|\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428239514 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 F := [-14 z + 7 x, -4 x y z - 8 x , 13 x y + 19 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 4 2 G := [13 y z - 18 x , -3 x z - 13 y , -20 z - 12 x ] > Problem := [F,G]; 4 2 2 3 Problem := [[-14 z + 7 x, -4 x y z - 8 x , 13 x y + 19 x z], 3 3 2 3 4 2 [13 y z - 18 x , -3 x z - 13 y , -20 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=4.3MB, alloc=32.3MB, time=0.18 memory used=27.0MB, alloc=32.3MB, time=0.53 memory used=48.5MB, alloc=32.3MB, time=0.85 memory used=68.8MB, alloc=56.3MB, time=1.18 memory used=111.1MB, alloc=60.3MB, time=1.81 memory used=149.1MB, alloc=84.3MB, time=2.38 memory used=211.8MB, alloc=92.3MB, time=3.30 memory used=273.1MB, alloc=116.3MB, time=4.37 memory used=348.5MB, alloc=116.3MB, time=5.51 memory used=414.9MB, alloc=372.3MB, time=6.54 memory used=500.9MB, alloc=396.3MB, time=7.90 memory used=606.9MB, alloc=420.3MB, time=9.50 memory used=733.6MB, alloc=444.3MB, time=11.50 memory used=877.5MB, alloc=468.3MB, time=13.91 memory used=998.6MB, alloc=468.3MB, time=15.88 memory used=1130.3MB, alloc=492.3MB, time=18.05 memory used=1261.2MB, alloc=492.3MB, time=20.23 memory used=1370.1MB, alloc=516.3MB, time=22.03 memory used=1471.4MB, alloc=516.3MB, time=23.75 memory used=1580.9MB, alloc=516.3MB, time=25.70 memory used=1668.3MB, alloc=540.3MB, time=27.25 memory used=1737.5MB, alloc=540.3MB, time=28.32 memory used=1815.4MB, alloc=540.3MB, time=29.82 memory used=1897.8MB, alloc=540.3MB, time=31.44 memory used=1954.2MB, alloc=540.3MB, time=32.51 memory used=1996.5MB, alloc=540.3MB, time=33.30 memory used=2059.1MB, alloc=540.3MB, time=34.70 memory used=2279.9MB, alloc=564.3MB, time=38.23 memory used=2499.9MB, alloc=588.3MB, time=41.93 memory used=2685.2MB, alloc=612.3MB, time=44.97 memory used=2910.3MB, alloc=636.3MB, time=49.45 memory used=3065.5MB, alloc=660.3MB, time=52.36 memory used=3241.5MB, alloc=684.3MB, time=55.78 memory used=3355.4MB, alloc=684.3MB, time=58.38 memory used=3483.8MB, alloc=684.3MB, time=61.16 memory used=3589.5MB, alloc=684.3MB, time=63.50 memory used=3715.1MB, alloc=684.3MB, time=66.45 memory used=3821.7MB, alloc=684.3MB, time=69.22 memory used=3899.6MB, alloc=684.3MB, time=71.43 memory used=4230.7MB, alloc=708.3MB, time=77.75 memory used=4577.5MB, alloc=732.3MB, time=84.46 memory used=4945.6MB, alloc=756.3MB, time=92.06 memory used=5326.5MB, alloc=780.3MB, time=100.62 memory used=5677.2MB, alloc=804.3MB, time=108.50 memory used=5999.7MB, alloc=828.3MB, time=115.75 memory used=6348.0MB, alloc=852.3MB, time=123.81 memory used=6652.1MB, alloc=876.3MB, time=131.02 memory used=6883.4MB, alloc=900.3MB, time=136.53 memory used=7106.4MB, alloc=924.3MB, time=142.30 memory used=7326.0MB, alloc=948.3MB, time=147.45 memory used=7508.1MB, alloc=972.3MB, time=152.23 memory used=7668.8MB, alloc=996.3MB, time=157.06 memory used=8250.9MB, alloc=1020.3MB, time=169.72 memory used=8838.7MB, alloc=1044.3MB, time=182.79 memory used=9443.8MB, alloc=1068.3MB, time=195.98 memory used=9960.6MB, alloc=1092.3MB, time=209.10 memory used=10418.2MB, alloc=1116.3MB, time=221.41 memory used=10953.4MB, alloc=1140.3MB, time=233.51 memory used=11555.9MB, alloc=1164.3MB, time=244.31 |\^/| 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(); 1428239814 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [-9 y - 12 y z, 3 x y z + 13 z , -6 y z + 14] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 G := [-2 y z + 10, -20 z - 5 z , 14 x y + 3 x z] > Problem := [F,G]; 2 2 3 2 2 Problem := [[-9 y - 12 y z, 3 x y z + 13 z , -6 y z + 14], 3 3 2 3 [-2 y z + 10, -20 z - 5 z , 14 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=0.18 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=47.8MB, alloc=32.3MB, time=0.80 memory used=68.4MB, alloc=32.3MB, time=1.11 memory used=87.1MB, alloc=56.3MB, time=1.41 memory used=125.0MB, alloc=60.3MB, time=2.00 memory used=159.4MB, alloc=84.3MB, time=2.53 memory used=214.5MB, alloc=84.3MB, time=3.39 memory used=268.7MB, alloc=84.3MB, time=4.24 memory used=322.8MB, alloc=84.3MB, time=5.10 memory used=375.8MB, alloc=108.3MB, time=5.96 memory used=450.5MB, alloc=116.3MB, time=7.20 memory used=522.7MB, alloc=116.3MB, time=8.39 memory used=593.6MB, alloc=140.3MB, time=9.58 memory used=684.4MB, alloc=140.3MB, time=11.09 memory used=771.5MB, alloc=164.3MB, time=12.60 memory used=879.2MB, alloc=188.3MB, time=14.47 memory used=974.9MB, alloc=444.3MB, time=16.13 memory used=1099.4MB, alloc=468.3MB, time=18.30 memory used=1244.3MB, alloc=492.3MB, time=21.04 memory used=1404.5MB, alloc=516.3MB, time=23.82 memory used=1570.7MB, alloc=540.3MB, time=26.98 memory used=1745.0MB, alloc=564.3MB, time=30.41 memory used=1926.5MB, alloc=588.3MB, time=33.92 memory used=2116.9MB, alloc=612.3MB, time=37.70 memory used=2313.0MB, alloc=636.3MB, time=41.63 memory used=2522.0MB, alloc=660.3MB, time=45.75 memory used=2753.4MB, alloc=684.3MB, time=49.70 memory used=2970.0MB, alloc=708.3MB, time=54.23 memory used=3186.1MB, alloc=732.3MB, time=58.88 memory used=3386.3MB, alloc=756.3MB, time=65.33 memory used=3583.6MB, alloc=780.3MB, time=72.51 memory used=3788.0MB, alloc=804.3MB, time=80.38 memory used=4002.3MB, alloc=828.3MB, time=88.94 memory used=4227.5MB, alloc=852.3MB, time=98.00 memory used=4464.9MB, alloc=876.3MB, time=108.00 memory used=4715.1MB, alloc=900.3MB, time=118.66 memory used=4978.3MB, alloc=924.3MB, time=129.97 memory used=5253.9MB, alloc=948.3MB, time=142.05 memory used=5544.9MB, alloc=972.3MB, time=154.80 memory used=5851.2MB, alloc=996.3MB, time=168.08 memory used=6173.6MB, alloc=1020.3MB, time=182.23 memory used=6509.3MB, alloc=1044.3MB, time=197.54 |\^/| 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(); 1428240114 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 F := [10 x y z + 3 y , 8 x y - 8 x, -6 x z + 16 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [4 x y + 11 y, -16 y - 9 y z , -16 x y ] > Problem := [F,G]; 2 3 2 2 2 2 Problem := [[10 x y z + 3 y , 8 x y - 8 x, -6 x z + 16 x y z], 3 2 2 2 [4 x y + 11 y, -16 y - 9 y z , -16 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.55 N1 := 209 > GB := Basis(F, plex(op(vars))); 2 2 3 GB := [27 x + 640 x, 640 x y + 27 x, 409600 y - 729 x y, 9 x y + 80 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=48.1MB, alloc=32.3MB, time=0.93 N2 := 75 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 2 2 H := [10 x y z + 3 y , 8 x y - 8 x, -6 x z + 16 x y z, 4 x y + 11 y, 3 2 2 2 -16 y - 9 y z , -16 x y ] > J:=[op(GB),op(G)]; 2 2 3 J := [27 x + 640 x, 640 x y + 27 x, 409600 y - 729 x y, 9 x y + 80 x z, 3 2 2 2 4 x y + 11 y, -16 y - 9 y z , -16 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 := [6, 14, 21, 4, 2, 3, 2, 5/6, 1, 1/2, 7/13, 9/13, 4/13, 7, 14, 19, 4, 2, 3, 2, 6/7, 6/7, 2/7, 3/5, 3/5, 2/15, 0, 2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=61.3MB, alloc=32.3MB, time=1.13 |\^/| 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(); 1428240116 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 3 4 2 2 F := [10 x y z + 13 y z , -12 z + 9 y , -20 x - 19 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 3 G := [20 y + 3 z , -19 x y z - 13 y z , -17 x + 4 y ] > Problem := [F,G]; 2 3 4 3 4 2 2 Problem := [[10 x y z + 13 y z , -12 z + 9 y , -20 x - 19 x z ], 2 2 2 2 3 3 [20 y + 3 z , -19 x y z - 13 y z , -17 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=0.52 memory used=48.3MB, alloc=32.3MB, time=0.84 memory used=68.4MB, alloc=32.3MB, time=1.14 memory used=88.5MB, alloc=60.3MB, time=1.44 memory used=129.5MB, alloc=60.3MB, time=2.06 memory used=167.6MB, alloc=84.3MB, time=2.64 memory used=209.3MB, alloc=84.3MB, time=3.27 memory used=267.9MB, alloc=116.3MB, time=4.22 memory used=342.7MB, alloc=372.3MB, time=5.42 memory used=420.6MB, alloc=396.3MB, time=6.71 memory used=514.7MB, alloc=420.3MB, time=8.52 memory used=627.2MB, alloc=444.3MB, time=10.61 memory used=751.3MB, alloc=468.3MB, time=13.02 memory used=877.8MB, alloc=492.3MB, time=16.67 memory used=1009.3MB, alloc=516.3MB, time=21.39 memory used=1155.4MB, alloc=540.3MB, time=27.15 memory used=1325.4MB, alloc=564.3MB, time=33.95 memory used=1519.4MB, alloc=564.3MB, time=41.52 memory used=1713.4MB, alloc=588.3MB, time=49.12 N1 := 5785 > GB := Basis(F, plex(op(vars))); 10 6 6 2 3 4 4 9 8 GB := [x , y x , -1600 x + 1083 x y , 8000 x y + 9633 y , 10 x + 13 x z, 5 4 4 2 2 2 3 4 3 10 x y + 13 x y z, 20 x + 19 x z , 10 x y z + 13 y z , 4 z - 3 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1939.0MB, alloc=588.3MB, time=55.57 memory used=2105.1MB, alloc=588.3MB, time=58.49 memory used=2258.9MB, alloc=588.3MB, time=61.12 memory used=2415.9MB, alloc=588.3MB, time=63.93 memory used=2585.7MB, alloc=612.3MB, time=67.45 memory used=2842.9MB, alloc=636.3MB, time=72.92 memory used=3102.0MB, alloc=660.3MB, time=80.50 memory used=3334.0MB, alloc=684.3MB, time=90.27 memory used=3575.1MB, alloc=708.3MB, time=101.07 |\^/| 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(); 1428240417 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [-12 x y - 16 z, 8 y z + 6 x y, 6 x z + 13 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 G := [3 x y z - 3 x z, 11 x y - 13 x , 13 x y z + 14 x z ] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[-12 x y - 16 z, 8 y z + 6 x y, 6 x z + 13 y z ], 2 2 3 2 2 3 [3 x y z - 3 x z, 11 x y - 13 x , 13 x y z + 14 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=77.1MB, alloc=68.3MB, time=1.30 memory used=124.5MB, alloc=68.3MB, time=2.02 memory used=169.9MB, alloc=68.3MB, time=2.71 memory used=214.8MB, alloc=92.3MB, time=3.40 memory used=281.4MB, alloc=100.3MB, time=4.44 memory used=345.6MB, alloc=124.3MB, time=5.41 memory used=431.5MB, alloc=148.3MB, time=6.91 memory used=534.1MB, alloc=172.3MB, time=8.86 memory used=648.0MB, alloc=196.3MB, time=12.80 N1 := 2167 > GB := Basis(F, plex(op(vars))); 9 2 2 3 GB := [5832 x y - 371293 x y, 6 x y + 13 x y , -9 x y + 26 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=777.0MB, alloc=196.3MB, time=16.46 N2 := 671 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 2 H := [-12 x y - 16 z, 8 y z + 6 x y, 6 x z + 13 y z , 3 x y z - 3 x z, 3 2 2 3 11 x y - 13 x , 13 x y z + 14 x z ] > J:=[op(GB),op(G)]; 9 2 2 3 J := [5832 x y - 371293 x y, 6 x y + 13 x y , -9 x y + 26 z, 2 2 3 2 2 3 3 x y z - 3 x z, 11 x y - 13 x , 13 x y z + 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 := [6, 17, 23, 4, 3, 2, 3, 1, 1, 5/6, 3/4, 7/12, 2/3, 6, 15, 29, 10, 9, 2, 3, 1, 1, 1/2, 11/12, 2/3, 5/12, 2, -6, -6] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=835.8MB, alloc=196.3MB, time=17.80 |\^/| 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(); 1428240471 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 2 F := [-6 x z - 12 y z, -17 z + 8, -2 z + 20 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 4 3 G := [-13 x + 4 x z , -11 x y + 11 y , -3 z + 14 y ] > Problem := [F,G]; 2 2 4 3 2 Problem := [[-6 x z - 12 y z, -17 z + 8, -2 z + 20 x ], 3 2 2 2 4 4 3 [-13 x + 4 x z , -11 x y + 11 y , -3 z + 14 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=27.0MB, alloc=32.3MB, time=0.53 memory used=48.5MB, alloc=32.3MB, time=0.85 memory used=68.9MB, alloc=32.3MB, time=1.17 memory used=88.4MB, alloc=56.3MB, time=1.50 memory used=128.0MB, alloc=60.3MB, time=2.12 memory used=164.2MB, alloc=84.3MB, time=2.71 memory used=203.6MB, alloc=84.3MB, time=3.31 memory used=262.5MB, alloc=92.3MB, time=4.27 memory used=322.1MB, alloc=116.3MB, time=5.20 memory used=401.5MB, alloc=116.3MB, time=6.45 memory used=479.3MB, alloc=140.3MB, time=7.68 memory used=548.7MB, alloc=140.3MB, time=8.76 memory used=613.7MB, alloc=420.3MB, time=9.76 memory used=740.0MB, alloc=444.3MB, time=11.49 memory used=877.1MB, alloc=468.3MB, time=13.58 memory used=1042.7MB, alloc=492.3MB, time=16.61 memory used=1203.0MB, alloc=516.3MB, time=19.87 memory used=1371.7MB, alloc=540.3MB, time=23.31 memory used=1548.0MB, alloc=564.3MB, time=26.90 memory used=1746.9MB, alloc=588.3MB, time=30.47 memory used=1941.5MB, alloc=612.3MB, time=34.46 memory used=2139.3MB, alloc=636.3MB, time=38.77 memory used=2331.2MB, alloc=660.3MB, time=43.72 memory used=2502.7MB, alloc=684.3MB, time=49.58 memory used=2680.3MB, alloc=708.3MB, time=56.27 memory used=2867.8MB, alloc=732.3MB, time=63.54 memory used=3066.8MB, alloc=756.3MB, time=71.41 memory used=3278.1MB, alloc=780.3MB, time=79.90 memory used=3502.5MB, alloc=804.3MB, time=88.98 memory used=3740.8MB, alloc=828.3MB, time=98.80 |\^/| 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(); 1428240771 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 4 2 2 2 F := [19 x y z + 11 x , -x y z + 7 z , -14 x y z - 9 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 G := [8 x + 1, -14 y z - 16 z , -10 y z - 3 z ] > Problem := [F,G]; 2 3 2 4 2 2 2 Problem := [[19 x y z + 11 x , -x y z + 7 z , -14 x y z - 9 y z ], 2 3 2 2 2 2 [8 x + 1, -14 y z - 16 z , -10 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=26.2MB, alloc=32.3MB, time=0.49 memory used=47.8MB, alloc=32.3MB, time=0.80 memory used=68.3MB, alloc=32.3MB, time=1.11 memory used=87.6MB, alloc=56.3MB, time=1.41 memory used=127.3MB, alloc=60.3MB, time=2.00 memory used=164.1MB, alloc=84.3MB, time=2.56 memory used=222.9MB, alloc=84.3MB, time=3.59 memory used=279.3MB, alloc=108.3MB, time=4.59 memory used=355.5MB, alloc=140.3MB, time=5.97 memory used=442.2MB, alloc=164.3MB, time=8.09 memory used=532.9MB, alloc=188.3MB, time=11.51 memory used=644.9MB, alloc=212.3MB, time=15.86 N1 := 3437 > GB := Basis(F, plex(op(vars))); 5 4 4 4 3 2 4 GB := [364952 x - 8019 x , 266 x y - 99 x , 171 x y - 1078 x , 4 4 2 3 2 2 2 26068 x z + 891 x , 19 x y z + 11 x , 14 x y z + 9 y z , 3 3 4 2 4 48538616 x z + 88209 x , -x y z + 7 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=782.8MB, alloc=212.3MB, time=20.83 memory used=902.7MB, alloc=468.3MB, time=22.68 memory used=1052.9MB, alloc=468.3MB, time=25.15 memory used=1199.2MB, alloc=492.3MB, time=27.54 memory used=1366.6MB, alloc=516.3MB, time=30.25 memory used=1543.9MB, alloc=540.3MB, time=33.18 memory used=1723.9MB, alloc=564.3MB, time=36.18 memory used=1884.2MB, alloc=564.3MB, time=38.86 memory used=2048.8MB, alloc=588.3MB, time=41.66 memory used=2191.3MB, alloc=588.3MB, time=44.09 memory used=2322.1MB, alloc=612.3MB, time=46.44 memory used=2450.5MB, alloc=612.3MB, time=48.50 memory used=2565.9MB, alloc=636.3MB, time=50.48 memory used=2671.3MB, alloc=636.3MB, time=52.31 memory used=2778.6MB, alloc=660.3MB, time=54.64 memory used=2916.4MB, alloc=660.3MB, time=57.60 memory used=3065.4MB, alloc=684.3MB, time=60.78 memory used=3232.5MB, alloc=708.3MB, time=64.36 memory used=3369.6MB, alloc=732.3MB, time=67.36 memory used=3516.0MB, alloc=756.3MB, time=70.50 memory used=3646.0MB, alloc=780.3MB, time=73.46 memory used=3777.9MB, alloc=804.3MB, time=76.45 memory used=3922.5MB, alloc=828.3MB, time=79.71 memory used=4036.8MB, alloc=852.3MB, time=82.47 memory used=4159.5MB, alloc=876.3MB, time=85.41 memory used=4247.9MB, alloc=900.3MB, time=87.78 memory used=4366.6MB, alloc=924.3MB, time=91.85 |\^/| 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(); 1428241071 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 F := [-14 y + 3, -5 y z - z , -11 x y - 15 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 G := [4 x - 2 z, 9 y z - 11 x y, 17 x y - 12 y ] > Problem := [F,G]; 4 2 2 Problem := [[-14 y + 3, -5 y z - z , -11 x y - 15 x], 2 2 2 4 [4 x - 2 z, 9 y z - 11 x y, 17 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=0.19 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=47.4MB, alloc=32.3MB, time=0.80 memory used=67.3MB, alloc=32.3MB, time=1.08 memory used=87.4MB, alloc=56.3MB, time=1.44 memory used=128.6MB, alloc=60.3MB, time=2.21 memory used=164.8MB, alloc=84.3MB, time=2.89 memory used=220.3MB, alloc=108.3MB, time=3.92 memory used=292.0MB, alloc=140.3MB, time=5.69 memory used=373.4MB, alloc=164.3MB, time=8.60 memory used=473.5MB, alloc=164.3MB, time=12.53 memory used=573.7MB, alloc=188.3MB, time=16.38 N1 := 3247 > GB := Basis(F, plex(op(vars))); 4 2 GB := [x, 14 y - 3, 5 y z + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=699.0MB, alloc=188.3MB, time=19.12 memory used=836.4MB, alloc=212.3MB, time=21.97 memory used=973.3MB, alloc=236.3MB, time=27.10 N2 := 2993 #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)]; 4 2 2 2 H := [-14 y + 3, -5 y z - z , -11 x y - 15 x, 4 x - 2 z, 9 y z - 11 x y, 2 2 4 17 x y - 12 y ] > J:=[op(GB),op(G)]; 4 2 2 2 2 4 J := [x, 14 y - 3, 5 y z + z , 4 x - 2 z, 9 y z - 11 x y, 17 x 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 := [6, 12, 17, 4, 2, 4, 2, 2/3, 5/6, 1/2, 5/12, 7/12, 1/3, 6, 11, 15, 4, 2, 4, 2, 2/3, 2/3, 1/2, 4/11, 6/11, 4/11, 1, 2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1117.9MB, alloc=236.3MB, time=32.72 |\^/| 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(); 1428241190 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-8 x z - 13 y , -2 y z - 12 y z, 12 x + 7 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [9 x y z - 4 z , -11 x y - 16 x y z, 17 x z - 13 y z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-8 x z - 13 y , -2 y z - 12 y z, 12 x + 7 x z], 2 2 2 2 2 [9 x y z - 4 z , -11 x y - 16 x y z, 17 x z - 13 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=48.0MB, alloc=32.3MB, time=0.82 memory used=68.1MB, alloc=32.3MB, time=1.13 memory used=87.0MB, alloc=56.3MB, time=1.44 memory used=126.8MB, alloc=60.3MB, time=2.08 memory used=164.8MB, alloc=84.3MB, time=2.68 memory used=221.5MB, alloc=84.3MB, time=3.59 memory used=275.7MB, alloc=116.3MB, time=4.50 memory used=351.4MB, alloc=116.3MB, time=5.78 memory used=422.5MB, alloc=140.3MB, time=7.10 memory used=508.0MB, alloc=164.3MB, time=8.62 memory used=608.8MB, alloc=188.3MB, time=10.43 memory used=720.8MB, alloc=468.3MB, time=12.48 memory used=847.7MB, alloc=492.3MB, time=14.82 memory used=985.1MB, alloc=516.3MB, time=17.34 memory used=1127.0MB, alloc=540.3MB, time=21.34 memory used=1272.7MB, alloc=564.3MB, time=26.16 memory used=1429.9MB, alloc=588.3MB, time=31.62 memory used=1600.6MB, alloc=612.3MB, time=37.89 memory used=1780.2MB, alloc=636.3MB, time=45.45 memory used=1983.7MB, alloc=660.3MB, time=54.04 memory used=2211.2MB, alloc=684.3MB, time=63.58 memory used=2462.6MB, alloc=708.3MB, time=74.01 memory used=2737.9MB, alloc=732.3MB, time=85.51 |\^/| 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(); 1428241490 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 3 4 F := [3 x y - 10 x y z, -2 y z + 7 x , 9 x z + 11 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 3 G := [8 x + 12 z , 13 y z - 10 z , -2 y - 13 z] > Problem := [F,G]; 2 2 2 3 3 3 4 Problem := [[3 x y - 10 x y z, -2 y z + 7 x , 9 x z + 11 z ], 3 2 2 2 4 3 [8 x + 12 z , 13 y z - 10 z , -2 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=0.17 memory used=26.6MB, alloc=32.3MB, time=0.48 memory used=47.9MB, alloc=32.3MB, time=0.79 memory used=68.1MB, alloc=32.3MB, time=1.08 memory used=87.5MB, alloc=56.3MB, time=1.39 memory used=127.6MB, alloc=60.3MB, time=1.98 memory used=165.1MB, alloc=60.3MB, time=2.53 memory used=202.2MB, alloc=84.3MB, time=3.08 memory used=262.6MB, alloc=92.3MB, time=3.98 memory used=318.4MB, alloc=116.3MB, time=4.81 memory used=396.4MB, alloc=116.3MB, time=5.95 memory used=475.2MB, alloc=116.3MB, time=7.08 memory used=551.8MB, alloc=140.3MB, time=8.24 memory used=636.6MB, alloc=396.3MB, time=9.56 memory used=735.3MB, alloc=420.3MB, time=11.03 memory used=874.2MB, alloc=444.3MB, time=12.60 memory used=1025.1MB, alloc=468.3MB, time=14.58 memory used=1181.1MB, alloc=492.3MB, time=16.96 memory used=1316.1MB, alloc=492.3MB, time=18.96 memory used=1428.9MB, alloc=516.3MB, time=20.30 memory used=1549.1MB, alloc=516.3MB, time=21.96 memory used=1685.0MB, alloc=540.3MB, time=24.31 memory used=1783.1MB, alloc=540.3MB, time=26.00 memory used=1889.6MB, alloc=540.3MB, time=27.83 memory used=2014.7MB, alloc=564.3MB, time=30.04 memory used=2122.7MB, alloc=564.3MB, time=31.95 memory used=2218.1MB, alloc=564.3MB, time=33.68 memory used=2302.2MB, alloc=564.3MB, time=35.29 memory used=2384.4MB, alloc=588.3MB, time=36.76 memory used=2471.2MB, alloc=588.3MB, time=38.54 memory used=2538.4MB, alloc=588.3MB, time=39.73 memory used=2600.0MB, alloc=588.3MB, time=40.75 memory used=2657.8MB, alloc=588.3MB, time=41.97 memory used=2720.0MB, alloc=588.3MB, time=43.33 memory used=2958.4MB, alloc=612.3MB, time=47.23 memory used=3168.4MB, alloc=636.3MB, time=50.48 memory used=3418.1MB, alloc=660.3MB, time=54.75 memory used=3657.1MB, alloc=684.3MB, time=59.29 memory used=3941.5MB, alloc=708.3MB, time=65.33 memory used=4217.0MB, alloc=732.3MB, time=71.24 memory used=4491.8MB, alloc=756.3MB, time=77.23 memory used=4764.4MB, alloc=780.3MB, time=83.44 memory used=5036.3MB, alloc=804.3MB, time=89.52 memory used=5310.2MB, alloc=828.3MB, time=95.87 |\^/| 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(); 1428241790 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 2 4 F := [-17 x z + 7 y , 10 x z - 16 z , -13 y + 3] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 3 2 3 G := [9 x + 12 x , -3 x - 2 y z , -14 x y z + 8 z ] > Problem := [F,G]; 2 2 4 3 2 4 Problem := [[-17 x z + 7 y , 10 x z - 16 z , -13 y + 3], 4 2 4 3 2 3 [9 x + 12 x , -3 x - 2 y z , -14 x y z + 8 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=48.2MB, alloc=32.3MB, time=0.83 memory used=69.1MB, alloc=32.3MB, time=1.16 memory used=89.6MB, alloc=56.3MB, time=1.49 memory used=130.2MB, alloc=60.3MB, time=2.11 memory used=169.2MB, alloc=60.3MB, time=2.70 memory used=207.1MB, alloc=84.3MB, time=3.28 memory used=268.2MB, alloc=92.3MB, time=4.15 memory used=330.7MB, alloc=92.3MB, time=5.01 memory used=390.4MB, alloc=116.3MB, time=5.88 memory used=478.4MB, alloc=140.3MB, time=7.26 memory used=577.8MB, alloc=164.3MB, time=9.00 memory used=694.5MB, alloc=188.3MB, time=11.08 memory used=819.7MB, alloc=444.3MB, time=13.21 memory used=949.4MB, alloc=468.3MB, time=15.39 memory used=1098.4MB, alloc=492.3MB, time=17.86 memory used=1256.3MB, alloc=516.3MB, time=20.73 memory used=1424.9MB, alloc=540.3MB, time=24.13 memory used=1583.2MB, alloc=564.3MB, time=28.97 memory used=1746.6MB, alloc=588.3MB, time=34.68 memory used=1922.0MB, alloc=612.3MB, time=40.96 memory used=2107.4MB, alloc=636.3MB, time=48.37 memory used=2311.6MB, alloc=660.3MB, time=57.03 memory used=2539.7MB, alloc=684.3MB, time=66.57 memory used=2791.8MB, alloc=708.3MB, time=76.94 memory used=3067.9MB, alloc=708.3MB, time=88.30 memory used=3343.8MB, alloc=732.3MB, time=99.71 |\^/| 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(); 1428242090 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 F := [-11 x y z - 12 x y , -15 x y z - 15 z , 17 y z - 3 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 2 G := [2 y z + 14, x z + 5 x y , -x y + 10 y z] > Problem := [F,G]; 2 2 2 3 2 3 Problem := [[-11 x y z - 12 x y , -15 x y z - 15 z , 17 y z - 3 z ], 2 2 2 3 2 2 2 [2 y z + 14, x z + 5 x y , -x 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=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=47.9MB, alloc=32.3MB, time=0.81 memory used=67.8MB, alloc=56.3MB, time=1.11 memory used=108.6MB, alloc=60.3MB, time=1.72 memory used=148.2MB, alloc=60.3MB, time=2.27 memory used=184.8MB, alloc=84.3MB, time=2.83 memory used=234.4MB, alloc=84.3MB, time=3.60 memory used=296.6MB, alloc=116.3MB, time=4.48 memory used=373.2MB, alloc=372.3MB, time=5.64 memory used=457.6MB, alloc=396.3MB, time=6.84 memory used=556.6MB, alloc=420.3MB, time=8.40 memory used=687.9MB, alloc=444.3MB, time=10.21 memory used=830.5MB, alloc=468.3MB, time=12.54 memory used=971.3MB, alloc=468.3MB, time=14.92 memory used=1100.8MB, alloc=492.3MB, time=17.11 memory used=1210.7MB, alloc=492.3MB, time=18.96 memory used=1310.7MB, alloc=516.3MB, time=20.69 memory used=1399.8MB, alloc=516.3MB, time=22.34 memory used=1499.1MB, alloc=516.3MB, time=24.17 memory used=1603.1MB, alloc=516.3MB, time=26.17 memory used=1684.1MB, alloc=540.3MB, time=27.79 memory used=1755.9MB, alloc=540.3MB, time=29.36 memory used=1822.0MB, alloc=540.3MB, time=30.64 memory used=1895.5MB, alloc=540.3MB, time=32.27 memory used=1953.2MB, alloc=540.3MB, time=33.53 memory used=2003.6MB, alloc=540.3MB, time=34.74 memory used=2208.1MB, alloc=564.3MB, time=38.36 memory used=2425.7MB, alloc=588.3MB, time=42.39 memory used=2637.2MB, alloc=612.3MB, time=46.63 memory used=2851.6MB, alloc=636.3MB, time=51.09 memory used=3070.5MB, alloc=660.3MB, time=55.70 memory used=3294.3MB, alloc=684.3MB, time=60.46 memory used=3540.1MB, alloc=708.3MB, time=65.35 memory used=3798.9MB, alloc=732.3MB, time=70.22 memory used=4042.0MB, alloc=756.3MB, time=75.64 memory used=4289.9MB, alloc=780.3MB, time=82.12 memory used=4504.3MB, alloc=804.3MB, time=90.31 memory used=4720.8MB, alloc=828.3MB, time=98.94 memory used=4945.5MB, alloc=852.3MB, time=108.35 |\^/| 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(); 1428242390 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 3 2 F := [-15 z + 8 y z, 15 z , 14 x y + 3 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 G := [17 x + 13 y, 3 x + 5, 8 x + 20 y] > Problem := [F,G]; 4 2 3 3 2 Problem := [[-15 z + 8 y z, 15 z , 14 x y + 3 x y z], 4 3 3 [17 x + 13 y, 3 x + 5, 8 x + 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=0.18 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=49.2MB, alloc=32.3MB, time=0.88 memory used=68.7MB, alloc=56.3MB, time=1.26 N1 := 657 > GB := Basis(F, plex(op(vars))); 3 2 3 GB := [x y , z y , z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 129 #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)]; 4 2 3 3 2 4 3 H := [-15 z + 8 y z, 15 z , 14 x y + 3 x y z, 17 x + 13 y, 3 x + 5, 3 8 x + 20 y] > J:=[op(GB),op(G)]; 3 2 3 4 3 3 J := [x y , z y , z , 17 x + 13 y, 3 x + 5, 8 x + 20 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, 11, 21, 4, 4, 3, 4, 2/3, 2/3, 1/2, 5/12, 5/12, 1/3, 6, 10, 20, 4, 4, 3, 3, 2/3, 2/3, 1/3, 1/3, 1/3, 1/6, 1, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=99.5MB, alloc=56.3MB, time=1.89 |\^/| 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(); 1428242396 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 3 2 F := [-4 y - 4 x z , -2 x z + 12 x z, 8 x z - 5 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 4 2 G := [-14 x y z - 2 x y , -14 z - 4 y, -z + 8 y z ] > Problem := [F,G]; 4 2 3 2 3 2 Problem := [[-4 y - 4 x z , -2 x z + 12 x z, 8 x z - 5 x z], 2 3 2 4 2 [-14 x y z - 2 x y , -14 z - 4 y, -z + 8 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.47 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=70.2MB, alloc=56.3MB, time=1.21 memory used=113.3MB, alloc=60.3MB, time=1.97 memory used=151.4MB, alloc=84.3MB, time=3.03 N1 := 1085 > GB := Basis(F, plex(op(vars))); 4 8 2 4 2 GB := [x y , y , x z, y + z x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=208.0MB, alloc=84.3MB, time=4.15 N2 := 729 #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)]; 4 2 3 2 3 2 2 3 H := [-4 y - 4 x z , -2 x z + 12 x z, 8 x z - 5 x z, -14 x y z - 2 x y , 2 4 2 -14 z - 4 y, -z + 8 y z ] > J:=[op(GB),op(G)]; J := [ 4 8 2 4 2 2 3 2 4 2 x y , y , x z, y + z x, -14 x y z - 2 x y , -14 z - 4 y, -z + 8 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 := [6, 14, 22, 4, 3, 4, 4, 2/3, 2/3, 1, 7/12, 5/12, 3/4, 7, 15, 30, 8, 2, 8, 4, 4/7, 6/7, 5/7, 5/14, 1/2, 3/7, -1, -8, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=266.4MB, alloc=84.3MB, time=5.34 |\^/| 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(); 1428242416 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 2 F := [-4 y z - 13 z , 2 y - 7 z , -5 x y z + 3 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 G := [-4 y z - 3 x z, -20 y + 3 x z, -17 x y - 15 x y z] > Problem := [F,G]; 2 2 3 3 2 2 Problem := [[-4 y z - 13 z , 2 y - 7 z , -5 x y z + 3 x y ], 3 2 3 3 [-4 y z - 3 x z, -20 y + 3 x z, -17 x y - 15 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.78 memory used=68.0MB, alloc=32.3MB, time=1.08 memory used=87.5MB, alloc=56.3MB, time=1.38 memory used=126.3MB, alloc=60.3MB, time=1.96 memory used=164.9MB, alloc=60.3MB, time=2.53 memory used=201.6MB, alloc=84.3MB, time=3.08 memory used=257.8MB, alloc=92.3MB, time=3.94 memory used=313.5MB, alloc=116.3MB, time=4.81 memory used=391.9MB, alloc=140.3MB, time=6.24 memory used=485.3MB, alloc=164.3MB, time=7.92 memory used=593.9MB, alloc=188.3MB, time=9.94 memory used=713.1MB, alloc=212.3MB, time=12.71 memory used=833.0MB, alloc=236.3MB, time=16.42 memory used=960.4MB, alloc=260.3MB, time=21.40 memory used=1110.7MB, alloc=284.3MB, time=27.31 memory used=1284.9MB, alloc=284.3MB, time=34.24 memory used=1459.2MB, alloc=308.3MB, time=41.25 memory used=1657.6MB, alloc=332.3MB, time=49.04 N1 := 5913 > GB := Basis(F, plex(op(vars))); 2 4 3 2 2 2 3 3 GB := [y x, 4 y + 13 y , x z , 4 y z + 13 z , -2 y + 7 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1848.1MB, alloc=332.3MB, time=54.79 memory used=2119.2MB, alloc=612.3MB, time=63.17 N2 := 2125 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 2 2 3 2 H := [-4 y z - 13 z , -7 z + 2 y , -5 x y z + 3 x y , -4 y z - 3 x z, 3 3 -20 y + 3 z x, -17 x y - 15 x y z] > J:=[op(GB),op(G)]; 2 4 3 2 2 2 3 3 3 2 J := [y x, 4 y + 13 y , x z , 4 y z + 13 z , -2 y + 7 z , -4 y z - 3 x z, 3 3 -20 y + 3 z x, -17 x y - 15 x 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 := [6, 16, 21, 4, 2, 3, 3, 2/3, 1, 1, 1/2, 2/3, 2/3, 8, 18, 27, 4, 2, 4, 3, 5/8, 7/8, 3/4, 3/8, 9/16, 1/2, -2, -6, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2132.9MB, alloc=612.3MB, time=63.70 |\^/| 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(); 1428242609 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [2 x z - 6 y, -19 x y, 5 - 7 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 3 G := [8 x + 15 y, -14 x + 6 x , -15 x y - 1] > Problem := [F,G]; 2 2 3 Problem := [[2 x z - 6 y, -19 x y, 5 - 7 y], 3 4 2 3 [8 x + 15 y, -14 x + 6 x , -15 x 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=4.2MB, alloc=32.3MB, time=0.17 memory used=27.4MB, alloc=32.3MB, time=0.56 memory used=48.9MB, alloc=56.3MB, time=0.95 N1 := 439 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 49 #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)]; H := [ 2 2 3 3 4 2 3 2 x z - 6 y, -19 y x , 5 - 7 y, 8 x + 15 y, -14 x + 6 x , -15 x y - 1] > J:=[op(GB),op(G)]; 3 4 2 3 J := [1, 8 x + 15 y, -14 x + 6 x , -15 x 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, 11, 20, 4, 4, 3, 2, 5/6, 5/6, 1/6, 6/13, 5/13, 1/13, 4, 5, 11, 4, 4, 3, 0, 3/4, 1/2, 0, 4/7, 2/7, 0, 6, 9, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=71.9MB, alloc=56.3MB, time=1.39 |\^/| 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(); 1428242613 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-2 x z + 4 x y , -14 y + 6 y z, 18 y z - 10 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 4 4 G := [7 x y + 12 y z , 11 y , -8 x + 5 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-2 x z + 4 x y , -14 y + 6 y z, 18 y z - 10 y z], 2 2 2 2 3 4 4 [7 x y + 12 y z , 11 y , -8 x + 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=47.7MB, alloc=32.3MB, time=0.81 memory used=67.8MB, alloc=32.3MB, time=1.12 memory used=87.2MB, alloc=56.3MB, time=1.43 memory used=129.4MB, alloc=60.3MB, time=2.13 memory used=168.4MB, alloc=84.3MB, time=2.85 memory used=227.3MB, alloc=84.3MB, time=3.92 memory used=280.9MB, alloc=108.3MB, time=4.87 memory used=349.9MB, alloc=140.3MB, time=6.44 memory used=427.1MB, alloc=164.3MB, time=9.05 memory used=523.6MB, alloc=164.3MB, time=12.59 memory used=620.1MB, alloc=188.3MB, time=16.14 N1 := 3383 > GB := Basis(F, plex(op(vars))); 2 2 2 3 2 2 2 2 GB := [49 x y - 10 x y , 21 y - 5 y , x z - 2 x y , -7 y + 3 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=743.3MB, alloc=188.3MB, time=19.27 memory used=888.1MB, alloc=212.3MB, time=22.60 N2 := 1409 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 2 H := [-2 x z + 4 x y , -14 y + 6 y z, 18 y z - 10 y z, 7 x y + 12 y z , 3 4 4 11 y , -8 x + 5 z ] > J:=[op(GB),op(G)]; 2 2 2 3 2 2 2 2 J := [49 x y - 10 x y , 21 y - 5 y , x z - 2 x y , -7 y + 3 y z, 2 2 2 2 3 4 4 7 x y + 12 y z , 11 y , -8 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 := [6, 13, 19, 4, 4, 3, 4, 1/2, 5/6, 5/6, 1/3, 2/3, 1/2, 7, 14, 23, 4, 4, 3, 4, 4/7, 6/7, 4/7, 3/7, 5/7, 2/7, -1, -4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=920.6MB, alloc=212.3MB, time=23.72 |\^/| 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(); 1428242681 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 2 3 F := [9 x z + 10 y z , -4 x - 19 y , x y + 15 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 2 G := [-6 x z - 4 x , -12 x y + 19 x z , -17 x y - z ] > Problem := [F,G]; 2 2 4 3 2 3 Problem := [[9 x z + 10 y z , -4 x - 19 y , x y + 15 y ], 3 3 2 2 3 2 [-6 x z - 4 x , -12 x y + 19 x z , -17 x y - z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.50 memory used=48.3MB, alloc=32.3MB, time=0.82 memory used=68.8MB, alloc=56.3MB, time=1.12 memory used=110.2MB, alloc=60.3MB, time=1.75 memory used=150.9MB, alloc=60.3MB, time=2.36 memory used=191.8MB, alloc=84.3MB, time=2.94 memory used=233.3MB, alloc=84.3MB, time=3.58 memory used=295.1MB, alloc=116.3MB, time=4.53 memory used=375.2MB, alloc=116.3MB, time=5.75 memory used=453.2MB, alloc=140.3MB, time=6.91 memory used=522.4MB, alloc=396.3MB, time=7.95 memory used=629.1MB, alloc=420.3MB, time=9.71 memory used=754.9MB, alloc=444.3MB, time=11.89 memory used=890.6MB, alloc=468.3MB, time=14.45 memory used=1039.9MB, alloc=492.3MB, time=17.23 memory used=1218.1MB, alloc=516.3MB, time=20.05 memory used=1408.1MB, alloc=540.3MB, time=23.30 memory used=1598.9MB, alloc=564.3MB, time=27.01 memory used=1799.1MB, alloc=588.3MB, time=30.85 memory used=1982.2MB, alloc=612.3MB, time=36.51 memory used=2165.5MB, alloc=636.3MB, time=42.85 memory used=2358.6MB, alloc=660.3MB, time=49.94 memory used=2564.6MB, alloc=684.3MB, time=57.69 memory used=2783.1MB, alloc=708.3MB, time=66.62 memory used=3011.9MB, alloc=732.3MB, time=76.70 memory used=3264.7MB, alloc=756.3MB, time=87.88 |\^/| 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(); 1428242981 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 F := [19 y z + 12, 8 x z - 20 y , 16 y + 15 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-11 x y z + 5 x z , -5 x y z - 10 x z, -4 x y + 8] > Problem := [F,G]; 2 2 3 4 Problem := [[19 y z + 12, 8 x z - 20 y , 16 y + 15 x], 2 2 2 [-11 x y z + 5 x z , -5 x y z - 10 x z, -4 x y + 8]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.47 memory used=47.3MB, alloc=32.3MB, time=0.76 memory used=68.2MB, alloc=32.3MB, time=1.06 memory used=88.0MB, alloc=56.3MB, time=1.37 memory used=127.9MB, alloc=60.3MB, time=1.96 memory used=169.1MB, alloc=84.3MB, time=2.69 memory used=227.9MB, alloc=84.3MB, time=3.75 memory used=281.4MB, alloc=108.3MB, time=4.75 memory used=352.9MB, alloc=140.3MB, time=6.09 memory used=439.7MB, alloc=164.3MB, time=8.08 memory used=533.1MB, alloc=188.3MB, time=11.09 memory used=638.6MB, alloc=212.3MB, time=15.26 memory used=768.2MB, alloc=212.3MB, time=20.31 memory used=897.7MB, alloc=236.3MB, time=25.43 memory used=1051.6MB, alloc=260.3MB, time=31.72 N1 := 4481 > GB := Basis(F, plex(op(vars))); 3 GB := [829275539111328125 x + 844424930131968, -45125 x + 8192 y, -21434375 x + 1048576 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1168.3MB, alloc=260.3MB, time=34.03 N2 := 1239 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 4 2 2 2 H := [19 z y + 12, 8 x z - 20 y , 16 y + 15 x, -11 x y z + 5 x z , -5 x y z - 10 x z, -4 x y + 8] > J:=[op(GB),op(G)]; 3 J := [829275539111328125 x + 844424930131968, -45125 x + 8192 y, 2 2 2 -21434375 x + 1048576 z, -11 x y z + 5 x z , -5 x y z - 10 x z, -4 x y + 8] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 19, 4, 2, 4, 2, 5/6, 1, 2/3, 7/12, 1/2, 1/2, 6, 13, 14, 4, 3, 1, 2, 1, 2/3, 1/2, 2/3, 1/3, 5/12, 2, 5, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1215.6MB, alloc=516.3MB, time=35.64 |\^/| 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(); 1428243097 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 4 2 F := [7 x - 5 y z , 9 x y z + 2 z , -20 x z - 18 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 3 G := [-7 x y z - 8 x , 19 x z - 7 y z , -18 x y - 10 x y] > Problem := [F,G]; 4 2 2 2 4 2 Problem := [[7 x - 5 y z , 9 x y z + 2 z , -20 x z - 18 z ], 2 2 2 2 2 2 3 [-7 x y z - 8 x , 19 x z - 7 y z , -18 x y - 10 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.78 memory used=68.3MB, alloc=32.3MB, time=1.09 memory used=88.4MB, alloc=56.3MB, time=1.40 memory used=128.7MB, alloc=60.3MB, time=1.99 memory used=166.2MB, alloc=84.3MB, time=2.54 memory used=216.0MB, alloc=84.3MB, time=3.38 memory used=274.0MB, alloc=116.3MB, time=4.46 memory used=350.7MB, alloc=140.3MB, time=5.86 memory used=445.9MB, alloc=164.3MB, time=7.65 memory used=557.2MB, alloc=188.3MB, time=9.68 memory used=682.8MB, alloc=212.3MB, time=11.98 memory used=796.0MB, alloc=492.3MB, time=14.41 memory used=932.7MB, alloc=516.3MB, time=18.50 memory used=1077.4MB, alloc=540.3MB, time=23.17 memory used=1229.5MB, alloc=564.3MB, time=29.21 memory used=1403.3MB, alloc=588.3MB, time=36.32 memory used=1601.1MB, alloc=612.3MB, time=44.43 memory used=1822.8MB, alloc=612.3MB, time=53.34 memory used=2044.5MB, alloc=612.3MB, time=62.33 memory used=2266.1MB, alloc=612.3MB, time=71.22 memory used=2487.7MB, alloc=636.3MB, time=80.26 memory used=2733.2MB, alloc=636.3MB, time=90.17 |\^/| 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(); 1428243397 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 3 F := [-2 x y + 17 x , 8 x y z - 13 x , 6 x z - 15 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 2 G := [16 y z + 9 y, 19 x + 11 y , -10 x + 3 x ] > Problem := [F,G]; 2 2 2 2 2 2 3 Problem := [[-2 x y + 17 x , 8 x y z - 13 x , 6 x z - 15 x ], 3 2 2 4 2 [16 y z + 9 y, 19 x + 11 y , -10 x + 3 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=48.4MB, alloc=32.3MB, time=0.82 memory used=70.0MB, alloc=56.3MB, time=1.19 memory used=114.7MB, alloc=60.3MB, time=1.98 memory used=154.0MB, alloc=84.3MB, time=2.88 N1 := 999 > GB := Basis(F, plex(op(vars))); 4 3 2 2 3 2 2 2 GB := [169 x - 835210 x , 2 x y - 17 x , -13 x + 578 x z, 8 x y z - 13 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=209.0MB, alloc=84.3MB, time=4.00 N2 := 623 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 3 3 H := [-2 x y + 17 x , 8 x y z - 13 x , 6 x z - 15 x , 16 y z + 9 y, 2 2 4 2 11 y + 19 x , -10 x + 3 x ] > J:=[op(GB),op(G)]; 4 3 2 2 3 2 2 2 J := [169 x - 835210 x , 2 x y - 17 x , -13 x + 578 x z, 8 x y z - 13 x , 3 2 2 4 2 16 y z + 9 y, 11 y + 19 x , -10 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, 12, 21, 4, 4, 2, 3, 5/6, 2/3, 1/2, 3/4, 5/12, 1/4, 7, 13, 24, 4, 4, 2, 3, 6/7, 4/7, 3/7, 11/14, 5/14, 3/14, -1, -3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=268.8MB, alloc=84.3MB, time=5.17 |\^/| 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(); 1428243413 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 F := [17 x - 19 x y z, -4 x + 3 y, -12 y + 14 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 3 2 G := [12 y z - 9 z , 15 x - 6 x y, 9 x y z - 2] > Problem := [F,G]; 3 2 3 Problem := [[17 x - 19 x y z, -4 x + 3 y, -12 y + 14 x], 2 3 4 3 2 [12 y z - 9 z , 15 x - 6 x y, 9 x y z - 2]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.81 memory used=67.9MB, alloc=32.3MB, time=1.10 memory used=87.5MB, alloc=56.3MB, time=1.41 memory used=130.5MB, alloc=60.3MB, time=2.17 memory used=168.0MB, alloc=84.3MB, time=2.85 memory used=225.6MB, alloc=84.3MB, time=3.87 memory used=277.6MB, alloc=108.3MB, time=4.85 memory used=347.6MB, alloc=140.3MB, time=6.23 memory used=430.7MB, alloc=164.3MB, time=8.62 memory used=526.0MB, alloc=188.3MB, time=12.03 memory used=639.8MB, alloc=188.3MB, time=16.42 memory used=753.5MB, alloc=188.3MB, time=20.99 memory used=867.2MB, alloc=212.3MB, time=25.59 N1 := 4375 > GB := Basis(F, plex(op(vars))); 6 2 GB := [128 x - 63 x, -4 x + 3 y, 76 x z - 51 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1006.9MB, alloc=212.3MB, time=30.56 memory used=1129.0MB, alloc=492.3MB, time=32.86 memory used=1302.4MB, alloc=516.3MB, time=37.41 memory used=1464.8MB, alloc=540.3MB, time=44.31 N2 := 3455 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 3 H := [17 x - 19 x y z, -4 x + 3 y, -12 y + 14 x, 12 y z - 9 z , 4 3 2 15 x - 6 x y, 9 z y x - 2] > J:=[op(GB),op(G)]; 6 2 2 3 4 3 J := [128 x - 63 x, -4 x + 3 y, 76 x z - 51 x, 12 y z - 9 z , 15 x - 6 x y, 2 9 z 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 := [6, 14, 19, 4, 4, 3, 3, 5/6, 1, 1/2, 7/12, 1/2, 1/3, 6, 12, 21, 6, 6, 1, 3, 5/6, 2/3, 1/2, 2/3, 1/3, 1/3, 2, -2, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1624.1MB, alloc=540.3MB, time=50.71 |\^/| 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(); 1428243563 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 2 F := [14 x z + 16 z , 2 x z + 14 z , -17 y z + 5 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [-5 x z - 7, -6 x z + 17 y z , 4 x y - 7 z ] > Problem := [F,G]; 3 3 2 2 3 2 Problem := [[14 x z + 16 z , 2 x z + 14 z , -17 y z + 5 y z ], 2 2 3 2 2 [-5 x z - 7, -6 x z + 17 y z , 4 x 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=48.0MB, alloc=32.3MB, time=0.82 memory used=68.4MB, alloc=32.3MB, time=1.12 memory used=87.4MB, alloc=56.3MB, time=1.42 memory used=127.0MB, alloc=60.3MB, time=2.02 memory used=165.2MB, alloc=84.3MB, time=2.58 memory used=210.7MB, alloc=84.3MB, time=3.32 memory used=269.1MB, alloc=108.3MB, time=4.42 memory used=347.2MB, alloc=140.3MB, time=5.89 memory used=437.4MB, alloc=164.3MB, time=7.80 memory used=531.8MB, alloc=188.3MB, time=11.05 memory used=642.4MB, alloc=188.3MB, time=15.39 memory used=753.1MB, alloc=212.3MB, time=19.68 N1 := 3459 > GB := Basis(F, plex(op(vars))); 4 3 3 2 2 2 3 3 GB := [x z + 7 x z, x y z, x z + 7 z , y z , 7 x z + 8 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=895.0MB, alloc=212.3MB, time=22.95 N2 := 1021 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 2 3 2 2 2 H := [14 x z + 16 z , 2 x z + 14 z , -17 y z + 5 y z , -5 x z - 7, 3 2 2 -6 x z + 17 y z , -7 z + 4 y x] > J:=[op(GB),op(G)]; 4 3 3 2 2 2 3 3 2 2 J := [x z + 7 x z, x y z, x z + 7 z , y z , 7 x z + 8 z , -5 x z - 7, 3 2 2 -6 x z + 17 y z , -7 z + 4 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 := [6, 14, 21, 4, 3, 1, 3, 5/6, 1/2, 1, 5/12, 1/3, 5/6, 8, 19, 30, 5, 4, 1, 3, 7/8, 1/2, 1, 8/17, 4/17, 12/17, -5, -9, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=973.5MB, alloc=212.3MB, time=24.95 |\^/| 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(); 1428243641 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [-4 x y z + 16 x z , 3 x y - 19 z , -10 x y + 12 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 G := [-19 y + 19 x y, -4 x y z - 9, -4 y z + 10 y ] > Problem := [F,G]; 2 2 2 3 2 Problem := [[-4 x y z + 16 x z , 3 x y - 19 z , -10 x y + 12 x], 3 3 3 [-19 y + 19 x y, -4 x y z - 9, -4 y z + 10 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=48.1MB, alloc=32.3MB, time=0.81 memory used=68.5MB, alloc=32.3MB, time=1.11 memory used=87.3MB, alloc=56.3MB, time=1.41 memory used=127.5MB, alloc=60.3MB, time=2.02 memory used=165.7MB, alloc=60.3MB, time=2.59 memory used=202.9MB, alloc=84.3MB, time=3.15 memory used=261.3MB, alloc=92.3MB, time=4.05 memory used=317.5MB, alloc=116.3MB, time=4.90 memory used=397.6MB, alloc=140.3MB, time=6.23 memory used=495.2MB, alloc=164.3MB, time=8.05 memory used=594.2MB, alloc=164.3MB, time=9.71 memory used=701.9MB, alloc=444.3MB, time=11.71 memory used=822.3MB, alloc=468.3MB, time=14.26 memory used=944.3MB, alloc=492.3MB, time=18.06 memory used=1073.6MB, alloc=516.3MB, time=23.00 memory used=1219.6MB, alloc=540.3MB, time=28.96 memory used=1389.4MB, alloc=564.3MB, time=35.93 memory used=1583.3MB, alloc=564.3MB, time=43.81 memory used=1777.1MB, alloc=588.3MB, time=51.68 memory used=1995.2MB, alloc=612.3MB, time=60.45 N1 := 6153 > GB := Basis(F, plex(op(vars))); 2 3 GB := [400 x - 57 x, 19 x y - 160 x, 10 x z - 3 x, 95 z - 18 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2240.3MB, alloc=612.3MB, time=65.05 memory used=2525.1MB, alloc=636.3MB, time=70.48 memory used=2793.0MB, alloc=660.3MB, time=80.32 memory used=3055.6MB, alloc=684.3MB, time=91.38 memory used=3342.3MB, alloc=708.3MB, 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(); 1428243941 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 2 4 F := [-11 x z - 6 z , -14 x y z + 17 z , 7 x y z + 10 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 3 2 2 G := [15 x - 17 x y , -14 x y + 14 y z , 6 x y z + 12 x y ] > Problem := [F,G]; 3 2 2 4 2 4 Problem := [[-11 x z - 6 z , -14 x y z + 17 z , 7 x y z + 10 y ], 4 3 2 2 3 2 2 [15 x - 17 x y , -14 x y + 14 y z , 6 x y z + 12 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.50 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=68.0MB, alloc=32.3MB, time=1.10 memory used=87.7MB, alloc=56.3MB, time=1.40 memory used=127.8MB, alloc=60.3MB, time=1.99 memory used=166.2MB, alloc=60.3MB, time=2.56 memory used=201.2MB, alloc=84.3MB, time=3.10 memory used=258.7MB, alloc=92.3MB, time=3.95 memory used=316.0MB, alloc=116.3MB, time=4.80 memory used=395.6MB, alloc=116.3MB, time=5.98 memory used=475.2MB, alloc=140.3MB, time=7.20 memory used=548.1MB, alloc=140.3MB, time=8.32 memory used=616.7MB, alloc=396.3MB, time=9.43 memory used=716.4MB, alloc=420.3MB, time=10.96 memory used=837.0MB, alloc=444.3MB, time=12.79 memory used=981.4MB, alloc=468.3MB, time=14.95 memory used=1111.6MB, alloc=492.3MB, time=16.99 memory used=1232.9MB, alloc=492.3MB, time=18.99 memory used=1352.2MB, alloc=516.3MB, time=20.98 memory used=1472.8MB, alloc=516.3MB, time=23.01 memory used=1576.1MB, alloc=540.3MB, time=24.69 memory used=1676.8MB, alloc=540.3MB, time=26.51 memory used=1756.0MB, alloc=564.3MB, time=28.30 memory used=1870.5MB, alloc=564.3MB, time=30.55 memory used=1982.8MB, alloc=588.3MB, time=32.96 memory used=2102.5MB, alloc=612.3MB, time=35.57 memory used=2227.0MB, alloc=636.3MB, time=38.27 memory used=2328.0MB, alloc=636.3MB, time=40.54 memory used=2441.4MB, alloc=660.3MB, time=43.08 memory used=2537.8MB, alloc=684.3MB, time=45.28 memory used=2642.2MB, alloc=684.3MB, time=47.63 memory used=2740.3MB, alloc=708.3MB, time=49.93 memory used=2825.1MB, alloc=732.3MB, time=52.01 memory used=2903.1MB, alloc=732.3MB, time=53.95 memory used=2984.2MB, alloc=756.3MB, time=55.99 memory used=3064.7MB, alloc=756.3MB, time=58.04 memory used=3370.8MB, alloc=780.3MB, time=66.19 memory used=3638.3MB, alloc=804.3MB, time=76.13 memory used=3909.3MB, alloc=828.3MB, time=86.77 memory used=4189.1MB, alloc=852.3MB, time=98.18 memory used=4478.6MB, alloc=876.3MB, time=110.14 |\^/| 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(); 1428244241 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 F := [-15 y + 14 x, -7 x z - 9 x y z, x y + 18 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 G := [-10 x z - 8, 14 x z + 15 x , -13 x y - 11 y z ] > Problem := [F,G]; 4 3 2 2 Problem := [[-15 y + 14 x, -7 x z - 9 x y z, x y + 18 y ], 3 3 3 2 [-10 x z - 8, 14 x z + 15 x , -13 x y - 11 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.79 memory used=69.1MB, alloc=32.3MB, time=1.10 memory used=89.6MB, alloc=32.3MB, time=1.41 memory used=108.8MB, alloc=56.3MB, time=1.70 memory used=152.8MB, alloc=60.3MB, time=2.49 memory used=192.4MB, alloc=84.3MB, time=3.18 memory used=251.0MB, alloc=84.3MB, time=4.24 memory used=302.6MB, alloc=108.3MB, time=5.42 memory used=366.2MB, alloc=132.3MB, time=7.67 memory used=451.7MB, alloc=132.3MB, time=10.78 N1 := 2357 > GB := Basis(F, plex(op(vars))); 4 2 2 2 GB := [5 x - 489888 x, x + 18 x y, -x + 324 y , z x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=539.4MB, alloc=140.3MB, time=12.43 memory used=640.5MB, alloc=164.3MB, time=15.07 N2 := 1179 #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)]; 4 3 2 2 H := [-15 y + 14 x, -7 x z - 9 x y z, x y + 18 y , -10 x z - 8, 3 3 3 2 14 x z + 15 x , -13 x y - 11 y z ] > J:=[op(GB),op(G)]; 4 2 2 2 J := [5 x - 489888 x, x + 18 x y, -x + 324 y , z x, -10 x z - 8, 3 3 3 2 14 x z + 15 x , -13 x y - 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 := [6, 14, 20, 4, 3, 4, 3, 1, 2/3, 2/3, 2/3, 1/2, 5/12, 7, 14, 20, 4, 4, 3, 3, 1, 3/7, 4/7, 5/7, 2/7, 2/7, 0, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=643.7MB, alloc=164.3MB, time=15.16 |\^/| 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(); 1428244287 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 2 F := [-14 x y - 20 x , -10 x y - 4 x y, 7 x z + 5 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 4 G := [18 x y - 5 x, 7 x z + 17 x y , -3 x y - 10 z ] > Problem := [F,G]; 2 2 2 2 2 3 2 2 Problem := [[-14 x y - 20 x , -10 x y - 4 x y, 7 x z + 5 y z ], 3 2 2 2 2 4 [18 x y - 5 x, 7 x z + 17 x y , -3 x y - 10 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.80 memory used=68.5MB, alloc=32.3MB, time=1.09 memory used=88.9MB, alloc=32.3MB, time=1.40 memory used=108.8MB, alloc=56.3MB, time=1.71 memory used=149.8MB, alloc=60.3MB, time=2.33 memory used=189.8MB, alloc=84.3MB, time=3.00 memory used=250.1MB, alloc=84.3MB, time=4.08 memory used=305.5MB, alloc=108.3MB, time=5.14 memory used=375.1MB, alloc=132.3MB, time=7.50 N1 := 1601 > GB := Basis(F, plex(op(vars))); 4 2 2 3 2 2 3 2 2 GB := [125 x + 14 x , -25 x + 7 x y, 343 x z + 3125 x z , 7 x z + 5 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=464.7MB, alloc=140.3MB, time=9.34 memory used=562.3MB, alloc=140.3MB, time=10.82 memory used=658.3MB, alloc=164.3MB, time=12.51 memory used=773.0MB, alloc=188.3MB, time=15.31 N2 := 1825 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 3 2 2 3 H := [-14 x y - 20 x , -10 x y - 4 x y, 7 x z + 5 y z , 18 x y - 5 x, 2 2 2 2 4 7 x z + 17 x y , -3 x y - 10 z ] > J:=[op(GB),op(G)]; 4 2 2 3 2 2 3 2 2 J := [125 x + 14 x , -25 x + 7 x y, 343 x z + 3125 x z , 7 x z + 5 y z , 3 2 2 2 2 4 18 x y - 5 x, 7 x z + 17 x y , -3 x y - 10 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 23, 4, 3, 3, 4, 1, 1, 1/2, 5/6, 7/12, 1/3, 7, 16, 25, 4, 4, 3, 4, 1, 5/7, 4/7, 6/7, 5/14, 3/7, -1, -2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=848.0MB, alloc=188.3MB, time=18.00 |\^/| 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(); 1428244340 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 4 3 F := [-18 x z + 16 x y , -7 y z - 13 y z , -16 x + 11 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 4 G := [18 y z - 4 z, 7 y z + 16 y z , 13 x + 8 y ] > Problem := [F,G]; 3 2 2 2 2 4 3 Problem := [[-18 x z + 16 x y , -7 y z - 13 y z , -16 x + 11 y z ], 3 2 2 4 4 [18 y z - 4 z, 7 y z + 16 y z , 13 x + 8 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.6MB, alloc=32.3MB, time=0.78 memory used=68.5MB, alloc=32.3MB, time=1.09 memory used=87.8MB, alloc=56.3MB, time=1.39 memory used=130.6MB, alloc=60.3MB, time=2.14 N1 := 555 > GB := Basis(F, plex(op(vars))); 8 4 4 4 5 3 GB := [6174 x + 24167 x , 7 x y + 13 x , -18 x + 11 x y , 5 2 2 2 2 2 3 2 -882 x z + 1859 x y z , 7 y z + 13 y z , 9 x z - 8 x y , 4 3 -16 x + 11 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=165.6MB, alloc=60.3MB, time=2.77 memory used=202.5MB, alloc=60.3MB, time=3.27 memory used=239.7MB, alloc=60.3MB, time=3.81 memory used=274.8MB, alloc=84.3MB, time=4.35 memory used=330.6MB, alloc=84.3MB, time=5.19 memory used=387.0MB, alloc=108.3MB, time=6.14 memory used=464.8MB, alloc=140.3MB, time=7.65 N2 := 1447 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 4 3 H := [-18 x z + 16 x y , -7 y z - 13 y z , -16 x + 11 y z , 18 y z - 4 z, 3 2 2 4 4 7 y z + 16 y z , 8 y + 13 x ] > J:=[op(GB),op(G)]; 8 4 4 4 5 3 J := [6174 x + 24167 x , 7 x y + 13 x , -18 x + 11 x y , 5 2 2 2 2 2 3 2 -882 x z + 1859 x y z , 7 y z + 13 y z , 9 x z - 8 x y , 4 3 3 2 2 4 4 -16 x + 11 y z , 18 y z - 4 z, 7 y z + 16 y z , 8 y + 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 := [6, 14, 22, 4, 4, 4, 3, 1/2, 1, 5/6, 1/3, 2/3, 2/3, 10, 22, 47, 8, 8, 4, 3, 7/10, 9/10, 3/5, 3/5, 11/20, 1/2, -8, -25, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=531.1MB, alloc=140.3MB, time=9.77 |\^/| 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(); 1428244371 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 4 2 4 F := [5 x - 9 x y , 4 y + 17 z , -13 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [12 x y z - 10 x z, -12 x y z + 16 y , 18 x y z - 15 y z] > Problem := [F,G]; 4 3 4 2 4 Problem := [[5 x - 9 x y , 4 y + 17 z , -13 z ], 2 3 [12 x y z - 10 x z, -12 x y z + 16 y , 18 x y z - 15 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 N1 := 203 > GB := Basis(F, plex(op(vars))); 10 7 2 4 3 8 4 2 GB := [x , x y , -5 x + 9 x y , y , 4 y + 17 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=48.3MB, alloc=32.3MB, time=0.88 memory used=68.4MB, alloc=32.3MB, time=1.18 N2 := 203 #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)]; 4 3 4 2 4 H := [5 x - 9 x y , 4 y + 17 z , -13 z , 12 x y z - 10 x z, 2 3 -12 x y z + 16 y , 18 x y z - 15 y z] > J:=[op(GB),op(G)]; 10 7 2 4 3 8 4 2 J := [x , x y , -5 x + 9 x y , y , 4 y + 17 z , 12 x y z - 10 x z, 2 3 -12 x y z + 16 y , 18 x y z - 15 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 := [6, 14, 22, 4, 4, 4, 4, 2/3, 5/6, 5/6, 1/2, 7/12, 7/12, 8, 17, 45, 10, 10, 8, 2, 3/4, 7/8, 1/2, 1/2, 9/16, 3/8, -3, -23, -6] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=81.8MB, alloc=32.3MB, time=1.41 |\^/| 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(); 1428244376 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 4 3 F := [-10 x z , -4 x z - 17 y z, -5 z - 13 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 2 G := [-18 x z + 15 y z , 18 x + 3 x z , -4 x y - 18 y ] > Problem := [F,G]; 2 2 2 2 2 4 3 Problem := [[-10 x z , -4 x z - 17 y z, -5 z - 13 z ], 2 2 4 3 2 [-18 x z + 15 y z , 18 x + 3 x z , -4 x 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=49.3MB, alloc=32.3MB, time=0.89 memory used=68.9MB, alloc=56.3MB, time=1.25 memory used=109.7MB, alloc=80.3MB, time=2.25 N1 := 893 > GB := Basis(F, plex(op(vars))); 2 2 2 4 3 GB := [z y , x z , 5 z + 13 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 197 #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 4 3 2 2 H := [-10 x z , -4 x z - 17 y z, -5 z - 13 z , -18 x z + 15 y z , 4 3 2 18 x + 3 x z , -4 x y - 18 y ] > J:=[op(GB),op(G)]; 2 2 2 4 3 2 2 4 3 J := [z y , x z , 5 z + 13 z , -18 x z + 15 y z , 18 x + 3 x z , 2 -4 x 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 := [6, 13, 21, 4, 4, 2, 4, 5/6, 1/2, 5/6, 6/13, 4/13, 8/13, 6, 12, 20, 4, 4, 2, 4, 2/3, 1/2, 5/6, 5/12, 1/3, 7/12, 1, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=136.3MB, alloc=80.3MB, time=2.70 |\^/| 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(); 1428244384 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [-13 x z - y z , 10 x z - z, -16 x y - 9 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [18 x z - 14 y z, 6 x y z + 8 x , -7 x z + 10 x z] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[-13 x z - y z , 10 x z - z, -16 x y - 9 x y z], 2 2 3 2 [18 x z - 14 y z, 6 x y z + 8 x , -7 x z + 10 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.78 memory used=69.0MB, alloc=56.3MB, time=1.13 memory used=111.8MB, alloc=60.3MB, time=1.87 memory used=150.5MB, alloc=84.3MB, time=2.55 memory used=208.1MB, alloc=108.3MB, time=3.56 memory used=282.4MB, alloc=132.3MB, time=5.46 memory used=365.5MB, alloc=132.3MB, time=8.68 memory used=448.5MB, alloc=156.3MB, time=11.97 N1 := 2749 > GB := Basis(F, plex(op(vars))); 7 2 2 2 4 2 2 3 4 2 GB := [2080 x y - 9 x y , 13 x y + x y , -2560 x y + 81 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=523.7MB, alloc=156.3MB, time=13.82 N2 := 551 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 2 H := [-13 x z - y z , 10 x z - z, -16 x y - 9 x y z, 18 x z - 14 y z, 2 3 2 6 x y z + 8 x , -7 x z + 10 x z] > J:=[op(GB),op(G)]; 7 2 2 2 4 2 2 3 4 2 J := [2080 x y - 9 x y , 13 x y + x y , -2560 x y + 81 z, 2 2 3 2 18 x z - 14 y z, 6 x y z + 8 x , -7 x z + 10 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 := [6, 16, 22, 4, 3, 2, 2, 1, 2/3, 1, 3/4, 5/12, 5/6, 6, 15, 31, 9, 7, 3, 1, 1, 5/6, 2/3, 5/6, 7/12, 1/2, 1, -9, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=562.1MB, alloc=164.3MB, time=14.60 |\^/| 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(); 1428244429 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 F := [18 x y - 3 y z, -12 x z + 15 y z , -19 x y z + 2 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 2 G := [18 x y - 7 x y z, -12 y - 20 y z , 5 x y z + 4 x ] > Problem := [F,G]; 3 3 2 2 2 2 Problem := [[18 x y - 3 y z, -12 x z + 15 y z , -19 x y z + 2 y ], 3 2 4 2 2 [18 x y - 7 x y z, -12 y - 20 y z , 5 x y z + 4 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.78 memory used=67.7MB, alloc=56.3MB, time=1.09 memory used=107.7MB, alloc=60.3MB, time=1.67 memory used=146.6MB, alloc=60.3MB, time=2.22 memory used=184.1MB, alloc=84.3MB, time=2.77 memory used=233.1MB, alloc=84.3MB, time=3.51 memory used=289.2MB, alloc=116.3MB, time=4.40 memory used=367.2MB, alloc=116.3MB, time=5.62 memory used=443.8MB, alloc=140.3MB, time=6.78 memory used=510.6MB, alloc=396.3MB, time=7.78 memory used=611.8MB, alloc=420.3MB, time=9.31 memory used=736.3MB, alloc=444.3MB, time=11.19 memory used=877.0MB, alloc=468.3MB, time=13.53 memory used=1014.8MB, alloc=492.3MB, time=15.84 memory used=1142.1MB, alloc=492.3MB, time=18.01 memory used=1262.0MB, alloc=492.3MB, time=20.20 memory used=1366.9MB, alloc=516.3MB, time=22.05 memory used=1476.7MB, alloc=516.3MB, time=24.09 memory used=1570.8MB, alloc=516.3MB, time=25.89 memory used=1656.7MB, alloc=516.3MB, time=27.55 memory used=1748.3MB, alloc=516.3MB, time=29.45 memory used=1821.4MB, alloc=540.3MB, time=31.02 memory used=1878.1MB, alloc=540.3MB, time=32.36 memory used=1939.6MB, alloc=540.3MB, time=33.77 memory used=2002.0MB, alloc=540.3MB, time=35.18 memory used=2044.7MB, alloc=540.3MB, time=36.28 memory used=2254.1MB, alloc=564.3MB, time=40.38 memory used=2481.7MB, alloc=588.3MB, time=44.95 memory used=2706.1MB, alloc=612.3MB, time=49.66 memory used=2929.6MB, alloc=636.3MB, time=54.41 memory used=3100.3MB, alloc=660.3MB, time=58.09 memory used=3284.9MB, alloc=684.3MB, time=62.24 memory used=3464.2MB, alloc=708.3MB, time=66.45 memory used=3608.3MB, alloc=732.3MB, time=69.77 memory used=3807.9MB, alloc=756.3MB, time=74.32 memory used=3965.7MB, alloc=780.3MB, time=77.83 memory used=4184.0MB, alloc=804.3MB, time=82.04 memory used=4378.8MB, alloc=828.3MB, time=86.42 memory used=4542.8MB, alloc=852.3MB, time=90.41 memory used=4734.8MB, alloc=876.3MB, time=95.08 memory used=5119.8MB, alloc=900.3MB, time=103.28 |\^/| 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(); 1428244729 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 3 F := [-20 z + 17 y , 18 x y z + 12 x z , -12 x y z - 20 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 3 2 G := [-2 x y - 13 x y z, -9 x - 18 y z, -18 y z - 9 x y] > Problem := [F,G]; 4 3 2 2 3 Problem := [[-20 z + 17 y , 18 x y z + 12 x z , -12 x y z - 20 x z ], 2 2 2 4 2 3 2 [-2 x y - 13 x y z, -9 x - 18 y z, -18 y z - 9 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.5MB, alloc=32.3MB, time=0.80 memory used=67.4MB, alloc=56.3MB, time=1.10 memory used=108.5MB, alloc=60.3MB, time=1.70 memory used=147.5MB, alloc=84.3MB, time=2.27 memory used=208.1MB, alloc=92.3MB, time=3.17 memory used=265.0MB, alloc=116.3MB, time=4.03 memory used=342.9MB, alloc=140.3MB, time=5.25 memory used=425.6MB, alloc=396.3MB, time=6.47 memory used=535.6MB, alloc=420.3MB, time=7.81 memory used=662.0MB, alloc=444.3MB, time=9.55 memory used=808.4MB, alloc=468.3MB, time=11.85 memory used=945.2MB, alloc=492.3MB, time=13.91 memory used=1061.5MB, alloc=492.3MB, time=15.74 memory used=1186.4MB, alloc=492.3MB, time=17.86 memory used=1297.7MB, alloc=516.3MB, time=19.81 memory used=1403.5MB, alloc=516.3MB, time=21.46 memory used=1514.4MB, alloc=540.3MB, time=22.67 memory used=1600.9MB, alloc=540.3MB, time=24.18 memory used=1672.4MB, alloc=540.3MB, time=25.38 memory used=1740.0MB, alloc=540.3MB, time=26.73 memory used=1802.0MB, alloc=564.3MB, time=27.81 memory used=1869.5MB, alloc=564.3MB, time=28.91 memory used=1941.8MB, alloc=588.3MB, time=29.90 memory used=2011.0MB, alloc=588.3MB, time=31.50 memory used=2247.6MB, alloc=612.3MB, time=34.57 memory used=2454.2MB, alloc=636.3MB, time=38.11 memory used=2670.2MB, alloc=660.3MB, time=41.37 memory used=2840.8MB, alloc=684.3MB, time=44.16 memory used=2995.8MB, alloc=708.3MB, time=46.49 memory used=3127.1MB, alloc=732.3MB, time=49.03 memory used=3292.3MB, alloc=756.3MB, time=51.76 memory used=3427.6MB, alloc=756.3MB, time=54.27 memory used=3561.3MB, alloc=756.3MB, time=57.04 memory used=3747.0MB, alloc=780.3MB, time=59.45 memory used=3943.9MB, alloc=804.3MB, time=61.69 memory used=4080.1MB, alloc=804.3MB, time=64.08 memory used=4178.9MB, alloc=828.3MB, time=66.00 memory used=4624.1MB, alloc=852.3MB, time=73.25 memory used=5108.5MB, alloc=876.3MB, time=79.29 memory used=5607.6MB, alloc=900.3MB, time=85.89 memory used=6060.2MB, alloc=924.3MB, time=94.55 memory used=6412.8MB, alloc=948.3MB, time=102.82 memory used=6868.4MB, alloc=972.3MB, time=110.46 |\^/| 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(); 1428245029 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [13 x z + 12 y z, 5 x y + 7 y, 16 y + 15 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 3 2 G := [-10 x y - 2 x , 16 y - 12 y , -16 x z + 12 x ] > Problem := [F,G]; 3 3 2 Problem := [[13 x z + 12 y z, 5 x y + 7 y, 16 y + 15 x], 3 2 4 3 3 2 [-10 x y - 2 x , 16 y - 12 y , -16 x 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=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=48.1MB, alloc=32.3MB, time=0.80 memory used=69.9MB, alloc=56.3MB, time=1.16 memory used=113.9MB, alloc=60.3MB, time=1.93 memory used=154.0MB, alloc=84.3MB, time=2.63 memory used=212.5MB, alloc=108.3MB, time=4.20 N1 := 1563 > GB := Basis(F, plex(op(vars))); GB := [ 2 2 3 3 5 x + 7 x, 5 x y + 7 y, 16 y + 15 x, 52 x z + 63 y z, 832 y z + 675 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=286.3MB, alloc=108.3MB, time=6.19 memory used=363.2MB, alloc=116.3MB, time=7.35 memory used=438.2MB, alloc=140.3MB, time=8.55 memory used=537.3MB, alloc=164.3MB, time=10.31 memory used=653.5MB, alloc=188.3MB, time=12.38 memory used=785.1MB, alloc=212.3MB, time=14.74 memory used=919.6MB, alloc=492.3MB, time=18.09 memory used=1058.0MB, alloc=516.3MB, time=22.64 memory used=1204.9MB, alloc=540.3MB, time=28.43 memory used=1375.9MB, alloc=564.3MB, time=35.13 memory used=1570.7MB, alloc=564.3MB, time=42.70 memory used=1765.6MB, alloc=588.3MB, time=50.26 memory used=1984.6MB, alloc=612.3MB, time=58.70 N2 := 6191 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 3 2 H := [13 x z + 12 y z, 5 x y + 7 y, 16 y + 15 x, -10 x y - 2 x , 4 3 3 2 16 y - 12 y , -16 x z + 12 x ] > J:=[op(GB),op(G)]; 2 2 3 J := [5 x + 7 x, 5 x y + 7 y, 16 y + 15 x, 52 x z + 63 y z, 3 3 2 4 3 3 2 832 y z + 675 x z, -10 x y - 2 x , 16 y - 12 y , -16 x z + 12 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, 20, 4, 3, 4, 3, 5/6, 5/6, 1/3, 7/12, 7/12, 1/4, 8, 16, 26, 4, 3, 4, 3, 7/8, 3/4, 3/8, 5/8, 1/2, 5/16, -4, -6, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2072.5MB, 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(); 1428245243 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 2 2 F := [-4 x - 3 x y, 10 x - 3 x y, 15 y z - 11 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 2 G := [17 y z - 16 x z, -7 x y - 4, 4 x - 5 x y z] > Problem := [F,G]; 4 2 4 2 2 Problem := [[-4 x - 3 x y, 10 x - 3 x y, 15 y z - 11 z], 3 2 2 4 2 [17 y z - 16 x z, -7 x y - 4, 4 x - 5 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.1MB, alloc=32.3MB, time=0.77 memory used=66.6MB, alloc=32.3MB, time=1.05 memory used=87.5MB, alloc=56.3MB, time=1.44 N1 := 649 > GB := Basis(F, plex(op(vars))); 5 4 4 2 2 GB := [5 x + 2 x , -10 x + 3 x y, 5 x z + 2 x z, 256 x z - 4125 x z, 2 2 15 y z - 11 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=129.3MB, alloc=60.3MB, time=2.40 memory used=167.2MB, alloc=60.3MB, time=2.93 memory used=204.2MB, alloc=84.3MB, time=3.47 memory used=261.8MB, alloc=92.3MB, time=4.35 memory used=322.0MB, alloc=116.3MB, time=5.38 memory used=400.2MB, alloc=140.3MB, time=6.76 memory used=488.7MB, alloc=164.3MB, time=9.58 N2 := 2265 #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)]; 4 2 4 2 2 3 H := [-4 x - 3 x y, 10 x - 3 x y, 15 y z - 11 z, 17 y z - 16 x z, 2 2 4 2 -7 x y - 4, 4 x - 5 x y z] > J:=[op(GB),op(G)]; 5 4 4 2 2 J := [5 x + 2 x , -10 x + 3 x y, 5 x z + 2 x z, 256 x z - 4125 x z, 2 2 3 2 2 4 2 15 y z - 11 z, 17 y z - 16 x z, -7 x y - 4, 4 x - 5 x 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 := [6, 14, 24, 4, 4, 3, 2, 5/6, 1, 1/2, 2/3, 1/2, 5/12, 8, 17, 31, 5, 5, 3, 2, 7/8, 5/8, 5/8, 3/4, 5/16, 9/16, -3, -7, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=587.8MB, alloc=164.3MB, time=12.93 |\^/| 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(); 1428245285 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 F := [3 x - 7 x y, -18 y z + 19 z , -10 x y z + 3 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [-3 x z + 11 y, 2 x y z - 5 y z , 6 x + 2 x y z] > Problem := [F,G]; 3 3 2 2 3 Problem := [[3 x - 7 x y, -18 y z + 19 z , -10 x y z + 3 z ], 2 2 2 2 3 [-3 x z + 11 y, 2 x y z - 5 y z , 6 x + 2 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=48.3MB, alloc=32.3MB, time=0.80 memory used=69.0MB, alloc=32.3MB, time=1.10 memory used=88.7MB, alloc=56.3MB, time=1.40 memory used=128.8MB, alloc=60.3MB, time=1.97 memory used=166.4MB, alloc=84.3MB, time=2.55 memory used=219.3MB, alloc=84.3MB, time=3.32 memory used=278.3MB, alloc=116.3MB, time=4.40 memory used=353.3MB, alloc=140.3MB, time=5.72 memory used=446.5MB, alloc=164.3MB, time=7.32 memory used=555.2MB, alloc=188.3MB, time=9.26 memory used=659.2MB, alloc=468.3MB, time=11.17 memory used=796.8MB, alloc=492.3MB, time=13.82 memory used=937.6MB, alloc=516.3MB, time=17.78 memory used=1083.6MB, alloc=540.3MB, time=22.59 memory used=1236.1MB, alloc=564.3MB, time=28.62 memory used=1408.7MB, alloc=588.3MB, time=35.82 memory used=1605.4MB, alloc=612.3MB, time=43.85 memory used=1825.9MB, alloc=612.3MB, time=52.91 memory used=2046.5MB, alloc=612.3MB, time=61.83 memory used=2267.0MB, alloc=636.3MB, time=70.74 memory used=2511.4MB, alloc=636.3MB, time=80.55 memory used=2755.7MB, alloc=660.3MB, time=90.42 |\^/| 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(); 1428245585 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [-14 y z + 16 x, -15 x y + 5 x , x y - 2 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [-10 x y z - 9 x y, 2 x y z - 20 x z, -z - 9 x y] > Problem := [F,G]; 3 2 2 2 2 Problem := [[-14 y z + 16 x, -15 x y + 5 x , x y - 2 x y z], 2 2 2 2 3 [-10 x y z - 9 x y, 2 x y z - 20 x z, -z - 9 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.79 memory used=68.3MB, alloc=32.3MB, time=1.08 memory used=87.9MB, alloc=56.3MB, time=1.38 memory used=127.5MB, alloc=60.3MB, time=1.98 memory used=163.8MB, alloc=84.3MB, time=2.53 memory used=221.3MB, alloc=84.3MB, time=3.48 memory used=277.7MB, alloc=108.3MB, time=4.46 memory used=353.4MB, alloc=140.3MB, time=5.82 memory used=446.2MB, alloc=164.3MB, time=7.50 memory used=555.2MB, alloc=188.3MB, time=9.45 memory used=677.8MB, alloc=212.3MB, time=11.67 memory used=804.5MB, alloc=236.3MB, time=14.92 memory used=933.9MB, alloc=260.3MB, time=18.97 memory used=1073.9MB, alloc=284.3MB, time=24.26 memory used=1229.3MB, alloc=308.3MB, time=30.59 memory used=1408.8MB, alloc=332.3MB, time=37.72 memory used=1612.2MB, alloc=332.3MB, time=45.85 memory used=1815.6MB, alloc=356.3MB, time=54.01 memory used=2042.9MB, alloc=356.3MB, time=63.02 memory used=2270.2MB, alloc=356.3MB, time=72.04 memory used=2497.5MB, alloc=380.3MB, time=81.10 |\^/| 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(); 1428245885 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [2 x y - 19 x y, -13 y z + 4 x y z, 18 x z + 19 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 3 2 G := [2 x y z + 12 z, -10 x - 20 x y , 9 x - y z ] > Problem := [F,G]; 2 3 2 2 Problem := [[2 x y - 19 x y, -13 y z + 4 x y z, 18 x z + 19 y z], 2 4 3 3 2 [2 x y z + 12 z, -10 x - 20 x y , 9 x - y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.78 memory used=68.4MB, alloc=32.3MB, time=1.08 memory used=88.3MB, alloc=32.3MB, time=1.37 memory used=107.5MB, alloc=56.3MB, time=1.68 memory used=147.2MB, alloc=60.3MB, time=2.26 memory used=187.6MB, alloc=84.3MB, time=2.99 memory used=248.1MB, alloc=84.3MB, time=4.03 memory used=304.6MB, alloc=108.3MB, time=5.05 memory used=379.0MB, alloc=140.3MB, time=6.54 memory used=461.6MB, alloc=164.3MB, time=9.11 memory used=557.7MB, alloc=164.3MB, time=12.70 memory used=653.8MB, alloc=188.3MB, time=16.31 N1 := 3169 > GB := Basis(F, plex(op(vars))); 2 6 5 2 GB := [2 x y - 19 x y, 5184 x y z - 1694173 x y z, -2592 x y z + 89167 y z, 2 2 4 2 3 18 x z + 19 y z, 144 x y z + 4693 x y z , 13 y z - 4 x y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=775.2MB, alloc=188.3MB, time=18.99 memory used=866.5MB, alloc=444.3MB, time=20.43 memory used=997.2MB, alloc=468.3MB, time=22.41 memory used=1155.9MB, alloc=492.3MB, time=25.03 memory used=1333.9MB, alloc=516.3MB, time=28.23 memory used=1522.7MB, alloc=540.3MB, time=31.69 memory used=1706.8MB, alloc=564.3MB, time=37.02 memory used=1882.9MB, alloc=588.3MB, time=43.70 memory used=2071.2MB, alloc=612.3MB, time=51.50 memory used=2283.4MB, alloc=636.3MB, time=60.25 memory used=2519.6MB, alloc=660.3MB, time=69.91 memory used=2779.8MB, alloc=684.3MB, time=80.47 memory used=3064.1MB, alloc=708.3MB, time=91.75 |\^/| 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(); 1428246185 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 F := [13 x y z + 18 y z, 6 z + 13, -15 x z + 16 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 2 G := [-6 x y z - 2 x z , -3 x y z - 19 z , -17 x - 19 x ] > Problem := [F,G]; 2 3 3 3 2 Problem := [[13 x y z + 18 y z, 6 z + 13, -15 x z + 16 y ], 2 2 4 3 2 [-6 x y z - 2 x z , -3 x y z - 19 z , -17 x - 19 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=67.9MB, alloc=32.3MB, time=1.10 memory used=87.6MB, alloc=56.3MB, time=1.41 memory used=128.3MB, alloc=60.3MB, time=1.98 memory used=166.9MB, alloc=84.3MB, time=2.55 memory used=213.0MB, alloc=84.3MB, time=3.21 memory used=273.1MB, alloc=116.3MB, time=4.30 memory used=355.6MB, alloc=116.3MB, time=5.63 memory used=427.6MB, alloc=140.3MB, time=6.94 memory used=511.1MB, alloc=164.3MB, time=9.23 memory used=601.3MB, alloc=188.3MB, time=12.80 memory used=715.6MB, alloc=212.3MB, time=17.30 N1 := 3071 > GB := Basis(F, plex(op(vars))); 8 5 4 3 7 2 2 GB := [597871125 x + 47525504 x , 13 x + 18 x y, 7381125 x + 1124864 x y , 2 3 3 2 2 2 3 3 13 x y + 18 y , 15 z x - 16 y , 32 y z + 65 x , 6 z + 13] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=835.8MB, alloc=212.3MB, time=20.06 memory used=992.2MB, alloc=468.3MB, time=22.47 memory used=1152.3MB, alloc=492.3MB, time=24.85 memory used=1285.0MB, alloc=516.3MB, time=26.69 memory used=1423.7MB, alloc=540.3MB, time=28.60 memory used=1554.5MB, alloc=540.3MB, time=30.62 memory used=1670.0MB, alloc=564.3MB, time=32.36 memory used=1782.2MB, alloc=564.3MB, time=34.14 memory used=1880.5MB, alloc=564.3MB, time=35.81 memory used=1981.1MB, alloc=564.3MB, time=37.44 memory used=2072.7MB, alloc=588.3MB, time=38.81 memory used=2148.6MB, alloc=588.3MB, time=40.06 memory used=2217.2MB, alloc=588.3MB, time=41.34 memory used=2276.0MB, alloc=588.3MB, time=42.51 memory used=2430.1MB, alloc=612.3MB, time=45.05 memory used=2535.9MB, alloc=636.3MB, time=47.35 memory used=2624.8MB, alloc=636.3MB, time=49.44 memory used=2735.4MB, alloc=660.3MB, time=52.00 memory used=2818.0MB, alloc=660.3MB, time=53.98 memory used=2910.4MB, alloc=684.3MB, time=56.24 memory used=3008.3MB, alloc=708.3MB, time=58.58 memory used=3099.7MB, alloc=708.3MB, time=60.56 memory used=3219.1MB, alloc=708.3MB, time=62.66 memory used=3503.4MB, alloc=732.3MB, time=70.07 memory used=3758.0MB, alloc=756.3MB, time=79.57 memory used=4011.7MB, alloc=780.3MB, time=89.78 memory used=4266.2MB, alloc=804.3MB, time=101.08 |\^/| 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(); 1428246485 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [-15 x z - 16 x , -5 y z - 13 x z, -20 x z - 19 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 4 G := [-2 y - 16 x y , 2 x y z - 18 y z, -5 x - 15 y z] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[-15 x z - 16 x , -5 y z - 13 x z, -20 x z - 19 z ], 4 2 2 3 4 [-2 y - 16 x y , 2 x y z - 18 y z, -5 x - 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=26.2MB, alloc=32.3MB, time=0.47 memory used=48.0MB, alloc=32.3MB, time=0.79 memory used=68.5MB, alloc=32.3MB, time=1.08 memory used=88.0MB, alloc=56.3MB, time=1.38 memory used=133.1MB, alloc=60.3MB, time=2.16 memory used=174.9MB, alloc=84.3MB, time=2.82 memory used=235.5MB, alloc=84.3MB, time=3.90 memory used=295.2MB, alloc=108.3MB, time=4.85 memory used=371.6MB, alloc=140.3MB, time=6.28 memory used=458.6MB, alloc=164.3MB, time=8.81 memory used=556.0MB, alloc=164.3MB, time=12.50 memory used=653.4MB, alloc=188.3MB, time=16.26 N1 := 3367 > GB := Basis(F, plex(op(vars))); 3 2 2 6 2 2 4 GB := [20 x + 19 x , 160000 x y - 2379351 x , 32000 x y + 183027 x z, 2 2 2 -6400 x y + 14079 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=777.6MB, alloc=188.3MB, time=20.37 memory used=883.4MB, alloc=444.3MB, time=22.04 memory used=1037.6MB, alloc=468.3MB, time=24.18 memory used=1203.4MB, alloc=492.3MB, time=26.90 memory used=1384.7MB, alloc=516.3MB, time=30.35 memory used=1548.9MB, alloc=540.3MB, time=36.22 memory used=1720.2MB, alloc=564.3MB, time=43.48 memory used=1915.5MB, alloc=588.3MB, time=51.58 N2 := 4875 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 4 2 H := [-15 x z - 16 x , -5 y z - 13 x z, -20 x z - 19 z , -2 y - 16 x y , 2 3 4 2 x y z - 18 y z, -5 x - 15 y z] > J:=[op(GB),op(G)]; 3 2 2 6 2 2 4 J := [20 x + 19 x , 160000 x y - 2379351 x , 32000 x y + 183027 x z, 2 2 2 4 2 2 3 4 -6400 x y + 14079 z , -2 y - 16 x y , 2 x y z - 18 y z, -5 x - 15 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 := [6, 15, 23, 4, 4, 4, 3, 1, 2/3, 5/6, 7/12, 1/2, 2/3, 7, 17, 33, 8, 4, 6, 2, 1, 6/7, 4/7, 5/7, 4/7, 5/14, -2, -10, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2129.3MB, alloc=588.3MB, time=59.92 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428246668 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 2 F := [13 x y z + 2 y z , -9 x y - 3 x y, 5 x y + 4 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [19 y z - 3 x, -2 x z - 15 x, -12 x z + z ] > Problem := [F,G]; 2 2 2 2 2 2 2 2 Problem := [[13 x y z + 2 y z , -9 x y - 3 x y, 5 x y + 4 x y ], 3 2 2 2 [19 y z - 3 x, -2 x z - 15 x, -12 x z + z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=48.5MB, alloc=32.3MB, time=0.84 memory used=69.6MB, alloc=56.3MB, time=1.22 N1 := 355 > GB := Basis(F, plex(op(vars))); GB := 2 2 2 2 2 [5 x y + 4 x y, 12 x y - 5 x y, 5 x y z - 26 x y z, 24 y z + 65 x y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=107.9MB, alloc=60.3MB, time=1.85 memory used=147.6MB, alloc=60.3MB, time=2.44 memory used=188.7MB, alloc=84.3MB, time=3.19 N2 := 573 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 2 3 H := [13 x y z + 2 y z , -9 x y - 3 x y, 5 x y + 4 x y , 19 y z - 3 x, 2 2 2 -2 x z - 15 x, -12 x z + z ] > J:=[op(GB),op(G)]; 2 2 2 2 2 J := [5 x y + 4 x y, 12 x y - 5 x y, 5 x y z - 26 x y z, 24 y z + 65 x y z, 3 2 2 2 19 y z - 3 x, -2 x z - 15 x, -12 x z + z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 22, 4, 2, 2, 3, 1, 2/3, 2/3, 3/4, 7/12, 1/2, 7, 17, 24, 4, 2, 2, 3, 1, 5/7, 5/7, 11/14, 9/14, 4/7, -3, -2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=200.9MB, alloc=84.3MB, time=3.54 |\^/| 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(); 1428246680 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 F := [-4 x y z + 7 y z, 4 x y - 20, 8 y z + 16 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [20 x y + 12 y, 11 x y z + 16 x , 11 x + 9 x] > Problem := [F,G]; 2 2 2 2 3 Problem := [[-4 x y z + 7 y z, 4 x y - 20, 8 y z + 16 x y], 3 2 3 2 [20 x y + 12 y, 11 x y z + 16 x , 11 x + 9 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=48.3MB, alloc=32.3MB, time=0.80 memory used=69.4MB, alloc=56.3MB, time=1.16 memory used=112.6MB, alloc=60.3MB, time=1.91 memory used=152.2MB, alloc=84.3MB, time=2.60 memory used=211.3MB, alloc=108.3MB, time=3.64 memory used=287.0MB, alloc=132.3MB, time=5.86 memory used=374.5MB, alloc=132.3MB, time=9.12 N1 := 2367 > GB := Basis(F, plex(op(vars))); 10 4 3 GB := [64 x - 6125, 8 x + 35 y, 2 x + 5 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=466.1MB, alloc=140.3MB, time=11.46 N2 := 527 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 3 H := [-4 x y z + 7 y z, 4 x y - 20, 8 y z + 16 x y, 20 x y + 12 y, 2 3 2 11 x y z + 16 x , 11 x + 9 x] > J:=[op(GB),op(G)]; 10 4 3 3 2 3 J := [64 x - 6125, 8 x + 35 y, 2 x + 5 z, 20 x y + 12 y, 11 x y z + 16 x , 2 11 x + 9 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 22, 4, 3, 3, 2, 1, 5/6, 1/2, 2/3, 2/3, 1/3, 6, 11, 27, 10, 10, 1, 2, 1, 1/2, 1/3, 2/3, 1/3, 1/6, 3, -5, -6] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=486.6MB, alloc=140.3MB, time=11.95 |\^/| 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(); 1428246719 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [11 x y - 14 y, -17 x y, -7 x y - 20 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [15 x z + 13 y z, 15 x y - 17 x y , 18 x y z + 3 x] > Problem := [F,G]; 3 2 2 2 Problem := [[11 x y - 14 y, -17 x y, -7 x y - 20 y z], 3 2 2 2 2 [15 x z + 13 y z, 15 x y - 17 x y , 18 x y z + 3 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=49.0MB, alloc=32.3MB, time=0.89 memory used=69.1MB, alloc=56.3MB, time=1.26 N1 := 713 > GB := Basis(F, plex(op(vars))); GB := [y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=110.0MB, alloc=60.3MB, time=2.19 N2 := 113 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 H := [11 x y - 14 y, -17 x y, -7 x y - 20 y z, 15 x z + 13 y z, 2 2 2 2 15 x y - 17 x y , 18 x y z + 3 x] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [y, 15 x z + 13 y z, 15 x y - 17 x y , 18 x y z + 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, 15, 22, 4, 3, 3, 2, 1, 1, 1/2, 8/13, 9/13, 4/13, 4, 9, 13, 4, 3, 2, 2, 3/4, 1, 1/2, 5/7, 5/7, 3/7, 6, 9, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=113.9MB, alloc=60.3MB, time=2.26 |\^/| 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(); 1428246725 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 2 2 F := [-9 y z - 19 z , -11 x y + 5 x , 9 x z - 15 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 4 2 G := [9 y z + 7 x z, 7 x - x z, 17 y + 2 x z ] > Problem := [F,G]; 3 3 2 2 2 2 2 2 Problem := [[-9 y z - 19 z , -11 x y + 5 x , 9 x z - 15 y z], 3 2 3 2 4 2 [9 y z + 7 x z, 7 x - x z, 17 y + 2 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.4MB, alloc=40.3MB, time=0.59 memory used=60.8MB, alloc=40.3MB, time=1.02 memory used=87.3MB, alloc=40.3MB, time=1.40 memory used=112.6MB, alloc=68.3MB, time=1.81 memory used=159.0MB, alloc=68.3MB, time=2.49 memory used=204.2MB, alloc=68.3MB, time=3.18 memory used=248.2MB, alloc=92.3MB, time=3.89 memory used=315.9MB, alloc=124.3MB, time=5.09 memory used=423.9MB, alloc=124.3MB, time=6.31 memory used=523.1MB, alloc=124.3MB, time=7.61 memory used=604.5MB, alloc=148.3MB, time=9.04 memory used=702.5MB, alloc=172.3MB, time=10.80 memory used=830.6MB, alloc=196.3MB, time=12.73 memory used=968.3MB, alloc=220.3MB, time=15.05 memory used=1073.1MB, alloc=500.3MB, time=17.25 memory used=1220.6MB, alloc=524.3MB, time=21.66 memory used=1373.0MB, alloc=548.3MB, time=27.00 memory used=1535.7MB, alloc=572.3MB, time=33.61 memory used=1720.6MB, alloc=596.3MB, time=41.16 memory used=1929.4MB, alloc=596.3MB, time=49.65 memory used=2138.2MB, alloc=596.3MB, time=58.13 memory used=2347.0MB, alloc=620.3MB, time=66.66 memory used=2579.7MB, alloc=620.3MB, time=76.15 memory used=2812.3MB, alloc=644.3MB, time=85.68 memory used=3068.8MB, alloc=644.3MB, time=95.98 |\^/| 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(); 1428247025 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [7 x y z - 18 y z, 11 x y z - 10 x y , -9 y - 12 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 2 G := [11 y z - 12 z, -6 y + 20, -2 x z + 16 x ] > Problem := [F,G]; 2 2 2 3 Problem := [[7 x y z - 18 y z, 11 x y z - 10 x y , -9 y - 12 x], 3 4 3 2 [11 y z - 12 z, -6 y + 20, -2 x z + 16 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=68.1MB, alloc=32.3MB, time=1.08 memory used=87.3MB, alloc=56.3MB, time=1.39 memory used=129.2MB, alloc=60.3MB, time=2.13 memory used=165.9MB, alloc=84.3MB, time=2.77 memory used=222.0MB, alloc=84.3MB, time=3.76 memory used=271.6MB, alloc=108.3MB, time=4.76 memory used=335.6MB, alloc=132.3MB, time=6.48 memory used=412.0MB, alloc=156.3MB, time=9.35 memory used=512.6MB, alloc=156.3MB, time=13.14 memory used=613.1MB, alloc=180.3MB, time=16.84 N1 := 3353 > GB := Basis(F, plex(op(vars))); 6 2 5 2 3 2 3 GB := [343 x + 4374 x , 49 x + 243 x y, 14 x + 27 x y , 3 y + 4 x, 5 3 1715 x + 24057 x z, 490 x + 2673 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=734.7MB, alloc=188.3MB, time=19.30 memory used=866.5MB, alloc=444.3MB, time=21.44 memory used=993.7MB, alloc=468.3MB, time=23.56 memory used=1144.1MB, alloc=492.3MB, time=25.98 memory used=1322.5MB, alloc=516.3MB, time=29.23 memory used=1500.0MB, alloc=540.3MB, time=32.73 memory used=1689.8MB, alloc=564.3MB, time=36.44 memory used=1883.6MB, alloc=588.3MB, time=40.32 memory used=2088.2MB, alloc=612.3MB, time=44.86 memory used=2275.5MB, alloc=636.3MB, time=51.55 memory used=2468.0MB, alloc=660.3MB, time=58.72 memory used=2672.1MB, alloc=684.3MB, time=66.80 memory used=2889.2MB, alloc=708.3MB, time=75.67 memory used=3115.7MB, alloc=732.3MB, time=85.46 memory used=3366.2MB, alloc=756.3MB, time=96.21 |\^/| 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(); 1428247325 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [-14 x y z - 8 z, 8 x z - 13 x y z , 18 x z - 19 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 G := [-2 y z + 19 x y, -19 x z - y z, 12 x + 16 y ] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[-14 x y z - 8 z, 8 x z - 13 x y z , 18 x z - 19 y ], 2 2 3 2 2 2 [-2 y z + 19 x y, -19 x z - y z, 12 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=26.6MB, alloc=32.3MB, time=0.48 memory used=48.1MB, alloc=32.3MB, time=0.79 memory used=68.4MB, alloc=32.3MB, time=1.09 memory used=88.1MB, alloc=56.3MB, time=1.39 memory used=128.9MB, alloc=60.3MB, time=1.99 memory used=167.1MB, alloc=60.3MB, time=2.56 memory used=203.5MB, alloc=84.3MB, time=3.13 memory used=265.5MB, alloc=84.3MB, time=4.19 memory used=322.4MB, alloc=108.3MB, time=5.18 memory used=398.4MB, alloc=140.3MB, time=6.54 memory used=492.3MB, alloc=140.3MB, time=8.19 memory used=579.4MB, alloc=164.3MB, time=9.74 memory used=682.8MB, alloc=188.3MB, time=11.64 memory used=795.3MB, alloc=468.3MB, time=14.19 memory used=914.9MB, alloc=492.3MB, time=17.77 memory used=1041.7MB, alloc=516.3MB, time=22.48 memory used=1185.6MB, alloc=540.3MB, time=28.29 memory used=1353.4MB, alloc=564.3MB, time=34.98 memory used=1545.1MB, alloc=564.3MB, time=42.58 memory used=1736.9MB, alloc=564.3MB, time=50.24 memory used=1928.6MB, alloc=588.3MB, time=57.87 memory used=2144.4MB, alloc=588.3MB, time=66.57 memory used=2360.3MB, alloc=612.3MB, time=75.36 N1 := 7357 > GB := Basis(F, plex(op(vars))); 4 2 2 2 3 2 GB := [119168 x y - 257049 y , -8 x y + 13 y , 133 y + 117 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2608.1MB, alloc=612.3MB, time=81.14 N2 := 1801 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 H := [-14 x y z - 8 z, 8 x z - 13 x y z , 18 z x - 19 y , 2 2 3 2 2 2 -2 y z + 19 x y, -19 x z - y z, 12 x + 16 y ] > J:=[op(GB),op(G)]; 4 2 2 2 3 2 J := [119168 x y - 257049 y , -8 x y + 13 y , 133 y + 117 z, 2 2 3 2 2 2 -2 y z + 19 x y, -19 x z - y z, 12 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 := [6, 17, 22, 4, 2, 2, 3, 1, 1, 5/6, 7/12, 7/12, 2/3, 6, 14, 21, 6, 4, 3, 3, 5/6, 1, 1/2, 5/12, 3/4, 1/3, 3, 1, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2748.3MB, alloc=612.3MB, time=86.11 |\^/| 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(); 1428247580 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 F := [-20 x - 19 z, -11 x y z + 18 y z , -12 x y - 11 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 G := [1 + 7 z, 17 z - 12, 15 x z + 5 x ] > Problem := [F,G]; 2 3 Problem := [[-20 x - 19 z, -11 x y z + 18 y z , -12 x y - 11 x y z], 4 3 3 [1 + 7 z, 17 z - 12, 15 x z + 5 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.47 memory used=47.5MB, alloc=32.3MB, time=0.81 memory used=67.9MB, alloc=56.3MB, time=1.19 memory used=107.8MB, alloc=80.3MB, time=1.89 memory used=164.5MB, alloc=80.3MB, time=3.62 N1 := 1671 > GB := Basis(F, plex(op(vars))); 2 GB := [y x , 19 z + 20 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=216.0MB, alloc=80.3MB, time=5.11 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)]; 2 3 H := [-20 x - 19 z, -11 x y z + 18 y z , -12 x y - 11 x y z, 7 z + 1, 4 3 3 17 z - 12, 15 x z + 5 x ] > J:=[op(GB),op(G)]; 2 4 3 3 J := [y x , 19 z + 20 x, 7 z + 1, 17 z - 12, 15 x z + 5 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 17, 4, 3, 1, 4, 2/3, 1/3, 1, 1/2, 1/3, 7/12, 5, 8, 13, 4, 3, 1, 4, 3/5, 1/5, 4/5, 2/5, 1/10, 2/5, 4, 4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=237.4MB, alloc=80.3MB, time=5.51 |\^/| 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(); 1428247597 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 F := [8 x y z + 19 x , 19 x z + 3 y z, 12 x + 20 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [-4 x y z + 6 x z , -11 x z - 7 x, -3 x y + 20 x ] > Problem := [F,G]; 2 2 3 3 2 Problem := [[8 x y z + 19 x , 19 x z + 3 y z, 12 x + 20 z], 2 2 2 2 3 [-4 x y z + 6 x z , -11 x z - 7 x, -3 x y + 20 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.80 memory used=67.6MB, alloc=32.3MB, time=1.09 memory used=86.9MB, alloc=56.3MB, time=1.39 memory used=126.9MB, alloc=60.3MB, time=1.99 memory used=164.6MB, alloc=60.3MB, time=2.53 memory used=200.9MB, alloc=84.3MB, time=3.16 memory used=257.9MB, alloc=108.3MB, time=4.20 memory used=331.7MB, alloc=132.3MB, time=6.37 N1 := 1565 > GB := Basis(F, plex(op(vars))); 11 2 9 2 2 GB := [4608 x + 45125 x , 192 x + 475 x y, 3 x + 5 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=419.4MB, alloc=140.3MB, time=8.48 N2 := 707 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 2 2 H := [8 x y z + 19 x , 19 x z + 3 y z, 12 x + 20 z, -4 x y z + 6 x z , 2 2 2 3 -11 x z - 7 x, -3 x y + 20 x ] > J:=[op(GB),op(G)]; 11 2 9 2 2 2 J := [4608 x + 45125 x , 192 x + 475 x y, 3 x + 5 z, -4 x y z + 6 x z , 2 2 2 3 -11 x z - 7 x, -3 x y + 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 := [6, 15, 20, 4, 3, 3, 2, 1, 2/3, 5/6, 5/6, 1/3, 7/12, 6, 12, 32, 11, 11, 2, 2, 1, 1/2, 1/2, 11/12, 1/4, 1/3, 3, -12, -7] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=489.3MB, alloc=140.3MB, time=9.94 |\^/| 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(); 1428247627 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 4 2 F := [13 x y z + 12 y z , -8 y + 19 x, 12 y + 6 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 3 3 3 G := [12 x + 10 x z, -3 x - 3 y , -11 x y + x z ] > Problem := [F,G]; 2 3 3 4 2 Problem := [[13 x y z + 12 y z , -8 y + 19 x, 12 y + 6 z ], 4 2 3 3 3 3 [12 x + 10 x z, -3 x - 3 y , -11 x y + x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=47.8MB, alloc=32.3MB, time=0.82 memory used=68.0MB, alloc=32.3MB, time=1.12 memory used=87.1MB, alloc=56.3MB, time=1.43 memory used=126.5MB, alloc=60.3MB, time=2.03 memory used=164.1MB, alloc=84.3MB, time=2.58 memory used=205.4MB, alloc=84.3MB, time=3.19 memory used=263.3MB, alloc=92.3MB, time=4.07 memory used=319.5MB, alloc=116.3MB, time=4.93 memory used=398.0MB, alloc=140.3MB, time=6.10 memory used=497.1MB, alloc=164.3MB, time=8.26 N1 := 869 > GB := Basis(F, plex(op(vars))); 5 3 4 3 3 GB := [4826809 x + 760032072 x , 169 x + 684 x y, 8 y - 19 x, 3 2 2 2 2 2 13 x + 12 x z, 13 x y + 12 x y z, 19 x y + 4 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=596.4MB, alloc=164.3MB, time=9.78 memory used=701.4MB, alloc=420.3MB, time=11.43 memory used=825.3MB, alloc=444.3MB, time=13.64 memory used=961.3MB, alloc=468.3MB, time=16.34 memory used=1093.1MB, alloc=492.3MB, time=20.98 memory used=1235.3MB, alloc=516.3MB, time=26.55 N2 := 3487 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 4 2 4 2 H := [13 x y z + 12 y z , -8 y + 19 x, 12 y + 6 z , 12 x + 10 x z, 3 3 3 3 -3 x - 3 y , -11 x y + x z ] > J:=[op(GB),op(G)]; 5 3 4 3 3 J := [4826809 x + 760032072 x , 169 x + 684 x y, 8 y - 19 x, 3 2 2 2 2 2 4 2 13 x + 12 x z, 13 x y + 12 x y z, 4 z + 19 y x, 12 x + 10 x z, 3 3 3 3 -3 x - 3 y , -11 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 := [6, 14, 22, 4, 4, 4, 3, 5/6, 5/6, 2/3, 7/12, 1/2, 5/12, 9, 20, 32, 5, 5, 3, 3, 1, 2/3, 5/9, 5/6, 7/18, 5/18, -6, -10, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1355.9MB, alloc=516.3MB, time=31.05 |\^/| 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(); 1428247724 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 F := [-11 x y - 13 x z, -6 y z + 3 x, -16 x z - 15 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [-20 x y z - 7 y z, -15 y z , -6 x y z - 6 x z ] > Problem := [F,G]; 2 2 3 3 Problem := [[-11 x y - 13 x z, -6 y z + 3 x, -16 x z - 15 y ], 2 2 2 3 [-20 x y z - 7 y z, -15 y z , -6 x y z - 6 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.55 memory used=49.0MB, alloc=32.3MB, time=0.91 memory used=70.6MB, alloc=56.3MB, time=1.31 N1 := 411 > GB := Basis(F, plex(op(vars))); 3 2 2 3 3 GB := [21296 x - 32955 x , 21296 x y - 32955 x y, 21296 x y - 32955 y , 4 2 3 2 2 2 195 y - 88 x , 11 x y + 13 x z, 2535 y z + 968 x , 2 y z - x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=110.9MB, alloc=60.3MB, time=1.98 memory used=152.0MB, alloc=60.3MB, time=2.64 memory used=192.2MB, alloc=84.3MB, time=3.38 N2 := 681 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 2 H := [-11 x y - 13 x z, -6 y z + 3 x, -16 x z - 15 y , -20 x y z - 7 y z, 2 2 3 -15 y z , -6 x y z - 6 x z ] > J:=[op(GB),op(G)]; 3 2 2 3 3 J := [21296 x - 32955 x , 21296 x y - 32955 x y, 21296 x y - 32955 y , 4 2 3 2 2 2 195 y - 88 x , 11 x y + 13 x z, 2535 z y + 968 x , 2 y z - x, 2 2 2 3 -20 x y z - 7 y z, -15 y z , -6 x y z - 6 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 := [6, 17, 21, 4, 2, 3, 3, 5/6, 1, 1, 7/13, 7/13, 8/13, 10, 24, 35, 4, 3, 4, 3, 9/10, 9/10, 3/5, 13/21, 4/7, 8/21, -7, -14, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=214.7MB, alloc=84.3MB, time=3.95 |\^/| 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(); 1428247738 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 3 F := [-3 x z - 12 x, -17 x - 16 y z, -16 y z - 6 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 G := [8 z - 20 z, 9 y + 4 y z, -16 x y - 20 x z] > Problem := [F,G]; 3 3 2 3 3 Problem := [[-3 x z - 12 x, -17 x - 16 y z, -16 y z - 6 x ], 3 2 3 3 [8 z - 20 z, 9 y + 4 y z, -16 x y - 20 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.51 memory used=48.2MB, alloc=32.3MB, time=0.82 memory used=69.0MB, alloc=32.3MB, time=1.15 memory used=88.9MB, alloc=56.3MB, time=1.46 memory used=128.9MB, alloc=60.3MB, time=2.11 memory used=167.0MB, alloc=84.3MB, time=2.72 memory used=213.5MB, alloc=84.3MB, time=3.44 memory used=271.2MB, alloc=92.3MB, time=4.39 memory used=329.7MB, alloc=116.3MB, time=5.29 memory used=397.9MB, alloc=140.3MB, time=6.41 memory used=457.5MB, alloc=396.3MB, time=7.43 memory used=561.0MB, alloc=420.3MB, time=9.05 memory used=682.2MB, alloc=444.3MB, time=10.86 memory used=817.8MB, alloc=468.3MB, time=12.97 memory used=929.4MB, alloc=468.3MB, time=14.66 memory used=1058.5MB, alloc=492.3MB, time=16.84 memory used=1175.9MB, alloc=492.3MB, time=18.76 memory used=1273.1MB, alloc=492.3MB, time=20.48 memory used=1362.4MB, alloc=516.3MB, time=22.10 memory used=1445.3MB, alloc=516.3MB, time=23.75 memory used=1524.5MB, alloc=516.3MB, time=25.28 memory used=1594.5MB, alloc=516.3MB, time=26.74 memory used=1664.4MB, alloc=516.3MB, time=28.23 memory used=1734.6MB, alloc=516.3MB, time=29.64 memory used=1785.5MB, alloc=516.3MB, time=30.80 memory used=1841.8MB, alloc=516.3MB, time=32.23 memory used=2033.5MB, alloc=540.3MB, time=35.91 memory used=2238.6MB, alloc=564.3MB, time=40.09 memory used=2466.5MB, alloc=588.3MB, time=44.41 memory used=2675.0MB, alloc=612.3MB, time=48.41 memory used=2871.1MB, alloc=636.3MB, time=52.02 memory used=3045.2MB, alloc=660.3MB, time=55.55 memory used=3228.8MB, alloc=684.3MB, time=59.55 memory used=3413.8MB, alloc=708.3MB, time=63.78 memory used=3571.5MB, alloc=732.3MB, time=67.56 memory used=3703.8MB, alloc=756.3MB, time=70.57 memory used=3882.6MB, alloc=780.3MB, time=74.84 memory used=4040.1MB, alloc=804.3MB, time=78.74 memory used=4259.6MB, alloc=828.3MB, time=83.97 memory used=4456.4MB, alloc=852.3MB, time=88.49 memory used=4635.4MB, alloc=876.3MB, time=92.81 memory used=4817.0MB, alloc=900.3MB, time=97.29 memory used=4986.7MB, alloc=924.3MB, time=101.75 |\^/| 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(); 1428248038 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 2 2 F := [-17 x - 4 x, -5 x + 12 x z, -5 y z + 8 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 3 G := [-10 x y z + 11 y z, -18 y - 18 x y, -11 x y + 5 x z ] > Problem := [F,G]; 4 4 2 2 Problem := [[-17 x - 4 x, -5 x + 12 x z, -5 y z + 8 y], 2 2 4 2 2 3 [-10 x y z + 11 y z, -18 y - 18 x y, -11 x y + 5 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=48.0MB, alloc=32.3MB, time=0.82 memory used=68.7MB, alloc=32.3MB, time=1.13 memory used=89.0MB, alloc=56.3MB, time=1.46 memory used=129.8MB, alloc=60.3MB, time=2.11 memory used=169.9MB, alloc=84.3MB, time=2.87 memory used=229.0MB, alloc=84.3MB, time=3.95 memory used=283.8MB, alloc=108.3MB, time=4.93 memory used=356.1MB, alloc=140.3MB, time=6.28 memory used=440.5MB, alloc=164.3MB, time=8.55 memory used=533.9MB, alloc=188.3MB, time=12.04 memory used=649.3MB, alloc=188.3MB, time=16.41 memory used=764.6MB, alloc=212.3MB, time=20.82 N1 := 3777 > GB := Basis(F, plex(op(vars))); 4 2 2 2 GB := [17 x + 4 x, 125 x y - 20808 x y, 51 x z + 5 x, 5 y z - 8 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=906.3MB, alloc=212.3MB, time=24.55 memory used=1024.0MB, alloc=468.3MB, time=26.64 memory used=1180.6MB, alloc=492.3MB, time=29.50 memory used=1330.9MB, alloc=516.3MB, time=35.27 N2 := 3107 #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)]; 4 4 2 2 2 2 H := [-17 x - 4 x, -5 x + 12 x z, -5 y z + 8 y, -10 x y z + 11 y z, 4 2 2 3 -18 y - 18 x y, -11 x y + 5 x z ] > J:=[op(GB),op(G)]; 4 2 2 2 J := [17 x + 4 x, 125 x y - 20808 x y, 51 x z + 5 x, 5 y z - 8 y, 2 2 4 2 2 3 -10 x y z + 11 y z, -18 y - 18 x y, -11 x y + 5 x z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 24, 4, 4, 4, 3, 5/6, 2/3, 2/3, 2/3, 7/12, 5/12, 7, 15, 25, 4, 4, 4, 3, 6/7, 5/7, 4/7, 5/7, 9/14, 5/14, -2, -1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1488.7MB, alloc=516.3MB, time=41.42 |\^/| 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(); 1428248173 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 2 F := [15 x y , -3 x y z - 6 y , 11 x y z - 12 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 2 2 G := [6 x y - 14 y z , y - 18 x y, -y z + 12 x y ] > Problem := [F,G]; 3 2 4 2 2 Problem := [[15 x y , -3 x y z - 6 y , 11 x y z - 12 x z ], 2 2 3 3 2 2 2 [6 x y - 14 y z , y - 18 x y, -y z + 12 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=48.3MB, alloc=32.3MB, time=0.81 memory used=69.3MB, alloc=32.3MB, time=1.12 memory used=89.4MB, alloc=56.3MB, time=1.43 memory used=132.1MB, alloc=60.3MB, time=2.13 memory used=175.9MB, alloc=84.3MB, time=2.82 memory used=239.8MB, alloc=84.3MB, time=3.92 memory used=295.4MB, alloc=108.3MB, time=5.00 memory used=361.3MB, alloc=132.3MB, time=7.29 memory used=444.6MB, alloc=156.3MB, time=10.49 N1 := 2309 > GB := Basis(F, plex(op(vars))); 3 6 2 4 4 2 GB := [x y , y , x y z + 2 y , z y , x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=556.0MB, alloc=164.3MB, time=12.69 N2 := 1067 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 4 2 2 2 2 3 H := [15 x y , -3 x y z - 6 y , 11 x y z - 12 x z , 6 x y - 14 y z , 3 2 2 2 y - 18 x y, -y z + 12 x y ] > J:=[op(GB),op(G)]; 3 6 2 4 4 2 2 2 3 3 J := [x y , y , x y z + 2 y , z y , x z , 6 x y - 14 y z , y - 18 x y, 2 2 2 -y z + 12 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 := [6, 16, 23, 4, 2, 4, 3, 1, 1, 2/3, 7/13, 10/13, 5/13, 8, 18, 33, 6, 2, 6, 3, 3/4, 7/8, 5/8, 3/8, 11/16, 5/16, -2, -10, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=641.9MB, alloc=164.3MB, time=14.83 |\^/| 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(); 1428248218 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 F := [-16 x y + 7 z , -11 x - 20 z , 13 x y - 15 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 3 G := [-3 y + 3 y z, 19 x z - 7 y , -5 x - 8 z] > Problem := [F,G]; 2 2 3 3 2 Problem := [[-16 x y + 7 z , -11 x - 20 z , 13 x y - 15 z], 4 3 2 2 3 [-3 y + 3 y z, 19 x z - 7 y , -5 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=4.4MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=48.1MB, alloc=32.3MB, time=0.82 memory used=68.3MB, alloc=32.3MB, time=1.11 memory used=87.7MB, alloc=56.3MB, time=1.41 memory used=127.7MB, alloc=60.3MB, time=2.01 memory used=165.8MB, alloc=84.3MB, time=2.58 memory used=207.8MB, alloc=84.3MB, time=3.14 memory used=265.5MB, alloc=116.3MB, time=4.07 memory used=348.5MB, alloc=116.3MB, time=5.27 memory used=428.1MB, alloc=140.3MB, time=6.48 memory used=503.4MB, alloc=396.3MB, time=7.66 memory used=605.5MB, alloc=420.3MB, time=9.21 memory used=732.3MB, alloc=444.3MB, time=11.04 memory used=872.4MB, alloc=468.3MB, time=13.25 memory used=1006.5MB, alloc=492.3MB, time=15.38 memory used=1130.3MB, alloc=516.3MB, time=17.42 memory used=1248.5MB, alloc=516.3MB, time=19.30 memory used=1367.5MB, alloc=540.3MB, time=21.28 memory used=1466.3MB, alloc=540.3MB, time=23.07 memory used=1564.7MB, alloc=540.3MB, time=25.08 memory used=1706.5MB, alloc=564.3MB, time=28.16 memory used=1835.5MB, alloc=588.3MB, time=30.93 memory used=1964.2MB, alloc=612.3MB, time=33.74 memory used=2102.7MB, alloc=636.3MB, time=36.80 memory used=2265.7MB, alloc=660.3MB, time=39.82 memory used=2392.8MB, alloc=684.3MB, time=42.62 memory used=2502.0MB, alloc=708.3MB, time=45.11 memory used=2637.0MB, alloc=732.3MB, time=49.36 memory used=2926.5MB, alloc=756.3MB, time=59.60 memory used=3215.1MB, alloc=780.3MB, time=70.85 memory used=3500.7MB, alloc=804.3MB, time=83.52 memory used=3805.9MB, alloc=828.3MB, time=97.17 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428248518 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [20 y z - 18 x z, 19 z + 12 y, 14 x y + 10 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 G := [-16 x y z + 15 z, 16 y z - 14 y, 8 z - 14 y ] > Problem := [F,G]; 2 3 2 2 Problem := [[20 y z - 18 x z, 19 z + 12 y, 14 x y + 10 y], 2 3 3 2 [-16 x y z + 15 z, 16 y z - 14 y, 8 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=26.2MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.82 memory used=68.9MB, alloc=32.3MB, time=1.12 memory used=88.8MB, alloc=56.3MB, time=1.43 memory used=129.5MB, alloc=60.3MB, time=2.05 memory used=170.8MB, alloc=60.3MB, time=2.64 memory used=208.9MB, alloc=84.3MB, time=3.22 memory used=269.7MB, alloc=92.3MB, time=4.15 memory used=328.8MB, alloc=116.3MB, time=5.04 memory used=409.0MB, alloc=140.3MB, time=6.40 memory used=506.7MB, alloc=164.3MB, time=8.22 memory used=619.5MB, alloc=188.3MB, time=10.35 memory used=745.4MB, alloc=212.3MB, time=12.71 memory used=866.9MB, alloc=492.3MB, time=15.04 memory used=1010.2MB, alloc=516.3MB, time=18.88 memory used=1153.6MB, alloc=540.3MB, time=23.71 memory used=1309.0MB, alloc=564.3MB, time=29.11 memory used=1473.8MB, alloc=588.3MB, time=35.76 memory used=1661.6MB, alloc=612.3MB, time=43.39 memory used=1873.4MB, alloc=636.3MB, time=51.93 memory used=2109.1MB, alloc=636.3MB, time=61.43 memory used=2344.8MB, alloc=660.3MB, time=71.26 memory used=2604.4MB, alloc=660.3MB, time=81.64 memory used=2864.0MB, alloc=660.3MB, time=92.03 memory used=3123.6MB, alloc=684.3MB, time=102.49 |\^/| 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(); 1428248818 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 F := [11 x y + 14 x z, 12 y, 12 x y + 7] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 G := [19 z - 16 x, 18 x z, 20 y z - 9 x ] > Problem := [F,G]; 2 Problem := [[11 x y + 14 x z, 12 y, 12 x y + 7], 3 3 2 2 2 [19 z - 16 x, 18 x z, 20 y z - 9 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=27.1MB, alloc=32.3MB, time=0.51 memory used=48.7MB, alloc=32.3MB, time=0.83 memory used=71.1MB, alloc=56.3MB, time=1.25 memory used=114.3MB, alloc=60.3MB, time=2.02 memory used=154.0MB, alloc=84.3MB, time=2.73 memory used=211.3MB, alloc=108.3MB, time=4.13 memory used=279.8MB, alloc=108.3MB, time=6.71 N1 := 1949 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 119 #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)]; H := [ 2 3 3 2 2 2 11 x y + 14 x z, 12 y, 12 y x + 7, 19 z - 16 x, 18 x z, 20 y z - 9 x ] > J:=[op(GB),op(G)]; 3 3 2 2 2 J := [1, 19 z - 16 x, 18 x z, 20 y 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, 13, 17, 4, 3, 2, 3, 5/6, 2/3, 2/3, 6/13, 4/13, 4/13, 4, 7, 11, 4, 3, 2, 3, 3/4, 1/4, 3/4, 3/8, 1/8, 3/8, 6, 6, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=321.8MB, alloc=108.3MB, time=7.86 |\^/| 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(); 1428248842 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 4 F := [-16 y z - 4 x z, -5 x z + 9 x, -9 x y + 2 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [15 x y z - x y , y z + 5 x , -20 x y + 7 x z] > Problem := [F,G]; 2 2 2 2 2 3 4 Problem := [[-16 y z - 4 x z, -5 x z + 9 x, -9 x y + 2 y ], 2 2 2 2 3 2 [15 x y z - x y , y z + 5 x , -20 x y + 7 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.50 memory used=48.5MB, alloc=32.3MB, time=0.83 memory used=68.7MB, alloc=56.3MB, time=1.14 memory used=109.8MB, alloc=60.3MB, time=1.75 memory used=147.4MB, alloc=84.3MB, time=2.32 memory used=206.1MB, alloc=92.3MB, time=3.25 memory used=264.0MB, alloc=116.3MB, time=4.15 memory used=321.9MB, alloc=116.3MB, time=4.86 memory used=397.6MB, alloc=396.3MB, time=6.01 memory used=502.5MB, alloc=396.3MB, time=7.55 memory used=604.5MB, alloc=420.3MB, time=9.16 memory used=734.1MB, alloc=444.3MB, time=11.02 memory used=855.6MB, alloc=468.3MB, time=12.86 memory used=979.3MB, alloc=492.3MB, time=14.64 memory used=1082.8MB, alloc=492.3MB, time=16.17 memory used=1179.5MB, alloc=492.3MB, time=17.69 memory used=1279.1MB, alloc=516.3MB, time=19.28 memory used=1363.3MB, alloc=516.3MB, time=20.69 memory used=1457.5MB, alloc=516.3MB, time=22.38 memory used=1524.7MB, alloc=516.3MB, time=23.56 memory used=1590.3MB, alloc=516.3MB, time=24.81 memory used=1644.1MB, alloc=540.3MB, time=25.73 memory used=1702.3MB, alloc=540.3MB, time=26.87 memory used=1759.3MB, alloc=540.3MB, time=27.92 memory used=1821.0MB, alloc=540.3MB, time=29.11 memory used=1862.7MB, alloc=540.3MB, time=30.11 memory used=2076.5MB, alloc=564.3MB, time=33.92 memory used=2271.0MB, alloc=588.3MB, time=37.86 memory used=2497.3MB, alloc=612.3MB, time=41.99 memory used=2779.2MB, alloc=636.3MB, time=45.90 memory used=3122.7MB, alloc=660.3MB, time=49.10 memory used=3471.9MB, alloc=684.3MB, time=53.27 memory used=3771.4MB, alloc=708.3MB, time=58.93 memory used=4058.6MB, alloc=732.3MB, time=64.82 memory used=4345.3MB, alloc=756.3MB, time=70.84 memory used=4647.2MB, alloc=780.3MB, time=76.94 memory used=5026.2MB, alloc=804.3MB, time=82.12 memory used=5401.6MB, alloc=828.3MB, time=88.47 memory used=5857.4MB, alloc=852.3MB, time=92.21 memory used=6344.9MB, alloc=876.3MB, time=96.00 memory used=6857.7MB, alloc=900.3MB, time=99.83 memory used=7394.9MB, alloc=924.3MB, time=103.66 memory used=7958.5MB, alloc=948.3MB, 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(); 1428249142 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [11 x y - 15 y z, 17 y z + 3 x z, 16 x y z - 12 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 G := [-5 x y z - 5 x z, 12 x y z - 3 x y, -10 z - 6 x y] > Problem := [F,G]; 3 2 3 2 Problem := [[11 x y - 15 y z, 17 y z + 3 x z, 16 x y z - 12 x z], 2 4 2 [-5 x y z - 5 x z, 12 x y z - 3 x y, -10 z - 6 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.5MB, alloc=32.3MB, time=0.79 memory used=68.4MB, alloc=32.3MB, time=1.11 memory used=87.4MB, alloc=56.3MB, time=1.41 memory used=126.6MB, alloc=60.3MB, time=2.02 memory used=166.3MB, alloc=60.3MB, time=2.60 memory used=203.1MB, alloc=84.3MB, time=3.17 memory used=261.1MB, alloc=92.3MB, time=4.11 memory used=315.7MB, alloc=116.3MB, time=4.96 memory used=390.8MB, alloc=140.3MB, time=6.15 memory used=487.9MB, alloc=164.3MB, time=7.88 memory used=599.0MB, alloc=188.3MB, time=9.88 memory used=719.1MB, alloc=468.3MB, time=12.05 memory used=859.1MB, alloc=492.3MB, time=14.55 memory used=1010.4MB, alloc=516.3MB, time=17.34 memory used=1159.5MB, alloc=540.3MB, time=21.68 memory used=1312.1MB, alloc=564.3MB, time=26.75 memory used=1474.2MB, alloc=588.3MB, time=32.87 memory used=1649.4MB, alloc=612.3MB, time=40.08 memory used=1848.6MB, alloc=636.3MB, time=48.34 memory used=2071.7MB, alloc=660.3MB, time=57.59 memory used=2318.8MB, alloc=684.3MB, time=67.62 memory used=2589.8MB, alloc=684.3MB, time=78.60 memory used=2860.7MB, alloc=684.3MB, time=89.62 |\^/| 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(); 1428249442 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 2 F := [-12 x y - 2 x z, 7 x z + 7 x y z , -10 x z + 18 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 2 2 G := [-x y - 7 x y , -5 y - 3 y z , 15 y ] > Problem := [F,G]; 2 2 2 2 2 2 2 2 Problem := [[-12 x y - 2 x z, 7 x z + 7 x y z , -10 x z + 18 y z], 3 2 4 2 2 2 [-x y - 7 x y , -5 y - 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=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.83 memory used=68.3MB, alloc=56.3MB, time=1.20 N1 := 347 > GB := Basis(F, plex(op(vars))); 3 4 2 4 2 5 2 4 2 2 2 GB := [10 x y + 3 x y , 10 x y - 3 x y , 6 x y + x z, 2 4 2 2 4 3 2 2 -20 x y + x y z, 20 x y + y z, 5 x z - 9 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=106.3MB, alloc=60.3MB, time=1.78 memory used=146.2MB, alloc=60.3MB, time=2.36 memory used=184.3MB, alloc=60.3MB, time=2.92 memory used=219.8MB, alloc=84.3MB, time=3.47 memory used=274.5MB, alloc=84.3MB, time=4.32 memory used=330.3MB, alloc=116.3MB, time=5.35 N2 := 1125 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 2 H := [-12 x y - 2 x z, 7 x z + 7 x y z , -10 x z + 18 y z, 3 2 4 2 2 2 -x y - 7 x y , -5 y - 3 y z , 15 y ] > J:=[op(GB),op(G)]; 3 4 2 4 2 5 2 4 2 2 2 J := [10 x y + 3 x y , 10 x y - 3 x y , 6 x y + x z, 2 4 2 2 4 3 2 2 3 2 -20 x y + x y z, 20 x y + y z, 5 x z - 9 y z, -x y - 7 x y , 4 2 2 2 -5 y - 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 := [6, 14, 21, 4, 3, 4, 2, 2/3, 1, 2/3, 7/12, 2/3, 1/2, 9, 21, 43, 7, 3, 5, 2, 7/9, 1, 5/9, 2/3, 5/6, 1/3, -7, -22, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=394.5MB, alloc=116.3MB, time=7.18 |\^/| 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(); 1428249464 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 F := [10 z + 18 z , 18 x y - 6 x , -15 x y + 18] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 2 3 G := [x y z + 18 y z, 9 z + 9 x z, -x z + 20 y z ] > Problem := [F,G]; 4 2 2 2 2 2 Problem := [[10 z + 18 z , 18 x y - 6 x , -15 x y + 18], 2 4 2 2 2 3 [x y z + 18 y z, 9 z + 9 x z, -x z + 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=26.2MB, alloc=32.3MB, time=0.48 memory used=47.6MB, alloc=32.3MB, time=0.80 memory used=68.1MB, alloc=32.3MB, time=1.10 memory used=88.5MB, alloc=32.3MB, time=1.41 memory used=107.3MB, alloc=56.3MB, time=1.70 memory used=149.5MB, alloc=60.3MB, time=2.43 memory used=188.8MB, alloc=84.3MB, time=3.14 memory used=248.8MB, alloc=84.3MB, time=4.22 memory used=300.7MB, alloc=108.3MB, time=5.44 memory used=364.6MB, alloc=132.3MB, time=7.81 N1 := 2163 > GB := Basis(F, plex(op(vars))); 2 4 2 GB := [5 x - 18, 3 y - 1, 5 z + 9 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=453.7MB, alloc=132.3MB, time=10.50 memory used=551.4MB, alloc=140.3MB, time=12.17 N2 := 1217 #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)]; 4 2 2 2 2 2 2 H := [10 z + 18 z , 18 x y - 6 x , -15 x y + 18, x y z + 18 y z, 4 2 2 2 3 9 z + 9 x z, -x z + 20 y z ] > J:=[op(GB),op(G)]; 2 4 2 2 4 2 J := [5 x - 18, 3 y - 1, 5 z + 9 z , x y z + 18 y z, 9 z + 9 x z, 2 2 3 -x z + 20 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 := [6, 13, 23, 4, 2, 2, 4, 5/6, 2/3, 2/3, 1/2, 5/12, 2/3, 6, 11, 19, 4, 2, 2, 4, 2/3, 1/2, 2/3, 1/3, 1/3, 2/3, 2, 4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=640.5MB, alloc=140.3MB, time=14.66 |\^/| 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(); 1428249506 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 3 F := [-18 x y z + 8 y z , 3 x y z + 6 x y z, 18 x y - 19 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [-4 x y z + 15 x , 19 x z - 18 x z, -4 x + 19 y] > Problem := [F,G]; 2 3 2 3 3 Problem := [[-18 x y z + 8 y z , 3 x y z + 6 x y z, 18 x y - 19 y z], 2 3 2 2 [-4 x y z + 15 x , 19 x z - 18 x z, -4 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=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=68.3MB, alloc=56.3MB, time=1.17 memory used=109.9MB, alloc=56.3MB, time=1.89 memory used=145.1MB, alloc=84.3MB, time=2.62 memory used=195.5MB, alloc=108.3MB, time=4.26 N1 := 1863 > GB := Basis(F, plex(op(vars))); 2 3 2 3 3 2 3 GB := [x y , x y z + 2 x y z, -18 x y + 19 y z, -9 x y z + 4 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=267.8MB, alloc=108.3MB, time=6.44 memory used=345.8MB, alloc=116.3MB, time=7.81 memory used=420.2MB, alloc=140.3MB, time=9.63 