory used=3324.5MB, alloc=764.3MB, time=100.98 memory used=3645.7MB, alloc=764.3MB, time=115.43 memory used=3966.9MB, alloc=764.3MB, time=130.10 memory used=4288.0MB, alloc=788.3MB, time=143.97 memory used=4632.9MB, alloc=788.3MB, time=158.86 memory used=4977.8MB, alloc=788.3MB, time=174.03 memory used=5322.6MB, alloc=812.3MB, time=189.77 memory used=5691.1MB, alloc=812.3MB, time=205.60 memory used=6059.6MB, alloc=836.3MB, time=221.95 |\^/| 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(); 1428487500 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-13 x - 16 x z + 3, -5 x + 8 x z + 7 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [11 x + 20 x + 11, 15 x y + y - 2] > Problem := [F,G]; 2 2 2 Problem := [[-13 x - 16 x z + 3, -5 x + 8 x z + 7 y ], 2 2 [11 x + 20 x + 11, 15 x y + y - 2]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=27.4MB, alloc=32.3MB, time=0.59 memory used=48.9MB, alloc=56.3MB, time=1.02 N1 := 349 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [-23 x + 14 y + 3, 16 z x + 13 x - 3] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 227 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-13 x - 16 x z + 3, -5 x + 8 x z + 7 y , 11 x + 20 x + 11, 2 y + 15 y x - 2] > J:=[op(GB),op(G)]; J := [ 2 2 2 2 2 -23 x + 14 y + 3, 16 z x + 13 x - 3, 11 x + 20 x + 11, y + 15 y x - 2] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 8, 2, 2, 2, 1, 1, 1/2, 1/2, 7/12, 1/4, 1/6, 4, 7, 8, 2, 2, 2, 1, 1, 1/2, 1/4, 1/2, 1/4, 1/12, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=84.5MB, alloc=60.3MB, time=1.71 |\^/| 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(); 1428487503 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [17 x y - 16 x z, 4 x z + 16 y - 19] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-10 y z - 4 x + 12, -15 x - 4 x z + 5 z ] > Problem := [F,G]; 2 Problem := [[17 x y - 16 x z, 4 x z + 16 y - 19], 2 2 [-10 y z - 4 x + 12, -15 x - 4 x z + 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.55 memory used=46.6MB, alloc=60.3MB, time=0.95 memory used=89.5MB, alloc=60.3MB, time=1.70 memory used=129.7MB, alloc=60.3MB, time=2.37 memory used=168.8MB, alloc=84.3MB, time=3.02 memory used=232.4MB, alloc=92.3MB, time=4.14 memory used=297.1MB, alloc=116.3MB, time=5.32 memory used=381.4MB, alloc=140.3MB, time=6.89 memory used=474.5MB, alloc=164.3MB, time=8.73 memory used=583.8MB, alloc=188.3MB, time=10.88 memory used=695.0MB, alloc=468.3MB, time=12.85 memory used=833.5MB, alloc=492.3MB, time=15.38 memory used=983.7MB, alloc=516.3MB, time=18.09 memory used=1147.2MB, alloc=540.3MB, time=21.01 memory used=1319.4MB, alloc=564.3MB, time=24.22 memory used=1501.3MB, alloc=588.3MB, time=27.67 memory used=1691.9MB, alloc=612.3MB, time=31.43 memory used=1886.3MB, alloc=636.3MB, time=36.08 memory used=2063.7MB, alloc=660.3MB, time=42.06 memory used=2250.0MB, alloc=684.3MB, time=48.82 memory used=2449.4MB, alloc=708.3MB, time=56.20 memory used=2663.0MB, alloc=732.3MB, time=64.60 memory used=2892.0MB, alloc=756.3MB, time=73.67 memory used=3136.0MB, alloc=780.3MB, time=83.25 memory used=3395.4MB, alloc=804.3MB, time=93.68 memory used=3670.4MB, alloc=828.3MB, time=104.90 memory used=3961.6MB, alloc=852.3MB, time=117.01 memory used=4269.2MB, alloc=876.3MB, time=129.91 memory used=4587.8MB, alloc=900.3MB, time=144.23 memory used=4929.9MB, alloc=924.3MB, time=159.41 memory used=5296.0MB, alloc=948.3MB, time=175.40 memory used=5686.1MB, alloc=972.3MB, time=192.02 |\^/| 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(); 1428487803 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [13 y - 10 x + 14 z, 4 x y - 16 y z - 10 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [12 y + 13 y z - y, 15 y - 16 y z + 11 y] > Problem := [F,G]; 2 Problem := [[13 y - 10 x + 14 z, 4 x y - 16 y z - 10 x], 2 2 [12 y + 13 y z - y, 15 y - 16 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=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.47 memory used=46.1MB, alloc=32.3MB, time=0.76 memory used=65.2MB, alloc=56.3MB, time=1.06 memory used=104.4MB, alloc=60.3MB, time=1.64 memory used=145.0MB, alloc=84.3MB, time=2.34 memory used=203.0MB, alloc=116.3MB, time=3.37 memory used=279.9MB, alloc=140.3MB, time=4.69 memory used=373.0MB, alloc=164.3MB, time=6.32 memory used=480.2MB, alloc=188.3MB, time=8.47 memory used=593.5MB, alloc=212.3MB, time=11.85 memory used=717.4MB, alloc=236.3MB, time=16.22 memory used=856.4MB, alloc=260.3MB, time=21.57 memory used=1019.2MB, alloc=260.3MB, time=27.84 memory used=1182.1MB, alloc=260.3MB, time=34.11 memory used=1344.9MB, alloc=284.3MB, time=40.36 memory used=1531.9MB, alloc=308.3MB, time=47.16 N1 := 5705 > GB := Basis(F, plex(op(vars))); 3 2 GB := [52 y - 26 x y - 35 x, 13 y - 10 x + 14 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1621.2MB, alloc=308.3MB, time=48.87 N2 := 1671 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [13 y - 10 x + 14 z, 4 x y - 16 y z - 10 x, 12 y + 13 y z - y, 2 15 y - 16 y z + 11 y] > J:=[op(GB),op(G)]; 3 2 2 J := [52 y - 26 x y - 35 x, 13 y - 10 x + 14 z, 12 y + 13 y z - y, 2 15 y - 16 y z + 11 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 1, 2, 1, 1/2, 1, 1, 1/4, 3/4, 1/3, 4, 9, 9, 3, 1, 3, 1, 1/2, 1, 3/4, 1/4, 3/4, 1/4, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1788.5MB, alloc=564.3MB, time=53.29 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428487871 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [15 x z + 9 y z - 7 x, -10 x + 15 y - 20 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [19 x - 12 x z - 19, -9 y z + z + 15] > Problem := [F,G]; 2 Problem := [[15 x z + 9 y z - 7 x, -10 x + 15 y - 20 z], 2 2 [19 x - 12 x z - 19, -9 y z + z + 15]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=46.7MB, alloc=56.3MB, time=0.80 memory used=87.9MB, alloc=60.3MB, time=1.39 memory used=126.7MB, alloc=84.3MB, time=1.98 memory used=170.7MB, alloc=84.3MB, time=2.62 memory used=233.2MB, alloc=92.3MB, time=3.54 memory used=294.0MB, alloc=116.3MB, time=4.44 memory used=376.9MB, alloc=116.3MB, time=5.75 memory used=449.0MB, alloc=396.3MB, time=6.88 memory used=551.0MB, alloc=420.3MB, time=8.67 memory used=667.6MB, alloc=444.3MB, time=10.72 memory used=795.6MB, alloc=468.3MB, time=12.96 memory used=937.4MB, alloc=492.3MB, time=15.48 memory used=1092.9MB, alloc=516.3MB, time=18.25 memory used=1260.3MB, alloc=540.3MB, time=21.39 memory used=1439.0MB, alloc=564.3MB, time=24.76 memory used=1627.8MB, alloc=588.3MB, time=28.37 memory used=1824.7MB, alloc=612.3MB, time=32.20 memory used=2001.6MB, alloc=636.3MB, time=35.66 memory used=2174.1MB, alloc=660.3MB, time=39.05 memory used=2339.6MB, alloc=684.3MB, time=42.79 memory used=2549.8MB, alloc=708.3MB, time=49.96 memory used=2765.4MB, alloc=732.3MB, time=58.12 memory used=2992.1MB, alloc=756.3MB, time=66.98 memory used=3233.0MB, alloc=780.3MB, time=76.50 memory used=3489.3MB, alloc=804.3MB, time=86.94 memory used=3760.1MB, alloc=828.3MB, time=97.85 memory used=4045.9MB, alloc=852.3MB, time=109.64 memory used=4347.6MB, alloc=876.3MB, time=122.54 memory used=4664.9MB, alloc=900.3MB, time=136.17 memory used=4998.1MB, alloc=924.3MB, time=150.31 memory used=5346.6MB, alloc=948.3MB, time=165.16 memory used=5706.1MB, alloc=972.3MB, time=181.24 |\^/| 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(); 1428488171 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [6 x + 14 x, 5 x y - 19 y z + 6 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [13 z + 11 x + 12 z, z + 16] > Problem := [F,G]; Problem := 2 2 2 [[6 x + 14 x, 5 x y - 19 y z + 6 x], [13 z + 11 x + 12 z, 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=49.5MB, alloc=32.3MB, time=0.90 N1 := 289 > GB := Basis(F, plex(op(vars))); 2 GB := [3 x + 7 x, -5 x y + 19 y z - 6 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=69.1MB, alloc=32.3MB, time=1.23 memory used=89.1MB, alloc=56.3MB, time=1.56 N2 := 289 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [6 x + 14 x, -19 z y + 5 y x + 6 x, 13 z + 12 z + 11 x, z + 16] > J:=[op(GB),op(G)]; 2 2 2 J := [3 x + 7 x, -5 x y + 19 y z - 6 x, 13 z + 12 z + 11 x, z + 16] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 7, 8, 2, 2, 1, 2, 3/4, 1/4, 3/4, 1/2, 1/5, 2/5, 4, 7, 8, 2, 2, 1, 2, 3/4, 1/4, 3/4, 1/2, 1/5, 2/5, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=111.4MB, alloc=56.3MB, time=1.95 |\^/| 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(); 1428488175 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-12 y - 2 y z - 10 z, 3 x z + 19 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [15 x z - 4, 13 z + 3 y + 4] > Problem := [F,G]; Problem := 2 2 2 [[-12 y - 2 y z - 10 z, 3 x z + 19 y ], [15 x z - 4, 13 z + 3 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=31.8MB, alloc=40.3MB, time=0.58 memory used=58.7MB, alloc=40.3MB, time=0.98 memory used=84.8MB, alloc=68.3MB, time=1.40 memory used=132.3MB, alloc=68.3MB, time=2.08 memory used=176.3MB, alloc=92.3MB, time=2.77 memory used=245.9MB, alloc=100.3MB, time=3.93 memory used=307.5MB, alloc=124.3MB, time=5.03 memory used=390.0MB, alloc=148.3MB, time=6.45 memory used=485.6MB, alloc=172.3MB, time=8.64 memory used=583.8MB, alloc=196.3MB, time=12.22 memory used=701.6MB, alloc=220.3MB, time=16.77 N1 := 3159 > GB := Basis(F, plex(op(vars))); 2 3 2 2 2 GB := [-18 x y + 19 y + 95 y , 3 z x + 19 y , z y + 6 y + 5 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=850.7MB, alloc=220.3MB, time=20.48 memory used=932.5MB, alloc=476.3MB, time=21.81 memory used=1100.0MB, alloc=500.3MB, time=24.65 memory used=1280.8MB, alloc=524.3MB, time=28.62 memory used=1444.7MB, alloc=548.3MB, time=35.33 N2 := 3159 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-12 y - 2 y z - 10 z, 3 z x + 19 y , 15 z x - 4, 13 z + 3 y + 4] > J:=[op(GB),op(G)]; 2 3 2 2 2 J := [-18 x y + 19 y + 95 y , 3 z x + 19 y , z y + 6 y + 5 z, 15 z x - 4, 2 13 z + 3 y + 4] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 1, 2, 2, 1/2, 3/4, 1, 1/5, 2/5, 1/2, 5, 11, 11, 3, 1, 3, 2, 3/5, 4/5, 4/5, 3/13, 7/13, 5/13, -2, -3, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1551.6MB, alloc=548.3MB, time=39.03 |\^/| 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(); 1428488240 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-5 y z + 8 z - 2, -6 x + 12 x y + 20 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [7 y - 9 x + 6, -5 x + 3 x + 14 z] > Problem := [F,G]; 2 Problem := [[-5 y z + 8 z - 2, -6 x + 12 x y + 20 y], 2 2 [7 y - 9 x + 6, -5 x + 3 x + 14 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=48.7MB, alloc=56.3MB, time=0.88 memory used=91.8MB, alloc=60.3MB, time=1.63 memory used=129.8MB, alloc=84.3MB, time=2.46 N1 := 1083 > GB := Basis(F, plex(op(vars))); GB := [ 2 2 -3 x + 6 x y + 10 y, 15 x z - 48 x z + 12 x - 80 z + 20, 5 z y - 8 z + 2] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=185.4MB, alloc=84.3MB, time=3.91 memory used=246.2MB, alloc=108.3MB, time=4.93 memory used=327.3MB, alloc=140.3MB, time=6.56 N2 := 1433 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 2 2 -5 y z + 8 z - 2, -6 x + 12 x y + 20 y, 7 y - 9 x + 6, -5 x + 3 x + 14 z ] > J:=[op(GB),op(G)]; 2 2 J := [-3 x + 6 x y + 10 y, 15 z x - 48 z x - 80 z + 12 x + 20, 2 2 5 z y - 8 z + 2, 7 y - 9 x + 6, -5 x + 3 x + 14 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 8, 2, 2, 2, 1, 3/4, 3/4, 1/2, 5/12, 1/3, 1/4, 5, 10, 11, 3, 2, 2, 1, 4/5, 3/5, 3/5, 8/17, 4/17, 6/17, -2, -3, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=383.2MB, alloc=140.3MB, time=8.24 |\^/| 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(); 1428488255 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [-4 x y - 18 x, 20 x y + 8 x z - 14] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [11 x y - 15 y + 18 z, -5 x z + 19 y z + 8 z ] > Problem := [F,G]; Problem := [[-4 x y - 18 x, 20 x y + 8 x z - 14], 2 2 [11 x y - 15 y + 18 z, -5 x z + 19 y z + 8 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.51 memory used=46.8MB, alloc=32.3MB, time=0.81 memory used=66.2MB, alloc=56.3MB, time=1.11 memory used=105.8MB, alloc=60.3MB, time=1.70 memory used=145.2MB, alloc=84.3MB, time=2.37 memory used=204.8MB, alloc=116.3MB, time=3.49 memory used=280.8MB, alloc=140.3MB, time=4.92 memory used=372.7MB, alloc=164.3MB, time=6.61 memory used=479.7MB, alloc=188.3MB, time=8.46 memory used=583.5MB, alloc=468.3MB, time=10.40 memory used=715.1MB, alloc=492.3MB, time=14.06 memory used=850.0MB, alloc=516.3MB, time=18.75 memory used=997.9MB, alloc=540.3MB, time=23.91 memory used=1157.7MB, alloc=564.3MB, time=30.11 memory used=1336.7MB, alloc=588.3MB, time=37.32 memory used=1539.7MB, alloc=588.3MB, time=45.44 memory used=1742.6MB, alloc=612.3MB, time=53.76 memory used=1969.5MB, alloc=612.3MB, time=62.80 memory used=2196.3MB, alloc=612.3MB, time=72.22 memory used=2423.1MB, alloc=636.3MB, time=81.19 memory used=2673.8MB, alloc=636.3MB, time=90.94 memory used=2924.7MB, alloc=660.3MB, time=100.73 N1 := 8847 > GB := Basis(F, plex(op(vars))); GB := [2 y + 9, 4 x z - 45 x - 7] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3205.1MB, alloc=660.3MB, time=109.67 memory used=3430.4MB, alloc=660.3MB, time=113.80 memory used=3735.6MB, alloc=684.3MB, time=122.99 memory used=4011.4MB, alloc=708.3MB, time=135.20 memory used=4311.4MB, alloc=732.3MB, time=147.78 N2 := 5395 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [-4 x y - 18 x, 20 x y + 8 x z - 14, -15 y + 11 y x + 18 z, 2 -5 x z + 19 y z + 8 z ] > J:=[op(GB),op(G)]; J := 2 2 [2 y + 9, 4 z x - 45 x - 7, -15 y + 11 y x + 18 z, -5 x z + 19 y z + 8 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 1, 2, 2, 1, 1, 3/4, 6/11, 5/11, 5/11, 4, 9, 7, 2, 1, 2, 2, 3/4, 3/4, 3/4, 4/11, 4/11, 5/11, 2, 1, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=4500.2MB, alloc=732.3MB, time=155.02 |\^/| 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(); 1428488488 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [12 x - 7 z + 4 z, -10 x z - 3 y + 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-9 x - 15 x y - 7 x z, 16 z + 17 x] > Problem := [F,G]; 2 2 2 2 Problem := [[12 x - 7 z + 4 z, -10 x z - 3 y + 2 z ], 2 2 [-9 x - 15 x y - 7 x z, 16 z + 17 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=60.3MB, time=0.81 memory used=89.1MB, alloc=60.3MB, time=1.38 memory used=132.1MB, alloc=92.3MB, time=1.97 memory used=198.8MB, alloc=92.3MB, time=2.89 memory used=263.3MB, alloc=116.3MB, time=3.83 memory used=340.8MB, alloc=372.3MB, time=4.97 memory used=426.7MB, alloc=396.3MB, time=6.42 memory used=530.0MB, alloc=420.3MB, time=8.15 memory used=646.2MB, alloc=444.3MB, time=10.13 memory used=784.3MB, alloc=468.3MB, time=12.39 memory used=944.5MB, alloc=492.3MB, time=14.80 memory used=1114.6MB, alloc=516.3MB, time=17.57 memory used=1278.8MB, alloc=540.3MB, time=21.26 memory used=1433.4MB, alloc=564.3MB, time=26.01 memory used=1595.5MB, alloc=588.3MB, time=31.55 memory used=1768.4MB, alloc=612.3MB, time=37.98 memory used=1953.4MB, alloc=636.3MB, time=45.82 memory used=2162.3MB, alloc=660.3MB, time=54.23 memory used=2395.1MB, alloc=684.3MB, time=64.14 memory used=2651.9MB, alloc=708.3MB, time=74.97 memory used=2932.7MB, alloc=708.3MB, time=86.37 memory used=3213.4MB, alloc=732.3MB, time=98.38 memory used=3518.0MB, alloc=732.3MB, time=111.23 memory used=3822.7MB, alloc=732.3MB, time=123.68 memory used=4127.3MB, alloc=756.3MB, time=136.35 memory used=4456.0MB, alloc=756.3MB, time=150.18 memory used=4784.5MB, alloc=780.3MB, time=164.23 memory used=5137.0MB, alloc=780.3MB, time=178.70 |\^/| 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(); 1428488788 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [10 x z + 4 y + 17 x, -11 x z + 15 x + 9 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-5 x + 16 y + 20 y z, 3 x + 3 y z - 15 y] > Problem := [F,G]; 2 Problem := [[10 x z + 4 y + 17 x, -11 x z + 15 x + 9 y], 2 2 2 [-5 x + 16 y + 20 y z, 3 x + 3 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=4.2MB, alloc=32.3MB, time=0.19 memory used=26.9MB, alloc=32.3MB, time=0.56 memory used=47.3MB, alloc=32.3MB, time=0.88 memory used=66.8MB, alloc=56.3MB, time=1.20 memory used=107.6MB, alloc=60.3MB, time=1.83 memory used=147.9MB, alloc=84.3MB, time=2.46 memory used=211.4MB, alloc=92.3MB, time=3.52 memory used=276.5MB, alloc=116.3MB, time=4.69 memory used=353.6MB, alloc=140.3MB, time=6.11 memory used=448.6MB, alloc=164.3MB, time=7.91 memory used=545.2MB, alloc=164.3MB, time=9.70 memory used=633.9MB, alloc=444.3MB, time=11.30 memory used=761.2MB, alloc=468.3MB, time=13.58 memory used=901.9MB, alloc=492.3MB, time=16.25 memory used=1053.3MB, alloc=516.3MB, time=20.33 memory used=1203.3MB, alloc=540.3MB, time=25.53 memory used=1365.9MB, alloc=564.3MB, time=31.61 memory used=1541.0MB, alloc=588.3MB, time=38.70 memory used=1731.0MB, alloc=612.3MB, time=46.87 memory used=1945.0MB, alloc=636.3MB, time=56.34 memory used=2182.9MB, alloc=636.3MB, time=67.09 memory used=2420.8MB, alloc=660.3MB, time=77.80 memory used=2682.7MB, alloc=660.3MB, time=88.90 memory used=2944.5MB, alloc=660.3MB, time=100.41 memory used=3206.3MB, alloc=684.3MB, time=112.05 memory used=3492.1MB, alloc=684.3MB, time=124.36 memory used=3778.0MB, alloc=708.3MB, time=136.16 N1 := 9587 > GB := Basis(F, plex(op(vars))); 2 GB := [44 y + 90 y + 337 x, 11 z x - 9 y - 15 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4100.2MB, alloc=708.3MB, time=146.02 N2 := 2567 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [10 z x + 4 y + 17 x, -11 x z + 15 x + 9 y, -5 x + 16 y + 20 y z, 2 3 x + 3 y z - 15 y] > J:=[op(GB),op(G)]; 2 2 2 J := [44 y + 90 y + 337 x, 11 z x - 9 y - 15 x, -5 x + 16 y + 20 y z, 2 3 x + 3 y z - 15 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 12, 8, 2, 2, 2, 1, 1, 1, 1, 1/2, 1/2, 1/3, 4, 11, 8, 2, 2, 2, 1, 1, 1, 3/4, 5/12, 7/12, 1/4, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=4436.7MB, alloc=708.3MB, time=158.76 |\^/| 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(); 1428488990 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-17 x + 20 x z - 6, 17 x y + 12 x z + 17 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-15 x + 4 y + 17 y, 9 x + 18 z] > Problem := [F,G]; 2 2 Problem := [[-17 x + 20 x z - 6, 17 x y + 12 x z + 17 y ], 2 2 2 [-15 x + 4 y + 17 y, 9 x + 18 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.54 memory used=48.9MB, alloc=32.3MB, time=0.96 memory used=68.9MB, alloc=56.3MB, time=1.33 N1 := 587 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [85 y + 85 y x + 51 x + 18, -17 x + 20 x z - 6] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.0MB, alloc=60.3MB, time=2.20 N2 := 105 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-17 x + 20 x z - 6, 12 z x + 17 y + 17 y x, -15 x + 4 y + 17 y, 2 9 x + 18 z] > J:=[op(GB),op(G)]; 2 2 2 2 2 J := [85 y + 85 y x + 51 x + 18, -17 x + 20 x z - 6, -15 x + 4 y + 17 y, 2 9 x + 18 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 1, 1, 1/2, 3/4, 6/11, 4/11, 3/11, 4, 8, 8, 2, 2, 2, 1, 1, 1/2, 1/2, 1/2, 1/3, 1/6, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=113.4MB, alloc=60.3MB, time=2.28 |\^/| 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(); 1428488993 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-16 x - 17 z - 17 y, 12 x y - 7 z - 14] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [12 x - 17 y z + 18, -13 z + 15 x + 2] > Problem := [F,G]; 2 2 Problem := [[-16 x - 17 z - 17 y, 12 x y - 7 z - 14], 2 2 [12 x - 17 y z + 18, -13 z + 15 x + 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=32.4MB, alloc=40.3MB, time=0.60 memory used=59.2MB, alloc=44.3MB, time=1.05 memory used=85.3MB, alloc=68.3MB, time=1.48 memory used=133.8MB, alloc=76.3MB, time=2.31 memory used=182.3MB, alloc=76.3MB, time=3.06 memory used=228.1MB, alloc=100.3MB, time=3.82 memory used=299.2MB, alloc=100.3MB, time=4.98 memory used=368.2MB, alloc=124.3MB, time=6.16 memory used=430.2MB, alloc=380.3MB, time=7.21 memory used=518.8MB, alloc=404.3MB, time=8.95 memory used=623.5MB, alloc=428.3MB, time=10.95 memory used=748.7MB, alloc=452.3MB, time=13.33 memory used=884.7MB, alloc=476.3MB, time=16.04 memory used=1026.1MB, alloc=500.3MB, time=19.80 memory used=1164.8MB, alloc=524.3MB, time=24.29 memory used=1310.8MB, alloc=548.3MB, time=29.94 memory used=1473.3MB, alloc=572.3MB, time=36.98 memory used=1659.8MB, alloc=596.3MB, time=44.93 memory used=1870.2MB, alloc=620.3MB, time=53.95 memory used=2104.6MB, alloc=620.3MB, time=63.95 memory used=2339.1MB, alloc=644.3MB, time=74.05 memory used=2597.8MB, alloc=644.3MB, time=84.44 N1 := 7361 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [2448 y x - 5712 y x + 784 x + 833 y + 3332, -12 x y + 7 z + 14] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2832.8MB, alloc=644.3MB, time=90.36 memory used=3148.7MB, alloc=668.3MB, time=100.37 N2 := 2819 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-16 x - 17 z - 17 y, 12 y x - 7 z - 14, -17 z y + 12 x + 18, 2 -13 z + 15 x + 2] > J:=[op(GB),op(G)]; 2 2 2 J := [2448 y x - 5712 y x + 784 x + 833 y + 3332, -12 x y + 7 z + 14, 2 2 -17 z y + 12 x + 18, -13 z + 15 x + 2] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 2, 1, 2, 1, 3/4, 1, 1/3, 1/4, 1/3, 4, 10, 10, 4, 2, 2, 2, 1, 3/4, 3/4, 3/7, 5/14, 3/14, 1, -2, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=3252.3MB, alloc=668.3MB, time=104.62 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428489128 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-13 x z + 8 z + 6, 2 x z - 3 z - 5 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [-12 x z + 13 y z + 13 y, 11 y z - 18 y] > Problem := [F,G]; 2 2 Problem := [[-13 x z + 8 z + 6, 2 x z - 3 z - 5 x], [-12 x z + 13 y z + 13 y, 11 y z - 18 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=47.5MB, alloc=32.3MB, time=0.83 memory used=67.9MB, alloc=56.3MB, time=1.18 memory used=112.3MB, alloc=60.3MB, time=1.97 memory used=152.3MB, alloc=84.3MB, time=2.68 memory used=210.8MB, alloc=108.3MB, time=3.80 memory used=280.3MB, alloc=132.3MB, time=6.11 memory used=368.5MB, alloc=156.3MB, time=9.24 N1 := 2209 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [1495 x + 1324 x - 1440 x + 324, 1495 x + 1324 x + 414 z - 720] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 827 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-13 x z + 8 z + 6, -3 z + 2 z x - 5 x, -12 x z + 13 y z + 13 y, 11 y z - 18 y] > J:=[op(GB),op(G)]; 3 2 2 J := [1495 x + 1324 x - 1440 x + 324, 1495 x + 414 z + 1324 x - 720, -12 x z + 13 y z + 13 y, 11 y z - 18 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 1, 1, 2, 3/4, 1/2, 1, 4/11, 4/11, 7/11, 4, 8, 9, 3, 3, 1, 1, 3/4, 1/2, 3/4, 6/13, 4/13, 4/13, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=465.8MB, alloc=164.3MB, time=11.16 |\^/| 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(); 1428489146 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-9 x + 10 y z - 13 y, -16 y + 11 z + 13 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-5 x + 20 x y + 12 z, -17 x + 8 x z - 2 y] > Problem := [F,G]; 2 2 2 Problem := [[-9 x + 10 y z - 13 y, -16 y + 11 z + 13 x], 2 2 [-5 x + 20 x y + 12 z, -17 x + 8 x z - 2 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=46.5MB, alloc=32.3MB, time=0.82 memory used=64.6MB, alloc=56.3MB, time=1.12 memory used=106.4MB, alloc=68.3MB, time=1.78 memory used=147.6MB, alloc=92.3MB, time=2.42 memory used=210.8MB, alloc=92.3MB, time=3.40 memory used=275.8MB, alloc=92.3MB, time=4.39 memory used=338.8MB, alloc=116.3MB, time=5.39 memory used=413.1MB, alloc=372.3MB, time=6.56 memory used=497.6MB, alloc=396.3MB, time=7.96 memory used=607.4MB, alloc=420.3MB, time=9.66 memory used=743.4MB, alloc=444.3MB, time=11.99 memory used=891.2MB, alloc=468.3MB, time=14.65 memory used=1046.0MB, alloc=492.3MB, time=17.51 memory used=1216.2MB, alloc=516.3MB, time=20.66 memory used=1395.5MB, alloc=540.3MB, time=24.16 memory used=1585.7MB, alloc=564.3MB, time=27.49 memory used=1774.7MB, alloc=588.3MB, time=31.19 memory used=1952.2MB, alloc=612.3MB, time=34.71 memory used=2131.5MB, alloc=636.3MB, time=38.21 memory used=2289.0MB, alloc=660.3MB, time=41.48 memory used=2427.5MB, alloc=684.3MB, time=44.34 memory used=2678.6MB, alloc=708.3MB, time=52.55 memory used=2921.3MB, alloc=732.3MB, time=61.69 memory used=3172.1MB, alloc=756.3MB, time=71.63 memory used=3436.1MB, alloc=780.3MB, time=82.47 memory used=3714.3MB, alloc=804.3MB, time=94.21 memory used=4006.5MB, alloc=828.3MB, time=106.65 memory used=4313.5MB, alloc=852.3MB, time=119.90 memory used=4636.4MB, alloc=876.3MB, time=133.94 memory used=4969.6MB, alloc=900.3MB, time=149.19 memory used=5322.3MB, alloc=924.3MB, time=165.64 memory used=5699.0MB, alloc=948.3MB, time=183.14 memory used=6099.6MB, alloc=972.3MB, time=201.63 |\^/| 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(); 1428489446 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [18 x - 4 y - 18, -4 x y - 10 y z - 4 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [15 x y - 15 y + 9 y z, -3 x + 17 x y - x z] > Problem := [F,G]; 2 2 2 Problem := [[18 x - 4 y - 18, -4 x y - 10 y z - 4 z ], 2 2 [15 x y - 15 y + 9 y z, -3 x + 17 x y - x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.80 memory used=68.5MB, alloc=56.3MB, time=1.18 memory used=110.6MB, alloc=60.3MB, time=1.92 memory used=147.1MB, alloc=84.3MB, time=2.93 N1 := 907 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [-9 x + 2 y + 9, 2 z + 5 z y + 2 y x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=202.6MB, alloc=84.3MB, time=3.82 memory used=264.4MB, alloc=116.3MB, time=5.06 N2 := 907 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [18 x - 4 y - 18, -4 x y - 10 y z - 4 z , 15 x y - 15 y + 9 y z, 2 -3 x + 17 x y - x z] > J:=[op(GB),op(G)]; 2 2 2 2 J := [-9 x + 2 y + 9, 2 z + 5 z y + 2 y x, 15 x y - 15 y + 9 y z, 2 -3 x + 17 x y - x z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 2, 2, 2, 1, 1, 3/4, 1/2, 7/12, 1/3, 4, 11, 8, 2, 2, 2, 2, 1, 1, 3/4, 1/2, 7/12, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=298.2MB, alloc=116.3MB, time=6.19 |\^/| 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(); 1428489456 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [11 y z + 13 z - 12 z, -8 x z - 9 z - 20] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-10 x z - 3 y z + 19 z, -2 z - 18 y - 6] > Problem := [F,G]; 2 Problem := [[11 y z + 13 z - 12 z, -8 x z - 9 z - 20], 2 [-10 x z - 3 y z + 19 z, -2 z - 18 y - 6]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.83 memory used=67.6MB, alloc=56.3MB, time=1.18 memory used=109.3MB, alloc=60.3MB, time=1.91 memory used=146.7MB, alloc=84.3MB, time=2.65 memory used=204.1MB, alloc=84.3MB, time=3.94 memory used=254.1MB, alloc=108.3MB, time=5.11 memory used=317.8MB, alloc=132.3MB, time=7.26 memory used=396.6MB, alloc=156.3MB, time=10.37 memory used=499.5MB, alloc=156.3MB, time=14.67 N1 := 3099 > GB := Basis(F, plex(op(vars))); GB := [88 y x + 99 y - 96 x - 368, 13 z + 11 y - 12] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=605.2MB, alloc=164.3MB, time=17.53 memory used=726.1MB, alloc=188.3MB, time=20.32 N2 := 1607 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [11 y z + 13 z - 12 z, -8 x z - 9 z - 20, -10 x z - 3 y z + 19 z, 2 -2 z - 18 y - 6] > J:=[op(GB),op(G)]; J := [88 y x + 99 y - 96 x - 368, 13 z + 11 y - 12, -10 x z - 3 y z + 19 z, 2 -2 z - 18 y - 6] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 1, 1, 2, 1/2, 3/4, 1, 1/6, 1/4, 3/4, 4, 9, 7, 2, 1, 1, 2, 1/2, 1, 3/4, 3/13, 5/13, 5/13, 0, 1, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=784.3MB, alloc=188.3MB, time=22.29 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428489494 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [9 y + y z - 4 z , -15 y - 14 z + 1] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-9 x + 18 x - 13 y, 6 x z + 15 y - 5] > Problem := [F,G]; 2 2 2 Problem := [[9 y + y z - 4 z , -15 y - 14 z + 1], 2 2 [-9 x + 18 x - 13 y, 6 x z + 15 y - 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=32.3MB, time=0.79 memory used=66.2MB, alloc=56.3MB, time=1.07 memory used=110.6MB, alloc=60.3MB, time=1.70 memory used=153.7MB, alloc=84.3MB, time=2.39 memory used=213.2MB, alloc=116.3MB, time=3.43 memory used=291.2MB, alloc=140.3MB, time=4.92 memory used=384.9MB, alloc=164.3MB, time=6.63 memory used=494.1MB, alloc=188.3MB, time=8.65 memory used=609.7MB, alloc=468.3MB, time=10.70 memory used=743.9MB, alloc=492.3MB, time=13.95 memory used=876.7MB, alloc=516.3MB, time=18.49 memory used=1022.8MB, alloc=540.3MB, time=23.47 memory used=1183.7MB, alloc=564.3MB, time=29.58 memory used=1356.1MB, alloc=588.3MB, time=37.57 memory used=1552.5MB, alloc=612.3MB, time=45.96 memory used=1772.9MB, alloc=612.3MB, time=55.32 memory used=1993.2MB, alloc=612.3MB, time=64.71 memory used=2213.5MB, alloc=636.3MB, time=73.93 memory used=2457.7MB, alloc=636.3MB, time=84.05 memory used=2702.0MB, alloc=636.3MB, time=94.10 memory used=2946.2MB, alloc=660.3MB, time=104.26 memory used=3214.4MB, alloc=660.3MB, time=115.60 memory used=3482.7MB, alloc=684.3MB, time=126.69 N1 := 9559 > GB := Basis(F, plex(op(vars))); 4 3 2 2 GB := [450 y + 105 y - 942 y - 7 y + 2, 15 y + 14 z - 1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3786.8MB, alloc=684.3MB, time=135.22 N2 := 1851 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-4 z + z y + 9 y , -15 y - 14 z + 1, -9 x + 18 x - 13 y, 2 6 z x + 15 y - 5] > J:=[op(GB),op(G)]; 4 3 2 2 2 J := [450 y + 105 y - 942 y - 7 y + 2, 15 y + 14 z - 1, -9 x + 18 x - 13 y, 2 6 z x + 15 y - 5] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 2, 1/2, 1, 3/4, 1/4, 5/12, 1/3, 4, 8, 10, 4, 2, 4, 1, 1/2, 1, 1/2, 3/14, 1/2, 1/7, 1, -2, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=3913.5MB, alloc=684.3MB, time=140.11 |\^/| 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(); 1428489700 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-4 x z - 7 x + z, 19 z + 12] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-19 x - 20 x z - 20 z, 17 x y + 2 z - 13] > Problem := [F,G]; Problem := [ 2 2 [-4 x z - 7 x + z, 19 z + 12], [-19 x - 20 x z - 20 z, 17 x y + 2 z - 13] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 N1 := 243 > GB := Basis(F, plex(op(vars))); 2 GB := [1123 x - 96 x + 12, -1123 x + 48 + 133 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=56.2MB, alloc=68.3MB, time=1.07 N2 := 201 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-4 x z - 7 x + z, 19 z + 12, -19 x - 20 x z - 20 z, 17 y x + 2 z - 13] > J:=[op(GB),op(G)]; 2 2 J := [1123 x - 96 x + 12, -1123 x + 48 + 133 z, -19 x - 20 x z - 20 z, 17 y x + 2 z - 13] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 8, 2, 2, 1, 2, 3/4, 1/4, 1, 5/11, 1/11, 6/11, 4, 8, 7, 2, 2, 1, 1, 1, 1/4, 3/4, 1/2, 1/12, 1/3, 0, 1, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=75.3MB, alloc=68.3MB, time=1.38 |\^/| 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(); 1428489702 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-9 x y - 15 x + 20 z, -11 y + 19] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-y + 5 y + 15 z, 20 x z + 8 x + 16 y] > Problem := [F,G]; 2 Problem := [[-9 x y - 15 x + 20 z, -11 y + 19], 2 [-y + 5 y + 15 z, 20 x z + 8 x + 16 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=48.0MB, alloc=56.3MB, time=0.86 memory used=91.8MB, alloc=60.3MB, time=1.59 memory used=131.4MB, alloc=84.3MB, time=2.26 memory used=188.2MB, alloc=108.3MB, time=3.28 memory used=262.5MB, alloc=108.3MB, time=5.70 memory used=328.9MB, alloc=132.3MB, time=8.13 N1 := 2019 > GB := Basis(F, plex(op(vars))); 2 GB := [11 y - 19, -9 x y - 15 x + 20 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=421.8MB, alloc=140.3MB, time=9.81 memory used=521.9MB, alloc=164.3MB, time=11.61 memory used=630.7MB, alloc=188.3MB, time=15.49 N2 := 2019 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-9 x y - 15 x + 20 z, -11 y + 19, -y + 5 y + 15 z, 20 x z + 8 x + 16 y] > J:=[op(GB),op(G)]; 2 2 J := [11 y - 19, -9 x y - 15 x + 20 z, -y + 5 y + 15 z, 20 x z + 8 x + 16 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 1, 2, 1, 1/2, 1, 3/4, 4/11, 5/11, 3/11, 4, 9, 8, 2, 1, 2, 1, 1/2, 1, 3/4, 4/11, 5/11, 3/11, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=671.9MB, alloc=188.3MB, time=16.88 |\^/| 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(); 1428489720 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-14 x - 15 y + 18, -19 x z + 10 z + 6 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [12 x y + 7 z - y, -3 x - 5 x z + 2 y z] > Problem := [F,G]; 2 2 Problem := [[-14 x - 15 y + 18, -19 x z + 10 z + 6 z], 2 2 [12 x y + 7 z - y, -3 x - 5 x z + 2 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.53 memory used=47.1MB, alloc=32.3MB, time=0.84 memory used=66.6MB, alloc=56.3MB, time=1.15 memory used=108.0MB, alloc=60.3MB, time=1.84 memory used=147.1MB, alloc=84.3MB, time=2.56 memory used=208.6MB, alloc=84.3MB, time=3.64 memory used=263.2MB, alloc=108.3MB, time=4.63 memory used=334.5MB, alloc=140.3MB, time=6.24 memory used=414.9MB, alloc=164.3MB, time=8.99 memory used=510.7MB, alloc=164.3MB, time=12.73 memory used=606.6MB, alloc=188.3MB, time=16.34 N1 := 3273 > GB := Basis(F, plex(op(vars))); 2 2 GB := [14 x + 15 y - 18, -19 x z + 10 z + 6 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=731.2MB, alloc=188.3MB, time=19.64 memory used=841.5MB, alloc=444.3MB, time=21.63 memory used=973.9MB, alloc=468.3MB, time=24.11 memory used=1111.3MB, alloc=492.3MB, time=28.72 memory used=1259.0MB, alloc=516.3MB, time=34.48 N2 := 3273 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-14 x - 15 y + 18, -19 x z + 10 z + 6 z, 7 z + 12 y x - y, 2 -3 x - 5 x z + 2 y z] > J:=[op(GB),op(G)]; 2 2 2 J := [14 x + 15 y - 18, -19 x z + 10 z + 6 z, 7 z + 12 y x - y, 2 -3 x - 5 x z + 2 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 1, 2, 1, 3/4, 3/4, 5/12, 1/3, 1/2, 4, 10, 8, 2, 2, 1, 2, 1, 3/4, 3/4, 5/12, 1/3, 1/2, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1338.2MB, alloc=516.3MB, time=37.23 |\^/| 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(); 1428489760 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [x y + 17 y - 20 z , 11 x + 17 x y + 10 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [4 x z - 8 y + 7 x, -14 x z - 17 x] > Problem := [F,G]; 2 2 2 Problem := [[x y + 17 y - 20 z , 11 x + 17 x y + 10 x], 2 [4 x z - 8 y + 7 x, -14 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.53 memory used=47.6MB, alloc=32.3MB, time=0.84 memory used=67.6MB, alloc=56.3MB, time=1.16 memory used=110.3MB, alloc=60.3MB, time=1.84 memory used=151.8MB, alloc=84.3MB, time=2.58 memory used=212.9MB, alloc=108.3MB, time=3.65 memory used=293.7MB, alloc=140.3MB, time=5.10 memory used=389.6MB, alloc=164.3MB, time=6.99 memory used=492.0MB, alloc=188.3MB, time=9.99 memory used=602.6MB, alloc=212.3MB, time=14.02 memory used=733.5MB, alloc=212.3MB, time=19.08 memory used=864.3MB, alloc=236.3MB, time=24.06 memory used=1019.3MB, alloc=260.3MB, time=29.88 N1 := 4339 > GB := Basis(F, plex(op(vars))); 2 2 2 2 GB := [11 x + 17 x y + 10 x, 11 x - 289 y + 340 z + 10 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1108.1MB, alloc=260.3MB, time=31.63 memory used=1315.3MB, alloc=540.3MB, time=36.27 N2 := 2605 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-20 z + 17 y + y x, 11 x + 17 x y + 10 x, 4 z x - 8 y + 7 x, -14 x z - 17 x] > J:=[op(GB),op(G)]; 2 2 2 2 2 J := [11 x + 17 x y + 10 x, 340 z - 289 y + 11 x + 10 x, 4 z x - 8 y + 7 x, -14 x z - 17 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 2, 2, 1, 3/4, 3/4, 8/11, 4/11, 3/11, 4, 10, 8, 2, 2, 2, 2, 1, 3/4, 3/4, 3/4, 1/4, 1/4, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1501.3MB, alloc=540.3MB, time=43.30 |\^/| 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(); 1428489810 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-13 y z + y, -16 x y - 19 x z - 11 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-z - 11 z + 8, -1 - 15 x + 8 y] > Problem := [F,G]; Problem := [ 2 2 [-13 y z + y, -16 x y - 19 x z - 11 y ], [-z - 11 z + 8, -1 - 15 x + 8 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.52 memory used=49.2MB, alloc=56.3MB, time=0.92 memory used=92.0MB, alloc=60.3MB, time=1.66 memory used=130.0MB, alloc=84.3MB, time=2.35 memory used=185.4MB, alloc=108.3MB, time=3.62 memory used=252.4MB, alloc=108.3MB, time=5.92 memory used=317.8MB, alloc=132.3MB, time=8.24 N1 := 2355 > GB := Basis(F, plex(op(vars))); 2 3 2 GB := [208 x y + 143 y + 19 x y, 19 z x + 11 y + 16 y x, 13 y z - y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=409.7MB, alloc=140.3MB, time=10.22 memory used=508.4MB, alloc=164.3MB, time=12.29 memory used=611.5MB, alloc=188.3MB, time=15.84 N2 := 2355 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-13 y z + y, -16 x y - 19 x z - 11 y , -z - 11 z + 8, -1 - 15 x + 8 y] > J:=[op(GB),op(G)]; 2 3 2 J := [208 x y + 143 y + 19 x y, 19 z x + 11 y + 16 y x, 13 y z - y, 2 -z - 11 z + 8, -1 - 15 x + 8 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 7, 2, 1, 2, 2, 1/2, 3/4, 3/4, 3/11, 5/11, 4/11, 5, 10, 10, 3, 1, 3, 2, 3/5, 4/5, 3/5, 5/14, 4/7, 2/7, -2, -3, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=689.3MB, alloc=188.3MB, time=18.38 |\^/| 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(); 1428489833 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [5 y z - 14 x + 6 y, 15 x y + 20 z - 16 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-12 y + 9 y z + y, -16 x z - 17 z - 12 z] > Problem := [F,G]; 2 Problem := [[5 y z - 14 x + 6 y, 15 x y + 20 z - 16 z], 2 2 [-12 y + 9 y z + y, -16 x z - 17 z - 12 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=46.9MB, alloc=32.3MB, time=0.81 memory used=66.1MB, alloc=56.3MB, time=1.12 memory used=104.0MB, alloc=60.3MB, time=1.72 memory used=140.1MB, alloc=84.3MB, time=2.30 memory used=198.1MB, alloc=92.3MB, time=3.27 memory used=254.4MB, alloc=116.3MB, time=4.16 memory used=331.6MB, alloc=140.3MB, time=5.45 memory used=423.2MB, alloc=396.3MB, time=7.02 memory used=520.7MB, alloc=420.3MB, time=8.78 memory used=630.8MB, alloc=444.3MB, time=10.77 memory used=753.1MB, alloc=468.3MB, time=13.00 memory used=887.5MB, alloc=492.3MB, time=15.55 memory used=1035.6MB, alloc=516.3MB, time=18.43 memory used=1201.9MB, alloc=540.3MB, time=21.65 memory used=1379.2MB, alloc=564.3MB, time=25.02 memory used=1560.0MB, alloc=588.3MB, time=28.48 memory used=1744.6MB, alloc=612.3MB, time=32.08 memory used=1934.6MB, alloc=636.3MB, time=35.87 memory used=2109.1MB, alloc=660.3MB, time=41.60 memory used=2286.9MB, alloc=684.3MB, time=48.24 memory used=2476.1MB, alloc=708.3MB, time=55.84 memory used=2678.2MB, alloc=732.3MB, time=63.68 memory used=2894.0MB, alloc=756.3MB, time=72.34 memory used=3124.1MB, alloc=780.3MB, time=81.74 memory used=3368.5MB, alloc=804.3MB, time=91.75 memory used=3628.2MB, alloc=828.3MB, time=102.67 memory used=3903.6MB, alloc=852.3MB, time=114.16 memory used=4194.9MB, alloc=876.3MB, time=126.48 memory used=4498.5MB, alloc=900.3MB, time=140.16 memory used=4822.0MB, alloc=924.3MB, time=155.01 memory used=5169.5MB, alloc=948.3MB, time=170.87 memory used=5540.9MB, alloc=972.3MB, time=187.84 memory used=5936.3MB, alloc=996.3MB, time=205.41 memory used=6355.5MB, alloc=1020.3MB, time=224.56 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428490133 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-15 x - 7 x z + 17 y, 10 x z + 16 z + 10 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-15 x + 12 y - 15, 10 x y - 9 y z] > Problem := [F,G]; 2 2 Problem := [[-15 x - 7 x z + 17 y, 10 x z + 16 z + 10 z], 2 [-15 x + 12 y - 15, 10 x y - 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.9MB, alloc=32.3MB, time=0.85 memory used=68.1MB, alloc=56.3MB, time=1.21 memory used=108.4MB, alloc=84.3MB, time=2.00 N1 := 1019 > GB := Basis(F, plex(op(vars))); 4 3 2 2 2 GB := [1275 x - 525 x - 3485 x y + 595 x y + 2312 y , 7 z x + 15 x - 17 y, 3 2 2 2 1275 x - 525 x - 1445 x y + 952 y z + 595 y, -75 x + 56 z + 85 y + 35 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=165.0MB, alloc=84.3MB, time=3.21 memory used=220.1MB, alloc=92.3MB, time=4.07 memory used=274.4MB, alloc=116.3MB, time=4.92 memory used=351.9MB, alloc=140.3MB, time=6.15 memory used=450.6MB, alloc=164.3MB, time=7.81 memory used=562.7MB, alloc=188.3MB, time=9.93 memory used=684.5MB, alloc=468.3MB, time=12.33 memory used=828.1MB, alloc=492.3MB, time=15.37 memory used=971.9MB, alloc=516.3MB, time=20.17 memory used=1119.0MB, alloc=540.3MB, time=25.98 memory used=1285.2MB, alloc=564.3MB, time=32.94 memory used=1475.3MB, alloc=588.3MB, time=40.48 memory used=1689.5MB, alloc=588.3MB, time=48.99 memory used=1903.8MB, alloc=612.3MB, time=57.91 N2 := 5989 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-15 x - 7 x z + 17 y, 10 x z + 16 z + 10 z, -15 x + 12 y - 15, 10 x y - 9 y z] > J:=[op(GB),op(G)]; 4 3 2 2 2 J := [1275 x - 525 x - 3485 x y + 595 x y + 2312 y , 7 z x + 15 x - 17 y, 3 2 2 2 1275 x + 952 z y - 1445 y x - 525 x + 595 y, -75 x + 56 z + 85 y + 35 z, 2 -15 x + 12 y - 15, 10 x y - 9 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 1, 2, 1, 3/4, 3/4, 5/11, 4/11, 5/11, 6, 16, 15, 4, 4, 2, 2, 1, 1, 2/3, 6/11, 1/2, 5/22, -6, -7, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1974.9MB, alloc=612.3MB, time=60.52 |\^/| 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(); 1428490206 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-11 x y - x - 17 y, -4 y - z - 17] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-13 y z + 5 z + 18, 2 y + 13 x + 12 z] > Problem := [F,G]; 2 Problem := [[-11 x y - x - 17 y, -4 y - z - 17], 2 [-13 y z + 5 z + 18, 2 y + 13 x + 12 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.52 memory used=47.2MB, alloc=32.3MB, time=0.85 memory used=67.5MB, alloc=56.3MB, time=1.24 memory used=109.5MB, alloc=60.3MB, time=2.06 memory used=147.5MB, alloc=84.3MB, time=2.79 memory used=204.4MB, alloc=108.3MB, time=4.22 memory used=272.2MB, alloc=132.3MB, time=6.78 N1 := 1681 > GB := Basis(F, plex(op(vars))); 2 GB := [11 y x + 17 y + x, 4 y + z + 17] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=365.6MB, alloc=140.3MB, time=8.45 memory used=464.7MB, alloc=164.3MB, time=10.50 N2 := 1681 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 2 -11 x y - x - 17 y, -4 y - z - 17, -13 y z + 5 z + 18, 2 y + 12 z + 13 x] > J:=[op(GB),op(G)]; 2 2 J := [11 y x + 17 y + x, 4 y + z + 17, -13 y z + 5 z + 18, 2 y + 12 z + 13 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 1, 2, 1, 1/2, 1, 3/4, 1/4, 5/12, 1/3, 4, 9, 8, 2, 1, 2, 1, 1/2, 1, 3/4, 1/4, 5/12, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=553.5MB, alloc=164.3MB, time=13.