N2 := 1863 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 3 3 H := [-18 x y z + 8 y z , 3 x y z + 6 x y z, 18 x y - 19 y z, 2 3 2 2 -4 x y z + 15 x , 19 x z - 18 x z, -4 x + 19 y] > J:=[op(GB),op(G)]; 2 3 2 3 3 2 3 J := [x y , x y z + 2 x y z, -18 x y + 19 y z, -9 x y z + 4 y z , 2 3 2 2 -4 x y z + 15 x , 19 x z - 18 x z, -4 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 := [6, 16, 21, 4, 3, 3, 3, 1, 5/6, 5/6, 3/4, 2/3, 2/3, 7, 18, 26, 5, 3, 3, 3, 1, 6/7, 5/7, 5/7, 9/14, 4/7, -2, -5, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=501.0MB, alloc=140.3MB, time=12.31 |\^/| 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(); 1428249542 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [20 x y z + 10 y , -7 x z - 18 x z, -2 z + 15 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 4 G := [13 y + 11, -7 x y - 9 y z, 15 y + 3 x] > Problem := [F,G]; 2 2 2 2 2 Problem := [[20 x y z + 10 y , -7 x z - 18 x z, -2 z + 15 x], 4 2 2 4 [13 y + 11, -7 x y - 9 y z, 15 y + 3 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=68.1MB, alloc=32.3MB, time=1.09 memory used=88.4MB, alloc=32.3MB, time=1.38 memory used=107.7MB, alloc=56.3MB, time=1.68 memory used=149.8MB, alloc=60.3MB, time=2.45 memory used=188.4MB, alloc=60.3MB, time=3.11 memory used=221.7MB, alloc=84.3MB, time=3.78 memory used=270.2MB, alloc=108.3MB, time=5.48 N1 := 1471 > GB := Basis(F, plex(op(vars))); 5 2 2 3 2 GB := [245 x - 216 x , y , 35 x + 12 x z, 2 z - 15 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=341.8MB, alloc=108.3MB, time=6.76 N2 := 539 #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 4 H := [20 x y z + 10 y , -7 x z - 18 x z, -2 z + 15 x, 13 y + 11, 2 2 4 -7 x y - 9 y z, 15 y + 3 x] > J:=[op(GB),op(G)]; 5 2 2 3 2 4 J := [245 x - 216 x , y , 35 x + 12 x z, 2 z - 15 x, 13 y + 11, 2 2 4 -7 x y - 9 y z, 15 y + 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, 13, 21, 4, 2, 4, 2, 5/6, 2/3, 2/3, 1/2, 1/2, 5/12, 7, 12, 23, 5, 5, 4, 2, 5/7, 4/7, 3/7, 1/2, 5/14, 3/14, 1, -2, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=370.0MB, alloc=108.3MB, time=7.36 |\^/| 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(); 1428249564 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [11 x y + 15 x y z, -19 x z + 15 x, 7 x y z + 15] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 2 2 2 2 2 G := [-15 x + 9 x z , 17 x - y z , 14 y z + 19 z ] > Problem := [F,G]; 2 2 2 3 Problem := [[11 x y + 15 x y z, -19 x z + 15 x, 7 x y z + 15], 4 2 4 2 2 2 2 2 [-15 x + 9 x z , 17 x - y z , 14 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=26.4MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=68.1MB, alloc=32.3MB, time=1.10 memory used=87.5MB, alloc=56.3MB, time=1.40 memory used=127.8MB, alloc=60.3MB, time=2.00 memory used=166.4MB, alloc=60.3MB, time=2.60 memory used=202.4MB, alloc=84.3MB, time=3.17 memory used=260.2MB, alloc=92.3MB, time=4.09 memory used=317.3MB, alloc=116.3MB, time=4.98 memory used=395.0MB, alloc=116.3MB, time=6.18 memory used=471.6MB, alloc=396.3MB, time=7.35 memory used=570.0MB, alloc=420.3MB, time=9.00 memory used=685.1MB, alloc=444.3MB, time=11.13 memory used=813.0MB, alloc=468.3MB, time=13.50 memory used=960.2MB, alloc=492.3MB, time=16.13 memory used=1116.9MB, alloc=516.3MB, time=19.08 memory used=1281.8MB, alloc=540.3MB, time=22.30 memory used=1457.6MB, alloc=564.3MB, time=25.72 memory used=1635.9MB, alloc=588.3MB, time=29.80 memory used=1802.5MB, alloc=612.3MB, time=34.98 memory used=1974.3MB, alloc=636.3MB, time=40.86 memory used=2156.4MB, alloc=660.3MB, time=47.37 memory used=2350.1MB, alloc=684.3MB, time=54.64 memory used=2554.8MB, alloc=708.3MB, time=62.80 memory used=2771.6MB, alloc=732.3MB, time=72.23 memory used=3012.4MB, alloc=756.3MB, time=82.61 memory used=3277.1MB, alloc=780.3MB, time=93.96 |\^/| 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(); 1428249864 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [15 y z - 18 z, -6 x y z - y, -11 y z - 17 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 G := [8 x y z - 9 z , 6 x z + 13 x y z, -13 x y z + 5 x ] > Problem := [F,G]; 3 2 2 2 Problem := [[15 y z - 18 z, -6 x y z - y, -11 y z - 17 x ], 3 3 2 2 2 [8 x y z - 9 z , 6 x z + 13 x y z, -13 x y z + 5 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=48.1MB, alloc=32.3MB, time=0.79 memory used=68.4MB, alloc=32.3MB, time=1.08 memory used=88.0MB, alloc=56.3MB, time=1.38 memory used=127.9MB, alloc=60.3MB, time=1.95 memory used=167.3MB, alloc=60.3MB, time=2.52 memory used=204.8MB, alloc=60.3MB, time=3.05 memory used=241.7MB, alloc=84.3MB, time=3.66 memory used=301.6MB, alloc=84.3MB, time=4.69 memory used=356.5MB, alloc=108.3MB, time=5.67 memory used=431.2MB, alloc=140.3MB, time=7.01 memory used=524.1MB, alloc=164.3MB, time=8.70 memory used=623.8MB, alloc=188.3MB, time=11.53 memory used=731.9MB, alloc=212.3MB, time=15.58 memory used=863.9MB, alloc=212.3MB, time=20.52 memory used=996.1MB, alloc=236.3MB, time=25.47 N1 := 4081 > GB := Basis(F, plex(op(vars))); 20 2 6 16 GB := [191017440 x + 1331 x , 612 x + 11 y, -31836240 x + 1331 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1148.5MB, alloc=236.3MB, time=28.97 memory used=1336.7MB, alloc=516.3MB, time=33.83 N2 := 1547 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 H := [15 y z - 18 z, -6 x y z - y, -11 y z - 17 x , 8 x y z - 9 z , 3 2 2 2 6 x z + 13 x y z, -13 x y z + 5 x ] > J:=[op(GB),op(G)]; 20 2 6 16 J := [191017440 x + 1331 x , 612 x + 11 y, -31836240 x + 1331 z, 3 3 2 2 2 8 x y z - 9 z , 6 x z + 13 x y z, -13 x y z + 5 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 17, 22, 4, 3, 3, 3, 5/6, 1, 1, 7/12, 7/12, 3/4, 6, 14, 53, 20, 20, 2, 3, 1, 2/3, 2/3, 3/4, 1/3, 1/2, 3, -31, -16] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1339.5MB, alloc=516.3MB, time=33.92 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428249970 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 3 F := [-10 x z - 2 y z , -18 x z - 18 x y z, -15 x y z - 16 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 4 G := [17 y , -19 x z + 12 y z, 20 y - 6] > Problem := [F,G]; 2 2 2 2 3 2 3 Problem := [[-10 x z - 2 y z , -18 x z - 18 x y z, -15 x y z - 16 z ], 4 2 2 4 [17 y , -19 x z + 12 y z, 20 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=26.0MB, alloc=32.3MB, time=0.47 memory used=49.5MB, alloc=32.3MB, time=0.86 memory used=70.6MB, alloc=56.3MB, time=1.23 memory used=112.1MB, alloc=56.3MB, time=2.21 N1 := 891 > GB := Basis(F, plex(op(vars))); 5 3 2 4 3 4 2 2 2 2 2 GB := [x z, x z + x y z, -5 x z + x y z, x z , 5 x z + y z , 3 15 x y z + 16 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=147.0MB, alloc=60.3MB, time=2.85 memory used=185.0MB, alloc=84.3MB, time=3.49 memory used=247.1MB, alloc=108.3MB, time=4.65 N2 := 1255 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 2 3 4 H := [-10 x z - 2 y z , -18 x z - 18 x y z, -15 x y z - 16 z , 17 y , 2 2 4 -19 x z + 12 y z, 20 y - 6] > J:=[op(GB),op(G)]; 5 3 2 4 3 4 2 2 2 2 2 J := [x z, x z + x y z, -5 x z + x y z, x z , 5 x z + y z , 3 4 2 2 4 15 x y z + 16 z , 17 y , -19 x z + 12 y z, 20 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 := [6, 14, 22, 4, 3, 4, 3, 2/3, 1, 2/3, 5/12, 1/2, 2/3, 9, 21, 39, 6, 5, 4, 3, 7/9, 7/9, 7/9, 1/2, 7/18, 2/3, -7, -17, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=308.3MB, alloc=108.3MB, time=6.52 |\^/| 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(); 1428249988 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 F := [-19 y z + 16 z, -7 x y z + y z , 5 x y + 8 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 4 G := [-19 x y - 18 x z , 15 x y + 16 x y z, -20 x y z - 9 y ] > Problem := [F,G]; 2 2 2 2 2 3 2 Problem := [[-19 y z + 16 z, -7 x y z + y z , 5 x y + 8 x y z], 3 3 3 2 2 4 [-19 x y - 18 x z , 15 x y + 16 x y z, -20 x 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.3MB, alloc=32.3MB, time=0.80 memory used=66.4MB, alloc=56.3MB, time=1.10 memory used=105.9MB, alloc=60.3MB, time=1.70 memory used=143.9MB, alloc=84.3MB, time=2.28 memory used=203.1MB, alloc=92.3MB, time=3.16 memory used=259.9MB, alloc=116.3MB, time=4.01 memory used=339.5MB, alloc=140.3MB, time=5.16 memory used=428.2MB, alloc=396.3MB, time=6.63 memory used=521.0MB, alloc=420.3MB, time=8.34 memory used=628.0MB, alloc=444.3MB, time=10.36 memory used=749.2MB, alloc=468.3MB, time=12.58 memory used=882.7MB, alloc=492.3MB, time=15.05 memory used=1028.2MB, alloc=516.3MB, time=17.75 memory used=1180.2MB, alloc=540.3MB, time=20.88 memory used=1326.9MB, alloc=564.3MB, time=25.45 memory used=1480.7MB, alloc=588.3MB, time=30.64 memory used=1646.5MB, alloc=612.3MB, time=36.57 memory used=1825.6MB, alloc=636.3MB, time=43.29 memory used=2014.2MB, alloc=660.3MB, time=51.30 memory used=2224.5MB, alloc=684.3MB, time=60.22 memory used=2458.8MB, alloc=708.3MB, time=70.18 memory used=2716.9MB, alloc=732.3MB, time=81.06 memory used=2999.1MB, alloc=756.3MB, time=93.01 |\^/| 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(); 1428250289 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 F := [-5 x z - 13 z, -11 y z + 15 x z , -2 x z + x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 4 2 2 G := [-20 x y - 10 z , 16 x y - 5 x y , 12 y + 15 y z ] > Problem := [F,G]; 2 2 3 2 2 2 2 Problem := [[-5 x z - 13 z, -11 y z + 15 x z , -2 x z + x y z], 2 3 2 4 2 2 [-20 x y - 10 z , 16 x y - 5 x y , 12 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=26.8MB, alloc=32.3MB, time=0.50 memory used=47.9MB, alloc=32.3MB, time=0.79 memory used=67.9MB, alloc=56.3MB, time=1.10 memory used=109.1MB, alloc=60.3MB, time=1.71 memory used=148.4MB, alloc=60.3MB, time=2.29 memory used=186.4MB, alloc=84.3MB, time=2.85 memory used=236.0MB, alloc=84.3MB, time=3.60 memory used=292.2MB, alloc=92.3MB, time=4.48 memory used=348.4MB, alloc=116.3MB, time=5.31 memory used=425.7MB, alloc=140.3MB, time=6.50 memory used=500.2MB, alloc=396.3MB, time=7.65 memory used=599.8MB, alloc=420.3MB, time=9.16 memory used=720.3MB, alloc=444.3MB, time=11.01 memory used=860.6MB, alloc=468.3MB, time=13.21 memory used=1010.5MB, alloc=492.3MB, time=15.59 memory used=1154.9MB, alloc=492.3MB, time=17.98 memory used=1279.2MB, alloc=516.3MB, time=20.15 memory used=1382.7MB, alloc=516.3MB, time=22.00 memory used=1486.8MB, alloc=516.3MB, time=23.91 memory used=1591.8MB, alloc=540.3MB, time=25.77 memory used=1688.0MB, alloc=540.3MB, time=27.57 memory used=1767.6MB, alloc=540.3MB, time=29.13 memory used=1846.7MB, alloc=564.3MB, time=30.88 memory used=1961.6MB, alloc=564.3MB, time=33.30 memory used=2082.2MB, alloc=588.3MB, time=35.86 memory used=2189.8MB, alloc=612.3MB, time=38.21 memory used=2283.5MB, alloc=612.3MB, time=40.28 memory used=2398.8MB, alloc=636.3MB, time=42.86 memory used=2486.4MB, alloc=660.3MB, time=45.49 memory used=2730.6MB, alloc=684.3MB, time=53.86 memory used=2967.1MB, alloc=708.3MB, time=63.55 memory used=3216.5MB, alloc=732.3MB, time=74.34 memory used=3489.7MB, alloc=756.3MB, time=86.16 |\^/| 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(); 1428250589 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 F := [5 y z - 15 x, -13 x z - 19 y z , 12 x + 18 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 3 2 G := [4 x y - 7 x z , -13 x + 3 z , -12 x y - 17 x y ] > Problem := [F,G]; 3 2 3 Problem := [[5 y z - 15 x, -13 x z - 19 y z , 12 x + 18 x y], 2 2 2 3 3 3 2 [4 x y - 7 x z , -13 x + 3 z , -12 x y - 17 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=48.0MB, alloc=32.3MB, time=0.79 memory used=68.7MB, alloc=32.3MB, time=1.11 memory used=88.7MB, alloc=56.3MB, time=1.43 memory used=129.7MB, alloc=60.3MB, time=2.05 memory used=169.0MB, alloc=60.3MB, time=2.65 memory used=206.7MB, alloc=84.3MB, time=3.24 memory used=266.3MB, alloc=92.3MB, time=4.23 memory used=322.7MB, alloc=116.3MB, time=5.25 memory used=399.0MB, alloc=140.3MB, time=6.65 memory used=491.0MB, alloc=164.3MB, time=8.44 memory used=589.7MB, alloc=188.3MB, time=11.62 memory used=699.8MB, alloc=212.3MB, time=15.93 memory used=834.0MB, alloc=212.3MB, time=21.12 N1 := 3425 > GB := Basis(F, plex(op(vars))); GB := [ 4 2 3 3 2 3 76 x + 351 x , 2 x + 3 x y, -38 x + 39 x z, y z - 3 x, 13 x z + 57 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=960.6MB, alloc=212.3MB, time=23.73 memory used=1112.0MB, alloc=468.3MB, time=26.14 memory used=1259.1MB, alloc=492.3MB, time=28.45 memory used=1431.9MB, alloc=516.3MB, time=31.57 memory used=1622.5MB, alloc=540.3MB, time=35.20 memory used=1814.8MB, alloc=564.3MB, time=40.14 memory used=1987.1MB, alloc=588.3MB, time=46.82 memory used=2172.9MB, alloc=612.3MB, time=54.58 memory used=2382.7MB, alloc=636.3MB, time=63.40 memory used=2616.6MB, alloc=660.3MB, time=72.98 N2 := 6001 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 2 2 H := [5 y z - 15 x, -13 x z - 19 y z , 12 x + 18 x y, 4 x y - 7 x z , 3 3 3 2 -13 x + 3 z , -12 x y - 17 x y ] > J:=[op(GB),op(G)]; 4 2 3 3 2 J := [76 x + 351 x , 2 x + 3 x y, -38 x + 39 x z, y z - 3 x, 3 2 2 2 3 3 3 2 13 x z + 57 x z, 4 x y - 7 x z , -13 x + 3 z , -12 x y - 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 := [6, 15, 20, 4, 3, 2, 3, 1, 5/6, 2/3, 3/4, 1/2, 5/12, 8, 17, 27, 4, 4, 2, 3, 1, 1/2, 5/8, 7/8, 5/16, 3/8, -2, -7, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2844.9MB, alloc=660.3MB, time=81.59 |\^/| 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(); 1428250828 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 4 2 F := [15 x y z + 9 x , -15 x y + 5 x y, -15 x + 10 x y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 2 G := [4 y z + 3 y z, 15 y z - 12, 3 x y z + 3 x z ] > Problem := [F,G]; 2 3 2 4 2 Problem := [[15 x y z + 9 x , -15 x y + 5 x y, -15 x + 10 x y z ], 2 2 2 3 2 2 2 [4 y z + 3 y z, 15 y z - 12, 3 x y z + 3 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.4MB, alloc=32.3MB, time=0.78 memory used=66.4MB, alloc=56.3MB, time=1.08 memory used=105.3MB, alloc=60.3MB, time=1.65 memory used=140.9MB, alloc=60.3MB, time=2.17 memory used=174.7MB, alloc=84.3MB, time=2.70 memory used=230.9MB, alloc=84.3MB, time=3.56 memory used=286.4MB, alloc=116.3MB, time=4.47 memory used=362.7MB, alloc=116.3MB, time=5.68 memory used=436.3MB, alloc=140.3MB, time=6.87 memory used=529.7MB, alloc=140.3MB, time=8.39 memory used=619.1MB, alloc=164.3MB, time=9.90 memory used=725.7MB, alloc=444.3MB, time=11.72 memory used=858.6MB, alloc=468.3MB, time=14.08 memory used=1000.9MB, alloc=492.3MB, time=16.67 memory used=1154.3MB, alloc=516.3MB, time=19.48 memory used=1317.8MB, alloc=540.3MB, time=22.50 memory used=1487.2MB, alloc=564.3MB, time=25.68 memory used=1663.9MB, alloc=588.3MB, time=29.09 memory used=1843.7MB, alloc=612.3MB, time=33.31 memory used=2010.7MB, alloc=636.3MB, time=38.76 memory used=2185.4MB, alloc=660.3MB, time=44.94 memory used=2371.3MB, alloc=684.3MB, time=51.76 memory used=2570.6MB, alloc=708.3MB, time=59.37 memory used=2784.1MB, alloc=732.3MB, time=67.59 memory used=3009.4MB, alloc=756.3MB, time=76.89 memory used=3248.7MB, alloc=780.3MB, time=87.38 |\^/| 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(); 1428251128 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 3 2 F := [4 x z + 14 x , 6 y z - 19 z , 9 x z - 10 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 3 2 G := [11 x y z - 20 z , -16 x y - 18 x z , 13 x z - 6 z ] > Problem := [F,G]; 3 2 2 2 4 3 2 Problem := [[4 x z + 14 x , 6 y z - 19 z , 9 x z - 10 x z], 2 3 3 2 3 2 [11 x y z - 20 z , -16 x y - 18 x z , 13 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=0.17 memory used=27.1MB, alloc=32.3MB, time=0.51 memory used=48.5MB, alloc=32.3MB, time=0.81 memory used=69.3MB, alloc=32.3MB, time=1.12 memory used=88.8MB, alloc=56.3MB, time=1.42 memory used=129.6MB, alloc=60.3MB, time=2.00 memory used=169.2MB, alloc=84.3MB, time=2.58 memory used=214.3MB, alloc=84.3MB, time=3.29 memory used=272.3MB, alloc=116.3MB, time=4.19 memory used=353.2MB, alloc=116.3MB, time=5.41 memory used=429.7MB, alloc=140.3MB, time=6.61 memory used=509.1MB, alloc=396.3MB, time=7.84 memory used=610.9MB, alloc=420.3MB, time=9.39 memory used=729.6MB, alloc=420.3MB, time=11.31 memory used=848.9MB, alloc=444.3MB, time=13.22 memory used=989.6MB, alloc=468.3MB, time=15.46 memory used=1147.8MB, alloc=468.3MB, time=18.04 memory used=1295.4MB, alloc=492.3MB, time=20.42 memory used=1420.0MB, alloc=516.3MB, time=22.55 memory used=1537.9MB, alloc=516.3MB, time=24.55 memory used=1635.5MB, alloc=516.3MB, time=26.25 memory used=1732.6MB, alloc=540.3MB, time=27.95 memory used=1849.4MB, alloc=540.3MB, time=30.28 memory used=2001.7MB, alloc=564.3MB, time=33.38 memory used=2174.3MB, alloc=588.3MB, time=36.96 memory used=2349.9MB, alloc=612.3MB, time=40.59 memory used=2502.2MB, alloc=636.3MB, time=43.88 memory used=2704.8MB, alloc=660.3MB, time=47.68 memory used=2853.7MB, alloc=684.3MB, time=50.78 memory used=3000.1MB, alloc=708.3MB, time=54.01 memory used=3136.7MB, alloc=732.3MB, time=57.00 memory used=3252.3MB, alloc=756.3MB, time=59.68 memory used=3378.3MB, alloc=780.3MB, time=62.54 memory used=3517.9MB, alloc=804.3MB, time=65.71 memory used=3624.8MB, alloc=828.3MB, time=68.13 memory used=3682.5MB, alloc=852.3MB, time=69.91 memory used=4017.3MB, alloc=876.3MB, time=81.17 memory used=4338.6MB, alloc=900.3MB, time=93.21 |\^/| 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(); 1428251428 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 3 4 F := [-3 x + 20 y , -17 x + 8, -x z - 4 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 G := [-2 x y z - 13 x y , -11 x + 16 x y , 12 x + 4 y z] > Problem := [F,G]; 3 3 4 3 4 Problem := [[-3 x + 20 y , -17 x + 8, -x z - 4 z ], 2 2 4 2 2 [-2 x y z - 13 x y , -11 x + 16 x y , 12 x + 4 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.4MB, alloc=32.3MB, time=0.78 memory used=67.7MB, alloc=32.3MB, time=1.07 memory used=88.8MB, alloc=56.3MB, time=1.46 memory used=129.5MB, alloc=60.3MB, time=2.17 memory used=167.3MB, alloc=84.3MB, time=2.84 memory used=223.2MB, alloc=108.3MB, time=4.04 memory used=290.6MB, alloc=132.3MB, time=6.42 N1 := 2219 > GB := Basis(F, plex(op(vars))); 4 3 3 3 4 GB := [17 x - 8, -3 x + 20 y , x z + 4 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=379.4MB, alloc=132.3MB, time=9.54 memory used=475.0MB, alloc=140.3MB, time=11.11 memory used=570.2MB, alloc=164.3MB, time=12.85 memory used=675.3MB, alloc=188.3MB, time=16.56 N2 := 2219 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 4 3 4 2 2 H := [-3 x + 20 y , -17 x + 8, -x z - 4 z , -2 x y z - 13 x y , 4 2 2 -11 x + 16 x y , 12 x + 4 y z] > J:=[op(GB),op(G)]; 4 3 3 3 4 2 2 J := [17 x - 8, -3 x + 20 y , x z + 4 z , -2 x y z - 13 x y , 4 2 2 -11 x + 16 x y , 12 x + 4 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 21, 4, 4, 3, 4, 1, 2/3, 1/2, 2/3, 5/12, 1/3, 6, 13, 21, 4, 4, 3, 4, 1, 2/3, 1/2, 2/3, 5/12, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=741.4MB, alloc=188.3MB, time=18.99 |\^/| 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(); 1428251483 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 3 2 F := [-18 x z + 4 y z , 13 z + 16 x y, -17 y - 14 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 2 G := [-6 x y + 11 x z , 18 x y - 5 x z, 13 x y z - 8 z] > Problem := [F,G]; 3 3 4 3 2 Problem := [[-18 x z + 4 y z , 13 z + 16 x y, -17 y - 14 z ], 2 2 2 2 3 2 2 [-6 x y + 11 x z , 18 x y - 5 x z, 13 x 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=0.17 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=48.5MB, alloc=32.3MB, time=0.83 memory used=69.0MB, alloc=32.3MB, time=1.13 memory used=88.8MB, alloc=56.3MB, time=1.44 memory used=129.8MB, alloc=60.3MB, time=2.04 memory used=166.4MB, alloc=84.3MB, time=2.58 memory used=207.9MB, alloc=84.3MB, time=3.18 memory used=268.0MB, alloc=92.3MB, time=4.08 memory used=327.0MB, alloc=116.3MB, time=4.96 memory used=407.7MB, alloc=116.3MB, time=6.17 memory used=484.3MB, alloc=396.3MB, time=7.33 memory used=585.4MB, alloc=396.3MB, time=8.85 memory used=686.0MB, alloc=420.3MB, time=10.39 memory used=810.9MB, alloc=444.3MB, time=12.25 memory used=953.4MB, alloc=468.3MB, time=14.50 memory used=1107.8MB, alloc=492.3MB, time=17.14 memory used=1271.5MB, alloc=516.3MB, time=20.33 memory used=1450.1MB, alloc=540.3MB, time=23.83 memory used=1629.1MB, alloc=564.3MB, time=27.33 memory used=1788.7MB, alloc=588.3MB, time=30.52 memory used=1961.2MB, alloc=612.3MB, time=33.95 memory used=2107.5MB, alloc=636.3MB, time=36.94 memory used=2257.0MB, alloc=660.3MB, time=40.08 memory used=2399.5MB, alloc=684.3MB, time=43.12 memory used=2540.9MB, alloc=708.3MB, time=46.11 memory used=2666.1MB, alloc=732.3MB, time=48.81 memory used=2775.6MB, alloc=756.3MB, time=51.26 memory used=2981.8MB, alloc=780.3MB, time=58.13 memory used=3249.3MB, alloc=804.3MB, time=68.39 memory used=3521.2MB, alloc=828.3MB, time=79.62 memory used=3800.9MB, alloc=852.3MB, time=91.12 memory used=4089.7MB, alloc=876.3MB, time=103.12 |\^/| 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(); 1428251783 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 F := [10 x y z - 13 x y, 8 x y - 12 y , 9 x y + 13 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [-7 z + 2 y , 2 x y z - 19 y , 2 x y z + 12 y ] > Problem := [F,G]; 2 2 2 3 2 3 Problem := [[10 x y z - 13 x y, 8 x y - 12 y , 9 x y + 13 y ], 3 2 3 2 [-7 z + 2 y , 2 x y z - 19 y , 2 x y z + 12 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.5MB, alloc=32.3MB, time=0.82 memory used=67.6MB, alloc=32.3MB, time=1.12 memory used=86.9MB, alloc=56.3MB, time=1.45 memory used=126.3MB, alloc=60.3MB, time=2.07 memory used=163.4MB, alloc=84.3MB, time=2.66 memory used=218.5MB, alloc=84.3MB, time=3.50 memory used=273.7MB, alloc=116.3MB, time=4.43 memory used=355.7MB, alloc=140.3MB, time=5.85 memory used=451.3MB, alloc=164.3MB, time=7.64 memory used=560.4MB, alloc=188.3MB, time=9.72 memory used=685.7MB, alloc=212.3MB, time=11.95 memory used=806.9MB, alloc=492.3MB, time=14.18 memory used=957.1MB, alloc=516.3MB, time=16.98 memory used=1116.0MB, alloc=540.3MB, time=20.48 memory used=1268.2MB, alloc=564.3MB, time=25.52 memory used=1429.5MB, alloc=588.3MB, time=31.24 memory used=1603.5MB, alloc=612.3MB, time=37.65 memory used=1791.8MB, alloc=636.3MB, time=44.85 memory used=1990.8MB, alloc=660.3MB, time=53.26 memory used=2212.0MB, alloc=684.3MB, time=62.54 memory used=2457.0MB, alloc=708.3MB, time=72.80 memory used=2726.0MB, alloc=732.3MB, time=84.01 memory used=3019.0MB, alloc=732.3MB, time=96.26 |\^/| 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(); 1428252083 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 3 F := [14 y - 2 x y , -20 x y + 11 y , -14 y z + 1] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 G := [-14 x z + 19 y z, 20 y z - 17 z , 18 y z - 10 y ] > Problem := [F,G]; 4 2 2 2 3 3 Problem := [[14 y - 2 x y , -20 x y + 11 y , -14 y z + 1], 2 2 3 3 3 [-14 x z + 19 y z, 20 y z - 17 z , 18 y z - 10 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.2MB, alloc=32.3MB, time=0.77 memory used=67.6MB, alloc=32.3MB, time=1.07 memory used=86.5MB, alloc=56.3MB, time=1.37 memory used=125.2MB, alloc=60.3MB, time=1.94 memory used=162.0MB, alloc=84.3MB, time=2.52 memory used=221.5MB, alloc=108.3MB, time=3.60 memory used=295.8MB, alloc=140.3MB, time=4.95 memory used=385.3MB, alloc=164.3MB, time=6.57 memory used=488.9MB, alloc=188.3MB, time=8.44 memory used=603.7MB, alloc=212.3MB, time=10.93 memory used=721.2MB, alloc=236.3MB, time=14.44 memory used=850.1MB, alloc=260.3MB, time=18.69 memory used=991.1MB, alloc=284.3MB, time=24.01 memory used=1151.3MB, alloc=308.3MB, time=30.37 memory used=1335.5MB, alloc=308.3MB, time=37.65 memory used=1519.6MB, alloc=332.3MB, time=44.93 memory used=1727.7MB, alloc=332.3MB, time=53.24 memory used=1935.7MB, alloc=332.3MB, time=61.46 memory used=2143.8MB, alloc=356.3MB, time=69.74 memory used=2375.8MB, alloc=356.3MB, time=78.93 memory used=2607.7MB, alloc=380.3MB, time=88.11 N1 := 8397 > GB := Basis(F, plex(op(vars))); 3 2 GB := [2800 x - 121, -20 x + 11 y, 11 z - 70] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2841.8MB, alloc=380.3MB, time=95.84 |\^/| 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(); 1428252383 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 2 F := [3 x y z - 16 z, 16 y - 10 x z, -18 x z - 19 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-17 x z + 7 y , -10 x y z - 2 x y z, -18 x y - 13 y ] > Problem := [F,G]; 2 4 3 2 Problem := [[3 x y z - 16 z, 16 y - 10 x z, -18 x z - 19 x y z], 2 2 2 2 [-17 x z + 7 y , -10 x y z - 2 x y z, -18 x y - 13 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=56.3MB, alloc=68.3MB, time=0.97 memory used=107.9MB, alloc=68.3MB, time=1.86 memory used=155.1MB, alloc=92.3MB, time=2.73 memory used=217.2MB, alloc=92.3MB, time=4.76 N1 := 1441 > GB := Basis(F, plex(op(vars))); 3 4 4 4 5 2 4 GB := [243 x y - 1444 y , 18 x y + 19 y , -486 x y + 1805 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=277.6MB, alloc=92.3MB, time=5.86 N2 := 695 #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 4 3 2 2 2 H := [3 x y z - 16 z, 16 y - 10 x z, -18 x z - 19 x y z, -17 x z + 7 y , 2 2 -10 x y z - 2 x y z, -18 x y - 13 y ] > J:=[op(GB),op(G)]; 3 4 4 4 5 2 4 J := [243 x y - 1444 y , 18 x y + 19 y , -486 x y + 1805 z, 2 2 2 2 -17 x z + 7 y , -10 x y z - 2 x y z, -18 x y - 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 := [6, 17, 21, 4, 3, 4, 2, 1, 1, 5/6, 2/3, 2/3, 2/3, 6, 15, 27, 7, 3, 5, 2, 1, 1, 1/2, 7/12, 5/6, 1/3, 2, -6, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=327.0MB, alloc=92.3MB, time=6.96 |\^/| 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(); 1428252407 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 3 F := [15 x z - 7 y z , -7 x - 16 y z, -11 y + 3 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [20 x z - 3 x, -10 x y - 4 z, 12 y z - 5 x ] > Problem := [F,G]; 2 2 2 4 2 3 Problem := [[15 x z - 7 y z , -7 x - 16 y z, -11 y + 3 x], 2 2 2 2 [20 x z - 3 x, -10 x y - 4 z, 12 y z - 5 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.80 memory used=68.2MB, alloc=32.3MB, time=1.10 memory used=87.7MB, alloc=56.3MB, time=1.41 memory used=127.9MB, alloc=60.3MB, time=2.02 memory used=166.8MB, alloc=60.3MB, time=2.60 memory used=204.8MB, alloc=84.3MB, time=3.19 memory used=267.2MB, alloc=92.3MB, time=4.08 memory used=324.2MB, alloc=116.3MB, time=4.94 memory used=404.4MB, alloc=140.3MB, time=6.22 memory used=506.1MB, alloc=164.3MB, time=8.05 memory used=621.0MB, alloc=188.3MB, time=10.10 memory used=735.0MB, alloc=468.3MB, time=12.28 memory used=876.8MB, alloc=492.3MB, time=14.97 memory used=1035.5MB, alloc=516.3MB, time=17.77 memory used=1200.8MB, alloc=540.3MB, time=20.82 memory used=1380.5MB, alloc=564.3MB, time=24.11 memory used=1556.5MB, alloc=588.3MB, time=29.18 memory used=1730.4MB, alloc=612.3MB, time=34.97 memory used=1914.2MB, alloc=636.3MB, time=41.49 memory used=2110.5MB, alloc=660.3MB, time=48.68 memory used=2320.5MB, alloc=684.3MB, time=56.78 memory used=2538.9MB, alloc=708.3MB, time=66.20 memory used=2781.1MB, alloc=732.3MB, time=76.53 memory used=3047.3MB, alloc=756.3MB, time=87.94 |\^/| 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(); 1428252707 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 3 2 F := [-10 x z - 13 x y, -6 z + 9 y z, 5 x y + 2 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [13 x - 17 x , -4 x y z - 3 x y, 12 x z - 17 x ] > Problem := [F,G]; 2 2 4 2 3 2 Problem := [[-10 x z - 13 x y, -6 z + 9 y z, 5 x y + 2 y z ], 3 2 2 2 2 [13 x - 17 x , -4 x y z - 3 x y, 12 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.8MB, alloc=32.3MB, time=0.80 memory used=68.6MB, alloc=56.3MB, time=1.12 memory used=109.5MB, alloc=60.3MB, time=1.72 memory used=148.1MB, alloc=84.3MB, time=2.32 memory used=206.1MB, alloc=92.3MB, time=3.23 memory used=260.8MB, alloc=116.3MB, time=4.08 memory used=339.3MB, alloc=140.3MB, time=5.50 memory used=434.8MB, alloc=164.3MB, time=7.26 memory used=542.5MB, alloc=188.3MB, time=9.29 memory used=656.9MB, alloc=212.3MB, time=12.50 memory used=775.1MB, alloc=236.3MB, time=17.00 memory used=917.3MB, alloc=236.3MB, time=22.36 memory used=1059.5MB, alloc=260.3MB, time=27.75 N1 := 4515 > GB := Basis(F, plex(op(vars))); 11 4 5 2 9 4 GB := [56250 x y + 28561 x y, -25 x y + 13 x y , 375 x y + 169 x y z, 6 3 2 2 3 2 4 2 -25 x y + 6 y z, 10 x z + 13 x y, 5 x y + 2 y z , 2 z - 3 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1229.5MB, alloc=260.3MB, time=33.47 memory used=1336.5MB, alloc=516.3MB, time=35.24 memory used=1513.3MB, alloc=516.3MB, time=37.95 memory used=1669.3MB, alloc=540.3MB, time=40.09 memory used=1827.0MB, alloc=564.3MB, time=42.50 memory used=1948.7MB, alloc=588.3MB, time=44.32 memory used=2064.8MB, alloc=588.3MB, time=46.26 memory used=2182.0MB, alloc=588.3MB, time=48.21 memory used=2289.2MB, alloc=588.3MB, time=50.13 memory used=2380.3MB, alloc=588.3MB, time=51.72 memory used=2469.2MB, alloc=612.3MB, time=53.44 memory used=2558.4MB, alloc=612.3MB, time=54.80 memory used=2653.0MB, alloc=612.3MB, time=56.27 memory used=2720.2MB, alloc=612.3MB, time=57.57 memory used=2783.7MB, alloc=612.3MB, time=58.88 memory used=2845.5MB, alloc=636.3MB, time=60.14 memory used=2923.4MB, alloc=636.3MB, time=61.64 memory used=2981.5MB, alloc=636.3MB, time=62.97 memory used=3034.0MB, alloc=636.3MB, time=64.10 memory used=3072.1MB, alloc=636.3MB, time=65.14 memory used=3305.7MB, alloc=660.3MB, time=68.79 memory used=3496.7MB, alloc=684.3MB, time=71.92 memory used=3695.3MB, alloc=708.3MB, time=75.44 memory used=3884.2MB, alloc=732.3MB, time=78.76 memory used=4034.7MB, alloc=732.3MB, time=81.45 memory used=4196.2MB, alloc=732.3MB, time=84.52 memory used=4329.5MB, alloc=756.3MB, time=87.09 memory used=4439.9MB, alloc=756.3MB, time=89.23 memory used=4559.1MB, alloc=756.3MB, time=91.80 memory used=4669.2MB, alloc=756.3MB, time=94.02 memory used=4779.2MB, alloc=756.3MB, time=96.50 memory used=4853.3MB, alloc=780.3MB, time=98.65 memory used=4941.7MB, alloc=780.3MB, time=100.77 memory used=5357.5MB, alloc=804.3MB, time=107.53 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428253007 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 3 2 4 F := [4 x - 2 x y z, 5 x y + 15 y z , -2 x y z - 15 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-8 x - 9, -13 x y z + y, -17 x z - 6 x] > Problem := [F,G]; 4 2 3 3 2 4 Problem := [[4 x - 2 x y z, 5 x y + 15 y z , -2 x y z - 15 y ], 2 2 2 [-8 x - 9, -13 x y z + y, -17 x z - 6 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=32.3MB, time=0.82 memory used=68.1MB, alloc=56.3MB, time=1.14 memory used=108.9MB, alloc=60.3MB, time=1.77 memory used=148.9MB, alloc=60.3MB, time=2.33 memory used=188.3MB, alloc=84.3MB, time=2.91 memory used=230.5MB, alloc=84.3MB, time=3.53 memory used=290.1MB, alloc=92.3MB, time=4.44 memory used=345.7MB, alloc=116.3MB, time=5.32 memory used=430.2MB, alloc=140.3MB, time=6.75 memory used=531.7MB, alloc=140.3MB, time=8.42 memory used=624.2MB, alloc=164.3MB, time=10.02 memory used=740.9MB, alloc=188.3MB, time=11.90 memory used=869.4MB, alloc=212.3MB, time=14.21 memory used=992.5MB, alloc=492.3MB, time=16.98 memory used=1131.6MB, alloc=516.3MB, time=21.22 memory used=1276.7MB, alloc=540.3MB, time=26.62 memory used=1437.7MB, alloc=564.3MB, time=33.03 memory used=1622.6MB, alloc=588.3MB, time=40.50 memory used=1831.5MB, alloc=588.3MB, time=48.65 memory used=2040.3MB, alloc=588.3MB, time=56.79 memory used=2249.2MB, alloc=612.3MB, time=65.06 memory used=2482.0MB, alloc=612.3MB, time=74.11 N1 := 7431 > GB := Basis(F, plex(op(vars))); 9 8 7 8 6 2 6 4 3 5 2 3 4 GB := [x , 1080 x + x y, -x + 45 x y , -x y + 45 x y , -x y + 45 x y , 6 5 7 7 4 4 4 2 8 x + 15 x y , 8 x + 675 y , 4 x z + 15 x y , -2 x + x y z, 4 4 2 4 3 3 -2 x y + 45 y z, 2 x y z + 15 y , x y + 3 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2724.7MB, alloc=612.3MB, time=82.07 memory used=3000.0MB, alloc=636.3MB, time=86.23 memory used=3296.9MB, alloc=660.3MB, time=90.58 memory used=3590.7MB, alloc=684.3MB, time=95.12 |\^/| 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(); 1428253307 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 4 3 F := [-20 x y - 10 y z, -20 x + 3 y , -17 x + x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 G := [20 x z + 4 y , -10 x y z - 17 y z , -18 x z - 3 x y z] > Problem := [F,G]; 3 3 3 4 3 Problem := [[-20 x y - 10 y z, -20 x + 3 y , -17 x + x ], 2 2 3 2 3 2 [20 x z + 4 y , -10 x y z - 17 y z , -18 x z - 3 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.79 memory used=67.9MB, alloc=32.3MB, time=1.07 memory used=87.7MB, alloc=56.3MB, time=1.43 memory used=130.7MB, alloc=60.3MB, time=2.19 memory used=169.6MB, alloc=84.3MB, time=2.89 memory used=229.3MB, alloc=84.3MB, time=3.95 memory used=285.3MB, alloc=108.3MB, time=4.96 memory used=352.0MB, alloc=132.3MB, time=6.92 memory used=431.3MB, alloc=156.3MB, time=10.04 memory used=534.7MB, alloc=156.3MB, time=14.11 N1 := 2909 > GB := Basis(F, plex(op(vars))); 4 3 3 3 3 2 3 3 GB := [17 x - x , -20 x + 3 y , 2 x y + 17 x z, 40 x + 51 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=610.9MB, alloc=156.3MB, time=16.14 memory used=707.7MB, alloc=420.3MB, time=17.77 memory used=817.4MB, alloc=444.3MB, time=19.73 memory used=946.9MB, alloc=468.3MB, time=22.06 memory used=1089.4MB, alloc=492.3MB, time=24.64 memory used=1239.0MB, alloc=516.3MB, time=29.02 memory used=1386.7MB, alloc=540.3MB, time=34.89 memory used=1554.2MB, alloc=564.3MB, time=41.79 memory used=1745.7MB, alloc=588.3MB, time=49.59 memory used=1961.3MB, alloc=612.3MB, time=58.26 N2 := 5465 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 3 4 3 2 2 3 H := [-20 x y - 10 y z, -20 x + 3 y , -17 x + x , 20 x z + 4 y , 2 3 2 -10 x y z - 17 y z , -18 x z - 3 x y z] > J:=[op(GB),op(G)]; 4 3 3 3 3 2 3 3 J := [17 x - x , -20 x + 3 y , 2 x y + 17 x z, 40 x + 51 z y, 2 2 3 2 3 2 20 x z + 4 y , -10 x y z - 17 y z , -18 x z - 3 x 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 := [6, 15, 22, 4, 4, 3, 2, 1, 5/6, 2/3, 2/3, 7/12, 1/2, 7, 18, 26, 5, 4, 3, 2, 1, 6/7, 5/7, 5/7, 1/2, 1/2, -3, -4, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2070.2MB, alloc=612.3MB, time=62.39 |\^/| 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(); 1428253483 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [17 x y z, 5 x y z - 18 x y z , 2 x y - 14 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 3 G := [-20 x - 19 x z, -x y - 4 y, 2 y ] > Problem := [F,G]; 2 2 2 2 Problem := [[17 x y z, 5 x y z - 18 x y z , 2 x y - 14 x], 4 3 3 3 [-20 x - 19 x z, -x y - 4 y, 2 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.52 memory used=48.4MB, alloc=32.3MB, time=0.88 memory used=66.5MB, alloc=56.3MB, time=1.23 N1 := 749 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [x y - 7 x, x z, -5 x y z + 18 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=104.2MB, alloc=56.3MB, time=2.00 memory used=144.6MB, alloc=84.3MB, time=2.74 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 2 4 3 H := [17 x y z, 5 x y z - 18 x y z , 2 x y - 14 x, -20 x - 19 x z, 3 3 -x y - 4 y, 2 y ] > J:=[op(GB),op(G)]; J := 2 2 2 4 3 3 3 [x y - 7 x, x z, -5 x y z + 18 x z , -20 x - 19 x z, -x y - 4 y, 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 := [6, 13, 22, 4, 4, 3, 2, 5/6, 5/6, 1/2, 4/7, 1/2, 2/7, 6, 12, 20, 4, 4, 3, 2, 5/6, 2/3, 1/2, 2/3, 5/12, 1/3, 1, 2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=163.1MB, alloc=84.3MB, time=3.24 |\^/| 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(); 1428253492 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 2 F := [9 x y , 3 x - 17, -x y - 19 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 G := [-13 x y - 5 y z , -5 x y - 18, -8 x y - 8 y ] > Problem := [F,G]; 2 4 2 2 2 Problem := [[9 x y , 3 x - 17, -x y - 19 x y], 2 2 3 3 2 [-13 x y - 5 y z , -5 x y - 18, -8 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=27.0MB, alloc=32.3MB, time=0.53 N1 := 133 > GB := Basis(F, plex(op(vars))); 4 GB := [3 x - 17, y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=48.1MB, alloc=32.3MB, time=0.89 N2 := 75 #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 4 2 2 2 2 2 3 H := [9 x y , 3 x - 17, -x y - 19 x y, -13 x y - 5 y z , -5 x y - 18, 3 2 -8 x y - 8 y ] > J:=[op(GB),op(G)]; 4 2 2 3 3 2 J := [3 x - 17, y, -13 x y - 5 y z , -5 x y - 18, -8 x y - 8 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 22, 4, 4, 3, 2, 1, 5/6, 1/6, 7/13, 8/13, 1/13, 5, 9, 16, 4, 4, 3, 2, 4/5, 4/5, 1/5, 4/9, 2/3, 1/9, 3, 6, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=58.8MB, alloc=32.3MB, time=1.07 |\^/| 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(); 1428253495 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 3 F := [-2 x z - 14 x y, 15 x + 14 x , -16 x + 8 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 G := [-19 x + y, 19 x y z + 9 x y, -13 x z - 5 x z ] > Problem := [F,G]; 2 4 2 3 Problem := [[-2 x z - 14 x y, 15 x + 14 x , -16 x + 8 x z], 3 3 [-19 x + y, 19 x y z + 9 x y, -13 x z - 5 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.79 N1 := 165 > GB := Basis(F, plex(op(vars))); 4 2 2 3 GB := [15 x + 14 x , -4 x + 15 x y, -2 x + x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=68.2MB, alloc=32.3MB, time=1.12 memory used=88.2MB, alloc=32.3MB, time=1.42 N2 := 113 #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 4 2 3 H := [-2 x z - 14 x y, 15 x + 14 x , -16 x + 8 x z, -19 x + y, 3 3 19 x y z + 9 x y, -13 x z - 5 x z ] > J:=[op(GB),op(G)]; 4 2 2 3 J := [15 x + 14 x , -4 x + 15 x y, -2 x + x z, -19 x + y, 19 x y z + 9 x y, 3 3 -13 x z - 5 x z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 18, 4, 4, 1, 3, 1, 1/2, 2/3, 11/12, 1/3, 5/12, 6, 12, 17, 4, 4, 1, 3, 1, 1/2, 1/2, 11/12, 1/3, 1/3, 1, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=91.7MB, alloc=32.3MB, time=1.48 |\^/| 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(); 1428253499 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 F := [-13 y + 8 x y, 8 x y z - 15 y z , 16 x z + 9 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 G := [18 y z - x z, -8 y z - 8 z , -8 x y z + 4 y z ] > Problem := [F,G]; 4 2 2 3 2 Problem := [[-13 y + 8 x y, 8 x y z - 15 y z , 16 x z + 9 x y], 3 2 3 2 2 [18 y z - x z, -8 y z - 8 z , -8 x y z + 4 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=47.5MB, alloc=32.3MB, time=0.79 memory used=67.6MB, alloc=32.3MB, time=1.08 memory used=87.1MB, alloc=56.3MB, time=1.38 memory used=126.4MB, alloc=60.3MB, time=1.97 memory used=165.1MB, alloc=84.3MB, time=2.60 memory used=223.1MB, alloc=84.3MB, time=3.61 memory used=275.7MB, alloc=108.3MB, time=4.54 memory used=346.3MB, alloc=140.3MB, time=5.96 memory used=426.4MB, alloc=164.3MB, time=8.42 memory used=520.5MB, alloc=188.3MB, time=11.96 memory used=638.8MB, alloc=188.3MB, time=16.46 N1 := 3253 > GB := Basis(F, plex(op(vars))); 8 4 5 3 2 GB := [3407872 x y + 2460375 x y, 128 x y + 135 x y , 6 2 3 4 2 3 2 -16384 x y + 18225 x y , 13 y - 8 x y, 16 x z + 9 x y, 5 2 2 2 1024 x y + 2025 x y z, -8 x y z + 15 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=757.7MB, alloc=188.3MB, time=19.10 memory used=854.5MB, alloc=444.3MB, time=20.63 memory used=983.4MB, alloc=468.3MB, time=22.60 memory used=1129.8MB, alloc=492.3MB, time=24.85 memory used=1301.9MB, alloc=516.3MB, time=27.89 memory used=1484.6MB, alloc=540.3MB, time=31.24 memory used=1679.6MB, alloc=564.3MB, time=35.01 memory used=1863.0MB, alloc=588.3MB, time=40.86 memory used=2046.2MB, alloc=612.3MB, time=51.19 memory used=2240.2MB, alloc=636.3MB, time=63.70 memory used=2458.2MB, alloc=660.3MB, time=77.64 memory used=2700.1MB, alloc=684.3MB, time=93.07 memory used=2966.0MB, alloc=708.3MB, time=109.94 |\^/| 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(); 1428253799 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 F := [11 x z - 17 x y z, x z - 11 z , -5 x y + 18 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 G := [4 z , 11 x z + 3 y z , 7 x y] > Problem := [F,G]; 2 3 2 3 2 Problem := [[11 x z - 17 x y z, x z - 11 z , -5 x y + 18 x z ], 3 3 2 2 2 [4 z , 11 x z + 3 y z , 7 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.29 memory used=26.8MB, alloc=32.3MB, time=0.86 memory used=48.7MB, alloc=32.3MB, time=1.48 memory used=69.0MB, alloc=56.3MB, time=2.13 memory used=115.3MB, alloc=60.3MB, time=3.28 N1 := 747 > GB := Basis(F, plex(op(vars))); 8 3 4 3 2 7 4 GB := [5 x y - 3366 x y, -11 x y + 17 x y , -5 x y + 198 x z, 2 7 2 -11 x z + 17 x y z, -25 x y + 60588 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=152.1MB, alloc=60.3MB, time=4.67 memory used=190.8MB, alloc=84.3MB, time=5.81 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 3 2 3 2 3 H := [11 x z - 17 x y z, x z - 11 z , -5 x y + 18 x z , 4 z , 3 2 2 2 11 x z + 3 y z , 7 y x ] > J:=[op(GB),op(G)]; 8 3 4 3 2 7 4 J := [5 x y - 3366 x y, -11 x y + 17 x y , -5 x y + 198 x z, 2 7 2 3 3 2 2 2 -11 x z + 17 x y z, -25 x y + 60588 z , 4 z , 11 x z + 3 y z , 7 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 := [6, 14, 21, 4, 3, 2, 3, 5/6, 2/3, 5/6, 7/13, 4/13, 8/13, 8, 19, 43, 9, 8, 2, 3, 7/8, 7/8, 5/8, 11/17, 9/17, 7/17, -5, -22, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=215.6MB, alloc=84.3MB, time=6.76 |\^/| 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(); 1428253821 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [-7 x z - 17 y z, -7 x z - 15, -11 x + 13 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 3 2 G := [-2 x - 13 x z , -19 x y - 13 x , 13 x y z - 12 x z ] > Problem := [F,G]; 2 2 3 Problem := [[-7 x z - 17 y z, -7 x z - 15, -11 x + 13 x y], 4 3 2 2 3 2 [-2 x - 13 x z , -19 x y - 13 x , 13 x y z - 12 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.85 memory used=48.0MB, alloc=32.3MB, time=1.40 memory used=69.0MB, alloc=32.3MB, time=1.95 memory used=88.9MB, alloc=56.3MB, time=2.48 memory used=132.5MB, alloc=60.3MB, time=3.80 memory used=172.8MB, alloc=84.3MB, time=5.06 N1 := 1077 > GB := Basis(F, plex(op(vars))); 2 GB := [187 x + 91, 3179 y - 637, 57967 z + 524535] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=231.4MB, alloc=84.3MB, time=7.74 memory used=289.7MB, alloc=84.3MB, time=9.32 memory used=350.7MB, alloc=108.3MB, time=11.64 N2 := 773 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 4 3 H := [-7 x z - 17 y z, -7 x z - 15, -11 x + 13 x y, -2 x - 13 x z , 2 2 3 2 -19 x y - 13 x , 13 x y z - 12 x z ] > J:=[op(GB),op(G)]; 2 4 3 J := [187 x + 91, 3179 y - 637, 57967 z + 524535, -2 x - 13 x z , 2 2 3 2 -19 x y - 13 x , 13 x y z - 12 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 := [6, 14, 20, 4, 4, 2, 3, 1, 2/3, 2/3, 5/6, 1/3, 1/2, 6, 10, 15, 4, 4, 2, 3, 2/3, 1/2, 1/2, 7/12, 1/4, 1/3, 4, 5, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=356.2MB, alloc=108.3MB, time=11.92 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428253853 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 F := [-9 x - 3 y z, -14 x y + 15 x y, 3 x z + 10 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 G := [8 x z - 7 x z, 14 x y z - 16 x z , -18 x y + 10 z ] > Problem := [F,G]; 4 3 2 2 Problem := [[-9 x - 3 y z, -14 x y + 15 x y, 3 x z + 10 y], 3 2 2 2 2 2 [8 x z - 7 x z, 14 x y z - 16 x z , -18 x y + 10 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=47.9MB, alloc=32.3MB, time=1.40 memory used=69.1MB, alloc=32.3MB, time=1.94 memory used=88.4MB, alloc=60.3MB, time=2.46 memory used=124.6MB, alloc=60.3MB, time=3.35 memory used=164.3MB, alloc=84.3MB, time=4.47 memory used=220.2MB, alloc=84.3MB, time=6.24 memory used=276.1MB, alloc=108.3MB, time=8.03 memory used=351.0MB, alloc=140.3MB, time=10.41 memory used=441.3MB, alloc=164.3MB, time=13.40 memory used=540.5MB, alloc=188.3MB, time=17.84 memory used=645.3MB, alloc=212.3MB, time=24.15 memory used=774.0MB, alloc=212.3MB, time=31.88 memory used=902.8MB, alloc=236.3MB, time=39.64 memory used=1055.7MB, alloc=260.3MB, time=48.89 N1 := 4533 > GB := Basis(F, plex(op(vars))); 7 6 3 2 2 2 2 6 3 GB := [14 x - 15 x , 14 x y - 15 x y, 14 x y - 15 x y , 18225 x + 5488 y , 5 2 4 2 9 x z - 10 y , 3 x + z y, 3 z x + 10 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1165.0MB, alloc=260.3MB, time=52.82 memory used=1357.3MB, alloc=516.3MB, time=57.87 memory used=1505.4MB, alloc=516.3MB, time=61.60 memory used=1655.2MB, alloc=540.3MB, time=65.56 memory used=1786.9MB, alloc=540.3MB, time=69.50 memory used=1988.6MB, alloc=564.3MB, time=76.04 memory used=2187.3MB, alloc=588.3MB, time=82.44 memory used=2377.8MB, alloc=612.3MB, time=88.75 memory used=2582.9MB, alloc=636.3MB, time=96.84 memory used=2792.4MB, alloc=660.3MB, time=108.14 |\^/| 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(); 1428254153 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-3 x z + 12 x z, -20 y z + x, 8 x z + 7 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 4 3 G := [-4 x y z - 4 x z , 15 x + 5 x z , -15 x - 3 x ] > Problem := [F,G]; 2 2 Problem := [[-3 x z + 12 x z, -20 y z + x, 8 x z + 7 x], 2 2 2 3 2 4 3 [-4 x y z - 4 x z , 15 x + 5 x z , -15 x - 3 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.85 memory used=47.5MB, alloc=32.3MB, time=1.38 memory used=68.0MB, alloc=56.3MB, time=1.99 memory used=109.8MB, alloc=56.3MB, time=3.25 memory used=146.0MB, alloc=80.3MB, time=4.88 N1 := 1061 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x - 4 x, 245 x y - 64 x, 8 x z + 7 x, 20 y z - x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=199.6MB, alloc=84.3MB, time=6.71 memory used=256.3MB, alloc=84.3MB, time=8.22 memory used=311.8MB, alloc=108.3MB, time=9.99 memory used=386.6MB, alloc=132.3MB, time=13.11 N2 := 1669 #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 z + 12 x z, -20 z y + x, 8 x z + 7 x, -4 x y z - 4 x z , 3 2 4 3 15 x + 5 x z , -15 x - 3 x ] > J:=[op(GB),op(G)]; 2 2 2 2 2 J := [x - 4 x, 245 x y - 64 x, 8 x z + 7 x, 20 y z - x, -4 x y z - 4 x z , 3 2 4 3 15 x + 5 x z , -15 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, 13, 19, 4, 4, 1, 2, 1, 1/3, 5/6, 11/12, 1/6, 7/12, 7, 14, 20, 4, 4, 1, 2, 1, 3/7, 4/7, 13/14, 3/14, 5/14, -1, -1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=446.1MB, alloc=132.3MB, time=16.44 |\^/| 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(); 1428254201 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 2 2 3 F := [-4 y - 4 x, 14 x y - 4 z , -18 x y + 5 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 2 2 G := [-16 x y + 11 x z , -3 z - 11 x z, -17 y z - y z ] > Problem := [F,G]; 3 2 2 4 2 2 3 Problem := [[-4 y - 4 x, 14 x y - 4 z , -18 x y + 5 y ], 3 3 3 3 2 2 [-16 x y + 11 x z , -3 z - 11 x z, -17 y z - y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.85 memory used=47.8MB, alloc=32.3MB, time=1.41 memory used=68.2MB, alloc=32.3MB, time=1.94 memory used=87.9MB, alloc=56.3MB, time=2.45 memory used=128.5MB, alloc=60.3MB, time=3.51 memory used=169.1MB, alloc=60.3MB, time=4.55 memory used=207.4MB, alloc=84.3MB, time=5.53 memory used=268.7MB, alloc=92.3MB, time=7.14 memory used=324.0MB, alloc=116.3MB, time=8.65 memory used=408.7MB, alloc=140.3MB, time=11.22 memory used=514.6MB, alloc=164.3MB, time=14.26 memory used=633.4MB, alloc=188.3MB, time=17.91 memory used=760.5MB, alloc=468.3MB, time=21.87 memory used=908.7MB, alloc=492.3MB, time=26.29 memory used=1076.9MB, alloc=516.3MB, time=30.92 memory used=1242.0MB, alloc=540.3MB, time=36.31 memory used=1399.9MB, alloc=564.3MB, time=43.55 memory used=1561.3MB, alloc=588.3MB, time=51.92 memory used=1732.6MB, alloc=612.3MB, time=61.68 memory used=1917.0MB, alloc=636.3MB, time=72.46 memory used=2112.3MB, alloc=660.3MB, time=85.03 |\^/| 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(); 1428254501 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 F := [2 z - 10 x z, 12 x y + x y z, 7 x y + 8 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 G := [x y z - 6 x z , 18 y + 4 x y, -11 x y + 14 x y] > Problem := [F,G]; 4 2 2 Problem := [[2 z - 10 x z, 12 x y + x y z, 7 x y + 8 x], 2 2 3 3 2 [x y z - 6 x z , 18 y + 4 x y, -11 x y + 14 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.80 memory used=47.6MB, alloc=32.3MB, time=1.33 memory used=68.7MB, alloc=56.3MB, time=1.93 memory used=112.3MB, alloc=60.3MB, time=3.25 memory used=150.5MB, alloc=84.3MB, time=4.44 memory used=204.0MB, alloc=108.3MB, time=7.15 N1 := 1487 > GB := Basis(F, plex(op(vars))); 3 4 2 GB := [1715 x - 884736 x, 7 x y + 8 x, 7 x z - 96 x, 7 z - 480 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=276.7MB, alloc=108.3MB, time=9.66 memory used=361.1MB, alloc=132.3MB, time=12.63 N2 := 1305 #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)]; 4 2 2 2 2 H := [2 z - 10 x z, 12 x y + x y z, 7 x y + 8 x, x y z - 6 x z , 3 3 2 18 y + 4 x y, -11 x y + 14 x y] > J:=[op(GB),op(G)]; 3 4 2 J := [1715 x - 884736 x, 7 x y + 8 x, 7 x z - 96 x, 7 z - 480 x , 2 2 3 3 2 x y z - 6 x z , 18 y + 4 x y, -11 x y + 14 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 := [6, 14, 20, 4, 2, 3, 4, 1, 5/6, 1/2, 5/6, 2/3, 5/12, 7, 14, 22, 4, 3, 3, 4, 1, 4/7, 3/7, 6/7, 3/7, 2/7, 0, -2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=398.9MB, alloc=132.3MB, time=14.60 |\^/| 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(); 1428254544 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 2 4 F := [-7 x z + z , -19 x z - 14 y z, -2 y + 3 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 G := [-6 x y + 13, 19 x y + 4 z , -14 x y z - 11 x z] > Problem := [F,G]; 3 4 2 2 2 4 Problem := [[-7 x z + z , -19 x z - 14 y z, -2 y + 3 x y], 3 3 3 2 2 [-6 x y + 13, 19 x y + 4 z , -14 x y z - 11 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.84 memory used=47.7MB, alloc=32.3MB, time=1.37 memory used=68.4MB, alloc=32.3MB, time=1.88 memory used=88.3MB, alloc=32.3MB, time=2.40 memory used=107.6MB, alloc=56.3MB, time=2.92 memory used=147.3MB, alloc=60.3MB, time=3.93 memory used=187.1MB, alloc=84.3MB, time=5.09 memory used=248.8MB, alloc=92.3MB, time=7.03 memory used=304.0MB, alloc=116.3MB, time=8.77 memory used=379.6MB, alloc=140.3MB, time=11.05 memory used=494.8MB, alloc=140.3MB, time=13.24 memory used=584.8MB, alloc=164.3MB, time=16.10 memory used=681.8MB, alloc=188.3MB, time=20.51 memory used=789.0MB, alloc=212.3MB, time=26.54 memory used=914.4MB, alloc=236.3MB, time=34.03 memory used=1063.7MB, alloc=236.3MB, time=42.84 memory used=1213.1MB, alloc=236.3MB, time=51.68 N1 := 4799 > GB := Basis(F, plex(op(vars))); 4 8 6 2 GB := [2 y - 3 x y, 6859 x y z + 18 x y z, -361 x y z + 6 x y z, 3 3 2 2 2 2 2 19 x y z + 2 y z, 19 x z + 14 y z, -7 x y z + x y z , 7 2 3 3 4 -17689 x y z + 6 y z , -7 x z + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1366.1MB, alloc=236.3MB, time=59.82 memory used=1470.6MB, alloc=492.3MB, time=62.63 memory used=1637.0MB, alloc=516.3MB, time=66.89 memory used=1830.0MB, alloc=540.3MB, time=72.20 memory used=2049.8MB, alloc=564.3MB, time=77.86 memory used=2287.8MB, alloc=588.3MB, time=84.15 memory used=2524.7MB, alloc=612.3MB, time=89.84 memory used=2823.5MB, alloc=636.3MB, time=97.37 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428254844 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 F := [18 y z + 16, -18 x + 16 x y z , 13 x y z - 17 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 G := [-6 x y + 8 z, -7 x z + 7 y z, -2 y z - 14] > Problem := [F,G]; 2 4 2 2 Problem := [[18 y z + 16, -18 x + 16 x y z , 13 x y z - 17 x], 3 2 3 [-6 x y + 8 z, -7 x z + 7 y z, -2 y z - 14]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.87 memory used=47.6MB, alloc=32.3MB, time=1.40 memory used=67.5MB, alloc=56.3MB, time=1.92 memory used=109.0MB, alloc=60.3MB, time=2.98 memory used=148.7MB, alloc=60.3MB, time=3.98 memory used=186.8MB, alloc=84.3MB, time=4.95 memory used=228.8MB, alloc=84.3MB, time=6.03 memory used=287.7MB, alloc=116.3MB, time=7.59 memory used=365.0MB, alloc=372.3MB, time=9.65 memory used=445.3MB, alloc=396.3MB, time=11.79 memory used=548.0MB, alloc=396.3MB, time=14.53 memory used=651.2MB, alloc=420.3MB, time=17.31 memory used=773.0MB, alloc=444.3MB, time=20.72 memory used=916.0MB, alloc=468.3MB, time=24.83 memory used=1058.4MB, alloc=492.3MB, time=28.84 memory used=1196.9MB, alloc=492.3MB, time=32.91 memory used=1329.9MB, alloc=516.3MB, time=36.98 memory used=1460.6MB, alloc=540.3MB, time=40.96 memory used=1571.9MB, alloc=540.3MB, time=44.53 memory used=1677.7MB, alloc=540.3MB, time=47.97 memory used=1788.5MB, alloc=564.3MB, time=51.55 memory used=1907.8MB, alloc=588.3MB, time=55.88 memory used=2035.9MB, alloc=588.3MB, time=60.17 memory used=2169.7MB, alloc=612.3MB, time=64.94 memory used=2294.9MB, alloc=636.3MB, time=69.50 memory used=2415.7MB, alloc=660.3MB, time=73.96 memory used=2513.8MB, alloc=684.3MB, time=77.77 memory used=2620.7MB, alloc=684.3MB, time=81.82 memory used=2716.0MB, alloc=708.3MB, time=85.57 memory used=2826.9MB, alloc=708.3MB, time=89.44 memory used=2942.0MB, alloc=732.3MB, time=93.33 memory used=3043.7MB, alloc=732.3MB, time=96.93 memory used=3142.5MB, alloc=756.3MB, time=100.69 memory used=3217.0MB, alloc=756.3MB, time=103.88 memory used=3309.4MB, alloc=780.3MB, time=107.70 memory used=3383.8MB, alloc=780.3MB, time=110.92 memory used=3463.7MB, alloc=804.3MB, time=114.49 |\^/| 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(); 1428255144 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 F := [-11 x y z - 17 x y , 11 y z - 17, -12 x z - 20 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [-13 x y + 20 y , -14 x y - 18 y z , 6 x z + 14 x y] > Problem := [F,G]; 2 3 2 3 2 Problem := [[-11 x y z - 17 x y , 11 y z - 17, -12 x z - 20 x z], 2 2 2 2 3 2 [-13 x y + 20 y , -14 x y - 18 y z , 6 x z + 14 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.84 memory used=47.6MB, alloc=32.3MB, time=1.38 memory used=68.8MB, alloc=32.3MB, time=1.92 memory used=88.1MB, alloc=56.3MB, time=2.44 memory used=128.3MB, alloc=60.3MB, time=3.46 memory used=167.8MB, alloc=84.3MB, time=4.57 memory used=226.9MB, alloc=84.3MB, time=6.36 memory used=280.8MB, alloc=108.3MB, time=8.03 memory used=352.2MB, alloc=140.3MB, time=10.93 memory used=431.5MB, alloc=164.3MB, time=15.71 N1 := 2165 > GB := Basis(F, plex(op(vars))); 2 4 2 2 GB := [3 x + 5 x, 3 x y - 5 x, -51 x y + 55 x z, 11 z y - 17] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=538.3MB, alloc=164.3MB, time=19.63 memory used=635.7MB, alloc=420.3MB, time=22.36 memory used=750.8MB, alloc=444.3MB, time=25.97 memory used=882.9MB, alloc=468.3MB, time=30.58 memory used=1013.3MB, alloc=492.3MB, time=37.99 memory used=1157.3MB, alloc=516.3MB, time=46.83 N2 := 3351 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 3 2 2 2 H := [-11 x y z - 17 x y , 11 z y - 17, -12 x z - 20 x z, -13 x y + 20 y , 2 2 3 2 -14 x y - 18 y z , 6 x z + 14 x y] > J:=[op(GB),op(G)]; 2 4 2 2 J := [3 x + 5 x, 3 x y - 5 x, -51 x y + 55 x z, 11 z y - 17, 2 2 2 2 3 2 -13 x y + 20 y , -14 x y - 18 y z , 6 x z + 14 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 := [6, 15, 21, 4, 3, 3, 3, 5/6, 5/6, 5/6, 2/3, 2/3, 1/2, 7, 16, 23, 5, 2, 4, 3, 6/7, 6/7, 4/7, 5/7, 4/7, 2/7, -1, -2, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1245.2MB, alloc=516.3MB, time=51.92 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428255283 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 F := [11 x z + 6 y z, -4 y z + 13 x y, -4 x z - 17 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-10 x z + 9 x y, 4 x y + 20 z , 14 x y z + 13 y z] > Problem := [F,G]; 2 3 2 2 2 2 Problem := [[11 x z + 6 y z, -4 y z + 13 x y, -4 x z - 17 y z ], 2 2 2 2 [-10 x z + 9 x y, 4 x y + 20 z , 14 x y z + 13 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.86 memory used=48.0MB, alloc=32.3MB, time=1.40 memory used=68.7MB, alloc=32.3MB, time=1.92 memory used=88.2MB, alloc=56.3MB, time=2.42 memory used=128.1MB, alloc=60.3MB, time=3.44 memory used=169.4MB, alloc=84.3MB, time=4.73 memory used=226.1MB, alloc=84.3MB, time=6.46 memory used=282.3MB, alloc=116.3MB, time=8.22 memory used=358.3MB, alloc=140.3MB, time=10.53 memory used=448.2MB, alloc=164.3MB, time=14.06 memory used=542.7MB, alloc=188.3MB, time=19.45 memory used=656.1MB, alloc=188.3MB, time=26.27 memory used=769.4MB, alloc=212.3MB, time=33.16 N1 := 3833 > GB := Basis(F, plex(op(vars))); 5 2 4 2 2 3 2 GB := [1536 x y - 702559 x y, 4 x y + 17 x y , -24 x y + 187 x y z, 3 2 2 2 96 x y + 3179 y z, 11 x z + 6 y z, -24 x y z + 187 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=910.0MB, alloc=212.3MB, time=40.21 memory used=1015.4MB, alloc=468.3MB, time=43.22 memory used=1166.2MB, alloc=492.3MB, time=47.81 memory used=1329.9MB, alloc=516.3MB, time=53.00 memory used=1505.1MB, alloc=540.3MB, time=60.95 memory used=1667.9MB, alloc=564.3MB, time=71.47 memory used=1854.7MB, alloc=588.3MB, time=83.36 memory used=2065.6MB, alloc=612.3MB, time=96.79 N2 := 5121 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 2 2 2 H := [11 x z + 6 y z, -4 y z + 13 x y, -4 x z - 17 y z , -10 x z + 9 x y, 2 2 2 4 x y + 20 z , 14 x y z + 13 y z] > J:=[op(GB),op(G)]; 5 2 4 2 2 3 2 J := [1536 x y - 702559 x y, 4 x y + 17 x y , -24 x y + 187 x y z, 3 2 2 2 96 x y + 3179 y z, 11 x z + 6 y z, -24 x y z + 187 y z , 2 2 2 2 -10 x z + 9 x y, 4 x y + 20 z , 14 x y z + 13 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 := [6, 18, 20, 4, 2, 3, 2, 1, 1, 1, 7/12, 2/3, 3/4, 9, 25, 34, 6, 5, 2, 2, 1, 1, 7/9, 13/18, 5/6, 5/9, -7, -14, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2203.9MB, alloc=612.3MB, time=105.17 |\^/| 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(); 1428255568 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [2 x y, 16 y z - 10 x , -13 y - 16] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 2 2 G := [-5 x y - 10 z , 14 x + 16 x , 2 x y + 18 z ] > Problem := [F,G]; 2 2 2 Problem := [[2 x y, 16 y z - 10 x , -13 y - 16], 2 2 3 3 2 2 2 [-5 x y - 10 z , 14 x + 16 x , 2 x y + 18 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.29 memory used=27.1MB, alloc=32.3MB, time=0.88 memory used=48.6MB, alloc=32.3MB, time=1.41 memory used=71.2MB, alloc=56.3MB, time=2.11 N1 := 515 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x, 13 y + 16, z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=116.4MB, alloc=60.3MB, time=3.55 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 2 2 2 3 3 2 H := [2 y x, 16 y z - 10 x , -13 y - 16, -5 x y - 10 z , 14 x + 16 x , 2 2 2 x y + 18 z ] > J:=[op(GB),op(G)]; 2 2 2 2 3 3 2 2 2 J := [x, 13 y + 16, z , -5 x y - 10 z , 14 x + 16 x , 2 x 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 := [6, 13, 17, 4, 3, 2, 3, 5/6, 5/6, 1/2, 6/13, 5/13, 3/13, 6, 10, 15, 4, 3, 2, 3, 2/3, 1/2, 1/2, 5/11, 3/11, 3/11, 3, 2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=144.0MB, alloc=60.3MB, time=4.29 |\^/| 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(); 1428255582 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [17 y z + 4, -7 x y - 5 x y, -x + 9 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 G := [15 x y z + 11 x y , 18 y + 2 y z, -11 y z + 3 y] > Problem := [F,G]; 3 3 2 Problem := [[17 y z + 4, -7 x y - 5 x y, -x + 9 x y], 2 2 4 2 [15 x y z + 11 x y , 18 y + 2 y z, -11 y z + 3 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.85 memory used=47.7MB, alloc=32.3MB, time=1.39 memory used=67.7MB, alloc=32.3MB, time=1.88 memory used=88.0MB, alloc=56.3MB, time=2.52 memory used=128.1MB, alloc=56.3MB, time=3.71 memory used=162.3MB, alloc=80.3MB, time=4.94 memory used=212.5MB, alloc=104.3MB, time=7.75 N1 := 1491 > GB := Basis(F, plex(op(vars))); 4 2 3 2 2 GB := [7 x + 405 x , -x + 9 x y, 7 x y + 5 x, -28 x y + 85 x z, 17 z y + 4] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=283.3MB, alloc=116.3MB, time=9.81 memory used=355.4MB, alloc=116.3MB, time=11.64 memory used=428.5MB, alloc=140.3MB, time=13.86 memory used=519.0MB, alloc=164.3MB, time=16.65 memory used=619.8MB, alloc=188.3MB, time=20.76 memory used=724.6MB, alloc=212.3MB, time=26.91 memory used=851.7MB, alloc=212.3MB, time=34.42 memory used=978.8MB, alloc=236.3MB, time=41.88 N2 := 3811 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 2 2 H := [17 z y + 4, -7 x y - 5 x y, -x + 9 x y, 15 x y z + 11 x y , 4 2 18 y + 2 y z, -11 y z + 3 y] > J:=[op(GB),op(G)]; 4 2 3 2 2 J := [7 x + 405 x , -x + 9 x y, 7 x y + 5 x, -28 x y + 85 x z, 17 z y + 4, 2 2 4 2 15 x y z + 11 x y , 18 y + 2 y z, -11 y 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 := [6, 13, 19, 4, 3, 4, 1, 1/2, 1, 2/3, 1/2, 5/6, 1/3, 8, 17, 24, 4, 4, 4, 1, 5/8, 7/8, 5/8, 5/8, 5/8, 5/16, -4, -5, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1023.3MB, alloc=236.3MB, time=44.25 |\^/| 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(); 1428255708 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 F := [12 x y z - y , -7 x y z + 16 x z, -13 z + 16 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 2 G := [15 y z - 7 z , -11 y + 16 x y, -15 x y + 9 x ] > Problem := [F,G]; 2 2 2 4 2 Problem := [[12 x y z - y , -7 x y z + 16 x z, -13 z + 16 y ], 3 2 3 2 2 2 [15 y z - 7 z , -11 y + 16 x y, -15 x y + 9 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.83 memory used=47.6MB, alloc=32.3MB, time=1.36 memory used=68.2MB, alloc=32.3MB, time=1.87 memory used=87.7MB, alloc=56.3MB, time=2.39 memory used=130.9MB, alloc=60.3MB, time=3.68 memory used=168.6MB, alloc=84.3MB, time=4.83 memory used=226.0MB, alloc=84.3MB, time=6.57 memory used=277.8MB, alloc=108.3MB, time=8.16 memory used=348.6MB, alloc=140.3MB, time=10.35 memory used=436.5MB, alloc=164.3MB, time=13.07 memory used=536.0MB, alloc=188.3MB, time=16.83 memory used=640.1MB, alloc=212.3MB, time=21.77 memory used=757.1MB, alloc=236.3MB, time=27.94 memory used=886.8MB, alloc=260.3MB, time=35.87 memory used=1040.5MB, alloc=260.3MB, time=45.23 memory used=1194.1MB, alloc=284.3MB, time=54.58 memory used=1371.8MB, alloc=284.3MB, time=65.34 memory used=1549.4MB, alloc=284.3MB, time=76.04 memory used=1727.0MB, alloc=308.3MB, time=86.82 memory used=1928.6MB, alloc=308.3MB, time=98.94 N1 := 7189 > GB := Basis(F, plex(op(vars))); 4 2 2 3 3 3 4 2 GB := [145152 x y - 13 x y , 145152 x y - 13 y , 7 y - 16 x y , 2 3 2 3 2 3 2 3 3 192 x z - 7 y , 12 x y z - y , -27648 x y + 13 y z, 13 y z - 192 x y , 4 2 13 z - 16 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2131.8MB, alloc=308.3MB, time=110.79 |\^/| 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(); 1428256008 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 2 2 F := [-12 z + 10 x , -5 y z + 13 y z , 15 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 G := [-13 x z, 2 x , 19 x z - 14 y ] > Problem := [F,G]; 4 3 3 2 2 2 Problem := [[-12 z + 10 x , -5 y z + 13 y z , 15 x y z], 3 2 3 [-13 x z, 2 x , 19 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=4.3MB, alloc=32.3MB, time=0.30 memory used=58.1MB, alloc=68.3MB, time=1.89 N1 := 499 > GB := Basis(F, plex(op(vars))); GB := [ 5 3 3 2 5 3 2 3 2 2 4 3 y x , y x , x y z, 150 y z - 2197 x y , -5 y z + 13 y z , 6 z - 5 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=104.7MB, alloc=68.3MB, time=3.26 memory used=152.8MB, alloc=92.3MB, time=4.63 N2 := 687 #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)]; 4 3 3 2 2 2 3 H := [-12 z + 10 x , -5 y z + 13 y z , 15 x y z, -13 x z, 2 x , 2 3 19 z x - 14 y ] > J:=[op(GB),op(G)]; 5 3 3 2 5 3 2 3 2 2 J := [y x , y x , x y z, 150 y z - 2197 x y , -5 y z + 13 y z , 4 3 3 2 3 6 z - 5 x , -13 x z, 2 x , 19 z 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 := [6, 13, 20, 4, 3, 3, 4, 5/6, 1/2, 5/6, 1/3, 4/15, 2/5, 9, 20, 38, 6, 5, 5, 4, 8/9, 2/3, 2/3, 2/5, 2/5, 7/20, -7, -18, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=194.8MB, alloc=92.3MB, time=6.16 |\^/| 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(); 1428256023 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 4 2 F := [17 x y z + 15 y z, 5 x - 17 x y, -20 x + 18 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 4 G := [9 x y z + x z , 18 x y + 11 x y , 12 x z + 20 y ] > Problem := [F,G]; 2 2 4 3 4 2 Problem := [[17 x y z + 15 y z, 5 x - 17 x y, -20 x + 18 y ], 2 2 3 2 2 3 4 [9 x y z + x z , 18 x y + 11 x y , 12 x z + 20 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.84 memory used=47.6MB, alloc=32.3MB, time=1.40 memory used=68.4MB, alloc=56.3MB, time=2.05 memory used=111.1MB, alloc=60.3MB, time=3.29 memory used=148.7MB, alloc=84.3MB, time=4.45 memory used=203.9MB, alloc=108.3MB, time=7.17 N1 := 1597 > GB := Basis(F, plex(op(vars))); 7 5 4 3 4 2 4 GB := [578 x - 45 x , -5 x + 17 x y, -10 x + 9 y , x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=278.2MB, alloc=108.3MB, time=10.36 memory used=358.9MB, alloc=140.3MB, time=12.78 N2 := 1427 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 4 3 4 2 2 2 H := [17 x y z + 15 y z, 5 x - 17 x y, -20 x + 18 y , 9 x y z + x z , 3 2 2 3 4 18 x y + 11 x y , 12 x z + 20 y ] > J:=[op(GB),op(G)]; 7 5 4 3 4 2 4 2 2 J := [578 x - 45 x , -5 x + 17 x y, -10 x + 9 y , x z, 9 x y z + x z , 3 2 2 3 4 18 x y + 11 x y , 12 x z + 20 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, 15, 24, 4, 4, 4, 2, 1, 1, 1/2, 3/4, 2/3, 5/12, 7, 15, 32, 7, 7, 4, 2, 1, 5/7, 3/7, 11/14, 3/7, 2/7, 0, -8, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=455.8MB, alloc=140.3MB, time=17.50 |\^/| 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(); 1428256072 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 3 F := [20 x y + 20 x z , 5 x z + 7 x y z , x y + 2 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 G := [x y - 4 y , -15 x z - 4 y, -15 x y z + 8] > Problem := [F,G]; 3 2 2 2 2 3 3 Problem := [[20 x y + 20 x z , 5 x z + 7 x y z , x y + 2 x ], 3 3 2 2 [x y - 4 y , -15 x z - 4 y, -15 x y z + 8]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.83 memory used=48.1MB, alloc=32.3MB, time=1.38 memory used=68.8MB, alloc=32.3MB, time=1.90 memory used=88.6MB, alloc=56.3MB, time=2.43 memory used=131.7MB, alloc=60.3MB, time=3.66 memory used=172.6MB, alloc=84.3MB, time=4.87 memory used=233.2MB, alloc=84.3MB, time=6.68 memory used=289.5MB, alloc=108.3MB, time=8.40 memory used=362.9MB, alloc=140.3MB, time=10.92 memory used=445.9MB, alloc=164.3MB, time=15.00 memory used=542.4MB, alloc=164.3MB, time=20.72 memory used=638.9MB, alloc=188.3MB, time=26.44 N1 := 3427 > GB := Basis(F, plex(op(vars))); 4 3 3 3 3 2 GB := [5 x - 14 x , x y + 2 x , -2 x + x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=763.0MB, alloc=188.3MB, time=32.60 memory used=874.7MB, alloc=444.3MB, time=35.91 memory used=1008.5MB, alloc=468.3MB, time=40.05 memory used=1158.2MB, alloc=492.3MB, time=46.68 memory used=1301.5MB, alloc=516.3MB, time=55.69 N2 := 3419 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 3 3 3 3 H := [20 x y + 20 x z , 5 x z + 7 x y z , x y + 2 x , x y - 4 y , 2 2 -15 x z - 4 y, -15 x y z + 8] > J:=[op(GB),op(G)]; 4 3 3 3 3 2 3 3 2 J := [5 x - 14 x , x y + 2 x , -2 x + x z , x y - 4 y , -15 x z - 4 y, 2 -15 x y z + 8] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 16, 23, 4, 3, 3, 2, 1, 1, 2/3, 3/4, 7/12, 5/12, 6, 13, 22, 4, 4, 3, 2, 1, 2/3, 1/2, 3/4, 5/12, 1/4, 3, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1456.4MB, alloc=516.3MB, time=64.95 |\^/| 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(); 1428256269 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 F := [-14 y z - 9 x z, -6 x y - 7 x z, 7 x y + 16 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [2 x y z - 9 x y, -3 x z + 3 z , -2 x y] > Problem := [F,G]; 3 3 2 3 2 Problem := [[-14 y z - 9 x z, -6 x y - 7 x z, 7 x y + 16 x z ], 2 2 2 3 2 [2 x y z - 9 x y, -3 x z + 3 z , -2 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=47.9MB, alloc=32.3MB, time=1.41 memory used=67.6MB, alloc=56.3MB, time=1.95 memory used=110.6MB, alloc=60.3MB, time=3.30 memory used=148.0MB, alloc=84.3MB, time=4.49 memory used=204.8MB, alloc=108.3MB, time=6.23 memory used=276.4MB, alloc=140.3MB, time=8.73 memory used=356.6MB, alloc=164.3MB, time=12.63 memory used=450.8MB, alloc=164.3MB, time=18.16 memory used=545.0MB, alloc=188.3MB, time=23.70 memory used=663.3MB, alloc=188.3MB, time=30.65 N1 := 3769 > GB := Basis(F, plex(op(vars))); 2 3 3 6 3 3 2 GB := [2401 x y - 2592 x y , 16807 x y + 11664 x y , 6 x y + 7 x z, 3 3 2 14 y z + 9 x z, 7 x y + 16 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=783.0MB, alloc=188.3MB, time=35.32 memory used=900.8MB, alloc=468.3MB, time=39.02 memory used=1045.7MB, alloc=492.3MB, time=43.70 memory used=1202.9MB, alloc=516.3MB, time=50.13 memory used=1350.7MB, alloc=540.3MB, time=58.51 memory used=1511.6MB, alloc=564.3MB, time=68.64 memory used=1696.5MB, alloc=588.3MB, time=80.28 memory used=1905.4MB, alloc=612.3MB, time=93.36 memory used=2138.3MB, alloc=636.3MB, time=107.96 |\^/| 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(); 1428256569 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [9 x y - 5 x y, -14 x y + x y z, 8 x y z - 16 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 G := [10 x y - 15 x y , 15 x y + 11 x y z, -10 x z + 12 x z] > Problem := [F,G]; 2 2 2 3 Problem := [[9 x y - 5 x y, -14 x y + x y z, 8 x y z - 16 x z ], 3 2 3 2 3 [10 x y - 15 x y , 15 x y + 11 x y z, -10 x z + 12 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=0.83 memory used=47.4MB, alloc=32.3MB, time=1.36 memory used=68.8MB, alloc=56.3MB, time=2.00 memory used=112.4MB, alloc=60.3MB, time=3.31 memory used=152.2MB, alloc=84.3MB, time=4.52 memory used=209.2MB, alloc=108.3MB, time=6.78 memory used=277.5MB, alloc=108.3MB, time=10.71 N1 := 1935 > GB := Basis(F, plex(op(vars))); 4 3 2 2 3 3 GB := [3528 x y - 5 x y, 9 x y - 5 x y, -14 x y + x y z, -7 x y + x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=347.0MB, alloc=108.3MB, time=13.24 memory used=424.8MB, alloc=140.3MB, time=15.60 N2 := 1223 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 3 2 H := [9 x y - 5 x y, -14 x y + x y z, 8 x y z - 16 x z , 10 x y - 15 x y , 3 2 3 15 x y + 11 x y z, -10 x z + 12 x z] > J:=[op(GB),op(G)]; 4 3 2 2 3 3 J := [3528 x y - 5 x y, 9 x y - 5 x y, -14 x y + x y z, -7 x y + x z , 3 2 3 2 3 10 x y - 15 x y , 15 x y + 11 x y z, -10 x z + 12 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 := [6, 15, 22, 4, 3, 3, 3, 1, 5/6, 2/3, 1, 3/4, 1/2, 7, 17, 27, 5, 4, 3, 3, 1, 6/7, 4/7, 1, 11/14, 5/14, -2, -5, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=499.2MB, alloc=140.3MB, time=19.18 |\^/| 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(); 1428256620 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-2 x y z - 13 y z, 4 y + 10 y z , -7 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 G := [-17 x z + 13 x y z, -9 y z + 6 y z , -y z + 19 x y z] > Problem := [F,G]; 2 2 3 2 Problem := [[-2 x y z - 13 y z, 4 y + 10 y z , -7 y], 3 3 2 3 [-17 x z + 13 x y z, -9 y z + 6 y z , -y z + 19 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.86 memory used=47.4MB, alloc=32.3MB, time=1.42 memory used=68.7MB, alloc=56.3MB, time=2.13 memory used=110.3MB, alloc=56.3MB, time=3.59 N1 := 835 > GB := Basis(F, plex(op(vars))); GB := [y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=145.8MB, alloc=56.3MB, time=4.93 N2 := 277 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 3 H := [-2 x y z - 13 y z, 4 y + 10 y z , -7 y, -17 x z + 13 x y z, 3 2 3 -9 y z + 6 y z , -y z + 19 x y z] > J:=[op(GB),op(G)]; 3 3 2 3 J := [y, -17 x z + 13 x y z, -9 y z + 6 y z , -y z + 19 x 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 := [6, 14, 20, 4, 1, 3, 3, 1/2, 1, 5/6, 1/3, 5/6, 3/4, 4, 9, 13, 4, 1, 1, 3, 1/2, 1, 3/4, 3/7, 6/7, 6/7, 5, 7, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=152.0MB, alloc=56.3MB, time=5.15 |\^/| 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(); 1428256633 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 F := [-12 x y + 12 y , -20 z - 5 x , -19 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 G := [-15 x z - 11 x z , -2 x y z - 8 x z, 13 y z + 8 x] > Problem := [F,G]; 2 2 4 2 Problem := [[-12 x y + 12 y , -20 z - 5 x , -19 y z], 3 3 2 2 2 2 [-15 x z - 11 x z , -2 x y z - 8 x z, 13 y z + 8 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=48.4MB, alloc=32.3MB, time=1.43 memory used=68.5MB, alloc=32.3MB, time=1.95 memory used=88.5MB, alloc=56.3MB, time=2.57 N1 := 323 > GB := Basis(F, plex(op(vars))); 2 2 4 2 GB := [y x , y , z y, 4 z + x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=129.3MB, alloc=60.3MB, time=3.86 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)]; 2 2 4 2 3 3 H := [-12 x y + 12 y , -20 z - 5 x , -19 z y, -15 x z - 11 x z , 2 2 2 2 -2 x y z - 8 x z, 13 z y + 8 x] > J:=[op(GB),op(G)]; 2 2 4 2 3 3 2 2 J := [y x , y , z y, 4 z + x , -15 x z - 11 x z , -2 x y z - 8 x z, 2 2 13 z y + 8 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 21, 4, 3, 2, 4, 5/6, 2/3, 5/6, 7/13, 5/13, 7/13, 7, 15, 23, 4, 3, 2, 4, 5/7, 5/7, 5/7, 1/2, 5/14, 1/2, -1, -2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=164.9MB, alloc=60.3MB, time=4.83 |\^/| 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(); 1428256645 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [13 x y - 10 x y z, -2 x y z + 15 z, 17 x z + 13 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 G := [-10 x y + 14 x y z, 3 y - 4 y z , 9 x] > Problem := [F,G]; 3 2 2 Problem := [[13 x y - 10 x y z, -2 x y z + 15 z, 17 x z + 13 x y z], 2 2 2 4 2 [-10 x y + 14 x y z, 3 y - 4 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=0.30 memory used=26.2MB, alloc=32.3MB, time=0.84 memory used=48.8MB, alloc=32.3MB, time=1.49 memory used=69.2MB, alloc=56.3MB, time=2.14 memory used=110.3MB, alloc=80.3MB, time=3.84 N1 := 943 > GB := Basis(F, plex(op(vars))); 3 3 3 2 3 4 2 3 GB := [34 x y + 195 x y , 17 x y + 13 x y , -26 x y + 1125 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=144.1MB, alloc=80.3MB, time=5.02 memory used=207.5MB, alloc=92.3MB, time=6.95 memory used=265.3MB, alloc=116.3MB, time=9.54 N2 := 1135 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 H := [13 x y - 10 x y z, -2 x y z + 15 z, 17 x z + 13 x y z, 2 2 2 4 2 -10 x y + 14 x y z, 3 y - 4 y z , 9 x] > J:=[op(GB),op(G)]; 3 3 3 2 3 4 2 3 J := [34 x y + 195 x y , 17 x y + 13 x y , -26 x y + 1125 z, 2 2 2 4 2 -10 x y + 14 x y z, 3 y - 4 y 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, 15, 19, 4, 2, 4, 2, 5/6, 5/6, 5/6, 2/3, 2/3, 7/12, 6, 13, 25, 6, 3, 4, 2, 5/6, 5/6, 1/2, 2/3, 3/4, 1/4, 2, -6, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=282.3MB, alloc=116.3MB, time=10.45 |\^/| 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(); 1428256673 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-2 x y + 15 x y, -9 x z - 4 x, 18 x y + 13 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 2 3 G := [12 y z - 10 z , -16 x - 14 y , 15 x z + 10 z] > Problem := [F,G]; 3 2 2 Problem := [[-2 x y + 15 x y, -9 x z - 4 x, 18 x y + 13 x y], 2 2 3 4 2 3 [12 y z - 10 z , -16 x - 14 y , 15 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=0.30 memory used=26.1MB, alloc=32.3MB, time=0.86 memory used=48.5MB, alloc=32.3MB, time=1.50 memory used=69.0MB, alloc=56.3MB, time=2.15 N1 := 739 > GB := Basis(F, plex(op(vars))); GB := [x y, 9 x z + 4 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.7MB, alloc=56.3MB, time=3.68 memory used=149.6MB, alloc=84.3MB, time=4.90 N2 := 559 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 3 H := [-2 x y + 15 x y, -9 x z - 4 x, 18 x y + 13 x y, 12 y z - 10 z , 4 2 3 -16 x - 14 y , 15 x z + 10 z] > J:=[op(GB),op(G)]; 2 2 3 4 2 3 J := [x y, 9 x z + 4 x, 12 y z - 10 z , -16 x - 14 y , 15 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, 12, 21, 4, 4, 2, 3, 5/6, 2/3, 1/2, 2/3, 1/2, 5/12, 5, 10, 16, 4, 4, 2, 3, 4/5, 3/5, 3/5, 1/2, 3/10, 1/2, 2, 5, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=166.3MB, alloc=84.3MB, time=5.55 |\^/| 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(); 1428256687 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 F := [11 y z + 17 z , -11 z + 17 z, 15 y z + x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 G := [-10 y + 3 z, 12 x y z + 6 x z , -14 x y - 5 z ] > Problem := [F,G]; 2 3 3 3 2 Problem := [[11 y z + 17 z , -11 z + 17 z, 15 y z + x z], 3 2 3 2 2 [-10 y + 3 z, 12 x y z + 6 x z , -14 x y - 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=27.1MB, alloc=32.3MB, time=0.90 memory used=48.4MB, alloc=32.3MB, time=1.44 memory used=68.9MB, alloc=32.3MB, time=1.97 memory used=87.9MB, alloc=56.3MB, time=2.49 memory used=127.0MB, alloc=60.3MB, time=3.54 memory used=164.6MB, alloc=60.3MB, time=4.54 memory used=200.8MB, alloc=60.3MB, time=5.47 memory used=235.4MB, alloc=84.3MB, time=6.39 memory used=290.3MB, alloc=84.3MB, time=7.84 memory used=343.5MB, alloc=116.3MB, time=9.34 memory used=418.5MB, alloc=116.3MB, time=11.40 memory used=494.0MB, alloc=116.3MB, time=13.45 memory used=566.8MB, alloc=140.3MB, time=15.48 memory used=664.1MB, alloc=140.3MB, time=18.09 memory used=756.1MB, alloc=140.3MB, time=20.67 memory used=847.7MB, alloc=164.3MB, time=23.18 memory used=935.7MB, alloc=420.3MB, time=25.55 memory used=1043.5MB, alloc=444.3MB, time=28.62 memory used=1172.6MB, alloc=468.3MB, time=32.19 memory used=1320.3MB, alloc=492.3MB, time=36.27 memory used=1485.0MB, alloc=516.3MB, time=40.99 memory used=1669.1MB, alloc=540.3MB, time=46.31 memory used=1871.3MB, alloc=564.3MB, time=53.17 memory used=2077.4MB, alloc=588.3MB, time=60.20 memory used=2297.3MB, alloc=612.3MB, time=67.43 memory used=2519.4MB, alloc=636.3MB, time=75.13 memory used=2744.2MB, alloc=660.3MB, time=83.06 memory used=2950.7MB, alloc=684.3MB, time=93.28 memory used=3155.4MB, alloc=708.3MB, time=104.52 memory used=3368.7MB, alloc=732.3MB, time=116.70 |\^/| 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(); 1428256987 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 2 2 3 F := [-8 x z + 7 z , 11 x y - 7 y z , -2 x z - 13 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 G := [18 x y z + 7 x, -4 x y - 14 y z , 17 x z + 20 x z ] > Problem := [F,G]; 2 2 3 3 2 2 2 3 Problem := [[-8 x z + 7 z , 11 x y - 7 y z , -2 x z - 13 y ], 2 3 2 2 2 2 [18 x y z + 7 x, -4 x y - 14 y z , 17 x z + 20 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.86 memory used=47.9MB, alloc=32.3MB, time=1.40 memory used=68.1MB, alloc=56.3MB, time=1.94 memory used=109.0MB, alloc=60.3MB, time=2.99 memory used=146.0MB, alloc=84.3MB, time=3.89 memory used=210.4MB, alloc=92.3MB, time=5.44 memory used=276.0MB, alloc=372.3MB, time=7.01 memory used=362.3MB, alloc=372.3MB, time=9.00 memory used=445.2MB, alloc=396.3MB, time=11.03 memory used=549.8MB, alloc=420.3MB, time=13.59 memory used=672.1MB, alloc=444.3MB, time=16.78 memory used=795.3MB, alloc=468.3MB, time=19.70 memory used=962.1MB, alloc=492.3MB, time=24.61 memory used=1129.9MB, alloc=516.3MB, time=29.98 memory used=1304.3MB, alloc=540.3MB, time=35.78 memory used=1489.3MB, alloc=564.3MB, time=42.01 memory used=1687.7MB, alloc=588.3MB, time=48.52 memory used=1930.3MB, alloc=612.3MB, time=54.68 memory used=2125.4MB, alloc=636.3MB, time=64.42 memory used=2320.5MB, alloc=660.3MB, time=75.24 memory used=2523.8MB, alloc=684.3MB, time=87.38 memory used=2734.4MB, alloc=708.3MB, time=101.11 |\^/| 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(); 1428257287 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 F := [-7 x y + 16 z, 5 y z - 12 z, -7 x z - 18 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 G := [-18 z - 12 x y z, 5 x y + 7 x z , 2 x y z - 18 x y] > Problem := [F,G]; 2 Problem := [[-7 x y + 16 z, 5 y z - 12 z, -7 x z - 18 x z], 4 3 2 2 2 [-18 z - 12 x y z, 5 x y + 7 x z , 2 x y z - 18 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.84 memory used=47.5MB, alloc=32.3MB, time=1.36 memory used=68.1MB, alloc=32.3MB, time=1.89 memory used=88.0MB, alloc=56.3MB, time=2.43 memory used=128.0MB, alloc=60.3MB, time=3.46 memory used=166.0MB, alloc=60.3MB, time=4.44 memory used=201.0MB, alloc=84.3MB, time=5.36 memory used=259.7MB, alloc=116.3MB, time=7.27 memory used=337.1MB, alloc=140.3MB, time=9.70 memory used=431.8MB, alloc=164.3MB, time=12.62 memory used=535.2MB, alloc=188.3MB, time=16.94 memory used=641.7MB, alloc=212.3MB, time=23.23 memory used=768.9MB, alloc=212.3MB, time=30.93 memory used=896.2MB, alloc=236.3MB, time=38.60 N1 := 4189 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [7 x y + 18 x y, 5 x y - 12 x y, -7 x y + 16 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1050.4MB, alloc=236.3MB, time=46.83 memory used=1158.7MB, alloc=492.3MB, time=49.85 memory used=1331.4MB, alloc=516.3MB, time=55.07 memory used=1524.5MB, alloc=540.3MB, time=61.91 memory used=1700.0MB, alloc=564.3MB, time=72.46 memory used=1891.8MB, alloc=588.3MB, time=84.56 N2 := 4189 #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 4 H := [-7 x y + 16 z, 5 y z - 12 z, -7 x z - 18 x z, -18 z - 12 x y z, 3 2 2 2 5 x y + 7 x z , 2 x y z - 18 x y] > J:=[op(GB),op(G)]; 3 2 2 4 J := [7 x y + 18 x y, 5 x y - 12 x y, -7 x y + 16 z, -18 z - 12 x y z, 3 2 2 2 5 x y + 7 x z , 2 x y z - 18 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 := [6, 16, 19, 4, 3, 2, 4, 5/6, 5/6, 1, 2/3, 1/2, 3/4, 6, 16, 21, 4, 3, 2, 4, 1, 1, 2/3, 5/6, 3/4, 5/12, 0, -2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2043.6MB, alloc=588.3MB, time=93.73 |\^/| 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(); 1428257569 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-10 y z + 5 z, 20 y z - 2 y, -19 x y + 8 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 3 G := [19 z - 19 x , 18 y z - 17 y , 5 x y z + 2 x ] > Problem := [F,G]; 2 2 2 2 Problem := [[-10 y z + 5 z, 20 y z - 2 y, -19 x y + 8 x y z], 3 2 3 3 2 3 [19 z - 19 x , 18 y z - 17 y , 5 x y z + 2 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.85 memory used=47.5MB, alloc=32.3MB, time=1.39 memory used=66.9MB, alloc=32.3MB, time=1.91 memory used=85.7MB, alloc=56.3MB, time=2.42 memory used=124.2MB, alloc=60.3MB, time=3.44 memory used=159.8MB, alloc=84.3MB, time=4.39 memory used=215.7MB, alloc=84.3MB, time=5.88 memory used=268.7MB, alloc=108.3MB, time=7.34 memory used=342.1MB, alloc=116.3MB, time=9.38 memory used=414.6MB, alloc=116.3MB, time=11.38 memory used=488.1MB, alloc=140.3MB, time=13.43 memory used=583.9MB, alloc=140.3MB, time=16.09 memory used=677.6MB, alloc=164.3MB, time=18.80 memory used=784.9MB, alloc=164.3MB, time=21.86 memory used=884.6MB, alloc=444.3MB, time=24.81 memory used=1021.2MB, alloc=444.3MB, time=28.66 memory used=1154.3MB, alloc=468.3MB, time=32.36 memory used=1312.3MB, alloc=492.3MB, time=36.44 memory used=1485.3MB, alloc=516.3MB, time=41.33 memory used=1682.9MB, alloc=540.3MB, time=46.51 memory used=1899.1MB, alloc=564.3MB, time=52.14 memory used=2118.7MB, alloc=588.3MB, time=58.51 memory used=2364.2MB, alloc=612.3MB, time=66.24 memory used=2628.6MB, alloc=636.3MB, time=73.52 memory used=2877.6MB, alloc=660.3MB, time=81.69 memory used=3124.6MB, alloc=684.3MB, time=90.01 memory used=3375.0MB, alloc=708.3MB, time=98.51 |\^/| 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(); 1428257869 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 4 4 F := [x z - 13 y z, 5 x z - 12 z , 17 x - 6 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 G := [-2 x + 10 x , 17 y z + 10 y , -2 - 20 x] > Problem := [F,G]; 2 3 4 4 4 Problem := [[x z - 13 y z, 5 x z - 12 z , 17 x - 6 y ], 4 2 2 2 [-2 x + 10 x , 17 y z + 10 y , -2 - 20 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.0MB, alloc=32.3MB, time=0.83 memory used=49.0MB, alloc=32.3MB, time=1.48 memory used=69.4MB, alloc=56.3MB, time=2.12 memory used=110.1MB, alloc=84.3MB, time=3.48 N1 := 1125 > GB := Basis(F, plex(op(vars))); 4 4 8 4 2 3 4 GB := [-17 x + 6 y , 6 x z - 485537 x z, -x z + 13 y z, -5 x z + 12 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=166.5MB, alloc=84.3MB, time=5.84 memory used=227.3MB, alloc=84.3MB, time=7.60 memory used=283.5MB, alloc=108.3MB, time=10.14 N2 := 1125 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 4 4 4 4 2 H := [x z - 13 y z, 5 x z - 12 z , -6 y + 17 x , -2 x + 10 x , 2 2 17 y z + 10 y , -2 - 20 x] > J:=[op(GB),op(G)]; 4 4 8 4 2 3 4 J := [-17 x + 6 y , 6 x z - 485537 x z, -x z + 13 y z, -5 x z + 12 z , 4 2 2 2 -2 x + 10 x , 17 y z + 10 y , -2 - 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 := [6, 11, 19, 4, 4, 4, 4, 5/6, 1/2, 1/2, 1/2, 1/3, 5/12, 7, 13, 28, 9, 8, 4, 4, 6/7, 3/7, 4/7, 4/7, 2/7, 1/2, -2, -9, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=291.3MB, alloc=108.3MB, time=10.51 |\^/| 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(); 1428257904 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 2 2 F := [11 z + 6 y, 9 x z + 3 x z , -15 x z - 5 x y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 2 2 2 G := [9 y - 18 z , 20 x - 3 x, 12 x y - 17 y z ] > Problem := [F,G]; 4 3 2 2 2 2 2 Problem := [[11 z + 6 y, 9 x z + 3 x z , -15 x z - 5 x y z ], 4 4 2 2 2 [9 y - 18 z , 20 x - 3 x, 12 x y - 17 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=48.3MB, alloc=32.3MB, time=1.41 memory used=68.6MB, alloc=56.3MB, time=1.95 memory used=111.1MB, alloc=60.3MB, time=3.06 memory used=153.0MB, alloc=84.3MB, time=4.36 memory used=216.3MB, alloc=84.3MB, time=6.23 memory used=274.5MB, alloc=108.3MB, time=7.93 memory used=349.9MB, alloc=132.3MB, time=10.23 memory used=438.2MB, alloc=164.3MB, time=13.07 memory used=531.5MB, alloc=188.3MB, time=16.96 memory used=634.1MB, alloc=212.3MB, time=22.07 memory used=748.9MB, alloc=236.3MB, time=28.88 memory used=887.7MB, alloc=236.3MB, time=37.10 memory used=1026.5MB, alloc=260.3MB, time=45.33 memory used=1189.2MB, alloc=260.3MB, time=54.93 memory used=1351.9MB, alloc=260.3MB, time=64.51 memory used=1514.6MB, alloc=284.3MB, time=74.15 memory used=1701.4MB, alloc=308.3MB, time=85.13 N1 := 6567 > GB := Basis(F, plex(op(vars))); 5 2 2 2 4 4 3 2 GB := [99 x y - 2 x y, 3 x y + x y , -x y + x z, 3 x y + x y z, 3 2 2 3 2 4 3 x z + x z , -9 x z + x y z , 11 z + 6 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1846.8MB, alloc=308.3MB, time=91.07 memory used=2077.0MB, alloc=564.3MB, time=97.46 |\^/| 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(); 1428258204 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 F := [16 x y z + 19 y , 20 x z + 14 x z , -2 y z + 8 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 2 G := [10 y z , 6 z + 9 y , -12 x y z - 15 x ] > Problem := [F,G]; 2 2 3 3 2 Problem := [[16 x y z + 19 y , 20 x z + 14 x z , -2 y z + 8 z ], 2 2 4 2 2 2 [10 y z , 6 z + 9 y , -12 x 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=0.30 memory used=26.5MB, alloc=32.3MB, time=0.89 memory used=47.8MB, alloc=32.3MB, time=1.43 memory used=68.0MB, alloc=32.3MB, time=1.97 memory used=87.3MB, alloc=56.3MB, time=2.50 memory used=126.5MB, alloc=60.3MB, time=3.52 memory used=166.2MB, alloc=92.3MB, time=4.58 memory used=226.8MB, alloc=92.3MB, time=6.13 memory used=288.1MB, alloc=116.3MB, time=7.63 memory used=360.8MB, alloc=372.3MB, time=9.50 memory used=438.4MB, alloc=396.3MB, time=11.59 memory used=538.0MB, alloc=420.3MB, time=14.25 memory used=660.4MB, alloc=444.3MB, time=17.97 memory used=790.5MB, alloc=468.3MB, time=22.35 memory used=918.9MB, alloc=492.3MB, time=29.78 N1 := 2239 > GB := Basis(F, plex(op(vars))); 3 2 2 2 3 3 2 2 4 3 3 GB := [4 x y + 19 x y , 4 x y + 19 y , 160 x y + 7 y , 640 x z + 7 x y , 2 2 3 2 2 16 x y z + 19 y , -y + 4 y z, -y z + 4 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1080.5MB, alloc=492.3MB, time=35.31 memory used=1254.0MB, alloc=492.3MB, time=40.06 memory used=1386.2MB, alloc=516.3MB, time=43.48 memory used=1508.0MB, alloc=516.3MB, time=46.49 memory used=1664.5MB, alloc=540.3MB, time=51.17 memory used=1841.1MB, alloc=564.3MB, time=57.12 memory used=2035.9MB, alloc=588.3MB, time=63.83 memory used=2242.6MB, alloc=612.3MB, time=75.57 memory used=2445.9MB, alloc=636.3MB, time=89.08 memory used=2673.2MB, alloc=660.3MB, time=104.31 |\^/| 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(); 1428258504 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 F := [-3 x y + 3 y z, -17 y z + 9 y , 3 y z + x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 2 G := [17 y + 9 x , 5 y - 17, 5 x y z - 13 y] > Problem := [F,G]; 2 3 3 2 Problem := [[-3 x y + 3 y z, -17 y z + 9 y , 3 y z + x y], 4 2 4 2 [17 y + 9 x , 5 y - 17, 5 x y z - 13 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.31 memory used=26.0MB, alloc=32.3MB, time=0.85 memory used=47.8MB, alloc=32.3MB, time=1.40 memory used=68.7MB, alloc=32.3MB, time=1.95 memory used=88.8MB, alloc=32.3MB, time=2.47 memory used=107.8MB, alloc=56.3MB, time=2.99 memory used=147.4MB, alloc=60.3MB, time=4.04 memory used=185.9MB, alloc=60.3MB, time=5.05 memory used=222.2MB, alloc=84.3MB, time=6.01 memory used=275.7MB, alloc=84.3MB, time=7.65 memory used=328.8MB, alloc=116.3MB, time=9.35 memory used=401.7MB, alloc=140.3MB, time=11.59 memory used=491.3MB, alloc=164.3MB, time=14.57 memory used=590.8MB, alloc=188.3MB, time=19.55 memory used=701.8MB, alloc=212.3MB, time=26.31 memory used=836.8MB, alloc=212.3MB, time=34.32 N1 := 3311 > GB := Basis(F, plex(op(vars))); GB := [ 7 4 2 6 3 4 289 x y + 243 x y, 17 x y + 27 x y , -289 x y + 729 y , 17 x y + 27 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=972.7MB, alloc=212.3MB, time=38.80 N2 := 795 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 2 4 2 4 H := [-3 x y + 3 y z, -17 y z + 9 y , 3 y z + x y, 17 y + 9 x , 5 y - 17, 2 5 x y z - 13 y] > J:=[op(GB),op(G)]; 7 4 2 6 3 J := [289 x y + 243 x y, 17 x y + 27 x y , -289 x y + 729 y , 4 4 2 4 2 17 x y + 27 y z, 17 y + 9 x , 5 y - 17, 5 x y 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 := [6, 14, 22, 4, 2, 4, 3, 2/3, 1, 2/3, 1/3, 5/6, 1/3, 7, 15, 37, 8, 7, 4, 1, 6/7, 1, 2/7, 4/7, 6/7, 1/7, -1, -15, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=995.0MB, alloc=468.3MB, time=39.99 |\^/| 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(); 1428258619 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 2 F := [-16 y + 17 y z, -8 x z - 8 x , 11 x - 11 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 G := [15 z - 12 y z, -2 x z + 15 x , 16 x y z + 6 x z ] > Problem := [F,G]; 4 2 2 2 3 2 Problem := [[-16 y + 17 y z, -8 x z - 8 x , 11 x - 11 y], 3 3 2 2 2 [15 z - 12 y z, -2 x z + 15 x , 16 x y z + 6 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.8MB, alloc=32.3MB, time=0.87 memory used=48.2MB, alloc=32.3MB, time=1.41 memory used=68.2MB, alloc=32.3MB, time=1.91 memory used=87.6MB, alloc=56.3MB, time=2.43 memory used=126.4MB, alloc=60.3MB, time=3.43 memory used=163.4MB, alloc=84.3MB, time=4.40 memory used=217.8MB, alloc=84.3MB, time=5.82 memory used=274.4MB, alloc=92.3MB, time=7.34 memory used=329.5MB, alloc=116.3MB, time=8.78 memory used=406.9MB, alloc=116.3MB, time=10.81 memory used=484.6MB, alloc=140.3MB, time=12.88 memory used=580.9MB, alloc=140.3MB, time=15.51 memory used=670.1MB, alloc=420.3MB, time=18.02 memory used=785.0MB, alloc=444.3MB, time=21.19 memory used=918.9MB, alloc=468.3MB, time=25.06 memory used=1074.6MB, alloc=492.3MB, time=30.02 memory used=1236.9MB, alloc=516.3MB, time=35.27 memory used=1408.3MB, alloc=540.3MB, time=40.84 memory used=1587.5MB, alloc=564.3MB, time=46.69 memory used=1769.2MB, alloc=588.3MB, time=52.89 memory used=1950.3MB, alloc=612.3MB, time=60.03 memory used=2116.6MB, alloc=636.3MB, time=68.65 memory used=2289.7MB, alloc=660.3MB, time=78.30 memory used=2474.0MB, alloc=684.3MB, time=88.91 memory used=2669.6MB, alloc=708.3MB, time=100.94 |\^/| 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(); 1428258919 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [-3 x y z + y , 9 x z - 3 x y , 3 x z + 11 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 2 G := [-6 x y - 4 y , -2 x y - 13 z , 9 x y + 14 x z ] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[-3 x y z + y , 9 x z - 3 x y , 3 x z + 11 y z ], 2 3 3 3 2 2 [-6 x y - 4 y , -2 x y - 13 z , 9 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=0.30 memory used=26.6MB, alloc=32.3MB, time=0.86 memory used=48.0MB, alloc=32.3MB, time=1.41 memory used=68.6MB, alloc=32.3MB, time=1.96 memory used=88.2MB, alloc=56.3MB, time=2.49 memory used=128.2MB, alloc=60.3MB, time=3.53 memory used=166.2MB, alloc=84.3MB, time=4.52 memory used=221.4MB, alloc=84.3MB, time=5.98 memory used=280.6MB, alloc=116.3MB, time=7.91 memory used=359.8MB, alloc=140.3MB, time=10.32 memory used=456.9MB, alloc=164.3MB, time=13.32 memory used=570.6MB, alloc=188.3MB, time=16.89 memory used=672.0MB, alloc=468.3MB, time=20.16 memory used=809.8MB, alloc=492.3MB, time=25.74 memory used=946.8MB, alloc=516.3MB, time=32.55 memory used=1088.2MB, alloc=540.3MB, time=41.25 memory used=1253.5MB, alloc=564.3MB, time=51.42 memory used=1442.8MB, alloc=564.3MB, time=62.93 memory used=1632.1MB, alloc=588.3MB, time=74.49 memory used=1845.4MB, alloc=588.3MB, time=87.52 memory used=2058.6MB, alloc=612.3MB, time=100.52 |\^/| 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(); 1428259219 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 F := [7 y - 15, 7 x y z + 19 y , -10 x y z - 11 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 2 2 G := [-14 z + 15 y z , 13 x y - 8 y z , -17 x y - x y ] > Problem := [F,G]; 4 2 4 Problem := [[7 y - 15, 7 x y z + 19 y , -10 x y z - 11 y z], 4 2 3 2 2 2 2 [-14 z + 15 y z , 13 x y - 8 y z , -17 x y - x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.86 memory used=47.5MB, alloc=32.3MB, time=1.39 memory used=68.4MB, alloc=32.3MB, time=1.94 memory used=89.9MB, alloc=56.3MB, time=2.63 memory used=132.6MB, alloc=60.3MB, time=3.98 memory used=172.8MB, alloc=84.3MB, time=5.24 memory used=229.9MB, alloc=108.3MB, time=7.34 memory used=296.6MB, alloc=108.3MB, time=11.29 N1 := 2035 > GB := Basis(F, plex(op(vars))); 4 2 GB := [10 x + 11, 7 y - 15, -190 y + 77 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=364.3MB, alloc=108.3MB, time=14.50 memory used=439.4MB, alloc=140.3MB, time=16.77 memory used=541.0MB, alloc=164.3MB, time=20.98 N2 := 1655 #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)]; 4 2 4 4 2 H := [7 y - 15, 7 x y z + 19 y , -10 x y z - 11 y z, -14 z + 15 y z , 3 2 2 2 2 13 x y - 8 y z , -17 x y - x y ] > J:=[op(GB),op(G)]; 4 2 4 2 3 2 J := [10 x + 11, 7 y - 15, -190 y + 77 z, -14 z + 15 y z , 13 x y - 8 y z , 2 2 2 -17 x y - 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 := [6, 14, 23, 4, 2, 4, 4, 2/3, 1, 2/3, 5/12, 5/6, 1/2, 6, 11, 19, 4, 2, 4, 4, 1/2, 5/6, 1/2, 1/3, 7/12, 1/3, 3, 4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=589.6MB, alloc=164.3MB, time=23.72 |\^/| 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(); 1428259283 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-2 x y, 8 x y + 14 y, -17 y z - 13 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [-4 x y + 12 x , -5 x z - 15 x , -12 x + 4 x y] > Problem := [F,G]; 2 2 2 2 Problem := [[-2 x y, 8 x y + 14 y, -17 y z - 13 x z], 2 2 2 2 3 2 [-4 x y + 12 x , -5 x z - 15 x , -12 x + 4 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.0MB, alloc=32.3MB, time=0.85 memory used=49.7MB, alloc=32.3MB, time=1.53 memory used=69.4MB, alloc=56.3MB, time=2.20 N1 := 533 > GB := Basis(F, plex(op(vars))); 2 GB := [y, z x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 121 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 H := [-2 x y, 8 x y + 14 y, -17 y z - 13 x z, -4 x y + 12 x , 2 2 3 2 -5 x z - 15 x , -12 x + 4 x y] > J:=[op(GB),op(G)]; 2 2 2 2 2 3 2 J := [y, z x , -4 x y + 12 x , -5 x z - 15 x , -12 x + 4 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 := [6, 13, 18, 4, 3, 2, 2, 1, 5/6, 1/3, 9/13, 6/13, 3/13, 5, 9, 13, 3, 3, 1, 2, 4/5, 3/5, 2/5, 7/9, 1/3, 2/9, 4, 5, 1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=93.8MB, alloc=56.3MB, time=3.00 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428259290 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 3 3 4 F := [-10 x y z + 5 z , -19 x y - 4 z , -17 x z - 18 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 3 3 G := [-17 x y + 20 z , 3 z + 13 x y, -11 x y - 19 y z] > Problem := [F,G]; 2 4 3 3 3 4 Problem := [[-10 x y z + 5 z , -19 x y - 4 z , -17 x z - 18 z ], 2 2 4 3 3 3 [-17 x y + 20 z , 3 z + 13 x y, -11 x y - 19 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.86 memory used=47.6MB, alloc=32.3MB, time=1.39 memory used=67.0MB, alloc=56.3MB, time=1.91 memory used=106.6MB, alloc=60.3MB, time=2.94 memory used=145.1MB, alloc=60.3MB, time=3.92 memory used=181.5MB, alloc=84.3MB, time=4.88 memory used=236.2MB, alloc=84.3MB, time=6.29 memory used=290.2MB, alloc=108.3MB, time=7.74 memory used=362.4MB, alloc=116.3MB, time=9.72 memory used=434.2MB, alloc=140.3MB, time=11.66 memory used=530.1MB, alloc=140.3MB, time=14.24 memory used=621.9MB, alloc=164.3MB, time=16.77 memory used=709.9MB, alloc=420.3MB, time=19.24 memory used=823.0MB, alloc=444.3MB, time=22.32 memory used=961.4MB, alloc=468.3MB, time=26.01 memory used=1116.7MB, alloc=492.3MB, time=30.21 memory used=1295.0MB, alloc=516.3MB, time=35.48 memory used=1490.4MB, alloc=540.3MB, time=41.09 memory used=1702.2MB, alloc=564.3MB, time=47.82 memory used=1933.9MB, alloc=588.3MB, time=54.70 memory used=2177.4MB, alloc=612.3MB, time=62.30 memory used=2441.5MB, alloc=636.3MB, time=70.84 memory used=2705.1MB, alloc=660.3MB, time=79.61 memory used=2970.3MB, alloc=684.3MB, time=88.71 memory used=3239.7MB, alloc=708.3MB, time=97.99 memory used=3511.6MB, alloc=732.3MB, time=107.31 |\^/| 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(); 1428259590 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 4 F := [16 z , 7 x z + 10 y z , -y + 12 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 4 4 3 G := [-7 x y z + 16 z , -5 x z + 18 z , 9 x + 13 y z ] > Problem := [F,G]; 2 3 2 2 4 Problem := [[16 z , 7 x z + 10 y z , -y + 12 x y z], 2 4 3 4 4 3 [-7 x y z + 16 z , -5 x z + 18 z , 9 x + 13 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.87 memory used=47.8MB, alloc=32.3MB, time=1.41 memory used=68.2MB, alloc=56.3MB, time=1.97 memory used=111.1MB, alloc=60.3MB, time=3.08 memory used=149.7MB, alloc=60.3MB, time=4.08 memory used=186.5MB, alloc=84.3MB, time=5.05 memory used=236.9MB, alloc=84.3MB, time=6.35 memory used=295.9MB, alloc=92.3MB, time=7.90 memory used=360.9MB, alloc=116.3MB, time=9.29 memory used=439.3MB, alloc=140.3MB, time=10.58 memory used=532.8MB, alloc=396.3MB, time=13.10 memory used=633.2MB, alloc=420.3MB, time=15.60 memory used=770.5MB, alloc=444.3MB, time=17.80 memory used=895.2MB, alloc=468.3MB, time=20.25 memory used=1039.4MB, alloc=492.3MB, time=23.55 memory used=1171.1MB, alloc=516.3MB, time=26.11 memory used=1326.7MB, alloc=516.3MB, time=28.57 memory used=1471.7MB, alloc=540.3MB, time=31.18 memory used=1626.4MB, alloc=564.3MB, time=33.52 memory used=1735.4MB, alloc=564.3MB, time=35.69 memory used=1837.9MB, alloc=564.3MB, time=37.89 memory used=1935.9MB, alloc=564.3MB, time=39.78 memory used=2042.6MB, alloc=588.3MB, time=41.86 memory used=2162.6MB, alloc=612.3MB, time=43.84 memory used=2294.1MB, alloc=612.3MB, time=45.57 memory used=2373.7MB, alloc=612.3MB, time=47.68 memory used=2472.7MB, alloc=636.3MB, time=51.31 memory used=2588.5MB, alloc=660.3MB, time=55.62 memory used=2692.5MB, alloc=660.3MB, time=59.53 memory used=2782.8MB, alloc=684.3MB, time=63.02 memory used=2881.5MB, alloc=708.3MB, time=66.85 memory used=2966.2MB, alloc=708.3MB, time=70.25 memory used=3049.4MB, alloc=732.3MB, time=73.62 memory used=3134.1MB, alloc=756.3MB, time=77.66 memory used=3427.1MB, alloc=780.3MB, time=93.21 memory used=3699.5MB, alloc=804.3MB, time=111.00 |\^/| 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(); 1428259890 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [20 y z - 10 z , 18 x y z - 18 x y, 14 x y z + 8 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 2 G := [3 z + 10 y z, -2 x z + 15 x , 16 x z - 15 x y] > Problem := [F,G]; 3 2 2 2 2 Problem := [[20 y z - 10 z , 18 x y z - 18 x y, 14 x y z + 8 x z], 3 3 3 3 2 [3 z + 10 y z, -2 x z + 15 x , 16 x z - 15 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.83 memory used=47.0MB, alloc=32.3MB, time=1.35 memory used=67.4MB, alloc=32.3MB, time=1.87 memory used=86.2MB, alloc=56.3MB, time=2.38 memory used=124.1MB, alloc=60.3MB, time=3.36 memory used=159.0MB, alloc=84.3MB, time=4.30 memory used=214.6MB, alloc=84.3MB, time=5.81 memory used=270.5MB, alloc=92.3MB, time=7.35 memory used=324.8MB, alloc=116.3MB, time=8.88 memory used=401.0MB, alloc=116.3MB, time=10.98 memory used=473.4MB, alloc=140.3MB, time=13.03 memory used=569.9MB, alloc=140.3MB, time=15.61 memory used=659.2MB, alloc=420.3MB, time=18.07 memory used=772.9MB, alloc=444.3MB, time=21.21 memory used=907.6MB, alloc=468.3MB, time=25.53 memory used=1050.2MB, alloc=492.3MB, time=30.07 memory used=1203.7MB, alloc=516.3MB, time=35.07 memory used=1366.9MB, alloc=540.3MB, time=40.48 memory used=1537.5MB, alloc=564.3MB, time=46.15 memory used=1718.2MB, alloc=588.3MB, time=52.17 memory used=1898.5MB, alloc=612.3MB, time=59.89 memory used=2068.9MB, alloc=636.3MB, time=68.87 memory used=2247.6MB, alloc=660.3MB, time=78.94 memory used=2438.7MB, alloc=684.3MB, time=90.16 memory used=2643.6MB, alloc=708.3MB, time=102.62 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428260190 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 F := [-8 y z + 15 y z , -8 y z + 20, 16 y + x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [-14 x, 15 y - 10 z , 7 x y z - 7 y] > Problem := [F,G]; 3 2 2 2 4 Problem := [[-8 y z + 15 y z , -8 y z + 20, 16 y + x z], 3 2 [-14 x, 15 y - 10 z , 7 x y z - 7 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.89 memory used=47.7MB, alloc=32.3MB, time=1.42 memory used=67.1MB, alloc=56.3MB, time=1.95 memory used=105.8MB, alloc=60.3MB, time=2.95 memory used=142.2MB, alloc=84.3MB, time=3.92 memory used=202.3MB, alloc=92.3MB, time=5.50 memory used=261.2MB, alloc=116.3MB, time=7.05 memory used=338.3MB, alloc=116.3MB, time=9.11 memory used=416.9MB, alloc=396.3MB, time=11.12 memory used=513.6MB, alloc=396.3MB, time=13.72 memory used=614.0MB, alloc=420.3MB, time=16.86 memory used=722.4MB, alloc=444.3MB, time=20.27 memory used=843.5MB, alloc=468.3MB, time=24.16 memory used=975.8MB, alloc=492.3MB, time=28.49 memory used=1119.5MB, alloc=516.3MB, time=33.19 memory used=1272.8MB, alloc=540.3MB, time=38.31 memory used=1434.7MB, alloc=564.3MB, time=43.66 memory used=1603.0MB, alloc=588.3MB, time=49.66 memory used=1760.7MB, alloc=612.3MB, time=57.45 memory used=1923.7MB, alloc=636.3MB, time=66.19 memory used=2097.7MB, alloc=660.3MB, time=75.91 memory used=2284.4MB, alloc=684.3MB, time=86.70 memory used=2484.8MB, alloc=708.3MB, time=98.51 memory used=2698.7MB, alloc=732.3MB, time=111.44 |\^/| 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(); 1428260490 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 4 2 F := [12 x z + 13 y z , -8 x - 18 z , 11 x - 16 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [12 y z - 11 z , x y + 3 y , -11 x y + 5 y z] > Problem := [F,G]; 2 2 2 2 3 2 4 2 Problem := [[12 x z + 13 y z , -8 x - 18 z , 11 x - 16 x z], 2 2 2 3 2 [12 y z - 11 z , x y + 3 y , -11 x y + 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.83 memory used=48.7MB, alloc=32.3MB, time=1.45 N1 := 305 > GB := Basis(F, plex(op(vars))); 6 5 5 3 2 4 2 3 2 GB := [1089 x + 1024 x , 12 x + 13 x y , -11 x + 16 x z, 4 x + 9 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=69.1MB, alloc=32.3MB, time=2.07 memory used=87.6MB, alloc=32.3MB, time=2.52 memory used=106.7MB, alloc=56.3MB, time=3.05 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)]; 2 2 2 2 3 2 4 2 2 2 H := [12 x z + 13 y z , -8 x - 18 z , 11 x - 16 x z, 12 y z - 11 z , 2 3 2 x y + 3 y , -11 x y + 5 y z] > J:=[op(GB),op(G)]; 6 5 5 3 2 4 2 3 2 J := [1089 x + 1024 x , 12 x + 13 x y , -11 x + 16 x z, 4 x + 9 z , 2 2 2 3 2 12 y z - 11 z , x y + 3 y , -11 x y + 5 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 20, 4, 4, 3, 2, 5/6, 2/3, 5/6, 1/2, 1/2, 7/12, 7, 14, 27, 6, 6, 3, 2, 6/7, 4/7, 4/7, 9/14, 3/7, 5/14, 0, -7, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=124.7MB, alloc=56.3MB, time=3.60 |\^/| 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(); 1428260500 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 F := [6 x z + 11 y z , -20 x y z + 14 y , -14 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 G := [19 x z + 12 x y, 18 z + 20 y, -15 x z - 8 x y z] > Problem := [F,G]; 3 3 2 4 Problem := [[6 x z + 11 y z , -20 x y z + 14 y , -14 x y z], 3 3 3 2 [19 x z + 12 x y, 18 z + 20 y, -15 x z - 8 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=27.0MB, alloc=32.3MB, time=0.90 memory used=48.6MB, alloc=32.3MB, time=1.45 memory used=70.2MB, alloc=32.3MB, time=2.01 memory used=89.5MB, alloc=56.3MB, time=2.50 memory used=131.1MB, alloc=60.3MB, time=3.51 memory used=172.2MB, alloc=92.3MB, time=4.58 memory used=236.2MB, alloc=92.3MB, time=6.13 memory used=298.7MB, alloc=116.3MB, time=7.62 memory used=375.9MB, alloc=372.3MB, time=9.47 memory used=455.1MB, alloc=396.3MB, time=11.74 memory used=549.9MB, alloc=420.3MB, time=14.72 memory used=662.5MB, alloc=444.3MB, time=18.24 memory used=784.1MB, alloc=468.3MB, time=23.97 memory used=908.1MB, alloc=492.3MB, time=31.49 memory used=1056.4MB, alloc=516.3MB, time=40.47 N1 := 3387 > GB := Basis(F, plex(op(vars))); 4 4 3 3 GB := [y , x z, x y z, 6 x z + 11 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1238.9MB, alloc=516.3MB, time=46.20 N2 := 1867 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 4 3 H := [6 x z + 11 y z , -20 x y z + 14 y , -14 x y z, 19 x z + 12 x y, 3 3 2 18 z + 20 y, -15 x z - 8 x y z] > J:=[op(GB),op(G)]; 4 4 3 3 3 3 J := [y , x z, x y z, 6 x z + 11 y z , 19 x z + 12 x y, 18 z + 20 y, 3 2 -15 x z - 8 x 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 := [6, 17, 22, 4, 3, 4, 3, 5/6, 1, 1, 1/2, 1/2, 4/7, 7, 17, 27, 5, 4, 4, 3, 5/7, 6/7, 6/7, 7/15, 2/5, 8/15, 0, -5, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1378.9MB, alloc=516.3MB, time=53.83 |\^/| 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(); 1428260643 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 F := [9 y - 13 z, -13 x z , 16 y + 4 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 4 G := [5 x , -6 x y z + 2 y z , -11 x ] > Problem := [F,G]; Problem := 2 4 3 2 2 2 2 4 [[9 y - 13 z, -13 x z , 16 y + 4 x ], [5 x , -6 x y z + 2 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); N1 := 207 > GB := Basis(F, plex(op(vars))); 4 2 4 3 GB := [x , y x, 4 y + x , 13 z - 9 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=33.2MB, alloc=40.3MB, time=1.13 N2 := 207 #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 4 3 2 2 2 2 4 H := [-13 z + 9 y, -13 x z , 16 y + 4 x , 5 x , -6 x y z + 2 y z , -11 x ] > J:=[op(GB),op(G)]; 4 2 4 3 2 2 2 2 4 J := [x , y x, 4 y + x , 13 z - 9 y, 5 x , -6 x y z + 2 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 := [6, 11, 18, 4, 4, 4, 2, 5/6, 1/2, 1/2, 5/13, 4/13, 4/13, 7, 12, 22, 4, 4, 4, 2, 6/7, 4/7, 2/7, 3/7, 5/14, 3/14, -1, -4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=49.8MB, alloc=40.3MB, time=1.60 |\^/| 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(); 1428260648 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-13 x z + 16 z, 20 x z - 4 x y, 8 y z + 9 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 3 2 G := [13 x z + 8 y z, 19 x y z + 11 y z , 7 x z + 17 y z ] > Problem := [F,G]; 3 2 2 Problem := [[-13 x z + 16 z, 20 x z - 4 x y, 8 y z + 9 x z], 2 2 3 2 2 2 3 2 [13 x z + 8 y z, 19 x y z + 11 y z , 7 x z + 17 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.85 memory used=48.0MB, alloc=32.3MB, time=1.42 memory used=67.6MB, alloc=56.3MB, time=1.92 memory used=109.8MB, alloc=60.3MB, time=2.95 memory used=147.1MB, alloc=84.3MB, time=3.93 memory used=209.3MB, alloc=92.3MB, time=5.56 memory used=275.6MB, alloc=116.3MB, time=7.06 memory used=344.1MB, alloc=116.3MB, time=8.57 memory used=400.1MB, alloc=372.3MB, time=9.91 memory used=484.8MB, alloc=396.3MB, time=11.91 memory used=591.8MB, alloc=420.3MB, time=14.48 memory used=718.8MB, alloc=444.3MB, time=17.61 memory used=830.1MB, alloc=468.3MB, time=20.39 memory used=933.8MB, alloc=468.3MB, time=23.04 memory used=1012.6MB, alloc=468.3MB, time=25.05 memory used=1097.8MB, alloc=492.3MB, time=27.38 memory used=1172.1MB, alloc=492.3MB, time=29.43 memory used=1257.7MB, alloc=492.3MB, time=31.74 memory used=1319.5MB, alloc=492.3MB, time=33.57 memory used=1385.5MB, alloc=492.3MB, time=35.58 memory used=1444.8MB, alloc=492.3MB, time=37.45 memory used=1513.8MB, alloc=516.3MB, time=39.60 memory used=1587.3MB, alloc=516.3MB, time=42.11 memory used=1673.8MB, alloc=540.3MB, time=45.29 memory used=1772.1MB, alloc=540.3MB, time=48.90 memory used=1849.6MB, alloc=564.3MB, time=51.85 memory used=1938.6MB, alloc=564.3MB, time=55.36 memory used=2131.5MB, alloc=588.3MB, time=62.07 memory used=2336.1MB, alloc=612.3MB, time=70.60 memory used=2520.8MB, alloc=636.3MB, time=80.85 memory used=2707.0MB, alloc=660.3MB, time=92.57 |\^/| 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(); 1428260948 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 4 F := [-13 x y - 12 y, 14 y - 1, 14 x z + 2 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [11 y - 4 x , -16 x + 15 y z, -19 x z + 20 y] > Problem := [F,G]; 2 2 4 3 4 Problem := [[-13 x y - 12 y, 14 y - 1, 14 x z + 2 y ], 3 2 2 2 [11 y - 4 x , -16 x + 15 y z, -19 x z + 20 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.31 memory used=26.9MB, alloc=32.3MB, time=0.89 memory used=48.8MB, alloc=32.3MB, time=1.44 memory used=69.6MB, alloc=60.3MB, time=2.01 memory used=111.6MB, alloc=60.3MB, time=3.04 memory used=152.8MB, alloc=60.3MB, time=4.07 memory used=193.4MB, alloc=84.3MB, time=5.12 memory used=233.6MB, alloc=84.3MB, time=6.23 memory used=295.5MB, alloc=116.3MB, time=8.10 memory used=372.0MB, alloc=116.3MB, time=10.47 memory used=453.8MB, alloc=140.3MB, time=12.61 memory used=586.6MB, alloc=140.3MB, time=14.11 memory used=715.7MB, alloc=140.3MB, time=15.74 memory used=807.1MB, alloc=164.3MB, time=18.57 memory used=914.2MB, alloc=188.3MB, time=22.93 memory used=1026.4MB, alloc=212.3MB, time=29.03 memory used=1151.9MB, alloc=236.3MB, time=36.72 memory used=1301.4MB, alloc=236.3MB, time=45.85 N1 := 4037 > GB := Basis(F, plex(op(vars))); 8 6 5 GB := [28561 x - 290304, 2197 x + 24192 y, 28561 x + 28449792 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1455.4MB, alloc=236.3MB, time=54.13 memory used=1555.0MB, alloc=492.3MB, time=57.17 memory used=1735.9MB, alloc=516.3MB, time=64.67 N2 := 1795 #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 4 3 4 3 2 H := [-13 x y - 12 y, 14 y - 1, 14 x z + 2 y , 11 y - 4 x , 2 2 -16 x + 15 y z, -19 x z + 20 y] > J:=[op(GB),op(G)]; 8 6 5 3 2 J := [28561 x - 290304, 2197 x + 24192 y, 28561 x + 28449792 z, 11 y - 4 x , 2 2 -16 x + 15 y z, -19 x z + 20 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, 20, 4, 3, 4, 2, 5/6, 1, 1/2, 5/12, 7/12, 1/4, 6, 13, 27, 8, 8, 3, 2, 1, 2/3, 1/2, 1/2, 1/3, 1/4, 1, -7, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1785.3MB, alloc=516.3MB, time=67.63 |\^/| 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(); 1428261122 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 2 F := [18 x z + 2 x y z , -14 x y z - 2 y z, -18 y z + 6 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 G := [14 x y z - 15 y z, 6 y , 8 y z - 16 y ] > Problem := [F,G]; 2 2 2 2 3 2 2 Problem := [[18 x z + 2 x y z , -14 x y z - 2 y z, -18 y z + 6 x ], 2 3 3 2 [14 x y z - 15 y z, 6 y , 8 y z - 16 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.0MB, alloc=32.3MB, time=0.84 memory used=48.0MB, alloc=32.3MB, time=1.50 memory used=67.5MB, alloc=56.3MB, time=2.18 N1 := 539 > GB := Basis(F, plex(op(vars))); 4 3 2 3 2 2 2 2 2 GB := [x , 7 x + x y, x z, 3 y z - x , 9 x z + x y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=105.3MB, alloc=60.3MB, time=3.30 N2 := 539 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 2 2 H := [18 x z + 2 x y z , -14 x y z - 2 y z, -18 y z + 6 x , 2 3 3 2 14 x y z - 15 y z, 6 y , 8 y z - 16 y ] > J:=[op(GB),op(G)]; 4 3 2 3 2 2 2 2 2 2 J := [x , 7 x + x y, x z, 3 y z - x , 9 x z + x y z , 14 x y z - 15 y z, 3 3 2 6 y , 8 y z - 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 := [6, 15, 22, 4, 2, 3, 2, 2/3, 1, 5/6, 5/12, 3/4, 2/3, 8, 17, 29, 4, 4, 3, 2, 3/4, 3/4, 5/8, 1/2, 1/2, 7/16, -2, -7, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=144.0MB, alloc=60.3MB, 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(); 1428261135 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 F := [14 y + y z, 17 y z - z , -11 x z + 20 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [-3 y z - 6 z , 11, -17 x y z - 9 z ] > Problem := [F,G]; 4 2 2 2 3 Problem := [[14 y + y z, 17 y z - z , -11 x z + 20 x z], 2 2 2 2 3 [-3 y z - 6 z , 11, -17 x y z - 9 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.86 memory used=47.1MB, alloc=32.3MB, time=1.39 memory used=67.4MB, alloc=56.3MB, time=1.97 memory used=111.2MB, alloc=60.3MB, time=3.35 memory used=149.8MB, alloc=84.3MB, time=4.54 memory used=206.3MB, alloc=84.3MB, time=6.27 memory used=255.2MB, alloc=108.3MB, time=7.84 memory used=319.4MB, alloc=132.3MB, time=10.41 memory used=395.6MB, alloc=156.3MB, time=14.38 memory used=490.3MB, alloc=156.3MB, time=19.83 memory used=584.8MB, alloc=180.3MB, time=25.32 memory used=703.4MB, alloc=180.3MB, time=32.14 memory used=821.9MB, alloc=204.3MB, time=38.92 N1 := 4209 > GB := Basis(F, plex(op(vars))); 4 6 4 2 4 2 GB := [x y , y , x z, 14 y + y z, 238 y + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 271 #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)]; 4 2 2 2 3 2 2 2 H := [14 y + y z, 17 y z - z , -11 x z + 20 x z, -3 y z - 6 z , 11, 2 3 -17 x y z - 9 z ] > J:=[op(GB),op(G)]; 4 6 4 2 4 2 2 2 2 J := [x y , y , x z, 14 y + y z, 238 y + z , -3 y z - 6 z , 11, 2 3 -17 x y z - 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 := [6, 11, 19, 4, 1, 4, 3, 1/3, 2/3, 5/6, 3/11, 5/11, 9/11, 8, 14, 29, 6, 1, 6, 3, 3/8, 3/4, 5/8, 1/5, 7/15, 7/15, -3, -10, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=875.6MB, alloc=212.3MB, time=40.83 |\^/| 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(); 1428261252 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 2 F := [7 y z + 7, 14 x y + 2 x , -14 x y + 11 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 4 G := [-2 x z + 3 y, 20 y z , -3 x y + 18 z ] > Problem := [F,G]; 2 2 2 3 3 2 2 Problem := [[7 y z + 7, 14 x y + 2 x , -14 x y + 11 y z ], 3 2 2 3 4 [-2 x z + 3 y, 20 y z , -3 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=0.30 memory used=27.0MB, alloc=32.3MB, time=0.91 memory used=48.9MB, alloc=32.3MB, time=1.45 memory used=67.9MB, alloc=56.3MB, time=1.96 memory used=110.2MB, alloc=60.3MB, time=3.01 memory used=150.5MB, alloc=60.3MB, time=4.01 memory used=189.8MB, alloc=84.3MB, time=5.02 memory used=226.1MB, alloc=84.3MB, time=5.91 memory used=287.1MB, alloc=92.3MB, time=7.43 memory used=349.7MB, alloc=116.3MB, time=8.84 memory used=431.5MB, alloc=116.3MB, time=10.86 memory used=511.1MB, alloc=140.3MB, time=13.12 memory used=622.5MB, alloc=164.3MB, time=15.78 memory used=750.8MB, alloc=420.3MB, time=18.93 memory used=868.5MB, alloc=444.3MB, time=22.33 memory used=1000.6MB, alloc=468.3MB, time=26.36 memory used=1149.2MB, alloc=492.3MB, time=30.83 memory used=1290.1MB, alloc=516.3MB, time=37.53 memory used=1434.8MB, alloc=540.3MB, time=45.80 memory used=1590.3MB, alloc=564.3MB, time=55.47 memory used=1769.9MB, alloc=588.3MB, time=66.56 memory used=1973.3MB, alloc=612.3MB, time=79.06 memory used=2200.8MB, alloc=612.3MB, time=92.87 |\^/| 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(); 1428261553 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 3 2 F := [5 x y + 6 x , -13 x y - 4 y , 18 x z + 6 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [-8 x z + 16 x , -2 x y z - x , -16 x - 14 x y] > Problem := [F,G]; 3 2 3 3 3 2 Problem := [[5 x y + 6 x , -13 x y - 4 y , 18 x z + 6 x y], 2 2 2 3 2 [-8 x z + 16 x , -2 x y z - x , -16 x - 14 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=26.7MB, alloc=32.3MB, time=0.87 memory used=48.6MB, alloc=32.3MB, time=1.43 memory used=69.5MB, alloc=32.3MB, time=1.96 memory used=89.2MB, alloc=56.3MB, time=2.51 memory used=133.4MB, alloc=60.3MB, time=3.86 memory used=178.3MB, alloc=84.3MB, time=5.02 memory used=241.6MB, alloc=84.3MB, time=6.93 memory used=294.4MB, alloc=108.3MB, time=8.88 memory used=358.6MB, alloc=132.3MB, time=12.51 N1 := 2209 > GB := Basis(F, plex(op(vars))); 3 2 3 2 3 2 GB := [13 x + 4 x , 10 y - 39 x , 3 x z + x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=445.7MB, alloc=132.3MB, time=17.27 memory used=542.4MB, alloc=140.3MB, time=19.99 memory used=643.9MB, alloc=164.3MB, time=23.27 N2 := 1377 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 3 3 2 2 2 H := [5 x y + 6 x , -13 x y - 4 y , 18 x z + 6 x y, -8 x z + 16 x , 2 3 2 -2 x y z - x , -16 x - 14 x y] > J:=[op(GB),op(G)]; 3 2 3 2 3 2 2 2 J := [13 x + 4 x , 10 y - 39 x , 3 x z + x y, -8 x z + 16 x , 2 3 2 -2 x y z - x , -16 x - 14 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 := [6, 14, 21, 4, 3, 3, 3, 1, 5/6, 1/2, 11/12, 1/2, 1/4, 6, 13, 19, 4, 3, 3, 3, 1, 2/3, 1/2, 11/12, 1/3, 1/4, 1, 2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=697.2MB, alloc=164.3MB, time=26.30 |\^/| 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(); 1428261642 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [-x y - 17 x y, 6 z + 12 x, -2 x y z + 4 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 G := [12 x y + 10 x z, -19 y z - 12, -8 x y - 9 x z ] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[-x y - 17 x y, 6 z + 12 x, -2 x y z + 4 x y ], 2 3 2 2 3 [12 x y + 10 x z, -19 y z - 12, -8 x y - 9 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.86 memory used=48.2MB, alloc=32.3MB, time=1.40 memory used=68.9MB, alloc=32.3MB, time=1.93 memory used=88.8MB, alloc=56.3MB, time=2.47 memory used=128.7MB, alloc=60.3MB, time=3.53 memory used=166.2MB, alloc=84.3MB, time=4.51 memory used=219.5MB, alloc=84.3MB, time=5.94 memory used=275.4MB, alloc=116.3MB, time=7.52 memory used=352.2MB, alloc=116.3MB, time=9.65 memory used=429.2MB, alloc=116.3MB, time=11.83 memory used=506.5MB, alloc=140.3MB, time=13.98 memory used=602.8MB, alloc=140.3MB, time=16.73 memory used=682.5MB, alloc=420.3MB, time=18.93 memory used=800.2MB, alloc=444.3MB, time=22.19 memory used=935.3MB, alloc=468.3MB, time=26.09 memory used=1092.6MB, alloc=492.3MB, time=30.54 memory used=1273.3MB, alloc=516.3MB, time=36.09 memory used=1458.5MB, alloc=540.3MB, time=42.18 memory used=1653.1MB, alloc=564.3MB, time=48.63 memory used=1838.2MB, alloc=588.3MB, time=54.93 memory used=2048.9MB, alloc=612.3MB, time=61.67 memory used=2238.2MB, alloc=636.3MB, time=68.32 memory used=2434.1MB, alloc=660.3MB, time=76.94 memory used=2639.1MB, alloc=684.3MB, time=88.08 memory used=2850.6MB, alloc=708.3MB, time=100.31 |\^/| 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(); 1428261942 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [-18 x y z - 13 x y, x y + 8 z, 2 x y z - 17 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 G := [-20 x y z + 8 z , -18 y z - 18, 20 x y - y z ] > Problem := [F,G]; 2 2 3 2 2 Problem := [[-18 x y z - 13 x y, x y + 8 z, 2 x y z - 17 x z ], 3 2 2 2 3 [-20 x y z + 8 z , -18 y z - 18, 20 x y - y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=47.6MB, alloc=32.3MB, time=1.39 memory used=68.0MB, alloc=32.3MB, time=1.91 memory used=87.1MB, alloc=56.3MB, time=2.44 memory used=126.5MB, alloc=60.3MB, time=3.47 memory used=162.8MB, alloc=84.3MB, time=4.45 memory used=206.0MB, alloc=84.3MB, time=5.60 memory used=263.6MB, alloc=92.3MB, time=7.14 memory used=318.7MB, alloc=116.3MB, time=8.66 memory used=395.1MB, alloc=140.3MB, time=10.74 memory used=490.8MB, alloc=140.3MB, time=13.42 memory used=583.8MB, alloc=164.3MB, time=16.05 memory used=657.6MB, alloc=420.3MB, time=18.01 memory used=771.9MB, alloc=444.3MB, time=21.17 memory used=916.8MB, alloc=468.3MB, time=24.91 memory used=1076.2MB, alloc=492.3MB, time=29.43 memory used=1257.7MB, alloc=516.3MB, time=34.79 memory used=1467.2MB, alloc=540.3MB, time=40.60 memory used=1690.1MB, alloc=564.3MB, time=47.53 memory used=1930.4MB, alloc=588.3MB, time=55.00 memory used=2198.4MB, alloc=612.3MB, time=63.39 memory used=2475.3MB, alloc=636.3MB, time=72.24 memory used=2764.4MB, alloc=660.3MB, time=81.81 memory used=3040.2MB, alloc=684.3MB, time=90.95 memory used=3289.6MB, alloc=708.3MB, time=99.51 memory used=3501.4MB, alloc=732.3MB, time=106.90 memory used=3708.6MB, alloc=756.3MB, time=113.80 memory used=3915.4MB, alloc=780.3MB, time=121.20 |\^/| 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(); 1428262242 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 F := [20 x + 8 y, 7 y - 18 y, 6 x z + 20 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [10 x z + 13, 5 x y + 15 x z , -6 x z + 9 y] > Problem := [F,G]; 3 4 2 2 Problem := [[20 x + 8 y, 7 y - 18 y, 6 x z + 20 y z], 2 2 2 2 3 [10 x z + 13, 5 x y + 15 x z , -6 x z + 9 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.0MB, alloc=40.3MB, time=1.00 memory used=60.1MB, alloc=40.3MB, time=1.69 memory used=86.6MB, alloc=40.3MB, time=2.36 memory used=112.2MB, alloc=68.3MB, time=3.05 memory used=157.6MB, alloc=68.3MB, time=4.23 memory used=201.1MB, alloc=68.3MB, time=5.38 memory used=244.2MB, alloc=92.3MB, time=6.54 memory used=308.4MB, alloc=100.3MB, time=8.26 memory used=370.1MB, alloc=100.3MB, time=9.89 memory used=430.4MB, alloc=124.3MB, time=11.54 memory used=514.6MB, alloc=148.3MB, time=14.17 memory used=616.2MB, alloc=172.3MB, time=17.39 memory used=738.4MB, alloc=196.3MB, time=21.06 memory used=858.1MB, alloc=476.3MB, time=25.72 memory used=987.6MB, alloc=500.3MB, time=33.01 memory used=1133.1MB, alloc=524.3MB, time=41.94 memory used=1302.7MB, alloc=548.3MB, time=52.17 N1 := 4117 > GB := Basis(F, plex(op(vars))); 12 3 3 3 2 2 GB := [875 x + 144 x , 5 x + 2 y, -25 x z + 3 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1501.6MB, alloc=548.3MB, time=59.49 memory used=1738.9MB, alloc=572.3MB, time=68.47 N2 := 2129 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 4 2 2 2 2 H := [20 x + 8 y, 7 y - 18 y, 6 x z + 20 y z, 10 z x + 13, 2 2 3 5 x y + 15 x z , -6 x z + 9 y] > J:=[op(GB),op(G)]; 12 3 3 3 2 2 2 2 J := [875 x + 144 x , 5 x + 2 y, -25 x z + 3 x z , 10 z x + 13, 2 2 3 5 x y + 15 x z , -6 x 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 := [6, 14, 22, 4, 3, 4, 3, 5/6, 5/6, 2/3, 1/2, 1/2, 5/12, 6, 13, 30, 12, 12, 1, 3, 1, 1/2, 2/3, 3/4, 1/4, 5/12, 1, -8, -8] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1835.6MB, alloc=572.3MB, time=74.25 |\^/| 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(); 1428262446 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 4 F := [2 x z - 13 x z , -y - 2 y, y + 5 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-7 y z + 2 x y, 20 x y - 17 z, 7 x y z + 17 x y ] > Problem := [F,G]; 2 2 4 4 Problem := [[2 x z - 13 x z , -y - 2 y, y + 5 x], 3 2 2 2 [-7 y z + 2 x y, 20 x y - 17 z, 7 x y z + 17 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.0MB, alloc=32.3MB, time=0.85 memory used=47.5MB, alloc=32.3MB, time=1.37 memory used=66.8MB, alloc=32.3MB, time=1.87 memory used=84.9MB, alloc=56.3MB, time=2.37 memory used=123.5MB, alloc=60.3MB, time=3.37 memory used=161.3MB, alloc=60.3MB, time=4.33 memory used=198.0MB, alloc=84.3MB, time=5.35 memory used=257.5MB, alloc=116.3MB, time=7.21 memory used=333.5MB, alloc=116.3MB, time=9.44 memory used=402.5MB, alloc=140.3MB, time=11.52 memory used=490.8MB, alloc=164.3MB, time=14.16 memory used=595.1MB, alloc=188.3MB, time=17.34 memory used=709.0MB, alloc=212.3MB, time=21.90 memory used=827.0MB, alloc=236.3MB, time=27.68 memory used=956.3MB, alloc=260.3MB, time=34.80 memory used=1100.2MB, alloc=284.3MB, time=43.82 memory used=1268.1MB, alloc=308.3MB, time=54.10 memory used=1459.8MB, alloc=308.3MB, time=65.78 memory used=1651.7MB, alloc=308.3MB, time=77.54 memory used=1843.4MB, alloc=332.3MB, time=89.29 memory used=2059.2MB, alloc=332.3MB, time=102.46 |\^/| 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(); 1428262746 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 3 F := [5 x z + 17 y , 4 x y - 8 x , -10 x y z + 17 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [18 x y + 8 z, -11 x y z - 20 y z, -18 x z] > Problem := [F,G]; 2 2 3 2 2 2 3 Problem := [[5 x z + 17 y , 4 x y - 8 x , -10 x y z + 17 z ], 2 2 2 3 [18 x y + 8 z, -11 x y z - 20 y z, -18 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.84 memory used=48.1MB, alloc=32.3MB, time=1.39 memory used=68.6MB, alloc=32.3MB, time=1.92 memory used=90.6MB, alloc=56.3MB, time=2.60 memory used=134.4MB, alloc=60.3MB, time=3.92 memory used=172.2MB, alloc=84.3MB, time=5.53 N1 := 993 > GB := Basis(F, plex(op(vars))); 6 2 2 2 4 3 4 2 2 GB := [25 x + 578 x , x y - 2 x , 100 x + 289 y , -20 x + 17 x z , 2 3 -20 x z + 17 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=227.0MB, alloc=84.3MB, time=7.30 memory used=289.6MB, alloc=108.3MB, time=9.17 memory used=369.3MB, alloc=140.3MB, time=12.08 memory used=453.6MB, alloc=164.3MB, time=16.91 N2 := 1869 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 2 3 2 2 H := [5 z x + 17 y , 4 x y - 8 x , -10 x y z + 17 z , 18 x y + 8 z, 2 3 -11 x y z - 20 y z, -18 x z] > J:=[op(GB),op(G)]; 6 2 2 2 4 3 4 2 2 J := [25 x + 578 x , x y - 2 x , 100 x + 289 y , -20 x + 17 x z , 2 3 2 2 2 3 -20 x z + 17 z , 18 x y + 8 z, -11 x y z - 20 y z, -18 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 := [6, 16, 21, 4, 2, 3, 3, 1, 5/6, 5/6, 7/13, 6/13, 7/13, 8, 17, 30, 6, 6, 3, 3, 1, 1/2, 5/8, 11/17, 5/17, 7/17, -1, -9, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=462.3MB, alloc=164.3MB, time=17.33 |\^/| 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(); 1428262800 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [4 x z + 12 y z, 5 y z + 9 x y, -8 x z - 13 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 3 2 G := [12 y - 11 y z, -16 x y + 5 y z , -9 x y - 16 y z] > Problem := [F,G]; 3 3 2 Problem := [[4 x z + 12 y z, 5 y z + 9 x y, -8 x z - 13 y z], 3 2 2 2 2 2 3 2 [12 y - 11 y z, -16 x y + 5 y z , -9 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=4.2MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.86 memory used=47.4MB, alloc=32.3MB, time=1.40 memory used=67.0MB, alloc=56.3MB, time=1.93 memory used=106.9MB, alloc=60.3MB, time=2.97 memory used=144.3MB, alloc=84.3MB, time=3.93 memory used=204.3MB, alloc=92.3MB, time=5.46 memory used=262.4MB, alloc=116.3MB, time=6.94 memory used=341.4MB, alloc=140.3MB, time=8.90 memory used=414.4MB, alloc=396.3MB, time=10.81 memory used=511.6MB, alloc=420.3MB, time=13.45 memory used=633.4MB, alloc=444.3MB, time=16.60 memory used=775.9MB, alloc=468.3MB, time=20.30 memory used=902.2MB, alloc=492.3MB, time=23.53 memory used=1036.1MB, alloc=492.3MB, time=26.96 memory used=1159.0MB, alloc=516.3MB, time=30.21 memory used=1260.2MB, alloc=516.3MB, time=32.88 memory used=1363.2MB, alloc=516.3MB, time=35.69 memory used=1470.8MB, alloc=516.3MB, time=38.83 memory used=1547.7MB, alloc=516.3MB, time=41.08 memory used=1631.2MB, alloc=540.3MB, time=43.76 memory used=1707.8MB, alloc=540.3MB, time=46.20 memory used=1780.2MB, alloc=540.3MB, time=48.45 memory used=1839.7MB, alloc=540.3MB, time=50.56 memory used=1905.9MB, alloc=540.3MB, time=52.87 memory used=1945.8MB, alloc=540.3MB, time=54.40 memory used=2149.0MB, alloc=564.3MB, time=60.60 memory used=2355.8MB, alloc=588.3MB, time=66.44 memory used=2597.0MB, alloc=612.3MB, time=74.07 memory used=2788.5MB, alloc=636.3MB, time=79.99 memory used=2974.1MB, alloc=660.3MB, time=85.88 memory used=3131.7MB, alloc=684.3MB, time=91.14 memory used=3263.7MB, alloc=708.3MB, time=95.49 memory used=3404.1MB, alloc=732.3MB, time=100.25 memory used=3544.4MB, alloc=756.3MB, time=105.71 memory used=3698.9MB, alloc=780.3MB, time=111.96 |\^/| 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(); 1428263100 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 2 F := [17 y z - 10 y z, -13 x z + 16 x y z, -16 x y + 4 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 G := [8 x z + 3 x , -13 x y z - 15 y z , 8 x y z + 5 x] > Problem := [F,G]; 3 2 3 2 3 2 Problem := [[17 y z - 10 y z, -13 x z + 16 x y z, -16 x y + 4 x y z], 3 3 2 2 2 [8 x z + 3 x , -13 x y z - 15 y z , 8 x y z + 5 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.8MB, alloc=40.3MB, time=0.98 memory used=59.6MB, alloc=40.3MB, time=1.69 memory used=86.2MB, alloc=40.3MB, time=2.37 memory used=110.3MB, alloc=64.3MB, time=3.02 memory used=154.8MB, alloc=68.3MB, time=4.19 memory used=197.4MB, alloc=68.3MB, time=5.33 memory used=238.5MB, alloc=92.3MB, time=6.44 memory used=299.3MB, alloc=92.3MB, time=8.07 memory used=358.3MB, alloc=124.3MB, time=9.71 memory used=436.2MB, alloc=148.3MB, time=11.83 memory used=537.4MB, alloc=172.3MB, time=14.91 memory used=646.5MB, alloc=196.3MB, time=18.33 memory used=753.5MB, alloc=476.3MB, time=21.76 memory used=892.2MB, alloc=500.3MB, time=26.16 memory used=1040.6MB, alloc=524.3MB, time=30.88 memory used=1197.9MB, alloc=548.3MB, time=35.97 memory used=1363.4MB, alloc=572.3MB, time=41.45 memory used=1534.1MB, alloc=596.3MB, time=47.11 memory used=1712.5MB, alloc=620.3MB, time=53.11 memory used=1889.4MB, alloc=644.3MB, time=60.89 memory used=2058.5MB, alloc=668.3MB, time=70.04 memory used=2237.0MB, alloc=692.3MB, time=80.33 memory used=2428.2MB, alloc=716.3MB, time=91.62 memory used=2633.2MB, alloc=740.3MB, time=104.05 |\^/| 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(); 1428263400 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 F := [-15 x z + 12 x , -15 x y z - 14 x y , -10 x z - 5 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [-19 y z + 9 x, x z - 18 x , -2 + 14 y] > Problem := [F,G]; 3 3 2 2 2 2 Problem := [[-15 x z + 12 x , -15 x y z - 14 x y , -10 x z - 5 y ], 3 3 2 [-19 y z + 9 x, x z - 18 x , -2 + 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=0.30 memory used=26.5MB, alloc=32.3MB, time=0.86 memory used=48.0MB, alloc=32.3MB, time=1.41 memory used=67.8MB, alloc=56.3MB, time=1.96 memory used=109.1MB, alloc=60.3MB, time=3.00 memory used=147.0MB, alloc=84.3MB, time=4.01 memory used=211.6MB, alloc=92.3MB, time=5.62 memory used=273.3MB, alloc=116.3MB, time=7.17 memory used=356.1MB, alloc=116.3MB, time=9.26 memory used=436.6MB, alloc=116.3MB, time=11.41 memory used=513.8MB, alloc=140.3MB, time=13.25 memory used=587.2MB, alloc=396.3MB, time=15.26 memory used=699.0MB, alloc=420.3MB, time=17.67 memory used=825.9MB, alloc=444.3MB, time=20.80 memory used=974.8MB, alloc=468.3MB, time=24.47 memory used=1087.8MB, alloc=468.3MB, time=27.11 memory used=1214.9MB, alloc=492.3MB, time=30.49 memory used=1317.4MB, alloc=492.3MB, time=32.88 memory used=1426.8MB, alloc=516.3MB, time=35.55 memory used=1511.8MB, alloc=516.3MB, time=37.87 memory used=1602.7MB, alloc=516.3MB, time=40.14 memory used=1687.2MB, alloc=516.3MB, time=42.38 memory used=1778.8MB, alloc=516.3MB, time=44.92 memory used=1851.3MB, alloc=516.3MB, time=47.08 memory used=1933.7MB, alloc=516.3MB, time=49.58 memory used=2007.9MB, alloc=540.3MB, time=51.93 memory used=2103.2MB, alloc=540.3MB, time=54.93 memory used=2214.3MB, alloc=564.3MB, time=58.50 memory used=2328.4MB, alloc=564.3MB, time=62.70 memory used=2425.9MB, alloc=588.3MB, time=66.38 memory used=2517.8MB, alloc=588.3MB, time=69.97 memory used=2625.7MB, alloc=612.3MB, time=74.01 memory used=2718.8MB, alloc=612.3MB, time=77.67 memory used=2819.4MB, alloc=636.3MB, time=81.71 memory used=3088.0MB, alloc=660.3MB, time=90.00 memory used=3377.8MB, alloc=684.3MB, time=98.34 memory used=3664.3MB, alloc=708.3MB, time=107.76 |\^/| 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(); 1428263700 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [-6 x z - 2 y , 9 y z + 18 y, -20 y z + 13 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 2 G := [-y z - 17 y , 15 x y z + 3 y z , -x z + 9 x y ] > Problem := [F,G]; 2 2 2 3 2 Problem := [[-6 x z - 2 y , 9 y z + 18 y, -20 y z + 13 z], 2 2 2 3 3 2 2 [-y z - 17 y , 15 x y z + 3 y z , -x z + 9 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.90 memory used=48.1MB, alloc=32.3MB, time=1.43 memory used=68.7MB, alloc=32.3MB, time=1.97 memory used=88.3MB, alloc=56.3MB, time=2.51 memory used=127.7MB, alloc=60.3MB, time=3.56 memory used=164.5MB, alloc=84.3MB, time=4.58 memory used=211.0MB, alloc=84.3MB, time=5.83 memory used=267.4MB, alloc=92.3MB, time=7.40 memory used=322.9MB, alloc=116.3MB, time=8.95 memory used=403.1MB, alloc=116.3MB, time=11.10 memory used=480.7MB, alloc=140.3MB, time=13.28 memory used=567.6MB, alloc=140.3MB, time=15.62 memory used=657.6MB, alloc=420.3MB, time=18.22 memory used=775.0MB, alloc=444.3MB, time=21.51 memory used=907.2MB, alloc=468.3MB, time=25.88 memory used=1052.0MB, alloc=492.3MB, time=30.64 memory used=1210.8MB, alloc=516.3MB, time=35.90 memory used=1376.4MB, alloc=540.3MB, time=42.74 memory used=1535.6MB, alloc=564.3MB, time=51.03 memory used=1700.9MB, alloc=588.3MB, time=60.93 memory used=1885.7MB, alloc=612.3MB, time=72.34 memory used=2094.5MB, alloc=636.3MB, time=85.15 memory used=2327.3MB, alloc=660.3MB, time=99.39 memory used=2584.0MB, alloc=660.3MB, time=115.11 |\^/| 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(); 1428264000 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-20 x y z - 10 y z, 12 x y z + 17 x y z, -11 x y - 18 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 3 G := [-3 x y z + 17, 15 x + x z , -19 x z - 1] > Problem := [F,G]; 2 2 3 2 Problem := [[-20 x y z - 10 y z, 12 x y z + 17 x y z, -11 x y - 18 x z], 2 4 2 3 [-3 x y z + 17, 15 x + x z , -19 x 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=26.5MB, alloc=32.3MB, time=0.87 memory used=48.2MB, alloc=32.3MB, time=1.43 memory used=68.1MB, alloc=56.3MB, time=1.95 memory used=111.0MB, alloc=60.3MB, time=3.01 memory used=153.4MB, alloc=60.3MB, time=4.03 memory used=198.4MB, alloc=84.3MB, time=5.16 memory used=270.5MB, alloc=84.3MB, time=6.72 memory used=329.6MB, alloc=108.3MB, time=8.53 memory used=413.0MB, alloc=140.3MB, time=10.87 memory used=496.6MB, alloc=164.3MB, time=15.51 N1 := 2105 > GB := Basis(F, plex(op(vars))); 4 3 2 GB := [x y , 11 x y + 18 x z, z y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=609.2MB, alloc=164.3MB, time=19.91 memory used=742.6MB, alloc=420.3MB, time=23.14 memory used=873.4MB, alloc=444.3MB, time=26.64 N2 := 1735 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 H := [-20 x y z - 10 y z, 12 x y z + 17 x y z, -11 x y - 18 x z, 2 4 2 3 -3 x y z + 17, 15 x + x z , -19 x z - 1] > J:=[op(GB),op(G)]; 4 3 2 2 4 2 3 J := [x y , 11 x y + 18 x z, z y, -3 x y z + 17, 15 x + x z , -19 x 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 := [6, 16, 24, 4, 4, 3, 3, 1, 2/3, 1, 3/4, 1/2, 2/3, 6, 14, 23, 5, 4, 4, 3, 5/6, 2/3, 5/6, 7/12, 1/3, 5/12, 2, 1, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=985.5MB, alloc=444.3MB, time=32.55 |\^/| 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(); 1428264087 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [18 x + 9 y, -18 x y z + 12 x y , x z + 14 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 2 2 G := [13 x z - 11 x z, 18 x z - 11 y, 10 x - x y ] > Problem := [F,G]; 3 2 2 2 Problem := [[18 x + 9 y, -18 x y z + 12 x y , x z + 14 x z], 3 3 4 2 2 [13 x z - 11 x z, 18 x z - 11 y, 10 x - x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.85 memory used=47.9MB, alloc=32.3MB, time=1.40 memory used=69.7MB, alloc=56.3MB, time=2.06 memory used=113.5MB, alloc=60.3MB, time=3.38 memory used=152.8MB, alloc=84.3MB, time=4.58 memory used=212.4MB, alloc=84.3MB, time=6.38 memory used=264.9MB, alloc=108.3MB, time=8.25 memory used=330.6MB, alloc=132.3MB, time=11.54 memory used=413.3MB, alloc=132.3MB, time=16.36 memory used=496.0MB, alloc=156.3MB, time=21.20 N1 := 2973 > GB := Basis(F, plex(op(vars))); 9 7 3 7 5 2 GB := [2 x - 21 x , 2 x + y, 4 x + 3 x z, x z + 14 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=603.0MB, alloc=164.3MB, time=25.50 memory used=720.2MB, alloc=188.3MB, time=29.12 memory used=853.1MB, alloc=212.3MB, time=35.59 memory used=991.2MB, alloc=236.3MB, time=43.85 N2 := 2681 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 H := [18 x + 9 y, -18 x y z + 12 x y , x z + 14 x z, 13 x z - 11 x z, 3 4 2 2 18 z x - 11 y, 10 x - x y ] > J:=[op(GB),op(G)]; 9 7 3 7 5 2 3 J := [2 x - 21 x , 2 x + y, 4 x + 3 x z, x z + 14 x z, 13 x z - 11 x z, 3 4 2 2 18 z x - 11 y, 10 x - 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 := [6, 14, 22, 4, 4, 2, 3, 1, 2/3, 2/3, 5/6, 5/12, 1/2, 7, 14, 34, 9, 9, 2, 3, 1, 3/7, 4/7, 6/7, 3/14, 3/7, 0, -12, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=998.5MB, alloc=236.3MB, time=44.22 |\^/| 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(); 1428264204 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 2 4 F := [16 x y - 2 x y z , -17 y - 6 x y z, 15 x z - 16 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 2 2 G := [-8 x z + 7 y, -11 x + 4 x y z , 12 y z - 7 z ] > Problem := [F,G]; 2 2 2 4 2 2 4 Problem := [[16 x y - 2 x y z , -17 y - 6 x y z, 15 x z - 16 y ], 2 4 2 2 2 2 [-8 x z + 7 y, -11 x + 4 x y z , 12 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=0.30 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=47.8MB, alloc=32.3MB, time=1.40 memory used=68.4MB, alloc=56.3MB, time=1.93 memory used=108.9MB, alloc=60.3MB, time=2.97 memory used=146.7MB, alloc=60.3MB, time=3.92 memory used=184.1MB, alloc=84.3MB, time=4.89 memory used=235.4MB, alloc=84.3MB, time=6.22 memory used=298.7MB, alloc=116.3MB, time=7.74 memory used=360.0MB, alloc=372.3MB, time=9.29 memory used=441.2MB, alloc=396.3MB, time=11.40 memory used=548.2MB, alloc=396.3MB, time=14.15 memory used=652.9MB, alloc=420.3MB, time=16.74 memory used=781.5MB, alloc=444.3MB, time=19.97 memory used=911.4MB, alloc=468.3MB, time=23.31 memory used=1034.8MB, alloc=468.3MB, time=26.56 memory used=1141.0MB, alloc=492.3MB, time=29.37 memory used=1241.5MB, alloc=492.3MB, time=31.65 memory used=1347.8MB, alloc=492.3MB, time=34.56 memory used=1422.0MB, alloc=516.3MB, time=36.67 memory used=1510.5MB, alloc=516.3MB, time=39.17 memory used=1581.1MB, alloc=516.3MB, time=41.18 memory used=1648.2MB, alloc=516.3MB, time=43.09 memory used=1713.5MB, alloc=516.3MB, time=45.03 memory used=1779.7MB, alloc=516.3MB, time=47.13 memory used=1837.3MB, alloc=516.3MB, time=49.09 memory used=1905.3MB, alloc=540.3MB, time=51.61 memory used=1990.7MB, alloc=540.3MB, time=54.78 memory used=2061.8MB, alloc=564.3MB, time=57.64 memory used=2280.2MB, alloc=588.3MB, time=64.43 memory used=2495.9MB, alloc=612.3MB, time=71.93 memory used=2718.9MB, alloc=636.3MB, time=79.86 memory used=2949.0MB, alloc=660.3MB, time=88.06 memory used=3184.5MB, alloc=684.3MB, time=96.55 memory used=3427.0MB, alloc=708.3MB, time=105.27 |\^/| 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(); 1428264504 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 F := [-16 x y z - 19, -16 x y z + 11 x z , -8 x z + 7 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 3 G := [17 x y z - 17 y , -15 y z - 9 y , 20 x z - 10 y ] > Problem := [F,G]; 2 2 2 3 2 2 Problem := [[-16 x y z - 19, -16 x y z + 11 x z , -8 x z + 7 x z ], 2 3 2 2 3 3 [17 x y z - 17 y , -15 y z - 9 y , 20 x z - 10 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.87 memory used=47.8MB, alloc=32.3MB, time=1.41 memory used=67.7MB, alloc=56.3MB, time=1.95 memory used=106.9MB, alloc=60.3MB, time=2.96 memory used=143.2MB, alloc=84.3MB, time=3.91 memory used=203.4MB, alloc=92.3MB, time=5.50 memory used=262.3MB, alloc=116.3MB, time=7.04 memory used=342.4MB, alloc=116.3MB, time=9.14 memory used=418.6MB, alloc=140.3MB, time=11.19 memory used=507.4MB, alloc=140.3MB, time=13.53 memory used=584.7MB, alloc=420.3MB, time=15.66 memory used=699.1MB, alloc=444.3MB, time=18.84 memory used=837.9MB, alloc=468.3MB, time=22.68 memory used=999.3MB, alloc=492.3MB, time=27.38 memory used=1143.7MB, alloc=516.3MB, time=31.57 memory used=1267.6MB, alloc=516.3MB, time=35.14 memory used=1402.4MB, alloc=516.3MB, time=39.32 memory used=1535.0MB, alloc=540.3MB, time=43.46 memory used=1637.9MB, alloc=540.3MB, time=46.70 memory used=1727.5MB, alloc=540.3MB, time=49.52 memory used=1826.8MB, alloc=540.3MB, time=53.03 memory used=1911.5MB, alloc=540.3MB, time=55.91 memory used=1981.0MB, alloc=540.3MB, time=58.37 memory used=2046.1MB, alloc=540.3MB, time=60.63 memory used=2093.9MB, alloc=540.3MB, time=62.48 memory used=2155.8MB, alloc=540.3MB, time=64.96 memory used=2363.0MB, alloc=564.3MB, time=71.46 memory used=2586.2MB, alloc=588.3MB, time=78.95 memory used=2813.3MB, alloc=612.3MB, time=86.68 memory used=3047.9MB, alloc=636.3MB, time=94.45 memory used=3233.2MB, alloc=660.3MB, time=100.94 memory used=3417.5MB, alloc=684.3MB, time=107.08 memory used=3583.9MB, alloc=708.3MB, time=112.64 |\^/| 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(); 1428264804 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 3 2 2 F := [-11 y z - 14 z , -14 x y - 14 y , -11 x y - 20 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [17 x y - 15 x z, -9 x y + 14, 9 y z + 8 z ] > Problem := [F,G]; 2 2 3 4 3 2 2 Problem := [[-11 y z - 14 z , -14 x y - 14 y , -11 x y - 20 x y ], 3 2 2 [17 x y - 15 x z, -9 x y + 14, 9 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=0.30 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=45.7MB, alloc=32.3MB, time=1.29 memory used=65.0MB, alloc=32.3MB, time=1.76 memory used=85.4MB, alloc=56.3MB, time=2.39 memory used=125.6MB, alloc=84.3MB, time=3.78 N1 := 855 > GB := Basis(F, plex(op(vars))); 5 3 2 2 3 4 2 GB := [x y, 11 x y + 20 x y , x y + y , z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=181.1MB, alloc=84.3MB, time=5.60 N2 := 417 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 4 3 2 2 H := [-11 y z - 14 z , -14 x y - 14 y , -11 x y - 20 x y , 17 x y - 15 x z, 3 2 2 -9 x y + 14, 9 y z + 8 z ] > J:=[op(GB),op(G)]; 5 3 2 2 3 4 2 3 J := [x y, 11 x y + 20 x y , x y + y , z , 17 x y - 15 x z, -9 x y + 14, 2 2 9 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, 20, 4, 3, 4, 2, 2/3, 1, 1/2, 1/2, 2/3, 5/12, 7, 14, 25, 6, 5, 4, 2, 5/7, 6/7, 3/7, 1/2, 4/7, 2/7, -1, -5, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=212.1MB, alloc=84.3MB, time=6.58 |\^/| 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(); 1428264822 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 2 F := [-11 x z - 12 y , -7 y z, 9 x z + 19 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 3 2 G := [15 x y - 12 y z, -5 x + 20 z , -3 y - 9 y z ] > Problem := [F,G]; 2 2 3 3 3 2 Problem := [[-11 x z - 12 y , -7 y z, 9 x z + 19 x z], 2 2 3 3 3 3 2 [15 x y - 12 y z, -5 x + 20 z , -3 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=0.30 memory used=26.8MB, alloc=32.3MB, time=0.89 memory used=47.7MB, alloc=32.3MB, time=1.44 memory used=68.3MB, alloc=56.3MB, time=1.94 memory used=110.6MB, alloc=60.3MB, time=2.99 memory used=150.8MB, alloc=84.3MB, time=4.07 memory used=216.3MB, alloc=92.3MB, time=5.63 memory used=279.0MB, alloc=116.3MB, time=7.12 memory used=348.8MB, alloc=116.3MB, time=8.86 memory used=419.9MB, alloc=396.3MB, time=10.74 memory used=527.9MB, alloc=420.3MB, time=13.17 memory used=654.6MB, alloc=444.3MB, time=16.33 memory used=803.4MB, alloc=468.3MB, time=20.52 memory used=952.5MB, alloc=492.3MB, time=25.34 memory used=1107.7MB, alloc=516.3MB, time=31.39 memory used=1246.9MB, alloc=540.3MB, time=39.73 memory used=1407.8MB, alloc=564.3MB, time=49.53 N1 := 3809 > GB := Basis(F, plex(op(vars))); 3 6 3 3 2 2 3 3 2 GB := [y x, y , x z, z y , 11 z x + 12 y , 9 x z + 19 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1618.7MB, alloc=564.3MB, time=58.96 memory used=1747.7MB, alloc=564.3MB, time=62.70 memory used=1867.2MB, alloc=564.3MB, time=66.09 memory used=1950.6MB, alloc=564.3MB, time=68.44 memory used=2053.2MB, alloc=564.3MB, time=71.56 memory used=2142.4MB, alloc=588.3MB, time=74.43 memory used=2218.6MB, alloc=588.3MB, time=77.00 memory used=2391.2MB, alloc=612.3MB, time=83.14 memory used=2557.1MB, alloc=636.3MB, time=90.04 memory used=2789.9MB, alloc=660.3MB, time=104.92 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428265122 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 F := [7 y z + 4 z, 2 x z + 20 y , -11 z - 9] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [5 z - 11 y , 18 y z + 9 y z, -9 x y + 5 y z] > Problem := [F,G]; 2 2 3 4 Problem := [[7 y z + 4 z, 2 x z + 20 y , -11 z - 9], 3 2 3 2 [5 z - 11 y , 18 y z + 9 y z, -9 x y + 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=48.0MB, alloc=32.3MB, time=1.41 memory used=68.9MB, alloc=32.3MB, time=1.95 memory used=88.6MB, alloc=56.3MB, time=2.49 memory used=128.6MB, alloc=60.3MB, time=3.53 memory used=167.0MB, alloc=60.3MB, time=4.53 memory used=203.3MB, alloc=84.3MB, time=5.50 memory used=259.6MB, alloc=92.3MB, time=7.03 memory used=315.1MB, alloc=116.3MB, time=8.50 memory used=395.8MB, alloc=116.3MB, time=10.57 memory used=470.4MB, alloc=396.3MB, time=12.50 memory used=572.7MB, alloc=420.3MB, time=15.14 memory used=698.0MB, alloc=444.3MB, time=18.42 memory used=838.6MB, alloc=468.3MB, time=22.26 memory used=994.1MB, alloc=492.3MB, time=26.44 memory used=1161.9MB, alloc=516.3MB, time=31.57 memory used=1335.6MB, alloc=540.3MB, time=39.58 N1 := 2203 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [3087 x - 70400, 7 y + 4, -441 x y + 1760 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1517.6MB, alloc=540.3MB, time=47.20 memory used=1743.7MB, alloc=540.3MB, time=55.56 N2 := 1259 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 4 3 2 3 H := [7 y z + 4 z, 2 x z + 20 y , -11 z - 9, 5 z - 11 y , 18 y z + 9 y z, 2 -9 x y + 5 y z] > J:=[op(GB),op(G)]; 2 2 2 3 2 J := [3087 x - 70400, 7 y + 4, -441 x y + 1760 z , 5 z - 11 y , 3 2 18 y z + 9 y z, -9 x y + 5 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 20, 4, 1, 3, 4, 1/3, 5/6, 1, 1/6, 7/12, 2/3, 6, 12, 16, 4, 2, 2, 3, 1/2, 5/6, 2/3, 1/4, 7/12, 5/12, 1, 4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1751.5MB, alloc=540.3MB, time=55.97 |\^/| 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(); 1428265265 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [-14 x y + 12 y z , 8 x + 20, 14 x - 2 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 G := [-15 x - z , 3 x z - y z, x z - 6 y ] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[-14 x y + 12 y z , 8 x + 20, 14 x - 2 z ], 4 3 2 2 [-15 x - z , 3 x z - y z, x z - 6 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.86 memory used=48.7MB, alloc=32.3MB, time=1.44 memory used=70.1MB, alloc=32.3MB, time=2.01 memory used=90.0MB, alloc=32.3MB, time=2.52 memory used=111.7MB, alloc=56.3MB, time=3.16 memory used=156.0MB, alloc=60.3MB, time=4.53 memory used=196.4MB, alloc=84.3MB, time=5.75 memory used=257.8MB, alloc=84.3MB, time=7.60 memory used=310.4MB, alloc=108.3MB, time=9.24 memory used=376.0MB, alloc=132.3MB, time=11.79 memory used=452.4MB, alloc=156.3MB, time=15.96 memory used=549.3MB, alloc=156.3MB, time=21.53 memory used=646.2MB, alloc=156.3MB, time=27.11 memory used=743.0MB, alloc=180.3MB, time=32.72 N1 := 3959 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [2 x + 5, y , 2 z + 35] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=866.3MB, alloc=188.3MB, time=38.27 N2 := 199 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 4 3 2 H := [-14 x y + 12 y z , 8 x + 20, 14 x - 2 z , -15 x - z , 3 x z - y z, 2 z x - 6 y ] > J:=[op(GB),op(G)]; 2 2 2 4 3 2 2 J := [2 x + 5, y , 2 z + 35, -15 x - z , 3 x z - y z, z x - 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 := [6, 14, 17, 4, 4, 2, 3, 1, 1/2, 5/6, 1/2, 1/3, 1/2, 6, 11, 15, 4, 4, 2, 3, 2/3, 1/2, 2/3, 1/3, 1/4, 5/12, 3, 2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=875.1MB, alloc=188.3MB, time=38.61 |\^/| 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(); 1428265363 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 2 2 F := [-9 x y - 13 x y , 6 y z - 7 z , 5 x y z + 20 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 4 2 3 G := [3 z - 7 x y, -7 x - z , -3 x z - 15 y ] > Problem := [F,G]; 3 2 2 3 2 2 2 Problem := [[-9 x y - 13 x y , 6 y z - 7 z , 5 x y z + 20 x y ], 4 4 4 2 3 [3 z - 7 x y, -7 x - z , -3 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=0.31 memory used=26.8MB, alloc=32.3MB, time=0.90 memory used=47.6MB, alloc=32.3MB, time=1.43 memory used=68.2MB, alloc=60.3MB, time=2.01 memory used=110.4MB, alloc=68.3MB, time=3.11 memory used=151.3MB, alloc=92.3MB, time=4.18 memory used=213.1MB, alloc=92.3MB, time=5.78 memory used=272.5MB, alloc=116.3MB, time=7.28 memory used=356.8MB, alloc=116.3MB, time=9.31 memory used=436.4MB, alloc=116.3MB, time=11.31 memory used=503.5MB, alloc=140.3MB, time=12.91 memory used=575.4MB, alloc=396.3MB, time=14.70 memory used=678.4MB, alloc=420.3MB, time=17.26 memory used=800.8MB, alloc=444.3MB, time=20.46 memory used=922.2MB, alloc=468.3MB, time=23.07 memory used=1050.7MB, alloc=468.3MB, time=26.37 memory used=1166.1MB, alloc=492.3MB, time=29.48 memory used=1253.6MB, alloc=492.3MB, time=31.67 memory used=1334.5MB, alloc=492.3MB, time=33.86 memory used=1393.6MB, alloc=492.3MB, time=35.59 memory used=1471.1MB, alloc=492.3MB, time=37.76 memory used=1530.2MB, alloc=516.3MB, time=39.30 memory used=1586.8MB, alloc=516.3MB, time=40.82 memory used=1659.1MB, alloc=516.3MB, time=43.15 memory used=1715.6MB, alloc=516.3MB, time=44.93 memory used=1771.2MB, alloc=516.3MB, time=47.04 memory used=1971.3MB, alloc=540.3MB, time=51.64 memory used=2185.4MB, alloc=564.3MB, time=56.97 memory used=2367.4MB, alloc=588.3MB, time=61.40 memory used=2548.4MB, alloc=612.3MB, time=65.48 memory used=2706.1MB, alloc=636.3MB, time=69.31 memory used=2864.2MB, alloc=660.3MB, time=73.51 memory used=2992.0MB, alloc=684.3MB, time=77.06 memory used=3110.1MB, alloc=684.3MB, time=80.69 memory used=3226.9MB, alloc=708.3MB, time=84.22 memory used=3355.1MB, alloc=708.3MB, time=88.65 memory used=3521.7MB, alloc=732.3MB, time=95.49 memory used=3834.5MB, alloc=756.3MB, time=106.81 memory used=4113.2MB, alloc=780.3MB, time=122.97 |\^/| 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(); 1428265664 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 3 F := [-17 x z + 3 y z , 3 x z - 3 y z , 16 z - 14 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 G := [-3 x y - 3, -13 x y + 14 x z , -7 z + 4 x y] > Problem := [F,G]; 3 3 3 2 3 Problem := [[-17 x z + 3 y z , 3 x z - 3 y z , 16 z - 14 z], 2 3 2 3 [-3 x y - 3, -13 x y + 14 x z , -7 z + 4 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.86 memory used=48.0MB, alloc=32.3MB, time=1.41 memory used=69.2MB, alloc=32.3MB, time=1.95 memory used=88.6MB, alloc=56.3MB, time=2.48 memory used=128.3MB, alloc=60.3MB, time=3.51 memory used=165.3MB, alloc=60.3MB, time=4.48 memory used=203.3MB, alloc=84.3MB, time=5.42 memory used=263.5MB, alloc=116.3MB, time=6.95 memory used=345.8MB, alloc=372.3MB, time=9.08 memory used=425.9MB, alloc=372.3MB, time=11.19 memory used=505.7MB, alloc=396.3MB, time=13.37 memory used=606.3MB, alloc=396.3MB, time=16.13 memory used=707.9MB, alloc=420.3MB, time=18.85 memory used=829.4MB, alloc=444.3MB, time=22.23 memory used=971.6MB, alloc=468.3MB, time=26.16 memory used=1133.7MB, alloc=492.3MB, time=30.65 memory used=1278.0MB, alloc=492.3MB, time=34.59 memory used=1404.0MB, alloc=516.3MB, time=38.12 memory used=1534.2MB, alloc=516.3MB, time=41.88 memory used=1645.1MB, alloc=540.3MB, time=45.18 memory used=1741.5MB, alloc=540.3MB, time=47.96 memory used=1828.4MB, alloc=540.3MB, time=50.43 memory used=1929.4MB, alloc=564.3MB, time=53.71 memory used=2038.3MB, alloc=564.3MB, time=57.62 memory used=2166.8MB, alloc=588.3MB, time=62.18 memory used=2303.3MB, alloc=612.3MB, time=67.05 memory used=2418.1MB, alloc=636.3MB, time=71.34 memory used=2521.7MB, alloc=660.3MB, time=75.29 memory used=2640.2MB, alloc=684.3MB, time=79.72 memory used=2755.5MB, alloc=708.3MB, time=84.05 memory used=2871.5MB, alloc=732.3MB, time=88.24 memory used=2974.9MB, alloc=732.3MB, time=92.23 |\^/| 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(); 1428265964 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 2 3 F := [9 x y + 19 x z , 18 x y + 6 z , -16 y z + 4 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [-9 y z + 11 y z , -16 x y z - 5 x y, 2 y z - 19 x] > Problem := [F,G]; 2 2 2 3 3 2 2 3 Problem := [[9 x y + 19 x z , 18 x y + 6 z , -16 y z + 4 z ], 2 2 3 2 2 [-9 y z + 11 y z , -16 x y z - 5 x y, 2 y z - 19 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, 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=67.9MB, alloc=56.3MB, time=1.94 memory used=107.7MB, alloc=60.3MB, time=2.98 memory used=144.9MB, alloc=84.3MB, time=3.95 memory used=204.1MB, alloc=92.3MB, time=5.49 memory used=259.7MB, alloc=116.3MB, time=6.96 memory used=340.4MB, alloc=116.3MB, time=8.96 memory used=412.0MB, alloc=140.3MB, time=10.87 memory used=504.4MB, alloc=140.3MB, time=13.33 memory used=595.8MB, alloc=164.3MB, time=15.81 memory used=679.7MB, alloc=164.3MB, time=18.07 memory used=752.1MB, alloc=420.3MB, time=20.05 memory used=866.2MB, alloc=444.3MB, time=23.16 memory used=1004.1MB, alloc=444.3MB, time=26.84 memory used=1135.4MB, alloc=468.3MB, time=30.53 memory used=1287.0MB, alloc=492.3MB, time=34.84 memory used=1456.0MB, alloc=516.3MB, time=39.67 memory used=1649.4MB, alloc=540.3MB, time=45.27 memory used=1862.8MB, alloc=564.3MB, time=51.73 memory used=2125.6MB, alloc=588.3MB, time=57.36 memory used=2401.7MB, alloc=612.3MB, time=64.05 memory used=2682.4MB, alloc=636.3MB, time=71.70 memory used=2946.3MB, alloc=660.3MB, time=80.59 memory used=3212.2MB, alloc=684.3MB, time=89.66 memory used=3480.1MB, alloc=708.3MB, time=98.73 memory used=3763.8MB, alloc=732.3MB, time=107.92 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428266264 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [11 x y + 4 y z , 17 y z + 8 x, 4 x y + 12 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 3 3 G := [3 x - 6 y z , 20 x z - 8 z, 3 y z + 14 x ] > Problem := [F,G]; 2 2 2 2 Problem := [[11 x y + 4 y z , 17 y z + 8 x, 4 x y + 12 x y z], 4 2 3 3 3 [3 x - 6 y z , 20 x z - 8 z, 3 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=0.31 memory used=26.6MB, alloc=32.3MB, time=0.87 memory used=47.8MB, alloc=32.3MB, time=1.41 memory used=68.1MB, alloc=32.3MB, time=1.92 memory used=86.8MB, alloc=56.3MB, time=2.44 memory used=125.7MB, alloc=60.3MB, time=3.47 memory used=162.7MB, alloc=60.3MB, time=4.44 memory used=200.0MB, alloc=84.3MB, time=5.42 memory used=258.5MB, alloc=92.3MB, time=7.01 memory used=315.0MB, alloc=92.3MB, time=8.48 memory used=372.4MB, alloc=116.3MB, time=10.00 memory used=449.8MB, alloc=116.3MB, time=12.06 memory used=526.4MB, alloc=140.3MB, time=14.10 memory used=611.0MB, alloc=396.3MB, time=16.40 memory used=705.5MB, alloc=420.3MB, time=18.95 memory used=820.3MB, alloc=444.3MB, time=22.32 memory used=953.5MB, alloc=468.3MB, time=26.54 memory used=1100.2MB, alloc=492.3MB, time=31.31 memory used=1257.7MB, alloc=516.3MB, time=37.01 memory used=1409.0MB, alloc=540.3MB, time=44.75 memory used=1563.6MB, alloc=564.3MB, time=54.29 memory used=1742.1MB, alloc=588.3MB, time=65.42 memory used=1944.7MB, alloc=612.3MB, time=78.02 memory used=2171.3MB, alloc=636.3MB, time=92.17 N1 := 5701 > GB := Basis(F, plex(op(vars))); GB := [ 5 4 4 2 3461931 x + 4096 x, 18513 x + 128 x y, -6171 x + 128 x z, 17 z y + 8 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2430.1MB, alloc=636.3MB, time=102.45 memory used=2647.0MB, alloc=636.3MB, time=108.95 |\^/| 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(); 1428266564 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 2 F := [19 x y - 4 x z, -19 x z , 17 z + 20 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 4 3 G := [18 y z + 3 x , 10 x y + 7 z , -15 y + x ] > Problem := [F,G]; 3 3 2 4 2 Problem := [[19 x y - 4 x z, -19 x z , 17 z + 20 y z ], 2 2 2 3 3 4 3 [18 y z + 3 x , 10 x y + 7 z , -15 y + x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.87 memory used=47.7MB, alloc=32.3MB, time=1.41 memory used=68.6MB, alloc=32.3MB, time=1.96 memory used=88.6MB, alloc=56.3MB, time=2.50 memory used=129.8MB, alloc=60.3MB, time=3.56 memory used=169.4MB, alloc=60.3MB, time=4.58 memory used=207.9MB, alloc=84.3MB, time=5.65 memory used=269.1MB, alloc=84.3MB, time=7.56 memory used=323.0MB, alloc=116.3MB, time=9.45 N1 := 1445 > GB := Basis(F, plex(op(vars))); 3 2 3 3 2 4 2 GB := [x y , -19 x y + 4 x z, x z , 17 z + 20 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=387.3MB, alloc=116.3MB, time=12.90 memory used=464.0MB, alloc=116.3MB, time=14.90 memory used=539.0MB, alloc=140.3MB, time=16.88 memory used=639.7MB, alloc=164.3MB, time=19.93 N2 := 1445 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 4 2 2 2 2 H := [19 x y - 4 x z, -19 x z , 17 z + 20 y z , 18 y z + 3 x , 3 3 4 3 10 y x + 7 z , -15 y + x ] > J:=[op(GB),op(G)]; 3 2 3 3 2 4 2 2 2 2 J := [x y , -19 x y + 4 x z, x z , 17 z + 20 y z , 18 y z + 3 x , 3 3 4 3 10 y x + 7 z , -15 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 := [6, 15, 23, 4, 3, 4, 4, 5/6, 5/6, 5/6, 6/13, 5/13, 6/13, 7, 17, 28, 5, 3, 4, 4, 6/7, 6/7, 5/7, 1/2, 3/7, 3/7, -2, -5, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=749.6MB, alloc=164.3MB, time=25.06 |\^/| 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(); 1428266640 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [20 x y + 20 x z, 2 x y - 3 y z, 19 y + 19 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [4 x y + 6 y z, -9 x z - 15 x y , 5 x y] > Problem := [F,G]; 2 2 2 3 Problem := [[20 x y + 20 x z, 2 x y - 3 y z, 19 y + 19 y z], 3 3 2 [4 x y + 6 y z, -9 x z - 15 x y , 5 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.87 memory used=47.6MB, alloc=32.3MB, time=1.40 memory used=67.9MB, alloc=56.3MB, time=1.98 memory used=110.8MB, alloc=60.3MB, time=3.34 memory used=149.2MB, alloc=84.3MB, time=4.55 memory used=206.3MB, alloc=108.3MB, time=6.70 memory used=273.3MB, alloc=132.3MB, time=10.70 N1 := 1785 > GB := Basis(F, plex(op(vars))); 2 2 3 2 2 2 GB := [2 x y + 3 y , x y + x z, -2 x y + 3 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=366.0MB, alloc=140.3MB, time=13.77 memory used=468.5MB, alloc=164.3MB, time=17.08 memory used=576.9MB, alloc=188.3MB, time=23.16 N2 := 1785 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 3 H := [20 x y + 20 x z, 2 x y - 3 y z, 19 y + 19 y z, 4 x y + 6 y z, 3 2 -9 x z - 15 x y , 5 x y] > J:=[op(GB),op(G)]; 2 2 3 2 2 2 3 J := [2 x y + 3 y , x y + x z, -2 x y + 3 y z, 4 x y + 6 y z, 3 2 -9 x z - 15 x y , 5 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 := [6, 16, 20, 4, 2, 3, 3, 5/6, 1, 5/6, 7/13, 9/13, 5/13, 6, 16, 21, 4, 2, 3, 3, 1, 1, 2/3, 8/13, 9/13, 4/13, 0, -1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=577.8MB, alloc=188.3MB, time=23.22 |\^/| 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(); 1428266705 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [9 x y z - 17 y, -4 y z + 4 x y, -7 y z + 16 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 3 2 2 G := [4 x z + 12 x z , -3 x y - 5 y z , -20 x y + 2 x z ] > Problem := [F,G]; 2 2 3 Problem := [[9 x y z - 17 y, -4 y z + 4 x y, -7 y z + 16 x z], 3 2 2 3 2 3 2 2 [4 x z + 12 x z , -3 x y - 5 y z , -20 x y + 2 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=47.8MB, alloc=32.3MB, time=1.39 memory used=67.5MB, alloc=56.3MB, time=1.92 memory used=107.1MB, alloc=60.3MB, time=2.94 memory used=142.4MB, alloc=84.3MB, time=3.87 memory used=199.5MB, alloc=92.3MB, time=5.40 memory used=255.2MB, alloc=92.3MB, time=6.83 memory used=312.0MB, alloc=116.3MB, time=8.32 memory used=389.0MB, alloc=116.3MB, time=10.36 memory used=464.5MB, alloc=140.3MB, time=12.36 memory used=554.4MB, alloc=420.3MB, time=14.80 memory used=669.8MB, alloc=420.3MB, time=17.92 memory used=786.4MB, alloc=444.3MB, time=21.11 memory used=932.7MB, alloc=468.3MB, time=25.20 memory used=1101.9MB, alloc=492.3MB, time=29.43 memory used=1287.2MB, alloc=516.3MB, time=34.38 memory used=1480.6MB, alloc=540.3MB, time=40.15 memory used=1671.2MB, alloc=564.3MB, time=46.48 memory used=1868.5MB, alloc=588.3MB, time=53.06 memory used=2072.5MB, alloc=612.3MB, time=59.92 memory used=2257.4MB, alloc=636.3MB, time=66.16 memory used=2443.1MB, alloc=660.3MB, time=72.85 memory used=2644.5MB, alloc=684.3MB, time=83.18 memory used=2845.9MB, alloc=708.3MB, time=94.62 memory used=3056.2MB, alloc=732.3MB, time=107.07 |\^/| 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(); 1428267005 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 F := [17 y + 15 z, 2 y z - 20 x z, 8 x y z - 10 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 G := [-8 x y - 14 x y , 2 y z + 11 x, -7 y + 18 x y] > Problem := [F,G]; 4 3 2 Problem := [[17 y + 15 z, 2 y z - 20 x z, 8 x y z - 10 x y z], 3 2 2 3 3 [-8 x y - 14 x y , 2 y z + 11 x, -7 y + 18 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.84 memory used=47.2MB, alloc=32.3MB, time=1.37 memory used=67.7MB, alloc=32.3MB, time=1.90 memory used=87.7MB, alloc=56.3MB, time=2.47 memory used=130.1MB, alloc=84.3MB, time=3.68 memory used=189.5MB, alloc=108.3MB, time=5.51 memory used=263.7MB, alloc=132.3MB, time=8.97 N1 := 1737 > GB := Basis(F, plex(op(vars))); 3 4 2 4 2 4 5 7 4 4 GB := [128 x y - 25 x y , -32 x y + 5 x y , y - 10 x y , 17 y + 15 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=354.6MB, alloc=132.3MB, time=13.01 memory used=456.7MB, alloc=164.3MB, time=15.92 memory used=577.4MB, alloc=188.3MB, time=21.55 N2 := 1335 #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)]; 4 3 2 3 2 2 H := [17 y + 15 z, 2 y z - 20 x z, 8 x y z - 10 x y z, -8 x y - 14 x y , 3 3 2 z y + 11 x, -7 y + 18 x y] > J:=[op(GB),op(G)]; 3 4 2 4 2 4 5 7 4 4 J := [128 x y - 25 x y , -32 x y + 5 x y , y - 10 x y , 17 y + 15 z, 3 2 2 3 3 -8 x y - 14 x y , 2 z y + 11 x, -7 y + 18 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 := [6, 15, 23, 4, 3, 4, 3, 5/6, 1, 2/3, 7/12, 3/4, 1/2, 7, 15, 35, 7, 3, 7, 3, 6/7, 1, 2/7, 9/14, 6/7, 1/7, 0, -12, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=583.5MB, alloc=188.3MB, time=21.87 |\^/| 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(); 1428267066 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 2 2 3 F := [-12 y z + 12 z , 2 x z + y z , 2 x y z - 16 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 G := [-13 z , -7 y z + 11 z , -4 x y + 6 x y z] > Problem := [F,G]; 3 4 3 2 2 3 Problem := [[-12 y z + 12 z , 2 x z + y z , 2 x y z - 16 y z ], 2 3 2 3 2 [-13 z , -7 y z + 11 z , -4 x y + 6 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=47.7MB, alloc=32.3MB, time=1.39 memory used=67.2MB, alloc=56.3MB, time=1.92 memory used=106.4MB, alloc=60.3MB, time=2.93 memory used=144.1MB, alloc=84.3MB, time=3.92 memory used=201.6MB, alloc=92.3MB, time=5.48 memory used=256.4MB, alloc=116.3MB, time=6.96 memory used=331.9MB, alloc=140.3MB, time=9.05 memory used=429.5MB, alloc=164.3MB, time=12.12 memory used=540.7MB, alloc=188.3MB, time=15.57 memory used=664.6MB, alloc=212.3MB, time=19.45 memory used=786.7MB, alloc=492.3MB, time=23.38 memory used=934.6MB, alloc=516.3MB, time=28.19 memory used=1090.3MB, alloc=540.3MB, time=33.24 memory used=1255.4MB, alloc=564.3MB, time=38.59 memory used=1418.0MB, alloc=588.3MB, time=46.18 memory used=1580.1MB, alloc=612.3MB, time=54.84 memory used=1752.0MB, alloc=636.3MB, time=64.70 memory used=1936.5MB, alloc=660.3MB, time=75.45 memory used=2135.0MB, alloc=684.3MB, time=87.32 memory used=2347.9MB, alloc=708.3MB, time=100.21 memory used=2570.1MB, alloc=732.3MB, time=115.02 |\^/| 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(); 1428267366 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 F := [-9 x + 2 z , 18 x y - y, -7 y z + 7 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 G := [3 z - 20 y, -4 x y z + 15 z , -5 x y z + 17 x ] > Problem := [F,G]; 4 2 2 2 2 Problem := [[-9 x + 2 z , 18 x y - y, -7 y z + 7 y z ], 3 3 2 2 [3 z - 20 y, -4 x y z + 15 z , -5 x 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=0.30 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=47.3MB, alloc=32.3MB, time=1.39 memory used=67.9MB, alloc=32.3MB, time=1.91 memory used=87.9MB, alloc=56.3MB, time=2.44 memory used=127.2MB, alloc=60.3MB, time=3.46 memory used=165.0MB, alloc=60.3MB, time=4.43 memory used=199.5MB, alloc=84.3MB, time=5.37 memory used=255.8MB, alloc=92.3MB, time=6.92 memory used=312.5MB, alloc=116.3MB, time=8.43 memory used=390.7MB, alloc=116.3MB, time=10.52 memory used=469.4MB, alloc=140.3MB, time=12.67 memory used=566.7MB, alloc=140.3MB, time=15.34 memory used=661.0MB, alloc=164.3MB, time=17.96 memory used=755.1MB, alloc=164.3MB, time=20.59 memory used=844.4MB, alloc=444.3MB, time=23.22 memory used=978.2MB, alloc=468.3MB, time=27.03 memory used=1130.7MB, alloc=492.3MB, time=31.46 memory used=1306.2MB, alloc=516.3MB, time=37.06 memory used=1494.3MB, alloc=540.3MB, time=42.69 memory used=1686.0MB, alloc=564.3MB, time=48.96 memory used=1884.8MB, alloc=588.3MB, time=55.62 memory used=2089.7MB, alloc=612.3MB, time=62.63 memory used=2299.4MB, alloc=636.3MB, time=69.92 memory used=2515.5MB, alloc=660.3MB, time=77.33 memory used=2746.9MB, alloc=684.3MB, time=84.81 memory used=2992.9MB, alloc=708.3MB, time=92.31 memory used=3254.6MB, alloc=732.3MB, time=99.76 memory used=3527.8MB, alloc=756.3MB, time=108.01 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428267666 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 3 F := [19 y - 16 y z, -10 x y z - 20 y z , -14 y z - 15] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 2 G := [-2 x y - 2 x z, 8 x y z + 14 y , 18 x y + x z] > Problem := [F,G]; 4 2 3 3 Problem := [[19 y - 16 y z, -10 x y z - 20 y z , -14 y z - 15], 2 2 2 4 2 2 [-2 x y - 2 x z, 8 x y z + 14 y , 18 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=0.30 memory used=26.9MB, alloc=32.3MB, time=0.89 memory used=48.3MB, alloc=32.3MB, time=1.42 memory used=68.5MB, alloc=32.3MB, time=1.93 memory used=87.2MB, alloc=60.3MB, time=2.43 memory used=128.0MB, alloc=60.3MB, time=3.43 memory used=168.6MB, alloc=92.3MB, time=4.50 memory used=231.3MB, alloc=92.3MB, time=6.01 memory used=286.1MB, alloc=116.3MB, time=7.47 memory used=362.7MB, alloc=116.3MB, time=9.42 memory used=438.2MB, alloc=140.3MB, time=11.34 memory used=499.9MB, alloc=396.3MB, time=12.91 memory used=603.0MB, alloc=420.3MB, time=15.48 memory used=727.7MB, alloc=444.3MB, time=18.57 memory used=848.7MB, alloc=468.3MB, time=21.57 memory used=962.6MB, alloc=468.3MB, time=24.49 memory used=1085.1MB, alloc=492.3MB, time=28.03 memory used=1186.9MB, alloc=492.3MB, time=31.07 memory used=1295.4MB, alloc=492.3MB, time=34.43 memory used=1400.1MB, alloc=492.3MB, time=37.68 memory used=1492.2MB, alloc=516.3MB, time=40.65 memory used=1594.2MB, alloc=516.3MB, time=44.01 memory used=1648.7MB, alloc=516.3MB, time=45.86 memory used=1719.1MB, alloc=516.3MB, time=48.22 memory used=1781.2MB, alloc=516.3MB, time=50.31 memory used=1838.1MB, alloc=516.3MB, time=52.19 memory used=1895.0MB, alloc=516.3MB, time=54.34 memory used=1932.6MB, alloc=516.3MB, time=55.72 memory used=2118.1MB, alloc=540.3MB, time=60.96 memory used=2326.7MB, alloc=564.3MB, time=67.22 memory used=2533.5MB, alloc=588.3MB, time=73.10 memory used=2720.0MB, alloc=612.3MB, time=78.75 memory used=2862.4MB, alloc=636.3MB, time=83.07 memory used=3035.2MB, alloc=660.3MB, time=88.39 memory used=3171.2MB, alloc=684.3MB, time=92.48 memory used=3303.5MB, alloc=708.3MB, time=96.99 memory used=3417.8MB, alloc=732.3MB, time=99.90 memory used=3549.9MB, alloc=732.3MB, time=104.67 memory used=3645.0MB, alloc=732.3MB, time=108.27 memory used=3751.2MB, alloc=756.3MB, time=111.91 memory used=4136.5MB, alloc=780.3MB, 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(); 1428267966 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 F := [-18 y z - 11 x y, -16 z + 4 x, -10 x z + 11 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [4 x y - 5 y z, -x z + z, 7 y + 3 z] > Problem := [F,G]; 2 2 3 2 2 2 Problem := [[-18 y z - 11 x y, -16 z + 4 x, -10 x z + 11 x z], 2 2 3 2 2 [4 x y - 5 y z, -x z + z, 7 y + 3 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.84 memory used=47.6MB, alloc=32.3MB, time=1.38 memory used=68.0MB, alloc=32.3MB, time=1.90 memory used=87.0MB, alloc=56.3MB, time=2.40 memory used=125.7MB, alloc=60.3MB, time=3.41 memory used=162.9MB, alloc=84.3MB, time=4.39 memory used=216.2MB, alloc=84.3MB, time=5.78 memory used=271.0MB, alloc=116.3MB, time=7.26 memory used=345.6MB, alloc=116.3MB, time=9.22 memory used=418.1MB, alloc=140.3MB, time=11.14 memory used=504.2MB, alloc=420.3MB, time=13.51 memory used=619.7MB, alloc=420.3MB, time=16.67 memory used=734.1MB, alloc=444.3MB, time=19.95 memory used=870.1MB, alloc=444.3MB, time=23.66 memory used=1005.1MB, alloc=468.3MB, time=27.35 memory used=1157.6MB, alloc=492.3MB, time=31.74 memory used=1304.0MB, alloc=516.3MB, time=35.96 memory used=1434.7MB, alloc=540.3MB, time=39.84 memory used=1565.0MB, alloc=564.3MB, time=44.08 memory used=1728.5MB, alloc=588.3MB, time=49.63 memory used=1915.6MB, alloc=612.3MB, time=56.04 memory used=2095.4MB, alloc=636.3MB, time=62.33 memory used=2264.9MB, alloc=660.3MB, time=68.35 memory used=2441.8MB, alloc=684.3MB, time=74.62 memory used=2608.7MB, alloc=708.3MB, time=80.70 memory used=2765.8MB, alloc=732.3MB, time=86.48 memory used=2905.4MB, alloc=756.3MB, time=91.66 memory used=3061.8MB, alloc=780.3MB, time=98.91 memory used=3336.4MB, alloc=804.3MB, time=114.07 |\^/| 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(); 1428268266 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 3 2 F := [-16 y z + 13 z , -12 x z + 3 y z , x z + 7 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 G := [14 y z - 6 z , -17 x z - 9 x z , -16 x y z - 11 x] > Problem := [F,G]; 2 2 2 2 2 2 3 2 Problem := [[-16 y z + 13 z , -12 x z + 3 y z , x z + 7 y z ], 3 3 2 2 2 2 [14 y z - 6 z , -17 x z - 9 x z , -16 x 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=0.30 memory used=26.0MB, alloc=32.3MB, time=0.82 memory used=47.4MB, alloc=32.3MB, time=1.34 memory used=67.9MB, alloc=32.3MB, time=1.87 memory used=88.5MB, alloc=56.3MB, time=2.52 memory used=129.5MB, alloc=60.3MB, time=3.75 memory used=166.9MB, alloc=84.3MB, time=4.90 memory used=223.0MB, alloc=108.3MB, time=7.12 memory used=291.0MB, alloc=108.3MB, time=11.09 N1 := 1983 > GB := Basis(F, plex(op(vars))); 6 5 4 3 2 2 3 3 GB := [x z, 1792 x z + 13 x y z, 13 x y z + 448 x y z, 13 x z + 112 y z, 2 2 -16 y z + 13 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=360.2MB, alloc=108.3MB, time=13.85 memory used=435.7MB, alloc=140.3MB, time=16.14 memory used=533.2MB, alloc=164.3MB, time=19.62 memory used=633.7MB, alloc=188.3MB, time=25.69 N2 := 1923 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 3 2 3 3 H := [-16 y z + 13 z , -12 x z + 3 y z , x z + 7 y z , 14 y z - 6 z , 2 2 2 2 -17 x z - 9 x z , -16 x y z - 11 x] > J:=[op(GB),op(G)]; 6 5 4 3 2 2 3 3 J := [x z, 1792 x z + 13 x y z, 13 x y z + 448 x y z, 13 x z + 112 y z, 2 2 3 3 2 2 2 2 -16 y z + 13 z , 14 y z - 6 z , -17 x z - 9 x z , -16 x 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 := [6, 15, 23, 4, 3, 2, 3, 2/3, 5/6, 1, 1/2, 5/12, 11/12, 8, 20, 37, 7, 6, 3, 3, 3/4, 3/4, 1, 5/8, 7/16, 7/8, -5, -14, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=639.0MB, alloc=188.3MB, time=25.95 |\^/| 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(); 1428268328 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 3 F := [-2 x z - 17 y z , -10 z + 18 z , 8 x y + 18 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 G := [3 x y - 4 z , 5 x y + 7 x y , -5 x y] > Problem := [F,G]; 2 2 4 3 3 Problem := [[-2 x z - 17 y z , -10 z + 18 z , 8 x y + 18 x z], 2 2 3 3 [3 x y - 4 z , 5 x y + 7 x y , -5 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.88 memory used=47.6MB, alloc=32.3MB, time=1.40 memory used=67.3MB, alloc=32.3MB, time=1.89 memory used=88.1MB, alloc=56.3MB, time=2.56 memory used=129.0MB, alloc=84.3MB, time=3.84 N1 := 1053 > GB := Basis(F, plex(op(vars))); 7 6 4 6 2 6 7 3 GB := [160 x y - 397953 x y , 2 x y + 17 x y , 4 x y + 9 x z, 6 2 4 3 32 x y + 1377 y z , 5 z - 9 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=186.9MB, alloc=84.3MB, time=6.27 memory used=245.2MB, alloc=84.3MB, time=7.75 memory used=301.0MB, alloc=116.3MB, time=9.25 memory used=379.7MB, alloc=116.3MB, time=11.22 memory used=459.2MB, alloc=140.3MB, time=13.61 memory used=558.1MB, alloc=164.3MB, time=16.68 memory used=663.0MB, alloc=188.3MB, time=21.13 memory used=769.1MB, alloc=212.3MB, time=27.61 memory used=899.5MB, alloc=236.3MB, time=35.53 N2 := 3217 #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 4 3 3 2 2 H := [-2 x z - 17 y z , -10 z + 18 z , 8 x y + 18 x z, 3 y x - 4 z , 3 3 5 x y + 7 x y , -5 y x] > J:=[op(GB),op(G)]; 7 6 4 6 2 6 7 3 J := [160 x y - 397953 x y , 2 x y + 17 x y , 4 x y + 9 x z, 6 2 4 3 2 2 3 3 32 x y + 1377 y z , 5 z - 9 z , 3 y x - 4 z , 5 x y + 7 x y , -5 y x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 20, 4, 3, 3, 4, 5/6, 5/6, 2/3, 7/13, 6/13, 6/13, 8, 18, 45, 13, 7, 7, 4, 7/8, 7/8, 1/2, 11/17, 11/17, 5/17, -4, -25, -9] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=932.5MB, alloc=236.3MB, time=37.35 |\^/| 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(); 1428268421 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [-19 x y + 11 x z, 19 x z + 13 x z , 7 x z + 9 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [19 x y z - 5 x y z, x y - 2 x, -9 x y - 6 y z] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[-19 x y + 11 x z, 19 x z + 13 x z , 7 x z + 9 x], 2 2 2 3 2 [19 x y z - 5 x y z, x y - 2 x, -9 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.82 memory used=47.1MB, alloc=32.3MB, time=1.33 memory used=68.2MB, alloc=56.3MB, time=1.97 memory used=110.2MB, alloc=60.3MB, time=3.22 memory used=145.9MB, alloc=84.3MB, time=4.45 memory used=196.5MB, alloc=108.3MB, time=7.26 N1 := 1435 > GB := Basis(F, plex(op(vars))); 2 2 GB := [19 x + 13 x, 133 x y + 99 x, 7 x z + 9 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=269.2MB, alloc=116.3MB, time=9.47 N2 := 719 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 H := [-19 x y + 11 x z, 19 x z + 13 x z , 7 x z + 9 x, 19 x y z - 5 x y z, 2 2 3 2 x y - 2 x, -9 x y - 6 y z] > J:=[op(GB),op(G)]; 2 2 2 J := [19 x + 13 x, 133 x y + 99 x, 7 x z + 9 x, 19 x y z - 5 x y z, 2 2 3 2 x y - 2 x, -9 x y - 6 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 := [6, 15, 22, 4, 2, 3, 2, 1, 2/3, 5/6, 11/12, 1/2, 7/12, 6, 13, 19, 4, 2, 3, 1, 1, 2/3, 1/2, 11/12, 1/2, 1/3, 2, 3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=298.2MB, alloc=116.3MB, time=10.72 |\^/| 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(); 1428268451 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 3 3 3 F := [-9 x y + 19 y , 14 x z - 20 y z , 13 x y + 11 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 4 G := [18 x z + 9 x z , 5 y z, 10 x y z - 15 z ] > Problem := [F,G]; 2 2 4 3 3 3 3 Problem := [[-9 x y + 19 y , 14 x z - 20 y z , 13 x y + 11 x ], 2 2 3 2 2 4 [18 x z + 9 x z , 5 y z, 10 x y z - 15 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.84 memory used=49.7MB, alloc=32.3MB, time=1.52 memory used=71.0MB, alloc=56.3MB, time=2.16 memory used=112.4MB, alloc=80.3MB, time=3.86 N1 := 911 > GB := Basis(F, plex(op(vars))); 7 5 5 3 3 3 GB := [123201 x - 829939 x , 1053 x + 3971 x y, 13 x y + 11 x , 2 2 4 3 3 3 3 -9 x y + 19 y , x z , -7 x z + 10 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=142.2MB, alloc=80.3MB, time=4.85 memory used=204.3MB, alloc=92.3MB, time=6.58 memory used=264.9MB, alloc=116.3MB, time=8.44 memory used=335.9MB, alloc=140.3MB, time=12.20 N2 := 1471 #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 4 3 3 3 3 2 2 3 H := [-9 x y + 19 y , 14 x z - 20 y z , 13 x y + 11 x , 18 x z + 9 x z , 2 2 4 5 y z, 10 x y z - 15 z ] > J:=[op(GB),op(G)]; 7 5 5 3 3 3 J := [123201 x - 829939 x , 1053 x + 3971 x y, 13 x y + 11 x , 2 2 4 3 3 3 3 2 2 3 2 -9 x y + 19 y , x z , -7 x z + 10 y z , 18 x z + 9 x z , 5 y z, 2 4 10 x y z - 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, 23, 4, 3, 4, 4, 5/6, 5/6, 2/3, 7/13, 6/13, 7/13, 9, 19, 41, 7, 7, 4, 4, 8/9, 2/3, 5/9, 12/19, 7/19, 8/19, -5, -18, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=345.1MB, alloc=140.3MB, time=12.65 |\^/| 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(); 1428268489 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 F := [-8 x - 2 x z , -17 x y + 6 y z, -4 x z - 3 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 3 G := [15 y z - 14 y , 2 y z + 13 x z , -20 x y z - 15 y ] > Problem := [F,G]; 3 2 3 2 2 Problem := [[-8 x - 2 x z , -17 x y + 6 y z, -4 x z - 3 y z ], 2 2 3 2 2 2 2 3 [15 y z - 14 y , 2 y z + 13 x z , -20 x 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=4.3MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=47.6MB, alloc=32.3MB, time=1.38 memory used=68.0MB, alloc=32.3MB, time=1.88 memory used=87.8MB, alloc=56.3MB, time=2.40 memory used=127.4MB, alloc=60.3MB, time=3.40 memory used=164.1MB, alloc=84.3MB, time=4.34 memory used=216.8MB, alloc=84.3MB, time=5.84 memory used=272.4MB, alloc=108.3MB, time=7.58 memory used=346.5MB, alloc=140.3MB, time=9.92 memory used=436.2MB, alloc=164.3MB, time=12.82 memory used=535.2MB, alloc=188.3MB, time=17.49 memory used=643.6MB, alloc=212.3MB, time=23.89 memory used=776.0MB, alloc=212.3MB, time=31.67 N1 := 3701 > GB := Basis(F, plex(op(vars))); GB := [ 7 3 4 3 6 3 4 3 2 289 x + 144 x , 4 x + 3 x y, -17 x + 6 x z, 34 x + 9 y z, 4 x + x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=911.5MB, alloc=212.3MB, time=38.93 memory used=1022.3MB, alloc=468.3MB, time=41.94 memory used=1172.0MB, alloc=492.3MB, time=45.97 memory used=1345.8MB, alloc=516.3MB, time=50.62 memory used=1540.7MB, alloc=540.3MB, time=56.15 memory used=1753.1MB, alloc=564.3MB, time=62.54 memory used=1966.4MB, alloc=588.3MB, time=69.50 memory used=2188.5MB, alloc=612.3MB, time=76.97 memory used=2397.8MB, alloc=636.3MB, time=87.82 memory used=2605.1MB, alloc=660.3MB, time=100.05 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428268789 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 F := [-16 x z + 15 z , 12 x y - 20 x z, -5 x y - 15 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 G := [6 x y z + 5 z , -17 x z + 4 x y, -19 x ] > Problem := [F,G]; 3 2 2 3 3 Problem := [[-16 x z + 15 z , 12 x y - 20 x z, -5 x y - 15 x ], 2 3 2 3 [6 x y z + 5 z , -17 x z + 4 x y, -19 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.84 memory used=47.4MB, alloc=32.3MB, time=1.36 memory used=67.7MB, alloc=32.3MB, time=1.87 memory used=87.2MB, alloc=56.3MB, time=2.38 memory used=128.2MB, alloc=60.3MB, time=3.51 memory used=168.7MB, alloc=84.3MB, time=4.76 memory used=229.5MB, alloc=108.3MB, time=6.60 memory used=304.1MB, alloc=140.3MB, time=9.14 memory used=385.4MB, alloc=164.3MB, time=13.41 memory used=484.7MB, alloc=164.3MB, time=19.16 N1 := 2983 > GB := Basis(F, plex(op(vars))); 5 3 3 3 2 4 2 GB := [16 x + 27 x , x y + 3 x , -3 x y + 5 x z, 48 x + 25 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=585.9MB, alloc=164.3MB, time=24.51 memory used=695.6MB, alloc=420.3MB, time=27.48 memory used=814.1MB, alloc=444.3MB, time=31.72 N2 := 1429 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 3 3 2 3 H := [-16 x z + 15 z , 12 x y - 20 x z, -5 x y - 15 x , 6 x y z + 5 z , 2 3 -17 x z + 4 x y, -19 x ] > J:=[op(GB),op(G)]; 5 3 3 3 2 4 2 J := [16 x + 27 x , x y + 3 x , -3 x y + 5 x z, 48 x + 25 z , 2 3 2 3 6 x y z + 5 z , -17 x z + 4 x y, -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 := [6, 14, 21, 4, 3, 2, 3, 1, 2/3, 2/3, 3/4, 1/3, 1/2, 7, 15, 26, 5, 5, 2, 3, 1, 4/7, 4/7, 11/14, 2/7, 5/14, -1, -5, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=864.5MB, alloc=444.3MB, time=34.59 |\^/| 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(); 1428268890 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 3 F := [-18 x z + 12, -19 x y - 4 y, 9 x + 18 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [5 x y + y z, 6 z, -18 y z + 3 x] > Problem := [F,G]; 2 3 4 3 Problem := [[-18 x z + 12, -19 x y - 4 y, 9 x + 18 x y ], 2 2 [5 x y + y z, 6 z, -18 y z + 3 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=48.8MB, alloc=32.3MB, time=1.50 memory used=69.8MB, alloc=56.3MB, time=2.15 memory used=110.9MB, alloc=84.3MB, time=3.50 N1 := 1003 > GB := Basis(F, plex(op(vars))); 3 3 GB := [19 x + 4, 19 y - 2, 6 z + 19 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=168.3MB, alloc=84.3MB, time=5.65 N2 := 731 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 4 3 H := [-18 x z + 12, -19 x y - 4 y, 9 x + 18 x y , 5 x y + y z, 6 z, 2 2 -18 y z + 3 x] > J:=[op(GB),op(G)]; 3 3 2 2 J := [19 x + 4, 19 y - 2, 6 z + 19 x, 5 x y + y z, 6 z, -18 y z + 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, 13, 18, 4, 4, 3, 2, 5/6, 2/3, 2/3, 1/2, 1/2, 1/3, 6, 11, 14, 4, 3, 3, 2, 2/3, 1/2, 2/3, 1/3, 1/3, 1/3, 2, 4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=229.1MB, alloc=84.3MB, time=7.77 |\^/| 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(); 1428268913 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [-15 x + 7 x y, x z - 16 x, -14 x z - 5 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 G := [10 x - y , 8 x y - 17 z, 17 x - 14 x z] > Problem := [F,G]; 3 2 2 2 Problem := [[-15 x + 7 x y, x z - 16 x, -14 x z - 5 y z], 3 2 2 2 3 2 [10 x - y , 8 x y - 17 z, 17 x - 14 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=47.5MB, alloc=32.3MB, time=1.38 memory used=67.4MB, alloc=32.3MB, time=1.88 memory used=86.6MB, alloc=56.3MB, time=2.37 memory used=126.0MB, alloc=60.3MB, time=3.38 memory used=164.6MB, alloc=60.3MB, time=4.34 memory used=201.2MB, alloc=84.3MB, time=5.29 memory used=258.5MB, alloc=92.3MB, time=6.83 memory used=311.5MB, alloc=116.3MB, time=8.23 memory used=388.5MB, alloc=140.3MB, time=10.60 memory used=480.3MB, alloc=164.3MB, time=13.44 memory used=585.8MB, alloc=188.3MB, time=16.75 memory used=702.4MB, alloc=212.3MB, time=20.45 memory used=829.3MB, alloc=236.3MB, time=24.69 memory used=955.9MB, alloc=260.3MB, time=30.50 memory used=1090.7MB, alloc=284.3MB, time=37.40 memory used=1237.7MB, alloc=308.3MB, time=45.43 memory used=1394.6MB, alloc=332.3MB, time=55.34 memory used=1575.5MB, alloc=356.3MB, time=66.68 memory used=1780.3MB, alloc=380.3MB, time=79.47 memory used=2009.0MB, alloc=380.3MB, time=93.65 memory used=2237.8MB, alloc=404.3MB, time=107.83 memory used=2490.5MB, alloc=404.3MB, time=123.40 |\^/| 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(); 1428269213 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [16 x y z - 13 x y, -6 x y - 19 y , -11 x y + 18 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 2 G := [-y - 16 y z, 20 x y + 13 x z, -16 y z - 18 y z ] > Problem := [F,G]; 2 2 2 3 2 Problem := [[16 x y z - 13 x y, -6 x y - 19 y , -11 x y + 18 x y], 4 2 2 3 2 2 [-y - 16 y z, 20 x y + 13 x z, -16 y z - 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=26.0MB, alloc=32.3MB, time=0.83 memory used=47.5MB, alloc=32.3MB, time=1.38 memory used=68.2MB, alloc=32.3MB, time=1.92 memory used=87.9MB, alloc=56.3MB, time=2.45 memory used=127.6MB, alloc=60.3MB, time=3.49 memory used=164.4MB, alloc=84.3MB, time=4.47 memory used=225.0MB, alloc=84.3MB, time=6.39 memory used=280.4MB, alloc=108.3MB, time=8.10 memory used=353.1MB, alloc=140.3MB, time=10.38 memory used=439.9MB, alloc=164.3MB, time=13.27 memory used=534.4MB, alloc=188.3MB, time=17.42 memory used=637.0MB, alloc=212.3MB, time=23.32 memory used=759.8MB, alloc=236.3MB, time=30.67 memory used=906.6MB, alloc=236.3MB, time=39.38 memory used=1053.5MB, alloc=260.3MB, time=48.17 memory used=1224.4MB, alloc=284.3MB, time=58.29 N1 := 5007 > GB := Basis(F, plex(op(vars))); 2 3 2 GB := [11 x y - 18 x y, 209 y + 108 x y, 88 x y z - 117 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1318.7MB, alloc=284.3MB, time=61.18 memory used=1538.4MB, alloc=564.3MB, time=68.21 memory used=1758.1MB, alloc=588.3MB, time=75.30 memory used=1975.1MB, alloc=612.3MB, time=84.79 memory used=2177.6MB, alloc=636.3MB, time=95.75 memory used=2385.4MB, alloc=660.3MB, time=108.51 memory used=2608.9MB, alloc=684.3MB, time=122.92 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428269513 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 3 F := [-12 y + 15 y z , -3 x + 14 x z , -16 x y + 12 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 2 2 2 3 G := [-2 x z - 2 z , 2 x z - 17 x z , 16 x z - 3 x ] > Problem := [F,G]; 4 3 3 2 3 Problem := [[-12 y + 15 y z , -3 x + 14 x z , -16 x y + 12 x z], 2 2 4 2 2 2 2 2 3 [-2 x z - 2 z , 2 x z - 17 x z , 16 x z - 3 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=48.1MB, alloc=32.3MB, time=1.40 memory used=69.2MB, alloc=32.3MB, time=1.96 memory used=88.6MB, alloc=56.3MB, time=2.48 memory used=128.7MB, alloc=60.3MB, time=3.54 memory used=165.9MB, alloc=84.3MB, time=4.54 memory used=220.6MB, alloc=84.3MB, time=6.00 memory used=277.9MB, alloc=108.3MB, time=7.77 memory used=353.3MB, alloc=132.3MB, time=10.18 memory used=448.0MB, alloc=164.3MB, time=13.20 memory used=559.1MB, alloc=188.3MB, time=16.70 memory used=674.2MB, alloc=212.3MB, time=21.23 memory used=791.4MB, alloc=236.3MB, time=27.14 memory used=918.2MB, alloc=260.3MB, time=34.77 memory used=1069.1MB, alloc=284.3MB, time=43.76 memory used=1243.9MB, alloc=284.3MB, time=54.11 memory used=1418.7MB, alloc=308.3MB, time=64.54 memory used=1617.4MB, alloc=308.3MB, time=76.26 N1 := 6185 > GB := Basis(F, plex(op(vars))); 5 3 3 4 4 6 3 3 GB := [5 x - 14 x , 5 x y - 14 x y , 224 x y - 27 x , -4 x y + 3 x z, 4 3 -4 y + 5 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1819.8MB, alloc=308.3MB, time=87.08 memory used=1923.5MB, alloc=564.3MB, time=90.18 memory used=2163.8MB, alloc=588.3MB, time=98.33 memory used=2388.1MB, alloc=612.3MB, time=111.87 N2 := 3203 #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)]; 4 3 3 2 3 2 2 4 H := [-12 y + 15 y z , -3 x + 14 x z , -16 x y + 12 x z, -2 x z - 2 z , 2 2 2 2 2 3 2 x z - 17 x z , 16 x z - 3 x ] > J:=[op(GB),op(G)]; 5 3 3 4 4 6 3 3 J := [5 x - 14 x , 5 x y - 14 x y , 224 x y - 27 x , -4 x y + 3 x z, 4 3 2 2 4 2 2 2 2 2 3 -4 y + 5 y z , -2 x z - 2 z , 2 x z - 17 x z , 16 x z - 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, 13, 23, 4, 3, 4, 4, 5/6, 1/3, 1, 3/4, 1/4, 2/3, 8, 16, 39, 7, 5, 6, 4, 7/8, 1/2, 5/8, 13/16, 3/8, 7/16, -3, -16, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2479.3MB, alloc=612.3MB, time=117.35 |\^/| 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(); 1428269797 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [4 x + 11 y, -18 x y + 15 y z , 7 x y z + y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 4 2 2 G := [18 x - 7 x z, 18 x z - 17 x z, 7 x + 20 x z ] > Problem := [F,G]; 2 3 2 2 Problem := [[4 x + 11 y, -18 x y + 15 y z , 7 x y z + y], 4 3 2 4 2 2 [18 x - 7 x z, 18 x z - 17 x z, 7 x + 20 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.32 memory used=26.3MB, alloc=32.3MB, time=0.88 memory used=48.7MB, alloc=32.3MB, time=1.52 memory used=69.4MB, alloc=56.3MB, time=2.18 N1 := 539 > GB := Basis(F, plex(op(vars))); 9 2 2 7 2 GB := [294 x - 5 x , 4 x + 11 y, 42 x + 5 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.1MB, alloc=60.3MB, time=3.48 N2 := 135 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 4 3 H := [4 x + 11 y, -18 x y + 15 y z , 7 x y z + y, 18 x - 7 x z, 2 4 2 2 18 x z - 17 x z, 7 x + 20 x z ] > J:=[op(GB),op(G)]; 9 2 2 7 2 4 3 J := [294 x - 5 x , 4 x + 11 y, 42 x + 5 x z, 18 x - 7 x z, 2 4 2 2 18 x z - 17 x z, 7 x + 20 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 := [6, 14, 21, 4, 4, 1, 2, 1, 1/2, 5/6, 3/4, 5/12, 1/2, 6, 11, 29, 9, 9, 1, 2, 1, 1/6, 2/3, 11/12, 1/12, 5/12, 3, -8, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=111.5MB, alloc=60.3MB, time=3.58 |\^/| 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(); 1428269805 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 4 3 3 F := [-18 x y z + 18 z , -x y - 12 y , 11 x y + x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [-3 x y z + 16 x z, 18 x y + 12 y, x y z + 19 z ] > Problem := [F,G]; 2 3 2 2 4 3 3 Problem := [[-18 x y z + 18 z , -x y - 12 y , 11 x y + x ], 2 2 2 3 [-3 x y z + 16 x z, 18 x y + 12 y, x y z + 19 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.85 memory used=47.6MB, alloc=32.3MB, time=1.38 memory used=69.9MB, alloc=32.3MB, time=2.01 N1 := 339 > GB := Basis(F, plex(op(vars))); 7 5 5 3 3 3 2 2 4 GB := [121 x + 1728 x , 11 x + 144 x y, 11 x y + x , x y + 12 y , 2 3 -x y z + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=90.4MB, alloc=56.3MB, time=2.73 memory used=130.6MB, alloc=60.3MB, time=3.74 memory used=169.7MB, alloc=60.3MB, time=4.71 memory used=211.8MB, alloc=84.3MB, time=6.01 memory used=273.5MB, alloc=108.3MB, time=8.52 N2 := 1007 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 4 3 3 2 H := [-18 x y z + 18 z , -x y - 12 y , 11 x y + x , -3 x y z + 16 x z, 2 2 3 18 x y + 12 y, x y z + 19 z ] > J:=[op(GB),op(G)]; 7 5 5 3 3 3 2 2 4 J := [121 x + 1728 x , 11 x + 144 x y, 11 x y + x , x y + 12 y , 2 3 2 2 2 3 -x y z + z , -3 x y z + 16 x z, 18 x y + 12 y, x y z + 19 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, 15, 23, 4, 3, 4, 3, 1, 1, 1/2, 2/3, 2/3, 1/2, 8, 18, 35, 7, 7, 4, 3, 1, 7/8, 3/8, 3/4, 9/16, 3/8, -3, -12, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=284.3MB, alloc=108.3MB, time=9.08 |\^/| 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(); 1428269826 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 F := [-4 x z + 13 y z , -13 x z - 6 y z, 15 x y + 12 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 4 G := [9 x y z + 4 y , -10 x y z + y z, 18 x z - 5 y ] > Problem := [F,G]; 2 2 2 2 2 3 2 Problem := [[-4 x z + 13 y z , -13 x z - 6 y z, 15 x y + 12 y z ], 3 2 3 4 [9 x y z + 4 y , -10 x y z + y z, 18 x z - 5 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.84 memory used=47.7MB, alloc=32.3MB, time=1.40 memory used=67.8MB, alloc=32.3MB, time=1.91 memory used=87.1MB, alloc=56.3MB, time=2.43 memory used=125.4MB, alloc=60.3MB, time=3.46 memory used=160.2MB, alloc=84.3MB, time=4.41 memory used=216.6MB, alloc=84.3MB, time=5.91 memory used=271.5MB, alloc=84.3MB, time=7.42 memory used=327.0MB, alloc=116.3MB, time=8.98 memory used=404.9MB, alloc=116.3MB, time=11.02 memory used=479.5MB, alloc=140.3MB, time=13.09 memory used=574.1MB, alloc=164.3MB, time=15.82 memory used=674.8MB, alloc=420.3MB, time=18.70 memory used=787.4MB, alloc=444.3MB, time=21.98 memory used=920.9MB, alloc=468.3MB, time=25.80 memory used=1077.3MB, alloc=492.3MB, time=30.75 memory used=1241.8MB, alloc=516.3MB, time=35.94 memory used=1418.1MB, alloc=540.3MB, time=41.56 memory used=1603.3MB, alloc=564.3MB, time=47.60 memory used=1801.1MB, alloc=588.3MB, time=53.95 memory used=2020.6MB, alloc=612.3MB, time=60.62 memory used=2244.3MB, alloc=636.3MB, time=67.54 memory used=2462.4MB, alloc=660.3MB, time=76.15 memory used=2662.0MB, alloc=684.3MB, time=86.60 memory used=2866.3MB, alloc=708.3MB, time=98.00 memory used=3081.0MB, alloc=732.3MB, time=110.58 memory used=3307.2MB, alloc=756.3MB, time=124.40 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428270126 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 F := [-14 x y - 12 z, 8 x y + 3 x z, 20 x y z + 14 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 G := [7 x z - 20 x , 5 x z - 10 x z, -8 x y - 11 y] > Problem := [F,G]; 3 2 Problem := [[-14 x y - 12 z, 8 x y + 3 x z, 20 x y z + 14 y z ], 3 3 3 2 2 [7 x z - 20 x , 5 x z - 10 x z, -8 x y - 11 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.83 memory used=47.7MB, alloc=32.3MB, time=1.38 memory used=68.3MB, alloc=32.3MB, time=1.89 memory used=87.5MB, alloc=56.3MB, time=2.40 memory used=127.7MB, alloc=60.3MB, time=3.56 memory used=166.3MB, alloc=84.3MB, time=4.74 memory used=224.0MB, alloc=108.3MB, time=6.51 memory used=296.0MB, alloc=140.3MB, time=8.79 memory used=378.8MB, alloc=164.3MB, time=12.12 memory used=468.1MB, alloc=188.3MB, time=17.32 memory used=581.3MB, alloc=188.3MB, time=23.89 memory used=694.6MB, alloc=212.3MB, time=30.50 N1 := 4057 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 2 GB := [16 x y - 7 x y, 49 x y - 60 x y , 7 y x + 6 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=833.5MB, alloc=212.3MB, time=38.06 N2 := 877 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 3 H := [-14 x y - 12 z, 8 x y + 3 x z, 20 x y z + 14 y z , 7 x z - 20 x , 3 2 2 5 x z - 10 x z, -8 x y - 11 y] > J:=[op(GB),op(G)]; 3 2 2 3 2 2 3 3 J := [16 x y - 7 x y, 49 x y - 60 x y , 7 y x + 6 z, 7 x z - 20 x , 3 2 2 5 x z - 10 x z, -8 x y - 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 := [6, 15, 20, 4, 3, 1, 3, 1, 2/3, 5/6, 3/4, 1/2, 7/12, 6, 13, 22, 5, 3, 3, 3, 1, 2/3, 1/2, 5/6, 7/12, 1/3, 2, -2, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=930.1MB, alloc=212.3MB, time=41.46 |\^/| 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(); 1428270236 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 3 3 F := [-20 x y + y z , 14 x y + 18 z , 8 x z + y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 3 3 G := [9 y z + 4 y z, -6 x - 3 x z , -15 x + 10 z ] > Problem := [F,G]; 3 2 2 2 3 3 3 Problem := [[-20 x y + y z , 14 x y + 18 z , 8 x z + y ], 2 2 4 2 2 3 3 [9 y z + 4 y z, -6 x - 3 x z , -15 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=0.31 memory used=26.9MB, alloc=32.3MB, time=0.90 memory used=48.2MB, alloc=32.3MB, time=1.45 memory used=68.9MB, alloc=32.3MB, time=1.98 memory used=88.6MB, alloc=56.3MB, time=2.51 memory used=130.0MB, alloc=60.3MB, time=3.56 memory used=169.6MB, alloc=60.3MB, time=4.56 memory used=210.0MB, alloc=84.3MB, time=5.58 memory used=270.5MB, alloc=92.3MB, time=7.13 memory used=332.9MB, alloc=116.3MB, time=8.62 memory used=406.8MB, alloc=116.3MB, time=10.22 memory used=469.2MB, alloc=372.3MB, time=11.55 memory used=550.6MB, alloc=396.3MB, time=13.55 memory used=659.9MB, alloc=420.3MB, time=16.04 memory used=789.8MB, alloc=444.3MB, time=19.16 memory used=919.0MB, alloc=468.3MB, time=22.07 memory used=1037.9MB, alloc=468.3MB, time=24.77 memory used=1120.6MB, alloc=492.3MB, time=26.77 memory used=1223.3MB, alloc=492.3MB, time=29.34 memory used=1311.2MB, alloc=492.3MB, time=31.19 memory used=1397.7MB, alloc=516.3MB, time=33.61 memory used=1467.7MB, alloc=516.3MB, time=35.86 memory used=1526.0MB, alloc=516.3MB, time=37.43 memory used=1589.2MB, alloc=516.3MB, time=39.12 memory used=1656.9MB, alloc=516.3MB, time=40.67 memory used=1727.1MB, alloc=516.3MB, time=42.94 memory used=1789.4MB, alloc=516.3MB, time=45.07 memory used=1826.8MB, alloc=516.3MB, time=46.52 memory used=1866.3MB, alloc=516.3MB, time=48.02 memory used=2048.5MB, alloc=540.3MB, time=52.24 memory used=2241.2MB, alloc=564.3MB, time=56.28 memory used=2422.3MB, alloc=588.3MB, time=60.51 memory used=2579.8MB, alloc=612.3MB, time=64.79 memory used=2730.6MB, alloc=636.3MB, time=68.47 memory used=2892.4MB, alloc=636.3MB, time=72.18 memory used=3052.6MB, alloc=636.3MB, time=76.17 memory used=3167.1MB, alloc=660.3MB, time=79.59 memory used=3289.9MB, alloc=660.3MB, time=83.29 memory used=3418.1MB, alloc=684.3MB, time=87.89 memory used=3545.6MB, alloc=684.3MB, time=92.64 memory used=3638.3MB, alloc=684.3MB, time=95.69 memory used=3744.5MB, alloc=684.3MB, time=99.47 memory used=4073.7MB, alloc=708.3MB, time=108.23 memory used=4422.8MB, alloc=732.3MB, time=116.82 memory used=4776.9MB, alloc=756.3MB, time=126.02 |\^/| 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(); 1428270536 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 4 F := [-16 y - 11 y z, -6 x y + 15 x z , -12 x + 10 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 G := [6 x y z + 18 x , 9 y - 7 y z, 3 x y + 14 x y] > Problem := [F,G]; 4 2 2 2 2 2 4 Problem := [[-16 y - 11 y z, -6 x y + 15 x z , -12 x + 10 y z], 2 3 2 3 2 [6 x y z + 18 x , 9 y - 7 y z, 3 x y + 14 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.86 memory used=47.7MB, alloc=32.3MB, time=1.42 memory used=67.4MB, alloc=56.3MB, time=1.94 memory used=109.0MB, alloc=60.3MB, time=3.03 memory used=147.8MB, alloc=60.3MB, time=4.03 memory used=185.2MB, alloc=84.3MB, time=5.02 memory used=232.6MB, alloc=84.3MB, time=6.28 memory used=289.2MB, alloc=116.3MB, time=7.85 memory used=367.9MB, alloc=116.3MB, time=9.92 memory used=447.1MB, alloc=140.3MB, time=12.29 memory used=542.1MB, alloc=164.3MB, time=15.36 memory used=646.2MB, alloc=188.3MB, time=18.71 memory used=751.3MB, alloc=468.3MB, time=22.15 memory used=886.3MB, alloc=492.3MB, time=26.51 memory used=1033.5MB, alloc=516.3MB, time=31.25 memory used=1192.9MB, alloc=540.3MB, time=36.44 memory used=1363.2MB, alloc=564.3MB, time=41.97 memory used=1537.4MB, alloc=588.3MB, time=47.87 memory used=1716.9MB, alloc=612.3MB, time=54.51 memory used=1883.9MB, alloc=636.3MB, time=63.27 memory used=2058.2MB, alloc=660.3MB, time=73.11 memory used=2244.1MB, alloc=684.3MB, time=83.91 memory used=2443.7MB, alloc=708.3MB, time=95.97 memory used=2657.2MB, alloc=732.3MB, time=108.89 |\^/| 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(); 1428270836 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 F := [6 x z - 6 y z, 14 y z + 5 x z , -16 y z - 5 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 2 G := [-19 x + 18 y z , 20 x + 4 z , -8 x z + 14 x y] > Problem := [F,G]; 3 3 2 3 Problem := [[6 x z - 6 y z, 14 y z + 5 x z , -16 y z - 5 x y], 4 3 3 2 2 [-19 x + 18 y z , 20 x + 4 z , -8 x z + 14 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.87 memory used=48.4MB, alloc=32.3MB, time=1.39 memory used=68.3MB, alloc=56.3MB, time=1.89 memory used=109.7MB, alloc=60.3MB, time=2.89 memory used=150.0MB, alloc=60.3MB, time=3.87 memory used=189.5MB, alloc=84.3MB, time=4.89 memory used=224.9MB, alloc=84.3MB, time=5.80 memory used=288.2MB, alloc=116.3MB, time=7.27 memory used=346.0MB, alloc=396.3MB, time=8.44 memory used=458.6MB, alloc=420.3MB, time=10.75 memory used=583.9MB, alloc=444.3MB, time=13.63 memory used=697.9MB, alloc=468.3MB, time=16.31 memory used=798.9MB, alloc=468.3MB, time=18.63 memory used=918.0MB, alloc=492.3MB, time=22.05 memory used=992.9MB, alloc=492.3MB, time=23.92 memory used=1078.5MB, alloc=492.3MB, time=26.05 memory used=1141.3MB, alloc=492.3MB, time=27.66 memory used=1205.6MB, alloc=492.3MB, time=29.60 memory used=1282.2MB, alloc=516.3MB, time=32.00 memory used=1335.9MB, alloc=516.3MB, time=33.64 memory used=1381.4MB, alloc=516.3MB, time=35.37 memory used=1429.2MB, alloc=516.3MB, time=37.16 memory used=1467.6MB, alloc=516.3MB, time=38.44 memory used=1514.7MB, alloc=516.3MB, time=40.34 memory used=1702.3MB, alloc=540.3MB, time=45.15 memory used=1867.6MB, alloc=564.3MB, time=49.45 memory used=2044.0MB, alloc=588.3MB, time=53.95 memory used=2198.3MB, alloc=612.3MB, time=57.80 memory used=2340.1MB, alloc=636.3MB, time=61.57 memory used=2464.1MB, alloc=660.3MB, time=65.63 memory used=2591.0MB, alloc=660.3MB, time=69.64 memory used=2708.8MB, alloc=684.3MB, time=73.11 memory used=2989.8MB, alloc=708.3MB, time=80.03 memory used=3211.1MB, alloc=732.3MB, time=87.69 memory used=3417.5MB, alloc=756.3MB, time=95.83 memory used=3594.0MB, alloc=780.3MB, time=103.06 memory used=3772.6MB, alloc=804.3MB, time=110.55 memory used=4173.8MB, alloc=828.3MB, time=122.06 memory used=4640.8MB, alloc=852.3MB, time=130.11 |\^/| 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(); 1428271136 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 3 3 F := [12 x - 19 y z, 11 x y - 3 x z , 11 x z - 16 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 G := [-11 y z - 7 z, 8 x - 16 x y , 12 x z - 18 x z] > Problem := [F,G]; 4 2 3 3 3 Problem := [[12 x - 19 y z, 11 x y - 3 x z , 11 x z - 16 x], 2 2 3 2 3 [-11 y z - 7 z, 8 x - 16 x y , 12 x z - 18 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=26.3MB, alloc=32.3MB, time=0.87 memory used=47.6MB, alloc=32.3MB, time=1.43 memory used=67.2MB, alloc=32.3MB, time=1.94 memory used=86.0MB, alloc=56.3MB, time=2.47 memory used=125.0MB, alloc=60.3MB, time=3.51 memory used=162.1MB, alloc=84.3MB, time=4.50 memory used=212.0MB, alloc=84.3MB, time=5.83 memory used=272.2MB, alloc=92.3MB, time=7.37 memory used=332.7MB, alloc=116.3MB, time=8.88 memory used=414.7MB, alloc=116.3MB, time=10.95 memory used=487.6MB, alloc=396.3MB, time=12.87 memory used=592.4MB, alloc=420.3MB, time=15.49 memory used=713.3MB, alloc=420.3MB, time=18.62 memory used=838.9MB, alloc=444.3MB, time=21.68 memory used=979.8MB, alloc=468.3MB, time=25.66 memory used=1132.4MB, alloc=492.3MB, time=30.62 memory used=1288.3MB, alloc=516.3MB, time=35.86 memory used=1455.4MB, alloc=540.3MB, time=41.48 memory used=1631.4MB, alloc=564.3MB, time=47.41 memory used=1813.9MB, alloc=588.3MB, time=53.67 memory used=2002.8MB, alloc=612.3MB, time=60.25 memory used=2200.6MB, alloc=636.3MB, time=67.12 memory used=2402.8MB, alloc=660.3MB, time=74.22 memory used=2595.1MB, alloc=684.3MB, time=80.99 memory used=2787.7MB, alloc=708.3MB, time=90.55 memory used=2979.1MB, alloc=732.3MB, time=101.08 memory used=3179.2MB, alloc=756.3MB, time=112.71 memory used=3390.4MB, alloc=780.3MB, 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(); 1428271436 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 4 2 F := [14 x z - 10 x z , 7 x z + 17 z , -17 y - 6 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 G := [13 x - 11 z, 15 x y z - 16 x z , -19 x y - 14 y ] > Problem := [F,G]; 3 2 2 2 4 4 2 Problem := [[14 x z - 10 x z , 7 x z + 17 z , -17 y - 6 y z], 3 2 3 3 2 [13 x - 11 z, 15 x y z - 16 x z , -19 x y - 14 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.85 memory used=47.5MB, alloc=32.3MB, time=1.39 memory used=68.0MB, alloc=32.3MB, time=1.91 memory used=87.3MB, alloc=56.3MB, time=2.44 memory used=127.5MB, alloc=60.3MB, time=3.51 memory used=165.6MB, alloc=60.3MB, time=4.50 memory used=202.2MB, alloc=84.3MB, time=5.48 memory used=257.4MB, alloc=84.3MB, time=6.94 memory used=313.0MB, alloc=108.3MB, time=8.73 memory used=385.5MB, alloc=132.3MB, time=11.07 memory used=474.0MB, alloc=156.3MB, time=13.93 memory used=547.4MB, alloc=188.3MB, time=16.41 memory used=657.9MB, alloc=212.3MB, time=21.14 memory used=775.0MB, alloc=236.3MB, time=27.34 memory used=906.9MB, alloc=260.3MB, time=35.19 memory used=1062.8MB, alloc=260.3MB, time=44.33 memory used=1218.7MB, alloc=260.3MB, time=53.37 memory used=1374.4MB, alloc=284.3MB, time=62.47 memory used=1554.1MB, alloc=284.3MB, time=72.83 N1 := 6051 > GB := Basis(F, plex(op(vars))); 3 6 6 8 6 10 2 6 GB := [343 x y + 425 x y , 119 x y + 30 x y , 4913 y + 252 x y , 4 2 3 2 2 3 2 2 2 4 17 y + 6 y z, 343 x z + 425 x z , 7 x z - 5 x z , 7 x z + 17 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1736.5MB, alloc=284.3MB, time=82.21 memory used=1838.1MB, alloc=540.3MB, time=85.14 memory used=2041.5MB, alloc=564.3MB, time=90.95 memory used=2261.0MB, alloc=588.3MB, time=98.17 memory used=2483.6MB, alloc=612.3MB, time=109.06 |\^/| 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(); 1428271736 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 4 4 F := [-12 x y - 7, 6 x z - 3 y z, 11 x + 7 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 2 2 G := [17 x y - 6 z , 19 x y - 8 y , -11 x y - 4 y z ] > Problem := [F,G]; 2 2 2 2 3 4 4 Problem := [[-12 x y - 7, 6 x z - 3 y z, 11 x + 7 y ], 2 2 2 2 2 2 2 2 2 [17 x y - 6 z , 19 x y - 8 y , -11 x y - 4 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.2MB, alloc=40.3MB, time=1.02 memory used=60.4MB, alloc=44.3MB, time=1.75 memory used=87.9MB, alloc=44.3MB, time=2.43 memory used=116.7MB, alloc=44.3MB, time=3.30 memory used=142.6MB, alloc=68.3MB, time=4.12 memory used=188.8MB, alloc=92.3MB, time=5.72 N1 := 1069 > GB := Basis(F, plex(op(vars))); 8 6 2 4 2 GB := [1584 x + 343, -132 x + 49 y , -66 x y z + 49 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=250.3MB, alloc=92.3MB, time=8.02 N2 := 441 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 4 4 2 2 2 H := [-12 x y - 7, 6 x z - 3 y z, 7 y + 11 x , 17 y x - 6 z , 2 2 2 2 2 2 19 x y - 8 y , -11 x y - 4 y z ] > J:=[op(GB),op(G)]; 8 6 2 4 2 2 2 2 J := [1584 x + 343, -132 x + 49 y , -66 x y z + 49 z , 17 y x - 6 z , 2 2 2 2 2 2 19 x y - 8 y , -11 x y - 4 y z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 23, 4, 4, 4, 2, 1, 1, 1/2, 1/2, 2/3, 1/3, 6, 14, 31, 8, 8, 2, 2, 1, 5/6, 1/2, 1/2, 7/12, 1/3, 1, -8, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=297.9MB, alloc=92.3MB, time=9.50 |\^/| 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(); 1428271762 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 F := [-x z - 7 x, 19 x y - 14 y z , -14 x - 6 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [11 x y z + 17 y z, -12 x y z + 10 x y, -9 x y - 3] > Problem := [F,G]; 3 2 4 2 Problem := [[-x z - 7 x, 19 x y - 14 y z , -14 x - 6 y z], 2 2 2 2 3 [11 x y z + 17 y z, -12 x y z + 10 x y, -9 x y - 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.88 memory used=48.4MB, alloc=32.3MB, time=1.43 memory used=68.7MB, alloc=32.3MB, time=1.95 memory used=88.4MB, alloc=32.3MB, time=2.45 memory used=109.2MB, alloc=56.3MB, time=3.13 memory used=151.6MB, alloc=60.3MB, time=4.42 memory used=189.4MB, alloc=84.3MB, time=5.58 memory used=246.6MB, alloc=108.3MB, time=7.35 memory used=316.1MB, alloc=132.3MB, time=10.17 memory used=395.4MB, alloc=132.3MB, time=14.66 memory used=474.8MB, alloc=156.3MB, time=19.22 memory used=578.4MB, alloc=180.3MB, time=24.90 N1 := 3171 > GB := Basis(F, plex(op(vars))); 7 4 4 5 2 GB := [19 x - 686 x , 19 x y - 686 x y, -x + 3 x y , x z + 7 x, 4 2 3 2 7 x + 3 z y , -19 x y + 14 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=690.0MB, alloc=188.3MB, time=27.97 memory used=833.7MB, alloc=468.3MB, time=32.39 memory used=979.6MB, alloc=492.3MB, time=39.81 memory used=1135.5MB, alloc=516.3MB, time=48.84 N2 := 3171 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 4 2 2 2 H := [-x z - 7 x, 19 x y - 14 y z , -14 x - 6 y z, 11 x y z + 17 y z, 2 2 3 -12 x y z + 10 x y, -9 x y - 3] > J:=[op(GB),op(G)]; 7 4 4 5 2 4 2 J := [19 x - 686 x , 19 x y - 686 x y, -x + 3 x y , x z + 7 x, 7 x + 3 z y , 3 2 2 2 2 2 3 -19 x y + 14 y z , 11 x y z + 17 y z, -12 x y z + 10 x y, -9 x 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 := [6, 16, 22, 4, 4, 3, 2, 1, 5/6, 5/6, 2/3, 2/3, 1/2, 9, 21, 39, 7, 7, 3, 2, 1, 7/9, 5/9, 7/9, 11/18, 1/3, -5, -17, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1167.7MB, alloc=516.3MB, time=50.54 |\^/| 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(); 1428271891 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 F := [-18 x , -x y z + 8 y z , -15 x y + 18 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 G := [-20 y z - 8 z , 20 x z - 15 x y z, -x y z - 2 x y] > Problem := [F,G]; 4 2 2 3 Problem := [[-18 x , -x y z + 8 y z , -15 x y + 18 y z], 3 3 3 2 2 [-20 y z - 8 z , 20 x z - 15 x y z, -x y z - 2 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, 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=67.3MB, alloc=56.3MB, time=1.93 memory used=106.1MB, alloc=60.3MB, time=2.93 memory used=142.6MB, alloc=84.3MB, time=3.87 memory used=201.4MB, alloc=92.3MB, time=5.44 memory used=259.8MB, alloc=92.3MB, time=6.91 memory used=316.8MB, alloc=116.3MB, time=8.40 memory used=395.9MB, alloc=116.3MB, time=10.43 memory used=471.0MB, alloc=140.3MB, time=12.43 memory used=559.6MB, alloc=396.3MB, time=14.79 memory used=654.1MB, alloc=420.3MB, time=17.24 memory used=772.7MB, alloc=444.3MB, time=20.81 memory used=899.0MB, alloc=468.3MB, time=24.84 memory used=1047.3MB, alloc=492.3MB, time=29.20 memory used=1200.0MB, alloc=516.3MB, time=34.16 memory used=1368.7MB, alloc=540.3MB, time=39.99 memory used=1520.1MB, alloc=564.3MB, time=47.59 memory used=1679.4MB, alloc=588.3MB, time=56.30 memory used=1844.6MB, alloc=612.3MB, time=66.75 memory used=2031.2MB, alloc=636.3MB, time=78.76 memory used=2241.7MB, alloc=660.3MB, time=92.15 memory used=2476.2MB, alloc=684.3MB, time=107.05 memory used=2734.6MB, alloc=708.3MB, time=123.43 |\^/| 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(); 1428272191 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 F := [-4 y + x z, -14 x y + 17 y z , -13 x y z + 7 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 G := [-19 y - 15 x y, -9 + 17 z, -4 z - 17 y z] > Problem := [F,G]; 4 3 3 2 Problem := [[-4 y + x z, -14 x y + 17 y z , -13 x y z + 7 y z ], 3 3 [-19 y - 15 x y, -9 + 17 z, -4 z - 17 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.86 memory used=47.4MB, alloc=32.3MB, time=1.39 memory used=66.9MB, alloc=56.3MB, time=1.91 memory used=106.6MB, alloc=60.3MB, time=2.93 memory used=144.7MB, alloc=60.3MB, time=3.92 memory used=182.2MB, alloc=84.3MB, time=4.86 memory used=227.0MB, alloc=84.3MB, time=6.00 memory used=285.0MB, alloc=116.3MB, time=7.54 memory used=362.6MB, alloc=116.3MB, time=9.51 memory used=425.1MB, alloc=140.3MB, time=10.96 memory used=516.1MB, alloc=420.3MB, time=13.25 memory used=632.0MB, alloc=444.3MB, time=16.86 memory used=757.2MB, alloc=468.3MB, time=20.86 memory used=910.4MB, alloc=492.3MB, time=25.05 memory used=1089.4MB, alloc=516.3MB, time=29.36 memory used=1265.1MB, alloc=540.3MB, time=34.79 memory used=1439.6MB, alloc=564.3MB, time=40.98 memory used=1601.1MB, alloc=588.3MB, time=48.91 memory used=1768.9MB, alloc=612.3MB, time=57.89 memory used=1948.0MB, alloc=636.3MB, time=67.93 memory used=2139.1MB, alloc=660.3MB, time=79.23 memory used=2341.5MB, alloc=684.3MB, time=92.16 memory used=2567.8MB, alloc=708.3MB, time=106.56 memory used=2818.1MB, alloc=732.3MB, time=122.46 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428272491 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [9 y + 18 z, -18 x y - 4 z , 16 x y z - 16 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 G := [-20 x - 16, -6 x y z + 11 x y z , -9 x + 9 y ] > Problem := [F,G]; 3 2 3 2 Problem := [[9 y + 18 z, -18 x y - 4 z , 16 x y z - 16 x z], 2 2 2 4 2 [-20 x - 16, -6 x y z + 11 x y z , -9 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=0.30 memory used=26.3MB, alloc=32.3MB, time=0.87 memory used=47.9MB, alloc=32.3MB, time=1.39 memory used=68.1MB, alloc=32.3MB, time=1.91 memory used=86.8MB, alloc=56.3MB, time=2.42 memory used=125.8MB, alloc=60.3MB, time=3.45 memory used=164.2MB, alloc=60.3MB, time=4.44 memory used=200.7MB, alloc=84.3MB, time=5.41 memory used=258.4MB, alloc=84.3MB, time=6.93 memory used=313.9MB, alloc=108.3MB, time=8.46 memory used=389.6MB, alloc=116.3MB, time=10.52 memory used=464.4MB, alloc=140.3MB, time=12.73 memory used=559.6MB, alloc=164.3MB, time=15.65 memory used=669.7MB, alloc=188.3MB, time=19.09 memory used=790.1MB, alloc=212.3MB, time=23.67 memory used=907.1MB, alloc=236.3MB, time=30.02 memory used=1037.2MB, alloc=260.3MB, time=37.98 memory used=1191.3MB, alloc=284.3MB, time=47.37 memory used=1369.5MB, alloc=308.3MB, time=58.16 N1 := 4799 > GB := Basis(F, plex(op(vars))); 5 3 3 3 3 5 3 9 2 3 GB := [9 x y - x y, 9 x y - x y , x y + 18 x y, y - 36 x y, y + 2 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1550.2MB, alloc=308.3MB, time=66.51 N2 := 1467 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 2 H := [9 y + 18 z, -18 x y - 4 z , 16 x y z - 16 x z, -20 x - 16, 2 2 4 2 -6 x y z + 11 x y z , -9 x + 9 y ] > J:=[op(GB),op(G)]; 5 3 3 3 3 5 3 9 2 3 J := [9 x y - x y, 9 x y - x y , x y + 18 x y, y - 36 x y, y + 2 z, 2 2 2 4 2 -20 x - 16, -6 x y z + 11 x y z , -9 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 := [6, 14, 20, 4, 4, 3, 3, 5/6, 5/6, 2/3, 7/12, 1/2, 1/2, 8, 16, 40, 9, 5, 9, 2, 7/8, 7/8, 1/4, 11/16, 3/4, 3/16, -2, -20, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1742.3MB, alloc=564.3MB, time=74.37 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428272669 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 F := [-15 x - 7 z, 8 x y z + 11 y, 16 x y z + 16] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 2 G := [-9 x y + 4 x z , -8 x y - x y z, 15 x y + 19 y z] > Problem := [F,G]; 4 2 Problem := [[-15 x - 7 z, 8 x y z + 11 y, 16 x y z + 16], 3 2 3 2 2 2 [-9 x y + 4 x z , -8 x y - x y z, 15 x y + 19 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.89 memory used=47.8MB, alloc=32.3MB, time=1.42 memory used=67.0MB, alloc=56.3MB, time=1.95 memory used=108.0MB, alloc=60.3MB, time=3.00 memory used=147.6MB, alloc=84.3MB, time=4.04 memory used=208.2MB, alloc=92.3MB, time=5.64 memory used=267.5MB, alloc=116.3MB, time=7.25 memory used=348.6MB, alloc=116.3MB, time=9.38 memory used=426.0MB, alloc=140.3MB, time=11.43 memory used=519.9MB, alloc=140.3MB, time=13.95 memory used=588.5MB, alloc=420.3MB, time=15.84 memory used=709.6MB, alloc=444.3MB, time=18.95 memory used=851.2MB, alloc=468.3MB, time=22.77 memory used=984.6MB, alloc=468.3MB, time=26.32 memory used=1121.2MB, alloc=492.3MB, time=30.18 memory used=1240.2MB, alloc=492.3MB, time=33.48 memory used=1372.2MB, alloc=516.3MB, time=37.21 memory used=1484.9MB, alloc=516.3MB, time=40.55 memory used=1588.6MB, alloc=540.3MB, time=43.65 memory used=1689.0MB, alloc=540.3MB, time=46.71 memory used=1793.1MB, alloc=564.3MB, time=50.34 memory used=1935.7MB, alloc=564.3MB, time=55.10 memory used=2060.5MB, alloc=588.3MB, time=59.56 memory used=2209.6MB, alloc=612.3MB, time=64.88 memory used=2345.5MB, alloc=636.3MB, time=69.93 memory used=2477.9MB, alloc=660.3MB, time=74.77 memory used=2588.4MB, alloc=684.3MB, time=78.95 memory used=2720.7MB, alloc=708.3MB, time=83.83 memory used=3003.6MB, alloc=732.3MB, time=90.13 memory used=3108.0MB, alloc=756.3MB, time=94.12 memory used=3252.8MB, alloc=756.3MB, time=99.10 memory used=3395.9MB, alloc=780.3MB, time=103.77 memory used=3480.6MB, alloc=804.3MB, time=107.47 memory used=3822.1MB, alloc=828.3MB, time=119.64 |\^/| 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(); 1428272969 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [4 x y - 13 y, 6 x y + 8 x z, -17 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [-16 x z - 18 y z , -2 x y z + 8 y z, 3 x + 10 z] > Problem := [F,G]; 2 2 3 Problem := [[4 x y - 13 y, 6 x y + 8 x z, -17 z], 2 2 2 2 3 2 [-16 x z - 18 y z , -2 x y z + 8 y z, 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=0.31 memory used=26.0MB, alloc=32.3MB, time=0.85 memory used=48.3MB, alloc=32.3MB, time=1.47 memory used=68.3MB, alloc=56.3MB, time=2.09 N1 := 815 > GB := Basis(F, plex(op(vars))); GB := [y, z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.2MB, alloc=56.3MB, time=3.80 N2 := 139 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 2 H := [4 x y - 13 y, 6 x y + 8 x z, -17 z, -16 x z - 18 y z , 2 3 2 -2 x y z + 8 y z, 3 x + 10 z] > J:=[op(GB),op(G)]; 2 2 2 2 3 2 J := [y, z, -16 x z - 18 y z , -2 x y z + 8 y z, 3 x + 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, 14, 19, 4, 3, 3, 2, 5/6, 2/3, 5/6, 1/2, 1/2, 7/12, 5, 10, 12, 4, 2, 3, 2, 3/5, 3/5, 4/5, 3/8, 1/2, 3/4, 4, 7, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=122.8MB, alloc=56.3MB, time=4.17 |\^/| 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(); 1428272979 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 F := [-6 x y z + 10 y z , -11 x - 3 y z, -17 x z + 6 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 G := [-9 x - 3 x y z, 20 x z + 2 x y , 3 x y + 18] > Problem := [F,G]; 2 2 2 3 2 3 Problem := [[-6 x y z + 10 y z , -11 x - 3 y z, -17 x z + 6 z], 3 3 2 3 [-9 x - 3 x y z, 20 x z + 2 x y , 3 x 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=0.31 memory used=26.4MB, alloc=32.3MB, time=0.88 memory used=47.7MB, alloc=32.3MB, time=1.41 memory used=68.1MB, alloc=56.3MB, time=1.95 memory used=108.4MB, alloc=60.3MB, time=3.02 memory used=147.3MB, alloc=84.3MB, time=4.00 memory used=206.7MB, alloc=92.3MB, time=5.57 memory used=265.9MB, alloc=116.3MB, time=7.12 memory used=346.1MB, alloc=116.3MB, time=9.16 memory used=424.4MB, alloc=140.3MB, time=11.27 memory used=524.5MB, alloc=164.3MB, time=14.39 memory used=648.8MB, alloc=188.3MB, time=17.68 memory used=776.0MB, alloc=468.3MB, time=21.74 memory used=916.2MB, alloc=492.3MB, time=26.12 memory used=1072.5MB, alloc=516.3MB, time=30.94 memory used=1238.9MB, alloc=540.3MB, time=37.40 memory used=1393.6MB, alloc=564.3MB, time=45.19 memory used=1557.9MB, alloc=588.3MB, time=54.05 memory used=1728.4MB, alloc=612.3MB, time=64.73 memory used=1921.4MB, alloc=636.3MB, time=76.87 memory used=2138.3MB, alloc=660.3MB, time=90.34 memory used=2379.1MB, alloc=684.3MB, time=105.34 memory used=2644.0MB, alloc=684.3MB, time=121.78 |\^/| 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(); 1428273279 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 4 3 F := [y z + 12 y z , 17 y - 13 z, 11 x + 4 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [2 y + 15 y, -16 x y + 9 x, 17 x - 11 x y] > Problem := [F,G]; 2 2 2 2 4 3 Problem := [[y z + 12 y z , 17 y - 13 z, 11 x + 4 z ], 3 2 3 2 [2 y + 15 y, -16 x y + 9 x, 17 x - 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=0.29 memory used=25.8MB, alloc=32.3MB, time=0.79 memory used=47.6MB, alloc=32.3MB, time=1.33 memory used=68.6MB, alloc=32.3MB, time=1.85 memory used=88.8MB, alloc=56.3MB, time=2.48 memory used=129.4MB, alloc=84.3MB, time=3.81 N1 := 821 > GB := Basis(F, plex(op(vars))); 8 4 4 4 5 4 GB := [24167 x + 58680557568 x , x y + 12 x , 235824 y - 24167 x , 2 -17 y + 13 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=185.5MB, alloc=84.3MB, time=5.64 N2 := 441 #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 4 3 3 2 H := [y z + 12 y z , 17 y - 13 z, 11 x + 4 z , 2 y + 15 y, -16 x y + 9 x, 3 2 17 x - 11 x y] > J:=[op(GB),op(G)]; 8 4 4 4 5 4 J := [24167 x + 58680557568 x , x y + 12 x , 235824 y - 24167 x , 2 3 2 3 2 -17 y + 13 z, 2 y + 15 y, -16 x y + 9 x, 17 x - 11 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 := [6, 11, 19, 4, 4, 3, 3, 1/2, 5/6, 1/2, 5/12, 7/12, 1/3, 7, 12, 29, 8, 8, 5, 1, 5/7, 6/7, 1/7, 9/14, 1/2, 1/14, -1, -10, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=222.4MB, alloc=84.3MB, time=6.82 |\^/| 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(); 1428273298 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 3 2 F := [-7 y z - z , -5 x - 17 x, 17 x z - 17 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 4 2 G := [-5 x y z + 8 x z , 19 x z - 9 x y z , -z + 3 y z ] > Problem := [F,G]; 2 2 4 2 3 2 Problem := [[-7 y z - z , -5 x - 17 x, 17 x z - 17 y z ], 2 2 2 2 2 2 4 2 [-5 x y z + 8 x z , 19 x z - 9 x y z , -z + 3 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.85 memory used=47.8MB, alloc=32.3MB, time=1.36 memory used=67.9MB, alloc=32.3MB, time=1.87 memory used=87.4MB, alloc=56.3MB, time=2.38 memory used=127.5MB, alloc=60.3MB, time=3.41 memory used=167.2MB, alloc=84.3MB, time=4.65 memory used=226.6MB, alloc=84.3MB, time=6.51 memory used=278.0MB, alloc=108.3MB, time=8.46 memory used=340.3MB, alloc=132.3MB, time=12.20 N1 := 1927 > GB := Basis(F, plex(op(vars))); 2 4 3 2 GB := [5 x + 17 x, 109375 x y z + 24137569 x z, -875 x y z + 4913 x z , 2 4 25 y z - 289 x z, 25 z + 2023 x y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=428.3MB, alloc=140.3MB, time=15.68 memory used=520.2MB, alloc=140.3MB, time=18.10 memory used=609.0MB, alloc=164.3MB, time=20.46 memory used=705.6MB, alloc=444.3MB, time=23.07 memory used=842.6MB, alloc=444.3MB, time=26.74 memory used=978.7MB, alloc=468.3MB, time=30.39 memory used=1137.3MB, alloc=468.3MB, time=34.57 memory used=1292.2MB, alloc=492.3MB, time=38.75 memory used=1463.5MB, alloc=516.3MB, time=43.52 memory used=1652.8MB, alloc=540.3MB, time=49.10 memory used=1867.3MB, alloc=564.3MB, time=55.12 memory used=2098.2MB, alloc=588.3MB, time=61.84 memory used=2347.4MB, alloc=612.3MB, time=69.84 memory used=2588.1MB, alloc=636.3MB, time=77.97 memory used=2834.4MB, alloc=660.3MB, time=86.21 memory used=3080.3MB, alloc=684.3MB, time=94.67 memory used=3328.7MB, alloc=708.3MB, time=103.29 memory used=3559.4MB, alloc=732.3MB, time=114.40 |\^/| 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(); 1428273598 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 2 F := [-11 x y - 15 x , -18 x - 6 y , 20 x + 13 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 2 G := [-5 x y + 20 x y z , 17 x y - 12 x y, -12 x y + 10 y z ] > Problem := [F,G]; 2 2 2 3 2 3 2 Problem := [[-11 x y - 15 x , -18 x - 6 y , 20 x + 13 y z ], 2 2 2 3 2 2 2 [-5 x y + 20 x y z , 17 x y - 12 x y, -12 x 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=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=48.0MB, alloc=32.3MB, time=1.41 memory used=68.7MB, alloc=32.3MB, time=1.94 memory used=88.3MB, alloc=56.3MB, time=2.47 memory used=132.0MB, alloc=60.3MB, time=3.81 memory used=173.1MB, alloc=84.3MB, time=5.08 memory used=233.7MB, alloc=108.3MB, time=6.99 memory used=306.1MB, alloc=108.3MB, time=10.63 N1 := 1895 > GB := Basis(F, plex(op(vars))); 5 2 3 2 2 2 2 2 3 GB := [11 x - 5 x , 3 x + y , 39 x z - 20 x y, 13 z y + 20 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=373.7MB, alloc=108.3MB, time=14.02 memory used=446.2MB, alloc=116.3MB, time=15.97 memory used=520.7MB, alloc=140.3MB, time=18.20 memory used=621.2MB, alloc=164.3MB, time=21.32 