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428490221 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-12 x + 16 x - 6, -6 x y + 6 y + 4] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [14 x - 11 x + 19 y, 3 x y - 7 y z + 2 y] > Problem := [F,G]; 2 Problem := [[-12 x + 16 x - 6, -6 x y + 6 y + 4], 2 [14 x - 11 x + 19 y, 3 x y - 7 y z + 2 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 N1 := 165 > GB := Basis(F, plex(op(vars))); 2 GB := [6 x - 8 x + 3, 3 y - 4 + 12 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=27.2MB, alloc=32.3MB, time=0.62 memory used=48.0MB, alloc=32.3MB, time=0.94 N2 := 201 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-12 x + 16 x - 6, -6 x y + 6 y + 4, 14 x + 19 y - 11 x, 3 x y - 7 y z + 2 y] > J:=[op(GB),op(G)]; 2 2 J := [6 x - 8 x + 3, 3 y + 12 x - 4, 14 x + 19 y - 11 x, 3 x y - 7 y z + 2 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 8, 2, 2, 1, 1, 1, 3/4, 1/4, 1/2, 1/2, 1/12, 4, 8, 7, 2, 2, 1, 1, 1, 3/4, 1/4, 1/2, 5/12, 1/12, 0, 1, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=51.9MB, alloc=32.3MB, time=1.02 |\^/| 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(); 1428490223 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [11 x - 8 y z - 4 x, 14 y z - 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-7 x + 2 x y - 20 x, 7 x z - 11 y - 12 y] > Problem := [F,G]; 2 2 Problem := [[11 x - 8 y z - 4 x, 14 y z - 6 z ], 2 2 [-7 x + 2 x y - 20 x, 7 x z - 11 y - 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.51 memory used=47.4MB, alloc=32.3MB, time=0.84 memory used=98.1MB, alloc=68.3MB, time=1.81 memory used=144.1MB, alloc=92.3MB, time=2.65 memory used=204.7MB, alloc=92.3MB, time=3.75 memory used=263.2MB, alloc=124.3MB, time=4.93 memory used=335.7MB, alloc=148.3MB, time=6.96 memory used=420.1MB, alloc=172.3MB, time=10.16 memory used=528.4MB, alloc=172.3MB, time=14.27 N1 := 3217 > GB := Basis(F, plex(op(vars))); 4 2 2 3 2 2 GB := [-363 x + 616 x y + 264 x - 224 x y - 48 x , 2 2 2 -77 x y + 33 x z + 28 x y - 12 x z, -11 x + 8 y z + 4 x, 2 2 -77 x + 24 z + 28 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=640.0MB, alloc=172.3MB, time=17.50 memory used=735.4MB, alloc=428.3MB, time=19.03 memory used=855.5MB, alloc=452.3MB, time=21.05 memory used=991.8MB, alloc=476.3MB, time=23.47 memory used=1144.4MB, alloc=500.3MB, time=26.42 memory used=1297.1MB, alloc=524.3MB, time=31.36 memory used=1449.8MB, alloc=548.3MB, time=37.45 memory used=1624.4MB, alloc=572.3MB, time=44.59 memory used=1823.0MB, alloc=596.3MB, time=52.63 memory used=2045.7MB, alloc=620.3MB, time=61.77 N2 := 5725 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-8 z y + 11 x - 4 x, 14 y z - 6 z , -7 x + 2 x y - 20 x, 2 7 z x - 11 y - 12 y] > J:=[op(GB),op(G)]; 4 2 2 3 2 2 J := [-363 x + 616 x y + 264 x - 224 x y - 48 x , 2 2 2 -77 x y + 33 x z + 28 x y - 12 x z, -11 x + 8 y z + 4 x, 2 2 2 2 -77 x + 24 z + 28 x, -7 x + 2 x y - 20 x, 7 z x - 11 y - 12 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 2, 2, 3/4, 1, 3/4, 6/11, 5/11, 4/11, 6, 15, 15, 17 4, 4, 2, 2, 1, 5/6, 2/3, --, 8/21, 5/21, -5, -7, -2] 21 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=2194.3MB, alloc=620.3MB, time=67.65 |\^/| 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(); 1428490301 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-7 x z + 16 y - 8, 11 y + 9 x + 7 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-2 y - 18 y - 18 z, -5 x + 13 x z - 13 y ] > Problem := [F,G]; 2 2 Problem := [[-7 x z + 16 y - 8, 11 y + 9 x + 7 z], 2 2 2 [-2 y - 18 y - 18 z, -5 x + 13 x z - 13 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.52 memory used=47.1MB, alloc=32.3MB, time=0.83 memory used=66.1MB, alloc=56.3MB, time=1.15 memory used=106.9MB, alloc=60.3MB, time=1.84 memory used=145.7MB, alloc=84.3MB, time=2.48 memory used=210.7MB, alloc=92.3MB, time=3.66 memory used=268.1MB, alloc=116.3MB, time=4.73 memory used=343.5MB, alloc=140.3MB, time=6.12 memory used=435.6MB, alloc=164.3MB, time=7.79 memory used=543.7MB, alloc=188.3MB, time=9.79 memory used=647.5MB, alloc=468.3MB, time=11.73 memory used=781.1MB, alloc=492.3MB, time=15.71 memory used=922.7MB, alloc=516.3MB, time=20.53 memory used=1074.1MB, alloc=540.3MB, time=26.56 memory used=1244.7MB, alloc=564.3MB, time=33.50 memory used=1439.3MB, alloc=564.3MB, time=41.37 memory used=1633.9MB, alloc=564.3MB, time=49.38 memory used=1828.4MB, alloc=588.3MB, time=57.30 memory used=2046.9MB, alloc=588.3MB, time=66.06 memory used=2265.3MB, alloc=612.3MB, time=74.96 N1 := 7257 > GB := Basis(F, plex(op(vars))); 2 2 2 2 GB := [11 y x + 16 y + 9 x - 8, 11 y + 7 z + 9 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2515.6MB, alloc=612.3MB, time=81.87 N2 := 2295 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-7 x z + 16 y - 8, 11 y + 7 z + 9 x, -2 y - 18 y - 18 z, 2 2 -5 x + 13 x z - 13 y ] > J:=[op(GB),op(G)]; 2 2 2 2 2 J := [11 y x + 16 y + 9 x - 8, 11 y + 7 z + 9 x, -2 y - 18 y - 18 z, 2 2 -5 x + 13 x z - 13 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 2, 2, 1, 3/4, 1, 1, 1/3, 5/12, 1/3, 4, 10, 9, 3, 2, 2, 1, 3/4, 1, 3/4, 5/13, 6/13, 3/13, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=2792.0MB, alloc=612.3MB, time=91.27 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428490403 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [13 x y - 10 z - 13 x, -4 x z - 6 y z + 10 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [10 x z + 6 y z - 16 z , 4 x z - 3 z + 5 x] > Problem := [F,G]; 2 2 Problem := [[13 x y - 10 z - 13 x, -4 x z - 6 y z + 10 z ], 2 2 [10 x z + 6 y z - 16 z , 4 x z - 3 z + 5 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.51 memory used=48.1MB, alloc=32.3MB, time=0.82 memory used=67.0MB, alloc=56.3MB, time=1.12 memory used=106.2MB, alloc=60.3MB, time=1.72 memory used=143.4MB, alloc=84.3MB, time=2.29 memory used=201.1MB, alloc=92.3MB, time=3.18 memory used=256.4MB, alloc=116.3MB, time=4.04 memory used=334.7MB, alloc=140.3MB, time=5.30 memory used=424.3MB, alloc=396.3MB, time=6.74 memory used=523.4MB, alloc=420.3MB, time=8.55 memory used=634.8MB, alloc=444.3MB, time=10.57 memory used=759.9MB, alloc=468.3MB, time=12.90 memory used=897.6MB, alloc=492.3MB, time=15.57 memory used=1044.8MB, alloc=516.3MB, time=18.41 memory used=1204.3MB, alloc=540.3MB, time=21.42 memory used=1373.9MB, alloc=564.3MB, time=24.65 memory used=1541.2MB, alloc=588.3MB, time=28.84 memory used=1698.4MB, alloc=612.3MB, time=33.95 memory used=1863.9MB, alloc=636.3MB, time=39.94 memory used=2041.9MB, alloc=660.3MB, time=46.60 memory used=2235.7MB, alloc=684.3MB, time=54.03 memory used=2444.3MB, alloc=708.3MB, time=62.24 memory used=2666.0MB, alloc=732.3MB, time=71.24 memory used=2898.6MB, alloc=756.3MB, time=81.66 memory used=3155.1MB, alloc=780.3MB, time=93.55 memory used=3435.6MB, alloc=804.3MB, time=105.51 memory used=3740.0MB, alloc=828.3MB, time=119.52 memory used=4068.4MB, alloc=852.3MB, time=133.93 memory used=4420.7MB, alloc=876.3MB, time=149.39 memory used=4797.0MB, alloc=900.3MB, time=165.90 memory used=5197.2MB, alloc=900.3MB, time=183.68 memory used=5597.3MB, alloc=900.3MB, time=201.62 memory used=5997.6MB, alloc=924.3MB, time=219.71 memory used=6421.6MB, alloc=924.3MB, time=238.83 |\^/| 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(); 1428490703 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [18 x - 3 x z + 18 y , -9 x + 9 x y + z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [y - 9 y z - 15 z, -14 x z - 2 x + 11 y] > Problem := [F,G]; 2 2 2 2 Problem := [[18 x - 3 x z + 18 y , -9 x + 9 x y + z ], 2 [y - 9 y z - 15 z, -14 x z - 2 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.54 memory used=46.1MB, alloc=32.3MB, time=0.86 memory used=64.0MB, alloc=56.3MB, time=1.16 memory used=106.5MB, alloc=60.3MB, time=1.85 memory used=146.8MB, alloc=84.3MB, time=2.60 memory used=214.3MB, alloc=92.3MB, time=3.61 memory used=278.2MB, alloc=92.3MB, time=4.58 memory used=342.9MB, alloc=116.3MB, time=5.56 memory used=412.4MB, alloc=372.3MB, time=6.71 memory used=497.6MB, alloc=396.3MB, time=8.07 memory used=610.4MB, alloc=420.3MB, time=9.72 memory used=757.8MB, alloc=420.3MB, time=11.39 memory used=866.4MB, alloc=420.3MB, time=11.97 memory used=968.7MB, alloc=420.3MB, time=12.43 memory used=1058.7MB, alloc=444.3MB, time=12.85 memory used=1173.9MB, alloc=444.3MB, time=13.34 memory used=1295.3MB, alloc=444.3MB, time=13.82 memory used=1417.6MB, alloc=444.3MB, time=14.27 memory used=1551.9MB, alloc=444.3MB, time=14.75 memory used=1691.2MB, alloc=444.3MB, time=15.24 memory used=1840.6MB, alloc=444.3MB, time=15.78 memory used=1996.0MB, alloc=444.3MB, time=16.31 memory used=2150.2MB, alloc=444.3MB, time=16.83 memory used=2312.8MB, alloc=444.3MB, time=17.39 memory used=2483.9MB, alloc=444.3MB, time=17.95 memory used=2664.7MB, alloc=444.3MB, time=18.57 memory used=2853.6MB, alloc=444.3MB, time=19.21 memory used=3041.2MB, alloc=444.3MB, time=19.85 memory used=3236.2MB, alloc=444.3MB, time=20.51 memory used=3440.3MB, alloc=444.3MB, time=21.19 memory used=3659.4MB, alloc=444.3MB, time=21.92 memory used=3888.4MB, alloc=444.3MB, time=22.66 memory used=4145.5MB, alloc=444.3MB, time=23.62 memory used=4428.3MB, alloc=444.3MB, time=24.58 memory used=4730.6MB, alloc=444.3MB, time=25.57 memory used=5106.2MB, alloc=444.3MB, time=26.86 memory used=5491.8MB, alloc=444.3MB, time=28.10 memory used=5863.4MB, alloc=444.3MB, time=29.31 memory used=6207.8MB, alloc=444.3MB, time=30.45 memory used=6559.9MB, alloc=444.3MB, time=31.58 memory used=6916.8MB, alloc=444.3MB, time=32.71 memory used=7272.5MB, alloc=444.3MB, time=33.88 memory used=7607.6MB, alloc=444.3MB, time=35.00 memory used=7950.2MB, alloc=444.3MB, time=36.16 memory used=8291.9MB, alloc=444.3MB, time=37.36 memory used=8640.6MB, alloc=444.3MB, time=38.51 memory used=8994.6MB, alloc=444.3MB, time=39.73 memory used=9357.3MB, alloc=444.3MB, time=40.94 memory used=9681.5MB, alloc=444.3MB, time=42.07 memory used=9990.7MB, alloc=444.3MB, time=43.18 memory used=10305.2MB, alloc=444.3MB, time=44.26 memory used=10624.3MB, alloc=444.3MB, time=45.38 memory used=10948.8MB, alloc=444.3MB, time=46.51 memory used=11276.5MB, alloc=444.3MB, time=47.69 memory used=11602.1MB, alloc=444.3MB, time=48.86 memory used=11930.4MB, alloc=444.3MB, time=50.02 memory used=12258.8MB, alloc=444.3MB, time=51.21 memory used=12590.1MB, alloc=444.3MB, time=52.40 memory used=12925.3MB, alloc=444.3MB, time=53.57 memory used=13260.7MB, alloc=444.3MB, time=54.79 memory used=13562.5MB, alloc=444.3MB, time=55.90 memory used=13862.7MB, alloc=444.3MB, time=56.98 memory used=14165.2MB, alloc=444.3MB, time=58.09 memory used=14470.6MB, alloc=444.3MB, time=59.20 memory used=14777.3MB, alloc=444.3MB, time=60.32 memory used=15085.5MB, alloc=444.3MB, time=61.48 memory used=15393.8MB, alloc=444.3MB, time=62.62 memory used=15703.9MB, alloc=444.3MB, time=63.78 memory used=16016.9MB, alloc=444.3MB, time=64.96 memory used=16327.2MB, alloc=444.3MB, time=66.11 memory used=16627.3MB, alloc=444.3MB, time=67.18 memory used=16929.6MB, alloc=444.3MB, time=68.32 memory used=17232.4MB, alloc=444.3MB, time=69.42 memory used=17536.1MB, alloc=444.3MB, time=70.54 memory used=17843.4MB, alloc=444.3MB, time=71.66 memory used=18152.0MB, alloc=444.3MB, time=72.79 memory used=18462.6MB, alloc=444.3MB, time=73.95 memory used=18775.3MB, alloc=444.3MB, time=75.09 memory used=19089.8MB, alloc=444.3MB, time=76.28 memory used=19406.1MB, alloc=444.3MB, time=77.44 memory used=19724.7MB, alloc=444.3MB, time=78.63 memory used=20045.1MB, alloc=444.3MB, time=79.80 memory used=20341.6MB, alloc=444.3MB, time=80.92 memory used=20619.4MB, alloc=444.3MB, time=81.97 memory used=20898.7MB, alloc=444.3MB, time=83.03 memory used=21179.2MB, alloc=444.3MB, time=84.12 memory used=21462.1MB, alloc=444.3MB, time=85.25 memory used=21746.3MB, alloc=444.3MB, time=86.36 memory used=22032.1MB, alloc=444.3MB, time=87.48 memory used=22319.9MB, alloc=444.3MB, time=88.61 memory used=22608.9MB, alloc=444.3MB, time=89.71 memory used=22899.8MB, alloc=444.3MB, time=90.83 memory used=23192.5MB, alloc=444.3MB, time=91.96 memory used=23487.4MB, alloc=444.3MB, time=93.10 memory used=23783.6MB, alloc=444.3MB, time=94.22 memory used=24080.9MB, alloc=444.3MB, time=95.35 memory used=24376.0MB, alloc=444.3MB, time=96.48 memory used=24672.5MB, alloc=444.3MB, time=97.64 memory used=24969.2MB, alloc=444.3MB, time=98.80 memory used=25265.1MB, alloc=444.3MB, time=99.98 memory used=25562.6MB, alloc=444.3MB, time=101.14 memory used=25861.2MB, alloc=444.3MB, time=102.32 memory used=26160.8MB, alloc=444.3MB, time=103.46 memory used=26454.9MB, alloc=444.3MB, time=104.62 memory used=26748.4MB, alloc=444.3MB, time=105.77 memory used=27044.0MB, alloc=444.3MB, time=106.92 memory used=27340.4MB, alloc=444.3MB, time=108.10 memory used=27637.3MB, alloc=444.3MB, time=109.28 memory used=27935.6MB, alloc=444.3MB, time=110.44 memory used=28235.1MB, alloc=444.3MB, time=111.61 memory used=28536.5MB, alloc=444.3MB, time=112.80 memory used=28837.9MB, alloc=444.3MB, time=114.00 memory used=29127.8MB, alloc=444.3MB, time=115.16 memory used=29418.7MB, alloc=444.3MB, time=116.33 memory used=29710.5MB, alloc=444.3MB, time=117.49 memory used=30003.4MB, alloc=444.3MB, time=118.66 memory used=30297.7MB, alloc=444.3MB, time=119.87 memory used=30592.5MB, alloc=444.3MB, time=121.05 memory used=30888.6MB, alloc=444.3MB, time=122.23 memory used=31185.7MB, alloc=444.3MB, time=123.44 memory used=31480.9MB, alloc=444.3MB, time=124.64 memory used=31777.4MB, alloc=444.3MB, time=125.85 memory used=32074.6MB, alloc=444.3MB, time=127.06 memory used=32372.1MB, alloc=444.3MB, time=128.26 memory used=32669.6MB, alloc=444.3MB, time=129.45 memory used=32967.5MB, alloc=444.3MB, time=130.66 memory used=33266.5MB, alloc=444.3MB, time=131.87 memory used=33567.3MB, alloc=444.3MB, time=133.09 memory used=33869.6MB, alloc=444.3MB, time=134.35 memory used=34171.8MB, alloc=444.3MB, time=135.66 memory used=34476.2MB, alloc=444.3MB, time=136.95 memory used=34781.4MB, alloc=444.3MB, time=138.26 memory used=35082.5MB, alloc=444.3MB, time=139.59 memory used=35368.9MB, alloc=444.3MB, time=140.91 memory used=35639.9MB, alloc=444.3MB, time=142.15 memory used=35911.6MB, alloc=444.3MB, time=143.38 memory used=36184.7MB, alloc=444.3MB, time=144.55 memory used=36457.9MB, alloc=444.3MB, time=145.74 memory used=36731.9MB, alloc=444.3MB, time=146.97 memory used=37007.0MB, alloc=444.3MB, time=148.17 memory used=37282.5MB, alloc=444.3MB, time=149.36 memory used=37558.7MB, alloc=444.3MB, time=150.57 memory used=37835.4MB, alloc=444.3MB, time=151.80 memory used=38113.4MB, alloc=444.3MB, time=153.00 memory used=38391.9MB, alloc=444.3MB, time=154.22 memory used=38671.5MB, alloc=444.3MB, time=155.45 memory used=38951.2MB, alloc=444.3MB, time=156.64 memory used=39229.3MB, alloc=444.3MB, time=157.86 memory used=39508.1MB, alloc=444.3MB, time=159.07 memory used=39787.8MB, alloc=444.3MB, time=160.30 memory used=40068.3MB, alloc=444.3MB, time=161.50 memory used=40349.7MB, alloc=444.3MB, time=162.78 memory used=40630.2MB, alloc=444.3MB, time=164.03 memory used=40910.8MB, alloc=444.3MB, time=165.24 memory used=41192.1MB, alloc=444.3MB, time=166.46 memory used=41474.9MB, alloc=444.3MB, time=167.72 memory used=41758.2MB, alloc=444.3MB, time=168.97 memory used=42040.8MB, alloc=444.3MB, time=170.18 memory used=42322.2MB, alloc=444.3MB, time=171.39 memory used=42604.4MB, alloc=444.3MB, time=172.61 memory used=42887.3MB, alloc=444.3MB, time=173.88 memory used=43170.3MB, alloc=444.3MB, time=175.11 memory used=43454.2MB, alloc=444.3MB, time=176.36 memory used=43738.4MB, alloc=444.3MB, time=177.65 memory used=44023.0MB, alloc=444.3MB, time=178.91 memory used=44308.4MB, alloc=444.3MB, time=180.16 memory used=44587.7MB, alloc=444.3MB, time=181.43 memory used=44864.9MB, alloc=444.3MB, time=182.69 memory used=45142.8MB, alloc=444.3MB, time=183.93 memory used=45421.5MB, alloc=444.3MB, time=185.20 memory used=45700.7MB, alloc=444.3MB, time=186.47 memory used=45980.1MB, alloc=444.3MB, time=187.74 memory used=46260.0MB, alloc=444.3MB, time=189.03 memory used=46541.0MB, alloc=444.3MB, time=190.32 memory used=46822.3MB, alloc=444.3MB, time=191.52 memory used=47104.2MB, alloc=444.3MB, time=192.75 memory used=47386.9MB, alloc=444.3MB, time=194.06 memory used=47670.6MB, alloc=444.3MB, time=195.38 memory used=47952.6MB, alloc=444.3MB, time=196.70 memory used=48234.8MB, alloc=444.3MB, time=198.00 memory used=48517.3MB, alloc=444.3MB, time=199.29 memory used=48800.4MB, alloc=444.3MB, time=200.62 memory used=49083.9MB, alloc=444.3MB, time=202.00 memory used=49368.7MB, alloc=444.3MB, time=203.29 memory used=49654.1MB, alloc=444.3MB, time=204.59 memory used=49939.9MB, alloc=444.3MB, time=205.90 memory used=50226.2MB, alloc=444.3MB, time=207.27 memory used=50506.4MB, alloc=444.3MB, time=208.62 memory used=50780.6MB, alloc=444.3MB, time=209.94 memory used=51054.5MB, alloc=444.3MB, time=211.25 memory used=51328.8MB, alloc=444.3MB, time=212.55 memory used=51603.7MB, alloc=444.3MB, time=213.88 memory used=51879.0MB, alloc=444.3MB, time=215.20 memory used=52154.7MB, alloc=444.3MB, time=216.52 memory used=52431.0MB, alloc=444.3MB, time=217.87 memory used=52708.1MB, alloc=444.3MB, time=219.22 memory used=52984.5MB, alloc=444.3MB, time=220.59 memory used=53260.9MB, alloc=444.3MB, time=221.94 memory used=53538.4MB, alloc=444.3MB, time=223.35 memory used=53816.6MB, alloc=444.3MB, time=224.77 memory used=54095.2MB, alloc=444.3MB, time=226.17 memory used=54374.0MB, alloc=444.3MB, time=227.58 memory used=54652.9MB, alloc=444.3MB, time=229.00 memory used=54929.8MB, alloc=444.3MB, time=230.39 memory used=55206.6MB, alloc=444.3MB, time=231.78 memory used=55484.1MB, alloc=444.3MB, time=233.20 memory used=55761.3MB, alloc=444.3MB, time=234.62 memory used=56039.3MB, alloc=444.3MB, time=236.04 memory used=56317.6MB, alloc=444.3MB, time=237.45 memory used=56596.6MB, alloc=444.3MB, time=238.85 memory used=56875.9MB, alloc=444.3MB, time=240.24 memory used=57155.8MB, alloc=444.3MB, time=241.64 memory used=57436.1MB, alloc=444.3MB, time=243.02 memory used=57715.7MB, alloc=444.3MB, time=244.42 memory used=57992.0MB, alloc=444.3MB, time=245.86 memory used=58268.4MB, alloc=444.3MB, time=247.29 memory used=58545.8MB, alloc=444.3MB, time=248.72 memory used=58823.4MB, alloc=444.3MB, time=250.15 memory used=59102.1MB, alloc=444.3MB, time=251.60 memory used=59380.8MB, alloc=444.3MB, time=253.03 memory used=59660.0MB, alloc=444.3MB, time=254.46 memory used=59940.1MB, alloc=444.3MB, time=255.88 memory used=60220.0MB, alloc=444.3MB, time=257.33 memory used=60498.8MB, alloc=444.3MB, time=258.76 memory used=60778.1MB, alloc=444.3MB, time=260.21 memory used=61058.0MB, alloc=444.3MB, time=261.68 memory used=61339.5MB, alloc=444.3MB, time=263.15 memory used=61620.7MB, alloc=444.3MB, time=264.61 memory used=61902.4MB, alloc=444.3MB, time=266.11 memory used=62179.6MB, alloc=444.3MB, time=267.57 memory used=62454.0MB, alloc=444.3MB, time=269.03 memory used=62728.5MB, alloc=444.3MB, time=270.48 memory used=63004.5MB, alloc=444.3MB, time=271.96 memory used=63280.6MB, alloc=444.3MB, time=273.57 |\^/| 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(); 1428491003 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [-2 x y - 17 x z - 7, 19 x z + 13 z - 5] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [18 x - 13 x z + 10 y, -12 x z + 8 y - 16 y z] > Problem := [F,G]; Problem := [[-2 x y - 17 x z - 7, 19 x z + 13 z - 5], 2 2 [18 x - 13 x z + 10 y, -12 x z + 8 y - 16 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=26.7MB, alloc=32.3MB, time=0.59 memory used=47.6MB, alloc=32.3MB, time=0.94 memory used=67.5MB, alloc=56.3MB, time=1.28 memory used=108.8MB, alloc=60.3MB, time=2.00 memory used=148.7MB, alloc=84.3MB, time=2.69 memory used=210.9MB, alloc=92.3MB, time=3.79 memory used=272.1MB, alloc=116.3MB, time=5.03 memory used=350.9MB, alloc=140.3MB, time=6.55 memory used=447.0MB, alloc=140.3MB, time=8.43 memory used=536.3MB, alloc=164.3MB, time=10.16 memory used=643.4MB, alloc=188.3MB, time=12.30 memory used=756.1MB, alloc=468.3MB, time=14.67 memory used=895.6MB, alloc=492.3MB, time=17.99 memory used=1036.5MB, alloc=516.3MB, time=23.27 memory used=1188.2MB, alloc=540.3MB, time=28.92 memory used=1350.0MB, alloc=564.3MB, time=35.92 memory used=1530.7MB, alloc=588.3MB, time=44.06 memory used=1735.3MB, alloc=588.3MB, time=53.13 memory used=1939.9MB, alloc=612.3MB, time=62.39 memory used=2168.5MB, alloc=612.3MB, time=71.85 memory used=2397.0MB, alloc=612.3MB, time=80.79 memory used=2625.4MB, alloc=636.3MB, time=90.10 memory used=2877.9MB, alloc=660.3MB, time=100.73 N1 := 8147 > GB := Basis(F, plex(op(vars))); 2 GB := [38 y x + 26 y x + 218 x + 91, -38 x y + 221 z - 218] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3168.1MB, alloc=660.3MB, time=110.28 memory used=3341.2MB, alloc=660.3MB, time=114.14 memory used=3593.7MB, alloc=684.3MB, time=122.32 memory used=3883.3MB, alloc=708.3MB, time=137.08 N2 := 4439 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [-2 x y - 17 x z - 7, 19 z x + 13 z - 5, -13 z x + 18 x + 10 y, 2 -12 x z + 8 y - 16 y z] > J:=[op(GB),op(G)]; 2 J := [38 y x + 26 y x + 218 x + 91, -38 x y + 221 z - 218, 2 2 -13 z x + 18 x + 10 y, -12 x z + 8 y - 16 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 2, 2, 1, 1, 3/4, 1, 1/2, 1/3, 1/2, 4, 11, 9, 3, 2, 2, 1, 1, 1, 3/4, 7/13, 6/13, 4/13, 0, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=4152.1MB, alloc=708.3MB, time=149.68 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428491195 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-19 z + 17 x + 18, -8 y + 13 x + 18 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [17 x y - 6 y + 7 z, 17 x + 9 x y - 17] > Problem := [F,G]; 2 2 Problem := [[-19 z + 17 x + 18, -8 y + 13 x + 18 z], 2 2 [17 x y - 6 y + 7 z, 17 x + 9 x y - 17]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=27.1MB, alloc=32.3MB, time=0.55 memory used=47.5MB, alloc=32.3MB, time=0.87 memory used=66.2MB, alloc=56.3MB, time=1.16 memory used=109.5MB, alloc=60.3MB, time=1.89 memory used=150.0MB, alloc=84.3MB, time=2.63 memory used=209.1MB, alloc=108.3MB, time=3.72 memory used=287.1MB, alloc=140.3MB, time=5.20 memory used=383.3MB, alloc=164.3MB, time=6.89 memory used=496.0MB, alloc=188.3MB, time=8.93 memory used=613.6MB, alloc=212.3MB, time=12.46 memory used=738.8MB, alloc=236.3MB, time=16.58 memory used=875.9MB, alloc=260.3MB, time=21.65 memory used=1029.6MB, alloc=284.3MB, time=27.81 memory used=1207.2MB, alloc=284.3MB, time=35.12 memory used=1384.8MB, alloc=284.3MB, time=42.35 memory used=1562.4MB, alloc=308.3MB, time=49.44 memory used=1764.0MB, alloc=308.3MB, time=57.32 memory used=1965.6MB, alloc=332.3MB, time=65.18 N1 := 6929 > GB := Basis(F, plex(op(vars))); 4 2 2 2 GB := [1216 y - 3952 y x + 3211 x - 5508 x - 5832, -8 y + 18 z + 13 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2150.8MB, alloc=332.3MB, time=71.38 N2 := 1399 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-19 z + 17 x + 18, -8 y + 18 z + 13 x, -6 y + 17 y x + 7 z, 2 9 y x + 17 x - 17] > J:=[op(GB),op(G)]; 4 2 2 2 J := [1216 y - 3952 y x + 3211 x - 5508 x - 5832, -8 y + 18 z + 13 x, 2 2 -6 y + 17 y x + 7 z, 9 y x + 17 x - 17] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 2, 2, 1, 3/4, 3/4, 5/12, 1/3, 1/4, 4, 10, 10, 4, 2, 4, 1, 1, 1, 1/2, 1/2, 3/7, 1/7, 0, -2, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=2304.4MB, alloc=588.3MB, time=75.97 |\^/| 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(); 1428491281 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-16 x - 10 x y + 14 x, -6 x y - 17 x + 15 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [20 y + 15 z + 6 z, 8 y - 14 y z + 15 z ] > Problem := [F,G]; 2 Problem := [[-16 x - 10 x y + 14 x, -6 x y - 17 x + 15 z], 2 2 2 2 [20 y + 15 z + 6 z, 8 y - 14 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.9MB, alloc=32.3MB, time=0.53 memory used=47.0MB, alloc=56.3MB, time=0.87 memory used=87.5MB, alloc=60.3MB, time=1.51 memory used=126.8MB, alloc=60.3MB, time=2.12 memory used=165.4MB, alloc=84.3MB, time=2.78 memory used=226.1MB, alloc=108.3MB, time=3.95 N1 := 865 > GB := Basis(F, plex(op(vars))); 2 2 GB := [8 x + 5 x y - 7 x, 48 x + 75 z - 127 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=301.7MB, alloc=116.3MB, time=5.58 memory used=382.2MB, alloc=116.3MB, time=6.86 memory used=462.5MB, alloc=140.3MB, time=8.48 N2 := 895 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-16 x - 10 x y + 14 x, -6 x y - 17 x + 15 z, 15 z + 20 y + 6 z, 2 2 15 z - 14 z y + 8 y ] > J:=[op(GB),op(G)]; 2 2 2 2 J := [8 x + 5 x y - 7 x, 48 x + 75 z - 127 x, 15 z + 20 y + 6 z, 2 2 15 z - 14 z y + 8 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 2, 1/2, 1, 3/4, 5/12, 5/12, 5/12, 4, 8, 8, 2, 2, 2, 2, 1/2, 3/4, 3/4, 5/12, 1/3, 5/12, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=483.6MB, alloc=140.3MB, time=9.10 |\^/| 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(); 1428491291 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-7 x y + 19 y z + 7 x, 4 z - 2 y + 5] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-19 y z + 2 z - 14 y, -18 x y - 12 y + 7] > Problem := [F,G]; 2 Problem := [[-7 x y + 19 y z + 7 x, 4 z - 2 y + 5], 2 [-19 y z + 2 z - 14 y, -18 x y - 12 y + 7]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=26.4MB, alloc=32.3MB, time=0.54 memory used=46.7MB, alloc=32.3MB, time=0.85 memory used=65.3MB, alloc=56.3MB, time=1.14 memory used=106.2MB, alloc=60.3MB, time=1.79 memory used=146.5MB, alloc=84.3MB, time=2.44 memory used=210.7MB, alloc=92.3MB, time=3.54 memory used=269.2MB, alloc=116.3MB, time=4.69 memory used=346.7MB, alloc=140.3MB, time=6.16 memory used=443.9MB, alloc=164.3MB, time=7.97 memory used=551.2MB, alloc=188.3MB, time=10.82 memory used=662.7MB, alloc=212.3MB, time=14.73 memory used=788.2MB, alloc=236.3MB, time=19.85 memory used=937.8MB, alloc=236.3MB, time=26.13 memory used=1087.5MB, alloc=260.3MB, time=32.09 N1 := 4341 > GB := Basis(F, plex(op(vars))); 2 2 2 3 2 2 GB := [-196 x y + 392 x y + 722 y - 196 x - 1805 y , 2 2 2 -196 x y + 196 x + 532 x z + 722 y - 1805 y, -7 x y + 19 y z + 7 x, 2 4 z - 2 y + 5] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1206.4MB, alloc=260.3MB, time=34.71 memory used=1411.4MB, alloc=516.3MB, time=37.98 memory used=1619.7MB, alloc=540.3MB, time=41.26 memory used=1856.4MB, alloc=564.3MB, time=44.95 memory used=2117.9MB, alloc=588.3MB, time=49.33 memory used=2371.2MB, alloc=612.3MB, time=54.01 memory used=2631.0MB, alloc=636.3MB, time=59.13 memory used=2907.0MB, alloc=660.3MB, time=64.20 memory used=3187.8MB, alloc=684.3MB, time=69.68 memory used=3453.4MB, alloc=708.3MB, time=77.49 memory used=3688.6MB, alloc=732.3MB, time=86.51 memory used=3930.7MB, alloc=756.3MB, time=96.73 memory used=4185.1MB, alloc=780.3MB, time=107.45 memory used=4452.9MB, alloc=804.3MB, time=119.04 memory used=4730.5MB, alloc=828.3MB, time=131.91 memory used=5021.6MB, alloc=852.3MB, time=146.42 memory used=5336.7MB, alloc=876.3MB, time=160.70 memory used=5675.7MB, alloc=900.3MB, time=176.06 memory used=6038.7MB, alloc=924.3MB, time=193.37 memory used=6425.6MB, alloc=948.3MB, time=211.60 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428491591 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-14 - y - 6 z, -11 y + 6 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [18 x + 5 y - 3, -4 y - 9 z + 16 x] > Problem := [F,G]; Problem := 2 2 2 2 2 [[-14 - y - 6 z, -11 y + 6 z], [18 x + 5 y - 3, -4 y - 9 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=47.5MB, alloc=32.3MB, time=0.82 memory used=67.5MB, alloc=56.3MB, time=1.14 memory used=109.7MB, alloc=60.3MB, time=1.87 memory used=148.4MB, alloc=84.3MB, time=2.53 memory used=205.0MB, alloc=108.3MB, time=3.72 N1 := 1541 > GB := Basis(F, plex(op(vars))); 2 GB := [11 y + y + 14, 6 z + y + 14] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=307.7MB, alloc=140.3MB, time=6.50 N2 := 387 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [-14 - y - 6 z, -11 y + 6 z, 5 y + 18 x - 3, -9 z - 4 y + 16 x] > J:=[op(GB),op(G)]; 2 2 2 2 2 J := [11 y + y + 14, 6 z + y + 14, 5 y + 18 x - 3, -9 z - 4 y + 16 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 2, 2, 2, 1/2, 1, 3/4, 2/11, 4/11, 3/11, 4, 8, 7, 2, 2, 2, 2, 1/2, 1, 1/2, 1/6, 5/12, 1/6, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=344.5MB, alloc=140.3MB, time=7.16 |\^/| 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(); 1428491604 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [14 - 11 x - 7 z, 7 x y - 13 x z + y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-6 x + 5 z + 1, -18 x + 12 y - 18 y] > Problem := [F,G]; 2 Problem := [[14 - 11 x - 7 z, 7 x y - 13 x z + y ], 2 2 2 [-6 x + 5 z + 1, -18 x + 12 y - 18 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=49.8MB, alloc=56.3MB, time=0.98 memory used=93.5MB, alloc=60.3MB, time=1.77 memory used=132.8MB, alloc=84.3MB, time=2.44 memory used=191.1MB, alloc=108.3MB, time=3.89 memory used=262.3MB, alloc=108.3MB, time=6.27 N1 := 1765 > GB := Basis(F, plex(op(vars))); 2 2 GB := [7 y + 49 y x + 143 x - 182 x, 7 z + 11 x - 14] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 507 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [14 - 11 x - 7 z, -13 z x + y + 7 y x, -6 x + 5 z + 1, 2 2 -18 x + 12 y - 18 y] > J:=[op(GB),op(G)]; 2 2 2 J := [7 y + 49 y x + 143 x - 182 x, 7 z + 11 x - 14, -6 x + 5 z + 1, 2 2 -18 x + 12 y - 18 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 2, 2, 1, 1, 1/2, 3/4, 5/12, 1/3, 1/4, 4, 8, 7, 2, 2, 2, 1, 1, 1/2, 1/2, 6/13, 4/13, 2/13, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=326.5MB, alloc=108.3MB, time=7.40 |\^/| 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(); 1428491618 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-11 x y - 9 x - 2 y, 15 x y + 13 y + z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [15 x z, 16 x - 16 x z + 4] > Problem := [F,G]; Problem := 2 2 2 [[-11 x y - 9 x - 2 y, 15 x y + 13 y + z ], [15 x z, 16 x - 16 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=4.1MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=49.6MB, alloc=32.3MB, time=0.89 memory used=70.2MB, alloc=56.3MB, time=1.25 N1 := 827 > GB := Basis(F, plex(op(vars))); 2 2 GB := [11 y x + 2 y + 9 x, 143 y + 11 z - 135 x - 30 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=141.2MB, alloc=92.3MB, time=2.68 memory used=213.3MB, alloc=92.3MB, time=4.13 N2 := 813 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-11 x y - 9 x - 2 y, z + 13 y + 15 y x, 15 z x, 16 x - 16 x z + 4] > J:=[op(GB),op(G)]; 2 2 J := [11 y x + 2 y + 9 x, 143 y + 11 z - 135 x - 30 y, 15 z x, 2 16 x - 16 x z + 4] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 2, 1, 1/2, 3/4, 1/2, 1/3, 1/4, 4, 9, 8, 2, 2, 2, 2, 1, 1/2, 3/4, 6/13, 4/13, 3/13, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=218.9MB, alloc=92.3MB, time=4.27 |\^/| 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(); 1428491625 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [12 x z - y - 11 y z, 10 y z + 15 z - 20] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-14 x y + 3 y z + 14 z, 6 y - 13 z - 11] > Problem := [F,G]; 2 2 Problem := [[12 x z - y - 11 y z, 10 y z + 15 z - 20], 2 2 [-14 x y + 3 y z + 14 z, 6 y - 13 z - 11]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.49 memory used=46.3MB, alloc=56.3MB, time=0.79 memory used=89.3MB, alloc=60.3MB, time=1.40 memory used=133.8MB, alloc=68.3MB, time=1.97 memory used=172.0MB, alloc=92.3MB, time=2.56 memory used=236.6MB, alloc=92.3MB, time=3.47 memory used=305.3MB, alloc=116.3MB, time=4.38 memory used=392.2MB, alloc=116.3MB, time=5.69 memory used=461.0MB, alloc=372.3MB, time=6.52 memory used=551.8MB, alloc=372.3MB, time=7.70 memory used=636.7MB, alloc=396.3MB, time=8.98 memory used=746.2MB, alloc=420.3MB, time=10.63 memory used=879.3MB, alloc=420.3MB, time=12.56 memory used=1010.0MB, alloc=444.3MB, time=14.41 memory used=1127.8MB, alloc=444.3MB, time=15.86 memory used=1266.4MB, alloc=468.3MB, time=17.91 memory used=1375.4MB, alloc=492.3MB, time=19.65 memory used=1485.1MB, alloc=492.3MB, time=21.37 memory used=1608.5MB, alloc=516.3MB, time=23.63 memory used=1725.8MB, alloc=516.3MB, time=25.83 memory used=1851.5MB, alloc=540.3MB, time=28.01 memory used=1955.3MB, alloc=564.3MB, time=29.96 memory used=2074.6MB, alloc=588.3MB, time=32.27 memory used=2184.6MB, alloc=588.3MB, time=34.51 memory used=2299.5MB, alloc=612.3MB, time=36.85 memory used=2425.9MB, alloc=636.3MB, time=39.45 memory used=2549.6MB, alloc=660.3MB, time=42.05 memory used=2648.8MB, alloc=684.3MB, time=44.24 memory used=2759.9MB, alloc=684.3MB, time=46.62 memory used=2868.0MB, alloc=708.3MB, time=48.95 memory used=2980.9MB, alloc=732.3MB, time=51.40 memory used=3077.2MB, alloc=732.3MB, time=53.58 memory used=3165.0MB, alloc=756.3MB, time=55.62 memory used=3261.3MB, alloc=756.3MB, time=57.77 memory used=3340.4MB, alloc=780.3MB, time=59.68 memory used=3420.8MB, alloc=780.3MB, time=61.62 memory used=3504.8MB, alloc=804.3MB, time=63.66 memory used=3583.1MB, alloc=804.3MB, time=65.56 memory used=3669.7MB, alloc=828.3MB, time=67.67 memory used=3744.8MB, alloc=828.3MB, time=69.64 memory used=4088.8MB, alloc=852.3MB, time=76.76 memory used=4428.9MB, alloc=876.3MB, time=83.55 memory used=4792.2MB, alloc=900.3MB, time=91.17 memory used=5150.5MB, alloc=924.3MB, time=98.98 memory used=5501.4MB, alloc=948.3MB, time=106.54 memory used=5852.1MB, alloc=972.3MB, time=114.48 memory used=6206.9MB, alloc=996.3MB, time=122.13 memory used=6533.8MB, alloc=1020.3MB, time=131.88 memory used=6818.3MB, alloc=1044.3MB, time=143.93 memory used=7109.1MB, alloc=1068.3MB, time=156.34 memory used=7409.3MB, alloc=1092.3MB, time=169.21 memory used=7720.7MB, alloc=1116.3MB, time=182.83 memory used=8044.5MB, alloc=1140.3MB, time=197.01 memory used=8381.2MB, alloc=1164.3MB, time=211.99 memory used=8732.0MB, alloc=1188.3MB, time=227.64 |\^/| 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(); 1428491925 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-16 y - 4 z - 6 z, -2 x z + 19 y z + 15 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [6 x + 14 x z, 4 z - 19 z - 6] > Problem := [F,G]; 2 2 Problem := [[-16 y - 4 z - 6 z, -2 x z + 19 y z + 15 z], 2 2 [6 x + 14 x z, 4 z - 19 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.6MB, alloc=32.3MB, time=0.80 memory used=66.8MB, alloc=56.3MB, time=1.10 memory used=109.2MB, alloc=60.3MB, time=1.86 memory used=146.1MB, alloc=84.3MB, time=2.54 memory used=201.9MB, alloc=108.3MB, time=3.54 memory used=270.0MB, alloc=132.3MB, time=5.12 memory used=348.2MB, alloc=156.3MB, time=7.70 memory used=445.4MB, alloc=156.3MB, time=11.21 memory used=542.5MB, alloc=156.3MB, time=14.53 memory used=639.8MB, alloc=180.3MB, time=17.86 N1 := 3621 > GB := Basis(F, plex(op(vars))); 2 3 2 2 2 GB := [-2 x y + 19 y + 15 y , -2 x z + 19 y z + 15 z, 2 z + 8 y + 3 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=695.7MB, alloc=180.3MB, time=18.98 memory used=834.1MB, alloc=188.3MB, time=21.40 memory used=957.3MB, alloc=212.3MB, time=24.54 memory used=1078.9MB, alloc=236.3MB, time=29.04 memory used=1224.6MB, alloc=260.3MB, time=34.39 N2 := 3621 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 2 2 2 -16 y - 4 z - 6 z, -2 x z + 19 y z + 15 z, 6 x + 14 x z, 4 z - 19 z - 6 ] > J:=[op(GB),op(G)]; 2 3 2 2 2 J := [-2 x y + 19 y + 15 y , -2 x z + 19 y z + 15 z, 2 z + 8 y + 3 z, 2 2 6 x + 14 x z, 4 z - 19 z - 6] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 8, 2, 2, 2, 2, 1/2, 1/2, 1, 3/11, 2/11, 8/11, 5, 10, 11, 3, 2, 3, 2, 3/5, 3/5, 4/5, 2/7, 5/14, 4/7, -2, -3, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1300.8MB, alloc=260.3MB, time=36.76 |\^/| 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(); 1428491967 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [3 x + 5 x z + 7 x, 5 z - x - 14] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [19 x y - 2 x - 11 z, -19 + 6 x] > Problem := [F,G]; Problem := 2 2 [[3 x + 5 x z + 7 x, 5 z - x - 14], [19 x y - 2 x - 11 z, -19 + 6 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=27.7MB, alloc=32.3MB, time=0.56 memory used=49.3MB, alloc=56.3MB, time=1.00 N1 := 457 > GB := Basis(F, plex(op(vars))); 3 2 2 2 GB := [9 x + 37 x - 21 x, 3 x + 5 x z + 7 x, 5 z - x - 14] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 457 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [3 x + 5 x z + 7 x, 5 z - x - 14, 19 y x - 11 z - 2 x, 6 x - 19] > J:=[op(GB),op(G)]; 3 2 2 2 J := [9 x + 37 x - 21 x, 3 x + 5 x z + 7 x, 5 z - x - 14, 19 y x - 11 z - 2 x, 6 x - 19] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 7, 2, 2, 1, 2, 1, 1/4, 3/4, 7/11, 1/11, 3/11, 5, 9, 10, 3, 3, 1, 2, 1, 1/5, 3/5, 5/7, 1/14, 3/14, -1, -3, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=100.8MB, alloc=92.3MB, time=1.95 |\^/| 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(); 1428491969 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [20 x y - x + 19 z, 6 x + 11 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [4 x y - 15 y - 20, 7 x - 4 y - 12 y z] > Problem := [F,G]; 2 2 Problem := [[20 x y - x + 19 z, 6 x + 11 y ], 2 2 2 [4 x y - 15 y - 20, 7 x - 4 y - 12 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=48.2MB, alloc=56.3MB, time=0.90 N1 := 387 > GB := Basis(F, plex(op(vars))); 2 2 GB := [11 y + 6 x , 20 y x + 19 z - x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=90.7MB, alloc=60.3MB, time=1.69 memory used=132.0MB, alloc=60.3MB, time=2.34 N2 := 387 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 2 2 2 2 20 y x + 19 z - x, 11 y + 6 x , -15 y + 4 y x - 20, -12 z y - 4 y + 7 x ] > J:=[op(GB),op(G)]; J := [ 2 2 2 2 2 11 y + 6 x , 20 y x + 19 z - x, -15 y + 4 y x - 20, -12 z y - 4 y + 7 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 2, 1, 1, 1, 1/2, 5/11, 6/11, 2/11, 4, 10, 8, 2, 2, 2, 1, 1, 1, 1/2, 5/11, 6/11, 2/11, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=155.8MB, alloc=60.3MB, time=2.76 |\^/| 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(); 1428491972 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [15 x - 9 x y + 17 x, 5 + 2 y + 13 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [10 x - 8 y z - 7 z, 15 x - 2 y + 19 z] > Problem := [F,G]; 2 Problem := [[15 x - 9 x y + 17 x, 5 + 2 y + 13 z], 2 [10 x - 8 y z - 7 z, 15 x - 2 y + 19 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=46.5MB, alloc=56.3MB, time=0.79 memory used=90.5MB, alloc=60.3MB, time=1.59 memory used=129.5MB, alloc=84.3MB, time=2.29 memory used=187.4MB, alloc=108.3MB, time=3.71 N1 := 1591 > GB := Basis(F, plex(op(vars))); 2 GB := [-15 x + 9 x y - 17 x, 13 z + 2 y + 5] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=257.5MB, alloc=108.3MB, time=6.01 memory used=336.2MB, alloc=140.3MB, time=7.34 memory used=436.7MB, alloc=164.3MB, time=9.61 N2 := 1591 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [15 x - 9 x y + 17 x, 13 z + 2 y + 5, -8 z y + 10 x - 7 z, 19 z - 2 y + 15 x] > J:=[op(GB),op(G)]; 2 2 J := [-15 x + 9 x y - 17 x, 13 z + 2 y + 5, -8 z y + 10 x - 7 z, 19 z - 2 y + 15 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 6, 2, 2, 1, 1, 3/4, 1, 3/4, 5/12, 1/3, 1/3, 4, 10, 6, 2, 2, 1, 1, 3/4, 1, 3/4, 5/12, 1/3, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=498.1MB, alloc=164.3MB, time=11.79 |\^/| 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(); 1428491985 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [19 x y + 4 y + 5 y z, -16 x - 18 y z - 15 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [5 x z - 3 z - 19, 14 x y - 19 z - 7 z] > Problem := [F,G]; 2 2 2 Problem := [[19 x y + 4 y + 5 y z, -16 x - 18 y z - 15 z ], 2 2 [5 x z - 3 z - 19, 14 x y - 19 z - 7 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.51 memory used=47.9MB, alloc=32.3MB, time=0.83 memory used=67.6MB, alloc=56.3MB, time=1.14 memory used=107.1MB, alloc=60.3MB, time=1.76 memory used=145.1MB, alloc=84.3MB, time=2.40 memory used=205.4MB, alloc=92.3MB, time=3.41 memory used=266.5MB, alloc=116.3MB, time=4.40 memory used=351.1MB, alloc=116.3MB, time=5.74 memory used=432.2MB, alloc=396.3MB, time=7.07 memory used=540.1MB, alloc=420.3MB, time=8.91 memory used=670.4MB, alloc=444.3MB, time=11.17 memory used=823.6MB, alloc=468.3MB, time=13.89 memory used=954.1MB, alloc=468.3MB, time=16.18 memory used=1101.8MB, alloc=492.3MB, time=18.83 memory used=1243.4MB, alloc=516.3MB, time=21.39 memory used=1396.5MB, alloc=540.3MB, time=24.30 memory used=1586.5MB, alloc=564.3MB, time=27.93 memory used=1768.6MB, alloc=588.3MB, time=31.29 memory used=1948.6MB, alloc=612.3MB, time=34.53 memory used=2104.7MB, alloc=636.3MB, time=37.53 memory used=2274.9MB, alloc=660.3MB, time=40.86 memory used=2516.9MB, alloc=684.3MB, time=48.25 memory used=2757.4MB, alloc=708.3MB, time=56.93 memory used=3005.6MB, alloc=732.3MB, time=66.23 memory used=3267.5MB, alloc=756.3MB, time=76.29 memory used=3533.8MB, alloc=780.3MB, time=87.61 memory used=3819.1MB, alloc=804.3MB, time=99.97 memory used=4128.4MB, alloc=828.3MB, time=113.58 memory used=4461.6MB, alloc=852.3MB, time=127.85 memory used=4818.7MB, alloc=876.3MB, time=143.06 memory used=5199.8MB, alloc=900.3MB, time=159.42 memory used=5604.8MB, alloc=900.3MB, time=177.19 memory used=6009.8MB, alloc=924.3MB, time=195.18 memory used=6438.7MB, alloc=924.3MB, time=214.17 memory used=6867.5MB, alloc=924.3MB, time=232.71 |\^/| 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(); 1428492285 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [12 y z - 8 x - 13 z, 15 y - 13 z + 11 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [3 x - 19 y z + 8 z , -14 x y + 9 y - 7 y] > Problem := [F,G]; 2 2 Problem := [[12 y z - 8 x - 13 z, 15 y - 13 z + 11 x], 2 2 2 [3 x - 19 y z + 8 z , -14 x y + 9 y - 7 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.56 memory used=47.4MB, alloc=32.3MB, time=0.90 memory used=66.4MB, alloc=56.3MB, time=1.23 memory used=107.4MB, alloc=60.3MB, time=1.87 memory used=147.4MB, alloc=84.3MB, time=2.49 memory used=208.8MB, alloc=92.3MB, time=3.49 memory used=272.6MB, alloc=116.3MB, time=4.46 memory used=357.3MB, alloc=140.3MB, time=5.77 memory used=446.0MB, alloc=420.3MB, time=7.32 memory used=567.3MB, alloc=444.3MB, time=9.53 memory used=705.4MB, alloc=468.3MB, time=12.18 memory used=855.0MB, alloc=492.3MB, time=14.88 memory used=1019.3MB, alloc=516.3MB, time=17.81 memory used=1199.5MB, alloc=540.3MB, time=21.01 memory used=1389.3MB, alloc=564.3MB, time=24.45 memory used=1583.9MB, alloc=588.3MB, time=28.35 memory used=1762.2MB, alloc=612.3MB, time=34.12 memory used=1948.1MB, alloc=636.3MB, time=40.70 memory used=2147.5MB, alloc=660.3MB, time=48.41 memory used=2361.4MB, alloc=684.3MB, time=56.63 memory used=2589.7MB, alloc=708.3MB, time=66.08 memory used=2833.3MB, alloc=732.3MB, time=76.39 memory used=3086.6MB, alloc=756.3MB, time=87.30 memory used=3362.6MB, alloc=780.3MB, time=99.55 memory used=3662.5MB, alloc=804.3MB, time=112.77 memory used=3986.4MB, alloc=828.3MB, time=126.60 memory used=4334.2MB, alloc=852.3MB, time=141.84 memory used=4706.0MB, alloc=852.3MB, time=158.01 memory used=5077.7MB, alloc=876.3MB, time=174.20 memory used=5473.3MB, alloc=876.3MB, time=192.11 |\^/| 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(); 1428492585 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [11 x + 2 y + 17 z, 12 x + 12 x y + 19 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [18 y z + 10 x, 14 x y + 7 z - 8 z] > Problem := [F,G]; 2 2 2 Problem := [[11 x + 2 y + 17 z, 12 x + 12 x y + 19 y z], 2 [18 y z + 10 x, 14 x y + 7 z - 8 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.57 memory used=46.6MB, alloc=56.3MB, time=0.89 memory used=88.1MB, alloc=60.3MB, time=1.50 memory used=162.6MB, alloc=100.3MB, time=2.61 memory used=236.1MB, alloc=100.3MB, time=3.68 memory used=311.0MB, alloc=124.3MB, time=4.74 memory used=374.7MB, alloc=380.3MB, time=5.73 memory used=471.9MB, alloc=404.3MB, time=7.20 memory used=591.7MB, alloc=428.3MB, time=9.04 memory used=717.1MB, alloc=452.3MB, time=11.28 memory used=863.4MB, alloc=476.3MB, time=13.74 memory used=1034.9MB, alloc=500.3MB, time=16.45 memory used=1204.4MB, alloc=524.3MB, time=19.46 memory used=1374.7MB, alloc=548.3MB, time=24.34 memory used=1544.1MB, alloc=572.3MB, time=30.42 memory used=1719.9MB, alloc=596.3MB, time=37.90 memory used=1912.8MB, alloc=620.3MB, time=46.08 memory used=2129.5MB, alloc=644.3MB, time=55.68 memory used=2370.2MB, alloc=668.3MB, time=65.67 memory used=2634.9MB, alloc=668.3MB, time=77.10 memory used=2899.6MB, alloc=692.3MB, time=88.32 memory used=3188.2MB, alloc=692.3MB, time=100.17 memory used=3477.0MB, alloc=716.3MB, time=112.04 N1 := 8601 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 GB := [38 y + 209 y x - 204 y x - 204 x , 2 y + 11 x + 17 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3703.6MB, alloc=716.3MB, time=118.89 memory used=3833.0MB, alloc=716.3MB, time=121.41 memory used=3992.0MB, alloc=716.3MB, time=124.76 N2 := 2933 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [2 y + 11 x + 17 z, 19 z y + 12 y x + 12 x , 18 y z + 10 x, 2 7 z + 14 y x - 8 z] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [38 y + 209 y x - 204 y x - 204 x , 2 y + 11 x + 17 z, 18 y z + 10 x, 2 7 z + 14 y x - 8 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 12, 8, 2, 2, 2, 2, 1, 1, 1, 5/11, 5/11, 5/11, 4, 11, 9, 3, 2, 3, 2, 1, 1, 3/4, 1/2, 1/2, 1/3, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=4307.1MB, alloc=716.3MB, time=137.08 |\^/| 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(); 1428492784 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [7 x - z - 11, -6 y z + 20 y - 14] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-16 x - 12 x y + 5 z, 1 - 7 x + y] > Problem := [F,G]; Problem := 2 2 [[7 x - z - 11, -6 y z + 20 y - 14], [-16 x - 12 x y + 5 z, 1 - 7 x + y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=46.5MB, alloc=32.3MB, time=0.79 memory used=67.0MB, alloc=56.3MB, time=1.18 memory used=107.9MB, alloc=60.3MB, time=1.87 memory used=145.3MB, alloc=84.3MB, time=2.51 memory used=201.5MB, alloc=108.3MB, time=3.55 memory used=271.5MB, alloc=132.3MB, time=5.66 memory used=358.3MB, alloc=132.3MB, time=8.58 N1 := 2255 > GB := Basis(F, plex(op(vars))); 2 2 GB := [21 y x - 43 y + 7, -7 x + z + 11] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 483 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [7 x - z - 11, -6 y z + 20 y - 14, -16 x - 12 x y + 5 z, 1 - 7 x + y] > J:=[op(GB),op(G)]; 2 2 2 J := [21 y x - 43 y + 7, -7 x + z + 11, -16 x - 12 x y + 5 z, 1 - 7 x + y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 2, 1, 1, 3/4, 3/4, 3/4, 1/3, 1/3, 1/4, 4, 9, 8, 3, 2, 1, 1, 1, 3/4, 1/2, 5/12, 1/3, 1/6, 0, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=435.7MB, alloc=140.3MB, time=10.25 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428492797 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [3 x y + 14 x z - 12 x, -10 x z + 11 z + 13] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [20 x + 14 z - 4, 4 x - 8 z - 5 z] > Problem := [F,G]; Problem := [[3 x y + 14 x z - 12 x, -10 x z + 11 z + 13], 2 2 2 [20 x + 14 z - 4, 4 x - 8 z - 5 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.48 memory used=47.9MB, alloc=32.3MB, time=0.84 memory used=67.7MB, alloc=56.3MB, time=1.19 memory used=108.8MB, alloc=84.3MB, time=1.89 memory used=167.5MB, alloc=84.3MB, time=3.59 N1 := 1457 > GB := Basis(F, plex(op(vars))); 2 2 GB := [30 x y - 120 x - 33 x y + 314 x, 15 x y - 60 x + 77 z + 91] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=221.6MB, alloc=84.3MB, time=4.75 memory used=279.7MB, alloc=108.3MB, time=5.81 N2 := 1185 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [3 x y + 14 x z - 12 x, -10 x z + 11 z + 13, 20 x + 14 z - 4, 2 2 -8 z + 4 x - 5 z] > J:=[op(GB),op(G)]; 2 2 J := [30 x y - 120 x - 33 x y + 314 x, 15 y x + 77 z - 60 x + 91, 2 2 2 20 x + 14 z - 4, -8 z + 4 x - 5 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 1, 2, 1, 1/4, 1, 1/2, 1/12, 1/2, 4, 9, 9, 3, 2, 1, 2, 1, 1/2, 3/4, 4/7, 3/14, 2/7, 0, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=344.1MB, alloc=108.3MB, time=7.68 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428492806 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-z + 15 y - 13 z, 8 x + 8 y - 11] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [17 x - 2 z + 11, -11 y z + 10] > Problem := [F,G]; Problem := 2 2 2 [[-z + 15 y - 13 z, 8 x + 8 y - 11], [17 x - 2 z + 11, -11 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=0.17 memory used=26.8MB, alloc=32.3MB, time=0.50 memory used=48.3MB, alloc=32.3MB, time=0.81 memory used=67.9MB, alloc=56.3MB, time=1.13 memory used=109.9MB, alloc=60.3MB, time=1.86 memory used=147.1MB, alloc=84.3MB, time=2.53 memory used=204.1MB, alloc=84.3MB, time=3.50 memory used=254.2MB, alloc=108.3MB, time=4.52 memory used=318.4MB, alloc=132.3MB, time=6.30 memory used=396.8MB, alloc=156.3MB, time=9.12 memory used=499.3MB, alloc=156.3MB, time=12.73 N1 := 3143 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [8 x + 8 y - 11, 120 x + 8 z + 104 z - 165] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=603.7MB, alloc=156.3MB, time=15.91 memory used=659.0MB, alloc=164.3MB, time=16.96 memory used=777.0MB, alloc=188.3MB, time=20.09 N2 := 1875 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-z - 13 z + 15 y, 8 x + 8 y - 11, 17 x - 2 z + 11, -11 y z + 10] > J:=[op(GB),op(G)]; 2 2 2 2 J := [8 x + 8 y - 11, 8 z + 120 x + 104 z - 165, 17 x - 2 z + 11, -11 y z + 10] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 8, 2, 2, 1, 2, 1/2, 3/4, 3/4, 2/11, 3/11, 4/11, 4, 8, 8, 2, 2, 1, 2, 3/4, 1/2, 3/4, 1/4, 1/6, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=848.2MB, alloc=188.3MB, time=22.88 |\^/| 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(); 1428492838 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [20 y z + 4 z + 10 y, 4 x z + 4 y + 15 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-2 x y + 7 y + 17 y z, 12 x z - 18 y + 8 y z] > Problem := [F,G]; 2 2 Problem := [[20 y z + 4 z + 10 y, 4 x z + 4 y + 15 z], 2 2 [-2 x y + 7 y + 17 y z, 12 x z - 18 y + 8 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=32.3MB, time=0.82 memory used=65.9MB, alloc=56.3MB, time=1.13 memory used=104.4MB, alloc=60.3MB, time=1.75 memory used=141.4MB, alloc=84.3MB, time=2.35 memory used=203.3MB, alloc=92.3MB, time=3.33 memory used=263.3MB, alloc=116.3MB, time=4.34 memory used=344.0MB, alloc=140.3MB, time=5.76 memory used=416.8MB, alloc=396.3MB, time=6.98 memory used=523.5MB, alloc=420.3MB, time=8.96 memory used=644.5MB, alloc=444.3MB, time=11.26 memory used=776.8MB, alloc=468.3MB, time=13.67 memory used=922.3MB, alloc=492.3MB, time=16.31 memory used=1084.3MB, alloc=516.3MB, time=19.22 memory used=1255.8MB, alloc=540.3MB, time=22.42 memory used=1437.6MB, alloc=564.3MB, time=25.87 memory used=1614.1MB, alloc=588.3MB, time=29.26 memory used=1788.5MB, alloc=612.3MB, time=32.58 memory used=1961.1MB, alloc=636.3MB, time=35.89 memory used=2126.7MB, alloc=660.3MB, time=39.09 memory used=2289.7MB, alloc=684.3MB, time=42.33 memory used=2434.1MB, alloc=708.3MB, time=45.45 memory used=2671.2MB, alloc=732.3MB, time=53.63 memory used=2910.6MB, alloc=756.3MB, time=62.81 memory used=3160.1MB, alloc=780.3MB, time=72.31 memory used=3422.1MB, alloc=804.3MB, time=83.19 memory used=3697.7MB, alloc=828.3MB, time=95.24 memory used=3987.0MB, alloc=852.3MB, time=107.12 memory used=4291.2MB, alloc=876.3MB, time=120.03 memory used=4610.9MB, alloc=900.3MB, time=133.51 memory used=4946.2MB, alloc=924.3MB, time=148.49 memory used=5297.6MB, alloc=948.3MB, time=165.25 memory used=5659.7MB, alloc=972.3MB, time=183.22 memory used=6042.4MB, alloc=996.3MB, time=200.35 memory used=6449.0MB, alloc=1020.3MB, time=218.54 |\^/| 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(); 1428493138 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [16 x + 7 y z + z , -11 x y + 19 y + z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-12 x y + 19 z - 15, -15 x - 17 x y + 12 z] > Problem := [F,G]; 2 2 2 2 Problem := [[16 x + 7 y z + z , -11 x y + 19 y + z ], 2 2 [-12 x y + 19 z - 15, -15 x - 17 x y + 12 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=27.0MB, alloc=32.3MB, time=0.50 memory used=48.1MB, alloc=56.3MB, time=0.83 memory used=90.5MB, alloc=60.3MB, time=1.46 memory used=130.8MB, alloc=84.3MB, time=2.05 memory used=170.7MB, alloc=84.3MB, time=2.66 memory used=236.8MB, alloc=116.3MB, time=3.64 memory used=304.8MB, alloc=372.3MB, time=4.62 memory used=391.0MB, alloc=396.3MB, time=5.97 memory used=500.1MB, alloc=420.3MB, time=7.61 memory used=637.0MB, alloc=420.3MB, time=9.58 memory used=767.2MB, alloc=444.3MB, time=11.66 memory used=893.3MB, alloc=468.3MB, time=13.66 memory used=1010.8MB, alloc=468.3MB, time=15.44 memory used=1123.5MB, alloc=492.3MB, time=17.13 memory used=1233.2MB, alloc=492.3MB, time=18.98 memory used=1329.4MB, alloc=492.3MB, time=20.60 memory used=1424.1MB, alloc=492.3MB, time=22.36 memory used=1519.6MB, alloc=516.3MB, time=24.06 memory used=1588.9MB, alloc=516.3MB, time=25.33 memory used=1665.5MB, alloc=516.3MB, time=26.73 memory used=1738.2MB, alloc=516.3MB, time=28.14 memory used=1805.4MB, alloc=516.3MB, time=29.33 memory used=1870.6MB, alloc=516.3MB, time=30.68 memory used=1970.5MB, alloc=540.3MB, time=32.70 memory used=2066.2MB, alloc=540.3MB, time=34.79 memory used=2153.5MB, alloc=564.3MB, time=36.72 memory used=2231.7MB, alloc=564.3MB, time=38.48 memory used=2313.7MB, alloc=588.3MB, time=40.32 memory used=2388.9MB, alloc=588.3MB, time=42.09 memory used=2616.7MB, alloc=612.3MB, time=46.47 memory used=2867.8MB, alloc=636.3MB, time=50.92 memory used=3112.3MB, alloc=660.3MB, time=55.79 memory used=3348.4MB, alloc=684.3MB, time=62.07 memory used=3563.3MB, alloc=708.3MB, time=69.77 memory used=3785.2MB, alloc=732.3MB, time=78.19 memory used=4018.1MB, alloc=756.3MB, time=87.30 memory used=4264.1MB, alloc=780.3MB, time=97.55 memory used=4523.8MB, alloc=804.3MB, time=108.27 memory used=4790.8MB, alloc=828.3MB, time=120.17 memory used=5081.8MB, alloc=852.3MB, time=133.11 memory used=5396.7MB, alloc=876.3MB, time=146.91 memory used=5735.5MB, alloc=900.3MB, time=161.83 memory used=6098.3MB, alloc=924.3MB, time=177.59 memory used=6485.1MB, alloc=948.3MB, time=194.32 memory used=6895.7MB, alloc=972.3MB, time=212.08 memory used=7330.4MB, alloc=996.3MB, time=230.93 |\^/| 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(); 1428493438 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-6 x y + 10 y - 4 x, 14 + 13 y - 9 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [5 y - 12 y z + 18 z , 6 x y + 17 x + 11 z] > Problem := [F,G]; 2 Problem := [[-6 x y + 10 y - 4 x, 14 + 13 y - 9 z], 2 2 [5 y - 12 y z + 18 z , 6 x y + 17 x + 11 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.9MB, alloc=32.3MB, time=0.82 memory used=67.5MB, alloc=56.3MB, time=1.15 N1 := 335 > GB := Basis(F, plex(op(vars))); 2 GB := [-3 x y + 5 y - 2 x, 9 z - 14 - 13 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=108.5MB, alloc=60.3MB, time=1.87 memory used=148.1MB, alloc=60.3MB, time=2.45 memory used=187.2MB, alloc=84.3MB, time=3.12 N2 := 335 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-6 x y + 10 y - 4 x, -9 z + 13 y + 14, 18 z - 12 z y + 5 y , 6 y x + 11 z + 17 x] > J:=[op(GB),op(G)]; 2 2 2 J := [-3 x y + 5 y - 2 x, 9 z - 14 - 13 y, 18 z - 12 z y + 5 y , 6 y x + 11 z + 17 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 1, 2, 2, 1/2, 1, 3/4, 1/3, 1/2, 1/3, 4, 9, 7, 2, 1, 2, 2, 1/2, 1, 3/4, 1/3, 1/2, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=192.3MB, alloc=84.3MB, time=3.25 |\^/| 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(); 1428493443 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [8 x y - 15 y z + 16, -9 x + 19 x z - 10 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [10 x z - y z + 5 z , -19 y z + 14 z + z] > Problem := [F,G]; 2 2 Problem := [[8 x y - 15 y z + 16, -9 x + 19 x z - 10 y ], 2 2 [10 x z - y z + 5 z , -19 y z + 14 z + z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=56.3MB, time=0.81 memory used=85.7MB, alloc=60.3MB, time=1.39 memory used=124.3MB, alloc=84.3MB, time=1.97 memory used=168.2MB, alloc=84.3MB, time=2.62 memory used=228.7MB, alloc=116.3MB, time=3.57 memory used=313.1MB, alloc=140.3MB, time=4.85 memory used=384.8MB, alloc=140.3MB, time=5.97 memory used=456.2MB, alloc=396.3MB, time=7.16 memory used=557.8MB, alloc=420.3MB, time=8.75 memory used=680.0MB, alloc=444.3MB, time=10.72 memory used=821.4MB, alloc=468.3MB, time=13.22 memory used=966.0MB, alloc=492.3MB, time=15.88 memory used=1128.9MB, alloc=516.3MB, time=18.73 memory used=1301.7MB, alloc=540.3MB, time=21.80 memory used=1475.3MB, alloc=564.3MB, time=25.61 memory used=1640.8MB, alloc=588.3MB, time=30.97 memory used=1813.9MB, alloc=612.3MB, time=37.07 memory used=1999.9MB, alloc=636.3MB, time=43.91 memory used=2192.5MB, alloc=660.3MB, time=51.89 memory used=2407.4MB, alloc=684.3MB, time=60.75 memory used=2646.2MB, alloc=708.3MB, time=70.64 memory used=2908.9MB, alloc=732.3MB, time=81.54 memory used=3195.7MB, alloc=756.3MB, time=93.37 memory used=3506.3MB, alloc=780.3MB, time=106.16 memory used=3840.9MB, alloc=780.3MB, time=119.87 memory used=4175.4MB, alloc=804.3MB, time=134.02 memory used=4533.8MB, alloc=804.3MB, time=148.80 memory used=4892.3MB, alloc=828.3MB, time=163.82 memory used=5274.6MB, alloc=828.3MB, time=179.13 memory used=5657.1MB, alloc=852.3MB, time=194.30 N1 := 11787 > GB := Basis(F, plex(op(vars))); 2 3 2 2 GB := [-17 x y + 150 y - 304 x, -9 x + 19 x z - 10 y , -8 x y + 15 y z - 16] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5836.7MB, alloc=852.3MB, time=199.20 memory used=5938.3MB, alloc=852.3MB, time=201.52 memory used=6040.0MB, alloc=852.3MB, time=203.77 memory used=6128.1MB, alloc=852.3MB, time=205.89 memory used=6218.5MB, alloc=852.3MB, time=207.91 memory used=6309.0MB, alloc=852.3MB, time=209.91 memory used=6387.2MB, alloc=852.3MB, time=211.85 memory used=6467.0MB, alloc=852.3MB, time=213.94 memory used=6545.9MB, alloc=852.3MB, time=215.92 memory used=6625.1MB, alloc=852.3MB, time=218.04 memory used=6711.1MB, alloc=852.3MB, time=220.26 memory used=6788.5MB, alloc=852.3MB, time=222.52 memory used=6866.7MB, alloc=852.3MB, time=224.46 memory used=6951.5MB, alloc=852.3MB, time=226.37 memory used=7355.7MB, alloc=876.3MB, time=236.38 memory used=7755.7MB, alloc=900.3MB, time=251.28 |\^/| 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(); 1428493743 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-14 y + 6 z - 13 y, 14 x z + 15 z - 5 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-13 y + 12 x, -13 y + 12 z + 18] > Problem := [F,G]; 2 2 2 Problem := [[-14 y + 6 z - 13 y, 14 x z + 15 z - 5 y], 2 2 [-13 y + 12 x, -13 y + 12 z + 18]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=46.5MB, alloc=56.3MB, time=0.83 memory used=87.6MB, alloc=60.3MB, time=1.44 memory used=128.7MB, alloc=60.3MB, time=2.01 memory used=168.1MB, alloc=84.3MB, time=2.60 memory used=235.0MB, alloc=92.3MB, time=3.61 memory used=297.5MB, alloc=116.3MB, time=4.63 memory used=376.4MB, alloc=140.3MB, time=5.97 memory used=471.4MB, alloc=164.3MB, time=7.60 memory used=579.2MB, alloc=188.3MB, time=9.52 memory used=701.7MB, alloc=212.3MB, time=11.70 memory used=805.6MB, alloc=492.3MB, time=13.64 memory used=956.6MB, alloc=516.3MB, time=16.35 memory used=1117.6MB, alloc=540.3MB, time=19.21 memory used=1291.2MB, alloc=564.3MB, time=22.28 memory used=1455.2MB, alloc=588.3MB, time=26.98 memory used=1619.9MB, alloc=612.3MB, time=32.43 memory used=1797.2MB, alloc=636.3MB, time=38.91 memory used=1990.2MB, alloc=660.3MB, time=45.79 memory used=2199.3MB, alloc=684.3MB, time=53.37 memory used=2424.0MB, alloc=708.3MB, time=62.02 memory used=2664.5MB, alloc=732.3MB, time=70.99 memory used=2919.5MB, alloc=756.3MB, time=80.59 memory used=3186.8MB, alloc=780.3MB, time=91.46 memory used=3478.1MB, alloc=804.3MB, time=103.32 memory used=3793.4MB, alloc=828.3MB, time=116.43 memory used=4132.5MB, alloc=852.3MB, time=130.82 memory used=4495.7MB, alloc=876.3MB, time=146.32 memory used=4882.8MB, alloc=876.3MB, time=162.76 memory used=5269.8MB, alloc=876.3MB, time=179.46 memory used=5656.8MB, alloc=876.3MB, time=195.84 memory used=6043.7MB, alloc=900.3MB, time=212.23 |\^/| 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(); 1428494043 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [12 x - 11 z - 4, 10 x y + 20 x z + 14 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [13 x - 20 x y - 12 x, 3 x z - 18 x - 12] > Problem := [F,G]; 2 Problem := [[12 x - 11 z - 4, 10 x y + 20 x z + 14 x], 2 [13 x - 20 x y - 12 x, 3 x z - 18 x - 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=27.0MB, alloc=32.3MB, time=0.53 memory used=48.6MB, alloc=56.3MB, time=0.90 N1 := 469 > GB := Basis(F, plex(op(vars))); 3 2 GB := [120 x + 55 x y + 37 x, -12 x + 11 z + 4] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 185 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [12 x - 11 z - 4, 10 x y + 20 x z + 14 x, 13 x - 20 x y - 12 x, 3 x z - 18 x - 12] > J:=[op(GB),op(G)]; 3 2 2 J := [120 x + 55 x y + 37 x, -12 x + 11 z + 4, 13 x - 20 x y - 12 x, 3 x z - 18 x - 12] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 1, 1, 1, 1/2, 3/4, 3/4, 1/6, 1/4, 4, 8, 9, 3, 3, 1, 1, 1, 1/2, 1/2, 3/4, 1/6, 1/6, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=83.9MB, alloc=56.3MB, time=1.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428494045 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-13 x z + 16 y - 10, 13 x + 4 x y - 13 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-12 x z - 2 y - 13 x, 8 x z + 8 y - 12 x] > Problem := [F,G]; 2 2 2 Problem := [[-13 x z + 16 y - 10, 13 x + 4 x y - 13 z ], 2 2 [-12 x z - 2 y - 13 x, 8 x z + 8 y - 12 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.5MB, alloc=32.3MB, time=0.82 memory used=67.1MB, alloc=60.3MB, time=1.10 memory used=111.2MB, alloc=68.3MB, time=1.73 memory used=153.3MB, alloc=92.3MB, time=2.32 memory used=219.3MB, alloc=92.3MB, time=3.24 memory used=284.2MB, alloc=116.3MB, time=4.17 memory used=347.1MB, alloc=116.3MB, time=4.94 memory used=414.8MB, alloc=372.3MB, time=5.94 memory used=505.6MB, alloc=396.3MB, time=7.31 memory used=623.3MB, alloc=420.3MB, time=8.98 memory used=758.5MB, alloc=444.3MB, time=10.89 memory used=888.7MB, alloc=468.3MB, time=13.20 memory used=1032.6MB, alloc=492.3MB, time=15.75 memory used=1202.7MB, alloc=516.3MB, time=18.51 memory used=1383.1MB, alloc=540.3MB, time=21.60 memory used=1580.5MB, alloc=564.3MB, time=25.02 memory used=1786.1MB, alloc=588.3MB, time=28.67 memory used=2002.3MB, alloc=612.3MB, time=32.22 memory used=2235.0MB, alloc=636.3MB, time=35.82 memory used=2419.0MB, alloc=660.3MB, time=39.28 memory used=2593.8MB, alloc=684.3MB, time=42.64 memory used=2797.0MB, alloc=708.3MB, time=48.01 memory used=3038.7MB, alloc=732.3MB, time=56.64 memory used=3285.9MB, alloc=756.3MB, time=66.08 memory used=3545.8MB, alloc=780.3MB, time=76.13 memory used=3818.6MB, alloc=804.3MB, time=86.97 memory used=4105.2MB, alloc=828.3MB, time=98.34 memory used=4405.3MB, alloc=852.3MB, time=110.47 memory used=4720.3MB, alloc=876.3MB, time=123.38 memory used=5050.3MB, alloc=900.3MB, time=137.08 memory used=5391.4MB, alloc=924.3MB, time=152.31 memory used=5750.6MB, alloc=948.3MB, time=168.38 memory used=6133.7MB, alloc=972.3MB, time=185.30 memory used=6540.8MB, alloc=996.3MB, time=203.67 memory used=6971.8MB, alloc=1020.3MB, time=222.10 memory used=7426.8MB, alloc=1044.3MB, time=241.39 |\^/| 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(); 1428494345 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [3 y - 8 y z + 20 x, 16 x y - 4 x z + 6 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [2 y z + 11 z - 4, 7 y - 17 y z + 16] > Problem := [F,G]; 2 Problem := [[3 y - 8 y z + 20 x, 16 x y - 4 x z + 6 z], 2 [2 y z + 11 z - 4, 7 y - 17 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=46.7MB, alloc=32.3MB, time=0.76 memory used=65.7MB, alloc=56.3MB, time=1.04 memory used=104.5MB, alloc=60.3MB, time=1.62 memory used=142.1MB, alloc=60.3MB, time=2.17 memory used=179.1MB, alloc=84.3MB, time=2.74 memory used=233.8MB, alloc=84.3MB, time=3.69 memory used=288.6MB, alloc=116.3MB, time=4.64 memory used=363.4MB, alloc=140.3MB, time=5.92 memory used=456.0MB, alloc=164.3MB, time=7.48 memory used=565.3MB, alloc=188.3MB, time=9.36 memory used=667.8MB, alloc=468.3MB, time=11.13 memory used=804.5MB, alloc=492.3MB, time=14.72 memory used=946.1MB, alloc=516.3MB, time=19.18 memory used=1098.0MB, alloc=540.3MB, time=24.75 memory used=1267.4MB, alloc=564.3MB, time=31.47 memory used=1460.8MB, alloc=564.3MB, time=38.95 memory used=1654.2MB, alloc=564.3MB, time=46.31 memory used=1847.5MB, alloc=588.3MB, time=53.76 memory used=2064.9MB, alloc=588.3MB, time=62.06 memory used=2282.3MB, alloc=612.3MB, time=70.41 N1 := 7179 > GB := Basis(F, plex(op(vars))); GB := 2 2 2 2 [58 x y - 40 x + 9 y + 60 x, -8 x y + 2 x z - 3 z, -3 y + 8 y z - 20 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2527.9MB, alloc=612.3MB, time=76.23 memory used=2730.2MB, alloc=612.3MB, time=79.81 memory used=2929.3MB, alloc=636.3MB, time=83.40 memory used=3140.3MB, alloc=660.3MB, time=87.66 memory used=3417.7MB, alloc=684.3MB, time=96.92 memory used=3686.8MB, alloc=708.3MB, time=107.82 memory used=3980.0MB, alloc=732.3MB, time=119.83 memory used=4297.2MB, alloc=756.3MB, time=132.83 memory used=4638.6MB, alloc=780.3MB, time=146.80 N2 := 7179 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [-8 z y + 3 y + 20 x, 16 x y - 4 x z + 6 z, 2 z y + 11 z - 4, 2 -17 z y + 7 y + 16] > J:=[op(GB),op(G)]; 2 2 2 2 J := [58 x y - 40 x + 9 y + 60 x, -8 x y + 2 x z - 3 z, -3 y + 8 y z - 20 x, 2 2 z y + 11 z - 4, -17 z y + 7 y + 16] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 1, 2, 1, 1/2, 1, 1, 1/4, 1/2, 1/2, 5, 12, 11, 3, 2, 2, 1, 3/5, 1, 4/5, 3/8, 1/2, 3/8, -2, -3, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=4800.1MB, alloc=780.3MB, time=153.07 |\^/| 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(); 1428494573 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [20 z + 15 y + 20 z, -11 x y - 2 x - 8] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [17 y z - 5 x - 10 z, 15 y - 7 z - 7] > Problem := [F,G]; 2 Problem := [[20 z + 15 y + 20 z, -11 x y - 2 x - 8], 2 2 [17 y z - 5 x - 10 z, 15 y - 7 z - 7]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.50 memory used=47.9MB, alloc=32.3MB, time=0.81 memory used=67.4MB, alloc=56.3MB, time=1.10 memory used=108.0MB, alloc=60.3MB, time=1.71 memory used=149.5MB, alloc=84.3MB, time=2.29 memory used=213.8MB, alloc=92.3MB, time=3.27 memory used=273.7MB, alloc=116.3MB, time=4.28 memory used=350.6MB, alloc=140.3MB, time=5.61 memory used=445.3MB, alloc=164.3MB, time=7.25 memory used=556.4MB, alloc=188.3MB, time=9.16 memory used=674.5MB, alloc=212.3MB, time=12.34 memory used=801.4MB, alloc=236.3MB, time=16.46 memory used=939.8MB, alloc=260.3MB, time=21.65 memory used=1102.2MB, alloc=260.3MB, time=27.65 memory used=1264.5MB, alloc=284.3MB, time=33.61 memory used=1451.0MB, alloc=284.3MB, time=40.49 N1 := 5549 > GB := Basis(F, plex(op(vars))); 2 GB := [11 y x + 2 x + 8, 4 z + 4 z + 3 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1644.3MB, alloc=284.3MB, time=46.21 memory used=1723.2MB, alloc=540.3MB, time=47.59 memory used=1922.0MB, alloc=564.3MB, time=50.94 memory used=2148.8MB, alloc=588.3MB, time=55.09 memory used=2382.4MB, alloc=612.3MB, time=62.44 memory used=2607.6MB, alloc=636.3MB, time=71.26 memory used=2856.9MB, alloc=660.3MB, time=81.06 memory used=3130.4MB, alloc=684.3MB, time=91.71 N2 := 5549 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [20 z + 15 y + 20 z, -11 x y - 2 x - 8, 17 y z - 5 x - 10 z, 2 2 -7 z + 15 y - 7] > J:=[op(GB),op(G)]; J := [ 2 2 2 11 y x + 2 x + 8, 4 z + 4 z + 3 y, 17 y z - 5 x - 10 z, -7 z + 15 y - 7] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 1, 2, 2, 1/2, 1, 3/4, 1/4, 1/3, 5/12, 4, 9, 8, 2, 1, 2, 2, 1/2, 1, 3/4, 1/4, 1/3, 5/12, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=3206.4MB, alloc=684.3MB, time=94.33 |\^/| 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(); 1428494671 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-17 x - 20 y - 9 z, -18 x z - y z - 16 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-14 x z + 13 z - x, 16 x + 8 y - 19 y] > Problem := [F,G]; 2 2 Problem := [[-17 x - 20 y - 9 z, -18 x z - y z - 16 x], 2 2 2 [-14 x z + 13 z - x, 16 x + 8 y - 19 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.1MB, alloc=32.3MB, time=0.81 memory used=67.0MB, alloc=56.3MB, time=1.12 memory used=110.0MB, alloc=68.3MB, time=1.73 memory used=150.0MB, alloc=92.3MB, time=2.36 memory used=217.4MB, alloc=92.3MB, time=3.47 memory used=275.1MB, alloc=116.3MB, time=4.45 memory used=353.5MB, alloc=140.3MB, time=5.77 memory used=467.6MB, alloc=140.3MB, time=7.15 memory used=567.7MB, alloc=164.3MB, time=8.72 memory used=676.6MB, alloc=188.3MB, time=10.94 memory used=789.2MB, alloc=212.3MB, time=14.31 memory used=913.2MB, alloc=236.3MB, time=18.58 memory used=1052.7MB, alloc=260.3MB, time=23.91 memory used=1216.2MB, alloc=260.3MB, time=30.14 memory used=1379.6MB, alloc=260.3MB, time=36.36 memory used=1543.1MB, alloc=284.3MB, time=42.63 N1 := 5543 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 2 GB := [20 y + 360 y x + 17 y x + 306 x - 144 x, 20 y + 17 x + 9 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1737.5MB, alloc=284.3MB, time=48.30 memory used=1967.3MB, alloc=564.3MB, time=53.18 N2 := 2527 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-17 x - 20 y - 9 z, -18 x z - y z - 16 x, -14 x z + 13 z - x, 2 2 8 y + 16 x - 19 y] > J:=[op(GB),op(G)]; 3 2 2 3 2 2 J := [20 y + 360 y x + 17 y x + 306 x - 144 x, 20 y + 17 x + 9 z, 2 2 2 -14 x z + 13 z - x, 8 y + 16 x - 19 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 2, 2, 1, 3/4, 3/4, 1/2, 1/3, 5/12, 4, 9, 9, 3, 3, 3, 2, 1, 3/4, 1/2, 4/7, 3/7, 3/14, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=2134.3MB, alloc=564.3MB, time=59.17 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428494733 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-18 x y + 16 x z - 8 y z, 13 x y + 13 z + 3 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-14 y z - 9 z + 2, 12 y + 5 y z] > Problem := [F,G]; 2 Problem := [[-18 x y + 16 x z - 8 y z, 13 x y + 13 z + 3 y], 2 2 [-14 y z - 9 z + 2, 12 y + 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=47.1MB, alloc=32.3MB, time=0.80 memory used=67.4MB, alloc=56.3MB, time=1.14 memory used=108.2MB, alloc=60.3MB, time=1.77 memory used=146.4MB, alloc=84.3MB, time=2.36 memory used=207.5MB, alloc=92.3MB, time=3.33 memory used=267.9MB, alloc=116.3MB, time=4.29 memory used=350.0MB, alloc=140.3MB, time=5.54 memory used=425.0MB, alloc=396.3MB, time=6.72 memory used=526.0MB, alloc=420.3MB, time=8.53 memory used=638.9MB, alloc=444.3MB, time=10.54 memory used=767.4MB, alloc=468.3MB, time=12.85 memory used=912.1MB, alloc=492.3MB, time=15.40 memory used=1070.0MB, alloc=516.3MB, time=18.15 memory used=1236.2MB, alloc=540.3MB, time=21.22 memory used=1405.1MB, alloc=564.3MB, time=25.53 memory used=1566.8MB, alloc=588.3MB, time=30.88 memory used=1738.6MB, alloc=612.3MB, time=36.84 memory used=1922.4MB, alloc=636.3MB, time=43.65 memory used=2120.3MB, alloc=660.3MB, time=51.21 memory used=2328.7MB, alloc=684.3MB, time=59.88 memory used=2561.0MB, alloc=708.3MB, time=70.00 memory used=2817.2MB, alloc=732.3MB, time=80.79 memory used=3097.4MB, alloc=756.3MB, time=92.55 memory used=3401.5MB, alloc=780.3MB, time=105.31 memory used=3729.5MB, alloc=780.3MB, time=118.93 memory used=4057.5MB, alloc=804.3MB, time=132.52 memory used=4409.4MB, alloc=804.3MB, time=146.94 memory used=4761.3MB, alloc=804.3MB, time=161.29 memory used=5113.2MB, alloc=828.3MB, time=175.61 memory used=5488.8MB, alloc=828.3MB, time=190.98 memory used=5864.4MB, alloc=828.3MB, time=206.24 memory used=6239.9MB, alloc=852.3MB, time=221.79 memory used=6639.4MB, alloc=876.3MB, time=238.25 memory used=7062.9MB, alloc=900.3MB, time=255.61 N1 := 13963 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 2 3 GB := [832 x y + 221 x y + 208 x y + 192 x y - 192 x y + 48 y , 2 2 2 2 -637 x y + 936 x z - 208 x y + 96 x y - 48 y , 4 z y - 8 z x + 9 y x, 2 13 z + 13 y x + 3 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7420.2MB, alloc=900.3MB, time=267.44 memory used=7542.7MB, alloc=900.3MB, time=270.37 memory used=7639.2MB, alloc=900.3MB, time=272.58 memory used=7743.7MB, alloc=900.3MB, time=274.83 memory used=7844.0MB, alloc=900.3MB, time=277.15 memory used=7934.1MB, alloc=900.3MB, time=279.28 |\^/| 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(); 1428495033 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-5 z + 15 x - 13 y, -14 x + 12 x z + 18 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-17 - 17 y - z, 10 x - 13 x + 7 y] > Problem := [F,G]; 2 2 2 Problem := [[-5 z + 15 x - 13 y, -14 x + 12 x z + 18 z ], 2 [-17 - 17 y - z, 10 x - 13 x + 7 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=67.3MB, alloc=56.3MB, time=1.11 memory used=110.2MB, alloc=84.3MB, time=1.81 memory used=165.7MB, alloc=84.3MB, time=2.80 memory used=223.4MB, alloc=108.3MB, time=3.80 memory used=300.5MB, alloc=140.3MB, time=5.19 memory used=394.2MB, alloc=164.3MB, time=6.88 memory used=503.7MB, alloc=188.3MB, time=8.88 memory used=622.2MB, alloc=212.3MB, time=11.52 memory used=740.9MB, alloc=236.3MB, time=15.14 memory used=871.6MB, alloc=260.3MB, time=19.38 memory used=1014.4MB, alloc=284.3MB, time=24.64 memory used=1175.1MB, alloc=308.3MB, time=31.01 memory used=1359.8MB, alloc=332.3MB, time=38.43 memory used=1568.3MB, alloc=332.3MB, time=46.58 memory used=1776.9MB, alloc=332.3MB, time=54.83 memory used=1985.4MB, alloc=332.3MB, time=63.05 memory used=2193.8MB, alloc=356.3MB, time=71.10 memory used=2426.3MB, alloc=356.3MB, time=80.14 memory used=2658.8MB, alloc=380.3MB, time=89.97 memory used=2915.6MB, alloc=404.3MB, time=100.28 N1 := 8667 > GB := Basis(F, plex(op(vars))); 4 2 3 2 2 GB := [1225 x + 10530 y x - 12150 x + 13689 y - 31590 y x + 18225 x , 2 -35 x + 30 x z + 135 x - 117 y, 3 2 2 245 x - 2430 x + 1287 x y + 702 y z + 3645 x - 3159 y, 5 z - 15 x + 13 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2989.9MB, alloc=404.3MB, time=102.13 memory used=3306.6MB, alloc=660.3MB, time=107.51 memory used=3614.8MB, alloc=684.3MB, time=113.41 memory used=3921.0MB, alloc=708.3MB, time=119.86 memory used=4229.0MB, alloc=732.3MB, time=126.41 memory used=4549.3MB, alloc=756.3MB, time=133.61 memory used=4828.7MB, alloc=780.3MB, time=143.80 memory used=5110.5MB, alloc=804.3MB, time=154.89 memory used=5401.5MB, alloc=828.3MB, time=166.65 memory used=5704.3MB, alloc=852.3MB, time=179.33 memory used=6014.7MB, alloc=876.3MB, time=192.67 memory used=6340.5MB, alloc=900.3MB, time=207.40 memory used=6690.3MB, alloc=924.3MB, time=222.71 |\^/| 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(); 1428495333 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [13 x - 14 x y - 6 z , 5 x z - 7 y - 16 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [12 z - 15, -6 x - 15 x y - 7 y z] > Problem := [F,G]; 2 2 Problem := [[13 x - 14 x y - 6 z , 5 x z - 7 y - 16 z], 2 2 [12 z - 15, -6 x - 15 x y - 7 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=32.3MB, time=0.83 memory used=66.9MB, alloc=60.3MB, time=1.14 memory used=107.9MB, alloc=60.3MB, time=1.72 memory used=147.1MB, alloc=84.3MB, time=2.29 memory used=208.6MB, alloc=92.3MB, time=3.29 memory used=270.5MB, alloc=116.3MB, time=4.24 memory used=347.9MB, alloc=116.3MB, time=5.39 memory used=419.0MB, alloc=396.3MB, time=6.54 memory used=524.8MB, alloc=420.3MB, time=8.38 memory used=642.0MB, alloc=444.3MB, time=10.42 memory used=774.1MB, alloc=468.3MB, time=12.69 memory used=917.9MB, alloc=492.3MB, time=15.21 memory used=1074.3MB, alloc=516.3MB, time=17.94 memory used=1239.7MB, alloc=540.3MB, time=20.86 memory used=1414.7MB, alloc=564.3MB, time=24.03 memory used=1598.6MB, alloc=588.3MB, time=27.39 memory used=1778.5MB, alloc=612.3MB, time=32.20 memory used=1951.8MB, alloc=636.3MB, time=37.92 memory used=2135.1MB, alloc=660.3MB, time=44.45 memory used=2331.0MB, alloc=684.3MB, time=51.63 memory used=2541.1MB, alloc=708.3MB, time=59.49 memory used=2766.0MB, alloc=732.3MB, time=68.05 memory used=3004.9MB, alloc=756.3MB, time=77.66 memory used=3257.9MB, alloc=780.3MB, time=88.70 memory used=3522.2MB, alloc=804.3MB, time=100.36 memory used=3810.5MB, alloc=828.3MB, time=112.72 memory used=4122.6MB, alloc=852.3MB, time=125.99 memory used=4458.8MB, alloc=876.3MB, time=140.24 memory used=4818.8MB, alloc=900.3MB, time=155.45 memory used=5202.7MB, alloc=924.3MB, time=171.66 memory used=5610.6MB, alloc=948.3MB, time=188.91 memory used=6042.5MB, alloc=948.3MB, time=207.17 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428495633 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-3 y + 11 z + 12 y, 11 x z - 20 y - 18 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-13 x + 19 x z + 16 y , -14 x y + 12 y - 5 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-3 y + 11 z + 12 y, 11 x z - 20 y - 18 z ], 2 2 2 2 [-13 x + 19 x z + 16 y , -14 x y + 12 y - 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.8MB, alloc=32.3MB, time=0.49 memory used=45.8MB, alloc=32.3MB, time=0.77 memory used=64.3MB, alloc=56.3MB, time=1.05 memory used=105.1MB, alloc=60.3MB, time=1.66 memory used=144.9MB, alloc=84.3MB, time=2.23 memory used=216.8MB, alloc=92.3MB, time=3.08 memory used=285.0MB, alloc=92.3MB, time=3.99 memory used=349.0MB, alloc=116.3MB, time=4.96 memory used=434.3MB, alloc=372.3MB, time=5.93 memory used=523.0MB, alloc=396.3MB, time=7.21 memory used=632.1MB, alloc=420.3MB, time=8.91 memory used=747.3MB, alloc=420.3MB, time=10.23 memory used=878.9MB, alloc=444.3MB, time=12.32 memory used=1010.1MB, alloc=468.3MB, time=14.33 memory used=1155.9MB, alloc=492.3MB, time=16.81 memory used=1330.5MB, alloc=516.3MB, time=20.27 memory used=1515.0MB, alloc=540.3MB, time=23.92 memory used=1681.8MB, alloc=564.3MB, time=26.74 memory used=1863.7MB, alloc=588.3MB, time=30.06 memory used=2035.0MB, alloc=612.3MB, time=33.40 memory used=2194.3MB, alloc=636.3MB, time=36.69 memory used=2415.2MB, alloc=660.3MB, time=43.93 memory used=2637.9MB, alloc=684.3MB, time=51.94 memory used=2868.7MB, alloc=708.3MB, time=60.88 memory used=3109.8MB, alloc=732.3MB, time=70.68 memory used=3356.3MB, alloc=756.3MB, time=81.72 memory used=3626.8MB, alloc=780.3MB, time=93.58 memory used=3921.3MB, alloc=804.3MB, time=106.72 memory used=4239.6MB, alloc=828.3MB, time=120.86 memory used=4582.0MB, alloc=852.3MB, time=136.15 memory used=4948.2MB, alloc=876.3MB, time=152.21 memory used=5338.4MB, alloc=876.3MB, time=168.67 memory used=5728.6MB, alloc=876.3MB, time=185.56 memory used=6118.6MB, alloc=900.3MB, time=203.32 memory used=6532.6MB, alloc=900.3MB, time=221.99 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428495933 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-4 x z - 14 y + 5 z , -12 y + 7 z - 6 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [13 y + 9 y z + 1, 9 x z + 2 y z - 17] > Problem := [F,G]; 2 2 2 2 Problem := [[-4 x z - 14 y + 5 z , -12 y + 7 z - 6 y], 2 [13 y + 9 y z + 1, 9 x z + 2 y z - 17]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.7MB, alloc=32.3MB, time=0.52 memory used=46.5MB, alloc=32.3MB, time=0.81 memory used=65.0MB, alloc=56.3MB, time=1.11 memory used=105.2MB, alloc=60.3MB, time=1.74 memory used=145.3MB, alloc=60.3MB, time=2.28 memory used=189.7MB, alloc=92.3MB, time=2.88 memory used=252.2MB, alloc=92.3MB, time=3.86 memory used=318.7MB, alloc=92.3MB, time=4.68 memory used=381.8MB, alloc=116.3MB, time=5.64 memory used=457.1MB, alloc=116.3MB, time=6.73 memory used=537.5MB, alloc=396.3MB, time=8.02 memory used=645.3MB, alloc=396.3MB, time=9.36 memory used=751.3MB, alloc=396.3MB, time=10.78 memory used=861.5MB, alloc=420.3MB, time=12.27 memory used=988.9MB, alloc=444.3MB, time=14.47 memory used=1115.0MB, alloc=444.3MB, time=16.36 memory used=1255.6MB, alloc=468.3MB, time=18.69 memory used=1413.8MB, alloc=492.3MB, time=21.41 memory used=1549.4MB, alloc=516.3MB, time=23.80 memory used=1709.0MB, alloc=540.3MB, time=26.81 memory used=1860.5MB, alloc=564.3MB, time=29.76 memory used=2015.7MB, alloc=588.3MB, time=32.79 memory used=2161.3MB, alloc=612.3MB, time=35.59 memory used=2305.3MB, alloc=636.3MB, time=38.50 memory used=2457.3MB, alloc=660.3MB, time=41.24 memory used=2592.0MB, alloc=684.3MB, time=43.89 memory used=2723.9MB, alloc=708.3MB, time=46.69 memory used=2860.7MB, alloc=732.3MB, time=49.61 memory used=2983.6MB, alloc=756.3MB, time=52.43 memory used=3104.6MB, alloc=780.3MB, time=55.21 memory used=3216.9MB, alloc=780.3MB, time=57.61 memory used=3330.2MB, alloc=804.3MB, time=60.08 memory used=3420.5MB, alloc=804.3MB, time=62.25 memory used=3526.6MB, alloc=828.3MB, time=64.44 memory used=3615.5MB, alloc=828.3MB, time=66.53 memory used=3724.7MB, alloc=852.3MB, time=68.97 memory used=3802.8MB, alloc=876.3MB, time=70.96 memory used=3903.2MB, alloc=876.3MB, time=73.20 memory used=3992.1MB, alloc=900.3MB, time=75.48 memory used=4080.7MB, alloc=900.3MB, time=77.75 memory used=4172.0MB, alloc=924.3MB, time=79.85 memory used=4280.5MB, alloc=948.3MB, time=83.22 memory used=4676.6MB, alloc=972.3MB, time=97.81 memory used=5065.0MB, alloc=996.3MB, time=113.60 memory used=5457.0MB, alloc=1020.3MB, time=129.81 memory used=5856.6MB, alloc=1044.3MB, time=146.78 memory used=6266.0MB, alloc=1068.3MB, time=164.59 memory used=6687.2MB, alloc=1092.3MB, time=183.13 memory used=7120.9MB, alloc=1116.3MB, time=202.85 memory used=7568.5MB, alloc=1140.3MB, time=223.04 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428496233 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [-3 x y + 12 y z, -20 x z + 11 y z + 8 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [14 y z - 11 z - 5 z, -2 x y + 4 x z + 20 z] > Problem := [F,G]; Problem := [[-3 x y + 12 y z, -20 x z + 11 y z + 8 z], 2 [14 y z - 11 z - 5 z, -2 x y + 4 x z + 20 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.20 memory used=25.8MB, alloc=32.3MB, time=0.52 memory used=46.4MB, alloc=32.3MB, time=0.85 memory used=66.8MB, alloc=56.3MB, time=1.24 memory used=107.6MB, alloc=60.3MB, time=1.99 memory used=144.5MB, alloc=84.3MB, time=2.70 memory used=199.6MB, alloc=108.3MB, time=3.99 memory used=267.0MB, alloc=132.3MB, time=6.65 memory used=353.7MB, alloc=132.3MB, time=10.32 N1 := 2359 > GB := Basis(F, plex(op(vars))); 2 2 GB := [-20 x y + 11 x y + 8 x y, -11 x y + 80 x z - 32 z, -x y + 4 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=439.3MB, alloc=140.3MB, time=12.22 memory used=534.9MB, alloc=164.3MB, time=14.04 memory used=646.7MB, alloc=444.3MB, time=16.19 memory used=772.6MB, alloc=468.3MB, time=19.82 memory used=895.9MB, alloc=492.3MB, time=25.35 memory used=1041.5MB, alloc=516.3MB, time=31.91 memory used=1211.4MB, alloc=540.3MB, time=39.01 N2 := 4045 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [-3 x y + 12 y z, -20 x z + 11 y z + 8 z, 14 y z - 11 z - 5 z, -2 x y + 4 x z + 20 z] > J:=[op(GB),op(G)]; 2 2 J := [-20 x y + 11 x y + 8 x y, -11 x y + 80 x z - 32 z, -x y + 4 y z, 2 14 y z - 11 z - 5 z, -2 x y + 4 x z + 20 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 1, 1, 2, 3/4, 1, 1, 4/11, 5/11, 9/11, 5, 13, 11, 3, 2, 2, 2, 4/5, 1, 4/5, 4/7, 4/7, 4/7, -2, -3, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1225.4MB, alloc=540.3MB, time=39.45 |\^/| 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(); 1428496300 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [2 x y - 6 y + 14 z , 16 x y + 5 y z - 17 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [20 y - 12 x - 16 z, 3 x y - 2 y + 17 z] > Problem := [F,G]; 2 2 Problem := [[2 x y - 6 y + 14 z , 16 x y + 5 y z - 17 z], 2 [20 y - 12 x - 16 z, 3 x y - 2 y + 17 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.53 memory used=45.3MB, alloc=56.3MB, time=0.85 memory used=85.1MB, alloc=60.3MB, time=1.47 memory used=123.3MB, alloc=84.3MB, time=2.09 memory used=164.2MB, alloc=84.3MB, time=2.77 memory used=224.7MB, alloc=92.3MB, time=3.73 memory used=284.4MB, alloc=116.3MB, time=4.66 memory used=366.1MB, alloc=116.3MB, time=6.07 memory used=436.2MB, alloc=396.3MB, time=7.27 memory used=546.1MB, alloc=420.3MB, time=9.22 memory used=664.1MB, alloc=444.3MB, time=11.46 memory used=796.6MB, alloc=468.3MB, time=13.90 memory used=950.0MB, alloc=492.3MB, time=16.63 memory used=1116.8MB, alloc=516.3MB, time=19.68 memory used=1293.7MB, alloc=540.3MB, time=23.15 memory used=1485.0MB, alloc=564.3MB, time=26.85 memory used=1679.9MB, alloc=588.3MB, time=30.61 memory used=1849.7MB, alloc=612.3MB, time=34.33 memory used=2022.5MB, alloc=636.3MB, time=37.98 memory used=2177.6MB, alloc=660.3MB, time=41.28 memory used=2395.3MB, alloc=684.3MB, time=49.01 memory used=2611.1MB, alloc=708.3MB, time=57.25 memory used=2836.7MB, alloc=732.3MB, time=66.33 memory used=3075.5MB, alloc=756.3MB, time=76.31 memory used=3328.5MB, alloc=780.3MB, time=86.73 memory used=3595.7MB, alloc=804.3MB, time=97.54 memory used=3877.7MB, alloc=828.3MB, time=109.96 memory used=4174.9MB, alloc=852.3MB, time=122.86 memory used=4488.0MB, alloc=876.3MB, time=136.65 memory used=4813.9MB, alloc=900.3MB, time=151.58 memory used=5157.8MB, alloc=924.3MB, time=167.15 memory used=5525.6MB, alloc=948.3MB, time=184.85 memory used=5917.4MB, alloc=972.3MB, time=203.67 memory used=6333.1MB, alloc=996.3MB, time=222.93 |\^/| 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(); 1428496600 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [5 x - 5 x z + 17 y z, 17 x - 8 y + 11 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-7 x + 15 x y - 15 y z, -13 + 6 x - 16 y] > Problem := [F,G]; 2 2 Problem := [[5 x - 5 x z + 17 y z, 17 x - 8 y + 11 z], 2 [-7 x + 15 x y - 15 y z, -13 + 6 x - 16 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.0MB, alloc=40.3MB, time=0.58 memory used=59.0MB, alloc=44.3MB, time=1.00 memory used=84.7MB, alloc=68.3MB, time=1.39 memory used=134.4MB, alloc=68.3MB, time=2.25 memory used=179.1MB, alloc=92.3MB, time=3.01 memory used=243.1MB, alloc=124.3MB, time=4.36 memory used=316.9MB, alloc=148.3MB, time=6.82 N1 := 1649 > GB := Basis(F, plex(op(vars))); 2 3 2 2 2 GB := [-289 y x + 85 x + 136 y - 40 y x + 55 x , 17 x + 11 z - 8 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=417.1MB, alloc=148.3MB, time=8.51 N2 := 833 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [17 z y - 5 z x + 5 x , 17 x + 11 z - 8 y, -7 x + 15 x y - 15 y z, -16 y + 6 x - 13] > J:=[op(GB),op(G)]; 2 3 2 2 2 J := [-289 y x + 85 x + 136 y - 40 y x + 55 x , 17 x + 11 z - 8 y, 2 -7 x + 15 x y - 15 y z, -16 y + 6 x - 13] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 7, 2, 2, 1, 1, 1, 1, 3/4, 1/2, 5/12, 1/3, 4, 10, 8, 3, 3, 2, 1, 1, 1, 1/2, 4/7, 1/2, 1/7, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=453.9MB, alloc=148.3MB, time=9.47 |\^/| 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(); 1428496611 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-x z + 18 x + 19, x y - 4 y - 11 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-20 y + 13 y - 20 z, 16 y - 5 z + 7] > Problem := [F,G]; 2 2 Problem := [[-x z + 18 x + 19, x y - 4 y - 11 z ], 2 2 [-20 y + 13 y - 20 z, 16 y - 5 z + 7]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.7MB, alloc=32.3MB, time=0.51 memory used=45.4MB, alloc=32.3MB, time=0.80 memory used=63.7MB, alloc=56.3MB, time=1.09 memory used=104.2MB, alloc=60.3MB, time=1.72 memory used=143.8MB, alloc=84.3MB, time=2.35 memory used=206.9MB, alloc=92.3MB, time=3.29 memory used=268.0MB, alloc=92.3MB, time=4.21 memory used=326.9MB, alloc=116.3MB, time=5.14 memory used=409.6MB, alloc=140.3MB, time=6.58 memory used=508.8MB, alloc=164.3MB, time=8.37 memory used=622.5MB, alloc=188.3MB, time=10.43 memory used=737.2MB, alloc=468.3MB, time=12.87 memory used=865.1MB, alloc=492.3MB, time=16.69 memory used=998.5MB, alloc=516.3MB, time=21.72 memory used=1154.1MB, alloc=540.3MB, time=27.65 memory used=1333.6MB, alloc=540.3MB, time=34.39 memory used=1513.1MB, alloc=564.3MB, time=40.98 N1 := 5321 > GB := Basis(F, plex(op(vars))); 3 2 2 2 GB := [-x y + 4 x y + 3564 x + 7524 x + 3971, 2 2 -x y + 4 x y + 3564 x + 209 z + 3762] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1730.6MB, alloc=564.3MB, time=46.77 N2 := 1553 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-x z + 18 x + 19, -11 z - 4 y + y x, -20 y + 13 y - 20 z, 2 16 y - 5 z + 7] > J:=[op(GB),op(G)]; 3 2 2 2 J := [-x y + 4 x y + 3564 x + 7524 x + 3971, 2 2 2 -x y + 4 x y + 3564 x + 209 z + 3762, -20 y + 13 y - 20 z, 2 16 y - 5 z + 7] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 1, 2, 2, 1/2, 3/4, 1, 1/4, 5/12, 1/3, 4, 9, 11, 4, 3, 2, 1, 1/2, 1, 3/4, 7/16, 7/16, 3/16, 0, -3, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1900.9MB, alloc=564.3MB, time=51.89 |\^/| 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(); 1428496666 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [15 x + 15 x z + 11 y z, -8 x + y - 18 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-7 + 7 y, -5 x z - 4 y - 9 z] > Problem := [F,G]; 2 2 Problem := [[15 x + 15 x z + 11 y z, -8 x + y - 18 z], 2 [-7 + 7 y, -5 x z - 4 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=32.0MB, alloc=40.3MB, time=0.60 memory used=58.8MB, alloc=44.3MB, time=1.02 memory used=85.5MB, alloc=68.3MB, time=1.62 memory used=134.1MB, alloc=68.3MB, time=2.53 memory used=179.0MB, alloc=92.3MB, time=3.32 memory used=243.4MB, alloc=124.3MB, time=4.70 memory used=322.4MB, alloc=148.3MB, time=7.32 N1 := 2117 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 GB := [-120 x - 88 x y + 270 x + 15 x y + 11 y , 8 x + 18 z - y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=416.6MB, alloc=148.3MB, time=10.84 N2 := 575 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [11 z y + 15 z x + 15 x , -8 x + y - 18 z, -7 + 7 y, -5 x z - 4 y - 9 z] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [-120 x - 88 x y + 270 x + 15 x y + 11 y , 8 x + 18 z - y, -7 + 7 y, 2 -5 x z - 4 y - 9 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 7, 2, 2, 2, 1, 3/4, 1, 3/4, 4/11, 4/11, 5/11, 4, 9, 8, 3, 3, 2, 1, 3/4, 1, 1/2, 6/13, 6/13, 3/13, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=498.2MB, alloc=148.3MB, time=12.50 |\^/| 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(); 1428496683 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-19 y - 13 z - 16, -11 x y + 2 y z - 4 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-2 x z - 11 y z - 13 z, -15 x + 19 y + 9 y z] > Problem := [F,G]; 2 2 Problem := [[-19 y - 13 z - 16, -11 x y + 2 y z - 4 x], 2 2 [-2 x z - 11 y z - 13 z, -15 x + 19 y + 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.22 memory used=26.6MB, alloc=32.3MB, time=0.56 memory used=48.0MB, alloc=32.3MB, time=0.89 memory used=66.9MB, alloc=56.3MB, time=1.20 memory used=107.4MB, alloc=60.3MB, time=1.85 memory used=146.2MB, alloc=60.3MB, time=2.50 memory used=184.0MB, alloc=84.3MB, time=3.11 memory used=225.6MB, alloc=84.3MB, time=3.76 memory used=284.7MB, alloc=116.3MB, time=4.87 memory used=360.7MB, alloc=140.3MB, time=6.48 memory used=452.9MB, alloc=164.3MB, time=8.86 memory used=549.6MB, alloc=188.3MB, time=12.48 N1 := 2157 > GB := Basis(F, plex(op(vars))); 4 2 2 2 2 2 GB := [76 y + 1573 y x + 1144 y x + 64 y + 208 x , 2 3 2 1573 x y + 76 y + 572 x + 104 x z + 64 y, -11 x y + 2 y z - 4 x, 2 2 13 z + 19 y + 16] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=656.6MB, alloc=188.3MB, time=14.42 memory used=802.4MB, alloc=444.3MB, time=16.61 memory used=946.9MB, alloc=468.3MB, time=18.74 memory used=1095.4MB, alloc=468.3MB, time=21.25 memory used=1239.1MB, alloc=492.3MB, time=23.63 memory used=1382.4MB, alloc=492.3MB, time=25.98 memory used=1512.3MB, alloc=516.3MB, time=27.91 memory used=1668.5MB, alloc=516.3MB, time=30.68 memory used=1806.0MB, alloc=540.3MB, time=33.23 memory used=1960.4MB, alloc=540.3MB, time=36.33 memory used=2110.5MB, alloc=564.3MB, time=39.35 memory used=2277.0MB, alloc=588.3MB, time=42.74 memory used=2442.7MB, alloc=612.3MB, time=46.46 memory used=2664.3MB, alloc=636.3MB, time=54.41 memory used=2881.9MB, alloc=660.3MB, time=64.19 memory used=3123.4MB, alloc=684.3MB, time=74.38 memory used=3389.0MB, alloc=708.3MB, time=86.41 N2 := 5781 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-19 y - 13 z - 16, -11 x y + 2 y z - 4 x, -2 x z - 11 y z - 13 z, 2 2 -15 x + 19 y + 9 y