memory used=726.7MB, alloc=188.3MB, time=26.99 N2 := 2165 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 2 3 2 2 2 H := [-11 x y - 15 x , -18 x - 6 y , 13 z y + 20 x , -5 x y + 20 x y z , 3 2 2 2 17 x y - 12 x y, -12 x y + 10 y z ] > J:=[op(GB),op(G)]; 5 2 3 2 2 2 2 2 3 J := [11 x - 5 x , 3 x + y , 39 x z - 20 x y, 13 z y + 20 x , 2 2 2 3 2 2 2 -5 x y + 20 x y z , 17 x y - 12 x y, -12 x y + 10 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 := [6, 15, 21, 4, 3, 3, 2, 1, 1, 1/2, 3/4, 3/4, 1/4, 7, 17, 26, 5, 5, 3, 2, 1, 6/7, 4/7, 11/14, 9/14, 2/7, -2, -5, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=788.8MB, alloc=188.3MB, time=30.59 |\^/| 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(); 1428273684 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 2 3 F := [-10 x z - x , 4 y - 20 z , -10 x y z - 11 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [8 z , 7 y z + 10 x z, 19 x z + 16 y z] > Problem := [F,G]; 3 3 3 3 2 3 Problem := [[-10 x z - x , 4 y - 20 z , -10 x y z - 11 y ], 2 2 2 2 3 2 [8 z , 7 y z + 10 x z, 19 x z + 16 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.31 memory used=27.3MB, alloc=32.3MB, time=0.91 memory used=48.7MB, alloc=36.3MB, time=1.49 memory used=69.8MB, alloc=60.3MB, time=2.05 memory used=113.0MB, alloc=60.3MB, time=3.12 memory used=153.3MB, alloc=84.3MB, time=4.20 memory used=213.9MB, alloc=92.3MB, time=5.81 memory used=273.3MB, alloc=116.3MB, time=7.32 memory used=347.0MB, alloc=116.3MB, time=9.13 memory used=418.8MB, alloc=372.3MB, time=10.85 memory used=498.1MB, alloc=396.3MB, time=12.95 memory used=610.2MB, alloc=420.3MB, time=15.42 memory used=744.8MB, alloc=420.3MB, time=18.31 memory used=878.4MB, alloc=444.3MB, time=20.92 memory used=1012.9MB, alloc=468.3MB, time=24.19 memory used=1142.5MB, alloc=492.3MB, time=27.29 memory used=1317.2MB, alloc=516.3MB, time=32.95 memory used=1493.5MB, alloc=540.3MB, time=38.77 memory used=1680.4MB, alloc=564.3MB, time=45.05 memory used=1878.4MB, alloc=588.3MB, time=51.78 memory used=2071.5MB, alloc=612.3MB, time=58.51 memory used=2258.4MB, alloc=636.3MB, time=64.88 memory used=2422.1MB, alloc=660.3MB, time=70.68 memory used=2606.5MB, alloc=684.3MB, time=78.98 memory used=2826.2MB, alloc=708.3MB, time=91.02 memory used=3049.5MB, alloc=732.3MB, time=104.18 memory used=3282.0MB, alloc=756.3MB, time=118.45 |\^/| 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(); 1428273984 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 F := [-12 x y z + 14 x y z, -6 x z + 14, -3 y - 14 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 G := [-10 z - 17 z, 16 x + 14 z, -3 x y - 3 y z] > Problem := [F,G]; 2 4 2 Problem := [[-12 x y z + 14 x y z, -6 x z + 14, -3 y - 14 y ], 4 3 [-10 z - 17 z, 16 x + 14 z, -3 x y - 3 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.0MB, alloc=32.3MB, time=0.83 memory used=46.9MB, alloc=32.3MB, time=1.35 memory used=67.1MB, alloc=32.3MB, time=1.87 memory used=87.1MB, alloc=56.3MB, time=2.53 memory used=127.9MB, alloc=56.3MB, time=3.76 memory used=164.1MB, alloc=80.3MB, time=4.92 memory used=194.4MB, alloc=84.3MB, time=5.95 memory used=242.0MB, alloc=108.3MB, time=8.30 memory used=308.9MB, alloc=108.3MB, time=12.04 N1 := 2247 > GB := Basis(F, plex(op(vars))); 4 2 GB := [x y - 2 y, 3 y + 14 y , 3 z x - 7, 6 y z - 7 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=376.3MB, alloc=108.3MB, time=14.93 memory used=449.6MB, alloc=140.3MB, time=17.12 memory used=547.4MB, alloc=164.3MB, time=20.30 memory used=649.6MB, alloc=188.3MB, time=25.95 N2 := 2247 #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 4 2 4 H := [-12 x y z + 14 x y z, -6 x z + 14, -3 y - 14 y , -10 z - 17 z, 3 16 x + 14 z, -3 x y - 3 y z] > J:=[op(GB),op(G)]; 4 2 4 J := [x y - 2 y, 3 y + 14 y , 3 z x - 7, 6 y z - 7 y, -10 z - 17 z, 3 16 x + 14 z, -3 x y - 3 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 := [6, 12, 19, 4, 1, 4, 4, 2/3, 1/2, 5/6, 5/12, 1/2, 7/12, 7, 13, 19, 4, 1, 4, 4, 4/7, 4/7, 5/7, 2/7, 4/7, 3/7, -1, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=701.8MB, alloc=188.3MB, time=28.77 |\^/| 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(); 1428274055 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 2 3 F := [-17 x y z + 9 x , -19 x y + x z, 14 x z - 14 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 3 2 G := [-3 x y z - 10 x z , 2 x + 11 x y z, -9 x y - 17 x y z] > Problem := [F,G]; 2 3 3 3 2 2 3 Problem := [[-17 x y z + 9 x , -19 x y + x z, 14 x z - 14 z ], 2 3 4 2 3 2 [-3 x y z - 10 x z , 2 x + 11 x y z, -9 x y - 17 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.89 memory used=47.5MB, alloc=32.3MB, time=1.43 memory used=67.2MB, alloc=56.3MB, time=1.95 memory used=109.1MB, alloc=60.3MB, time=3.02 memory used=148.0MB, alloc=60.3MB, time=4.02 memory used=185.4MB, alloc=84.3MB, time=5.00 memory used=233.8MB, alloc=84.3MB, time=6.32 memory used=291.5MB, alloc=116.3MB, time=7.84 memory used=364.9MB, alloc=372.3MB, time=9.75 memory used=442.4MB, alloc=396.3MB, time=11.79 memory used=546.1MB, alloc=420.3MB, time=14.40 memory used=668.2MB, alloc=444.3MB, time=17.54 memory used=806.8MB, alloc=468.3MB, time=21.08 memory used=944.2MB, alloc=492.3MB, time=24.90 memory used=1061.0MB, alloc=516.3MB, time=28.14 memory used=1149.7MB, alloc=516.3MB, time=30.70 memory used=1299.4MB, alloc=540.3MB, time=35.85 memory used=1478.7MB, alloc=564.3MB, time=42.02 memory used=1649.2MB, alloc=588.3MB, time=47.74 memory used=1804.3MB, alloc=612.3MB, time=53.29 memory used=1988.1MB, alloc=636.3MB, time=62.15 memory used=2195.1MB, alloc=660.3MB, time=73.60 memory used=2404.8MB, alloc=684.3MB, time=86.69 memory used=2625.9MB, alloc=708.3MB, time=101.39 memory used=2870.9MB, alloc=732.3MB, time=117.73 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428274355 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 2 F := [-15 y z + 17, 11 y - 12 z , -16 x y z + 3 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 3 2 G := [9 x y - 7 y , 20 y + 9 x z, -2 x y - 17 y z ] > Problem := [F,G]; 2 2 4 3 2 Problem := [[-15 y z + 17, 11 y - 12 z , -16 x y z + 3 x z], 2 3 4 2 3 2 [9 x y - 7 y , 20 y + 9 x z, -2 x y - 17 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.88 memory used=48.9MB, alloc=32.3MB, time=1.45 memory used=69.8MB, alloc=32.3MB, time=1.99 memory used=90.1MB, alloc=56.3MB, time=2.54 memory used=131.4MB, alloc=60.3MB, time=3.62 memory used=172.1MB, alloc=84.3MB, time=4.71 memory used=211.3MB, alloc=84.3MB, time=5.73 memory used=273.9MB, alloc=92.3MB, time=7.33 memory used=334.2MB, alloc=116.3MB, time=8.90 memory used=418.8MB, alloc=116.3MB, time=11.06 memory used=494.4MB, alloc=396.3MB, time=13.01 memory used=600.2MB, alloc=420.3MB, time=15.70 memory used=732.3MB, alloc=444.3MB, time=19.51 memory used=877.6MB, alloc=468.3MB, time=23.60 memory used=1029.3MB, alloc=492.3MB, time=28.36 memory used=1193.8MB, alloc=516.3MB, time=33.55 memory used=1370.6MB, alloc=540.3MB, time=39.13 memory used=1576.0MB, alloc=564.3MB, time=44.33 memory used=1766.4MB, alloc=588.3MB, time=50.98 memory used=1945.4MB, alloc=612.3MB, time=59.57 memory used=2127.9MB, alloc=636.3MB, time=69.30 memory used=2320.4MB, alloc=660.3MB, time=80.08 memory used=2523.9MB, alloc=684.3MB, time=92.03 memory used=2737.1MB, alloc=708.3MB, time=105.76 |\^/| 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(); 1428274656 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [19 x y z - 15 z , 8 x y - 10 y, 3 x z + 12 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 3 G := [-6 x z - 11 y, 2 x + 4 x y z, -6 x y - 7 z ] > Problem := [F,G]; 2 2 2 3 2 Problem := [[19 x y z - 15 z , 8 x y - 10 y, 3 x z + 12 x y ], 3 4 2 3 [-6 x z - 11 y, 2 x + 4 x y z, -6 x 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=4.2MB, alloc=32.3MB, time=0.30 memory used=26.9MB, alloc=32.3MB, time=0.87 memory used=48.0MB, alloc=32.3MB, time=1.39 memory used=68.3MB, alloc=56.3MB, time=1.92 memory used=110.7MB, alloc=60.3MB, time=2.96 memory used=144.9MB, alloc=60.3MB, time=3.76 memory used=186.8MB, alloc=92.3MB, time=4.84 memory used=250.3MB, alloc=92.3MB, time=6.38 memory used=310.0MB, alloc=116.3MB, time=7.90 memory used=386.0MB, alloc=372.3MB, time=9.79 memory used=469.6MB, alloc=396.3MB, time=11.77 memory used=583.6MB, alloc=420.3MB, time=14.28 memory used=709.6MB, alloc=444.3MB, time=17.44 memory used=831.9MB, alloc=444.3MB, time=20.36 memory used=962.3MB, alloc=468.3MB, time=23.61 memory used=1078.5MB, alloc=492.3MB, time=26.62 memory used=1189.7MB, alloc=492.3MB, time=29.35 memory used=1279.7MB, alloc=492.3MB, time=31.67 memory used=1376.5MB, alloc=516.3MB, time=34.32 memory used=1453.9MB, alloc=516.3MB, time=36.36 memory used=1518.5MB, alloc=516.3MB, time=38.31 memory used=1582.5MB, alloc=516.3MB, time=40.54 memory used=1678.0MB, alloc=540.3MB, time=44.03 memory used=1785.3MB, alloc=564.3MB, time=48.02 memory used=1880.9MB, alloc=564.3MB, time=51.66 memory used=1978.0MB, alloc=588.3MB, time=55.43 memory used=2052.8MB, alloc=588.3MB, time=58.38 memory used=2154.5MB, alloc=612.3MB, time=61.67 memory used=2231.1MB, alloc=612.3MB, time=64.67 memory used=2322.0MB, alloc=636.3MB, time=68.26 memory used=2400.1MB, alloc=636.3MB, time=71.57 memory used=2649.9MB, alloc=660.3MB, time=79.81 memory used=2878.8MB, alloc=684.3MB, time=91.55 memory used=3102.4MB, alloc=708.3MB, time=104.48 |\^/| 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(); 1428274956 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 3 2 2 F := [-15 x - 12 y z, -2 y z - 3 x , 5 x y - 3 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [9 x y z + 17 x y z, 15 y - 7 z, -13 x z + 8 y z ] > Problem := [F,G]; 4 3 3 3 2 2 Problem := [[-15 x - 12 y z, -2 y z - 3 x , 5 x y - 3 x z ], 2 2 3 2 2 [9 x y z + 17 x y z, 15 y - 7 z, -13 x z + 8 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.87 memory used=48.4MB, alloc=32.3MB, time=1.41 memory used=69.1MB, alloc=56.3MB, time=1.96 memory used=110.2MB, alloc=60.3MB, time=3.00 memory used=148.3MB, alloc=84.3MB, time=4.00 memory used=208.4MB, alloc=92.3MB, time=5.60 memory used=270.0MB, alloc=116.3MB, time=7.08 memory used=349.9MB, alloc=116.3MB, time=8.98 memory used=427.3MB, alloc=396.3MB, time=10.85 memory used=530.7MB, alloc=420.3MB, time=13.54 memory used=661.7MB, alloc=444.3MB, time=16.70 memory used=790.1MB, alloc=468.3MB, time=19.62 memory used=918.1MB, alloc=492.3MB, time=22.75 memory used=1028.9MB, alloc=492.3MB, time=25.30 memory used=1138.6MB, alloc=492.3MB, time=28.12 memory used=1232.2MB, alloc=516.3MB, time=30.50 memory used=1328.9MB, alloc=516.3MB, time=33.13 memory used=1407.0MB, alloc=516.3MB, time=35.23 memory used=1478.8MB, alloc=516.3MB, time=37.37 memory used=1546.8MB, alloc=516.3MB, time=39.51 memory used=1604.8MB, alloc=516.3MB, time=41.46 memory used=1661.1MB, alloc=516.3MB, time=43.16 memory used=1719.6MB, alloc=540.3MB, time=45.30 memory used=1765.0MB, alloc=540.3MB, time=47.13 memory used=1807.3MB, alloc=540.3MB, time=48.74 memory used=2020.3MB, alloc=564.3MB, time=54.62 memory used=2212.2MB, alloc=588.3MB, time=59.55 memory used=2471.8MB, alloc=612.3MB, time=67.83 memory used=2698.4MB, alloc=636.3MB, time=76.02 memory used=2930.5MB, alloc=660.3MB, time=84.43 memory used=3168.2MB, alloc=684.3MB, time=93.22 memory used=3410.1MB, alloc=708.3MB, time=102.18 memory used=3680.7MB, alloc=732.3MB, time=110.96 memory used=3909.8MB, alloc=756.3MB, time=119.37 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428275256 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 F := [-7 y z - 17 z , -16 x y z - 12 x z , 14 z + x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 2 G := [-6 y z - 3 x z, -x y z + 5 z , -17 x y + 15 x y z ] > Problem := [F,G]; 2 2 2 2 3 Problem := [[-7 y z - 17 z , -16 x y z - 12 x z , 14 z + x y], 2 2 4 3 2 [-6 y z - 3 x z, -x y z + 5 z , -17 x y + 15 x y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=47.6MB, alloc=32.3MB, time=1.37 memory used=68.4MB, alloc=32.3MB, time=1.91 memory used=88.8MB, alloc=32.3MB, time=2.44 memory used=108.1MB, alloc=56.3MB, time=2.96 memory used=147.3MB, alloc=60.3MB, time=4.00 memory used=183.7MB, alloc=84.3MB, time=4.98 memory used=243.9MB, alloc=116.3MB, time=6.81 memory used=325.5MB, alloc=140.3MB, time=9.31 memory used=424.1MB, alloc=164.3MB, time=12.38 memory used=538.4MB, alloc=188.3MB, time=15.95 memory used=668.1MB, alloc=212.3MB, time=20.00 memory used=776.9MB, alloc=492.3MB, time=23.53 memory used=920.7MB, alloc=516.3MB, time=29.66 memory used=1064.3MB, alloc=540.3MB, time=36.89 memory used=1218.2MB, alloc=564.3MB, time=45.22 memory used=1381.3MB, alloc=588.3MB, time=55.30 memory used=1566.7MB, alloc=612.3MB, time=66.76 memory used=1776.0MB, alloc=636.3MB, time=79.58 memory used=2009.2MB, alloc=636.3MB, time=93.72 memory used=2242.4MB, alloc=636.3MB, time=107.88 memory used=2475.6MB, alloc=660.3MB, time=122.04 |\^/| 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(); 1428275556 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 4 F := [15 y + 7 z , 5 x + 10 x y, 19 z - 17 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 2 G := [-6 x y z + 18 z , 18 x + 10 x y z , 15 x y - 10 y] > Problem := [F,G]; 2 2 4 2 4 Problem := [[15 y + 7 z , 5 x + 10 x y, 19 z - 17 x], 2 3 4 2 2 [-6 x y z + 18 z , 18 x + 10 x y z , 15 x y - 10 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.84 memory used=47.7MB, alloc=32.3MB, time=1.36 memory used=68.1MB, alloc=32.3MB, time=1.88 memory used=87.6MB, alloc=56.3MB, time=2.37 memory used=128.0MB, alloc=60.3MB, time=3.38 memory used=168.0MB, alloc=84.3MB, time=4.39 memory used=215.9MB, alloc=84.3MB, time=5.71 memory used=278.4MB, alloc=108.3MB, time=7.53 memory used=375.7MB, alloc=108.3MB, time=9.22 memory used=454.7MB, alloc=140.3MB, time=11.63 memory used=552.1MB, alloc=140.3MB, time=14.55 memory used=638.8MB, alloc=164.3MB, time=17.44 memory used=732.4MB, alloc=188.3MB, time=21.55 memory used=833.7MB, alloc=212.3MB, time=27.32 memory used=957.2MB, alloc=236.3MB, time=34.50 memory used=1104.8MB, alloc=236.3MB, time=43.03 memory used=1252.4MB, alloc=260.3MB, time=51.74 N1 := 4689 > GB := Basis(F, plex(op(vars))); 10 3 4 2 4 2 2 GB := [4275 x - 13328 x , x + 2 x y, 4275 y - 833 x, 7 z + 15 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1419.6MB, alloc=260.3MB, time=58.98 N2 := 1179 #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 4 2 4 2 3 H := [7 z + 15 y , 5 x + 10 x y, 19 z - 17 x, -6 x y z + 18 z , 4 2 2 18 x + 10 x y z , 15 x y - 10 y] > J:=[op(GB),op(G)]; 10 3 4 2 4 2 2 J := [4275 x - 13328 x , x + 2 x y, 4275 y - 833 x, 7 z + 15 y , 2 3 4 2 2 -6 x y z + 18 z , 18 x + 10 x y z , 15 x y - 10 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 21, 4, 4, 2, 4, 5/6, 5/6, 2/3, 7/12, 1/2, 5/12, 7, 15, 31, 10, 10, 4, 3, 6/7, 6/7, 3/7, 9/14, 1/2, 2/7, -1, -10, -6] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1557.7MB, alloc=516.3MB, time=64.54 |\^/| 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(); 1428275723 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 3 2 F := [11 x y - 3 x z , 9 x y - 20 y , -11 x y + 19 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 G := [11 y + 12 x, -15 y z - 14, x y - 18 x z] > Problem := [F,G]; 2 2 3 4 3 2 Problem := [[11 x y - 3 x z , 9 x y - 20 y , -11 x y + 19 x ], 3 [11 y + 12 x, -15 y z - 14, x y - 18 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.85 memory used=47.5MB, alloc=32.3MB, time=1.40 memory used=68.0MB, alloc=32.3MB, time=1.91 memory used=88.4MB, alloc=56.3MB, time=2.57 memory used=130.6MB, alloc=60.3MB, time=3.86 memory used=168.3MB, alloc=84.3MB, time=5.05 memory used=223.3MB, alloc=108.3MB, time=7.44 memory used=292.9MB, alloc=108.3MB, time=11.44 N1 := 1835 > GB := Basis(F, plex(op(vars))); 4 2 3 2 3 4 2 2 GB := [99 x - 380 x , -9 x + 20 x y, -9 x y + 20 y , -11 x y + 3 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=362.3MB, alloc=116.3MB, time=13.58 memory used=442.1MB, alloc=140.3MB, time=16.52 N2 := 1227 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 4 3 2 3 H := [11 x y - 3 x z , 9 x y - 20 y , -11 x y + 19 x , 11 y + 12 x, -15 y z - 14, x y - 18 x z] > J:=[op(GB),op(G)]; 4 2 3 2 3 4 2 2 J := [99 x - 380 x , -9 x + 20 x y, -9 x y + 20 y , -11 x y + 3 x z , 3 11 y + 12 x, -15 y z - 14, x y - 18 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 := [6, 14, 18, 4, 3, 4, 2, 5/6, 1, 1/2, 2/3, 7/12, 1/4, 7, 15, 21, 4, 4, 4, 2, 6/7, 6/7, 3/7, 5/7, 1/2, 3/14, -1, -3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=473.9MB, alloc=140.3MB, time=18.33 |\^/| 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(); 1428275769 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 F := [16 x z - 9 y z, 2 y z + 8 z, -19 z - 9 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 2 G := [-11 x y - 5 z , 11 y - 19 z , 11 y z + 3 y z] > Problem := [F,G]; 2 2 2 4 2 Problem := [[16 x z - 9 y z, 2 y z + 8 z, -19 z - 9 x ], 2 2 3 2 2 2 2 2 [-11 x y - 5 z , 11 y - 19 z , 11 y z + 3 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.85 memory used=48.1MB, alloc=32.3MB, time=1.40 memory used=68.6MB, alloc=32.3MB, time=1.93 memory used=87.9MB, alloc=56.3MB, time=2.45 memory used=126.7MB, alloc=60.3MB, time=3.49 memory used=163.3MB, alloc=60.3MB, time=4.46 memory used=199.1MB, alloc=84.3MB, time=5.41 memory used=256.3MB, alloc=84.3MB, time=6.93 memory used=312.4MB, alloc=116.3MB, time=8.44 memory used=389.7MB, alloc=116.3MB, time=10.50 memory used=463.9MB, alloc=140.3MB, time=12.50 memory used=559.5MB, alloc=164.3MB, time=15.16 memory used=655.5MB, alloc=420.3MB, time=17.74 memory used=768.1MB, alloc=444.3MB, time=21.13 memory used=897.7MB, alloc=468.3MB, time=25.23 memory used=1028.5MB, alloc=492.3MB, time=31.42 memory used=1162.5MB, alloc=516.3MB, time=39.36 memory used=1320.7MB, alloc=540.3MB, time=48.73 N1 := 3565 > GB := Basis(F, plex(op(vars))); 12 2 2 2 2 8 GB := [4096 x + 13851 x , x y + 4 x , 256 x y + 1539 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1505.8MB, alloc=540.3MB, time=54.14 memory used=1736.4MB, alloc=564.3MB, time=61.93 memory used=1941.1MB, alloc=588.3MB, time=73.95 memory used=2156.7MB, alloc=612.3MB, time=87.43 N2 := 4405 #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 4 2 2 2 3 H := [16 x z - 9 y z, 2 y z + 8 z, -19 z - 9 x , -11 x y - 5 z , 2 2 2 2 2 -19 z + 11 y , 11 y z + 3 y z] > J:=[op(GB),op(G)]; 12 2 2 2 2 8 2 2 3 J := [4096 x + 13851 x , x y + 4 x , 256 y x + 1539 z, -11 x y - 5 z , 2 2 2 2 2 -19 z + 11 y , 11 y z + 3 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 := [6, 14, 21, 4, 2, 2, 4, 1/2, 5/6, 1, 1/4, 1/2, 3/4, 6, 13, 35, 12, 12, 2, 3, 2/3, 5/6, 2/3, 1/2, 1/2, 5/12, 1, -14, -8] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2328.9MB, alloc=612.3MB, time=97.58 |\^/| 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(); 1428276019 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 F := [11 y z + 14 z, -19 x y + 19 y , 7 y z - 9 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 2 G := [20 y z , 8 x y + 15 y , 5 z + 12 x] > Problem := [F,G]; 2 2 3 3 2 Problem := [[11 y z + 14 z, -19 x y + 19 y , 7 y z - 9 y z ], 3 3 4 2 [20 y z , 8 x y + 15 y , 5 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=25.9MB, alloc=32.3MB, time=0.83 memory used=48.5MB, alloc=32.3MB, time=1.51 N1 := 285 > GB := Basis(F, plex(op(vars))); 2 3 2 2 3 2 GB := [-x y + y , 11 x z + 14 z, 11 y z + 14 z, 7 z - 9 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=66.3MB, alloc=32.3MB, time=1.98 memory used=86.0MB, alloc=56.3MB, time=2.56 N2 := 285 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 2 3 H := [11 y z + 14 z, -19 x y + 19 y , 7 y z - 9 y z , 20 y z , 3 4 2 8 x y + 15 y , 5 z + 12 x] > J:=[op(GB),op(G)]; 2 3 2 2 3 2 3 J := [-x y + y , 11 x z + 14 z, 11 y z + 14 z, 7 z - 9 z , 20 y z , 3 4 2 8 x y + 15 y , 5 z + 12 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, 20, 4, 3, 4, 3, 1/2, 5/6, 2/3, 3/13, 8/13, 6/13, 7, 13, 22, 4, 3, 4, 3, 4/7, 4/7, 5/7, 4/15, 2/5, 8/15, -1, -2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=96.6MB, alloc=56.3MB, time=2.90 |\^/| 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(); 1428314142 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [7 x y z - 3 y, 7 x z - 4 y z, -15 x + 16 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 G := [12 y z - 17 x z , -17 y z - 12 y, -4 x y + 13 x z] > Problem := [F,G]; 2 2 2 3 Problem := [[7 x y z - 3 y, 7 x z - 4 y z, -15 x + 16 x y], 3 2 2 2 2 2 [12 y z - 17 x z , -17 y z - 12 y, -4 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=0.17 memory used=26.7MB, alloc=32.3MB, time=0.48 memory used=47.4MB, alloc=32.3MB, time=0.77 memory used=67.8MB, alloc=32.3MB, time=1.06 memory used=86.9MB, alloc=56.3MB, time=1.35 memory used=127.0MB, alloc=60.3MB, time=1.92 memory used=164.4MB, alloc=60.3MB, time=2.49 memory used=201.3MB, alloc=84.3MB, time=3.06 memory used=258.8MB, alloc=92.3MB, time=4.00 memory used=315.1MB, alloc=116.3MB, time=4.85 memory used=393.6MB, alloc=116.3MB, time=6.07 memory used=470.4MB, alloc=140.3MB, time=7.33 memory used=565.3MB, alloc=140.3MB, time=8.93 memory used=647.1MB, alloc=420.3MB, time=10.26 memory used=761.1MB, alloc=444.3MB, time=12.46 memory used=885.7MB, alloc=468.3MB, time=14.84 memory used=1022.3MB, alloc=492.3MB, time=17.38 memory used=1171.0MB, alloc=516.3MB, time=20.10 memory used=1329.4MB, alloc=540.3MB, time=23.19 memory used=1497.2MB, alloc=564.3MB, time=26.47 memory used=1672.9MB, alloc=588.3MB, time=30.26 memory used=1840.1MB, alloc=612.3MB, time=35.60 memory used=2013.9MB, alloc=636.3MB, time=41.68 memory used=2199.0MB, alloc=660.3MB, time=48.48 memory used=2397.8MB, alloc=684.3MB, time=56.36 memory used=2610.2MB, alloc=708.3MB, time=64.96 memory used=2831.9MB, alloc=732.3MB, time=75.06 memory used=3077.7MB, alloc=756.3MB, time=85.90 memory used=3347.3MB, alloc=780.3MB, time=98.06 memory used=3641.0MB, alloc=804.3MB, time=111.64 memory used=3958.5MB, alloc=828.3MB, time=125.42 memory used=4300.0MB, alloc=852.3MB, time=139.80 memory used=4665.5MB, alloc=876.3MB, time=155.91 memory used=5054.8MB, alloc=876.3MB, time=173.18 memory used=5444.2MB, alloc=876.3MB, time=191.04 memory used=5833.4MB, alloc=876.3MB, time=207.64 memory used=6222.7MB, alloc=900.3MB, time=224.36 memory used=6635.9MB, alloc=900.3MB, time=241.62 memory used=7048.8MB, alloc=900.3MB, time=259.08 |\^/| 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(); 1428314442 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 F := [5 x y z + 18 z, 20 y z - 7, -19 x + 13 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [-17 x z + 3 y, 14 x y - 19 x y, 16 x y + 3] > Problem := [F,G]; 2 4 Problem := [[5 x y z + 18 z, 20 y z - 7, -19 x + 13 z], 2 2 3 [-17 x z + 3 y, 14 x y - 19 x y, 16 x y + 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.49 memory used=47.8MB, alloc=32.3MB, time=0.82 memory used=68.8MB, alloc=32.3MB, time=1.13 memory used=88.8MB, alloc=56.3MB, time=1.45 memory used=135.9MB, alloc=60.3MB, time=2.19 memory used=176.8MB, alloc=84.3MB, time=2.90 memory used=238.5MB, alloc=84.3MB, time=3.94 memory used=295.2MB, alloc=108.3MB, time=5.03 memory used=362.7MB, alloc=132.3MB, time=7.21 memory used=447.2MB, alloc=132.3MB, time=10.23 N1 := 2305 > GB := Basis(F, plex(op(vars))); 2 GB := [24624 x - 455, 2275 y + 443232 x, 31912704 z - 15925] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=535.9MB, alloc=140.3MB, time=12.02 N2 := 465 #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 4 2 H := [5 x y z + 18 z, 20 z y - 7, -19 x + 13 z, -17 x z + 3 y, 2 3 14 x y - 19 x y, 16 y x + 3] > J:=[op(GB),op(G)]; 2 2 J := [24624 x - 455, 2275 y + 443232 x, 31912704 z - 15925, -17 x z + 3 y, 2 3 14 x y - 19 x y, 16 y x + 3] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 20, 4, 4, 3, 2, 5/6, 5/6, 2/3, 1/2, 1/2, 5/12, 6, 11, 14, 4, 2, 3, 2, 5/6, 2/3, 1/3, 1/2, 5/12, 1/6, 3, 6, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=541.9MB, alloc=140.3MB, time=12.19 |\^/| 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(); 1428314456 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 2 F := [18 y z - 5 y, 9 x z - 6 x , 12 x z - 18 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 G := [16 y z + 4 z , 16 x y + 2 x y , -10 y z - 6 x ] > Problem := [F,G]; 2 2 3 2 2 2 2 2 Problem := [[18 y z - 5 y, 9 x z - 6 x , 12 x z - 18 y z ], 2 2 2 2 2 3 2 [16 y z + 4 z , 16 x y + 2 x y , -10 y z - 6 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.51 memory used=47.9MB, alloc=32.3MB, time=0.81 memory used=67.4MB, alloc=56.3MB, time=1.14 memory used=110.0MB, alloc=60.3MB, time=1.71 memory used=150.6MB, alloc=84.3MB, time=2.30 memory used=213.2MB, alloc=92.3MB, time=3.19 memory used=273.7MB, alloc=92.3MB, time=4.08 memory used=334.4MB, alloc=116.3MB, time=4.88 memory used=411.7MB, alloc=396.3MB, time=6.00 memory used=517.2MB, alloc=420.3MB, time=7.82 memory used=631.4MB, alloc=444.3MB, time=9.83 memory used=761.4MB, alloc=468.3MB, time=12.09 memory used=903.3MB, alloc=492.3MB, time=14.64 memory used=1053.4MB, alloc=516.3MB, time=17.84 memory used=1199.2MB, alloc=540.3MB, time=22.28 memory used=1353.8MB, alloc=564.3MB, time=27.43 memory used=1516.5MB, alloc=588.3MB, time=33.63 memory used=1699.0MB, alloc=612.3MB, time=40.79 memory used=1905.4MB, alloc=636.3MB, time=48.80 memory used=2135.8MB, alloc=660.3MB, time=57.75 memory used=2390.1MB, alloc=660.3MB, time=67.54 memory used=2644.4MB, alloc=660.3MB, time=77.28 memory used=2898.7MB, alloc=684.3MB, time=87.43 memory used=3176.9MB, alloc=684.3MB, time=98.17 memory used=3455.0MB, alloc=708.3MB, time=108.79 memory used=3757.1MB, alloc=732.3MB, time=120.34 N1 := 9507 > GB := Basis(F, plex(op(vars))); 13 3 6 10 3 GB := [1990656 x - 15625 x , -1152 x + 125 y, -13824 x + 625 x z, 6 2 2 3 2 -96 x + 25 x z , 3 x z - 2 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3949.5MB, alloc=732.3MB, time=124.61 memory used=4090.4MB, alloc=732.3MB, time=127.07 memory used=4213.0MB, alloc=732.3MB, time=129.17 memory used=4329.5MB, alloc=732.3MB, time=131.08 memory used=4443.2MB, alloc=732.3MB, time=133.05 memory used=4556.7MB, alloc=732.3MB, time=135.15 memory used=4726.9MB, alloc=732.3MB, time=138.68 memory used=4908.8MB, alloc=756.3MB, time=142.53 memory used=5089.0MB, alloc=780.3MB, time=146.39 memory used=5280.6MB, alloc=804.3MB, time=150.76 memory used=5424.7MB, alloc=828.3MB, time=154.38 memory used=5600.9MB, alloc=852.3MB, time=160.37 memory used=5894.9MB, alloc=876.3MB, time=171.22 memory used=6113.0MB, alloc=900.3MB, time=179.99 memory used=6491.5MB, alloc=924.3MB, time=195.91 memory used=6880.3MB, alloc=948.3MB, time=212.93 memory used=7293.1MB, alloc=972.3MB, time=230.77 memory used=7729.8MB, alloc=996.3MB, time=249.61 memory used=8190.4MB, alloc=1020.3MB, time=269.42 |\^/| 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(); 1428314756 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 2 F := [19 x y z - 17 y z , 9 z + 15, 19 x y - 14 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 2 G := [-7 y z - 16 y z, -7 x y - 16 x y z , -19 x y + 3 x z] > Problem := [F,G]; 2 3 4 2 2 Problem := [[19 x y z - 17 y z , 9 z + 15, 19 x y - 14 y ], 3 2 2 2 2 3 2 [-7 y z - 16 y z, -7 x y - 16 x y z , -19 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=26.1MB, alloc=32.3MB, time=0.48 memory used=47.5MB, alloc=32.3MB, time=0.78 memory used=67.6MB, alloc=32.3MB, time=1.08 memory used=86.5MB, alloc=56.3MB, time=1.37 memory used=125.3MB, alloc=60.3MB, time=1.96 memory used=162.9MB, alloc=84.3MB, time=2.60 memory used=223.9MB, alloc=84.3MB, time=3.69 memory used=277.1MB, alloc=108.3MB, time=4.67 memory used=342.5MB, alloc=132.3MB, time=6.76 N1 := 1897 > GB := Basis(F, plex(op(vars))); 4 2 2 4 GB := [390963 x y + 417605 y, -19 x y + 14 y , -19 x y + 17 y z, 3 z + 5] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=427.6MB, alloc=132.3MB, time=9.04 memory used=522.3MB, alloc=140.3MB, time=10.47 memory used=619.1MB, alloc=164.3MB, time=12.10 memory used=734.1MB, alloc=188.3MB, time=14.81 N2 := 1897 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 4 2 2 3 2 H := [19 x y z - 17 y z , 9 z + 15, 19 x y - 14 y , -7 y z - 16 y z, 2 2 2 3 2 -7 x y - 16 x y z , -19 x y + 3 x z] > J:=[op(GB),op(G)]; 4 2 2 4 J := [390963 x y + 417605 y, -19 x y + 14 y , -19 x y + 17 y z, 3 z + 5, 3 2 2 2 2 3 2 -7 y z - 16 y z, -7 x y - 16 x y z , -19 x y + 3 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 := [6, 14, 23, 4, 3, 3, 4, 2/3, 5/6, 5/6, 1/2, 3/4, 7/12, 7, 16, 26, 5, 4, 3, 4, 5/7, 6/7, 5/7, 1/2, 11/14, 3/7, -2, -3, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=809.2MB, alloc=188.3MB, time=17.09 |\^/| 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(); 1428314775 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [-8 x z , -5 x z + 1, 18 x y z + 10 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 3 G := [2 x + 9 y z , 14 x y z - 13 x y z , 6 x z - 10 y] > Problem := [F,G]; 3 3 2 Problem := [[-8 x z , -5 x z + 1, 18 x y z + 10 y z], 4 2 2 2 2 3 [2 x + 9 y z , 14 x y z - 13 x y z , 6 x z - 10 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.51 memory used=48.3MB, alloc=32.3MB, time=0.82 memory used=69.2MB, alloc=60.3MB, time=1.14 memory used=111.5MB, alloc=60.3MB, time=1.74 N1 := 319 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=151.4MB, alloc=60.3MB, time=2.42 N2 := 111 #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)]; 3 3 2 2 2 4 H := [-8 z x, -5 x z + 1, 18 x y z + 10 y z, 9 z y + 2 x , 2 2 3 14 x y z - 13 x y z , 6 x z - 10 y] > J:=[op(GB),op(G)]; 2 2 4 2 2 3 J := [1, 9 z y + 2 x , 14 x y z - 13 x y z , 6 x z - 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 := [6, 16, 24, 4, 4, 2, 3, 1, 2/3, 1, 7/13, 6/13, 8/13, 4, 9, 12, 4, 4, 2, 2, 3/4, 3/4, 3/4, 4/7, 4/7, 4/7, 7, 12, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=168.7MB, alloc=60.3MB, time=2.67 |\^/| 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(); 1428314778 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 4 2 F := [17 y z + 9 z , -18 x z + 15 y , -19 y z + 7 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [-16 y z + 7 x , 6 z - 14, 20 x y] > Problem := [F,G]; 2 3 2 2 4 2 Problem := [[17 y z + 9 z , -18 x z + 15 y , -19 y z + 7 x y], 3 3 2 [-16 y z + 7 x , 6 z - 14, 20 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=0.16 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.80 memory used=67.8MB, alloc=32.3MB, time=1.09 memory used=87.2MB, alloc=56.3MB, time=1.40 memory used=127.6MB, alloc=60.3MB, time=1.99 memory used=163.4MB, alloc=84.3MB, time=2.54 memory used=212.6MB, alloc=84.3MB, time=3.28 memory used=269.9MB, alloc=92.3MB, time=4.12 memory used=325.0MB, alloc=116.3MB, time=4.97 memory used=403.2MB, alloc=140.3MB, time=6.16 memory used=495.4MB, alloc=396.3MB, time=7.55 memory used=593.2MB, alloc=420.3MB, time=9.09 memory used=709.3MB, alloc=444.3MB, time=10.96 memory used=857.4MB, alloc=468.3MB, time=13.43 memory used=1026.4MB, alloc=492.3MB, time=15.72 memory used=1194.6MB, alloc=516.3MB, time=18.64 memory used=1370.8MB, alloc=540.3MB, time=21.85 memory used=1555.5MB, alloc=564.3MB, time=25.30 memory used=1747.3MB, alloc=588.3MB, time=28.94 memory used=1945.9MB, alloc=612.3MB, time=32.64 memory used=2149.8MB, alloc=636.3MB, time=36.46 memory used=2366.2MB, alloc=660.3MB, time=40.20 memory used=2613.2MB, alloc=684.3MB, time=43.90 memory used=2871.7MB, alloc=708.3MB, time=48.07 memory used=3072.9MB, alloc=732.3MB, time=51.81 memory used=3331.8MB, alloc=756.3MB, time=57.02 memory used=3594.2MB, alloc=780.3MB, time=62.20 memory used=3866.4MB, alloc=804.3MB, time=67.89 memory used=4090.8MB, alloc=828.3MB, time=75.47 memory used=4317.2MB, alloc=852.3MB, time=83.74 memory used=4551.8MB, alloc=876.3MB, time=92.87 memory used=4797.4MB, alloc=900.3MB, time=102.31 memory used=5054.1MB, alloc=924.3MB, time=112.34 memory used=5323.7MB, alloc=948.3MB, time=123.13 memory used=5606.4MB, alloc=972.3MB, time=134.58 memory used=5902.4MB, alloc=996.3MB, time=147.26 memory used=6212.4MB, alloc=1020.3MB, time=160.00 memory used=6536.1MB, alloc=1044.3MB, time=173.37 memory used=6874.0MB, alloc=1068.3MB, time=188.12 memory used=7226.4MB, alloc=1092.3MB, time=204.71 memory used=7593.4MB, alloc=1116.3MB, time=220.62 memory used=7975.1MB, alloc=1140.3MB, time=238.28 memory used=8369.5MB, alloc=1164.3MB, time=255.36 memory used=8777.1MB, alloc=1188.3MB, time=273.76 |\^/| 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(); 1428315078 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [-16 y z , 19 y z + 7 x, 11 x z - 16 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 3 4 G := [-9 z - 20 z , -4 y z - 10, -9 x z - 5 y ] > Problem := [F,G]; 3 3 2 Problem := [[-16 y z , 19 y z + 7 x, 11 x z - 16 x ], 4 3 2 3 4 [-9 z - 20 z , -4 y z - 10, -9 x z - 5 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.80 memory used=67.6MB, alloc=32.3MB, time=1.08 memory used=86.1MB, alloc=56.3MB, time=1.37 memory used=125.3MB, alloc=60.3MB, time=1.97 memory used=163.6MB, alloc=84.3MB, time=2.52 memory used=209.4MB, alloc=84.3MB, time=3.24 memory used=270.7MB, alloc=116.3MB, time=4.15 memory used=353.6MB, alloc=116.3MB, time=5.38 memory used=433.1MB, alloc=140.3MB, time=6.63 memory used=511.9MB, alloc=396.3MB, time=7.79 memory used=612.6MB, alloc=420.3MB, time=9.33 memory used=741.4MB, alloc=444.3MB, time=10.96 memory used=892.9MB, alloc=468.3MB, time=12.89 memory used=1050.0MB, alloc=468.3MB, time=14.74 memory used=1212.2MB, alloc=492.3MB, time=17.41 memory used=1370.9MB, alloc=516.3MB, time=20.34 memory used=1555.1MB, alloc=540.3MB, time=23.32 memory used=1740.0MB, alloc=564.3MB, time=26.77 memory used=1925.0MB, alloc=588.3MB, time=31.33 memory used=2095.4MB, alloc=612.3MB, time=36.97 memory used=2272.0MB, alloc=636.3MB, time=43.37 memory used=2455.8MB, alloc=660.3MB, time=50.77 memory used=2663.6MB, alloc=684.3MB, time=59.07 memory used=2895.4MB, alloc=708.3MB, time=68.33 memory used=3151.1MB, alloc=732.3MB, time=78.53 memory used=3430.7MB, alloc=756.3MB, time=89.89 memory used=3734.2MB, alloc=780.3MB, time=102.24 memory used=4061.8MB, alloc=804.3MB, time=115.51 memory used=4413.2MB, alloc=804.3MB, time=129.81 memory used=4764.7MB, alloc=828.3MB, time=143.71 N1 := 10365 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x , 19 z y + 7 x, x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5150.2MB, alloc=828.3MB, time=157.63 memory used=5299.8MB, alloc=828.3MB, time=160.64 memory used=5454.7MB, alloc=828.3MB, time=163.97 N2 := 2877 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 4 3 2 H := [-16 y z , 19 z y + 7 x, 11 x z - 16 x , -9 z - 20 z , -4 y z - 10, 3 4 -9 x z - 5 y ] > J:=[op(GB),op(G)]; 2 2 4 3 2 3 4 J := [x , 19 z y + 7 x, x z , -9 z - 20 z , -4 y z - 10, -9 x 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 := [6, 13, 21, 4, 2, 4, 4, 1/2, 2/3, 1, 4/13, 4/13, 7/13, 6, 12, 18, 4, 2, 4, 4, 2/3, 1/2, 5/6, 1/3, 1/4, 1/2, 1, 3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=5766.3MB, alloc=828.3MB, time=176.08 |\^/| 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(); 1428315260 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 F := [20 z + 15 x z, -15 x y - 19 z , 17 x y z - 19 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [14 x y - 4 x, -10 x z + 11 y, -18 x z + 2 y z] > Problem := [F,G]; 4 2 2 2 2 2 Problem := [[20 z + 15 x z, -15 x y - 19 z , 17 x y z - 19 y z], 3 2 2 [14 x y - 4 x, -10 x z + 11 y, -18 x z + 2 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=48.0MB, alloc=32.3MB, time=0.77 memory used=69.1MB, alloc=32.3MB, time=1.08 memory used=89.2MB, alloc=56.3MB, time=1.39 memory used=130.1MB, alloc=60.3MB, time=1.98 memory used=169.8MB, alloc=60.3MB, time=2.56 memory used=209.6MB, alloc=84.3MB, time=3.23 memory used=270.9MB, alloc=84.3MB, time=4.31 memory used=327.0MB, alloc=108.3MB, time=5.30 memory used=403.0MB, alloc=140.3MB, time=6.66 memory used=493.8MB, alloc=164.3MB, time=8.39 memory used=592.7MB, alloc=188.3MB, time=11.08 memory used=699.3MB, alloc=212.3MB, time=14.94 memory used=828.7MB, alloc=212.3MB, time=19.66 memory used=958.0MB, alloc=236.3MB, time=24.54 memory used=1111.7MB, alloc=260.3MB, time=30.12 N1 := 4415 > GB := Basis(F, plex(op(vars))); 14 2 3 2 5 2 3 3 GB := [144825414000 x y + 322687697779 x y , -17 x y + 19 x y , 5 2 4 6 2 2 -289 x y + 361 x y , 86700 x y + 130321 x z, 8 2 2 2 2 25056300 x y + 47045881 y z, 15 y x + 19 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1219.0MB, alloc=260.3MB, time=32.00 memory used=1415.6MB, alloc=516.3MB, time=35.07 memory used=1614.3MB, alloc=540.3MB, time=38.19 memory used=1848.8MB, alloc=564.3MB, time=41.74 memory used=2095.6MB, alloc=588.3MB, time=45.79 memory used=2333.7MB, alloc=612.3MB, time=50.32 memory used=2581.2MB, alloc=636.3MB, time=54.86 memory used=2813.4MB, alloc=660.3MB, time=62.01 memory used=3035.5MB, alloc=684.3MB, time=70.04 memory used=3263.8MB, alloc=708.3MB, time=78.92 memory used=3499.6MB, alloc=732.3MB, time=88.78 memory used=3759.4MB, alloc=756.3MB, time=99.78 memory used=4043.1MB, alloc=780.3MB, time=111.69 memory used=4350.8MB, alloc=804.3MB, time=125.85 memory used=4682.4MB, alloc=828.3MB, time=141.48 memory used=5037.9MB, alloc=852.3MB, time=156.86 memory used=5417.5MB, alloc=876.3MB, time=173.42 memory used=5820.9MB, alloc=876.3MB, time=190.11 memory used=6224.3MB, alloc=900.3MB, time=206.66 memory used=6651.7MB, alloc=900.3MB, time=224.18 memory used=7078.9MB, alloc=924.3MB, time=241.63 N2 := 12599 #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)]; 4 2 2 2 2 2 3 H := [20 z + 15 x z, -15 x y - 19 z , 17 x y z - 19 y z, 14 x y - 4 x, 2 2 -10 x z + 11 y, -18 x z + 2 y z] > J:=[op(GB),op(G)]; 14 2 3 2 5 2 3 3 J := [144825414000 x y + 322687697779 x y , -17 x y + 19 x y , 5 2 4 6 2 2 -289 x y + 361 x y , 86700 x y + 130321 x z, 8 2 2 2 2 3 25056300 x y + 47045881 y z, 15 y x + 19 z , 14 x y - 4 x, 2 2 -10 x z + 11 y, -18 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 := [6, 16, 21, 4, 3, 2, 4, 1, 5/6, 5/6, 7/12, 1/2, 2/3, 9, 23, 61, 16, 14, 4, 2, 1, 1, 5/9, 7/9, 13/18, 1/3, -7, -40, -12] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=7498.6MB, alloc=924.3MB, time=257.88 |\^/| 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(); 1428315535 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 F := [-17 x y - 20 z, 8 - 20 y, -5 x - 14 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 3 3 3 G := [2 x y - 10 z , 13 x y z + 16 y z , 4 x z - 4 y z] > Problem := [F,G]; 2 4 3 Problem := [[-17 x y - 20 z, 8 - 20 y, -5 x - 14 y ], 2 2 4 2 3 3 3 [2 x y - 10 z , 13 x y z + 16 y z , 4 x z - 4 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=47.5MB, alloc=32.3MB, time=0.77 memory used=68.0MB, alloc=32.3MB, time=1.06 memory used=87.8MB, alloc=32.3MB, time=1.35 memory used=107.2MB, alloc=32.3MB, time=1.63 memory used=125.8MB, alloc=56.3MB, time=1.92 memory used=168.8MB, alloc=60.3MB, time=2.67 memory used=209.5MB, alloc=84.3MB, time=3.37 memory used=271.6MB, alloc=84.3MB, time=4.41 memory used=326.2MB, alloc=108.3MB, time=5.37 memory used=394.0MB, alloc=140.3MB, time=7.17 memory used=471.2MB, alloc=164.3MB, time=10.04 memory used=571.9MB, alloc=164.3MB, time=13.86 N1 := 3125 > GB := Basis(F, plex(op(vars))); 4 GB := [625 x + 112, 5 y - 2, 125 z + 17 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=674.2MB, alloc=164.3MB, time=17.27 memory used=789.6MB, alloc=188.3MB, time=19.15 N2 := 1237 #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 4 3 2 2 4 H := [-17 x y - 20 z, 8 - 20 y, -5 x - 14 y , 2 x y - 10 z , 2 3 3 3 13 x y z + 16 y z , 4 x z - 4 y z] > J:=[op(GB),op(G)]; 4 2 2 4 2 3 J := [625 x + 112, 5 y - 2, 125 z + 17 x, 2 x y - 10 z , 13 x y z + 16 y z , 3 3 4 x z - 4 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 20, 4, 4, 3, 4, 5/6, 1, 2/3, 5/12, 7/12, 1/2, 6, 13, 18, 4, 4, 3, 4, 5/6, 2/3, 2/3, 5/12, 5/12, 1/2, 2, 2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=856.4MB, alloc=188.3MB, time=20.98 |\^/| 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(); 1428315557 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-13 y z + 2 x y , 11 y z - 7 x, x y - 5] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 4 2 2 2 G := [5 x z + 8 z , 2 y - 5 x, 6 x y + 9 x y ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-13 y z + 2 x y , 11 y z - 7 x, x y - 5], 2 2 4 4 2 2 2 [5 x z + 8 z , 2 y - 5 x, 6 x y + 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=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.78 memory used=69.5MB, alloc=56.3MB, time=1.17 memory used=114.4MB, alloc=56.3MB, time=1.95 memory used=155.1MB, alloc=84.3MB, time=2.67 memory used=211.3MB, alloc=84.3MB, time=4.37 N1 := 1439 > GB := Basis(F, plex(op(vars))); 2 GB := [8281 x - 2420, 22 y - 91, 107653 z - 4840] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=263.6MB, alloc=84.3MB, time=5.43 N2 := 441 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 4 4 H := [-13 y z + 2 x y , 11 y z - 7 x, y x - 5, 5 x z + 8 z , 2 y - 5 x, 2 2 2 6 x y + 9 x y ] > J:=[op(GB),op(G)]; 2 2 2 4 4 J := [8281 x - 2420, 22 y - 91, 107653 z - 4840, 5 x z + 8 z , 2 y - 5 x, 2 2 2 6 x y + 9 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 := [6, 14, 22, 4, 2, 4, 4, 1, 5/6, 1/2, 7/12, 7/12, 1/3, 6, 9, 16, 4, 2, 4, 4, 2/3, 1/2, 1/3, 5/12, 1/3, 1/4, 5, 6, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=288.3MB, alloc=84.3MB, time=5.91 |\^/| 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(); 1428315563 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 3 F := [4 y z + 18 x y, 20 x y - 6 x z, -19 y z + 18 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 G := [-4 x y + 3 y z, 18 x z + 2 x z , -10 x y + 16 y z] > Problem := [F,G]; 3 2 3 3 3 Problem := [[4 y z + 18 x y, 20 x y - 6 x z, -19 y z + 18 x ], 2 2 2 2 2 2 2 [-4 x y + 3 y z, 18 x z + 2 x z , -10 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=26.2MB, alloc=32.3MB, time=0.48 memory used=47.0MB, alloc=32.3MB, time=0.78 memory used=66.7MB, alloc=56.3MB, time=1.09 memory used=105.8MB, alloc=60.3MB, time=1.69 memory used=142.1MB, alloc=84.3MB, time=2.25 memory used=198.6MB, alloc=84.3MB, time=3.10 memory used=253.9MB, alloc=92.3MB, time=3.96 memory used=307.7MB, alloc=116.3MB, time=4.76 memory used=381.4MB, alloc=116.3MB, time=5.89 memory used=452.9MB, alloc=140.3MB, time=7.02 memory used=544.2MB, alloc=140.3MB, time=8.48 memory used=631.6MB, alloc=164.3MB, time=9.92 memory used=738.8MB, alloc=188.3MB, time=11.74 memory used=837.9MB, alloc=444.3MB, time=13.52 memory used=961.7MB, alloc=468.3MB, time=15.79 memory used=1102.2MB, alloc=492.3MB, time=18.36 memory used=1256.6MB, alloc=516.3MB, time=21.10 memory used=1440.5MB, alloc=540.3MB, time=23.84 memory used=1670.5MB, alloc=564.3MB, time=25.90 memory used=1935.5MB, alloc=588.3MB, time=27.92 memory used=2211.4MB, alloc=588.3MB, time=31.30 memory used=2491.5MB, alloc=612.3MB, time=34.06 memory used=2743.6MB, alloc=636.3MB, time=38.67 memory used=2999.9MB, alloc=660.3MB, time=43.38 memory used=3298.5MB, alloc=684.3MB, time=47.51 memory used=3548.4MB, alloc=708.3MB, time=54.78 memory used=3784.4MB, alloc=732.3MB, time=62.96 memory used=4026.2MB, alloc=756.3MB, time=71.81 memory used=4278.0MB, alloc=780.3MB, time=81.32 memory used=4539.6MB, alloc=804.3MB, time=91.54 memory used=4810.4MB, alloc=828.3MB, time=103.08 memory used=5105.1MB, alloc=852.3MB, time=115.95 memory used=5423.8MB, alloc=876.3MB, time=129.48 memory used=5766.4MB, alloc=900.3MB, time=143.99 memory used=6133.0MB, alloc=924.3MB, time=159.66 memory used=6523.5MB, alloc=948.3MB, time=176.23 memory used=6938.0MB, alloc=972.3MB, time=193.85 memory used=7376.3MB, alloc=996.3MB, time=212.24 memory used=7838.7MB, alloc=996.3MB, time=231.56 memory used=8300.9MB, alloc=996.3MB, time=250.86 memory used=8763.1MB, alloc=1020.3MB, time=270.33 |\^/| 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(); 1428315863 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 2 F := [-8 x y + 6 y , -13 y z + 4 z , 13 x y z + y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 G := [15 x y z, -15 x z - 13 y z , 17 y - 18 x z] > Problem := [F,G]; 2 3 4 2 2 Problem := [[-8 x y + 6 y , -13 y z + 4 z , 13 x y z + y z ], 3 2 4 2 [15 x y z, -15 x z - 13 y z , 17 y - 18 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.9MB, alloc=32.3MB, time=0.51 memory used=48.1MB, alloc=32.3MB, time=0.83 memory used=67.2MB, alloc=56.3MB, time=1.12 memory used=107.0MB, alloc=60.3MB, time=1.74 memory used=142.8MB, alloc=84.3MB, time=2.26 memory used=207.4MB, alloc=116.3MB, time=3.25 memory used=290.1MB, alloc=116.3MB, time=4.62 memory used=366.9MB, alloc=140.3MB, time=5.90 memory used=448.6MB, alloc=164.3MB, time=8.53 N1 := 2243 > GB := Basis(F, plex(op(vars))); GB := [ 2 6 3 2 2 2 4 -4 x y + 3 y , 4563 x y z + 16 x y z, 13 x y z + y z , -52 x y z + 9 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=548.7MB, alloc=164.3MB, time=11.67 memory used=632.5MB, alloc=420.3MB, time=12.87 memory used=754.5MB, alloc=444.3MB, time=14.52 memory used=909.9MB, alloc=468.3MB, time=16.70 memory used=1090.0MB, alloc=492.3MB, time=19.20 memory used=1289.6MB, alloc=516.3MB, time=22.71 N2 := 2497 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 4 2 2 H := [-8 x y + 6 y , -13 y z + 4 z , 13 x y z + y z , 15 x y z, 3 2 4 2 -15 x z - 13 y z , 17 y - 18 x z] > J:=[op(GB),op(G)]; 2 6 3 2 2 J := [-4 x y + 3 y , 4563 x y z + 16 x y z, 13 x y z + y z , 2 4 3 2 4 2 -52 x y z + 9 z , 15 x y z, -15 x z - 13 y z , 17 y - 18 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 := [6, 16, 21, 4, 3, 4, 4, 5/6, 1, 5/6, 5/14, 4/7, 4/7, 7, 20, 29, 8, 6, 4, 4, 1, 1, 6/7, 1/2, 5/8, 5/8, -4, -8, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1435.7MB, alloc=516.3MB, time=28.09 |\^/| 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(); 1428315893 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 F := [-x - 3 x z, 10 x + 2 x z, -13 x z - 12 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 3 2 G := [-5 y z - 10 y z , -6 z + 16 y z , 11 x z + 3 y ] > Problem := [F,G]; 3 4 2 Problem := [[-x - 3 x z, 10 x + 2 x z, -13 x z - 12 z], 2 2 4 2 3 2 [-5 y z - 10 y z , -6 z + 16 y z , 11 x z + 3 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.46 memory used=47.9MB, alloc=32.3MB, time=0.77 memory used=68.1MB, alloc=56.3MB, time=1.09 memory used=108.1MB, alloc=60.3MB, time=1.69 memory used=145.6MB, alloc=84.3MB, time=2.25 memory used=202.1MB, alloc=92.3MB, time=3.09 memory used=257.6MB, alloc=116.3MB, time=3.92 memory used=337.5MB, alloc=116.3MB, time=5.13 memory used=415.6MB, alloc=140.3MB, time=6.32 memory used=510.9MB, alloc=164.3MB, time=7.85 memory used=595.8MB, alloc=420.3MB, time=9.13 memory used=710.4MB, alloc=444.3MB, time=10.98 memory used=846.3MB, alloc=468.3MB, time=13.12 memory used=997.6MB, alloc=492.3MB, time=15.69 memory used=1168.8MB, alloc=516.3MB, time=18.58 memory used=1356.0MB, alloc=540.3MB, time=21.82 memory used=1562.2MB, alloc=564.3MB, time=25.51 memory used=1765.4MB, alloc=588.3MB, time=29.26 memory used=1968.1MB, alloc=612.3MB, time=33.10 memory used=2175.7MB, alloc=636.3MB, time=37.03 memory used=2397.0MB, alloc=660.3MB, time=41.06 memory used=2634.3MB, alloc=684.3MB, time=45.33 memory used=2866.7MB, alloc=708.3MB, time=49.77 memory used=3096.8MB, alloc=732.3MB, time=54.36 memory used=3325.6MB, alloc=756.3MB, time=58.90 memory used=3555.8MB, alloc=780.3MB, time=63.55 memory used=3789.1MB, alloc=804.3MB, time=68.29 memory used=4029.6MB, alloc=828.3MB, time=73.21 memory used=4267.5MB, alloc=852.3MB, time=78.75 memory used=4463.2MB, alloc=876.3MB, time=85.57 memory used=4663.6MB, alloc=900.3MB, time=93.02 memory used=4874.2MB, alloc=924.3MB, time=101.28 memory used=5097.0MB, alloc=948.3MB, time=110.30 memory used=5332.3MB, alloc=972.3MB, time=119.99 memory used=5581.3MB, alloc=996.3MB, time=130.30 memory used=5844.1MB, alloc=1020.3MB, time=141.16 memory used=6120.7MB, alloc=1044.3MB, time=153.56 memory used=6411.3MB, alloc=1068.3MB, time=167.83 memory used=6716.4MB, alloc=1092.3MB, time=181.82 memory used=7035.5MB, alloc=1116.3MB, time=196.47 memory used=7369.7MB, alloc=1140.3MB, time=211.47 memory used=7718.8MB, alloc=1164.3MB, time=227.56 memory used=8082.9MB, alloc=1188.3MB, time=244.59 memory used=8461.7MB, alloc=1212.3MB, time=262.48 |\^/| 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(); 1428316193 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [10 y z + 9 x y, -3, y z + 11 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-13 x y z + 15 x y z, 16 x z - 18 x y, 20 x y z + 7 x y] > Problem := [F,G]; 3 3 2 Problem := [[10 y z + 9 x y, -3, y z + 11 y z ], 2 2 2 2 [-13 x y z + 15 x y z, 16 x z - 18 x y, 20 x y z + 7 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=54.8MB, alloc=68.3MB, time=0.99 memory used=107.5MB, alloc=68.3MB, time=1.97 memory used=156.4MB, alloc=92.3MB, time=2.96 memory used=223.6MB, alloc=124.3MB, time=4.25 memory used=299.1MB, alloc=148.3MB, time=6.74 memory used=391.2MB, alloc=148.3MB, time=10.11 N1 := 2415 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 145 #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)]; 3 3 2 2 H := [10 y z + 9 x y, -3, y z + 11 y z , -13 x y z + 15 x y z, 2 2 2 16 x z - 18 x y, 20 x y z + 7 x y] > J:=[op(GB),op(G)]; 2 2 2 2 J := [1, -13 x y z + 15 x y z, 16 x z - 18 x y, 20 x y z + 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 := [6, 14, 19, 4, 2, 2, 3, 2/3, 5/6, 5/6, 7/11, 9/11, 7/11, 4, 9, 11, 4, 2, 2, 2, 3/4, 3/4, 3/4, 6/7, 5/7, 4/7, 5, 8, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=432.4MB, alloc=148.3MB, time=11.12 |\^/| 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(); 1428316207 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [x + 8, -14 x y - 5 x z, 20 x + 5 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 4 4 G := [11 y + 7 y, -x z - 2 y , -14 x - 19 y ] > Problem := [F,G]; 2 2 3 2 Problem := [[x + 8, -14 x y - 5 x z, 20 x + 5 y ], 2 3 3 4 4 [11 y + 7 y, -x z - 2 y , -14 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=47.9MB, alloc=32.3MB, time=0.81 memory used=69.9MB, alloc=56.3MB, time=1.23 N1 := 373 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x + 8, y - 32 x, 5 z + 448 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=110.4MB, alloc=60.3MB, time=1.90 memory used=151.9MB, alloc=60.3MB, time=2.57 N2 := 293 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 3 3 H := [x + 8, -14 x y - 5 x z, 20 x + 5 y , 11 y + 7 y, -x z - 2 y , 4 4 -14 x - 19 y ] > J:=[op(GB),op(G)]; J := 2 2 2 3 3 4 4 [x + 8, y - 32 x, 5 z + 448 x, 11 y + 7 y, -x z - 2 y , -14 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 := [6, 12, 18, 4, 4, 4, 3, 5/6, 5/6, 1/3, 1/2, 1/2, 1/6, 6, 11, 15, 4, 4, 4, 3, 5/6, 2/3, 1/3, 5/12, 5/12, 1/6, 1, 3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=154.0MB, alloc=60.3MB, time=2.63 |\^/| 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(); 1428316209 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 4 2 2 F := [10 x z + 10 x y , 20 x y + 8 y , -4 x - 9 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 G := [-7 y z - 20 y z, 12 y z - 10 y , -17 x + 5 z] > Problem := [F,G]; 2 2 3 2 2 4 2 2 Problem := [[10 x z + 10 x y , 20 x y + 8 y , -4 x - 9 y ], 3 2 2 2 3 [-7 y z - 20 y z, 12 y z - 10 y , -17 x + 5 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.9MB, alloc=32.3MB, time=0.79 memory used=68.9MB, alloc=32.3MB, time=1.09 memory used=89.0MB, alloc=56.3MB, time=1.42 memory used=131.1MB, alloc=60.3MB, time=2.19 memory used=169.2MB, alloc=84.3MB, time=2.89 N1 := 1017 > GB := Basis(F, plex(op(vars))); 4 2 2 3 2 2 GB := [x , 9 y + 4 x , -4 x y + 9 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=225.1MB, alloc=84.3MB, time=4.15 N2 := 427 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 4 2 2 3 2 H := [10 x z + 10 x y , 20 x y + 8 y , -4 x - 9 y , -7 y z - 20 y z, 2 2 3 12 y z - 10 y , -17 x + 5 z] > J:=[op(GB),op(G)]; 4 2 2 3 2 2 3 2 2 2 3 J := [x , 9 y + 4 x , -4 x y + 9 x z , -7 y z - 20 y z, 12 y z - 10 y , -17 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 := [6, 13, 19, 4, 2, 4, 2, 2/3, 5/6, 2/3, 5/12, 2/3, 5/12, 6, 12, 19, 4, 4, 3, 2, 2/3, 2/3, 2/3, 5/12, 1/2, 5/12, 1, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=285.2MB, alloc=84.3MB, time=5.25 |\^/| 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(); 1428316216 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-13 x z - 19 x z, 13 x z - 11 y z , 20 y z + 12 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 2 G := [-10 y z - 14 x y, -y z + 7 y , 4 x y + 13 y ] > Problem := [F,G]; 2 2 2 2 Problem := [[-13 x z - 19 x z, 13 x z - 11 y z , 20 y z + 12 y z], 3 2 2 3 2 2 [-10 y z - 14 x y, -y z + 7 y , 4 x y + 13 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.52 memory used=48.9MB, alloc=32.3MB, time=0.93 memory used=69.0MB, alloc=56.3MB, time=1.31 N1 := 545 > GB := Basis(F, plex(op(vars))); 2 2 2 2 GB := [13 x z + 19 x z, 5 y z + 3 y z, z x, z y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=108.1MB, alloc=60.3MB, time=2.10 N2 := 277 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 H := [-13 x z - 19 x z, 13 x z - 11 y z , 20 y z + 12 y z, -10 y z - 14 x y, 2 2 3 2 2 -y z + 7 y , 4 x y + 13 y ] > J:=[op(GB),op(G)]; 2 2 2 2 3 J := [13 x z + 19 x z, 5 y z + 3 y z, z x, z y, -10 y z - 14 x y, 2 2 3 2 2 -y z + 7 y , 4 x y + 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 := [6, 14, 20, 4, 2, 3, 2, 2/3, 5/6, 5/6, 5/12, 3/4, 2/3, 7, 15, 23, 4, 2, 3, 2, 4/7, 5/7, 6/7, 5/14, 9/14, 4/7, -1, -3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=121.1MB, 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(); 1428316219 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 4 F := [19 x - 7 x y , 15 x z + 7 y, 12 x z - 10 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 G := [17 y z , -5 x z - 17 y , 8 x y z + 12 x z] > Problem := [F,G]; 3 2 2 2 2 2 4 Problem := [[19 x - 7 x y , 15 x z + 7 y, 12 x z - 10 y ], 3 3 2 2 2 [17 y z , -5 x z - 17 y , 8 x y z + 12 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.70 memory used=48.6MB, alloc=32.3MB, time=1.08 memory used=69.3MB, alloc=32.3MB, time=1.44 memory used=88.2MB, alloc=56.3MB, time=1.74 memory used=130.6MB, alloc=60.3MB, time=2.46 memory used=169.2MB, alloc=84.3MB, time=3.14 memory used=228.8MB, alloc=84.3MB, time=4.18 memory used=284.1MB, alloc=108.3MB, time=5.19 memory used=359.2MB, alloc=116.3MB, time=6.54 memory used=426.7MB, alloc=140.3MB, time=7.95 memory used=504.5MB, alloc=164.3MB, time=10.21 memory used=593.6MB, alloc=188.3MB, time=13.93 memory used=706.7MB, alloc=188.3MB, time=18.52 memory used=819.8MB, alloc=212.3MB, time=22.99 N1 := 4001 > GB := Basis(F, plex(op(vars))); 9 3 4 4 2 2 GB := [4286875 x - 67228 x , 9025 x + 686 y, -1805 x + 294 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=960.4MB, alloc=212.3MB, time=27.08 memory used=1126.5MB, alloc=236.3MB, time=31.04 N2 := 1443 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 4 3 H := [19 x - 7 x y , 15 z x + 7 y, 12 x z - 10 y , 17 y z , 3 2 2 2 -5 x z - 17 y , 8 x y z + 12 x z] > J:=[op(GB),op(G)]; 9 3 4 4 2 2 3 J := [4286875 x - 67228 x , 9025 x + 686 y, -1805 x + 294 x z , 17 y z , 3 2 2 2 -5 x z - 17 y , 8 x y z + 12 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 := [6, 16, 23, 4, 3, 4, 3, 5/6, 1, 5/6, 7/13, 6/13, 6/13, 6, 13, 29, 9, 9, 2, 3, 5/6, 2/3, 2/3, 8/13, 4/13, 5/13, 3, -6, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1132.3MB, alloc=236.3MB, time=31.22 |\^/| 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(); 1428316253 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 F := [15 x y - 14 x, 10 x y z, -3 x y + 16 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [3 y z - 20, 12 x y + 20 y , 8 x y z - 14 y z] > Problem := [F,G]; 2 3 3 Problem := [[15 x y - 14 x, 10 x y z, -3 x y + 16 y ], 2 2 2 2 3 [3 y z - 20, 12 x y + 20 y , 8 x y 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=0.16 memory used=26.3MB, alloc=32.3MB, time=0.47 memory used=48.9MB, alloc=32.3MB, time=0.88 memory used=69.0MB, alloc=56.3MB, time=1.26 memory used=109.9MB, alloc=84.3MB, time=2.01 N1 := 1187 > GB := Basis(F, plex(op(vars))); 2 3 GB := [3 x - 16 x, 15 x y - 14 x, 2250 y - 343 x, z x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=168.3MB, alloc=84.3MB, time=3.42 memory used=227.2MB, alloc=92.3MB, time=4.32 memory used=284.6MB, alloc=116.3MB, time=5.29 memory used=358.3MB, alloc=140.3MB, time=7.35 N2 := 1421 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 2 2 2 H := [15 x y - 14 x, 10 x y z, -3 x y + 16 y , 3 z y - 20, 12 x y + 20 y , 2 3 8 x y z - 14 y z] > J:=[op(GB),op(G)]; 2 3 2 2 J := [3 x - 16 x, 15 x y - 14 x, 2250 y - 343 x, z x, 3 z y - 20, 2 2 3 12 x y + 20 y , 8 x y z - 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 := [6, 14, 20, 4, 2, 3, 2, 5/6, 1, 1/2, 3/7, 9/14, 2/7, 7, 14, 19, 4, 2, 3, 2, 6/7, 5/7, 3/7, 4/7, 1/2, 2/7, 0, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=363.4MB, alloc=140.3MB, time=7.48 |\^/| 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(); 1428316261 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [2 x y + 7 z , 8 y z , -9 x y z + 3 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [10 y z + 9 z , -15 x z - 5 x, 2 x y + 14 y z] > Problem := [F,G]; 2 3 2 2 2 Problem := [[2 x y + 7 z , 8 y z , -9 x y z + 3 x z], 2 2 2 2 [10 y z + 9 z , -15 x z - 5 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=48.2MB, alloc=32.3MB, time=0.81 memory used=68.4MB, alloc=32.3MB, time=1.11 memory used=87.0MB, alloc=56.3MB, time=1.41 memory used=126.6MB, alloc=60.3MB, time=2.02 memory used=165.8MB, alloc=84.3MB, time=2.72 memory used=223.6MB, alloc=108.3MB, time=3.89 N1 := 1375 > GB := Basis(F, plex(op(vars))); 2 2 4 2 2 3 2 GB := [y x , y x, z x, y z , 7 z + 2 y x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=294.2MB, alloc=108.3MB, time=6.05 N2 := 187 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 2 H := [7 z + 2 y x, 8 y z , -9 x y z + 3 x z, 10 y z + 9 z , -15 x z - 5 x, 2 2 2 x y + 14 y z] > J:=[op(GB),op(G)]; 2 2 4 2 2 3 2 2 2 J := [y x , y x, z x, y z , 7 z + 2 y x, 10 y z + 9 z , -15 x z - 5 x, 2 2 2 x 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 := [6, 15, 19, 4, 2, 2, 3, 2/3, 5/6, 1, 6/13, 6/13, 8/13, 8, 18, 26, 5, 2, 4, 3, 3/4, 3/4, 3/4, 7/16, 7/16, 7/16, -3, -7, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=359.3MB, alloc=116.3MB, time=7.10 |\^/| 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(); 1428316269 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [10 x y + 18 x y z, 10 x y z - 20 z, -11 x y z - 20 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 G := [16 x - 10 y z, -10 y z + 2 z, -13 x y - 10 x] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[10 x y + 18 x y z, 10 x y z - 20 z, -11 x y z - 20 x z ], 4 2 3 [16 x - 10 y z, -10 y z + 2 z, -13 x y - 10 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=47.6MB, alloc=32.3MB, time=0.80 memory used=67.8MB, alloc=32.3MB, time=1.09 memory used=88.5MB, alloc=56.3MB, time=1.47 memory used=129.9MB, alloc=60.3MB, time=2.18 memory used=167.8MB, alloc=84.3MB, time=2.81 memory used=224.1MB, alloc=108.3MB, time=3.91 memory used=296.4MB, alloc=132.3MB, time=6.09 memory used=382.7MB, alloc=132.3MB, time=9.40 N1 := 2567 > GB := Basis(F, plex(op(vars))); 9 3 7 3 2 6 GB := [25 x y - 99 x y, -50 x y + 99 x y , 5 x y + 36 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=471.1MB, alloc=132.3MB, time=12.20 memory used=565.2MB, alloc=164.3MB, time=13.91 N2 := 987 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 H := [10 x y + 18 x y z, 10 x y z - 20 z, -11 x y z - 20 x z , 4 2 3 16 x - 10 y z, -10 y z + 2 z, -13 x y - 10 x] > J:=[op(GB),op(G)]; 9 3 7 3 2 6 4 J := [25 x y - 99 x y, -50 x y + 99 x y , 5 y x + 36 z, 16 x - 10 y z, 2 3 -10 y z + 2 z, -13 x y - 10 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 16, 23, 4, 4, 2, 2, 5/6, 1, 5/6, 2/3, 7/12, 2/3, 6, 14, 36, 10, 9, 2, 1, 5/6, 1, 1/2, 2/3, 2/3, 1/3, 2, -13, -6] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=604.3MB, alloc=164.3MB, time=15.06 |\^/| 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(); 1428316286 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 F := [16 x y + 16 x y, -17 x z + 3 z, -11 x z + 10 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 G := [2 x y + 14 x z, 3 x y z + 15 x y, -3 x y z + 3 x ] > Problem := [F,G]; 2 3 3 Problem := [[16 x y + 16 x y, -17 x z + 3 z, -11 x z + 10 y], 3 2 2 3 [2 x y + 14 x z, 3 x y z + 15 x y, -3 x y z + 3 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.47 memory used=48.3MB, alloc=32.3MB, time=0.80 memory used=69.9MB, alloc=60.3MB, time=1.13 memory used=111.4MB, alloc=60.3MB, time=1.74 memory used=152.2MB, alloc=60.3MB, time=2.34 memory used=190.9MB, alloc=84.3MB, time=3.04 memory used=248.3MB, alloc=108.3MB, time=4.07 memory used=323.9MB, alloc=116.3MB, time=5.42 memory used=393.1MB, alloc=140.3MB, time=6.78 memory used=478.7MB, alloc=164.3MB, time=8.48 memory used=575.5MB, alloc=188.3MB, time=11.45 memory used=680.8MB, alloc=212.3MB, time=15.45 memory used=802.9MB, alloc=236.3MB, time=20.48 memory used=948.9MB, alloc=236.3MB, time=26.78 memory used=1094.9MB, alloc=260.3MB, time=32.98 memory used=1265.1MB, alloc=260.3MB, time=39.91 N1 := 5071 > GB := Basis(F, plex(op(vars))); GB := [y, z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 515 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 3 H := [16 x y + 16 x y, -17 x z + 3 z, -11 x z + 10 y, 2 x y + 14 x z, 2 2 3 3 x y z + 15 x y, -3 x y z + 3 x ] > J:=[op(GB),op(G)]; 3 2 2 3 J := [y, z, 2 x y + 14 x z, 3 x y z + 15 x y, -3 x y z + 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, 16, 23, 4, 3, 3, 2, 1, 5/6, 5/6, 5/6, 7/12, 1/2, 5, 11, 14, 4, 3, 3, 2, 3/5, 4/5, 4/5, 3/4, 5/8, 1/2, 5, 9, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1375.6MB, alloc=260.3MB, time=42.98 |\^/| 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(); 1428316337 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 F := [x z - 11 z , 3 + 19 z, 12 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 G := [-13 x y z - 15, 16 y z - 16 x z , 15 x y + 2 z] > Problem := [F,G]; 2 2 4 2 Problem := [[x z - 11 z , 3 + 19 z, 12 x z], 2 3 2 3 [-13 x y z - 15, 16 y z - 16 x z , 15 x y + 2 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.5MB, alloc=32.3MB, time=0.83 memory used=67.4MB, alloc=32.3MB, time=1.13 memory used=87.0MB, alloc=56.3MB, time=1.44 memory used=128.2MB, alloc=60.3MB, time=2.09 memory used=166.9MB, alloc=84.3MB, time=2.67 memory used=217.9MB, alloc=84.3MB, time=3.52 memory used=277.5MB, alloc=116.3MB, time=4.60 memory used=358.5MB, alloc=116.3MB, time=5.87 memory used=436.1MB, alloc=140.3MB, time=7.48 memory used=534.0MB, alloc=164.3MB, time=9.13 memory used=641.9MB, alloc=188.3MB, time=11.21 memory used=760.8MB, alloc=468.3MB, time=13.46 memory used=916.7MB, alloc=492.3MB, time=15.74 memory used=1122.6MB, alloc=492.3MB, time=17.41 memory used=1328.5MB, alloc=492.3MB, time=18.91 memory used=1530.6MB, alloc=492.3MB, time=20.27 memory used=1706.2MB, alloc=516.3MB, time=22.66 memory used=1873.0MB, alloc=540.3MB, time=25.78 memory used=2049.7MB, alloc=564.3MB, time=29.30 memory used=2224.2MB, alloc=588.3MB, time=34.09 memory used=2391.8MB, alloc=612.3MB, time=39.88 memory used=2567.7MB, alloc=636.3MB, time=46.53 memory used=2755.5MB, alloc=660.3MB, time=53.94 memory used=2956.4MB, alloc=684.3MB, time=61.69 memory used=3166.4MB, alloc=708.3MB, time=70.85 memory used=3396.3MB, alloc=732.3MB, time=81.24 memory used=3650.2MB, alloc=756.3MB, time=92.63 memory used=3928.0MB, alloc=780.3MB, time=104.88 memory used=4229.7MB, alloc=804.3MB, time=117.43 memory used=4555.4MB, alloc=828.3MB, time=130.91 memory used=4905.1MB, alloc=828.3MB, time=145.16 memory used=5254.6MB, alloc=852.3MB, time=159.43 memory used=5628.1MB, alloc=852.3MB, time=174.48 memory used=6001.6MB, alloc=852.3MB, time=189.55 memory used=6375.1MB, alloc=852.3MB, time=204.56 memory used=6748.4MB, alloc=876.3MB, time=219.97 memory used=7145.7MB, alloc=876.3MB, time=236.15 memory used=7543.0MB, alloc=876.3MB, time=252.27 memory used=7940.2MB, alloc=900.3MB, time=268.40 |\^/| 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(); 1428316638 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 F := [3 x z, -4 x y + 11 x , -11 x z - 5 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 G := [19 x y + 3 z , -18 x z + 8 y , -5 x y - 10 x z] > Problem := [F,G]; 2 2 2 3 3 2 Problem := [[3 x z, -4 x y + 11 x , -11 x z - 5 x ], 2 3 2 3 2 [19 x y + 3 z , -18 x z + 8 y , -5 x y - 10 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.51 memory used=48.7MB, alloc=32.3MB, time=0.83 memory used=68.8MB, alloc=32.3MB, time=1.13 memory used=87.4MB, alloc=56.3MB, time=1.41 memory used=128.9MB, alloc=60.3MB, time=2.02 memory used=169.9MB, alloc=84.3MB, time=2.58 memory used=212.2MB, alloc=84.3MB, time=3.21 memory used=272.6MB, alloc=92.3MB, time=4.08 memory used=332.3MB, alloc=116.3MB, time=4.95 memory used=414.2MB, alloc=140.3MB, time=6.08 memory used=517.0MB, alloc=420.3MB, time=7.91 memory used=640.6MB, alloc=444.3MB, time=9.92 memory used=772.7MB, alloc=468.3MB, time=12.28 memory used=920.5MB, alloc=492.3MB, time=14.91 memory used=1075.8MB, alloc=516.3MB, time=18.40 memory used=1222.0MB, alloc=540.3MB, time=22.96 memory used=1375.7MB, alloc=564.3MB, time=28.58 memory used=1544.4MB, alloc=588.3MB, time=35.11 memory used=1737.1MB, alloc=612.3MB, time=42.71 memory used=1953.8MB, alloc=636.3MB, time=51.28 memory used=2194.4MB, alloc=636.3MB, time=60.69 memory used=2435.0MB, alloc=636.3MB, time=70.03 memory used=2675.4MB, alloc=660.3MB, time=79.44 memory used=2940.0MB, alloc=684.3MB, time=89.61 N1 := 7993 > GB := Basis(F, plex(op(vars))); 3 2 2 2 3 2 GB := [x , y x , x z, 11 x z + 5 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3146.4MB, alloc=684.3MB, time=94.20 memory used=3313.6MB, alloc=684.3MB, time=97.07 memory used=3528.7MB, alloc=684.3MB, time=101.07 memory used=3835.6MB, alloc=708.3MB, time=113.07 N2 := 4109 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 3 2 3 2 H := [3 x z, -4 x y + 11 x , -11 x z - 5 x , 3 z + 19 y x, 2 3 2 -18 x z + 8 y , -5 x y - 10 x z] > J:=[op(GB),op(G)]; 3 2 2 2 3 2 3 2 2 3 J := [x , y x , x z, 11 x z + 5 x , 3 z + 19 y x, -18 x z + 8 y , 2 -5 x y - 10 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 := [6, 15, 20, 4, 3, 3, 3, 1, 2/3, 5/6, 9/13, 4/13, 5/13, 7, 16, 23, 4, 3, 3, 3, 1, 4/7, 5/7, 9/14, 2/7, 5/14, -1, -3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=4096.3MB, alloc=708.3MB, time=123.66 |\^/| 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(); 1428316773 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 F := [18 x y + 9 z , -10 x + 8 y z, -11 y z + 9 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 2 G := [14 x y + 9 y , 14 y z + 13 y z , -17 x y z + 5 y ] > Problem := [F,G]; 3 3 2 3 Problem := [[18 x y + 9 z , -10 x + 8 y z, -11 y z + 9 z], 3 3 3 2 2 2 [14 x y + 9 y , 14 y z + 13 y z , -17 x y z + 5 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.9MB, alloc=32.3MB, time=0.48 memory used=48.1MB, alloc=32.3MB, time=0.78 memory used=68.5MB, alloc=32.3MB, time=1.07 memory used=88.5MB, alloc=56.3MB, time=1.37 memory used=130.3MB, alloc=60.3MB, time=1.96 memory used=169.9MB, alloc=84.3MB, time=2.54 memory used=214.2MB, alloc=84.3MB, time=3.18 memory used=269.7MB, alloc=116.3MB, time=4.05 memory used=350.8MB, alloc=116.3MB, time=5.23 memory used=422.5MB, alloc=140.3MB, time=6.24 memory used=492.3MB, alloc=396.3MB, time=7.29 memory used=594.6MB, alloc=420.3MB, time=8.78 memory used=721.4MB, alloc=444.3MB, time=10.69 memory used=866.8MB, alloc=444.3MB, time=12.93 memory used=1000.1MB, alloc=468.3MB, time=15.09 memory used=1126.6MB, alloc=492.3MB, time=17.08 memory used=1240.4MB, alloc=492.3MB, time=19.01 memory used=1359.5MB, alloc=492.3MB, time=20.98 memory used=1450.8MB, alloc=516.3MB, time=22.52 memory used=1533.7MB, alloc=516.3MB, time=23.92 memory used=1611.7MB, alloc=516.3MB, time=25.37 memory used=1695.9MB, alloc=516.3MB, time=26.98 memory used=1756.4MB, alloc=516.3MB, time=28.16 memory used=1821.0MB, alloc=540.3MB, time=29.46 memory used=1869.8MB, alloc=540.3MB, time=30.52 memory used=1918.5MB, alloc=540.3MB, time=31.47 memory used=1976.3MB, alloc=540.3MB, time=32.74 memory used=2182.0MB, alloc=564.3MB, time=36.72 memory used=2385.4MB, alloc=588.3MB, time=40.75 memory used=2596.2MB, alloc=612.3MB, time=45.05 memory used=2816.5MB, alloc=636.3MB, time=49.48 memory used=3044.3MB, alloc=660.3MB, time=54.06 memory used=3285.2MB, alloc=684.3MB, time=58.83 memory used=3526.8MB, alloc=708.3MB, time=63.75 memory used=3764.0MB, alloc=732.3MB, time=69.85 memory used=3975.8MB, alloc=756.3MB, time=77.47 memory used=4192.7MB, alloc=780.3MB, time=85.70 memory used=4420.5MB, alloc=804.3MB, time=94.84 memory used=4660.8MB, alloc=828.3MB, time=104.95 memory used=4913.8MB, alloc=852.3MB, time=115.60 memory used=5180.8MB, alloc=876.3MB, time=127.36 memory used=5461.9MB, alloc=900.3MB, time=139.97 memory used=5753.6MB, alloc=924.3MB, time=153.01 memory used=6060.2MB, alloc=948.3MB, time=167.23 memory used=6390.8MB, alloc=972.3MB, time=182.55 memory used=6745.4MB, alloc=996.3MB, time=199.36 memory used=7123.8MB, alloc=1020.3MB, time=218.35 memory used=7526.3MB, alloc=1044.3MB, time=237.61 memory used=7952.6MB, alloc=1068.3MB, time=257.84 memory used=8402.9MB, alloc=1092.3MB, time=279.30 |\^/| 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(); 1428317073 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [18 x y z + 7 x y, 15 x y - 14 y , -12 x y + 12 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 4 2 G := [-18 x y z + 8 y z , -12 x y - 9 x z, 10 z - 17 y ] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[18 x y z + 7 x y, 15 x y - 14 y , -12 x y + 12 y z], 2 3 3 3 4 2 [-18 x y z + 8 y z , -12 x y - 9 x z, 10 z - 17 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=48.3MB, alloc=32.3MB, time=0.82 memory used=68.6MB, alloc=32.3MB, time=1.11 memory used=87.6MB, alloc=56.3MB, time=1.45 memory used=126.7MB, alloc=60.3MB, time=2.27 memory used=163.9MB, alloc=60.3MB, time=2.91 memory used=199.7MB, alloc=84.3MB, time=3.46 memory used=255.4MB, alloc=84.3MB, time=4.33 memory used=307.0MB, alloc=108.3MB, time=5.35 memory used=382.0MB, alloc=140.3MB, time=6.76 memory used=475.0MB, alloc=164.3MB, time=8.73 memory used=580.9MB, alloc=188.3MB, time=10.88 memory used=700.1MB, alloc=212.3MB, time=13.27 memory used=823.0MB, alloc=492.3MB, time=15.72 memory used=966.0MB, alloc=516.3MB, time=18.57 memory used=1118.7MB, alloc=540.3MB, time=21.64 memory used=1278.9MB, alloc=564.3MB, time=25.02 memory used=1447.4MB, alloc=588.3MB, time=28.37 memory used=1618.2MB, alloc=612.3MB, time=32.56 memory used=1776.0MB, alloc=636.3MB, time=37.95 memory used=1940.6MB, alloc=660.3MB, time=44.00 memory used=2116.9MB, alloc=684.3MB, time=50.88 memory used=2305.9MB, alloc=708.3MB, time=58.38 memory used=2509.1MB, alloc=732.3MB, time=66.63 memory used=2726.5MB, alloc=756.3MB, time=75.89 memory used=2958.1MB, alloc=780.3MB, time=85.44 memory used=3204.7MB, alloc=804.3MB, time=95.77 memory used=3463.6MB, alloc=828.3MB, time=107.42 memory used=3741.6MB, alloc=852.3MB, time=120.23 memory used=4043.6MB, alloc=876.3MB, time=133.90 memory used=4369.6MB, alloc=900.3MB, time=149.16 memory used=4719.4MB, alloc=924.3MB, time=164.96 memory used=5093.3MB, alloc=948.3MB, time=181.77 memory used=5491.0MB, alloc=972.3MB, time=199.62 memory used=5912.8MB, alloc=996.3MB, time=218.47 memory used=6358.4MB, alloc=996.3MB, time=238.22 memory used=6804.1MB, alloc=1020.3MB, time=257.98 |\^/| 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(); 1428317373 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 F := [-16 y - 1, 12 x z + 19 y z, -12 y + 19 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [4 y + 3 x y, 20 y + 20 x, -17 z + 2 x ] > Problem := [F,G]; 2 3 4 2 Problem := [[-16 y - 1, 12 x z + 19 y z, -12 y + 19 x z ], 3 2 3 2 [4 y + 3 x y, 20 y + 20 x, -17 z + 2 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.81 memory used=68.7MB, alloc=32.3MB, time=1.13 memory used=88.9MB, alloc=56.3MB, time=1.45 memory used=129.3MB, alloc=60.3MB, time=2.08 memory used=166.8MB, alloc=84.3MB, time=2.68 memory used=228.6MB, alloc=84.3MB, time=3.84 memory used=286.4MB, alloc=108.3MB, time=4.88 memory used=362.9MB, alloc=140.3MB, time=6.35 memory used=449.3MB, alloc=164.3MB, time=9.27 N1 := 2281 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 51 #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 3 4 2 3 H := [-16 y - 1, 12 x z + 19 y z, -12 y + 19 z x, 4 y + 3 x y, 2 3 2 20 y + 20 x, -17 z + 2 x ] > J:=[op(GB),op(G)]; 3 2 3 2 J := [1, 4 y + 3 x y, 20 y + 20 x, -17 z + 2 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 18, 4, 2, 4, 3, 5/6, 5/6, 1/2, 5/12, 1/2, 1/3, 4, 6, 8, 3, 2, 3, 3, 3/4, 1/2, 1/4, 3/7, 3/7, 1/7, 7, 10, 1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=548.0MB, alloc=164.3MB, time=12.73 |\^/| 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(); 1428317389 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 3 F := [-15 y z + 8 x y, -3 x + 13 z , -12 y - 9 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 2 4 G := [8 y z - 20 z , 9 x z + 2 y , -20 x y + 2 y ] > Problem := [F,G]; 3 2 4 3 3 Problem := [[-15 y z + 8 x y, -3 x + 13 z , -12 y - 9 x], 2 2 3 3 2 2 4 [8 y z - 20 z , 9 x z + 2 y , -20 x y + 2 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=47.9MB, alloc=32.3MB, time=0.86 memory used=68.5MB, alloc=32.3MB, time=1.18 memory used=88.1MB, alloc=56.3MB, time=1.49 memory used=128.5MB, alloc=60.3MB, time=2.12 memory used=167.2MB, alloc=84.3MB, time=2.72 memory used=212.9MB, alloc=84.3MB, time=3.42 memory used=277.0MB, alloc=116.3MB, time=4.31 memory used=350.2MB, alloc=372.3MB, time=5.42 memory used=433.0MB, alloc=396.3MB, time=6.63 memory used=541.1MB, alloc=420.3MB, time=8.38 memory used=663.2MB, alloc=444.3MB, time=10.65 memory used=794.4MB, alloc=468.3MB, time=13.19 memory used=939.8MB, alloc=492.3MB, time=15.99 memory used=1100.6MB, alloc=516.3MB, time=19.05 memory used=1282.8MB, alloc=540.3MB, time=22.24 memory used=1469.0MB, alloc=564.3MB, time=26.01 memory used=1663.5MB, alloc=588.3MB, time=30.07 memory used=1863.4MB, alloc=612.3MB, time=34.32 memory used=2048.3MB, alloc=636.3MB, time=40.51 memory used=2237.1MB, alloc=660.3MB, time=47.35 memory used=2437.2MB, alloc=684.3MB, time=55.12 memory used=2651.0MB, alloc=708.3MB, time=63.86 memory used=2879.6MB, alloc=732.3MB, time=73.14 memory used=3123.2MB, alloc=756.3MB, time=83.13 memory used=3381.5MB, alloc=780.3MB, time=93.86 memory used=3649.7MB, alloc=804.3MB, time=105.80 memory used=3941.8MB, alloc=828.3MB, time=118.80 memory used=4258.0MB, alloc=852.3MB, time=133.16 memory used=4598.0MB, alloc=876.3MB, time=149.12 memory used=4962.0MB, alloc=900.3MB, time=166.98 memory used=5349.9MB, alloc=924.3MB, time=184.59 memory used=5761.8MB, alloc=924.3MB, time=202.72 memory used=6173.6MB, alloc=924.3MB, time=221.71 memory used=6585.4MB, alloc=948.3MB, time=240.46 |\^/| 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(); 1428317689 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 4 F := [-8 y - 4 x y z, 7 x z + 2 x z, 3 y + 11 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 G := [-11 y z + 18 z, 4 y z - 15 z , -9 x + x y z] > Problem := [F,G]; 4 3 4 Problem := [[-8 y - 4 x y z, 7 x z + 2 x z, 3 y + 11 y], 3 2 2 4 3 [-11 y z + 18 z, 4 y z - 15 z , -9 x + x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.54 memory used=48.2MB, alloc=32.3MB, time=0.88 memory used=67.8MB, alloc=56.3MB, time=1.20 memory used=107.5MB, alloc=60.3MB, time=1.85 memory used=145.6MB, alloc=60.3MB, time=2.44 memory used=183.6MB, alloc=84.3MB, time=3.06 memory used=234.2MB, alloc=84.3MB, time=3.87 memory used=292.8MB, alloc=92.3MB, time=4.79 memory used=348.1MB, alloc=116.3MB, time=5.66 memory used=428.2MB, alloc=140.3MB, time=7.19 memory used=524.3MB, alloc=164.3MB, time=9.10 memory used=635.6MB, alloc=188.3MB, time=11.23 memory used=760.8MB, alloc=212.3MB, time=13.62 memory used=866.8MB, alloc=492.3MB, time=15.81 memory used=1009.3MB, alloc=516.3MB, time=20.25 memory used=1158.4MB, alloc=540.3MB, time=25.34 memory used=1314.7MB, alloc=564.3MB, time=31.72 memory used=1494.9MB, alloc=588.3MB, time=39.00 memory used=1699.1MB, alloc=588.3MB, time=47.11 memory used=1903.3MB, alloc=612.3MB, time=55.30 memory used=2131.4MB, alloc=612.3MB, time=64.44 memory used=2359.4MB, alloc=612.3MB, time=73.64 memory used=2587.3MB, alloc=636.3MB, time=82.86 memory used=2839.8MB, alloc=660.3MB, time=92.90 N1 := 7929 > GB := Basis(F, plex(op(vars))); 2 4 3 GB := [9 x y + 1694 y, 3 y + 11 y, 3 x y + 77 y z, 7 x z + 2 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3035.0MB, alloc=660.3MB, time=96.55 memory used=3363.6MB, alloc=684.3MB, time=104.38 memory used=3648.3MB, alloc=708.3MB, time=116.56 N2 := 4271 #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)]; 4 3 4 3 H := [-8 y - 4 x y z, 7 x z + 2 x z, 3 y + 11 y, -11 y z + 18 z, 2 2 4 3 4 y z - 15 z , -9 x + x y z] > J:=[op(GB),op(G)]; 2 4 3 J := [9 x y + 1694 y, 3 y + 11 y, 3 x y + 77 y z, 7 x z + 2 x z, 3 2 2 4 3 -11 y z + 18 z, 4 y z - 15 z , -9 x + x 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 := [6, 13, 23, 4, 3, 4, 4, 1/2, 5/6, 5/6, 5/12, 7/12, 2/3, 7, 15, 24, 4, 3, 4, 4, 4/7, 6/7, 5/7, 3/7, 9/14, 4/7, -2, -1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3857.6MB, alloc=708.3MB, time=125.39 |\^/| 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(); 1428317827 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 F := [14 x z + 19 y , 3 y z + x y, -18 x y z - 9 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 4 2 G := [2 x y - 4 y z , 15 y z + 17 x y, -17 x - 7 x y ] > Problem := [F,G]; 3 2 3 2 2 Problem := [[14 x z + 19 y , 3 y z + x y, -18 x y z - 9 z], 2 2 3 3 2 4 2 [2 x y - 4 y z , 15 y z + 17 x y, -17 x - 7 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.20 memory used=26.4MB, alloc=32.3MB, time=0.56 memory used=48.1MB, alloc=32.3MB, time=0.89 memory used=68.8MB, alloc=56.3MB, time=1.21 memory used=111.3MB, alloc=60.3MB, time=1.87 memory used=150.7MB, alloc=60.3MB, time=2.51 memory used=191.7MB, alloc=92.3MB, time=3.15 memory used=258.6MB, alloc=92.3MB, time=4.06 memory used=316.9MB, alloc=116.3MB, time=4.82 memory used=394.8MB, alloc=372.3MB, time=6.06 memory used=473.1MB, alloc=396.3MB, time=7.30 memory used=578.3MB, alloc=420.3MB, time=8.87 memory used=702.1MB, alloc=444.3MB, time=11.20 memory used=835.4MB, alloc=468.3MB, time=13.88 memory used=983.6MB, alloc=492.3MB, time=16.87 memory used=1144.6MB, alloc=516.3MB, time=20.07 memory used=1305.5MB, alloc=540.3MB, time=24.65 memory used=1462.6MB, alloc=564.3MB, time=30.20 memory used=1627.8MB, alloc=588.3MB, time=36.85 memory used=1807.4MB, alloc=612.3MB, time=44.65 memory used=2011.0MB, alloc=636.3MB, time=53.45 memory used=2238.6MB, alloc=660.3MB, time=63.36 memory used=2490.1MB, alloc=684.3MB, time=74.19 memory used=2765.5MB, alloc=684.3MB, time=85.80 memory used=3041.0MB, alloc=684.3MB, time=97.71 memory used=3316.5MB, alloc=708.3MB, time=109.47 N1 := 8697 > GB := Basis(F, plex(op(vars))); 6 2 4 2 2 3 3 4 GB := [28 x y + 57 x y, 28 x y + 57 y , -14 x y + 57 y , 28 x z + 57 z, 3 2 3 2 3 -14 x z + 57 y z, -2 x y + 3 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3628.8MB, alloc=708.3MB, time=120.78 memory used=3775.4MB, alloc=708.3MB, time=123.80 N2 := 1643 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 2 2 2 3 H := [14 z x + 19 y , 3 y z + x y, -18 x y z - 9 z, 2 x y - 4 y z , 3 2 4 2 15 y z + 17 x y, -17 x - 7 x y ] > J:=[op(GB),op(G)]; 6 2 4 2 2 3 3 4 J := [28 x y + 57 x y, 28 x y + 57 y , -14 x y + 57 y , 28 x z + 57 z, 3 2 3 2 3 2 2 3 3 2 -14 x z + 57 y z, -2 x y + 3 z , 2 x y - 4 y z , 15 y z + 17 x y, 4 2 -17 x - 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 := [6, 17, 24, 4, 4, 3, 3, 1, 1, 5/6, 7/12, 3/4, 1/2, 9, 22, 43, 7, 6, 3, 3, 1, 8/9, 5/9, 11/18, 13/18, 7/18, -5, -19, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3927.2MB, alloc=708.3MB, time=128.99 |\^/| 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(); 1428317979 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 F := [-3 x + 7 x z, 3 x z + 16 z , 20 x y + 19 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 3 2 G := [16 y - 12 z , 4 y z - 10 x z , -8 y + 2 y ] > Problem := [F,G]; 4 3 3 2 Problem := [[-3 x + 7 x z, 3 x z + 16 z , 20 x y + 19 x], 4 3 3 2 3 2 [16 y - 12 z , 4 y z - 10 x z , -8 y + 2 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.51 memory used=47.5MB, alloc=32.3MB, time=0.85 memory used=67.7MB, alloc=56.3MB, time=1.19 memory used=108.7MB, alloc=60.3MB, time=1.86 memory used=147.9MB, alloc=60.3MB, time=2.49 memory used=183.6MB, alloc=84.3MB, time=3.08 memory used=229.3MB, alloc=84.3MB, time=3.79 memory used=287.2MB, alloc=116.3MB, time=4.88 memory used=363.1MB, alloc=140.3MB, time=6.32 memory used=458.8MB, alloc=164.3MB, time=8.10 memory used=565.5MB, alloc=188.3MB, time=10.36 memory used=675.2MB, alloc=212.3MB, time=13.68 memory used=791.2MB, alloc=236.3MB, time=18.13 memory used=931.2MB, alloc=260.3MB, time=23.52 memory used=1095.3MB, alloc=260.3MB, time=29.95 memory used=1259.4MB, alloc=284.3MB, time=36.56 N1 := 4875 > GB := Basis(F, plex(op(vars))); 7 5 4 3 4 2 GB := [7 x + 16 x , 20 x y + 19 x, -3 x + 7 x z, 9 x + 112 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1401.8MB, alloc=284.3MB, time=40.04 memory used=1617.4MB, alloc=540.3MB, time=43.74 memory used=1836.3MB, alloc=564.3MB, time=49.71 N2 := 1945 #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)]; 4 3 3 2 4 3 H := [-3 x + 7 x z, 3 x z + 16 z , 20 x y + 19 x, 16 y - 12 z , 3 2 3 2 4 y z - 10 x z , -8 y + 2 y ] > J:=[op(GB),op(G)]; 7 5 4 3 4 2 4 3 J := [7 x + 16 x , 20 x y + 19 x, -3 x + 7 x z, 9 x + 112 z , 16 y - 12 z , 3 2 3 2 4 y z - 10 x z , -8 y + 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 := [6, 12, 21, 4, 4, 4, 3, 2/3, 2/3, 2/3, 1/2, 5/12, 1/2, 7, 13, 28, 7, 7, 4, 3, 5/7, 4/7, 4/7, 4/7, 5/14, 5/14, -1, -7, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1886.8MB, alloc=564.3MB, time=51.56 |\^/| 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(); 1428318043 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 2 2 F := [-9 y z + 20 z , 2 x y - 11 z , x y + 6 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 3 G := [16 y z - 12 x , 17 x - 4 y , 7 x y - 14 z] > Problem := [F,G]; 3 3 3 3 2 2 Problem := [[-9 y z + 20 z , 2 x y - 11 z , x y + 6 x y z], 2 2 4 3 3 [16 y z - 12 x , 17 x - 4 y , 7 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=67.8MB, alloc=32.3MB, time=1.11 memory used=86.7MB, alloc=56.3MB, time=1.41 memory used=126.5MB, alloc=60.3MB, time=2.03 memory used=165.8MB, alloc=60.3MB, time=2.63 memory used=201.4MB, alloc=84.3MB, time=3.19 memory used=258.3MB, alloc=92.3MB, time=4.06 memory used=318.5MB, alloc=116.3MB, time=5.13 memory used=395.3MB, alloc=140.3MB, time=6.51 memory used=493.6MB, alloc=164.3MB, time=8.22 memory used=602.7MB, alloc=188.3MB, time=10.29 memory used=722.2MB, alloc=212.3MB, time=13.63 memory used=845.1MB, alloc=236.3MB, time=18.24 memory used=982.8MB, alloc=260.3MB, time=23.94 memory used=1144.5MB, alloc=260.3MB, time=30.55 memory used=1306.2MB, alloc=284.3MB, time=37.16 memory used=1492.0MB, alloc=284.3MB, time=44.68 N1 := 5369 > GB := Basis(F, plex(op(vars))); GB := 4 3 2 3 4 3 2 2 3 3 [11 x y + 432 x y , 9 x y - 20 x y , x y + 6 x y z, -2 x y + 11 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1635.2MB, alloc=284.3MB, time=48.48 memory used=1844.8MB, alloc=540.3MB, time=51.97 memory used=2056.3MB, alloc=564.3MB, time=55.93 memory used=2279.4MB, alloc=588.3MB, time=62.68 memory used=2482.0MB, alloc=612.3MB, time=71.76 memory used=2708.9MB, alloc=636.3MB, time=82.05 N2 := 4353 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 3 3 2 2 2 2 H := [-9 y z + 20 z , 2 y x - 11 z , x y + 6 x y z, 16 y z - 12 x , 4 3 3 17 x - 4 y , 7 x y - 14 z] > J:=[op(GB),op(G)]; 4 3 2 3 4 3 2 2 3 3 J := [11 x y + 432 x y , 9 x y - 20 x y , x y + 6 x y z, -2 x y + 11 z , 2 2 4 3 3 16 y z - 12 x , 17 x - 4 y , 7 x y - 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 := [6, 16, 23, 4, 4, 3, 3, 5/6, 1, 5/6, 1/2, 7/12, 1/2, 7, 18, 31, 7, 4, 4, 3, 1, 1, 4/7, 5/7, 5/7, 2/7, -2, -8, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2772.3MB, alloc=636.3MB, time=84.72 |\^/| 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(); 1428318139 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [-15 x y - 6 x z , 12 x z + 10 z , 15 x y z - 5 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [12 y , 12 y z + 6 x , -4 x y - 19] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[-15 x y - 6 x z , 12 x z + 10 z , 15 x y z - 5 y z ], 3 2 2 2 [12 y , 12 y z + 6 x , -4 x 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.54 memory used=48.6MB, alloc=32.3MB, time=0.91 memory used=70.2MB, alloc=56.3MB, time=1.35 N1 := 449 > GB := Basis(F, plex(op(vars))); 2 3 3 7 4 4 2 6 3 GB := [6 x y + 5 x y , 72 x y + 125 x y , -x y + x y z, 6 x y + 5 x y z, 3 2 -3 x y + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=110.5MB, alloc=60.3MB, time=2.09 memory used=150.2MB, alloc=60.3MB, time=2.70 memory used=188.8MB, alloc=84.3MB, time=3.33 memory used=229.1MB, alloc=84.3MB, time=3.97 memory used=289.6MB, alloc=92.3MB, time=4.91 memory used=347.4MB, alloc=116.3MB, time=5.84 memory used=429.0MB, alloc=140.3MB, time=7.11 memory used=525.3MB, alloc=164.3MB, time=9.23 N2 := 1061 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 3 H := [-15 x y - 6 x z , 12 x z + 10 z , 15 x y z - 5 y z , 12 y , 2 2 2 12 y z + 6 x , -4 x y - 19] > J:=[op(GB),op(G)]; 2 3 3 7 4 4 2 6 3 J := [6 x y + 5 x y , 72 x y + 125 x y , -x y + x y z, 6 x y + 5 x y z, 3 2 3 2 2 2 -3 x y + z , 12 y , 12 y z + 6 x , -4 x 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 := [6, 14, 20, 4, 2, 3, 2, 5/6, 5/6, 2/3, 1/2, 1/2, 1/2, 8, 19, 38, 8, 2, 7, 2, 7/8, 1, 1/2, 11/16, 3/4, 1/4, -5, -18, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=549.9MB, alloc=164.3MB, time=10.00 |\^/| 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(); 1428318150 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-x z - 2 y, 13 y z - 12 x, 12 x y z + 13 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 G := [-9 x y - 20 x , 5 x z - 10 x , 6 x z - 17 y ] > Problem := [F,G]; 2 2 2 Problem := [[-x z - 2 y, 13 y z - 12 x, 12 x y z + 13 x y ], 2 2 2 2 2 2 2 [-9 x y - 20 x , 5 x z - 10 x , 6 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.81 memory used=68.0MB, alloc=32.3MB, time=1.11 memory used=86.8MB, alloc=56.3MB, time=1.42 memory used=126.2MB, alloc=60.3MB, time=2.04 memory used=164.2MB, alloc=60.3MB, time=2.63 memory used=200.9MB, alloc=84.3MB, time=3.22 memory used=258.3MB, alloc=92.3MB, time=4.15 memory used=313.6MB, alloc=116.3MB, time=5.04 memory used=390.3MB, alloc=140.3MB, time=6.30 memory used=487.4MB, alloc=164.3MB, time=8.17 memory used=599.4MB, alloc=188.3MB, time=10.30 memory used=724.3MB, alloc=468.3MB, time=12.66 memory used=866.1MB, alloc=492.3MB, time=15.37 memory used=1017.2MB, alloc=516.3MB, time=18.74 memory used=1167.6MB, alloc=540.3MB, time=23.30 memory used=1323.4MB, alloc=564.3MB, time=28.49 memory used=1484.7MB, alloc=588.3MB, time=34.92 memory used=1665.2MB, alloc=612.3MB, time=42.33 memory used=1869.6MB, alloc=636.3MB, time=50.68 memory used=2098.0MB, alloc=660.3MB, time=60.09 memory used=2350.4MB, alloc=660.3MB, time=70.36 memory used=2602.6MB, alloc=660.3MB, time=80.62 memory used=2854.9MB, alloc=684.3MB, time=90.88 memory used=3131.2MB, alloc=684.3MB, time=102.07 memory used=3407.3MB, alloc=708.3MB, time=113.29 memory used=3707.5MB, alloc=708.3MB, time=125.40 memory used=4008.1MB, alloc=732.3MB, time=137.31 N1 := 10059 > GB := Basis(F, plex(op(vars))); 2 GB := [2197 x + 3456 x, 169 y + 144 x, 12 x z + 13 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 725 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 H := [-x z - 2 y, 13 y z - 12 x, 12 x y z + 13 x y , -9 x y - 20 x , 2 2 2 2 5 x z - 10 x , 6 z x - 17 y ] > J:=[op(GB),op(G)]; 2 2 2 2 J := [2197 x + 3456 x, 169 y + 144 x, 12 x z + 13 x, -9 x y - 20 x , 2 2 2 2 5 x z - 10 x , 6 z x - 17 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, 16, 19, 4, 2, 2, 2, 1, 5/6, 5/6, 3/4, 1/2, 5/12, 6, 12, 15, 4, 2, 2, 2, 1, 1/2, 1/2, 5/6, 1/4, 1/4, 4, 4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=4178.5MB, alloc=732.3MB, time=141.91 |\^/| 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(); 1428318306 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [6 x z + 2 y, 6 z + 20 y, -8 x y z + 20 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 2 2 G := [-13 z - 8 z, 6 x y + 14 z , -12 y z - 14 y ] > Problem := [F,G]; 3 2 2 3 Problem := [[6 x z + 2 y, 6 z + 20 y, -8 x y z + 20 y z ], 2 2 2 4 2 2 2 [-13 z - 8 z, 6 x y + 14 z , -12 y z - 14 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=47.1MB, alloc=32.3MB, time=0.83 memory used=66.9MB, alloc=32.3MB, time=1.14 memory used=86.1MB, alloc=56.3MB, time=1.44 memory used=124.8MB, alloc=60.3MB, time=2.06 memory used=161.2MB, alloc=60.3MB, time=2.65 memory used=195.4MB, alloc=84.3MB, time=3.21 memory used=251.9MB, alloc=92.3MB, time=4.15 memory used=306.8MB, alloc=116.3MB, time=5.05 memory used=383.2MB, alloc=116.3MB, time=6.26 memory used=456.7MB, alloc=140.3MB, time=7.51 memory used=551.7MB, alloc=140.3MB, time=9.04 memory used=644.1MB, alloc=164.3MB, time=10.62 memory used=734.9MB, alloc=188.3MB, time=12.29 memory used=857.5MB, alloc=468.3MB, time=14.79 memory used=1002.7MB, alloc=492.3MB, time=17.77 memory used=1156.1MB, alloc=516.3MB, time=21.66 memory used=1300.0MB, alloc=540.3MB, time=26.92 memory used=1452.8MB, alloc=564.3MB, time=33.30 memory used=1629.6MB, alloc=588.3MB, time=40.55 memory used=1830.4MB, alloc=612.3MB, time=48.69 memory used=2055.3MB, alloc=636.3MB, time=57.77 N1 := 5771 > GB := Basis(F, plex(op(vars))); GB := 10 9 6 2 3 3 2 [3 x y + 25 x y, 30 x y + y , 3 z x + y, -10 x y + y z, 3 z + 10 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2314.7MB, alloc=636.3MB, time=64.08 memory used=2614.7MB, alloc=636.3MB, time=69.27 memory used=2911.1MB, alloc=660.3MB, time=76.12 memory used=3165.8MB, alloc=684.3MB, time=86.94 N2 := 3781 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 3 2 H := [6 x z + 2 y, 6 z + 20 y, -8 x y z + 20 y z , -13 z - 8 z, 2 2 4 2 2 2 6 x y + 14 z , -12 y z - 14 y ] > J:=[op(GB),op(G)]; 10 9 6 2 3 3 2 J := [3 x y + 25 x y, 30 x y + y , 3 z x + y, -10 x y + y z, 3 z + 10 y, 2 2 2 4 2 2 2 -13 z - 8 z, 6 x y + 14 z , -12 y z - 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 := [6, 14, 20, 4, 3, 2, 4, 1/2, 5/6, 1, 1/4, 7/12, 2/3, 8, 18, 38, 11, 10, 2, 4, 5/8, 7/8, 3/4, 3/8, 11/16, 7/16, -4, -18, -7] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3321.6MB, alloc=684.3MB, 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(); 1428318413 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 2 2 F := [12 x z - 9 x z , -12 x + 11 x y z, 12 x y z - 8 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 G := [15 x z - x, 5 x y + 16 x , -x - 2 x y z] > Problem := [F,G]; 3 3 4 2 2 Problem := [[12 x z - 9 x z , -12 x + 11 x y z, 12 x y z - 8 y z], 3 2 4 [15 x z - x, 5 x y + 16 x , -x - 2 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.81 memory used=68.1MB, alloc=32.3MB, time=1.12 memory used=88.0MB, alloc=56.3MB, time=1.43 memory used=128.4MB, alloc=60.3MB, time=2.07 memory used=168.7MB, alloc=84.3MB, time=2.81 memory used=227.9MB, alloc=108.3MB, time=3.92 memory used=305.1MB, alloc=116.3MB, time=5.41 memory used=374.9MB, alloc=140.3MB, time=6.72 memory used=461.6MB, alloc=164.3MB, time=8.40 memory used=563.9MB, alloc=188.3MB, time=10.50 memory used=669.7MB, alloc=212.3MB, time=14.14 memory used=785.8MB, alloc=236.3MB, time=18.01 memory used=913.0MB, alloc=260.3MB, time=23.00 memory used=1058.2MB, alloc=284.3MB, time=28.98 memory used=1227.4MB, alloc=284.3MB, time=35.95 memory used=1396.6MB, alloc=308.3MB, time=42.73 memory used=1589.7MB, alloc=308.3MB, time=50.42 memory used=1782.8MB, alloc=308.3MB, time=59.13 memory used=1975.8MB, alloc=332.3MB, time=67.18 memory used=2192.9MB, alloc=332.3MB, time=76.54 memory used=2410.0MB, alloc=356.3MB, time=85.49 memory used=2651.1MB, alloc=380.3MB, time=95.28 N1 := 8239 > GB := Basis(F, plex(op(vars))); 6 4 4 4 4 5 2 4 5 3 GB := [3 x - 2 x , 121 x y - 48 x , -11 x y + 6 x z, -33 x y + 8 y z, 3 3 -4 x z + 3 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2718.2MB, alloc=380.3MB, time=96.83 memory used=2921.5MB, alloc=636.3MB, time=100.46 memory used=3101.0MB, alloc=636.3MB, time=103.85 memory used=3271.3MB, alloc=636.3MB, time=106.94 memory used=3426.8MB, alloc=660.3MB, time=110.18 memory used=3623.7MB, alloc=684.3MB, time=114.29 memory used=3851.0MB, alloc=708.3MB, time=119.00 memory used=4067.4MB, alloc=732.3MB, time=123.51 memory used=4278.4MB, alloc=756.3MB, time=128.12 memory used=4480.9MB, alloc=780.3MB, time=132.51 memory used=4687.3MB, alloc=804.3MB, time=136.58 memory used=5094.3MB, alloc=828.3MB, time=140.67 memory used=5487.5MB, alloc=852.3MB, time=144.96 memory used=5895.7MB, alloc=876.3MB, time=149.44 memory used=6189.5MB, alloc=900.3MB, time=153.17 memory used=6470.6MB, alloc=924.3MB, time=164.12 memory used=6838.9MB, alloc=948.3MB, time=179.05 memory used=7220.6MB, alloc=972.3MB, time=195.09 memory used=7606.7MB, alloc=996.3MB, time=211.50 memory used=8000.6MB, alloc=1020.3MB, time=229.15 memory used=8404.0MB, alloc=1044.3MB, time=247.61 |\^/| 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(); 1428318713 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 2 F := [16 x y + 7 z , -9 y + 2 z , 20 x y z - 19 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 4 3 G := [19 x y z + 6 x , -20 x y - 18 y z , -6 y - 14 z ] > Problem := [F,G]; 3 3 3 3 2 Problem := [[16 x y + 7 z , -9 y + 2 z , 20 x y z - 19 x], 2 3 2 2 4 3 [19 x y z + 6 x , -20 x y - 18 y z , -6 y - 14 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.6MB, alloc=40.3MB, time=0.69 memory used=62.5MB, alloc=44.3MB, time=1.18 memory used=90.6MB, alloc=44.3MB, time=1.62 memory used=120.1MB, alloc=68.3MB, time=2.06 memory used=167.2MB, alloc=68.3MB, time=2.87 memory used=211.9MB, alloc=68.3MB, time=3.66 memory used=249.7MB, alloc=92.3MB, time=4.26 memory used=327.1MB, alloc=100.3MB, time=5.35 memory used=400.3MB, alloc=124.3MB, time=6.44 memory used=474.6MB, alloc=124.3MB, time=7.40 memory used=545.8MB, alloc=380.3MB, time=8.43 memory used=629.9MB, alloc=404.3MB, time=9.95 memory used=746.4MB, alloc=404.3MB, time=11.74 memory used=865.2MB, alloc=428.3MB, time=13.33 memory used=1005.7MB, alloc=452.3MB, time=15.24 memory used=1158.4MB, alloc=476.3MB, time=17.48 memory used=1284.9MB, alloc=476.3MB, time=19.07 memory used=1413.2MB, alloc=500.3MB, time=20.68 memory used=1553.3MB, alloc=500.3MB, time=22.21 memory used=1671.9MB, alloc=500.3MB, time=24.07 memory used=1788.8MB, alloc=524.3MB, time=25.38 memory used=1911.2MB, alloc=524.3MB, time=26.83 memory used=2003.3MB, alloc=524.3MB, time=28.15 memory used=2093.0MB, alloc=548.3MB, time=29.85 memory used=2173.2MB, alloc=548.3MB, time=31.12 memory used=2283.5MB, alloc=548.3MB, time=33.14 memory used=2367.4MB, alloc=548.3MB, time=34.78 memory used=2427.5MB, alloc=548.3MB, time=35.97 memory used=2502.2MB, alloc=548.3MB, time=37.45 memory used=2566.4MB, alloc=572.3MB, time=38.73 memory used=2621.3MB, alloc=572.3MB, time=39.73 memory used=2697.1MB, alloc=572.3MB, time=40.89 memory used=2937.7MB, alloc=596.3MB, time=44.27 memory used=3172.5MB, alloc=620.3MB, time=47.83 memory used=3378.5MB, alloc=644.3MB, time=50.45 memory used=3568.7MB, alloc=668.3MB, time=53.72 memory used=3743.6MB, alloc=692.3MB, time=57.52 memory used=3903.6MB, alloc=716.3MB, time=60.85 memory used=4031.8MB, alloc=740.3MB, time=63.30 memory used=4171.9MB, alloc=740.3MB, time=66.06 memory used=4303.3MB, alloc=740.3MB, time=68.34 memory used=4421.3MB, alloc=740.3MB, time=70.41 memory used=4541.3MB, alloc=764.3MB, time=72.89 memory used=4946.3MB, alloc=788.3MB, time=79.47 memory used=5359.9MB, alloc=812.3MB, time=84.78 memory used=5772.8MB, alloc=836.3MB, time=92.28 memory used=6168.7MB, alloc=860.3MB, time=97.72 memory used=6589.6MB, alloc=884.3MB, time=103.98 memory used=6955.0MB, alloc=908.3MB, time=108.86 memory used=7334.5MB, alloc=932.3MB, time=114.35 memory used=7729.8MB, alloc=956.3MB, time=120.86 memory used=8077.7MB, alloc=980.3MB, time=125.86 memory used=8421.5MB, alloc=1004.3MB, time=130.57 memory used=8656.6MB, alloc=1028.3MB, time=135.53 memory used=8907.2MB, alloc=1052.3MB, time=140.81 memory used=9457.4MB, alloc=1076.3MB, time=151.67 memory used=9981.8MB, alloc=1100.3MB, time=163.66 memory used=10620.5MB, alloc=1124.3MB, time=174.47 memory used=11225.7MB, alloc=1148.3MB, time=184.20 memory used=11810.5MB, alloc=1172.3MB, time=193.75 memory used=12407.0MB, alloc=1196.3MB, time=202.82 memory used=13072.9MB, alloc=1220.3MB, time=214.47 memory used=13692.0MB, alloc=1244.3MB, time=227.29 memory used=14259.7MB, alloc=1268.3MB, time=239.13 memory used=14804.5MB, alloc=1292.3MB, time=250.56 memory used=15400.6MB, alloc=1316.3MB, time=263.25 |\^/| 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(); 1428319014 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 4 2 F := [-14 y z + x, -7 x y - 16 y , 15 z - 7 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 G := [-18 y z + 16 y, -18 y z + 16 z, 6 z - 7 y ] > Problem := [F,G]; 2 2 2 4 4 2 Problem := [[-14 y z + x, -7 x y - 16 y , 15 z - 7 x ], 2 2 4 3 [-18 y z + 16 y, -18 y z + 16 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=32.0MB, alloc=40.3MB, time=0.60 memory used=60.4MB, alloc=40.3MB, time=1.03 memory used=87.8MB, alloc=40.3MB, time=1.46 memory used=114.4MB, alloc=68.3MB, time=1.91 memory used=160.2MB, alloc=68.3MB, time=2.61 memory used=205.6MB, alloc=92.3MB, time=3.45 memory used=272.3MB, alloc=92.3MB, time=4.68 memory used=332.9MB, alloc=116.3MB, time=5.85 memory used=412.8MB, alloc=148.3MB, time=7.38 memory used=510.8MB, alloc=172.3MB, time=9.19 memory used=620.8MB, alloc=196.3MB, time=11.39 memory used=733.9MB, alloc=220.3MB, time=14.65 memory used=854.7MB, alloc=244.3MB, time=18.92 memory used=989.8MB, alloc=268.3MB, time=24.39 memory used=1148.8MB, alloc=268.3MB, time=30.74 memory used=1307.8MB, alloc=292.3MB, time=37.01 memory used=1490.8MB, alloc=292.3MB, time=44.36 memory used=1673.7MB, alloc=292.3MB, time=51.65 memory used=1856.6MB, alloc=316.3MB, time=58.93 memory used=2063.4MB, alloc=340.3MB, time=66.87 N1 := 6975 > GB := Basis(F, plex(op(vars))); 4 2 2 2 2 3 3 4 2 GB := [2401 x + 60 x , 1372 x y - 15 x , 7 x y + 16 x y , 3136 y + 15 x , 2 2 2 4 2 -98 x y + 15 x z , 14 y z - x, 15 z - 7 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2192.9MB, alloc=340.3MB, time=69.68 memory used=2447.6MB, alloc=596.3MB, time=74.01 memory used=2708.6MB, alloc=620.3MB, time=78.27 memory used=2992.3MB, alloc=644.3MB, time=83.55 memory used=3278.0MB, alloc=668.3MB, time=89.21 memory used=3566.9MB, alloc=692.3MB, time=94.94 memory used=3853.9MB, alloc=716.3MB, time=102.08 memory used=4100.9MB, alloc=740.3MB, time=111.54 memory used=4347.8MB, alloc=764.3MB, time=121.36 memory used=4598.2MB, alloc=788.3MB, time=132.44 memory used=4853.5MB, alloc=812.3MB, time=144.47 memory used=5132.7MB, alloc=836.3MB, time=157.05 memory used=5435.9MB, alloc=860.3MB, time=171.03 memory used=5763.0MB, alloc=884.3MB, time=185.97 memory used=6114.1MB, alloc=908.3MB, time=201.93 memory used=6489.1MB, alloc=932.3MB, time=218.71 memory used=6888.0MB, alloc=956.3MB, time=236.55 memory used=7310.9MB, alloc=980.3MB, time=255.28 |\^/| 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(); 1428319314 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 4 F := [11 x y z - 18 x , -13 x z - 10 x y z, -7 y - 13 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [19 x z + 8, -5 x - 6 x, 0] > Problem := [F,G]; 2 3 2 2 2 4 Problem := [[11 x y z - 18 x , -13 x z - 10 x y z, -7 y - 13 y], 2 3 [19 x z + 8, -5 x - 6 x, 0]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [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=48.1MB, alloc=32.3MB, time=0.82 memory used=69.1MB, alloc=56.3MB, time=1.21 N1 := 563 > GB := Basis(F, plex(op(vars))); 12 3 6 3 4 GB := [1750329 x + 2162875 x , -63 x + 55 x y, 7 y + 13 y, 8 3 9 2 2 3 7938 x + 7865 x z, 500094 x + 432575 x y z, 143 x z + 180 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=110.3MB, alloc=60.3MB, time=2.03 memory used=149.4MB, alloc=60.3MB, time=2.60 memory used=189.5MB, alloc=84.3MB, time=3.32 N2 := 723 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 2 4 2 H := [11 x y z - 18 x , -13 x z - 10 x y z, -7 y - 13 y, 19 z x + 8, 3 -5 x - 6 x, 0] > J:=[op(GB),op(G)]; 12 3 6 3 4 J := [1750329 x + 2162875 x , -63 x + 55 x y, 7 y + 13 y, 8 3 9 2 2 3 7938 x + 7865 x z, 500094 x + 432575 x y z, 143 x z + 180 x , 2 3 19 z x + 8, -5 x - 6 x, 0] > > 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, 10, -infinity, 4, 3, 4, 2, 2/3, 1/2, 1/2, 7/11, 4/11, 4/11, 9, 14, -infinity, 12, 12, 4, 2, 7/9, 1/3, 4/9, 13/17, 4/17, 4/17, -4, undefined, -8] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=232.4MB, alloc=84.3MB, time=4.29 |\^/| 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(); 1428319319 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 4 2 F := [17 x y z - 20, 6 z - 5 x z, -9 x - 7 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [-4 x y + 10 x z , -15 x + 3 y z, -3 z + 2 z ] > Problem := [F,G]; 2 4 2 4 2 Problem := [[17 x y z - 20, 6 z - 5 x z, -9 x - 7 x z], 2 2 2 3 2 [-4 x y + 10 x z , -15 x + 3 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.50 memory used=47.9MB, alloc=32.3MB, time=0.82 memory used=68.0MB, alloc=56.3MB, time=1.15 memory used=107.9MB, alloc=60.3MB, time=1.77 memory used=145.5MB, alloc=60.3MB, time=2.35 memory used=181.4MB, alloc=84.3MB, time=2.91 memory used=236.9MB, alloc=84.3MB, time=3.79 memory used=289.2MB, alloc=116.3MB, time=4.62 memory used=363.9MB, alloc=140.3MB, time=5.79 memory used=460.0MB, alloc=140.3MB, time=7.29 memory used=551.7MB, alloc=420.3MB, time=8.75 memory used=669.6MB, alloc=420.3MB, time=10.63 memory used=785.7MB, alloc=444.3MB, time=12.58 memory used=922.0MB, alloc=468.3MB, time=14.86 memory used=1078.1MB, alloc=492.3MB, time=17.56 memory used=1249.4MB, alloc=516.3MB, time=20.69 memory used=1411.4MB, alloc=540.3MB, time=23.68 memory used=1573.6MB, alloc=564.3MB, time=26.95 memory used=1778.1MB, alloc=588.3MB, time=31.11 memory used=1977.7MB, alloc=612.3MB, time=35.20 memory used=2151.2MB, alloc=636.3MB, time=38.90 memory used=2329.5MB, alloc=660.3MB, time=42.62 memory used=2516.7MB, alloc=684.3MB, time=46.56 memory used=2687.2MB, alloc=708.3MB, time=50.18 memory used=2853.7MB, alloc=732.3MB, time=53.71 memory used=3018.3MB, alloc=756.3MB, time=57.27 memory used=3178.2MB, alloc=780.3MB, time=62.04 memory used=3439.3MB, alloc=804.3MB, time=71.52 memory used=3701.0MB, alloc=828.3MB, time=81.49 memory used=3969.9MB, alloc=852.3MB, time=92.29 memory used=4248.0MB, alloc=876.3MB, time=103.74 memory used=4537.3MB, alloc=900.3MB, time=115.80 memory used=4838.5MB, alloc=924.3MB, time=128.62 memory used=5152.4MB, alloc=948.3MB, time=142.01 memory used=5473.1MB, alloc=972.3MB, time=156.66 memory used=5811.7MB, alloc=996.3MB, time=172.74 memory used=6174.2MB, alloc=1020.3MB, time=189.85 memory used=6560.6MB, alloc=1044.3MB, time=207.75 memory used=6971.0MB, alloc=1068.3MB, time=226.75 memory used=7405.4MB, alloc=1092.3MB, time=246.61 memory used=7863.7MB, alloc=1116.3MB, time=267.42 |\^/| 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(); 1428319619 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 3 F := [-17 x y + y z, -13 x + 12 y , -5 x y - 15 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 3 G := [8 x z - 5 y z , 3 x y + 7 z , 10 y z - 6 y] > Problem := [F,G]; 3 2 2 2 2 2 3 Problem := [[-17 x y + y z, -13 x + 12 y , -5 x y - 15 z ], 2 2 3 3 3 3 [8 x z - 5 y z , 3 x y + 7 z , 10 y z - 6 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.52 memory used=47.8MB, alloc=32.3MB, time=0.83 memory used=68.6MB, alloc=60.3MB, time=1.16 memory used=110.6MB, alloc=68.3MB, time=1.79 memory used=151.9MB, alloc=92.3MB, time=2.39 memory used=218.0MB, alloc=92.3MB, time=3.27 memory used=278.1MB, alloc=116.3MB, time=4.15 memory used=344.7MB, alloc=116.3MB, time=5.08 memory used=401.6MB, alloc=372.3MB, time=5.78 memory used=488.5MB, alloc=396.3MB, time=6.98 memory used=598.1MB, alloc=420.3MB, time=8.56 memory used=718.9MB, alloc=444.3MB, time=10.14 memory used=838.4MB, alloc=444.3MB, time=11.70 memory used=945.0MB, alloc=468.3MB, time=12.91 memory used=1047.5MB, alloc=468.3MB, time=14.28 memory used=1140.0MB, alloc=492.3MB, time=15.76 memory used=1220.8MB, alloc=492.3MB, time=17.05 memory used=1302.9MB, alloc=492.3MB, time=18.48 memory used=1362.7MB, alloc=492.3MB, time=19.57 memory used=1443.5MB, alloc=492.3MB, time=20.91 memory used=1494.8MB, alloc=492.3MB, time=21.92 memory used=1554.7MB, alloc=516.3MB, time=23.12 memory used=1619.1MB, alloc=516.3MB, time=24.41 memory used=1677.6MB, alloc=516.3MB, time=25.56 memory used=1725.1MB, alloc=516.3MB, time=26.37 memory used=1777.0MB, alloc=516.3MB, time=27.51 memory used=1951.9MB, alloc=540.3MB, time=30.33 memory used=2135.4MB, alloc=564.3MB, time=33.10 memory used=2304.5MB, alloc=588.3MB, time=36.14 memory used=2538.2MB, alloc=612.3MB, time=41.23 memory used=2756.2MB, alloc=636.3MB, time=46.26 memory used=3002.7MB, alloc=660.3MB, time=51.64 memory used=3231.9MB, alloc=684.3MB, time=57.23 memory used=3450.0MB, alloc=708.3MB, time=65.39 memory used=3657.4MB, alloc=732.3MB, time=74.21 memory used=3872.7MB, alloc=756.3MB, time=83.97 memory used=4090.7MB, alloc=780.3MB, time=94.72 memory used=4329.2MB, alloc=804.3MB, time=106.72 memory used=4591.6MB, alloc=828.3MB, time=119.81 memory used=4877.9MB, alloc=852.3MB, time=133.97 memory used=5188.2MB, alloc=876.3MB, time=149.27 memory used=5522.4MB, alloc=900.3MB, time=165.59 memory used=5880.5MB, alloc=924.3MB, time=182.91 memory used=6262.6MB, alloc=948.3MB, time=200.77 memory used=6668.6MB, alloc=972.3MB, time=219.98 memory used=7098.6MB, alloc=996.3MB, time=240.30 |\^/| 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(); 1428319919 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 2 F := [-14 x z + 18 x , -12 x y - 8 y z , -4 x z + 19] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 G := [-9 x z , -18 x y - 15, -18 x y z - 4 x ] > Problem := [F,G]; 3 2 3 2 2 2 Problem := [[-14 x z + 18 x , -12 x y - 8 y z , -4 x z + 19], 2 2 2 2 2 3 [-9 x z , -18 x y - 15, -18 x y z - 4 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.53 memory used=47.9MB, alloc=32.3MB, time=0.84 memory used=68.1MB, alloc=32.3MB, time=1.15 memory used=88.5MB, alloc=56.3MB, time=1.56 memory used=131.2MB, alloc=60.3MB, time=2.39 memory used=168.9MB, alloc=84.3MB, time=3.15 N1 := 1183 > GB := Basis(F, plex(op(vars))); 2 GB := [931 x - 324, 14274217991299 y + 66119763456 y, 36 z - 133] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=221.4MB, alloc=84.3MB, time=4.68 N2 := 413 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 2 2 2 2 H := [-14 x z + 18 x , -12 x y - 8 y z , -4 x z + 19, -9 x z , 2 2 2 3 -18 x y - 15, -18 x y z - 4 x ] > J:=[op(GB),op(G)]; 2 2 2 J := [931 x - 324, 14274217991299 y + 66119763456 y, 36 z - 133, -9 x z , 2 2 2 3 -18 x y - 15, -18 x y z - 4 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 23, 4, 3, 2, 2, 1, 1/2, 5/6, 8/13, 4/13, 5/13, 6, 10, 16, 4, 3, 2, 2, 2/3, 1/2, 1/2, 5/13, 4/13, 3/13, 4, 7, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=263.5MB, alloc=84.3MB, time=5.45 |\^/| 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(); 1428319927 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [11 x y z + 12 x, -x y z - 4 x z, 14 x y z - 10 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [15 x z + 4 x y z, -10 - 7 z, -16 y z + 9 x z] > Problem := [F,G]; 2 2 2 3 Problem := [[11 x y z + 12 x, -x y z - 4 x z, 14 x y z - 10 z ], 3 2 2 [15 x z + 4 x y z, -10 - 7 z, -16 y z + 9 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=32.3MB, time=0.82 memory used=66.9MB, alloc=56.3MB, time=1.14 memory used=107.2MB, alloc=60.3MB, time=1.76 memory used=145.8MB, alloc=60.3MB, time=2.36 memory used=182.6MB, alloc=84.3MB, time=2.94 memory used=237.1MB, alloc=84.3MB, time=3.80 memory used=292.5MB, alloc=116.3MB, time=4.68 memory used=369.6MB, alloc=116.3MB, time=5.88 memory used=444.5MB, alloc=140.3MB, time=7.10 memory used=539.3MB, alloc=164.3MB, time=8.64 memory used=633.4MB, alloc=188.3MB, time=10.53 memory used=736.4MB, alloc=468.3MB, time=12.55 memory used=879.0MB, alloc=492.3MB, time=15.30 memory used=1033.0MB, alloc=516.3MB, time=18.41 memory used=1195.1MB, alloc=540.3MB, time=21.75 memory used=1360.2MB, alloc=564.3MB, time=26.34 memory used=1517.0MB, alloc=588.3MB, time=31.84 memory used=1682.9MB, alloc=612.3MB, time=38.26 memory used=1861.1MB, alloc=636.3MB, time=45.18 memory used=2048.1MB, alloc=660.3MB, time=53.36 memory used=2255.7MB, alloc=684.3MB, time=62.61 memory used=2487.4MB, alloc=708.3MB, time=72.92 memory used=2742.9MB, alloc=732.3MB, time=84.27 memory used=3022.4MB, alloc=756.3MB, time=96.67 memory used=3325.9MB, alloc=780.3MB, time=110.80 memory used=3653.3MB, alloc=780.3MB, time=125.80 memory used=3980.6MB, alloc=780.3MB, time=140.95 memory used=4308.0MB, alloc=804.3MB, time=156.33 memory used=4659.2MB, alloc=804.3MB, time=171.56 memory used=5010.5MB, alloc=804.3MB, time=186.02 memory used=5361.7MB, alloc=828.3MB, time=200.16 memory used=5736.8MB, alloc=828.3MB, time=215.19 memory used=6111.9MB, alloc=852.3MB, time=230.68 memory used=6510.9MB, alloc=876.3MB, time=247.63 |\^/| 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(); 1428320227 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 F := [-3 x - 2 z , 19 x y - 18 y, -18 x z - 20 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 G := [-12 y z, 11 y z - 4, -4 z - z ] > Problem := [F,G]; 3 2 3 3 2 Problem := [[-3 x - 2 z , 19 x y - 18 y, -18 x z - 20 x z ], 3 4 2 [-12 y z, 11 y z - 4, -4 z - z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=32.3MB, time=0.83 memory used=69.0MB, alloc=56.3MB, time=1.24 memory used=110.9MB, alloc=60.3MB, time=2.10 N1 := 733 > GB := Basis(F, plex(op(vars))); 7 4 3 2 3 4 4 GB := [243 x + 200 x , 243 x y + 200 y, 2187 x y + 1900 y , 9 