z] > J:=[op(GB),op(G)]; 4 2 2 2 2 2 J := [76 y + 1573 y x + 1144 y x + 64 y + 208 x , 3 2 2 76 y + 1573 y x + 104 z x + 572 x + 64 y, -11 x y + 2 y z - 4 x, 2 2 2 2 13 z + 19 y + 16, -2 x z - 11 y z - 13 z, -15 x + 19 y + 9 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 2, 2, 2, 3/4, 1, 1, 1/3, 1/2, 1/2, 6, 16, 15, 4, 2, 13 4, 2, 5/6, 1, 5/6, 5/11, --, 7/22, -5, -7, -2] 22 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=3521.9MB, alloc=708.3MB, time=91.78 |\^/| 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(); 1428496784 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [6 x + 3 y z + 18 z, x y - 15 z - 10] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [7 + 4 z, 11 y z + 13 z - 12 z] > Problem := [F,G]; Problem := 2 2 [[6 x + 3 y z + 18 z, x y - 15 z - 10], [7 + 4 z, 11 y z + 13 z - 12 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.48 memory used=45.7MB, alloc=32.3MB, time=0.76 memory used=63.7MB, alloc=56.3MB, time=1.04 memory used=102.2MB, alloc=60.3MB, time=1.61 memory used=138.9MB, alloc=84.3MB, time=2.19 memory used=196.1MB, alloc=116.3MB, time=3.12 memory used=275.5MB, alloc=140.3MB, time=4.54 memory used=368.5MB, alloc=164.3MB, time=6.18 memory used=475.2MB, alloc=188.3MB, time=8.08 memory used=584.7MB, alloc=468.3MB, time=10.00 memory used=715.6MB, alloc=492.3MB, time=12.38 memory used=853.0MB, alloc=516.3MB, time=15.41 memory used=987.3MB, alloc=540.3MB, time=19.96 memory used=1131.9MB, alloc=564.3MB, time=25.36 memory used=1290.2MB, alloc=588.3MB, time=30.96 memory used=1463.2MB, alloc=612.3MB, time=37.56 memory used=1647.8MB, alloc=636.3MB, time=45.81 memory used=1854.3MB, alloc=660.3MB, time=55.09 memory used=2084.7MB, alloc=684.3MB, time=65.35 memory used=2339.1MB, alloc=708.3MB, time=76.35 memory used=2617.4MB, alloc=708.3MB, time=88.72 memory used=2895.7MB, alloc=708.3MB, time=101.09 memory used=3174.0MB, alloc=732.3MB, time=113.08 memory used=3476.2MB, alloc=732.3MB, time=125.46 memory used=3778.2MB, alloc=732.3MB, time=137.07 memory used=4080.1MB, alloc=756.3MB, time=148.82 memory used=4406.0MB, alloc=756.3MB, time=161.91 memory used=4731.9MB, alloc=780.3MB, time=174.60 memory used=5081.8MB, alloc=780.3MB, time=188.09 memory used=5431.4MB, alloc=804.3MB, time=201.88 memory used=5805.3MB, alloc=828.3MB, time=217.05 N1 := 12801 > GB := Basis(F, plex(op(vars))); 2 2 GB := [y x + 6 y x + 30 x - 10 y - 60, -x y + 15 z + 10] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6034.2MB, alloc=828.3MB, time=222.68 memory used=6497.1MB, alloc=828.3MB, time=241.75 N2 := 3595 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [6 x + 3 y z + 18 z, y x - 15 z - 10, 4 z + 7, 11 y z + 13 z - 12 z] > J:=[op(GB),op(G)]; 2 2 J := [y x + 6 y x + 30 x - 10 y - 60, -x y + 15 z + 10, 4 z + 7, 2 11 y z + 13 z - 12 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 2, 1, 2, 1/2, 3/4, 1, 2/11, 3/11, 7/11, 4, 8, 8, 3, 2, 2, 2, 1/2, 3/4, 3/4, 4/13, 5/13, 5/13, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=6552.2MB, alloc=828.3MB, time=243.81 |\^/| 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(); 1428497073 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-3 x - 12 x y - 9 x, -2 x y - 8 x z - 9 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-8 y - y + 16, 14 x - 8 y + 9] > Problem := [F,G]; 2 Problem := [[-3 x - 12 x y - 9 x, -2 x y - 8 x z - 9 y z], 2 2 [-8 y - y + 16, 14 x - 8 y + 9]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=48.3MB, alloc=32.3MB, time=0.88 memory used=67.9MB, alloc=56.3MB, time=1.24 N1 := 485 > GB := Basis(F, plex(op(vars))); 2 3 2 2 GB := [x + 4 x y + 3 x, -2 x + 23 x z - 6 x - 27 x z, 2 -x + 16 x z + 18 y z - 3 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=107.4MB, alloc=60.3MB, time=1.98 memory used=148.9MB, alloc=84.3MB, time=2.70 memory used=211.2MB, alloc=84.3MB, time=4.25 N2 := 847 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-3 x - 12 x y - 9 x, -2 x y - 8 x z - 9 y z, -8 y - y + 16, 2 14 x - 8 y + 9] > J:=[op(GB),op(G)]; 2 3 2 2 J := [x + 4 x y + 3 x, -2 x + 23 x z - 6 x - 27 x z, 2 2 2 -x + 16 x z + 18 y z - 3 x, -8 y - y + 16, 14 x - 8 y + 9] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 8, 2, 2, 2, 1, 3/4, 1, 1/4, 1/2, 1/2, 1/6, 5, 10, 11, 3, 11 3, 2, 1, 4/5, 4/5, 2/5, --, 5/17, 4/17, -2, -3, -1] 17 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=216.8MB, alloc=84.3MB, time=4.40 |\^/| 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(); 1428497078 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [-12 y z - 19 y + 9 z, -18 + y - 5 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-7 x - 12 z, -13 x y - 11 x z + 11 z] > Problem := [F,G]; Problem := [[-12 y z - 19 y + 9 z, -18 + y - 5 z], 2 [-7 x - 12 z, -13 x y - 11 x z + 11 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=46.2MB, alloc=56.3MB, time=0.82 memory used=87.2MB, alloc=60.3MB, time=1.45 memory used=125.8MB, alloc=60.3MB, time=2.08 memory used=164.7MB, alloc=84.3MB, time=2.83 memory used=223.3MB, alloc=116.3MB, time=3.91 memory used=299.2MB, alloc=140.3MB, time=5.30 memory used=392.6MB, alloc=164.3MB, time=7.04 memory used=500.8MB, alloc=188.3MB, time=9.04 memory used=621.8MB, alloc=212.3MB, time=11.48 memory used=744.2MB, alloc=492.3MB, time=14.41 memory used=878.9MB, alloc=516.3MB, time=18.77 memory used=1025.3MB, alloc=540.3MB, time=23.81 memory used=1186.5MB, alloc=564.3MB, time=29.53 memory used=1358.8MB, alloc=588.3MB, time=36.41 memory used=1553.5MB, alloc=612.3MB, time=44.82 memory used=1772.3MB, alloc=612.3MB, time=53.64 memory used=1990.9MB, alloc=636.3MB, time=62.53 memory used=2233.5MB, alloc=636.3MB, time=73.18 memory used=2476.1MB, alloc=636.3MB, time=83.63 memory used=2718.7MB, alloc=660.3MB, time=93.38 memory used=2985.1MB, alloc=660.3MB, time=104.42 memory used=3251.7MB, alloc=684.3MB, time=115.10 memory used=3542.2MB, alloc=684.3MB, time=126.60 N1 := 9655 > GB := Basis(F, plex(op(vars))); 2 GB := [6 y - 65 y + 81, 5 z + 18 - y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3842.4MB, alloc=684.3MB, time=135.34 N2 := 1931 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 -12 y z - 19 y + 9 z, -5 z + y - 18, -7 x - 12 z, -13 x y - 11 x z + 11 z] > J:=[op(GB),op(G)]; 2 2 J := [6 y - 65 y + 81, 5 z + 18 - y, -7 x - 12 z, -13 x y - 11 x z + 11 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 2, 1, 1, 1/2, 3/4, 1, 3/11, 4/11, 6/11, 4, 8, 7, 2, 2, 2, 1, 1/2, 3/4, 3/4, 3/11, 4/11, 4/11, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=3996.3MB, alloc=684.3MB, time=140.83 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428497238 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-3 x - 18 y + 4, -3 z - 11 x - 9 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-11 x + 5 y - 12 y z, -9 y + 14 z - 19] > Problem := [F,G]; 2 2 2 Problem := [[-3 x - 18 y + 4, -3 z - 11 x - 9 z], 2 2 2 2 [-11 x + 5 y - 12 y z, -9 y + 14 z - 19]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=27.2MB, alloc=32.3MB, time=0.53 memory used=48.4MB, alloc=32.3MB, time=0.89 memory used=67.5MB, alloc=56.3MB, time=1.20 memory used=108.5MB, alloc=60.3MB, time=1.83 memory used=149.8MB, alloc=60.3MB, time=2.37 memory used=192.2MB, alloc=92.3MB, time=3.03 memory used=265.3MB, alloc=92.3MB, time=4.13 memory used=329.5MB, alloc=116.3MB, time=5.38 memory used=412.3MB, alloc=140.3MB, time=6.93 memory used=511.6MB, alloc=164.3MB, time=8.67 memory used=626.5MB, alloc=188.3MB, time=10.71 memory used=760.6MB, alloc=468.3MB, time=13.00 memory used=899.4MB, alloc=492.3MB, time=15.86 memory used=1034.1MB, alloc=516.3MB, time=19.99 memory used=1178.9MB, alloc=540.3MB, time=24.91 memory used=1335.5MB, alloc=564.3MB, time=31.33 memory used=1506.7MB, alloc=588.3MB, time=38.29 memory used=1701.9MB, alloc=612.3MB, time=46.08 memory used=1921.0MB, alloc=612.3MB, time=54.71 memory used=2140.2MB, alloc=636.3MB, time=63.18 memory used=2383.2MB, alloc=636.3MB, time=72.60 memory used=2626.2MB, alloc=636.3MB, time=82.52 memory used=2869.3MB, alloc=660.3MB, time=91.99 memory used=3136.2MB, alloc=660.3MB, time=103.14 memory used=3403.2MB, alloc=684.3MB, time=113.39 memory used=3694.2MB, alloc=708.3MB, time=125.17 N1 := 9617 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [18 y + 3 x - 4, 3 z + 9 z + 11 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3916.4MB, alloc=708.3MB, time=130.64 memory used=4104.2MB, alloc=708.3MB, time=134.06 memory used=4325.0MB, alloc=708.3MB, time=138.60 memory used=4542.3MB, alloc=708.3MB, time=143.09 memory used=4866.7MB, alloc=732.3MB, time=153.42 memory used=5164.8MB, alloc=756.3MB, time=166.49 memory used=5472.5MB, alloc=780.3MB, time=180.42 memory used=5804.1MB, alloc=804.3MB, time=195.17 memory used=6159.7MB, alloc=828.3MB, time=211.27 memory used=6539.3MB, alloc=852.3MB, time=227.50 memory used=6942.8MB, alloc=876.3MB, time=244.90 |\^/| 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(); 1428497538 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [15 y - 6 y - 13, -15 x z + 3 z - 18 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [16 + 4 x - 12 y, -9 x + 16 y + 9 z] > Problem := [F,G]; 2 2 Problem := [[15 y - 6 y - 13, -15 x z + 3 z - 18 x], [16 + 4 x - 12 y, -9 x + 16 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=4.2MB, alloc=32.3MB, time=0.17 memory used=27.1MB, alloc=32.3MB, time=0.55 memory used=49.7MB, alloc=56.3MB, time=0.96 memory used=93.2MB, alloc=60.3MB, time=1.75 memory used=130.3MB, alloc=84.3MB, time=2.80 N1 := 1213 > GB := Basis(F, plex(op(vars))); 2 2 GB := [15 y - 6 y - 13, -5 x z + z - 6 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=187.7MB, alloc=84.3MB, time=4.35 memory used=247.9MB, alloc=108.3MB, time=5.57 N2 := 1213 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 2 15 y - 6 y - 13, -15 x z + 3 z - 18 x, 16 + 4 x - 12 y, -9 x + 16 y + 9 z ] > J:=[op(GB),op(G)]; 2 2 J := [15 y - 6 y - 13, -5 x z + z - 6 x, 16 + 4 x - 12 y, -9 x + 16 y + 9 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 6, 2, 1, 2, 2, 3/4, 3/4, 1/2, 1/3, 1/3, 1/4, 4, 8, 6, 2, 1, 2, 2, 3/4, 3/4, 1/2, 1/3, 1/3, 1/4, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=312.8MB, alloc=108.3MB, time=7.74 |\^/| 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(); 1428497549 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-12 x y - x + 9 z, -2 x + 7 y z + z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [5 x - 9 y - 11, 3 x y - 3 x z - 2 z] > Problem := [F,G]; 2 Problem := [[-12 x y - x + 9 z, -2 x + 7 y z + z], 2 2 [5 x - 9 y - 11, 3 x y - 3 x z - 2 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.23 memory used=26.5MB, alloc=32.3MB, time=0.62 memory used=47.2MB, alloc=32.3MB, time=0.97 memory used=66.7MB, alloc=56.3MB, time=1.31 memory used=109.5MB, alloc=60.3MB, time=2.13 memory used=147.4MB, alloc=84.3MB, time=2.89 memory used=208.0MB, alloc=92.3MB, time=4.06 memory used=262.7MB, alloc=116.3MB, time=5.05 memory used=336.2MB, alloc=140.3MB, time=6.66 memory used=421.5MB, alloc=164.3MB, time=9.55 memory used=519.6MB, alloc=164.3MB, time=14.18 memory used=617.8MB, alloc=188.3MB, time=18.42 N1 := 3121 > GB := Basis(F, plex(op(vars))); 2 2 GB := [84 x y - 18 x + 19 x y + x, -12 x y - x + 9 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=745.9MB, alloc=188.3MB, time=21.69 N2 := 749 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-12 x y - x + 9 z, -2 x + 7 y z + z, -9 y + 5 x - 11, -3 z x + 3 y x - 2 z] > J:=[op(GB),op(G)]; 2 2 2 2 J := [84 x y - 18 x + 19 x y + x, -12 x y - x + 9 z, -9 y + 5 x - 11, -3 z x + 3 y x - 2 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 2, 2, 1, 1, 1, 3/4, 1/2, 1/3, 5/12, 4, 10, 9, 3, 2, 2, 1, 1, 1, 1/2, 9/13, 5/13, 3/13, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=780.8MB, alloc=188.3MB, time=22.70 |\^/| 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(); 1428497579 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [2 y + 7 y, 9 x + 16 x z - 10 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [8 x + 19 y - 17, -6 x + 19 y z + 7 z] > Problem := [F,G]; 2 2 Problem := [[2 y + 7 y, 9 x + 16 x z - 10 x], 2 2 2 [8 x + 19 y - 17, -6 x + 19 y z + 7 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=49.1MB, alloc=32.3MB, time=0.92 memory used=68.6MB, alloc=56.3MB, time=1.30 memory used=109.6MB, alloc=60.3MB, time=2.06 memory used=145.8MB, alloc=84.3MB, time=3.09 N1 := 1269 > GB := Basis(F, plex(op(vars))); 2 2 GB := [2 y + 7 y, 9 x + 16 x z - 10 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=200.8MB, alloc=84.3MB, time=4.74 memory used=259.5MB, alloc=116.3MB, time=5.80 memory used=339.7MB, alloc=140.3MB, time=7.94 N2 := 1269 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := 2 2 2 2 2 [2 y + 7 y, 9 x + 16 x z - 10 x, 19 y + 8 x - 17, -6 x + 19 y z + 7 z] > J:=[op(GB),op(G)]; J := 2 2 2 2 2 [2 y + 7 y, 9 x + 16 x z - 10 x, 19 y + 8 x - 17, -6 x + 19 y z + 7 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 8, 2, 2, 2, 1, 3/4, 3/4, 1/2, 5/11, 4/11, 3/11, 4, 8, 8, 2, 2, 2, 1, 3/4, 3/4, 1/2, 5/11, 4/11, 3/11, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=370.4MB, alloc=140.3MB, time=8.94 |\^/| 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(); 1428497589 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [-9 x + 11 y - 5 z, 11 x z + 16 x + 2 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-14 x - 20 z - 12 x, -20 z + 9 y] > Problem := [F,G]; Problem := [[-9 x + 11 y - 5 z, 11 x z + 16 x + 2 z], 2 2 2 [-14 x - 20 z - 12 x, -20 z + 9 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.52 memory used=46.1MB, alloc=56.3MB, time=0.84 memory used=86.5MB, alloc=60.3MB, time=1.54 memory used=127.4MB, alloc=84.3MB, time=2.31 memory used=190.2MB, alloc=84.3MB, time=3.49 memory used=247.0MB, alloc=108.3MB, time=4.59 memory used=319.7MB, alloc=140.3MB, time=6.16 memory used=405.5MB, alloc=164.3MB, time=8.58 memory used=499.2MB, alloc=188.3MB, time=12.25 memory used=617.0MB, alloc=188.3MB, time=16.83 N1 := 3441 > GB := Basis(F, plex(op(vars))); 2 GB := [-99 x + 121 x y + 62 x + 22 y, 5 z - 11 y + 9 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=737.2MB, alloc=188.3MB, time=21.11 memory used=854.2MB, alloc=468.3MB, time=23.32 memory used=1013.3MB, alloc=492.3MB, time=28.68 N2 := 1925 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 2 2 -9 x + 11 y - 5 z, 11 z x + 2 z + 16 x, -14 x - 20 z - 12 x, -20 z + 9 y ] > J:=[op(GB),op(G)]; 2 2 2 J := [-99 x + 121 x y + 62 x + 22 y, 5 z - 11 y + 9 x, -14 x - 20 z - 12 x, 2 -20 z + 9 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 2, 1, 2, 3/4, 1/2, 1, 5/11, 2/11, 5/11, 4, 9, 7, 2, 2, 1, 2, 3/4, 3/4, 3/4, 1/2, 1/3, 1/4, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1043.6MB, alloc=492.3MB, time=29.82 |\^/| 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(); 1428497623 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-17 x + 7 x y - 8, 14 y z - 19 y - 20] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [18 x + 8 z - 6 x, 8 x y + 3 y - 15 z] > Problem := [F,G]; 2 Problem := [[-17 x + 7 x y - 8, 14 y z - 19 y - 20], 2 2 [18 x + 8 z - 6 x, 8 x y + 3 y - 15 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.54 memory used=48.0MB, alloc=32.3MB, time=0.85 memory used=68.0MB, alloc=32.3MB, time=1.15 memory used=87.8MB, alloc=56.3MB, time=1.54 memory used=130.2MB, alloc=60.3MB, time=2.35 memory used=168.7MB, alloc=84.3MB, time=3.10 memory used=225.0MB, alloc=108.3MB, time=4.99 N1 := 1345 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [-17 x + 7 x y - 8, 238 x z - 323 x - 140 x + 112 z - 152, 14 z y - 19 y - 20] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=298.0MB, alloc=116.3MB, time=6.78 memory used=374.9MB, alloc=116.3MB, time=8.11 memory used=453.1MB, alloc=140.3MB, time=9.51 memory used=548.1MB, alloc=164.3MB, time=11.78 N2 := 1959 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-17 x + 7 x y - 8, 14 z y - 19 y - 20, 18 x + 8 z - 6 x, 8 y x - 15 z + 3 y] > J:=[op(GB),op(G)]; 2 2 2 J := [-17 x + 7 x y - 8, 238 z x - 323 x + 112 z - 140 x - 152, 2 2 14 z y - 19 y - 20, 18 x + 8 z - 6 x, 8 y x - 15 z + 3 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 1, 2, 3/4, 3/4, 3/4, 5/12, 5/12, 1/4, 5, 11, 11, 3, 2, 1, 2, 4/5, 3/5, 4/5, 8/17, 5/17, 5/17, -2, -3, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=641.5MB, alloc=164.3MB, time=15.11 |\^/| 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(); 1428497641 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [8 x y - 9 x + 5 z, 9 x z + 6 y - 3] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [19 x - 3 y - 13 z, 14 x + 12 x y + 9] > Problem := [F,G]; Problem := [[8 x y - 9 x + 5 z, 9 x z + 6 y - 3], 2 2 2 [19 x - 3 y - 13 z, 14 x + 12 x y + 9]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=26.6MB, alloc=32.3MB, time=0.65 memory used=48.0MB, alloc=32.3MB, time=1.02 memory used=68.1MB, alloc=56.3MB, time=1.44 memory used=109.4MB, alloc=60.3MB, time=2.26 memory used=147.2MB, alloc=84.3MB, time=2.99 memory used=204.8MB, alloc=108.3MB, time=4.66 memory used=273.6MB, alloc=132.3MB, time=7.64 N1 := 1747 > GB := Basis(F, plex(op(vars))); 2 2 GB := [24 y x - 27 x - 10 y + 5, 8 y x + 5 z - 9 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=369.5MB, alloc=140.3MB, time=9.78 N2 := 739 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [8 y x + 5 z - 9 x, 9 x z + 6 y - 3, -3 y + 19 x - 13 z, 2 12 y x + 14 x + 9] > J:=[op(GB),op(G)]; 2 2 2 2 J := [24 y x - 27 x - 10 y + 5, 8 y x + 5 z - 9 x, -3 y + 19 x - 13 z, 2 12 y x + 14 x + 9] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 2, 2, 1, 1, 1, 3/4, 1/2, 1/3, 1/4, 4, 10, 9, 3, 2, 2, 1, 1, 1, 1/2, 7/13, 5/13, 2/13, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=382.2MB, alloc=140.3MB, time=10.20 |\^/| 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(); 1428497654 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-4 x z - 5 z - 18 x, 5 y z - 14 z + 9 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [5 x y - x - 8 y, -6 y - 10 x - 2] > Problem := [F,G]; 2 2 Problem := [[-4 x z - 5 z - 18 x, 5 y z - 14 z + 9 y], 2 [5 x y - x - 8 y, -6 y - 10 x - 2]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.53 memory used=47.7MB, alloc=32.3MB, time=0.87 memory used=68.0MB, alloc=56.3MB, time=1.32 memory used=113.1MB, alloc=60.3MB, time=2.19 memory used=153.2MB, alloc=84.3MB, time=2.91 memory used=209.9MB, alloc=108.3MB, time=4.43 N1 := 1655 > GB := Basis(F, plex(op(vars))); 2 2 2 2 GB := [50 y x + 112 y x + 75 y + 840 y x + 2352 x , -10 x y + 28 x z - 84 x - 15 y, 4 x y + 5 y z + 84 x + 15 y, 2 2 x y + 7 z + 42 x + 3 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=282.0MB, alloc=108.3MB, time=6.75 memory used=356.3MB, alloc=116.3MB, time=7.89 memory used=433.0MB, alloc=140.3MB, time=9.26 memory used=532.3MB, alloc=164.3MB, time=11.13 memory used=643.3MB, alloc=188.3MB, time=14.97 N2 := 2355 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-4 x z - 5 z - 18 x, -14 z + 5 z y + 9 y, 5 y x - 8 y - x, 2 -6 y - 10 x - 2] > J:=[op(GB),op(G)]; 2 2 2 2 J := [50 y x + 112 y x + 75 y + 840 y x + 2352 x , -10 x y + 28 x z - 84 x - 15 y, 5 z y + 4 y x + 15 y + 84 x, 2 2 7 z + 2 y x + 3 y + 42 x, 5 y x - 8 y - x, -6 y - 10 x - 2] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 8, 2, 1, 2, 2, 3/4, 3/4, 1/2, 5/12, 5/12, 1/3, 6, 15, 13, 14 14 3, 2, 2, 2, 1, 1, 1/2, --, --, 3/23, -7, -5, -1] 23 23 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=755.9MB, alloc=188.3MB, time=19.54 |\^/| 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(); 1428497678 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-2 x + 10 y z + 16 y, x z - 9 z - 11 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [7 y + 12 z - 15, -13 x z - y z - 10 x] > Problem := [F,G]; 2 2 Problem := [[-2 x + 10 y z + 16 y, x z - 9 z - 11 z], 2 [7 y + 12 z - 15, -13 x z - y z - 10 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=46.9MB, alloc=32.3MB, time=0.82 memory used=65.3MB, alloc=56.3MB, time=1.11 memory used=104.7MB, alloc=60.3MB, time=1.71 memory used=142.7MB, alloc=84.3MB, time=2.36 memory used=203.0MB, alloc=92.3MB, time=3.50 memory used=262.5MB, alloc=116.3MB, time=4.65 memory used=343.3MB, alloc=116.3MB, time=6.19 memory used=421.8MB, alloc=140.3MB, time=7.71 memory used=495.1MB, alloc=140.3MB, time=9.04 memory used=561.5MB, alloc=420.3MB, time=10.38 memory used=684.6MB, alloc=444.3MB, time=12.70 memory used=816.8MB, alloc=468.3MB, time=15.04 memory used=957.2MB, alloc=492.3MB, time=17.78 memory used=1109.4MB, alloc=516.3MB, time=20.74 memory used=1270.4MB, alloc=540.3MB, time=23.88 memory used=1442.2MB, alloc=564.3MB, time=27.23 memory used=1622.9MB, alloc=588.3MB, time=30.71 memory used=1813.1MB, alloc=612.3MB, time=34.59 memory used=2002.2MB, alloc=636.3MB, time=38.58 memory used=2175.6MB, alloc=660.3MB, time=42.28 memory used=2392.0MB, alloc=684.3MB, time=46.96 memory used=2615.2MB, alloc=708.3MB, time=51.53 memory used=2834.1MB, alloc=732.3MB, time=56.54 memory used=3024.6MB, alloc=756.3MB, time=64.12 memory used=3223.2MB, alloc=780.3MB, time=73.31 memory used=3434.1MB, alloc=804.3MB, time=82.62 memory used=3659.6MB, alloc=828.3MB, time=92.90 memory used=3899.6MB, alloc=852.3MB, time=103.16 memory used=4153.8MB, alloc=876.3MB, time=113.86 memory used=4423.8MB, alloc=900.3MB, time=125.44 memory used=4709.4MB, alloc=924.3MB, time=137.91 memory used=5010.9MB, alloc=948.3MB, time=150.86 memory used=5328.6MB, alloc=972.3MB, time=164.36 memory used=5662.6MB, alloc=996.3MB, time=178.44 memory used=6012.8MB, alloc=1020.3MB, time=193.40 memory used=6379.9MB, alloc=1044.3MB, time=210.07 memory used=6762.9MB, alloc=1068.3MB, time=227.27 |\^/| 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(); 1428497979 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-4 x + y - 11 y, 2 x z - 9 y + 11] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [14 x - 7 x z + 4 y, 19 x + 17 x z - 14 y z] > Problem := [F,G]; 2 2 Problem := [[-4 x + y - 11 y, 2 x z - 9 y + 11], 2 2 [14 x - 7 x z + 4 y, 19 x + 17 x z - 14 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.21 memory used=26.7MB, alloc=32.3MB, time=0.58 memory used=47.7MB, alloc=32.3MB, time=0.91 memory used=67.6MB, alloc=56.3MB, time=1.28 memory used=111.4MB, alloc=60.3MB, time=2.17 memory used=150.3MB, alloc=84.3MB, time=2.88 memory used=210.1MB, alloc=92.3MB, time=3.98 memory used=266.6MB, alloc=116.3MB, time=5.03 memory used=340.8MB, alloc=140.3MB, time=7.02 memory used=423.4MB, alloc=164.3MB, time=10.23 N1 := 2423 > GB := Basis(F, plex(op(vars))); 2 2 GB := [-4 x + y - 11 y, 2 z x - 9 y + 11] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=534.5MB, alloc=164.3MB, time=13.58 memory used=631.6MB, alloc=420.3MB, time=15.29 memory used=745.8MB, alloc=444.3MB, time=17.39 memory used=880.5MB, alloc=468.3MB, time=22.15 N2 := 2423 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-4 x + y - 11 y, 2 z x - 9 y + 11, -7 z x + 14 x + 4 y, 2 -14 z y + 17 z x + 19 x ] > J:=[op(GB),op(G)]; 2 2 2 J := [-4 x + y - 11 y, 2 z x - 9 y + 11, -7 z x + 14 x + 4 y, 2 -14 z y + 17 z x + 19 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 2, 2, 1, 1, 1, 3/4, 1/2, 5/12, 1/3, 4, 11, 8, 2, 2, 2, 1, 1, 1, 3/4, 1/2, 5/12, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=995.5MB, alloc=468.3MB, time=26.75 |\^/| 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(); 1428498013 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-6 y z + 18 z - 17 x, 4 x y + 8 x - 19 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [7 x z - 20 y + 18, -19 y z - 3 z + 3] > Problem := [F,G]; 2 Problem := [[-6 y z + 18 z - 17 x, 4 x y + 8 x - 19 y], [7 x z - 20 y + 18, -19 y z - 3 z + 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.53 memory used=47.5MB, alloc=32.3MB, time=0.87 memory used=66.7MB, alloc=56.3MB, time=1.21 memory used=107.3MB, alloc=60.3MB, time=1.89 memory used=146.3MB, alloc=84.3MB, time=2.56 memory used=210.1MB, alloc=116.3MB, time=3.80 memory used=290.1MB, alloc=116.3MB, time=5.34 memory used=365.5MB, alloc=140.3MB, time=6.82 memory used=460.1MB, alloc=164.3MB, time=8.54 memory used=562.2MB, alloc=188.3MB, time=10.68 memory used=686.6MB, alloc=212.3MB, time=14.65 memory used=813.5MB, alloc=236.3MB, time=19.75 memory used=951.1MB, alloc=260.3MB, time=25.48 memory used=1104.1MB, alloc=284.3MB, time=32.15 memory used=1281.0MB, alloc=284.3MB, time=40.06 memory used=1457.9MB, alloc=308.3MB, time=48.28 memory used=1658.8MB, alloc=308.3MB, time=57.20 memory used=1859.8MB, alloc=332.3MB, time=66.26 N1 := 6355 > GB := Basis(F, plex(op(vars))); 2 GB := [4 y x - 19 y + 8 x, -6 y z + 18 z - 17 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2031.4MB, alloc=332.3MB, time=72.12 memory used=2293.7MB, alloc=588.3MB, time=78.13 memory used=2539.5MB, alloc=612.3MB, time=84.03 memory used=2794.6MB, alloc=636.3MB, time=93.68 memory used=3035.1MB, alloc=660.3MB, time=104.91 memory used=3294.3MB, alloc=684.3MB, time=116.89 memory used=3577.5MB, alloc=708.3MB, time=131.17 memory used=3885.0MB, alloc=732.3MB, time=144.84 N2 := 6355 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [-6 y z + 18 z - 17 x, 4 y x - 19 y + 8 x, 7 z x - 20 y + 18, -19 y z - 3 z + 3] > J:=[op(GB),op(G)]; 2 J := [4 y x - 19 y + 8 x, -6 y z + 18 z - 17 x, 7 z x - 20 y + 18, -19 y z - 3 z + 3] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 1, 1, 2, 3/4, 1, 3/4, 1/3, 5/12, 5/12, 4, 10, 8, 2, 1, 1, 2, 3/4, 1, 3/4, 1/3, 5/12, 5/12, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=3924.5MB, alloc=732.3MB, time=146.83 |\^/| 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(); 1428498195 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-11 x - 6 x y + 19 z , 13 y - 3 x + 3 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-19 y z - 4 z + 5, 14 x - 20 x z - 17 y] > Problem := [F,G]; 2 2 2 Problem := [[-11 x - 6 x y + 19 z , 13 y - 3 x + 3 z], 2 [-19 y z - 4 z + 5, 14 x - 20 x z - 17 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.2MB, alloc=44.3MB, time=0.76 memory used=57.7MB, alloc=44.3MB, time=1.17 memory used=84.6MB, alloc=68.3MB, time=1.55 memory used=135.7MB, alloc=76.3MB, time=2.57 memory used=184.8MB, alloc=76.3MB, time=3.36 memory used=236.4MB, alloc=100.3MB, time=4.28 memory used=309.4MB, alloc=100.3MB, time=5.69 memory used=377.1MB, alloc=124.3MB, time=6.74 memory used=453.5MB, alloc=380.3MB, time=7.99 memory used=547.9MB, alloc=404.3MB, time=9.36 memory used=664.3MB, alloc=428.3MB, time=11.30 memory used=805.3MB, alloc=452.3MB, time=14.23 memory used=946.7MB, alloc=476.3MB, time=17.14 memory used=1100.1MB, alloc=500.3MB, time=20.67 memory used=1268.1MB, alloc=524.3MB, time=24.49 memory used=1449.6MB, alloc=548.3MB, time=27.87 memory used=1633.2MB, alloc=572.3MB, time=31.49 memory used=1805.8MB, alloc=596.3MB, time=34.94 memory used=1969.0MB, alloc=620.3MB, time=38.39 memory used=2120.6MB, alloc=644.3MB, time=41.73 memory used=2328.1MB, alloc=668.3MB, time=48.13 memory used=2543.5MB, alloc=692.3MB, time=56.29 memory used=2767.5MB, alloc=716.3MB, time=65.16 memory used=3004.2MB, alloc=740.3MB, time=74.94 memory used=3254.5MB, alloc=764.3MB, time=86.61 memory used=3518.8MB, alloc=788.3MB, time=98.71 memory used=3797.4MB, alloc=812.3MB, time=110.79 memory used=4090.8MB, alloc=836.3MB, time=125.44 memory used=4393.3MB, alloc=860.3MB, time=140.64 memory used=4719.8MB, alloc=884.3MB, time=155.59 memory used=5070.2MB, alloc=908.3MB, time=171.15 memory used=5444.5MB, alloc=932.3MB, time=187.76 memory used=5842.8MB, alloc=956.3MB, time=205.54 memory used=6265.0MB, alloc=980.3MB, time=224.50 |\^/| 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(); 1428498495 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [5 x y - 16 z - 7, -9 x z - 3 z - 15 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [-2 x y - 3 y - 16, 18 x y + 9 x z - 14 y] > Problem := [F,G]; 2 Problem := [[5 x y - 16 z - 7, -9 x z - 3 z - 15 z], [-2 x y - 3 y - 16, 18 x y + 9 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.4MB, alloc=32.3MB, time=0.81 memory used=67.3MB, alloc=56.3MB, time=1.15 memory used=109.7MB, alloc=60.3MB, time=1.89 memory used=147.4MB, alloc=84.3MB, time=2.61 memory used=204.8MB, alloc=108.3MB, time=3.80 memory used=278.4MB, alloc=140.3MB, time=5.94 memory used=360.3MB, alloc=140.3MB, time=9.28 memory used=440.1MB, alloc=164.3MB, time=12.57 N1 := 2873 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [25 x y + 240 x y + 330 x y - 336 x - 511, -5 x y + 16 z + 7] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=547.3MB, alloc=164.3MB, time=15.81 N2 := 941 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [5 y x - 16 z - 7, -9 x z - 3 z - 15 z, -2 x y - 3 y - 16, 9 z x + 18 y x - 14 y] > J:=[op(GB),op(G)]; 2 2 2 J := [25 x y + 240 x y + 330 x y - 336 x - 511, -5 x y + 16 z + 7, -2 x y - 3 y - 16, 9 z x + 18 y x - 14 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 1, 1, 2, 1, 3/4, 3/4, 5/12, 5/12, 5/12, 4, 10, 10, 4, 2, 2, 1, 1, 1, 1/2, 4/7, 4/7, 1/7, 0, -2, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=651.7MB, alloc=164.3MB, time=18.07 |\^/| 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(); 1428498522 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-9 x y + 6 y + 13 y z, 20 x z + 14 y + 11 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [15 x z - 20 y + 7, x + 6 y - 4 z] > Problem := [F,G]; 2 2 2 Problem := [[-9 x y + 6 y + 13 y z, 20 x z + 14 y + 11 z ], 2 [15 x z - 20 y + 7, x + 6 y - 4 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.49 memory used=47.8MB, alloc=32.3MB, time=0.81 memory used=68.2MB, alloc=56.3MB, time=1.16 memory used=111.2MB, alloc=60.3MB, time=1.81 memory used=152.6MB, alloc=84.3MB, time=2.44 memory used=214.7MB, alloc=92.3MB, time=3.40 memory used=276.7MB, alloc=116.3MB, time=4.54 memory used=357.5MB, alloc=140.3MB, time=6.10 memory used=451.0MB, alloc=164.3MB, time=7.77 memory used=557.6MB, alloc=188.3MB, time=9.59 memory used=664.2MB, alloc=468.3MB, time=11.50 memory used=811.4MB, alloc=492.3MB, time=14.03 memory used=966.8MB, alloc=516.3MB, time=16.94 memory used=1123.7MB, alloc=540.3MB, time=21.73 memory used=1286.2MB, alloc=564.3MB, time=27.55 memory used=1461.6MB, alloc=588.3MB, time=34.48 memory used=1645.9MB, alloc=612.3MB, time=42.31 memory used=1851.4MB, alloc=636.3MB, time=51.00 memory used=2080.8MB, alloc=660.3MB, time=60.80 memory used=2334.2MB, alloc=660.3MB, time=71.25 memory used=2587.6MB, alloc=684.3MB, time=81.71 memory used=2864.8MB, alloc=684.3MB, time=93.00 memory used=3141.9MB, alloc=684.3MB, time=104.03 memory used=3419.0MB, alloc=708.3MB, time=115.11 memory used=3720.0MB, alloc=708.3MB, time=126.90 memory used=4021.1MB, alloc=732.3MB, time=138.88 N1 := 10299 > GB := Basis(F, plex(op(vars))); 2 2 3 2 GB := [3231 x y - 2748 x y + 2762 y , -9 x y + 6 y + 13 y z, 2 2 11 z + 20 z x + 14 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4348.7MB, alloc=732.3MB, time=151.23 memory used=4710.0MB, alloc=732.3MB, time=157.61 memory used=5068.7MB, alloc=756.3MB, time=164.30 memory used=5437.6MB, alloc=780.3MB, time=173.29 memory used=5771.3MB, alloc=804.3MB, time=185.92 memory used=6097.4MB, alloc=828.3MB, time=199.89 memory used=6443.8MB, alloc=852.3MB, time=214.49 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428498822 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-5 z - 16 x, 5 y + 4 y + 18] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-17 x - 13 x y + 14, -18 x y + 18 x - 16 y] > Problem := [F,G]; 2 2 Problem := [[-5 z - 16 x, 5 y + 4 y + 18], 2 [-17 x - 13 x y + 14, -18 x y + 18 x - 16 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); N1 := 167 > GB := Basis(F, plex(op(vars))); 2 2 GB := [5 y + 4 y + 18, 5 z + 16 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=33.7MB, alloc=40.3MB, time=0.65 N2 := 167 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 2 2 -5 z - 16 x, 5 y + 4 y + 18, -17 x - 13 x y + 14, -18 x y + 18 x - 16 y] > J:=[op(GB),op(G)]; J := 2 2 2 [5 y + 4 y + 18, 5 z + 16 x, -17 x - 13 x y + 14, -18 x y + 18 x - 16 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 7, 8, 2, 2, 2, 2, 3/4, 3/4, 1/4, 5/11, 5/11, 1/11, 4, 7, 8, 2, 2, 2, 2, 3/4, 3/4, 1/4, 5/11, 5/11, 1/11, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=55.6MB, alloc=40.3MB, time=1.00 |\^/| 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(); 1428498823 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-8 y z - z + 10, 10 x + 12 z - 1] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [16 x z + 16 z - 9, 20 x z + 20 y + 11 x] > Problem := [F,G]; 2 2 2 Problem := [[-8 y z - z + 10, 10 x + 12 z - 1], 2 2 [16 x z + 16 z - 9, 20 x z + 20 y + 11 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=27.1MB, alloc=32.3MB, time=0.51 memory used=48.2MB, alloc=32.3MB, time=0.82 memory used=68.2MB, alloc=56.3MB, time=1.14 memory used=109.8MB, alloc=60.3MB, time=1.75 memory used=148.2MB, alloc=60.3MB, time=2.30 memory used=188.1MB, alloc=92.3MB, time=2.90 memory used=253.5MB, alloc=92.3MB, time=3.81 memory used=317.8MB, alloc=116.3MB, time=4.74 memory used=389.1MB, alloc=372.3MB, time=5.79 memory used=471.4MB, alloc=396.3MB, time=7.27 memory used=568.4MB, alloc=420.3MB, time=8.99 memory used=684.0MB, alloc=444.3MB, time=11.02 memory used=809.3MB, alloc=468.3MB, time=13.53 memory used=935.9MB, alloc=492.3MB, time=17.23 memory used=1064.5MB, alloc=516.3MB, time=22.11 memory used=1215.0MB, alloc=540.3MB, time=27.87 memory used=1389.4MB, alloc=540.3MB, time=34.65 memory used=1563.9MB, alloc=564.3MB, time=41.27 memory used=1762.2MB, alloc=588.3MB, time=48.97 N1 := 5743 > GB := Basis(F, plex(op(vars))); 2 2 4 2 2 GB := [7680 y x + 100 x - 768 y + 2380 x + 14161, 2 2 2 2 2 80 x y + 10 x z - 8 y + 119 z, -10 x + 96 y z - 119, 12 z + 10 x - 1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1989.6MB, alloc=588.3MB, time=53.92 memory used=2121.1MB, alloc=588.3MB, time=56.05 memory used=2260.8MB, alloc=588.3MB, time=58.28 memory used=2370.0MB, alloc=588.3MB, time=60.15 memory used=2501.0MB, alloc=588.3MB, time=62.23 memory used=2653.2MB, alloc=612.3MB, time=65.06 memory used=2855.6MB, alloc=636.3MB, time=68.88 memory used=3028.8MB, alloc=660.3MB, time=72.25 memory used=3233.3MB, alloc=684.3MB, time=76.33 memory used=3423.2MB, alloc=708.3MB, time=80.96 memory used=3719.2MB, alloc=732.3MB, time=91.54 memory used=4002.7MB, alloc=756.3MB, time=103.81 memory used=4305.8MB, alloc=780.3MB, time=117.02 memory used=4632.8MB, alloc=804.3MB, time=131.30 memory used=4983.8MB, alloc=828.3MB, time=146.66 memory used=5358.9MB, alloc=852.3MB, time=162.80 memory used=5758.1MB, alloc=876.3MB, time=179.59 memory used=6181.4MB, alloc=900.3MB, time=197.52 N2 := 9573 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-8 y z - z + 10, 12 z + 10 x - 1, 16 z + 16 z x - 9, 2 20 z x + 20 y + 11 x] > J:=[op(GB),op(G)]; 2 2 4 2 2 J := [7680 y x + 100 x - 768 y + 2380 x + 14161, 2 2 2 2 2 10 z x + 80 y x + 119 z - 8 y, -10 x + 96 y z - 119, 12 z + 10 x - 1, 2 2 16 z + 16 z x - 9, 20 z x + 20 y + 11 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 2, 3/4, 1/2, 1, 1/3, 1/6, 1/2, 6, 15, 15, 4, 10 4, 2, 2, 1, 2/3, 5/6, --, 2/7, 1/3, -6, -7, -2] 21 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=6217.6MB, alloc=900.3MB, time=198.82 |\^/| 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(); 1428499059 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-10 y - 18 z + 20, 4 x z + 16 z - 1] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-10 y z + 17 x + 9, -3 x y + 17 y - 2] > Problem := [F,G]; 2 2 Problem := [[-10 y - 18 z + 20, 4 x z + 16 z - 1], 2 [-10 y z + 17 x + 9, -3 x y + 17 y - 2]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.6MB, alloc=32.3MB, time=0.84 memory used=67.8MB, alloc=56.3MB, time=1.18 memory used=110.8MB, alloc=60.3MB, time=1.90 memory used=154.6MB, alloc=84.3MB, time=2.63 memory used=216.3MB, alloc=116.3MB, time=3.76 memory used=297.3MB, alloc=116.3MB, time=5.09 memory used=373.5MB, alloc=140.3MB, time=6.38 memory used=464.8MB, alloc=164.3MB, time=7.96 memory used=577.4MB, alloc=188.3MB, time=9.86 memory used=701.1MB, alloc=468.3MB, time=12.01 memory used=825.9MB, alloc=492.3MB, time=15.68 memory used=960.4MB, alloc=516.3MB, time=20.00 memory used=1109.1MB, alloc=540.3MB, time=25.05 memory used=1270.3MB, alloc=564.3MB, time=31.18 memory used=1450.8MB, alloc=588.3MB, time=38.24 memory used=1655.3MB, alloc=588.3MB, time=46.12 memory used=1859.7MB, alloc=612.3MB, time=53.93 memory used=2088.1MB, alloc=612.3MB, time=62.70 memory used=2316.4MB, alloc=612.3MB, time=71.41 memory used=2544.7MB, alloc=636.3MB, time=80.28 memory used=2797.0MB, alloc=636.3MB, time=90.10 memory used=3049.3MB, alloc=660.3MB, time=99.96 memory used=3325.8MB, alloc=684.3MB, time=111.01 N1 := 9147 > GB := Basis(F, plex(op(vars))); 4 2 2 2 GB := [400 y - 180 x y - 1600 y + 360 x + 1519, 5 y + 9 z - 10] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3633.4MB, alloc=684.3MB, time=118.90 N2 := 2721 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-10 y - 18 z + 20, 16 z + 4 z x - 1, -10 z y + 17 x + 9, 2 -3 x y + 17 y - 2] > J:=[op(GB),op(G)]; 4 2 2 2 J := [400 y - 180 x y - 1600 y + 360 x + 1519, 5 y + 9 z - 10, 2 -10 z y + 17 x + 9, -3 x y + 17 y - 2] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 1, 2, 2, 3/4, 3/4, 3/4, 1/4, 1/3, 1/3, 4, 9, 10, 4, 1, 4, 1, 3/4, 1, 1/2, 2/7, 1/2, 1/7, 0, -2, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=3939.7MB, alloc=684.3MB, time=133.09 |\^/| 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(); 1428499210 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-12 x y - 3 y + 16 y, -10 x y + 8 x z - 5 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [7 y - 2 y z - 19, -5 x + 12 y + 15] > Problem := [F,G]; 2 Problem := [[-12 x y - 3 y + 16 y, -10 x y + 8 x z - 5 z], 2 2 2 [7 y - 2 y z - 19, -5 x + 12 y + 15]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.52 memory used=48.7MB, alloc=32.3MB, time=0.93 memory used=68.5MB, alloc=56.3MB, time=1.33 memory used=110.4MB, alloc=84.3MB, time=2.56 N1 := 751 > GB := Basis(F, plex(op(vars))); 2 GB := [12 x y + 3 y - 16 y, -10 x y + 8 x z - 5 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=168.9MB, alloc=84.3MB, time=3.69 N2 := 751 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-12 x y - 3 y + 16 y, -10 x y + 8 x z - 5 z, -2 z y + 7 y - 19, 2 2 -5 x + 12 y + 15] > J:=[op(GB),op(G)]; 2 2 J := [12 x y + 3 y - 16 y, -10 x y + 8 x z - 5 z, -2 z y + 7 y - 19, 2 2 -5 x + 12 y + 15] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 1, 3/4, 1, 1/2, 1/3, 7/12, 1/4, 4, 9, 8, 2, 2, 2, 1, 3/4, 1, 1/2, 1/3, 7/12, 1/4, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=218.9MB, alloc=84.3MB, time=5.19 |\^/| 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(); 1428499217 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [11 y z + 16 z + 10, 15 x - 7 y z + 3 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [18 x - 12 y + 19 z, -6 x - 8 x z - 15 y] > Problem := [F,G]; 2 2 Problem := [[11 y z + 16 z + 10, 15 x - 7 y z + 3 y], 2 2 2 [18 x - 12 y + 19 z, -6 x - 8 x z - 15 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.4MB, alloc=44.3MB, time=0.68 memory used=59.0MB, alloc=44.3MB, time=1.16 memory used=86.4MB, alloc=68.3MB, time=1.61 memory used=137.0MB, alloc=76.3MB, time=2.46 memory used=186.5MB, alloc=100.3MB, time=3.27 memory used=259.3MB, alloc=100.3MB, time=4.41 memory used=321.6MB, alloc=356.3MB, time=5.38 memory used=394.1MB, alloc=380.3MB, time=6.59 memory used=491.3MB, alloc=380.3MB, time=8.12 memory used=585.8MB, alloc=404.3MB, time=9.66 memory used=703.7MB, alloc=428.3MB, time=11.59 memory used=844.4MB, alloc=452.3MB, time=14.36 memory used=986.2MB, alloc=476.3MB, time=17.44 memory used=1137.6MB, alloc=500.3MB, time=20.53 memory used=1301.4MB, alloc=524.3MB, time=23.92 memory used=1475.5MB, alloc=548.3MB, time=27.58 memory used=1645.5MB, alloc=572.3MB, time=31.11 memory used=1812.0MB, alloc=596.3MB, time=34.49 memory used=1966.3MB, alloc=620.3MB, time=37.84 memory used=2116.7MB, alloc=644.3MB, time=41.39 memory used=2329.5MB, alloc=668.3MB, time=48.49 memory used=2545.6MB, alloc=692.3MB, time=56.43 memory used=2774.3MB, alloc=716.3MB, time=65.23 memory used=3017.3MB, alloc=740.3MB, time=75.30 memory used=3274.5MB, alloc=764.3MB, time=85.81 memory used=3546.4MB, alloc=788.3MB, time=96.92 memory used=3826.4MB, alloc=812.3MB, time=109.65 memory used=4127.7MB, alloc=836.3MB, time=123.06 memory used=4452.8MB, alloc=860.3MB, time=137.81 memory used=4802.0MB, alloc=884.3MB, time=153.94 memory used=5175.0MB, alloc=908.3MB, time=170.46 memory used=5572.0MB, alloc=932.3MB, time=188.37 memory used=5992.9MB, alloc=932.3MB, 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(); 1428499517 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [6 x y - 16 y - 8 y z, 15 x z + 13 y + 6 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-2 x - 20 x y - 10 y, -11 x - 5 y - 16 y] > Problem := [F,G]; 2 2 2 Problem := [[6 x y - 16 y - 8 y z, 15 x z + 13 y + 6 z ], 2 2 2 [-2 x - 20 x y - 10 y, -11 x - 5 y - 16 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.4MB, alloc=32.3MB, time=0.83 memory used=69.0MB, alloc=56.3MB, time=1.23 memory used=110.0MB, alloc=60.3MB, time=1.96 memory used=147.5MB, alloc=84.3MB, time=2.62 memory used=205.1MB, alloc=116.3MB, time=3.67 memory used=278.7MB, alloc=140.3MB, time=5.84 memory used=364.2MB, alloc=140.3MB, time=9.13 N1 := 2413 > GB := Basis(F, plex(op(vars))); GB := [ 2 2 3 2 2 2 117 x y - 384 x y + 296 y , -3 x y + 8 y + 4 y z, 6 z + 15 z x + 13 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=452.6MB, alloc=140.3MB, time=12.03 memory used=547.6MB, alloc=164.3MB, time=13.81 memory used=666.0MB, alloc=188.3MB, time=16.16 memory used=788.5MB, alloc=212.3MB, time=20.68 N2 := 2413 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [6 x y - 16 y - 8 y z, 6 z + 15 z x + 13 y , -2 x - 20 x y - 10 y, 2 2 -11 x - 5 y - 16 y] > J:=[op(GB),op(G)]; 2 2 3 2 J := [117 x y - 384 x y + 296 y , -3 x y + 8 y + 4 y z, 2 2 2 2 2 6 z + 15 z x + 13 y , -2 x - 20 x y - 10 y, -11 x - 5 y - 16 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 2, 2, 1, 1, 1/2, 5/12, 2/3, 1/4, 5, 12, 11, 3, 11 2, 3, 2, 1, 1, 2/5, 7/15, --, 1/5, -2, -3, -1] 15 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=868.0MB, alloc=212.3MB, time=23.66 |\^/| 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(); 1428499557 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [13 y z - y, -18 z + y + 13 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [20 x - 4 y + 13 z , 8 x y - 2 y + 12 x] > Problem := [F,G]; 2 Problem := [[13 y z - y, -18 z + y + 13 z], 2 2 2 2 [20 x - 4 y + 13 z , 8 x y - 2 y + 12 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.53 memory used=47.9MB, alloc=32.3MB, time=0.84 memory used=67.4MB, alloc=56.3MB, time=1.16 memory used=108.1MB, alloc=60.3MB, time=1.79 memory used=146.3MB, alloc=84.3MB, time=2.38 memory used=210.2MB, alloc=116.3MB, time=3.59 memory used=287.9MB, alloc=140.3MB, time=5.03 memory used=383.4MB, alloc=164.3MB, time=6.69 memory used=496.9MB, alloc=188.3MB, time=8.64 memory used=620.4MB, alloc=212.3MB, time=10.82 memory used=749.2MB, alloc=236.3MB, time=13.74 memory used=875.7MB, alloc=260.3MB, time=17.64 memory used=1013.8MB, alloc=284.3MB, time=22.16 memory used=1165.9MB, alloc=308.3MB, time=27.49 memory used=1332.2MB, alloc=332.3MB, time=33.90 memory used=1514.5MB, alloc=356.3MB, time=41.95 memory used=1720.7MB, alloc=380.3MB, time=50.21 memory used=1951.0MB, alloc=380.3MB, time=59.42 memory used=2181.2MB, alloc=404.3MB, time=68.73 memory used=2435.3MB, alloc=404.3MB, time=79.27 memory used=2689.4MB, alloc=404.3MB, time=89.97 memory used=2943.4MB, alloc=404.3MB, time=100.42 memory used=3197.4MB, alloc=428.3MB, time=110.71 memory used=3475.4MB, alloc=428.3MB, time=122.04 memory used=3753.2MB, alloc=452.3MB, time=133.78 memory used=4054.9MB, alloc=452.3MB, time=146.41 memory used=4356.6MB, alloc=476.3MB, time=158.69 N1 := 10951 > GB := Basis(F, plex(op(vars))); 2 2 GB := [169 y + 151 y, 13 y z - y, 18 z - y - 13 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4524.4MB, alloc=476.3MB, time=164.53 memory used=4902.6MB, alloc=732.3MB, time=171.92 memory used=5269.1MB, alloc=756.3MB, time=180.33 memory used=5590.2MB, alloc=780.3MB, time=192.39 memory used=5907.4MB, alloc=804.3MB, time=205.25 memory used=6236.8MB, alloc=828.3MB, time=219.58 memory used=6590.2MB, alloc=852.3MB, time=235.07 |\^/| 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(); 1428499857 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-8 y + y z + 5 z , -16 x + 9 x z + 19 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-20 x - 11 x z - 3 y, -18 y z - 19 z - 14 x] > Problem := [F,G]; 2 2 2 Problem := [[-8 y + y z + 5 z , -16 x + 9 x z + 19 y], 2 2 [-20 x - 11 x z - 3 y, -18 y z - 19 z - 14 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.53 memory used=47.1MB, alloc=56.3MB, time=0.86 memory used=88.1MB, alloc=60.3MB, time=1.48 memory used=128.3MB, alloc=92.3MB, time=2.12 memory used=194.2MB, alloc=92.3MB, time=3.08 memory used=257.2MB, alloc=116.3MB, time=4.07 memory used=326.5MB, alloc=372.3MB, time=5.25 