x z + 10 x , 3 2 9 y z + 10 y, 3 x + 2 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=145.0MB, alloc=60.3MB, time=2.78 memory used=183.0MB, alloc=84.3MB, time=3.41 N2 := 669 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 3 2 3 H := [-3 x - 2 z , 19 x y - 18 y, -18 x z - 20 x z , -12 z y, 11 z y - 4, 4 2 -4 z - z ] > J:=[op(GB),op(G)]; 7 4 3 2 3 4 4 J := [243 x + 200 x , 243 x y + 200 y, 2187 x y + 1900 y , 9 x z + 10 x , 3 2 3 4 2 9 y z + 10 y, 3 x + 2 z , -12 z y, 11 z y - 4, -4 z - z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 11, 21, 4, 3, 3, 4, 1/2, 1/2, 5/6, 4/13, 4/13, 7/13, 9, 16, 34, 7, 7, 3, 4, 5/9, 5/9, 2/3, 7/19, 8/19, 7/19, -5, -13, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=237.9MB, alloc=84.3MB, time=4.58 |\^/| 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(); 1428320233 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 F := [8 y + x z, 2 z + x, -5 x y + 15 x y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 G := [-7 y z - 18 x , 3 x y - 17 x y , 9 x y z - 15 x z ] > Problem := [F,G]; 3 3 3 2 Problem := [[8 y + x z, 2 z + x, -5 x y + 15 x y z ], 2 2 2 2 2 2 2 [-7 y z - 18 x , 3 x y - 17 x y , 9 x y z - 15 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=48.5MB, alloc=32.3MB, time=0.86 memory used=68.7MB, alloc=56.3MB, time=1.19 memory used=109.4MB, alloc=60.3MB, time=1.84 memory used=147.2MB, alloc=84.3MB, time=2.47 memory used=206.1MB, alloc=92.3MB, time=3.43 memory used=264.0MB, alloc=116.3MB, time=4.36 memory used=344.4MB, alloc=116.3MB, time=5.62 memory used=423.0MB, alloc=396.3MB, time=6.76 memory used=525.4MB, alloc=420.3MB, time=8.37 memory used=653.7MB, alloc=444.3MB, time=10.29 memory used=792.0MB, alloc=468.3MB, time=13.01 memory used=953.0MB, alloc=492.3MB, time=15.94 memory used=1104.1MB, alloc=516.3MB, time=20.29 memory used=1243.6MB, alloc=540.3MB, time=26.02 memory used=1406.0MB, alloc=564.3MB, time=32.81 memory used=1592.5MB, alloc=588.3MB, time=40.41 N1 := 4741 > GB := Basis(F, plex(op(vars))); 7 3 6 2 6 2 3 5 4 GB := [4 x - 27 x , 4 x y - 27 x y, -x + 36 x y , -x y + 36 x y , 7 4 3 4 3 3 2 2 3 192 y - x y, 8 y + z x, 24 y z + x y, 16 y z - x , 2 z + x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1820.9MB, alloc=588.3MB, time=46.94 memory used=1970.7MB, alloc=588.3MB, time=49.41 memory used=2094.9MB, alloc=588.3MB, time=51.55 memory used=2222.6MB, alloc=588.3MB, time=53.55 memory used=2327.2MB, alloc=612.3MB, time=55.26 memory used=2439.9MB, alloc=612.3MB, time=56.65 memory used=2552.2MB, alloc=636.3MB, time=58.26 memory used=2655.5MB, alloc=636.3MB, time=60.38 memory used=2748.2MB, alloc=636.3MB, time=61.93 memory used=2842.6MB, alloc=660.3MB, time=63.65 memory used=2915.3MB, alloc=660.3MB, time=65.05 memory used=2995.8MB, alloc=660.3MB, time=66.70 memory used=3063.1MB, alloc=660.3MB, time=68.13 memory used=3119.4MB, alloc=660.3MB, time=69.41 memory used=3175.9MB, alloc=660.3MB, time=70.70 memory used=3237.8MB, alloc=660.3MB, time=72.21 memory used=3436.2MB, alloc=684.3MB, time=75.49 memory used=3624.2MB, alloc=708.3MB, time=78.89 memory used=3798.7MB, alloc=732.3MB, time=81.98 memory used=3957.8MB, alloc=756.3MB, time=84.90 memory used=4127.6MB, alloc=780.3MB, time=87.56 memory used=4374.0MB, alloc=804.3MB, time=90.26 memory used=4553.9MB, alloc=828.3MB, time=95.48 memory used=4675.4MB, alloc=852.3MB, time=97.84 memory used=4792.6MB, alloc=852.3MB, time=100.77 memory used=4909.5MB, alloc=852.3MB, time=103.80 memory used=5006.1MB, alloc=852.3MB, time=106.33 memory used=5091.0MB, alloc=852.3MB, time=108.40 memory used=5552.7MB, alloc=876.3MB, time=116.24 memory used=5952.3MB, alloc=900.3MB, time=123.26 memory used=6341.1MB, alloc=924.3MB, time=130.15 memory used=6680.7MB, alloc=948.3MB, time=136.58 memory used=6938.6MB, alloc=972.3MB, time=141.77 memory used=7212.2MB, alloc=996.3MB, time=147.52 memory used=7465.6MB, alloc=1020.3MB, time=152.89 memory used=8039.0MB, alloc=1044.3MB, time=163.50 memory used=8597.5MB, alloc=1068.3MB, time=175.27 memory used=9083.6MB, alloc=1092.3MB, time=187.20 memory used=9595.6MB, alloc=1116.3MB, time=199.33 memory used=10025.4MB, alloc=1140.3MB, time=215.33 memory used=10383.5MB, alloc=1164.3MB, time=232.54 memory used=10733.5MB, alloc=1188.3MB, time=251.11 memory used=11092.2MB, alloc=1212.3MB, time=271.69 |\^/| 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(); 1428320533 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [17 x y z - 19 x y , -x y z + 4 y , 15 x y z - 6 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 G := [-9 x y + 4 y, -7 y z + 6, 10 y z + 3 z ] > Problem := [F,G]; 2 2 3 2 Problem := [[17 x y z - 19 x y , -x y z + 4 y , 15 x y z - 6 y], 2 2 3 3 3 [-9 x y + 4 y, -7 y z + 6, 10 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=4.2MB, alloc=32.3MB, time=0.19 memory used=26.4MB, alloc=32.3MB, time=0.52 memory used=48.1MB, alloc=32.3MB, time=0.84 memory used=68.5MB, alloc=56.3MB, time=1.16 memory used=108.2MB, alloc=60.3MB, time=1.81 memory used=146.3MB, alloc=60.3MB, time=2.40 memory used=187.8MB, alloc=92.3MB, time=2.99 memory used=252.8MB, alloc=92.3MB, time=3.89 memory used=309.5MB, alloc=116.3MB, time=4.83 memory used=387.7MB, alloc=116.3MB, time=6.14 memory used=467.9MB, alloc=140.3MB, time=7.60 memory used=561.6MB, alloc=164.3MB, time=9.44 memory used=676.0MB, alloc=188.3MB, time=11.50 memory used=796.0MB, alloc=468.3MB, time=13.79 memory used=936.0MB, alloc=492.3MB, time=16.34 memory used=1120.1MB, alloc=516.3MB, time=18.94 memory used=1282.0MB, alloc=540.3MB, time=23.54 memory used=1442.3MB, alloc=564.3MB, time=28.81 memory used=1610.2MB, alloc=588.3MB, time=35.09 memory used=1790.1MB, alloc=612.3MB, time=42.50 memory used=1993.9MB, alloc=636.3MB, time=51.19 memory used=2221.6MB, alloc=660.3MB, time=60.76 memory used=2473.3MB, alloc=660.3MB, time=70.86 memory used=2725.0MB, alloc=660.3MB, time=81.50 memory used=2976.6MB, alloc=684.3MB, time=92.08 memory used=3252.2MB, alloc=684.3MB, time=103.54 memory used=3527.8MB, alloc=708.3MB, time=114.97 memory used=3827.4MB, alloc=708.3MB, time=127.39 memory used=4127.3MB, alloc=732.3MB, time=139.78 N1 := 9987 > GB := Basis(F, plex(op(vars))); GB := [ 5 4 2 2 16290125 x y - 10690688 y, -171475 x y + 314432 y , -1805 x y + 2312 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 1107 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 2 H := [17 x y z - 19 x y , -x y z + 4 y , 15 x y z - 6 y, -9 x y + 4 y, 3 3 3 -7 y z + 6, 10 y z + 3 z ] > J:=[op(GB),op(G)]; 5 4 2 J := [16290125 x y - 10690688 y, -171475 x y + 314432 y , 2 2 2 3 3 3 -1805 x y + 2312 y z, -9 x y + 4 y, -7 y z + 6, 10 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, 15, 23, 4, 2, 3, 3, 2/3, 1, 5/6, 5/12, 5/6, 1/2, 6, 13, 26, 6, 5, 3, 3, 2/3, 1, 1/2, 1/3, 5/6, 1/3, 2, -3, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=4367.0MB, alloc=732.3MB, time=146.74 |\^/| 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(); 1428320720 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 4 F := [-6 y + 20 y z , -18 x y z - 4 x z, 14 x y z + 13 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [6 y z + 5 x z, 8 x y z + 4 x z, 11 x y z - 11 x y] > Problem := [F,G]; 4 3 2 2 4 Problem := [[-6 y + 20 y z , -18 x y z - 4 x z, 14 x y z + 13 y ], 3 2 2 2 2 [6 y z + 5 x z, 8 x y z + 4 x z, 11 x y z - 11 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.82 memory used=67.5MB, alloc=32.3MB, time=1.12 memory used=86.2MB, alloc=56.3MB, time=1.44 memory used=125.0MB, alloc=60.3MB, time=2.05 memory used=160.5MB, alloc=60.3MB, time=2.61 memory used=194.4MB, alloc=84.3MB, time=3.18 memory used=251.9MB, alloc=108.3MB, time=4.32 memory used=326.3MB, alloc=132.3MB, time=5.72 memory used=415.0MB, alloc=164.3MB, time=7.46 memory used=513.5MB, alloc=188.3MB, time=10.07 memory used=618.2MB, alloc=212.3MB, time=13.81 memory used=738.7MB, alloc=236.3MB, time=18.56 memory used=883.2MB, alloc=236.3MB, time=24.24 memory used=1027.7MB, alloc=260.3MB, time=29.92 memory used=1196.2MB, alloc=284.3MB, time=36.36 N1 := 4917 > GB := Basis(F, plex(op(vars))); 6 4 4 3 4 5 GB := [1543790178 x y + 120670225 y , -18522 x y + 10985 y , 4 5 4 4 4 3 -117 y + 28 x z, 24504606 x y + 9282325 y z, -3 y + 10 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1310.0MB, alloc=284.3MB, time=38.63 memory used=1530.2MB, alloc=540.3MB, time=42.45 memory used=1753.7MB, alloc=564.3MB, time=46.22 memory used=1996.6MB, alloc=588.3MB, time=50.43 memory used=2263.3MB, alloc=612.3MB, time=54.76 memory used=2525.5MB, alloc=636.3MB, time=59.87 memory used=2781.8MB, alloc=660.3MB, time=64.99 memory used=3027.6MB, alloc=684.3MB, time=71.66 memory used=3239.5MB, alloc=708.3MB, time=79.56 memory used=3456.7MB, alloc=732.3MB, time=88.20 memory used=3677.4MB, alloc=756.3MB, time=97.97 memory used=3917.6MB, alloc=780.3MB, time=108.65 memory used=4181.8MB, alloc=804.3MB, time=120.37 memory used=4469.9MB, alloc=828.3MB, time=133.69 memory used=4782.0MB, alloc=852.3MB, time=148.05 memory used=5118.0MB, alloc=876.3MB, time=163.13 memory used=5477.9MB, alloc=900.3MB, time=179.26 memory used=5861.8MB, alloc=924.3MB, time=196.43 memory used=6269.6MB, alloc=948.3MB, time=213.54 memory used=6701.4MB, alloc=972.3MB, time=230.46 memory used=7157.1MB, alloc=996.3MB, time=249.19 |\^/| 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(); 1428321020 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 F := [-14 y z - 20 y , -3 x - 6 x y, 15 y z - 10 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 2 G := [6 x y - x z , -20 x z + 17 x y , -14 y + 11 x y] > Problem := [F,G]; 2 2 3 2 3 2 Problem := [[-14 y z - 20 y , -3 x - 6 x y, 15 y z - 10 z ], 3 2 2 2 4 2 [6 x y - x z , -20 x z + 17 x y , -14 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=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=32.3MB, time=0.84 memory used=68.3MB, alloc=32.3MB, time=1.16 memory used=86.9MB, alloc=56.3MB, time=1.47 memory used=126.8MB, alloc=60.3MB, time=2.14 memory used=165.9MB, alloc=60.3MB, time=2.75 memory used=203.5MB, alloc=84.3MB, time=3.43 memory used=260.5MB, alloc=92.3MB, time=4.44 memory used=315.3MB, alloc=116.3MB, time=5.38 memory used=393.6MB, alloc=140.3MB, time=7.06 memory used=487.8MB, alloc=164.3MB, time=9.02 memory used=596.1MB, alloc=188.3MB, time=11.18 memory used=711.5MB, alloc=212.3MB, time=14.64 memory used=831.4MB, alloc=236.3MB, time=19.70 memory used=973.1MB, alloc=260.3MB, time=25.73 memory used=1138.6MB, alloc=260.3MB, time=32.57 memory used=1304.3MB, alloc=284.3MB, time=39.45 N1 := 4775 > GB := Basis(F, plex(op(vars))); 9 4 3 2 7 2 7 4 GB := [63 x - 1280 x , x + 2 x y, 63 y + 40 y , 3 x + 16 x z, 5 2 6 2 -3 y + 2 y z, -9 y + 4 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1409.8MB, alloc=284.3MB, time=41.91 memory used=1599.3MB, alloc=540.3MB, time=45.08 memory used=1772.6MB, alloc=540.3MB, time=48.15 memory used=1934.4MB, alloc=540.3MB, time=51.00 memory used=2118.6MB, alloc=564.3MB, time=54.34 memory used=2300.6MB, alloc=588.3MB, time=57.63 memory used=2488.0MB, alloc=612.3MB, time=61.62 memory used=2692.7MB, alloc=636.3MB, time=65.60 memory used=2888.8MB, alloc=660.3MB, time=69.46 memory used=3119.8MB, alloc=684.3MB, time=76.09 memory used=3368.3MB, alloc=708.3MB, time=85.20 memory used=3615.8MB, alloc=732.3MB, time=95.35 memory used=3879.2MB, alloc=756.3MB, time=106.54 memory used=4166.4MB, alloc=780.3MB, time=118.84 memory used=4477.6MB, alloc=804.3MB, time=132.27 memory used=4812.8MB, alloc=828.3MB, time=147.01 memory used=5171.9MB, alloc=852.3MB, time=162.43 memory used=5554.9MB, alloc=876.3MB, time=178.92 memory used=5962.0MB, alloc=900.3MB, time=196.22 N2 := 10379 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 3 2 3 2 H := [-14 y z - 20 y , -3 x - 6 x y, 15 y z - 10 z , 6 x y - x z , 2 2 4 2 -20 x z + 17 x y , -14 y + 11 x y] > J:=[op(GB),op(G)]; 9 4 3 2 7 2 7 4 J := [63 x - 1280 x , x + 2 x y, 63 y + 40 y , 3 x + 16 x z, 5 2 6 2 3 2 2 2 -3 y + 2 y z, -9 y + 4 z , 6 x y - x z , -20 x z + 17 x y , 4 2 -14 y + 11 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 := [6, 14, 21, 4, 3, 4, 2, 2/3, 1, 2/3, 7/12, 2/3, 5/12, 9, 18, 48, 9, 9, 7, 2, 2/3, 7/9, 5/9, 11/18, 5/9, 5/18, -4, -27, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=6333.1MB, alloc=900.3MB, time=209.91 |\^/| 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(); 1428321258 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-5 x y + 13 x y z , 13 x z - 6 y , -18 x y z + 16 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 G := [-7 x z + 4 y z, -16 z , -2 x y + 8 z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-5 x y + 13 x y z , 13 x z - 6 y , -18 x y z + 16 z ], 2 4 2 2 [-7 x z + 4 y z, -16 z , -2 x y + 8 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.8MB, alloc=32.3MB, time=0.79 memory used=67.9MB, alloc=32.3MB, time=1.07 memory used=87.1MB, alloc=56.3MB, time=1.35 memory used=127.0MB, alloc=60.3MB, time=1.91 memory used=164.9MB, alloc=60.3MB, time=2.44 memory used=200.4MB, alloc=84.3MB, time=2.99 memory used=255.9MB, alloc=116.3MB, time=3.86 memory used=333.6MB, alloc=140.3MB, time=5.18 memory used=426.9MB, alloc=164.3MB, time=6.80 memory used=537.1MB, alloc=188.3MB, time=8.67 memory used=650.8MB, alloc=468.3MB, time=10.61 memory used=789.3MB, alloc=492.3MB, time=12.99 memory used=937.2MB, alloc=516.3MB, time=15.82 memory used=1083.7MB, alloc=540.3MB, time=20.20 memory used=1236.7MB, alloc=564.3MB, time=25.20 memory used=1399.8MB, alloc=588.3MB, time=30.95 memory used=1572.6MB, alloc=612.3MB, time=37.89 memory used=1769.4MB, alloc=636.3MB, time=45.97 memory used=1990.1MB, alloc=660.3MB, time=55.00 memory used=2234.7MB, alloc=684.3MB, time=64.84 memory used=2503.3MB, alloc=684.3MB, time=75.60 memory used=2771.8MB, alloc=684.3MB, time=86.34 memory used=3040.3MB, alloc=708.3MB, time=97.22 memory used=3332.7MB, alloc=708.3MB, time=108.85 memory used=3625.1MB, alloc=708.3MB, time=120.46 memory used=3917.6MB, alloc=732.3MB, time=132.08 memory used=4234.1MB, alloc=732.3MB, time=144.65 memory used=4550.4MB, alloc=756.3MB, time=157.25 N1 := 11297 > GB := Basis(F, plex(op(vars))); 5 2 2 2 4 2 2 3 4 2 4 GB := [41067 x y - 5120 x y , -39 x y + 16 x y , -1521 x y + 256 y , 2 3 2 3 2 13 z x - 6 y , -9 x y + 8 y z, -27 y + 52 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4895.3MB, alloc=756.3MB, time=167.99 memory used=5087.0MB, alloc=756.3MB, time=171.98 memory used=5294.3MB, alloc=780.3MB, time=176.78 memory used=5672.7MB, alloc=804.3MB, time=192.38 N2 := 4863 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 H := [-5 x y + 13 x y z , 13 z x - 6 y , -18 x y z + 16 z , -7 x z + 4 y z, 4 2 2 -16 z , -2 x y + 8 z] > J:=[op(GB),op(G)]; 5 2 2 2 4 2 2 3 4 2 4 J := [41067 x y - 5120 x y , -39 x y + 16 x y , -1521 x y + 256 y , 2 3 2 3 2 2 4 13 z x - 6 y , -9 x y + 8 y z, -27 y + 52 z , -7 x z + 4 y z, -16 z , 2 2 -2 x y + 8 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 16, 20, 4, 2, 2, 4, 5/6, 5/6, 1, 1/2, 1/2, 2/3, 9, 21, 39, 7, 5, 4, 4, 7/9, 8/9, 2/3, 1/2, 2/3, 7/18, -5, -19, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=6000.8MB, alloc=804.3MB, time=206.09 |\^/| 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(); 1428321474 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 F := [13 x y z + 3 x y , 2 x z - 16 z, 5 x y + 9 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 3 4 G := [12 y - 7 y , -19 z + 4, -7 x y - 17 y ] > Problem := [F,G]; 2 2 3 3 2 Problem := [[13 x y z + 3 x y , 2 x z - 16 z, 5 x y + 9 x y ], 4 3 2 3 4 [12 y - 7 y , -19 z + 4, -7 x y - 17 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=25.7MB, alloc=32.3MB, time=0.46 memory used=48.4MB, alloc=32.3MB, time=0.84 memory used=67.5MB, alloc=56.3MB, time=1.22 N1 := 675 > GB := Basis(F, plex(op(vars))); 4 2 2 3 2 3 3 2 2 GB := [x y - 8 x y , 5 x y + 9 x y , x z - 8 z, 3 x y + 104 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=104.4MB, alloc=56.3MB, time=1.84 memory used=145.8MB, alloc=84.3MB, time=2.54 N2 := 949 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 2 4 3 H := [13 x y z + 3 x y , 2 x z - 16 z, 5 x y + 9 x y , 12 y - 7 y , 2 3 4 -19 z + 4, -7 x y - 17 y ] > J:=[op(GB),op(G)]; 4 2 2 3 2 3 3 2 2 J := [x y - 8 x y , 5 x y + 9 x y , x z - 8 z, 3 x y + 104 y z, 4 3 2 3 4 12 y - 7 y , -19 z + 4, -7 x y - 17 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, 11, 22, 4, 3, 4, 2, 2/3, 2/3, 1/2, 1/2, 2/3, 1/3, 7, 13, 29, 6, 4, 4, 2, 5/7, 5/7, 3/7, 1/2, 5/7, 2/7, -2, -7, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=184.8MB, alloc=84.3MB, time=3.47 |\^/| 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(); 1428321478 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 2 2 2 F := [15 y z - 14 z , 4 z - 14 z , -3 x y z + 13 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 3 G := [14 z - 12 y z, 12 x y - 9 y z, 14 x y - 8 x z] > Problem := [F,G]; 2 3 4 2 2 2 2 Problem := [[15 y z - 14 z , 4 z - 14 z , -3 x y z + 13 x z ], 4 2 2 3 3 [14 z - 12 y z, 12 x y - 9 y z, 14 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=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=47.6MB, alloc=32.3MB, time=0.78 memory used=66.8MB, alloc=56.3MB, time=1.07 memory used=106.5MB, alloc=60.3MB, time=1.65 memory used=143.5MB, alloc=60.3MB, time=2.19 memory used=177.3MB, alloc=84.3MB, time=2.71 memory used=231.1MB, alloc=84.3MB, time=3.53 memory used=281.3MB, alloc=108.3MB, time=4.29 memory used=355.2MB, alloc=116.3MB, time=5.44 memory used=428.1MB, alloc=116.3MB, time=6.58 memory used=498.5MB, alloc=140.3MB, time=7.71 memory used=592.0MB, alloc=140.3MB, time=9.20 memory used=683.4MB, alloc=140.3MB, time=10.69 memory used=771.8MB, alloc=164.3MB, time=12.05 memory used=877.9MB, alloc=420.3MB, time=13.76 memory used=983.4MB, alloc=444.3MB, time=15.51 memory used=1107.6MB, alloc=468.3MB, time=17.57 memory used=1248.9MB, alloc=492.3MB, time=19.99 memory used=1411.7MB, alloc=516.3MB, time=22.79 memory used=1599.1MB, alloc=540.3MB, time=26.15 memory used=1780.5MB, alloc=564.3MB, time=29.55 memory used=1965.5MB, alloc=588.3MB, time=33.03 memory used=2154.0MB, alloc=612.3MB, time=36.64 memory used=2346.3MB, alloc=636.3MB, time=40.37 memory used=2543.0MB, alloc=660.3MB, time=44.21 memory used=2743.5MB, alloc=684.3MB, time=48.14 memory used=2946.0MB, alloc=708.3MB, time=52.23 memory used=3151.4MB, alloc=732.3MB, time=56.42 memory used=3359.6MB, alloc=756.3MB, time=60.82 memory used=3570.4MB, alloc=780.3MB, time=65.37 memory used=3782.6MB, alloc=804.3MB, time=69.78 memory used=3996.9MB, alloc=828.3MB, time=74.34 memory used=4213.6MB, alloc=852.3MB, time=79.00 memory used=4431.3MB, alloc=876.3MB, time=83.78 memory used=4651.3MB, alloc=900.3MB, time=88.64 memory used=4872.6MB, alloc=924.3MB, time=93.48 memory used=5095.0MB, alloc=948.3MB, time=98.45 memory used=5318.9MB, alloc=972.3MB, time=103.50 memory used=5543.1MB, alloc=996.3MB, time=108.60 memory used=5768.5MB, alloc=1020.3MB, time=113.88 memory used=5995.1MB, alloc=1044.3MB, time=119.23 memory used=6222.2MB, alloc=1068.3MB, time=124.56 memory used=6448.1MB, alloc=1092.3MB, time=129.82 memory used=6675.3MB, alloc=1116.3MB, time=135.17 memory used=6903.8MB, alloc=1140.3MB, time=140.56 memory used=7130.8MB, alloc=1164.3MB, time=146.05 memory used=7359.1MB, alloc=1188.3MB, time=151.63 memory used=7591.5MB, alloc=1212.3MB, time=157.18 memory used=7819.6MB, alloc=1236.3MB, time=162.76 memory used=8003.7MB, alloc=1260.3MB, time=169.24 memory used=8182.3MB, alloc=1284.3MB, time=176.61 memory used=8371.0MB, alloc=1308.3MB, time=184.62 memory used=8571.2MB, alloc=1332.3MB, time=193.14 memory used=8783.4MB, alloc=1356.3MB, time=202.42 memory used=9008.7MB, alloc=1380.3MB, time=212.30 memory used=9247.6MB, alloc=1404.3MB, time=222.86 memory used=9500.3MB, alloc=1428.3MB, time=234.14 memory used=9767.1MB, alloc=1452.3MB, time=246.29 memory used=10047.7MB, alloc=1476.3MB, time=259.04 memory used=10342.1MB, alloc=1500.3MB, time=272.31 memory used=10651.0MB, alloc=1524.3MB, time=286.45 memory used=10974.3MB, alloc=1548.3MB, time=301.14 |\^/| 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(); 1428321778 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-20 y z , 12 x z + 19 x y, -8 x y z + 19 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 4 3 3 3 G := [7 y z + 15 z , -11 x - 16 x z , 16 x z + 2 z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-20 y z , 12 x z + 19 x y, -8 x y z + 19 x], 2 2 4 4 3 3 3 [7 y z + 15 z , -11 x - 16 x z , 16 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=4.3MB, alloc=32.3MB, time=0.17 memory used=27.0MB, alloc=32.3MB, time=0.51 memory used=48.4MB, alloc=32.3MB, time=0.82 memory used=68.5MB, alloc=32.3MB, time=1.12 memory used=87.8MB, alloc=56.3MB, time=1.42 memory used=127.8MB, alloc=60.3MB, time=2.04 memory used=165.9MB, alloc=60.3MB, time=2.63 memory used=203.8MB, alloc=84.3MB, time=3.24 memory used=263.5MB, alloc=92.3MB, time=4.17 memory used=320.8MB, alloc=92.3MB, time=5.04 memory used=375.4MB, alloc=116.3MB, time=5.89 memory used=451.1MB, alloc=116.3MB, time=7.07 memory used=526.2MB, alloc=140.3MB, time=8.27 memory used=624.0MB, alloc=164.3MB, time=10.13 memory used=737.4MB, alloc=188.3MB, time=12.26 memory used=865.8MB, alloc=212.3MB, time=14.69 memory used=994.6MB, alloc=492.3MB, time=17.70 memory used=1125.5MB, alloc=516.3MB, time=21.92 memory used=1266.3MB, alloc=540.3MB, time=27.22 memory used=1431.1MB, alloc=564.3MB, time=33.43 memory used=1619.9MB, alloc=564.3MB, time=40.49 memory used=1808.7MB, alloc=588.3MB, time=47.63 memory used=2021.7MB, alloc=612.3MB, time=55.53 N1 := 5959 > GB := Basis(F, plex(op(vars))); 2 GB := [x, y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 119 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 4 H := [-20 y z , 12 x z + 19 x y, -8 x y z + 19 x, 7 y z + 15 z , 4 3 3 3 -11 x - 16 x z , 16 x z + 2 z ] > J:=[op(GB),op(G)]; 2 2 2 4 4 3 3 3 J := [x, y z , 7 y z + 15 z , -11 x - 16 x z , 16 x z + 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, 14, 23, 4, 4, 2, 4, 2/3, 2/3, 1, 7/13, 4/13, 8/13, 5, 9, 16, 4, 4, 2, 4, 3/5, 2/5, 4/5, 4/9, 2/9, 2/3, 5, 7, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2076.8MB, alloc=612.3MB, time=56.87 |\^/| 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(); 1428321841 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [2 y + 10 y , 2 x y z + 17 x z , -x z - 17 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 2 2 G := [x z + 17 y, -6 x + 5 x , -15 x y - 19 z ] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[2 y + 10 y , 2 x y z + 17 x z , -x z - 17 x], 2 4 2 2 2 2 [x z + 17 y, -6 x + 5 x , -15 x y - 19 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.78 memory used=68.4MB, alloc=32.3MB, time=1.08 memory used=88.3MB, alloc=56.3MB, time=1.38 memory used=130.4MB, alloc=60.3MB, time=2.07 memory used=170.3MB, alloc=84.3MB, time=2.77 memory used=229.5MB, alloc=84.3MB, time=3.81 memory used=283.5MB, alloc=108.3MB, time=4.91 memory used=347.5MB, alloc=132.3MB, time=7.16 N1 := 2045 > GB := Basis(F, plex(op(vars))); 2 3 2 GB := [2500 x + 4913 x, x y + 5 x, y + 5 y , 17 x z + 50 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=435.7MB, alloc=132.3MB, time=9.64 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)]; 3 2 2 2 2 2 2 H := [2 y + 10 y , 2 x y z + 17 x z , -x z - 17 x, z x + 17 y, 4 2 2 2 2 -6 x + 5 x , -15 x y - 19 z ] > J:=[op(GB),op(G)]; 2 3 2 2 J := [2500 x + 4913 x, x y + 5 x, y + 5 y , 17 x z + 50 x, z x + 17 y, 4 2 2 2 2 -6 x + 5 x , -15 x y - 19 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, 22, 4, 4, 3, 2, 5/6, 2/3, 2/3, 2/3, 5/12, 5/12, 7, 13, 20, 4, 4, 3, 2, 6/7, 4/7, 3/7, 5/7, 5/14, 3/14, 0, 2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=466.5MB, alloc=132.3MB, time=10.15 |\^/| 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(); 1428321851 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 2 2 2 F := [-9 x y z - 8 y , -11 x z + 8 y z , x y + 4 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [-7 x z - 9, 5 x z + 19, 18 y + y z ] > Problem := [F,G]; 2 4 3 2 2 2 Problem := [[-9 x y z - 8 y , -11 x z + 8 y z , x y + 4 y ], 3 2 3 2 [-7 x z - 9, 5 x z + 19, 18 y + y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.49 memory used=48.1MB, alloc=32.3MB, time=0.79 memory used=67.2MB, alloc=56.3MB, time=1.08 memory used=108.7MB, alloc=60.3MB, time=1.69 memory used=147.4MB, alloc=60.3MB, time=2.24 memory used=185.0MB, alloc=84.3MB, time=2.80 memory used=236.0MB, alloc=84.3MB, time=3.56 memory used=296.0MB, alloc=116.3MB, time=4.42 memory used=378.2MB, alloc=396.3MB, time=5.56 memory used=482.6MB, alloc=396.3MB, time=7.02 memory used=593.9MB, alloc=420.3MB, time=8.38 memory used=720.7MB, alloc=444.3MB, time=10.13 memory used=853.6MB, alloc=468.3MB, time=11.94 memory used=986.4MB, alloc=492.3MB, time=13.67 memory used=1113.8MB, alloc=492.3MB, time=15.41 memory used=1210.8MB, alloc=516.3MB, time=16.78 memory used=1308.6MB, alloc=516.3MB, time=18.39 memory used=1391.2MB, alloc=516.3MB, time=19.48 memory used=1479.4MB, alloc=516.3MB, time=20.99 memory used=1543.3MB, alloc=540.3MB, time=22.08 memory used=1613.8MB, alloc=540.3MB, time=23.32 memory used=1670.2MB, alloc=540.3MB, time=24.42 memory used=1738.2MB, alloc=540.3MB, time=25.70 memory used=1859.8MB, alloc=564.3MB, time=28.20 memory used=1975.2MB, alloc=564.3MB, time=30.69 memory used=2100.4MB, alloc=588.3MB, time=33.17 memory used=2300.4MB, alloc=612.3MB, time=39.90 memory used=2497.4MB, alloc=636.3MB, time=46.76 N1 := 4185 > GB := Basis(F, plex(op(vars))); 10 7 2 2 7 5 6 2 GB := [x y + 396 x y, x y + 4 y , x y + 18 x z, -x y + 72 x y z, 3 2 -11 x z + 8 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2726.3MB, alloc=636.3MB, time=52.98 memory used=2818.7MB, alloc=636.3MB, time=54.59 memory used=2888.6MB, alloc=636.3MB, time=55.92 memory used=2963.5MB, alloc=636.3MB, time=57.25 memory used=3027.2MB, alloc=636.3MB, time=58.57 memory used=3282.7MB, alloc=660.3MB, time=62.23 memory used=3527.3MB, alloc=684.3MB, time=65.80 memory used=3748.1MB, alloc=708.3MB, time=69.07 memory used=3914.9MB, alloc=732.3MB, time=71.61 memory used=4102.1MB, alloc=756.3MB, time=74.44 memory used=4387.2MB, alloc=780.3MB, time=79.39 memory used=4724.0MB, alloc=804.3MB, time=87.08 memory used=5022.8MB, alloc=828.3MB, time=98.22 memory used=5345.5MB, alloc=852.3MB, time=109.83 memory used=5692.8MB, alloc=876.3MB, time=121.77 N2 := 6003 #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 4 3 2 2 2 3 H := [-9 x y z - 8 y , -11 x z + 8 y z , x y + 4 y , -7 x z - 9, 2 3 2 5 z x + 19, 18 y + y z ] > J:=[op(GB),op(G)]; 10 7 2 2 7 5 6 2 J := [x y + 396 x y, x y + 4 y , x y + 18 x z, -x y + 72 x y z, 3 2 3 2 3 2 -11 x z + 8 y z , -7 x z - 9, 5 z x + 19, 18 y + y z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 21, 4, 3, 4, 3, 5/6, 2/3, 5/6, 5/12, 7/12, 1/2, 8, 19, 43, 11, 10, 3, 3, 7/8, 3/4, 3/4, 5/8, 5/8, 7/16, -5, -22, -7] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=5696.0MB, alloc=876.3MB, time=121.88 |\^/| 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(); 1428321973 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [12 x - 10 z , 7 x y - 5 y , 11 x z - 13 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 G := [-6 x y z + 14 x z, -17 x y z , -16 x z + 19 y ] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[12 x - 10 z , 7 x y - 5 y , 11 x z - 13 x], 2 3 4 [-6 x y z + 14 x z, -17 x y z , -16 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=26.5MB, alloc=32.3MB, time=0.43 memory used=48.4MB, alloc=32.3MB, time=0.69 memory used=70.1MB, alloc=56.3MB, time=1.02 memory used=117.2MB, alloc=60.3MB, time=1.65 memory used=157.9MB, alloc=84.3MB, time=2.21 memory used=215.4MB, alloc=84.3MB, time=3.43 memory used=264.6MB, alloc=108.3MB, time=4.59 N1 := 1667 > GB := Basis(F, plex(op(vars))); 4 2 2 2 GB := [66 x - 65 x, y , -6 x + 5 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 579 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 H := [12 x - 10 z , 7 x y - 5 y , 11 x z - 13 x, -6 x y z + 14 x z, 2 3 4 -17 x y z , -16 x z + 19 y ] > J:=[op(GB),op(G)]; 4 2 2 2 2 J := [66 x - 65 x, y , -6 x + 5 z , -6 x y z + 14 x z, -17 x y z , 3 4 -16 x z + 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 := [6, 15, 21, 4, 2, 4, 3, 1, 2/3, 5/6, 4/7, 5/14, 3/7, 6, 13, 19, 4, 4, 4, 3, 5/6, 2/3, 2/3, 1/2, 2/7, 5/14, 2, 2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=337.1MB, alloc=116.3MB, time=5.66 |\^/| 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(); 1428321979 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 F := [12 y z , 16 x + 7 z, -7 x - 5] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 G := [2 x y z + x z , 8 y z - 18 x , -5 x z - x ] > Problem := [F,G]; 3 3 Problem := [[12 y z , 16 x + 7 z, -7 x - 5], 2 3 2 2 2 2 [2 x y z + x z , 8 y z - 18 x , -5 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=0.16 memory used=26.4MB, alloc=32.3MB, time=0.43 memory used=47.6MB, alloc=32.3MB, time=0.66 memory used=69.1MB, alloc=56.3MB, time=0.98 memory used=112.7MB, alloc=60.3MB, time=1.60 memory used=151.1MB, alloc=84.3MB, time=2.21 memory used=206.2MB, alloc=108.3MB, time=3.34 memory used=274.8MB, alloc=108.3MB, time=5.18 N1 := 2043 > GB := Basis(F, plex(op(vars))); 3 GB := [7 x + 5, y, 7 z + 16 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=344.4MB, alloc=108.3MB, time=6.27 memory used=422.6MB, alloc=140.3MB, time=7.40 memory used=519.8MB, alloc=164.3MB, time=9.43 N2 := 2043 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 3 2 2 H := [12 y z , 7 z + 16 x, -7 x - 5, 2 x y z + x z , 8 y z - 18 x , 2 2 -5 x z - x ] > J:=[op(GB),op(G)]; 3 2 3 2 2 2 2 J := [7 x + 5, y, 7 z + 16 x, 2 x y z + x z , 8 y z - 18 x , -5 x z - x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 18, 4, 3, 1, 3, 5/6, 1/2, 5/6, 7/13, 3/13, 6/13, 6, 12, 15, 4, 3, 1, 3, 5/6, 1/2, 2/3, 7/11, 3/11, 5/11, 1, 3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=606.1MB, 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(); 1428321991 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 F := [-17 x y - 9 y z , 6 x y + 11 x y, -6 x y - 15 x y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 2 2 G := [8 x y - 15 x , 20 x y + 15 z , x y + 3 x z ] > Problem := [F,G]; 3 2 2 2 3 2 Problem := [[-17 x y - 9 y z , 6 x y + 11 x y, -6 x y - 15 x y z ], 3 3 2 3 2 2 2 [8 x y - 15 x , 20 x y + 15 z , 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=0.16 memory used=26.5MB, alloc=32.3MB, time=0.44 memory used=48.1MB, alloc=32.3MB, time=0.68 memory used=69.0MB, alloc=32.3MB, time=0.92 memory used=89.0MB, alloc=56.3MB, time=1.17 memory used=133.5MB, alloc=60.3MB, time=1.78 memory used=175.2MB, alloc=84.3MB, time=2.38 memory used=234.0MB, alloc=108.3MB, time=3.32 memory used=301.6MB, alloc=132.3MB, time=4.87 N1 := 1649 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [85 x y - 18 x y, 108 x y + 935 x y, 104976 y z + 14861825 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=396.0MB, alloc=140.3MB, time=6.17 memory used=502.8MB, alloc=164.3MB, time=7.74 memory used=607.1MB, alloc=188.3MB, time=10.59 N2 := 2027 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 2 3 3 H := [-17 x y - 9 y z , 6 x y + 11 x y, -6 x y - 15 x y z , 8 x y - 15 x , 2 3 2 2 2 20 x y + 15 z , x y + 3 x z ] > J:=[op(GB),op(G)]; 2 2 2 J := [85 x y - 18 x y, 108 x y + 935 x y, 104976 y z + 14861825 x y, 3 3 2 3 2 2 2 8 x y - 15 x , 20 x y + 15 z , x y + 3 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 := [6, 16, 23, 4, 3, 3, 3, 1, 1, 2/3, 5/6, 3/4, 1/3, 6, 15, 20, 4, 3, 2, 3, 1, 1, 1/2, 5/6, 3/4, 1/4, 1, 3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=638.2MB, alloc=188.3MB, time=11.15 |\^/| 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(); 1428322003 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 F := [-11 y z - 7 x z, 16 x + 13 y, -6 x z - y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 G := [-18 x y z - 14 y z, -9 x y - 4 z , 17 z + 20 x] > Problem := [F,G]; 2 4 2 2 Problem := [[-11 y z - 7 x z, 16 x + 13 y, -6 x z - y ], 2 3 3 3 2 [-18 x y z - 14 y z, -9 x y - 4 z , 17 z + 20 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.2MB, alloc=32.3MB, time=0.38 memory used=47.9MB, alloc=32.3MB, time=0.64 memory used=69.1MB, alloc=32.3MB, time=0.91 memory used=89.5MB, alloc=32.3MB, time=1.16 memory used=109.2MB, alloc=56.3MB, time=1.39 memory used=149.9MB, alloc=60.3MB, time=1.86 memory used=190.8MB, alloc=84.3MB, time=2.45 memory used=254.6MB, alloc=84.3MB, time=3.34 memory used=312.6MB, alloc=108.3MB, time=4.15 memory used=390.3MB, alloc=140.3MB, time=5.27 memory used=483.4MB, alloc=164.3MB, time=6.66 memory used=584.4MB, alloc=188.3MB, time=8.83 memory used=691.1MB, alloc=212.3MB, time=12.04 memory used=819.5MB, alloc=212.3MB, time=15.95 memory used=947.8MB, alloc=236.3MB, time=19.71 memory used=1100.2MB, alloc=236.3MB, time=24.24 N1 := 4795 > GB := Basis(F, plex(op(vars))); GB := 15 8 4 8 8 2 [2816 x + 1183 x , 16 x + 13 y, 2816 x z + 1183 x z, 128 x + 507 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1255.6MB, alloc=236.3MB, time=27.91 memory used=1385.5MB, alloc=492.3MB, time=29.79 N2 := 1465 #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 4 2 2 2 3 H := [-11 y z - 7 x z, 16 x + 13 y, -6 x z - y , -18 x y z - 14 y z, 3 3 2 -9 x y - 4 z , 17 z + 20 x] > J:=[op(GB),op(G)]; 15 8 4 8 8 2 J := [2816 x + 1183 x , 16 x + 13 y, 2816 x z + 1183 x z, 128 x + 507 x z , 2 3 3 3 2 -18 x y z - 14 y z, -9 x y - 4 z , 17 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 := [6, 16, 20, 4, 4, 3, 3, 1, 5/6, 5/6, 1/2, 1/2, 7/12, 7, 15, 46, 15, 15, 3, 3, 1, 3/7, 5/7, 5/7, 2/7, 1/2, 1, -26, -11] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1479.7MB, alloc=492.3MB, time=31.74 |\^/| 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(); 1428322036 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [-3 x y + 9 z , 16 x y - 8 y , -5 z - 20] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 2 G := [-17 x z + 6 y z , -8 x z - 11 x y , -5 x + 12 z ] > Problem := [F,G]; 3 2 2 2 2 Problem := [[-3 x y + 9 z , 16 x y - 8 y , -5 z - 20], 3 2 3 2 2 2 [-17 x z + 6 y z , -8 x z - 11 x y , -5 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=4.3MB, alloc=32.3MB, time=0.16 memory used=26.7MB, alloc=32.3MB, time=0.44 memory used=48.2MB, alloc=32.3MB, time=0.68 memory used=67.8MB, alloc=56.3MB, time=0.91 memory used=110.1MB, alloc=60.3MB, time=1.39 memory used=150.3MB, alloc=84.3MB, time=1.85 memory used=213.5MB, alloc=92.3MB, time=2.58 memory used=272.3MB, alloc=116.3MB, time=3.26 memory used=352.8MB, alloc=116.3MB, time=4.18 memory used=429.8MB, alloc=396.3MB, time=5.08 memory used=529.6MB, alloc=420.3MB, time=6.24 memory used=656.3MB, alloc=444.3MB, time=7.90 memory used=790.5MB, alloc=468.3MB, time=9.91 memory used=942.6MB, alloc=492.3MB, time=12.02 memory used=1102.7MB, alloc=516.3MB, time=14.35 memory used=1279.5MB, alloc=540.3MB, time=17.02 memory used=1444.2MB, alloc=564.3MB, time=21.08 memory used=1612.1MB, alloc=588.3MB, time=25.72 memory used=1787.7MB, alloc=612.3MB, time=31.18 memory used=1977.7MB, alloc=636.3MB, time=37.46 memory used=2191.8MB, alloc=660.3MB, time=44.60 memory used=2429.7MB, alloc=684.3MB, time=52.41 memory used=2691.7MB, alloc=684.3MB, time=61.07 memory used=2953.6MB, alloc=708.3MB, time=69.70 memory used=3239.4MB, alloc=708.3MB, time=79.04 memory used=3525.2MB, alloc=708.3MB, time=88.45 memory used=3810.9MB, alloc=732.3MB, time=98.03 memory used=4120.7MB, alloc=756.3MB, time=108.27 memory used=4454.4MB, alloc=756.3MB, time=119.12 N1 := 10453 > GB := Basis(F, plex(op(vars))); 3 2 GB := [2 x - 1, y + 24, z + 4] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4754.9MB, alloc=756.3MB, time=125.48 memory used=4992.9MB, alloc=756.3MB, time=129.66 N2 := 3099 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 3 2 H := [-3 x y + 9 z , 16 x y - 8 y , -5 z - 20, -17 x z + 6 y z , 3 2 2 2 -8 x z - 11 x y , -5 x + 12 z ] > J:=[op(GB),op(G)]; 3 2 3 2 3 2 J := [2 x - 1, y + 24, z + 4, -17 x z + 6 y z , -8 x z - 11 x y , 2 2 -5 x + 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 := [6, 14, 19, 4, 3, 3, 3, 5/6, 2/3, 5/6, 1/2, 5/12, 1/2, 6, 11, 16, 4, 3, 3, 3, 2/3, 1/2, 2/3, 5/12, 1/4, 5/12, 3, 3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=5278.4MB, alloc=756.3MB, time=137.94 |\^/| 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(); 1428322179 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [-13 x y - 18 y z , -7 x y - 15 x y z, 9 x y z + 4 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 3 G := [-6 y z - 19 z , -7 z - 20 x, 8 x z + 19 x ] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[-13 x y - 18 y z , -7 x y - 15 x y z, 9 x y z + 4 x ], 3 2 4 3 3 [-6 y z - 19 z , -7 z - 20 x, 8 x z + 19 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=27.0MB, alloc=32.3MB, time=0.43 memory used=47.8MB, alloc=32.3MB, time=0.69 memory used=67.4MB, alloc=56.3MB, time=0.95 memory used=107.9MB, alloc=60.3MB, time=1.46 memory used=146.4MB, alloc=60.3MB, time=1.92 memory used=184.8MB, alloc=84.3MB, time=2.36 memory used=229.7MB, alloc=84.3MB, time=2.91 memory used=287.1MB, alloc=92.3MB, time=3.63 memory used=344.4MB, alloc=116.3MB, time=4.30 memory used=424.2MB, alloc=116.3MB, time=5.26 memory used=508.1MB, alloc=140.3MB, time=6.19 memory used=584.1MB, alloc=140.3MB, time=7.04 memory used=669.5MB, alloc=420.3MB, time=8.09 memory used=796.3MB, alloc=444.3MB, time=9.44 memory used=932.2MB, alloc=444.3MB, time=11.02 memory used=1077.1MB, alloc=468.3MB, time=12.97 memory used=1229.4MB, alloc=492.3MB, time=15.12 memory used=1398.1MB, alloc=516.3MB, time=17.46 memory used=1578.8MB, alloc=540.3MB, time=20.15 memory used=1750.3MB, alloc=564.3MB, time=23.86 memory used=1913.3MB, alloc=588.3MB, time=28.18 memory used=2080.1MB, alloc=612.3MB, time=33.55 memory used=2267.6MB, alloc=636.3MB, time=39.75 memory used=2479.0MB, alloc=660.3MB, time=46.73 memory used=2714.4MB, alloc=684.3MB, time=54.51 memory used=2973.7MB, alloc=708.3MB, time=63.03 memory used=3257.1MB, alloc=708.3MB, time=72.34 memory used=3540.2MB, alloc=732.3MB, time=81.61 memory used=3847.1MB, alloc=756.3MB, time=91.71 N1 := 8849 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 2 2 2 2 GB := [x , 21 x y - 20 x , z x , 9 x y z + 4 x , 13 x y + 18 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4188.2MB, alloc=756.3MB, time=99.69 memory used=4333.1MB, alloc=756.3MB, time=102.00 memory used=4471.8MB, alloc=756.3MB, time=104.07 memory used=4599.8MB, alloc=756.3MB, time=105.73 memory used=4744.6MB, alloc=756.3MB, time=107.95 memory used=4996.3MB, alloc=756.3MB, time=111.91 memory used=5249.5MB, alloc=780.3MB, time=115.95 memory used=5607.2MB, alloc=804.3MB, time=127.61 memory used=5955.3MB, alloc=828.3MB, time=140.32 memory used=6327.5MB, alloc=852.3MB, time=153.39 N2 := 6277 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 H := [-13 x y - 18 y z , -7 x y - 15 x y z, 9 x y z + 4 x , 3 2 4 3 3 -6 y z - 19 z , -7 z - 20 x, 8 x z + 19 x ] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 2 2 2 J := [x , 21 x y - 20 x , z x , 9 x y z + 4 x , 13 x y + 18 y z , 3 2 4 3 3 -6 y z - 19 z , -7 z - 20 x, 8 x 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 := [6, 15, 23, 4, 3, 3, 4, 5/6, 2/3, 1, 2/3, 1/2, 7/12, 8, 17, 29, 4, 3, 3, 4, 7/8, 1/2, 3/4, 5/8, 5/16, 7/16, -2, -6, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=6503.3MB, alloc=852.3MB, time=158.47 |\^/| 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(); 1428322342 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-20 x y z - 20 z, 18 x + 9 x, -6 x z - 8 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [-20 x y + 17 z, -10 x y, 5 x z + 17 x] > Problem := [F,G]; 2 2 2 Problem := [[-20 x y z - 20 z, 18 x + 9 x, -6 x z - 8 y z], 2 3 [-20 x y + 17 z, -10 x y, 5 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=26.3MB, alloc=32.3MB, time=0.46 memory used=48.3MB, alloc=32.3MB, time=0.74 memory used=68.7MB, alloc=56.3MB, time=1.04 N1 := 557 > GB := Basis(F, plex(op(vars))); 2 2 GB := [2 x + x, 2 x z + z, 16 y z + 3 z, 3 z + 32 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=108.3MB, alloc=60.3MB, time=1.66 memory used=149.9MB, alloc=84.3MB, time=2.26 N2 := 829 #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 x y z - 20 z, 18 x + 9 x, -6 x z - 8 y z, -20 x y + 17 z, -10 x y, 3 5 x z + 17 x] > J:=[op(GB),op(G)]; 2 2 2 J := [2 x + x, 2 x z + z, 16 y z + 3 z, 3 z + 32 z, -20 x y + 17 z, -10 x y, 3 5 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 := [6, 14, 18, 4, 3, 1, 2, 1, 2/3, 2/3, 8/13, 4/13, 6/13, 7, 13, 17, 4, 3, 1, 2, 5/7, 3/7, 5/7, 7/15, 1/5, 8/15, 1, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=180.4MB, alloc=84.3MB, time=2.85 |\^/| 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(); 1428322346 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 F := [-4 z - 4 z, -18 x z + 10 y , 19 x y + 8 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [14 x y + 20 z, -9 x z - 5 y , -20 x y - 9 x z] > Problem := [F,G]; 4 2 2 2 2 Problem := [[-4 z - 4 z, -18 x z + 10 y , 19 x y + 8 x z], 2 2 2 3 [14 x y + 20 z, -9 x z - 5 y , -20 x y - 9 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.1MB, alloc=32.3MB, time=0.38 memory used=47.1MB, alloc=32.3MB, time=0.60 memory used=67.4MB, alloc=32.3MB, time=0.84 memory used=86.1MB, alloc=56.3MB, time=1.10 memory used=124.2MB, alloc=60.3MB, time=1.57 memory used=160.4MB, alloc=60.3MB, time=2.00 memory used=194.5MB, alloc=84.3MB, time=2.42 memory used=250.9MB, alloc=92.3MB, time=3.10 memory used=305.6MB, alloc=116.3MB, time=3.77 memory used=384.4MB, alloc=116.3MB, time=4.72 memory used=462.2MB, alloc=140.3MB, time=5.68 memory used=551.4MB, alloc=140.3MB, time=6.81 memory used=627.6MB, alloc=420.3MB, time=7.81 memory used=742.2MB, alloc=444.3MB, time=9.38 memory used=876.6MB, alloc=468.3MB, time=11.08 memory used=1033.8MB, alloc=492.3MB, time=13.09 memory used=1165.2MB, alloc=492.3MB, time=14.77 memory used=1300.4MB, alloc=516.3MB, time=16.56 memory used=1440.6MB, alloc=516.3MB, time=18.59 memory used=1559.6MB, alloc=516.3MB, time=20.30 memory used=1662.6MB, alloc=540.3MB, time=21.84 memory used=1771.0MB, alloc=540.3MB, time=23.47 memory used=1867.4MB, alloc=540.3MB, time=24.95 memory used=1948.4MB, alloc=540.3MB, time=26.29 memory used=2019.8MB, alloc=540.3MB, time=27.53 memory used=2078.4MB, alloc=540.3MB, time=28.55 memory used=2142.5MB, alloc=540.3MB, time=29.68 memory used=2195.6MB, alloc=540.3MB, time=30.69 memory used=2240.1MB, alloc=540.3MB, time=31.73 memory used=2444.7MB, alloc=564.3MB, time=34.70 memory used=2668.0MB, alloc=588.3MB, time=38.01 memory used=2892.1MB, alloc=612.3MB, time=41.61 memory used=3068.1MB, alloc=636.3MB, time=44.57 memory used=3229.4MB, alloc=660.3MB, time=47.26 memory used=3407.3MB, alloc=684.3MB, time=50.40 memory used=3544.9MB, alloc=708.3MB, time=52.95 memory used=3708.8MB, alloc=732.3MB, time=55.96 memory used=3830.1MB, alloc=756.3MB, time=58.32 memory used=3986.5MB, alloc=756.3MB, time=61.44 memory used=4177.2MB, alloc=780.3MB, time=65.19 memory used=4363.1MB, alloc=804.3MB, time=68.90 memory used=4552.4MB, alloc=828.3MB, time=72.71 memory used=4905.5MB, alloc=852.3MB, time=79.06 memory used=5249.5MB, alloc=876.3MB, time=85.57 memory used=5589.5MB, alloc=900.3MB, time=91.83 memory used=5910.1MB, alloc=924.3MB, time=100.56 memory used=6199.2MB, alloc=948.3MB, time=110.12 memory used=6487.8MB, alloc=972.3MB, time=120.43 memory used=6782.0MB, alloc=996.3MB, time=131.14 memory used=7083.9MB, alloc=1020.3MB, time=142.19 memory used=7396.4MB, alloc=1044.3MB, time=153.91 memory used=7720.5MB, alloc=1068.3MB, time=166.13 memory used=8057.3MB, alloc=1092.3MB, time=178.87 memory used=8398.5MB, alloc=1116.3MB, time=192.74 memory used=8759.2MB, alloc=1140.3MB, time=208.77 memory used=9143.8MB, alloc=1164.3MB, time=224.07 memory used=9552.4MB, alloc=1188.3MB, time=239.89 memory used=9984.9MB, alloc=1212.3MB, time=256.58 memory used=10441.3MB, alloc=1236.3MB, time=274.34 memory used=10921.7MB, alloc=1260.3MB, time=294.57 |\^/| 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(); 1428322646 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 4 F := [-18 x + 6 y, -9 y z + 17 y, -13 z + 5] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 3 G := [13 x y z - 11 x y , -19 y z - 20 y , -6 x z + 15 y z ] > Problem := [F,G]; 4 2 2 4 Problem := [[-18 x + 6 y, -9 y z + 17 y, -13 z + 5], 2 2 2 2 3 3 [13 x y z - 11 x y , -19 y z - 20 y , -6 x z + 15 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.53 memory used=47.9MB, alloc=32.3MB, time=0.86 memory used=67.9MB, alloc=32.3MB, time=1.20 memory used=86.6MB, alloc=56.3MB, time=1.52 memory used=124.9MB, alloc=60.3MB, time=2.16 memory used=162.1MB, alloc=84.3MB, time=2.89 memory used=219.4MB, alloc=108.3MB, time=4.08 memory used=293.7MB, alloc=108.3MB, time=5.65 memory used=359.8MB, alloc=132.3MB, time=7.01 memory used=442.7MB, alloc=164.3MB, time=8.75 memory used=540.6MB, alloc=188.3MB, time=10.63 memory used=651.9MB, alloc=212.3MB, time=12.84 memory used=772.7MB, alloc=236.3MB, time=15.50 memory used=894.8MB, alloc=260.3MB, time=19.39 memory used=1024.4MB, alloc=284.3MB, time=23.76 memory used=1165.0MB, alloc=308.3MB, time=28.00 memory used=1318.0MB, alloc=332.3MB, time=32.49 memory used=1481.0MB, alloc=356.3MB, time=38.01 memory used=1666.9MB, alloc=380.3MB, time=44.20 memory used=1876.8MB, alloc=404.3MB, time=51.03 memory used=2110.6MB, alloc=428.3MB, time=58.54 memory used=2368.3MB, alloc=428.3MB, time=66.85 memory used=2626.0MB, alloc=428.3MB, time=75.18 memory used=2883.6MB, alloc=452.3MB, time=83.40 memory used=3165.1MB, alloc=452.3MB, time=92.38 memory used=3446.5MB, alloc=452.3MB, time=101.34 memory used=3728.0MB, alloc=452.3MB, time=110.43 memory used=4009.4MB, alloc=476.3MB, time=119.51 memory used=4314.7MB, alloc=476.3MB, time=129.44 memory used=4619.9MB, alloc=476.3MB, time=139.47 memory used=4924.9MB, alloc=500.3MB, time=149.52 memory used=5253.9MB, alloc=500.3MB, time=160.14 memory used=5582.8MB, alloc=524.3MB, time=170.69 memory used=5935.6MB, alloc=524.3MB, time=181.87 memory used=6288.4MB, alloc=548.3MB, time=193.03 N1 := 13871 > GB := Basis(F, plex(op(vars))); 12 4 4 8 4 2 4 GB := [3645 x - 3757 x , -3 x + y, -135 x + 221 x z , 13 z - 5] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6514.4MB, alloc=548.3MB, time=199.01 memory used=6964.2MB, alloc=828.3MB, time=207.87 memory used=7365.0MB, alloc=852.3MB, time=221.38 N2 := 5527 #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)]; 4 2 2 4 2 2 H := [-18 x + 6 y, -9 y z + 17 y, -13 z + 5, 13 x y z - 11 x y , 2 2 3 3 -19 y z - 20 y , -6 x z + 15 y z ] > J:=[op(GB),op(G)]; 12 4 4 8 4 2 4 J := [3645 x - 3757 x , -3 x + y, -135 x + 221 x z , 13 z - 5, 2 2 2 2 3 3 13 x y z - 11 x y , -19 y z - 20 y , -6 x z + 15 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 := [6, 13, 23, 4, 4, 2, 4, 1/2, 5/6, 5/6, 1/3, 2/3, 1/2, 7, 14, 39, 12, 12, 2, 4, 5/7, 4/7, 5/7, 4/7, 3/7, 3/7, -1, -16, -8] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=7746.8MB, alloc=852.3MB, time=233.26 |\^/| 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(); 1428322896 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [8 x z + 17 y z, -8 x z - 15, 11 y - 6 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 3 G := [-16 x z - 17 y z, -8 x y z - 5 z , -6 x y - 14 x z] > Problem := [F,G]; 3 3 2 Problem := [[8 x z + 17 y z, -8 x z - 15, 11 y - 6 z], 2 2 2 2 3 3 [-16 x z - 17 y z, -8 x y z - 5 z , -6 x y - 14 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.1MB, alloc=32.3MB, time=0.44 memory used=47.9MB, alloc=32.3MB, time=0.67 memory used=68.7MB, alloc=32.3MB, time=0.92 memory used=88.3MB, alloc=56.3MB, time=1.16 memory used=127.7MB, alloc=60.3MB, time=1.65 memory used=166.0MB, alloc=84.3MB, time=2.26 memory used=223.6MB, alloc=84.3MB, time=3.08 memory used=275.9MB, alloc=108.3MB, time=3.90 memory used=347.2MB, alloc=140.3MB, time=4.98 memory used=434.4MB, alloc=164.3MB, time=6.33 memory used=533.0MB, alloc=188.3MB, time=8.43 memory used=637.8MB, alloc=212.3MB, time=11.40 memory used=758.9MB, alloc=236.3MB, time=15.21 memory used=903.9MB, alloc=236.3MB, time=19.79 memory used=1048.8MB, alloc=236.3MB, time=24.43 memory used=1193.8MB, alloc=260.3MB, time=29.03 memory used=1362.9MB, alloc=284.3MB, time=34.01 N1 := 5535 > GB := Basis(F, plex(op(vars))); 9 4 4 GB := [907039232 x + 711048375, -1936 x + 2295 y, -10648 x + 6885 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1494.9MB, alloc=284.3MB, time=36.24 N2 := 1541 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 2 2 H := [8 x z + 17 y z, -8 x z - 15, -6 z + 11 y, -16 x z - 17 y z, 2 2 3 3 -8 x y z - 5 z , -6 x y - 14 x z] > J:=[op(GB),op(G)]; 9 4 4 J := [907039232 x + 711048375, -1936 x + 2295 y, -10648 x + 6885 z, 2 2 2 2 3 3 -16 x z - 17 y z, -8 x y z - 5 z , -6 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 := [6, 16, 20, 4, 3, 3, 2, 5/6, 5/6, 1, 1/2, 5/12, 3/4, 6, 14, 29, 9, 9, 1, 2, 1, 2/3, 2/3, 7/12, 1/3, 1/2, 2, -9, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1630.4MB, alloc=540.3MB, time=38.80 |\^/| 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(); 1428322937 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 F := [19 z + y z, 4 x z + 6 x z, 19 x y z + 4 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 G := [6 x z - 13 x z, 8 x y - 3 x z , -15 x - 11 x z ] > Problem := [F,G]; 4 2 3 2 2 Problem := [[19 z + y z, 4 x z + 6 x z, 19 x y z + 4 y z ], 3 3 2 3 2 [6 x z - 13 x z, 8 x y - 3 x z , -15 x - 11 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.43 memory used=47.9MB, alloc=32.3MB, time=0.66 memory used=68.5MB, alloc=32.3MB, time=0.93 memory used=87.9MB, alloc=56.3MB, time=1.16 memory used=131.7MB, alloc=60.3MB, time=1.80 N1 := 629 > GB := Basis(F, plex(op(vars))); 2 3 3 4 GB := [19 x z + 4 x z, 19 x y z + 4 y z, 32 y z - 185193 x z, 2 2 3 2 4 2 -2 x y z + 57 x z , -2 y z + 57 y z , 19 z + y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=169.3MB, alloc=60.3MB, time=2.36 memory used=207.1MB, alloc=60.3MB, time=2.80 memory used=244.1MB, alloc=84.3MB, time=3.23 memory used=293.1MB, alloc=84.3MB, time=3.81 memory used=349.1MB, alloc=92.3MB, time=4.48 memory used=404.8MB, alloc=116.3MB, time=5.16 memory used=482.7MB, alloc=140.3MB, time=6.25 memory used=583.4MB, alloc=164.3MB, time=7.67 memory used=691.3MB, alloc=188.3MB, time=10.13 memory used=804.5MB, alloc=212.3MB, time=13.28 N2 := 2333 #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)]; 4 2 3 2 2 3 H := [19 z + y z, 4 x z + 6 x z, 19 x y z + 4 y z , 6 x z - 13 x z, 3 2 3 2 8 x y - 3 x z , -15 x - 11 x z ] > J:=[op(GB),op(G)]; 2 3 3 4 J := [19 x z + 4 x z, 19 x y z + 4 y z, 32 y z - 185193 x z, 2 2 3 2 4 2 3 -2 x y z + 57 x z , -2 y z + 57 y z , 19 z + y z, 6 x z - 13 x z, 3 2 3 2 8 x y - 3 x z , -15 x - 11 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 := [6, 14, 23, 4, 3, 2, 4, 5/6, 1/2, 1, 3/4, 1/3, 5/6, 9, 22, 36, 5, 3, 4, 4, 7/9, 2/3, 1, 2/3, 4/9, 8/9, -8, -13, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=805.2MB, alloc=212.3MB, time=13.31 |\^/| 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(); 1428322951 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 3 F := [15 x z - 10, -6 y z + 13 y z , 19 x y + 7 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 G := [x y, -6 x y - 16 x z, 15 x z - 9 x z] > Problem := [F,G]; 3 3 2 2 3 3 Problem := [[15 x z - 10, -6 y z + 13 y z , 19 x y + 7 x z], 2 3 3 [x y, -6 x y - 16 x z, 15 x z - 9 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.4MB, alloc=32.3MB, time=0.40 memory used=48.7MB, alloc=32.3MB, time=0.74 memory used=68.9MB, alloc=56.3MB, time=1.04 N1 := 823 > GB := Basis(F, plex(op(vars))); memory used=110.2MB, alloc=56.3MB, time=1.80 GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 87 #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)]; 3 3 2 2 3 3 2 H := [15 x z - 10, -6 y z + 13 y z , 19 x y + 7 x z, y x , 3 3 -6 x y - 16 x z, 15 x z - 9 x z] > J:=[op(GB),op(G)]; 2 3 3 J := [1, y x , -6 x y - 16 x z, 15 x z - 9 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 := [6, 14, 23, 4, 3, 3, 3, 5/6, 2/3, 5/6, 2/3, 5/12, 7/12, 4, 7, 11, 4, 3, 1, 1, 3/4, 1/2, 1/2, 5/7, 2/7, 3/7, 7, 12, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=120.9MB, 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(); 1428322953 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [-17 x y z + 8 z, 8 z + 2, -4 y z - 12 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 3 G := [-8 y z - 13 x z, 20 x + 6 x y, x y + 19 y ] > Problem := [F,G]; 2 2 3 Problem := [[-17 x y z + 8 z, 8 z + 2, -4 y z - 12 x y], 2 3 2 3 3 [-8 y z - 13 x z, 20 x + 6 x y, x 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=0.14 memory used=26.0MB, alloc=32.3MB, time=0.38 memory used=48.2MB, alloc=32.3MB, time=0.70 memory used=69.8MB, alloc=56.3MB, time=1.03 N1 := 509 > GB := Basis(F, plex(op(vars))); 2 GB := [576 x + 1, 17 y + 4608, -12 x + z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.1MB, alloc=60.3MB, time=1.57 N2 := 475 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 H := [-17 x y z + 8 z, 8 z + 2, -4 y z - 12 x y, -8 y z - 13 x z, 3 2 3 3 20 x + 6 x y, x y + 19 y ] > J:=[op(GB),op(G)]; 2 2 3 2 J := [576 x + 1, 17 y + 4608, -12 x + z, -8 y z - 13 x z, 20 x + 6 x y, 3 3 x 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 := [6, 14, 20, 4, 3, 3, 3, 5/6, 5/6, 2/3, 1/2, 7/12, 1/2, 6, 11, 14, 4, 3, 3, 1, 5/6, 2/3, 1/3, 1/2, 5/12, 1/4, 3, 6, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=147.0MB, alloc=60.3MB, time=2.10 |\^/| 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(); 1428322955 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 2 2 F := [12 x z - 6 y , -8 y z - 6 z, 14 x y z - 10 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [10 x y z - 3 z, 4 x y - 16 y , x y - 18 y z] > Problem := [F,G]; 2 2 4 3 2 2 Problem := [[12 x z - 6 y , -8 y z - 6 z, 14 x y z - 10 x y z], 2 2 2 3 2 [10 x y z - 3 z, 4 x y - 16 y , 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=4.3MB, alloc=32.3MB, time=0.14 memory used=26.2MB, alloc=32.3MB, time=0.40 memory used=48.0MB, alloc=32.3MB, time=0.64 memory used=68.8MB, alloc=32.3MB, time=0.86 memory used=89.1MB, alloc=56.3MB, time=1.12 memory used=129.0MB, alloc=60.3MB, time=1.62 memory used=169.8MB, alloc=84.3MB, time=2.22 memory used=230.7MB, alloc=84.3MB, time=3.06 memory used=287.5MB, alloc=108.3MB, time=3.95 memory used=363.3MB, alloc=140.3MB, time=5.06 memory used=457.3MB, alloc=164.3MB, time=6.59 memory used=556.8MB, alloc=188.3MB, time=9.01 memory used=664.2MB, alloc=212.3MB, time=12.58 memory used=795.5MB, alloc=212.3MB, time=16.82 memory used=926.9MB, alloc=236.3MB, time=21.07 N1 := 4309 > GB := Basis(F, plex(op(vars))); 3 4 4 4 5 3 GB := [33614 x y + 9375 y , -7 x y + 5 y , 33614 x z + 9375 z, 4 2 -7 x z + 5 y z, 16807 x y + 9375 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1086.1MB, alloc=236.3MB, time=24.99 N2 := 937 #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 4 3 2 2 2 H := [12 x z - 6 y , -8 y z - 6 z, 14 x y z - 10 x y z, 10 x y z - 3 z, 2 2 3 2 4 x y - 16 y , x y - 18 y z] > J:=[op(GB),op(G)]; 3 4 4 4 5 3 J := [33614 x y + 9375 y , -7 x y + 5 y , 33614 x z + 9375 z, 4 2 2 2 2 3 -7 x z + 5 y z, 16807 y x + 9375 z , 10 x y z - 3 z, 4 x y - 16 y , 2 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 := [6, 16, 23, 4, 2, 4, 3, 5/6, 1, 5/6, 1/2, 3/4, 2/3, 8, 20, 34, 7, 3, 5, 2, 1, 7/8, 5/8, 1/2, 11/16, 1/2, -4, -11, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1209.1MB, alloc=236.3MB, time=27.01 |\^/| 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(); 1428322983 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [17 x y + 8 y z , -17 y + 12 z, 14 x z - 18] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [-19 x - 8, 11 x y + 3 x z, -20 y z + 14 x] > Problem := [F,G]; 3 2 2 2 2 Problem := [[17 x y + 8 y z , -17 y + 12 z, 14 x z - 18], 2 2 2 2 3 [-19 x - 8, 11 x y + 3 x z, -20 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=26.9MB, alloc=32.3MB, time=0.45 memory used=48.6MB, alloc=32.3MB, time=0.72 memory used=69.5MB, alloc=32.3MB, time=0.96 memory used=88.7MB, alloc=56.3MB, time=1.22 memory used=127.6MB, alloc=60.3MB, time=1.66 memory used=166.9MB, alloc=84.3MB, time=2.12 memory used=207.2MB, alloc=84.3MB, time=2.57 memory used=271.0MB, alloc=92.3MB, time=3.40 memory used=333.0MB, alloc=116.3MB, time=4.12 memory used=411.8MB, alloc=116.3MB, time=5.01 memory used=487.6MB, alloc=396.3MB, time=5.95 memory used=594.3MB, alloc=420.3MB, time=7.10 memory used=726.0MB, alloc=444.3MB, time=8.64 memory used=868.7MB, alloc=468.3MB, time=10.36 memory used=1009.4MB, alloc=492.3MB, time=12.17 memory used=1174.8MB, alloc=516.3MB, time=14.62 memory used=1354.6MB, alloc=540.3MB, time=17.49 memory used=1525.5MB, alloc=564.3MB, time=20.19 memory used=1701.5MB, alloc=588.3MB, time=23.08 memory used=1896.6MB, alloc=612.3MB, time=26.26 memory used=2099.4MB, alloc=636.3MB, time=31.77 memory used=2302.4MB, alloc=660.3MB, time=37.98 memory used=2508.1MB, alloc=684.3MB, time=44.94 memory used=2725.4MB, alloc=708.3MB, time=52.74 memory used=2966.6MB, alloc=732.3MB, time=61.31 memory used=3231.7MB, alloc=756.3MB, time=70.74 memory used=3520.8MB, alloc=780.3MB, time=80.96 memory used=3833.9MB, alloc=804.3MB, time=91.97 memory used=4170.8MB, alloc=828.3MB, time=103.73 memory used=4531.8MB, alloc=828.3MB, time=116.40 memory used=4892.6MB, alloc=852.3MB, time=129.05 memory used=5277.3MB, alloc=852.3MB, time=142.50 memory used=5661.8MB, alloc=876.3MB, time=155.59 memory used=6070.2MB, alloc=900.3MB, time=169.28 N1 := 12079 > GB := Basis(F, plex(op(vars))); 7 5 3 GB := [99127 x - 20736, 833 x + 288 y, -119 x + 48 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6386.2MB, alloc=900.3MB, time=177.79 N2 := 945 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 H := [17 x y + 8 y z , -17 y + 12 z, 14 x z - 18, -19 x - 8, 2 2 2 3 11 x y + 3 x z, -20 y z + 14 x] > J:=[op(GB),op(G)]; 7 5 3 2 J := [99127 x - 20736, 833 x + 288 y, -119 x + 48 z, -19 x - 8, 2 2 2 3 11 x y + 3 x z, -20 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 := [6, 14, 19, 4, 2, 3, 3, 5/6, 2/3, 5/6, 1/2, 5/12, 5/12, 6, 12, 25, 7, 7, 2, 3, 1, 1/2, 1/2, 7/12, 1/4, 1/4, 2, -6, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=6492.3MB, alloc=900.3MB, time=179.60 |\^/| 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(); 1428323168 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 3 F := [-6 y z , -2 y z - 14 z , 17 x y + 20 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 3 4 2 G := [-4 x y + 16 y , 18 x y + 11 x , -9 y - 5 x y ] > Problem := [F,G]; 2 3 3 3 3 Problem := [[-6 y z , -2 y z - 14 z , 17 x y + 20 x ], 3 4 3 3 4 2 [-4 x y + 16 y , 18 x y + 11 x , -9 y - 5 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.41 memory used=47.6MB, alloc=32.3MB, time=0.69 memory used=65.7MB, alloc=56.3MB, time=0.91 N1 := 693 > GB := Basis(F, plex(op(vars))); 3 3 3 2 2 3 GB := [17 x y + 20 x , x z , y z , z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=103.8MB, alloc=56.3MB, time=1.50 N2 := 447 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 3 3 3 4 H := [-6 y z , -2 y z - 14 z , 17 x y + 20 x , -4 x y + 16 y , 3 3 4 2 18 x y + 11 x , -9 y - 5 x y ] > J:=[op(GB),op(G)]; 3 3 3 2 2 3 3 4 3 3 J := [17 x y + 20 x , x z , y z , z , -4 x y + 16 y , 18 x y + 11 x , 4 2 -9 y - 5 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 := [6, 12, 23, 4, 3, 4, 3, 2/3, 1, 1/3, 6/13, 8/13, 3/13, 7, 13, 27, 5, 3, 4, 3, 5/7, 5/7, 3/7, 1/2, 1/2, 3/14, -1, -4, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=142.1MB, alloc=60.3MB, time=2.02 |\^/| 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(); 1428323170 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [4 x y z - 17 x z , 14 x y z - 14 y z , -14 y z + y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 4 3 G := [13 x z - 14 x y , 8 x + 8 y , -6 y + 15 y z ] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[4 x y z - 17 x z , 14 x y z - 14 y z , -14 y z + y z], 2 2 2 4 2 4 3 [13 x z - 14 x y , 8 x + 8 y , -6 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=0.15 memory used=26.1MB, alloc=32.3MB, time=0.40 memory used=47.6MB, alloc=32.3MB, time=0.66 memory used=67.8MB, alloc=32.3MB, time=0.91 memory used=86.5MB, alloc=56.3MB, time=1.18 memory used=125.8MB, alloc=60.3MB, time=1.76 memory used=164.1MB, alloc=60.3MB, time=2.27 memory used=200.7MB, alloc=84.3MB, time=2.72 memory used=257.3MB, alloc=92.3MB, time=3.45 memory used=313.7MB, alloc=116.3MB, time=4.21 memory used=393.3MB, alloc=140.3MB, time=5.24 memory used=485.4MB, alloc=164.3MB, time=6.52 memory used=588.0MB, alloc=188.3MB, time=8.25 memory used=693.6MB, alloc=212.3MB, time=10.85 memory used=807.0MB, alloc=236.3MB, time=14.35 memory used=944.4MB, alloc=260.3MB, time=18.90 memory used=1105.8MB, alloc=260.3MB, time=23.74 memory used=1267.2MB, alloc=284.3MB, time=28.81 N1 := 5295 > GB := Basis(F, plex(op(vars))); GB := [ 4 3 3 2 2 2 2 2 14 x y z - x y z, -833 x y z + y z, -4 x y z + 17 x z , -x y z + y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1455.8MB, alloc=284.3MB, time=33.87 memory used=1561.3MB, alloc=540.3MB, time=35.25 memory used=1788.8MB, alloc=564.3MB, time=40.13 N2 := 2009 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 H := [4 x y z - 17 x z , 14 x y z - 14 y z , -14 y z + y z, 2 2 2 4 2 4 3 13 x z - 14 x y , 8 x + 8 y , -6 y + 15 y z ] > J:=[op(GB),op(G)]; 4 3 3 2 2 2 2 J := [14 x y z - x y z, -833 x y z + y z, -4 x y z + 17 x z , 2 2 2 2 4 2 4 3 -x y z + y z , 13 x z - 14 x y , 8 x + 8 y , -6 y + 15 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 := [6, 15, 23, 4, 4, 4, 3, 2/3, 1, 5/6, 1/2, 3/4, 2/3, 7, 19, 30, 6, 4, 4, 3, 6/7, 1, 6/7, 9/14, 11/14, 5/7, -4, -7, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1821.9MB, alloc=564.3MB, time=40.93 |\^/| 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(); 1428323213 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-14 x y z - 20 x y z, 2 y z - 7 y, 14 x y z + 19 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 G := [-4 x z - 19 z , -4 x z + 5 z, -19 x y + 4 z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-14 x y z - 20 x y z, 2 y z - 7 y, 14 x y z + 19 x z ], 2 3 3 3 [-4 x z - 19 z , -4 x z + 5 z, -19 x y + 4 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.1MB, alloc=32.3MB, time=0.43 memory used=47.3MB, alloc=32.3MB, time=0.66 memory used=67.6MB, alloc=32.3MB, time=0.90 memory used=86.5MB, alloc=56.3MB, time=1.15 memory used=125.7MB, alloc=60.3MB, time=1.62 memory used=162.2MB, alloc=84.3MB, time=2.11 memory used=217.2MB, alloc=84.3MB, time=2.90 memory used=272.1MB, alloc=108.3MB, time=3.70 memory used=345.0MB, alloc=132.3MB, time=4.83 memory used=438.2MB, alloc=164.3MB, time=6.13 memory used=543.5MB, alloc=188.3MB, time=7.68 memory used=661.4MB, alloc=212.3MB, time=9.43 memory used=784.2MB, alloc=236.3MB, time=12.10 memory used=913.4MB, alloc=260.3MB, time=15.41 memory used=1050.2MB, alloc=284.3MB, time=20.39 memory used=1210.9MB, alloc=308.3MB, time=27.01 memory used=1395.6MB, alloc=308.3MB, time=34.53 memory used=1580.3MB, alloc=332.3MB, time=41.32 memory used=1789.0MB, alloc=332.3MB, time=48.13 memory used=1997.5MB, alloc=332.3MB, time=55.74 memory used=2206.2MB, alloc=356.3MB, time=63.04 memory used=2438.6MB, alloc=380.3MB, time=70.41 N1 := 7911 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [y x, z x, 2 y z - 7 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2657.9MB, alloc=380.3MB, time=75.42 N2 := 1403 #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 x y z - 20 x y z, 2 y z - 7 y, 14 x y z + 19 x z , 2 3 3 3 -4 x z - 19 z , -4 x z + 5 z, -19 x y + 4 z] > J:=[op(GB),op(G)]; 2 2 2 2 3 3 3 J := [y x, z x, 2 y z - 7 y, -4 x z - 19 z , -4 x z + 5 z, -19 x y + 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, 15, 23, 4, 3, 2, 3, 5/6, 2/3, 1, 7/12, 1/2, 5/6, 6, 13, 20, 4, 3, 2, 3, 5/6, 1/2, 5/6, 5/12, 1/3, 7/12, 2, 3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2781.8MB, alloc=636.3MB, time=77.82 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428323298 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-19 x y z + 17 x , 20 y z , -17 x y + 5 x y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 G := [17 x y, 9 x + 2 y z , -5 y z + 2 z ] > Problem := [F,G]; 2 2 3 2 Problem := [[-19 x y z + 17 x , 20 y z , -17 x y + 5 x y z ], 2 3 2 2 3 [17 x y, 9 x + 2 y z , -5 y z + 2 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.8MB, alloc=32.3MB, time=0.39 memory used=48.3MB, alloc=32.3MB, time=0.63 memory used=68.5MB, alloc=32.3MB, time=0.86 memory used=90.0MB, alloc=56.3MB, time=1.22 memory used=132.4MB, alloc=60.3MB, time=1.88 memory used=170.4MB, alloc=84.3MB, time=2.44 memory used=228.9MB, alloc=84.3MB, time=3.29 memory used=281.7MB, alloc=108.3MB, time=4.05 memory used=353.1MB, alloc=132.3MB, time=5.10 memory used=440.1MB, alloc=164.3MB, time=6.40 memory used=535.8MB, alloc=188.3MB, time=8.41 memory used=640.8MB, alloc=212.3MB, time=11.00 memory used=756.2MB, alloc=236.3MB, time=14.71 memory used=895.6MB, alloc=236.3MB, time=19.10 memory used=1035.0MB, alloc=236.3MB, time=23.91 memory used=1174.3MB, alloc=260.3MB, time=28.51 memory used=1337.6MB, alloc=260.3MB, time=33.62 memory used=1500.9MB, alloc=260.3MB, time=40.27 memory used=1664.1MB, alloc=284.3MB, time=47.02 memory used=1851.3MB, alloc=308.3MB, time=54.82 N1 := 6935 > GB := Basis(F, plex(op(vars))); 3 2 2 2 GB := [x , z x , 19 x y z - 17 x , z y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 583 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 2 3 H := [-19 x y z + 17 x , 20 z y, -17 x y + 5 x y z , 17 x y, 2 z y + 9 x , 2 3 -5 y z + 2 z ] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 3 2 3 J := [x , z x , 19 x y z - 17 x , z y, 17 x y, 2 z y + 9 x , -5 y z + 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, 15, 19, 4, 3, 2, 3, 2/3, 1, 5/6, 3/7, 1/2, 3/7, 7, 15, 21, 3, 3, 2, 3, 5/7, 5/7, 5/7, 2/5, 1/3, 2/5, 0, -2, 1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1989.6MB, alloc=308.3MB, time=58.25 |\^/| 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(); 1428323361 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 3 F := [-9 x z + 16 x, -17 y z + 6 z, -16 x - 11 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 3 2 G := [-5 y z - 9 z, -16 x - 14 z , 4 x z - 4 y z] > Problem := [F,G]; 3 3 4 3 Problem := [[-9 x z + 16 x, -17 y z + 6 z, -16 x - 11 x ], 2 2 4 3 3 2 [-5 y z - 9 z, -16 x - 14 z , 4 x z - 4 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.2MB, alloc=32.3MB, time=0.41 memory used=47.6MB, alloc=32.3MB, time=0.65 memory used=68.1MB, alloc=32.3MB, time=0.93 memory used=87.7MB, alloc=56.3MB, time=1.17 memory used=127.5MB, alloc=60.3MB, time=1.68 memory used=167.9MB, alloc=84.3MB, time=2.26 memory used=227.6MB, alloc=84.3MB, time=3.16 memory used=283.4MB, alloc=108.3MB, time=3.99 memory used=357.2MB, alloc=132.3MB, time=5.09 memory used=447.5MB, alloc=164.3MB, time=6.50 memory used=547.6MB, alloc=188.3MB, time=8.64 memory used=653.9MB, alloc=212.3MB, time=11.77 memory used=780.0MB, alloc=212.3MB, time=15.58 memory used=906.0MB, alloc=236.3MB, time=19.44 memory used=1056.0MB, alloc=236.3MB, time=23.96 memory used=1206.2MB, alloc=260.3MB, time=28.12 N1 := 4897 > GB := Basis(F, plex(op(vars))); 4 3 3 3 3 GB := [16 x + 11 x , 17 x y - 6 x, 17 y z - 6 z, 9 x z - 16 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1313.5MB, alloc=260.3MB, time=29.63 memory used=1513.1MB, alloc=516.3MB, time=32.52 memory used=1701.7MB, alloc=540.3MB, time=35.67 memory used=1879.4MB, alloc=564.3MB, time=40.77 memory used=2067.7MB, alloc=588.3MB, time=46.79 memory used=2280.1MB, alloc=612.3MB, time=53.30 N2 := 4897 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 4 3 2 2 H := [-9 x z + 16 x, -17 y z + 6 z, -16 x - 11 x , -5 y z - 9 z, 4 3 3 2 -16 x - 14 z , 4 x z - 4 y z] > J:=[op(GB),op(G)]; 4 3 3 3 3 J := [16 x + 11 x , 17 x y - 6 x, 17 y z - 6 z, 9 x z - 16 x, 2 2 4 3 3 2 -5 y z - 9 z, -16 x - 14 z , 4 x z - 4 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 24, 4, 4, 3, 3, 2/3, 1/2, 5/6, 1/2, 1/4, 2/3, 7, 14, 28, 4, 4, 3, 3, 5/7, 4/7, 5/7, 4/7, 2/7, 4/7, -2, -4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2427.4MB, alloc=612.3MB, time=57.18 |\^/| 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(); 1428323420 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 4 2 F := [-9 x y z - 2 y z, 4 x y + 8 x z , 6 y - 5 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 2 G := [15 x y z - 2 z, 3 y - 16 x z, -13 x z - 12 x z] > Problem := [F,G]; 2 3 2 2 4 2 Problem := [[-9 x y z - 2 y z, 4 x y + 8 x z , 6 y - 5 x y], 2 4 3 2 [15 x y z - 2 z, 3 y - 16 x z, -13 x z - 12 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=0.16 memory used=26.2MB, alloc=32.3MB, time=0.41 memory used=47.9MB, alloc=32.3MB, time=0.69 memory used=68.3MB, alloc=32.3MB, time=0.93 memory used=88.7MB, alloc=56.3MB, time=1.21 N1 := 385 > GB := Basis(F, plex(op(vars))); 6 4 5 3 2 4 2 3 GB := [6561 x y + 50 x y, -243 x y + 10 x y , 9 x y + 2 x y , 4 2 4 2 2 2 2 6 y - 5 x y, 6561 x y z + 50 x y z, 27 x y z + 5 x y z, 2 3 2 2 9 x y z + 2 y z, x y + 2 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=129.2MB, alloc=60.3MB, time=1.78 memory used=167.2MB, alloc=60.3MB, time=2.16 memory used=205.7MB, alloc=60.3MB, time=2.57 memory used=243.8MB, alloc=84.3MB, time=3.02 memory used=304.3MB, alloc=84.3MB, time=3.88 memory used=359.6MB, alloc=108.3MB, time=4.84 N2 := 1015 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 4 2 2 H := [-9 x y z - 2 y z, 4 x y + 8 x z , 6 y - 5 x y, 15 x y z - 2 z, 4 3 2 3 y - 16 x z, -13 x z - 12 x z] > J:=[op(GB),op(G)]; 6 4 5 3 2 4 2 3 J := [6561 x y + 50 x y, -243 x y + 10 x y , 9 x y + 2 x y , 4 2 4 2 2 2 2 6 y - 5 x y, 6561 x y z + 50 x y z, 27 x y z + 5 x y z, 2 3 2 2 2 4 9 x y z + 2 y z, x y + 2 x z , 15 x y z - 2 z, 3 y - 16 x z, 3 2 -13 x z - 12 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 := [6, 16, 23, 4, 3, 4, 2, 1, 5/6, 5/6, 2/3, 7/12, 2/3, 11, 28, 52, 7, 6, 4, 2, 1, 10/11, 7/11, 9/11, 17/22, 6/11, -12, -29, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=380.8MB, alloc=108.3MB, time=5.26 |\^/| 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(); 1428323426 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [15 y , 6 y z + 6 x y, 13 x y z - 11] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [8 x y + 13 y , -8 x y z - 14 z, 13 x y - 4 y] > Problem := [F,G]; 2 3 2 2 Problem := [[15 y , 6 y z + 6 x y, 13 x y z - 11], 3 2 2 2 [8 x y + 13 y , -8 x y z - 14 z, 13 x y - 4 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.7MB, alloc=32.3MB, time=0.44 memory used=49.0MB, alloc=32.3MB, time=0.73 N1 := 485 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=68.9MB, alloc=56.3MB, time=1.05 N2 := 183 #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 3 2 2 3 2 2 H := [15 y , 6 y z + 6 x y, 13 z y x - 11, 8 x y + 13 y , -8 x y z - 14 z, 2 13 x y - 4 y] > J:=[op(GB),op(G)]; 3 2 2 2 J := [1, 8 x y + 13 y , -8 x y z - 14 z, 13 x y - 4 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 21, 4, 3, 3, 1, 5/6, 1, 1/2, 5/12, 3/4, 1/3, 4, 7, 11, 4, 3, 2, 1, 3/4, 3/4, 1/4, 3/7, 5/7, 2/7, 7, 10, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=87.9MB, alloc=56.3MB, time=1.30 |\^/| 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(); 1428323427 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 2 2 F := [4 y z + 11 y z , -10 x z + 18 x y z, -11 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [10 x y z - 11 x y, -18 y z - 6 y z , -15 x y z - 4] > Problem := [F,G]; 3 2 2 3 2 2 2 Problem := [[4 y z + 11 y z , -10 x z + 18 x y z, -11 x z ], 2 2 3 2 [10 x y z - 11 x y, -18 y z - 6 y z , -15 x y z - 4]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.38 memory used=47.5MB, alloc=32.3MB, time=0.63 memory used=67.5MB, alloc=56.3MB, time=0.88 memory used=108.2MB, alloc=60.3MB, time=1.37 memory used=148.1MB, alloc=84.3MB, time=1.98 memory used=207.1MB, alloc=84.3MB, time=2.82 memory used=260.2MB, alloc=108.3MB, time=3.63 memory used=328.6MB, alloc=132.3MB, time=5.22 memory used=408.8MB, alloc=156.3MB, time=7.77 memory used=513.2MB, alloc=180.3MB, time=10.54 N1 := 2731 > GB := Basis(F, plex(op(vars))); 5 3 2 2 2 3 2 2 GB := [z x , -5 x z + 9 x y z, x z , 4 y z + 11 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=634.3MB, alloc=188.3MB, time=12.12 memory used=774.1MB, alloc=468.3MB, time=14.15 memory used=919.4MB, alloc=492.3MB, time=18.30 N2 := 2731 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 3 2 2 2 2 2 H := [4 y z + 11 y z , -10 x z + 18 x y z, -11 x z , 10 x y z - 11 x y, 3 2 -18 y z - 6 y z , -15 x y z - 4] > J:=[op(GB),op(G)]; 5 3 2 2 2 3 2 2 2 2 J := [z x , -5 x z + 9 x y z, x z , 4 y z + 11 y z , 10 x y z - 11 x y, 3 2 -18 y z - 6 y z , -15 x y 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 := [6, 15, 23, 4, 3, 3, 2, 2/3, 5/6, 1, 6/13, 8/13, 9/13, 7, 17, 29, 6, 5, 3, 2, 5/7, 5/7, 1, 1/2, 4/7, 5/7, -2, -6, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1029.3MB, alloc=492.3MB, time=21.04 |\^/| 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(); 1428323449 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 2 4 F := [19 x y z + 2 z , -14 x + 13 x y , 15 x + 20 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 2 2 G := [-18 x y + 2 y z , -6 y + 6 x, -15 x z - 8 x z ] > Problem := [F,G]; 2 4 3 2 4 Problem := [[19 x y z + 2 z , -14 x + 13 x y , 15 x + 20 y z], 3 3 3 3 2 2 [-18 x y + 2 y z , -6 y + 6 x, -15 x z - 8 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.42 memory used=47.9MB, alloc=32.3MB, time=0.65 memory used=68.6MB, alloc=32.3MB, time=0.89 memory used=88.5MB, alloc=56.3MB, time=1.13 memory used=129.5MB, alloc=60.3MB, time=1.61 memory used=170.3MB, alloc=60.3MB, time=2.07 memory used=210.5MB, alloc=84.3MB, time=2.56 memory used=271.8MB, alloc=92.3MB, time=3.32 memory used=331.3MB, alloc=116.3MB, time=4.13 memory used=411.1MB, alloc=140.3MB, time=5.29 memory used=506.9MB, alloc=164.3MB, time=6.72 memory used=618.8MB, alloc=188.3MB, time=8.44 memory used=732.5MB, alloc=468.3MB, time=10.21 memory used=864.1MB, alloc=492.3MB, time=13.20 memory used=1000.7MB, alloc=516.3MB, time=17.00 memory used=1145.7MB, alloc=540.3MB, time=21.78 memory used=1314.8MB, alloc=564.3MB, time=27.33 memory used=1507.7MB, alloc=564.3MB, time=33.43 memory used=1700.7MB, alloc=564.3MB, time=39.67 memory used=1893.6MB, alloc=588.3MB, time=45.82 memory used=2110.6MB, alloc=612.3MB, time=52.86 N1 := 6907 > GB := Basis(F, plex(op(vars))); 19 7 14 7 GB := [270672597 x - 198814171136 x , -4563 x + 119168 x y, 3 2 5 3 4 5 4 -14 x + 13 x y , 39 x y + 56 x z, 3 x + 4 z y, -57 x y + 8 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2357.8MB, alloc=612.3MB, time=58.59 memory used=2623.8MB, alloc=612.3MB, time=62.15 memory used=2897.6MB, alloc=636.3MB, time=65.62 memory used=3189.3MB, alloc=660.3MB, time=69.30 memory used=3453.5MB, alloc=684.3MB, time=72.60 memory used=3695.8MB, alloc=708.3MB, time=75.80 memory used=3928.8MB, alloc=732.3MB, time=78.92 memory used=4116.4MB, alloc=756.3MB, time=81.72 memory used=4305.8MB, alloc=780.3MB, time=84.57 memory used=4474.5MB, alloc=804.3MB, time=87.25 memory used=4634.3MB, alloc=804.3MB, time=89.95 memory used=4791.7MB, alloc=828.3MB, time=92.46 memory used=4906.3MB, alloc=828.3MB, time=94.55 memory used=5026.7MB, alloc=828.3MB, time=96.72 memory used=5150.5MB, alloc=828.3MB, time=99.08 memory used=5270.2MB, alloc=852.3MB, time=101.29 memory used=5351.2MB, alloc=852.3MB, time=103.06 memory used=5451.2MB, alloc=852.3MB, time=105.16 memory used=5897.5MB, alloc=876.3MB, time=112.55 memory used=6311.9MB, alloc=900.3MB, time=120.22 memory used=6716.8MB, alloc=924.3MB, time=127.97 memory used=7109.8MB, alloc=948.3MB, time=135.58 memory used=7495.3MB, alloc=972.3MB, time=143.45 memory used=7822.1MB, alloc=996.3MB, time=154.37 memory used=8140.8MB, alloc=1020.3MB, time=165.84 memory used=8463.4MB, alloc=1044.3MB, time=177.90 memory used=8794.2MB, alloc=1068.3MB, time=190.46 memory used=9135.7MB, alloc=1092.3MB, time=203.52 memory used=9489.5MB, alloc=1116.3MB, time=217.74 memory used=9855.7MB, alloc=1140.3MB, time=232.86 memory used=10232.7MB, alloc=1164.3MB, time=247.45 memory used=10619.7MB, alloc=1188.3MB, time=263.27 memory used=11030.6MB, alloc=1212.3MB, time=279.99 memory used=11465.5MB, alloc=1236.3MB, time=297.60 |\^/| 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(); 1428323749 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 3 F := [-2 x y + 14 x y , 16 x z + 6 x , 19 x - 16 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 G := [-19 x + 18 x z, -18 z , -17 z + 14] > Problem := [F,G]; 3 2 3 3 3 Problem := [[-2 x y + 14 x y , 16 x z + 6 x , 19 x - 16 x y z], 4 2 3 [-19 x + 18 x z, -18 z , -17 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.46 memory used=48.7MB, alloc=32.3MB, time=0.84 memory used=68.8MB, alloc=56.3MB, time=1.20 N1 := 827 > GB := Basis(F, plex(op(vars))); 5 3 2 3 3 3 GB := [x , y x , y x, 8 x z + 3 x , -19 x + 16 x y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.1MB, alloc=56.3MB, time=2.06 memory used=148.8MB, alloc=84.3MB, time=2.73 N2 := 499 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 3 3 4 H := [-2 x y + 14 x y , 16 x z + 6 x , 19 x - 16 x y z, -19 x + 18 x z, 2 3 -18 z , -17 z + 14] > J:=[op(GB),op(G)]; 5 3 2 3 3 3 4 2 J := [x , y x , y x, 8 x z + 3 x , -19 x + 16 x y z, -19 x + 18 x z, -18 z , 3 -17 z + 14] > > 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, 20, 4, 4, 2, 3, 2/3, 1/3, 5/6, 2/3, 1/4, 5/12, 8, 14, 28, 5, 5, 2, 3, 3/4, 3/8, 5/8, 9/16, 3/16, 5/16, -3, -8, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=158.0MB, alloc=84.3MB, time=2.94 |\^/| 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(); 1428323752 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 F := [16 x y z + 8 x z, 19 x z + 10 x z, 18 x + 10 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 G := [0, 8 z - 5 y z, 4 x y z - 4 z ] > Problem := [F,G]; 2 2 2 4 Problem := [[16 x y z + 8 x z, 19 x z + 10 x z, 18 x + 10 x], 4 2 4 [0, 8 z - 5 y z, 4 x y z - 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=48.8MB, alloc=56.3MB, time=0.91 N1 := 405 > GB := Basis(F, plex(op(vars))); 4 GB := [9 x + 5 x, z x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); 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 4 4 H := [16 x y z + 8 x z, 19 x z + 10 x z, 18 x + 10 x, 0, 8 z - 5 y z, 2 4 4 x y z - 4 z ] > J:=[op(GB),op(G)]; 4 4 2 4 J := [9 x + 5 x, z x, 0, 8 z - 5 y z, 4 x 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, 11, -infinity, 4, 4, 1, 4, 2/3, 1/2, 2/3, 7/11, 3/11, 8/11, 5, 8, -infinity, 4, 4, 1, 4, 3/5, 2/5, 3/5, 4/9, 2/9, 5/9, 3, undefined, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=72.6MB, alloc=56.3MB, time=1.34 |\^/| 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(); 1428323754 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [-8 x z - 8 x y z , 8 x y - 2 x y z, -18 x y z + 19 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 G := [x y z + 19 z, -9 x y z + 6 x z, 2 y + 9 z] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[-8 x z - 8 x y z , 8 x y - 2 x y z, -18 x y z + 19 x y z], 2 2 2 4 [x y z + 19 z, -9 x y z + 6 x z, 2 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=0.17 memory used=26.3MB, alloc=32.3MB, time=0.43 memory used=47.6MB, alloc=32.3MB, time=0.71 memory used=67.5MB, alloc=32.3MB, time=1.01 memory used=86.9MB, alloc=56.3MB, time=1.30 memory used=126.2MB, alloc=60.3MB, time=1.82 memory used=163.2MB, alloc=60.3MB, time=2.34 memory used=200.6MB, alloc=84.3MB, time=3.01 memory used=257.8MB, alloc=108.3MB, time=3.98 memory used=339.5MB, alloc=140.3MB, time=5.25 memory used=428.5MB, alloc=164.3MB, time=7.24 memory used=521.6MB, alloc=188.3MB, time=10.49 memory used=634.4MB, alloc=188.3MB, time=14.63 memory used=747.2MB, alloc=212.3MB, time=18.55 N1 := 3529 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 3 2 2 2 2 2 GB := [72 x y - 19 x y , 72 x y + 19 x y , 4 x y + x y z, 2 2 2 2 2 2 -4 x y + x y z, 18 x z + 19 x y z, 18 x y z - 19 x y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=885.0MB, alloc=212.3MB, time=20.53 memory used=994.9MB, alloc=468.3MB, time=21.95 memory used=1143.2MB, alloc=492.3MB, time=23.95 memory used=1315.7MB, alloc=492.3MB, time=26.35 memory used=1481.0MB, alloc=516.3MB, time=28.67 memory used=1666.9MB, alloc=540.3MB, time=31.21 memory used=1869.4MB, alloc=564.3MB, time=33.95 memory used=2093.1MB, alloc=588.3MB, time=37.34 memory used=2337.9MB, alloc=612.3MB, time=40.91 memory used=2578.1MB, alloc=636.3MB, time=44.50 memory used=2818.1MB, alloc=660.3MB, time=48.22 memory used=3094.5MB, alloc=684.3MB, time=51.73 memory used=3354.4MB, alloc=708.3MB, time=55.62 memory used=3596.9MB, alloc=732.3MB, time=61.01 memory used=3812.5MB, alloc=756.3MB, time=67.41 memory used=4033.8MB, alloc=780.3MB, time=74.34 memory used=4265.2MB, alloc=804.3MB, time=82.06 memory used=4507.4MB, alloc=828.3MB, time=90.27 memory used=4761.9MB, alloc=852.3MB, time=98.74 memory used=5029.0MB, alloc=876.3MB, time=107.93 memory used=5304.5MB, alloc=900.3MB, time=118.02 memory used=5603.9MB, alloc=924.3MB, time=129.03 memory used=5927.3MB, alloc=948.3MB, time=140.81 memory used=6274.6MB, alloc=972.3MB, time=153.46 memory used=6645.9MB, alloc=996.3MB, time=166.92 memory used=7041.0MB, alloc=1020.3MB, time=181.13 memory used=7460.2MB, alloc=1044.3MB, time=196.21 memory used=7903.2MB, alloc=1068.3MB, time=212.18 memory used=8370.2MB, alloc=1092.3MB, time=228.88 memory used=8861.2MB, alloc=1116.3MB, time=246.40 memory used=9376.1MB, alloc=1140.3MB, time=264.67 memory used=9914.9MB, alloc=1164.3MB, time=283.63 |\^/| 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(); 1428324054 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 F := [-7 x - y , -16 x y + 5 x y z, 18 y z + 15 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 G := [-4 x + 3 x y , 5 x y z + 5 x y, -11 x - 3 x ] > Problem := [F,G]; 3 3 2 2 2 2 Problem := [[-7 x - y , -16 x y + 5 x y z, 18 y z + 15 z], 4 2 2 3 2 [-4 x + 3 x y , 5 x y z + 5 x y, -11 x - 3 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.45 memory used=47.4MB, alloc=32.3MB, time=0.74 memory used=68.0MB, alloc=56.3MB, time=1.13 N1 := 293 > GB := Basis(F, plex(op(vars))); 11 5 8 5 8 2 2 3 3 GB := [10584 x + 125 x , -42 x + 5 x y, -1764 x + 25 x y , y + 7 x , 9 7112448 x + 3125 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=106.5MB, alloc=60.3MB, time=1.71 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)]; 3 3 2 2 2 2 4 2 H := [-7 x - y , -16 x y + 5 x y z, 18 y z + 15 z, -4 x + 3 x y , 2 3 2 5 x y z + 5 x y, -11 x - 3 x ] > J:=[op(GB),op(G)]; 11 5 8 5 8 2 2 3 3 J := [10584 x + 125 x , -42 x + 5 x y, -1764 x + 25 x y , y + 7 x , 9 4 2 2 3 2 7112448 x + 3125 z, -4 x + 3 x y , 5 x y z + 5 x y, -11 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, 13, 21, 4, 4, 3, 2, 5/6, 5/6, 1/2, 3/4, 7/12, 1/3, 8, 15, 50, 11, 11, 3, 2, 1, 5/8, 1/4, 7/8, 3/8, 1/8, -2, -29, -7] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=145.8MB, alloc=60.3MB, time=2.36 |\^/| 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(); 1428324056 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 2 2 F := [-15 y - 18 z , 10 x y - 3 y , 10 x y - 16 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 2 3 G := [-13 x y - x y z , -11 x y + 17 y z , -12 y z - 20 y z ] > Problem := [F,G]; 3 3 2 2 2 2 2 2 Problem := [[-15 y - 18 z , 10 x y - 3 y , 10 x y - 16 x y], 3 2 3 3 2 2 3 [-13 x y - x y z , -11 x y + 17 y z , -12 y z - 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=26.3MB, alloc=32.3MB, time=0.46 memory used=48.1MB, alloc=32.3MB, time=0.77 memory used=69.1MB, alloc=32.3MB, time=1.07 memory used=90.1MB, alloc=56.3MB, time=1.44 memory used=132.7MB, alloc=60.3MB, time=2.19 N1 := 725 > GB := Basis(F, plex(op(vars))); 4 2 2 2 2 3 GB := [10 x y - 3 x y, -16 x y + 3 y , 64 x y + 9 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=167.8MB, alloc=60.3MB, time=2.89 memory used=205.4MB, alloc=84.3MB, time=3.45 memory used=267.3MB, alloc=92.3MB, time=4.41 memory used=328.8MB, alloc=116.3MB, time=5.47 memory used=405.8MB, alloc=140.3MB, time=7.80 N2 := 1411 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 2 2 2 2 2 3 2 H := [-15 y - 18 z , 10 x y - 3 y , 10 x y - 16 x y, -13 x y - x y z , 3 3 2 2 3 -11 x y + 17 y z , -12 y z - 20 y z ] > J:=[op(GB),op(G)]; 4 2 2 2 3 2 3 2 J := [10 x y - 3 x y, -16 x y + 3 y , 9 z + 64 y x , -13 x y - x y z , 3 3 2 2 3 -11 x y + 17 y z , -12 y z - 20 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 := [6, 14, 23, 4, 3, 3, 3, 2/3, 1, 2/3, 1/2, 11/12, 5/12, 6, 15, 23, 5, 4, 2, 3, 5/6, 1, 2/3, 7/12, 11/12, 5/12, -1, 0, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=426.0MB, alloc=140.3MB, time=8.40 |\^/| 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(); 1428324065 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 F := [11 x y z - 19 x y z, -7 x y - 12 x y, 12 y z + 17 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [5 x y - 9 x y z, -10 x y - 10 y , -6 x y + 17 y] > Problem := [F,G]; 2 2 2 3 2 2 Problem := [[11 x y z - 19 x y z, -7 x y - 12 x y, 12 y z + 17 y z ], 2 3 2 2 [5 x y - 9 x y z, -10 x y - 10 y , -6 x y + 17 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.46 memory used=48.6MB, alloc=32.3MB, time=0.84 memory used=68.2MB, alloc=56.3MB, time=1.19 memory used=108.7MB, alloc=84.3MB, time=1.91 memory used=165.8MB, alloc=84.3MB, time=3.82 N1 := 1385 > GB := Basis(F, plex(op(vars))); 2 2 2 2 GB := [7 x y + 12 x y, 133 x y z + 132 x y z, 11 x y z - 19 x y z, 2 3 2 2 187 x y z + 228 x y z, 12 y z + 17 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=218.0MB, alloc=84.3MB, time=4.53 memory used=276.0MB, alloc=108.3MB, time=5.33 memory used=352.9MB, alloc=132.3MB, time=6.88 N2 := 1749 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 2 H := [11 x y z - 19 x y z, -7 x y - 12 x y, 12 y z + 17 y z , 2 3 2 2 5 x y - 9 x y z, -10 x y - 10 y , -6 x y + 17 y] > J:=[op(GB),op(G)]; 2 2 2 2 J := [7 x y + 12 x y, 133 x y z + 132 x y z, 11 x y z - 19 x y z, 2 3 2 2 2 187 x y z + 228 x y z, 12 y z + 17 y z , 5 x y - 9 x y z, 3 2 2 -10 x y - 10 y , -6 x y + 17 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, 22, 4, 2, 3, 2, 5/6, 1, 1/2, 2/3, 1, 5/12, 8, 20, 30, 4, 2, 3, 2, 7/8, 1, 5/8, 3/4, 1, 9/16, -6, -8, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=414.0MB, alloc=132.3MB, time=8.21 |\^/| 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(); 1428324074 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 2 3 F := [-x - 2 y z , -2 x z + 11 z, 15 x y - 9 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 G := [-4 y + 10 y z , -11 y - 3 x , -17 y - 6 z] > Problem := [F,G]; 4 2 2 3 2 2 3 Problem := [[-x - 2 y z , -2 x z + 11 z, 15 x y - 9 x z ], 4 2 2 3 2 [-4 y + 10 y z , -11 y - 3 x , -17 y - 6 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=26.4MB, alloc=32.3MB, time=0.44 memory used=47.7MB, alloc=32.3MB, time=0.71 memory used=67.8MB, alloc=32.3MB, time=0.98 memory used=87.6MB, alloc=56.3MB, time=1.23 memory used=128.3MB, alloc=60.3MB, time=1.70 memory used=169.5MB, alloc=84.3MB, time=2.23 memory used=231.5MB, alloc=108.3MB, time=3.12 N1 := 1025 > GB := Basis(F, plex(op(vars))); GB := 7 4 5 2 2 2 2 10 6 3 4 [2 x - 11 x , 2 x y - 11 x y , 800 x y + 1089 x , 40 x y + 363 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=307.8MB, alloc=116.3MB, time=4.37 memory used=390.5MB, alloc=140.3MB, time=5.46 N2 := 837 #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)]; 4 2 2 3 2 2 3 4 2 2 H := [-x - 2 y z , -2 x z + 11 z, 15 x y - 9 x z , -4 y + 10 y z , 3 2 -11 y - 3 x , -17 y - 6 z] > J:=[op(GB),op(G)]; 7 4 5 2 2 2 2 10 6 4 3 J := [2 x - 11 x , 2 x y - 11 x y , 800 x y + 1089 x , 40 y x + 363 z, 4 2 2 3 2 -4 y + 10 y z , -11 y - 3 x , -17 y - 6 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 20, 4, 4, 4, 3, 2/3, 5/6, 5/6, 5/12, 1/2, 1/2, 7, 14, 41, 12, 7, 10, 2, 5/7, 6/7, 3/7, 4/7, 4/7, 3/14, 0, -21, -8] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=416.1MB, alloc=140.3MB, time=5.95 |\^/| 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(); 1428324080 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 4 F := [-16 x y z + 6 x , -2 y z + 10, -6 x y z + y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-y z - z, 5 y z - 20 x z, -3 x y z - 16 x ] > Problem := [F,G]; 2 3 2 2 4 Problem := [[-16 x y z + 6 x , -2 y z + 10, -6 x y z + y ], 2 2 2 2 [-y z - z, 5 y z - 20 x z, -3 x 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=0.16 memory used=26.4MB, alloc=32.3MB, time=0.43 memory used=47.2MB, alloc=32.3MB, time=0.65 memory used=67.0MB, alloc=32.3MB, time=0.89 memory used=86.7MB, alloc=56.3MB, time=1.11 memory used=126.4MB, alloc=60.3MB, time=1.57 memory used=163.5MB, alloc=60.3MB, time=1.99 memory used=200.7MB, alloc=84.3MB, time=2.44 memory used=258.4MB, alloc=92.3MB, time=3.14 memory used=314.5MB, alloc=92.3MB, time=3.76 memory used=370.3MB, alloc=116.3MB, time=4.44 memory used=462.5MB, alloc=116.3MB, time=5.36 memory used=537.9MB, alloc=140.3MB, time=5.70 memory used=655.3MB, alloc=140.3MB, time=6.04 memory used=761.0MB, alloc=140.3MB, time=6.31 memory used=850.2MB, alloc=140.3MB, time=6.55 memory used=948.2MB, alloc=140.3MB, time=6.78 memory used=1055.6MB, alloc=140.3MB, time=7.04 memory used=1173.2MB, alloc=140.3MB, time=7.29 memory used=1299.9MB, alloc=140.3MB, time=7.55 memory used=1436.5MB, alloc=140.3MB, time=7.82 memory used=1555.5MB, alloc=152.0MB, time=8.07 memory used=1624.1MB, alloc=155.8MB, time=8.24 memory used=1688.6MB, alloc=155.8MB, time=8.40 memory used=1752.7MB, alloc=155.8MB, time=8.56 memory used=1817.7MB, alloc=155.8MB, time=8.71 memory used=1883.6MB, alloc=155.8MB, time=8.85 memory used=1950.7MB, alloc=155.8MB, time=8.99 memory used=2019.2MB, alloc=155.8MB, time=9.16 memory used=2088.8MB, alloc=155.8MB, time=9.30 memory used=2159.8MB, alloc=155.8MB, time=9.48 memory used=2232.3MB, alloc=155.8MB, time=9.65 memory used=2306.4MB, alloc=155.8MB, time=9.82 memory used=2381.9MB, alloc=155.8MB, time=9.98 memory used=2458.6MB, alloc=155.8MB, time=10.13 memory used=2536.9MB, alloc=155.8MB, time=10.28 memory used=2616.8MB, alloc=155.8MB, time=10.45 memory used=2697.8MB, alloc=155.8MB, time=10.61 memory used=2780.8MB, alloc=155.8MB, time=10.77 memory used=2865.5MB, alloc=155.8MB, time=10.93 memory used=2951.6MB, alloc=155.8MB, time=11.08 memory used=3039.2MB, alloc=155.8MB, time=11.24 memory used=3128.1MB, alloc=155.8MB, time=11.38 memory used=3218.9MB, alloc=155.8MB, time=11.53 memory used=3311.2MB, alloc=155.8MB, time=11.70 memory used=3405.1MB, alloc=155.8MB, time=11.86 memory used=3500.2MB, alloc=155.8MB, time=12.03 memory used=3596.5MB, alloc=155.8MB, time=12.18 memory used=3693.9MB, alloc=155.8MB, time=12.34 memory used=3792.8MB, alloc=155.8MB, time=12.49 memory used=3893.2MB, alloc=155.8MB, time=12.65 memory used=3995.6MB, alloc=155.8MB, time=12.81 memory used=4099.2MB, alloc=155.8MB, time=12.98 memory used=4203.7MB, alloc=155.8MB, time=13.14 memory used=4309.8MB, alloc=155.8MB, time=13.31 memory used=4417.8MB, alloc=155.8MB, time=13.47 memory used=4466.4MB, alloc=155.8MB, time=13.58 memory used=4485.6MB, alloc=155.8MB, time=13.67 memory used=4503.4MB, alloc=155.8MB, time=13.75 memory used=4520.9MB, alloc=155.8MB, time=13.84 memory used=4538.0MB, alloc=155.8MB, time=13.92 memory used=4554.7MB, alloc=155.8MB, time=14.00 memory used=4571.0MB, alloc=155.8MB, time=14.08 memory used=4587.0MB, alloc=155.8MB, time=14.16 memory used=4602.6MB, alloc=155.8MB, time=14.24 memory used=4618.0MB, alloc=155.8MB, time=14.32 memory used=4633.1MB, alloc=155.8MB, time=14.40 memory used=4647.8MB, alloc=155.8MB, time=14.48 memory used=4662.3MB, alloc=155.8MB, time=14.55 memory used=4676.5MB, alloc=155.8MB, time=14.63 memory used=4690.5MB, alloc=155.8MB, time=14.70 memory used=4704.2MB, alloc=155.8MB, time=14.78 memory used=4717.8MB, alloc=155.8MB, time=14.85 memory used=4731.2MB, alloc=155.8MB, time=14.94 memory used=4744.4MB, alloc=155.8MB, time=15.03 memory used=4757.5MB, alloc=155.8MB, time=15.11 memory used=4770.6MB, alloc=155.8MB, time=15.19 memory used=4783.4MB, alloc=155.8MB, time=15.26 memory used=4796.3MB, alloc=155.8MB, time=15.34 memory used=4808.9MB, alloc=155.8MB, time=15.42 memory used=4821.6MB, alloc=155.8MB, time=15.49 memory used=4834.1MB, alloc=155.8MB, time=15.57 memory used=4846.7MB, alloc=155.8MB, time=15.65 memory used=4859.1MB, alloc=155.8MB, time=15.73 memory used=4871.5MB, alloc=155.8MB, time=15.80 memory used=4883.8MB, alloc=155.8MB, time=15.88 memory used=4896.1MB, alloc=155.8MB, time=15.96 memory used=4908.4MB, alloc=155.8MB, time=16.03 memory used=4920.6MB, alloc=155.8MB, time=16.11 memory used=4932.9MB, alloc=155.8MB, time=16.19 memory used=4945.1MB, alloc=155.8MB, time=16.27 memory used=4957.3MB, alloc=155.8MB, time=16.34 memory used=4969.4MB, alloc=155.8MB, time=16.43 memory used=4981.4MB, alloc=155.8MB, time=16.51 memory used=4993.4MB, alloc=155.8MB, time=16.59 memory used=5005.3MB, alloc=155.8MB, time=16.67 memory used=5017.4MB, alloc=155.8MB, time=16.75 memory used=5029.4MB, alloc=155.8MB, time=16.83 memory used=5041.4MB, alloc=155.8MB, time=16.91 memory used=5053.5MB, alloc=155.8MB, time=16.99 memory used=5065.5MB, alloc=155.8MB, time=17.06 memory used=5077.3MB, alloc=155.8MB, time=17.16 memory used=5089.2MB, alloc=155.8MB, time=17.23 memory used=5101.2MB, alloc=155.8MB, time=17.31 memory used=5113.2MB, alloc=155.8MB, time=17.39 memory used=5125.2MB, alloc=155.8MB, time=17.47 memory used=5137.2MB, alloc=155.8MB, time=17.55 memory used=5149.2MB, alloc=155.8MB, time=17.63 memory used=5161.3MB, alloc=155.8MB, time=17.70 memory used=5173.2MB, alloc=155.8MB, time=17.78 memory used=5185.2MB, alloc=155.8MB, time=17.86 memory used=5197.2MB, alloc=155.8MB, time=17.95 memory used=5209.2MB, alloc=155.8MB, time=18.02 memory used=5221.3MB, alloc=155.8MB, time=18.10 memory used=5233.3MB, alloc=155.8MB, time=18.17 memory used=5245.4MB, alloc=155.8MB, time=18.25 memory used=5257.4MB, alloc=155.8MB, time=18.34 memory used=5269.4MB, alloc=155.8MB, time=18.41 memory used=5281.5MB, alloc=155.8MB, time=18.47 memory used=5293.5MB, alloc=155.8MB, time=18.55 memory used=5305.4MB, alloc=155.8MB, time=18.63 memory used=5317.5MB, alloc=155.8MB, time=18.71 memory used=5329.6MB, alloc=155.8MB, time=18.79 memory used=5341.6MB, alloc=155.8MB, time=18.86 memory used=5353.7MB, alloc=155.8MB, time=18.93 memory used=5365.7MB, alloc=155.8MB, time=19.02 memory used=5377.9MB, alloc=155.8MB, time=19.09 memory used=5389.9MB, alloc=155.8MB, time=19.16 memory used=5402.1MB, alloc=155.8MB, time=19.25 memory used=5414.2MB, alloc=155.8MB, time=19.32 memory used=5426.4MB, alloc=155.8MB, time=19.39 memory used=5438.5MB, alloc=155.8MB, time=19.46 memory used=5450.6MB, alloc=155.8MB, time=19.54 memory used=5462.8MB, alloc=155.8MB, time=19.61 memory used=5475.0MB, alloc=155.8MB, time=19.68 memory used=5487.2MB, alloc=155.8MB, time=19.75 memory used=5499.5MB, alloc=155.8MB, time=19.83 memory used=5511.6MB, alloc=155.8MB, time=19.91 memory used=5523.9MB, alloc=155.8MB, time=19.99 memory used=5536.1MB, alloc=155.8MB, time=20.06 memory used=5548.4MB, alloc=155.8MB, time=20.14 memory used=5560.6MB, alloc=155.8MB, time=20.22 memory used=5572.9MB, alloc=155.8MB, time=20.30 memory used=5585.2MB, alloc=155.8MB, time=20.39 memory used=5597.5MB, alloc=155.8MB, time=20.46 memory used=5609.8MB, alloc=155.8MB, time=20.55 memory used=5622.1MB, alloc=155.8MB, time=20.62 memory used=5634.5MB, alloc=155.8MB, time=20.70 memory used=5647.0MB, alloc=155.8MB, time=20.79 memory used=5659.4MB, alloc=155.8MB, time=20.87 memory used=5671.8MB, alloc=155.8MB, time=20.95 memory used=5684.2MB, alloc=155.8MB, time=21.03 memory used=5696.6MB, alloc=155.8MB, time=21.11 memory used=5709.0MB, alloc=155.8MB, time=21.19 memory used=5721.5MB, alloc=155.8MB, time=21.26 memory used=5733.9MB, alloc=155.8MB, time=21.35 memory used=5746.4MB, alloc=155.8MB, time=21.43 memory used=5758.8MB, alloc=155.8MB, time=21.50 memory used=5771.2MB, alloc=155.8MB, time=21.59 memory used=5783.7MB, alloc=155.8MB, time=21.67 memory used=5796.3MB, alloc=155.8MB, time=21.73 memory used=5808.7MB, alloc=155.8MB, time=21.81 memory used=5821.3MB, alloc=155.8MB, time=21.88 memory used=5833.8MB, alloc=155.8MB, time=21.95 memory used=5846.3MB, alloc=155.8MB, time=22.03 memory used=5859.0MB, alloc=155.8MB, time=22.10 memory used=5871.6MB, alloc=155.8MB, time=22.17 memory used=5884.4MB, alloc=155.8MB, time=22.25 memory used=5897.1MB, alloc=155.8MB, time=22.33 memory used=5909.8MB, alloc=155.8MB, time=22.41 memory used=5922.7MB, alloc=155.8MB, time=22.48 memory used=5935.4MB, alloc=155.8MB, time=22.56 memory used=5948.2MB, alloc=155.8MB, time=22.64 memory used=5961.1MB, alloc=155.8MB, time=22.71 memory used=5974.0MB, alloc=155.8MB, time=22.79 memory used=5986.8MB, alloc=155.8MB, time=22.88 memory used=5999.8MB, alloc=155.8MB, time=22.95 memory used=6012.7MB, alloc=155.8MB, time=23.03 memory used=6025.7MB, alloc=155.8MB, time=23.11 memory used=6038.8MB, alloc=155.8MB, time=23.19 memory used=6051.7MB, alloc=155.8MB, time=23.26 memory used=6064.6MB, alloc=155.8MB, time=23.34 memory used=6077.6MB, alloc=155.8MB, time=23.41 memory used=6090.5MB, alloc=155.8MB, time=23.49 memory used=6103.5MB, alloc=155.8MB, time=23.57 memory used=6116.4MB, alloc=155.8MB, time=23.65 memory used=6129.5MB, alloc=155.8MB, time=23.73 memory used=6142.5MB, alloc=155.8MB, time=23.80 memory used=6155.6MB, alloc=155.8MB, time=23.88 memory used=6168.7MB, alloc=155.8MB, time=23.95 memory used=6181.7MB, alloc=155.8MB, time=24.03 memory used=6194.8MB, alloc=155.8MB, time=24.11 memory used=6208.0MB, alloc=155.8MB, time=24.18 memory used=6221.2MB, alloc=155.8MB, time=24.26 memory used=6234.3MB, alloc=155.8MB, time=24.34 memory used=6247.4MB, alloc=155.8MB, time=24.41 memory used=6260.5MB, alloc=155.8MB, time=24.48 memory used=6273.8MB, alloc=155.8MB, time=24.56 memory used=6287.1MB, alloc=155.8MB, time=24.63 memory used=6300.3MB, alloc=155.8MB, time=24.70 memory used=6313.6MB, alloc=155.8MB, time=24.78 memory used=6326.8MB, alloc=155.8MB, time=24.85 memory used=6340.0MB, alloc=155.8MB, time=24.93 memory used=6353.3MB, alloc=155.8MB, time=25.00 memory used=6366.5MB, alloc=155.8MB, time=25.07 memory used=6379.9MB, alloc=155.8MB, time=25.14 memory used=6393.2MB, alloc=155.8MB, time=25.22 memory used=6406.6MB, alloc=155.8MB, time=25.29 memory used=6419.8MB, alloc=155.8MB, time=25.37 memory used=6433.2MB, alloc=155.8MB, time=25.45 memory used=6446.5MB, alloc=155.8MB, time=25.52 memory used=6459.7MB, alloc=155.8MB, time=25.60 memory used=6473.1MB, alloc=155.8MB, time=25.67 memory used=6486.3MB, alloc=155.8MB, time=25.76 memory used=6499.7MB, alloc=155.8MB, time=25.83 memory used=6513.1MB, alloc=155.8MB, time=25.91 memory used=6526.3MB, alloc=155.8MB, time=25.99 memory used=6539.7MB, alloc=155.8MB, time=26.07 memory used=6553.2MB, alloc=155.8MB, time=26.15 memory used=6566.7MB, alloc=155.8MB, time=26.23 memory used=6580.2MB, alloc=155.8MB, time=26.30 memory used=6593.6MB, alloc=155.8MB, time=26.38 memory used=6607.2MB, alloc=155.8MB, time=26.46 memory used=6620.5MB, alloc=155.8MB, time=26.54 memory used=6633.9MB, alloc=155.8MB, time=26.61 memory used=6647.4MB, alloc=155.8MB, time=26.68 memory used=6660.9MB, alloc=155.8MB, time=26.76 memory used=6674.5MB, alloc=155.8MB, time=26.83 memory used=6688.1MB, alloc=155.8MB, time=26.91 memory used=6701.5MB, alloc=155.8MB, time=26.98 memory used=6715.2MB, alloc=155.8MB, time=27.06 memory used=6728.7MB, alloc=155.8MB, time=27.14 memory used=6742.4MB, alloc=155.8MB, time=27.21 memory used=6756.2MB, alloc=155.8MB, time=27.29 memory used=6769.8MB, alloc=155.8MB, time=27.37 memory used=6783.5MB, alloc=155.8MB, time=27.45 memory used=6797.2MB, alloc=155.8MB, time=27.53 memory used=6811.0MB, alloc=155.8MB, time=27.60 memory used=6824.7MB, alloc=155.8MB, time=27.68 memory used=6838.5MB, alloc=155.8MB, time=27.76 memory used=6852.2MB, alloc=155.8MB, time=27.84 memory used=6866.1MB, alloc=155.8MB, time=27.92 memory used=6879.9MB, alloc=155.8MB, time=28.00 memory used=6893.6MB, alloc=155.8MB, time=28.08 memory used=6907.5MB, alloc=155.8MB, time=28.15 memory used=6921.4MB, alloc=155.8MB, time=28.23 memory used=6935.4MB, alloc=155.8MB, time=28.30 memory used=6949.5MB, alloc=155.8MB, time=28.37 memory used=6963.6MB, alloc=155.8MB, time=28.44 memory used=6977.6MB, alloc=155.8MB, time=28.52 memory used=6991.7MB, alloc=155.8MB, time=28.60 memory used=7005.8MB, alloc=155.8MB, time=28.67 memory used=7019.8MB, alloc=155.8MB, time=28.74 memory used=7034.0MB, alloc=155.8MB, time=28.81 memory used=7048.1MB, alloc=155.8MB, time=28.88 memory used=7062.2MB, alloc=155.8MB, time=28.96 memory used=7076.3MB, alloc=155.8MB, time=29.04 memory used=7090.4MB, alloc=155.8MB, time=29.12 memory used=7104.5MB, alloc=155.8MB, time=29.20 memory used=7118.5MB, alloc=155.8MB, time=29.28 memory used=7132.6MB, alloc=155.8MB, time=29.36 memory used=7146.6MB, alloc=155.8MB, time=29.44 memory used=7160.7MB, alloc=155.8MB, time=29.51 memory used=7174.8MB, alloc=155.8MB, time=29.59 memory used=7188.9MB, alloc=155.8MB, time=29.68 memory used=7202.9MB, alloc=155.8MB, time=29.75 memory used=7217.1MB, alloc=155.8MB, time=29.83 memory used=7231.2MB, alloc=155.8MB, time=29.90 memory used=7245.5MB, alloc=155.8MB, time=29.98 memory used=7259.8MB, alloc=155.8MB, time=30.06 memory used=7274.0MB, alloc=155.8MB, time=30.14 memory used=7288.3MB, alloc=155.8MB, time=30.23 memory used=7302.5MB, alloc=155.8MB, time=30.30 memory used=7316.8MB, alloc=155.8MB, time=30.38 memory used=7331.1MB, alloc=155.8MB, time=30.45 memory used=7345.5MB, alloc=155.8MB, time=30.52 memory used=7359.8MB, alloc=155.8MB, time=30.60 memory used=7374.2MB, alloc=155.8MB, time=30.67 memory used=7388.6MB, alloc=155.8MB, time=30.76 memory used=7403.0MB, alloc=155.8MB, time=30.84 memory used=7417.4MB, alloc=155.8MB, time=30.93 memory used=7431.9MB, alloc=155.8MB, time=31.00 memory used=7446.3MB, alloc=155.8MB, time=31.08 memory used=7460.7MB, alloc=155.8MB, time=31.16 memory used=7475.1MB, alloc=155.8MB, time=31.24 memory used=7489.5MB, alloc=155.8MB, time=31.33 memory used=7504.0MB, alloc=155.8MB, time=31.41 memory used=7518.4MB, alloc=155.8MB, time=31.49 memory used=7532.9MB, alloc=155.8MB, time=31.57 memory used=7547.5MB, alloc=155.8MB, time=31.65 memory used=7562.1MB, alloc=155.8MB, time=31.74 memory used=7576.7MB, alloc=155.8MB, time=31.82 memory used=7591.3MB, alloc=155.8MB, time=31.90 memory used=7606.0MB, alloc=155.8MB, time=31.99 memory used=7620.5MB, alloc=155.8MB, time=32.07 memory used=7635.2MB, alloc=155.8MB, time=32.15 memory used=7649.8MB, alloc=155.8MB, time=32.22 memory used=7664.5MB, alloc=155.8MB, time=32.30 memory used=7679.0MB, alloc=155.8MB, time=32.38 memory used=7693.8MB, alloc=155.8MB, time=32.45 memory used=7708.5MB, alloc=155.8MB, time=32.53 memory used=7723.2MB, alloc=155.8MB, time=32.61 memory used=7737.8MB, alloc=155.8MB, time=32.70 memory used=7752.4MB, alloc=155.8MB, time=32.78 memory used=7767.1MB, alloc=155.8MB, time=32.86 memory used=7781.7MB, alloc=155.8MB, time=32.94 memory used=7796.4MB, alloc=155.8MB, time=33.03 memory used=7811.1MB, alloc=155.8MB, time=33.10 memory used=7825.7MB, alloc=155.8MB, time=33.18 memory used=7840.5MB, alloc=155.8MB, time=33.25 memory used=7855.2MB, alloc=155.8MB, time=33.33 memory used=7870.0MB, alloc=155.8MB, time=33.40 memory used=7884.9MB, alloc=155.8MB, time=33.49 memory used=7899.6MB, alloc=155.8MB, time=33.56 memory used=7914.5MB, alloc=155.8MB, time=33.64 memory used=7929.5MB, alloc=155.8MB, time=33.72 memory used=7944.4MB, alloc=155.8MB, time=33.79 memory used=7959.2MB, alloc=155.8MB, time=33.87 memory used=7974.2MB, alloc=155.8MB, time=33.95 memory used=7989.2MB, alloc=155.8MB, time=34.03 memory used=8004.0MB, alloc=155.8MB, time=34.11 memory used=8019.0MB, alloc=155.8MB, time=34.20 memory used=8033.9MB, alloc=155.8MB, time=34.27 memory used=8049.0MB, alloc=155.8MB, time=34.34 memory used=8064.0MB, alloc=155.8MB, time=34.42 memory used=8079.1MB, alloc=155.8MB, time=34.49 memory used=8094.2MB, alloc=155.8MB, time=34.57 memory used=8109.3MB, alloc=155.8MB, time=34.66 memory used=8124.4MB, alloc=155.8MB, time=34.73 memory used=8139.5MB, alloc=155.8MB, time=34.82 memory used=8154.6MB, alloc=155.8MB, time=34.90 memory used=8169.7MB, alloc=155.8MB, time=34.97 memory used=8184.9MB, alloc=155.8MB, time=35.05 memory used=8200.0MB, alloc=155.8MB, time=35.12 memory used=8215.2MB, alloc=155.8MB, time=35.18 memory used=8230.4MB, alloc=155.8MB, time=35.25 memory used=8245.5MB, alloc=155.8MB, time=35.32 memory used=8260.8MB, alloc=155.8MB, time=35.39 memory used=8275.8MB, alloc=155.8MB, time=35.47 memory used=8291.0MB, alloc=155.8MB, time=35.55 memory used=8306.2MB, alloc=155.8MB, time=35.62 memory used=8321.4MB, alloc=155.8MB, time=35.69 memory used=8336.6MB, alloc=155.8MB, time=35.77 memory used=8351.7MB, alloc=155.8MB, time=35.84 memory used=8366.8MB, alloc=155.8MB, time=35.91 memory used=8382.1MB, alloc=155.8MB, time=35.99 memory used=8397.2MB, alloc=155.8MB, time=36.07 memory used=8412.5MB, alloc=155.8MB, time=36.15 memory used=8427.8MB, alloc=155.8MB, time=36.23 memory used=8443.0MB, alloc=155.8MB, time=36.31 memory used=8458.3MB, alloc=155.8MB, time=36.39 memory used=8473.7MB, alloc=155.8MB, time=36.48 memory used=8489.0MB, alloc=155.8MB, time=36.55 memory used=8504.4MB, alloc=155.8MB, time=36.63 memory used=8519.8MB, alloc=155.8MB, time=36.71 memory used=8535.2MB, alloc=155.8MB, time=36.79 memory used=8550.7MB, alloc=155.8MB, time=36.87 memory used=8566.1MB, alloc=155.8MB, time=36.95 memory used=8581.8MB, alloc=155.8MB, time=37.04 memory used=8597.2MB, alloc=155.8MB, time=37.12 memory used=8612.8MB, alloc=155.8MB, time=37.20 memory used=8628.4MB, alloc=155.8MB, time=37.28 memory used=8644.0MB, alloc=155.8MB, time=37.35 memory used=8659.5MB, alloc=155.8MB, time=37.43 memory used=8674.9MB, alloc=155.8MB, time=37.51 memory used=8690.5MB, alloc=155.8MB, time=37.60 memory used=8706.1MB, alloc=155.8MB, time=37.67 memory used=8721.7MB, alloc=155.8MB, time=37.75 memory used=8737.4MB, alloc=155.8MB, time=37.83 memory used=8753.0MB, alloc=155.8MB, time=37.91 memory used=8768.9MB, alloc=155.8MB, time=37.99 memory used=8784.5MB, alloc=155.8MB, 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alloc=155.8MB, time=39.72 memory used=9134.4MB, alloc=155.8MB, time=39.80 memory used=9150.6MB, alloc=155.8MB, time=39.87 memory used=9166.7MB, alloc=155.8MB, time=39.95 memory used=9182.8MB, alloc=155.8MB, time=40.02 memory used=9198.7MB, alloc=155.8MB, time=40.10 memory used=9214.7MB, alloc=155.8MB, time=40.18 memory used=9230.9MB, alloc=155.8MB, time=40.26 memory used=9246.9MB, alloc=155.8MB, time=40.33 memory used=9263.2MB, alloc=155.8MB, time=40.41 memory used=9279.3MB, alloc=155.8MB, time=40.48 memory used=9295.4MB, alloc=155.8MB, time=40.55 memory used=9311.6MB, alloc=155.8MB, time=40.63 memory used=9327.8MB, alloc=155.8MB, time=40.71 memory used=9343.9MB, alloc=155.8MB, time=40.78 memory used=9358.8MB, alloc=155.8MB, time=40.85 memory used=9373.5MB, alloc=155.8MB, time=40.92 memory used=9388.0MB, alloc=155.8MB, time=40.99 memory used=9402.2MB, alloc=155.8MB, time=41.06 memory used=9416.3MB, alloc=155.8MB, time=41.13 memory used=9430.2MB, alloc=155.8MB, time=41.20 memory used=9444.0MB, alloc=155.8MB, time=41.27 memory used=9457.6MB, alloc=155.8MB, time=41.34 memory used=9470.9MB, alloc=155.8MB, time=41.41 memory used=9484.0MB, alloc=155.8MB, time=41.48 memory used=9497.1MB, alloc=155.8MB, time=41.55 memory used=9510.0MB, alloc=155.8MB, time=41.62 memory used=9522.9MB, alloc=155.8MB, time=41.69 memory used=9535.5MB, alloc=155.8MB, time=41.77 memory used=9547.9MB, alloc=155.8MB, time=41.83 memory used=9560.2MB, alloc=155.8MB, time=41.92 memory used=9572.3MB, alloc=155.8MB, time=41.98 memory used=9584.3MB, alloc=155.8MB, time=42.05 memory used=9596.2MB, alloc=155.8MB, time=42.12 memory used=9607.9MB, alloc=155.8MB, time=42.19 memory used=9619.6MB, alloc=155.8MB, time=42.26 memory used=9631.1MB, alloc=155.8MB, time=42.33 memory used=9642.5MB, alloc=155.8MB, time=42.42 memory used=9653.8MB, alloc=155.8MB, time=42.50 memory used=9665.0MB, alloc=155.8MB, time=42.58 memory used=9676.1MB, alloc=155.8MB, time=42.66 memory used=9687.0MB, alloc=155.8MB, time=42.74 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time=48.88 memory used=10529.8MB, alloc=155.8MB, time=48.96 memory used=10540.1MB, alloc=155.8MB, time=49.03 memory used=10550.3MB, alloc=155.8MB, time=49.10 memory used=10560.4MB, alloc=155.8MB, time=49.17 memory used=10570.7MB, alloc=155.8MB, time=49.24 memory used=10580.9MB, alloc=155.8MB, time=49.31 memory used=10591.2MB, alloc=155.8MB, time=49.38 memory used=10601.4MB, alloc=155.8MB, time=49.45 memory used=10611.6MB, alloc=155.8MB, time=49.51 memory used=10622.0MB, alloc=155.8MB, time=49.58 memory used=10632.4MB, alloc=155.8MB, time=49.66 memory used=10642.8MB, alloc=155.8MB, time=49.73 memory used=10653.0MB, alloc=155.8MB, time=49.80 memory used=10663.3MB, alloc=155.8MB, time=49.88 memory used=10673.7MB, alloc=155.8MB, time=49.94 memory used=10684.1MB, alloc=155.8MB, time=50.01 memory used=10694.4MB, alloc=155.8MB, time=50.08 memory used=10704.7MB, alloc=155.8MB, time=50.14 memory used=10715.0MB, alloc=155.8MB, time=50.22 memory used=10725.3MB, alloc=155.8MB, time=50.29 memory 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alloc=155.8MB, time=51.79 memory used=10955.0MB, alloc=155.8MB, time=51.86 memory used=10965.5MB, alloc=155.8MB, time=51.94 memory used=10976.0MB, alloc=155.8MB, time=52.02 memory used=10986.5MB, alloc=155.8MB, time=52.09 memory used=10997.1MB, alloc=155.8MB, time=52.17 memory used=11007.8MB, alloc=155.8MB, time=52.24 memory used=11018.4MB, alloc=155.8MB, time=52.32 memory used=11029.0MB, alloc=155.8MB, time=52.39 memory used=11039.5MB, alloc=155.8MB, time=52.46 memory used=11050.1MB, alloc=155.8MB, time=52.54 memory used=11060.7MB, alloc=155.8MB, time=52.62 memory used=11071.4MB, alloc=155.8MB, time=52.70 memory used=11082.1MB, alloc=155.8MB, time=52.78 memory used=11092.7MB, alloc=155.8MB, time=52.85 memory used=11103.2MB, alloc=155.8MB, time=52.93 memory used=11113.7MB, alloc=155.8MB, time=53.01 memory used=11124.2MB, alloc=155.8MB, time=53.09 memory used=11134.9MB, alloc=155.8MB, time=53.17 memory used=11145.6MB, alloc=155.8MB, time=53.24 memory used=11156.2MB, alloc=155.8MB, time=53.32 memory used=11166.9MB, alloc=155.8MB, time=53.40 memory used=11177.5MB, alloc=155.8MB, time=53.48 memory used=11188.1MB, alloc=155.8MB, time=53.55 memory used=11198.9MB, alloc=155.8MB, time=53.63 memory used=11209.6MB, alloc=155.8MB, time=53.70 memory used=11220.4MB, alloc=155.8MB, time=53.77 memory used=11231.1MB, alloc=155.8MB, time=53.85 memory used=11241.6MB, alloc=155.8MB, time=53.93 memory used=11252.3MB, alloc=155.8MB, time=54.00 memory used=11263.0MB, alloc=155.8MB, time=54.08 memory used=11273.7MB, alloc=155.8MB, time=54.15 memory used=11284.4MB, alloc=155.8MB, time=54.23 memory used=11295.0MB, alloc=155.8MB, time=54.31 memory used=11305.6MB, alloc=155.8MB, time=54.38 memory used=11316.3MB, alloc=155.8MB, time=54.46 memory used=11327.1MB, alloc=155.8MB, time=54.53 memory used=11338.0MB, alloc=155.8MB, time=54.62 memory used=11348.8MB, alloc=155.8MB, time=54.69 memory used=11359.6MB, alloc=155.8MB, time=54.77 memory used=11370.2MB, alloc=155.8MB, time=54.84 memory 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time=57.82 memory used=11829.9MB, alloc=155.8MB, time=57.89 memory used=11841.0MB, alloc=155.8MB, time=57.96 memory used=11852.0MB, alloc=155.8MB, time=58.04 memory used=11862.9MB, alloc=155.8MB, time=58.10 memory used=11874.0MB, alloc=155.8MB, time=58.18 memory used=11885.0MB, alloc=155.8MB, time=58.26 memory used=11896.0MB, alloc=155.8MB, time=58.33 memory used=11907.1MB, alloc=155.8MB, time=58.39 memory used=11918.2MB, alloc=155.8MB, time=58.47 memory used=11929.3MB, alloc=155.8MB, time=58.53 memory used=11940.2MB, alloc=155.8MB, time=58.60 memory used=11951.3MB, alloc=155.8MB, time=58.67 memory used=11962.4MB, alloc=155.8MB, time=58.74 memory used=11973.6MB, alloc=155.8MB, time=58.81 memory used=11984.7MB, alloc=155.8MB, time=58.88 memory used=11995.9MB, alloc=155.8MB, time=58.94 memory used=12007.1MB, alloc=155.8MB, time=59.01 memory used=12018.4MB, alloc=155.8MB, time=59.08 memory used=12029.6MB, alloc=155.8MB, time=59.15 memory used=12040.9MB, alloc=155.8MB, time=59.22 memory 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alloc=155.8MB, time=60.78 memory used=12288.8MB, alloc=155.8MB, time=60.85 memory used=12300.3MB, alloc=155.8MB, time=60.93 memory used=12311.7MB, alloc=155.8MB, time=61.01 memory used=12323.2MB, alloc=155.8MB, time=61.09 memory used=12334.7MB, alloc=155.8MB, time=61.16 memory used=12346.2MB, alloc=155.8MB, time=61.24 memory used=12357.7MB, alloc=155.8MB, time=61.32 memory used=12369.1MB, alloc=155.8MB, time=61.39 memory used=12380.7MB, alloc=155.8MB, time=61.48 memory used=12392.2MB, alloc=155.8MB, time=61.55 memory used=12403.6MB, alloc=155.8MB, time=61.62 memory used=12415.2MB, alloc=155.8MB, time=61.69 memory used=12426.7MB, alloc=155.8MB, time=61.77 memory used=12438.2MB, alloc=155.8MB, time=61.84 memory used=12449.7MB, alloc=155.8MB, time=61.92 memory used=12461.3MB, alloc=155.8MB, time=61.99 memory used=12472.8MB, alloc=155.8MB, time=62.06 memory used=12484.3MB, alloc=155.8MB, time=62.14 memory used=12495.9MB, alloc=155.8MB, time=62.21 memory used=12507.5MB, alloc=155.8MB, 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time=66.82 memory used=13233.0MB, alloc=155.8MB, time=66.89 memory used=13244.9MB, alloc=155.8MB, time=66.96 memory used=13256.8MB, alloc=155.8MB, time=67.03 memory used=13268.7MB, alloc=155.8MB, time=67.11 memory used=13280.6MB, alloc=155.8MB, time=67.18 memory used=13292.5MB, alloc=155.8MB, time=67.25 memory used=13304.4MB, alloc=155.8MB, time=67.32 memory used=13316.3MB, alloc=155.8MB, time=67.39 memory used=13328.2MB, alloc=155.8MB, time=67.46 memory used=13340.1MB, alloc=155.8MB, time=67.53 memory used=13352.0MB, alloc=155.8MB, time=67.60 memory used=13364.0MB, alloc=155.8MB, time=67.67 memory used=13376.0MB, alloc=155.8MB, time=67.74 memory used=13387.9MB, alloc=155.8MB, time=67.82 memory used=13399.9MB, alloc=155.8MB, time=67.89 memory used=13411.9MB, alloc=155.8MB, time=67.96 memory used=13423.9MB, alloc=155.8MB, time=68.03 memory used=13435.9MB, alloc=155.8MB, time=68.10 memory used=13447.9MB, alloc=155.8MB, time=68.18 memory used=13459.9MB, alloc=155.8MB, time=68.26 memory 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alloc=155.8MB, time=69.79 memory used=13725.7MB, alloc=155.8MB, time=69.86 memory used=13737.9MB, alloc=155.8MB, time=69.94 memory used=13750.0MB, alloc=155.8MB, time=70.01 memory used=13762.1MB, alloc=155.8MB, time=70.08 memory used=13774.3MB, alloc=155.8MB, time=70.15 memory used=13786.5MB, alloc=155.8MB, time=70.23 memory used=13798.6MB, alloc=155.8MB, time=70.30 memory used=13810.8MB, alloc=155.8MB, time=70.38 memory used=13823.0MB, alloc=155.8MB, time=70.46 memory used=13835.3MB, alloc=155.8MB, time=70.54 memory used=13847.5MB, alloc=155.8MB, time=70.63 memory used=13859.7MB, alloc=155.8MB, time=70.70 memory used=13871.9MB, alloc=155.8MB, time=70.77 memory used=13884.1MB, alloc=155.8MB, time=70.85 memory used=13896.4MB, alloc=155.8MB, time=70.93 memory used=13908.6MB, alloc=155.8MB, time=71.00 memory used=13920.8MB, alloc=155.8MB, time=71.07 memory used=13933.1MB, alloc=155.8MB, time=71.15 memory used=13945.3MB, alloc=155.8MB, time=71.21 memory used=13957.5MB, alloc=155.8MB, 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time=80.39 memory used=15505.7MB, alloc=155.8MB, time=80.46 memory used=15518.6MB, alloc=155.8MB, time=80.53 memory used=15531.5MB, alloc=155.8MB, time=80.60 memory used=15544.5MB, alloc=155.8MB, time=80.67 memory used=15557.4MB, alloc=155.8MB, time=80.74 memory used=15570.3MB, alloc=155.8MB, time=80.81 memory used=15583.2MB, alloc=155.8MB, time=80.87 memory used=15596.2MB, alloc=155.8MB, time=80.95 memory used=15609.1MB, alloc=155.8MB, time=81.02 memory used=15622.0MB, alloc=155.8MB, time=81.08 memory used=15634.9MB, alloc=155.8MB, time=81.15 memory used=15647.8MB, alloc=155.8MB, time=81.21 memory used=15660.8MB, alloc=155.8MB, time=81.28 memory used=15673.7MB, alloc=155.8MB, time=81.35 memory used=15686.7MB, alloc=155.8MB, time=81.42 memory used=15699.7MB, alloc=155.8MB, time=81.49 memory used=15712.7MB, alloc=155.8MB, time=81.56 memory used=15725.8MB, alloc=155.8MB, time=81.63 memory used=15738.7MB, alloc=155.8MB, time=81.70 memory used=15751.7MB, alloc=155.8MB, time=81.77 memory 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alloc=155.8MB, time=83.25 memory used=16038.0MB, alloc=155.8MB, time=83.32 memory used=16049.6MB, alloc=155.8MB, time=83.39 memory used=16060.9MB, alloc=155.8MB, time=83.47 memory used=16071.7MB, alloc=155.8MB, time=83.54 memory used=16080.1MB, alloc=155.8MB, time=83.61 memory used=16087.7MB, alloc=155.8MB, time=83.68 memory used=16095.3MB, alloc=155.8MB, time=83.75 memory used=16102.6MB, alloc=155.8MB, time=83.82 memory used=16109.7MB, alloc=155.8MB, time=83.90 memory used=16116.8MB, alloc=155.8MB, time=83.97 memory used=16123.8MB, alloc=155.8MB, time=84.04 memory used=16130.7MB, alloc=155.8MB, time=84.11 memory used=16137.5MB, alloc=155.8MB, time=84.18 memory used=16144.2MB, alloc=155.8MB, time=84.26 memory used=16150.9MB, alloc=155.8MB, time=84.34 memory used=16157.5MB, alloc=155.8MB, time=84.41 memory used=16164.1MB, alloc=155.8MB, time=84.49 memory used=16170.6MB, alloc=155.8MB, time=84.56 memory used=16177.1MB, alloc=155.8MB, time=84.64 memory used=16183.2MB, alloc=155.8MB, 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alloc=155.8MB, time=92.04 memory used=16597.6MB, alloc=155.8MB, time=92.11 memory used=16600.5MB, alloc=155.8MB, time=92.18 memory used=16603.4MB, alloc=155.8MB, time=92.25 memory used=16606.3MB, alloc=155.8MB, time=92.32 memory used=16609.3MB, alloc=155.8MB, time=92.39 memory used=16612.3MB, alloc=155.8MB, time=92.45 memory used=16615.6MB, alloc=155.8MB, time=92.52 memory used=16618.7MB, alloc=155.8MB, time=92.58 memory used=16622.0MB, alloc=155.8MB, time=92.65 memory used=16625.7MB, alloc=155.8MB, time=92.72 memory used=16629.5MB, alloc=155.8MB, time=92.79 memory used=16633.0MB, alloc=155.8MB, time=92.86 memory used=16636.5MB, alloc=155.8MB, time=92.93 memory used=16639.9MB, alloc=155.8MB, time=93.00 memory used=16643.4MB, alloc=155.8MB, time=93.07 memory used=16646.8MB, alloc=155.8MB, time=93.13 memory used=16650.2MB, alloc=155.8MB, time=93.20 memory used=16653.5MB, alloc=155.8MB, time=93.27 memory used=16657.1MB, alloc=155.8MB, time=93.34 memory used=16660.4MB, alloc=155.8MB, time=93.41 memory used=16664.0MB, alloc=155.8MB, time=93.47 memory used=16667.4MB, alloc=155.8MB, time=93.54 memory used=16670.6MB, alloc=155.8MB, time=93.61 memory used=16673.9MB, alloc=155.8MB, time=93.68 memory used=16677.5MB, alloc=155.8MB, time=93.74 memory used=16681.1MB, alloc=155.8MB, time=93.81 memory used=16684.7MB, alloc=155.8MB, time=93.88 memory used=16688.0MB, alloc=155.8MB, time=93.95 memory used=16691.4MB, alloc=155.8MB, time=94.02 memory used=16694.9MB, alloc=155.8MB, time=94.09 memory used=16698.5MB, alloc=155.8MB, time=94.16 memory used=16701.9MB, alloc=155.8MB, time=94.24 memory used=16705.3MB, alloc=155.8MB, time=94.31 memory used=16708.8MB, alloc=155.8MB, time=94.39 memory used=16712.2MB, alloc=155.8MB, time=94.47 memory used=16715.7MB, alloc=155.8MB, time=94.54 memory used=16719.2MB, alloc=155.8MB, time=94.61 memory used=16722.6MB, alloc=155.8MB, time=94.67 memory used=16726.0MB, alloc=155.8MB, time=94.73 memory used=16729.5MB, alloc=155.8MB, time=94.81 memory 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memory used=116556.5MB, alloc=411.8MB, time=305.80 memory used=116976.0MB, alloc=411.8MB, time=306.11 memory used=117397.1MB, alloc=411.8MB, time=306.46 memory used=117819.4MB, alloc=411.8MB, time=306.80 memory used=118243.1MB, alloc=411.8MB, time=307.12 memory used=118668.6MB, alloc=411.8MB, time=307.46 memory used=119094.6MB, alloc=411.8MB, time=307.78 memory used=119521.3MB, alloc=411.8MB, time=308.09 memory used=119948.7MB, alloc=411.8MB, time=308.41 memory used=120377.6MB, alloc=411.8MB, time=308.75 memory used=120808.1MB, alloc=411.8MB, time=309.08 memory used=121239.8MB, alloc=411.8MB, time=309.42 memory used=121673.1MB, alloc=411.8MB, time=309.75 memory used=122106.9MB, alloc=411.8MB, time=310.07 memory used=122541.9MB, alloc=411.8MB, time=310.40 memory used=122977.3MB, alloc=411.8MB, time=310.72 memory used=123413.6MB, alloc=411.8MB, time=311.06 memory used=123850.9MB, alloc=411.8MB, time=311.37 memory used=124289.0MB, alloc=411.8MB, time=311.71 memory used=124728.0MB, alloc=411.8MB, time=312.04 memory used=125167.4MB, alloc=411.8MB, time=312.36 memory used=125607.6MB, alloc=411.8MB, time=312.71 memory used=126048.9MB, alloc=411.8MB, time=313.04 memory used=126491.2MB, alloc=411.8MB, time=313.37 memory used=126934.9MB, alloc=411.8MB, time=313.71 memory used=127379.4MB, alloc=411.8MB, time=314.05 memory used=127824.3MB, alloc=411.8MB, time=314.37 memory used=128270.1MB, alloc=411.8MB, time=314.71 memory used=128716.1MB, alloc=411.8MB, time=315.07 memory used=129163.1MB, alloc=411.8MB, time=315.41 memory used=129611.1MB, alloc=411.8MB, time=315.75 memory used=130060.0MB, alloc=411.8MB, time=316.07 memory used=130510.8MB, alloc=411.8MB, time=316.41 memory used=130961.9MB, alloc=411.8MB, time=316.75 memory used=131413.7MB, alloc=411.8MB, time=317.08 memory used=131866.2MB, alloc=411.8MB, time=317.41 memory used=132319.9MB, alloc=411.8MB, time=317.74 memory used=132773.9MB, alloc=411.8MB, time=318.07 memory used=133228.7MB, alloc=411.8MB, time=318.39 memory used=133685.0MB, alloc=411.8MB, time=318.74 memory used=134141.9MB, alloc=411.8MB, time=319.08 memory used=134599.8MB, alloc=411.8MB, time=319.41 memory used=135058.6MB, alloc=411.8MB, time=319.74 memory used=135517.9MB, alloc=411.8MB, time=320.08 memory used=135978.0MB, alloc=411.8MB, time=320.44 memory used=136438.8MB, alloc=411.8MB, time=320.78 memory used=136900.1MB, alloc=411.8MB, time=321.13 memory used=137362.9MB, alloc=411.8MB, time=321.48 memory used=137826.2MB, alloc=411.8MB, time=321.81 memory used=138231.3MB, alloc=411.8MB, time=322.13 memory used=138597.7MB, alloc=411.8MB, time=322.40 memory used=138964.6MB, alloc=411.8MB, time=322.70 memory used=139332.4MB, alloc=411.8MB, time=322.99 memory used=139699.7MB, alloc=411.8MB, time=323.28 memory used=140067.7MB, alloc=411.8MB, time=323.60 memory used=140436.1MB, alloc=411.8MB, time=323.89 memory used=140804.7MB, alloc=411.8MB, time=324.17 memory used=141173.0MB, alloc=411.8MB, time=324.45 memory used=141542.8MB, alloc=411.8MB, time=324.75 memory used=141914.3MB, alloc=411.8MB, time=325.06 memory used=142285.2MB, alloc=411.8MB, time=325.37 memory used=142656.4MB, alloc=411.8MB, time=325.66 memory used=143027.6MB, alloc=411.8MB, time=325.94 memory used=143398.8MB, alloc=411.8MB, time=326.23 memory used=143771.3MB, alloc=411.8MB, time=326.53 memory used=144143.4MB, alloc=411.8MB, time=326.81 memory used=144516.9MB, alloc=411.8MB, time=327.09 memory used=144891.0MB, alloc=411.8MB, time=327.39 memory used=145265.8MB, alloc=411.8MB, time=327.69 memory used=145640.2MB, alloc=411.8MB, time=327.99 memory used=146014.3MB, alloc=411.8MB, time=328.27 memory used=146391.1MB, alloc=411.8MB, time=328.57 memory used=146767.2MB, alloc=411.8MB, time=328.87 memory used=147144.4MB, alloc=411.8MB, time=329.17 memory used=147522.3MB, alloc=411.8MB, time=329.46 memory used=147899.4MB, alloc=411.8MB, time=329.75 memory used=148277.7MB, alloc=411.8MB, time=330.04 memory used=148656.4MB, alloc=411.8MB, time=330.34 memory used=149035.8MB, alloc=411.8MB, time=330.62 memory used=149415.3MB, alloc=411.8MB, time=330.91 memory used=149794.8MB, alloc=411.8MB, time=331.23 memory used=150175.6MB, alloc=411.8MB, time=331.53 memory used=150556.7MB, alloc=411.8MB, time=331.83 memory used=150938.7MB, alloc=411.8MB, time=332.13 memory used=151320.8MB, alloc=411.8MB, time=332.41 memory used=151704.1MB, alloc=411.8MB, time=332.71 memory used=152087.0MB, alloc=411.8MB, time=333.00 memory used=152469.5MB, alloc=411.8MB, time=333.29 memory used=152854.5MB, alloc=411.8MB, time=333.58 memory used=153239.3MB, alloc=411.8MB, time=333.87 memory used=153625.0MB, alloc=411.8MB, time=334.17 memory used=154011.0MB, alloc=411.8MB, time=334.46 memory used=154396.6MB, alloc=411.8MB, time=334.76 memory used=154783.2MB, alloc=411.8MB, time=335.08 memory used=155171.2MB, alloc=411.8MB, time=335.38 memory used=155558.8MB, alloc=411.8MB, time=335.68 memory used=155947.7MB, alloc=411.8MB, time=335.99 memory used=156336.5MB, alloc=411.8MB, time=336.31 memory used=156727.1MB, alloc=411.8MB, time=336.60 memory used=157117.0MB, alloc=411.8MB, time=336.90 memory used=157507.8MB, alloc=411.8MB, time=337.20 memory used=157899.9MB, alloc=411.8MB, time=337.51 memory used=158291.4MB, alloc=411.8MB, time=337.80 memory used=158683.1MB, alloc=411.8MB, time=338.08 memory used=159075.4MB, alloc=411.8MB, time=338.38 memory used=159467.9MB, alloc=411.8MB, time=338.67 memory used=159862.1MB, alloc=411.8MB, time=338.97 memory used=160256.0MB, alloc=411.8MB, time=339.26 memory used=160649.5MB, alloc=411.8MB, time=339.55 memory used=161044.7MB, alloc=411.8MB, time=339.85 memory used=161439.7MB, alloc=411.8MB, time=340.17 memory used=161834.1MB, alloc=411.8MB, time=340.48 memory used=162242.6MB, alloc=411.8MB, time=340.80 memory used=162651.8MB, alloc=411.8MB, time=341.11 memory used=163063.0MB, alloc=411.8MB, time=341.42 memory used=163475.5MB, alloc=411.8MB, time=341.73 memory used=163889.2MB, alloc=411.8MB, time=342.04 memory used=164305.2MB, alloc=411.8MB, time=342.36 memory used=164721.4MB, alloc=411.8MB, time=342.67 memory used=165138.5MB, alloc=411.8MB, time=342.98 memory used=165556.2MB, alloc=411.8MB, time=343.31 memory used=165975.1MB, alloc=411.8MB, time=343.62 memory used=166395.1MB, alloc=411.8MB, time=343.92 memory used=166815.8MB, alloc=411.8MB, time=344.24 memory used=167236.9MB, alloc=411.8MB, time=344.56 memory used=167659.4MB, alloc=411.8MB, time=344.86 memory used=168082.1MB, alloc=411.8MB, time=345.17 memory used=168504.4MB, alloc=411.8MB, time=345.48 memory used=168927.8MB, alloc=411.8MB, time=345.81 memory used=169352.3MB, alloc=411.8MB, time=346.13 memory used=169777.4MB, alloc=411.8MB, time=346.46 memory used=170202.9MB, alloc=411.8MB, time=346.77 memory used=170629.3MB, alloc=411.8MB, time=347.08 memory used=171057.0MB, alloc=411.8MB, time=347.39 memory used=171485.9MB, alloc=411.8MB, time=347.71 memory used=171915.8MB, alloc=411.8MB, time=348.03 memory used=172345.7MB, alloc=411.8MB, time=348.32 memory used=172775.9MB, alloc=411.8MB, time=348.64 memory used=173206.5MB, alloc=411.8MB, time=348.97 memory used=173637.7MB, alloc=411.8MB, time=349.33 memory used=174069.4MB, alloc=411.8MB, time=349.65 memory used=174501.9MB, alloc=411.8MB, time=349.98 memory used=174935.3MB, alloc=411.8MB, time=350.31 memory used=175369.5MB, alloc=411.8MB, time=350.64 memory used=175804.0MB, alloc=411.8MB, time=350.95 memory used=176239.1MB, alloc=411.8MB, time=351.27 memory used=176674.7MB, alloc=411.8MB, time=351.59 memory used=177111.8MB, alloc=411.8MB, time=351.91 memory used=177549.0MB, alloc=411.8MB, time=352.21 memory used=177986.5MB, alloc=411.8MB, time=352.55 memory used=178424.5MB, alloc=411.8MB, time=352.88 memory used=178863.4MB, alloc=411.8MB, time=353.21 memory used=179302.0MB, alloc=411.8MB, time=353.52 memory used=179741.3MB, alloc=411.8MB, time=353.84 memory used=180180.9MB, alloc=411.8MB, time=354.15 memory used=180622.4MB, alloc=411.8MB, time=354.47 memory used=181064.3MB, alloc=411.8MB, time=354.80 memory used=181506.9MB, alloc=411.8MB, time=355.12 memory used=181950.2MB, alloc=411.8MB, time=355.44 memory used=182393.6MB, alloc=411.8MB, time=355.76 memory used=182837.9MB, alloc=411.8MB, time=356.10 memory used=183282.7MB, alloc=411.8MB, time=356.44 memory used=183727.5MB, alloc=411.8MB, time=356.75 memory used=184172.1MB, alloc=411.8MB, time=357.09 memory used=184618.3MB, alloc=411.8MB, time=357.41 memory used=185065.2MB, alloc=411.8MB, time=357.75 memory used=185512.8MB, alloc=411.8MB, time=358.08 memory used=185961.3MB, alloc=411.8MB, time=358.39 memory used=186410.3MB, alloc=411.8MB, time=358.72 memory used=186859.8MB, alloc=411.8MB, time=359.06 memory used=187305.0MB, alloc=411.8MB, time=359.38 memory used=187681.7MB, alloc=411.8MB, time=359.67 memory used=188041.6MB, alloc=411.8MB, time=359.97 memory used=188403.8MB, alloc=411.8MB, time=360.24 memory used=188763.4MB, alloc=411.8MB, time=360.52 memory used=189124.0MB, alloc=411.8MB, time=360.79 memory used=189484.4MB, alloc=411.8MB, time=361.08 memory used=189846.1MB, alloc=411.8MB, time=361.35 memory used=190208.1MB, alloc=411.8MB, time=361.63 memory used=190570.6MB, alloc=411.8MB, time=361.91 memory used=190933.2MB, alloc=411.8MB, time=362.19 memory used=191296.2MB, alloc=411.8MB, time=362.49 memory used=191659.9MB, alloc=411.8MB, time=362.78 memory used=192024.0MB, alloc=411.8MB, time=363.07 memory used=192389.9MB, alloc=411.8MB, time=363.35 |\^/| 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(); 1428324380 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 2 F := [x - 10 x z, 10 z - 9 y, 12 x z + 4 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-8 x y z + 11 x y z, -y z + 20 z, -12 x y + 3 y] > Problem := [F,G]; 4 2 3 2 2 2 Problem := [[x - 10 x z, 10 z - 9 y, 12 x z + 4 z ], 2 2 [-8 x y z + 11 x y z, -y z + 20 z, -12 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.49 memory used=48.0MB, alloc=32.3MB, time=0.76 memory used=69.0MB, alloc=56.3MB, time=1.07 memory used=111.0MB, alloc=60.3MB, time=1.65 memory used=147.0MB, alloc=84.3MB, time=2.22 memory used=198.3MB, alloc=108.3MB, time=3.50 N1 := 1595 > GB := Basis(F, plex(op(vars))); 8 6 6 4 2 6 2 GB := [3 x + x , -x + 900 y, -x + 10 x z, 3 x + 100 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=271.0MB, alloc=108.3MB, time=4.54 memory used=353.5MB, alloc=132.3MB, time=5.87 N2 := 883 #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)]; 4 2 3 2 2 2 2 H := [x - 10 x z, 10 z - 9 y, 12 x z + 4 z , -8 x y z + 11 x y z, 2 -y z + 20 z, -12 x y + 3 y] > J:=[op(GB),op(G)]; 8 6 6 4 2 6 2 J := [3 x + x , -x + 900 y, -x + 10 x z, 3 x + 100 z , 2 2 -8 x y z + 11 x y z, -y z + 20 z, -12 x y + 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 := [6, 13, 20, 4, 4, 2, 3, 2/3, 2/3, 5/6, 1/2, 1/2, 2/3, 7, 14, 33, 8, 8, 2, 2, 6/7, 4/7, 4/7, 9/14, 3/7, 3/7, -1, -13, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=365.0MB, alloc=132.3MB, time=6.10 |\^/| 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(); 1428324387 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 2 F := [7 x z + 17 x y z, 19 x - 3 x y z, -y z - 14 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 4 2 2 G := [14 x y + 7 x y z, -8 x y + 5 y z, 10 y + 13 y z ] > Problem := [F,G]; 3 2 4 2 2 Problem := [[7 x z + 17 x y z, 19 x - 3 x y z, -y z - 14 x], 2 2 2 3 4 2 2 [14 x y + 7 x y z, -8 x y + 5 y z, 10 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=32.0MB, alloc=40.3MB, time=0.49 memory used=59.8MB, alloc=40.3MB, time=0.80 memory used=86.9MB, alloc=40.3MB, time=1.08 memory used=112.8MB, alloc=44.3MB, time=1.42 memory used=138.7MB, alloc=68.3MB, time=1.72 memory used=185.3MB, alloc=76.3MB, time=2.27 memory used=229.7MB, alloc=100.3MB, time=2.82 memory used=297.7MB, alloc=100.3MB, time=3.57 memory used=362.0MB, alloc=124.3MB, time=4.33 memory used=438.2MB, alloc=148.3MB, time=5.26 memory used=507.9MB, alloc=404.3MB, time=6.15 memory used=610.3MB, alloc=428.3MB, time=7.59 memory used=725.6MB, alloc=452.3MB, time=9.36 memory used=852.5MB, alloc=476.3MB, time=11.43 memory used=981.0MB, alloc=500.3MB, time=14.81 memory used=1114.6MB, alloc=524.3MB, time=19.00 memory used=1272.1MB, alloc=548.3MB, time=24.03 memory used=1453.7MB, alloc=572.3MB, time=29.49 N1 := 4711 > GB := Basis(F, plex(op(vars))); 4 2 2 2 2 3 2 2 GB := [19 x + 42 x , 323 x y - 294 x , 323 x + 21 x z, z y + 14 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1668.8MB, alloc=572.3MB, time=33.55 memory used=1857.4MB, alloc=572.3MB, time=36.23 memory used=2101.2MB, alloc=596.3MB, time=41.62 N2 := 2659 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 4 2 2 2 2 2 H := [7 x z + 17 x y z, 19 x - 3 x y z, -y z - 14 x, 14 x y + 7 x y z, 3 4 2 2 -8 x y + 5 y z, 10 y + 13 y z ] > J:=[op(GB),op(G)]; 4 2 2 2 2 3 2 2 J := [19 x + 42 x , 323 x y - 294 x , 323 x + 21 x z, z y + 14 x, 2 2 2 3 4 2 2 14 x y + 7 x y z, -8 x y + 5 y z, 10 y + 13 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 := [6, 17, 23, 4, 4, 4, 2, 5/6, 1, 1, 2/3, 3/4, 7/12, 7, 16, 26, 4, 4, 4, 2, 6/7, 5/7, 5/7, 5/7, 4/7, 5/14, 1, -3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2245.6MB, alloc=596.3MB, time=45.74 |\^/| 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(); 1428324434 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 F := [-9 x - x y z, 17 y z, -20 y - 5 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 2 G := [13 y + 9 x z, -13 x y z + 6 x , -14 x z + 4 x y z] > Problem := [F,G]; 4 3 2 Problem := [[-9 x - x y z, 17 y z, -20 y - 5 y z], 4 2 2 2 3 2 [13 y + 9 x z, -13 x y z + 6 x , -14 x z + 4 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.7MB, alloc=32.3MB, time=0.43 memory used=47.7MB, alloc=32.3MB, time=0.68 memory used=68.1MB, alloc=56.3MB, time=0.92 memory used=109.1MB, alloc=60.3MB, time=1.39 memory used=149.3MB, alloc=84.3MB, time=1.97 memory used=207.9MB, alloc=116.3MB, time=2.78 memory used=282.1MB, alloc=116.3MB, time=4.45 N1 := 1709 > GB := Basis(F, plex(op(vars))); 4 3 GB := [x , y , z y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 171 #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)]; 4 3 2 4 2 2 2 H := [-9 x - x y z, 17 z y, -20 y - 5 y z, 13 y + 9 z x , -13 x y z + 6 x , 3 2 -14 x z + 4 x y z] > J:=[op(GB),op(G)]; 4 3 4 2 2 2 3 2 J := [x , y , z y, 13 y + 9 z x , -13 x y z + 6 x , -14 x z + 4 x 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 := [6, 16, 21, 4, 4, 4, 1, 2/3, 1, 1, 7/13, 7/13, 7/13, 6, 13, 21, 4, 4, 4, 1, 2/3, 5/6, 2/3, 1/2, 5/12, 5/12, 3, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=339.0MB, alloc=116.3MB, time=5.46 |\^/| 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(); 1428324440 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 F := [19 x z + 11 y z, 18 y z - 7 y, 20 y z - 9] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 2 2 G := [18 x y + 6 x y , -19 x + 12 x y, 6 x y z] > Problem := [F,G]; 2 3 Problem := [[19 x z + 11 y z, 18 y z - 7 y, 20 y z - 9], 2 2 3 4 2 2 [18 x y + 6 x y , -19 x + 12 x y, 6 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.1MB, alloc=32.3MB, time=0.43 memory used=48.1MB, alloc=32.3MB, time=0.71 memory used=67.2MB, alloc=56.3MB, time=0.99 N1 := 837 > GB := Basis(F, plex(op(vars))); 6 2 GB := [480130 x + 107811, 19 x + 11 y, 18 z - 7] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=107.4MB, alloc=56.3MB, time=1.65 N2 := 265 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 3 H := [19 x z + 11 y z, 18 y z - 7 y, 20 z y - 9, 18 x y + 6 x y , 4 2 2 -19 x + 12 x y, 6 x y z] > J:=[op(GB),op(G)]; 6 2 2 2 3 J := [480130 x + 107811, 19 x + 11 y, 18 z - 7, 18 x y + 6 x y , 4 2 2 -19 x + 12 x y, 6 x 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 := [6, 14, 21, 4, 4, 3, 1, 2/3, 1, 2/3, 3/7, 4/7, 5/14, 6, 11, 21, 6, 6, 3, 1, 5/6, 2/3, 1/3, 1/2, 5/14, 1/7, 3, 0, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=135.6MB, alloc=56.3MB, time=2.02 |\^/| 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(); 1428324442 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 2 3 4 F := [x y - 16 z , -11 y z + 7 x , 8 x y - 17 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [-4 x z, 13 x y z + 18 x y, 9 x y - x z] > Problem := [F,G]; 3 4 2 2 2 3 4 Problem := [[x y - 16 z , -11 y z + 7 x , 8 x y - 17 y ], 2 2 3 2 [-4 x z, 13 x y z + 18 x y, 9 x y - x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.0MB, alloc=44.3MB, time=0.47 memory used=59.0MB, alloc=44.3MB, time=0.80 memory used=85.7MB, alloc=68.3MB, time=1.11 memory used=141.0MB, alloc=76.3MB, time=1.61 memory used=186.1MB, alloc=100.3MB, time=2.10 memory used=256.0MB, alloc=100.3MB, time=2.88 memory used=331.3MB, alloc=124.3MB, time=3.48 memory used=398.5MB, alloc=124.3MB, time=4.17 memory used=463.2MB, alloc=404.3MB, time=4.93 memory used=576.6MB, alloc=404.3MB, time=6.40 memory used=674.1MB, alloc=428.3MB, time=7.76 memory used=793.3MB, alloc=452.3MB, time=9.40 memory used=927.4MB, alloc=476.3MB, time=11.39 memory used=1062.7MB, alloc=500.3MB, time=14.39 memory used=1196.3MB, alloc=524.3MB, time=18.39 memory used=1344.3MB, alloc=548.3MB, time=23.06 memory used=1516.3MB, alloc=572.3MB, time=28.42 memory used=1712.3MB, alloc=572.3MB, time=34.60 memory used=1908.4MB, alloc=596.3MB, time=40.69 N1 := 5739 > GB := Basis(F, plex(op(vars))); 16 4 13 4 GB := [907039232 x - 48275934539777 x , -1874048 x + 3409076657 x y, 8 2 2 3 4 10 2 2 -3872 x + 240737 x y , -8 x y + 17 y , -21296 x + 28647703 x z , 2 2 2 3 4 11 y z - 7 x , -x y + 16 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2146.8MB, alloc=596.3MB, time=44.94 memory used=2262.2MB, alloc=596.3MB, time=46.35 memory used=2368.6MB, alloc=596.3MB, time=47.52 memory used=2471.0MB, alloc=620.3MB, time=48.92 memory used=2577.7MB, alloc=620.3MB, time=50.15 memory used=2663.5MB, alloc=620.3MB, time=51.35 memory used=2753.9MB, alloc=644.3MB, time=52.53 memory used=2835.1MB, alloc=644.3MB, time=53.62 memory used=2906.5MB, alloc=644.3MB, time=54.82 memory used=2976.6MB, alloc=644.3MB, time=55.98 memory used=3046.3MB, alloc=644.3MB, time=56.96 memory used=3095.6MB, alloc=644.3MB, time=57.97 memory used=3160.3MB, alloc=644.3MB, time=59.11 memory used=3196.0MB, alloc=668.3MB, time=60.00 memory used=3408.1MB, alloc=692.3MB, time=62.76 memory used=3594.1MB, alloc=716.3MB, time=65.14 memory used=3780.5MB, alloc=740.3MB, time=67.26 memory used=3977.2MB, alloc=764.3MB, time=69.58 memory used=4128.3MB, alloc=788.3MB, time=71.68 memory used=4261.5MB, alloc=812.3MB, time=74.07 memory used=4387.3MB, alloc=836.3MB, time=76.27 memory used=4486.8MB, alloc=836.3MB, time=78.00 memory used=4590.5MB, alloc=836.3MB, time=79.99 memory used=4665.0MB, alloc=836.3MB, time=81.65 memory used=4762.1MB, alloc=836.3MB, time=83.71 memory used=5206.1MB, alloc=860.3MB, time=88.78 memory used=5556.8MB, alloc=884.3MB, time=93.47 memory used=5921.9MB, alloc=908.3MB, time=98.15 memory used=6229.2MB, alloc=932.3MB, time=102.51 memory used=6512.0MB, alloc=956.3MB, time=106.94 memory used=6774.0MB, alloc=980.3MB, time=111.15 memory used=7034.9MB, alloc=1004.3MB, time=115.37 memory used=7219.8MB, alloc=1028.3MB, time=119.23 memory used=7425.4MB, alloc=1052.3MB, time=123.05 memory used=8042.3MB, alloc=1076.3MB, time=130.29 memory used=8650.6MB, alloc=1100.3MB, time=138.73 memory used=9266.1MB, alloc=1124.3MB, time=146.95 memory used=9870.9MB, alloc=1148.3MB, time=154.63 memory used=10482.3MB, alloc=1172.3MB, time=162.95 memory used=11076.7MB, alloc=1196.3MB, time=172.26 memory used=11648.0MB, alloc=1220.3MB, time=181.08 memory used=12182.5MB, alloc=1244.3MB, time=189.88 memory used=12745.2MB, alloc=1268.3MB, time=199.01 memory used=13256.6MB, alloc=1292.3MB, time=205.17 memory used=13820.5MB, alloc=1316.3MB, time=211.47 memory used=14388.3MB, alloc=1340.3MB, time=217.80 memory used=14993.7MB, alloc=1364.3MB, time=223.97 memory used=15771.5MB, alloc=1388.3MB, time=232.77 memory used=16449.8MB, alloc=1412.3MB, time=245.10 memory used=16962.6MB, alloc=1436.3MB, time=257.78 memory used=17592.3MB, alloc=1460.3MB, time=270.22 memory used=18338.4MB, alloc=1484.3MB, time=281.78 memory used=18892.5MB, alloc=1508.3MB, time=294.87 memory used=19391.6MB, alloc=1532.3MB, time=307.69 memory used=20144.6MB, alloc=1556.3MB, time=319.04 |\^/| 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(); 1428324742 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 F := [-4 x y z - 5 y z, 15 x y z - 15 y , 19 x y z + 15 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 4 G := [-8 x y - 9 y z, -12 x z - 3 x y , 19 x z + 18 y ] > Problem := [F,G]; 2 2 2 4 Problem := [[-4 x y z - 5 y z, 15 x y z - 15 y , 19 x y z + 15 y], 3 2 2 2 2 3 4 [-8 x y - 9 y z, -12 x z - 3 x y , 19 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=0.17 memory used=26.6MB, alloc=32.3MB, time=0.48 memory used=47.9MB, alloc=32.3MB, time=0.79 memory used=67.7MB, alloc=32.3MB, time=1.07 memory used=86.9MB, alloc=56.3MB, time=1.35 memory used=126.4MB, alloc=60.3MB, time=1.89 memory used=164.0MB, alloc=84.3MB, time=2.41 memory used=205.1MB, alloc=84.3MB, time=3.00 memory used=265.1MB, alloc=92.3MB, time=3.84 memory used=323.7MB, alloc=116.3MB, time=4.71 memory used=403.8MB, alloc=116.3MB, time=5.83 memory used=474.8MB, alloc=396.3MB, time=6.88 memory used=574.0MB, alloc=420.3MB, time=8.28 memory used=688.8MB, alloc=420.3MB, time=10.10 memory used=811.0MB, alloc=444.3MB, time=11.87 memory used=949.2MB, alloc=468.3MB, time=13.66 memory used=1062.2MB, alloc=468.3MB, time=14.96 memory used=1182.8MB, alloc=492.3MB, time=16.50 memory used=1293.2MB, alloc=492.3MB, time=17.91 memory used=1402.9MB, alloc=516.3MB, time=19.35 memory used=1503.7MB, alloc=516.3MB, time=20.74 memory used=1605.8MB, alloc=516.3MB, time=22.23 memory used=1693.1MB, alloc=516.3MB, time=23.45 memory used=1773.6MB, alloc=516.3MB, time=24.68 memory used=1836.0MB, alloc=516.3MB, time=25.63 memory used=1910.5MB, alloc=516.3MB, time=26.83 memory used=1979.6MB, alloc=516.3MB, time=28.01 memory used=2044.4MB, alloc=516.3MB, time=29.17 memory used=2116.2MB, alloc=516.3MB, time=30.47 memory used=2166.6MB, alloc=516.3MB, time=31.43 memory used=2361.2MB, alloc=540.3MB, time=34.14 memory used=2562.5MB, alloc=564.3MB, time=37.19 memory used=2779.4MB, alloc=588.3MB, time=40.36 memory used=2974.4MB, alloc=612.3MB, time=43.21 memory used=3134.3MB, alloc=636.3MB, time=45.61 memory used=3319.1MB, alloc=660.3MB, time=48.85 memory used=3460.6MB, alloc=684.3MB, time=51.16 memory used=3616.4MB, alloc=708.3MB, time=53.83 memory used=3746.4MB, alloc=708.3MB, time=56.29 memory used=3870.1MB, alloc=708.3MB, time=58.62 memory used=3971.3MB, alloc=732.3MB, time=60.74 memory used=4105.0MB, alloc=732.3MB, time=63.73 memory used=4471.1MB, alloc=756.3MB, time=69.62 memory used=4848.3MB, alloc=780.3MB, time=75.69 memory used=5241.3MB, alloc=804.3MB, time=81.89 memory used=5569.6MB, alloc=828.3MB, time=86.96 memory used=5976.9MB, alloc=852.3MB, time=93.99 memory used=6386.6MB, alloc=876.3MB, time=100.39 memory used=6747.3MB, alloc=900.3MB, time=107.28 memory used=7100.4MB, alloc=924.3MB, time=114.26 memory used=7451.9MB, alloc=948.3MB, time=121.45 memory used=7804.2MB, alloc=972.3MB, time=128.75 memory used=8160.0MB, alloc=996.3MB, time=136.27 memory used=8513.4MB, alloc=1020.3MB, time=144.27 memory used=8867.3MB, alloc=1044.3MB, time=151.72 memory used=9223.0MB, alloc=1068.3MB, time=159.25 memory used=9589.9MB, alloc=1092.3MB, time=166.77 memory used=10048.5MB, alloc=1116.3MB, time=173.58 memory used=10564.6MB, alloc=1140.3MB, time=179.32 memory used=11048.7MB, alloc=1164.3MB, time=187.53 memory used=11438.9MB, alloc=1188.3MB, time=195.84 memory used=11827.1MB, alloc=1212.3MB, time=204.21 memory used=12226.4MB, alloc=1236.3MB, time=213.05 memory used=12583.1MB, alloc=1260.3MB, time=226.28 memory used=12910.0MB, alloc=1284.3MB, time=240.07 memory used=13237.0MB, alloc=1308.3MB, time=253.95 memory used=13569.5MB, alloc=1332.3MB, time=267.27 memory used=13910.5MB, alloc=1356.3MB, time=281.31 memory used=14261.9MB, alloc=1380.3MB, time=295.70 |\^/| 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(); 1428325042 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 F := [-7 x y - 9 x, -3 x z - 12 x y, -15 y z + 9 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 4 2 G := [-15 x z + 9 x y , 8 x z - 9 y z, 12 z + 13 x z] > Problem := [F,G]; 3 3 2 3 2 Problem := [[-7 x y - 9 x, -3 x z - 12 x y, -15 y z + 9 y ], 2 2 3 3 4 2 [-15 x z + 9 x y , 8 x z - 9 y z, 12 z + 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=0.17 memory used=26.9MB, alloc=32.3MB, time=0.49 memory used=48.6MB, alloc=32.3MB, time=0.79 memory used=69.8MB, alloc=32.3MB, time=1.09 memory used=90.4MB, alloc=56.3MB, time=1.39 memory used=130.8MB, alloc=60.3MB, time=1.94 memory used=170.0MB, alloc=84.3MB, time=2.45 memory used=209.4MB, alloc=84.3MB, time=2.98 memory used=271.4MB, alloc=92.3MB, time=3.86 memory used=332.1MB, alloc=116.3MB, time=4.68 memory used=416.9MB, alloc=116.3MB, time=6.04 memory used=500.7MB, alloc=140.3MB, time=7.18 memory used=598.2MB, alloc=164.3MB, time=8.66 memory used=711.2MB, alloc=188.3MB, time=10.35 memory used=819.5MB, alloc=468.3MB, time=12.04 memory used=954.6MB, alloc=492.3MB, time=14.99 memory used=1090.5MB, alloc=516.3MB, time=18.75 memory used=1233.0MB, alloc=540.3MB, time=23.34 memory used=1397.6MB, alloc=564.3MB, time=28.71 memory used=1586.1MB, alloc=564.3MB, time=34.85 memory used=1774.6MB, alloc=588.3MB, time=40.91 memory used=1987.0MB, alloc=588.3MB, time=47.56 memory used=2199.5MB, alloc=612.3MB, time=54.38 memory used=2436.3MB, alloc=636.3MB, time=61.42 N1 := 7069 > GB := Basis(F, plex(op(vars))); 2 3 3 2 GB := [20 x + 3 x, 7 x y + 400 x, 7 x z + 240 x, 5 y z - 3 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2624.1MB, alloc=636.3MB, time=64.12 memory used=2872.6MB, alloc=636.3MB, time=68.19 memory used=3147.5MB, alloc=660.3MB, time=76.54 memory used=3416.9MB, alloc=684.3MB, time=85.90 N2 := 4595 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 3 2 2 2 H := [-7 x y - 9 x, -3 x z - 12 x y, -15 y z + 9 y , -15 x z + 9 x y , 3 3 4 2 8 x z - 9 y z, 12 z + 13 x z] > J:=[op(GB),op(G)]; 2 3 3 2 J := [20 x + 3 x, 7 x y + 400 x, 7 x z + 240 x, 5 y z - 3 y , 2 2 3 3 4 2 -15 x z + 9 x y , 8 x z - 9 y z, 12 z + 13 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 := [6, 15, 23, 4, 3, 3, 4, 5/6, 5/6, 5/6, 2/3, 1/2, 7/12, 7, 15, 23, 4, 3, 3, 4, 6/7, 4/7, 5/7, 5/7, 5/14, 1/2, 0, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3588.8MB, alloc=684.3MB, time=90.82 |\^/| 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(); 1428325137 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 4 2 F := [-5 y + 8 z , 17 x y + 16 x , -6 x - 11 x y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 3 G := [18 z - 5 x, 17 z + 2 x , 10 x z - 9 y ] > Problem := [F,G]; 2 2 2 2 4 2 Problem := [[-5 y + 8 z , 17 x y + 16 x , -6 x - 11 x y z ], 3 3 2 3 3 [18 z - 5 x, 17 z + 2 x , 10 x z - 9 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=27.1MB, alloc=32.3MB, time=0.49 memory used=48.3MB, alloc=32.3MB, time=0.73 memory used=68.7MB, alloc=32.3MB, time=0.99 memory used=89.2MB, alloc=60.3MB, time=1.27 memory used=130.5MB, alloc=60.3MB, time=1.76 memory used=169.8MB, alloc=60.3MB, time=2.23 memory used=208.3MB, alloc=84.3MB, time=2.67 memory used=267.7MB, alloc=116.3MB, time=3.38 memory used=347.8MB, alloc=372.3MB, time=4.33 memory used=430.5MB, alloc=396.3MB, time=5.33 memory used=540.7MB, alloc=420.3MB, time=6.51 memory used=671.7MB, alloc=444.3MB, time=7.97 memory used=811.4MB, alloc=444.3MB, time=9.38 memory used=948.8MB, alloc=468.3MB, time=11.36 memory used=1077.9MB, alloc=492.3MB, time=13.31 memory used=1183.3MB, alloc=492.3MB, time=14.53 memory used=1277.9MB, alloc=492.3MB, time=15.77 memory used=1410.4MB, alloc=516.3MB, time=17.83 memory used=1583.6MB, alloc=540.3MB, time=20.70 memory used=1752.2MB, alloc=564.3MB, time=23.53 memory used=1934.0MB, alloc=588.3MB, time=26.64 memory used=2106.5MB, alloc=612.3MB, time=29.52 memory used=2264.5MB, alloc=636.3MB, time=32.17 memory used=2442.0MB, alloc=660.3MB, time=35.11 memory used=2586.2MB, alloc=684.3MB, time=37.67 memory used=2738.8MB, alloc=708.3MB, time=40.37 memory used=2862.0MB, alloc=732.3MB, time=43.03 memory used=3066.9MB, alloc=756.3MB, time=48.80 memory used=3285.0MB, alloc=780.3MB, time=55.65 memory used=3567.1MB, alloc=804.3MB, time=64.58 memory used=3856.0MB, alloc=828.3MB, time=74.08 memory used=4155.5MB, alloc=852.3MB, time=83.99 memory used=4458.3MB, alloc=876.3MB, time=95.02 memory used=4781.4MB, alloc=900.3MB, time=106.78 memory used=5128.4MB, alloc=924.3MB, time=119.47 memory used=5499.4MB, alloc=948.3MB, time=132.82 memory used=5894.2MB, alloc=972.3MB, time=147.07 memory used=6313.1MB, alloc=996.3MB, time=162.11 memory used=6755.9MB, alloc=1020.3MB, time=178.07 memory used=7222.6MB, alloc=1020.3MB, time=194.82 memory used=7689.4MB, alloc=1020.3MB, time=211.42 memory used=8156.0MB, alloc=1044.3MB, time=228.22 memory used=8646.5MB, alloc=1044.3MB, time=245.54 memory used=9137.0MB, alloc=1044.3MB, time=263.06 memory used=9627.3MB, alloc=1068.3MB, time=280.71 |\^/| 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(); 1428325437 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 2 F := [18 x y z - 15 x y , 19 x y - 5 x y , -4 x y + 5 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 4 G := [-11 x z - 19 y , -x y + 18 z, 8 z - 11 x z] > Problem := [F,G]; 2 2 3 3 3 2 Problem := [[18 x y z - 15 x y , 19 x y - 5 x y , -4 x y + 5 z ], 2 3 2 4 [-11 x z - 19 y , -x y + 18 z, 8 z - 11 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=48.2MB, alloc=32.3MB, time=0.79 memory used=69.0MB, alloc=32.3MB, time=1.08 memory used=89.0MB, alloc=56.3MB, time=1.38 memory used=129.1MB, alloc=60.3MB, time=1.96 memory used=168.2MB, alloc=84.3MB, time=2.50 memory used=216.7MB, alloc=84.3MB, time=3.20 memory used=277.3MB, alloc=116.3MB, time=4.12 memory used=359.1MB, alloc=116.3MB, time=5.35 memory used=441.0MB, alloc=140.3MB, time=6.57 memory used=515.8MB, alloc=396.3MB, time=7.72 memory used=618.4MB, alloc=420.3MB, time=9.20 memory used=741.0MB, alloc=444.3MB, time=10.74 memory used=885.4MB, alloc=468.3MB, time=12.83 memory used=1039.7MB, alloc=492.3MB, time=15.14 memory used=1191.8MB, alloc=516.3MB, time=17.20 memory used=1378.9MB, alloc=540.3MB, time=19.90 memory used=1563.0MB, alloc=564.3MB, time=22.86 memory used=1733.3MB, alloc=588.3MB, time=25.65 memory used=1954.0MB, alloc=612.3MB, time=28.60 memory used=2181.3MB, alloc=636.3MB, time=31.61 memory used=2354.5MB, alloc=660.3MB, time=34.47 memory used=2523.2MB, alloc=684.3MB, time=37.26 memory used=2783.5MB, alloc=708.3MB, time=44.35 memory used=3037.7MB, alloc=732.3MB, time=52.09 memory used=3299.1MB, alloc=756.3MB, time=60.54 memory used=3564.1MB, alloc=780.3MB, time=69.85 memory used=3844.2MB, alloc=804.3MB, time=80.14 memory used=4148.3MB, alloc=828.3MB, time=91.50 memory used=4476.2MB, alloc=852.3MB, time=104.55 memory used=4828.1MB, alloc=876.3MB, time=117.10 memory used=5204.0MB, alloc=900.3MB, time=130.41 memory used=5603.8MB, alloc=900.3MB, time=144.75 memory used=6003.5MB, alloc=924.3MB, time=158.97 memory used=6427.2MB, alloc=924.3MB, time=174.03 memory used=6850.8MB, alloc=924.3MB, time=190.76 memory used=7274.4MB, alloc=948.3MB, time=208.10 memory used=7721.9MB, alloc=948.3MB, time=225.42 memory used=8169.3MB, alloc=972.3MB, time=243.08 memory used=8640.7MB, alloc=972.3MB, time=260.39 memory used=9112.1MB, alloc=996.3MB, time=276.88 |\^/| 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(); 1428325737 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 3 F := [17 x y z + 3 y z , -3 x y - 8 x z, -17 y z + 9 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [20 x y z - 5 x , -16 x z + 9 y z, 2 x y z - 2 x] > Problem := [F,G]; 2 3 3 2 3 Problem := [[17 x y z + 3 y z , -3 x y - 8 x z, -17 y z + 9 y], 2 3 2 2 [20 x y z - 5 x , -16 x z + 9 y z, 2 x y z - 2 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.53 memory used=47.4MB, alloc=32.3MB, time=0.83 memory used=66.9MB, alloc=56.3MB, time=1.14 memory used=105.6MB, alloc=60.3MB, time=1.69 memory used=141.7MB, alloc=84.3MB, time=2.23 memory used=198.1MB, alloc=92.3MB, time=3.10 memory used=252.4MB, alloc=116.3MB, time=4.04 memory used=328.5MB, alloc=116.3MB, time=5.25 memory used=399.9MB, alloc=140.3MB, time=6.55 memory used=492.6MB, alloc=140.3MB, time=8.14 memory used=584.7MB, alloc=164.3MB, time=9.53 memory used=664.5MB, alloc=164.3MB, time=10.60 memory used=736.9MB, alloc=420.3MB, time=11.75 memory used=847.0MB, alloc=444.3MB, time=13.61 memory used=981.3MB, alloc=468.3MB, time=15.98 memory used=1141.5MB, alloc=492.3MB, time=18.84 memory used=1319.7MB, alloc=516.3MB, time=22.55 memory used=1518.2MB, alloc=540.3MB, time=26.19 memory used=1734.1MB, alloc=564.3MB, time=30.62 memory used=1965.4MB, alloc=588.3MB, time=35.19 memory used=2208.0MB, alloc=612.3MB, time=39.30 memory used=2465.5MB, alloc=636.3MB, time=43.86 memory used=2710.9MB, alloc=660.3MB, time=48.41 memory used=2961.9MB, alloc=684.3MB, time=53.08 memory used=3216.5MB, alloc=708.3MB, time=58.31 memory used=3487.4MB, alloc=732.3MB, time=62.98 memory used=3679.9MB, alloc=756.3MB, time=64.48 memory used=3913.4MB, alloc=780.3MB, time=65.71 memory used=4165.4MB, alloc=804.3MB, time=66.89 memory used=4507.5MB, alloc=828.3MB, time=68.23 memory used=4995.8MB, alloc=852.3MB, time=69.78 memory used=5321.1MB, alloc=891.8MB, time=71.02 memory used=5671.6MB, alloc=891.8MB, time=72.18 memory used=6051.4MB, alloc=891.8MB, time=73.57 memory used=6461.1MB, alloc=891.8MB, time=74.91 memory used=6884.4MB, alloc=891.8MB, time=76.27 memory used=7327.0MB, alloc=891.8MB, time=77.57 memory used=7796.7MB, alloc=891.8MB, time=78.81 memory used=8292.9MB, alloc=891.8MB, time=79.99 memory used=8815.7MB, alloc=891.8MB, time=81.25 memory used=9126.5MB, alloc=891.8MB, time=82.22 memory used=9374.5MB, alloc=891.8MB, time=83.13 memory used=9626.1MB, alloc=891.8MB, time=84.06 memory used=9882.4MB, alloc=891.8MB, time=84.98 memory used=10143.5MB, alloc=891.8MB, time=85.86 memory used=10409.6MB, alloc=891.8MB, time=86.76 memory used=10680.7MB, alloc=891.8MB, time=87.66 memory used=10957.0MB, alloc=891.8MB, time=88.59 memory used=11238.5MB, alloc=891.8MB, time=89.50 memory used=11525.1MB, alloc=891.8MB, time=90.46 memory used=11817.0MB, alloc=891.8MB, time=91.42 memory used=12111.1MB, alloc=891.8MB, time=92.34 memory used=12406.5MB, alloc=891.8MB, time=93.28 memory used=12706.8MB, alloc=891.8MB, time=94.45 memory used=13012.2MB, alloc=891.8MB, time=95.65 memory used=13322.2MB, alloc=891.8MB, time=96.82 memory used=13637.3MB, alloc=891.8MB, time=97.85 memory used=13957.5MB, alloc=891.8MB, time=98.91 memory used=14282.6MB, alloc=891.8MB, time=99.90 memory used=14612.6MB, alloc=891.8MB, time=101.24 memory used=14947.5MB, alloc=891.8MB, time=102.27 memory used=15287.4MB, alloc=891.8MB, time=103.31 memory used=15632.0MB, alloc=891.8MB, time=104.36 memory used=15930.7MB, alloc=891.8MB, time=105.35 memory used=16229.2MB, alloc=891.8MB, time=106.30 memory used=16530.2MB, alloc=891.8MB, time=107.28 memory used=16834.1MB, alloc=891.8MB, time=108.26 memory used=17141.1MB, alloc=891.8MB, time=109.25 memory used=17451.5MB, alloc=891.8MB, time=110.21 memory used=17765.7MB, alloc=891.8MB, time=111.47 memory used=18083.0MB, alloc=891.8MB, time=112.45 memory used=18403.7MB, alloc=891.8MB, time=113.41 memory used=18728.2MB, alloc=891.8MB, time=114.37 memory used=19056.1MB, alloc=891.8MB, time=115.67 memory used=19387.3MB, alloc=891.8MB, time=116.84 memory used=19721.9MB, alloc=891.8MB, time=117.81 memory used=20058.9MB, alloc=891.8MB, time=118.76 memory used=20394.2MB, alloc=891.8MB, time=119.86 memory used=20733.3MB, alloc=891.8MB, time=120.98 memory used=21075.9MB, alloc=891.8MB, time=121.98 memory used=21421.5MB, alloc=891.8MB, time=122.97 memory used=21770.7MB, alloc=891.8MB, time=123.93 memory used=22123.4MB, alloc=891.8MB, time=124.92 memory used=22479.3MB, alloc=891.8MB, time=125.94 memory used=22838.5MB, alloc=891.8MB, time=126.96 memory used=23201.4MB, alloc=891.8MB, time=127.90 memory used=23567.7MB, alloc=891.8MB, time=128.88 memory used=23937.0MB, alloc=891.8MB, time=129.97 memory used=24309.5MB, alloc=891.8MB, time=131.05 memory used=24685.7MB, alloc=891.8MB, time=132.15 memory used=25026.5MB, alloc=891.8MB, time=133.20 memory used=25309.0MB, alloc=891.8MB, time=134.15 memory used=25592.2MB, alloc=891.8MB, time=135.13 memory used=25876.5MB, alloc=891.8MB, time=136.09 memory used=26162.2MB, alloc=891.8MB, time=137.06 memory used=26449.0MB, alloc=891.8MB, time=138.01 memory used=26737.4MB, alloc=891.8MB, time=139.21 memory used=27027.5MB, alloc=891.8MB, time=140.20 memory used=27319.0MB, alloc=891.8MB, time=141.13 memory used=27612.4MB, alloc=891.8MB, time=142.18 memory used=27907.0MB, alloc=891.8MB, time=143.45 memory used=28203.6MB, alloc=891.8MB, time=144.45 memory used=28501.9MB, alloc=891.8MB, time=145.43 memory used=28802.2MB, alloc=891.8MB, time=146.40 memory used=29103.7MB, alloc=891.8MB, time=147.32 memory used=29407.3MB, alloc=891.8MB, time=148.32 memory used=29712.7MB, alloc=891.8MB, time=149.37 memory used=30020.0MB, alloc=891.8MB, time=150.32 memory used=30329.1MB, alloc=891.8MB, time=151.26 memory used=30639.6MB, alloc=891.8MB, time=152.21 memory used=30948.0MB, alloc=891.8MB, time=153.14 memory used=31258.6MB, alloc=891.8MB, time=154.06 memory used=31570.6MB, alloc=891.8MB, time=155.15 memory used=31884.4MB, alloc=891.8MB, time=156.08 memory used=32199.9MB, alloc=891.8MB, time=157.00 memory used=32517.1MB, alloc=891.8MB, time=157.94 memory used=32836.3MB, alloc=891.8MB, time=158.92 memory used=33157.1MB, alloc=891.8MB, time=159.87 memory used=33479.7MB, alloc=891.8MB, time=161.17 memory used=33804.1MB, alloc=891.8MB, time=162.38 memory used=34130.2MB, alloc=891.8MB, time=163.54 memory used=34457.7MB, alloc=891.8MB, time=164.58 memory used=34787.3MB, alloc=891.8MB, time=165.61 memory used=35118.6MB, alloc=891.8MB, time=166.67 memory used=35451.4MB, alloc=891.8MB, time=167.86 memory used=35786.3MB, alloc=891.8MB, time=168.94 memory used=36122.6MB, alloc=891.8MB, time=169.99 memory used=36460.8MB, alloc=891.8MB, time=171.04 memory used=36800.9MB, alloc=891.8MB, time=172.12 memory used=37117.9MB, alloc=891.8MB, time=173.12 memory used=37427.9MB, alloc=891.8MB, time=174.02 memory used=37739.8MB, alloc=891.8MB, time=175.07 memory used=38052.0MB, alloc=891.8MB, time=176.12 memory used=38366.0MB, alloc=891.8MB, time=177.06 memory used=38681.2MB, alloc=891.8MB, time=178.06 memory used=38997.4MB, alloc=891.8MB, time=179.28 memory used=39314.6MB, alloc=891.8MB, time=180.30 memory used=39633.2MB, alloc=891.8MB, time=181.33 memory used=39953.2MB, alloc=891.8MB, time=182.36 memory used=40274.5MB, alloc=891.8MB, time=183.71 memory used=40597.3MB, alloc=891.8MB, time=184.71 memory used=40921.4MB, alloc=891.8MB, time=185.73 memory used=41247.1MB, alloc=891.8MB, time=186.73 memory used=41574.0MB, alloc=891.8MB, time=187.76 memory used=41902.3MB, alloc=891.8MB, time=188.74 memory used=42232.1MB, alloc=891.8MB, time=189.73 memory used=42563.3MB, alloc=891.8MB, time=190.80 memory used=42895.7MB, alloc=891.8MB, time=191.88 memory used=43229.8MB, alloc=891.8MB, time=192.88 memory used=43565.2MB, alloc=891.8MB, time=193.91 memory used=43901.4MB, alloc=891.8MB, time=195.20 memory used=44236.6MB, alloc=891.8MB, time=196.28 memory used=44572.9MB, alloc=891.8MB, time=197.27 memory used=44910.6MB, alloc=891.8MB, time=198.49 memory used=45250.2MB, alloc=891.8MB, time=199.68 memory used=45591.7MB, alloc=891.8MB, time=200.66 memory used=45934.1MB, alloc=891.8MB, time=201.71 memory used=46277.5MB, alloc=891.8MB, time=202.67 memory used=46622.4MB, alloc=891.8MB, time=203.64 memory used=46969.1MB, alloc=891.8MB, time=204.75 memory used=47317.4MB, alloc=891.8MB, time=205.96 memory used=47666.7MB, alloc=891.8MB, time=206.92 memory used=48017.3MB, alloc=891.8MB, time=208.07 memory used=48369.9MB, alloc=891.8MB, time=209.02 memory used=48723.7MB, alloc=891.8MB, time=210.06 memory used=49078.4MB, alloc=891.8MB, time=211.17 memory used=49435.1MB, alloc=891.8MB, time=212.51 memory used=49793.2MB, alloc=891.8MB, time=213.59 memory used=50152.3MB, alloc=891.8MB, time=214.63 memory used=50512.3MB, alloc=891.8MB, time=215.73 memory used=50874.3MB, alloc=891.8MB, time=216.75 memory used=51237.7MB, alloc=891.8MB, time=217.75 memory used=51553.0MB, alloc=891.8MB, time=218.78 memory used=51844.3MB, alloc=891.8MB, time=219.74 memory used=52135.6MB, alloc=891.8MB, time=220.72 memory used=52427.6MB, alloc=891.8MB, time=221.69 memory used=52719.3MB, alloc=891.8MB, time=222.77 memory used=53011.9MB, alloc=891.8MB, time=223.80 memory used=53304.7MB, alloc=891.8MB, time=225.09 memory used=53598.1MB, alloc=891.8MB, time=226.26 memory used=53891.9MB, alloc=891.8MB, time=227.66 memory used=54186.5MB, alloc=891.8MB, time=228.97 memory used=54481.7MB, alloc=891.8MB, time=230.18 memory used=54777.8MB, alloc=891.8MB, time=231.14 memory used=55075.0MB, alloc=891.8MB, time=232.05 memory used=55373.1MB, alloc=891.8MB, time=233.18 memory used=55672.2MB, alloc=891.8MB, time=234.42 memory used=55971.4MB, alloc=891.8MB, time=235.32 memory used=56271.6MB, alloc=891.8MB, time=236.27 memory used=56572.3MB, alloc=891.8MB, time=237.23 memory used=56874.1MB, alloc=891.8MB, time=238.14 memory used=57177.0MB, alloc=891.8MB, time=239.07 memory used=57480.2MB, alloc=891.8MB, time=240.15 memory used=57784.8MB, alloc=891.8MB, time=241.15 memory used=58089.8MB, alloc=891.8MB, time=242.17 memory used=58395.5MB, alloc=891.8MB, time=243.15 memory used=58702.1MB, alloc=891.8MB, time=244.17 memory used=59009.5MB, alloc=891.8MB, time=245.70 memory used=59317.7MB, alloc=891.8MB, time=246.96 memory used=59627.0MB, alloc=891.8MB, time=247.99 memory used=59934.7MB, alloc=891.8MB, time=248.98 memory used=60242.7MB, alloc=891.8MB, time=249.97 memory used=60551.9MB, alloc=891.8MB, time=250.94 memory used=60861.5MB, alloc=891.8MB, time=251.93 memory used=61172.3MB, alloc=891.8MB, time=252.93 memory used=61484.0MB, alloc=891.8MB, time=253.91 memory used=61796.6MB, alloc=891.8MB, time=254.87 memory used=62109.6MB, alloc=891.8MB, time=255.92 memory used=62424.0MB, alloc=891.8MB, time=256.94 memory used=62738.8MB, alloc=891.8MB, time=257.88 memory used=63054.8MB, alloc=891.8MB, time=258.88 memory used=63371.5MB, alloc=891.8MB, time=259.83 memory used=63688.8MB, alloc=891.8MB, time=260.76 memory used=64007.1MB, alloc=891.8MB, time=261.72 memory used=64326.4MB, alloc=891.8MB, time=262.65 memory used=64646.4MB, alloc=891.8MB, time=263.60 memory used=64966.7MB, alloc=891.8MB, time=264.54 memory used=65287.8MB, alloc=891.8MB, time=265.46 memory used=65609.8MB, alloc=891.8MB, time=266.39 memory used=65932.5MB, alloc=891.8MB, time=267.32 memory used=66256.3MB, alloc=891.8MB, time=268.26 memory used=66580.7MB, alloc=891.8MB, time=269.22 memory used=66906.9MB, alloc=891.8MB, time=270.12 memory used=67233.6MB, alloc=891.8MB, time=271.05 memory used=67560.7MB, alloc=891.8MB, time=271.96 memory used=67889.2MB, alloc=891.8MB, time=272.94 memory used=68218.6MB, alloc=891.8MB, time=273.94 memory used=68547.5MB, alloc=891.8MB, time=274.93 memory used=68859.0MB, alloc=891.8MB, time=275.89 memory used=69168.0MB, alloc=891.8MB, time=276.81 memory used=69478.8MB, alloc=891.8MB, time=277.78 memory used=69789.5MB, alloc=891.8MB, time=278.73 memory used=70102.1MB, alloc=891.8MB, time=279.65 memory used=70414.6MB, alloc=891.8MB, time=280.60 memory used=70728.3MB, alloc=891.8MB, time=281.56 memory used=71042.0MB, alloc=891.8MB, time=282.48 memory used=71356.8MB, alloc=891.8MB, time=283.41 memory used=71671.8MB, alloc=891.8MB, time=284.34 memory used=71987.7MB, alloc=891.8MB, time=285.27 memory used=72304.7MB, alloc=891.8MB, time=286.19 memory used=72621.5MB, alloc=891.8MB, time=287.13 memory used=72939.7MB, alloc=891.8MB, time=288.03 memory used=73258.6MB, alloc=891.8MB, time=288.96 memory used=73577.9MB, alloc=891.8MB, time=289.85 memory used=73898.8MB, alloc=891.8MB, time=290.82 memory used=74219.4MB, alloc=891.8MB, time=291.84 memory used=74541.4MB, alloc=891.8MB, time=292.83 memory used=74863.8MB, alloc=891.8MB, time=293.85 memory used=75186.7MB, alloc=891.8MB, time=294.80 memory used=75511.2MB, alloc=891.8MB, time=295.78 memory used=75835.1MB, alloc=891.8MB, time=296.74 memory used=76160.8MB, alloc=891.8MB, time=297.68 memory used=76487.1MB, alloc=891.8MB, time=298.61 memory used=76813.7MB, alloc=891.8MB, time=299.56 memory used=77141.7MB, alloc=891.8MB, time=300.52 memory used=77469.7MB, alloc=891.8MB, time=301.51 memory used=77799.0MB, alloc=891.8MB, time=302.43 memory used=78129.0MB, alloc=891.8MB, time=303.36 memory used=78457.7MB, alloc=891.8MB, time=304.27 memory used=78787.1MB, alloc=891.8MB, time=305.19 memory used=79117.2MB, alloc=891.8MB, time=306.12 memory used=79448.1MB, alloc=891.8MB, time=307.05 memory used=79779.6MB, alloc=891.8MB, time=307.97 memory used=80111.8MB, alloc=891.8MB, time=308.87 memory used=80444.8MB, alloc=891.8MB, time=309.91 memory used=80778.5MB, alloc=891.8MB, time=310.90 memory used=81112.8MB, alloc=891.8MB, time=311.93 memory used=81447.9MB, alloc=891.8MB, time=312.94 memory used=81784.1MB, alloc=891.8MB, time=313.91 memory used=82121.3MB, alloc=891.8MB, time=314.97 memory used=82459.3MB, alloc=891.8MB, time=316.09 memory used=82797.8MB, alloc=891.8MB, time=317.11 memory used=83136.9MB, alloc=891.8MB, time=318.11 memory used=83476.3MB, alloc=891.8MB, time=319.09 memory used=83816.6MB, alloc=891.8MB, time=320.07 memory used=84157.5MB, alloc=891.8MB, time=321.08 memory used=84499.2MB, alloc=891.8MB, time=322.05 memory used=84841.6MB, alloc=891.8MB, time=323.15 memory used=85184.7MB, alloc=891.8MB, time=324.15 memory used=85528.3MB, alloc=891.8MB, time=325.24 memory used=85873.0MB, alloc=891.8MB, time=326.23 memory used=86218.2MB, alloc=891.8MB, time=327.37 memory used=86564.3MB, alloc=891.8MB, time=328.36 memory used=86911.0MB, alloc=891.8MB, time=329.35 memory used=87258.2MB, alloc=891.8MB, time=330.34 memory used=87606.3MB, alloc=891.8MB, time=331.32 memory used=87955.3MB, alloc=891.8MB, time=332.29 memory used=88293.0MB, alloc=891.8MB, time=333.23 memory used=88585.5MB, alloc=891.8MB, time=334.15 memory used=88874.6MB, alloc=891.8MB, time=335.07 memory used=89164.3MB, alloc=891.8MB, time=335.97 memory used=89453.7MB, alloc=891.8MB, time=336.88 memory used=89743.8MB, alloc=891.8MB, time=337.78 memory used=90033.7MB, alloc=891.8MB, time=338.69 memory used=90324.1MB, alloc=891.8MB, time=339.62 memory used=90615.6MB, alloc=891.8MB, time=340.62 memory used=90907.0MB, alloc=891.8MB, time=341.63 memory used=91197.8MB, alloc=891.8MB, time=342.64 memory used=91489.3MB, alloc=891.8MB, time=343.60 memory used=91781.6MB, alloc=891.8MB, time=344.55 memory used=92074.2MB, alloc=891.8MB, time=345.49 memory used=92366.6MB, alloc=891.8MB, time=346.44 memory used=92660.1MB, alloc=891.8MB, time=347.42 memory used=92953.9MB, alloc=891.8MB, time=348.37 memory used=93248.1MB, alloc=891.8MB, time=349.32 memory used=93542.4MB, alloc=891.8MB, time=350.27 memory used=93837.1MB, alloc=891.8MB, time=351.25 memory used=94131.7MB, alloc=891.8MB, time=352.18 memory used=94427.4MB, alloc=891.8MB, time=353.13 memory used=94723.2MB, alloc=891.8MB, time=354.08 memory used=95019.5MB, alloc=891.8MB, time=355.02 memory used=95316.7MB, alloc=891.8MB, time=355.98 |\^/| 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(); 1428326037 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [14 x , -17 x y z - 12 x z, 7 y z - 17 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [0, 2 x y + 19 y z, -2 x y + 15 x z ] > Problem := [F,G]; 3 2 2 2 Problem := [[14 x , -17 x y z - 12 x z, 7 y z - 17 x y], 2 2 3 2 2 [0, 2 x y + 19 y z, -2 x y + 15 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.24 memory used=26.4MB, alloc=32.3MB, time=0.56 memory used=49.8MB, alloc=32.3MB, time=1.14 memory used=70.3MB, alloc=56.3MB, time=1.63 N1 := 723 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [x , x z, 7 y z - 17 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=110.6MB, alloc=60.3MB, time=2.30 N2 := 325 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 H := [14 x , -17 x y z - 12 x z, 7 y z - 17 x y, 0, 2 x y + 19 y z, 3 2 2 -2 x y + 15 x z ] > J:=[op(GB),op(G)]; 3 2 2 2 2 3 2 2 J := [x , x z, 7 y z - 17 x y, 0, 2 x y + 19 y z, -2 x y + 15 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 := [6, 13, -infinity, 4, 3, 2, 2, 5/6, 2/3, 2/3, 7/11, 6/11, 5/11, 6, 12, -infinity, 4, 3, 2, 2, 5/6, 1/2, 2/3, 6/11, 5/11, 4/11, 1, undefined, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=137.6MB, alloc=60.3MB, time=2.70 |\^/| 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(); 1428326040 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 2 2 F := [-17 x y + 3 y z, -3 y + 10 z , -5 y z + 4 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 G := [19 x z - 19 x z, -8 y z + 2 z , -10 x y + 18 x y] > Problem := [F,G]; 2 4 3 2 2 Problem := [[-17 x y + 3 y z, -3 y + 10 z , -5 y z + 4 x y z], 2 2 2 2 2 3 [19 x z - 19 x z, -8 y z + 2 z , -10 x y + 18 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=0.20 memory used=26.1MB, alloc=32.3MB, time=0.56 memory used=47.5MB, alloc=32.3MB, time=0.82 memory used=67.4MB, alloc=32.3MB, time=1.07 memory used=86.4MB, alloc=56.3MB, time=1.34 memory used=124.9MB, alloc=60.3MB, time=1.97 memory used=161.1MB, alloc=84.3MB, time=2.60 memory used=217.9MB, alloc=84.3MB, time=3.69 memory used=273.0MB, alloc=116.3MB, time=4.62 memory used=349.0MB, alloc=116.3MB, time=5.62 memory used=422.3MB, alloc=140.3MB, time=6.61 memory used=519.9MB, alloc=164.3MB, time=8.02 memory used=632.0MB, alloc=188.3MB, time=9.86 memory used=753.0MB, alloc=212.3MB, time=12.08 memory used=884.6MB, alloc=492.3MB, time=14.35 memory used=1027.4MB, alloc=516.3MB, time=16.86 memory used=1185.1MB, alloc=540.3MB, time=19.45 memory used=1347.4MB, alloc=564.3MB, time=22.27 memory used=1514.6MB, alloc=588.3MB, time=25.08 memory used=1688.5MB, alloc=612.3MB, time=28.22 memory used=1861.6MB, alloc=636.3MB, time=32.97 memory used=2023.2MB, alloc=660.3MB, time=38.32 memory used=2194.6MB, alloc=684.3MB, time=44.35 memory used=2378.5MB, alloc=708.3MB, time=50.72 memory used=2576.3MB, alloc=732.3MB, time=58.18 memory used=2788.7MB, alloc=756.3MB, time=66.17 memory used=3015.4MB, alloc=780.3MB, time=74.85 memory used=3257.4MB, alloc=804.3MB, time=84.59 memory used=3514.9MB, alloc=828.3MB, time=94.88 memory used=3788.3MB, alloc=852.3MB, time=107.07 memory used=4076.9MB, alloc=876.3MB, time=120.01 memory used=4378.4MB, alloc=900.3MB, time=132.90 memory used=4703.7MB, alloc=924.3MB, time=146.94 memory used=5053.0MB, alloc=948.3MB, time=162.91 memory used=5426.3MB, alloc=972.3MB, time=180.28 memory used=5823.5MB, alloc=996.3MB, time=198.14 memory used=6244.6MB, alloc=1020.3MB, time=216.67 memory used=6689.8MB, alloc=1044.3MB, time=236.86 memory used=7158.8MB, alloc=1068.3MB, time=258.37 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428326340 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [6 x y + 3 x, 5 y + 3 x, 2 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 G := [-4 x z + 11 x y , 19 x y z - 7 x , -8 x + 4 y z ] > Problem := [F,G]; 2 2 2 Problem := [[6 x y + 3 x, 5 y + 3 x, 2 z], 2 2 2 3 3 2 [-4 x z + 11 x y , 19 x y z - 7 x , -8 x + 4 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=26.3MB, alloc=32.3MB, time=0.57 memory used=48.0MB, alloc=32.3MB, time=0.93 memory used=68.8MB, alloc=56.3MB, time=1.29 memory used=112.4MB, alloc=60.3MB, time=2.10 memory used=152.5MB, alloc=84.3MB, time=3.09 memory used=212.4MB, alloc=84.3MB, time=4.44 memory used=268.3MB, alloc=108.3MB, time=5.73 memory used=340.8MB, alloc=140.3MB, time=7.87 memory used=420.9MB, alloc=164.3MB, time=11.42 memory used=525.0MB, alloc=164.3MB, time=15.63 N1 := 2663 > GB := Basis(F, plex(op(vars))); 3 2 GB := [6 x - 5 x, 5 y + 3 x, z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=627.6MB, alloc=164.3MB, time=17.44 memory used=746.3MB, alloc=444.3MB, time=20.58 N2 := 1491 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 3 H := [6 x y + 3 x, 5 y + 3 x, 2 z, -4 x z + 11 x y , 19 x y z - 7 x , 3 2 -8 x + 4 y z ] > J:=[op(GB),op(G)]; 3 2 2 2 2 3 J := [6 x - 5 x, 5 y + 3 x, z, -4 x z + 11 x y , 19 x y z - 7 x , 3 2 -8 x + 4 y z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 17, 4, 3, 2, 2, 5/6, 5/6, 2/3, 2/3, 5/12, 1/3, 6, 13, 16, 4, 3, 2, 2, 5/6, 2/3, 2/3, 8/11, 4/11, 4/11, 1, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=775.3MB, alloc=444.3MB, time=21.64 |\^/| 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(); 1428326365 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [2 x z - 8 y , -18 y z + 11 y z, 12 x y - x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 2 G := [9 x - 13 y , -20 x z - 15 y , 3 x z - z ] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[2 x z - 8 y , -18 y z + 11 y z, 12 x y - x], 4 2 2 2 3 2 [9 x - 13 y , -20 x z - 15 y , 3 x z - z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.9MB, alloc=40.3MB, time=0.55 memory used=59.6MB, alloc=40.3MB, time=0.96 memory used=86.6MB, alloc=40.3MB, time=1.33 memory used=111.6MB, alloc=64.3MB, time=1.70 memory used=157.0MB, alloc=68.3MB, time=2.35 memory used=202.2MB, alloc=92.3MB, time=3.13 memory used=264.1MB, alloc=92.3MB, time=4.15 memory used=321.1MB, alloc=116.3MB, time=5.11 memory used=396.2MB, alloc=148.3MB, time=6.39 memory used=488.2MB, alloc=172.3MB, time=7.98 memory used=593.0MB, alloc=196.3MB, time=10.36 memory used=703.3MB, alloc=220.3MB, time=13.16 memory used=821.8MB, alloc=244.3MB, time=17.12 memory used=962.3MB, alloc=268.3MB, time=22.08 memory used=1126.8MB, alloc=268.3MB, time=27.79 memory used=1291.2MB, alloc=268.3MB, time=33.50 memory used=1455.5MB, alloc=292.3MB, time=39.16 memory used=1643.7MB, alloc=292.3MB, time=45.53 N1 := 6397 > GB := Basis(F, plex(op(vars))); 3 2 GB := [121 x - 108 x, 1296 y - 121 x, 18 x z - 11 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1834.1MB, alloc=292.3MB, time=51.21 N2 := 1251 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 4 2 H := [2 x z - 8 y , -18 y z + 11 y z, 12 x y - x, 9 x - 13 y , 2 2 3 2 -20 x z - 15 y , 3 x z - z ] > J:=[op(GB),op(G)]; 3 2 4 2 J := [121 x - 108 x, 1296 y - 121 x, 18 x z - 11 x, 9 x - 13 y , 2 2 3 2 -20 x z - 15 y , 3 x z - z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 22, 4, 4, 2, 3, 5/6, 5/6, 2/3, 1/2, 1/2, 1/2, 6, 12, 18, 4, 4, 2, 3, 1, 1/2, 1/2, 2/3, 1/4, 1/3, 2, 4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1986.1MB, alloc=292.3MB, time=54.49 |\^/| 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(); 1428326423 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 F := [-3 x y z + 2 x, -14 y z - 9 y , -20 x y z - 3 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [-6 x y - 12 y z, -15 z + 5 x, -12 x z - 12 x y z] > Problem := [F,G]; 2 3 3 2 Problem := [[-3 x y z + 2 x, -14 y z - 9 y , -20 x y z - 3 z ], 2 2 3 2 [-6 x y - 12 y z, -15 z + 5 x, -12 x z - 12 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.19 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=47.6MB, alloc=32.3MB, time=0.85 memory used=67.4MB, alloc=56.3MB, time=1.22 memory used=107.2MB, alloc=60.3MB, time=1.80 memory used=144.8MB, alloc=60.3MB, time=2.31 memory used=179.6MB, alloc=84.3MB, time=2.85 memory used=232.5MB, alloc=84.3MB, time=3.53 memory used=289.3MB, alloc=116.3MB, time=4.38 memory used=367.1MB, alloc=116.3MB, time=5.35 memory used=442.5MB, alloc=140.3MB, time=6.34 memory used=533.0MB, alloc=396.3MB, time=7.51 memory used=626.9MB, alloc=420.3MB, time=9.18 memory used=739.3MB, alloc=444.3MB, time=11.01 memory used=869.2MB, alloc=468.3MB, time=12.80 memory used=1009.9MB, alloc=492.3MB, time=14.80 memory used=1159.6MB, alloc=516.3MB, time=17.23 memory used=1315.3MB, alloc=540.3MB, time=20.01 memory used=1463.4MB, alloc=564.3MB, time=23.99 memory used=1619.3MB, alloc=588.3MB, time=28.53 memory used=1787.5MB, alloc=612.3MB, time=33.71 memory used=1963.2MB, alloc=636.3MB, time=40.58 memory used=2162.2MB, alloc=660.3MB, time=47.66 memory used=2385.2MB, alloc=684.3MB, time=55.86 memory used=2632.1MB, alloc=708.3MB, time=65.51 memory used=2902.9MB, alloc=732.3MB, time=76.66 memory used=3197.7MB, alloc=732.3MB, time=87.47 memory used=3492.4MB, alloc=756.3MB, time=97.62 memory used=3811.2MB, alloc=756.3MB, time=108.21 memory used=4129.8MB, alloc=756.3MB, time=118.70 memory used=4448.4MB, alloc=780.3MB, time=128.92 memory used=4790.7MB, alloc=780.3MB, time=139.70 memory used=5133.0MB, alloc=804.3MB, time=150.28 memory used=5499.2MB, alloc=828.3MB, time=161.37 N1 := 11921 > GB := Basis(F, plex(op(vars))); 3 2 3 GB := [2195200 x + 19683 x, 7840 x + 729 x y, 19683 y - 219520 x, 2 2 14 x z + 9 x, 11200 x + 243 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5762.0MB, alloc=828.3MB, time=166.22 N2 := 1849 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 2 2 2 H := [-3 x y z + 2 x, -14 y z - 9 y , -20 x y z - 3 z , -6 x y - 12 y z, 3 2 -15 z + 5 x, -12 x z - 12 x y z] > J:=[op(GB),op(G)]; 3 2 3 J := [2195200 x + 19683 x, 7840 x + 729 x y, 19683 y - 219520 x, 2 2 2 2 3 14 x z + 9 x, 243 z + 11200 x , -6 x y - 12 y z, -15 z + 5 x, 2 -12 x z - 12 x 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 := [6, 16, 20, 4, 2, 3, 3, 5/6, 5/6, 1, 7/12, 7/12, 2/3, 8, 17, 21, 3, 3, 3, 3, 1, 1/2, 5/8, 3/4, 5/16, 3/8, -1, -1, 1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=5991.5MB, alloc=828.3MB, time=170.69 |\^/| 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(); 1428326605 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 F := [2 x y z - 5 x , -15 y z + 7 x y z, -10 x y z + 16 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 G := [-5 x + 15 x y, 14 x z + 7 x y, 6 x z + 9 x y ] > Problem := [F,G]; 2 3 2 2 2 2 Problem := [[2 x y z - 5 x , -15 y z + 7 x y z, -10 x y z + 16 x y z], 4 2 2 2 2 2 [-5 x + 15 x y, 14 x z + 7 x y, 6 x z + 9 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=48.0MB, alloc=32.3MB, time=0.73 memory used=68.2MB, alloc=32.3MB, time=0.95 memory used=88.0MB, alloc=56.3MB, time=1.19 memory used=128.2MB, alloc=60.3MB, time=1.63 memory used=167.6MB, alloc=84.3MB, time=2.10 memory used=215.3MB, alloc=84.3MB, time=2.68 memory used=273.4MB, alloc=92.3MB, time=3.35 memory used=330.4MB, alloc=116.3MB, time=4.08 memory used=411.6MB, alloc=140.3MB, time=5.14 memory used=506.7MB, alloc=164.3MB, time=6.46 memory used=610.1MB, alloc=188.3MB, time=7.98 memory used=722.8MB, alloc=468.3MB, time=9.55 memory used=865.7MB, alloc=492.3MB, time=11.55 memory used=1019.4MB, alloc=516.3MB, time=14.02 memory used=1172.5MB, alloc=540.3MB, time=17.88 memory used=1332.2MB, alloc=564.3MB, time=22.35 memory used=1498.9MB, alloc=588.3MB, time=27.73 memory used=1689.6MB, alloc=612.3MB, time=33.93 memory used=1904.2MB, alloc=636.3MB, time=40.69 memory used=2142.8MB, alloc=636.3MB, time=48.20 memory used=2381.3MB, alloc=660.3MB, time=55.70 memory used=2643.9MB, alloc=660.3MB, time=64.05 memory used=2906.3MB, alloc=684.3MB, time=72.19 memory used=3192.9MB, alloc=684.3MB, time=80.82 N1 := 8699 > GB := Basis(F, plex(op(vars))); 5 4 4 3 4 4 4 2 GB := [5625 x - 784 x , -5 x + 8 x y, 75 x z - 56 x , -375 x + 112 x y z, 4 2 2 3 2 2 -1875 x + 896 x y z, 2 x y z - 5 x , 15 y z - 7 x y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3487.2MB, alloc=684.3MB, time=86.62 memory used=3814.5MB, alloc=708.3MB, time=90.96 memory used=4125.2MB, alloc=732.3MB, time=94.94 memory used=4379.3MB, alloc=756.3MB, time=98.21 memory used=4627.9MB, alloc=780.3MB, time=101.62 memory used=4854.4MB, alloc=804.3MB, time=104.96 memory used=5031.3MB, alloc=828.3MB, time=107.55 memory used=5231.4MB, alloc=852.3MB, time=110.66 memory used=5412.4MB, alloc=876.3MB, time=113.64 memory used=5573.1MB, alloc=876.3MB, time=116.43 memory used=5721.3MB, alloc=900.3MB, time=118.98 memory used=5890.5MB, alloc=900.3MB, time=122.11 memory used=6396.0MB, alloc=924.3MB, time=129.65 memory used=6885.8MB, alloc=948.3MB, time=138.25 memory used=7295.2MB, alloc=972.3MB, time=144.71 memory used=7672.4MB, alloc=996.3MB, time=150.68 memory used=8013.1MB, alloc=1020.3MB, time=155.94 memory used=8607.0MB, alloc=1044.3MB, time=164.55 memory used=9212.2MB, alloc=1068.3MB, time=173.52 memory used=9827.1MB, alloc=1092.3MB, time=182.46 memory used=10444.8MB, alloc=1116.3MB, time=192.46 memory used=11067.0MB, alloc=1140.3MB, time=203.81 memory used=11689.5MB, alloc=1164.3MB, time=214.19 memory used=12312.4MB, alloc=1188.3MB, time=224.44 memory used=12958.2MB, alloc=1212.3MB, time=236.14 memory used=13602.5MB, alloc=1236.3MB, time=249.50 memory used=14226.1MB, alloc=1260.3MB, time=263.96 memory used=14776.3MB, alloc=1284.3MB, time=276.39 memory used=15397.1MB, alloc=1308.3MB, time=288.77 |\^/| 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(); 1428326905 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [-x + x z, 5 x y + 5 x z, -3 x y + 20 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 G := [-3 y z - 6 x, 15 x y z - 13 x z, 7 x y z - 14 y ] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[-x + x z, 5 x y + 5 x z, -3 x y + 20 x], 2 2 2 2 2 3 [-3 y z - 6 x, 15 x y z - 13 x z, 7 x 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=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=47.6MB, alloc=32.3MB, time=0.82 memory used=67.8MB, alloc=32.3MB, time=1.13 memory used=87.2MB, alloc=56.3MB, time=1.43 memory used=126.8MB, alloc=60.3MB, time=2.02 memory used=162.6MB, alloc=84.3MB, time=2.57 memory used=216.0MB, alloc=84.3MB, time=3.34 memory used=273.1MB, alloc=116.3MB, time=4.22 memory used=351.8MB, alloc=116.3MB, time=5.41 memory used=429.0MB, alloc=140.3MB, time=6.31 memory used=525.6MB, alloc=140.3MB, time=7.52 memory used=615.1MB, alloc=164.3MB, time=8.64 memory used=702.9MB, alloc=420.3MB, time=9.69 memory used=817.7MB, alloc=444.3MB, time=11.33 memory used=942.6MB, alloc=468.3MB, time=13.23 memory used=1079.6MB, alloc=492.3MB, time=15.25 memory used=1227.9MB, alloc=516.3MB, time=17.47 memory used=1386.3MB, alloc=540.3MB, time=19.82 memory used=1551.0MB, alloc=564.3MB, time=22.52 memory used=1713.4MB, alloc=588.3MB, time=26.44 memory used=1879.6MB, alloc=612.3MB, time=31.00 memory used=2055.4MB, alloc=636.3MB, time=36.26 memory used=2243.0MB, alloc=660.3MB, time=42.14 memory used=2440.7MB, alloc=684.3MB, time=48.83 memory used=2661.0MB, alloc=708.3MB, time=56.38 memory used=2905.3MB, alloc=732.3MB, time=64.57 memory used=3173.5MB, alloc=756.3MB, time=73.60 memory used=3465.6MB, alloc=780.3MB, time=83.39 memory used=3781.8MB, alloc=804.3MB, time=93.97 memory used=4121.8MB, alloc=804.3MB, time=105.39 memory used=4461.7MB, alloc=804.3MB, time=116.99 memory used=4801.7MB, alloc=828.3MB, time=128.31 memory used=5165.6MB, alloc=828.3MB, time=140.68 memory used=5529.4MB, alloc=828.3MB, time=152.97 memory used=5893.0MB, alloc=852.3MB, time=165.10 memory used=6280.5MB, alloc=852.3MB, time=177.97 memory used=6668.1MB, alloc=876.3MB, time=190.97 memory used=7079.6MB, alloc=876.3MB, time=204.94 memory used=7491.0MB, alloc=900.3MB, time=218.66 N1 := 14487 > GB := Basis(F, plex(op(vars))); 4 3 2 3 GB := [3 x + 20 x, x + x y , -x + x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7933.7MB, alloc=900.3MB, time=231.75 memory used=8464.0MB, alloc=900.3MB, time=244.46 N2 := 3455 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 2 2 H := [-x + x z, 5 x y + 5 x z, -3 x y + 20 x, -3 y z - 6 x, 2 2 2 3 15 x y z - 13 x z, 7 x y z - 14 y ] > J:=[op(GB),op(G)]; 4 3 2 3 2 2 2 2 J := [3 x + 20 x, x + x y , -x + x z, -3 y z - 6 x, 15 x y z - 13 x z, 2 3 7 x y z - 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 := [6, 16, 23, 4, 3, 3, 2, 1, 5/6, 5/6, 5/6, 1/2, 1/2, 6, 14, 22, 4, 4, 3, 2, 1, 2/3, 2/3, 5/6, 5/12, 5/12, 2, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=8620.9MB, alloc=900.3MB, time=249.16 |\^/| 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(); 1428327171 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [17 x y + 5 x , 11 x y z + 14 y z, 6 x y - 13 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 G := [14 x + 16 x y , y z - 16 z, 20 x y z - 18] > Problem := [F,G]; 3 3 2 Problem := [[17 x y + 5 x , 11 x y z + 14 y z, 6 x y - 13 x z], 4 3 3 2 [14 x + 16 x y , y z - 16 z, 20 x 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.41 memory used=47.4MB, alloc=32.3MB, time=0.65 memory used=67.4MB, alloc=32.3MB, time=0.86 memory used=85.9MB, alloc=56.3MB, time=1.09 memory used=125.9MB, alloc=60.3MB, time=1.52 memory used=164.1MB, alloc=60.3MB, time=1.94 memory used=200.3MB, alloc=84.3MB, time=2.37 memory used=260.5MB, alloc=92.3MB, time=3.19 memory used=314.6MB, alloc=116.3MB, time=3.97 memory used=387.6MB, alloc=140.3MB, time=5.08 memory used=478.4MB, alloc=164.3MB, time=6.42 memory used=584.1MB, alloc=188.3MB, time=8.07 memory used=696.5MB, alloc=212.3MB, time=10.66 memory used=815.1MB, alloc=236.3MB, time=14.39 memory used=956.5MB, alloc=236.3MB, time=18.74 memory used=1097.8MB, alloc=260.3MB, time=23.17 memory used=1263.1MB, alloc=260.3MB, time=28.31 memory used=1428.7MB, alloc=284.3MB, time=32.91 N1 := 5229 > GB := Basis(F, plex(op(vars))); 8 3 7 3 4 2 GB := [179685 x - 12810707 x , 5445 x + 140777 x y, -165 x + 1547 x y , 3 -6 x y + 13 x z, -990 x + 20111 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1521.3MB, alloc=284.3MB, time=34.31 memory used=1729.8MB, alloc=540.3MB, time=36.82 memory used=1940.4MB, alloc=564.3MB, time=39.92 memory used=2163.3MB, alloc=588.3MB, time=44.19 memory used=2364.2MB, alloc=612.3MB, time=50.78 memory used=2581.4MB, alloc=636.3MB, time=58.22 memory used=2822.9MB, alloc=660.3MB, time=66.20 N2 := 5021 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 4 3 H := [17 x y + 5 x , 11 x y z + 14 y z, 6 x y - 13 x z, 14 x + 16 x y , 3 2 y z - 16 z, 20 x y z - 18] > J:=[op(GB),op(G)]; 8 3 7 3 4 2 J := [179685 x - 12810707 x , 5445 x + 140777 x y, -165 x + 1547 x y , 3 4 3 3 -6 x y + 13 x z, -990 x + 20111 y z, 14 x + 16 x y , y z - 16 z, 2 20 x y z - 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, 15, 22, 4, 4, 3, 3, 5/6, 1, 2/3, 2/3, 7/12, 1/2, 8, 18, 36, 8, 8, 3, 3, 7/8, 7/8, 1/2, 3/4, 7/16, 5/16, -3, -14, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2885.4MB, alloc=660.3MB, time=67.98 |\^/| 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(); 1428327244 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 F := [6 x y z + 6 x z, 7 y z - 4 x z, 10 x y z + 19 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 G := [-12 x z + 20 z , 8 x y + 11 x z , 19 y - 2] > Problem := [F,G]; 2 2 3 2 3 Problem := [[6 x y z + 6 x z, 7 y z - 4 x z, 10 x y z + 19 x y ], 2 2 3 3 2 [-12 x z + 20 z , 8 x y + 11 x z , 19 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=0.15 memory used=26.2MB, alloc=32.3MB, time=0.41 memory used=47.7MB, alloc=32.3MB, time=0.68 memory used=67.9MB, alloc=32.3MB, time=0.90 memory used=87.5MB, alloc=56.3MB, time=1.16 memory used=127.4MB, alloc=60.3MB, time=1.60 memory used=166.7MB, alloc=60.3MB, time=2.06 memory used=205.5MB, alloc=84.3MB, time=2.49 memory used=264.5MB, alloc=92.3MB, time=3.17 memory used=322.4MB, alloc=116.3MB, time=3.85 memory used=399.3MB, alloc=116.3MB, time=4.76 memory used=475.9MB, alloc=140.3MB, time=5.76 memory used=579.0MB, alloc=164.3MB, time=7.13 memory used=691.2MB, alloc=188.3MB, time=8.72 memory used=809.5MB, alloc=468.3MB, time=10.42 memory used=951.3MB, alloc=492.3MB, time=12.55 memory used=1106.1MB, alloc=516.3MB, time=14.85 memory used=1271.5MB, alloc=540.3MB, time=17.33 memory used=1446.4MB, alloc=564.3MB, time=20.80 memory used=1608.4MB, alloc=588.3MB, time=25.11 memory used=1780.1MB, alloc=612.3MB, time=30.10 memory used=1965.0MB, alloc=636.3MB, time=35.63 memory used=2161.8MB, alloc=660.3MB, time=42.07 memory used=2376.1MB, alloc=684.3MB, time=49.31 memory used=2614.4MB, alloc=708.3MB, time=57.36 memory used=2876.5MB, alloc=732.3MB, time=66.03 memory used=3162.7MB, alloc=756.3MB, time=75.96 memory used=3472.8MB, alloc=756.3MB, time=88.28 memory used=3782.8MB, alloc=756.3MB, time=98.50 memory used=4092.8MB, alloc=780.3MB, time=108.63 memory used=4426.7MB, alloc=780.3MB, time=119.55 memory used=4760.6MB, alloc=780.3MB, time=130.33 memory used=5094.4MB, alloc=804.3MB, time=141.11 memory used=5452.0MB, alloc=804.3MB, time=152.80 memory used=5809.4MB, alloc=828.3MB, time=164.41 memory used=6190.7MB, alloc=828.3MB, time=176.51 memory used=6572.0MB, alloc=852.3MB, time=188.46 N1 := 13395 > GB := Basis(F, plex(op(vars))); 4 3 3 4 3 3 2 GB := [400 x y + 2527 x y , x y + x y , -19 x y + 10 x z, 3 3 3 3 -40 x y + 133 x y z, 7 y z - 4 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6985.3MB, alloc=852.3MB, time=198.07 memory used=7127.3MB, alloc=852.3MB, time=200.51 memory used=7249.3MB, alloc=852.3MB, time=202.62 memory used=7361.4MB, alloc=852.3MB, time=204.70 memory used=7474.0MB, alloc=852.3MB, time=206.60 memory used=7578.8MB, alloc=852.3MB, time=208.39 memory used=7675.9MB, alloc=852.3MB, time=210.17 memory used=7790.5MB, alloc=852.3MB, time=212.70 memory used=7891.0MB, alloc=852.3MB, time=214.84 memory used=8001.2MB, alloc=852.3MB, time=217.21 memory used=8065.8MB, alloc=852.3MB, time=218.86 memory used=8152.5MB, alloc=852.3MB, time=220.61 memory used=8225.5MB, alloc=852.3MB, time=222.27 memory used=8295.1MB, alloc=852.3MB, time=223.89 memory used=8352.9MB, alloc=852.3MB, time=225.25 memory used=8393.5MB, alloc=852.3MB, time=226.66 memory used=8454.6MB, alloc=852.3MB, time=228.52 memory used=8722.3MB, alloc=876.3MB, time=232.80 memory used=8983.8MB, alloc=900.3MB, time=237.07 memory used=9404.8MB, alloc=924.3MB, time=243.45 memory used=9768.2MB, alloc=948.3MB, time=249.76 memory used=10210.7MB, alloc=972.3MB, time=257.84 memory used=10677.8MB, alloc=996.3MB, time=265.35 memory used=11119.9MB, alloc=1020.3MB, time=272.93 memory used=11563.3MB, alloc=1044.3MB, time=280.53 |\^/| 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(); 1428327544 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 F := [9 x y z + 13 x z, 16 x z + 7 y z , 15 y - 9 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 G := [3 y z + 4, 3 x y + 3 z, x - 12 x] > Problem := [F,G]; 2 2 3 3 3 Problem := [[9 x y z + 13 x z, 16 x z + 7 y z , 15 y - 9 y], 3 3 [3 y z + 4, 3 x y + 3 z, x - 12 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=48.0MB, alloc=32.3MB, time=0.77 memory used=68.3MB, alloc=32.3MB, time=1.06 memory used=87.8MB, alloc=56.3MB, time=1.34 memory used=131.3MB, alloc=60.3MB, time=2.11 memory used=170.0MB, alloc=84.3MB, time=2.79 memory used=229.0MB, alloc=84.3MB, time=3.83 memory used=283.6MB, alloc=108.3MB, time=4.81 memory used=354.1MB, alloc=140.3MB, time=6.42 memory used=434.4MB, alloc=164.3MB, time=9.13 memory used=532.2MB, alloc=164.3MB, time=12.02 memory used=630.1MB, alloc=188.3MB, time=14.73 N1 := 3355 > GB := Basis(F, plex(op(vars))); 3 2 3 GB := [5 y - 3 y, x z, z y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 485 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 3 3 H := [9 x y z + 13 x z, 16 x z + 7 y z , 15 y - 9 y, 3 z y + 4, 3 3 x y + 3 z, x - 12 x] > J:=[op(GB),op(G)]; 3 2 3 3 3 J := [5 y - 3 y, x z, z y, 3 z y + 4, 3 x y + 3 z, x - 12 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, 20, 4, 3, 3, 3, 2/3, 5/6, 2/3, 1/2, 1/2, 1/2, 6, 11, 19, 4, 3, 3, 3, 1/2, 2/3, 2/3, 1/3, 5/12, 1/3, 2, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=749.2MB, alloc=188.3MB, time=16.90 |\^/| 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(); 1428327562 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 F := [13 x y z - 7 x , 6 y z - 7 z, -y z + 6 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 4 G := [-14 x z + 17 x z , 2 x y z - 8 z , -5 y - 20 x y] > Problem := [F,G]; 2 2 3 3 Problem := [[13 x y z - 7 x , 6 y z - 7 z, -y z + 6 x y], 2 2 2 2 4 [-14 x z + 17 x z , 2 x y z - 8 z , -5 y - 20 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=26.1MB, alloc=32.3MB, time=0.42 memory used=47.5MB, alloc=32.3MB, time=0.67 memory used=67.8MB, alloc=32.3MB, time=0.91 memory used=86.6MB, alloc=56.3MB, time=1.15 memory used=125.7MB, alloc=60.3MB, time=1.58 memory used=164.5MB, alloc=60.3MB, time=2.01 memory used=200.7MB, alloc=84.3MB, time=2.50 memory used=258.2MB, alloc=92.3MB, time=3.18 memory used=316.5MB, alloc=116.3MB, time=4.02 memory used=391.8MB, alloc=140.3MB, time=5.07 memory used=485.1MB, alloc=164.3MB, time=6.39 memory used=594.8MB, alloc=188.3MB, time=7.91 memory used=717.7MB, alloc=468.3MB, time=9.65 memory used=851.6MB, alloc=492.3MB, time=12.06 memory used=982.3MB, alloc=516.3MB, time=15.30 memory used=1124.5MB, alloc=540.3MB, time=19.06 memory used=1275.5MB, alloc=564.3MB, time=23.68 memory used=1450.6MB, alloc=588.3MB, time=29.05 memory used=1649.5MB, alloc=612.3MB, time=35.26 memory used=1872.5MB, alloc=612.3MB, time=42.15 memory used=2095.4MB, alloc=612.3MB, time=48.95 memory used=2318.3MB, alloc=636.3MB, time=55.66 memory used=2565.1MB, alloc=636.3MB, time=63.16 memory used=2811.7MB, alloc=660.3MB, time=70.46 memory used=3082.5MB, alloc=684.3MB, time=77.84 N1 := 8609 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 4 2 2 GB := [49 x - 13182 x , 6 x y - 7 x , 6 x y - 7 x y, -78 x y + 7 x z, 3 2 2 2 3 3 6 y z - 7 z, -6 x y + 13 x z , -36 x y + 7 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3364.6MB, alloc=684.3MB, time=81.76 memory used=3687.1MB, alloc=684.3MB, time=86.32 memory used=4010.3MB, alloc=708.3MB, time=91.40 memory used=4332.9MB, alloc=732.3MB, time=96.53 memory used=4650.7MB, alloc=756.3MB, time=103.95 memory used=4932.9MB, alloc=780.3MB, time=112.31 memory used=5214.9MB, alloc=804.3MB, time=121.39 memory used=5499.2MB, alloc=828.3MB, time=131.68 memory used=5807.4MB, alloc=852.3MB, time=142.69 memory used=6139.5MB, alloc=876.3MB, time=154.47 memory used=6495.5MB, alloc=900.3MB, time=166.85 memory used=6875.6MB, alloc=924.3MB, time=180.12 memory used=7279.4MB, alloc=948.3MB, time=194.10 memory used=7707.3MB, alloc=972.3MB, time=208.92 memory used=8159.0MB, alloc=996.3MB, time=224.64 memory used=8634.8MB, alloc=1020.3MB, time=241.22 memory used=9134.4MB, alloc=1044.3MB, time=258.56 memory used=9657.8MB, alloc=1068.3MB, time=276.54 |\^/| 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(); 1428327862 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 F := [9 y z + 17 x , 19 x z - 17 x z, 4 y - 8 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 3 G := [-7 x y - 4 x , -x z + 3 y , -8 x y z + 6 z ] > Problem := [F,G]; 3 3 2 2 2 2 Problem := [[9 y z + 17 x , 19 x z - 17 x z, 4 y - 8 z ], 3 2 2 2 2 2 3 [-7 x y - 4 x , -x z + 3 y , -8 x y z + 6 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=27.0MB, alloc=32.3MB, time=0.49 memory used=48.5MB, alloc=32.3MB, time=0.79 memory used=68.8MB, alloc=32.3MB, time=1.09 memory used=88.1MB, alloc=56.3MB, time=1.36 memory used=127.5MB, alloc=60.3MB, time=1.96 memory used=165.3MB, alloc=84.3MB, time=2.53 memory used=218.8MB, alloc=84.3MB, time=3.38 memory used=278.2MB, alloc=116.3MB, time=4.29 memory used=359.6MB, alloc=116.3MB, time=5.50 memory used=437.2MB, alloc=140.3MB, time=6.70 memory used=516.5MB, alloc=396.3MB, time=7.89 memory used=614.2MB, alloc=420.3MB, time=9.39 memory used=736.3MB, alloc=444.3MB, time=11.25 memory used=878.0MB, alloc=468.3MB, time=13.48 memory used=1025.7MB, alloc=492.3MB, time=15.68 memory used=1188.1MB, alloc=516.3MB, time=18.43 memory used=1373.1MB, alloc=540.3MB, time=21.70 memory used=1568.1MB, alloc=564.3MB, time=24.73 memory used=1761.7MB, alloc=588.3MB, time=27.74 memory used=1957.5MB, alloc=612.3MB, time=30.83 memory used=2138.2MB, alloc=636.3MB, time=33.76 memory used=2319.9MB, alloc=660.3MB, time=36.75 memory used=2476.0MB, alloc=684.3MB, time=39.28 memory used=2655.5MB, alloc=708.3MB, time=42.08 memory used=2803.4MB, alloc=732.3MB, time=44.65 memory used=2953.3MB, alloc=756.3MB, time=47.26 memory used=3115.1MB, alloc=780.3MB, time=50.24 memory used=3263.0MB, alloc=804.3MB, time=52.87 memory used=3408.9MB, alloc=828.3MB, time=55.63 memory used=3728.5MB, alloc=852.3MB, time=61.36 memory used=4013.5MB, alloc=876.3MB, time=69.16 memory used=4291.5MB, alloc=900.3MB, time=77.53 memory used=4574.4MB, alloc=924.3MB, time=86.45 memory used=4864.3MB, alloc=948.3MB, time=95.93 memory used=5163.8MB, alloc=972.3MB, time=105.76 memory used=5474.6MB, alloc=996.3MB, time=116.07 memory used=5797.6MB, alloc=1020.3MB, time=127.12 memory used=6133.6MB, alloc=1044.3MB, time=138.82 memory used=6481.9MB, alloc=1068.3MB, time=150.81 memory used=6843.8MB, alloc=1092.3MB, time=163.50 memory used=7219.6MB, alloc=1116.3MB, time=176.62 memory used=7609.1MB, alloc=1140.3MB, time=190.49 memory used=8007.0MB, alloc=1164.3MB, time=205.08 memory used=8423.9MB, alloc=1188.3MB, time=220.40 memory used=8864.7MB, alloc=1212.3MB, time=236.92 memory used=9329.5MB, alloc=1236.3MB, time=254.17 memory used=9818.2MB, alloc=1260.3MB, time=272.34 |\^/| 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(); 1428328162 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-9 x z - 3 x y , -3 x - 11 y z , -11 - 6 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 G := [-7 x z + 15 x z, 13 x y z - 18, 13 z + 12 x y z] > Problem := [F,G]; 2 2 3 2 Problem := [[-9 x z - 3 x y , -3 x - 11 y z , -11 - 6 x], 3 2 4 [-7 x z + 15 x z, 13 x y z - 18, 13 z + 12 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.49 memory used=48.0MB, alloc=32.3MB, time=0.77 memory used=68.0MB, alloc=56.3MB, time=1.05 memory used=109.4MB, alloc=60.3MB, time=1.63 memory used=149.8MB, alloc=84.3MB, time=2.18 memory used=214.8MB, alloc=92.3MB, time=3.08 memory used=279.7MB, alloc=116.3MB, time=3.94 memory used=354.4MB, alloc=116.3MB, time=4.95 memory used=419.2MB, alloc=396.3MB, time=5.81 memory used=523.5MB, alloc=420.3MB, time=7.30 memory used=651.2MB, alloc=444.3MB, time=9.10 memory used=778.8MB, alloc=468.3MB, time=10.88 memory used=898.9MB, alloc=492.3MB, time=12.32 memory used=1018.5MB, alloc=492.3MB, time=13.89 memory used=1174.5MB, alloc=516.3MB, time=16.24 memory used=1352.2MB, alloc=540.3MB, time=18.93 memory used=1484.9MB, alloc=564.3MB, time=20.99 memory used=1638.9MB, alloc=588.3MB, time=23.46 memory used=1796.3MB, alloc=612.3MB, time=26.01 memory used=1949.3MB, alloc=636.3MB, time=28.60 memory used=2136.8MB, alloc=660.3MB, time=33.20 memory used=2357.1MB, alloc=684.3MB, time=39.66 memory used=2581.9MB, alloc=708.3MB, time=46.63 memory used=2812.2MB, alloc=732.3MB, time=54.36 memory used=3053.2MB, alloc=756.3MB, time=62.94 memory used=3318.1MB, alloc=780.3MB, time=72.36 memory used=3607.0MB, alloc=804.3MB, time=82.58 memory used=3919.8MB, alloc=828.3MB, time=93.56 memory used=4256.5MB, alloc=852.3MB, time=105.34 memory used=4617.2MB, alloc=876.3MB, time=117.85 memory used=5001.7MB, alloc=876.3MB, time=131.22 memory used=5386.3MB, alloc=876.3MB, time=144.46 memory used=5770.8MB, alloc=900.3MB, time=157.78 memory used=6179.2MB, alloc=900.3MB, time=171.80 memory used=6587.7MB, alloc=900.3MB, time=185.83 memory used=6996.0MB, alloc=924.3MB, time=199.87 memory used=7428.4MB, alloc=924.3MB, time=214.68 memory used=7860.7MB, alloc=948.3MB, time=229.28 memory used=8317.0MB, alloc=972.3MB, time=244.80 memory used=8797.4MB, alloc=996.3MB, time=261.28 N1 := 15389 > GB := Basis(F, plex(op(vars))); 5 2 GB := [6 x + 11, 288 y - 14641, -2 y + 11 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=9097.7MB, alloc=996.3MB, time=269.82 memory used=9484.3MB, alloc=996.3MB, time=276.22 |\^/| 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(); 1428328462 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [-18 x y + x y, -17 x y z + 2 y z , -10 x y - 16 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 G := [8 x y z, 3 x y + 15 z , -16 x y - 9 y z] > Problem := [F,G]; 2 2 3 2 2 Problem := [[-18 x y + x y, -17 x y z + 2 y z , -10 x y - 16 y z ], 2 3 3 2 2 [8 x y z, 3 x y + 15 z , -16 x y - 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.79 memory used=70.0MB, alloc=56.3MB, time=1.18 N1 := 429 > GB := Basis(F, plex(op(vars))); 4 2 3 2 2 2 GB := [x y, 18 x y - x y, -17 x y + 2 x y z, 5 x y + 8 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=110.3MB, alloc=60.3MB, time=1.82 memory used=152.8MB, alloc=60.3MB, time=2.51 N2 := 429 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 2 H := [-18 x y + x y, -17 x y z + 2 y z , -10 x y - 16 y z , 8 x y z, 3 3 2 2 3 x y + 15 z , -16 x y - 9 y z] > J:=[op(GB),op(G)]; 4 2 3 2 2 2 2 J := [x y, 18 x y - x y, -17 x y + 2 x y z, 5 x y + 8 y z , 8 x y z, 3 3 2 2 3 x y + 15 z , -16 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 := [6, 17, 21, 4, 2, 3, 3, 1, 1, 5/6, 1/2, 5/7, 3/7, 7, 19, 26, 5, 4, 3, 3, 1, 1, 5/7, 9/16, 11/16, 5/16, -2, -5, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=162.9MB, alloc=60.3MB, time=2.72 |\^/| 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(); 1428328465 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 3 3 F := [8 y z - x , 2 x z + 12 x y, 11 y z + 11 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 3 G := [-10 x y - 9 x y, -15 y z - 12 y, 2 y - 3 y z] > Problem := [F,G]; 3 3 3 2 3 3 Problem := [[8 y z - x , 2 x z + 12 x y, 11 y z + 11 z ], 3 2 2 2 4 3 [-10 x y - 9 x y, -15 y z - 12 y, 2 y - 3 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=48.1MB, alloc=32.3MB, time=0.79 memory used=68.1MB, alloc=32.3MB, time=1.07 memory used=87.8MB, alloc=56.3MB, time=1.38 memory used=128.2MB, alloc=60.3MB, time=1.96 memory used=164.9MB, alloc=60.3MB, time=2.53 memory used=200.4MB, alloc=84.3MB, time=3.06 memory used=256.9MB, alloc=92.3MB, time=3.91 memory used=312.3MB, alloc=116.3MB, time=4.76 memory used=389.6MB, alloc=140.3MB, time=6.12 memory used=489.2MB, alloc=164.3MB, time=7.72 memory used=604.2MB, alloc=188.3MB, time=9.64 memory used=725.8MB, alloc=212.3MB, time=11.92 memory used=845.6MB, alloc=236.3MB, time=15.19 memory used=977.8MB, alloc=260.3MB, time=19.26 memory used=1134.0MB, alloc=284.3MB, time=24.18 memory used=1314.2MB, alloc=284.3MB, time=29.73 memory used=1494.7MB, alloc=308.3MB, time=34.98 N1 := 5181 > GB := Basis(F, plex(op(vars))); 5 3 4 2 3 3 GB := [x + 48 x , -x + 48 x y, x + 8 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1591.0MB, alloc=308.3MB, time=36.48 N2 := 685 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 3 2 3 3 3 2 H := [8 y z - x , 2 x z + 12 x y, 11 y z + 11 z , -10 x y - 9 x y, 2 2 4 3 -15 y z - 12 y, 2 y - 3 y z] > J:=[op(GB),op(G)]; 5 3 4 2 3 3 3 2 2 2 J := [x + 48 x , -x + 48 x y, x + 8 z , -10 x y - 9 x y, -15 y z - 12 y, 4 3 2 y - 3 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 := [6, 14, 24, 4, 3, 4, 3, 1/2, 1, 5/6, 5/12, 3/4, 1/2, 6, 11, 24, 5, 5, 4, 3, 2/3, 2/3, 1/2, 7/12, 7/12, 1/4, 3, 0, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1693.9MB, alloc=564.3MB, time=37.96 |\^/| 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(); 1428328506 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 F := [-6 x y - 17 x z, -10 y - 19 z , -18 x y z - 5 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 G := [14 x z + 5 y z, -11 x y + 7 x z, 2 z + 19 x y z] > Problem := [F,G]; 4 2 Problem := [[-6 x y - 17 x z, -10 y - 19 z , -18 x y z - 5 x z], 3 3 2 4 [14 x z + 5 y z, -11 x y + 7 x z, 2 z + 19 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.8MB, alloc=40.3MB, time=0.45 memory used=60.9MB, alloc=40.3MB, time=0.80 memory used=88.3MB, alloc=44.3MB, time=1.14 memory used=114.5MB, alloc=68.3MB, time=1.47 memory used=160.4MB, alloc=68.3MB, time=1.99 memory used=204.1MB, alloc=92.3MB, time=2.55 memory used=246.2MB, alloc=92.3MB, time=3.11 memory used=312.3MB, alloc=124.3MB, time=4.07 memory used=395.8MB, alloc=148.3MB, time=5.26 memory used=490.7MB, alloc=172.3MB, time=7.41 memory used=594.9MB, alloc=196.3MB, time=10.32 N1 := 2385 > GB := Basis(F, plex(op(vars))); 4 2 GB := [y x, z x, 10 y + 19 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 243 #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)]; 4 2 3 3 H := [-6 x y - 17 x z, -10 y - 19 z , -18 x y z - 5 x z, 14 x z + 5 y z, 2 4 -11 x y + 7 x z, 2 z + 19 x y z] > J:=[op(GB),op(G)]; 4 2 3 3 2 J := [y x, z x, 10 y + 19 z , 14 x z + 5 y z, -11 x y + 7 x z, 4 2 z + 19 x 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 := [6, 17, 20, 4, 3, 4, 4, 5/6, 1, 1, 2/3, 1/2, 3/4, 6, 15, 19, 4, 3, 4, 4, 5/6, 5/6, 5/6, 1/2, 5/12, 7/12, 2, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=665.6MB, alloc=196.3MB, time=11.31 |\^/| 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(); 1428328518 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [10 x y z - 10 x y z, -10 x y + 15 z , 4 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 3 2 G := [-2 x y + 3 x z, 4 x + 17 x z , -16 x y + x ] > Problem := [F,G]; 2 2 2 2 Problem := [[10 x y z - 10 x y z, -10 x y + 15 z , 4 y z], 3 4 2 3 2 [-2 x y + 3 x z, 4 x + 17 x z , -16 x y + x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.4MB, alloc=32.3MB, time=0.42 memory used=48.6MB, alloc=32.3MB, time=0.72 memory used=69.5MB, alloc=56.3MB, time=1.02 N1 := 403 > GB := Basis(F, plex(op(vars))); 3 3 2 3 4 2 2 2 2 GB := [x y - x y , y x, x y z - x y z, y z, -2 x y + 3 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=108.0MB, alloc=60.3MB, time=1.46 N2 := 403 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 H := [10 x y z - 10 x y z, -10 x y + 15 z , 4 y z, -2 x y + 3 x z, 4 2 3 2 4 x + 17 x z , -16 x y + x ] > J:=[op(GB),op(G)]; 3 3 2 3 4 2 2 2 2 J := [x y - x y , y x, x y z - x y z, y z, -2 x y + 3 z , 3 4 2 3 2 -2 x y + 3 x z, 4 x + 17 x z , -16 x y + x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 22, 4, 4, 3, 2, 5/6, 5/6, 5/6, 9/13, 6/13, 6/13, 8, 19, 33, 6, 4, 4, 2, 7/8, 7/8, 5/8, 3/4, 9/16, 3/8, -4, -11, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=141.7MB, alloc=60.3MB, time=1.90 |\^/| 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(); 1428328520 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 F := [14 x z + 7 x, 7 y z + 19 y , -19 x z + 6 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 2 2 G := [-19 x y z + 4 x , -5 y - 2 x z , x y z - x y] > Problem := [F,G]; 3 3 2 2 2 2 Problem := [[14 x z + 7 x, 7 y z + 19 y , -19 x z + 6 y z ], 2 3 4 2 2 2 [-19 x y z + 4 x , -5 y - 2 x z , x y z - x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.42 memory used=48.9MB, alloc=60.3MB, time=0.67 memory used=92.2MB, alloc=60.3MB, time=1.14 memory used=134.4MB, alloc=92.3MB, time=1.71 memory used=198.5MB, alloc=116.3MB, time=2.43 memory used=282.2MB, alloc=116.3MB, time=3.42 memory used=357.4MB, alloc=396.3MB, time=4.34 memory used=457.2MB, alloc=420.3MB, time=5.54 memory used=579.5MB, alloc=444.3MB, time=7.07 memory used=716.4MB, alloc=468.3MB, time=9.02 memory used=861.0MB, alloc=492.3MB, time=11.13 memory used=1015.0MB, alloc=516.3MB, time=13.39 memory used=1179.3MB, alloc=540.3MB, time=15.87 memory used=1347.1MB, alloc=564.3MB, time=19.01 memory used=1503.9MB, alloc=588.3MB, time=22.94 memory used=1668.2MB, alloc=612.3MB, time=27.45 memory used=1843.6MB, alloc=636.3MB, time=32.69 memory used=2024.8MB, alloc=660.3MB, time=38.76 memory used=2229.6MB, alloc=684.3MB, time=45.58 memory used=2458.3MB, alloc=708.3MB, time=53.07 memory used=2710.9MB, alloc=732.3MB, time=61.45 memory used=2987.5MB, alloc=756.3MB, time=70.71 memory used=3288.0MB, alloc=780.3MB, time=80.71 memory used=3612.5MB, alloc=780.3MB, time=91.34 memory used=3936.9MB, alloc=804.3MB, time=102.17 memory used=4285.3MB, alloc=804.3MB, time=113.62 memory used=4633.6MB, alloc=804.3MB, time=125.05 memory used=4981.7MB, alloc=828.3MB, time=136.42 memory used=5353.7MB, alloc=828.3MB, time=148.54 memory used=5725.8MB, alloc=852.3MB, time=160.55 memory used=6121.8MB, alloc=876.3MB, time=173.38 memory used=6542.2MB, alloc=900.3MB, time=186.68 N1 := 13247 > GB := Basis(F, plex(op(vars))); 4 2 3 2 3 2 2 2 GB := [x , x y, -19 x + 6 x y , y , 2 x z + x, 24 y z - 19 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6655.7MB, alloc=900.3MB, time=188.99 memory used=6760.0MB, alloc=900.3MB, time=190.96 memory used=6859.2MB, alloc=900.3MB, time=192.88 memory used=6949.1MB, alloc=900.3MB, time=194.56 memory used=7036.5MB, alloc=900.3MB, time=196.39 memory used=7156.6MB, alloc=900.3MB, time=198.66 memory used=7266.5MB, alloc=900.3MB, time=201.07 memory used=7389.5MB, alloc=900.3MB, time=203.69 memory used=7506.7MB, alloc=900.3MB, time=206.01 memory used=7605.0MB, alloc=900.3MB, time=208.15 memory used=7710.2MB, alloc=900.3MB, time=210.47 memory used=7856.9MB, alloc=924.3MB, time=214.77 memory used=8323.0MB, alloc=948.3MB, time=229.98 memory used=8776.0MB, alloc=972.3MB, time=246.44 memory used=9252.9MB, alloc=996.3MB, time=263.51 memory used=9753.7MB, alloc=1020.3MB, time=281.53 |\^/| 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(); 1428328820 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 F := [x y - 19 z , -6 z, -15 + 11 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 G := [-8 x z - 8 y, -4 y + 8 y z, x z + 10 x] > Problem := [F,G]; 3 4 Problem := [[x y - 19 z , -6 z, -15 + 11 z], 3 4 2 2 [-8 x z - 8 y, -4 y + 8 y z, x z + 10 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.48 memory used=48.1MB, alloc=32.3MB, time=0.80 memory used=67.8MB, alloc=56.3MB, time=1.09 memory used=108.3MB, alloc=60.3MB, time=1.68 memory used=146.2MB, alloc=84.3MB, time=2.23 memory used=203.7MB, alloc=92.3MB, time=3.13 memory used=264.8MB, alloc=116.3MB, time=3.99 memory used=348.6MB, alloc=116.3MB, time=5.12 memory used=426.2MB, alloc=116.3MB, time=6.31 memory used=505.6MB, alloc=140.3MB, time=7.48 memory used=604.4MB, alloc=140.3MB, time=8.97 memory used=681.2MB, alloc=164.3MB, time=10.04 memory used=768.1MB, alloc=420.3MB, time=11.32 memory used=889.3MB, alloc=444.3MB, time=12.93 memory used=1024.3MB, alloc=468.3MB, time=15.00 memory used=1190.7MB, alloc=492.3MB, time=17.53 memory used=1410.6MB, alloc=492.3MB, time=18.99 memory used=1634.9MB, alloc=492.3MB, time=20.48 memory used=1844.6MB, alloc=492.3MB, time=22.37 memory used=2039.3MB, alloc=516.3MB, time=24.45 memory used=2231.2MB, alloc=540.3MB, time=26.92 memory used=2429.3MB, alloc=564.3MB, time=29.66 memory used=2644.0MB, alloc=588.3MB, time=32.60 memory used=2858.4MB, alloc=612.3MB, time=35.97 memory used=3056.8MB, alloc=636.3MB, time=40.96 memory used=3252.1MB, alloc=660.3MB, time=46.36 memory used=3454.9MB, alloc=684.3MB, time=52.32 memory used=3666.6MB, alloc=708.3MB, time=59.11 memory used=3891.8MB, alloc=732.3MB, time=66.78 memory used=4140.9MB, alloc=756.3MB, time=74.97 memory used=4414.0MB, alloc=780.3MB, time=84.04 memory used=4710.9MB, alloc=804.3MB, time=93.75 memory used=5031.9MB, alloc=828.3MB, time=104.37 memory used=5376.7MB, alloc=852.3MB, time=115.69 memory used=5745.6MB, alloc=852.3MB, time=127.63 memory used=6114.4MB, alloc=876.3MB, time=139.67 memory used=6507.1MB, alloc=876.3MB, time=152.45 memory used=6899.7MB, alloc=876.3MB, time=165.22 memory used=7292.3MB, alloc=900.3MB, time=178.19 memory used=7708.9MB, alloc=900.3MB, time=191.92 memory used=8125.6MB, alloc=924.3MB, time=205.66 memory used=8566.2MB, alloc=948.3MB, time=220.11 memory used=9030.8MB, alloc=972.3MB, time=235.09 N1 := 14697 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 343 #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)]; H := [ 4 3 3 4 2 2 -19 z + y x , -6 z, 11 z - 15, -8 x z - 8 y, -4 y + 8 y z, x z + 10 x] > J:=[op(GB),op(G)]; 3 4 2 2 J := [1, -8 x z - 8 y, -4 y + 8 y z, 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, 12, 18, 4, 3, 4, 4, 1/2, 1/2, 1, 1/3, 1/3, 1/2, 4, 7, 12, 4, 2, 4, 3, 1/2, 1/2, 3/4, 3/7, 3/7, 3/7, 5, 6, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=9418.8MB, alloc=972.3MB, time=245.65 |\^/| 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(); 1428329083 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 F := [15 y z + 5 x y, -18 z + 18 x y z, -16 x y + 3 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 2 3 G := [-5 z + 7 x , 7 z + 20 x , 15 y - 3 x y] > Problem := [F,G]; 3 2 4 3 Problem := [[15 y z + 5 x y, -18 z + 18 x y z, -16 x y + 3 y z], 4 2 4 2 3 [-5 z + 7 x , 7 z + 20 x , 15 y - 3 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.46 memory used=47.9MB, alloc=32.3MB, time=0.68 memory used=68.6MB, alloc=32.3MB, time=0.93 memory used=89.1MB, alloc=60.3MB, time=1.20 memory used=130.0MB, alloc=60.3MB, time=1.74 memory used=168.7MB, alloc=60.3MB, time=2.14 memory used=207.4MB, alloc=84.3MB, time=2.58 memory used=267.5MB, alloc=92.3MB, time=3.32 memory used=325.7MB, alloc=92.3MB, time=4.00 memory used=382.3MB, alloc=116.3MB, time=4.67 memory used=463.1MB, alloc=116.3MB, time=5.58 memory used=540.2MB, alloc=140.3MB, time=6.46 memory used=633.7MB, alloc=396.3MB, time=7.61 memory used=733.9MB, alloc=420.3MB, time=8.99 memory used=857.4MB, alloc=444.3MB, time=10.54 memory used=995.6MB, alloc=468.3MB, time=12.38 memory used=1147.3MB, alloc=492.3MB, time=14.55 memory used=1293.9MB, alloc=516.3MB, time=17.63 memory used=1438.7MB, alloc=540.3MB, time=21.71 memory used=1594.2MB, alloc=564.3MB, time=26.54 memory used=1773.7MB, alloc=588.3MB, time=32.23 memory used=1977.1MB, alloc=612.3MB, time=38.49 memory used=2204.6MB, alloc=612.3MB, time=45.50 memory used=2432.1MB, alloc=636.3MB, time=52.30 N1 := 6775 > GB := Basis(F, plex(op(vars))); GB := 9 2 3 2 2 3 4 4 [4096 x y + 6561 x y, x y + 3 x y , -16 x y + 3 y z, -16 x y + 27 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2696.8MB, alloc=636.3MB, time=58.09 memory used=2863.7MB, alloc=636.3MB, time=60.23 memory used=3078.9MB, alloc=636.3MB, time=63.37 memory used=3353.0MB, alloc=660.3MB, time=68.15 memory used=3621.9MB, alloc=684.3MB, time=77.19 memory used=3901.3MB, alloc=708.3MB, time=83.47 N2 := 4419 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 4 3 4 2 H := [15 y z + 5 x y, -18 z + 18 x y z, -16 x y + 3 y z, -5 z + 7 x , 4 2 3 7 z + 20 x , 15 y - 3 x y] > J:=[op(GB),op(G)]; 9 2 3 2 2 3 4 4 J := [4096 x y + 6561 x y, x y + 3 x y , -16 x y + 3 y z, -16 x y + 27 z , 4 2 4 2 3 -5 z + 7 x , 7 z + 20 x , 15 y - 3 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 := [6, 15, 23, 4, 2, 3, 4, 1, 2/3, 5/6, 1/2, 7/12, 1/2, 7, 16, 34, 10, 9, 3, 4, 1, 5/7, 4/7, 9/14, 9/14, 2/7, -1, -11, -6] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3957.3MB, alloc=708.3MB, time=84.42 |\^/| 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(); 1428329172 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 3 3 3 F := [-5 x - 7 x y z, 8 x - 7 x y, -2 x y - 9 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 4 G := [18 y z + 3 x , 20 x y - 18 z , -20 x y z - 3 z ] > Problem := [F,G]; 4 2 4 3 3 3 Problem := [[-5 x - 7 x y z, 8 x - 7 x y, -2 x y - 9 z ], 3 2 3 2 2 4 [18 y z + 3 x , 20 x y - 18 z , -20 x 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=4.2MB, alloc=32.3MB, time=0.14 memory used=26.9MB, alloc=32.3MB, time=0.35 memory used=48.6MB, alloc=32.3MB, time=0.53 memory used=68.5MB, alloc=56.3MB, time=0.71 memory used=111.0MB, alloc=60.3MB, time=1.06 memory used=151.4MB, alloc=84.3MB, time=1.41 memory used=214.0MB, alloc=92.3MB, time=1.95 memory used=277.5MB, alloc=116.3MB, time=2.45 memory used=347.4MB, alloc=116.3MB, time=2.98 memory used=433.1MB, alloc=372.3MB, time=3.43 memory used=522.7MB, alloc=396.3MB, time=3.95 memory used=634.4MB, alloc=420.3MB, time=4.78 memory used=760.7MB, alloc=444.3MB, time=5.84 memory used=907.6MB, alloc=468.3MB, time=7.11 memory used=1046.1MB, alloc=492.3MB, time=8.40 memory used=1166.4MB, alloc=492.3MB, time=9.44 memory used=1278.1MB, alloc=516.3MB, time=10.38 memory used=1390.2MB, alloc=516.3MB, time=11.31 memory used=1507.6MB, alloc=540.3MB, time=12.33 memory used=1644.3MB, alloc=540.3MB, time=13.17 memory used=1752.1MB, alloc=540.3MB, time=13.98 memory used=1929.9MB, alloc=564.3MB, time=14.87 memory used=2061.3MB, alloc=564.3MB, time=15.70 memory used=2206.7MB, alloc=564.3MB, time=16.62 memory used=2284.0MB, alloc=588.3MB, time=17.43 memory used=2358.6MB, alloc=588.3MB, time=18.12 memory used=2454.8MB, alloc=588.3MB, time=19.13 memory used=2522.2MB, alloc=588.3MB, time=19.89 memory used=2580.4MB, alloc=588.3MB, time=20.54 memory used=2638.5MB, alloc=588.3MB, time=21.19 memory used=2691.8MB, alloc=588.3MB, time=21.91 memory used=2742.2MB, alloc=588.3MB, time=22.70 memory used=2953.0MB, alloc=612.3MB, time=24.67 memory used=3125.2MB, alloc=636.3MB, time=26.48 memory used=3295.1MB, alloc=660.3MB, time=28.35 memory used=3457.4MB, alloc=684.3MB, time=29.82 memory used=3610.7MB, alloc=708.3MB, time=31.36 memory used=3750.7MB, alloc=708.3MB, time=32.84 memory used=3899.5MB, alloc=708.3MB, time=34.45 memory used=4040.6MB, alloc=732.3MB, time=36.21 memory used=4143.4MB, alloc=732.3MB, time=37.54 memory used=4243.7MB, alloc=732.3MB, time=38.99 memory used=4354.0MB, alloc=732.3MB, time=40.27 memory used=4457.4MB, alloc=756.3MB, time=41.78 memory used=4861.4MB, alloc=780.3MB, time=45.17 memory used=5255.1MB, alloc=804.3MB, time=48.11 memory used=5688.0MB, alloc=828.3MB, time=51.94 memory used=6088.6MB, alloc=852.3MB, time=55.16 memory used=6447.5MB, alloc=876.3MB, time=58.91 memory used=6775.0MB, alloc=900.3MB, time=62.53 memory used=7081.5MB, alloc=924.3MB, time=65.88 memory used=7608.8MB, alloc=948.3MB, time=70.79 memory used=7995.6MB, alloc=972.3MB, time=76.68 memory used=8383.9MB, alloc=996.3MB, time=82.64 memory used=8870.2MB, alloc=1020.3MB, time=87.99 memory used=9387.9MB, alloc=1044.3MB, time=93.19 memory used=9854.9MB, alloc=1068.3MB, time=99.70 memory used=10278.8MB, alloc=1092.3MB, time=106.23 memory used=10701.9MB, alloc=1116.3MB, time=112.85 memory used=11120.4MB, alloc=1140.3MB, time=119.57 memory used=11564.6MB, alloc=1164.3MB, time=126.89 memory used=11877.0MB, alloc=1188.3MB, time=135.87 memory used=12186.2MB, alloc=1212.3MB, time=145.30 memory used=12501.3MB, alloc=1236.3MB, time=155.07 memory used=12825.2MB, alloc=1260.3MB, time=165.20 memory used=13160.6MB, alloc=1284.3MB, time=175.78 memory used=13508.8MB, alloc=1308.3MB, time=186.82 memory used=13869.8MB, alloc=1332.3MB, time=198.65 memory used=14245.2MB, alloc=1356.3MB, time=210.71 memory used=14634.4MB, alloc=1380.3MB, time=223.04 memory used=15038.7MB, alloc=1404.3MB, time=235.86 memory used=15452.9MB, alloc=1428.3MB, time=249.41 memory used=15881.1MB, alloc=1452.3MB, time=263.62 memory used=16333.2MB, alloc=1476.3MB, time=278.42 memory used=16809.3MB, alloc=1500.3MB, time=293.95 memory used=17309.3MB, alloc=1524.3MB, time=310.18 |\^/| 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(); 1428329472 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 4 2 F := [16 x z - 4 x y, -12 x y + 14 x y, 9 x + 19 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 G := [-4 x z + 15 y, 13 y - 17 y z, 20 x y - 14 y ] > Problem := [F,G]; 3 2 3 4 2 Problem := [[16 x z - 4 x y, -12 x y + 14 x y, 9 x + 19 y ], 3 3 2 2 3 [-4 x z + 15 y, 13 y - 17 y z, 20 x y - 14 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.7MB, alloc=32.3MB, time=0.39 memory used=48.0MB, alloc=32.3MB, time=0.62 memory used=69.3MB, alloc=32.3MB, time=0.85 memory used=89.7MB, alloc=56.3MB, time=1.10 memory used=133.8MB, alloc=60.3MB, time=1.71 memory used=173.4MB, alloc=84.3MB, time=2.23 memory used=232.3MB, alloc=108.3MB, time=3.48 N1 := 1327 > GB := Basis(F, plex(op(vars))); 7 5 3 4 2 3 2 GB := [6 x - 7 x , 6 x y - 7 x y, 9 x + 19 y , 4 x z - x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=306.9MB, alloc=108.3MB, time=4.79 memory used=388.2MB, alloc=116.3MB, time=5.61 memory used=466.8MB, alloc=140.3MB, time=6.46 N2 := 1327 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 4 2 3 H := [16 x z - 4 x y, -12 x y + 14 x y, 9 x + 19 y , -4 x z + 15 y, 3 2 2 3 13 y - 17 y z, 20 x y - 14 y ] > J:=[op(GB),op(G)]; 7 5 3 4 2 3 2 3 J := [6 x - 7 x , 6 x y - 7 x y, 9 x + 19 y , 4 x z - x y, -4 x z + 15 y, 3 2 2 3 13 y - 17 y z, 20 x y - 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 := [6, 14, 23, 4, 4, 3, 3, 5/6, 1, 1/2, 7/12, 3/4, 1/4, 7, 15, 30, 7, 7, 3, 3, 6/7, 6/7, 3/7, 9/14, 9/14, 3/14, -1, -7, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=524.3MB, alloc=140.3MB, time=7.28 |\^/| 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(); 1428329480 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 F := [-13 y + 19 x z, 9 z - 16 y, -17 y z - 10 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 G := [-3 x z + 18 y z , -5 x y + 10 y z, -4 x y z + 5 y] > Problem := [F,G]; 4 2 3 2 Problem := [[-13 y + 19 x z, 9 z - 16 y, -17 y z - 10 x ], 3 3 2 2 2 [-3 x z + 18 y z , -5 x y + 10 y z, -4 x y z + 5 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.12 memory used=26.3MB, alloc=32.3MB, time=0.31 memory used=47.6MB, alloc=32.3MB, time=0.50 memory used=68.3MB, alloc=56.3MB, time=0.70 memory used=112.7MB, alloc=68.3MB, time=1.08 memory used=151.5MB, alloc=92.3MB, time=1.47 memory used=215.2MB, alloc=92.3MB, time=2.01 memory used=277.7MB, alloc=116.3MB, time=2.55 memory used=358.7MB, alloc=116.3MB, time=3.28 memory used=434.2MB, alloc=396.3MB, time=3.96 memory