memory used=415.3MB, alloc=396.3MB, time=6.62 memory used=526.8MB, alloc=420.3MB, time=8.34 memory used=662.4MB, alloc=420.3MB, time=10.41 memory used=794.1MB, alloc=444.3MB, time=12.68 memory used=948.5MB, alloc=468.3MB, time=15.40 memory used=1104.5MB, alloc=492.3MB, time=18.29 memory used=1274.1MB, alloc=516.3MB, time=21.57 memory used=1445.0MB, alloc=540.3MB, time=24.91 memory used=1605.5MB, alloc=564.3MB, time=28.07 memory used=1770.7MB, alloc=588.3MB, time=31.32 memory used=1922.1MB, alloc=612.3MB, time=34.35 memory used=2076.5MB, alloc=636.3MB, time=37.49 memory used=2230.4MB, alloc=660.3MB, time=40.37 memory used=2371.5MB, alloc=684.3MB, time=43.38 memory used=2505.5MB, alloc=708.3MB, time=46.30 memory used=2645.2MB, alloc=732.3MB, time=49.37 memory used=2773.6MB, alloc=756.3MB, time=52.31 memory used=2890.2MB, alloc=780.3MB, time=55.23 memory used=3029.4MB, alloc=804.3MB, time=59.43 memory used=3269.7MB, alloc=828.3MB, time=68.63 memory used=3505.7MB, alloc=852.3MB, time=77.91 memory used=3701.9MB, alloc=876.3MB, time=86.00 memory used=4042.6MB, alloc=900.3MB, time=99.55 memory used=4391.0MB, alloc=924.3MB, time=113.91 memory used=4749.7MB, alloc=948.3MB, time=129.02 memory used=5123.3MB, alloc=972.3MB, time=144.85 memory used=5511.1MB, alloc=996.3MB, time=161.69 memory used=5912.8MB, alloc=1020.3MB, time=180.25 memory used=6319.2MB, alloc=1044.3MB, time=200.17 memory used=6749.5MB, alloc=1068.3MB, time=219.71 memory used=7203.8MB, alloc=1092.3MB, time=239.99 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428500157 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [10 z + 2 x + 15, -14 x + 20 x y + 8] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [16 - 18 y - 20 z, 16 x y + 9 z + 4 y] > Problem := [F,G]; 2 2 Problem := [[10 z + 2 x + 15, -14 x + 20 x y + 8], 2 [16 - 18 y - 20 z, 16 x y + 9 z + 4 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=47.2MB, alloc=32.3MB, time=0.80 memory used=67.3MB, alloc=56.3MB, time=1.13 memory used=111.0MB, alloc=60.3MB, time=1.90 memory used=149.4MB, alloc=84.3MB, time=2.59 memory used=207.1MB, alloc=108.3MB, time=4.09 N1 := 1499 > GB := Basis(F, plex(op(vars))); 2 2 GB := [-7 x + 10 x y + 4, 10 z + 2 x + 15] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=280.5MB, alloc=108.3MB, time=6.15 memory used=360.0MB, alloc=140.3MB, time=7.50 memory used=459.5MB, alloc=164.3MB, time=9.78 N2 := 1499 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [10 z + 2 x + 15, -14 x + 20 x y + 8, 16 - 18 y - 20 z, 2 9 z + 16 y x + 4 y] > J:=[op(GB),op(G)]; J := [ 2 2 2 -7 x + 10 x y + 4, 10 z + 2 x + 15, 16 - 18 y - 20 z, 9 z + 16 y x + 4 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 2, 1, 2, 3/4, 3/4, 3/4, 1/3, 1/3, 1/4, 4, 9, 7, 2, 2, 1, 2, 3/4, 3/4, 3/4, 1/3, 1/3, 1/4, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=510.8MB, alloc=164.3MB, time=11.40 |\^/| 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(); 1428500175 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [19 x y + 4 x z - 6 y , x - 18 x y + 15] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [6 x - 16 y - 13 x, 19 x - 16 x + 17 y] > Problem := [F,G]; 2 2 Problem := [[19 x y + 4 x z - 6 y , x - 18 x y + 15], 2 2 2 [6 x - 16 y - 13 x, 19 x - 16 x + 17 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=27.4MB, alloc=32.3MB, time=0.55 N1 := 285 > GB := Basis(F, plex(op(vars))); 2 3 3 GB := [-x + 18 x y - 15, x - 5832 y + 15 x + 15660 y + 3240 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=48.9MB, alloc=32.3MB, time=0.95 memory used=69.2MB, alloc=56.3MB, time=1.29 N2 := 291 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [4 z x - 6 y + 19 y x, -18 y x + x + 15, -16 y + 6 x - 13 x, 2 19 x + 17 y - 16 x] > J:=[op(GB),op(G)]; 2 3 3 J := [-x + 18 x y - 15, -5832 y + x + 3240 z + 15660 y + 15 x, 2 2 2 -16 y + 6 x - 13 x, 19 x + 17 y - 16 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 1, 1, 1, 1/4, 2/3, 5/12, 1/12, 4, 9, 9, 3, 3, 3, 1, 1, 1, 1/4, 4/7, 5/14, 1/14, 0, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=89.0MB, alloc=56.3MB, time=1.64 |\^/| 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(); 1428500177 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [3 - 13 x + 5 y, -10 y + 4 y z - 7] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [7 x + 11 x z + 5 y, 4 x - 15 x y - 14 x z] > Problem := [F,G]; 2 Problem := [[3 - 13 x + 5 y, -10 y + 4 y z - 7], 2 2 [7 x + 11 x z + 5 y, 4 x - 15 x y - 14 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.3MB, alloc=32.3MB, time=0.81 memory used=67.3MB, alloc=56.3MB, time=1.15 memory used=108.7MB, alloc=60.3MB, time=1.85 memory used=146.3MB, alloc=84.3MB, time=2.50 memory used=203.2MB, alloc=108.3MB, time=4.18 N1 := 1395 > GB := Basis(F, plex(op(vars))); 2 GB := [3 - 13 x + 5 y, -338 x + 52 x z + 156 x - 12 z - 53] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=278.0MB, alloc=108.3MB, time=5.98 N2 := 717 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [3 - 13 x + 5 y, -10 y + 4 y z - 7, 11 z x + 7 x + 5 y, 2 4 x - 15 x y - 14 x z] > J:=[op(GB),op(G)]; 2 2 J := [3 - 13 x + 5 y, -338 x + 52 x z + 156 x - 12 z - 53, 11 z x + 7 x + 5 y, 2 4 x - 15 x y - 14 x z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 7, 2, 2, 2, 1, 3/4, 1, 3/4, 1/2, 5/12, 1/4, 4, 10, 7, 2, 2, 1, 1, 1, 3/4, 3/4, 9/14, 3/14, 2/7, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=337.9MB, alloc=108.3MB, time=7.35 |\^/| 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(); 1428500188 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-11 x z - 11 y z + 8 x, x - z + 6] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-12 x + 12 x z - 8 y , 11 x - 7 y z - 18 y] > Problem := [F,G]; 2 Problem := [[-11 x z - 11 y z + 8 x, x - z + 6], 2 2 2 [-12 x + 12 x z - 8 y , 11 x - 7 y z - 18 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=46.6MB, alloc=32.3MB, time=0.80 memory used=66.2MB, alloc=56.3MB, time=1.11 memory used=107.6MB, alloc=60.3MB, time=1.73 memory used=147.6MB, alloc=84.3MB, time=2.33 memory used=209.9MB, alloc=92.3MB, time=3.28 memory used=270.0MB, alloc=116.3MB, time=4.20 memory used=353.1MB, alloc=140.3MB, time=5.62 memory used=451.4MB, alloc=140.3MB, time=7.34 memory used=540.0MB, alloc=164.3MB, time=9.29 memory used=633.3MB, alloc=188.3MB, time=12.63 memory used=744.6MB, alloc=212.3MB, time=16.96 N1 := 2853 > GB := Basis(F, plex(op(vars))); 2 3 2 GB := [11 y x + 11 x + 66 y + 58 x, -x + z - 6] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=859.6MB, alloc=212.3MB, time=19.58 N2 := 449 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-11 x z - 11 y z + 8 x, x - z + 6, -12 x + 12 x z - 8 y , 2 -7 z y + 11 x - 18 y] > J:=[op(GB),op(G)]; 2 3 2 2 2 J := [11 y x + 11 x + 66 y + 58 x, -x + z - 6, -12 x + 12 x z - 8 y , 2 -7 z y + 11 x - 18 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 2, 2, 1, 1, 3/4, 1, 1/2, 1/3, 5/12, 4, 10, 9, 3, 3, 2, 1, 1, 3/4, 3/4, 7/13, 5/13, 3/13, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=896.3MB, alloc=468.3MB, time=20.30 |\^/| 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(); 1428500214 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [5 x y - 7 y z + 14 x, -14 x y - 2 x z + 11] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-5 y - 9 y z + 9 y, 17 x - 14 y z + 13 x] > Problem := [F,G]; Problem := [[5 x y - 7 y z + 14 x, -14 x y - 2 x z + 11], 2 2 [-5 y - 9 y z + 9 y, 17 x - 14 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.49 memory used=46.8MB, alloc=32.3MB, time=0.79 memory used=66.0MB, alloc=56.3MB, time=1.09 memory used=106.8MB, alloc=60.3MB, time=1.71 memory used=146.7MB, alloc=84.3MB, time=2.32 memory used=209.7MB, alloc=92.3MB, time=3.41 memory used=266.0MB, alloc=116.3MB, time=4.39 memory used=341.5MB, alloc=140.3MB, time=5.70 memory used=435.0MB, alloc=164.3MB, time=7.35 memory used=543.0MB, alloc=188.3MB, time=9.99 memory used=655.0MB, alloc=212.3MB, time=13.80 memory used=779.3MB, alloc=236.3MB, time=18.71 memory used=927.5MB, alloc=236.3MB, time=24.49 memory used=1075.8MB, alloc=260.3MB, time=30.31 N1 := 4547 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [98 y x + 10 y x + 28 x - 77 y, 2 z x + 14 y x - 11, -5 x y + 7 y z - 14 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1249.9MB, alloc=260.3MB, time=35.11 memory used=1444.4MB, alloc=540.3MB, time=38.39 memory used=1654.8MB, alloc=564.3MB, time=42.24 memory used=1874.9MB, alloc=588.3MB, time=49.71 memory used=2091.1MB, alloc=612.3MB, time=58.63 memory used=2331.5MB, alloc=636.3MB, time=68.42 N2 := 4547 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [-7 z y + 5 y x + 14 x, -14 x y - 2 x z + 11, -5 y - 9 y z + 9 y, 2 -14 z y + 17 x + 13 x] > J:=[op(GB),op(G)]; 2 2 2 J := [98 y x + 10 y x + 28 x - 77 y, 2 z x + 14 y x - 11, 2 2 -5 x y + 7 y z - 14 x, -5 y - 9 y z + 9 y, -14 z y + 17 x + 13 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 2, 2, 1, 3/4, 1, 1, 1/2, 7/12, 1/3, 5, 13, 11, 3, 2, 2, 1, 4/5, 1, 4/5, 9/16, 5/8, 1/4, -2, -3, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=2371.4MB, alloc=636.3MB, time=69.77 |\^/| 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(); 1428500302 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [-18 x y - 16 y z + 14 x, 9 y z + 6 y - 10 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [2 y + 6 z + 5 z, 7 x - x z - x] > Problem := [F,G]; Problem := [[-18 x y - 16 y z + 14 x, 9 y z + 6 y - 10 z], 2 2 2 [2 y + 6 z + 5 z, 7 x - x z - x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=46.8MB, alloc=32.3MB, time=0.79 memory used=65.4MB, alloc=56.3MB, time=1.08 memory used=104.9MB, alloc=60.3MB, time=1.69 memory used=143.0MB, alloc=84.3MB, time=2.28 memory used=202.2MB, alloc=92.3MB, time=3.24 memory used=261.6MB, alloc=116.3MB, time=4.17 memory used=343.4MB, alloc=116.3MB, time=5.43 memory used=425.2MB, alloc=140.3MB, time=6.86 memory used=520.9MB, alloc=164.3MB, time=8.56 memory used=632.4MB, alloc=188.3MB, time=10.51 memory used=747.9MB, alloc=468.3MB, time=12.58 memory used=887.6MB, alloc=492.3MB, time=15.07 memory used=1038.6MB, alloc=516.3MB, time=17.81 memory used=1201.1MB, alloc=540.3MB, time=20.78 memory used=1368.3MB, alloc=564.3MB, time=24.83 memory used=1526.8MB, alloc=588.3MB, time=29.96 memory used=1696.6MB, alloc=612.3MB, time=35.77 memory used=1879.7MB, alloc=636.3MB, time=42.36 memory used=2077.8MB, alloc=660.3MB, time=49.66 memory used=2291.6MB, alloc=684.3MB, time=57.75 memory used=2516.0MB, alloc=708.3MB, time=67.01 memory used=2763.5MB, alloc=732.3MB, time=77.19 memory used=3034.9MB, alloc=756.3MB, time=88.30 memory used=3330.3MB, alloc=780.3MB, time=100.40 memory used=3649.6MB, alloc=804.3MB, time=113.39 memory used=3992.9MB, alloc=804.3MB, time=127.80 memory used=4336.0MB, alloc=804.3MB, time=141.91 memory used=4679.2MB, alloc=828.3MB, time=156.08 memory used=5046.4MB, alloc=828.3MB, time=171.03 memory used=5413.4MB, alloc=828.3MB, time=185.87 memory used=5780.5MB, alloc=828.3MB, time=200.66 memory used=6147.4MB, alloc=852.3MB, time=215.49 memory used=6538.1MB, alloc=852.3MB, time=231.32 memory used=6929.0MB, alloc=876.3MB, time=247.00 memory used=7343.7MB, alloc=876.3MB, time=263.60 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428500602 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [3 y + 7 y z - 12 z , -16 x z - 15 x - 19 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [20 x z - 3 y + 4, -5 y z - 17 z + 12] > Problem := [F,G]; 2 2 Problem := [[3 y + 7 y z - 12 z , -16 x z - 15 x - 19 y], [20 x z - 3 y + 4, -5 y z - 17 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=46.7MB, alloc=56.3MB, time=0.82 memory used=87.9MB, alloc=60.3MB, time=1.44 memory used=128.6MB, alloc=60.3MB, time=2.05 memory used=167.8MB, alloc=84.3MB, time=2.65 memory used=229.9MB, alloc=92.3MB, time=3.62 memory used=290.5MB, alloc=116.3MB, time=4.57 memory used=377.0MB, alloc=140.3MB, time=6.07 memory used=473.2MB, alloc=420.3MB, time=7.77 memory used=586.3MB, alloc=444.3MB, time=9.77 memory used=715.1MB, alloc=468.3MB, time=12.03 memory used=856.6MB, alloc=492.3MB, time=14.57 memory used=1010.6MB, alloc=516.3MB, time=17.39 memory used=1175.6MB, alloc=540.3MB, time=20.40 memory used=1353.3MB, alloc=564.3MB, time=23.65 memory used=1539.0MB, alloc=588.3MB, time=27.32 memory used=1713.5MB, alloc=612.3MB, time=32.81 memory used=1894.1MB, alloc=636.3MB, time=39.19 memory used=2086.8MB, alloc=660.3MB, time=46.39 memory used=2293.8MB, alloc=684.3MB, time=54.47 memory used=2515.5MB, alloc=708.3MB, time=63.21 memory used=2752.6MB, alloc=732.3MB, time=72.60 memory used=3001.9MB, alloc=756.3MB, time=83.12 memory used=3268.8MB, alloc=780.3MB, time=94.55 memory used=3559.8MB, alloc=804.3MB, time=106.99 memory used=3874.6MB, alloc=828.3MB, time=120.59 memory used=4213.3MB, alloc=852.3MB, time=135.43 memory used=4576.0MB, alloc=876.3MB, time=151.40 memory used=4962.7MB, alloc=876.3MB, time=168.62 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428500902 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-8 y + 13 z - 19, 2 y - 13 x + 14] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-7 x + 17 y - 9 y z, -10 y z - 7 x - 9 y] > Problem := [F,G]; 2 2 2 Problem := [[-8 y + 13 z - 19, 2 y - 13 x + 14], 2 2 [-7 x + 17 y - 9 y z, -10 y z - 7 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=48.1MB, alloc=32.3MB, time=0.83 memory used=67.7MB, alloc=56.3MB, time=1.14 memory used=109.5MB, alloc=60.3MB, time=1.73 memory used=148.0MB, alloc=84.3MB, time=2.27 memory used=215.2MB, alloc=116.3MB, time=3.43 memory used=296.6MB, alloc=116.3MB, time=4.94 memory used=369.6MB, alloc=140.3MB, time=6.33 memory used=461.6MB, alloc=164.3MB, time=8.08 memory used=568.4MB, alloc=188.3MB, time=10.00 memory used=686.2MB, alloc=212.3MB, time=13.15 memory used=810.6MB, alloc=236.3MB, time=17.13 memory used=945.6MB, alloc=260.3MB, time=22.40 memory used=1099.9MB, alloc=284.3MB, time=28.69 memory used=1278.1MB, alloc=284.3MB, time=37.03 memory used=1456.4MB, alloc=308.3MB, time=45.51 memory used=1658.5MB, alloc=308.3MB, time=54.84 memory used=1860.7MB, alloc=332.3MB, time=63.63 N1 := 6503 > GB := Basis(F, plex(op(vars))); 2 2 GB := [2 y - 13 x + 14, 13 z - 52 x + 37] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2039.5MB, alloc=332.3MB, time=70.33 memory used=2298.0MB, alloc=612.3MB, time=75.08 memory used=2572.5MB, alloc=636.3MB, time=81.22 memory used=2823.2MB, alloc=660.3MB, time=90.73 memory used=3079.1MB, alloc=684.3MB, time=101.64 memory used=3359.1MB, alloc=708.3MB, time=114.04 memory used=3663.3MB, alloc=732.3MB, time=128.09 N2 := 6099 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [-8 y + 13 z - 19, 2 y - 13 x + 14, -7 x + 17 y - 9 y z, -10 y z - 7 x - 9 y] > J:=[op(GB),op(G)]; 2 2 2 2 J := [2 y - 13 x + 14, 13 z - 52 x + 37, -7 x + 17 y - 9 y z, -10 y z - 7 x - 9 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 2, 2, 3/4, 1, 3/4, 1/4, 1/2, 1/4, 4, 10, 8, 2, 2, 2, 2, 1, 3/4, 3/4, 1/3, 5/12, 1/4, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=3721.6MB, alloc=732.3MB, time=130.19 |\^/| 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(); 1428501070 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-5 - 2 y + 3 z, 19 y + 16 y z + 12] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-16 y + 20 y z + 5, 5 x z + 5 z - 15 y] > Problem := [F,G]; 2 Problem := [[-5 - 2 y + 3 z, 19 y + 16 y z + 12], 2 2 [-16 y + 20 y z + 5, 5 x z + 5 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=4.3MB, alloc=32.3MB, time=0.21 memory used=25.5MB, alloc=32.3MB, time=0.63 memory used=45.6MB, alloc=56.3MB, time=0.95 memory used=86.2MB, alloc=60.3MB, time=1.69 memory used=125.8MB, alloc=60.3MB, time=2.30 memory used=163.9MB, alloc=84.3MB, time=2.93 memory used=225.2MB, alloc=92.3MB, time=3.94 memory used=289.0MB, alloc=116.3MB, time=5.05 memory used=371.7MB, alloc=140.3MB, time=6.41 memory used=469.8MB, alloc=164.3MB, time=8.47 memory used=574.8MB, alloc=188.3MB, time=10.45 memory used=685.0MB, alloc=468.3MB, time=12.41 memory used=832.2MB, alloc=492.3MB, time=14.97 memory used=982.1MB, alloc=516.3MB, time=18.85 memory used=1128.5MB, alloc=540.3MB, time=23.83 memory used=1287.5MB, alloc=564.3MB, time=29.37 memory used=1455.0MB, alloc=588.3MB, time=36.51 memory used=1645.6MB, alloc=612.3MB, time=44.80 memory used=1860.1MB, alloc=636.3MB, time=54.06 memory used=2098.5MB, alloc=636.3MB, time=64.22 memory used=2336.8MB, alloc=636.3MB, time=74.20 memory used=2575.2MB, alloc=660.3MB, time=83.77 memory used=2837.5MB, alloc=660.3MB, time=94.09 memory used=3099.8MB, alloc=684.3MB, time=104.30 memory used=3386.2MB, alloc=684.3MB, time=115.45 memory used=3672.7MB, alloc=708.3MB, time=125.95 N1 := 9433 > GB := Basis(F, plex(op(vars))); 2 GB := [89 y + 80 y + 36, -5 - 2 y + 3 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3984.8MB, alloc=708.3MB, time=131.91 memory used=4334.2MB, alloc=732.3MB, time=143.98 memory used=4661.0MB, alloc=756.3MB, time=157.91 N2 := 4765 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-5 - 2 y + 3 z, 16 z y + 19 y + 12, -16 y + 20 y z + 5, 2 5 x z + 5 z - 15 y] > J:=[op(GB),op(G)]; J := [ 2 2 2 89 y + 80 y + 36, -5 - 2 y + 3 z, -16 y + 20 y z + 5, 5 x z + 5 z - 15 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 1, 2, 2, 1/4, 1, 1, 1/12, 1/2, 5/12, 4, 8, 7, 2, 1, 2, 2, 1/4, 1, 3/4, 1/12, 1/2, 1/3, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=4829.0MB, alloc=756.3MB, time=164.51 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428501283 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-14 x z - 3 y + 15 z , -11 x - 7 y z - 12 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-14 x + 16 x y - 14, 18 x z - 12 x - 1] > Problem := [F,G]; 2 2 2 Problem := [[-14 x z - 3 y + 15 z , -11 x - 7 y z - 12 y], 2 [-14 x + 16 x y - 14, 18 x z - 12 x - 1]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=48.2MB, alloc=32.3MB, time=0.82 memory used=68.9MB, alloc=56.3MB, time=1.13 memory used=110.4MB, alloc=60.3MB, time=1.75 memory used=152.5MB, alloc=84.3MB, time=2.40 memory used=225.1MB, alloc=92.3MB, time=3.32 memory used=286.2MB, alloc=116.3MB, time=4.27 memory used=366.5MB, alloc=116.3MB, time=5.61 memory used=445.7MB, alloc=140.3MB, time=6.85 memory used=547.2MB, alloc=164.3MB, time=8.45 memory used=674.4MB, alloc=164.3MB, time=10.15 memory used=798.0MB, alloc=188.3MB, time=11.81 memory used=915.4MB, alloc=468.3MB, time=13.93 memory used=1046.4MB, alloc=492.3MB, time=17.58 memory used=1186.0MB, alloc=516.3MB, time=22.03 memory used=1337.6MB, alloc=540.3MB, time=27.46 memory used=1503.8MB, alloc=564.3MB, time=34.31 memory used=1694.0MB, alloc=564.3MB, time=42.31 memory used=1884.2MB, alloc=588.3MB, time=50.04 memory used=2098.4MB, alloc=588.3MB, time=58.24 memory used=2312.4MB, alloc=588.3MB, time=66.66 memory used=2526.6MB, alloc=612.3MB, time=75.33 memory used=2764.6MB, alloc=636.3MB, time=85.44 N1 := 7785 > GB := Basis(F, plex(op(vars))); 4 3 4 2 2 2 GB := [-1815 x - 1078 x y + 147 y - 3960 x y - 1176 x y - 2160 y , 3 2 3 2 -1078 x + 1155 x z + 147 y - 1980 x - 1176 x y - 2160 y, 2 2 2 7 z y + 11 x + 12 y, -14 x z - 3 y + 15 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3040.6MB, alloc=636.3MB, time=93.24 memory used=3337.8MB, alloc=636.3MB, time=98.30 memory used=3656.3MB, alloc=660.3MB, time=103.53 memory used=3955.6MB, alloc=684.3MB, time=109.38 memory used=4274.4MB, alloc=708.3MB, time=115.46 memory used=4626.7MB, alloc=732.3MB, time=121.32 memory used=4994.8MB, alloc=756.3MB, time=127.19 memory used=5362.1MB, alloc=780.3MB, time=133.40 memory used=5705.2MB, alloc=804.3MB, time=141.89 memory used=6006.6MB, alloc=828.3MB, time=153.73 memory used=6309.0MB, alloc=852.3MB, time=165.93 memory used=6620.7MB, alloc=876.3MB, time=178.93 memory used=6943.9MB, alloc=900.3MB, time=192.43 memory used=7279.7MB, alloc=924.3MB, time=206.52 memory used=7625.6MB, alloc=948.3MB, time=221.60 memory used=7984.8MB, alloc=972.3MB, time=238.05 memory used=8368.0MB, alloc=996.3MB, time=255.42 |\^/| 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(); 1428501583 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-15 x y + 17 y z + 6 x, x - 8 x + 14 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [8 x y - 8 z - 7 z, -17 x z - 14 y z - 2 x] > Problem := [F,G]; 2 Problem := [[-15 x y + 17 y z + 6 x, x - 8 x + 14 z], 2 [8 x y - 8 z - 7 z, -17 x z - 14 y z - 2 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=46.3MB, alloc=56.3MB, time=0.81 memory used=87.0MB, alloc=60.3MB, time=1.43 memory used=126.1MB, alloc=84.3MB, time=2.04 memory used=171.0MB, alloc=84.3MB, time=2.74 memory used=231.6MB, alloc=92.3MB, time=3.72 memory used=292.1MB, alloc=116.3MB, time=4.67 memory used=374.4MB, alloc=140.3MB, time=5.99 memory used=448.0MB, alloc=396.3MB, time=7.24 memory used=546.8MB, alloc=420.3MB, time=9.08 memory used=659.0MB, alloc=444.3MB, time=11.14 memory used=785.7MB, alloc=468.3MB, time=13.49 memory used=931.3MB, alloc=492.3MB, time=16.16 memory used=1089.0MB, alloc=516.3MB, time=18.97 memory used=1264.7MB, alloc=540.3MB, time=22.09 memory used=1454.2MB, alloc=564.3MB, time=25.50 memory used=1650.0MB, alloc=588.3MB, time=29.36 memory used=1828.1MB, alloc=612.3MB, time=35.11 memory used=2013.8MB, alloc=636.3MB, time=41.50 memory used=2211.1MB, alloc=660.3MB, time=48.83 memory used=2423.0MB, alloc=684.3MB, time=57.42 memory used=2650.0MB, alloc=708.3MB, time=66.71 memory used=2890.1MB, alloc=732.3MB, time=76.82 memory used=3144.2MB, alloc=756.3MB, time=88.14 memory used=3422.2MB, alloc=780.3MB, time=100.49 memory used=3724.2MB, alloc=804.3MB, time=113.58 memory used=4050.0MB, alloc=828.3MB, time=127.84 memory used=4399.9MB, alloc=852.3MB, time=143.24 memory used=4773.7MB, alloc=852.3MB, time=159.84 memory used=5147.4MB, alloc=852.3MB, time=176.44 memory used=5521.1MB, alloc=876.3MB, time=192.08 memory used=5918.8MB, alloc=876.3MB, time=209.38 memory used=6316.3MB, alloc=876.3MB, time=227.56 memory used=6713.7MB, alloc=900.3MB, time=245.47 |\^/| 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(); 1428501883 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-13 x z + 19 z - 17, -18 z - 14] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-4 x z - 11 z - 1, -16 y - 9 y + 4] > Problem := [F,G]; Problem := [ 2 2 2 [-13 x z + 19 z - 17, -18 z - 14], [-4 x z - 11 z - 1, -16 y - 9 y + 4]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=27.6MB, alloc=32.3MB, time=0.58 N1 := 215 > GB := Basis(F, plex(op(vars))); 2 GB := [63 x + 484, -7 x + 22 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=48.6MB, alloc=32.3MB, time=0.94 N2 := 145 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-13 x z + 19 z - 17, -18 z - 14, -4 x z - 11 z - 1, -16 y - 9 y + 4] > J:=[op(GB),op(G)]; 2 2 J := [63 x + 484, -7 x + 22 z, -4 x z - 11 z - 1, -16 y - 9 y + 4] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 6, 8, 2, 1, 2, 2, 1/2, 1/4, 3/4, 2/11, 2/11, 5/11, 4, 6, 7, 2, 2, 2, 1, 3/4, 1/4, 1/2, 3/10, 1/5, 3/10, 0, 1, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=49.7MB, alloc=32.3MB, time=0.97 |\^/| 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(); 1428501885 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-15 x z + 12 y + 4 z, -6 - 5 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [11 x + 16 x + 4 z, -15 x y + 2 y - 6 x] > Problem := [F,G]; 2 Problem := [[-15 x z + 12 y + 4 z, -6 - 5 y], 2 2 [11 x + 16 x + 4 z, -15 x y + 2 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=49.0MB, alloc=32.3MB, time=0.95 memory used=69.2MB, alloc=56.3MB, time=1.32 memory used=111.0MB, alloc=80.3MB, time=2.38 N1 := 825 > GB := Basis(F, plex(op(vars))); GB := [5 y + 6, 375 x z - 100 z - 432] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=141.8MB, alloc=80.3MB, time=2.95 N2 := 307 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := 2 2 2 [-15 x z + 12 y + 4 z, -6 - 5 y, 11 x + 4 z + 16 x, -15 x y + 2 y - 6 x] > J:=[op(GB),op(G)]; 2 2 J := [5 y + 6, 375 z x - 100 z - 432, 11 x + 4 z + 16 x, -15 x y + 2 y - 6 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 7, 2, 2, 2, 1, 3/4, 3/4, 1/2, 5/11, 4/11, 3/11, 4, 7, 7, 2, 2, 2, 1, 3/4, 1/2, 1/2, 5/11, 3/11, 3/11, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=154.9MB, alloc=84.3MB, time=3.19 |\^/| 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(); 1428501889 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-8 y - 9 y z + 13 y, -12 x - 3 z + 10 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [3 y + 4 y z + 18 z , 14 y + 20 y + 15] > Problem := [F,G]; 2 2 2 Problem := [[-8 y - 9 y z + 13 y, -12 x - 3 z + 10 x], 2 2 2 [3 y + 4 y z + 18 z , 14 y + 20 y + 15]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.53 memory used=47.5MB, alloc=32.3MB, time=0.84 memory used=67.3MB, alloc=56.3MB, time=1.16 N1 := 115 > GB := Basis(F, plex(op(vars))); 2 3 2 2 GB := [324 x y + 64 y - 270 x y - 208 y + 169 y, 8 y + 9 y z - 13 y, 2 2 3 z + 12 x - 10 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=106.7MB, alloc=60.3MB, time=1.77 memory used=147.5MB, alloc=60.3MB, time=2.39 N2 := 115 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [-8 y - 9 y z + 13 y, -12 x - 3 z + 10 x, 18 z + 4 z y + 3 y , 2 14 y + 20 y + 15] > J:=[op(GB),op(G)]; 2 3 2 2 J := [324 x y + 64 y - 270 x y - 208 y + 169 y, 8 y + 9 y z - 13 y, 2 2 2 2 2 3 z + 12 x - 10 x, 18 z + 4 z y + 3 y , 14 y + 20 y + 15] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 7, 8, 2, 2, 2, 2, 1/4, 3/4, 3/4, 1/6, 7/12, 1/3, 5, 9, 11, 3, 12 2, 3, 2, 2/5, 4/5, 3/5, 4/17, --, 4/17, -2, -3, -1] 17 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=151.4MB, alloc=60.3MB, time=2.47 |\^/| 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(); 1428501891 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [5 + 18 y + 15 z, -5 y + 12 y z - 3] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-9 y - 8 z, x y + 14 z ] > Problem := [F,G]; 2 2 2 Problem := [[5 + 18 y + 15 z, -5 y + 12 y z - 3], [-9 y - 8 z, x y + 14 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=46.4MB, alloc=32.3MB, time=0.80 memory used=64.6MB, alloc=56.3MB, time=1.09 memory used=104.0MB, alloc=60.3MB, time=1.70 memory used=144.1MB, alloc=84.3MB, time=2.40 memory used=203.5MB, alloc=116.3MB, time=3.50 memory used=282.2MB, alloc=116.3MB, time=4.85 memory used=352.4MB, alloc=140.3MB, time=6.18 memory used=433.8MB, alloc=164.3MB, time=8.40 memory used=525.0MB, alloc=188.3MB, time=11.83 memory used=637.8MB, alloc=188.3MB, time=16.21 memory used=750.7MB, alloc=212.3MB, time=20.55 N1 := 3775 > GB := Basis(F, plex(op(vars))); 2 GB := [97 y + 20 y + 15, 15 z + 18 y + 5] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=893.3MB, alloc=212.3MB, time=24.60 N2 := 667 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [15 z + 18 y + 5, -5 y + 12 y z - 3, -9 y - 8 z, 14 z + y x] > J:=[op(GB),op(G)]; 2 2 2 J := [97 y + 20 y + 15, 15 z + 18 y + 5, -9 y - 8 z, 14 z + y x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 1, 2, 2, 1/4, 1, 1, 1/10, 1/2, 2/5, 4, 8, 7, 2, 1, 2, 2, 1/4, 1, 3/4, 1/10, 1/2, 3/10, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=930.2MB, alloc=212.3MB, time=25.52 |\^/| 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(); 1428501920 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-18 x y - 15 x z - 10 y, 3 x - 6 y - 19 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-3 x z + 12 z - 3, 8 x + 3 x y + 8 y] > Problem := [F,G]; 2 2 Problem := [[-18 x y - 15 x z - 10 y, 3 x - 6 y - 19 y], 2 [-3 x z + 12 z - 3, 8 x + 3 x y + 8 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=49.1MB, alloc=32.3MB, time=0.89 memory used=69.4MB, alloc=56.3MB, time=1.24 memory used=110.6MB, alloc=60.3MB, time=2.00 N1 := 927 > GB := Basis(F, plex(op(vars))); 2 2 GB := [-3 x + 6 y + 19 y, 15 z x + 18 y x + 10 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=145.1MB, alloc=84.3MB, time=2.97 memory used=207.8MB, alloc=92.3MB, time=4.00 memory used=267.6MB, alloc=116.3MB, time=5.43 N2 := 927 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-18 x y - 15 x z - 10 y, -6 y + 3 x - 19 y, -3 x z + 12 z - 3, 2 3 y x + 8 x + 8 y] > J:=[op(GB),op(G)]; 2 2 J := [-3 x + 6 y + 19 y, 15 z x + 18 y x + 10 y, -3 x z + 12 z - 3, 2 3 y x + 8 x + 8 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 1, 1, 3/4, 1/2, 1/2, 1/2, 1/4, 4, 9, 8, 2, 2, 2, 1, 1, 3/4, 1/2, 1/2, 1/2, 1/4, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=275.7MB, alloc=116.3MB, time=5.63 |\^/| 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(); 1428501926 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [19 + 18 x - 16 z, 12 x z + 19 y z + 9 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-9 y z - 8 z + 5, -11 x z - 12 x - 3 y] > Problem := [F,G]; Problem := [[19 + 18 x - 16 z, 12 x z + 19 y z + 9 z], 2 [-9 y z - 8 z + 5, -11 x z - 12 x - 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.3MB, alloc=32.3MB, time=0.80 memory used=66.6MB, alloc=56.3MB, time=1.11 memory used=106.1MB, alloc=84.3MB, time=1.75 memory used=163.5MB, alloc=84.3MB, time=2.74 memory used=219.1MB, alloc=108.3MB, time=3.71 memory used=293.1MB, alloc=140.3MB, time=5.03 memory used=380.3MB, alloc=164.3MB, time=6.96 memory used=473.4MB, alloc=188.3MB, time=9.84 memory used=579.0MB, alloc=212.3MB, time=13.74 memory used=708.5MB, alloc=212.3MB, time=18.57 memory used=838.0MB, alloc=236.3MB, time=23.32 N1 := 4381 > GB := Basis(F, plex(op(vars))); 2 GB := [216 x + 342 x y + 390 x + 361 y + 171, 16 z - 18 x - 19] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=996.3MB, alloc=236.3MB, time=28.54 memory used=1090.5MB, alloc=492.3MB, time=30.29 memory used=1268.8MB, alloc=516.3MB, time=34.93 N2 := 2481 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [-16 z + 18 x + 19, 12 x z + 19 y z + 9 z, -9 y z - 8 z + 5, -11 x z - 12 x - 3 y] > J:=[op(GB),op(G)]; 2 J := [216 x + 342 x y + 390 x + 361 y + 171, 16 z - 18 x - 19, 2 -9 y z - 8 z + 5, -11 x z - 12 x - 3 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 7, 2, 1, 1, 2, 3/4, 3/4, 1, 1/3, 1/4, 7/12, 4, 9, 7, 2, 2, 1, 2, 3/4, 3/4, 3/4, 3/7, 2/7, 2/7, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1405.6MB, alloc=516.3MB, time=40.41 |\^/| 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(); 1428501969 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-17 x - 12 x z - 20 z , -9 x y - 19 x z + 11 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-11 x z - 2 z - 3 y, -10 y - 6 z + 15] > Problem := [F,G]; 2 2 Problem := [[-17 x - 12 x z - 20 z , -9 x y - 19 x z + 11 z], 2 2 2 [-11 x z - 2 z - 3 y, -10 y - 6 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=31.7MB, alloc=44.3MB, time=0.60 memory used=58.5MB, alloc=44.3MB, time=1.00 memory used=82.5MB, alloc=68.3MB, time=1.39 memory used=131.2MB, alloc=76.3MB, time=2.15 memory used=180.8MB, alloc=100.3MB, time=2.89 memory used=254.8MB, alloc=100.3MB, time=3.99 memory used=329.3MB, alloc=100.3MB, time=5.10 memory used=398.8MB, alloc=124.3MB, time=6.20 memory used=484.0MB, alloc=380.3MB, time=7.62 memory used=576.4MB, alloc=404.3MB, time=9.05 memory used=698.4MB, alloc=404.3MB, time=10.90 memory used=809.8MB, alloc=428.3MB, time=12.77 memory used=947.9MB, alloc=452.3MB, time=15.16 memory used=1090.5MB, alloc=476.3MB, time=17.87 memory used=1248.0MB, alloc=500.3MB, time=20.83 memory used=1413.5MB, alloc=524.3MB, time=24.68 memory used=1571.8MB, alloc=548.3MB, time=30.06 memory used=1733.8MB, alloc=572.3MB, time=36.58 memory used=1919.6MB, alloc=596.3MB, time=44.07 memory used=2129.6MB, alloc=620.3MB, time=52.41 N1 := 5509 > GB := Basis(F, plex(op(vars))); 4 3 2 2 3 2 2 GB := [6137 x - 2052 x y + 1620 x y - 7106 x + 1188 x y + 2057 x , 19 z x + 9 y x - 11 z, 3 2 2 2 -6137 x + 2052 x y - 1620 x y + 3553 x + 1980 y z, 2 2 323 x - 108 x y + 380 z + 132 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2365.3MB, alloc=620.3MB, time=61.58 memory used=2502.7MB, alloc=620.3MB, time=63.76 memory used=2631.0MB, alloc=620.3MB, time=65.79 memory used=2797.0MB, alloc=620.3MB, time=68.05 memory used=2924.4MB, alloc=620.3MB, time=70.32 memory used=3046.9MB, alloc=620.3MB, time=72.54 memory used=3175.6MB, alloc=620.3MB, time=74.58 memory used=3278.9MB, alloc=620.3MB, time=76.62 memory used=3387.7MB, alloc=620.3MB, time=78.58 memory used=3508.1MB, alloc=620.3MB, time=80.28 memory used=3649.4MB, alloc=620.3MB, time=82.29 memory used=3731.4MB, alloc=644.3MB, time=83.85 memory used=3827.4MB, alloc=644.3MB, time=85.93 memory used=3938.4MB, alloc=644.3MB, time=87.80 memory used=4027.0MB, alloc=644.3MB, time=89.12 memory used=4123.0MB, alloc=644.3MB, time=90.81 memory used=4237.9MB, alloc=668.3MB, time=92.48 memory used=4311.6MB, alloc=668.3MB, time=94.14 memory used=4382.5MB, alloc=668.3MB, time=95.34 memory used=4458.3MB, alloc=668.3MB, time=96.82 memory used=4532.7MB, alloc=668.3MB, time=98.55 memory used=4590.0MB, alloc=668.3MB, time=99.67 memory used=4668.5MB, alloc=668.3MB, time=101.40 memory used=4731.6MB, alloc=668.3MB, time=102.80 memory used=4805.0MB, alloc=668.3MB, time=104.07 memory used=4866.1MB, alloc=668.3MB, time=105.95 memory used=5101.0MB, alloc=692.3MB, time=110.52 memory used=5331.1MB, alloc=716.3MB, time=115.03 memory used=5527.9MB, alloc=740.3MB, time=118.74 memory used=5860.7MB, alloc=740.3MB, time=123.25 memory used=6137.7MB, alloc=764.3MB, time=126.42 memory used=6453.5MB, alloc=764.3MB, time=129.63 memory used=6636.4MB, alloc=764.3MB, time=132.35 memory used=6810.8MB, alloc=788.3MB, time=135.71 memory used=6977.6MB, alloc=788.3MB, time=139.48 memory used=7162.6MB, alloc=788.3MB, time=144.09 memory used=7324.3MB, alloc=788.3MB, time=147.95 memory used=7520.0MB, alloc=812.3MB, time=152.98 memory used=7675.8MB, alloc=812.3MB, time=156.72 memory used=7804.5MB, alloc=812.3MB, time=160.14 memory used=7940.2MB, alloc=812.3MB, time=163.33 memory used=8074.6MB, alloc=812.3MB, time=167.36 memory used=8204.2MB, alloc=836.3MB, time=170.28 memory used=8305.5MB, alloc=836.3MB, time=173.66 memory used=8437.9MB, alloc=836.3MB, time=177.62 memory used=8935.5MB, alloc=860.3MB, time=190.09 memory used=9430.3MB, alloc=884.3MB, time=200.74 memory used=9917.5MB, alloc=908.3MB, time=211.51 memory used=10469.8MB, alloc=932.3MB, time=220.51 memory used=10925.3MB, alloc=956.3MB, time=232.17 memory used=11339.6MB, alloc=980.3MB, time=243.52 memory used=11764.1MB, alloc=1004.3MB, time=253.87 memory used=12136.2MB, alloc=1028.3MB, time=263.90 |\^/| 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(); 1428502269 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [3 x y - 8 y z + 13 z , 4 x z - 15 z - 6 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-x y + 19 y z + 12 y, -13 x + 3 x y - 6 y z] > Problem := [F,G]; 2 2 Problem := [[3 x y - 8 y z + 13 z , 4 x z - 15 z - 6 z], 2 [-x y + 19 y z + 12 y, -13 x + 3 x y - 6 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=47.2MB, alloc=32.3MB, time=0.85 memory used=66.3MB, alloc=56.3MB, time=1.18 memory used=106.1MB, alloc=60.3MB, time=1.83 memory used=143.8MB, alloc=84.3MB, time=2.46 memory used=203.7MB, alloc=116.3MB, time=3.55 memory used=284.6MB, alloc=140.3MB, time=5.16 memory used=381.6MB, alloc=164.3MB, time=7.29 memory used=494.1MB, alloc=188.3MB, time=9.66 memory used=621.6MB, alloc=212.3MB, time=12.02 memory used=745.9MB, alloc=492.3MB, time=15.37 memory used=877.0MB, alloc=516.3MB, time=20.01 memory used=1017.9MB, alloc=540.3MB, time=25.79 memory used=1170.8MB, alloc=564.3MB, time=32.77 memory used=1347.6MB, alloc=588.3MB, time=41.17 memory used=1548.4MB, alloc=612.3MB, time=50.26 memory used=1773.1MB, alloc=612.3MB, time=59.85 memory used=1997.8MB, alloc=612.3MB, time=69.45 memory used=2222.5MB, alloc=636.3MB, time=79.72 memory used=2471.2MB, alloc=636.3MB, time=90.77 memory used=2719.9MB, alloc=660.3MB, time=101.11 memory used=2992.7MB, alloc=684.3MB, time=112.42 N1 := 8699 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 GB := [208 x y + 195 x y - 624 x y + 720 x y + 468 x y, 2 2 13 x y + 52 x z + 48 x y - 78 x z, -45 x y - 52 x z + 120 y z + 78 z, 2 -4 x z + 15 z + 6 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3281.6MB, alloc=684.3MB, time=118.44 memory used=3622.4MB, alloc=708.3MB, time=125.68 memory used=3963.2MB, alloc=732.3MB, time=133.23 memory used=4309.5MB, alloc=756.3MB, time=141.69 memory used=4612.7MB, alloc=780.3MB, time=153.89 memory used=4910.2MB, alloc=804.3MB, time=166.88 memory used=5213.8MB, alloc=828.3MB, time=181.41 memory used=5541.4MB, alloc=852.3MB, time=196.30 memory used=5892.9MB, alloc=876.3MB, time=211.81 |\^/| 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(); 1428502569 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [5 x y + 19 x z + 20 y z, -6 x - 2 x z - 11 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [10 x y - 4 y z - 2 y, -6 x y + 5 x - 6 z] > Problem := [F,G]; 2 Problem := [[5 x y + 19 x z + 20 y z, -6 x - 2 x z - 11 y], [10 x y - 4 y z - 2 y, -6 x y + 5 x - 6 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.49 memory used=46.5MB, alloc=32.3MB, time=0.80 memory used=65.6MB, alloc=56.3MB, time=1.11 memory used=105.5MB, alloc=60.3MB, time=1.72 memory used=143.6MB, alloc=84.3MB, time=2.32 memory used=204.9MB, alloc=116.3MB, time=3.46 memory used=285.8MB, alloc=140.3MB, time=4.91 memory used=382.1MB, alloc=164.3MB, time=6.69 memory used=495.1MB, alloc=188.3MB, time=8.68 memory used=602.3MB, alloc=468.3MB, time=10.67 memory used=745.1MB, alloc=492.3MB, time=13.25 memory used=898.2MB, alloc=516.3MB, time=17.04 memory used=1049.4MB, alloc=540.3MB, time=22.02 memory used=1212.1MB, alloc=564.3MB, time=27.75 memory used=1387.2MB, alloc=588.3MB, time=34.44 memory used=1576.5MB, alloc=612.3MB, time=42.62 memory used=1789.7MB, alloc=636.3MB, time=52.06 memory used=2026.9MB, alloc=636.3MB, time=61.96 memory used=2264.0MB, alloc=660.3MB, time=72.42 memory used=2525.1MB, alloc=660.3MB, time=83.09 memory used=2786.2MB, alloc=660.3MB, time=93.44 memory used=3047.0MB, alloc=684.3MB, time=104.21 memory used=3331.9MB, alloc=684.3MB, time=115.72 memory used=3616.8MB, alloc=708.3MB, time=126.92 N1 := 9575 > GB := Basis(F, plex(op(vars))); 2 3 2 2 GB := [110 y x + 114 x + 220 y + 209 y x, 2 z x + 6 x + 11 y, 2 -114 x + 10 x y + 40 y z - 209 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3935.3MB, alloc=708.3MB, time=135.35 memory used=4126.4MB, alloc=708.3MB, time=139.10 memory used=4322.7MB, alloc=732.3MB, time=142.89 memory used=4680.5MB, alloc=756.3MB, time=155.78 memory used=5017.1MB, alloc=780.3MB, time=170.21 memory used=5377.6MB, alloc=804.3MB, time=185.47 memory used=5762.7MB, alloc=828.3MB, time=201.44 N2 := 6609 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [20 z y + 19 z x + 5 y x, -6 x - 2 x z - 11 y, 10 x y - 4 y z - 2 y, -6 x y + 5 x - 6 z] > J:=[op(GB),op(G)]; 2 3 2 2 J := [110 y x + 114 x + 220 y + 209 y x, 2 z x + 6 x + 11 y, 2 -114 x + 10 x y + 40 y z - 209 y, 10 x y - 4 y z - 2 y, -6 x y + 5 x - 6 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 12, 8, 2, 2, 1, 1, 1, 1, 1, 7/12, 7/12, 5/12, 5, 14, 11, 3, 10 11 3, 2, 1, 1, 1, 4/5, --, --, 4/17, -2, -3, -1] 17 17 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=5792.0MB, alloc=828.3MB, time=202.33 |\^/| 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(); 1428502854 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [20 x z + 14 y - 13 z, -13 - x + 2 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [4 x - 8 x z + 8 z , 16 y z - 19] > Problem := [F,G]; Problem := 2 2 [[20 x z + 14 y - 13 z, -13 - x + 2 y], [4 x - 8 x z + 8 z , 16 y z - 19]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.5MB, alloc=32.3MB, time=0.81 memory used=68.7MB, alloc=56.3MB, time=1.18 N1 := 451 > GB := Basis(F, plex(op(vars))); GB := [-13 - x + 2 y, 20 z x - 13 z + 7 x + 91] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=110.7MB, alloc=60.3MB, time=1.94 memory used=152.0MB, alloc=60.3MB, time=2.58 N2 := 299 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [20 z x - 13 z + 14 y, -13 - x + 2 y, 4 x - 8 x z + 8 z , 16 z y - 19] > J:=[op(GB),op(G)]; J := 2 2 [-13 - x + 2 y, 20 z x - 13 z + 7 x + 91, 4 x - 8 x z + 8 z , 16 z y - 19] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 2, 1, 2, 3/4, 3/4, 3/4, 4/11, 3/11, 5/11, 4, 8, 7, 2, 2, 1, 2, 3/4, 1/2, 3/4, 5/12, 1/6, 5/12, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=160.8MB, alloc=60.3MB, time=2.75 |\^/| 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(); 1428502858 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [10 x y - y z + 20 x, 19 x y - 4] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [3 y z + 2 y, -8 x z + 8 y z - 1] > Problem := [F,G]; Problem := [[10 x y - y z + 20 x, 19 x y - 4], [3 y z + 2 y, -8 x z + 8 y z - 1]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=47.5MB, alloc=32.3MB, time=0.78 memory used=68.1MB, alloc=56.3MB, time=1.15 memory used=109.5MB, alloc=60.3MB, time=1.84 memory used=147.7MB, alloc=84.3MB, time=2.49 memory used=205.1MB, alloc=116.3MB, time=3.58 memory used=278.3MB, alloc=140.3MB, time=5.91 memory used=365.7MB, alloc=140.3MB, time=9.27 N1 := 2257 > GB := Basis(F, plex(op(vars))); 2 GB := [19 y x - 4, -95 x - 10 x + z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=455.6MB, alloc=140.3MB, time=11.23 memory used=554.4MB, alloc=164.3MB, time=13.58 N2 := 1455 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [-z y + 10 y x + 20 x, 19 y x - 4, 3 y z + 2 y, -8 x z + 8 y z - 1] > J:=[op(GB),op(G)]; 2 J := [19 y x - 4, -95 x - 10 x + z, 3 y z + 2 y, -8 x z + 8 y z - 1] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 1, 1, 1, 3/4, 1, 3/4, 2/5, 3/5, 2/5, 4, 9, 8, 2, 2, 1, 1, 3/4, 3/4, 3/4, 2/5, 2/5, 2/5, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=593.1MB, alloc=164.3MB, time=14.86 |\^/| 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(); 1428502878 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-x y - 8 y - 7 z, 8 x z + 14] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [-6 x z + 5 z, 10 x y + 9 x z + 11 y] > Problem := [F,G]; Problem := 2 [[-x y - 8 y - 7 z, 8 x z + 14], [-6 x z + 5 z, 10 x y + 9 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.47 memory used=48.0MB, alloc=32.3MB, time=0.82 memory used=68.1MB, alloc=56.3MB, time=1.17 memory used=109.3MB, alloc=84.3MB, time=1.87 N1 := 1173 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [32 y x + 4 y x - 49, 8 y + y x + 7 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=168.9MB, alloc=84.3MB, time=3.46 memory used=228.2MB, alloc=84.3MB, time=4.39 N2 := 767 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [-x y - 8 y - 7 z, 8 x z + 14, -6 x z + 5 z, 9 z x + 10 y x + 11 y] > J:=[op(GB),op(G)]; 2 2 2 J := [32 y x + 4 y x - 49, 8 y + y x + 7 z, -6 x z + 5 z, 9 z x + 10 y x + 11 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 1, 2, 1, 1, 1/2, 1, 1/2, 2/5, 1/2, 4, 10, 9, 3, 2, 2, 1, 1, 3/4, 3/4, 6/11, 6/11, 4/11, 0, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=264.3MB, alloc=84.3MB, time=5.24 |\^/| 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(); 1428502887 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-13 - 11 x + 3 z, -18 y - y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [6 y + 5 z + 2, 2 y z + 7 z + 6] > Problem := [F,G]; Problem := 2 2 2 2 [[-13 - 11 x + 3 z, -18 y - y z], [6 y + 5 z + 2, 2 y z + 7 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.2MB, alloc=32.3MB, time=0.80 memory used=66.3MB, alloc=56.3MB, time=1.09 memory used=105.7MB, alloc=60.3MB, time=1.67 memory used=142.8MB, alloc=84.3MB, time=2.23 memory used=202.4MB, alloc=84.3MB, time=3.24 N1 := 715 > GB := Basis(F, plex(op(vars))); 2 GB := [11 x y + 54 y + 13 y, -13 - 11 x + 3 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=255.9MB, alloc=84.3MB, time=4.31 memory used=314.9MB, alloc=92.3MB, time=5.21 memory used=372.6MB, alloc=116.3MB, time=6.21 N2 := 519 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-13 - 11 x + 3 z, -18 y - y z, 5 z + 6 y + 2, 7 z + 2 z y + 6] > J:=[op(GB),op(G)]; J := [ 2 2 2 2 11 x y + 54 y + 13 y, -13 - 11 x + 3 z, 5 z + 6 y + 2, 7 z + 2 z y + 6] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 7, 2, 1, 2, 2, 1/4, 3/4, 1, 1/11, 4/11, 5/11, 4, 8, 7, 2, 1, 2, 2, 1/2, 3/4, 3/4, 1/6, 5/12, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=389.8MB, alloc=116.3MB, time=6.59 |\^/| 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(); 1428502897 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-20 x + 14 x y + 13 y , 11 y z - 13 z + 15] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [4 x + 18 z + 12, -19 x y - 9 y - z] > Problem := [F,G]; 2 2 2 Problem := [[-20 x + 14 x y + 13 y , 11 y z - 13 z + 15], 2 2 [4 x + 18 z + 12, -19 x y - 9 y - z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=27.1MB, alloc=32.3MB, time=0.51 memory used=48.5MB, alloc=32.3MB, time=0.83 memory used=69.2MB, alloc=60.3MB, time=1.16 memory used=110.7MB, alloc=60.3MB, time=1.78 memory used=152.7MB, alloc=84.3MB, time=2.53 memory used=214.3MB, alloc=84.3MB, time=3.59 memory used=268.7MB, alloc=108.3MB, time=4.71 memory used=334.2MB, alloc=132.3MB, time=6.97 N1 := 1703 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [-20 x + 14 x y + 13 y , -11 y z + 13 z - 15] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=426.1MB, alloc=140.3MB, time=8.71 memory used=528.9MB, alloc=140.3MB, time=10.43 memory used=624.4MB, alloc=164.3MB, time=12.35 N2 := 1703 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [-20 x + 14 x y + 13 y , -13 z + 11 z y + 15, 4 x + 18 z + 12, -19 x y - 9 y - z] > J:=[op(GB),op(G)]; 2 2 2 2 2 J := [-20 x + 14 x y + 13 y , -11 y z + 13 z - 15, 4 x + 18 z + 12, -19 x y - 9 y - z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 2, 3/4, 3/4, 3/4, 1/3, 5/12, 1/3, 4, 9, 8, 2, 2, 2, 2, 3/4, 3/4, 3/4, 1/3, 5/12, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=706.8MB, alloc=164.3MB, time=14.87 |\^/| 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(); 1428502915 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-13 x y - 16 y + 18, y + 8 z + 8 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [9 y + 15 z + 9 y, 20 y z + 6 x + 17 z] > Problem := [F,G]; 2 2 Problem := [[-13 x y - 16 y + 18, y + 8 z + 8 z], 2 2 [9 y + 15 z + 9 y, 20 y z + 6 x + 17 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.4MB, alloc=32.3MB, time=0.79 memory used=66.7MB, alloc=56.3MB, time=1.09 memory used=107.0MB, alloc=60.3MB, time=1.69 memory used=145.9MB, alloc=84.3MB, time=2.26 memory used=207.2MB, alloc=92.3MB, time=3.17 memory used=269.7MB, alloc=116.3MB, time=4.24 memory used=348.1MB, alloc=140.3MB, time=5.59 memory used=444.9MB, alloc=164.3MB, time=7.26 memory used=559.5MB, alloc=188.3MB, time=9.23 memory used=685.2MB, alloc=212.3MB, time=11.46 memory used=813.0MB, alloc=236.3MB, time=15.12 memory used=950.4MB, alloc=260.3MB, time=19.51 memory used=1099.3MB, alloc=284.3MB, time=24.97 memory used=1265.4MB, alloc=308.3MB, time=31.46 memory used=1455.4MB, alloc=308.3MB, time=38.85 memory used=1645.4MB, alloc=332.3MB, time=46.27 memory used=1859.4MB, alloc=332.3MB, time=54.60 memory used=2073.3MB, alloc=332.3MB, time=62.91 memory used=2287.2MB, alloc=356.3MB, time=71.23 memory used=2525.4MB, alloc=380.3MB, time=80.24 N1 := 7491 > GB := Basis(F, plex(op(vars))); 2 2 GB := [13 y x + 16 y - 18, 8 z + y + 8 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2589.8MB, alloc=380.3MB, time=81.60 memory used=2778.3MB, alloc=636.3MB, time=84.87 memory used=3039.9MB, alloc=636.3MB, time=89.83 memory used=3322.9MB, alloc=660.3MB, time=96.70 memory used=3578.8MB, alloc=684.3MB, time=105.86 memory used=3837.4MB, alloc=708.3MB, time=116.28 memory used=4120.0MB, alloc=732.3MB, time=127.70 memory used=4426.5MB, alloc=756.3MB, time=140.22 memory used=4757.0MB, alloc=780.3MB, time=154.11 N2 := 7491 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-13 x y - 16 y + 18, 8 z + y + 8 z, 9 y + 15 z + 9 y, 20 z y + 17 z + 6 x] > J:=[op(GB),op(G)]; 2 2 2 2 J := [13 y x + 16 y - 18, 8 z + y + 8 z, 9 y + 15 z + 9 y, 20 z y + 17 z + 6 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 1, 2, 2, 1/2, 1, 3/4, 1/6, 1/2, 5/12, 4, 9, 8, 2, 1, 2, 2, 1/2, 1, 3/4, 1/6, 1/2, 5/12, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=5043.5MB, alloc=780.3MB, time=165.23 |\^/| 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(); 1428503162 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-10 y + 13 z + 19 y, -14 x z - 13 y + 6] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [12 + 15 y - 15 z, -11 x y - 7 y + 3] > Problem := [F,G]; 2 2 Problem := [[-10 y + 13 z + 19 y, -14 x z - 13 y + 6], [12 + 15 y - 15 z, -11 x y - 7 y + 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=47.6MB, alloc=32.3MB, time=0.84 memory used=67.1MB, alloc=56.3MB, time=1.13 memory used=108.5MB, alloc=60.3MB, time=1.83 memory used=145.8MB, alloc=84.3MB, time=2.52 memory used=203.6MB, alloc=108.3MB, time=3.62 memory used=279.2MB, alloc=140.3MB, time=5.06 memory used=370.3MB, alloc=164.3MB, time=7.14 memory used=468.8MB, alloc=188.3MB, time=10.45 memory used=578.2MB, alloc=212.3MB, time=15.51 memory used=711.7MB, alloc=212.3MB, time=20.90 memory used=845.2MB, alloc=236.3MB, time=26.15 N1 := 4159 > GB := Basis(F, plex(op(vars))); 2 2 2 2 GB := [1960 y x - 3724 y x - 2197 y + 2028 y - 468, 14 z x + 13 y - 6, 2 2 2 140 x y - 266 x y + 169 y z - 78 z, -10 y + 13 z + 19 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1007.7MB, alloc=236.3MB, time=30.59 memory used=1104.5MB, alloc=492.3MB, time=32.22 memory used=1276.8MB, alloc=516.3MB, time=35.38 memory used=1466.3MB, alloc=540.3MB, time=38.93 memory used=1664.6MB, alloc=564.3MB, time=42.83 memory used=1872.1MB, alloc=588.3MB, time=49.23 memory used=2072.2MB, alloc=612.3MB, time=57.14 memory used=2276.3MB, alloc=636.3MB, time=66.41 memory used=2504.4MB, alloc=660.3MB, time=76.56 memory used=2756.5MB, alloc=684.3MB, time=88.22 memory used=3032.6MB, alloc=708.3MB, time=101.08 memory used=3332.6MB, alloc=732.3MB, time=114.20 memory used=3656.8MB, alloc=756.3MB, time=127.57 N2 := 7969 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-10 y + 13 z + 19 y, -14 x z - 13 y + 6, 12 + 15 y - 15 z, -11 x y - 7 y + 3] > J:=[op(GB),op(G)]; 2 2 2 2 J := [1960 y x - 3724 y x - 2197 y + 2028 y - 468, 14 z x + 13 y - 6, 2 2 2 140 y x + 169 z y - 266 y x - 78 z, -10 y + 13 z + 19 y, 12 + 15 y - 15 z, -11 x y - 7 y + 3] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 1, 2, 2, 1/2, 1, 3/4, 1/6, 1/2, 1/4, 6, 14, 14, 4, 13 2, 2, 2, 2/3, 1, 2/3, 2/7, --, 5/21, -5, -7, -2] 21 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=3766.4MB, alloc=756.3MB, time=131.68 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428503321 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [18 x z - 14 y + 14 z , -y + 2 z - 18 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [13 x - 16 x y - 17, -8 + 10 y + 5 z] > Problem := [F,G]; 2 2 2 2 Problem := [[18 x z - 14 y + 14 z , -y + 2 z - 18 y], 2 [13 x - 16 x y - 17, -8 + 10 y + 5 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.49 memory used=47.8MB, alloc=32.3MB, time=0.80 memory used=67.5MB, alloc=56.3MB, time=1.10 memory used=108.2MB, alloc=60.3MB, time=1.72 memory used=146.3MB, alloc=84.3MB, time=2.31 memory used=209.7MB, alloc=116.3MB, time=3.40 memory used=291.9MB, alloc=140.3MB, time=4.83 memory used=389.9MB, alloc=164.3MB, time=6.52 memory used=503.0MB, alloc=188.3MB, time=8.54 memory used=611.5MB, alloc=468.3MB, time=10.50 memory used=752.5MB, alloc=492.3MB, time=13.07 memory used=898.2MB, alloc=516.3MB, time=16.42 memory used=1038.7MB, alloc=540.3MB, time=20.86 memory used=1190.2MB, alloc=564.3MB, time=25.98 memory used=1355.4MB, alloc=588.3MB, time=31.82 memory used=1534.4MB, alloc=612.3MB, time=38.62 memory used=1727.8MB, alloc=636.3MB, time=46.44 memory used=1945.2MB, alloc=660.3MB, time=55.07 memory used=2186.5MB, alloc=684.3MB, time=64.52 memory used=2451.7MB, alloc=684.3MB, time=75.25 memory used=2716.9MB, alloc=684.3MB, time=85.81 memory used=2982.0MB, alloc=708.3MB, time=96.34 memory used=3271.1MB, alloc=708.3MB, time=108.18 memory used=3560.2MB, alloc=708.3MB, time=119.86 memory used=3849.3MB, alloc=732.3MB, time=131.30 memory used=4162.2MB, alloc=732.3MB, time=143.72 memory used=4475.2MB, alloc=756.3MB, time=156.39 memory used=4812.2MB, alloc=756.3MB, time=169.72 memory used=5149.0MB, alloc=780.3MB, time=183.46 N1 := 12107 > GB := Basis(F, plex(op(vars))); 2 2 4 2 3 2 GB := [-162 x y + 49 y - 2916 x y - 1764 y + 15876 y , 2 2 2 18 z x - 7 y + 126 y, -9 x y + 7 y z - 162 x y - 126 y z, 2 2 -y + 2 z - 18 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5519.2MB, alloc=780.3MB, time=195.18 memory used=5697.6MB, alloc=780.3MB, time=198.76 memory used=5872.9MB, alloc=780.3MB, time=202.48 memory used=6035.3MB, alloc=804.3MB, time=205.93 memory used=6192.2MB, alloc=828.3MB, time=209.26 memory used=6358.1MB, alloc=852.3MB, time=213.14 memory used=6520.7MB, alloc=876.3MB, time=216.85 memory used=6685.8MB, alloc=900.3MB, time=221.11 memory used=7027.2MB, alloc=924.3MB, time=234.05 memory used=7468.6MB, alloc=948.3MB, time=252.23 |\^/| 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(); 1428503621 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [8 x y + 5 y - 14 y, -10 x z + 13 y - 20 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [3 x y - 20 z - 18, -11 y + 5 y] > Problem := [F,G]; 2 2 2 Problem := [[8 x y + 5 y - 14 y, -10 x z + 13 y - 20 z ], 2 [3 x y - 20 z - 18, -11 y + 5 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.3MB, alloc=56.3MB, time=0.83 memory used=91.8MB, alloc=60.3MB, time=1.58 memory used=132.0MB, alloc=84.3MB, time=2.26 memory used=190.1MB, alloc=108.3MB, time=3.44 memory used=258.9MB, alloc=132.3MB, time=5.82 N1 := 1917 > GB := Basis(F, plex(op(vars))); 2 2 GB := [8 x y + 5 y - 14 y, 52 x y + 25 x z + 50 z - 91 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=352.7MB, alloc=140.3MB, time=8.18 memory used=454.4MB, alloc=164.3MB, time=9.95 memory used=572.0MB, alloc=188.3MB, time=12.81 memory used=686.8MB, alloc=212.3MB, time=17.46 N2 := 2533 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [8 x y + 5 y - 14 y, -10 x z + 13 y - 20 z , 3 y x - 20 z - 18, 2 -11 y + 5 y] > J:=[op(GB),op(G)]; 2 2 J := [8 x y + 5 y - 14 y, 50 z + 25 z x + 52 y x - 91 y, 3 y x - 20 z - 18, 2 -11 y + 5 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 1, 2, 2, 3/4, 1, 1/2, 3/11, 7/11, 3/11, 4, 9, 8, 2, 1, 2, 2, 3/4, 1, 1/2, 1/3, 2/3, 1/4, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=748.9MB, alloc=212.3MB, time=19.59 |\^/| 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(); 1428503650 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-2 x z + 8 z + 4, -16 y z - x - 17] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [y + 3 y + 19 z, 6 x - 14 x y - 13] > Problem := [F,G]; 2 Problem := [[-2 x z + 8 z + 4, -16 y z - x - 17], 2 2 [y + 3 y + 19 z, 6 x - 14 x 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=47.4MB, alloc=32.3MB, time=0.80 memory used=67.0MB, alloc=56.3MB, time=1.11 memory used=109.7MB, alloc=60.3MB, time=1.77 memory used=149.9MB, alloc=84.3MB, time=2.45 memory used=211.1MB, alloc=108.3MB, time=3.47 memory used=290.3MB, alloc=140.3MB, time=4.83 memory used=384.0MB, alloc=164.3MB, time=6.72 memory used=483.9MB, alloc=188.3MB, time=9.79 memory used=594.9MB, alloc=188.3MB, time=13.87 memory used=705.9MB, alloc=212.3MB, time=17.93 memory used=841.0MB, alloc=236.3MB, time=22.74 N1 := 3941 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [4 y x + 128 y + 68 y x + x + 34 x + 289, 2 -x + 4 x z - 17 x - 32 y + 68 z, 16 z y + x + 17, 2 2 -x + 16 z - 17 x - 32 y + 68 z + 8] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=974.2MB, alloc=236.3MB, time=25.52 memory used=1153.6MB, alloc=492.3MB, time=28.34 memory used=1330.6MB, alloc=516.3MB, time=31.34 memory used=1531.0MB, alloc=540.3MB, time=34.87 memory used=1736.5MB, alloc=564.3MB, time=38.52 memory used=1949.3MB, alloc=588.3MB, time=42.38 memory used=2174.7MB, alloc=612.3MB, time=46.47 memory used=2408.4MB, alloc=636.3MB, time=50.73 memory used=2634.4MB, alloc=660.3MB, time=57.29 memory used=2847.5MB, alloc=684.3MB, time=65.13 memory used=3070.9MB, alloc=708.3MB, time=73.55 memory used=3307.2MB, alloc=732.3MB, time=83.18 memory used=3557.2MB, alloc=756.3MB, time=93.25 memory used=3818.6MB, alloc=780.3MB, time=104.06 memory used=4093.2MB, alloc=804.3MB, time=115.91 memory used=4391.7MB, alloc=828.3MB, time=129.02 memory used=4714.1MB, alloc=852.3MB, time=142.86 memory used=5060.5MB, alloc=876.3MB, time=157.74 memory used=5430.8MB, alloc=900.3MB, time=173.79 memory used=5825.1MB, alloc=924.3MB, time=190.75 memory used=6243.2MB, alloc=948.3MB, time=208.70 memory used=6685.4MB, alloc=972.3MB, time=227.44 |\^/| 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(); 1428503950 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [15 y z - 18 z - 15 z, 20 x y + 4 x z - 6 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-8 x + 15 y + 2 y z, 7 x + 20 y - 15 y z] > Problem := [F,G]; 2 Problem := [[15 y z - 18 z - 15 z, 20 x y + 4 x z - 6 y z], 2 2 2 2 [-8 x + 15 y + 2 y z, 7 x + 20 y - 15 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=46.7MB, alloc=32.3MB, time=0.79 memory used=65.8MB, alloc=56.3MB, time=1.10 memory used=104.1MB, alloc=60.3MB, time=1.69 memory used=140.2MB, alloc=84.3MB, time=2.25 memory used=198.9MB, alloc=92.3MB, time=3.20 memory used=259.4MB, alloc=116.3MB, time=4.13 memory used=343.4MB, alloc=116.3MB, time=5.38 memory used=420.2MB, alloc=396.3MB, time=6.58 memory used=525.6MB, alloc=420.3MB, time=8.21 memory used=652.2MB, alloc=444.3MB, time=10.48 memory used=782.5MB, alloc=468.3MB, time=12.91 memory used=926.6MB, alloc=492.3MB, time=15.50 memory used=1083.6MB, alloc=516.3MB, time=18.36 memory used=1251.9MB, alloc=540.3MB, time=21.52 memory used=1426.4MB, alloc=564.3MB, time=25.19 memory used=1593.0MB, alloc=588.3MB, time=30.59 memory used=1767.4MB, alloc=612.3MB, time=36.60 memory used=1954.4MB, alloc=636.3MB, time=43.45 memory used=2155.2MB, alloc=660.3MB, time=51.07 memory used=2363.9MB, alloc=684.3MB, time=59.84 memory used=2596.7MB, alloc=708.3MB, time=69.62 memory used=2853.3MB, alloc=732.3MB, time=80.41 memory used=3133.8MB, alloc=756.3MB, time=92.02 memory used=3438.4MB, alloc=780.3MB, time=104.70 memory used=3766.9MB, alloc=780.3MB, time=118.37 memory used=4095.2MB, alloc=804.3MB, time=131.98 memory used=4447.7MB, alloc=804.3MB, time=146.73 memory used=4799.9MB, alloc=804.3MB, time=161.38 memory used=5152.2MB, alloc=828.3MB, time=176.17 memory used=5528.2MB, alloc=828.3MB, time=192.01 memory used=5904.2MB, alloc=852.3MB, time=207.87 memory used=6304.1MB, alloc=852.3MB, time=224.55 memory used=6703.8MB, alloc=876.3MB, time=241.43 N1 := 13545 > GB := Basis(F, plex(op(vars))); 2 2 3 2 2 2 2 2 GB := [-14 x y + 3 x y + 2 x y - 3 x y , 20 x y + 4 x z - 5 x y + 5 x y, 2 -10 x y - 2 x z + 3 y z, -50 x y - 10 x z + 18 z + 15 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7144.8MB, alloc=876.3MB, time=257.47 memory used=7246.3MB, alloc=876.3MB, time=259.97 memory used=7341.0MB, alloc=876.3MB, time=262.25 memory used=7443.1MB, alloc=876.3MB, time=264.67 memory used=7519.8MB, alloc=876.3MB, time=266.32 memory used=7596.2MB, alloc=876.3MB, time=268.35 |\^/| 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(); 1428504250 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-9 x y - 11 y - y z, -20 x y - 13 y z - 15 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [20 x - 18 x z, -11 y - 5 z - 19 x] > Problem := [F,G]; 2 Problem := [[-9 x y - 11 y - y z, -20 x y - 13 y z - 15 z], 2 2 2 [20 x - 18 x z, -11 y - 5 z - 19 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=56.3MB, time=0.84 memory used=87.5MB, alloc=60.3MB, time=1.47 memory used=125.3MB, alloc=84.3MB, time=2.09 memory used=170.6MB, alloc=84.3MB, time=2.82 memory used=227.9MB, alloc=116.3MB, time=3.82 memory used=310.3MB, alloc=140.3MB, time=5.25 memory used=410.6MB, alloc=164.3MB, time=7.17 memory used=518.4MB, alloc=444.3MB, time=9.12 memory used=649.4MB, alloc=468.3MB, time=11.48 memory used=791.1MB, alloc=492.3MB, time=14.07 memory used=940.2MB, alloc=516.3MB, time=17.76 memory used=1086.3MB, alloc=540.3MB, time=22.62 memory used=1242.6MB, alloc=564.3MB, time=28.27 memory used=1409.3MB, alloc=588.3MB, time=34.80 memory used=1593.7MB, alloc=612.3MB, time=42.68 memory used=1802.1MB, alloc=636.3MB, time=51.89 memory used=2034.5MB, alloc=660.3MB, time=62.09 memory used=2290.8MB, alloc=660.3MB, time=72.73 memory used=2547.0MB, alloc=660.3MB, time=84.12 memory used=2803.3MB, alloc=684.3MB, time=94.89 memory used=3083.5MB, alloc=684.3MB, time=106.34 memory used=3363.7MB, alloc=708.3MB, time=118.50 memory used=3668.0MB, alloc=732.3MB, time=130.77 N1 := 9471 > GB := Basis(F, plex(op(vars))); 2 3 2 2 GB := [97 x y + 143 y + 135 x y + 165 y , -97 x y - 143 y + 15 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4023.8MB, alloc=732.3MB, time=138.61 memory used=4408.5MB, alloc=756.3MB, time=148.85 memory used=4737.9MB, alloc=780.3MB, time=163.49 memory used=5089.7MB, alloc=804.3MB, time=179.22 N2 := 5559 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-9 x y - 11 y - y z, -20 x y - 13 y z - 15 z, 20 x - 18 x z, 2 2 -11 y - 5 z - 19 x] > J:=[op(GB),op(G)]; 2 3 2 2 J := [97 x y + 143 y + 135 x y + 165 y , -97 x y - 143 y + 15 z, 2 2 2 20 x - 18 x z, -11 y - 5 z - 19 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 2, 2, 2, 1, 3/4, 1, 5/11, 6/11, 5/11, 4, 10, 9, 3, 2, 3, 2, 1, 3/4, 3/4, 1/2, 7/12, 1/4, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=5264.4MB, alloc=804.3MB, time=186.71 |\^/| 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(); 1428504479 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [2 y - 11 z + 20, 20 x + 6 x y + 20 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-11 y z + 5 z + 13, 14 x y + 11 y + 10 y] > Problem := [F,G]; 2 2 2 2 Problem := [[2 y - 11 z + 20, 20 x + 6 x y + 20 z ], 2 [-11 y z + 5 z + 13, 14 x y + 11 y + 10 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.53 memory used=47.1MB, alloc=32.3MB, time=0.86 memory used=66.2MB, alloc=56.3MB, time=1.18 memory used=105.8MB, alloc=60.3MB, time=1.82 memory used=144.2MB, alloc=84.3MB, time=2.44 memory used=206.5MB, alloc=92.3MB, time=3.58 memory used=266.2MB, alloc=116.3MB, time=4.69 memory used=343.1MB, alloc=140.3MB, time=6.21 memory used=426.2MB, alloc=164.3MB, time=9.07 N1 := 2043 > GB := Basis(F, plex(op(vars))); 2 2 2 2 GB := [20 y + 33 y x + 110 x + 200, 10 z + 3 y x + 10 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=534.2MB, alloc=164.3MB, time=11.75 N2 := 455 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-11 z + 2 y + 20, 20 x + 6 x y + 20 z , -11 y z + 5 z + 13, 2 14 x y + 11 y + 10 y] > J:=[op(GB),op(G)]; 2 2 2 2 J := [20 y + 33 y x + 110 x + 200, 10 z + 3 y x + 10 x , -11 y z + 5 z + 13, 2 14 x y + 11 y + 10 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 2, 1/2, 1, 3/4, 1/4, 1/2, 1/3, 4, 9, 8, 2, 2, 2, 2, 3/4, 1, 1/2, 5/13, 7/13, 3/13, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=610.8MB, alloc=164.3MB, time=13.11 |\^/| 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(); 1428504494 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [20 x z - 18 z + 3 z, -8 x z + 4 y z - 13] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-3 x z - 16 y z + 15, -19 z + 7 x + 19 z] > Problem := [F,G]; 2 Problem := [[20 x z - 18 z + 3 z, -8 x z + 4 y z - 13], 2 [-3 x z - 16 y z + 15, -19 z + 7 x + 19 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=32.3MB, time=0.82 memory used=66.4MB, alloc=56.3MB, time=1.14 memory used=106.9MB, alloc=60.3MB, time=1.77 memory used=146.3MB, alloc=84.3MB, time=2.46 memory used=207.2MB, alloc=92.3MB, time=3.61 memory used=263.7MB, alloc=116.3MB, time=4.65 memory used=340.5MB, alloc=140.3MB, time=6.04 memory used=433.9MB, alloc=164.3MB, time=7.70 memory used=540.9MB, alloc=188.3MB, time=9.89 memory used=652.6MB, alloc=212.3MB, time=13.09 memory used=772.0MB, alloc=236.3MB, time=17.33 memory used=907.0MB, alloc=260.3MB, time=22.57 memory used=1065.9MB, alloc=260.3MB, time=28.85 memory used=1224.8MB, alloc=284.3MB, time=35.01 memory used=1407.7MB, alloc=284.3MB, time=42.11 memory used=1590.5MB, alloc=284.3MB, time=49.17 memory used=1773.6MB, alloc=308.3MB, time=56.27 N1 := 6403 > GB := Basis(F, plex(op(vars))); 2 GB := [-80 x + 40 x y - 12 x + 6 y - 117, 18 z - 20 x - 3] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1901.2MB, alloc=308.3MB, time=59.29 N2 := 953 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [20 x z - 18 z + 3 z, -8 x z + 4 y z - 13, -3 x z - 16 y z + 15, 2 -19 z + 19 z + 7 x] > J:=[op(GB),op(G)]; 2 J := [-80 x + 40 x y - 12 x + 6 y - 117, 18 z - 20 x - 3, -3 x z - 16 y z + 15, 2 -19 z + 19 z + 7 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 1, 1, 2, 1, 1/2, 1, 1/3, 1/6, 3/4, 4, 9, 7, 2, 2, 1, 2, 1, 1/2, 3/4, 3/7, 3/14, 5/14, 1, 1, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1942.1MB, alloc=564.3MB, time=60.48 |\^/| 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(); 1428504559 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-20 y - 4 y z - 7 x, 16 x - 13 y + 5 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [6 x + 19 x z + 9 z , -x y - 7 y + 9 z ] > Problem := [F,G]; 2 2 2 Problem := [[-20 y - 4 y z - 7 x, 16 x - 13 y + 5 y], 2 2 2 2 [6 x + 19 x z + 9 z , -x y - 7 y + 9 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=46.6MB, alloc=32.3MB, time=0.81 memory used=66.1MB, alloc=56.3MB, time=1.13 memory used=107.7MB, alloc=60.3MB, time=1.77 memory used=149.7MB, alloc=60.3MB, time=2.34 memory used=191.0MB, alloc=84.3MB, time=2.93 memory used=233.4MB, alloc=84.3MB, time=3.65 memory used=302.9MB, alloc=116.3MB, time=4.74 memory used=392.0MB, alloc=140.3MB, time=6.19 memory used=496.8MB, alloc=140.3MB, time=7.94 memory used=590.8MB, alloc=164.3MB, time=9.67 memory used=707.4MB, alloc=188.3MB, time=11.69 memory used=812.2MB, alloc=468.3MB, time=13.56 memory used=957.9MB, alloc=492.3MB, time=16.25 memory used=1137.1MB, alloc=516.3MB, time=19.08 memory used=1336.6MB, alloc=540.3MB, time=22.04 memory used=1537.2MB, alloc=564.3MB, time=25.71 memory used=1734.6MB, alloc=588.3MB, time=30.61 memory used=1911.9MB, alloc=612.3MB, time=36.72 memory used=2098.7MB, alloc=636.3MB, time=43.34 memory used=2298.8MB, alloc=660.3MB, time=50.58 memory used=2513.5MB, alloc=684.3MB, time=58.71 memory used=2743.2MB, alloc=708.3MB, time=67.57 memory used=2983.4MB, alloc=732.3MB, time=77.59 memory used=3247.6MB, alloc=756.3MB, time=88.61 memory used=3535.7MB, alloc=780.3MB, time=100.54 memory used=3847.7MB, alloc=804.3MB, time=113.46 memory used=4183.7MB, alloc=828.3MB, time=127.33 memory used=4543.6MB, alloc=828.3MB, time=142.47 memory used=4903.4MB, alloc=828.3MB, time=157.38 memory used=5263.2MB, alloc=828.3MB, time=172.30 memory used=5623.1MB, alloc=852.3MB, time=187.69 memory used=6006.8MB, alloc=852.3MB, time=203.96 memory used=6390.5MB, alloc=852.3MB, time=220.32 memory used=6774.1MB, alloc=876.3MB, time=236.46 memory used=7181.5MB, alloc=876.3MB, time=253.83 |\^/| 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(); 1428504859 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [13 x y - 11 y - 14 y z, -13 x z + z + 3] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [12 x - y , -18 x + 11 y z] > Problem := [F,G]; Problem := [ 2 2 2 2 2 [13 x y - 11 y - 14 y z, -13 x z + z + 3], [12 x - y , -18 x + 11 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=48.3MB, alloc=32.3MB, time=0.86 memory used=69.7MB, alloc=56.3MB, time=1.25 memory used=112.3MB, alloc=60.3MB, time=1.99 memory used=150.7MB, alloc=84.3MB, time=2.67 memory used=208.8MB, alloc=108.3MB, time=3.75 memory used=280.4MB, alloc=132.3MB, time=5.98 memory used=367.6MB, alloc=132.3MB, time=9.14 N1 := 2327 > GB := Basis(F, plex(op(vars))); 2 2 3 2 GB := [-2197 x y + 1716 x y + 121 y + 588 y, -13 x y + 11 y + 14 y z, 2 -13 x z + z + 3] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=457.1MB, alloc=140.3MB, time=10.92 memory used=555.1MB, alloc=164.3MB, time=12.62 memory used=672.6MB, alloc=188.3MB, time=15.58 memory used=789.9MB, alloc=212.3MB, time=19.95 N2 := 2327 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [13 x y - 11 y - 14 y z, -13 x z + z + 3, -y + 12 x , -18 x + 11 y z] > J:=[op(GB),op(G)]; 2 2 3 2 J := [-2197 x y + 1716 x y + 121 y + 588 y, -13 x y + 11 y + 14 y z, 2 2 2 2 -13 x z + z + 3, -y + 12 x , -18 x + 11 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 2, 2, 1, 3/4, 3/4, 2/5, 1/2, 2/5, 5, 12, 11, 3, 2, 3, 2, 1, 4/5, 3/5, 3/7, 9/14, 2/7, -2, -3, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=802.3MB, alloc=212.3MB, time=20.30 |\^/| 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(); 1428504885 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-13 x - 9 x z + y , 17 x y - 19 y + 18 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [x - 5 x + 10 z, 15 x - x z + 10 x] > Problem := [F,G]; 2 2 Problem := [[-13 x - 9 x z + y , 17 x y - 19 y + 18 z], 2 2 [x - 5 x + 10 z, 15 x - x z + 10 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.50 memory used=46.0MB, alloc=32.3MB, time=0.80 memory used=65.7MB, alloc=56.3MB, time=1.12 memory used=108.7MB, alloc=60.3MB, time=1.88 memory used=146.6MB, alloc=84.3MB, time=2.53 memory used=204.9MB, alloc=108.3MB, time=3.56 memory used=282.3MB, alloc=116.3MB, time=4.91 memory used=349.9MB, alloc=140.3MB, time=6.44 memory used=429.5MB, alloc=164.3MB, time=8.74 memory used=520.5MB, alloc=188.3MB, time=12.18 memory used=635.3MB, alloc=188.3MB, time=16.41 memory used=749.9MB, alloc=212.3MB, time=20.73 N1 := 4079 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [17 y x + 2 y - 19 y x - 26 x , 17 y x + 18 z - 19 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=890.4MB, alloc=212.3MB, time=25.48 N2 := 947 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-13 x - 9 x z + y , 17 y x + 18 z - 19 y, x + 10 z - 5 x, 2 15 x - x z + 10 x] > J:=[op(GB),op(G)]; 2 2 2 2 J := [17 y x + 2 y - 19 y x - 26 x , 17 y x + 18 z - 19 y, x + 10 z - 5 x, 2 15 x - x z + 10 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 2, 1, 1, 1/2, 1, 2/3, 1/4, 1/3, 4, 9, 9, 3, 2, 2, 1, 1, 1/2, 3/4, 9/13, 5/13, 3/13, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=997.7MB, alloc=212.3MB, time=27.75 |\^/| 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(); 1428504920 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [20 x - 8 y - z , 19 x + 4 y - 15 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [3 y z + 2 x - 15, 7 y + 9 y z + 2 y] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[20 x - 8 y - z , 19 x + 4 y - 15 z ], 2 [3 y z + 2 x - 15, 7 y + 9 y z + 2 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.51 memory used=47.6MB, alloc=56.3MB, time=0.85 memory used=87.7MB, alloc=60.3MB, time=1.53 memory used=128.8MB, alloc=92.3MB, time=2.20 memory used=191.7MB, alloc=92.3MB, time=3.23 memory used=255.2MB, alloc=116.3MB, time=4.23 memory used=332.2MB, alloc=372.3MB, time=5.46 memory used=416.6MB, alloc=396.3MB, time=6.82 memory used=521.1MB, alloc=420.3MB, time=8.61 memory used=651.0MB, alloc=444.3MB, time=10.83 memory used=790.5MB, alloc=468.3MB, time=13.36 memory used=939.4MB, alloc=492.3MB, time=16.11 memory used=1100.4MB, alloc=516.3MB, time=19.18 memory used=1277.0MB, alloc=540.3MB, time=22.80 memory used=1461.4MB, alloc=564.3MB, time=26.59 memory used=1651.9MB, alloc=588.3MB, time=30.50 memory used=1837.2MB, alloc=612.3MB, time=34.08 memory used=2031.7MB, alloc=636.3MB, time=39.94 memory used=2219.9MB, alloc=660.3MB, time=47.06 memory used=2417.4MB, alloc=684.3MB, time=54.52 memory used=2628.7MB, alloc=708.3MB, time=63.02 memory used=2854.5MB, alloc=732.3MB, time=72.18 memory used=3094.5MB, alloc=756.3MB, time=81.69 memory used=3348.5MB, alloc=780.3MB, time=91.85 memory used=3611.5MB, alloc=804.3MB, time=103.37 memory used=3894.6MB, alloc=828.3MB, time=116.00 memory used=4201.6MB, alloc=852.3MB, time=129.57 memory used=4532.6MB, alloc=876.3MB, time=144.05 memory used=4887.6MB, alloc=900.3MB, time=159.63 memory used=5266.4MB, alloc=924.3MB, time=176.01 memory used=5669.2MB, alloc=948.3MB, time=193.33 memory used=6095.9MB, alloc=972.3MB, time=211.93 memory used=6546.6MB, alloc=972.3MB, time=231.63 |\^/| 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(); 1428505220 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-16 x y + 14 y + 10 y z, 4 x z + y - 18] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-6 y - 13 x - 20 z, -16 x y + 11 z - 19] > Problem := [F,G]; 2 2 Problem := [[-16 x y + 14 y + 10 y z, 4 x z + y - 18], 2 2 [-6 y - 13 x - 20 z, -16 x y + 11 z - 19]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=46.7MB, alloc=32.3MB, time=0.80 memory used=66.2MB, alloc=56.3MB, time=1.10 memory used=107.4MB, alloc=60.3MB, time=1.72 memory used=146.5MB, alloc=84.3MB, time=2.32 memory used=210.6MB, alloc=92.3MB, time=3.30 memory used=273.0MB, alloc=116.3MB, time=4.26 memory used=342.7MB, alloc=116.3MB, time=5.31 memory used=411.9MB, alloc=396.3MB, time=6.36 memory used=521.1MB, alloc=420.3MB, time=8.00 memory used=652.9MB, alloc=444.3MB, time=10.29 memory used=789.4MB, alloc=468.3MB, time=12.71 memory used=936.0MB, alloc=492.3MB, time=15.34 memory used=1096.1MB, alloc=516.3MB, time=18.25 memory used=1267.4MB, alloc=540.3MB, time=21.38 memory used=1449.5MB, alloc=564.3MB, time=24.76 memory used=1636.4MB, alloc=588.3MB, time=28.21 memory used=1800.1MB, alloc=612.3MB, time=31.33 memory used=1961.9MB, alloc=636.3MB, time=34.46 memory used=2170.1MB, alloc=660.3MB, time=40.21 memory used=2370.5MB, alloc=684.3MB, time=47.27 memory used=2580.8MB, alloc=708.3MB, time=55.48 memory used=2804.2MB, alloc=732.3MB, time=64.20 memory used=3041.6MB, alloc=756.3MB, time=73.68 memory used=3293.4MB, alloc=780.3MB, time=83.96 memory used=3559.7MB, alloc=804.3MB, time=94.90 memory used=3842.3MB, alloc=828.3MB, time=106.57 memory used=4140.4MB, alloc=852.3MB, time=119.07 memory used=4446.8MB, alloc=876.3MB, time=132.82 memory used=4776.8MB, alloc=900.3MB, time=147.40 memory used=5130.9MB, alloc=924.3MB, time=163.20 memory used=5508.8MB, alloc=948.3MB, time=180.14 memory used=5910.7MB, alloc=972.3MB, time=198.07 memory used=6336.5MB, alloc=996.3MB, time=217.19 |\^/| 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(); 1428505520 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-2 x + 12 x + 20, 11 x y - 10 x z - 15 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [12 y + 9 z + 2 y, 20 x z - z - 16 z] > Problem := [F,G]; 2 Problem := [[-2 x + 12 x + 20, 11 x y - 10 x z - 15 y z], 2 2 2 [12 y + 9 z + 2 y, 20 x z - z - 16 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.6MB, alloc=32.3MB, time=0.83 memory used=67.3MB, alloc=56.3MB, time=1.14 memory used=110.0MB, alloc=60.3MB, time=1.87 memory used=148.2MB, alloc=84.3MB, time=2.55 memory used=207.5MB, alloc=108.3MB, time=3.56 memory used=281.4MB, alloc=132.3MB, time=5.41 memory used=363.5MB, alloc=132.3MB, time=8.34 N1 := 2431 > GB := Basis(F, plex(op(vars))); 2 GB := [x - 6 x - 10, -11 x y + 10 x z + 15 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=447.6MB, alloc=132.3MB, time=10.96 memory used=540.3MB, alloc=164.3MB, time=12.49 memory used=657.8MB, alloc=188.3MB, time=14.58 memory used=781.1MB, alloc=212.3MB, time=18.76 N2 := 2431 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-2 x + 12 x + 20, -15 z y - 10 z x + 11 y x, 9 z + 12 y + 2 y, 2 20 x z - z - 16 z] > J:=[op(GB),op(G)]; 2 2 2 J := [x - 6 x - 10, -11 x y + 10 x z + 15 y z, 9 z + 12 y + 2 y, 2 20 x z - z - 16 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 8, 2, 2, 2, 2, 3/4, 1/2, 3/4, 5/12, 1/3, 1/2, 4, 8, 8, 2, 2, 2, 2, 3/4, 1/2, 3/4, 5/12, 1/3, 1/2, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=867.4MB, alloc=212.3MB, time=21.53 |\^/| 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(); 1428505545 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-10 z + 14 x + 3 z, -16 x z + 9 x + 15 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-13 x - 9 y - 17 x, -14 x - 18 x + 20] > Problem := [F,G]; 2 Problem := [[-10 z + 14 x + 3 z, -16 x z + 9 x + 15 y], 2 2 2 [-13 x - 9 y - 17 x, -14 x - 18 x + 20]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.53 N1 := 233 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [-1792 x + 189 x + 990 x y + 1125 y , 16 z x - 15 y - 9 x, 2 2 -1792 x + 1200 y z + 189 x + 315 y, 10 z - 14 x - 3 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=48.3MB, alloc=32.3MB, time=0.90 memory used=67.9MB, alloc=56.3MB, time=1.21 memory used=110.5MB, alloc=60.3MB, time=1.92 N2 := 493 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-10 z + 3 z + 14 x, -16 x z + 9 x + 15 y, -13 x - 9 y - 17 x, 2 -14 x - 18 x + 20] > J:=[op(GB),op(G)]; 3 2 2 J := [-1792 x + 189 x + 990 x y + 1125 y , 16 z x - 15 y - 9 x, 2 2 -1792 x + 1200 y z + 189 x + 315 y, 10 z - 14 x - 3 z, 2 2 2 -13 x - 9 y - 17 x, -14 x - 18 x + 20] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 8, 2, 2, 2, 2, 1, 1/2, 1/2, 7/12, 1/6, 1/4, 6, 13, 13, 3, 3, 2, 2, 1, 2/3, 1/2, 3/5, 3/10, 1/5, -5, -5, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=129.1MB, alloc=60.3MB, time=2.32 |\^/| 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(); 1428505547 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-7 x y + 18 x z - 18 y, 11 x + 4 x z - x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-2 x - 7 y z - 3, -6 y z + 9 z - 6 y] > Problem := [F,G]; 2 Problem := [[-7 x y + 18 x z - 18 y, 11 x + 4 x z - x], 2 2 [-2 x - 7 y z - 3, -6 y z + 9 z - 6 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=46.2MB, alloc=32.3MB, time=0.80 memory used=65.2MB, alloc=56.3MB, time=1.10 memory used=106.4MB, alloc=60.3MB, time=1.72 memory used=145.4MB, alloc=84.3MB, time=2.35 memory used=206.4MB, alloc=92.3MB, time=3.32 memory used=266.4MB, alloc=116.3MB, time=4.30 memory used=346.0MB, alloc=140.3MB, time=5.71 memory used=441.8MB, alloc=164.3MB, time=7.39 memory used=553.1MB, alloc=188.3MB, time=9.33 memory used=664.7MB, alloc=468.3MB, time=11.35 memory used=800.0MB, alloc=492.3MB, time=15.01 memory used=938.9MB, alloc=516.3MB, time=19.45 memory used=1085.5MB, alloc=540.3MB, time=25.07 memory used=1253.0MB, alloc=564.3MB, time=31.63 memory used=1444.5MB, alloc=564.3MB, time=39.06 memory used=1636.0MB, alloc=588.3MB, time=46.54 memory used=1851.4MB, alloc=588.3MB, time=54.87 memory used=2066.9MB, alloc=612.3MB, time=63.26 N1 := 6999 > GB := Basis(F, plex(op(vars))); 2 2 GB := [14 y x + 99 x + 36 y - 9 x, 11 x + 4 x z - x, 2 -1089 x + 56 y z + 99 x - 410 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2310.9MB, alloc=612.3MB, time=71.55 memory used=2588.2MB, alloc=612.3MB, time=76.19 memory used=2857.4MB, alloc=636.3MB, time=81.29 memory used=3132.4MB, alloc=660.3MB, time=86.40 memory used=3410.2MB, alloc=684.3MB, time=94.47 memory used=3664.7MB, alloc=708.3MB, time=103.85 memory used=3917.8MB, alloc=732.3MB, time=114.66 memory used=4192.8MB, alloc=756.3MB, time=126.67 memory used=4491.6MB, alloc=780.3MB, time=139.57 memory used=4814.5MB, alloc=804.3MB, time=153.31 memory used=5161.3MB, alloc=828.3MB, time=168.07 memory used=5532.0MB, alloc=852.3MB, time=183.94 memory used=5926.7MB, alloc=876.3MB, time=200.69 N2 := 9693 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-7 x y + 18 x z - 18 y, 11 x + 4 x z - x, -2 x - 7 y z - 3, 2 -6 y z + 9 z - 6 y] > J:=[op(GB),op(G)]; 2 2 J := [14 y x + 99 x + 36 y - 9 x, 11 x + 4 x z - x, 2 2 2 -1089 x + 56 y z + 99 x - 410 y, -2 x - 7 y z - 3, -6 y z + 9 z - 6 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 1, 2, 3/4, 3/4, 1, 1/2, 5/12, 5/12, 5, 12, 10, 2, 2, 1, 2, 4/5, 4/5, 4/5, 9/17, 7/17, 5/17, -2, -2, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=6207.1MB, alloc=876.3MB, time=211.93 |\^/| 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(); 1428505792 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-2 y + 11 z - 10, 4 x + 12 x y - 18] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [11 y + 3 z - 12 y, -x y - 5 y z + 4 z] > Problem := [F,G]; 2 2 Problem := [[-2 y + 11 z - 10, 4 x + 12 x y - 18], 2 2 [11 y + 3 z - 12 y, -x y - 5 y z + 4 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.53 memory used=46.8MB, alloc=32.3MB, time=0.86 memory used=66.5MB, alloc=56.3MB, time=1.19 memory used=107.3MB, alloc=60.3MB, time=1.82 memory used=146.9MB, alloc=84.3MB, time=2.45 memory used=211.0MB, alloc=92.3MB, time=3.66 memory used=267.1MB, alloc=116.3MB, time=4.70 memory used=342.2MB, alloc=140.3MB, time=6.09 memory used=434.8MB, alloc=164.3MB, time=7.79 memory used=539.2MB, alloc=188.3MB, time=10.33 memory used=649.3MB, alloc=212.3MB, time=13.70 memory used=771.1MB, alloc=236.3MB, time=18.16 memory used=912.2MB, alloc=236.3MB, time=23.53 memory used=1053.2MB, alloc=260.3MB, time=29.04 memory used=1218.2MB, alloc=260.3MB, time=35.30 memory used=1383.1MB, alloc=284.3MB, time=41.60 N1 := 5437 > GB := Basis(F, plex(op(vars))); 2 2 GB := [6 y x + 2 x - 9, -2 y + 11 z - 10] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1549.8MB, alloc=284.3MB, time=46.29 memory used=1769.2MB, alloc=540.3MB, time=50.26 memory used=1976.6MB, alloc=564.3MB, time=54.36 memory used=2177.9MB, alloc=588.3MB, time=61.12 memory used=2380.3MB, alloc=612.3MB, time=69.28 memory used=2606.7MB, alloc=636.3MB, time=78.37 memory used=2857.3MB, alloc=660.3MB, time=88.45 N2 := 5437 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-2 y + 11 z - 10, 4 x + 12 x y - 18, 3 z + 11 y - 12 y, -x y - 5 y z + 4 z] > J:=[op(GB),op(G)]; 2 2 2 2 J := [6 y x + 2 x - 9, -2 y + 11 z - 10, 3 z + 11 y - 12 y, -x y - 5 y z + 4 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 2, 1/2, 1, 3/4, 1/4, 1/2, 1/3, 4, 9, 8, 2, 2, 2, 2, 1/2, 1, 3/4, 1/4, 1/2, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=2953.6MB, alloc=660.3MB, time=91.96 |\^/| 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(); 1428505890 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-4 x y + 17 x - 13 y, -17 y + 6 y z - 20 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [9 x z + 3 y - 13 z, -12 y + 8 y z - 14 x] > Problem := [F,G]; 2 2 Problem := [[-4 x y + 17 x - 13 y, -17 y + 6 y z - 20 z ], 2 2 [9 x z + 3 y - 13 z, -12 y + 8 y z - 14 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=46.9MB, alloc=32.3MB, time=0.79 memory used=66.2MB, alloc=56.3MB, time=1.11 memory used=109.2MB, alloc=60.3MB, time=1.88 N1 := 533 > GB := Basis(F, plex(op(vars))); 2 2 GB := [4 y x + 13 y - 17 x, 20 z - 6 z y + 17 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=147.8MB, alloc=60.3MB, time=2.66 memory used=185.4MB, alloc=84.3MB, time=3.25 memory used=232.0MB, alloc=84.3MB, time=4.02 N2 := 533 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-4 x y + 17 x - 13 y, -17 y + 6 y z - 20 z , 9 z x + 3 y - 13 z, 2 -12 y + 8 y z - 14 x] > J:=[op(GB),op(G)]; 2 2 2 J := [4 y x + 13 y - 17 x, 20 z - 6 z y + 17 y , 9 z x + 3 y - 13 z, 2 -12 y + 8 y z - 14 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 1, 2, 2, 3/4, 1, 3/4, 1/3, 7/12, 5/12, 4, 10, 8, 2, 1, 2, 2, 3/4, 1, 3/4, 1/3, 7/12, 5/12, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=276.8MB, alloc=84.3MB, time=4.89 |\^/| 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(); 1428505895 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [13 x y + 9 x z + 17 z , -13 x y + 9 x z + 6 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-x y + 20 x z - y, 15 x y - 14 z - 15 z] > Problem := [F,G]; 2 Problem := [[13 x y + 9 x z + 17 z , -13 x y + 9 x z + 6 y z], 2 [-x y + 20 x z - y, 15 x y - 14 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.1MB, alloc=56.3MB, time=0.83 memory used=86.8MB, alloc=60.3MB, time=1.43 memory used=125.4MB, alloc=84.3MB, time=2.03 memory used=172.4MB, alloc=84.3MB, time=2.78 memory used=231.5MB, alloc=116.3MB, time=3.74 memory used=314.0MB, alloc=116.3MB, time=5.05 memory used=394.6MB, alloc=140.3MB, time=6.38 memory used=491.0MB, alloc=420.3MB, time=8.13 memory used=618.3MB, alloc=444.3MB, time=10.44 memory used=766.2MB, alloc=468.3MB, time=13.01 memory used=930.4MB, alloc=492.3MB, time=16.12 memory used=1102.4MB, alloc=516.3MB, time=19.37 memory used=1283.8MB, alloc=540.3MB, time=22.70 memory used=1472.6MB, alloc=564.3MB, time=26.22 memory used=1660.5MB, alloc=588.3MB, time=29.82 memory used=1838.9MB, alloc=612.3MB, time=33.22 memory used=1998.3MB, alloc=636.3MB, time=36.29 memory used=2163.7MB, alloc=660.3MB, time=39.45 memory used=2313.0MB, alloc=684.3MB, time=42.44 memory used=2448.6MB, alloc=708.3MB, time=45.20 memory used=2598.7MB, alloc=732.3MB, time=48.27 memory used=2723.6MB, alloc=756.3MB, time=50.93 memory used=2846.7MB, alloc=780.3MB, time=53.58 memory used=2961.2MB, alloc=804.3MB, time=56.07 memory used=3130.1MB, alloc=828.3MB, time=61.15 memory used=3437.1MB, alloc=852.3MB, time=72.17 memory used=3770.2MB, alloc=876.3MB, time=84.84 memory used=4110.3MB, alloc=900.3MB, time=98.58 memory used=4458.6MB, alloc=924.3MB, time=112.64 memory used=4817.9MB, alloc=948.3MB, time=127.57 memory used=5189.9MB, alloc=972.3MB, time=143.20 memory used=5575.6MB, alloc=996.3MB, time=159.55 memory used=5975.6MB, alloc=1020.3MB, time=176.75 memory used=6389.5MB, alloc=1044.3MB, time=195.03 memory used=6814.2MB, alloc=1068.3MB, time=214.46 memory used=7262.7MB, alloc=1092.3MB, time=234.95 memory used=7735.2MB, alloc=1116.3MB, time=255.92 memory used=8231.6MB, alloc=1140.3MB, time=277.99 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428506195 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-7 y + 19 y + 18 z, x y + 15 z - 12 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [x - 20 y - 16 z, -5 x y + 20 y z - 17 x] > Problem := [F,G]; 2 2 Problem := [[-7 y + 19 y + 18 z, x y + 15 z - 12 x], 2 [x - 20 y - 16 z, -5 x y + 20 y z - 17 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.1MB, alloc=32.3MB, time=0.81 memory used=65.7MB, alloc=56.3MB, time=1.11 memory used=108.0MB, alloc=60.3MB, time=1.72 memory used=143.5MB, alloc=84.3MB, time=2.24 memory used=207.0MB, alloc=92.3MB, time=3.20 memory used=270.8MB, alloc=116.3MB, time=4.14 memory used=347.5MB, alloc=116.3MB, time=5.29 memory used=412.3MB, alloc=372.3MB, time=6.28 memory used=494.4MB, alloc=396.3MB, time=7.58 memory used=603.1MB, alloc=420.3MB, time=9.51 memory used=720.3MB, alloc=444.3MB, time=11.64 memory used=853.2MB, alloc=468.3MB, time=14.10 memory used=1005.1MB, alloc=492.3MB, time=16.81 memory used=1165.7MB, alloc=516.3MB, time=19.84 memory used=1336.9MB, alloc=540.3MB, time=23.13 memory used=1509.5MB, alloc=564.3MB, time=27.64 memory used=1673.5MB, alloc=588.3MB, time=33.06 memory used=1847.3MB, alloc=612.3MB, time=39.29 memory used=2034.0MB, alloc=636.3MB, time=46.22 memory used=2234.6MB, alloc=660.3MB, time=54.00 memory used=2443.6MB, alloc=684.3MB, time=62.98 memory used=2676.6MB, alloc=708.3MB, time=72.93 memory used=2933.5MB, alloc=732.3MB, time=84.00 memory used=3214.3MB, alloc=756.3MB, time=96.03 memory used=3519.1MB, alloc=780.3MB, time=109.04 memory used=3847.8MB, alloc=780.3MB, time=123.51 memory used=4176.5MB, alloc=804.3MB, time=138.60 memory used=4529.1MB, alloc=804.3MB, time=153.67 memory used=4881.7MB, alloc=804.3MB, time=168.56 memory used=5234.1MB, alloc=828.3MB, time=183.82 memory used=5610.4MB, alloc=828.3MB, time=200.95 memory used=5986.5MB, alloc=852.3MB, time=216.75 memory used=6386.8MB, alloc=852.3MB, time=233.19 memory used=6786.9MB, alloc=876.3MB, time=249.74 |\^/| 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(); 1428506495 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-4 y z + 16 z + 9 x, 5 x y - 10 y + 16 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-11 x - 13 y - 13 z, -2 y z + 3 z - 2 z] > Problem := [F,G]; 2 2 2 Problem := [[-4 y z + 16 z + 9 x, 5 x y - 10 y + 16 z ], 2 2 [-11 x - 13 y - 13 z, -2 y z + 3 z - 2 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=27.2MB, alloc=32.3MB, time=0.52 memory used=47.9MB, alloc=32.3MB, time=0.83 memory used=67.1MB, alloc=56.3MB, time=1.14 memory used=105.7MB, alloc=60.3MB, time=1.75 memory used=142.0MB, alloc=84.3MB, time=2.33 memory used=201.7MB, alloc=92.3MB, time=3.27 memory used=261.3MB, alloc=116.3MB, time=4.24 memory used=344.5MB, alloc=116.3MB, time=5.58 memory used=425.7MB, alloc=140.3MB, time=6.94 memory used=515.7MB, alloc=140.3MB, time=8.49 memory used=588.3MB, alloc=420.3MB, time=9.78 memory used=709.1MB, alloc=444.3MB, time=11.90 memory used=856.3MB, alloc=468.3MB, time=14.44 memory used=1013.2MB, alloc=492.3MB, time=17.10 memory used=1149.0MB, alloc=516.3MB, time=19.45 memory used=1295.0MB, alloc=540.3MB, time=22.16 memory used=1430.0MB, alloc=564.3MB, time=24.75 memory used=1605.7MB, alloc=588.3MB, time=27.89 memory used=1763.8MB, alloc=612.3MB, time=30.67 memory used=1895.6MB, alloc=636.3MB, time=33.29 memory used=2032.5MB, alloc=660.3MB, time=36.06 memory used=2181.8MB, alloc=684.3MB, time=39.23 memory used=2323.9MB, alloc=708.3MB, time=42.37 memory used=2453.2MB, alloc=732.3MB, time=45.10 memory used=2568.3MB, alloc=756.3MB, time=47.63 memory used=2697.5MB, alloc=780.3MB, time=50.43 memory used=2816.1MB, alloc=804.3MB, time=53.14 memory used=2933.5MB, alloc=828.3MB, time=55.82 memory used=3037.8MB, alloc=852.3MB, time=58.29 memory used=3127.2MB, alloc=876.3MB, time=60.49 memory used=3226.3MB, alloc=876.3MB, time=62.82 memory used=3311.8MB, alloc=900.3MB, time=64.94 memory used=3397.7MB, alloc=924.3MB, time=67.12 memory used=3485.4MB, alloc=924.3MB, time=69.46 memory used=3556.6MB, alloc=948.3MB, time=71.52 memory used=3923.2MB, alloc=972.3MB, time=79.06 memory used=4253.3MB, alloc=996.3MB, time=86.46 memory used=4664.2MB, alloc=1020.3MB, time=97.84 memory used=5008.3MB, alloc=1044.3MB, time=112.10 memory used=5349.7MB, alloc=1068.3MB, time=125.87 memory used=5696.2MB, alloc=1092.3MB, time=140.73 memory used=6050.6MB, alloc=1116.3MB, time=156.27 memory used=6415.5MB, alloc=1140.3MB, time=172.19 memory used=6792.3MB, alloc=1164.3MB, time=189.34 |\^/| 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(); 1428506796 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-20 x y - 6 x - 13, -12 y z - 13 z - 10 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [4 x z + 17 y z + 11, -13 x z - 8 y - 3 y] > Problem := [F,G]; 2 Problem := [[-20 x y - 6 x - 13, -12 y z - 13 z - 10 x], 2 [4 x z + 17 y z + 11, -13 x z - 8 y - 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.20 memory used=26.8MB, alloc=32.3MB, time=0.59 memory used=47.4MB, alloc=60.3MB, time=0.92 memory used=89.7MB, alloc=60.3MB, time=1.54 memory used=131.2MB, alloc=84.3MB, time=2.17 memory used=169.5MB, alloc=84.3MB, time=2.75 memory used=235.3MB, alloc=116.3MB, time=3.98 memory used=320.9MB, alloc=116.3MB, time=5.63 memory used=397.8MB, alloc=140.3MB, time=7.09 memory used=493.6MB, alloc=164.3MB, time=8.85 memory used=600.3MB, alloc=188.3MB, time=10.72 memory used=695.4MB, alloc=444.3MB, time=12.55 memory used=820.6MB, alloc=468.3MB, time=14.90 memory used=951.9MB, alloc=492.3MB, time=19.07 memory used=1090.6MB, alloc=516.3MB, time=23.85 memory used=1243.4MB, alloc=540.3MB, time=29.57 memory used=1410.8MB, alloc=564.3MB, time=37.09 memory used=1602.1MB, alloc=564.3MB, time=45.76 memory used=1793.4MB, alloc=588.3MB, time=53.96 memory used=2008.6MB, alloc=588.3MB, time=63.43 memory used=2223.8MB, alloc=612.3MB, time=73.84 memory used=2463.1MB, alloc=612.3MB, time=83.64 N1 := 7363 > GB := Basis(F, plex(op(vars))); 2 GB := [20 y x + 6 x + 13, 13 z + 12 z y + 10 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2714.5MB, alloc=612.3MB, time=92.75 memory used=2998.0MB, alloc=636.3MB, time=97.94 memory used=3288.8MB, alloc=660.3MB, time=103.18 memory used=3592.4MB, alloc=684.3MB, time=110.72 memory used=3870.0MB, alloc=708.3MB, time=121.31 memory used=4150.8MB, alloc=732.3MB, time=133.01 memory used=4455.7MB, alloc=756.3MB, time=147.12 memory used=4784.4MB, alloc=780.3MB, time=161.73 memory used=5137.2MB, alloc=804.3MB, time=177.34 |\^/| 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(); 1428507096 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-13 z + 17 x - 10, 20 x + 9 x + 3 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [6 y z + 20 z - 15 x, 2 x - 12 z - 5] > Problem := [F,G]; 2 2 Problem := [[-13 z + 17 x - 10, 20 x + 9 x + 3 y], 2 2 [6 y z + 20 z - 15 x, 2 x - 12 z - 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.53 memory used=47.1MB, alloc=32.3MB, time=0.84 memory used=67.3MB, alloc=56.3MB, time=1.20 memory used=110.0MB, alloc=60.3MB, time=1.96 memory used=150.4MB, alloc=84.3MB, time=2.65 memory used=208.7MB, alloc=108.3MB, time=3.80 memory used=277.0MB, alloc=132.3MB, time=6.30 N1 := 1883 > GB := Basis(F, plex(op(vars))); 2 2 GB := [20 x + 3 y + 9 x, 13 z - 17 x + 10] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=369.4MB, alloc=140.3MB, time=8.53 memory used=474.0MB, alloc=140.3MB, time=10.60 memory used=567.3MB, alloc=164.3MB, time=13.29 N2 := 1883 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-13 z + 17 x - 10, 20 x + 3 y + 9 x, 6 y z + 20 z - 15 x, 2 2 x - 12 z - 5] > J:=[op(GB),op(G)]; J := [ 2 2 2 2 20 x + 3 y + 9 x, 13 z - 17 x + 10, 6 y z + 20 z - 15 x, 2 x - 12 z - 5 ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 1, 2, 1, 1/2, 3/4, 5/12, 1/6, 1/3, 4, 9, 8, 2, 2, 1, 2, 1, 1/2, 3/4, 5/12, 1/6, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=629.3MB, alloc=164.3MB, time=15.41 |\^/| 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(); 1428507116 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-2 x - 6 x z - 8 x, 20 x z - 6 z + 13 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [-17 x y + 12 x z + 17 y z, 6 y z + y - 18] > Problem := [F,G]; 2 2 Problem := [[-2 x - 6 x z - 8 x, 20 x z - 6 z + 13 x], [-17 x y + 12 x z + 17 y z, 6 y z + y - 18]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=46.7MB, alloc=32.3MB, time=0.80 memory used=65.7MB, alloc=56.3MB, time=1.11 memory used=105.0MB, alloc=60.3MB, time=1.71 memory used=142.7MB, alloc=84.3MB, time=2.30 memory used=205.9MB, alloc=92.3MB, time=3.40 memory used=263.4MB, alloc=116.3MB, time=4.45 memory used=339.3MB, alloc=140.3MB, time=5.77 memory used=431.9MB, alloc=164.3MB, time=7.39 memory used=541.9MB, alloc=188.3MB, time=9.27 memory used=668.4MB, alloc=212.3MB, time=11.45 memory used=795.1MB, alloc=492.3MB, time=14.32 memory used=928.9MB, alloc=516.3MB, time=18.59 memory used=1073.4MB, alloc=540.3MB, time=23.62 memory used=1230.6MB, alloc=564.3MB, time=30.11 memory used=1403.1MB, alloc=588.3MB, time=38.11 memory used=1599.6MB, alloc=612.3MB, time=46.53 memory used=1820.0MB, alloc=612.3MB, time=55.09 memory used=2040.4MB, alloc=612.3MB, time=63.59 memory used=2260.7MB, alloc=636.3MB, time=72.84 memory used=2505.0MB, alloc=636.3MB, time=82.44 memory used=2749.2MB, alloc=636.3MB, time=91.87 memory used=2993.5MB, alloc=660.3MB, time=101.59 memory used=3261.5MB, alloc=684.3MB, time=112.05 memory used=3553.8MB, alloc=708.3MB, time=123.13 N1 := 9451 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 GB := [22 x + 57 x + 32 x, x + 3 x z + 4 x, 20 x + 18 z + 41 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3724.5MB, alloc=708.3MB, time=126.33 memory used=3946.4MB, alloc=708.3MB, time=130.69 memory used=4176.2MB, alloc=732.3MB, time=135.61 memory used=4512.9MB, alloc=756.3MB, time=148.67 memory used=4847.7MB, alloc=780.3MB, time=162.62 memory used=5206.5MB, alloc=804.3MB, time=177.68 N2 := 6439 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-2 x - 6 x z - 8 x, -6 z + 20 z x + 13 x, -17 x y + 12 x z + 17 y z, 6 z y + y - 18] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [22 x + 57 x + 32 x, x + 3 x z + 4 x, 18 z + 20 x + 41 x, -17 x y + 12 x z + 17 y z, 6 z y + y - 18] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 1, 2, 3/4, 1/2, 1, 7/12, 1/3, 1/2, 5, 10, 11, 3, 3, 1, 2, 4/5, 2/5, 4/5, 2/3, 4/15, 1/3, -1, -3, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=5482.3MB, alloc=804.3MB, time=188.23 |\^/| 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(); 1428507325 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [12 z - 12 x - 8 z, -15 x y - 3 y + 13 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-6 x y + 16 y z - 4 y, -4 x - 20 y + 6 y] > Problem := [F,G]; 2 Problem := [[12 z - 12 x - 8 z, -15 x y - 3 y + 13 z], 2 2 [-6 x y + 16 y z - 4 y, -4 x - 20 y + 6 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=48.1MB, alloc=32.3MB, time=0.85 memory used=69.4MB, alloc=56.3MB, time=1.23 memory used=113.3MB, alloc=60.3MB, time=1.98 memory used=149.9MB, alloc=84.3MB, time=2.88 N1 := 1259 > GB := Basis(F, plex(op(vars))); GB := 2 2 2 2 [225 y x + 90 y x + 9 y - 130 y x - 26 y - 169 x, -15 x y - 3 y + 13 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=205.1MB, alloc=84.3MB, time=4.30 memory used=264.4MB, alloc=108.3MB, time=5.33 N2 := 839 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [12 z - 12 x - 8 z, -15 x y - 3 y + 13 z, -6 x y + 16 y z - 4 y, 2 2 -4 x - 20 y + 6 y] > J:=[op(GB),op(G)]; 2 2 2 2 J := [225 y x + 90 y x + 9 y - 130 y x - 26 y - 169 x, -15 x y - 3 y + 13 z, 2 2 -6 x y + 16 y z - 4 y, -4 x - 20 y + 6 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 2, 2, 1, 3/4, 3/4, 1/3, 7/12, 1/3, 4, 10, 10, 4, 2, 2, 1, 1, 1, 1/2, 7/15, 4/5, 2/15, 0, -2, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=306.0MB, alloc=108.3MB, time=6.42 |\^/| 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(); 1428507332 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [5 x y - 5 y z - 8, 11 + 2 x + 7 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [7 x - 8 x y - 20 z , 6 x z - 12 y + 14 y z] > Problem := [F,G]; Problem := [[5 x y - 5 y z - 8, 11 + 2 x + 7 y], 2 2 2 [7 x - 8 x y - 20 z , 6 x z - 12 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.9MB, alloc=32.3MB, time=0.53 memory used=47.8MB, alloc=32.3MB, time=0.85 memory used=67.4MB, alloc=56.3MB, time=1.17 memory used=109.8MB, alloc=60.3MB, time=1.82 memory used=150.8MB, alloc=84.3MB, time=2.46 memory used=218.2MB, alloc=92.3MB, time=3.59 memory used=277.6MB, alloc=116.3MB, time=4.66 memory used=357.8MB, alloc=140.3MB, time=6.09 memory used=455.3MB, alloc=164.3MB, time=7.82 memory used=555.8MB, alloc=188.3MB, time=9.59 memory used=641.6MB, alloc=444.3MB, time=11.12 memory used=769.5MB, alloc=468.3MB, time=13.31 memory used=898.0MB, alloc=492.3MB, time=17.04 memory used=1036.1MB, alloc=516.3MB, time=21.53 memory used=1186.5MB, alloc=540.3MB, time=26.84 memory used=1350.5MB, alloc=564.3MB, time=33.21 memory used=1538.5MB, alloc=588.3MB, time=40.53 memory used=1750.4MB, alloc=588.3MB, time=48.89 memory used=1962.3MB, alloc=588.3MB, time=57.24 memory used=2174.1MB, alloc=612.3MB, time=65.61 memory used=2409.8MB, alloc=612.3MB, time=74.79 memory used=2645.6MB, alloc=636.3MB, time=84.07 N1 := 7861 > GB := Basis(F, plex(op(vars))); 2 GB := [7 y + 2 x + 11, -10 x + 10 x z - 55 x + 55 z - 56] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2916.2MB, alloc=636.3MB, time=91.65 memory used=3216.9MB, alloc=660.3MB, time=97.36 memory used=3523.1MB, alloc=684.3MB, time=107.91 memory used=3813.0MB, alloc=708.3MB, time=120.09 N2 := 4611 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-5 z y + 5 y x - 8, 7 y + 2 x + 11, -20 z - 8 y x + 7 x , 2 6 x z - 12 y + 14 y z] > J:=[op(GB),op(G)]; 2 2 2 J := [7 y + 2 x + 11, -10 x + 10 x z - 55 x + 55 z - 56, -20 z - 8 y x + 7 x , 2 6 x z - 12 y + 14 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 7, 2, 2, 2, 2, 1, 1, 3/4, 5/12, 1/2, 1/3, 4, 10, 7, 2, 2, 2, 2, 1, 3/4, 3/4, 1/2, 2/7, 5/14, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=3995.0MB, alloc=708.3MB, time=127.20 |\^/| 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(); 1428507477 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [20 z + 2 x - 16 z, -2 x y - 19 z + 2] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-3 x + 15 x y - 4 x z, 18 y - 4 x + 2 z] > Problem := [F,G]; 2 Problem := [[20 z + 2 x - 16 z, -2 x y - 19 z + 2], 2 2 [-3 x + 15 x y - 4 x z, 18 y - 4 x + 2 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=47.3MB, alloc=32.3MB, time=0.80 memory used=66.9MB, alloc=56.3MB, time=1.10 memory used=108.6MB, alloc=60.3MB, time=1.71 memory used=148.8MB, alloc=60.3MB, time=2.29 memory used=188.0MB, alloc=84.3MB, time=2.93 memory used=236.1MB, alloc=84.3MB, time=3.75 memory used=294.2MB, alloc=116.3MB, time=4.77 memory used=378.3MB, alloc=140.3MB, time=6.04 memory used=475.2MB, alloc=164.3MB, time=7.65 memory used=583.2MB, alloc=444.3MB, time=9.47 memory used=708.5MB, alloc=468.3MB, time=11.62 memory used=843.9MB, alloc=492.3MB, time=13.98 memory used=982.3MB, alloc=516.3MB, time=17.91 memory used=1126.6MB, alloc=540.3MB, time=22.55 memory used=1283.6MB, alloc=564.3MB, time=27.91 memory used=1452.8MB, alloc=588.3MB, time=34.28 memory used=1638.6MB, alloc=612.3MB, time=41.67 memory used=1848.4MB, alloc=636.3MB, time=50.04 memory used=2082.0MB, alloc=636.3MB, time=59.30 memory used=2315.7MB, alloc=660.3MB, time=68.54 memory used=2573.3MB, alloc=660.3MB, time=78.77 memory used=2830.8MB, alloc=660.3MB, time=89.52 memory used=3088.2MB, alloc=684.3MB, time=100.06 memory used=3369.5MB, alloc=684.3MB, time=111.52 memory used=3650.8MB, alloc=684.3MB, time=122.97 memory used=3932.1MB, alloc=708.3MB, time=134.71 memory used=4237.3MB, alloc=732.3MB, time=146.92 N1 := 10757 > GB := Basis(F, plex(op(vars))); 2 2 GB := [40 y x + 224 y x + 361 x - 264, 2 y x + 19 z - 2] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4577.5MB, alloc=732.3MB, time=158.19 N2 := 2169 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [20 z + 2 x - 16 z, -2 x y - 19 z + 2, -3 x + 15 x y - 4 x z, 2 18 y - 4 x + 2 z] > J:=[op(GB),op(G)]; 2 2 J := [40 y x + 224 y x + 361 x - 264, 2 y x + 19 z - 2, 2 2 -3 x + 15 x y - 4 x z, 18 y - 4 x + 2 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 2, 2, 2, 1, 3/4, 1, 1/2, 1/4, 5/12, 4, 11, 10, 4, 2, 2, 1, 1, 1, 3/4, 8/13, 5/13, 3/13, 0, -2, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=4847.0MB, alloc=732.3MB, time=166.97 |\^/| 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(); 1428507686 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [9 x + 9 y + 2 y, 3 + 18 x + 4 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [19 z + 14 z + 7, -x + 9 x + 6] > Problem := [F,G]; Problem := 2 2 2 2 [[9 x + 9 y + 2 y, 3 + 18 x + 4 y], [19 z + 14 z + 7, -x + 9 x + 6]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 N1 := 35 > GB := Basis(F, plex(op(vars))); 2 GB := [1020 x + 276 x + 19, 4 y + 18 x + 3] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 15 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [9 y + 9 x + 2 y, 4 y + 18 x + 3, 19 z + 14 z + 7, -x + 9 x + 6] > J:=[op(GB),op(G)]; 2 2 2 J := [1020 x + 276 x + 19, 4 y + 18 x + 3, 19 z + 14 z + 7, -x + 9 x + 6] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 6, 7, 2, 2, 2, 2, 3/4, 1/2, 1/4, 1/3, 1/4, 1/6, 4, 5, 7, 2, 2, 1, 2, 3/4, 1/4, 1/4, 5/12, 1/12, 1/6, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=22.8MB, alloc=32.3MB, time=0.56 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428507687 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-7 x z + 11 y - 15, -14 x - 3 y + 16] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [7 x - 15 z - 17 x, -20 x + 20 x y + 18 y z] > Problem := [F,G]; 2 2 Problem := [[-7 x z + 11 y - 15, -14 x - 3 y + 16], 2 2 2 [7 x - 15 z - 17 x, -20 x + 20 x y + 18 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=27.1MB, alloc=32.3MB, time=0.52 memory used=48.6MB, alloc=32.3MB, time=0.84 memory used=68.5MB, alloc=56.3MB, time=1.15 memory used=110.6MB, alloc=60.3MB, time=1.85 memory used=151.9MB, alloc=84.3MB, time=2.59 memory used=213.0MB, alloc=92.3MB, time=3.67 memory used=269.3MB, alloc=116.3MB, time=4.67 memory used=344.3MB, alloc=140.3MB, time=5.98 memory used=436.2MB, alloc=164.3MB, time=7.92 memory used=535.8MB, alloc=188.3MB, time=10.87 memory used=645.3MB, alloc=212.3MB, time=15.07 memory used=778.4MB, alloc=212.3MB, time=20.93 memory used=911.4MB, alloc=236.3MB, time=26.24 N1 := 4303 > GB := Basis(F, plex(op(vars))); 2 2 GB := [3 y + 14 x - 16, 7 z x - 11 y + 15] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1074.5MB, alloc=236.3MB, time=31.41 memory used=1171.4MB, alloc=492.3MB, time=33.18 memory used=1345.7MB, alloc=516.3MB, time=36.36 memory used=1535.4MB, alloc=540.3MB, time=41.23 memory used=1712.9MB, alloc=564.3MB, time=48.08 memory used=1909.5MB, alloc=588.3MB, time=55.97 N2 := 4303 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-7 x z + 11 y - 15, -14 x - 3 y + 16, -15 z + 7 x - 17 x, 2 -20 x + 20 x y + 18 y z] > J:=[op(GB),op(G)]; 2 2 2 2 J := [3 y + 14 x - 16, 7 z x - 11 y + 15, -15 z + 7 x - 17 x, 2 -20 x + 20 x y + 18 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 2, 2, 1, 3/4, 3/4, 1/2, 1/3, 1/4, 4, 10, 8, 2, 2, 2, 2, 1, 3/4, 3/4, 1/2, 1/3, 1/4, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=2067.3MB, alloc=588.3MB, time=61.67 |\^/| 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(); 1428507755 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [3 x y + 12 y + 6 z, -13 y z + 10 x + 19 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [2 y - 5 z + 7, 19 x - 8 x z - 15 z ] > Problem := [F,G]; Problem := [[3 x y + 12 y + 6 z, -13 y z + 10 x + 19 y], 2 2 2 2 [2 y - 5 z + 7, 19 x - 8 x z - 15 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.52 memory used=45.8MB, alloc=56.3MB, time=0.83 memory used=85.5MB, alloc=60.3MB, time=1.46 memory used=125.5MB, alloc=84.3MB, time=2.09 memory used=169.1MB, alloc=84.3MB, time=2.79 memory used=233.7MB, alloc=92.3MB, time=4.11 memory used=295.4MB, alloc=116.3MB, time=5.22 memory used=379.1MB, alloc=116.3MB, time=6.65 memory used=452.5MB, alloc=372.3MB, time=7.99 memory used=536.2MB, alloc=396.3MB, time=9.62 memory used=650.8MB, alloc=420.3MB, time=11.44 memory used=784.2MB, alloc=444.3MB, time=13.84 memory used=933.5MB, alloc=468.3MB, time=16.43 memory used=1093.5MB, alloc=492.3MB, time=19.38 memory used=1268.3MB, alloc=516.3MB, time=22.43 memory used=1453.2MB, alloc=540.3MB, time=26.29 memory used=1645.4MB, alloc=564.3MB, time=30.74 memory used=1859.6MB, alloc=588.3MB, time=34.64 memory used=2070.0MB, alloc=612.3MB, time=38.65 memory used=2296.9MB, alloc=636.3MB, time=42.80 memory used=2501.7MB, alloc=660.3MB, time=46.90 memory used=2695.6MB, alloc=684.3MB, time=50.56 memory used=2869.6MB, alloc=708.3MB, time=54.36 memory used=3124.8MB, alloc=732.3MB, time=59.33 memory used=3375.1MB, alloc=756.3MB, time=64.52 memory used=3593.0MB, alloc=780.3MB, time=71.82 memory used=3810.9MB, alloc=804.3MB, time=79.88 memory used=4038.5MB, alloc=828.3MB, time=88.70 memory used=4278.3MB, alloc=852.3MB, time=98.82 memory used=4531.1MB, alloc=876.3MB, time=109.06 memory used=4797.3MB, alloc=900.3MB, time=119.96 memory used=5077.9MB, alloc=924.3MB, time=132.29 memory used=5373.3MB, alloc=948.3MB, time=145.48 memory used=5683.6MB, alloc=972.3MB, time=158.89 memory used=6009.3MB, alloc=996.3MB, time=173.96 memory used=6350.3MB, alloc=1020.3MB, time=190.32 memory used=6706.5MB, alloc=1044.3MB, time=207.61 memory used=7078.2MB, alloc=1068.3MB, time=223.96 memory used=7465.2MB, alloc=1092.3MB, time=240.65 |\^/| 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(); 1428508055 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-10 z - y + 20, 12 x + 10 x - 10 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [7 y z + 16 z + x, 14 x z - 20 z + 14] > Problem := [F,G]; 2 2 Problem := [[-10 z - y + 20, 12 x + 10 x - 10 z], 2 2 [7 y z + 16 z + x, 14 x z - 20 z + 14]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.50 memory used=46.7MB, alloc=56.3MB, time=0.81 memory used=87.9MB, alloc=60.3MB, time=1.43 memory used=128.7MB, alloc=60.3MB, time=2.03 memory used=168.0MB, alloc=84.3MB, time=2.63 memory used=229.8MB, alloc=92.3MB, time=3.59 memory used=289.5MB, alloc=116.3MB, time=4.51 memory used=372.0MB, alloc=116.3MB, time=5.80 memory used=455.6MB, alloc=140.3MB, time=7.20 memory used=547.0MB, alloc=164.3MB, time=8.74 memory used=656.7MB, alloc=444.3MB, time=10.63 memory used=792.5MB, alloc=468.3MB, time=12.91 memory used=938.9MB, alloc=492.3MB, time=15.43 memory used=1099.7MB, alloc=516.3MB, time=18.20 memory used=1279.1MB, alloc=540.3MB, time=21.21 memory used=1467.3MB, alloc=564.3MB, time=24.48 memory used=1659.1MB, alloc=588.3MB, time=27.93 memory used=1858.8MB, alloc=612.3MB, time=31.59 memory used=2068.6MB, alloc=636.3MB, time=35.61 memory used=2292.9MB, alloc=660.3MB, time=39.90 memory used=2489.8MB, alloc=684.3MB, time=45.73 memory used=2680.6MB, alloc=708.3MB, time=52.32 memory used=2879.6MB, alloc=732.3MB, time=59.50 memory used=3090.1MB, alloc=756.3MB, time=67.36 memory used=3313.5MB, alloc=780.3MB, time=76.10 memory used=3549.5MB, alloc=804.3MB, time=85.39 memory used=3799.7MB, alloc=828.3MB, time=95.35 memory used=4064.2MB, alloc=852.3MB, time=106.04 memory used=4343.4MB, alloc=876.3MB, time=117.71 memory used=4637.2MB, alloc=900.3MB, time=130.13 memory used=4946.3MB, alloc=924.3MB, time=143.30 memory used=5265.3MB, alloc=948.3MB, time=157.32 memory used=5606.8MB, alloc=972.3MB, time=172.09 memory used=5972.2MB, alloc=996.3MB, time=187.48 |\^/| 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(); 1428508355 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-5 x - 18 x z + 14, 2 x y + 6 z + 15 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-12 x y + 2 y + 3, -2 x - 9 y + 10 y] > Problem := [F,G]; 2 2 Problem := [[-5 x - 18 x z + 14, 2 x y + 6 z + 15 z], 2 2 [-12 x y + 2 y + 3, -2 x - 9 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=32.1MB, alloc=40.3MB, time=0.58 memory used=61.5MB, alloc=44.3MB, time=1.05 memory used=89.4MB, alloc=68.3MB, time=1.51 memory used=139.7MB, alloc=68.3MB, time=2.27 memory used=183.0MB, alloc=92.3MB, time=3.08 memory used=240.5MB, alloc=116.3MB, time=4.76 N1 := 1745 > GB := Basis(F, plex(op(vars))); 3 4 3 2 GB := [108 y x + 25 x - 225 x - 140 x + 630 x + 196, 3 2 2 25 x + 108 x y - 225 x - 70 x + 252 z + 630] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=323.3MB, alloc=116.3MB, time=6.59 N2 := 555 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-5 x - 18 x z + 14, 6 z + 2 y x + 15 z, -12 x y + 2 y + 3, 2 2 -2 x - 9 y + 10 y] > J:=[op(GB),op(G)]; 3 4 3 2 J := [108 y x + 25 x - 225 x - 140 x + 630 x + 196, 2 3 2 108 y x + 25 x - 225 x + 252 z - 70 x + 630, -12 x y + 2 y + 3, 2 2 -2 x - 9 y + 10 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 2, 1, 3/4, 1/2, 5/12, 5/12, 1/4, 4, 9, 11, 4, 11 4, 2, 1, 1, 1, 1/4, --, 1/3, 1/18, 0, -3, -2] 18 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=369.3MB, alloc=116.3MB, time=7.42 |\^/| 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(); 1428508363 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [9 x z - 12 y z, 4 x + 18 y - 15] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-8 x - 17 y + 6 x, -14 y + 16 y z + 9 y] > Problem := [F,G]; 2 Problem := [[9 x z - 12 y z, 4 x + 18 y - 15], 2 2 2 [-8 x - 17 y + 6 x, -14 y + 16 y z + 9 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.6MB, alloc=32.3MB, time=0.80 memory used=66.7MB, alloc=56.3MB, time=1.13 memory used=106.6MB, alloc=80.3MB, time=1.97 N1 := 873 > GB := Basis(F, plex(op(vars))); 2 2 GB := [4 x + 18 y - 15, 8 x z + 27 x z - 30 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=142.5MB, alloc=80.3MB, time=2.62 N2 := 541 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [9 x z - 12 y z, 4 x + 18 y - 15, -8 x - 17 y + 6 x, 2 -14 y + 16 y z + 9 y] > J:=[op(GB),op(G)]; 2 2 2 2 J := [4 x + 18 y - 15, 8 x z + 27 x z - 30 z, -8 x - 17 y + 6 x, 2 -14 y + 16 y z + 9 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 1, 3/4, 1, 1/2, 4/11, 6/11, 3/11, 4, 8, 9, 3, 2, 2, 1, 3/4, 3/4, 1/2, 5/12, 5/12, 1/3, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=185.8MB, alloc=84.3MB, time=3.48 |\^/| 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(); 1428508367 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [7 y z - 7 x + 5, -9 x y - 10 y z - 10] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-8 x y + 12 x, 20 x y + 17 x z - 4 z ] > Problem := [F,G]; Problem := [[7 y z - 7 x + 5, -9 x y - 10 y z - 10], 2 [-8 x y + 12 x, 20 x y + 17 x z - 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.46 memory used=47.4MB, alloc=32.3MB, time=0.73 memory used=67.1MB, alloc=56.3MB, time=1.05 memory used=108.8MB, alloc=60.3MB, time=1.70 memory used=147.3MB, alloc=84.3MB, time=2.38 memory used=205.5MB, alloc=116.3MB, time=3.38 memory used=282.8MB, alloc=140.3MB, time=4.67 memory used=377.8MB, alloc=164.3MB, time=6.30 memory used=487.0MB, alloc=188.3MB, time=8.59 memory used=601.8MB, alloc=212.3MB, time=12.03 memory used=727.0MB, alloc=236.3MB, time=16.53 memory used=871.7MB, alloc=236.3MB, time=21.97 memory used=1016.4MB, alloc=260.3MB, time=27.85 memory used=1185.0MB, alloc=260.3MB, time=34.24 memory used=1354.1MB, alloc=284.3MB, time=40.04 N1 := 5173 > GB := Basis(F, plex(op(vars))); 2 GB := [63 y x + 70 x + 20, 63 x + 70 x z - 45 x + 20 z, 7 y z - 7 x + 5] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1437.7MB, alloc=284.3MB, time=41.50 memory used=1655.9MB, alloc=564.3MB, time=45.17 memory used=1880.3MB, alloc=588.3MB, time=52.56 memory used=2106.7MB, alloc=612.3MB, time=61.61 N2 := 3543 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [7 y z - 7 x + 5, -9 x y - 10 y z - 10, -8 x y + 12 x, 2 -4 z + 17 z x + 20 y x] > J:=[op(GB),op(G)]; 2 J := [63 y x + 70 x + 20, 70 z x + 63 x + 20 z - 45 x, 7 y z - 7 x + 5, 2 -8 x y + 12 x, -4 z + 17 z x + 20 y x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 1, 1, 2, 1, 1, 3/4, 6/11, 5/11, 4/11, 5, 12, 10, 2, 2, 1, 2, 1, 4/5, 3/5, 2/3, 4/15, 1/3, -1, -2, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=2114.4MB, alloc=612.3MB, time=61.84 |\^/| 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(); 1428508433 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [17 x + 7 x + 6, -x - 6 y z - 16 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-6 + x - 13 y, -14 x - 18 x z - 3 y] > Problem := [F,G]; 2 2 2 Problem := [[17 x + 7 x + 6, -x - 6 y z - 16 z ], 2 [-6 + x - 13 y, -14 x - 18 x z - 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.9MB, alloc=32.3MB, time=0.53 memory used=49.0MB, alloc=56.3MB, time=0.91 memory used=93.5MB, alloc=60.3MB, time=1.64 memory used=133.3MB, alloc=84.3MB, time=2.35 N1 := 1043 > GB := Basis(F, plex(op(vars))); 2 2 GB := [17 x + 7 x + 6, 102 y z + 272 z - 7 x - 6] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=190.4MB, alloc=84.3MB, time=3.67 memory used=253.5MB, alloc=116.3MB, time=4.75 N2 := 843 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 2 2 2 17 x + 7 x + 6, -x - 6 y z - 16 z , -13 y + x - 6, -14 x - 18 x z - 3 y] > J:=[op(GB),op(G)]; 2 2 J := [17 x + 7 x + 6, 102 y z + 272 z - 7 x - 6, -13 y + x - 6, 2 -14 x - 18 x z - 3 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 2, 1, 2, 1, 3/4, 1/2, 1/2, 1/4, 1/4, 4, 9, 7, 2, 2, 1, 2, 1, 3/4, 1/2, 6/13, 3/13, 3/13, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=294.3MB, alloc=116.3MB, time=5.60 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428508439 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [7 y + 11 x - 16 y, 14 z - 2 x + 12] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [18 x - 9 x y + 13 y, -20 z - 16 z] > Problem := [F,G]; 2 2 Problem := [[7 y + 11 x - 16 y, 14 z - 2 x + 12], 2 2 [18 x - 9 x y + 13 y, -20 z - 16 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.4MB, alloc=40.3MB, time=0.59 N1 := 305 > GB := Basis(F, plex(op(vars))); 2 2 GB := [7 y - 16 y + 11 x, 7 z - x + 6] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=59.9MB, alloc=40.3MB, time=1.05 memory used=87.8MB, alloc=64.3MB, time=1.53 N2 := 305 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 2 2 2 7 y - 16 y + 11 x, 14 z - 2 x + 12, -9 y x + 18 x + 13 y, -20 z - 16 z] > J:=[op(GB),op(G)]; 2 2 2 2 J := [7 y - 16 y + 11 x, 7 z - x + 6, -9 y x + 18 x + 13 y, -20 z - 16 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 7, 8, 2, 2, 2, 2, 3/4, 1/2, 1/2, 4/11, 4/11, 3/11, 4, 7, 8, 2, 2, 2, 2, 3/4, 1/2, 1/2, 4/11, 4/11, 3/11, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=88.2MB, alloc=64.3MB, time=1.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428508441 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-2 x - 13 x z + 9 z, -11 x + 14 y z + 7 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-19 x y + 16 x z + 16 y, -7 x z - 4 z + 3 y] > Problem := [F,G]; 2 2 Problem := [[-2 x - 13 x z + 9 z, -11 x + 14 y z + 7 y], 2 [-19 x y + 16 x z + 16 y, -7 x z - 4 z + 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.48 memory used=46.1MB, alloc=56.3MB, time=0.80 memory used=85.2MB, alloc=60.3MB, time=1.43 memory used=124.4MB, alloc=84.3MB, time=2.05 memory used=171.8MB, alloc=84.3MB, time=2.76 memory used=231.9MB, alloc=116.3MB, time=3.69 memory used=314.3MB, alloc=116.3MB, time=4.95 memory used=396.3MB, alloc=140.3MB, time=6.32 memory used=492.3MB, alloc=164.3MB, time=7.89 memory used=608.3MB, alloc=188.3MB, time=9.75 memory used=718.1MB, alloc=468.3MB, time=11.66 memory used=865.3MB, alloc=492.3MB, time=14.58 memory used=1024.1MB, alloc=516.3MB, time=17.76 memory used=1195.5MB, alloc=540.3MB, time=21.24 memory used=1378.9MB, alloc=564.3MB, time=25.03 memory used=1557.2MB, alloc=588.3MB, time=31.25 memory used=1738.8MB, alloc=612.3MB, time=38.30 memory used=1932.5MB, alloc=636.3MB, time=45.32 memory used=2139.6MB, alloc=660.3MB, time=53.22 memory used=2360.8MB, alloc=684.3MB, time=62.25 memory used=2591.7MB, alloc=708.3MB, time=72.74 memory used=2846.6MB, alloc=732.3MB, time=83.95 memory used=3125.4MB, alloc=756.3MB, time=96.18 memory used=3428.2MB, alloc=780.3MB, time=109.51 memory used=3754.8MB, alloc=780.3MB, time=124.65 memory used=4081.5MB, alloc=804.3MB, time=139.67 memory used=4432.1MB, alloc=804.3MB, time=156.03 memory used=4782.7MB, alloc=804.3MB, time=171.65 memory used=5133.2MB, alloc=828.3MB, time=186.39 memory used=5507.5MB, alloc=828.3MB, time=201.87 memory used=5881.8MB, alloc=828.3MB, time=217.31 |\^/| 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(); 1428508741 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-11 x y + 7 x z - 17 z , -17 x - 6 y + 14 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-11 y - 6 z + 11 y, 8 y z - 8 z - 2 y] > Problem := [F,G]; 2 2 2 Problem := [[-11 x y + 7 x z - 17 z , -17 x - 6 y + 14 x], 2 2 2 [-11 y - 6 z + 11 y, 8 y z - 8 z - 2 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=46.6MB, alloc=32.3MB, time=0.78 memory used=66.1MB, alloc=56.3MB, time=1.08 memory used=106.2MB, alloc=60.3MB, time=1.67 memory used=158.2MB, alloc=92.3MB, time=2.44 memory used=226.9MB, alloc=100.3MB, time=3.55 memory used=294.0MB, alloc=124.3MB, time=4.74 memory used=379.1MB, alloc=148.3MB, time=6.30 memory used=471.9MB, alloc=172.3MB, time=9.30 N1 := 2269 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [6 y + 17 x - 14 x, 17 z - 7 z x + 11 y x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=582.1MB, alloc=172.3MB, time=13.13 memory used=677.6MB, alloc=428.3MB, time=14.67 memory used=802.7MB, alloc=452.3MB, time=16.67 memory used=951.8MB, alloc=476.3MB, time=19.58 memory used=1094.4MB, alloc=500.3MB, time=24.72 N2 := 2269 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [-11 x y + 7 x z - 17 z , -17 x - 6 y + 14 x, -11 y - 6 z + 11 y, 2 8 y z - 8 z - 2 y] > J:=[op(GB),op(G)]; 2 2 2 2 2 J := [6 y + 17 x - 14 x, 17 z - 7 z x + 11 y x, -11 y - 6 z + 11 y, 2 8 y z - 8 z - 2 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 2, 1/2, 1, 3/4, 1/3, 1/2, 5/12, 4, 9, 8, 2, 2, 2, 2, 1/2, 1, 3/4, 1/3, 1/2, 5/12, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1118.2MB, alloc=500.3MB, time=25.41 |\^/| 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(); 1428508776 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [12 x - 11 x y - 12 y z, -x - x z - 5 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [x y + 18 y z - 20 z, 17 - 6 y] > Problem := [F,G]; 2 2 2 Problem := [[12 x - 11 x y - 12 y z, -x - x z - 5 z ], [x y + 18 y z - 20 z, 17 - 6 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=47.4MB, alloc=32.3MB, time=0.78 memory used=68.2MB, alloc=56.3MB, time=1.15 N1 := 199 > GB := Basis(F, plex(op(vars))); 4 3 2 2 3 2 2 GB := [720 x - 1176 x y + 617 x y , -516 x + 617 x y + 720 x z, 2 2 2 -12 x + 11 x y + 12 y z, 5 z + z x + x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=107.3MB, alloc=60.3MB, time=1.72 memory used=146.4MB, alloc=60.3MB, time=2.30 memory used=183.8MB, alloc=84.3MB, time=2.86 memory used=239.8MB, alloc=84.3MB, time=3.89 N2 := 563 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := 2 2 2 [-12 z y - 11 y x + 12 x , -x - x z - 5 z , 18 z y + y x - 20 z, 17 - 6 y] > J:=[op(GB),op(G)]; 4 3 2 2 3 2 2 J := [720 x - 1176 x y + 617 x y , -516 x + 617 x y + 720 x z, 2 2 2 -12 x + 11 x y + 12 y z, 5 z + z x + x , 18 z y + y x - 20 z, 17 - 6 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 2, 1, 2, 3/4, 3/4, 3/4, 5/11, 5/11, 5/11, 6, 14, 14, 11 4, 4, 2, 2, 5/6, 5/6, 2/3, --, 8/17, 6/17, -5, -7, -2] 17 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=275.5MB, alloc=84.3MB, time=4.60 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428508782 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [14 x z + 2 y , -16 x y + 11 y - 12 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-10 x z - 15 z + 19 y, -7 x z - 19 y z - 18 y] > Problem := [F,G]; 2 2 Problem := [[14 x z + 2 y , -16 x y + 11 y - 12 x], 2 [-10 x z - 15 z + 19 y, -7 x z - 19 y z - 18 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.49 memory used=48.5MB, alloc=32.3MB, time=0.81 memory used=68.4MB, alloc=56.3MB, time=1.11 memory used=108.5MB, alloc=60.3MB, time=1.69 memory used=146.9MB, alloc=84.3MB, time=2.27 memory used=211.1MB, alloc=116.3MB, time=3.37 memory used=292.0MB, alloc=116.3MB, time=4.68 memory used=366.1MB, alloc=140.3MB, time=5.94 memory used=459.7MB, alloc=164.3MB, time=7.51 memory used=565.1MB, alloc=188.3MB, time=9.44 memory used=667.4MB, alloc=468.3MB, time=11.22 memory used=808.2MB, alloc=492.3MB, time=14.77 memory used=949.6MB, alloc=516.3MB, time=19.93 memory used=1102.7MB, alloc=540.3MB, time=25.87 memory used=1269.1MB, alloc=564.3MB, time=32.93 memory used=1459.5MB, alloc=564.3MB, time=40.66 memory used=1649.9MB, alloc=588.3MB, time=48.21 memory used=1864.3MB, alloc=588.3MB, time=56.57 memory used=2078.6MB, alloc=612.3MB, time=65.07 memory used=2317.0MB, alloc=612.3MB, time=74.64 N1 := 7245 > GB := Basis(F, plex(op(vars))); 2 GB := [-16 x y + 11 y - 12 x, 16 x y + 77 x z + 12 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2566.1MB, alloc=612.3MB, time=81.50 memory used=2841.8MB, alloc=636.3MB, time=86.76 memory used=3118.9MB, alloc=660.3MB, time=91.97 memory used=3407.9MB, alloc=684.3MB, time=100.75 memory used=3675.4MB, alloc=708.3MB, time=111.52 memory used=3945.3MB, alloc=732.3MB, time=123.94 memory used=4239.1MB, alloc=756.3MB, time=137.03 memory used=4556.9MB, alloc=780.3MB, time=151.59 memory used=4898.7MB, alloc=804.3MB, time=167.56 memory used=5264.4MB, alloc=828.3MB, time=183.80 N2 := 8637 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [14 x z + 2 y , -16 x y + 11 y - 12 x, -10 x z - 15 z + 19 y, -7 x z - 19 y z - 18 y] > J:=[op(GB),op(G)]; 2 2 J := [-16 x y + 11 y - 12 x, 16 x y + 77 x z + 12 x, -10 x z - 15 z + 19 y, -7 x z - 19 y z - 18 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 1, 2, 2, 1, 1, 3/4, 5/11, 6/11, 5/11, 4, 11, 8, 2, 1, 2, 2, 1, 1, 3/4, 7/12, 1/2, 5/12, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=5642.1MB, alloc=828.3MB, time=198.95 |\^/| 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(); 1428509013 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-12 x - 19 x y + 15 z, -10 x y + 9 y z + 18 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-6 y + 6 z + 12, 14 x z - 6 x - 13 z] > Problem := [F,G]; 2 Problem := [[-12 x - 19 x y + 15 z, -10 x y + 9 y z + 18 y], 2 2 [-6 y + 6 z + 12, 14 x z - 6 x - 13 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.6MB, alloc=32.3MB, time=0.50 memory used=46.0MB, alloc=56.3MB, time=0.81 memory used=88.2MB, alloc=60.3MB, time=1.46 memory used=129.2MB, alloc=60.3MB, time=2.11 memory used=168.2MB, alloc=84.3MB, time=2.72 memory used=228.2MB, alloc=116.3MB, time=3.71 memory used=311.9MB, alloc=140.3MB, time=5.16 memory used=409.1MB, alloc=164.3MB, time=6.85 memory used=521.3MB, alloc=188.3MB, time=8.83 memory used=648.0MB, alloc=212.3MB, time=11.03 memory used=767.7MB, alloc=492.3MB, time=13.18 memory used=917.3MB, alloc=516.3MB, time=15.99 memory used=1076.2MB, alloc=540.3MB, time=19.39 memory used=1228.9MB, alloc=564.3MB, time=24.11 memory used=1390.6MB, alloc=588.3MB, time=29.82 memory used=1565.2MB, alloc=612.3MB, time=36.38 memory used=1754.5MB, alloc=636.3MB, time=43.87 memory used=1959.6MB, alloc=660.3MB, time=52.21 memory used=2175.5MB, alloc=684.3MB, time=61.57 memory used=2415.4MB, alloc=708.3MB, time=72.32 memory used=2679.1MB, alloc=732.3MB, time=83.63 memory used=2966.9MB, alloc=756.3MB, time=96.40 memory used=3278.6MB, alloc=756.3MB, time=109.70 memory used=3590.2MB, alloc=756.3MB, time=122.56 memory used=3901.9MB, alloc=756.3MB, time=135.38 memory used=4213.5MB, alloc=780.3MB, time=148.21 memory used=4548.9MB, alloc=780.3MB, time=161.82 memory used=4884.2MB, alloc=780.3MB, time=175.41 memory used=5219.6MB, alloc=804.3MB, time=189.03 memory used=5578.9MB, alloc=804.3MB, time=203.50 memory used=5938.1MB, alloc=804.3MB, time=217.94 memory used=6297.4MB, alloc=828.3MB, time=232.34 memory used=6680.6MB, alloc=852.3MB, time=247.71 |\^/| 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(); 1428509313 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-14 + 9 x - z, 7 x + 9 y - 2 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-12 x + 20 x y - 6 x z, 10 x + 3 y z - 4 y] > Problem := [F,G]; 2 2 2 Problem := [[-14 + 9 x - z, 7 x + 9 y - 2 z ], 2 2 [-12 x + 20 x y - 6 x z, 10 x + 3 y z - 4 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=46.7MB, alloc=56.3MB, time=0.83 memory used=87.6MB, alloc=60.3MB, time=1.45 memory used=127.2MB, alloc=84.3MB, time=2.06 memory used=168.3MB, alloc=84.3MB, time=2.70 memory used=229.7MB, alloc=116.3MB, time=3.69 memory used=308.6MB, alloc=372.3MB, time=4.89 memory used=393.5MB, alloc=396.3MB, time=6.37 memory used=492.1MB, alloc=420.3MB, time=8.10 memory used=613.8MB, alloc=444.3MB, time=10.12 memory used=747.2MB, alloc=468.3MB, time=12.41 memory used=887.6MB, alloc=492.3MB, time=14.98 memory used=1039.4MB, alloc=516.3MB, time=18.20 memory used=1184.9MB, alloc=540.3MB, time=22.80 memory used=1339.5MB, alloc=564.3MB, time=28.08 memory used=1505.7MB, alloc=588.3MB, time=34.47 memory used=1683.6MB, alloc=612.3MB, time=41.92 memory used=1885.5MB, alloc=636.3MB, time=50.31 memory used=2111.3MB, alloc=660.3MB, time=59.55 memory used=2361.1MB, alloc=684.3MB, time=69.83 memory used=2634.7MB, alloc=684.3MB, time=81.02 memory used=2908.3MB, alloc=684.3MB, time=92.32 memory used=3182.0MB, alloc=708.3MB, time=103.51 memory used=3479.6MB, alloc=708.3MB, time=115.72 memory used=3777.3MB, alloc=732.3MB, time=127.81 memory used=4098.9MB, alloc=756.3MB, time=140.95 N1 := 10161 > GB := Basis(F, plex(op(vars))); 2 2 GB := [-155 x + 9 y + 504 x - 392, z - 9 x + 14] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4399.7MB, alloc=756.3MB, time=149.59 N2 := 1483 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-z + 9 x - 14, -2 z + 9 y + 7 x , -12 x + 20 x y - 6 x z, 2 3 z y + 10 x - 4 y] > J:=[op(GB),op(G)]; 2 2 2 J := [-155 x + 9 y + 504 x - 392, z - 9 x + 14, -12 x + 20 x y - 6 x z, 2 3 z y + 10 x - 4 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 7, 2, 2, 2, 2, 1, 3/4, 1, 1/2, 1/3, 1/3, 4, 10, 7, 2, 2, 2, 1, 1, 3/4, 3/4, 7/13, 4/13, 3/13, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=4462.6MB, alloc=756.3MB, time=152.13 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428509491 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-7 z + 2 z - 5, x + 10 y - 2 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [-19 x y + 9 z, -11 x z - 10 x + 15 z] > Problem := [F,G]; Problem := 2 [[-7 z + 2 z - 5, x + 10 y - 2 z], [-19 x y + 9 z, -11 x z - 10 x + 15 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=46.6MB, alloc=56.3MB, time=0.82 N1 := 349 > GB := Basis(F, plex(op(vars))); 2 2 GB := [700 y + 140 y x + 7 x - 40 y - 4 x + 20, 2 z - 10 y - x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=89.3MB, alloc=60.3MB, time=1.61 memory used=129.1MB, alloc=60.3MB, time=2.23 N2 := 349 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [-7 z + 2 z - 5, -2 z + 10 y + x, -19 x y + 9 z, -11 x z - 10 x + 15 z] > J:=[op(GB),op(G)]; 2 2 J := [700 y + 140 y x + 7 x - 40 y - 4 x + 20, 2 z - 10 y - x, -19 x y + 9 z, -11 x z - 10 x + 15 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 1, 1, 2, 3/4, 1/2, 1, 4/11, 2/11, 6/11, 4, 10, 7, 2, 2, 2, 1, 1, 3/4, 3/4, 1/2, 5/14, 2/7, -1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=145.8MB, alloc=60.3MB, time=2.53 |\^/| 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(); 1428509494 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [20 x - 16 x z + 7, -5 x - 17 x y - 10 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [9 x + 13 x z + 12 x, 14 x + 12 z + 12 z] > Problem := [F,G]; 2 2 2 Problem := [[20 x - 16 x z + 7, -5 x - 17 x y - 10 y ], 2 2 2 [9 x + 13 x z + 12 x, 14 x + 12 z + 12 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=27.7MB, alloc=32.3MB, time=0.56 N1 := 391 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [10 y + 17 y x + 5 x , -20 x + 16 x z - 7] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=49.2MB, alloc=32.3MB, time=0.98 memory used=68.5MB, alloc=56.3MB, time=1.31 N2 := 391 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-16 z x + 20 x + 7, -5 x - 17 x y - 10 y , 9 x + 13 x z + 12 x, 2 2 14 x + 12 z + 12 z] > J:=[op(GB),op(G)]; 2 2 2 2 J := [10 y + 17 y x + 5 x , -20 x + 16 x z - 7, 9 x + 13 x z + 12 x, 2 2 14 x + 12 z + 12 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 8, 2, 2, 2, 2, 1, 1/4, 3/4, 2/3, 1/6, 1/3, 4, 8, 8, 2, 2, 2, 2, 1, 1/4, 3/4, 2/3, 1/6, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=91.5MB, alloc=56.3MB, time=1.72 |\^/| 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(); 1428509496 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-6 x z + 18 z, 9 x - 8 y - 14] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [12 x + 2 y - 2 z, -16 y - 8 y z - 15 x] > Problem := [F,G]; 2 2 Problem := [[-6 x z + 18 z, 9 x - 8 y - 14], 2 [12 x + 2 y - 2 z, -16 y - 8 y z - 15 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.3MB, alloc=32.3MB, time=0.80 memory used=67.5MB, alloc=56.3MB, time=1.18 memory used=107.5MB, alloc=84.3MB, time=1.91 memory used=166.7MB, alloc=108.3MB, time=3.42 N1 := 1495 > GB := Basis(F, plex(op(vars))); 2 2 GB := [-9 x + 8 y + 14, x z - 3 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=240.2MB, alloc=108.3MB, time=5.56 memory used=318.8MB, alloc=140.3MB, time=6.94 memory used=418.3MB, alloc=164.3MB, time=9.98 N2 := 1495 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := 2 2 2 [-6 x z + 18 z, -8 y + 9 x - 14, 12 x + 2 y - 2 z, -16 y - 8 y z - 15 x] > J:=[op(GB),op(G)]; 2 2 2 J := [-9 x + 8 y + 14, x z - 3 z, 12 x + 2 y - 2 z, -16 y - 8 y z - 15 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 7, 2, 2, 2, 1, 1, 3/4, 3/4, 4/11, 4/11, 4/11, 4, 10, 7, 2, 2, 2, 1, 1, 3/4, 3/4, 4/11, 4/11, 4/11, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=433.4MB, alloc=164.3MB, time=10.44 |\^/| 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(); 1428509508 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-10 z - 7 y - 19 z, -20 x z - 9 y z - 16 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [5 x z + 18 z + 6, -9 x - 3 x z + 17 y ] > Problem := [F,G]; 2 Problem := [[-10 z - 7 y - 19 z, -20 x z - 9 y z - 16 z], 2 2 2 [5 x z + 18 z + 6, -9 x - 3 x z + 17 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.0MB, alloc=56.3MB, time=0.82 memory used=88.1MB, alloc=60.3MB, time=1.45 memory used=127.4MB, alloc=60.3MB, time=2.04 memory used=165.2MB, alloc=84.3MB, time=2.63 memory used=226.0MB, alloc=92.3MB, time=3.55 memory used=286.0MB, alloc=116.3MB, time=4.49 memory used=368.6MB, alloc=140.3MB, time=5.98 memory used=463.5MB, alloc=164.3MB, time=7.69 memory used=572.1MB, alloc=188.3MB, time=9.67 memory used=691.9MB, alloc=468.3MB, time=11.89 memory used=832.5MB, alloc=492.3MB, time=14.47 memory used=985.9MB, alloc=516.3MB, time=17.23 memory used=1135.1MB, alloc=540.3MB, time=21.60 memory used=1289.0MB, alloc=564.3MB, time=26.93 memory used=1457.7MB, alloc=588.3MB, time=32.74 memory used=1639.7MB, alloc=612.3MB, time=39.26 memory used=1830.4MB, alloc=636.3MB, time=46.83 memory used=2042.8MB, alloc=660.3MB, time=55.55 memory used=2279.2MB, alloc=684.3MB, time=65.19 memory used=2539.6MB, alloc=708.3MB, time=75.79 memory used=2823.9MB, alloc=708.3MB, time=87.21 memory used=3108.2MB, alloc=708.3MB, time=98.61 memory used=3392.4MB, alloc=708.3MB, time=110.01 memory used=3676.7MB, alloc=732.3MB, time=121.45 memory used=3984.7MB, alloc=732.3MB, time=133.69 memory used=4292.6MB, alloc=732.3MB, time=146.29 memory used=4600.6MB, alloc=756.3MB, time=158.66 memory used=4932.5MB, alloc=756.3MB, time=172.24 memory used=5264.2MB, alloc=780.3MB, time=186.06 memory used=5620.1MB, alloc=804.3MB, time=200.70 N1 := 12349 > GB := Basis(F, plex(op(vars))); 2 2 GB := [20 x y + 9 y + 16 y, 20 x z + 9 y z + 16 z, 10 z + 19 z + 7 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6005.4MB, alloc=804.3MB, time=209.81 memory used=6431.7MB, alloc=828.3MB, time=218.25 memory used=6871.3MB, alloc=852.3MB, time=228.95 memory used=7261.5MB, alloc=876.3MB, time=243.60 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428509808 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [14 x - 3 x + 17 y, 2 x + 8 x z + 19 y z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [x + 17 y z + 19 y, -2 x y + 10 x z + y] > Problem := [F,G]; 2 2 Problem := [[14 x - 3 x + 17 y, 2 x + 8 x z + 19 y z], 2 [x + 17 y z + 19 y, -2 x y + 10 x z + y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=32.3MB, time=0.85 memory used=66.4MB, alloc=56.3MB, time=1.20 memory used=109.0MB, alloc=60.3MB, time=1.97 memory used=148.7MB, alloc=84.3MB, time=2.71 memory used=208.4MB, alloc=92.3MB, time=3.82 memory used=264.4MB, alloc=116.3MB, time=4.86 memory used=339.9MB, alloc=140.3MB, time=6.61 memory used=426.6MB, alloc=164.3MB, time=9.75 memory used=527.1MB, alloc=164.3MB, time=13.46 N1 := 2789 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [14 x + 17 y - 3 x, 266 x z - 34 x - 193 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=631.0MB, alloc=164.3MB, time=16.46 memory used=745.7MB, alloc=188.3MB, time=18.43 memory used=883.9MB, alloc=212.3MB, time=22.04 N2 := 2007 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [14 x + 17 y - 3 x, 19 z y + 8 z x + 2 x , 17 z y + x + 19 y, -2 x y + 10 x z + y] > J:=[op(GB),op(G)]; 2 2 2 2 J := [14 x + 17 y - 3 x, 266 x z - 34 x - 193 x z, 17 z y + x + 19 y, -2 x y + 10 x z + y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 11, 8, 2, 2, 1, 1, 1, 1, 3/4, 7/12, 1/2, 1/3, 4, 10, 9, 3, 2, 1, 1, 1, 3/4, 3/4, 2/3, 5/12, 1/3, 1, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=967.8MB, alloc=212.3MB, time=25.07 |\^/| 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(); 1428509842 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [14 x + 18 z + 11 x, -12 x - 3 x - 19 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; G := [16 y z + 3 z, -2 y z - 20 x - 5] > Problem := [F,G]; 2 2 2 Problem := [[14 x + 18 z + 11 x, -12 x - 3 x - 19 z], [16 y z + 3 z, -2 y z - 20 x - 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=48.9MB, alloc=32.3MB, time=0.85 memory used=69.7MB, alloc=56.3MB, time=1.22 memory used=110.8MB, alloc=84.3MB, time=2.05 N1 := 1091 > GB := Basis(F, plex(op(vars))); 4 3 2 2 GB := [2592 x + 1296 x + 5216 x + 3971 x, 12 x + 19 z + 3 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=168.4MB, alloc=84.3MB, time=3.34 N2 := 339 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 2 2 18 z + 14 x + 11 x, -12 x - 3 x - 19 z, 16 y z + 3 z, -2 y z - 20 x - 5] > J:=[op(GB),op(G)]; 4 3 2 2 J := [2592 x + 1296 x + 5216 x + 3971 x, 12 x + 19 z + 3 x, 16 y z + 3 z, -2 y z - 20 x - 5] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 1, 2, 3/4, 1/2, 1, 5/11, 2/11, 5/11, 4, 8, 10, 4, 4, 1, 1, 3/4, 1/2, 3/4, 7/12, 1/6, 1/3, 1, -2, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=179.3MB, alloc=84.3MB, time=3.