used=545.7MB, alloc=420.3MB, time=4.67 memory used=669.2MB, alloc=444.3MB, time=5.71 memory used=785.2MB, alloc=468.3MB, time=6.64 memory used=900.3MB, alloc=492.3MB, time=7.37 memory used=1011.2MB, alloc=492.3MB, time=8.42 memory used=1097.3MB, alloc=492.3MB, time=9.21 memory used=1190.3MB, alloc=492.3MB, time=10.04 memory used=1279.5MB, alloc=492.3MB, time=10.83 memory used=1352.0MB, alloc=516.3MB, time=11.58 memory used=1410.5MB, alloc=516.3MB, time=12.31 memory used=1479.2MB, alloc=516.3MB, time=12.99 memory used=1550.2MB, alloc=516.3MB, time=13.79 memory used=1606.4MB, alloc=516.3MB, time=14.47 memory used=1658.4MB, alloc=516.3MB, time=15.21 memory used=1849.4MB, alloc=540.3MB, time=17.07 memory used=2025.2MB, alloc=564.3MB, time=18.81 memory used=2184.8MB, alloc=588.3MB, time=20.45 memory used=2372.3MB, alloc=612.3MB, time=22.50 memory used=2521.8MB, alloc=636.3MB, time=24.21 memory used=2663.8MB, alloc=660.3MB, time=25.82 memory used=2830.7MB, alloc=684.3MB, time=27.22 memory used=2973.1MB, alloc=708.3MB, time=28.75 memory used=3073.4MB, alloc=708.3MB, time=30.19 memory used=3184.2MB, alloc=708.3MB, time=31.55 memory used=3265.3MB, alloc=732.3MB, time=32.98 memory used=3625.4MB, alloc=756.3MB, time=37.42 memory used=3986.2MB, alloc=780.3MB, time=41.50 memory used=4304.2MB, alloc=804.3MB, time=45.96 memory used=4624.3MB, alloc=828.3MB, time=50.50 memory used=4947.5MB, alloc=852.3MB, time=55.06 memory used=5338.0MB, alloc=876.3MB, time=59.31 memory used=5735.6MB, alloc=900.3MB, time=64.54 memory used=6028.3MB, alloc=924.3MB, time=71.88 memory used=6315.4MB, alloc=948.3MB, time=79.61 memory used=6606.9MB, alloc=972.3MB, time=87.78 memory used=6906.8MB, alloc=996.3MB, time=96.23 memory used=7218.0MB, alloc=1020.3MB, time=105.10 memory used=7534.8MB, alloc=1044.3MB, time=114.63 memory used=7866.1MB, alloc=1068.3MB, time=124.78 memory used=8221.3MB, alloc=1092.3MB, time=135.58 memory used=8600.5MB, alloc=1116.3MB, time=147.00 memory used=9003.5MB, alloc=1140.3MB, time=159.05 memory used=9430.5MB, alloc=1164.3MB, time=171.75 memory used=9881.5MB, alloc=1188.3MB, time=185.10 memory used=10356.4MB, alloc=1212.3MB, time=199.16 memory used=10855.2MB, alloc=1236.3MB, time=213.82 memory used=11378.0MB, alloc=1260.3MB, time=229.08 memory used=11924.7MB, alloc=1284.3MB, time=244.94 memory used=12495.4MB, alloc=1308.3MB, time=261.47 memory used=13089.9MB, alloc=1332.3MB, time=278.63 memory used=13708.4MB, alloc=1356.3MB, time=296.38 |\^/| 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(); 1428329780 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 2 3 F := [8 z + 3 x , -16 y + 4 x y z, 20 x y - 18 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 G := [2 x z - 12 x y, 8 x y z - 14 y , 16 y + 13 x y] > Problem := [F,G]; 4 2 4 2 3 Problem := [[8 z + 3 x , -16 y + 4 x y z, 20 x y - 18 y ], 3 2 4 3 [2 x z - 12 x y, 8 x y z - 14 y , 16 y + 13 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=26.6MB, alloc=32.3MB, time=0.46 memory used=48.0MB, alloc=32.3MB, time=0.73 memory used=68.5MB, alloc=56.3MB, time=1.00 memory used=110.0MB, alloc=60.3MB, time=1.45 memory used=150.3MB, alloc=60.3MB, time=1.79 memory used=189.7MB, alloc=84.3MB, time=2.14 memory used=227.6MB, alloc=84.3MB, time=2.47 memory used=295.5MB, alloc=92.3MB, time=2.98 memory used=356.8MB, alloc=116.3MB, time=3.52 memory used=438.5MB, alloc=116.3MB, time=4.29 memory used=516.7MB, alloc=140.3MB, time=5.06 memory used=579.3MB, alloc=140.3MB, time=5.68 memory used=650.0MB, alloc=396.3MB, time=6.39 memory used=750.3MB, alloc=420.3MB, time=7.45 memory used=861.5MB, alloc=444.3MB, time=8.70 memory used=985.6MB, alloc=468.3MB, time=10.54 memory used=1107.1MB, alloc=492.3MB, time=12.82 N1 := 2511 > GB := Basis(F, plex(op(vars))); 9 3 2 3 2 2 GB := [2048000000 x y + 1594323 x y, -10 x y + 9 y , -40 x y + 9 x y z, 4 2 8 z + 3 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1265.8MB, alloc=492.3MB, time=14.51 memory used=1408.9MB, alloc=492.3MB, time=15.93 memory used=1555.1MB, alloc=516.3MB, time=17.35 memory used=1710.1MB, alloc=516.3MB, time=18.93 memory used=1840.6MB, alloc=540.3MB, time=20.34 memory used=2048.7MB, alloc=564.3MB, time=23.17 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)]; 4 2 4 2 3 3 H := [8 z + 3 x , -16 y + 4 x y z, 20 x y - 18 y , 2 x z - 12 x y, 2 4 3 8 x y z - 14 y , 16 y + 13 x y] > J:=[op(GB),op(G)]; 9 3 2 3 2 2 J := [2048000000 x y + 1594323 x y, -10 x y + 9 y , -40 x y + 9 x y z, 4 2 3 2 4 3 8 z + 3 x , 2 x z - 12 x y, 8 x y z - 14 y , 16 y + 13 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 := [6, 15, 22, 4, 2, 4, 4, 1, 5/6, 2/3, 7/12, 3/4, 1/3, 7, 17, 32, 10, 9, 4, 4, 1, 6/7, 4/7, 5/7, 11/14, 2/7, -2, -10, -6] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2162.4MB, alloc=564.3MB, time=25.15 |\^/| 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(); 1428329805 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 3 2 F := [-10 x y z + 14 y , 9 x y - 4 z , -17 y z + 8 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 2 G := [15 x z + 16 z , 5 y z - 18 x z, -7 x y z ] > Problem := [F,G]; 2 2 2 2 3 3 2 Problem := [[-10 x y z + 14 y , 9 x y - 4 z , -17 y z + 8 x y ], 3 4 2 2 2 [15 x z + 16 z , 5 y z - 18 x z, -7 x y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.4MB, alloc=32.3MB, time=0.34 memory used=47.8MB, alloc=32.3MB, time=0.52 memory used=67.6MB, alloc=32.3MB, time=0.69 memory used=87.7MB, alloc=56.3MB, time=0.88 memory used=127.1MB, alloc=60.3MB, time=1.22 memory used=167.2MB, alloc=92.3MB, time=1.56 memory used=231.8MB, alloc=116.3MB, time=2.05 memory used=305.0MB, alloc=116.3MB, time=2.64 memory used=380.3MB, alloc=372.3MB, time=3.30 memory used=466.1MB, alloc=396.3MB, time=4.02 memory used=580.9MB, alloc=420.3MB, time=4.88 memory used=710.3MB, alloc=444.3MB, time=5.92 memory used=852.4MB, alloc=468.3MB, time=7.19 memory used=968.3MB, alloc=492.3MB, time=8.21 memory used=1085.4MB, alloc=492.3MB, time=9.29 memory used=1192.6MB, alloc=516.3MB, time=10.32 memory used=1283.5MB, alloc=516.3MB, time=11.26 memory used=1379.6MB, alloc=516.3MB, time=12.34 memory used=1545.5MB, alloc=540.3MB, time=14.18 memory used=1692.3MB, alloc=564.3MB, time=15.93 memory used=1847.3MB, alloc=588.3MB, time=17.77 memory used=1970.7MB, alloc=612.3MB, time=19.39 memory used=2071.0MB, alloc=636.3MB, time=20.78 memory used=2273.6MB, alloc=660.3MB, time=24.82 memory used=2504.4MB, alloc=684.3MB, time=30.26 memory used=2734.0MB, alloc=708.3MB, time=36.48 memory used=2987.5MB, alloc=732.3MB, time=43.25 memory used=3265.0MB, alloc=756.3MB, time=50.58 memory used=3566.5MB, alloc=780.3MB, time=58.48 memory used=3891.8MB, alloc=780.3MB, time=66.97 memory used=4217.1MB, alloc=804.3MB, time=75.36 memory used=4566.4MB, alloc=804.3MB, time=84.21 memory used=4915.6MB, alloc=828.3MB, time=92.58 N1 := 9817 > GB := Basis(F, plex(op(vars))); 10 2 2 8 2 3 2 2 GB := [172125 x y - 43904 x y , -1125 x y + 1372 y , 5 x y z - 7 y , 7 2 2 3 2 2 2 2 2 3 -225 x y + 196 x y z, -40 x y + 119 y z , -9 x y + 4 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5108.2MB, alloc=828.3MB, time=96.00 memory used=5192.3MB, alloc=828.3MB, time=97.47 memory used=5277.4MB, alloc=828.3MB, time=98.95 memory used=5346.1MB, alloc=828.3MB, time=100.07 memory used=5401.1MB, alloc=828.3MB, time=101.15 memory used=5466.3MB, alloc=828.3MB, time=102.28 memory used=5513.8MB, alloc=828.3MB, time=103.26 memory used=5768.7MB, alloc=828.3MB, time=106.18 memory used=6004.3MB, alloc=828.3MB, time=108.81 memory used=6210.7MB, alloc=828.3MB, time=111.37 memory used=6390.1MB, alloc=852.3MB, time=113.62 memory used=6581.2MB, alloc=852.3MB, time=116.14 memory used=6910.0MB, alloc=876.3MB, time=120.55 memory used=7228.8MB, alloc=900.3MB, time=125.00 memory used=7582.8MB, alloc=924.3MB, time=129.58 memory used=7989.7MB, alloc=948.3MB, time=133.96 memory used=8414.6MB, alloc=972.3MB, time=143.88 memory used=8813.6MB, alloc=996.3MB, time=154.31 memory used=9195.5MB, alloc=1020.3MB, time=165.38 memory used=9596.6MB, alloc=1044.3MB, time=177.01 memory used=10021.7MB, alloc=1068.3MB, time=189.28 memory used=10470.7MB, alloc=1092.3MB, time=202.13 memory used=10943.7MB, alloc=1116.3MB, time=215.62 memory used=11440.6MB, alloc=1140.3MB, time=229.77 memory used=11961.4MB, alloc=1164.3MB, time=244.53 memory used=12506.2MB, alloc=1188.3MB, time=259.91 memory used=13074.8MB, alloc=1212.3MB, time=275.88 memory used=13667.4MB, alloc=1236.3MB, time=292.46 memory used=14283.9MB, alloc=1260.3MB, time=309.59 |\^/| 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(); 1428330105 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 4 F := [7 x y - 2 x y z, -11 y z - 6 x z, 7 z - 10 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 G := [10 x - 5, 3 x y + 2 z , -18 x - 2] > Problem := [F,G]; 2 2 2 2 2 4 Problem := [[7 x y - 2 x y z, -11 y z - 6 x z, 7 z - 10 y], 3 2 2 2 4 [10 x - 5, 3 x y + 2 z , -18 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=0.14 memory used=26.0MB, alloc=32.3MB, time=0.35 memory used=47.7MB, alloc=32.3MB, time=0.59 memory used=68.3MB, alloc=32.3MB, time=0.84 memory used=87.4MB, alloc=56.3MB, time=1.09 memory used=130.7MB, alloc=60.3MB, time=1.70 memory used=169.4MB, alloc=84.3MB, time=2.21 memory used=226.6MB, alloc=108.3MB, time=3.13 memory used=294.0MB, alloc=132.3MB, time=4.78 N1 := 1641 > GB := Basis(F, plex(op(vars))); 4 3 3 2 2 2 4 3 GB := [7203 x y + 440 x y, 7203 x y + 440 x y , 1210 x y - 3087 x y, 6 2 3 3 3 2 2 2 1210 y - 3087 x y , -7 x y + 2 x z, -7 x y + 2 x y z, 3 5 2 2 2 2 3 3 11 y z + 6 x y, -605 y + 126 x z , 11 y z + 6 x z, 21 x z + 55 y , 4 7 z - 10 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=383.5MB, alloc=140.3MB, time=5.73 memory used=480.9MB, alloc=140.3MB, time=6.79 memory used=575.5MB, alloc=140.3MB, time=7.88 memory used=674.7MB, alloc=164.3MB, time=9.20 memory used=794.4MB, alloc=188.3MB, time=10.92 memory used=904.0MB, alloc=468.3MB, time=12.58 memory used=1038.9MB, alloc=492.3MB, time=16.22 memory used=1182.7MB, alloc=516.3MB, time=20.59 memory used=1350.7MB, alloc=540.3MB, time=24.60 N2 := 3889 #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 4 3 H := [7 x y - 2 x y z, -11 y z - 6 x z, 7 z - 10 y, 10 x - 5, 2 2 2 4 3 y x + 2 z , -18 x - 2] > J:=[op(GB),op(G)]; 4 3 3 2 2 2 4 3 J := [7203 x y + 440 x y, 7203 x y + 440 x y , 1210 x y - 3087 x y, 6 2 3 3 3 2 2 2 1210 y - 3087 x y , -7 x y + 2 x z, -7 x y + 2 x y z, 3 5 2 2 2 2 3 3 11 y z + 6 x y, -605 y + 126 z x , 11 y z + 6 x z, 21 z x + 55 y , 4 3 2 2 2 4 7 z - 10 y, 10 x - 5, 3 y x + 2 z , -18 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 := [6, 13, 23, 4, 4, 2, 4, 5/6, 2/3, 2/3, 1/2, 5/12, 5/12, 14, 33, 61, 6, 4, 6, 4, 13/14, 6/7, 4/7, 9/14, 9/14, 9/28, -20, -38, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1383.8MB, alloc=540.3MB, time=25.09 |\^/| 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(); 1428330132 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 3 2 F := [-12 x y - 2 x y z , 13 x + 9 y , -7 y z + 7 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 2 4 2 G := [17 y z - 11 z , -13 y z + 11 x z , -5 y + 20 x y] > Problem := [F,G]; 3 2 4 2 3 2 Problem := [[-12 x y - 2 x y z , 13 x + 9 y , -7 y z + 7 x y], 3 4 3 2 4 2 [17 y z - 11 z , -13 y z + 11 x z , -5 y + 20 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=0.11 memory used=26.8MB, alloc=32.3MB, time=0.32 memory used=48.1MB, alloc=32.3MB, time=0.53 memory used=69.3MB, alloc=32.3MB, time=0.71 memory used=89.9MB, alloc=60.3MB, time=0.90 memory used=130.7MB, alloc=60.3MB, time=1.24 memory used=170.7MB, alloc=60.3MB, time=1.57 memory used=209.5MB, alloc=84.3MB, time=1.91 memory used=277.8MB, alloc=92.3MB, time=2.42 memory used=344.6MB, alloc=116.3MB, time=2.90 memory used=419.7MB, alloc=116.3MB, time=3.55 memory used=497.5MB, alloc=140.3MB, time=4.38 memory used=589.5MB, alloc=164.3MB, time=5.48 N1 := 1399 > GB := Basis(F, plex(op(vars))); 15 7 11 3 4 2 GB := [17576 x - 27 x , 17576 x y - 27 x y, 13 x + 9 y , 13 7 9 3 9 5 2 -676 x + 9 x z, -676 x y + 9 x y z, -26 x + 3 x z , 5 2 4 3 6 3 2 -26 x y + 3 x y z , x z - x , y z - x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=691.7MB, alloc=164.3MB, time=6.70 memory used=781.4MB, alloc=420.3MB, time=7.57 memory used=905.3MB, alloc=444.3MB, time=8.65 memory used=1045.7MB, alloc=468.3MB, time=9.97 memory used=1149.8MB, alloc=468.3MB, time=10.91 memory used=1261.7MB, alloc=492.3MB, time=11.73 memory used=1369.2MB, alloc=492.3MB, time=12.72 memory used=1480.9MB, alloc=516.3MB, time=13.74 memory used=1578.8MB, alloc=516.3MB, time=14.72 memory used=1673.8MB, alloc=516.3MB, time=15.71 memory used=1765.3MB, alloc=516.3MB, time=16.68 memory used=1836.2MB, alloc=516.3MB, time=17.46 memory used=1907.1MB, alloc=540.3MB, time=18.35 memory used=1975.6MB, alloc=540.3MB, time=19.20 memory used=2038.9MB, alloc=540.3MB, time=20.00 memory used=2098.8MB, alloc=540.3MB, time=20.76 memory used=2158.7MB, alloc=540.3MB, time=21.55 memory used=2241.4MB, alloc=564.3MB, time=22.75 memory used=2357.6MB, alloc=588.3MB, time=24.44 memory used=2476.7MB, alloc=612.3MB, time=26.16 memory used=2706.0MB, alloc=636.3MB, time=28.52 memory used=2964.6MB, alloc=660.3MB, time=31.83 memory used=3219.1MB, alloc=684.3MB, time=35.42 memory used=3443.2MB, alloc=708.3MB, time=40.21 memory used=3667.0MB, alloc=732.3MB, time=45.49 memory used=3898.2MB, alloc=756.3MB, time=51.26 memory used=4131.6MB, alloc=780.3MB, time=57.75 memory used=4389.1MB, alloc=804.3MB, time=64.79 memory used=4670.4MB, alloc=828.3MB, time=72.46 memory used=4975.7MB, alloc=852.3MB, time=80.71 memory used=5304.9MB, alloc=876.3MB, time=89.54 memory used=5658.0MB, alloc=900.3MB, time=98.97 memory used=6035.1MB, alloc=924.3MB, time=109.01 memory used=6436.1MB, alloc=948.3MB, time=119.59 memory used=6861.0MB, alloc=972.3MB, time=130.69 memory used=7309.9MB, alloc=972.3MB, time=142.34 memory used=7758.8MB, alloc=972.3MB, time=153.88 memory used=8207.6MB, alloc=996.3MB, time=165.42 memory used=8680.6MB, alloc=996.3MB, time=177.32 memory used=9153.4MB, alloc=1020.3MB, time=189.17 memory used=9650.2MB, alloc=1044.3MB, time=201.36 N2 := 15293 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 4 2 3 2 3 4 H := [-12 x y - 2 x y z , 13 x + 9 y , -7 y z + 7 x y, 17 y z - 11 z , 3 2 4 2 -13 y z + 11 x z , -5 y + 20 x y] > J:=[op(GB),op(G)]; 15 7 11 3 4 2 13 7 J := [17576 x - 27 x , 17576 x y - 27 x y, 13 x + 9 y , -676 x + 9 x z, 9 3 9 5 2 5 2 4 3 6 -676 x y + 9 x y z, -26 x + 3 x z , -26 x y + 3 x y z , x z - x , 3 2 3 4 3 2 4 2 y z - x y, 17 y z - 11 z , -13 y z + 11 x z , -5 y + 20 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 := [6, 15, 24, 4, 4, 4, 4, 5/6, 1, 2/3, 1/2, 3/4, 1/2, 12, 27, 92, 15, 15, 4, 4, 11/12, 2/3, 2/3, 3/4, 13/24, 5/12, -12, -68, -11] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=10143.6MB, alloc=1044.3MB, time=211.38 |\^/| 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(); 1428330337 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [-5 x y z - 13 x z , -15 y + 7 y z, -8 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 4 G := [2 x y z - 14 x y, 9 x + 4 z , -19 y + 19 x y z] > Problem := [F,G]; 2 3 2 2 Problem := [[-5 x y z - 13 x z , -15 y + 7 y z, -8 x y ], 2 2 3 3 4 [2 x y z - 14 x y, 9 x + 4 z , -19 y + 19 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.7MB, alloc=32.3MB, time=0.36 memory used=48.6MB, alloc=60.3MB, time=0.56 memory used=90.3MB, alloc=60.3MB, time=0.93 memory used=128.2MB, alloc=84.3MB, time=1.28 memory used=170.3MB, alloc=84.3MB, time=1.68 memory used=227.7MB, alloc=116.3MB, time=2.25 memory used=309.3MB, alloc=396.3MB, time=2.99 memory used=411.0MB, alloc=420.3MB, time=4.11 memory used=523.4MB, alloc=444.3MB, time=5.34 memory used=648.9MB, alloc=468.3MB, time=6.70 memory used=787.3MB, alloc=492.3MB, time=8.23 memory used=934.3MB, alloc=516.3MB, time=10.20 memory used=1076.6MB, alloc=540.3MB, time=12.91 memory used=1228.1MB, alloc=564.3MB, time=16.11 memory used=1387.1MB, alloc=588.3MB, time=20.02 memory used=1567.3MB, alloc=612.3MB, time=24.54 memory used=1771.5MB, alloc=636.3MB, time=29.58 memory used=1999.5MB, alloc=660.3MB, time=35.18 memory used=2251.6MB, alloc=660.3MB, time=41.33 memory used=2503.6MB, alloc=684.3MB, time=47.46 memory used=2779.7MB, alloc=684.3MB, time=54.12 memory used=3055.6MB, alloc=684.3MB, time=60.71 memory used=3331.4MB, alloc=708.3MB, time=67.20 memory used=3631.0MB, alloc=732.3MB, time=73.81 N1 := 9703 > GB := Basis(F, plex(op(vars))); 2 2 3 GB := [x y , -15 y + 7 y z, x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3898.1MB, alloc=732.3MB, time=77.82 memory used=4286.0MB, alloc=756.3MB, time=85.08 N2 := 3083 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 2 2 H := [-5 x y z - 13 x z , -15 y + 7 y z, -8 x y , 2 x y z - 14 x y, 3 3 4 4 z + 9 x , -19 y + 19 x y z] > J:=[op(GB),op(G)]; 2 2 3 2 2 3 3 J := [x y , -15 y + 7 y z, x z , 2 x y z - 14 x y, 4 z + 9 x , 4 -19 y + 19 x 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 := [6, 15, 20, 4, 3, 4, 3, 5/6, 5/6, 5/6, 7/13, 8/13, 6/13, 6, 14, 20, 4, 3, 4, 3, 5/6, 2/3, 5/6, 1/2, 7/12, 5/12, 1, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=4368.8MB, alloc=756.3MB, time=86.63 |\^/| 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(); 1428330422 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 F := [18 x y - x y, -2 x z + 5 x , -15 y z + 6 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 3 2 G := [-10 x + 17 y , 13 y + 18 z, 19 y z - 14 x z ] > Problem := [F,G]; 3 3 2 2 Problem := [[18 x y - x y, -2 x z + 5 x , -15 y z + 6 x z], 4 3 3 3 2 [-10 x + 17 y , 13 y + 18 z, 19 y z - 14 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.2MB, alloc=32.3MB, time=0.32 memory used=48.0MB, alloc=32.3MB, time=0.50 memory used=68.4MB, alloc=32.3MB, time=0.67 memory used=87.7MB, alloc=32.3MB, time=0.83 memory used=107.6MB, alloc=56.3MB, time=1.04 memory used=149.1MB, alloc=60.3MB, time=1.47 memory used=186.0MB, alloc=84.3MB, time=1.85 memory used=242.5MB, alloc=84.3MB, time=2.44 memory used=293.8MB, alloc=108.3MB, time=3.01 memory used=359.8MB, alloc=132.3MB, time=4.02 memory used=437.9MB, alloc=156.3MB, time=5.58 memory used=540.1MB, alloc=156.3MB, time=7.46 N1 := 3155 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 3 2 2 GB := [36 x - 5 x , 18 x y - x , 18 x y - x y, x z - 18 x , 2 2 -648 x y + 5 x y z, 5 y z - 2 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=644.3MB, alloc=156.3MB, time=9.00 memory used=686.9MB, alloc=164.3MB, time=9.46 memory used=774.2MB, alloc=420.3MB, time=10.27 memory used=880.6MB, alloc=444.3MB, time=11.32 memory used=1011.2MB, alloc=468.3MB, time=12.75 memory used=1154.7MB, alloc=492.3MB, time=14.29 memory used=1308.1MB, alloc=516.3MB, time=16.23 memory used=1454.4MB, alloc=540.3MB, time=19.01 memory used=1607.6MB, alloc=564.3MB, time=22.51 memory used=1775.4MB, alloc=588.3MB, time=26.57 memory used=1967.2MB, alloc=612.3MB, time=31.18 memory used=2183.0MB, alloc=636.3MB, time=36.32 memory used=2422.7MB, alloc=660.3MB, time=41.88 memory used=2686.4MB, alloc=660.3MB, time=47.91 memory used=2950.2MB, alloc=684.3MB, time=53.56 N2 := 7611 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 2 4 3 H := [18 x y - x y, -2 x z + 5 x , -15 y z + 6 x z, -10 x + 17 y , 3 3 2 13 y + 18 z, 19 y z - 14 x z ] > J:=[op(GB),op(G)]; 3 2 2 2 2 3 2 2 J := [36 x - 5 x , 18 x y - x , 18 x y - x y, x z - 18 x , 2 2 4 3 3 -648 x y + 5 x y z, 5 y z - 2 x z, -10 x + 17 y , 13 y + 18 z, 3 2 19 y z - 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 := [6, 14, 22, 4, 4, 3, 2, 5/6, 5/6, 2/3, 7/12, 1/2, 1/2, 9, 20, 31, 4, 4, 3, 2, 8/9, 7/9, 5/9, 13/18, 1/2, 7/18, -6, -9, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3091.1MB, alloc=684.3MB, time=55.94 |\^/| 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(); 1428330477 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 F := [-16 x y + 17 x z, -13 y + 9 z, 18 x z + 15 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 G := [-6 x z + 20 x z , x z - 17 y z, -2 x z + 13 x y ] > Problem := [F,G]; 3 3 4 Problem := [[-16 x y + 17 x z, -13 y + 9 z, 18 x z + 15 y ], 3 2 2 2 2 2 [-6 x z + 20 x z , x z - 17 y z, -2 x z + 13 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=0.14 memory used=26.3MB, alloc=32.3MB, time=0.33 memory used=47.1MB, alloc=32.3MB, time=0.49 memory used=66.8MB, alloc=32.3MB, time=0.66 memory used=85.5MB, alloc=56.3MB, time=0.83 memory used=123.6MB, alloc=60.3MB, time=1.15 memory used=158.1MB, alloc=84.3MB, time=1.45 memory used=211.6MB, alloc=84.3MB, time=1.91 memory used=264.7MB, alloc=116.3MB, time=2.42 memory used=340.5MB, alloc=116.3MB, time=3.11 memory used=414.3MB, alloc=140.3MB, time=3.79 memory used=510.5MB, alloc=140.3MB, time=4.70 memory used=605.2MB, alloc=164.3MB, time=5.61 memory used=697.8MB, alloc=420.3MB, time=6.53 memory used=808.7MB, alloc=444.3MB, time=7.61 memory used=939.4MB, alloc=468.3MB, time=8.91 memory used=1091.8MB, alloc=492.3MB, time=10.42 memory used=1261.6MB, alloc=516.3MB, time=12.18 memory used=1450.3MB, alloc=540.3MB, time=14.21 memory used=1654.1MB, alloc=564.3MB, time=16.37 memory used=1875.5MB, alloc=588.3MB, time=18.85 memory used=2101.2MB, alloc=612.3MB, time=21.48 memory used=2324.7MB, alloc=636.3MB, time=24.18 memory used=2562.5MB, alloc=660.3MB, time=27.01 memory used=2803.4MB, alloc=684.3MB, time=30.15 memory used=3041.2MB, alloc=708.3MB, time=33.15 memory used=3283.3MB, alloc=732.3MB, time=36.25 memory used=3523.6MB, alloc=756.3MB, time=39.72 memory used=3736.2MB, alloc=780.3MB, time=44.37 memory used=3951.2MB, alloc=804.3MB, time=49.57 memory used=4175.1MB, alloc=828.3MB, time=55.28 memory used=4410.2MB, alloc=852.3MB, time=61.38 memory used=4657.2MB, alloc=876.3MB, time=67.86 memory used=4916.9MB, alloc=900.3MB, time=74.80 memory used=5190.5MB, alloc=924.3MB, time=82.15 memory used=5478.3MB, alloc=948.3MB, time=89.97 memory used=5778.4MB, alloc=972.3MB, time=98.40 memory used=6090.0MB, alloc=996.3MB, time=107.50 memory used=6425.6MB, alloc=1020.3MB, time=117.25 memory used=6785.1MB, alloc=1044.3MB, time=127.66 memory used=7168.6MB, alloc=1068.3MB, time=138.63 memory used=7575.9MB, alloc=1092.3MB, time=150.32 memory used=8007.2MB, alloc=1116.3MB, time=162.64 memory used=8462.6MB, alloc=1140.3MB, time=175.64 memory used=8941.8MB, alloc=1164.3MB, time=189.29 memory used=9444.9MB, alloc=1188.3MB, time=203.56 memory used=9972.0MB, alloc=1212.3MB, time=218.54 memory used=10523.0MB, alloc=1236.3MB, time=234.11 memory used=11098.0MB, alloc=1260.3MB, time=250.38 memory used=11696.9MB, alloc=1284.3MB, time=267.33 memory used=12319.7MB, alloc=1308.3MB, time=284.84 memory used=12966.5MB, alloc=1332.3MB, time=302.97 |\^/| 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(); 1428330777 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 F := [-5 y z - 14 y z , 17 y + 2, -3 y + 2] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 4 G := [13 x y + 3 y, 19 x y - 6 y z, -x z + 4 z ] > Problem := [F,G]; 3 2 2 4 3 Problem := [[-5 y z - 14 y z , 17 y + 2, -3 y + 2], 2 3 2 3 4 [13 x y + 3 y, 19 x y - 6 y z, -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=0.15 memory used=26.3MB, alloc=32.3MB, time=0.41 memory used=47.6MB, alloc=32.3MB, time=0.64 memory used=68.1MB, alloc=32.3MB, time=0.86 memory used=88.4MB, alloc=56.3MB, time=1.16 memory used=130.3MB, alloc=60.3MB, time=1.74 memory used=166.4MB, alloc=84.3MB, time=2.38 N1 := 1081 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 71 #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)]; 3 2 2 4 3 2 3 2 H := [-5 y z - 14 y z , 17 y + 2, -3 y + 2, 13 x y + 3 y, 19 x y - 6 y z, 3 4 -x z + 4 z ] > J:=[op(GB),op(G)]; 2 3 2 3 4 J := [1, 13 x y + 3 y, 19 x y - 6 y z, -x 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, 11, 22, 4, 3, 4, 4, 1/2, 5/6, 1/2, 1/4, 2/3, 5/12, 4, 7, 11, 4, 3, 2, 4, 3/4, 1/2, 1/2, 3/7, 4/7, 3/7, 4, 11, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=201.7MB, alloc=84.3MB, time=2.96 |\^/| 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(); 1428330780 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 F := [-11 y z - 7 x, -16 x y - 10 x y z, 6 y + 17 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 4 G := [19 y z - 11 x , -11 y z - 3 y z, 11 z + 15 x z] > Problem := [F,G]; 2 2 2 4 Problem := [[-11 y z - 7 x, -16 x y - 10 x y z, 6 y + 17 z], 3 2 3 2 4 [19 y z - 11 x , -11 y z - 3 y z, 11 z + 15 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.5MB, alloc=32.3MB, time=0.44 memory used=47.9MB, alloc=32.3MB, time=0.68 memory used=68.6MB, alloc=56.3MB, time=0.93 memory used=108.1MB, alloc=60.3MB, time=1.40 memory used=145.9MB, alloc=84.3MB, time=1.84 memory used=209.7MB, alloc=92.3MB, time=2.55 memory used=265.4MB, alloc=116.3MB, time=3.20 memory used=344.8MB, alloc=116.3MB, time=4.14 memory used=427.2MB, alloc=140.3MB, time=5.18 memory used=510.6MB, alloc=140.3MB, time=6.07 memory used=579.1MB, alloc=420.3MB, time=6.79 memory used=716.0MB, alloc=444.3MB, time=8.22 memory used=846.9MB, alloc=444.3MB, time=9.52 memory used=989.2MB, alloc=468.3MB, time=10.69 memory used=1124.0MB, alloc=492.3MB, time=12.13 memory used=1236.9MB, alloc=492.3MB, time=13.32 memory used=1349.1MB, alloc=516.3MB, time=14.75 memory used=1459.8MB, alloc=516.3MB, time=16.13 memory used=1547.0MB, alloc=516.3MB, time=17.11 memory used=1636.9MB, alloc=540.3MB, time=17.97 memory used=1728.1MB, alloc=540.3MB, time=19.02 memory used=1800.7MB, alloc=540.3MB, time=19.86 memory used=1871.4MB, alloc=540.3MB, time=20.52 memory used=1947.9MB, alloc=564.3MB, time=21.22 memory used=2043.2MB, alloc=564.3MB, time=21.94 memory used=2124.4MB, alloc=564.3MB, time=22.99 memory used=2187.2MB, alloc=588.3MB, time=23.88 memory used=2246.0MB, alloc=588.3MB, time=24.77 memory used=2459.5MB, alloc=612.3MB, time=26.90 memory used=2731.5MB, alloc=636.3MB, time=28.70 memory used=2991.8MB, alloc=660.3MB, time=30.49 memory used=3191.8MB, alloc=684.3MB, time=32.63 memory used=3477.2MB, alloc=708.3MB, time=36.05 memory used=3757.8MB, alloc=732.3MB, time=39.79 memory used=4067.6MB, alloc=756.3MB, time=43.49 memory used=4426.7MB, alloc=780.3MB, time=46.93 memory used=4740.6MB, alloc=804.3MB, time=50.88 memory used=5006.7MB, alloc=828.3MB, time=54.66 memory used=5268.5MB, alloc=852.3MB, time=57.78 memory used=5569.3MB, alloc=876.3MB, time=64.44 memory used=5853.4MB, alloc=900.3MB, time=71.78 memory used=6141.9MB, alloc=924.3MB, time=79.57 memory used=6439.0MB, alloc=948.3MB, time=87.69 memory used=6746.6MB, alloc=972.3MB, time=96.25 memory used=7061.6MB, alloc=996.3MB, time=105.46 memory used=7389.4MB, alloc=1020.3MB, time=115.39 memory used=7741.1MB, alloc=1044.3MB, time=125.98 memory used=8116.7MB, alloc=1068.3MB, time=137.23 memory used=8516.3MB, alloc=1092.3MB, time=149.16 memory used=8939.8MB, alloc=1116.3MB, time=161.74 memory used=9387.3MB, alloc=1140.3MB, time=174.99 memory used=9858.6MB, alloc=1164.3MB, time=188.88 memory used=10353.9MB, alloc=1188.3MB, time=203.44 memory used=10873.2MB, alloc=1212.3MB, time=218.67 memory used=11416.3MB, alloc=1236.3MB, time=234.53 memory used=11983.4MB, alloc=1260.3MB, time=251.08 memory used=12574.4MB, alloc=1284.3MB, time=268.28 memory used=13189.4MB, alloc=1308.3MB, time=286.13 memory used=13828.2MB, alloc=1332.3MB, time=304.64 |\^/| 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(); 1428331080 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [6 x z - 19 x, -9 y z - 16, 7 y z - 12 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 G := [15 z - 14 x , -3 x y z + 7 z , -8 y z - 16 y] > Problem := [F,G]; 2 2 3 2 Problem := [[6 x z - 19 x, -9 y z - 16, 7 y z - 12 x z], 4 3 2 2 2 [15 z - 14 x , -3 x y z + 7 z , -8 y z - 16 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=26.4MB, alloc=32.3MB, time=0.37 memory used=48.0MB, alloc=32.3MB, time=0.60 memory used=68.1MB, alloc=32.3MB, time=0.81 memory used=87.3MB, alloc=32.3MB, time=1.03 memory used=106.2MB, alloc=56.3MB, time=1.28 memory used=143.4MB, alloc=60.3MB, time=1.71 memory used=178.6MB, alloc=84.3MB, time=2.17 memory used=235.6MB, alloc=108.3MB, time=3.01 memory used=312.3MB, alloc=108.3MB, time=4.10 memory used=382.2MB, alloc=132.3MB, time=5.12 memory used=470.2MB, alloc=164.3MB, time=6.41 memory used=573.9MB, alloc=188.3MB, time=7.89 memory used=685.6MB, alloc=212.3MB, time=9.77 memory used=799.3MB, alloc=236.3MB, time=12.25 memory used=922.9MB, alloc=260.3MB, time=15.34 memory used=1055.4MB, alloc=284.3MB, time=19.48 memory used=1211.1MB, alloc=308.3MB, time=23.41 memory used=1390.7MB, alloc=332.3MB, time=27.79 memory used=1594.2MB, alloc=332.3MB, time=32.73 memory used=1797.8MB, alloc=332.3MB, time=37.67 memory used=2001.3MB, alloc=356.3MB, time=42.61 memory used=2228.8MB, alloc=356.3MB, time=48.13 memory used=2456.2MB, alloc=356.3MB, time=53.63 memory used=2683.5MB, alloc=380.3MB, time=58.74 memory used=2934.8MB, alloc=404.3MB, time=63.83 N1 := 8835 > GB := Basis(F, plex(op(vars))); 2 2 GB := [27 x + 28, 57 y + 32, 6 z - 19] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 525 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 4 3 H := [6 x z - 19 x, -9 y z - 16, 7 y z - 12 x z, 15 z - 14 x , 2 2 2 -3 x y z + 7 z , -8 y z - 16 y] > J:=[op(GB),op(G)]; 2 2 4 3 2 2 J := [27 x + 28, 57 y + 32, 6 z - 19, 15 z - 14 x , -3 x y z + 7 z , 2 -8 y z - 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 := [6, 14, 21, 4, 3, 1, 4, 2/3, 2/3, 1, 5/12, 5/12, 2/3, 6, 10, 16, 4, 3, 1, 4, 1/2, 1/2, 2/3, 1/4, 1/3, 5/12, 4, 5, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3088.1MB, alloc=404.3MB, time=65.93 |\^/| 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(); 1428331147 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 4 2 F := [-20 x z - 4 y , -18 x y - y , -12 x z - 3 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-12 x - 14 x z, -6 x y z - 17 x z , -18 x y - 10 x z] > Problem := [F,G]; 2 3 3 4 2 Problem := [[-20 x z - 4 y , -18 x y - y , -12 x z - 3 y z], 2 2 2 2 [-12 x - 14 x z, -6 x y z - 17 x z , -18 x y - 10 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.0MB, alloc=32.3MB, time=0.32 memory used=47.4MB, alloc=32.3MB, time=0.50 memory used=67.5MB, alloc=32.3MB, time=0.68 memory used=86.0MB, alloc=56.3MB, time=0.85 memory used=125.0MB, alloc=60.3MB, time=1.19 memory used=162.2MB, alloc=60.3MB, time=1.52 memory used=196.5MB, alloc=84.3MB, time=1.83 memory used=252.3MB, alloc=116.3MB, time=2.40 memory used=328.8MB, alloc=140.3MB, time=3.21 memory used=421.0MB, alloc=164.3MB, time=4.16 memory used=528.1MB, alloc=188.3MB, time=5.30 memory used=647.9MB, alloc=212.3MB, time=6.59 memory used=756.3MB, alloc=492.3MB, time=7.83 memory used=896.7MB, alloc=516.3MB, time=10.19 memory used=1041.5MB, alloc=540.3MB, time=13.07 memory used=1196.2MB, alloc=564.3MB, time=16.60 memory used=1365.1MB, alloc=588.3MB, time=20.77 memory used=1558.0MB, alloc=612.3MB, time=25.49 memory used=1774.9MB, alloc=612.3MB, time=30.74 memory used=1991.7MB, alloc=636.3MB, time=35.98 memory used=2232.5MB, alloc=636.3MB, time=41.75 memory used=2473.2MB, alloc=636.3MB, time=47.50 memory used=2713.9MB, alloc=660.3MB, time=53.24 memory used=2978.6MB, alloc=660.3MB, time=59.46 memory used=3243.4MB, alloc=684.3MB, time=65.48 memory used=3532.2MB, alloc=708.3MB, time=71.40 N1 := 9539 > GB := Basis(F, plex(op(vars))); 6 3 5 3 2 3 4 2 3 GB := [20736 x y - 125 x y, 72 x y + 5 x y , 18 x y + y , 5 z x + y , 5 3 2 2 -373248 x y + 625 x y z, 1296 x y + 25 y z, 4 x z + y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3830.0MB, alloc=708.3MB, time=74.62 memory used=4178.6MB, alloc=708.3MB, time=78.15 memory used=4520.0MB, alloc=732.3MB, time=81.76 memory used=4825.0MB, alloc=756.3MB, time=85.10 memory used=5124.6MB, alloc=780.3MB, time=88.45 memory used=5398.6MB, alloc=804.3MB, time=91.52 memory used=5625.2MB, alloc=828.3MB, time=94.24 memory used=5836.9MB, alloc=852.3MB, time=96.74 memory used=6020.4MB, alloc=876.3MB, time=99.13 memory used=6210.9MB, alloc=900.3MB, time=101.72 memory used=6396.3MB, alloc=900.3MB, time=104.42 memory used=6903.8MB, alloc=924.3MB, time=110.55 memory used=7342.7MB, alloc=948.3MB, time=115.60 memory used=7762.2MB, alloc=972.3MB, time=120.49 memory used=8160.0MB, alloc=996.3MB, time=125.51 memory used=8539.8MB, alloc=1020.3MB, time=130.52 memory used=9137.3MB, alloc=1044.3MB, time=138.06 memory used=9751.2MB, alloc=1068.3MB, time=145.53 memory used=10361.7MB, alloc=1092.3MB, time=153.61 memory used=10968.9MB, alloc=1116.3MB, time=162.00 memory used=11585.0MB, alloc=1140.3MB, time=170.97 memory used=12206.9MB, alloc=1164.3MB, time=180.10 memory used=12834.2MB, alloc=1188.3MB, time=189.19 memory used=13419.9MB, alloc=1212.3MB, time=198.19 memory used=14023.1MB, alloc=1236.3MB, time=207.54 memory used=14523.2MB, alloc=1260.3MB, time=216.91 memory used=14937.9MB, alloc=1284.3MB, time=225.32 memory used=15318.5MB, alloc=1308.3MB, time=233.53 memory used=15689.4MB, alloc=1332.3MB, time=241.60 memory used=16099.0MB, alloc=1356.3MB, time=250.02 memory used=16579.0MB, alloc=1380.3MB, time=258.78 memory used=17138.1MB, alloc=1404.3MB, time=267.60 memory used=17658.4MB, alloc=1428.3MB, time=276.76 memory used=18126.7MB, alloc=1452.3MB, time=285.88 memory used=18561.0MB, alloc=1476.3MB, time=294.72 memory used=18935.2MB, alloc=1500.3MB, time=303.28 memory used=19292.0MB, alloc=1524.3MB, time=311.66 memory used=19634.8MB, alloc=1548.3MB, time=320.10 |\^/| 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(); 1428331447 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 F := [12 y z - 16, 8 y - 9 x y z, -x z + z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [6 y z - 2 y, -x z + 17 y z, 4 y z - 18 x y] > Problem := [F,G]; 2 4 2 2 Problem := [[12 y z - 16, 8 y - 9 x y z, -x z + z ], 2 2 2 2 [6 y z - 2 y, -x z + 17 y z, 4 y z - 18 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=0.14 memory used=26.8MB, alloc=32.3MB, time=0.37 memory used=47.4MB, alloc=32.3MB, time=0.60 memory used=67.7MB, alloc=32.3MB, time=0.83 memory used=86.5MB, alloc=56.3MB, time=1.10 memory used=125.7MB, alloc=60.3MB, time=1.56 memory used=162.3MB, alloc=60.3MB, time=1.87 memory used=197.9MB, alloc=84.3MB, time=2.19 memory used=257.5MB, alloc=92.3MB, time=2.73 memory used=313.6MB, alloc=116.3MB, time=3.25 memory used=393.0MB, alloc=116.3MB, time=3.96 memory used=470.6MB, alloc=396.3MB, time=4.67 memory used=571.4MB, alloc=420.3MB, time=5.58 memory used=691.7MB, alloc=444.3MB, time=6.71 memory used=828.5MB, alloc=444.3MB, time=8.06 memory used=962.1MB, alloc=468.3MB, time=9.39 memory used=1110.5MB, alloc=492.3MB, time=10.84 memory used=1283.4MB, alloc=516.3MB, time=12.73 memory used=1464.3MB, alloc=540.3MB, time=14.79 memory used=1644.3MB, alloc=564.3MB, time=16.93 memory used=1837.8MB, alloc=588.3MB, time=19.26 memory used=2065.5MB, alloc=612.3MB, time=21.54 memory used=2277.2MB, alloc=636.3MB, time=23.81 memory used=2447.1MB, alloc=660.3MB, time=25.88 memory used=2617.8MB, alloc=684.3MB, time=28.05 memory used=2776.4MB, alloc=708.3MB, time=30.14 memory used=2927.5MB, alloc=732.3MB, time=32.19 memory used=3075.4MB, alloc=756.3MB, time=34.18 memory used=3235.3MB, alloc=780.3MB, time=36.26 memory used=3364.7MB, alloc=804.3MB, time=38.36 memory used=3654.5MB, alloc=828.3MB, time=44.84 memory used=3940.1MB, alloc=852.3MB, time=51.72 memory used=4232.4MB, alloc=876.3MB, time=59.08 memory used=4533.3MB, alloc=900.3MB, time=66.69 memory used=4844.8MB, alloc=924.3MB, time=74.76 memory used=5168.7MB, alloc=948.3MB, time=83.31 memory used=5505.2MB, alloc=972.3MB, time=92.31 memory used=5855.5MB, alloc=996.3MB, time=101.77 memory used=6217.6MB, alloc=1020.3MB, time=111.75 memory used=6589.6MB, alloc=1044.3MB, time=122.30 memory used=6985.7MB, alloc=1068.3MB, time=133.52 memory used=7405.6MB, alloc=1092.3MB, time=145.36 memory used=7849.6MB, alloc=1116.3MB, time=157.82 memory used=8317.4MB, alloc=1140.3MB, time=170.95 memory used=8809.1MB, alloc=1164.3MB, time=184.70 memory used=9324.9MB, alloc=1188.3MB, time=199.10 memory used=9864.5MB, alloc=1212.3MB, time=214.21 memory used=10428.1MB, alloc=1236.3MB, time=229.94 memory used=11015.6MB, alloc=1260.3MB, time=246.26 memory used=11627.1MB, alloc=1260.3MB, time=263.26 memory used=12238.5MB, alloc=1260.3MB, time=280.24 memory used=12849.9MB, alloc=1284.3MB, time=297.28 |\^/| 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(); 1428331747 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 2 2 3 F := [5 x y + 5 z , -12 x - 3 x y, 16 x z + 9 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 2 G := [-3 x y - 3 y z , -13 x - 13 x z , -5 x y z - 19 x z] > Problem := [F,G]; 3 3 4 2 2 3 Problem := [[5 x y + 5 z , -12 x - 3 x y, 16 x z + 9 x z ], 3 2 4 2 2 [-3 x y - 3 y z , -13 x - 13 x z , -5 x y z - 19 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.4MB, alloc=32.3MB, time=0.39 memory used=47.8MB, alloc=32.3MB, time=0.62 memory used=67.9MB, alloc=32.3MB, time=0.84 memory used=87.0MB, alloc=56.3MB, time=1.07 memory used=126.2MB, alloc=60.3MB, time=1.50 memory used=164.4MB, alloc=60.3MB, time=1.92 memory used=201.1MB, alloc=84.3MB, time=2.34 memory used=258.4MB, alloc=84.3MB, time=3.02 memory used=313.8MB, alloc=108.3MB, time=3.72 memory used=392.6MB, alloc=140.3MB, time=4.81 memory used=489.6MB, alloc=164.3MB, time=6.21 memory used=601.2MB, alloc=188.3MB, time=7.78 memory used=724.0MB, alloc=212.3MB, time=9.65 memory used=850.0MB, alloc=236.3MB, time=11.61 memory used=977.8MB, alloc=260.3MB, time=14.01 memory used=1113.4MB, alloc=284.3MB, time=17.12 memory used=1268.0MB, alloc=308.3MB, time=20.82 memory used=1446.6MB, alloc=332.3MB, time=25.03 memory used=1649.1MB, alloc=332.3MB, time=29.78 memory used=1851.6MB, alloc=356.3MB, time=34.48 memory used=2078.1MB, alloc=356.3MB, time=39.74 memory used=2304.6MB, alloc=356.3MB, time=44.89 memory used=2531.0MB, alloc=380.3MB, time=49.93 memory used=2781.5MB, alloc=404.3MB, time=55.22 N1 := 8181 > GB := Basis(F, plex(op(vars))); 20 13 4 12 11 11 2 2 GB := [729 x + 64 x , 4 x + x y, 16 x + 9 x z, 36 x + x z , 10 3 -64 x + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2895.3MB, alloc=404.3MB, time=56.78 memory used=3202.5MB, alloc=660.3MB, time=59.91 memory used=3518.7MB, alloc=684.3MB, time=63.58 memory used=3833.1MB, alloc=708.3MB, time=67.51 memory used=4114.9MB, alloc=732.3MB, time=73.22 memory used=4381.4MB, alloc=756.3MB, time=79.90 memory used=4663.2MB, alloc=780.3MB, time=87.16 memory used=4968.9MB, alloc=804.3MB, time=94.98 memory used=5298.6MB, alloc=828.3MB, time=103.32 memory used=5652.2MB, alloc=852.3MB, time=112.20 memory used=6029.7MB, alloc=876.3MB, time=121.63 memory used=6431.3MB, alloc=900.3MB, time=131.58 memory used=6856.8MB, alloc=924.3MB, time=142.05 memory used=7306.3MB, alloc=948.3MB, time=152.86 memory used=7780.0MB, alloc=972.3MB, time=163.37 N2 := 11619 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 4 2 2 3 3 2 H := [5 x y + 5 z , -12 x - 3 x y, 16 x z + 9 x z , -3 x y - 3 y z , 4 2 2 -13 x - 13 x z , -5 x y z - 19 x z] > J:=[op(GB),op(G)]; 20 13 4 12 11 11 2 2 J := [729 x + 64 x , 4 x + x y, 16 x + 9 x z, 36 x + x z , 10 3 3 2 4 2 2 -64 x + z , -3 x y - 3 y z , -13 x - 13 x z , -5 x y z - 19 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 := [6, 15, 24, 4, 4, 3, 3, 1, 2/3, 5/6, 5/6, 5/12, 7/12, 8, 17, 69, 20, 20, 3, 3, 1, 3/8, 3/4, 7/8, 1/4, 7/16, -2, -45, -16] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=7880.2MB, alloc=972.3MB, time=165.02 |\^/| 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(); 1428331911 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 3 F := [-3 x y + 1, 16 x z + 4 z , -13 z + 20 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-7 y z + 15 x y, -17 x z - 7 y z, 13 y z + 9 z ] > Problem := [F,G]; 2 2 3 4 3 Problem := [[-3 x y + 1, 16 x z + 4 z , -13 z + 20 z ], 2 2 2 2 2 [-7 y z + 15 x y, -17 x z - 7 y z, 13 y z + 9 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.1MB, alloc=32.3MB, time=0.36 memory used=47.7MB, alloc=32.3MB, time=0.53 memory used=68.3MB, alloc=32.3MB, time=0.70 memory used=88.1MB, alloc=32.3MB, time=0.87 memory used=107.0MB, alloc=56.3MB, time=1.06 memory used=148.9MB, alloc=60.3MB, time=1.50 memory used=186.3MB, alloc=84.3MB, time=1.89 memory used=240.1MB, alloc=108.3MB, time=2.64 N1 := 1413 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [3 y x - 1, 169 x z + 100 z, 300 y z + 169 z, 13 z - 20 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=311.4MB, alloc=108.3MB, time=3.35 memory used=391.8MB, alloc=116.3MB, time=4.19 memory used=466.2MB, alloc=140.3MB, time=5.03 memory used=546.2MB, alloc=164.3MB, time=6.44 N2 := 2257 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 4 3 2 H := [-3 x y + 1, 16 x z + 4 z , -13 z + 20 z , -7 y z + 15 x y, 2 2 2 2 -17 x z - 7 y z, 13 y z + 9 z ] > J:=[op(GB),op(G)]; 2 2 2 J := [3 y x - 1, 169 x z + 100 z, 300 y z + 169 z, 13 z - 20 z, 2 2 2 2 2 -7 y z + 15 x y, -17 x z - 7 y z, 13 y z + 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 := [6, 13, 20, 4, 2, 1, 4, 2/3, 2/3, 5/6, 1/3, 5/12, 3/4, 7, 15, 20, 4, 2, 1, 2, 4/7, 5/7, 6/7, 2/7, 3/7, 11/14, -2, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=619.6MB, alloc=164.3MB, time=7.50 |\^/| 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(); 1428331918 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 F := [10 y z + 14, -11 x y z - 8 y z , 7 y z - 20 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 2 G := [10 x z - 13 y z, 8 x z - 6 x y, -17 x - 7 x z ] > Problem := [F,G]; 2 2 2 3 2 2 Problem := [[10 y z + 14, -11 x y z - 8 y z , 7 y z - 20 y], 2 2 3 4 2 [10 x z - 13 y z, 8 x z - 6 x y, -17 x - 7 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=27.3MB, alloc=32.3MB, time=0.35 memory used=48.9MB, alloc=32.3MB, time=0.53 memory used=70.1MB, alloc=60.3MB, time=0.72 memory used=111.5MB, alloc=60.3MB, time=1.06 memory used=151.1MB, alloc=84.3MB, time=1.40 memory used=216.1MB, alloc=116.3MB, time=1.96 memory used=287.3MB, alloc=372.3MB, time=2.56 memory used=376.0MB, alloc=396.3MB, time=3.30 memory used=485.1MB, alloc=420.3MB, time=4.25 memory used=614.4MB, alloc=444.3MB, time=5.40 memory used=742.4MB, alloc=468.3MB, time=6.53 memory used=857.2MB, alloc=468.3MB, time=7.55 memory used=955.7MB, alloc=492.3MB, time=8.50 memory used=1051.3MB, alloc=492.3MB, time=9.46 memory used=1137.9MB, alloc=492.3MB, time=10.36 memory used=1199.4MB, alloc=492.3MB, time=11.01 memory used=1273.4MB, alloc=492.3MB, time=11.82 memory used=1322.4MB, alloc=516.3MB, time=12.41 memory used=1383.9MB, alloc=516.3MB, time=13.18 memory used=1444.3MB, alloc=516.3MB, time=13.94 memory used=1486.5MB, alloc=516.3MB, time=14.53 memory used=1687.8MB, alloc=540.3MB, time=16.36 memory used=1863.0MB, alloc=564.3MB, time=18.08 memory used=2022.3MB, alloc=588.3MB, time=19.79 memory used=2163.2MB, alloc=612.3MB, time=21.34 memory used=2311.6MB, alloc=636.3MB, time=23.22 memory used=2407.1MB, alloc=636.3MB, time=24.47 memory used=2523.2MB, alloc=636.3MB, time=26.00 memory used=2613.5MB, alloc=636.3MB, time=27.27 memory used=2700.7MB, alloc=636.3MB, time=28.69 memory used=3011.5MB, alloc=660.3MB, time=31.69 memory used=3330.3MB, alloc=684.3MB, time=34.90 memory used=3653.6MB, alloc=708.3MB, time=38.45 memory used=3913.3MB, alloc=732.3MB, time=41.62 memory used=4163.1MB, alloc=756.3MB, time=44.76 memory used=4390.0MB, alloc=780.3MB, time=47.77 memory used=4609.7MB, alloc=804.3MB, time=50.91 memory used=4814.4MB, alloc=828.3MB, time=54.19 memory used=5240.4MB, alloc=852.3MB, time=59.09 memory used=5671.4MB, alloc=876.3MB, time=64.48 memory used=6115.6MB, alloc=900.3MB, time=70.17 memory used=6569.0MB, alloc=924.3MB, time=76.06 memory used=7029.3MB, alloc=948.3MB, time=82.28 memory used=7484.0MB, alloc=972.3MB, time=88.97 memory used=7954.3MB, alloc=996.3MB, time=95.72 memory used=8413.4MB, alloc=1020.3MB, time=102.36 memory used=8753.2MB, alloc=1044.3MB, time=108.27 memory used=9182.6MB, alloc=1068.3MB, time=116.09 memory used=9496.7MB, alloc=1092.3MB, time=123.21 memory used=9813.4MB, alloc=1116.3MB, time=130.41 memory used=10132.9MB, alloc=1140.3MB, time=137.67 memory used=10452.7MB, alloc=1164.3MB, time=145.01 memory used=10817.2MB, alloc=1188.3MB, time=152.64 memory used=11141.5MB, alloc=1212.3MB, time=160.22 memory used=11472.2MB, alloc=1236.3MB, time=167.95 memory used=11787.3MB, alloc=1260.3MB, time=177.66 memory used=12069.7MB, alloc=1284.3MB, time=187.99 memory used=12353.9MB, alloc=1308.3MB, time=198.76 memory used=12646.5MB, alloc=1332.3MB, time=209.84 memory used=12948.2MB, alloc=1356.3MB, time=221.32 memory used=13261.8MB, alloc=1380.3MB, time=233.25 memory used=13587.6MB, alloc=1404.3MB, time=245.74 memory used=13924.9MB, alloc=1428.3MB, time=258.76 memory used=14279.9MB, alloc=1452.3MB, time=272.17 memory used=14650.8MB, alloc=1476.3MB, time=286.09 memory used=15038.7MB, alloc=1500.3MB, time=300.53 memory used=15442.8MB, alloc=1524.3MB, time=315.61 memory used=15857.6MB, alloc=1548.3MB, time=331.41 |\^/| 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(); 1428332218 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [6 x y z + 20 z, 2 y, 11 x y z - 16 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 2 G := [18 x + 15 x y, -14 z - 7 y, -16 x z - 7 x y] > Problem := [F,G]; 2 2 2 Problem := [[6 x y z + 20 z, 2 y, 11 x y z - 16 z ], 2 4 3 2 [18 x + 15 x y, -14 z - 7 y, -16 x z - 7 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.38 memory used=47.4MB, alloc=32.3MB, time=0.63 memory used=67.9MB, alloc=56.3MB, time=0.90 memory used=109.6MB, alloc=60.3MB, time=1.40 memory used=150.3MB, alloc=60.3MB, time=1.86 memory used=187.9MB, alloc=84.3MB, time=2.32 memory used=242.5MB, alloc=108.3MB, time=3.08 memory used=320.3MB, alloc=116.3MB, time=4.13 memory used=392.3MB, alloc=140.3MB, time=5.14 memory used=481.6MB, alloc=164.3MB, time=6.41 memory used=584.9MB, alloc=188.3MB, time=8.16 memory used=694.0MB, alloc=212.3MB, time=10.82 memory used=809.2MB, alloc=236.3MB, time=14.52 memory used=948.5MB, alloc=260.3MB, time=17.66 memory used=1111.6MB, alloc=260.3MB, time=21.24 memory used=1274.8MB, alloc=284.3MB, time=24.67 N1 := 5201 > GB := Basis(F, plex(op(vars))); GB := [y, z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 191 #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 4 H := [6 x y z + 20 z, 2 y, 11 x y z - 16 z , 18 x + 15 x y, -14 z - 7 y, 3 2 -16 x z - 7 x y] > J:=[op(GB),op(G)]; 2 4 3 2 J := [y, z, 18 x + 15 x y, -14 z - 7 y, -16 x z - 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 := [6, 14, 19, 4, 3, 1, 4, 2/3, 1, 2/3, 1/2, 1/2, 1/2, 5, 9, 12, 4, 3, 1, 4, 2/5, 4/5, 3/5, 1/2, 1/2, 3/8, 5, 7, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1447.2MB, alloc=284.3MB, time=27.35 |\^/| 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(); 1428332246 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [y z + 7 y, 18 x z - 12 y z, -14 x y z + 19 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 G := [19 y z + 7 y z , 14 z, 14 x + 4 y ] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[y z + 7 y, 18 x z - 12 y z, -14 x y z + 19 x y], 2 2 4 3 [19 y z + 7 y z , 14 z, 14 x + 4 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=26.7MB, alloc=32.3MB, time=0.35 memory used=47.7MB, alloc=32.3MB, time=0.54 memory used=67.9MB, alloc=56.3MB, time=0.72 memory used=109.9MB, alloc=60.3MB, time=1.10 memory used=154.3MB, alloc=92.3MB, time=1.54 memory used=221.6MB, alloc=100.3MB, time=2.29 memory used=282.2MB, alloc=124.3MB, time=2.95 memory used=358.4MB, alloc=148.3MB, time=3.94 memory used=440.4MB, alloc=172.3MB, time=5.52 memory used=545.2MB, alloc=196.3MB, time=7.33 N1 := 2813 > GB := Basis(F, plex(op(vars))); 3 2 2 3 4 2 3 2 2 GB := [y x , y x , x y , y , 3 x y z - 2 y , 14 x y z - 19 x y, 3 2 2 2 2 3 19 y z + 147 x y , 3 x z - 2 y z, y z + 7 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=667.0MB, alloc=196.3MB, time=8.63 memory used=816.7MB, alloc=476.3MB, time=10.00 memory used=986.5MB, alloc=500.3MB, time=11.64 memory used=1178.4MB, alloc=524.3MB, time=13.62 memory used=1366.3MB, alloc=548.3MB, time=15.74 memory used=1562.7MB, alloc=572.3MB, time=18.07 memory used=1750.1MB, alloc=596.3MB, time=21.68 memory used=1932.8MB, alloc=620.3MB, time=26.13 memory used=2130.5MB, alloc=644.3MB, time=31.13 memory used=2352.1MB, alloc=668.3MB, time=36.72 memory used=2597.8MB, alloc=692.3MB, time=42.88 memory used=2867.3MB, alloc=716.3MB, time=49.44 memory used=3160.8MB, alloc=740.3MB, time=56.36 memory used=3478.5MB, alloc=764.3MB, time=62.85 N2 := 7881 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 2 2 H := [y z + 7 y, 18 x z - 12 y z, -14 x y z + 19 x y, 19 y z + 7 y z , 4 3 14 z, 14 x + 4 y ] > J:=[op(GB),op(G)]; 3 2 2 3 4 2 3 2 2 J := [y x , y x , x y , y , 3 x y z - 2 y , 14 x y z - 19 x y, 3 2 2 2 2 3 2 2 19 y z + 147 x y , 3 x z - 2 y z, y z + 7 y, 19 y z + 7 y z , 14 z, 4 3 14 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 := [6, 13, 20, 4, 4, 3, 3, 1/2, 5/6, 5/6, 1/3, 2/3, 7/12, 12, 26, 44, 4, 4, 4, 3, 2/3, 11/12, 7/12, 3/8, 2/3, 3/8, -13, -24, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3482.4MB, alloc=764.3MB, time=62.93 |\^/| 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(); 1428332308 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [2 x z + 12 x z, 2 x - 4 y z , 5 x z - 4] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 G := [4 x - 6 x y z, -15 x y + 11 x y , 12 y z + 18 x z] > Problem := [F,G]; 2 2 3 2 2 Problem := [[2 x z + 12 x z, 2 x - 4 y z , 5 x z - 4], 4 2 3 2 2 [4 x - 6 x y z, -15 x y + 11 x y , 12 y z + 18 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=0.14 memory used=26.3MB, alloc=32.3MB, time=0.33 memory used=47.9MB, alloc=32.3MB, time=0.52 memory used=67.7MB, alloc=32.3MB, time=0.68 memory used=86.2MB, alloc=56.3MB, time=0.85 memory used=124.0MB, alloc=60.3MB, time=1.18 memory used=160.1MB, alloc=84.3MB, time=1.50 memory used=208.9MB, alloc=84.3MB, time=1.94 memory used=265.2MB, alloc=116.3MB, time=2.48 memory used=342.8MB, alloc=116.3MB, time=3.17 memory used=420.1MB, alloc=140.3MB, time=3.89 memory used=497.9MB, alloc=396.3MB, time=4.64 memory used=590.8MB, alloc=420.3MB, time=5.53 memory used=705.5MB, alloc=444.3MB, time=6.62 memory used=838.1MB, alloc=468.3MB, time=8.12 memory used=979.8MB, alloc=492.3MB, time=9.69 memory used=1140.6MB, alloc=516.3MB, time=11.41 memory used=1308.1MB, alloc=540.3MB, time=13.29 memory used=1487.5MB, alloc=564.3MB, time=15.40 memory used=1678.7MB, alloc=588.3MB, time=17.66 memory used=1885.8MB, alloc=612.3MB, time=20.04 memory used=2073.9MB, alloc=636.3MB, time=23.71 memory used=2263.6MB, alloc=660.3MB, time=27.86 memory used=2461.6MB, alloc=684.3MB, time=32.50 memory used=2670.6MB, alloc=708.3MB, time=37.62 memory used=2888.6MB, alloc=732.3MB, time=43.30 memory used=3120.9MB, alloc=756.3MB, time=49.57 memory used=3377.1MB, alloc=780.3MB, time=56.49 memory used=3657.3MB, alloc=804.3MB, time=64.07 memory used=3961.4MB, alloc=828.3MB, time=72.21 memory used=4289.4MB, alloc=852.3MB, time=80.96 memory used=4641.4MB, alloc=876.3MB, time=90.34 memory used=5017.3MB, alloc=900.3MB, time=100.32 memory used=5417.2MB, alloc=900.3MB, time=110.90 memory used=5817.0MB, alloc=924.3MB, time=121.52 memory used=6240.7MB, alloc=924.3MB, time=132.71 memory used=6664.3MB, alloc=924.3MB, time=143.88 memory used=7088.0MB, alloc=924.3MB, time=155.07 memory used=7511.4MB, alloc=948.3MB, time=166.24 memory used=7958.6MB, alloc=948.3MB, time=177.85 memory used=8405.9MB, alloc=972.3MB, time=189.62 memory used=8876.9MB, alloc=972.3MB, time=202.01 memory used=9347.7MB, alloc=996.3MB, time=214.44 memory used=9842.6MB, alloc=996.3MB, time=227.44 memory used=10337.3MB, alloc=1020.3MB, time=240.09 memory used=10856.4MB, alloc=1044.3MB, time=252.63 N1 := 17657 > GB := Basis(F, plex(op(vars))); GB := [x - 45, 8 y - 20503125, 15 z + 2] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 1427 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 4 2 H := [2 x z + 12 x z, 2 x - 4 y z , 5 z x - 4, 4 x - 6 x y z, 3 2 2 -15 x y + 11 x y , 12 y z + 18 x z] > J:=[op(GB),op(G)]; 4 2 3 2 J := [x - 45, 8 y - 20503125, 15 z + 2, 4 x - 6 x y z, -15 x y + 11 x y , 2 12 y z + 18 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 := [6, 15, 21, 4, 4, 3, 2, 1, 2/3, 5/6, 3/4, 5/12, 7/12, 6, 11, 14, 4, 4, 3, 2, 2/3, 2/3, 1/2, 1/2, 5/12, 1/3, 4, 7, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=11335.8MB, alloc=1044.3MB, time=260.64 |\^/| 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(); 1428332564 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 4 3 F := [9 x z - 16 y , 15 x y + 12 x, 14 x + 8 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 3 G := [-6 x y - 5 x, -4 x z + 7 y z , -7 x y - 13 x y ] > Problem := [F,G]; 3 4 3 4 3 Problem := [[9 x z - 16 y , 15 x y + 12 x, 14 x + 8 x z], 3 3 2 2 2 2 3 [-6 x y - 5 x, -4 x z + 7 y z , -7 x y - 13 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=0.14 memory used=26.2MB, alloc=32.3MB, time=0.31 memory used=47.7MB, alloc=32.3MB, time=0.50 memory used=68.3MB, alloc=32.3MB, time=0.70 memory used=88.2MB, alloc=56.3MB, time=0.90 memory used=131.1MB, alloc=60.3MB, time=1.33 memory used=170.7MB, alloc=84.3MB, time=1.76 memory used=229.3MB, alloc=108.3MB, time=2.41 N1 := 1439 > GB := Basis(F, plex(op(vars))); 13 5 GB := [18386112189375 x + 274877906944 x, -15435 x + 4096 x y, 4 4 2 1024 y + 3087 x , 7 x + 4 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=301.0MB, alloc=108.3MB, time=3.39 memory used=376.3MB, alloc=116.3MB, time=4.06 N2 := 353 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 4 3 4 3 3 H := [9 z x - 16 y , 15 x y + 12 x, 14 x + 8 x z, -6 x y - 5 x, 3 2 2 2 2 3 -4 x z + 7 y z , -7 x y - 13 x y ] > J:=[op(GB),op(G)]; 13 5 J := [18386112189375 x + 274877906944 x, -15435 x + 4096 x y, 4 4 2 3 3 2 2 1024 y + 3087 x , 7 x + 4 x z, -6 x y - 5 x, -4 x z + 7 y z , 2 2 3 -7 x y - 13 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 := [6, 14, 24, 4, 4, 4, 3, 1, 5/6, 1/2, 5/6, 1/2, 1/3, 7, 14, 36, 13, 13, 4, 2, 1, 5/7, 2/7, 6/7, 3/7, 3/14, 0, -12, -9] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=388.0MB, alloc=116.3MB, time=4.19 |\^/| 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(); 1428332568 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 2 3 2 F := [9 x - 19 y , -6 x y z - 17 z , 8 x y z - 16 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-17 x y + 14 x , -20 x y - 12 y, 4 x y z + 2 x] > Problem := [F,G]; 4 4 2 3 2 Problem := [[9 x - 19 y , -6 x y z - 17 z , 8 x y z - 16 x y], 3 2 2 2 [-17 x y + 14 x , -20 x y - 12 y, 4 x 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=0.12 memory used=26.1MB, alloc=32.3MB, time=0.29 memory used=47.4MB, alloc=32.3MB, time=0.46 memory used=67.7MB, alloc=32.3MB, time=0.63 memory used=87.7MB, alloc=56.3MB, time=0.81 memory used=128.3MB, alloc=60.3MB, time=1.15 memory used=166.6MB, alloc=60.3MB, time=1.50 memory used=205.2MB, alloc=84.3MB, time=1.95 memory used=262.2MB, alloc=108.3MB, time=2.56 memory used=337.2MB, alloc=140.3MB, time=3.38 memory used=429.1MB, alloc=164.3MB, time=4.36 memory used=533.8MB, alloc=188.3MB, time=5.77 memory used=643.6MB, alloc=212.3MB, time=7.80 memory used=762.5MB, alloc=236.3MB, time=10.49 memory used=904.3MB, alloc=236.3MB, time=13.68 memory used=1046.0MB, alloc=260.3MB, time=16.84 memory used=1211.9MB, alloc=260.3MB, time=20.41 memory used=1377.8MB, alloc=284.3MB, time=23.69 N1 := 5375 > GB := Basis(F, plex(op(vars))); 11 5 7 6 2 4 4 GB := [81 x - 5491 x , 81 x y - 5491 x y, 27 x + 323 x y , -9 x + 19 y , 6 5 7 2 3 6 x y + 17 x z, -162 x + 5491 x y z, -72 x y + 289 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1505.1MB, alloc=284.3MB, time=25.23 memory used=1690.3MB, alloc=540.3MB, time=27.02 memory used=1847.4MB, alloc=540.3MB, time=28.56 memory used=2008.6MB, alloc=564.3MB, time=30.19 memory used=2156.1MB, alloc=564.3MB, time=31.67 memory used=2297.2MB, alloc=588.3MB, time=33.16 memory used=2424.3MB, alloc=588.3MB, time=34.48 memory used=2566.3MB, alloc=612.3MB, time=36.31 memory used=2724.1MB, alloc=636.3MB, time=38.32 memory used=2871.9MB, alloc=660.3MB, time=40.32 memory used=2996.5MB, alloc=684.3MB, time=42.01 memory used=3150.0MB, alloc=708.3MB, time=43.99 memory used=3305.1MB, alloc=708.3MB, time=45.78 memory used=3445.7MB, alloc=732.3MB, time=47.70 memory used=3575.5MB, alloc=756.3MB, time=49.53 memory used=3695.2MB, alloc=780.3MB, time=51.59 memory used=3986.6MB, alloc=804.3MB, time=58.38 memory used=4322.2MB, alloc=828.3MB, time=67.01 memory used=4664.8MB, alloc=852.3MB, time=76.18 memory used=5009.6MB, alloc=876.3MB, time=86.26 memory used=5373.2MB, alloc=900.3MB, time=96.97 memory used=5760.6MB, alloc=924.3MB, time=108.31 memory used=6172.1MB, alloc=948.3MB, time=120.30 memory used=6607.4MB, alloc=948.3MB, time=132.94 memory used=7042.7MB, alloc=948.3MB, time=145.55 memory used=7478.0MB, alloc=972.3MB, time=158.14 memory used=7937.2MB, alloc=972.3MB, time=171.32 memory used=8396.4MB, alloc=996.3MB, time=184.42 memory used=8879.6MB, alloc=996.3MB, time=198.28 memory used=9362.7MB, alloc=1020.3MB, time=212.02 memory used=9869.5MB, alloc=1020.3MB, time=225.89 memory used=10376.4MB, alloc=1044.3MB, time=239.55 memory used=10907.3MB, alloc=1068.3MB, time=253.48 N2 := 15535 #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)]; 4 4 2 3 2 3 2 H := [-19 y + 9 x , -6 x y z - 17 z , 8 x y z - 16 x y, -17 x y + 14 x , 2 2 -20 x y - 12 y, 4 x y z + 2 x] > J:=[op(GB),op(G)]; 11 5 7 6 2 4 4 J := [81 x - 5491 x , 81 x y - 5491 x y, 27 x + 323 x y , -9 x + 19 y , 6 5 7 2 3 3 2 6 x y + 17 x z, -162 x + 5491 x y z, -72 x y + 289 z , -17 x y + 14 x , 2 2 -20 x y - 12 y, 4 x y z + 2 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 23, 4, 4, 4, 3, 1, 1, 1/2, 3/4, 2/3, 1/3, 10, 23, 57, 11, 11, 4, 3, 1, 9/10, 2/5, 17/20, 11/20, 1/5, -8, -34, -7] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=11206.4MB, alloc=1068.3MB, time=259.96 |\^/| 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(); 1428332823 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-x z - 18 y z, 4 - 14 y, 14 x z + 14 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 4 G := [19 z + 4 z, 7 x z + 17 y z, 10 x + 9 z ] > Problem := [F,G]; 2 2 Problem := [[-x z - 18 y z, 4 - 14 y, 14 x z + 14 y z], 3 3 2 4 4 [19 z + 4 z, 7 x z + 17 y z, 10 x + 9 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.2MB, alloc=32.3MB, time=0.35 memory used=47.7MB, alloc=32.3MB, time=0.53 memory used=68.2MB, alloc=32.3MB, time=0.70 memory used=88.2MB, alloc=56.3MB, time=0.91 N1 := 379 > GB := Basis(F, plex(op(vars))); GB := [7 y - 2, z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=130.0MB, alloc=60.3MB, time=1.36 N2 := 121 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 2 H := [-x z - 18 y z, 4 - 14 y, 14 x z + 14 y z, 19 z + 4 z, 7 x z + 17 y z, 4 4 9 z + 10 x ] > J:=[op(GB),op(G)]; 3 3 2 4 4 J := [7 y - 2, z, 19 z + 4 z, 7 x z + 17 y z, 9 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, 17, 4, 4, 2, 4, 2/3, 2/3, 5/6, 1/3, 1/3, 3/4, 5, 8, 13, 4, 4, 2, 4, 2/5, 2/5, 4/5, 2/9, 2/9, 2/3, 5, 4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=162.2MB, alloc=60.3MB, 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(); 1428332825 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 3 F := [-10 x y + 5 y z, -4 x y + 2 y z, -6 x z - 17 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 2 G := [-13 x y + 2 y z , 14 x + 3 x z, -4 y z - 8 x y] > Problem := [F,G]; 3 3 3 3 3 Problem := [[-10 x y + 5 y z, -4 x y + 2 y z, -6 x z - 17 y z ], 3 2 4 2 2 [-13 x y + 2 y z , 14 x + 3 x z, -4 y z - 8 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.11 memory used=26.7MB, alloc=32.3MB, time=0.30 memory used=47.7MB, alloc=32.3MB, time=0.47 memory used=67.1MB, alloc=56.3MB, time=0.65 memory used=106.0MB, alloc=60.3MB, time=1.04 memory used=143.1MB, alloc=60.3MB, time=1.36 memory used=180.6MB, alloc=84.3MB, time=1.68 memory used=228.8MB, alloc=84.3MB, time=2.10 memory used=287.4MB, alloc=116.3MB, time=2.64 memory used=365.8MB, alloc=116.3MB, time=3.33 memory used=440.4MB, alloc=140.3MB, time=4.02 memory used=531.8MB, alloc=396.3MB, time=4.88 memory used=628.2MB, alloc=420.3MB, time=5.75 memory used=738.7MB, alloc=444.3MB, time=6.80 memory used=876.3MB, alloc=468.3MB, time=8.07 memory used=1031.4MB, alloc=492.3MB, time=9.53 memory used=1176.9MB, alloc=516.3MB, time=10.93 memory used=1305.7MB, alloc=516.3MB, time=12.20 memory used=1434.4MB, alloc=516.3MB, time=13.52 memory used=1563.3MB, alloc=540.3MB, time=14.91 memory used=1676.8MB, alloc=540.3MB, time=16.16 memory used=1775.7MB, alloc=540.3MB, time=17.29 memory used=1867.8MB, alloc=540.3MB, time=18.37 memory used=1965.4MB, alloc=540.3MB, time=19.52 memory used=2037.1MB, alloc=540.3MB, time=20.39 memory used=2105.5MB, alloc=540.3MB, time=21.29 memory used=2181.1MB, alloc=564.3MB, time=22.31 memory used=2250.8MB, alloc=564.3MB, time=23.25 memory used=2308.4MB, alloc=564.3MB, time=24.11 memory used=2536.1MB, alloc=588.3MB, time=26.57 memory used=2752.8MB, alloc=612.3MB, time=29.00 memory used=2990.9MB, alloc=636.3MB, time=31.77 memory used=3180.9MB, alloc=660.3MB, time=34.04 memory used=3334.5MB, alloc=684.3MB, time=36.05 memory used=3479.4MB, alloc=708.3MB, time=37.91 memory used=3601.0MB, alloc=732.3MB, time=39.65 memory used=3704.9MB, alloc=732.3MB, time=41.19 memory used=3821.9MB, alloc=756.3MB, time=42.88 memory used=3955.1MB, alloc=756.3MB, time=44.98 memory used=4109.3MB, alloc=780.3MB, time=47.40 memory used=4307.4MB, alloc=804.3MB, time=50.56 memory used=4661.9MB, alloc=828.3MB, time=55.40 memory used=5082.8MB, alloc=852.3MB, time=59.51 memory used=5572.9MB, alloc=876.3MB, time=62.47 memory used=6095.3MB, alloc=900.3MB, time=65.50 memory used=6614.2MB, alloc=924.3MB, time=69.56 memory used=7113.6MB, alloc=948.3MB, time=74.97 memory used=7578.3MB, alloc=972.3MB, time=81.13 memory used=8014.1MB, alloc=996.3MB, time=87.40 memory used=8433.9MB, alloc=1020.3MB, time=93.54 memory used=8843.8MB, alloc=1044.3MB, time=99.61 memory used=9306.4MB, alloc=1068.3MB, time=104.74 memory used=9783.7MB, alloc=1092.3MB, time=107.96 memory used=10295.7MB, alloc=1116.3MB, time=112.52 memory used=10686.2MB, alloc=1140.3MB, time=122.36 memory used=11065.7MB, alloc=1164.3MB, time=132.72 memory used=11444.2MB, alloc=1188.3MB, time=143.44 memory used=11825.1MB, alloc=1212.3MB, time=154.26 memory used=12212.5MB, alloc=1236.3MB, time=165.40 memory used=12607.5MB, alloc=1260.3MB, time=176.80 memory used=13011.2MB, alloc=1284.3MB, time=188.54 memory used=13425.2MB, alloc=1308.3MB, time=200.70 memory used=13850.0MB, alloc=1332.3MB, time=213.22 memory used=14286.2MB, alloc=1356.3MB, time=226.16 memory used=14734.9MB, alloc=1380.3MB, time=239.55 memory used=15196.1MB, alloc=1404.3MB, time=253.39 memory used=15669.9MB, alloc=1428.3MB, time=267.75 memory used=16146.6MB, alloc=1452.3MB, time=282.78 memory used=16646.5MB, alloc=1476.3MB, time=298.50 memory used=17170.4MB, alloc=1500.3MB, time=314.84 |\^/| 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(); 1428333125 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-7 x y z, -3 x y - 12 z, -11 y z + 18] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 G := [-12 y , 15 z + 19 y , -13 x + 15 y] > Problem := [F,G]; 3 2 2 Problem := [[-7 x y z, -3 x y - 12 z, -11 y z + 18], 2 4 2 [-12 y , 15 z + 19 y , -13 x + 15 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=27.1MB, alloc=32.3MB, time=0.41 memory used=48.8MB, alloc=32.3MB, time=0.67 memory used=69.7MB, alloc=56.3MB, time=0.99 memory used=111.8MB, alloc=60.3MB, time=1.60 N1 := 691 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 19 #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)]; 3 2 2 2 4 2 H := [-7 x y z, -3 x y - 12 z, -11 y z + 18, -12 y , 15 z + 19 y , -13 x + 15 y] > J:=[op(GB),op(G)]; 2 4 2 J := [1, -12 y , 15 z + 19 y , -13 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 := [6, 13, 18, 4, 3, 2, 4, 1/2, 1, 2/3, 3/14, 3/7, 2/7, 4, 5, 7, 4, 1, 2, 4, 1/4, 3/4, 1/4, 1/7, 3/7, 1/7, 8, 11, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=120.8MB, alloc=60.3MB, 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(); 1428333127 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 F := [8 x y z + 8 y z, 12 x z - 16 x z, -20 x y z - 2 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [-4 x y - 4 y , 20 x z + 11 x , -11 x y z + 11 y ] > Problem := [F,G]; 2 3 2 2 2 2 Problem := [[8 x y z + 8 y z, 12 x z - 16 x z, -20 x y z - 2 x y ], 2 2 2 2 3 [-4 x y - 4 y , 20 x z + 11 x , -11 x y z + 11 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.42 memory used=47.5MB, alloc=32.3MB, time=0.66 memory used=67.9MB, alloc=32.3MB, time=0.90 memory used=87.3MB, alloc=56.3MB, time=1.15 memory used=126.6MB, alloc=60.3MB, time=1.60 memory used=162.7MB, alloc=84.3MB, time=2.04 memory used=220.3MB, alloc=108.3MB, time=2.80 memory used=295.8MB, alloc=140.3MB, time=3.86 memory used=386.1MB, alloc=164.3MB, time=5.10 memory used=490.4MB, alloc=188.3MB, time=6.52 memory used=608.4MB, alloc=212.3MB, time=8.14 memory used=735.5MB, alloc=236.3MB, time=10.36 memory used=861.2MB, alloc=260.3MB, time=13.22 memory used=997.0MB, alloc=284.3MB, time=16.81 memory used=1140.9MB, alloc=308.3MB, time=20.23 memory used=1308.8MB, alloc=332.3MB, time=24.17 memory used=1500.7MB, alloc=356.3MB, time=28.66 memory used=1716.5MB, alloc=356.3MB, time=33.67 memory used=1932.2MB, alloc=356.3MB, time=38.67 memory used=2147.8MB, alloc=380.3MB, time=43.68 memory used=2387.4MB, alloc=380.3MB, time=49.17 memory used=2626.8MB, alloc=380.3MB, time=54.60 memory used=2866.2MB, alloc=404.3MB, time=59.98 memory used=3129.3MB, alloc=428.3MB, time=65.75 memory used=3416.6MB, alloc=452.3MB, time=71.45 N1 := 9631 > GB := Basis(F, plex(op(vars))); 2 2 2 4 2 3 GB := [3 x y + 40 x y , 3 x y + 4 x y , -3 x y + 40 x y z, 3 3 2 2 -3 x y + 400 y z, 3 x z - 4 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3546.9MB, alloc=452.3MB, time=73.24 memory used=3899.6MB, alloc=708.3MB, time=77.01 memory used=4243.7MB, alloc=732.3MB, time=80.99 memory used=4590.2MB, alloc=756.3MB, time=85.54 memory used=4893.5MB, alloc=780.3MB, time=92.04 memory used=5188.4MB, alloc=804.3MB, time=99.36 memory used=5494.7MB, alloc=828.3MB, time=107.26 memory used=5825.1MB, alloc=852.3MB, time=115.71 memory used=6179.4MB, alloc=876.3MB, time=124.70 memory used=6557.7MB, alloc=900.3MB, time=134.18 memory used=6959.9MB, alloc=924.3MB, time=144.12 memory used=7386.2MB, alloc=948.3MB, time=154.49 memory used=7836.5MB, alloc=972.3MB, time=165.26 memory used=8310.8MB, alloc=996.3MB, time=176.38 memory used=8809.1MB, alloc=1020.3MB, time=187.61 N2 := 12461 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 2 2 2 H := [8 x y z + 8 y z, 12 x z - 16 x z, -20 x y z - 2 x y , -4 x y - 4 y , 2 2 2 3 20 x z + 11 x , -11 x y z + 11 y ] > J:=[op(GB),op(G)]; 2 2 2 4 2 3 J := [3 x y + 40 x y , 3 x y + 4 x y , -3 x y + 40 x y z, 3 3 2 2 2 2 2 -3 x y + 400 y z, 3 x z - 4 x z, -4 x y - 4 y , 20 x z + 11 x , 2 3 -11 x 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 := [6, 15, 21, 4, 2, 3, 2, 1, 2/3, 5/6, 3/4, 2/3, 7/12, 8, 19, 30, 5, 2, 4, 2, 1, 3/4, 5/8, 13/16, 3/4, 3/8, -4, -9, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=9174.0MB, alloc=1020.3MB, time=194.42 |\^/| 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(); 1428333320 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 2 2 2 F := [-3 y z + 2 z , 6 x y - 17 y z, 12 x y - 15 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 2 G := [-17 z + 13 y z, -3 x z - 4 z , -17 y z] > Problem := [F,G]; 2 3 3 2 2 2 2 2 Problem := [[-3 y z + 2 z , 6 x y - 17 y z, 12 x y - 15 x z ], 3 3 4 2 [-17 z + 13 y z, -3 x z - 4 z , -17 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.4MB, alloc=32.3MB, time=0.37 memory used=47.4MB, alloc=32.3MB, time=0.54 memory used=67.2MB, alloc=32.3MB, time=0.71 memory used=86.5MB, alloc=56.3MB, time=0.89 memory used=126.5MB, alloc=60.3MB, time=1.27 memory used=164.8MB, alloc=84.3MB, time=1.68 memory used=223.4MB, alloc=108.3MB, time=2.31 memory used=299.9MB, alloc=140.3MB, time=3.15 memory used=392.6MB, alloc=164.3MB, time=4.14 memory used=498.9MB, alloc=188.3MB, time=5.31 memory used=617.0MB, alloc=212.3MB, time=6.65 memory used=736.4MB, alloc=236.3MB, time=8.42 memory used=858.6MB, alloc=260.3MB, time=10.68 memory used=991.3MB, alloc=284.3MB, time=13.40 memory used=1135.1MB, alloc=308.3MB, time=16.76 memory used=1294.7MB, alloc=332.3MB, time=20.77 memory used=1478.4MB, alloc=356.3MB, time=25.36 memory used=1685.9MB, alloc=380.3MB, time=30.55 memory used=1917.4MB, alloc=380.3MB, time=36.27 memory used=2148.9MB, alloc=380.3MB, time=41.98 memory used=2380.4MB, alloc=380.3MB, time=47.64 memory used=2611.8MB, alloc=404.3MB, time=53.26 memory used=2867.2MB, alloc=404.3MB, time=59.43 memory used=3122.5MB, alloc=404.3MB, time=65.61 memory used=3377.7MB, alloc=428.3MB, time=71.80 memory used=3657.0MB, alloc=428.3MB, time=78.47 memory used=3936.2MB, alloc=428.3MB, time=85.11 memory used=4215.4MB, alloc=452.3MB, time=91.68 memory used=4518.5MB, alloc=476.3MB, time=98.58 N1 := 11751 > GB := Basis(F, plex(op(vars))); GB := [ 3 3 2 4 5 3 2 2 2 2 2 3 3 x y , x y , x y , -6 x y + 17 y z, -4 x y + 5 x z , -9 x y + 17 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4811.4MB, alloc=476.3MB, time=103.90 memory used=5168.7MB, alloc=732.3MB, time=108.06 memory used=5534.6MB, alloc=756.3MB, time=113.35 memory used=5851.8MB, alloc=780.3MB, time=121.16 memory used=6175.7MB, alloc=804.3MB, time=129.62 memory used=6523.4MB, alloc=828.3MB, time=138.61 memory used=6895.1MB, alloc=852.3MB, time=148.00 memory used=7291.1MB, alloc=876.3MB, time=157.56 N2 := 8141 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 2 2 2 2 2 3 H := [-3 y z + 2 z , 6 x y - 17 y z, 12 x y - 15 x z , -17 z + 13 y z, 3 4 2 -3 x z - 4 z , -17 z y ] > J:=[op(GB),op(G)]; 3 3 4 2 5 3 2 2 2 2 2 J := [x y , y x , x y , -6 x y + 17 y z, -4 x y + 5 x z , 3 3 3 3 4 2 -9 x y + 17 z , -17 z + 13 y z, -3 x z - 4 z , -17 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 := [6, 14, 21, 4, 2, 3, 4, 1/2, 5/6, 1, 4/13, 6/13, 9/13, 9, 21, 40, 6, 3, 5, 4, 7/9, 8/9, 2/3, 8/19, 9/19, 8/19, -7, -19, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=7441.0MB, alloc=876.3MB, time=160.37 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428333478 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 F := [14 x z - 19 x y, 13 x y z - 15 y , -14 x - 10 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 3 4 3 G := [-20 x - 3 x z , 19 y z - 5 y , -16 x + 4 y z ] > Problem := [F,G]; 3 2 2 2 3 2 Problem := [[14 x z - 19 x y, 13 x y z - 15 y , -14 x - 10 y z], 4 3 2 2 3 4 3 [-20 x - 3 x z , 19 y z - 5 y , -16 x + 4 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=27.5MB, alloc=32.3MB, time=0.37 memory used=49.7MB, alloc=32.3MB, time=0.57 memory used=70.4MB, alloc=56.3MB, time=0.76 memory used=111.9MB, alloc=60.3MB, time=1.13 memory used=151.5MB, alloc=84.3MB, time=1.47 memory used=215.0MB, alloc=92.3MB, time=2.03 memory used=280.6MB, alloc=92.3MB, time=2.58 memory used=338.0MB, alloc=116.3MB, time=3.13 memory used=415.7MB, alloc=372.3MB, time=3.79 memory used=500.2MB, alloc=396.3MB, time=4.53 memory used=602.8MB, alloc=420.3MB, time=5.46 memory used=730.3MB, alloc=444.3MB, time=6.55 memory used=861.9MB, alloc=468.3MB, time=7.64 memory used=999.6MB, alloc=468.3MB, time=8.87 memory used=1111.7MB, alloc=492.3MB, time=9.89 memory used=1212.4MB, alloc=492.3MB, time=10.85 memory used=1298.9MB, alloc=492.3MB, time=11.65 memory used=1384.0MB, alloc=516.3MB, time=12.33 memory used=1468.7MB, alloc=516.3MB, time=13.25 memory used=1553.2MB, alloc=516.3MB, time=14.18 memory used=1631.9MB, alloc=516.3MB, time=15.11 memory used=1705.2MB, alloc=516.3MB, time=16.00 memory used=1761.5MB, alloc=516.3MB, time=16.71 memory used=1815.5MB, alloc=516.3MB, time=17.30 memory used=1869.8MB, alloc=516.3MB, time=17.96 memory used=2071.3MB, alloc=540.3MB, time=19.81 memory used=2258.8MB, alloc=564.3MB, time=21.42 memory used=2450.6MB, alloc=588.3MB, time=23.48 memory used=2619.9MB, alloc=612.3MB, time=25.19 memory used=2788.0MB, alloc=636.3MB, time=27.17 memory used=2929.6MB, alloc=660.3MB, time=28.87 memory used=3064.0MB, alloc=684.3MB, time=30.52 memory used=3188.0MB, alloc=684.3MB, time=31.96 memory used=3303.6MB, alloc=708.3MB, time=33.55 memory used=3394.3MB, alloc=708.3MB, time=34.95 memory used=3763.3MB, alloc=732.3MB, time=38.50 memory used=4169.8MB, alloc=756.3MB, time=42.01 memory used=4554.5MB, alloc=780.3MB, time=45.92 memory used=4891.2MB, alloc=804.3MB, time=49.70 memory used=5195.5MB, alloc=828.3MB, time=53.48 memory used=5477.8MB, alloc=852.3MB, time=57.04 memory used=5693.7MB, alloc=876.3MB, time=60.04 memory used=5932.6MB, alloc=900.3MB, time=63.57 memory used=6149.8MB, alloc=924.3MB, time=66.80 memory used=6378.8MB, alloc=948.3MB, time=70.41 memory used=6905.4MB, alloc=972.3MB, time=76.34 memory used=7431.8MB, alloc=996.3MB, time=82.25 memory used=7973.2MB, alloc=1020.3MB, time=88.59 memory used=8520.6MB, alloc=1044.3MB, time=95.39 memory used=9059.3MB, alloc=1068.3MB, time=101.70 memory used=9592.0MB, alloc=1092.3MB, time=108.73 memory used=10145.5MB, alloc=1116.3MB, time=116.25 memory used=10685.0MB, alloc=1140.3MB, time=123.85 memory used=11101.2MB, alloc=1164.3MB, time=131.66 memory used=11434.4MB, alloc=1188.3MB, time=139.21 memory used=11808.2MB, alloc=1212.3MB, time=146.88 memory used=12290.1MB, alloc=1236.3MB, time=154.78 memory used=12838.3MB, alloc=1260.3MB, time=162.63 memory used=13430.1MB, alloc=1284.3MB, time=170.27 memory used=14049.8MB, alloc=1308.3MB, time=178.18 memory used=14657.2MB, alloc=1332.3MB, time=186.84 memory used=15204.2MB, alloc=1356.3MB, time=196.08 memory used=15666.0MB, alloc=1380.3MB, time=205.41 memory used=16094.9MB, alloc=1404.3MB, time=214.79 memory used=16496.4MB, alloc=1428.3MB, time=225.42 memory used=16825.7MB, alloc=1452.3MB, time=237.23 memory used=17154.2MB, alloc=1476.3MB, time=249.50 memory used=17489.5MB, alloc=1500.3MB, time=261.99 memory used=17833.6MB, alloc=1524.3MB, time=274.85 memory used=18189.3MB, alloc=1548.3MB, time=288.16 memory used=18557.3MB, alloc=1572.3MB, time=302.19 memory used=18939.1MB, alloc=1596.3MB, time=316.69 memory used=19334.9MB, alloc=1620.3MB, time=331.61 |\^/| 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(); 1428333778 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 3 F := [-6 y + 3 z , 9 y + 8 y z, 8 x + 10 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 2 G := [8 x y - 19 z , 10 x + 4 y , 3 x y + 16 x y] > Problem := [F,G]; 3 3 2 4 3 Problem := [[-6 y + 3 z , 9 y + 8 y z, 8 x + 10 z ], 3 3 3 3 2 [8 x y - 19 z , 10 x + 4 y , 3 x y + 16 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.6MB, alloc=32.3MB, time=0.40 memory used=48.4MB, alloc=32.3MB, time=0.66 memory used=71.0MB, alloc=56.3MB, time=0.98 memory used=114.0MB, alloc=84.3MB, time=1.63 N1 := 985 > GB := Basis(F, plex(op(vars))); 8 4 4 3 4 2 4 3 GB := [x , y x , 2 x + 5 y , x z, 9 y + 8 y z, 4 x + 5 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=172.6MB, alloc=84.3MB, time=2.52 memory used=234.2MB, alloc=92.3MB, time=3.35 N2 := 1019 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 4 3 3 3 3 3 H := [-6 y + 3 z , 9 y + 8 y z, 8 x + 10 z , 8 y x - 19 z , 10 x + 4 y , 2 3 x y + 16 x y] > J:=[op(GB),op(G)]; 8 4 4 3 4 2 4 3 3 3 J := [x , y x , 2 x + 5 y , x z, 9 y + 8 y z, 4 x + 5 z , 8 y x - 19 z , 3 3 2 10 x + 4 y , 3 x y + 16 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 := [6, 13, 19, 4, 4, 3, 3, 2/3, 5/6, 2/3, 5/12, 7/12, 1/3, 9, 18, 38, 8, 8, 3, 3, 8/9, 2/3, 4/9, 1/2, 4/9, 2/9, -5, -19, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=286.2MB, alloc=92.3MB, time=4.25 |\^/| 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(); 1428333782 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [-3 x z - 8 z , 16 y z , -17 x z + 15 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 2 G := [6 x z - 20 x z , 8 x z - 10 x y z, 10 x z - 16 y z] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[-3 x z - 8 z , 16 y z , -17 x z + 15 x y z], 2 2 2 3 2 2 2 [6 x z - 20 x z , 8 x z - 10 x y z, 10 x z - 16 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.44 N1 := 187 > GB := Basis(F, plex(op(vars))); 3 3 2 GB := [3 x y z + 8 x y z, x y z, 45 x y z + 136 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=47.6MB, alloc=32.3MB, time=0.66 N2 := 187 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 2 2 2 H := [-3 x z - 8 z , 16 y z , -17 x z + 15 x y z, 6 x z - 20 x z , 3 2 2 2 8 x z - 10 x y z, 10 x z - 16 y z] > J:=[op(GB),op(G)]; 3 3 2 2 2 2 J := [3 x y z + 8 x y z, x y z, 45 x y z + 136 z , 6 x z - 20 x z , 3 2 2 2 8 x z - 10 x y z, 10 x z - 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 := [6, 15, 24, 4, 3, 2, 2, 5/6, 2/3, 1, 8/13, 4/13, 11/13, 6, 17, 25, 5, 3, 3, 2, 1, 5/6, 1, 9/13, 6/13, 11/13, -2, -1, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=60.9MB, alloc=32.3MB, time=0.84 |\^/| 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(); 1428333783 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 2 F := [-16 y z + 18 z, 13 x y - 7 x z , 2 x + 8 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 G := [13 x - 9 y z , 9 x y, 11 y + 5 y] > Problem := [F,G]; 2 2 3 2 2 3 2 Problem := [[-16 y z + 18 z, 13 x y - 7 x z , 2 x + 8 y z], 3 2 2 4 [13 x - 9 y z , 9 x y, 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=4.3MB, alloc=32.3MB, time=0.15 memory used=26.7MB, alloc=32.3MB, time=0.38 memory used=48.3MB, alloc=32.3MB, time=0.62 memory used=70.2MB, alloc=36.3MB, time=0.87 memory used=88.6MB, alloc=60.3MB, time=1.08 memory used=130.5MB, alloc=60.3MB, time=1.54 memory used=172.5MB, alloc=84.3MB, time=2.09 memory used=226.5MB, alloc=84.3MB, time=2.91 memory used=284.0MB, alloc=108.3MB, time=3.89 memory used=360.6MB, alloc=140.3MB, time=5.14 memory used=453.7MB, alloc=164.3MB, time=6.43 memory used=559.0MB, alloc=188.3MB, time=7.85 memory used=666.9MB, alloc=212.3MB, time=9.89 memory used=784.5MB, alloc=236.3MB, time=12.58 memory used=926.0MB, alloc=236.3MB, time=15.75 memory used=1067.5MB, alloc=260.3MB, time=18.89 memory used=1233.1MB, alloc=260.3MB, time=22.39 memory used=1398.7MB, alloc=284.3MB, time=25.65 N1 := 5517 > GB := Basis(F, plex(op(vars))); 6 3 3 5 5 4 3 GB := [2 x + 9 x , 416 x y + 63 x , 208 x y + 567 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1548.1MB, alloc=284.3MB, time=27.62 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 3 2 2 3 2 2 3 H := [-16 y z + 18 z, 13 x y - 7 x z , 2 x + 8 y z, -9 z y + 13 x , 2 4 9 y x , 11 y + 5 y] > J:=[op(GB),op(G)]; 6 3 3 5 5 3 4 2 3 J := [2 x + 9 x , 416 x y + 63 x , 208 y x + 567 z, -9 z y + 13 x , 2 4 9 y x , 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 := [6, 14, 21, 4, 3, 4, 2, 2/3, 1, 2/3, 5/13, 7/13, 5/13, 6, 12, 31, 8, 6, 5, 2, 5/6, 5/6, 1/3, 7/13, 6/13, 2/13, 2, -10, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1558.4MB, alloc=540.3MB, time=27.81 |\^/| 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(); 1428333811 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [11 z + 18 y, -4 x z - 7 x, 15 x z + 20] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 G := [4 x y z + 5 y z, 19 x y + 5 z , -2 x y - 3 y ] > Problem := [F,G]; 3 2 2 3 Problem := [[11 z + 18 y, -4 x z - 7 x, 15 x z + 20], 2 3 3 [4 x y z + 5 y z, 19 x y + 5 z , -2 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=0.11 memory used=26.2MB, alloc=32.3MB, time=0.29 memory used=48.0MB, alloc=32.3MB, time=0.48 memory used=69.0MB, alloc=32.3MB, time=0.68 memory used=89.1MB, alloc=56.3MB, time=0.87 memory used=130.3MB, alloc=60.3MB, time=1.23 memory used=168.7MB, alloc=60.3MB, time=1.56 memory used=206.4MB, alloc=84.3MB, time=1.97 memory used=264.4MB, alloc=108.3MB, time=2.60 memory used=341.1MB, alloc=116.3MB, time=3.43 memory used=411.2MB, alloc=140.3MB, time=4.19 memory used=499.2MB, alloc=164.3MB, time=5.13 memory used=596.4MB, alloc=188.3MB, time=6.60 memory used=700.7MB, alloc=212.3MB, time=8.75 memory used=822.2MB, alloc=236.3MB, time=11.41 memory used=967.8MB, alloc=236.3MB, time=14.53 memory used=1113.3MB, alloc=236.3MB, time=17.58 memory used=1258.8MB, alloc=260.3MB, time=20.45 N1 := 5217 > GB := Basis(F, plex(op(vars))); 5 2 GB := [63 x + 64, 384 y - 539 x, -21 x + 16 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1434.5MB, alloc=260.3MB, time=22.96 N2 := 683 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 3 H := [11 z + 18 y, -4 x z - 7 x, 15 x z + 20, 4 x y z + 5 y z, 2 3 3 5 z + 19 y x, -2 x y - 3 y ] > J:=[op(GB),op(G)]; 5 2 2 J := [63 x + 64, 384 y - 539 x, -21 x + 16 z, 4 x y z + 5 y z, 5 z + 19 y x, 3 3 -2 x y - 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 := [6, 14, 20, 4, 3, 3, 3, 5/6, 2/3, 5/6, 1/2, 1/2, 1/2, 6, 13, 17, 5, 5, 3, 2, 1, 2/3, 1/2, 1/2, 1/2, 1/3, 1, 3, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1469.5MB, alloc=260.3MB, time=23.38 |\^/| 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(); 1428333834 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 2 F := [13 x y - 11 x y z, 8 x z - 3 y z , 15 x y + 3 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 2 2 G := [-2 x + 16 y , 19 x z - 13 x , -17 x y z - 20 x z ] > Problem := [F,G]; 3 2 2 2 3 2 2 Problem := [[13 x y - 11 x y z, 8 x z - 3 y z , 15 x y + 3 y z ], 2 2 3 3 2 2 2 [-2 x + 16 y , 19 x z - 13 x , -17 x y z - 20 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.6MB, alloc=32.3MB, time=0.33 memory used=47.3MB, alloc=32.3MB, time=0.51 memory used=65.2MB, alloc=56.3MB, time=0.68 memory used=103.6MB, alloc=60.3MB, time=1.03 memory used=141.6MB, alloc=84.3MB, time=1.37 memory used=199.6MB, alloc=92.3MB, time=1.92 memory used=258.0MB, alloc=116.3MB, time=2.47 memory used=336.9MB, alloc=116.3MB, time=3.21 memory used=412.9MB, alloc=140.3MB, time=3.96 memory used=508.6MB, alloc=164.3MB, time=4.91 memory used=576.7MB, alloc=420.3MB, time=5.58 memory used=693.2MB, alloc=444.3MB, time=6.86 memory used=821.1MB, alloc=468.3MB, time=8.26 memory used=971.3MB, alloc=492.3MB, time=9.78 memory used=1132.5MB, alloc=516.3MB, time=11.51 memory used=1301.6MB, alloc=540.3MB, time=13.47 memory used=1469.0MB, alloc=564.3MB, time=16.44 memory used=1636.8MB, alloc=588.3MB, time=19.93 memory used=1812.2MB, alloc=612.3MB, time=24.13 memory used=2001.0MB, alloc=636.3MB, time=28.90 memory used=2213.8MB, alloc=660.3MB, time=34.27 memory used=2450.6MB, alloc=684.3MB, time=40.15 memory used=2711.2MB, alloc=708.3MB, time=46.63 memory used=2995.9MB, alloc=708.3MB, time=53.62 memory used=3280.5MB, alloc=732.3MB, time=60.57 memory used=3589.0MB, alloc=732.3MB, time=68.10 memory used=3897.6MB, alloc=756.3MB, time=75.59 memory used=4230.2MB, alloc=756.3MB, time=83.53 memory used=4562.7MB, alloc=780.3MB, time=91.04 N1 := 10583 > GB := Basis(F, plex(op(vars))); 4 2 3 4 3 2 3 2 GB := [y x , y x , z x , 15 x y + 8 x y z, -13 x y + 11 x y z, 2 2 -8 x z + 3 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4926.1MB, alloc=780.3MB, time=96.31 memory used=5364.1MB, alloc=804.3MB, time=102.17 memory used=5743.2MB, alloc=828.3MB, time=111.39 N2 := 5099 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 2 2 2 2 H := [13 x y - 11 x y z, 8 x z - 3 y z , 15 x y + 3 y z , -2 x + 16 y , 3 3 2 2 2 19 x z - 13 x , -17 x y z - 20 x z ] > J:=[op(GB),op(G)]; 4 2 3 4 3 2 3 2 J := [y x , y x , z x , 15 x y + 8 x y z, -13 x y + 11 x y z, 2 2 2 2 3 3 2 2 2 -8 x z + 3 y z , -2 x + 16 y , 19 x z - 13 x , -17 x y z - 20 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 := [6, 16, 21, 4, 3, 2, 3, 1, 5/6, 5/6, 3/4, 7/12, 7/12, 9, 22, 36, 5, 4, 2, 3, 1, 7/9, 2/3, 13/18, 1/2, 4/9, -6, -15, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=6091.9MB, alloc=828.3MB, time=118.48 |\^/| 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(); 1428333951 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 F := [19 y z + 20 x, 10 y + 12 y , 11 x y - 17 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 4 4 G := [17 y + 19 y z , 5 z + 5 y , -16 x + 14 z ] > Problem := [F,G]; 2 4 3 Problem := [[19 y z + 20 x, 10 y + 12 y , 11 x y - 17 x z], 4 2 3 2 4 4 [17 y + 19 y z , 5 z + 5 y , -16 x + 14 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.4MB, alloc=32.3MB, time=0.34 memory used=48.1MB, alloc=32.3MB, time=0.53 memory used=68.7MB, alloc=32.3MB, time=0.71 memory used=87.8MB, alloc=56.3MB, time=0.89 memory used=125.2MB, alloc=60.3MB, time=1.22 memory used=162.0MB, alloc=84.3MB, time=1.54 memory used=209.8MB, alloc=84.3MB, time=1.98 memory used=272.0MB, alloc=92.3MB, time=2.54 memory used=329.9MB, alloc=92.3MB, time=3.08 memory used=392.4MB, alloc=116.3MB, time=3.62 memory used=476.1MB, alloc=116.3MB, time=4.37 memory used=560.7MB, alloc=140.3MB, time=5.02 memory used=624.5MB, alloc=396.3MB, time=5.54 memory used=730.4MB, alloc=420.3MB, time=6.45 memory used=852.1MB, alloc=420.3MB, time=7.56 memory used=981.1MB, alloc=444.3MB, time=8.62 memory used=1122.8MB, alloc=468.3MB, time=9.88 memory used=1257.2MB, alloc=492.3MB, time=11.20 memory used=1385.7MB, alloc=492.3MB, time=12.41 memory used=1525.8MB, alloc=516.3MB, time=13.91 memory used=1658.4MB, alloc=540.3MB, time=15.26 memory used=1811.9MB, alloc=540.3MB, time=16.52 memory used=1973.0MB, alloc=564.3MB, time=18.42 memory used=2182.4MB, alloc=588.3MB, time=20.95 memory used=2390.8MB, alloc=612.3MB, time=23.49 memory used=2578.1MB, alloc=636.3MB, time=25.90 memory used=2762.8MB, alloc=660.3MB, time=28.23 memory used=2936.1MB, alloc=684.3MB, time=30.46 memory used=3106.0MB, alloc=708.3MB, time=32.69 memory used=3253.1MB, alloc=732.3MB, time=34.71 memory used=3402.8MB, alloc=756.3MB, time=36.80 memory used=3552.2MB, alloc=780.3MB, time=38.87 memory used=3695.3MB, alloc=804.3MB, time=40.87 memory used=3834.9MB, alloc=828.3MB, time=42.89 memory used=3921.0MB, alloc=852.3MB, time=44.35 memory used=4044.1MB, alloc=876.3MB, time=46.21 memory used=4126.9MB, alloc=900.3MB, time=47.80 memory used=4473.6MB, alloc=924.3MB, time=55.52 memory used=4810.6MB, alloc=948.3MB, time=63.72 memory used=5150.9MB, alloc=972.3MB, time=72.29 memory used=5499.1MB, alloc=996.3MB, time=81.17 memory used=5857.6MB, alloc=1020.3MB, time=90.43 memory used=6227.4MB, alloc=1044.3MB, time=100.18 memory used=6609.3MB, alloc=1068.3MB, time=110.37 memory used=7004.1MB, alloc=1092.3MB, time=120.97 memory used=7412.0MB, alloc=1116.3MB, time=131.89 memory used=7833.9MB, alloc=1140.3MB, time=143.24 memory used=8266.7MB, alloc=1164.3MB, time=155.18 memory used=8712.5MB, alloc=1188.3MB, time=167.73 memory used=9182.2MB, alloc=1212.3MB, time=180.90 memory used=9675.9MB, alloc=1236.3MB, time=194.79 memory used=10193.5MB, alloc=1260.3MB, time=209.25 memory used=10735.1MB, alloc=1284.3MB, time=224.39 memory used=11300.6MB, alloc=1308.3MB, time=240.13 memory used=11890.1MB, alloc=1332.3MB, time=256.50 memory used=12503.4MB, alloc=1356.3MB, time=273.57 memory used=13140.7MB, alloc=1380.3MB, time=291.37 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428334251 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 3 F := [-18 y z + 11 x z, 19 x z - 5 x z , -13 x y - 8 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 G := [5 x y - 10, -8 x y z - 14 y , 13 y z] > Problem := [F,G]; 3 2 2 2 2 3 Problem := [[-18 y z + 11 x z, 19 x z - 5 x z , -13 x y - 8 x y z], 2 2 3 3 [5 x y - 10, -8 x y z - 14 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=4.3MB, alloc=32.3MB, time=0.15 memory used=26.2MB, alloc=32.3MB, time=0.38 memory used=49.1MB, alloc=32.3MB, time=0.74 memory used=69.7MB, alloc=56.3MB, time=1.04 N1 := 737 > GB := Basis(F, plex(op(vars))); 4 3 3 3 2 5 5 6 3 3 GB := [19 x y - 5 x y , 19 x y - 5 x y , 18 x y - 11 x y , 5 3 3 3 2 117 x y + 44 x z, 13 x y + 8 x y z, 18 y z - 11 x z, 3 4 2 -61009 x y + 1600 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=111.2MB, alloc=60.3MB, time=1.69 memory used=148.5MB, alloc=60.3MB, time=1.99 memory used=185.9MB, alloc=84.3MB, time=2.33 memory used=235.8MB, alloc=84.3MB, time=2.77 memory used=293.3MB, alloc=92.3MB, time=3.31 memory used=348.1MB, alloc=116.3MB, time=3.80 memory used=433.1MB, alloc=116.3MB, time=4.65 memory used=509.1MB, alloc=140.3MB, time=5.45 memory used=600.3MB, alloc=164.3MB, time=6.46 memory used=706.7MB, alloc=188.3MB, time=7.66 memory used=814.9MB, alloc=468.3MB, time=9.00 memory used=938.8MB, alloc=492.3MB, time=11.17 memory used=1067.0MB, alloc=516.3MB, time=14.02 memory used=1212.7MB, alloc=540.3MB, time=17.46 memory used=1382.4MB, alloc=564.3MB, time=21.38 memory used=1576.2MB, alloc=564.3MB, time=25.93 memory used=1769.9MB, alloc=564.3MB, time=30.30 memory used=1963.7MB, alloc=588.3MB, time=34.45 N2 := 6653 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 3 2 H := [-18 y z + 11 x z, 19 x z - 5 x z , -13 x y - 8 x y z, 5 x y - 10, 2 3 3 -8 x y z - 14 y , 13 y z] > J:=[op(GB),op(G)]; 4 3 3 3 2 5 5 6 3 3 J := [19 x y - 5 x y , 19 x y - 5 x y , 18 x y - 11 x y , 5 3 3 3 2 117 x y + 44 x z, 13 x y + 8 x y z, 18 y z - 11 x z, 3 4 2 2 2 3 3 -61009 x y + 1600 x z , 5 x y - 10, -8 x y z - 14 y , 13 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 := [6, 15, 23, 4, 2, 3, 2, 5/6, 5/6, 5/6, 7/13, 7/13, 7/13, 10, 25, 53, 7, 4, 6, 2, 9/10, 1, 3/5, 5/7, 5/7, 1/3, -10, -30, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2177.0MB, alloc=588.3MB, time=38.20 |\^/| 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(); 1428334288 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 3 F := [4 y z + 17 x y , 17 x z - 9 y z, 7 x y - 6 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 4 3 G := [-12 x y - 18 x, 3 x y + 6 x z , 4 y + 6 y z] > Problem := [F,G]; 3 2 3 2 2 3 Problem := [[4 y z + 17 x y , 17 x z - 9 y z, 7 x y - 6 x z ], 2 3 2 4 3 [-12 x y - 18 x, 3 x y + 6 x z , 4 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=4.3MB, alloc=32.3MB, time=0.11 memory used=26.4MB, alloc=32.3MB, time=0.29 memory used=47.9MB, alloc=32.3MB, time=0.48 memory used=68.1MB, alloc=32.3MB, time=0.67 memory used=87.4MB, alloc=56.3MB, time=0.88 memory used=126.3MB, alloc=60.3MB, time=1.22 memory used=165.5MB, alloc=60.3MB, time=1.56 memory used=202.9MB, alloc=84.3MB, time=1.90 memory used=261.2MB, alloc=92.3MB, time=2.43 memory used=317.4MB, alloc=116.3MB, time=2.94 memory used=394.4MB, alloc=116.3MB, time=3.64 memory used=471.3MB, alloc=140.3MB, time=4.50 memory used=563.6MB, alloc=164.3MB, time=5.52 memory used=672.4MB, alloc=444.3MB, time=6.74 memory used=795.8MB, alloc=468.3MB, time=8.13 memory used=929.0MB, alloc=492.3MB, time=9.77 memory used=1060.1MB, alloc=516.3MB, time=12.17 memory used=1200.1MB, alloc=540.3MB, time=15.06 memory used=1349.3MB, alloc=564.3MB, time=18.63 memory used=1518.3MB, alloc=588.3MB, time=22.77 memory used=1711.4MB, alloc=612.3MB, time=27.44 memory used=1928.4MB, alloc=636.3MB, time=32.67 memory used=2169.3MB, alloc=636.3MB, time=38.41 memory used=2410.1MB, alloc=636.3MB, time=44.11 memory used=2650.8MB, alloc=660.3MB, time=49.74 memory used=2915.5MB, alloc=660.3MB, time=55.77 memory used=3180.3MB, alloc=684.3MB, time=61.27 N1 := 8691 > GB := Basis(F, plex(op(vars))); 14 2 2 4 2 3 12 2 7 GB := [64736 x y + 177147 x y , -17 x y + 9 x y , -56 x y + 243 x z, 3 2 2 3 -17 x z + 9 y z, -7 x y + 6 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3468.7MB, alloc=684.3MB, time=64.80 memory used=3791.4MB, alloc=684.3MB, time=68.16 memory used=4110.3MB, alloc=708.3MB, time=72.09 memory used=4426.5MB, alloc=732.3MB, time=76.04 memory used=4737.9MB, alloc=756.3MB, time=82.46 memory used=5034.1MB, alloc=780.3MB, time=89.82 memory used=5330.8MB, alloc=804.3MB, time=97.89 memory used=5651.5MB, alloc=828.3MB, time=106.55 memory used=5996.2MB, alloc=852.3MB, time=115.76 memory used=6364.7MB, alloc=876.3MB, time=125.57 memory used=6757.3MB, alloc=900.3MB, time=135.95 memory used=7173.7MB, alloc=924.3MB, time=146.86 memory used=7614.2MB, alloc=948.3MB, time=158.21 memory used=8078.5MB, alloc=972.3MB, time=169.64 N2 := 11227 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 2 3 2 H := [4 y z + 17 x y , 17 x z - 9 y z, 7 x y - 6 x z , -12 x y - 18 x, 3 2 4 3 3 x y + 6 x z , 4 y + 6 y z] > J:=[op(GB),op(G)]; 14 2 2 4 2 3 12 2 7 J := [64736 x y + 177147 x y , -17 x y + 9 x y , -56 x y + 243 x z, 3 2 2 3 2 3 2 -17 x z + 9 y z, -7 x y + 6 x z , -12 x y - 18 x, 3 x y + 6 x z , 4 3 4 y + 6 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 := [6, 16, 23, 4, 3, 4, 3, 5/6, 1, 5/6, 2/3, 2/3, 1/2, 8, 20, 55, 16, 14, 4, 3, 7/8, 1, 5/8, 13/16, 11/16, 3/8, -4, -32, -12] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=8355.5MB, alloc=972.3MB, time=175.10 |\^/| 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(); 1428334461 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 2 2 F := [-5 x y - y , -18 x y z - 4 x z , -13 x y + 19 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [5 x y z - 17 y z, 9 x y, 20 x y + 12 x] > Problem := [F,G]; 2 3 2 2 2 2 2 2 Problem := [[-5 x y - y , -18 x y z - 4 x z , -13 x y + 19 x ], 2 2 2 [5 x y z - 17 y z, 9 x y, 20 x 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=4.3MB, alloc=32.3MB, time=0.16 memory used=26.2MB, alloc=32.3MB, time=0.37 memory used=47.7MB, alloc=56.3MB, time=0.59 N1 := 443 > GB := Basis(F, plex(op(vars))); 4 2 2 2 2 2 3 2 2 2 GB := [65 x + 19 x , 13 x y - 19 x , 5 x y + y , 9 x y z + 2 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=87.7MB, alloc=60.3MB, time=0.98 N2 := 443 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 2 2 2 2 2 H := [-5 x y - y , -18 x y z - 4 x z , -13 x y + 19 x , 5 x y z - 17 y z, 2 2 9 x y, 20 x y + 12 x] > J:=[op(GB),op(G)]; 4 2 2 2 2 2 3 2 2 2 J := [65 x + 19 x , 13 x y - 19 x , 5 x y + y , 9 x y z + 2 x z , 2 2 2 5 x y z - 17 y z, 9 x y, 20 x y + 12 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, 21, 4, 2, 3, 2, 1, 1, 1/3, 9/13, 8/13, 4/13, 7, 15, 25, 4, 4, 3, 2, 1, 6/7, 2/7, 11/15, 8/15, 4/15, -1, -4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=113.8MB, alloc=60.3MB, time=1.24 |\^/| 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(); 1428334462 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [13 y z - 7 x, x z - 5 x y z , -8 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 4 3 G := [-2 x y z - 11 x z, -13 x y - 3 y , -3 y + 3 z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[13 y z - 7 x, x z - 5 x y z , -8 x y z], 2 2 2 3 4 3 [-2 x y z - 11 x z, -13 x y - 3 y , -3 y + 3 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.11 memory used=26.5MB, alloc=32.3MB, time=0.29 memory used=48.5MB, alloc=32.3MB, time=0.49 memory used=70.3MB, alloc=56.3MB, time=0.73 N1 := 617 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 2 2 GB := [x , x y, x y z, 13 x z - 35 x , 13 y z - 7 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=111.7MB, alloc=60.3MB, time=1.19 memory used=151.5MB, alloc=60.3MB, time=1.52 memory used=191.5MB, alloc=84.3MB, time=1.91 memory used=254.0MB, alloc=84.3MB, time=2.61 memory used=307.2MB, alloc=108.3MB, time=3.28 memory used=369.6MB, alloc=132.3MB, time=4.32 N2 := 1857 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 H := [13 y z - 7 x, x z - 5 x y z , -8 x y z, -2 x y z - 11 x z, 2 3 4 3 -13 x y - 3 y , -3 y + 3 z ] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 2 2 2 J := [x , x y, x y z, 13 x z - 35 x , 13 y z - 7 x, -2 x y z - 11 x z, 2 3 4 3 -13 x y - 3 y , -3 y + 3 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 16, 22, 4, 2, 4, 3, 5/6, 1, 5/6, 1/2, 1/2, 1/2, 8, 18, 28, 4, 3, 4, 3, 7/8, 3/4, 5/8, 9/17, 7/17, 6/17, -2, -6, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=405.1MB, alloc=132.3MB, time=4.82 |\^/| 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(); 1428334467 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 4 2 2 F := [-9 y - 18 z , 7 x - 13 y z , 14 x - 2 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 2 2 3 G := [11 x z - 6 y , 18 y + 15 y z, -7 x y - 10 y z ] > Problem := [F,G]; 3 3 3 2 4 2 2 Problem := [[-9 y - 18 z , 7 x - 13 y z , 14 x - 2 x y ], 3 2 4 3 2 2 3 [11 x z - 6 y , 18 y + 15 y z, -7 x 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=4.2MB, alloc=32.3MB, time=0.11 memory used=26.9MB, alloc=32.3MB, time=0.31 memory used=48.2MB, alloc=32.3MB, time=0.49 memory used=69.4MB, alloc=32.3MB, time=0.67 memory used=89.2MB, alloc=60.3MB, time=0.85 memory used=130.2MB, alloc=60.3MB, time=1.19 memory used=171.6MB, alloc=68.3MB, time=1.55 memory used=211.6MB, alloc=92.3MB, time=1.90 memory used=276.2MB, alloc=92.3MB, time=2.47 memory used=336.5MB, alloc=116.3MB, time=3.04 memory used=403.3MB, alloc=116.3MB, time=3.56 memory used=466.0MB, alloc=396.3MB, time=4.06 memory used=576.8MB, alloc=420.3MB, time=4.90 memory used=703.6MB, alloc=444.3MB, time=5.81 memory used=828.7MB, alloc=444.3MB, time=6.78 memory used=927.8MB, alloc=468.3MB, time=7.62 memory used=1050.5MB, alloc=492.3MB, time=8.65 memory used=1145.5MB, alloc=492.3MB, time=9.50 memory used=1233.6MB, alloc=492.3MB, time=10.35 memory used=1311.1MB, alloc=492.3MB, time=11.13 memory used=1374.9MB, alloc=492.3MB, time=11.83 memory used=1455.2MB, alloc=516.3MB, time=12.68 memory used=1524.7MB, alloc=516.3MB, time=13.43 memory used=1622.0MB, alloc=516.3MB, time=14.14 memory used=1699.3MB, alloc=516.3MB, time=14.84 memory used=1757.5MB, alloc=516.3MB, time=15.57 memory used=1809.8MB, alloc=516.3MB, time=16.29 memory used=2019.5MB, alloc=540.3MB, time=17.84 memory used=2230.0MB, alloc=564.3MB, time=20.06 memory used=2417.6MB, alloc=588.3MB, time=22.56 memory used=2616.7MB, alloc=612.3MB, time=25.19 memory used=2827.0MB, alloc=636.3MB, time=27.97 memory used=3046.2MB, alloc=660.3MB, time=30.96 memory used=3273.0MB, alloc=684.3MB, time=34.17 memory used=3481.3MB, alloc=708.3MB, time=38.79 memory used=3690.1MB, alloc=732.3MB, time=44.06 memory used=3908.7MB, alloc=756.3MB, time=49.88 memory used=4140.0MB, alloc=780.3MB, time=56.17 memory used=4377.2MB, alloc=804.3MB, time=63.13 memory used=4635.3MB, alloc=828.3MB, time=70.76 memory used=4917.3MB, alloc=852.3MB, time=79.03 memory used=5223.3MB, alloc=876.3MB, time=87.95 memory used=5553.2MB, alloc=900.3MB, time=97.48 memory used=5907.0MB, alloc=924.3MB, time=107.66 memory used=6284.8MB, alloc=948.3MB, time=118.46 memory used=6686.5MB, alloc=972.3MB, time=129.84 memory used=7112.1MB, alloc=996.3MB, time=141.82 memory used=7561.7MB, alloc=1020.3MB, time=154.40 memory used=8035.0MB, alloc=1044.3MB, time=167.60 memory used=8532.2MB, alloc=1068.3MB, time=181.30 memory used=9053.5MB, alloc=1068.3MB, time=195.45 memory used=9574.6MB, alloc=1092.3MB, time=209.47 memory used=10119.9MB, alloc=1116.3MB, time=223.70 N1 := 15211 > GB := Basis(F, plex(op(vars))); 8 7 6 4 2 2 6 6 3 4 GB := [x , -107653 x + 4 x y, -7 x + x y , -343 x + y , 14 z x + 13 y , 5 4 6 5 3 2 3 3 14 x y + 169 x y z, 98 x + 169 y z, -7 x + 13 y z , 2 z + y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=10740.4MB, alloc=1116.3MB, time=233.69 memory used=11440.6MB, alloc=1140.3MB, time=241.37 memory used=12144.8MB, alloc=1164.3MB, time=248.17 memory used=12845.3MB, alloc=1188.3MB, time=255.18 memory used=13539.0MB, alloc=1212.3MB, time=263.41 memory used=14235.6MB, alloc=1236.3MB, time=271.03 memory used=14866.2MB, alloc=1260.3MB, time=277.47 memory used=15503.7MB, alloc=1284.3MB, time=283.91 memory used=16154.2MB, alloc=1308.3MB, time=291.85 memory used=16827.2MB, alloc=1332.3MB, time=300.03 memory used=17454.1MB, alloc=1356.3MB, time=307.29 memory used=17957.1MB, alloc=1380.3MB, time=314.20 |\^/| 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(); 1428334767 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 3 2 F := [11 x y z - y z , -9 y - 17 y z , 2 y z - 17 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 G := [-6 x z + 14 x, -15 y - 10 y z, 15 x z ] > Problem := [F,G]; 2 2 2 4 3 2 Problem := [[11 x y z - y z , -9 y - 17 y z , 2 y z - 17 y z], 3 4 2 [-6 x z + 14 x, -15 y - 10 y z, 15 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.46 memory used=47.6MB, alloc=32.3MB, time=0.76 memory used=69.2MB, alloc=56.3MB, time=1.04 memory used=111.7MB, alloc=56.3MB, time=1.63 memory used=147.3MB, alloc=80.3MB, time=2.25 memory used=199.1MB, alloc=104.3MB, time=3.47 N1 := 1491 > GB := Basis(F, plex(op(vars))); 4 4 5 4 2 GB := [22 x y - 17 y , 2 y - 17 y , 22 x y z - 17 y z, 2 y z - 17 y z, 4 3 9 y + 17 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=224.6MB, alloc=104.3MB, time=3.75 N2 := 525 #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 4 3 2 3 H := [11 x y z - y z , -9 y - 17 y z , 2 y z - 17 y z, -6 x z + 14 x, 4 2 -15 y - 10 y z, 15 x z ] > J:=[op(GB),op(G)]; 4 4 5 4 2 J := [22 x y - 17 y , 2 y - 17 y , 22 x y z - 17 y z, 2 y z - 17 y z, 4 3 3 4 2 9 y + 17 y z , -6 x z + 14 x, -15 y - 10 y z, 15 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 := [6, 13, 22, 4, 1, 4, 3, 1/2, 2/3, 1, 4/13, 8/13, 8/13, 8, 16, 31, 5, 1, 5, 3, 1/2, 3/4, 3/4, 5/17, 12/17, 8/17, -3, -9, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=267.3MB, alloc=108.3MB, 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(); 1428334771 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 F := [4 x y - 19 y z , -11 x y - 3 z, 9 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 G := [-10 x z - 11 y z , 7 x - 7 x z, 14 y z + 14 x y z] > Problem := [F,G]; 3 2 2 2 3 Problem := [[4 x y - 19 y z , -11 x y - 3 z, 9 y ], 3 2 2 4 3 [-10 x z - 11 y z , 7 x - 7 x z, 14 y z + 14 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=26.8MB, alloc=32.3MB, time=0.36 memory used=47.4MB, alloc=32.3MB, time=0.53 memory used=67.4MB, alloc=32.3MB, time=0.71 memory used=86.6MB, alloc=56.3MB, time=0.89 memory used=126.3MB, alloc=60.3MB, time=1.25 memory used=165.7MB, alloc=84.3MB, time=1.59 memory used=203.9MB, alloc=84.3MB, time=1.94 memory used=264.1MB, alloc=116.3MB, time=2.47 memory used=344.7MB, alloc=116.3MB, time=3.21 memory used=407.1MB, alloc=140.3MB, time=3.78 memory used=479.7MB, alloc=396.3MB, time=4.45 memory used=579.3MB, alloc=420.3MB, time=5.47 memory used=700.6MB, alloc=444.3MB, time=6.68 memory used=826.6MB, alloc=468.3MB, time=8.07 memory used=966.1MB, alloc=492.3MB, time=9.63 memory used=1121.2MB, alloc=516.3MB, time=11.32 memory used=1276.9MB, alloc=540.3MB, time=13.49 memory used=1426.7MB, alloc=564.3MB, time=16.38 memory used=1583.8MB, alloc=588.3MB, time=19.77 memory used=1748.9MB, alloc=612.3MB, time=23.88 memory used=1933.4MB, alloc=636.3MB, time=28.55 memory used=2141.8MB, alloc=660.3MB, time=33.74 memory used=2374.1MB, alloc=684.3MB, time=39.50 memory used=2630.4MB, alloc=708.3MB, time=45.94 memory used=2910.6MB, alloc=708.3MB, time=52.84 memory used=3190.8MB, alloc=732.3MB, time=59.68 memory used=3495.0MB, alloc=732.3MB, time=67.07 memory used=3799.0MB, alloc=732.3MB, time=74.54 memory used=4102.9MB, alloc=756.3MB, time=81.91 memory used=4430.7MB, alloc=780.3MB, time=89.60 memory used=4782.7MB, alloc=804.3MB, time=96.86 N1 := 10879 > GB := Basis(F, plex(op(vars))); 3 3 2 GB := [y x , y , 11 y x + 3 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 1275 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 3 2 2 H := [4 x y - 19 y z , -11 x y - 3 z, 9 y , -10 x z - 11 y z , 4 3 7 x - 7 x z, 14 y z + 14 x y z] > J:=[op(GB),op(G)]; 3 3 2 3 2 2 4 J := [y x , y , 11 y x + 3 z, -10 x z - 11 y z , 7 x - 7 x z, 3 14 y z + 14 x 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 := [6, 15, 22, 4, 4, 3, 3, 5/6, 5/6, 5/6, 1/2, 7/12, 7/12, 6, 14, 22, 4, 4, 3, 3, 5/6, 5/6, 2/3, 1/2, 1/2, 1/2, 1, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=5001.3MB, alloc=804.3MB, time=99.49 |\^/| 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(); 1428334869 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [7 x z - 20 y , 14 x z - 10 y z, -19 y z - 11 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [20 y z - 19 x y, 0, -15 x y - 13 x y z] > Problem := [F,G]; 2 2 2 2 Problem := [[7 x z - 20 y , 14 x z - 10 y z, -19 y z - 11 z], 3 2 3 2 [20 y z - 19 x y, 0, -15 x y - 13 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.6MB, alloc=32.3MB, time=0.34 memory used=48.2MB, alloc=32.3MB, time=0.54 memory used=69.0MB, alloc=56.3MB, time=0.73 memory used=110.9MB, alloc=60.3MB, time=1.10 memory used=150.2MB, alloc=84.3MB, time=1.45 memory used=212.9MB, alloc=116.3MB, time=2.15 memory used=291.2MB, alloc=116.3MB, time=2.97 memory used=362.2MB, alloc=140.3MB, time=3.74 memory used=450.9MB, alloc=164.3MB, time=4.70 memory used=555.0MB, alloc=188.3MB, time=5.85 memory used=662.1MB, alloc=468.3MB, time=7.06 memory used=789.3MB, alloc=492.3MB, time=9.05 memory used=920.9MB, alloc=516.3MB, time=11.61 memory used=1063.3MB, alloc=540.3MB, time=14.67 memory used=1218.0MB, alloc=564.3MB, time=18.41 memory used=1396.7MB, alloc=588.3MB, time=22.68 memory used=1599.3MB, alloc=588.3MB, time=27.48 memory used=1801.9MB, alloc=588.3MB, time=32.26 memory used=2004.5MB, alloc=612.3MB, time=37.01 memory used=2231.0MB, alloc=612.3MB, time=42.29 memory used=2457.5MB, alloc=612.3MB, time=47.51 memory used=2684.0MB, alloc=636.3MB, time=52.73 memory used=2934.3MB, alloc=636.3MB, time=58.31 memory used=3184.6MB, alloc=660.3MB, time=63.55 N1 := 9219 > GB := Basis(F, plex(op(vars))); 2 2 2 2 3 2 GB := [495292 x y - 15125 y , -7 x y + 5 y , 37642192 x y + 166375 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3466.2MB, alloc=660.3MB, time=67.57 N2 := 1341 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 2 H := [7 z x - 20 y , 14 x z - 10 y z, -19 y z - 11 z, 20 y z - 19 x y, 0, 3 2 -15 x y - 13 x y z] > J:=[op(GB),op(G)]; 2 2 2 2 3 2 J := [495292 x y - 15125 y , -7 x y + 5 y , 37642192 y x + 166375 z, 3 2 3 2 20 y z - 19 x y, 0, -15 x y - 13 x 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 := [6, 14, -infinity, 4, 3, 3, 2, 2/3, 5/6, 5/6, 5/11, 7/11, 7/11, 6, 13, -infinity, 4, 3, 3, 1, 5/6, 5/6, 1/2, 6/11, 9/11, 3/11, 1, undefined, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3500.5MB, alloc=660.3MB, time=68.14 |\^/| 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(); 1428334936 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 F := [-10 x y + 16 y, -14 x y - 11 y z , -11 x z - 4] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 4 3 G := [-18 x y - 2 x y, -4 x z + 5 x y, 4 z - 13 y ] > Problem := [F,G]; 3 2 2 2 2 2 2 Problem := [[-10 x y + 16 y, -14 x y - 11 y z , -11 x z - 4], 2 2 2 3 4 3 [-18 x y - 2 x y, -4 x z + 5 x y, 4 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=0.14 memory used=26.4MB, alloc=32.3MB, time=0.33 memory used=48.2MB, alloc=32.3MB, time=0.52 memory used=68.7MB, alloc=32.3MB, time=0.70 memory used=88.4MB, alloc=56.3MB, time=0.89 memory used=128.7MB, alloc=60.3MB, time=1.25 memory used=167.5MB, alloc=84.3MB, time=1.66 memory used=226.7MB, alloc=84.3MB, time=2.30 N1 := 879 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 GB := [5 x y - 8 y, y , 11 z x + 4, 22 y z + 5 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=280.0MB, alloc=84.3MB, time=2.91 memory used=337.8MB, alloc=92.3MB, time=3.45 memory used=392.7MB, alloc=116.3MB, time=3.97 memory used=473.8MB, alloc=140.3MB, time=4.84 memory used=569.2MB, alloc=164.3MB, time=6.06 N2 := 1709 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 2 2 2 2 H := [-10 x y + 16 y, -14 x y - 11 y z , -11 x z - 4, -18 x y - 2 x y, 3 4 3 -4 x z + 5 x y, 4 z - 13 y ] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 2 2 J := [5 x y - 8 y, y , 11 z x + 4, 22 y z + 5 x y, -18 x y - 2 x y, 3 4 3 -4 x z + 5 x y, 4 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 := [6, 14, 24, 4, 3, 3, 4, 5/6, 5/6, 2/3, 7/12, 2/3, 1/3, 7, 15, 25, 4, 3, 3, 4, 5/7, 6/7, 4/7, 1/2, 9/14, 2/7, -1, -1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=638.0MB, alloc=164.3MB, time=7.06 |\^/| 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(); 1428334943 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 F := [12 x y z - 19 y , -19 y z + 14 x y, -7 x y - 16 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [-17 x y + y, 6 x y z, -10 x y + 18 y z ] > Problem := [F,G]; 2 2 3 2 3 Problem := [[12 x y z - 19 y , -19 y z + 14 x y, -7 x y - 16 x], 3 3 2 [-17 x y + y, 6 x y z, -10 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=4.3MB, alloc=32.3MB, time=0.14 memory used=26.7MB, alloc=32.3MB, time=0.33 memory used=48.7MB, alloc=32.3MB, time=0.52 memory used=69.8MB, alloc=32.3MB, time=0.71 memory used=90.4MB, alloc=56.3MB, time=0.89 memory used=135.8MB, alloc=60.3MB, time=1.37 memory used=176.1MB, alloc=84.3MB, time=1.79 memory used=236.6MB, alloc=108.3MB, time=2.43 memory used=311.5MB, alloc=132.3MB, time=3.56 memory used=398.1MB, alloc=132.3MB, time=5.00 N1 := 2293 > GB := Basis(F, plex(op(vars))); 16 14 GB := [2470629 x + 449511424 x, -352947 x + 28094464 x y, 11 2 7 50421 x + 1755904 y , -343 x + 2432 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=486.9MB, alloc=140.3MB, time=6.03 N2 := 503 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 3 3 H := [12 x y z - 19 y , -19 y z + 14 x y, -7 x y - 16 x, -17 x y + y, 3 2 6 x y z, -10 x y + 18 y z ] > J:=[op(GB),op(G)]; 16 14 J := [2470629 x + 449511424 x, -352947 x + 28094464 x y, 11 2 7 3 50421 x + 1755904 y , -343 x + 2432 x z, -17 x y + y, 6 x y z, 3 2 -10 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 := [6, 16, 23, 4, 3, 3, 2, 1, 1, 2/3, 1/2, 5/7, 2/7, 7, 15, 59, 16, 16, 3, 2, 1, 5/7, 3/7, 5/8, 7/16, 3/16, 1, -36, -12] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=504.9MB, alloc=140.3MB, time=6.24 |\^/| 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(); 1428334949 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 F := [-19 x y + 12 x z, -17 x y, 4 x z - 20 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [4 x z , 14 x y + 8 x y , 17 x y + 4 x y] > Problem := [F,G]; 3 2 3 Problem := [[-19 x y + 12 x z, -17 x y, 4 x z - 20 y z], 2 2 2 2 3 2 [4 x z , 14 x y + 8 x y , 17 x y + 4 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.11 memory used=26.9MB, alloc=32.3MB, time=0.31 N1 := 291 > GB := Basis(F, plex(op(vars))); 2 4 3 GB := [x y, x y , -19 x y + 12 x z, z y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=48.4MB, alloc=32.3MB, time=0.55 N2 := 155 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 2 2 2 H := [-19 x y + 12 x z, -17 x y, 4 x z - 20 y z, 4 x z , 14 x y + 8 x y , 3 2 17 x y + 4 x y] > J:=[op(GB),op(G)]; 2 4 3 2 2 2 2 J := [x y, x y , -19 x y + 12 x z, z y, 4 x z , 14 x y + 8 x y , 3 2 17 x y + 4 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 := [6, 14, 22, 4, 3, 3, 2, 1, 5/6, 1/2, 9/14, 1/2, 2/7, 7, 15, 25, 5, 2, 4, 2, 6/7, 6/7, 3/7, 3/5, 