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428509847 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [10 x z - z - 17 x, 13 x z - 16 y z + 4 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-x - 17 x z + 15 x, 5 x y + 8 z + 11 z] > Problem := [F,G]; 2 Problem := [[10 x z - z - 17 x, 13 x z - 16 y z + 4 z], 2 2 [-x - 17 x z + 15 x, 5 x y + 8 z + 11 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.78 memory used=67.4MB, alloc=56.3MB, time=1.09 memory used=110.2MB, alloc=60.3MB, time=1.83 memory used=150.5MB, alloc=84.3MB, time=2.57 memory used=213.2MB, alloc=108.3MB, time=3.63 memory used=293.3MB, alloc=140.3MB, time=5.05 memory used=381.5MB, alloc=164.3MB, time=7.15 memory used=475.3MB, alloc=188.3MB, time=10.40 memory used=586.4MB, alloc=188.3MB, time=14.61 memory used=697.5MB, alloc=212.3MB, time=19.15 memory used=832.7MB, alloc=212.3MB, time=24.16 N1 := 4331 > GB := Basis(F, plex(op(vars))); 2 2 GB := [-13 x + 16 x y - 4 x, -13 x z + 16 y z - 4 z, -10 x z + z + 17 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=971.4MB, alloc=212.3MB, time=28.11 memory used=1090.9MB, alloc=468.3MB, time=30.17 memory used=1243.4MB, alloc=492.3MB, time=32.87 memory used=1395.0MB, alloc=516.3MB, time=38.08 memory used=1552.6MB, alloc=540.3MB, time=44.58 memory used=1734.3MB, alloc=564.3MB, time=51.99 N2 := 4331 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-z + 10 z x - 17 x, 13 x z - 16 y z + 4 z, -x - 17 x z + 15 x, 2 8 z + 5 y x + 11 z] > J:=[op(GB),op(G)]; 2 2 J := [-13 x + 16 x y - 4 x, -13 x z + 16 y z - 4 z, -10 x z + z + 17 x, 2 2 -x - 17 x z + 15 x, 8 z + 5 y x + 11 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 1, 2, 1, 1/2, 1, 7/12, 1/6, 2/3, 5, 12, 10, 2, 2, 1, 2, 1, 3/5, 4/5, 2/3, 1/5, 8/15, -2, -2, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1847.7MB, alloc=564.3MB, time=56.39 |\^/| 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(); 1428509914 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [6 x z + 17 y z + 14 x, -20 y z - 5 y + 7 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [11 x z + 13 z, -20 x - 18 y - 11] > Problem := [F,G]; Problem := [[6 x z + 17 y z + 14 x, -20 y z - 5 y + 7 z], 2 [11 x z + 13 z, -20 x - 18 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.53 memory used=48.8MB, alloc=32.3MB, time=0.90 memory used=69.1MB, alloc=56.3MB, time=1.31 memory used=110.2MB, alloc=84.3MB, time=2.18 N1 := 913 > GB := Basis(F, plex(op(vars))); GB := [ 2 -250 x y + 85 y + 98 x, 120 x z + 280 x - 85 y + 119 z, 20 z y - 7 z + 5 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=167.2MB, alloc=84.3MB, time=3.43 memory used=227.8MB, alloc=116.3MB, time=4.56 memory used=308.6MB, alloc=140.3MB, time=6.82 N2 := 1307 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [17 z y + 6 z x + 14 x, -20 y z - 5 y + 7 z, 11 x z + 13 z, 2 -20 x - 18 y - 11] > J:=[op(GB),op(G)]; 2 J := [-250 x y + 85 y + 98 x, 120 z x + 119 z - 85 y + 280 x, 2 20 z y - 7 z + 5 y, 11 x z + 13 z, -20 x - 18 y - 11] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 1, 1, 3/4, 3/4, 3/4, 4/11, 4/11, 6/11, 5, 11, 10, 2, 2, 2, 1, 4/5, 4/5, 3/5, 2/5, 2/5, 2/5, -2, -2, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=333.1MB, alloc=140.3MB, time=7.64 |\^/| 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(); 1428509923 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [-5 y z + 13 y, -4 x z - 16 y z - 14] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-5 y + 11 z - 12 y, 20 x + 3 y z + 19 z] > Problem := [F,G]; Problem := [[-5 y z + 13 y, -4 x z - 16 y z - 14], 2 2 2 [-5 y + 11 z - 12 y, 20 x + 3 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=46.9MB, alloc=32.3MB, time=0.79 memory used=65.9MB, alloc=56.3MB, time=1.09 memory used=105.4MB, alloc=60.3MB, time=1.70 memory used=142.9MB, alloc=84.3MB, time=2.27 memory used=204.3MB, alloc=92.3MB, time=3.20 memory used=263.6MB, alloc=116.3MB, time=4.10 memory used=345.5MB, alloc=116.3MB, time=5.29 memory used=421.7MB, alloc=396.3MB, time=6.47 memory used=529.8MB, alloc=420.3MB, time=8.24 memory used=646.4MB, alloc=444.3MB, time=10.33 memory used=775.9MB, alloc=468.3MB, time=12.72 memory used=918.2MB, alloc=492.3MB, time=15.32 memory used=1076.0MB, alloc=516.3MB, time=18.20 memory used=1242.1MB, alloc=540.3MB, time=21.30 memory used=1422.9MB, alloc=564.3MB, time=24.68 memory used=1612.2MB, alloc=588.3MB, time=28.25 memory used=1797.6MB, alloc=612.3MB, time=33.45 memory used=1975.1MB, alloc=636.3MB, time=39.57 memory used=2163.5MB, alloc=660.3MB, time=46.41 memory used=2365.5MB, alloc=684.3MB, time=54.07 memory used=2582.8MB, alloc=708.3MB, time=62.43 memory used=2815.7MB, alloc=732.3MB, time=71.67 memory used=3064.0MB, alloc=756.3MB, time=81.68 memory used=3324.0MB, alloc=780.3MB, time=92.83 memory used=3601.7MB, alloc=804.3MB, time=105.13 memory used=3903.4MB, alloc=828.3MB, time=118.84 memory used=4229.0MB, alloc=852.3MB, time=132.83 memory used=4578.5MB, alloc=876.3MB, time=147.52 memory used=4952.0MB, alloc=900.3MB, time=163.64 memory used=5349.5MB, alloc=924.3MB, time=181.72 memory used=5770.8MB, alloc=924.3MB, time=201.33 memory used=6192.1MB, alloc=924.3MB, time=220.29 memory used=6613.4MB, alloc=924.3MB, time=238.76 |\^/| 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(); 1428510223 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [-8 y z + 3 z + 1, 16 y z + 11 y + 13] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [8 y - 20 y - 3 z, 7 x z + 10 x - 4] > Problem := [F,G]; Problem := [[-8 y z + 3 z + 1, 16 y z + 11 y + 13], 2 [8 y - 20 y - 3 z, 7 x z + 10 x - 4]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=46.4MB, alloc=32.3MB, time=0.81 memory used=65.2MB, alloc=56.3MB, time=1.11 memory used=104.3MB, alloc=60.3MB, time=1.70 memory used=144.3MB, alloc=84.3MB, time=2.41 memory used=202.4MB, alloc=84.3MB, time=3.44 memory used=253.9MB, alloc=108.3MB, time=4.38 memory used=324.3MB, alloc=140.3MB, time=5.67 memory used=412.0MB, alloc=164.3MB, time=7.26 memory used=515.8MB, alloc=188.3MB, time=9.12 memory used=633.8MB, alloc=212.3MB, time=11.23 memory used=763.6MB, alloc=236.3MB, time=14.31 memory used=894.2MB, alloc=260.3MB, time=18.78 memory used=1038.0MB, alloc=284.3MB, time=23.73 memory used=1196.6MB, alloc=308.3MB, time=29.36 memory used=1368.6MB, alloc=332.3MB, time=35.88 memory used=1559.1MB, alloc=356.3MB, time=43.42 memory used=1773.5MB, alloc=356.3MB, time=51.71 memory used=1987.9MB, alloc=380.3MB, time=60.23 memory used=2226.2MB, alloc=380.3MB, time=69.59 memory used=2464.5MB, alloc=380.3MB, time=79.08 memory used=2702.8MB, alloc=380.3MB, time=89.12 memory used=2941.1MB, alloc=404.3MB, time=98.73 memory used=3203.2MB, alloc=404.3MB, time=109.62 memory used=3465.5MB, alloc=428.3MB, time=120.88 memory used=3751.7MB, alloc=428.3MB, time=132.30 memory used=4038.1MB, alloc=452.3MB, time=144.09 N1 := 10213 > GB := Basis(F, plex(op(vars))); 2 GB := [88 y + 87 y - 39, 6 z + 15 + 11 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4113.2MB, alloc=452.3MB, time=146.23 N2 := 785 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := 2 [-8 y z + 3 z + 1, 16 z y + 11 y + 13, 8 y - 3 z - 20 y, 7 z x + 10 x - 4] > J:=[op(GB),op(G)]; 2 2 J := [88 y + 87 y - 39, 6 z + 11 y + 15, 8 y - 3 z - 20 y, 7 z x + 10 x - 4] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 8, 2, 1, 2, 1, 1/4, 3/4, 1, 1/6, 5/12, 5/12, 4, 7, 7, 2, 1, 2, 1, 1/4, 3/4, 3/4, 1/6, 5/12, 1/4, 1, 1, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=4159.3MB, alloc=708.3MB, time=147.43 |\^/| 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(); 1428510411 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [3 z + 17 y - 5 z, -x + 18 x y - 7 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-17 y z - y - 17 z, -2 x + 8 y + 8 z] > Problem := [F,G]; 2 2 2 Problem := [[3 z + 17 y - 5 z, -x + 18 x y - 7 y ], 2 2 [-17 y z - y - 17 z, -2 x + 8 y + 8 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.52 memory used=46.6MB, alloc=56.3MB, time=0.84 memory used=88.5MB, alloc=60.3MB, time=1.49 memory used=130.5MB, alloc=60.3MB, time=2.10 memory used=169.5MB, alloc=84.3MB, time=2.78 memory used=234.9MB, alloc=116.3MB, time=3.96 memory used=314.8MB, alloc=140.3MB, time=5.36 memory used=409.5MB, alloc=164.3MB, time=7.09 memory used=519.4MB, alloc=188.3MB, time=9.11 memory used=637.7MB, alloc=468.3MB, time=11.25 memory used=773.0MB, alloc=492.3MB, time=13.70 memory used=913.6MB, alloc=516.3MB, time=17.93 memory used=1060.5MB, alloc=540.3MB, time=23.21 memory used=1220.9MB, alloc=564.3MB, time=29.13 memory used=1396.7MB, alloc=588.3MB, time=35.60 memory used=1584.6MB, alloc=612.3MB, time=43.54 memory used=1794.5MB, alloc=636.3MB, time=52.52 memory used=2028.3MB, alloc=636.3MB, time=62.45 memory used=2262.0MB, alloc=660.3MB, time=72.23 memory used=2519.8MB, alloc=660.3MB, time=83.36 memory used=2777.5MB, alloc=660.3MB, time=94.28 memory used=3035.2MB, alloc=660.3MB, time=105.93 memory used=3292.8MB, alloc=684.3MB, time=117.65 memory used=3574.3MB, alloc=684.3MB, time=129.02 memory used=3855.9MB, alloc=708.3MB, time=141.21 memory used=4161.5MB, alloc=708.3MB, time=153.54 N1 := 10645 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [7 y - 18 y x + x , 3 z - 5 z + 17 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4468.0MB, alloc=708.3MB, time=165.64 memory used=4612.5MB, alloc=708.3MB, time=168.46 memory used=4799.7MB, alloc=708.3MB, time=172.34 memory used=4983.8MB, alloc=732.3MB, time=176.20 memory used=5188.9MB, alloc=756.3MB, time=180.58 memory used=5546.4MB, alloc=780.3MB, time=192.79 memory used=5885.1MB, alloc=804.3MB, time=205.83 |\^/| 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(); 1428510711 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-5 z + 10 x - 9 y, 7 x + 19 y z + 8 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [13 x y - 5 x - 11 z, 6 y - 3 z + 2] > Problem := [F,G]; 2 2 Problem := [[-5 z + 10 x - 9 y, 7 x + 19 y z + 8 y], 2 2 [13 x y - 5 x - 11 z, 6 y - 3 z + 2]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.19 memory used=26.2MB, alloc=32.3MB, time=0.51 memory used=46.8MB, alloc=32.3MB, time=0.81 memory used=65.4MB, alloc=56.3MB, time=1.10 memory used=106.5MB, alloc=60.3MB, time=1.77 memory used=141.1MB, alloc=84.3MB, time=2.28 memory used=205.1MB, alloc=92.3MB, time=3.31 memory used=270.6MB, alloc=116.3MB, time=4.30 memory used=335.5MB, alloc=116.3MB, time=5.30 memory used=402.1MB, alloc=372.3MB, time=6.34 memory used=485.0MB, alloc=396.3MB, time=7.66 memory used=596.9MB, alloc=396.3MB, time=9.29 memory used=703.6MB, alloc=420.3MB, time=10.91 memory used=832.7MB, alloc=444.3MB, time=12.97 memory used=978.5MB, alloc=468.3MB, time=15.58 memory used=1126.3MB, alloc=492.3MB, time=18.36 memory used=1296.4MB, alloc=516.3MB, time=21.47 memory used=1457.8MB, alloc=540.3MB, time=24.57 memory used=1609.1MB, alloc=564.3MB, time=27.62 memory used=1768.9MB, alloc=588.3MB, time=31.15 memory used=1953.8MB, alloc=612.3MB, time=37.34 memory used=2142.1MB, alloc=636.3MB, time=44.41 memory used=2339.8MB, alloc=660.3MB, time=52.07 memory used=2549.3MB, alloc=684.3MB, time=60.32 memory used=2763.2MB, alloc=708.3MB, time=69.92 memory used=3000.4MB, alloc=732.3MB, time=80.47 memory used=3261.6MB, alloc=756.3MB, time=92.05 memory used=3546.7MB, alloc=780.3MB, time=104.74 memory used=3855.7MB, alloc=804.3MB, time=118.31 memory used=4188.8MB, alloc=828.3MB, time=133.11 memory used=4545.6MB, alloc=828.3MB, time=149.09 memory used=4902.5MB, alloc=852.3MB, time=165.46 memory used=5283.3MB, alloc=852.3MB, time=182.44 memory used=5664.0MB, alloc=852.3MB, time=199.15 |\^/| 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(); 1428511011 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-10 x y + 10 y z + 16, -2 z + 17 x - 6 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-8 y z - 14 y + 15 z, -15 x y - 7 y + 6 x] > Problem := [F,G]; 2 Problem := [[-10 x y + 10 y z + 16, -2 z + 17 x - 6 z], 2 [-8 y z - 14 y + 15 z, -15 x y - 7 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=4.2MB, alloc=32.3MB, time=0.23 memory used=26.5MB, alloc=32.3MB, time=0.62 memory used=47.7MB, alloc=32.3MB, time=0.99 memory used=67.8MB, alloc=56.3MB, time=1.33 memory used=107.7MB, alloc=60.3MB, time=2.04 memory used=149.3MB, alloc=84.3MB, time=2.97 memory used=209.4MB, alloc=92.3MB, time=4.27 memory used=265.7MB, alloc=116.3MB, time=5.52 memory used=341.5MB, alloc=140.3MB, time=7.05 memory used=434.9MB, alloc=164.3MB, time=8.83 memory used=537.8MB, alloc=188.3MB, time=11.98 memory used=649.9MB, alloc=212.3MB, time=16.26 memory used=773.9MB, alloc=236.3MB, time=22.20 memory used=922.1MB, alloc=236.3MB, time=29.14 memory used=1070.2MB, alloc=260.3MB, time=35.96 memory used=1242.3MB, alloc=260.3MB, time=42.80 N1 := 5099 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [50 y x - 275 y x - 160 y x - 240 y + 128, 2 -10 x y + 55 x y + 16 x + 16 z + 48] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1400.7MB, alloc=260.3MB, time=46.81 memory used=1604.1MB, alloc=540.3MB, time=51.65 N2 := 2131 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 H := [-10 x y + 10 y z + 16, -2 z - 6 z + 17 x, -8 y z - 14 y + 15 z, 2 -15 x y - 7 y + 6 x] > J:=[op(GB),op(G)]; 2 2 2 J := [50 y x - 275 y x - 160 y x - 240 y + 128, 2 -10 x y + 55 x y + 16 x + 16 z + 48, -8 y z - 14 y + 15 z, 2 -15 x y - 7 y + 6 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 1, 2, 2, 3/4, 3/4, 3/4, 1/3, 1/2, 5/12, 4, 9, 11, 4, 2, 2, 1, 3/4, 1, 1/2, 1/2, 5/8, 3/16, 0, -3, -2] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1725.6MB, alloc=540.3MB, time=57.15 |\^/| 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(); 1428511091 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-10 y - 8 y + 4, -5 y z + 11 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-9 x - x y - 12, -13 x y + 8 y + 5 z ] > Problem := [F,G]; 2 Problem := [[-10 y - 8 y + 4, -5 y z + 11 x], 2 2 2 [-9 x - x y - 12, -13 x y + 8 y + 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.52 memory used=47.6MB, alloc=32.3MB, time=0.87 memory used=68.6MB, alloc=56.3MB, time=1.31 N1 := 519 > GB := Basis(F, plex(op(vars))); 2 GB := [5 y + 4 y - 2, -55 x y - 44 x + 10 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=110.3MB, alloc=60.3MB, time=2.30 memory used=149.3MB, alloc=60.3MB, time=2.92 memory used=187.5MB, alloc=84.3MB, time=3.63 N2 := 553 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-10 y - 8 y + 4, -5 z y + 11 x, -9 x - x y - 12, -13 x y + 8 y + 5 z ] > J:=[op(GB),op(G)]; 2 2 J := [5 y + 4 y - 2, -55 x y - 44 x + 10 z, -9 x - x y - 12, 2 2 -13 x y + 8 y + 5 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 2, 3/4, 1, 1/2, 4/11, 6/11, 2/11, 4, 9, 8, 2, 2, 2, 2, 3/4, 1, 1/2, 5/12, 1/2, 1/6, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=221.5MB, alloc=84.3MB, time=4.50 |\^/| 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(); 1428511099 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [5 x + 6 y - 13 y z, -11 x z - 12] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [17 y + 16, -7 y - 6 y + 18 z] > Problem := [F,G]; Problem := 2 2 2 2 [[5 x + 6 y - 13 y z, -11 x z - 12], [17 y + 16, -7 y - 6 y + 18 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.20 memory used=27.0MB, alloc=32.3MB, time=0.55 memory used=48.0MB, alloc=32.3MB, time=0.91 memory used=68.3MB, alloc=56.3MB, time=1.27 memory used=109.7MB, alloc=60.3MB, time=2.11 N1 := 581 > GB := Basis(F, plex(op(vars))); 2 3 2 2 GB := [66 y x + 55 x + 156 y, 11 z x + 12, -5 x - 6 y + 13 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=145.2MB, alloc=60.3MB, time=2.84 memory used=183.0MB, alloc=84.3MB, time=3.54 memory used=233.4MB, alloc=84.3MB, time=4.44 N2 := 581 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-13 z y + 6 y + 5 x , -11 x z - 12, 17 y + 16, -7 y - 6 y + 18 z] > J:=[op(GB),op(G)]; 2 3 2 2 2 J := [66 y x + 55 x + 156 y, 11 z x + 12, -5 x - 6 y + 13 y z, 17 y + 16, 2 -7 y - 6 y + 18 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 8, 2, 2, 2, 1, 1/2, 3/4, 3/4, 1/5, 1/2, 3/10, 5, 10, 11, 3, 3, 2, 1, 3/5, 4/5, 3/5, 4/13, 7/13, 3/13, -2, -3, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=253.3MB, alloc=84.3MB, time=4.96 |\^/| 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(); 1428511106 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-18 y + 18 y z - 2 x, 14 x + 8 z + 6 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [5 z - 15 x - 3, -14 x z + 19 y - 19 z ] > Problem := [F,G]; 2 2 2 Problem := [[-18 y + 18 y z - 2 x, 14 x + 8 z + 6 x], 2 2 2 [5 z - 15 x - 3, -14 x z + 19 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.54 memory used=47.9MB, alloc=32.3MB, time=0.88 memory used=68.2MB, alloc=56.3MB, time=1.23 memory used=109.8MB, alloc=60.3MB, time=1.91 memory used=148.3MB, alloc=84.3MB, time=2.55 memory used=213.1MB, alloc=92.3MB, time=3.61 memory used=275.5MB, alloc=116.3MB, time=4.69 memory used=351.7MB, alloc=116.3MB, time=5.87 memory used=439.0MB, alloc=396.3MB, time=7.48 memory used=549.4MB, alloc=420.3MB, time=9.52 memory used=669.9MB, alloc=444.3MB, time=11.87 memory used=810.3MB, alloc=468.3MB, time=14.60 memory used=975.6MB, alloc=492.3MB, time=17.35 memory used=1160.3MB, alloc=516.3MB, time=20.42 memory used=1364.4MB, alloc=540.3MB, time=23.77 memory used=1568.0MB, alloc=564.3MB, time=27.57 memory used=1800.5MB, alloc=588.3MB, time=31.09 memory used=2044.5MB, alloc=612.3MB, time=34.83 memory used=2292.5MB, alloc=636.3MB, time=39.17 memory used=2546.8MB, alloc=660.3MB, time=43.71 memory used=2779.4MB, alloc=684.3MB, time=49.96 memory used=2990.4MB, alloc=708.3MB, time=57.23 memory used=3208.7MB, alloc=732.3MB, time=65.52 memory used=3436.2MB, alloc=756.3MB, time=74.62 memory used=3674.9MB, alloc=780.3MB, time=83.97 memory used=3925.3MB, alloc=804.3MB, time=94.02 memory used=4189.2MB, alloc=828.3MB, time=104.80 memory used=4466.6MB, alloc=852.3MB, time=116.20 memory used=4757.4MB, alloc=876.3MB, time=128.76 memory used=5059.8MB, alloc=900.3MB, time=142.75 memory used=5384.8MB, alloc=924.3MB, time=158.46 |\^/| 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(); 1428511406 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [19 x y + 13 x z - 18 y, 15 x z - 15 z + 12] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-18 x + 10 x y - x z, 2 y - 17 y z - 9 x] > Problem := [F,G]; 2 Problem := [[19 x y + 13 x z - 18 y, 15 x z - 15 z + 12], 2 2 [-18 x + 10 x y - x z, 2 y - 17 y z - 9 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.52 memory used=46.9MB, alloc=56.3MB, time=0.87 memory used=88.7MB, alloc=60.3MB, time=1.54 memory used=128.7MB, alloc=60.3MB, time=2.17 memory used=167.3MB, alloc=84.3MB, time=2.83 memory used=228.1MB, alloc=92.3MB, time=3.86 memory used=291.8MB, alloc=116.3MB, time=4.97 memory used=375.6MB, alloc=140.3MB, time=6.39 memory used=477.2MB, alloc=164.3MB, time=8.11 memory used=592.4MB, alloc=188.3MB, time=10.16 memory used=704.3MB, alloc=468.3MB, time=12.20 memory used=848.5MB, alloc=492.3MB, time=14.91 memory used=1014.2MB, alloc=516.3MB, time=17.93 memory used=1193.0MB, alloc=540.3MB, time=21.17 memory used=1394.2MB, alloc=564.3MB, time=24.60 memory used=1597.8MB, alloc=588.3MB, time=28.35 memory used=1807.1MB, alloc=612.3MB, time=33.15 memory used=1995.6MB, alloc=636.3MB, time=39.85 memory used=2190.7MB, alloc=660.3MB, time=47.38 memory used=2397.9MB, alloc=684.3MB, time=55.36 memory used=2619.3MB, alloc=708.3MB, time=64.24 memory used=2855.6MB, alloc=732.3MB, time=74.13 memory used=3106.5MB, alloc=756.3MB, time=84.72 memory used=3370.7MB, alloc=780.3MB, time=96.47 memory used=3650.3MB, alloc=804.3MB, time=109.11 memory used=3953.9MB, alloc=828.3MB, time=122.68 memory used=4281.4MB, alloc=852.3MB, time=136.86 memory used=4632.8MB, alloc=876.3MB, time=151.86 memory used=5008.2MB, alloc=900.3MB, time=167.97 |\^/| 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(); 1428511706 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; F := [-x y - 4 x z + 7, 7 x z - 15 y z - 20 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [10 x - 5 y + 20 z , -16 x z + 8 y - 6 z ] > Problem := [F,G]; Problem := [[-x y - 4 x z + 7, 7 x z - 15 y z - 20 x], 2 2 2 2 2 [10 x - 5 y + 20 z , -16 x z + 8 y - 6 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.1MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=47.7MB, alloc=60.3MB, time=0.84 memory used=90.3MB, alloc=60.3MB, time=1.45 memory used=133.4MB, alloc=92.3MB, time=2.08 memory used=200.5MB, alloc=92.3MB, time=3.01 memory used=267.6MB, alloc=116.3MB, time=3.98 memory used=334.2MB, alloc=372.3MB, time=4.97 memory used=427.2MB, alloc=396.3MB, time=6.26 memory used=541.3MB, alloc=420.3MB, time=7.92 memory used=664.2MB, alloc=420.3MB, time=9.81 memory used=775.7MB, alloc=444.3MB, time=11.49 memory used=894.2MB, alloc=444.3MB, time=13.31 memory used=1010.3MB, alloc=468.3MB, time=15.11 memory used=1118.3MB, alloc=468.3MB, time=16.83 memory used=1206.9MB, alloc=468.3MB, time=18.41 memory used=1287.5MB, alloc=468.3MB, time=19.72 memory used=1373.9MB, alloc=492.3MB, time=21.24 memory used=1451.9MB, alloc=492.3MB, time=22.55 memory used=1558.1MB, alloc=492.3MB, time=24.72 memory used=1673.6MB, alloc=516.3MB, time=27.30 memory used=1794.3MB, alloc=540.3MB, time=29.97 memory used=1895.3MB, alloc=564.3MB, time=32.18 memory used=2001.1MB, alloc=564.3MB, time=34.53 memory used=2092.0MB, alloc=588.3MB, time=36.62 memory used=2184.0MB, alloc=588.3MB, time=38.68 memory used=2294.4MB, alloc=612.3MB, time=41.26 memory used=2390.2MB, alloc=636.3MB, time=43.35 memory used=2483.1MB, alloc=636.3MB, time=45.42 memory used=2563.0MB, alloc=660.3MB, time=47.23 memory used=2658.3MB, alloc=684.3MB, time=49.89 memory used=2820.4MB, alloc=708.3MB, time=55.56 memory used=3088.6MB, alloc=732.3MB, time=65.75 memory used=3360.4MB, alloc=756.3MB, time=76.44 memory used=3637.5MB, alloc=780.3MB, time=88.04 memory used=3926.2MB, alloc=804.3MB, time=100.68 memory used=4238.9MB, alloc=828.3MB, time=114.28 memory used=4575.5MB, alloc=852.3MB, time=129.08 memory used=4936.0MB, alloc=852.3MB, time=144.64 memory used=5296.5MB, alloc=852.3MB, time=161.40 memory used=5656.9MB, alloc=876.3MB, time=177.67 memory used=6041.3MB, alloc=876.3MB, time=195.49 memory used=6425.7MB, alloc=876.3MB, time=212.99 memory used=6809.9MB, alloc=900.3MB, time=229.86 |\^/| 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(); 1428520480 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [5 x + 4 z + 19 y, 10 y + 18 y z - 19 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [20 x + 11 x y + 20 y, 20 y - 13 z - 17 x] > Problem := [F,G]; 2 2 2 Problem := [[5 x + 4 z + 19 y, 10 y + 18 y z - 19 x], 2 2 2 [20 x + 11 x y + 20 y, 20 y - 13 z - 17 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.51 memory used=46.2MB, alloc=32.3MB, time=0.80 memory used=65.5MB, alloc=56.3MB, time=1.09 memory used=107.4MB, alloc=60.3MB, time=1.72 memory used=148.0MB, alloc=60.3MB, time=2.31 memory used=187.2MB, alloc=84.3MB, time=2.90 memory used=252.8MB, alloc=116.3MB, time=4.08 memory used=338.3MB, alloc=116.3MB, time=5.57 memory used=415.8MB, alloc=140.3MB, time=6.97 memory used=510.4MB, alloc=164.3MB, time=8.72 memory used=622.9MB, alloc=444.3MB, time=10.79 memory used=750.8MB, alloc=468.3MB, time=13.18 memory used=879.8MB, alloc=492.3MB, time=17.21 memory used=1019.2MB, alloc=516.3MB, time=21.99 memory used=1169.1MB, alloc=540.3MB, time=27.90 memory used=1339.8MB, alloc=564.3MB, time=35.16 memory used=1534.4MB, alloc=564.3MB, time=43.14 memory used=1729.1MB, alloc=564.3MB, time=50.88 memory used=1923.7MB, alloc=588.3MB, time=58.66 memory used=2142.4MB, alloc=588.3MB, time=67.68 memory used=2361.2MB, alloc=612.3MB, time=76.12 N1 := 7021 > GB := Basis(F, plex(op(vars))); 4 2 2 3 2 2 GB := [100 y + 405 y x + 1539 y - 380 y x + 361 x , 2 3 2 2 405 x y + 100 y - 190 x y + 342 x z + 1539 y , 10 y + 18 y z - 19 x, 2 2 4 z + 5 x + 19 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2609.0MB, alloc=612.3MB, time=80.33 memory used=2899.5MB, alloc=636.3MB, time=84.84 memory used=3191.7MB, alloc=660.3MB, time=88.74 memory used=3521.3MB, alloc=684.3MB, time=92.33 memory used=3924.8MB, alloc=708.3MB, time=97.68 memory used=4329.7MB, alloc=732.3MB, time=103.18 memory used=4742.4MB, alloc=756.3MB, time=110.22 memory used=5158.1MB, alloc=780.3MB, time=117.38 memory used=5548.4MB, alloc=804.3MB, time=124.88 memory used=5954.2MB, alloc=828.3MB, time=132.08 memory used=6341.3MB, alloc=852.3MB, time=139.17 memory used=6761.0MB, alloc=876.3MB, time=146.31 memory used=7153.0MB, alloc=900.3MB, time=158.42 memory used=7487.8MB, alloc=924.3MB, time=171.69 memory used=7822.5MB, alloc=948.3MB, time=185.93 memory used=8166.5MB, alloc=972.3MB, time=200.96 memory used=8522.9MB, alloc=996.3MB, time=216.65 memory used=8891.4MB, alloc=1020.3MB, time=233.06 memory used=9273.3MB, alloc=1044.3MB, time=250.18 |\^/| 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(); 1428520780 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [13 x - 8 x - 15, 7 x y + 12 x z + 7 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-5 x + 20 z + 9 x, -20 y - 7 z + 5 y] > Problem := [F,G]; 2 2 Problem := [[13 x - 8 x - 15, 7 x y + 12 x z + 7 y ], 2 2 2 2 [-5 x + 20 z + 9 x, -20 y - 7 z + 5 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.52 memory used=47.0MB, alloc=56.3MB, time=0.83 memory used=89.4MB, alloc=60.3MB, time=1.55 memory used=129.4MB, alloc=84.3MB, time=2.26 memory used=190.0MB, alloc=84.3MB, time=3.36 memory used=244.8MB, alloc=108.3MB, time=4.44 memory used=312.3MB, alloc=132.3MB, time=6.58 memory used=395.5MB, alloc=132.3MB, time=9.56 N1 := 2339 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [13 x - 8 x - 15, 91 x y - 56 y + 105 y + 180 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=484.0MB, alloc=140.3MB, time=11.54 memory used=580.2MB, alloc=164.3MB, time=13.16 memory used=701.0MB, alloc=188.3MB, time=15.29 memory used=829.2MB, alloc=212.3MB, time=19.20 memory used=960.9MB, alloc=236.3MB, time=24.20 N2 := 2811 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [13 x - 8 x - 15, 12 z x + 7 y + 7 y x, -5 x + 20 z + 9 x, 2 2 -20 y - 7 z + 5 y] > J:=[op(GB),op(G)]; 2 2 2 2 2 J := [13 x - 8 x - 15, 91 y x - 56 y + 180 z + 105 y, -5 x + 20 z + 9 x, 2 2 -20 y - 7 z + 5 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 8, 8, 2, 2, 2, 2, 3/4, 1/2, 3/4, 1/2, 1/3, 1/4, 4, 8, 9, 3, 2, 2, 2, 3/4, 1/2, 3/4, 5/13, 5/13, 3/13, 0, -1, -1] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1008.8MB, alloc=236.3MB, time=25.59 |\^/| 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(); 1428520811 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-17 y + 12 z - 19 y, 6 x z - 19 y z + 5 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [5 x z + 2 y z - 18 x, -11 x - 20 y - 20 z] > Problem := [F,G]; 2 2 2 Problem := [[-17 y + 12 z - 19 y, 6 x z - 19 y z + 5 z ], 2 [5 x z + 2 y z - 18 x, -11 x - 20 y - 20 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=56.3MB, time=0.81 memory used=85.5MB, alloc=60.3MB, time=1.40 memory used=124.5MB, alloc=84.3MB, time=1.97 memory used=173.6MB, alloc=84.3MB, time=2.69 memory used=233.1MB, alloc=116.3MB, time=3.62 memory used=315.4MB, alloc=116.3MB, time=4.86 memory used=395.1MB, alloc=140.3MB, time=6.17 memory used=478.5MB, alloc=396.3MB, time=7.57 memory used=578.0MB, alloc=420.3MB, time=9.30 memory used=700.9MB, alloc=444.3MB, time=11.43 memory used=844.5MB, alloc=468.3MB, time=13.91 memory used=1012.4MB, alloc=492.3MB, time=16.87 memory used=1160.5MB, alloc=516.3MB, time=19.51 memory used=1333.8MB, alloc=540.3MB, time=22.73 memory used=1512.2MB, alloc=564.3MB, time=26.10 memory used=1679.1MB, alloc=588.3MB, time=29.35 memory used=1853.4MB, alloc=612.3MB, time=32.68 memory used=2018.1MB, alloc=636.3MB, time=35.88 memory used=2169.8MB, alloc=660.3MB, time=39.00 memory used=2317.6MB, alloc=684.3MB, time=42.12 memory used=2456.4MB, alloc=708.3MB, time=45.17 memory used=2586.5MB, alloc=732.3MB, time=48.04 memory used=2704.6MB, alloc=756.3MB, time=50.67 memory used=2819.6MB, alloc=780.3MB, time=53.30 memory used=2938.7MB, alloc=804.3MB, time=55.99 memory used=3046.9MB, alloc=828.3MB, time=58.56 memory used=3141.7MB, alloc=852.3MB, time=60.79 memory used=3470.4MB, alloc=876.3MB, time=72.09 memory used=3781.2MB, alloc=900.3MB, time=83.94 memory used=4098.0MB, alloc=924.3MB, time=96.97 memory used=4423.9MB, alloc=948.3MB, time=110.73 memory used=4761.7MB, alloc=972.3MB, time=124.67 memory used=5111.9MB, alloc=996.3MB, time=139.40 memory used=5474.8MB, alloc=1020.3MB, time=154.69 memory used=5851.4MB, alloc=1044.3MB, time=170.79 memory used=6242.3MB, alloc=1068.3MB, time=187.75 memory used=6646.9MB, alloc=1092.3MB, time=204.96 memory used=7065.6MB, alloc=1116.3MB, time=223.74 memory used=7498.9MB, alloc=1140.3MB, time=242.45 |\^/| 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(); 1428521111 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [19 y z - 18 z - 8 x, 20 + 7 x] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-3 x y - 2 y - 6 z , 19 x + 2 x y + 5 y] > Problem := [F,G]; 2 Problem := [[19 y z - 18 z - 8 x, 20 + 7 x], 2 2 2 [-3 x y - 2 y - 6 z , 19 x + 2 x y + 5 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=55.1MB, alloc=68.3MB, time=0.98 memory used=107.6MB, alloc=68.3MB, time=1.88 memory used=153.6MB, alloc=92.3MB, time=2.71 memory used=214.5MB, alloc=116.3MB, time=4.60 N1 := 1251 > GB := Basis(F, plex(op(vars))); 2 GB := [7 x + 20, -133 y z + 126 z - 160] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=298.9MB, alloc=124.3MB, time=6.03 memory used=385.8MB, alloc=148.3MB, time=8.21 N2 := 1141 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := 2 2 2 2 [19 y z - 18 z - 8 x, 7 x + 20, -3 x y - 2 y - 6 z , 2 y x + 19 x + 5 y] > J:=[op(GB),op(G)]; 2 2 2 J := [7 x + 20, -133 y z + 126 z - 160, -3 x y - 2 y - 6 z , 2 2 y x + 19 x + 5 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 2, 2, 2, 1, 3/4, 1/2, 5/11, 5/11, 3/11, 4, 8, 7, 2, 2, 2, 2, 3/4, 3/4, 1/2, 4/11, 5/11, 3/11, 1, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=396.9MB, alloc=148.3MB, time=8.52 |\^/| 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(); 1428521123 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-18 y + 17 y z - 11 y, x y - 12 y z - 20 z ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-13 x z + 19 y + 4 x, -10 x - 9 y + 19 y] > Problem := [F,G]; 2 2 Problem := [[-18 y + 17 y z - 11 y, x y - 12 y z - 20 z ], 2 2 2 [-13 x z + 19 y + 4 x, -10 x - 9 y + 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=4.1MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=47.4MB, alloc=32.3MB, time=0.82 memory used=68.0MB, alloc=56.3MB, time=1.14 memory used=110.4MB, alloc=60.3MB, time=1.79 memory used=152.0MB, alloc=84.3MB, time=2.48 memory used=214.3MB, alloc=116.3MB, time=3.56 memory used=294.1MB, alloc=116.3MB, time=4.92 memory used=367.4MB, alloc=140.3MB, time=6.19 memory used=456.3MB, alloc=164.3MB, time=8.10 memory used=552.5MB, alloc=188.3MB, time=11.02 memory used=658.0MB, alloc=212.3MB, time=15.08 memory used=787.3MB, alloc=212.3MB, time=20.09 memory used=916.6MB, alloc=236.3MB, time=25.12 N1 := 4269 > GB := Basis(F, plex(op(vars))); 2 3 2 2 GB := [-289 x y + 10152 y + 10164 y + 2420 y, -18 y + 17 y z - 11 y, 2 2 -17 x y + 216 y + 340 z + 132 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1074.6MB, alloc=236.3MB, time=30.18 memory used=1153.3MB, alloc=492.3MB, time=31.54 memory used=1332.8MB, alloc=516.3MB, time=34.68 memory used=1525.2MB, alloc=540.3MB, time=40.66 N2 := 2795 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-18 y + 17 y z - 11 y, -20 z - 12 z y + y x, -13 x z + 19 y + 4 x, 2 2 -10 x - 9 y + 19 y] > J:=[op(GB),op(G)]; 2 3 2 2 J := [-289 x y + 10152 y + 10164 y + 2420 y, -18 y + 17 y z - 11 y, 2 2 2 -17 x y + 216 y + 340 z + 132 y, -13 x z + 19 y + 4 x, 2 2 -10 x - 9 y + 19 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 2, 2, 3/4, 1, 3/4, 1/3, 2/3, 1/3, 5, 12, 11, 3, 13 2, 3, 2, 4/5, 1, 3/5, 5/17, --, 3/17, -2, -3, -1] 17 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=1679.3MB, alloc=540.3MB, time=46.57 |\^/| 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(); 1428521182 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [-11 x - 8 x y + 17 y, -19 x + 17 y - 14 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-8 y + 8 y z - 5, -17 y z - 9 z + 3] > Problem := [F,G]; 2 Problem := [[-11 x - 8 x y + 17 y, -19 x + 17 y - 14 z], 2 2 [-8 y + 8 y z - 5, -17 y z - 9 z + 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.5MB, alloc=32.3MB, time=0.82 memory used=67.8MB, alloc=56.3MB, time=1.15 memory used=108.7MB, alloc=60.3MB, time=1.78 memory used=147.5MB, alloc=84.3MB, time=2.48 memory used=205.0MB, alloc=116.3MB, time=3.56 memory used=276.0MB, alloc=140.3MB, time=5.89 N1 := 1675 > GB := Basis(F, plex(op(vars))); 2 GB := [8 y x + 11 x - 17 y, 14 z - 17 y + 19 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=368.1MB, alloc=140.3MB, time=7.91 memory used=469.0MB, alloc=420.3MB, time=9.64 memory used=585.5MB, alloc=444.3MB, time=13.10 N2 := 1675 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-11 x - 8 x y + 17 y, -19 x + 17 y - 14 z, -8 y + 8 y z - 5, 2 -17 y z - 9 z + 3] > J:=[op(GB),op(G)]; 2 2 J := [8 y x + 11 x - 17 y, 14 z - 17 y + 19 x, -8 y + 8 y z - 5, 2 -17 y z - 9 z + 3] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 2, 2, 2, 1/2, 1, 3/4, 1/4, 1/2, 1/3, 4, 9, 7, 2, 2, 2, 2, 1/2, 1, 3/4, 1/4, 1/2, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=613.3MB, alloc=444.3MB, time=14.03 |\^/| 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(); 1428521203 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-13 x y - 16 z - 9 z, 3 x - 16 x z + 13 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-11 z - 10 y - 3, 19 x + x z - 15 y] > Problem := [F,G]; 2 2 2 Problem := [[-13 x y - 16 z - 9 z, 3 x - 16 x z + 13 y ], 2 2 [-11 z - 10 y - 3, 19 x + x z - 15 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=27.3MB, alloc=32.3MB, time=0.54 memory used=48.8MB, alloc=32.3MB, time=0.87 memory used=66.7MB, alloc=56.3MB, time=1.15 memory used=110.2MB, alloc=68.3MB, time=1.79 memory used=149.6MB, alloc=92.3MB, time=2.44 memory used=217.2MB, alloc=92.3MB, time=3.40 memory used=281.6MB, alloc=116.3MB, time=4.42 memory used=358.3MB, alloc=116.3MB, time=5.57 memory used=429.4MB, alloc=372.3MB, time=6.69 memory used=517.3MB, alloc=396.3MB, time=8.02 memory used=627.9MB, alloc=396.3MB, time=9.40 memory used=737.2MB, alloc=420.3MB, time=11.13 memory used=861.6MB, alloc=444.3MB, time=13.10 memory used=1002.6MB, alloc=468.3MB, time=15.52 memory used=1154.4MB, alloc=492.3MB, time=18.35 memory used=1320.0MB, alloc=516.3MB, time=21.38 memory used=1500.2MB, alloc=540.3MB, time=24.74 memory used=1685.4MB, alloc=564.3MB, time=28.47 memory used=1867.3MB, alloc=588.3MB, time=34.39 memory used=2054.5MB, alloc=612.3MB, time=41.07 memory used=2245.3MB, alloc=636.3MB, time=48.98 memory used=2456.9MB, alloc=660.3MB, time=57.89 memory used=2692.4MB, alloc=684.3MB, time=67.77 memory used=2951.9MB, alloc=708.3MB, time=78.65 memory used=3235.3MB, alloc=732.3MB, time=90.46 memory used=3542.6MB, alloc=732.3MB, time=103.25 memory used=3849.9MB, alloc=756.3MB, time=116.08 memory used=4181.1MB, alloc=780.3MB, time=129.68 N1 := 9167 > GB := Basis(F, plex(op(vars))); 4 2 2 3 4 2 3 GB := [169 y + 78 y x + 208 y x + 9 x + 117 y x + 27 x , 2 2 -3 x + 16 x z - 13 y , 3 2 2 2 2 2 2 9 x + 208 x y + 39 x y + 208 y z + 27 x + 117 y , 16 z + 13 y x + 9 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4421.2MB, alloc=780.3MB, time=137.21 memory used=4526.9MB, alloc=780.3MB, time=139.28 memory used=4625.7MB, alloc=780.3MB, time=141.17 memory used=4719.1MB, alloc=780.3MB, time=143.00 memory used=4815.4MB, alloc=780.3MB, time=144.89 memory used=4906.4MB, alloc=780.3MB, time=146.45 memory used=4988.0MB, alloc=780.3MB, time=148.01 memory used=5071.3MB, alloc=780.3MB, time=149.68 memory used=5148.2MB, alloc=780.3MB, time=151.23 memory used=5216.0MB, alloc=780.3MB, time=152.66 memory used=5315.6MB, alloc=780.3MB, time=154.06 memory used=5384.7MB, alloc=780.3MB, time=155.51 memory used=5445.9MB, alloc=780.3MB, time=156.65 memory used=5556.2MB, alloc=780.3MB, time=158.32 memory used=5610.3MB, alloc=780.3MB, time=159.67 memory used=5664.0MB, alloc=780.3MB, time=161.09 memory used=5710.1MB, alloc=780.3MB, time=162.37 memory used=5771.5MB, alloc=780.3MB, time=163.65 memory used=5830.5MB, alloc=780.3MB, time=165.16 memory used=5893.9MB, alloc=780.3MB, time=166.86 memory used=5941.9MB, alloc=780.3MB, time=168.09 memory used=6160.4MB, alloc=780.3MB, time=171.63 memory used=6414.1MB, alloc=780.3MB, time=175.07 memory used=6596.9MB, alloc=804.3MB, time=178.39 memory used=6795.8MB, alloc=828.3MB, time=181.92 memory used=7090.0MB, alloc=828.3MB, time=186.20 memory used=7279.3MB, alloc=828.3MB, time=189.20 memory used=7427.2MB, alloc=852.3MB, time=192.07 memory used=7615.5MB, alloc=852.3MB, time=196.28 memory used=7783.2MB, alloc=876.3MB, time=199.66 memory used=8002.4MB, alloc=876.3MB, time=202.86 memory used=8170.5MB, alloc=876.3MB, time=206.10 memory used=8300.2MB, alloc=876.3MB, time=209.21 memory used=8465.3MB, alloc=900.3MB, time=212.18 memory used=8609.9MB, alloc=900.3MB, time=215.35 memory used=8810.3MB, alloc=900.3MB, time=218.32 memory used=9296.0MB, alloc=924.3MB, time=227.26 memory used=9788.6MB, alloc=948.3MB, time=238.08 memory used=10151.7MB, alloc=972.3MB, time=246.21 memory used=10580.5MB, alloc=996.3MB, time=254.61 memory used=10902.7MB, alloc=1020.3MB, time=257.65 memory used=11531.7MB, alloc=1044.3MB, time=269.89 memory used=12208.5MB, alloc=1068.3MB, time=282.69 memory used=12775.2MB, alloc=1092.3MB, time=293.53 |\^/| 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(); 1428521503 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [10 y z - 9 x + 5 y, 18 x y + 5 y - 13 y] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 G := [-11 x z - y z, 7 x + 17 x y] > Problem := [F,G]; Problem := [ 2 2 [10 y z - 9 x + 5 y, 18 x y + 5 y - 13 y], [-11 x z - y z, 7 x + 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=32.4MB, alloc=40.3MB, time=0.62 memory used=60.5MB, alloc=64.3MB, time=1.16 N1 := 493 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [18 x + 5 x y - 13 x, -324 x + 25 y + 234 x - 65 y, 2 2 36 x z + 27 x - 26 x z - 13 x, 10 y z - 9 x + 5 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=105.9MB, alloc=68.3MB, time=1.92 memory used=154.8MB, alloc=68.3MB, time=2.79 memory used=198.8MB, alloc=92.3MB, time=4.04 N2 := 935 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [10 y z - 9 x + 5 y, 18 x y + 5 y - 13 y, -11 x z - y z, 7 x + 17 x y] > J:=[op(GB),op(G)]; 2 2 2 J := [18 x + 5 x y - 13 x, -324 x + 25 y + 234 x - 65 y, 2 2 36 x z + 27 x - 26 x z - 13 x, 10 y z - 9 x + 5 y, -11 x z - y z, 2 7 x + 17 x y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 10, 8, 2, 2, 2, 1, 1, 1, 1/2, 1/2, 7/10, 3/10, 6, 14, 13, 3, 13 2, 2, 1, 1, 5/6, 1/2, --, 7/18, 5/18, -4, -5, -1] 18 > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=204.8MB, alloc=92.3MB, time=4.20 |\^/| 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(); 1428521509 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 F := [6 y - 11 y z - 15 y, -10 y z - 7 y - 17] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [14 y - 10 z + x, -5 x - 2 z] > Problem := [F,G]; Problem := [ 2 2 2 [6 y - 11 y z - 15 y, -10 y z - 7 y - 17], [14 y - 10 z + x, -5 x - 2 z] ] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=47.1MB, alloc=32.3MB, time=0.84 memory used=66.3MB, alloc=56.3MB, time=1.16 memory used=106.1MB, alloc=60.3MB, time=1.80 memory used=143.9MB, alloc=84.3MB, time=2.41 memory used=203.1MB, alloc=92.3MB, time=3.38 memory used=261.3MB, alloc=116.3MB, time=4.40 memory used=338.0MB, alloc=140.3MB, time=5.81 memory used=431.0MB, alloc=164.3MB, time=7.51 memory used=540.7MB, alloc=188.3MB, time=9.49 memory used=654.0MB, alloc=468.3MB, time=11.56 memory used=789.5MB, alloc=492.3MB, time=14.32 memory used=921.8MB, alloc=516.3MB, time=18.40 memory used=1064.1MB, alloc=540.3MB, time=23.24 memory used=1218.1MB, alloc=564.3MB, time=29.06 memory used=1387.4MB, alloc=588.3MB, time=35.92 memory used=1580.6MB, alloc=612.3MB, time=43.65 memory used=1797.8MB, alloc=612.3MB, time=52.51 memory used=2015.0MB, alloc=636.3MB, time=61.81 memory used=2256.1MB, alloc=636.3MB, time=71.99 memory used=2497.3MB, alloc=636.3MB, time=81.78 memory used=2738.2MB, alloc=660.3MB, time=91.30 memory used=3003.2MB, alloc=684.3MB, time=101.73 memory used=3292.0MB, alloc=708.3MB, time=112.97 N1 := 9109 > GB := Basis(F, plex(op(vars))); 2 GB := [60 y - 73 y + 187, 11 z + 15 - 6 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 1473 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [6 y - 11 y z - 15 y, -10 y z - 7 y - 17, -10 z + 14 y + x, -5 x - 2 z] > J:=[op(GB),op(G)]; 2 2 2 J := [60 y - 73 y + 187, 11 z + 15 - 6 y, -10 z + 14 y + x, -5 x - 2 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 7, 2, 1, 2, 2, 1/2, 3/4, 1, 2/11, 6/11, 4/11, 4, 8, 6, 2, 1, 2, 2, 1/2, 3/4, 3/4, 2/11, 4/11, 3/11, 1, 1, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=3598.4MB, alloc=708.3MB, time=121.15 |\^/| 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(); 1428521644 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-5 x + 3 x y, -10 x + 5 x + 7 z] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [14 x y + 12 x z + 9 z , 14 x + 15 y + 15 y] > Problem := [F,G]; 2 2 Problem := [[-5 x + 3 x y, -10 x + 5 x + 7 z], 2 2 2 [14 x y + 12 x z + 9 z , 14 x + 15 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=49.1MB, alloc=32.3MB, time=0.89 memory used=69.9MB, alloc=56.3MB, time=1.26 N1 := 649 > GB := Basis(F, plex(op(vars))); 2 2 GB := [-5 x + 3 x y, -10 x + 5 x + 7 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=110.8MB, alloc=60.3MB, time=2.10 memory used=151.5MB, alloc=60.3MB, time=2.78 memory used=191.2MB, alloc=84.3MB, time=3.65 N2 := 649 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-5 x + 3 x y, -10 x + 5 x + 7 z, 9 z + 12 z x + 14 y x, 2 2 15 y + 14 x + 15 y] > J:=[op(GB),op(G)]; 2 2 2 J := [-5 x + 3 x y, -10 x + 5 x + 7 z, 9 z + 12 z x + 14 y x, 2 2 15 y + 14 x + 15 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 2, 1, 3/4, 1/2, 7/11, 4/11, 3/11, 4, 9, 8, 2, 2, 2, 2, 1, 3/4, 1/2, 7/11, 4/11, 3/11, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=194.8MB, alloc=84.3MB, time=3.74 |\^/| 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(); 1428521648 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [10 z + 8 x, -x - 4 x y - 4 y ] > G := [ randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=3, degree=2, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-4 x + 14 x - 9 z, -4 x + 16 y z + 11 x] > Problem := [F,G]; 2 2 2 Problem := [[10 z + 8 x, -x - 4 x y - 4 y ], 2 2 [-4 x + 14 x - 9 z, -4 x + 16 y z + 11 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=49.8MB, alloc=32.3MB, time=0.90 memory used=69.6MB, alloc=56.3MB, time=1.30 N1 := 491 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [x + 4 x y + 4 y , 5 z + 4 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=108.5MB, alloc=60.3MB, time=1.99 N2 := 491 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 2 2 2 2 10 z + 8 x, -x - 4 x y - 4 y , -4 x + 14 x - 9 z, -4 x + 16 y z + 11 x] > J:=[op(GB),op(G)]; 2 2 2 2 2 J := [x + 4 x y + 4 y , 5 z + 4 x, -4 x + 14 x - 9 z, -4 x + 16 y z + 11 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [4, 9, 8, 2, 2, 2, 2, 1, 1/2, 3/4, 7/11, 3/11, 3/11, 4, 9, 8, 2, 2, 2, 2, 1, 1/2, 3/4, 7/11, 3/11, 3/11, 0, 0, 0] > save(F, G, cat("ranSet/32", convert(F, string),".txt")); > quit memory used=144.7MB, alloc=60.3MB, time=2.70