8/15, 1/5, -1, -3, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=62.2MB, alloc=32.3MB, time=0.69 |\^/| 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(); 1428334950 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 2 F := [-8 z , 3 x z + 2 y z , -6 x y - 4 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 G := [-14 x z + 15, -20 x y + 14 x , 15 x y z + 16 z ] > Problem := [F,G]; 3 3 2 2 3 2 Problem := [[-8 z , 3 x z + 2 y z , -6 x y - 4 x y z], 3 2 2 3 2 [-14 x z + 15, -20 x y + 14 x , 15 x 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=32.2MB, alloc=40.3MB, time=0.36 memory used=61.1MB, alloc=44.3MB, time=0.62 memory used=88.4MB, alloc=68.3MB, time=0.86 memory used=136.2MB, alloc=76.3MB, time=1.30 memory used=182.2MB, alloc=100.3MB, time=1.72 memory used=250.7MB, alloc=100.3MB, time=2.44 memory used=311.7MB, alloc=124.3MB, time=3.11 memory used=390.3MB, alloc=148.3MB, time=4.00 memory used=482.0MB, alloc=172.3MB, time=5.51 memory used=583.2MB, alloc=196.3MB, time=7.47 N1 := 3025 > GB := Basis(F, plex(op(vars))); 5 3 3 2 2 2 3 GB := [y x , x y z, 3 x y + 2 x y z, z y , z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=709.6MB, alloc=196.3MB, time=9.46 N2 := 855 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 2 3 2 3 H := [-8 z , 3 x z + 2 y z , -6 x y - 4 x y z, -14 x z + 15, 2 2 3 2 -20 x y + 14 x , 15 x y z + 16 z ] > J:=[op(GB),op(G)]; 5 3 3 2 2 2 3 3 J := [y x , x y z, 3 x y + 2 x y z, z y , z , -14 x z + 15, 2 2 3 2 -20 x y + 14 x , 15 x y 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 := [6, 14, 22, 4, 3, 2, 3, 5/6, 2/3, 5/6, 7/12, 5/12, 7/12, 8, 18, 33, 6, 5, 2, 3, 3/4, 3/4, 3/4, 8/17, 7/17, 7/17, -4, -11, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=819.9MB, alloc=196.3MB, time=10.65 |\^/| 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(); 1428334960 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 3 F := [10 x + 4 y z , 8 x y + 5 x y z, -17 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 G := [16 x y, 2 x z + 11 y z, -3 y z + 15 z ] > Problem := [F,G]; 4 2 2 2 2 3 Problem := [[10 x + 4 y z , 8 x y + 5 x y z, -17 x y], 3 3 3 2 [16 x y, 2 x z + 11 y z, -3 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=0.13 memory used=27.0MB, alloc=32.3MB, time=0.34 memory used=48.4MB, alloc=56.3MB, time=0.52 memory used=91.2MB, alloc=60.3MB, time=0.89 memory used=133.4MB, alloc=68.3MB, time=1.28 memory used=171.2MB, alloc=92.3MB, time=1.70 N1 := 695 > GB := Basis(F, plex(op(vars))); 5 3 2 2 2 2 4 GB := [x , y x , 8 x y + 5 x y z, 2 z y + 5 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=227.6MB, alloc=92.3MB, time=2.30 memory used=290.3MB, alloc=116.3MB, time=2.86 memory used=373.1MB, alloc=116.3MB, time=3.70 N2 := 695 #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)]; 4 2 2 2 2 3 3 3 H := [10 x + 4 y z , 8 x y + 5 x y z, -17 y x , 16 y x , 2 x z + 11 y z, 3 2 -3 y z + 15 z ] > J:=[op(GB),op(G)]; 5 3 2 2 2 2 4 3 3 J := [x , y x , 8 x y + 5 x y z, 2 z y + 5 x , 16 y x , 2 x z + 11 y z, 3 2 -3 y z + 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, 15, 24, 4, 4, 3, 3, 5/6, 1, 2/3, 3/7, 1/2, 3/7, 7, 16, 29, 5, 5, 3, 3, 6/7, 6/7, 4/7, 7/15, 7/15, 2/5, -1, -5, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=402.9MB, alloc=116.3MB, time=4.04 |\^/| 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(); 1428334964 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 3 F := [8 x y z + 11 x , -18 x z - 11 y z , -7 x y z + 10 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 G := [20 x y z - 14 y z, 15 x - 16 x y z, -14 y + 8 x] > Problem := [F,G]; 2 2 2 2 3 2 3 Problem := [[8 x y z + 11 x , -18 x z - 11 y z , -7 x y z + 10 y ], 2 3 3 [20 x y z - 14 y z, 15 x - 16 x y z, -14 y + 8 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.12 memory used=26.7MB, alloc=32.3MB, time=0.34 memory used=48.3MB, alloc=32.3MB, time=0.53 memory used=68.7MB, alloc=56.3MB, time=0.71 memory used=109.0MB, alloc=60.3MB, time=1.06 memory used=148.3MB, alloc=84.3MB, time=1.39 memory used=207.8MB, alloc=92.3MB, time=1.91 memory used=265.5MB, alloc=116.3MB, time=2.44 memory used=345.0MB, alloc=116.3MB, time=3.30 memory used=417.7MB, alloc=140.3MB, time=4.09 memory used=509.0MB, alloc=164.3MB, time=5.10 memory used=617.0MB, alloc=444.3MB, time=6.31 memory used=734.5MB, alloc=468.3MB, time=8.23 memory used=853.6MB, alloc=492.3MB, time=10.92 memory used=991.7MB, alloc=516.3MB, time=14.09 memory used=1153.8MB, alloc=516.3MB, time=17.66 memory used=1315.9MB, alloc=540.3MB, time=21.06 N1 := 5171 > GB := Basis(F, plex(op(vars))); 10 3 6 3 GB := [1393140695040 x - 181561972207 x , 2592 x + 1331 x y, 8 2 2 3 2 -6718464 x + 1771561 x y , 80 y + 77 x , 8 2 2 2 -9674588160 x + 1500512167 x z, 8 x y z + 11 x , 7 3 1209323520 x + 136410197 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1506.3MB, alloc=540.3MB, time=24.18 memory used=1712.5MB, alloc=540.3MB, time=26.16 memory used=1917.8MB, alloc=564.3MB, time=28.09 memory used=2140.5MB, alloc=588.3MB, time=30.25 memory used=2391.3MB, alloc=612.3MB, time=32.93 memory used=2657.1MB, alloc=636.3MB, time=36.01 memory used=2927.0MB, alloc=660.3MB, time=39.43 memory used=3172.3MB, alloc=684.3MB, time=44.64 memory used=3411.5MB, alloc=708.3MB, time=50.53 memory used=3665.1MB, alloc=732.3MB, time=57.05 memory used=3942.7MB, alloc=756.3MB, time=64.13 memory used=4244.2MB, alloc=780.3MB, time=71.79 memory used=4569.7MB, alloc=804.3MB, time=79.92 memory used=4919.2MB, alloc=828.3MB, time=88.48 memory used=5292.9MB, alloc=852.3MB, time=97.05 N2 := 9045 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 2 3 H := [8 x y z + 11 x , -18 x z - 11 y z , -7 x y z + 10 y , 2 3 3 20 x y z - 14 y z, 15 x - 16 x y z, -14 y + 8 x] > J:=[op(GB),op(G)]; 10 3 6 3 J := [1393140695040 x - 181561972207 x , 2592 x + 1331 x y, 8 2 2 3 2 -6718464 x + 1771561 x y , 80 y + 77 x , 8 2 2 2 -9674588160 x + 1500512167 x z, 8 x y z + 11 x , 7 3 2 3 1209323520 x + 136410197 z y, 20 x y z - 14 y z, 15 x - 16 x y z, 3 -14 y + 8 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 17, 21, 4, 3, 3, 3, 1, 1, 5/6, 2/3, 2/3, 7/12, 10, 23, 55, 10, 10, 3, 3, 1, 4/5, 1/2, 4/5, 9/20, 3/10, -6, -34, -6] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=5453.3MB, alloc=852.3MB, time=99.83 |\^/| 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(); 1428335062 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 F := [-2 y z - 2 y z, -10 x - 18 x, -11 x z + 13 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [-20 y + 6 y z, -11 x z - 7 z, -18 x y + 6 z ] > Problem := [F,G]; 3 2 3 3 2 Problem := [[-2 y z - 2 y z, -10 x - 18 x, -11 x z + 13 x ], 2 2 3 2 [-20 y + 6 y z, -11 x z - 7 z, -18 x y + 6 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.2MB, alloc=32.3MB, time=0.33 memory used=48.0MB, alloc=32.3MB, time=0.52 memory used=69.2MB, alloc=56.3MB, time=0.73 memory used=113.3MB, alloc=60.3MB, time=1.20 memory used=150.8MB, alloc=84.3MB, time=1.66 N1 := 1109 > GB := Basis(F, plex(op(vars))); 3 3 2 3 2 3 2 GB := [5 x + 9 x, x y + x y , y z + y z, 11 x z - 13 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=205.7MB, alloc=84.3MB, time=2.27 memory used=266.2MB, alloc=92.3MB, time=2.89 memory used=323.9MB, alloc=116.3MB, time=3.61 N2 := 1109 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 3 2 2 H := [-2 y z - 2 y z, -10 x - 18 x, -11 x z + 13 x , -20 y + 6 y z, 2 3 2 -11 x z - 7 z, -18 x y + 6 z ] > J:=[op(GB),op(G)]; 3 3 2 3 2 3 2 2 J := [5 x + 9 x, x y + x y , y z + y z, 11 x z - 13 x , -20 y + 6 y z, 2 3 2 -11 x z - 7 z, -18 x y + 6 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 20, 4, 3, 3, 3, 2/3, 1/2, 5/6, 1/2, 5/12, 7/12, 7, 14, 24, 4, 3, 3, 3, 5/7, 4/7, 5/7, 4/7, 1/2, 1/2, -2, -4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=344.5MB, alloc=116.3MB, time=3.89 |\^/| 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(); 1428335066 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 F := [-10 x , 17 y z, 18 x z - 14 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 3 G := [x y - 11 x z, 4 y + 18 y z, -4 x y] > Problem := [F,G]; 3 2 3 3 Problem := [[-10 x , 17 y z, 18 x z - 14 x z ], 3 4 2 3 [x y - 11 x z, 4 y + 18 y z, -4 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=27.6MB, alloc=32.3MB, time=0.37 memory used=49.4MB, alloc=56.3MB, time=0.60 N1 := 659 > GB := Basis(F, plex(op(vars))); 3 2 3 GB := [x , y z, x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 71 #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 := [ 3 2 3 3 3 4 2 3 -10 x , 17 y z, 18 x z - 14 x z , x y - 11 x z, 4 y + 18 y z, -4 x y] > J:=[op(GB),op(G)]; 3 2 3 3 4 2 3 J := [x , y z, x z , x y - 11 x z, 4 y + 18 y z, -4 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 := [6, 12, 22, 4, 3, 4, 3, 2/3, 2/3, 2/3, 3/7, 5/14, 5/14, 6, 12, 22, 4, 3, 4, 3, 2/3, 2/3, 2/3, 5/13, 5/13, 4/13, 0, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=81.3MB, alloc=56.3MB, time=0.94 |\^/| 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(); 1428335067 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 F := [-18 x z - 17 y z, 18 y z + 4 x y z, -19 x y - 12 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 3 G := [-19 x y - 10 y z, 2 x y z + 14 y , 7 y z - 12 z ] > Problem := [F,G]; 2 2 3 2 2 2 2 Problem := [[-18 x z - 17 y z, 18 y z + 4 x y z, -19 x y - 12 x y], 3 3 2 2 3 3 [-19 x y - 10 y z, 2 x y z + 14 y , 7 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=4.3MB, alloc=32.3MB, time=0.11 memory used=26.6MB, alloc=32.3MB, time=0.30 memory used=47.6MB, alloc=32.3MB, time=0.48 memory used=68.1MB, alloc=32.3MB, time=0.66 memory used=87.8MB, alloc=56.3MB, time=0.84 memory used=129.0MB, alloc=60.3MB, time=1.20 memory used=166.9MB, alloc=60.3MB, time=1.55 memory used=203.3MB, alloc=84.3MB, time=1.91 memory used=262.2MB, alloc=116.3MB, time=2.44 memory used=338.6MB, alloc=372.3MB, time=3.09 memory used=419.9MB, alloc=396.3MB, time=3.81 memory used=527.2MB, alloc=420.3MB, time=4.71 memory used=656.5MB, alloc=444.3MB, time=5.82 memory used=794.8MB, alloc=444.3MB, time=7.08 memory used=913.3MB, alloc=468.3MB, time=8.12 memory used=1031.3MB, alloc=492.3MB, time=9.23 memory used=1148.7MB, alloc=492.3MB, time=10.36 memory used=1276.3MB, alloc=516.3MB, time=11.71 memory used=1385.1MB, alloc=516.3MB, time=12.85 memory used=1471.4MB, alloc=516.3MB, time=13.76 memory used=1549.7MB, alloc=540.3MB, time=14.62 memory used=1617.0MB, alloc=540.3MB, time=15.45 memory used=1711.0MB, alloc=540.3MB, time=16.72 memory used=1829.5MB, alloc=564.3MB, time=18.18 memory used=1948.9MB, alloc=588.3MB, time=19.75 memory used=2064.9MB, alloc=612.3MB, time=21.33 memory used=2178.3MB, alloc=612.3MB, time=22.89 memory used=2270.9MB, alloc=636.3MB, time=24.28 memory used=2375.1MB, alloc=660.3MB, time=25.81 memory used=2465.3MB, alloc=660.3MB, time=27.17 memory used=2564.6MB, alloc=684.3MB, time=28.60 memory used=2661.5MB, alloc=684.3MB, time=29.95 memory used=2949.6MB, alloc=708.3MB, time=33.18 memory used=3217.9MB, alloc=732.3MB, time=36.63 memory used=3526.4MB, alloc=756.3MB, time=39.94 memory used=3788.0MB, alloc=780.3MB, time=45.44 memory used=4040.5MB, alloc=804.3MB, time=51.49 memory used=4299.0MB, alloc=828.3MB, time=58.15 memory used=4566.1MB, alloc=852.3MB, time=65.08 memory used=4843.4MB, alloc=876.3MB, time=72.40 memory used=5134.6MB, alloc=900.3MB, time=80.15 memory used=5440.0MB, alloc=924.3MB, time=88.49 memory used=5754.6MB, alloc=948.3MB, time=97.40 memory used=6088.4MB, alloc=972.3MB, time=106.95 memory used=6446.1MB, alloc=996.3MB, time=117.14 memory used=6827.8MB, alloc=1020.3MB, time=127.97 memory used=7233.3MB, alloc=1044.3MB, time=139.50 memory used=7662.9MB, alloc=1068.3MB, time=151.63 memory used=8116.4MB, alloc=1092.3MB, time=164.39 memory used=8593.8MB, alloc=1116.3MB, time=177.74 memory used=9095.1MB, alloc=1140.3MB, time=191.76 memory used=9620.4MB, alloc=1164.3MB, time=206.44 memory used=10169.6MB, alloc=1188.3MB, time=221.68 memory used=10742.7MB, alloc=1188.3MB, time=237.62 memory used=11315.8MB, alloc=1188.3MB, time=253.52 memory used=11888.8MB, alloc=1212.3MB, time=269.50 memory used=12485.9MB, alloc=1212.3MB, time=286.03 memory used=13082.9MB, alloc=1212.3MB, time=302.68 |\^/| 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(); 1428335367 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 F := [x + 8 z, -14 x , -3 x z - 2 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [11 x y z + 4 y z, 6 x y - x, 2 x z + 10 y] > Problem := [F,G]; 4 3 3 2 Problem := [[x + 8 z, -14 x , -3 x z - 2 x ], 2 2 3 2 [11 x y z + 4 y z, 6 x y - x, 2 x z + 10 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=26.3MB, alloc=32.3MB, time=0.39 memory used=49.1MB, alloc=32.3MB, time=0.70 memory used=69.8MB, alloc=56.3MB, time=1.01 N1 := 825 > GB := Basis(F, plex(op(vars))); 2 GB := [x , z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 101 #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)]; 4 3 3 2 2 2 3 H := [x + 8 z, -14 x , -3 x z - 2 x , 11 x y z + 4 y z, 6 x y - x, 2 2 x z + 10 y] > J:=[op(GB),op(G)]; 2 2 2 3 2 J := [x , z, 11 x y z + 4 y z, 6 x y - x, 2 x z + 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 := [6, 13, 22, 4, 4, 2, 3, 1, 1/2, 2/3, 2/3, 1/3, 5/12, 5, 10, 14, 4, 3, 2, 1, 4/5, 3/5, 3/5, 5/9, 4/9, 4/9, 3, 8, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=125.9MB, alloc=92.3MB, time=1.87 |\^/| 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(); 1428335369 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [-6 x z + 10 x y z, 13 x z , 16 x y + 6 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 4 G := [-12 x z - y z, -12 x z + 6 x z, -11 x z - 19 z ] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[-6 x z + 10 x y z, 13 x z , 16 x y + 6 z ], 2 3 2 3 4 [-12 x z - y z, -12 x z + 6 x z, -11 x z - 19 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.6MB, alloc=32.3MB, time=0.43 memory used=47.4MB, alloc=32.3MB, time=0.67 memory used=67.1MB, alloc=56.3MB, time=0.88 memory used=105.9MB, alloc=60.3MB, time=1.33 memory used=142.4MB, alloc=84.3MB, time=1.74 memory used=200.4MB, alloc=92.3MB, time=2.41 memory used=256.2MB, alloc=116.3MB, time=3.08 memory used=332.0MB, alloc=116.3MB, time=3.93 memory used=408.7MB, alloc=140.3MB, time=4.87 memory used=504.1MB, alloc=164.3MB, time=6.18 memory used=634.3MB, alloc=164.3MB, time=7.57 memory used=743.2MB, alloc=188.3MB, time=9.07 memory used=865.1MB, alloc=212.3MB, time=10.77 memory used=989.4MB, alloc=492.3MB, time=12.51 memory used=1129.1MB, alloc=516.3MB, time=14.58 memory used=1266.9MB, alloc=540.3MB, time=17.22 memory used=1413.1MB, alloc=564.3MB, time=20.44 memory used=1568.7MB, alloc=588.3MB, time=24.24 memory used=1748.4MB, alloc=612.3MB, time=28.62 memory used=1952.0MB, alloc=636.3MB, time=33.91 memory used=2179.5MB, alloc=660.3MB, time=39.37 memory used=2431.0MB, alloc=660.3MB, time=45.36 memory used=2682.4MB, alloc=660.3MB, time=51.35 memory used=2933.8MB, alloc=684.3MB, time=57.30 memory used=3209.2MB, alloc=684.3MB, time=63.72 memory used=3484.6MB, alloc=708.3MB, time=70.07 memory used=3784.0MB, alloc=732.3MB, time=76.71 N1 := 9959 > GB := Basis(F, plex(op(vars))); 4 3 3 2 2 2 GB := [y x , y x , z x y , 8 y x + 3 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4118.0MB, alloc=732.3MB, time=82.38 N2 := 1895 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 2 H := [-6 x z + 10 x y z, 13 x z , 16 x y + 6 z , -12 x z - y z, 3 2 3 4 -12 x z + 6 x z, -11 x z - 19 z ] > J:=[op(GB),op(G)]; 4 3 3 2 2 2 2 3 2 J := [y x , y x , z x y , 8 y x + 3 z , -12 x z - y z, -12 x z + 6 x z, 3 4 -11 x z - 19 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, 15, 22, 4, 2, 2, 4, 1, 1/2, 1, 8/13, 3/13, 10/13, 7, 17, 29, 6, 4, 3, 4, 1, 5/7, 5/7, 8/15, 1/3, 8/15, -2, -7, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=4325.4MB, alloc=732.3MB, time=85.31 |\^/| 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(); 1428335454 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 4 2 2 F := [-5 x z - 18 y , 18 x y z + 20 y z , 12 x - 10 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [x z - 18 z, -2 x y z - 12 x z , 16 x y + 4 x y ] > Problem := [F,G]; 3 3 2 2 2 4 2 2 Problem := [[-5 x z - 18 y , 18 x y z + 20 y z , 12 x - 10 x y ], 2 2 2 2 [x z - 18 z, -2 x y z - 12 x z , 16 x y + 4 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.3MB, alloc=32.3MB, time=0.32 memory used=49.1MB, alloc=32.3MB, time=0.58 memory used=69.3MB, alloc=56.3MB, time=0.81 N1 := 665 > GB := Basis(F, plex(op(vars))); 7 6 5 4 2 2 4 5 2 5 GB := [x , 9 x + 10 x y, -6 x + 5 x y , 9 x y + 10 y , z x , 4 2 3 2 2 2 2 3 3 4 x z + 3 x y z , 9 x y z + 10 y z , 5 z x + 18 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.1MB, alloc=56.3MB, time=1.24 memory used=148.8MB, alloc=84.3MB, time=1.65 N2 := 777 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 2 2 4 2 2 H := [-5 x z - 18 y , 18 x y z + 20 y z , 12 x - 10 x y , x z - 18 z, 2 2 2 2 -2 x y z - 12 x z , 16 x y + 4 x y ] > J:=[op(GB),op(G)]; 7 6 5 4 2 2 4 5 2 5 J := [x , 9 x + 10 x y, -6 x + 5 x y , 9 x y + 10 y , z x , 4 2 3 2 2 2 2 3 3 4 x z + 3 x y z , 9 x y z + 10 y z , 5 z x + 18 y , x z - 18 z, 2 2 2 2 -2 x y z - 12 x z , 16 x y + 4 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 := [6, 15, 21, 4, 4, 3, 3, 1, 5/6, 2/3, 3/4, 7/12, 7/12, 11, 25, 52, 7, 7, 5, 3, 1, 8/11, 6/11, 8/11, 1/2, 5/11, -10, -31, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=205.2MB, alloc=84.3MB, time=2.27 |\^/| 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(); 1428335457 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 3 2 F := [11 x y + 10 x , -13 x - 6 x y z, -x z - 15 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [12 x z + 7 z , 11 x + 4 z , -9 x + 7 x y ] > Problem := [F,G]; 2 2 4 2 3 2 Problem := [[11 x y + 10 x , -13 x - 6 x y z, -x z - 15 x y z], 2 2 2 3 2 [12 x z + 7 z , 11 x + 4 z , -9 x + 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=32.3MB, alloc=40.3MB, time=0.33 memory used=62.0MB, alloc=40.3MB, time=0.60 memory used=90.3MB, alloc=40.3MB, time=0.90 memory used=115.6MB, alloc=64.3MB, time=1.17 N1 := 809 > GB := Basis(F, plex(op(vars))); 6 4 2 2 5 2 4 2 GB := [121 x + 1500 x , 11 x y + 10 x , 1573 x + 600 x z, 13 x + 6 x y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=158.6MB, alloc=64.3MB, time=1.63 memory used=204.6MB, alloc=68.3MB, time=2.07 memory used=249.8MB, alloc=92.3MB, time=2.55 N2 := 1085 #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 4 2 3 2 2 H := [11 x y + 10 x , -13 x - 6 x y z, -x z - 15 x y z, 12 x z + 7 z , 2 2 3 2 4 z + 11 x , -9 x + 7 x y ] > J:=[op(GB),op(G)]; 6 4 2 2 5 2 4 2 J := [121 x + 1500 x , 11 x y + 10 x , 1573 x + 600 x z, 13 x + 6 x y z, 2 2 2 3 2 12 x z + 7 z , 4 z + 11 x , -9 x + 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 := [6, 14, 18, 4, 4, 2, 2, 1, 2/3, 2/3, 5/6, 1/3, 1/2, 7, 14, 25, 6, 6, 2, 2, 1, 3/7, 4/7, 6/7, 3/14, 5/14, 0, -7, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=298.8MB, alloc=92.3MB, time=3.22 |\^/| 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(); 1428335460 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 2 F := [9 x z - 9 x y , -4 x y + 15 x y, 10 x z + 15] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 4 G := [-11 z + 2 x , -14 x z - 2 y, -x + 6 x y z] > Problem := [F,G]; 3 3 3 2 2 2 Problem := [[9 x z - 9 x y , -4 x y + 15 x y, 10 x z + 15], 4 2 3 4 [-11 z + 2 x , -14 x z - 2 y, -x + 6 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.11 memory used=26.8MB, alloc=32.3MB, time=0.31 memory used=48.3MB, alloc=32.3MB, time=0.50 memory used=98.2MB, alloc=68.3MB, time=0.95 memory used=145.9MB, alloc=68.3MB, time=1.37 memory used=191.5MB, alloc=68.3MB, time=1.77 memory used=237.3MB, alloc=100.3MB, time=2.20 memory used=304.4MB, alloc=100.3MB, time=2.80 memory used=369.7MB, alloc=124.3MB, time=3.41 memory used=444.5MB, alloc=380.3MB, time=4.10 memory used=531.2MB, alloc=404.3MB, time=4.95 memory used=640.7MB, alloc=428.3MB, time=5.95 memory used=775.0MB, alloc=452.3MB, time=7.16 memory used=922.3MB, alloc=476.3MB, time=8.54 memory used=1057.4MB, alloc=476.3MB, time=9.85 memory used=1187.9MB, alloc=500.3MB, time=11.09 memory used=1315.1MB, alloc=500.3MB, time=12.39 memory used=1435.6MB, alloc=500.3MB, time=13.62 memory used=1535.1MB, alloc=524.3MB, time=14.67 memory used=1616.4MB, alloc=524.3MB, time=15.61 memory used=1701.8MB, alloc=524.3MB, time=16.62 memory used=1779.2MB, alloc=524.3MB, time=17.52 memory used=1863.4MB, alloc=548.3MB, time=18.56 memory used=1928.3MB, alloc=548.3MB, time=19.44 memory used=2038.6MB, alloc=548.3MB, time=20.96 memory used=2153.6MB, alloc=572.3MB, time=22.45 memory used=2249.4MB, alloc=572.3MB, time=23.80 memory used=2377.3MB, alloc=596.3MB, time=25.53 memory used=2484.3MB, alloc=596.3MB, time=27.03 memory used=2599.7MB, alloc=620.3MB, time=28.64 memory used=2716.5MB, alloc=620.3MB, time=30.22 memory used=2820.5MB, alloc=644.3MB, time=31.74 memory used=3075.1MB, alloc=668.3MB, time=34.89 memory used=3342.9MB, alloc=692.3MB, time=38.22 memory used=3604.5MB, alloc=716.3MB, time=43.13 memory used=3847.3MB, alloc=740.3MB, time=48.79 memory used=4097.5MB, alloc=764.3MB, time=55.01 memory used=4359.5MB, alloc=788.3MB, time=61.80 memory used=4628.8MB, alloc=812.3MB, time=69.20 memory used=4912.4MB, alloc=836.3MB, time=77.23 memory used=5219.9MB, alloc=860.3MB, time=85.91 memory used=5551.4MB, alloc=884.3MB, time=95.21 memory used=5906.7MB, alloc=908.3MB, time=105.12 memory used=6286.1MB, alloc=932.3MB, time=115.69 memory used=6689.4MB, alloc=956.3MB, time=126.86 memory used=7116.6MB, alloc=980.3MB, time=138.66 memory used=7567.8MB, alloc=980.3MB, time=151.05 memory used=8018.8MB, alloc=1004.3MB, time=163.43 memory used=8493.8MB, alloc=1004.3MB, time=176.35 memory used=8968.8MB, alloc=1004.3MB, time=189.30 memory used=9443.7MB, alloc=1028.3MB, time=202.12 memory used=9942.5MB, alloc=1028.3MB, time=215.38 memory used=10441.0MB, alloc=1052.3MB, time=228.75 memory used=10963.5MB, alloc=1076.3MB, time=242.39 memory used=11510.0MB, alloc=1100.3MB, time=256.29 N1 := 16615 > GB := Basis(F, plex(op(vars))); 2 GB := [1125 x + 32, 75 y + 8, 128 z + 16875 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=12109.3MB, alloc=1100.3MB, time=267.22 memory used=12857.9MB, alloc=1100.3MB, time=275.85 memory used=13541.8MB, alloc=1124.3MB, time=291.62 memory used=14154.8MB, alloc=1148.3MB, time=307.76 |\^/| 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(); 1428335760 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 F := [16 x z + 8, 10 y z + 11 x , 19 x z - 20 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-12 x + 19 y z , -16 x z , 3 x y z - 4 x z] > Problem := [F,G]; 2 2 2 3 3 2 Problem := [[16 x z + 8, 10 y z + 11 x , 19 x z - 20 x z], 3 2 2 2 [-12 x + 19 y z , -16 x z , 3 x y z - 4 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.42 memory used=48.0MB, alloc=32.3MB, time=0.68 memory used=68.5MB, alloc=32.3MB, time=0.91 memory used=88.1MB, alloc=56.3MB, time=1.17 memory used=131.1MB, alloc=60.3MB, time=1.78 memory used=171.3MB, alloc=84.3MB, time=2.45 memory used=232.4MB, alloc=84.3MB, time=3.41 memory used=288.2MB, alloc=108.3MB, time=4.32 memory used=358.5MB, alloc=132.3MB, time=5.76 memory used=441.4MB, alloc=132.3MB, time=7.27 memory used=524.6MB, alloc=156.3MB, time=8.62 N1 := 2665 > GB := Basis(F, plex(op(vars))); 5 2 2 3 GB := [80 x - 19, 200 y + 209 x , 40 x + 19 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=581.8MB, alloc=156.3MB, time=9.26 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 2 3 3 2 3 2 H := [16 x z + 8, 10 z y + 11 x , 19 x z - 20 x z, -12 x + 19 y z , 2 2 -16 x z , 3 x y z - 4 x z] > J:=[op(GB),op(G)]; 5 2 2 3 3 2 2 J := [80 x - 19, 200 y + 209 x , 40 x + 19 z, -12 x + 19 y z , -16 x z , 2 3 x y z - 4 x z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 21, 4, 3, 2, 3, 1, 1/2, 1, 8/13, 3/13, 8/13, 6, 13, 20, 5, 5, 2, 2, 1, 1/2, 2/3, 7/13, 3/13, 5/13, 2, 1, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=601.6MB, alloc=164.3MB, time=9.49 |\^/| 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(); 1428335770 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 4 2 F := [-18 x y + 15 y z , -13 x y - 14 y , x y z - 4 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 3 2 G := [14 x y - 11 y z, 6 x y z + 16 y , -11 x z - 5 z ] > Problem := [F,G]; 2 2 3 3 4 2 Problem := [[-18 x y + 15 y z , -13 x y - 14 y , x y z - 4 y], 2 2 2 4 3 2 [14 x y - 11 y z, 6 x y z + 16 y , -11 x z - 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.6MB, alloc=32.3MB, time=0.34 memory used=47.4MB, alloc=32.3MB, time=0.52 memory used=67.6MB, alloc=32.3MB, time=0.69 memory used=86.8MB, alloc=56.3MB, time=0.87 memory used=126.9MB, alloc=60.3MB, time=1.22 memory used=168.4MB, alloc=92.3MB, time=1.57 memory used=228.7MB, alloc=92.3MB, time=2.10 memory used=289.0MB, alloc=116.3MB, time=2.65 memory used=367.3MB, alloc=372.3MB, time=3.33 memory used=447.8MB, alloc=396.3MB, time=4.06 memory used=554.6MB, alloc=420.3MB, time=4.97 memory used=678.8MB, alloc=420.3MB, time=6.11 memory used=801.9MB, alloc=444.3MB, time=7.25 memory used=939.7MB, alloc=468.3MB, time=8.54 memory used=1059.3MB, alloc=492.3MB, time=9.70 memory used=1166.6MB, alloc=492.3MB, time=10.74 memory used=1300.9MB, alloc=516.3MB, time=12.34 memory used=1473.5MB, alloc=540.3MB, time=14.43 memory used=1643.3MB, alloc=564.3MB, time=16.37 memory used=1810.1MB, alloc=588.3MB, time=18.38 memory used=1976.7MB, alloc=612.3MB, time=20.48 memory used=2140.3MB, alloc=636.3MB, time=22.57 memory used=2275.2MB, alloc=660.3MB, time=24.34 memory used=2428.8MB, alloc=684.3MB, time=26.36 memory used=2563.6MB, alloc=708.3MB, time=28.20 memory used=2709.3MB, alloc=732.3MB, time=30.19 memory used=2847.2MB, alloc=756.3MB, time=32.08 memory used=2986.6MB, alloc=780.3MB, time=34.92 memory used=3188.6MB, alloc=804.3MB, time=39.52 memory used=3485.3MB, alloc=828.3MB, time=46.48 memory used=3785.0MB, alloc=852.3MB, time=53.85 memory used=4092.2MB, alloc=876.3MB, time=61.46 memory used=4409.0MB, alloc=900.3MB, time=69.54 memory used=4737.1MB, alloc=924.3MB, time=78.06 memory used=5068.6MB, alloc=948.3MB, time=87.22 memory used=5422.6MB, alloc=972.3MB, time=96.98 memory used=5800.5MB, alloc=996.3MB, time=107.39 memory used=6202.4MB, alloc=1020.3MB, time=118.38 memory used=6628.2MB, alloc=1044.3MB, time=130.01 memory used=7077.9MB, alloc=1068.3MB, time=142.25 memory used=7551.6MB, alloc=1092.3MB, time=155.08 memory used=8049.2MB, alloc=1116.3MB, time=168.52 memory used=8570.8MB, alloc=1116.3MB, time=182.66 memory used=9092.3MB, alloc=1116.3MB, time=196.74 memory used=9613.8MB, alloc=1140.3MB, time=210.76 memory used=10159.2MB, alloc=1140.3MB, time=225.42 memory used=10704.5MB, alloc=1140.3MB, time=240.05 memory used=11249.9MB, alloc=1140.3MB, time=254.62 memory used=11795.2MB, alloc=1164.3MB, time=269.53 memory used=12364.4MB, alloc=1164.3MB, time=285.10 memory used=12933.5MB, alloc=1164.3MB, time=300.41 |\^/| 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(); 1428336070 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-18 x z + 13 z , -4 x y z + 5 x y, 12 y z - 10 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 3 G := [-8 y z + y , 10 y - 10 z , 18 y z - 11 y] > Problem := [F,G]; 2 2 3 2 Problem := [[-18 x z + 13 z , -4 x y z + 5 x y, 12 y z - 10 y z], 2 2 3 3 3 3 [-8 y z + y , 10 y - 10 z , 18 y z - 11 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.5MB, alloc=32.3MB, time=0.41 memory used=47.2MB, alloc=32.3MB, time=0.62 memory used=66.6MB, alloc=32.3MB, time=0.84 memory used=85.2MB, alloc=56.3MB, time=1.06 memory used=123.0MB, alloc=60.3MB, time=1.50 memory used=157.9MB, alloc=60.3MB, time=1.92 memory used=191.4MB, alloc=84.3MB, time=2.35 memory used=244.3MB, alloc=84.3MB, time=2.98 memory used=295.8MB, alloc=108.3MB, time=3.64 memory used=368.6MB, alloc=116.3MB, time=4.53 memory used=439.2MB, alloc=140.3MB, time=5.40 memory used=530.0MB, alloc=140.3MB, time=6.56 memory used=615.5MB, alloc=164.3MB, time=7.62 memory used=721.1MB, alloc=164.3MB, time=8.91 memory used=825.7MB, alloc=188.3MB, time=10.26 memory used=929.0MB, alloc=444.3MB, time=11.64 memory used=1051.2MB, alloc=468.3MB, time=12.81 memory used=1193.4MB, alloc=492.3MB, time=14.32 memory used=1356.0MB, alloc=516.3MB, time=16.18 memory used=1523.2MB, alloc=540.3MB, time=18.10 memory used=1695.2MB, alloc=564.3MB, time=20.15 memory used=1871.7MB, alloc=588.3MB, time=22.24 memory used=2050.3MB, alloc=612.3MB, time=24.41 memory used=2232.8MB, alloc=636.3MB, time=26.68 memory used=2409.2MB, alloc=660.3MB, time=29.19 memory used=2565.5MB, alloc=684.3MB, time=32.33 memory used=2728.3MB, alloc=708.3MB, time=35.89 memory used=2901.2MB, alloc=732.3MB, time=39.87 memory used=3085.4MB, alloc=756.3MB, time=44.27 memory used=3282.1MB, alloc=780.3MB, time=49.07 memory used=3491.9MB, alloc=804.3MB, time=54.41 memory used=3715.8MB, alloc=828.3MB, time=60.11 memory used=3953.8MB, alloc=852.3MB, time=67.19 memory used=4205.1MB, alloc=876.3MB, time=75.00 memory used=4468.8MB, alloc=900.3MB, time=82.66 memory used=4756.4MB, alloc=924.3MB, time=90.50 memory used=5067.9MB, alloc=948.3MB, time=98.86 memory used=5403.4MB, alloc=972.3MB, time=107.89 memory used=5762.8MB, alloc=996.3MB, time=118.01 memory used=6146.2MB, alloc=1020.3MB, time=128.65 memory used=6553.5MB, alloc=1044.3MB, time=140.12 memory used=6984.8MB, alloc=1068.3MB, time=151.47 memory used=7440.0MB, alloc=1092.3MB, time=163.37 memory used=7919.1MB, alloc=1116.3MB, time=175.84 memory used=8422.1MB, alloc=1140.3MB, time=188.91 memory used=8949.2MB, alloc=1140.3MB, time=202.77 memory used=9476.0MB, alloc=1140.3MB, time=216.59 memory used=10002.8MB, alloc=1164.3MB, time=230.26 memory used=10553.5MB, alloc=1164.3MB, time=244.96 memory used=11104.2MB, alloc=1164.3MB, time=259.15 memory used=11654.9MB, alloc=1164.3MB, time=273.34 memory used=12205.6MB, alloc=1188.3MB, time=287.52 memory used=12780.2MB, alloc=1188.3MB, time=302.29 |\^/| 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(); 1428336370 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [-4 x z - 15 y z, 17 z - 16 y , -10 x y + x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 2 G := [-6 y z + 13 y z, -15 z - 8 z , 8 x y - 7 y] > Problem := [F,G]; 3 2 2 2 Problem := [[-4 x z - 15 y z, 17 z - 16 y , -10 x y + x z], 3 4 3 2 [-6 y z + 13 y z, -15 z - 8 z , 8 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=0.13 memory used=26.2MB, alloc=32.3MB, time=0.35 memory used=47.9MB, alloc=32.3MB, time=0.59 memory used=68.4MB, alloc=32.3MB, time=0.82 memory used=87.9MB, alloc=56.3MB, time=1.06 memory used=128.8MB, alloc=60.3MB, time=1.58 memory used=167.7MB, alloc=84.3MB, time=2.15 memory used=225.9MB, alloc=108.3MB, time=2.96 memory used=299.1MB, alloc=140.3MB, time=4.16 memory used=380.1MB, alloc=164.3MB, time=6.35 memory used=480.1MB, alloc=164.3MB, time=9.05 N1 := 2879 > GB := Basis(F, plex(op(vars))); 8 2 2 2 3 2 2 2 2 GB := [2176 x y - 405 x y , 4 x y + 15 y , -10 x y + x z, 8 x y + 3 y z, 3 2 17 z - 16 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=581.8MB, alloc=164.3MB, time=10.95 memory used=690.1MB, alloc=164.3MB, time=12.18 memory used=796.6MB, alloc=188.3MB, time=13.37 memory used=898.8MB, alloc=468.3MB, time=14.80 memory used=1049.7MB, alloc=492.3MB, time=16.78 memory used=1209.9MB, alloc=516.3MB, time=18.57 memory used=1371.1MB, alloc=540.3MB, time=21.31 memory used=1532.2MB, alloc=564.3MB, time=24.80 memory used=1702.9MB, alloc=588.3MB, time=29.01 memory used=1897.7MB, alloc=612.3MB, time=33.79 memory used=2116.4MB, alloc=636.3MB, time=39.06 memory used=2359.1MB, alloc=660.3MB, time=44.78 memory used=2625.8MB, alloc=660.3MB, time=50.95 memory used=2892.8MB, alloc=684.3MB, time=56.61 N2 := 7287 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 H := [-4 x z - 15 y z, 17 z - 16 y , -10 x y + x z, -6 y z + 13 y z, 4 3 2 -15 z - 8 z , 8 x y - 7 y] > J:=[op(GB),op(G)]; 8 2 2 2 3 2 2 2 2 J := [2176 x y - 405 x y , 4 x y + 15 y , -10 x y + x z, 8 x y + 3 y z, 3 2 3 4 3 2 17 z - 16 y , -6 y z + 13 y z, -15 z - 8 z , 8 x y - 7 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 20, 4, 2, 3, 4, 1/2, 5/6, 5/6, 1/3, 7/12, 2/3, 8, 17, 35, 10, 8, 3, 4, 5/8, 7/8, 5/8, 7/16, 3/4, 7/16, -4, -15, -6] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2918.8MB, alloc=684.3MB, time=57.01 |\^/| 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(); 1428336427 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [12 x z + 11 z, -13 x y z - 12 y z, 17 y z + 14 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 G := [-14 x y - 3 x z, 10 x y + 2 x y z , 7 x y z + 17 x z ] > Problem := [F,G]; 2 2 3 2 Problem := [[12 x z + 11 z, -13 x y z - 12 y z, 17 y z + 14 x y], 2 3 2 2 3 [-14 x y - 3 x z, 10 x y + 2 x y z , 7 x y z + 17 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.35 memory used=48.3MB, alloc=32.3MB, time=0.56 memory used=69.6MB, alloc=32.3MB, time=0.75 memory used=90.2MB, alloc=56.3MB, time=0.95 memory used=132.0MB, alloc=60.3MB, time=1.32 memory used=171.8MB, alloc=60.3MB, time=1.70 memory used=210.8MB, alloc=84.3MB, time=2.12 memory used=269.2MB, alloc=108.3MB, time=2.79 N1 := 1011 > GB := Basis(F, plex(op(vars))); 4 2 3 2 2 2 GB := [12 x y + 11 x y, 13 x y + 12 x y , 12 x z + 11 z, 2 3 2 13 x y z + 12 y z, 17 y z + 14 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=341.3MB, alloc=108.3MB, time=3.54 memory used=422.5MB, alloc=116.3MB, time=4.30 memory used=502.6MB, alloc=116.3MB, time=5.11 memory used=576.5MB, alloc=140.3MB, time=6.03 N2 := 1011 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 H := [12 x z + 11 z, -13 x y z - 12 y z, 17 y z + 14 x y, -14 x y - 3 x z, 3 2 2 3 10 x y + 2 x y z , 7 x y z + 17 x z ] > J:=[op(GB),op(G)]; 4 2 3 2 2 2 2 J := [12 x y + 11 x y, 13 x y + 12 x y , 12 x z + 11 z, 13 x y z + 12 y z, 3 2 2 3 2 2 3 17 y z + 14 x y, -14 x y - 3 x z, 10 x y + 2 x y z , 7 x y z + 17 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 := [6, 17, 21, 4, 2, 3, 3, 1, 5/6, 1, 3/4, 2/3, 3/4, 8, 21, 30, 5, 4, 3, 3, 1, 7/8, 3/4, 13/16, 3/4, 9/16, -4, -9, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=579.8MB, alloc=140.3MB, time=6.08 |\^/| 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(); 1428336434 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 2 2 2 F := [2 z - 10 y , 10 y + 7 x, 2 x y - 4 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 G := [20 y + 5 y, 3 x + 8 x y z, -15 x y z + 5 y z ] > Problem := [F,G]; 4 2 4 2 2 2 Problem := [[2 z - 10 y , 10 y + 7 x, 2 x y - 4 y z], 3 3 2 3 [20 y + 5 y, 3 x + 8 x y z, -15 x y z + 5 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.0MB, alloc=32.3MB, time=0.34 memory used=47.6MB, alloc=32.3MB, time=0.53 memory used=68.0MB, alloc=32.3MB, time=0.71 memory used=87.7MB, alloc=56.3MB, time=0.90 memory used=126.4MB, alloc=60.3MB, time=1.24 memory used=163.2MB, alloc=84.3MB, time=1.57 memory used=217.1MB, alloc=108.3MB, time=2.11 memory used=295.2MB, alloc=140.3MB, time=2.98 memory used=387.6MB, alloc=164.3MB, time=3.97 memory used=497.7MB, alloc=188.3MB, time=5.29 memory used=616.6MB, alloc=212.3MB, time=6.76 memory used=737.7MB, alloc=236.3MB, time=8.92 memory used=866.9MB, alloc=260.3MB, time=11.56 memory used=1005.1MB, alloc=284.3MB, time=14.97 memory used=1165.4MB, alloc=308.3MB, time=18.84 memory used=1349.6MB, alloc=332.3MB, time=24.25 memory used=1557.9MB, alloc=332.3MB, time=29.83 memory used=1766.1MB, alloc=332.3MB, time=35.00 memory used=1974.2MB, alloc=356.3MB, time=40.00 memory used=2206.4MB, alloc=356.3MB, time=45.19 memory used=2438.3MB, alloc=380.3MB, time=50.50 N1 := 8097 > GB := Basis(F, plex(op(vars))); 16 9 2 4 3 10 2 GB := [x + 4480 x, -x + 80 x y , 10 y + 7 x, -x + 2 x z, -x + 160 y z, 4 2 z - 5 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2697.5MB, alloc=380.3MB, time=55.36 memory used=2780.6MB, alloc=636.3MB, time=56.43 memory used=3063.7MB, alloc=636.3MB, time=59.36 memory used=3340.4MB, alloc=660.3MB, time=62.19 memory used=3655.8MB, alloc=684.3MB, time=65.17 memory used=3942.7MB, alloc=708.3MB, time=67.78 memory used=4199.1MB, alloc=732.3MB, time=70.15 memory used=4548.5MB, alloc=756.3MB, time=74.31 memory used=4942.6MB, alloc=780.3MB, time=78.19 memory used=5303.9MB, alloc=804.3MB, time=82.66 memory used=5610.1MB, alloc=828.3MB, time=89.44 memory used=5906.6MB, alloc=852.3MB, time=96.81 memory used=6200.8MB, alloc=876.3MB, time=105.24 memory used=6505.3MB, alloc=900.3MB, time=114.27 memory used=6833.7MB, alloc=924.3MB, time=124.42 memory used=7185.9MB, alloc=948.3MB, time=134.39 memory used=7562.2MB, alloc=972.3MB, time=145.58 memory used=7962.4MB, alloc=996.3MB, time=156.94 memory used=8386.4MB, alloc=1020.3MB, time=169.16 memory used=8834.5MB, alloc=1044.3MB, time=182.38 memory used=9306.4MB, alloc=1068.3MB, time=195.62 memory used=9802.3MB, alloc=1092.3MB, time=209.08 memory used=10322.2MB, alloc=1116.3MB, time=222.96 memory used=10865.9MB, alloc=1140.3MB, time=237.39 memory used=11433.6MB, alloc=1164.3MB, time=252.24 memory used=12025.2MB, alloc=1188.3MB, time=267.27 memory used=12640.9MB, alloc=1212.3MB, time=283.05 N2 := 15955 #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)]; 4 2 4 2 2 2 3 3 H := [2 z - 10 y , 10 y + 7 x, 2 x y - 4 y z, 20 y + 5 y, 3 x + 8 x y z, 2 3 -15 x y z + 5 y z ] > J:=[op(GB),op(G)]; 16 9 2 4 3 10 2 J := [x + 4480 x, -x + 80 x y , 10 y + 7 x, -x + 2 x z, -x + 160 y z, 4 2 3 3 2 3 z - 5 y , 20 y + 5 y, 3 x + 8 x y z, -15 x y z + 5 y z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 22, 4, 3, 4, 4, 2/3, 1, 2/3, 5/12, 3/4, 5/12, 9, 19, 56, 16, 16, 4, 4, 7/9, 7/9, 5/9, 11/18, 1/2, 1/3, -5, -34, -12] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=12871.9MB, alloc=1212.3MB, time=289.13 |\^/| 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(); 1428336718 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 F := [16 x y - 8 y , 5 x z - 14 z, -9 x + 2 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [18 x y + 2 x y, -17 y - 15 z, -10 y z - 2 x y] > Problem := [F,G]; 2 3 2 3 Problem := [[16 x y - 8 y , 5 x z - 14 z, -9 x + 2 z], 3 2 2 2 [18 x y + 2 x y, -17 y - 15 z, -10 y z - 2 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.45 memory used=47.6MB, alloc=32.3MB, time=0.68 memory used=67.9MB, alloc=32.3MB, time=0.86 memory used=88.1MB, alloc=56.3MB, time=1.08 memory used=130.7MB, alloc=60.3MB, time=1.55 memory used=167.6MB, alloc=84.3MB, time=1.96 N1 := 1263 > GB := Basis(F, plex(op(vars))); 5 3 2 3 3 GB := [5 x - 14 x , -2 x y + y , -9 x + 2 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=219.8MB, alloc=84.3MB, time=2.97 memory used=275.8MB, alloc=84.3MB, time=3.56 memory used=333.8MB, alloc=108.3MB, time=4.41 N2 := 1003 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 3 3 H := [16 x y - 8 y , 5 x z - 14 z, -9 x + 2 z, 18 x y + 2 x y, -17 y - 15 z, 2 2 2 -10 y z - 2 x y] > J:=[op(GB),op(G)]; 5 3 2 3 3 3 J := [5 x - 14 x , -2 x y + y , -9 x + 2 z, 18 x y + 2 x y, -17 y - 15 z, 2 2 2 -10 y z - 2 x y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 18, 4, 3, 3, 2, 5/6, 2/3, 2/3, 1/2, 7/12, 5/12, 6, 12, 20, 5, 5, 3, 2, 5/6, 2/3, 1/2, 7/12, 7/12, 1/4, 1, -2, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=396.1MB, alloc=108.3MB, time=5.31 |\^/| 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(); 1428336723 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [-6 z + 12, -16 x y z + 4 x y, -20 y z - 4 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 3 G := [6 y z - 12 x , 17 z + 18 x, -15 x y z - 13 x z ] > Problem := [F,G]; 2 2 3 Problem := [[-6 z + 12, -16 x y z + 4 x y, -20 y z - 4 x], 3 2 4 2 3 [6 y z - 12 x , 17 z + 18 x, -15 x y z - 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=0.12 memory used=27.0MB, alloc=32.3MB, time=0.41 memory used=48.4MB, alloc=32.3MB, time=0.64 memory used=68.3MB, alloc=56.3MB, time=0.86 memory used=108.6MB, alloc=60.3MB, time=1.23 memory used=146.9MB, alloc=84.3MB, time=1.58 memory used=208.5MB, alloc=92.3MB, time=2.31 memory used=267.4MB, alloc=116.3MB, time=3.08 memory used=348.1MB, alloc=116.3MB, time=4.05 memory used=427.3MB, alloc=140.3MB, time=4.97 memory used=509.1MB, alloc=140.3MB, time=5.99 memory used=576.1MB, alloc=420.3MB, time=6.77 memory used=698.9MB, alloc=444.3MB, time=7.95 memory used=835.8MB, alloc=468.3MB, time=9.35 memory used=984.0MB, alloc=492.3MB, time=10.83 memory used=1131.3MB, alloc=516.3MB, time=12.50 memory used=1255.6MB, alloc=516.3MB, time=13.98 memory used=1384.9MB, alloc=540.3MB, time=15.43 memory used=1483.6MB, alloc=540.3MB, time=16.55 memory used=1596.5MB, alloc=540.3MB, time=18.03 memory used=1696.5MB, alloc=540.3MB, time=19.29 memory used=1772.3MB, alloc=540.3MB, time=20.29 memory used=1841.8MB, alloc=540.3MB, time=21.28 memory used=1905.2MB, alloc=540.3MB, time=22.24 memory used=1962.2MB, alloc=540.3MB, time=23.05 memory used=2019.4MB, alloc=564.3MB, time=23.75 memory used=2095.6MB, alloc=564.3MB, time=25.14 memory used=2157.6MB, alloc=564.3MB, time=26.45 memory used=2214.8MB, alloc=564.3MB, time=27.45 memory used=2438.1MB, alloc=588.3MB, time=30.09 memory used=2654.8MB, alloc=612.3MB, time=32.47 memory used=2861.7MB, alloc=636.3MB, time=35.03 memory used=3064.7MB, alloc=660.3MB, time=37.70 memory used=3211.8MB, alloc=684.3MB, time=39.67 memory used=3371.9MB, alloc=708.3MB, time=42.02 memory used=3503.2MB, alloc=708.3MB, time=44.21 memory used=3648.7MB, alloc=732.3MB, time=46.64 memory used=3768.4MB, alloc=732.3MB, time=48.75 memory used=3869.5MB, alloc=732.3MB, time=50.84 memory used=3958.4MB, alloc=732.3MB, time=52.79 memory used=4312.4MB, alloc=756.3MB, time=57.60 memory used=4674.6MB, alloc=780.3MB, time=62.19 memory used=5073.9MB, alloc=804.3MB, time=65.61 memory used=5483.8MB, alloc=828.3MB, time=69.67 memory used=5865.5MB, alloc=852.3MB, time=74.91 memory used=6229.2MB, alloc=876.3MB, time=80.12 memory used=6571.2MB, alloc=900.3MB, time=85.62 memory used=6905.4MB, alloc=924.3MB, time=91.27 memory used=7281.7MB, alloc=948.3MB, time=96.59 memory used=7664.5MB, alloc=972.3MB, time=101.41 memory used=8002.8MB, alloc=996.3MB, time=106.78 memory used=8333.1MB, alloc=1020.3MB, time=113.30 memory used=8603.2MB, alloc=1044.3MB, time=120.65 memory used=8870.2MB, alloc=1068.3MB, time=128.37 memory used=9141.9MB, alloc=1092.3MB, time=136.58 memory used=9421.6MB, alloc=1116.3MB, time=145.19 memory used=9711.1MB, alloc=1140.3MB, time=153.70 memory used=10012.2MB, alloc=1164.3MB, time=162.55 memory used=10325.0MB, alloc=1188.3MB, time=171.80 memory used=10650.1MB, alloc=1212.3MB, time=181.34 memory used=10988.4MB, alloc=1236.3MB, time=191.53 memory used=11338.7MB, alloc=1260.3MB, time=203.07 memory used=11702.3MB, alloc=1284.3MB, time=214.54 memory used=12082.0MB, alloc=1308.3MB, time=229.08 memory used=12477.6MB, alloc=1332.3MB, time=242.11 memory used=12889.0MB, alloc=1356.3MB, time=257.32 memory used=13313.0MB, alloc=1380.3MB, time=273.00 memory used=13753.5MB, alloc=1404.3MB, time=289.21 memory used=14217.9MB, alloc=1428.3MB, time=306.39 |\^/| 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(); 1428337024 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [10 x y + 19 x z, -11 x y z - 12 y , 3 y z + 19 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 3 2 G := [4 x y - 17 x y, 13 y z - 6 z , -17 x z - 20 y z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[10 x y + 19 x z, -11 x y z - 12 y , 3 y z + 19 z ], 2 2 2 4 3 2 [4 x y - 17 x y, 13 y z - 6 z , -17 x z - 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=0.14 memory used=26.3MB, alloc=32.3MB, time=0.40 memory used=48.1MB, alloc=32.3MB, time=0.74 memory used=68.1MB, alloc=56.3MB, time=1.05 memory used=108.1MB, alloc=60.3MB, time=1.53 memory used=144.8MB, alloc=60.3MB, time=2.17 memory used=180.4MB, alloc=84.3MB, time=2.62 memory used=233.9MB, alloc=84.3MB, time=3.39 memory used=290.5MB, alloc=92.3MB, time=4.10 memory used=346.0MB, alloc=116.3MB, time=4.77 memory used=422.8MB, alloc=140.3MB, time=5.72 memory used=522.6MB, alloc=164.3MB, time=7.42 memory used=632.9MB, alloc=188.3MB, time=9.37 memory used=724.4MB, alloc=468.3MB, time=10.93 memory used=864.1MB, alloc=492.3MB, time=13.40 memory used=1015.0MB, alloc=516.3MB, time=15.89 memory used=1174.0MB, alloc=540.3MB, time=18.35 memory used=1341.6MB, alloc=564.3MB, time=21.01 memory used=1516.3MB, alloc=588.3MB, time=23.74 memory used=1695.7MB, alloc=612.3MB, time=26.16 memory used=1863.0MB, alloc=636.3MB, time=29.96 memory used=2034.1MB, alloc=660.3MB, time=34.88 memory used=2216.2MB, alloc=684.3MB, time=39.51 memory used=2410.9MB, alloc=708.3MB, time=45.11 memory used=2619.0MB, alloc=732.3MB, time=51.42 memory used=2840.8MB, alloc=756.3MB, time=58.16 memory used=3076.8MB, alloc=780.3MB, time=64.56 memory used=3327.4MB, alloc=804.3MB, time=72.35 memory used=3587.9MB, alloc=828.3MB, time=80.82 memory used=3872.4MB, alloc=852.3MB, time=89.85 memory used=4180.9MB, alloc=876.3MB, time=99.61 memory used=4513.3MB, alloc=900.3MB, time=109.18 memory used=4869.6MB, alloc=924.3MB, time=120.22 memory used=5249.9MB, alloc=948.3MB, time=133.35 memory used=5654.1MB, alloc=972.3MB, time=145.62 memory used=6082.3MB, alloc=996.3MB, time=159.89 memory used=6534.4MB, alloc=996.3MB, time=173.86 memory used=6986.5MB, alloc=1020.3MB, time=186.84 memory used=7462.5MB, alloc=1020.3MB, time=203.08 memory used=7938.5MB, alloc=1020.3MB, time=218.81 memory used=8414.4MB, alloc=1020.3MB, time=234.21 memory used=8890.3MB, alloc=1020.3MB, time=249.24 memory used=9366.1MB, alloc=1044.3MB, time=264.47 memory used=9865.7MB, alloc=1044.3MB, time=281.04 |\^/| 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(); 1428337324 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 F := [15 x , 16 y z + 13 x z, 13 x z - 9 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [-5 x y z + 9 x y , -3 x y + 18 z, 12 x y z + 20 x y z ] > Problem := [F,G]; 4 2 2 2 2 Problem := [[15 x , 16 y z + 13 x z, 13 x z - 9 z ], 2 2 2 2 2 2 [-5 x y z + 9 x y , -3 x y + 18 z, 12 x y z + 20 x y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.57 memory used=47.8MB, alloc=32.3MB, time=0.89 memory used=67.6MB, alloc=56.3MB, time=1.16 memory used=107.7MB, alloc=60.3MB, time=1.75 memory used=146.0MB, alloc=84.3MB, time=2.25 memory used=205.5MB, alloc=92.3MB, time=2.88 memory used=264.6MB, alloc=92.3MB, time=3.45 memory used=320.7MB, alloc=116.3MB, time=3.98 memory used=397.3MB, alloc=116.3MB, time=4.74 memory used=470.9MB, alloc=140.3MB, time=5.47 memory used=565.7MB, alloc=164.3MB, time=6.38 memory used=658.8MB, alloc=164.3MB, time=7.72 memory used=763.4MB, alloc=444.3MB, time=9.67 memory used=891.8MB, alloc=468.3MB, time=11.65 memory used=1028.7MB, alloc=492.3MB, time=13.74 memory used=1176.6MB, alloc=516.3MB, time=15.79 memory used=1353.9MB, alloc=540.3MB, time=17.58 memory used=1526.2MB, alloc=564.3MB, time=19.65 memory used=1709.5MB, alloc=588.3MB, time=21.98 memory used=1875.9MB, alloc=612.3MB, time=25.40 memory used=2047.7MB, alloc=636.3MB, time=29.33 memory used=2230.7MB, alloc=660.3MB, time=33.68 memory used=2427.1MB, alloc=684.3MB, time=38.77 memory used=2637.5MB, alloc=708.3MB, time=44.15 memory used=2859.6MB, alloc=732.3MB, time=50.67 memory used=3098.6MB, alloc=756.3MB, time=58.30 memory used=3361.5MB, alloc=780.3MB, time=67.00 memory used=3648.4MB, alloc=804.3MB, time=75.27 memory used=3959.2MB, alloc=828.3MB, time=83.87 memory used=4293.9MB, alloc=852.3MB, time=93.01 memory used=4652.7MB, alloc=876.3MB, time=102.76 memory used=5035.3MB, alloc=876.3MB, time=113.17 memory used=5417.9MB, alloc=900.3MB, time=124.30 memory used=5824.5MB, alloc=900.3MB, time=135.30 memory used=6231.1MB, alloc=900.3MB, time=148.69 memory used=6637.6MB, alloc=900.3MB, time=161.85 memory used=7043.8MB, alloc=924.3MB, time=173.91 memory used=7474.0MB, alloc=924.3MB, time=186.38 memory used=7904.1MB, alloc=924.3MB, time=200.43 memory used=8333.9MB, alloc=948.3MB, time=215.80 memory used=8787.8MB, alloc=948.3MB, time=230.57 memory used=9241.5MB, alloc=972.3MB, time=245.42 memory used=9719.2MB, alloc=972.3MB, time=258.39 memory used=10196.8MB, alloc=996.3MB, time=270.75 memory used=10698.6MB, alloc=1020.3MB, time=284.38 N1 := 17725 > GB := Basis(F, plex(op(vars))); 4 2 GB := [x , z x, z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 427 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 4 2 2 2 2 2 2 H := [15 x , 16 y z + 13 x z, 13 x z - 9 z , -5 x y z + 9 x y , 2 2 2 2 -3 x y + 18 z, 12 x y z + 20 x y z ] > J:=[op(GB),op(G)]; 4 2 2 2 2 2 2 2 J := [x , z x, z , -5 x y z + 9 x y , -3 x y + 18 z, 12 x y z + 20 x 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 := [6, 15, 23, 4, 4, 2, 2, 1, 2/3, 5/6, 2/3, 1/2, 2/3, 6, 13, 20, 4, 4, 2, 2, 5/6, 1/2, 5/6, 7/12, 5/12, 1/2, 2, 3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=11181.3MB, alloc=1020.3MB, time=295.67 |\^/| 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(); 1428337621 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 2 F := [5 x y - 3 x y , 15 y + 14 x, -18 x + 18 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 3 4 2 G := [-12 x + 3 x , -13 y z + 17 y z , 18 x + 9 x y z] > Problem := [F,G]; 3 2 2 4 3 2 Problem := [[5 x y - 3 x y , 15 y + 14 x, -18 x + 18 y z], 4 3 3 3 4 2 [-12 x + 3 x , -13 y z + 17 y z , 18 x + 9 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.38 memory used=48.4MB, alloc=32.3MB, time=0.62 memory used=70.4MB, alloc=56.3MB, time=0.88 memory used=113.0MB, alloc=60.3MB, time=1.37 memory used=150.0MB, alloc=84.3MB, time=1.81 memory used=201.0MB, alloc=108.3MB, time=2.66 N1 := 1485 > GB := Basis(F, plex(op(vars))); 6 3 4 3 4 2 2 4 GB := [3125 x + 378 x , -5 x + 3 x y, -25 x + 9 x y , 15 y + 14 x, 5 3 2 125 x + 42 x z, -x + y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=274.3MB, alloc=116.3MB, time=3.43 memory used=352.0MB, alloc=116.3MB, time=4.15 memory used=427.9MB, alloc=140.3MB, time=4.96 memory used=522.7MB, alloc=164.3MB, time=6.17 memory used=631.5MB, alloc=188.3MB, time=7.41 memory used=753.0MB, alloc=212.3MB, time=8.81 memory used=867.5MB, alloc=492.3MB, time=10.24 memory used=1001.4MB, alloc=516.3MB, time=13.10 memory used=1142.2MB, alloc=540.3MB, time=16.09 memory used=1292.4MB, alloc=564.3MB, time=20.36 memory used=1461.8MB, alloc=588.3MB, time=25.12 memory used=1655.2MB, alloc=612.3MB, time=30.99 memory used=1872.5MB, alloc=612.3MB, time=36.67 memory used=2089.8MB, alloc=636.3MB, time=43.04 memory used=2331.0MB, alloc=636.3MB, time=49.05 memory used=2572.1MB, alloc=636.3MB, time=55.99 memory used=2813.2MB, alloc=660.3MB, time=62.18 memory used=3078.4MB, alloc=684.3MB, time=68.67 N2 := 8981 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 4 3 2 4 3 H := [5 x y - 3 x y , 15 y + 14 x, -18 x + 18 y z, -12 x + 3 x , 3 3 4 2 -13 y z + 17 y z , 18 x + 9 x y z] > J:=[op(GB),op(G)]; 6 3 4 3 4 2 2 4 J := [3125 x + 378 x , -5 x + 3 x y, -25 x + 9 x y , 15 y + 14 x, 5 3 2 4 3 3 3 125 x + 42 x z, -x + y z, -12 x + 3 x , -13 y z + 17 y z , 4 2 18 x + 9 x 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 := [6, 13, 23, 4, 4, 4, 3, 5/6, 5/6, 1/2, 2/3, 7/12, 1/3, 9, 18, 38, 6, 6, 4, 3, 8/9, 2/3, 4/9, 7/9, 7/18, 5/18, -5, -15, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3347.3MB, alloc=684.3MB, time=73.99 |\^/| 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(); 1428337695 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [14 x y, -11 x y z + 13 x z, -14 y z - y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 G := [15 z - y z, 3 x y z - 7 y z , 11 x y + 7 x z] > Problem := [F,G]; 2 2 2 3 2 Problem := [[14 x y, -11 x y z + 13 x z, -14 y z - y z ], 4 2 2 2 [15 z - y z, 3 x y z - 7 y z , 11 x y + 7 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=26.1MB, alloc=32.3MB, time=0.35 memory used=47.4MB, alloc=32.3MB, time=0.55 memory used=67.3MB, alloc=32.3MB, time=0.73 memory used=85.5MB, alloc=56.3MB, time=0.90 memory used=125.3MB, alloc=60.3MB, time=1.33 memory used=161.4MB, alloc=84.3MB, time=1.73 memory used=217.3MB, alloc=108.3MB, time=2.37 memory used=288.0MB, alloc=132.3MB, time=3.46 memory used=369.0MB, alloc=132.3MB, time=5.14 memory used=450.0MB, alloc=156.3MB, time=6.55 N1 := 2583 > GB := Basis(F, plex(op(vars))); 2 2 3 2 GB := [x y, x z, 14 y z + y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=554.3MB, alloc=164.3MB, time=7.67 memory used=672.1MB, alloc=188.3MB, time=9.40 N2 := 1705 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 4 H := [14 x y, -11 x y z + 13 x z, -14 y z - y z , 15 z - y z, 2 2 2 3 x y z - 7 y z , 11 x y + 7 x z] > J:=[op(GB),op(G)]; J := [ 2 2 3 2 4 2 2 2 x y, x z, 14 y z + y z , 15 z - y z, 3 x y z - 7 y z , 11 x y + 7 x z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 21, 4, 2, 2, 4, 2/3, 1, 5/6, 6/13, 8/13, 9/13, 6, 14, 20, 4, 2, 2, 4, 2/3, 5/6, 5/6, 5/12, 7/12, 2/3, 1, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=716.0MB, alloc=188.3MB, time=10.06 |\^/| 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(); 1428337705 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 3 2 F := [11 x z - 20 y , 11 y - 14 z, 20 x z - 5 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 G := [17 x z + 17 y z, -4 y + 3, -5 x z - 18 y z ] > Problem := [F,G]; 3 4 3 3 2 Problem := [[11 x z - 20 y , 11 y - 14 z, 20 x z - 5 x y ], 3 3 2 2 2 [17 x z + 17 y z, -4 y + 3, -5 x z - 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=0.14 memory used=26.3MB, alloc=32.3MB, time=0.37 memory used=48.0MB, alloc=32.3MB, time=0.58 memory used=68.7MB, alloc=32.3MB, time=0.77 memory used=88.0MB, alloc=56.3MB, time=0.97 memory used=126.6MB, alloc=60.3MB, time=1.33 memory used=165.2MB, alloc=60.3MB, time=1.67 memory used=201.3MB, alloc=84.3MB, time=2.03 memory used=260.1MB, alloc=92.3MB, time=2.60 memory used=317.2MB, alloc=116.3MB, time=3.19 memory used=395.6MB, alloc=116.3MB, time=4.09 memory used=471.8MB, alloc=140.3MB, time=5.16 memory used=570.9MB, alloc=164.3MB, time=6.28 memory used=677.1MB, alloc=444.3MB, time=7.50 memory used=804.9MB, alloc=468.3MB, time=8.90 memory used=947.7MB, alloc=492.3MB, time=10.49 memory used=1102.4MB, alloc=516.3MB, time=12.67 memory used=1276.1MB, alloc=540.3MB, time=14.62 memory used=1453.5MB, alloc=564.3MB, time=18.19 memory used=1621.4MB, alloc=588.3MB, time=22.13 memory used=1799.8MB, alloc=612.3MB, time=26.48 memory used=1990.7MB, alloc=636.3MB, time=31.33 memory used=2192.4MB, alloc=660.3MB, time=36.95 memory used=2418.2MB, alloc=684.3MB, time=43.17 memory used=2667.8MB, alloc=708.3MB, time=51.03 memory used=2941.4MB, alloc=732.3MB, time=59.67 memory used=3239.0MB, alloc=732.3MB, time=67.77 memory used=3536.5MB, alloc=756.3MB, time=75.71 memory used=3858.0MB, alloc=756.3MB, time=84.25 memory used=4179.4MB, alloc=756.3MB, time=92.76 memory used=4500.7MB, alloc=780.3MB, time=101.29 memory used=4846.1MB, alloc=780.3MB, time=110.16 memory used=5191.3MB, alloc=804.3MB, time=118.94 memory used=5560.4MB, alloc=804.3MB, time=129.46 memory used=5929.7MB, alloc=828.3MB, time=138.73 N1 := 12253 > GB := Basis(F, plex(op(vars))); 10 2 2 8 2 3 5 2 4 GB := [56320 x y - 49 x y , -2560 x y + 7 x y , -1280 x y + 11 y , 3 -11 y + 14 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6329.6MB, alloc=828.3MB, time=144.54 N2 := 2621 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 4 3 3 2 3 3 H := [11 z x - 20 y , 11 y - 14 z, 20 x z - 5 x y , 17 x z + 17 y z, 2 2 2 -4 y + 3, -5 x z - 18 y z ] > J:=[op(GB),op(G)]; 10 2 2 8 2 3 5 2 4 J := [56320 x y - 49 x y , -2560 x y + 7 x y , -1280 x y + 11 y , 3 3 3 2 2 2 -11 y + 14 z, 17 x z + 17 y z, -4 y + 3, -5 x z - 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 := [6, 15, 20, 4, 3, 4, 3, 2/3, 1, 5/6, 5/12, 1/2, 7/12, 7, 15, 41, 12, 10, 4, 3, 5/7, 1, 3/7, 1/2, 5/7, 5/14, 0, -21, -8] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=6499.1MB, alloc=828.3MB, time=148.19 |\^/| 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(); 1428337853 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 F := [17 x + 11 z, -9 x y - 14 x y z, -18 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 G := [-11 x z + 9 x y , -x y - 6 z, 10 x y z + 18 x ] > Problem := [F,G]; 2 Problem := [[17 x + 11 z, -9 x y - 14 x y z, -18 x y z], 2 2 2 2 2 2 2 [-11 x z + 9 x y , -x y - 6 z, 10 x y 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=0.14 memory used=26.4MB, alloc=32.3MB, time=0.37 memory used=48.2MB, alloc=32.3MB, time=0.60 memory used=68.6MB, alloc=56.3MB, time=0.80 memory used=108.3MB, alloc=60.3MB, time=1.15 memory used=145.4MB, alloc=84.3MB, time=1.50 memory used=201.9MB, alloc=84.3MB, time=2.01 memory used=255.3MB, alloc=108.3MB, time=2.54 memory used=332.2MB, alloc=140.3MB, time=3.37 memory used=427.0MB, alloc=164.3MB, time=4.41 memory used=535.9MB, alloc=188.3MB, time=5.59 memory used=659.4MB, alloc=212.3MB, time=6.93 memory used=795.2MB, alloc=236.3MB, time=8.46 memory used=942.4MB, alloc=516.3MB, time=10.18 memory used=1100.3MB, alloc=540.3MB, time=12.02 memory used=1268.3MB, alloc=564.3MB, time=13.95 memory used=1445.5MB, alloc=588.3MB, time=16.09 memory used=1613.1MB, alloc=612.3MB, time=19.22 memory used=1784.9MB, alloc=636.3MB, time=22.85 memory used=1966.5MB, alloc=660.3MB, time=27.01 memory used=2160.1MB, alloc=684.3MB, time=31.58 memory used=2367.2MB, alloc=708.3MB, time=36.64 memory used=2587.7MB, alloc=732.3MB, time=43.33 memory used=2818.7MB, alloc=756.3MB, time=50.74 memory used=3070.2MB, alloc=780.3MB, time=58.14 memory used=3345.7MB, alloc=804.3MB, time=66.56 memory used=3645.1MB, alloc=828.3MB, time=75.48 memory used=3968.4MB, alloc=852.3MB, time=85.13 memory used=4315.6MB, alloc=876.3MB, time=96.43 memory used=4686.9MB, alloc=900.3MB, time=108.02 memory used=5082.0MB, alloc=900.3MB, time=119.07 memory used=5477.1MB, alloc=900.3MB, time=130.01 memory used=5872.2MB, alloc=900.3MB, time=141.94 memory used=6267.3MB, alloc=924.3MB, time=153.91 memory used=6686.3MB, alloc=924.3MB, time=166.71 memory used=7105.2MB, alloc=924.3MB, time=179.29 memory used=7524.2MB, alloc=924.3MB, time=190.80 memory used=7942.9MB, alloc=948.3MB, time=203.05 memory used=8385.5MB, alloc=948.3MB, time=214.83 memory used=8828.0MB, alloc=948.3MB, time=226.77 memory used=9270.5MB, alloc=972.3MB, time=238.79 memory used=9736.8MB, alloc=972.3MB, time=251.85 memory used=10203.0MB, alloc=972.3MB, time=265.95 memory used=10669.1MB, alloc=996.3MB, time=279.42 memory used=11159.2MB, alloc=996.3MB, time=292.83 |\^/| 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(); 1428338153 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 F := [-y , -19 x - 8 y, 18 x y z - 16 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 4 2 2 3 G := [14 x y - 19 z , -5 x + 12 z, 20 x z + 8 z ] > Problem := [F,G]; 2 4 2 Problem := [[-y , -19 x - 8 y, 18 x y z - 16 y z ], 2 2 4 4 2 2 3 [14 x y - 19 z , -5 x + 12 z, 20 x z + 8 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.3MB, alloc=32.3MB, time=0.41 memory used=47.8MB, alloc=32.3MB, time=0.62 memory used=67.8MB, alloc=56.3MB, time=0.86 memory used=111.0MB, alloc=60.3MB, time=1.49 memory used=149.6MB, alloc=84.3MB, time=2.17 memory used=208.7MB, alloc=84.3MB, time=3.02 memory used=261.7MB, alloc=108.3MB, time=3.92 memory used=361.6MB, alloc=172.3MB, time=5.66 memory used=465.4MB, alloc=196.3MB, time=8.21 memory used=579.7MB, alloc=196.3MB, time=10.94 memory used=694.0MB, alloc=220.3MB, time=13.73 memory used=832.1MB, alloc=220.3MB, time=16.87 memory used=970.3MB, alloc=244.3MB, time=20.08 N1 := 4827 > GB := Basis(F, plex(op(vars))); 8 4 5 4 2 GB := [x , 19 x + 8 y, -9 x z + 8 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1135.9MB, alloc=244.3MB, time=22.62 memory used=1305.1MB, alloc=500.3MB, time=24.59 memory used=1478.4MB, alloc=524.3MB, time=27.16 memory used=1635.9MB, alloc=548.3MB, time=30.97 memory used=1812.5MB, alloc=572.3MB, time=35.25 memory used=2013.2MB, alloc=596.3MB, time=40.02 N2 := 4827 #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 4 2 4 2 2 4 H := [-y , -19 x - 8 y, 18 x y z - 16 y z , -19 z + 14 y x , -5 x + 12 z, 2 2 3 20 x z + 8 z ] > J:=[op(GB),op(G)]; 8 4 5 4 2 4 2 2 4 J := [x , 19 x + 8 y, -9 x z + 8 x z , -19 z + 14 y x , -5 x + 12 z, 2 2 3 20 x 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, 21, 4, 4, 2, 4, 5/6, 2/3, 2/3, 5/12, 5/12, 1/2, 6, 12, 30, 8, 8, 2, 4, 1, 1/3, 2/3, 7/12, 1/6, 1/2, 1, -9, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2136.7MB, alloc=596.3MB, time=42.25 |\^/| 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(); 1428338195 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 3 F := [-7 x y - 3 z , 2 x z - 15 x z , -15 y z - 2 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 G := [-10 x y z - x, -x - 8 y, -17 x z - 17 x y ] > Problem := [F,G]; 2 2 3 2 2 2 3 Problem := [[-7 x y - 3 z , 2 x z - 15 x z , -15 y z - 2 z ], 2 3 3 2 2 [-10 x y z - x, -x - 8 y, -17 x z - 17 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.35 memory used=47.5MB, alloc=32.3MB, time=0.57 memory used=67.8MB, alloc=32.3MB, time=0.78 memory used=86.9MB, alloc=56.3MB, time=0.97 memory used=125.0MB, alloc=60.3MB, time=1.33 memory used=160.9MB, alloc=84.3MB, time=1.66 memory used=218.0MB, alloc=84.3MB, time=2.18 memory used=275.1MB, alloc=92.3MB, time=2.70 memory used=329.1MB, alloc=116.3MB, time=3.21 memory used=404.2MB, alloc=116.3MB, time=3.89 memory used=476.4MB, alloc=140.3MB, time=4.58 memory used=568.1MB, alloc=140.3MB, time=5.47 memory used=660.4MB, alloc=164.3MB, time=6.44 memory used=774.0MB, alloc=188.3MB, time=7.69 memory used=898.3MB, alloc=468.3MB, time=9.06 memory used=1035.9MB, alloc=492.3MB, time=10.62 memory used=1184.7MB, alloc=516.3MB, time=12.71 memory used=1348.4MB, alloc=540.3MB, time=14.69 memory used=1513.2MB, alloc=564.3MB, time=16.86 memory used=1687.1MB, alloc=588.3MB, time=19.18 memory used=1847.5MB, alloc=612.3MB, time=22.34 memory used=2014.0MB, alloc=636.3MB, time=26.00 memory used=2191.5MB, alloc=660.3MB, time=30.86 memory used=2381.1MB, alloc=684.3MB, time=36.29 memory used=2587.0MB, alloc=708.3MB, time=41.57 memory used=2807.3MB, alloc=732.3MB, time=47.31 memory used=3045.0MB, alloc=756.3MB, time=54.43 memory used=3306.7MB, alloc=780.3MB, time=62.86 memory used=3592.3MB, alloc=804.3MB, time=71.31 memory used=3901.8MB, alloc=828.3MB, time=81.16 memory used=4235.2MB, alloc=852.3MB, time=91.52 memory used=4592.7MB, alloc=876.3MB, time=101.16 memory used=4974.0MB, alloc=876.3MB, time=112.37 memory used=5355.3MB, alloc=876.3MB, time=124.00 memory used=5736.6MB, alloc=900.3MB, time=134.71 memory used=6141.8MB, alloc=900.3MB, time=146.79 memory used=6546.9MB, alloc=900.3MB, time=157.60 memory used=6952.1MB, alloc=924.3MB, time=169.95 memory used=7381.2MB, alloc=924.3MB, time=181.34 memory used=7810.2MB, alloc=924.3MB, time=193.57 memory used=8239.2MB, alloc=948.3MB, time=206.27 memory used=8691.9MB, alloc=948.3MB, time=218.20 memory used=9144.6MB, alloc=972.3MB, time=229.46 memory used=9621.2MB, alloc=972.3MB, time=243.78 memory used=10097.8MB, alloc=996.3MB, time=258.09 memory used=10598.7MB, alloc=1020.3MB, time=272.64 N1 := 17585 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 4 2 2 6 2 2 GB := [28 x y - 675 x y , x y + x y , 675 x y - 28 x y , 4 2 2 2 15 x y + 2 x y z, 7 y x + 3 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=11133.4MB, alloc=1020.3MB, time=284.31 memory used=11735.3MB, alloc=1020.3MB, time=292.78 |\^/| 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(); 1428338495 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 3 2 F := [-9 x y + 11 z , 9 x z + 8 x y z, 4 y z - 17 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 G := [11 x - 17 x y , 8 x y - 16 y, 16 x y - 14 x z] > Problem := [F,G]; 2 2 3 2 2 2 3 2 Problem := [[-9 x y + 11 z , 9 x z + 8 x y z, 4 y z - 17 x y ], 3 2 2 2 2 2 [11 x - 17 x y , 8 x y - 16 y, 16 x y - 14 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.5MB, alloc=32.3MB, time=0.37 memory used=48.2MB, alloc=32.3MB, time=0.61 memory used=68.6MB, alloc=32.3MB, time=0.86 memory used=88.1MB, alloc=56.3MB, time=1.09 memory used=128.6MB, alloc=60.3MB, time=1.54 memory used=167.6MB, alloc=84.3MB, time=2.00 memory used=208.5MB, alloc=84.3MB, time=2.47 memory used=267.8MB, alloc=92.3MB, time=3.25 memory used=325.0MB, alloc=116.3MB, time=3.96 memory used=405.6MB, alloc=140.3MB, time=4.93 memory used=492.5MB, alloc=420.3MB, time=6.30 memory used=609.4MB, alloc=444.3MB, time=8.04 memory used=740.4MB, alloc=468.3MB, time=9.96 memory used=885.0MB, alloc=492.3MB, time=12.20 memory used=1036.8MB, alloc=516.3MB, time=14.49 memory used=1182.7MB, alloc=540.3MB, time=17.55 memory used=1338.8MB, alloc=564.3MB, time=21.41 memory used=1503.0MB, alloc=588.3MB, time=25.84 memory used=1691.3MB, alloc=612.3MB, time=30.72 memory used=1903.5MB, alloc=636.3MB, time=37.41 memory used=2139.6MB, alloc=636.3MB, time=45.07 memory used=2375.7MB, alloc=660.3MB, time=51.41 memory used=2635.8MB, alloc=660.3MB, time=58.20 memory used=2895.8MB, alloc=684.3MB, time=64.65 memory used=3180.0MB, alloc=708.3MB, time=71.57 N1 := 8733 > GB := Basis(F, plex(op(vars))); 10 2 2 9 2 3 GB := [43046721 x y + 26902281142 x y , 4782969 x y + 575449864 x y , 7 2 2 7 2 2 2 2 2 3 -59049 x y + 1538636 x y z, 13122 x y + 384659 x z , -9 x y + 11 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3498.1MB, alloc=708.3MB, time=76.61 memory used=3661.8MB, alloc=708.3MB, time=78.57 memory used=3832.5MB, alloc=708.3MB, time=80.62 memory used=4033.3MB, alloc=732.3MB, time=83.36 memory used=4228.6MB, alloc=756.3MB, time=86.18 memory used=4418.9MB, alloc=780.3MB, time=88.92 memory used=4716.9MB, alloc=804.3MB, time=95.68 memory used=5070.8MB, alloc=828.3MB, time=105.25 memory used=5434.3MB, alloc=852.3MB, time=115.44 memory used=5821.8MB, alloc=876.3MB, time=126.17 memory used=6233.3MB, alloc=900.3MB, time=137.35 memory used=6668.7MB, alloc=924.3MB, time=149.06 memory used=7127.9MB, alloc=948.3MB, time=161.45 N2 := 9737 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 2 3 2 3 2 H := [-9 x y + 11 z , 9 x z + 8 x y z, 4 y z - 17 x y , 11 x - 17 x y , 2 2 2 2 8 x y - 16 y, 16 x y - 14 x z] > J:=[op(GB),op(G)]; 10 2 2 9 2 3 J := [43046721 x y + 26902281142 x y , 4782969 x y + 575449864 x y , 7 2 2 7 2 2 2 2 2 3 -59049 x y + 1538636 x y z, 13122 x y + 384659 x z , -9 x y + 11 z , 3 2 2 2 2 2 11 x - 17 x y , 8 x y - 16 y, 16 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 := [6, 16, 22, 4, 3, 2, 3, 1, 1, 2/3, 3/4, 2/3, 5/12, 8, 20, 55, 12, 10, 3, 3, 1, 1, 1/2, 7/8, 3/4, 1/4, -4, -33, -8] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=7451.4MB, alloc=948.3MB, time=169.76 |\^/| 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(); 1428338664 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 3 4 F := [7 x y - 9 x z , 10 x y + 17 y z, -2 x y + 20 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 4 G := [-11 x y - 18 y z, -3 x y - 11 z , -18 y - 3] > Problem := [F,G]; 2 2 2 2 2 3 3 4 Problem := [[7 x y - 9 x z , 10 x y + 17 y z, -2 x y + 20 y ], 2 2 3 2 4 [-11 x y - 18 y z, -3 x y - 11 z , -18 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=0.15 memory used=26.7MB, alloc=32.3MB, time=0.41 memory used=48.1MB, alloc=32.3MB, time=0.59 memory used=68.0MB, alloc=32.3MB, time=0.77 memory used=87.2MB, alloc=56.3MB, time=0.94 memory used=127.1MB, alloc=60.3MB, time=1.29 memory used=165.7MB, alloc=60.3MB, time=1.62 memory used=202.2MB, alloc=84.3MB, time=1.95 memory used=262.8MB, alloc=92.3MB, time=2.63 memory used=319.8MB, alloc=116.3MB, time=3.25 memory used=396.8MB, alloc=140.3MB, time=4.11 memory used=487.3MB, alloc=164.3MB, time=5.42 memory used=580.2MB, alloc=188.3MB, time=7.48 memory used=695.1MB, alloc=212.3MB, time=9.95 N1 := 3051 > GB := Basis(F, plex(op(vars))); 8 5 7 4 2 GB := [8279186167 x y - 7290000000000 x y, -4092529 x y + 810000000 x y , 3 4 3 2 3 2 2 3 2 2 2 -x y + 10 y , 17 x y z + 100 x y , 10 x y + 17 y z, -7 x y + 9 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=837.4MB, alloc=212.3MB, time=11.64 memory used=955.1MB, alloc=468.3MB, time=12.78 memory used=1109.5MB, alloc=468.3MB, time=14.29 memory used=1261.3MB, alloc=492.3MB, time=15.73 memory used=1432.3MB, alloc=516.3MB, time=17.46 memory used=1625.7MB, alloc=540.3MB, time=19.44 memory used=1841.9MB, alloc=564.3MB, time=22.10 memory used=2069.6MB, alloc=588.3MB, time=24.76 memory used=2305.9MB, alloc=612.3MB, time=28.25 memory used=2547.3MB, alloc=636.3MB, time=31.36 memory used=2779.4MB, alloc=660.3MB, time=36.03 memory used=3002.1MB, alloc=684.3MB, time=42.03 memory used=3231.6MB, alloc=708.3MB, time=48.51 memory used=3463.2MB, alloc=732.3MB, time=55.80 memory used=3715.2MB, alloc=756.3MB, time=63.06 memory used=3991.2MB, alloc=780.3MB, time=70.70 memory used=4291.1MB, alloc=804.3MB, time=78.84 memory used=4614.9MB, alloc=828.3MB, time=88.40 memory used=4962.7MB, alloc=852.3MB, time=97.80 memory used=5334.4MB, alloc=876.3MB, time=107.71 memory used=5730.1MB, alloc=900.3MB, time=118.17 memory used=6149.6MB, alloc=900.3MB, time=130.87 memory used=6569.2MB, alloc=924.3MB, time=144.38 memory used=7012.6MB, alloc=924.3MB, time=156.16 memory used=7455.9MB, alloc=948.3MB, time=167.49 memory used=7923.4MB, alloc=972.3MB, time=178.66 N2 := 13265 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 3 3 4 2 2 H := [7 x y - 9 x z , 10 x y + 17 y z, -2 x y + 20 y , -11 x y - 18 y z, 3 2 4 -3 x y - 11 z , -18 y - 3] > J:=[op(GB),op(G)]; 8 5 7 4 2 J := [8279186167 x y - 7290000000000 x y, -4092529 x y + 810000000 x y , 3 4 3 2 3 2 2 3 2 2 2 -x y + 10 y , 17 x y z + 100 x y , 10 x y + 17 y z, -7 x y + 9 x z , 2 2 3 2 4 -11 x y - 18 y z, -3 x y - 11 z , -18 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 := [6, 15, 24, 4, 3, 4, 2, 5/6, 1, 2/3, 1/2, 3/4, 1/3, 9, 22, 46, 9, 8, 4, 2, 8/9, 1, 5/9, 2/3, 5/6, 5/18, -7, -22, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=7985.1MB, alloc=972.3MB, time=179.73 |\^/| 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(); 1428338842 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 3 F := [-x z - 11 y , 8 x y + 4 x , 3 x - 10 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 G := [-7 x y + 14 x z , -6 x + 16 y z , -15 x y z + 20] > Problem := [F,G]; 2 3 2 2 3 3 Problem := [[-x z - 11 y , 8 x y + 4 x , 3 x - 10 y ], 2 2 4 2 2 [-7 x y + 14 x z , -6 x + 16 y z , -15 x 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=0.15 memory used=26.8MB, alloc=32.3MB, time=0.40 memory used=48.2MB, alloc=32.3MB, time=0.59 memory used=68.9MB, alloc=32.3MB, time=0.77 memory used=89.8MB, alloc=60.3MB, time=0.97 memory used=130.7MB, alloc=60.3MB, time=1.33 memory used=170.9MB, alloc=92.3MB, time=1.71 memory used=236.0MB, alloc=92.3MB, time=2.26 memory used=296.4MB, alloc=92.3MB, time=2.79 memory used=356.3MB, alloc=116.3MB, time=3.34 memory used=436.8MB, alloc=116.3MB, time=4.07 memory used=520.8MB, alloc=140.3MB, time=4.95 memory used=616.9MB, alloc=164.3MB, time=6.01 memory used=722.9MB, alloc=420.3MB, time=7.18 memory used=834.3MB, alloc=444.3MB, time=8.40 memory used=956.3MB, alloc=468.3MB, time=10.23 memory used=1078.2MB, alloc=492.3MB, time=12.92 memory used=1213.1MB, alloc=516.3MB, time=16.18 memory used=1372.1MB, alloc=540.3MB, time=19.73 memory used=1555.1MB, alloc=564.3MB, time=23.25 N1 := 4601 > GB := Basis(F, plex(op(vars))); GB := 6 3 4 2 2 2 3 3 3 2 [18 x + 25 x , 3 x + 5 x y, 2 x y + x , -3 x + 10 y , 33 x + 10 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1771.7MB, alloc=564.3MB, time=25.59 memory used=2008.8MB, alloc=564.3MB, time=27.84 memory used=2245.7MB, alloc=588.3MB, time=30.52 memory used=2504.2MB, alloc=612.3MB, time=33.36 memory used=2750.4MB, alloc=636.3MB, time=38.53 memory used=2987.7MB, alloc=660.3MB, time=44.15 N2 := 4405 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 3 3 2 2 H := [-x z - 11 y , 8 x y + 4 x , -10 y + 3 x , -7 x y + 14 x z , 4 2 2 -6 x + 16 y z , -15 x y z + 20] > J:=[op(GB),op(G)]; 6 3 4 2 2 2 3 3 3 2 J := [18 x + 25 x , 3 x + 5 x y, 2 x y + x , -3 x + 10 y , 33 x + 10 x z , 2 2 4 2 2 -7 x y + 14 x z , -6 x + 16 y z , -15 x y z + 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 := [6, 16, 20, 4, 4, 3, 2, 1, 1, 2/3, 2/3, 1/2, 1/3, 8, 18, 30, 6, 6, 3, 2, 1, 3/4, 1/2, 13/16, 3/8, 1/4, -2, -10, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3209.5MB, alloc=660.3MB, time=48.32 |\^/| 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(); 1428338890 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 3 F := [14 x + 14 y z , -9 x + 7, -5 y z - 18 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 G := [-18 y z + 5 z, -8 x z - 10 y z, 9 x y z - 5 x y ] > Problem := [F,G]; 4 3 2 3 Problem := [[14 x + 14 y z , -9 x + 7, -5 y z - 18 x y z], 3 3 2 2 3 [-18 y z + 5 z, -8 x z - 10 y z, 9 x y z - 5 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.8MB, alloc=32.3MB, time=0.38 memory used=48.5MB, alloc=32.3MB, time=0.59 memory used=68.7MB, alloc=56.3MB, time=0.78 memory used=110.7MB, alloc=68.3MB, time=1.16 memory used=151.8MB, alloc=68.3MB, time=1.51 memory used=194.5MB, alloc=92.3MB, time=1.85 memory used=257.9MB, alloc=92.3MB, time=2.38 memory used=321.2MB, alloc=116.3MB, time=2.92 memory used=403.4MB, alloc=140.3MB, time=3.66 memory used=507.2MB, alloc=140.3MB, time=4.72 memory used=609.4MB, alloc=164.3MB, time=5.74 memory used=721.7MB, alloc=188.3MB, time=6.98 memory used=827.1MB, alloc=468.3MB, time=8.21 memory used=970.5MB, alloc=492.3MB, time=9.79 memory used=1118.4MB, alloc=516.3MB, time=12.06 memory used=1262.2MB, alloc=540.3MB, time=14.87 memory used=1412.2MB, alloc=564.3MB, time=18.35 memory used=1578.3MB, alloc=588.3MB, time=22.41 memory used=1768.4MB, alloc=612.3MB, time=27.01 memory used=1982.4MB, alloc=636.3MB, time=32.23 memory used=2220.4MB, alloc=636.3MB, time=38.03 memory used=2458.3MB, alloc=636.3MB, time=43.67 memory used=2696.3MB, alloc=660.3MB, time=49.44 memory used=2958.2MB, alloc=684.3MB, time=57.40 memory used=3244.3MB, alloc=708.3MB, time=65.90 N1 := 8631 > GB := Basis(F, plex(op(vars))); 2 2 GB := [9 x - 7, 472392 y + 6125 x, 2916 y + 175 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3567.7MB, alloc=708.3MB, time=70.47 memory used=3921.4MB, alloc=732.3MB, time=78.16 N2 := 3219 #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)]; 4 3 2 3 3 H := [14 x + 14 y z , -9 x + 7, -5 y z - 18 x y z, -18 y z + 5 z, 3 2 2 3 -8 x z - 10 y z, 9 x y z - 5 x y ] > J:=[op(GB),op(G)]; 2 2 3 J := [9 x - 7, 472392 y + 6125 x, 175 z + 2916 y, -18 y z + 5 z, 3 2 2 3 -8 x z - 10 y z, 9 x y z - 5 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 := [6, 15, 22, 4, 4, 3, 3, 5/6, 5/6, 5/6, 1/2, 7/12, 2/3, 6, 13, 17, 4, 3, 3, 3, 2/3, 5/6, 2/3, 5/12, 1/2, 1/2, 2, 5, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3986.9MB, alloc=732.3MB, time=79.32 |\^/| 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(); 1428338968 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 4 2 F := [9 x z + 14 x y, 13 x y + 13 y , 11 x + 19 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [13 x y z - 6 y z, -15 y z - 16 x, -4 x y z + 7 y ] > Problem := [F,G]; 3 3 4 4 2 Problem := [[9 x z + 14 x y, 13 x y + 13 y , 11 x + 19 z ], 2 3 2 2 [13 x y z - 6 y z, -15 y z - 16 x, -4 x y z + 7 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=26.5MB, alloc=32.3MB, time=0.35 memory used=47.6MB, alloc=32.3MB, time=0.59 memory used=68.0MB, alloc=56.3MB, time=0.81 memory used=109.9MB, alloc=60.3MB, time=1.18 memory used=150.3MB, alloc=84.3MB, time=1.55 memory used=210.8MB, alloc=92.3MB, time=2.10 memory used=275.2MB, alloc=116.3MB, time=2.64 memory used=357.1MB, alloc=116.3MB, time=3.37 memory used=423.4MB, alloc=396.3MB, time=4.02 memory used=528.8MB, alloc=396.3MB, time=4.97 memory used=639.3MB, alloc=420.3MB, time=5.94 memory used=764.4MB, alloc=444.3MB, time=7.11 memory used=898.0MB, alloc=468.3MB, time=8.74 memory used=1026.8MB, alloc=492.3MB, time=10.09 memory used=1146.5MB, alloc=492.3MB, time=11.54 memory used=1248.4MB, alloc=492.3MB, time=12.57 memory used=1349.3MB, alloc=516.3MB, time=13.94 memory used=1438.2MB, alloc=516.3MB, time=14.97 memory used=1525.9MB, alloc=516.3MB, time=15.96 memory used=1596.5MB, alloc=516.3MB, time=16.85 memory used=1657.9MB, alloc=540.3MB, time=17.54 memory used=1715.0MB, alloc=540.3MB, time=18.32 memory used=1780.6MB, alloc=540.3MB, time=19.05 memory used=1847.2MB, alloc=540.3MB, time=19.95 memory used=1919.7MB, alloc=540.3MB, time=20.85 memory used=1997.7MB, alloc=564.3MB, time=22.02 memory used=2082.2MB, alloc=564.3MB, time=23.32 memory used=2290.1MB, alloc=588.3MB, time=26.01 memory used=2504.7MB, alloc=612.3MB, time=29.09 memory used=2719.3MB, alloc=636.3MB, time=33.80 memory used=2917.3MB, alloc=660.3MB, time=38.61 memory used=3116.8MB, alloc=684.3MB, time=44.15 memory used=3340.2MB, alloc=708.3MB, time=50.51 memory used=3587.6MB, alloc=732.3MB, time=57.29 memory used=3859.0MB, alloc=756.3MB, time=64.45 memory used=4154.4MB, alloc=780.3MB, time=72.45 memory used=4473.6MB, alloc=804.3MB, time=80.93 N1 := 8107 > GB := Basis(F, plex(op(vars))); 32 22 25 14 GB := [107811 x + 1344364 x , -107811 x + 1344364 x y, 13 2 13 4 5 107811 x + 1344364 x y , -107811 x y + 1344364 y , 99 x z - 266 x y, 9 4 2 1089 x + 5054 x y z, 11 x + 19 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4850.6MB, alloc=804.3MB, time=86.95 memory used=5073.0MB, alloc=804.3MB, time=89.49 memory used=5282.4MB, alloc=804.3MB, time=91.92 memory used=5471.3MB, alloc=804.3MB, time=94.18 memory used=5678.5MB, alloc=828.3MB, time=96.66 memory used=5870.2MB, alloc=852.3MB, time=99.01 memory used=6012.3MB, alloc=852.3MB, time=100.88 memory used=6146.7MB, alloc=876.3MB, time=102.75 memory used=6259.0MB, alloc=876.3MB, time=104.44 memory used=6362.7MB, alloc=876.3MB, time=106.22 memory used=6461.4MB, alloc=876.3MB, time=107.98 memory used=6562.7MB, alloc=876.3MB, time=109.92 memory used=6952.0MB, alloc=900.3MB, time=113.97 memory used=7324.4MB, alloc=924.3MB, time=118.02 memory used=7669.7MB, alloc=948.3MB, time=121.78 memory used=8005.4MB, alloc=972.3MB, time=125.88 memory used=8299.3MB, alloc=996.3MB, time=129.39 memory used=8575.0MB, alloc=1020.3MB, time=133.20 memory used=9211.1MB, alloc=1044.3MB, time=140.19 memory used=9848.9MB, alloc=1068.3MB, time=146.78 memory used=10501.3MB, alloc=1092.3MB, time=154.05 memory used=11153.0MB, alloc=1116.3MB, time=161.66 memory used=11812.3MB, alloc=1140.3MB, time=169.54 memory used=12491.5MB, alloc=1164.3MB, time=177.47 memory used=13066.1MB, alloc=1188.3MB, time=185.15 memory used=13587.0MB, alloc=1212.3MB, time=192.63 memory used=14159.3MB, alloc=1236.3MB, time=200.83 memory used=14599.5MB, alloc=1260.3MB, time=208.05 memory used=14923.1MB, alloc=1284.3MB, time=214.31 memory used=15416.1MB, alloc=1308.3MB, time=221.57 memory used=15866.1MB, alloc=1332.3MB, time=229.22 memory used=16268.4MB, alloc=1356.3MB, time=236.57 memory used=16600.4MB, alloc=1380.3MB, time=243.12 memory used=16936.0MB, alloc=1404.3MB, time=249.23 memory used=17263.5MB, alloc=1428.3MB, time=257.03 memory used=17790.6MB, alloc=1452.3MB, time=268.36 memory used=18213.9MB, alloc=1476.3MB, time=278.05 memory used=18785.2MB, alloc=1500.3MB, time=288.73 memory used=19380.0MB, alloc=1524.3MB, time=299.32 memory used=19828.4MB, alloc=1548.3MB, time=309.49 memory used=20317.3MB, alloc=1572.3MB, time=320.02 |\^/| 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(); 1428339268 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 3 2 F := [-15 x z - 16 x , -8 y z - 13 x z, -3 x y + 2 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 3 G := [6 x z + 4 x y , 12 x y - 17 y z, 7 y + 4 z] > Problem := [F,G]; 3 3 3 2 3 2 Problem := [[-15 x z - 16 x , -8 y z - 13 x z, -3 x y + 2 y z ], 2 2 3 3 2 3 [6 x z + 4 x y , 12 x y - 17 y z, 7 y + 4 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=26.9MB, alloc=32.3MB, time=0.49 memory used=48.3MB, alloc=32.3MB, time=0.77 memory used=68.7MB, alloc=32.3MB, time=1.01 memory used=87.8MB, alloc=56.3MB, time=1.25 memory used=125.9MB, alloc=60.3MB, time=1.71 memory used=166.0MB, alloc=84.3MB, time=2.17 memory used=202.3MB, alloc=84.3MB, time=2.67 memory used=266.2MB, alloc=92.3MB, time=3.24 memory used=327.1MB, alloc=116.3MB, time=3.80 memory used=407.4MB, alloc=116.3MB, time=4.53 memory used=474.5MB, alloc=396.3MB, time=5.16 memory used=577.9MB, alloc=420.3MB, time=6.10 memory used=704.2MB, alloc=444.3MB, time=7.26 memory used=849.2MB, alloc=468.3MB, time=8.59 memory used=986.3MB, alloc=492.3MB, time=9.87 memory used=1114.2MB, alloc=492.3MB, time=11.08 memory used=1203.7MB, alloc=516.3MB, time=11.89 memory used=1303.5MB, alloc=516.3MB, time=12.89 memory used=1385.9MB, alloc=516.3MB, time=13.84 memory used=1450.0MB, alloc=540.3MB, time=14.56 memory used=1530.0MB, alloc=540.3MB, time=15.46 memory used=1606.5MB, alloc=540.3MB, time=16.40 memory used=1656.6MB, alloc=540.3MB, time=17.04 memory used=1695.1MB, alloc=540.3MB, time=17.63 memory used=1906.2MB, alloc=564.3MB, time=19.93 memory used=2102.9MB, alloc=588.3MB, time=21.93 memory used=2282.8MB, alloc=612.3MB, time=23.89 memory used=2436.6MB, alloc=636.3MB, time=25.63 memory used=2582.8MB, alloc=660.3MB, time=27.42 memory used=2722.3MB, alloc=684.3MB, time=29.14 memory used=2824.8MB, alloc=684.3MB, time=30.50 memory used=2942.0MB, alloc=684.3MB, time=32.12 memory used=3046.0MB, alloc=684.3MB, time=33.81 memory used=3385.1MB, alloc=708.3MB, time=37.33 memory used=3739.9MB, alloc=732.3MB, time=41.24 memory used=4101.1MB, alloc=756.3MB, time=45.19 memory used=4432.8MB, alloc=780.3MB, time=49.05 memory used=4727.7MB, alloc=804.3MB, time=52.64 memory used=4955.3MB, alloc=828.3MB, time=55.76 memory used=5216.9MB, alloc=852.3MB, time=59.32 memory used=5466.0MB, alloc=876.3MB, time=62.81 memory used=5691.9MB, alloc=900.3MB, time=66.24 memory used=5880.5MB, alloc=924.3MB, time=69.64 memory used=6381.4MB, alloc=948.3MB, time=75.86 memory used=6892.8MB, alloc=972.3MB, time=82.31 memory used=7410.3MB, alloc=996.3MB, time=89.01 memory used=7949.1MB, alloc=1020.3MB, time=95.76 memory used=8485.6MB, alloc=1044.3MB, time=102.86 memory used=8903.4MB, alloc=1068.3MB, time=110.23 memory used=9256.6MB, alloc=1092.3MB, time=117.11 memory used=9634.0MB, alloc=1116.3MB, time=124.18 memory used=10080.7MB, alloc=1140.3MB, time=131.42 memory used=10454.4MB, alloc=1164.3MB, time=138.64 memory used=10817.7MB, alloc=1188.3MB, time=145.79 memory used=11172.7MB, alloc=1212.3MB, time=153.08 memory used=11522.0MB, alloc=1236.3MB, time=160.85 memory used=11863.5MB, alloc=1260.3MB, time=168.58 memory used=12200.8MB, alloc=1284.3MB, time=176.29 memory used=12533.1MB, alloc=1308.3MB, time=183.91 memory used=12860.6MB, alloc=1332.3MB, time=191.19 memory used=13187.3MB, alloc=1356.3MB, time=198.50 memory used=13493.3MB, alloc=1380.3MB, time=207.20 memory used=13750.4MB, alloc=1404.3MB, time=216.68 memory used=14013.2MB, alloc=1428.3MB, time=226.63 memory used=14287.1MB, alloc=1452.3MB, time=237.01 memory used=14575.0MB, alloc=1476.3MB, time=247.71 memory used=14871.3MB, alloc=1500.3MB, time=258.62 memory used=15177.6MB, alloc=1524.3MB, time=270.01 memory used=15495.6MB, alloc=1548.3MB, time=281.80 memory used=15825.5MB, alloc=1572.3MB, time=294.74 memory used=16167.7MB, alloc=1596.3MB, time=308.43 memory used=16522.7MB, alloc=1620.3MB, time=321.71 |\^/| 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(); 1428339568 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [12 x z - 17 x z, -3 x y - 3 x y z, 5 x y z - 19 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 G := [-5 x y - z, 12 y z + 1, x z + 13 x ] > Problem := [F,G]; 2 3 2 2 2 Problem := [[12 x z - 17 x z, -3 x y - 3 x y z, 5 x y z - 19 x y ], 2 3 3 2 [-5 x y - z, 12 y z + 1, x z + 13 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=47.2MB, alloc=32.3MB, time=0.76 memory used=66.5MB, alloc=56.3MB, time=0.99 memory used=105.9MB, alloc=60.3MB, time=1.47 memory used=142.7MB, alloc=60.3MB, time=1.96 memory used=178.6MB, alloc=84.3MB, time=2.39 memory used=228.1MB, alloc=84.3MB, time=2.93 memory used=282.1MB, alloc=116.3MB, time=3.83 memory used=356.7MB, alloc=116.3MB, time=4.70 memory used=436.0MB, alloc=140.3MB, time=5.66 memory used=531.3MB, alloc=164.3MB, time=6.89 memory used=645.3MB, alloc=188.3MB, time=8.28 memory used=771.5MB, alloc=212.3MB, time=9.68 memory used=906.6MB, alloc=236.3MB, time=11.67 memory used=1053.3MB, alloc=260.3MB, time=13.38 memory used=1211.6MB, alloc=284.3MB, time=15.17 memory used=1334.8MB, alloc=564.3MB, time=17.30 memory used=1486.4MB, alloc=588.3MB, time=20.36 memory used=1646.3MB, alloc=612.3MB, time=23.87 memory used=1817.9MB, alloc=636.3MB, time=27.77 memory used=2003.1MB, alloc=660.3MB, time=32.04 memory used=2201.8MB, alloc=684.3MB, time=36.79 memory used=2412.0MB, alloc=708.3MB, time=42.25 memory used=2646.1MB, alloc=732.3MB, time=48.29 memory used=2904.3MB, alloc=756.3MB, time=56.01 memory used=3186.4MB, alloc=780.3MB, time=64.06 memory used=3492.3MB, alloc=804.3MB, time=72.01 memory used=3822.3MB, alloc=804.3MB, time=80.56 memory used=4152.3MB, alloc=828.3MB, time=89.79 memory used=4506.1MB, alloc=828.3MB, time=99.49 memory used=4859.9MB, alloc=828.3MB, time=111.12 memory used=5213.7MB, alloc=828.3MB, time=122.56 memory used=5567.5MB, alloc=852.3MB, time=131.77 memory used=5945.2MB, alloc=852.3MB, time=142.50 memory used=6322.6MB, alloc=852.3MB, time=153.38 memory used=6700.0MB, alloc=876.3MB, time=163.43 memory used=7101.3MB, alloc=876.3MB, time=173.87 memory used=7502.6MB, alloc=876.3MB, time=184.45 memory used=7903.7MB, alloc=900.3MB, time=194.75 memory used=8328.6MB, alloc=900.3MB, time=206.56 memory used=8753.5MB, alloc=924.3MB, time=217.96 memory used=9202.3MB, alloc=924.3MB, time=231.69 memory used=9651.2MB, alloc=948.3MB, time=245.21 memory used=10124.5MB, alloc=972.3MB, time=260.07 N1 := 17379 > GB := Basis(F, plex(op(vars))); 4 3 2 3 2 2 GB := [12 x y + 17 x y, y x, x y + x y z, 12 x z - 17 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=10634.2MB, alloc=972.3MB, time=271.00 memory used=11207.1MB, alloc=996.3MB, time=287.91 |\^/| 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(); 1428339868 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 F := [-16 x y - 6 x z , 15 y + 2 y z, -5 x y z - 13 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 4 2 G := [-2 x z + 19 y , -3 y z - 5 y z , 9 z + 15 x z ] > Problem := [F,G]; 3 2 3 2 2 Problem := [[-16 x y - 6 x z , 15 y + 2 y z, -5 x y z - 13 x ], 3 2 3 2 4 2 [-2 x z + 19 y , -3 y z - 5 y z , 9 z + 15 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.4MB, alloc=32.3MB, time=0.43 memory used=47.6MB, alloc=32.3MB, time=0.69 memory used=67.5MB, alloc=32.3MB, time=0.93 memory used=86.1MB, alloc=56.3MB, time=1.17 memory used=124.1MB, alloc=60.3MB, time=1.64 memory used=159.5MB, alloc=84.3MB, time=2.09 memory used=215.7MB, alloc=84.3MB, time=2.77 memory used=268.9MB, alloc=108.3MB, time=3.45 memory used=343.5MB, alloc=116.3MB, time=4.48 memory used=422.9MB, alloc=140.3MB, time=5.53 memory used=508.0MB, alloc=396.3MB, time=6.72 memory used=605.1MB, alloc=420.3MB, time=7.76 memory used=726.2MB, alloc=420.3MB, time=8.95 memory used=845.7MB, alloc=444.3MB, time=10.21 memory used=983.5MB, alloc=468.3MB, time=11.66 memory used=1144.0MB, alloc=492.3MB, time=13.39 memory used=1322.8MB, alloc=516.3MB, time=15.40 memory used=1480.9MB, alloc=540.3MB, time=17.18 memory used=1640.7MB, alloc=564.3MB, time=19.06 memory used=1790.4MB, alloc=564.3MB, time=20.86 memory used=1941.8MB, alloc=588.3MB, time=22.85 memory used=2056.0MB, alloc=588.3MB, time=24.23 memory used=2180.0MB, alloc=588.3MB, time=25.88 memory used=2285.1MB, alloc=588.3MB, time=27.30 memory used=2393.8MB, alloc=612.3MB, time=28.82 memory used=2454.8MB, alloc=612.3MB, time=29.73 memory used=2548.7MB, alloc=612.3MB, time=31.09 memory used=2642.6MB, alloc=612.3MB, time=32.45 memory used=2759.8MB, alloc=636.3MB, time=34.56 memory used=2861.6MB, alloc=636.3MB, time=36.15 memory used=2926.4MB, alloc=636.3MB, time=37.18 memory used=3004.3MB, alloc=636.3MB, time=38.53 memory used=3078.0MB, alloc=660.3MB, time=39.68 memory used=3153.0MB, alloc=660.3MB, time=40.88 memory used=3232.4MB, alloc=660.3MB, time=42.24 memory used=3286.2MB, alloc=660.3MB, time=43.20 memory used=3574.0MB, alloc=684.3MB, time=46.89 memory used=3855.8MB, alloc=708.3MB, time=51.23 memory used=4136.2MB, alloc=732.3MB, time=56.90 memory used=4414.5MB, alloc=756.3MB, time=61.89 memory used=4691.8MB, alloc=780.3MB, time=66.55 memory used=4968.5MB, alloc=804.3MB, time=71.28 memory used=5246.5MB, alloc=828.3MB, time=76.41 memory used=5530.2MB, alloc=852.3MB, time=81.14 memory used=5812.9MB, alloc=876.3MB, time=85.39 memory used=6090.2MB, alloc=900.3MB, time=90.40 memory used=6369.7MB, alloc=924.3MB, time=95.16 memory used=6630.2MB, alloc=948.3MB, time=101.16 memory used=6866.9MB, alloc=972.3MB, time=108.16 memory used=7108.2MB, alloc=996.3MB, time=115.56 memory used=7357.5MB, alloc=1020.3MB, time=123.21 memory used=7617.1MB, alloc=1044.3MB, time=130.55 memory used=7888.1MB, alloc=1068.3MB, time=138.89 memory used=8171.6MB, alloc=1092.3MB, time=147.34 memory used=8468.2MB, alloc=1116.3MB, time=157.40 memory used=8778.5MB, alloc=1140.3MB, time=167.83 memory used=9101.7MB, alloc=1164.3MB, time=178.44 memory used=9438.9MB, alloc=1188.3MB, time=188.60 memory used=9790.6MB, alloc=1212.3MB, time=198.91 memory used=10156.3MB, alloc=1236.3MB, time=209.71 memory used=10536.1MB, alloc=1260.3MB, time=221.92 memory used=10932.1MB, alloc=1284.3MB, time=234.59 memory used=11344.2MB, alloc=1308.3MB, time=246.97 memory used=11772.5MB, alloc=1332.3MB, time=260.99 memory used=12216.0MB, alloc=1356.3MB, time=274.97 memory used=12675.9MB, alloc=1380.3MB, time=291.20 |\^/| 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(); 1428340169 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 3 F := [-3 x - 17 y z, 10 x y z - 10 y , 20 x y + 12 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 G := [-2 z + 12 y z, 16 x y + 12 x z, 16 x y z - x z ] > Problem := [F,G]; 4 3 2 3 Problem := [[-3 x - 17 y z, 10 x y z - 10 y , 20 x y + 12 y z], 4 3 2 2 2 [-2 z + 12 y z, 16 x y + 12 x z, 16 x y z - x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.39 memory used=47.4MB, alloc=32.3MB, time=0.62 memory used=67.4MB, alloc=56.3MB, time=0.92 memory used=107.9MB, alloc=60.3MB, time=1.39 memory used=145.6MB, alloc=60.3MB, time=1.84 memory used=181.2MB, alloc=84.3MB, time=2.31 memory used=236.5MB, alloc=84.3MB, time=3.06 memory used=291.1MB, alloc=108.3MB, time=3.80 memory used=367.9MB, alloc=116.3MB, time=4.83 memory used=442.5MB, alloc=140.3MB, time=5.70 memory used=527.9MB, alloc=396.3MB, time=6.67 memory used=621.4MB, alloc=420.3MB, time=7.71 memory used=737.5MB, alloc=444.3MB, time=9.15 memory used=878.3MB, alloc=468.3MB, time=11.04 memory used=1046.7MB, alloc=492.3MB, time=12.67 memory used=1216.5MB, alloc=516.3MB, time=14.79 memory used=1390.0MB, alloc=540.3MB, time=16.93 memory used=1572.4MB, alloc=564.3MB, time=19.47 memory used=1768.9MB, alloc=588.3MB, time=22.49 memory used=1948.8MB, alloc=612.3MB, time=26.99 memory used=2130.4MB, alloc=636.3MB, time=31.36 memory used=2321.4MB, alloc=660.3MB, time=36.14 memory used=2521.1MB, alloc=684.3MB, time=41.28 memory used=2733.3MB, alloc=708.3MB, time=47.04 memory used=2969.6MB, alloc=732.3MB, time=53.39 memory used=3229.7MB, alloc=756.3MB, time=61.29 memory used=3513.8MB, alloc=780.3MB, time=69.99 memory used=3821.9MB, alloc=804.3MB, time=78.76 memory used=4153.9MB, alloc=828.3MB, time=87.61 memory used=4509.8MB, alloc=828.3MB, time=97.86 memory used=4865.7MB, alloc=852.3MB, time=108.20 memory used=5245.4MB, alloc=852.3MB, time=118.90 memory used=5625.2MB, alloc=852.3MB, time=129.28 memory used=6004.7MB, alloc=876.3MB, time=139.06 memory used=6408.1MB, alloc=876.3MB, time=149.42 memory used=6811.6MB, alloc=900.3MB, time=159.63 memory used=7238.9MB, alloc=900.3MB, time=170.61 memory used=7666.2MB, alloc=924.3MB, time=181.17 memory used=8118.1MB, alloc=948.3MB, time=191.00 N1 := 14577 > GB := Basis(F, plex(op(vars))); 7 4 4 4 3 3 GB := [112890625 x - 59049 x , 2125 x y - 81 x , -25 x y + 9 y , 5 4 5 x + 3 x z, 5 x y + 3 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=8256.3MB, alloc=948.3MB, time=193.24 N2 := 2351 #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)]; 4 3 2 3 4 H := [-3 x - 17 y z, 10 x y z - 10 y , 20 x y + 12 y z, -2 z + 12 y z, 3 2 2 2 16 x y + 12 x z, 16 x y z - x z ] > J:=[op(GB),op(G)]; 7 4 4 4 3 3 J := [112890625 x - 59049 x , 2125 x y - 81 x , -25 x y + 9 y , 5 4 4 3 2 5 x + 3 x z, 5 x y + 3 y z, -2 z + 12 y z, 16 x y + 12 x z, 2 2 16 x y z - 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 := [6, 17, 22, 4, 4, 3, 4, 5/6, 1, 1, 7/12, 2/3, 2/3, 8, 18, 35, 7, 7, 3, 4, 7/8, 3/4, 5/8, 3/4, 1/2, 7/16, -1, -13, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=8517.9MB, alloc=948.3MB, time=198.68 |\^/| 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(); 1428340367 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 2 2 F := [-10 x y z + 8 z , 8 x y z + 2 z , -7 x y z - 18 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 3 G := [-7 x y + 7 y z , -11 x z + 15 y z, 16 x - 19 x y z] > Problem := [F,G]; 2 4 2 2 2 2 Problem := [[-10 x y z + 8 z , 8 x y z + 2 z , -7 x y z - 18 x ], 3 3 3 3 3 [-7 x y + 7 y z , -11 x z + 15 y z, 16 x - 19 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.21 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=48.5MB, alloc=32.3MB, time=0.75 memory used=69.6MB, alloc=32.3MB, time=0.94 memory used=89.8MB, alloc=56.3MB, time=1.13 memory used=130.5MB, alloc=60.3MB, time=1.49 memory used=169.8MB, alloc=60.3MB, time=1.84 memory used=205.9MB, alloc=84.3MB, time=2.17 memory used=264.2MB, alloc=92.3MB, time=2.71 memory used=321.6MB, alloc=92.3MB, time=3.21 memory used=379.2MB, alloc=116.3MB, time=3.71 memory used=458.4MB, alloc=116.3MB, time=4.41 memory used=533.1MB, alloc=140.3MB, time=5.07 memory used=621.0MB, alloc=420.3MB, time=5.87 memory used=742.7MB, alloc=444.3MB, time=7.20 memory used=875.5MB, alloc=468.3MB, time=8.71 memory used=1023.5MB, alloc=492.3MB, time=10.38 memory used=1182.2MB, alloc=516.3MB, time=12.32 memory used=1340.2MB, alloc=540.3MB, time=15.65 memory used=1497.6MB, alloc=564.3MB, time=19.46 memory used=1667.1MB, alloc=588.3MB, time=23.89 memory used=1860.6MB, alloc=612.3MB, time=29.19 memory used=2078.1MB, alloc=636.3MB, time=36.09 memory used=2319.6MB, alloc=636.3MB, time=44.47 memory used=2561.0MB, alloc=660.3MB, time=51.71 memory used=2826.5MB, alloc=684.3MB, time=58.50 N1 := 7395 > GB := Basis(F, plex(op(vars))); 6 2 5 2 3 2 GB := [23887872 x - 1715 x , 5971968 x + 1715 x y, -72 x + 7 x z, 4 2 2 2 -107495424 x + 12005 x y z, -5184 x + 49 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3030.1MB, alloc=684.3MB, time=61.06 memory used=3158.6MB, alloc=684.3MB, time=62.51 memory used=3276.1MB, alloc=684.3MB, time=63.80 memory used=3376.8MB, alloc=684.3MB, time=64.92 memory used=3491.8MB, alloc=684.3MB, time=66.14 memory used=3569.4MB, alloc=684.3MB, time=67.22 memory used=3650.7MB, alloc=684.3MB, time=68.33 memory used=3741.2MB, alloc=684.3MB, time=69.60 memory used=3867.9MB, alloc=684.3MB, time=70.65 memory used=3932.8MB, alloc=684.3MB, time=71.53 memory used=3977.3MB, alloc=684.3MB, time=72.25 memory used=4033.7MB, alloc=708.3MB, time=73.00 memory used=4094.0MB, alloc=708.3MB, time=73.97 memory used=4146.7MB, alloc=708.3MB, time=74.89 memory used=4361.8MB, alloc=732.3MB, time=76.87 memory used=4549.7MB, alloc=756.3MB, time=78.73 memory used=4808.0MB, alloc=780.3MB, time=80.79 memory used=4992.9MB, alloc=804.3MB, time=83.18 memory used=5337.1MB, alloc=828.3MB, time=87.95 memory used=5684.7MB, alloc=852.3MB, time=92.58 memory used=6054.6MB, alloc=876.3MB, time=100.98 memory used=6373.5MB, alloc=900.3MB, time=110.48 memory used=6716.3MB, alloc=924.3MB, time=120.64 memory used=7083.0MB, alloc=948.3MB, time=132.48 memory used=7473.8MB, alloc=972.3MB, time=144.70 memory used=7889.3MB, alloc=996.3MB, time=157.96 N2 := 8387 #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 4 2 2 2 2 3 3 H := [-10 x y z + 8 z , 8 x y z + 2 z , -7 x y z - 18 x , -7 x y + 7 y z , 3 3 3 -11 x z + 15 y z, 16 x - 19 x y z] > J:=[op(GB),op(G)]; 6 2 5 2 3 2 J := [23887872 x - 1715 x , 5971968 x + 1715 x y, -72 x + 7 x z, 4 2 2 2 3 3 -107495424 x + 12005 x y z, -5184 x + 49 z , -7 x y + 7 y z , 3 3 3 -11 x z + 15 y z, 16 x - 19 x 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 := [6, 18, 23, 4, 3, 3, 4, 1, 1, 1, 2/3, 7/12, 3/4, 8, 19, 31, 6, 6, 3, 3, 1, 5/8, 3/4, 13/16, 3/8, 7/16, -1, -8, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=7896.8MB, alloc=996.3MB, time=158.11 |\^/| 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(); 1428340524 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 F := [15 x y - 10 x z, 17 x y z + 6 z , -11 y + 9 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [15 y - 19 y z, -x y z + 2 y z, 14 x y + 3 z] > Problem := [F,G]; 3 2 4 3 Problem := [[15 x y - 10 x z, 17 x y z + 6 z , -11 y + 9 z], 2 2 2 [15 y - 19 y z, -x y z + 2 y z, 14 x y + 3 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.1MB, alloc=32.3MB, time=0.38 memory used=48.0MB, alloc=32.3MB, time=0.58 memory used=68.7MB, alloc=32.3MB, time=0.88 memory used=88.1MB, alloc=56.3MB, time=1.18 memory used=127.8MB, alloc=60.3MB, time=1.57 memory used=163.9MB, alloc=60.3MB, time=1.88 memory used=197.9MB, alloc=84.3MB, time=2.20 memory used=253.7MB, alloc=108.3MB, time=2.83 memory used=329.2MB, alloc=140.3MB, time=3.77 memory used=420.7MB, alloc=164.3MB, time=4.80 memory used=529.6MB, alloc=188.3MB, time=6.01 memory used=640.9MB, alloc=468.3MB, time=7.38 memory used=770.6MB, alloc=492.3MB, time=9.27 memory used=898.9MB, alloc=516.3MB, time=12.37 memory used=1037.0MB, alloc=540.3MB, time=15.35 memory used=1183.3MB, alloc=564.3MB, time=19.97 memory used=1352.5MB, alloc=588.3MB, time=24.57 memory used=1545.6MB, alloc=612.3MB, time=30.01 memory used=1762.6MB, alloc=612.3MB, time=36.52 memory used=1979.6MB, alloc=636.3MB, time=43.02 memory used=2220.6MB, alloc=636.3MB, time=49.14 memory used=2461.6MB, alloc=636.3MB, time=55.06 memory used=2702.5MB, alloc=660.3MB, time=61.26 memory used=2967.6MB, alloc=684.3MB, time=68.06 memory used=3256.8MB, alloc=708.3MB, time=74.57 N1 := 9099 > GB := Basis(F, plex(op(vars))); 16 8 13 8 2 3 3 GB := [19683 x y - 25432 x y, 729 x y + 748 x y , -27 x y + 22 x y , 12 7 3 2576816 y + 9034497 x y, -11 y + 9 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3427.2MB, alloc=708.3MB, time=76.41 memory used=3639.2MB, alloc=708.3MB, time=79.08 N2 := 2935 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 4 3 2 H := [15 x y - 10 x z, 17 x y z + 6 z , -11 y + 9 z, 15 y - 19 y z, 2 2 -x y z + 2 y z, 14 y x + 3 z] > J:=[op(GB),op(G)]; 16 8 13 8 2 3 3 J := [19683 x y - 25432 x y, 729 x y + 748 x y , -27 x y + 22 x y , 12 7 3 2 2 2576816 y + 9034497 x y, -11 y + 9 z, 15 y - 19 y z, -x y z + 2 y z, 2 14 y x + 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, 16, 19, 4, 3, 3, 4, 2/3, 1, 1, 5/12, 2/3, 2/3, 8, 18, 58, 17, 16, 12, 1, 3/4, 1, 1/2, 9/16, 7/8, 5/16, -2, -39, -13] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3911.7MB, alloc=708.3MB, time=85.18 |\^/| 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(); 1428351911 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-4 x y - 15 x, 14 y + 20 y, -z - 15] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 G := [9 y - 12, -11 y - 6 x y, 12 x y - 13 x z] > Problem := [F,G]; 2 2 3 2 Problem := [[-4 x y - 15 x, 14 y + 20 y, -z - 15], 2 4 2 2 [9 y - 12, -11 y - 6 x y, 12 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=0.14 memory used=26.4MB, alloc=32.3MB, time=0.33 memory used=47.4MB, alloc=32.3MB, time=0.51 memory used=68.5MB, alloc=56.3MB, time=0.75 N1 := 399 > GB := Basis(F, plex(op(vars))); 2 2 3 2 GB := [8 x - 21 x, 7 x y + 10 x, 7 y + 10 y, z + 15] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.2MB, alloc=60.3MB, time=1.17 memory used=150.2MB, alloc=60.3MB, time=1.55 N2 := 225 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 4 H := [-4 x y - 15 x, 14 y + 20 y, -z - 15, 9 y - 12, -11 y - 6 x y, 2 2 12 x y - 13 x z] > J:=[op(GB),op(G)]; 2 2 3 2 2 J := [8 x - 21 x, 7 x y + 10 x, 7 y + 10 y, z + 15, 9 y - 12, 4 2 2 -11 y - 6 x y, 12 x y - 13 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 := [6, 10, 19, 4, 2, 4, 2, 1/2, 5/6, 1/3, 5/12, 7/12, 1/6, 7, 11, 20, 4, 2, 4, 2, 4/7, 5/7, 2/7, 1/2, 1/2, 1/7, -1, -1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=152.1MB, alloc=60.3MB, time=1.58 |\^/| 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(); 1428351912 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 4 F := [-12 x y - 7 x z, 13 x + 17 z, 12 y - 2] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 2 2 4 G := [9 z + 12 x y, -19 z + 10 y z , -20 x y z - 9 y ] > Problem := [F,G]; 2 2 2 3 4 Problem := [[-12 x y - 7 x z, 13 x + 17 z, 12 y - 2], 4 2 4 2 2 4 [9 z + 12 x y, -19 z + 10 y z , -20 x 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=0.12 memory used=26.4MB, alloc=32.3MB, time=0.35 memory used=48.2MB, alloc=32.3MB, time=0.54 memory used=67.9MB, alloc=56.3MB, time=0.74 memory used=108.5MB, alloc=60.3MB, time=1.14 memory used=147.5MB, alloc=60.3MB, time=1.47 memory used=185.0MB, alloc=84.3MB, time=1.82 memory used=236.6MB, alloc=84.3MB, time=2.29 memory used=294.7MB, alloc=116.3MB, time=2.85 memory used=367.9MB, alloc=372.3MB, time=3.49 memory used=448.9MB, alloc=396.3MB, time=4.43 memory used=556.6MB, alloc=420.3MB, time=5.35 memory used=687.8MB, alloc=420.3MB, time=6.79 memory used=812.8MB, alloc=444.3MB, time=8.58 memory used=943.9MB, alloc=468.3MB, time=10.25 memory used=1072.3MB, alloc=492.3MB, time=12.03 memory used=1193.7MB, alloc=492.3MB, time=13.59 memory used=1298.7MB, alloc=492.3MB, time=15.25 memory used=1409.8MB, alloc=516.3MB, time=16.82 memory used=1499.5MB, alloc=516.3MB, time=18.21 memory used=1596.5MB, alloc=516.3MB, time=19.50 memory used=1660.0MB, alloc=516.3MB, time=20.58 memory used=1737.8MB, alloc=516.3MB, time=21.85 memory used=1815.1MB, alloc=540.3MB, time=23.10 memory used=1888.9MB, alloc=540.3MB, time=24.12 memory used=1950.4MB, alloc=540.3MB, time=25.00 memory used=2005.1MB, alloc=540.3MB, time=25.91 memory used=2053.4MB, alloc=540.3MB, time=26.54 memory used=2109.4MB, alloc=540.3MB, time=27.42 memory used=2332.2MB, alloc=564.3MB, time=30.44 memory used=2553.1MB, alloc=588.3MB, time=33.10 memory used=2748.8MB, alloc=612.3MB, time=35.19 memory used=2946.2MB, alloc=636.3MB, time=37.21 memory used=3146.4MB, alloc=660.3MB, time=39.41 memory used=3393.6MB, alloc=684.3MB, time=42.66 memory used=3657.6MB, alloc=708.3MB, time=46.22 memory used=3942.0MB, alloc=732.3MB, time=50.88 memory used=4273.1MB, alloc=756.3MB, time=54.34 memory used=4579.9MB, alloc=780.3MB, time=58.82 memory used=4834.3MB, alloc=804.3MB, time=63.29 memory used=5042.0MB, alloc=828.3MB, time=66.45 memory used=5242.7MB, alloc=852.3MB, time=70.28 memory used=5523.4MB, alloc=876.3MB, time=78.95 memory used=5793.1MB, alloc=900.3MB, time=86.83 memory used=6068.5MB, alloc=924.3MB, time=94.36 memory used=6353.4MB, alloc=948.3MB, time=102.29 memory used=6649.5MB, alloc=972.3MB, time=110.56 memory used=6958.2MB, alloc=996.3MB, time=119.36 memory used=7280.3MB, alloc=1020.3MB, time=128.60 memory used=7616.4MB, alloc=1044.3MB, time=138.28 memory used=7961.2MB, alloc=1068.3MB, time=148.71 memory used=8324.4MB, alloc=1092.3MB, time=159.84 memory used=8711.4MB, alloc=1116.3MB, time=171.70 memory used=9122.4MB, alloc=1140.3MB, time=184.17 memory used=9557.3MB, alloc=1164.3MB, time=198.33 memory used=10016.2MB, alloc=1188.3MB, time=217.06 memory used=10499.0MB, alloc=1212.3MB, time=235.48 memory used=11005.7MB, alloc=1236.3MB, time=251.85 memory used=11536.4MB, alloc=1260.3MB, time=268.46 memory used=12090.9MB, alloc=1284.3MB, time=285.13 |\^/| 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(); 1428352212 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 2 F := [7 y - 2 x , 20 x z + 18 x , -14 x z - 5 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 4 2 2 G := [4 y z + 14 z , z + 15 x y, -6 x + 9 x y ] > Problem := [F,G]; 3 2 3 2 2 2 Problem := [[7 y - 2 x , 20 x z + 18 x , -14 x z - 5 x z], 3 2 4 2 4 2 2 [4 y z + 14 z , z + 15 x y, -6 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.44 memory used=48.3MB, alloc=32.3MB, time=0.68 memory used=68.8MB, alloc=32.3MB, time=0.87 memory used=89.2MB, alloc=56.3MB, time=1.06 memory used=129.8MB, alloc=60.3MB, time=1.42 memory used=168.7MB, alloc=60.3MB, time=1.75 memory used=205.4MB, alloc=84.3MB, time=2.08 memory used=264.2MB, alloc=92.3MB, time=2.61 memory used=321.3MB, alloc=116.3MB, time=3.13 memory used=401.1MB, alloc=140.3MB, time=3.96 memory used=502.3MB, alloc=164.3MB, time=5.00 memory used=617.1MB, alloc=188.3MB, time=6.25 memory used=772.1MB, alloc=188.3MB, time=7.37 memory used=903.7MB, alloc=212.3MB, time=8.69 memory used=1036.7MB, alloc=492.3MB, time=10.10 memory used=1180.2MB, alloc=516.3MB, time=12.52 memory used=1327.7MB, alloc=540.3MB, time=15.52 memory used=1482.4MB, alloc=564.3MB, time=19.20 memory used=1659.9MB, alloc=588.3MB, time=23.45 memory used=1861.4MB, alloc=588.3MB, time=28.22 memory used=2062.9MB, alloc=612.3MB, time=32.97 memory used=2288.3MB, alloc=612.3MB, time=38.35 memory used=2513.8MB, alloc=636.3MB, time=43.61 memory used=2763.2MB, alloc=636.3MB, time=49.26 memory used=3013.0MB, alloc=660.3MB, time=54.03 N1 := 7915 > GB := Basis(F, plex(op(vars))); 6 2 3 2 4 GB := [12348 x - 625 x , 7 y - 2 x , 882 x + 125 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3277.5MB, alloc=660.3MB, time=57.15 memory used=3587.7MB, alloc=684.3MB, time=63.73 N2 := 3387 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 2 2 3 2 H := [7 y - 2 x , 20 x z + 18 x , -14 x z - 5 x z, 4 y z + 14 z , 4 2 4 2 2 z + 15 y x , -6 x + 9 x y ] > J:=[op(GB),op(G)]; 6 2 3 2 4 3 2 J := [12348 x - 625 x , 7 y - 2 x , 882 x + 125 x z, 4 y z + 14 z , 4 2 4 2 2 z + 15 y x , -6 x + 9 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 := [6, 13, 23, 4, 4, 3, 4, 5/6, 2/3, 2/3, 2/3, 1/3, 1/2, 6, 12, 25, 6, 6, 3, 4, 5/6, 2/3, 1/2, 2/3, 1/3, 1/3, 1, -2, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3724.6MB, alloc=684.3MB, time=66.27 |\^/| 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(); 1428352278 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 4 F := [20 x z - 19 x , 8 z , -19 y - x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 3 2 G := [11 x y - 4 y , y - 8 z , y z + 2 y z] > Problem := [F,G]; 2 2 4 4 Problem := [[20 x z - 19 x , 8 z , -19 y - x z], 2 2 4 3 3 2 [11 x y - 4 y , y - 8 z , y z + 2 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.1MB, alloc=40.3MB, time=0.37 memory used=60.3MB, alloc=40.3MB, time=0.63 memory used=86.8MB, alloc=40.3MB, time=0.93 memory used=112.4MB, alloc=68.3MB, time=1.23 memory used=156.8MB, alloc=68.3MB, time=1.68 memory used=200.7MB, alloc=92.3MB, time=2.12 memory used=242.6MB, alloc=92.3MB, time=2.49 memory used=309.6MB, alloc=124.3MB, time=3.20 memory used=398.2MB, alloc=124.3MB, time=4.12 memory used=477.9MB, alloc=148.3MB, time=4.99 memory used=568.1MB, alloc=172.3MB, time=6.23 memory used=661.5MB, alloc=196.3MB, time=8.13 memory used=776.8MB, alloc=220.3MB, time=10.36 N1 := 3403 > GB := Basis(F, plex(op(vars))); 3 4 2 8 4 4 2 4 GB := [x , y x , y , 19 y + z x, 20 y z + x , z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=920.1MB, alloc=220.3MB, time=12.46 memory used=1002.8MB, alloc=476.3MB, time=13.30 memory used=1167.6MB, alloc=476.3MB, time=14.82 memory used=1330.7MB, alloc=500.3MB, time=16.60 memory used=1505.5MB, alloc=524.3MB, time=19.18 memory used=1665.4MB, alloc=548.3MB, time=22.65 N2 := 3099 #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 4 4 2 2 4 3 3 H := [20 x z - 19 x , 8 z , -19 y - x z, 11 x y - 4 y , y - 8 z , 2 y z + 2 y z] > J:=[op(GB),op(G)]; 3 4 2 8 4 4 2 4 2 2 4 3 3 J := [x , y x , y , 19 y + z x, 20 z y + x , z , 11 x y - 4 y , y - 8 z , 2 y z + 2 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 21, 4, 2, 4, 4, 1/2, 2/3, 5/6, 1/3, 1/2, 1/2, 9, 17, 40, 8, 3, 8, 4, 5/9, 7/9, 5/9, 5/18, 1/2, 1/3, -5, -19, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1750.1MB, alloc=548.3MB, time=24.02 |\^/| 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(); 1428352301 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 2 F := [-11 y z - 10 y z , -12 x z - 17 y z, -20 x z - 16 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 4 G := [-16 x + 15, -15 x y z - 5 y z , 16 y + 17 x z] > Problem := [F,G]; 3 3 2 2 2 2 Problem := [[-11 y z - 10 y z , -12 x z - 17 y z, -20 x z - 16 y ], 4 2 3 4 [-16 x + 15, -15 x y z - 5 y z , 16 y + 17 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.4MB, alloc=32.3MB, time=0.36 memory used=47.4MB, alloc=32.3MB, time=0.53 memory used=68.1MB, alloc=32.3MB, time=0.71 memory used=87.9MB, alloc=56.3MB, time=0.89 memory used=128.1MB, alloc=60.3MB, time=1.23 memory used=166.2MB, alloc=60.3MB, time=1.54 memory used=205.0MB, alloc=60.3MB, time=1.87 memory used=241.8MB, alloc=84.3MB, time=2.18 memory used=280.9MB, alloc=84.3MB, time=2.51 memory used=339.6MB, alloc=116.3MB, time=3.18 memory used=416.7MB, alloc=116.3MB, time=4.01 memory used=486.9MB, alloc=140.3MB, time=4.95 N1 := 1763 > GB := Basis(F, plex(op(vars))); 3 2 2 2 3 GB := [y , 85 x y z - 48 y , y z, 12 x z + 17 y z, y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=566.3MB, alloc=140.3MB, time=6.18 memory used=661.5MB, alloc=164.3MB, time=7.11 memory used=770.8MB, alloc=444.3MB, time=8.46 memory used=896.4MB, alloc=468.3MB, time=10.80 N2 := 2271 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 2 2 2 4 H := [-11 y z - 10 y z , -12 x z - 17 y z, -20 x z - 16 y , -16 x + 15, 2 3 4 -15 x y z - 5 y z , 16 y + 17 z x] > J:=[op(GB),op(G)]; 3 2 2 2 3 4 J := [y , 85 x y z - 48 y , y z, 12 x z + 17 y z, y z , -16 x + 15, 2 3 4 -15 x y z - 5 y z , 16 y + 17 z x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 23, 4, 4, 4, 3, 5/6, 5/6, 5/6, 5/12, 7/12, 2/3, 8, 18, 28, 4, 4, 4, 3, 5/8, 7/8, 3/4, 5/16, 9/16, 1/2, -3, -5, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=949.8MB, alloc=468.3MB, time=11.60 |\^/| 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(); 1428352313 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 F := [20 x y + 5 z, 12 x z + 10 z , -3 x z + 20 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 3 G := [6 x y + 9 x, 11 x y z + 20 z , 17 x y z + 19 z ] > Problem := [F,G]; 3 3 3 Problem := [[20 x y + 5 z, 12 x z + 10 z , -3 x z + 20 x], 2 4 2 3 [6 x y + 9 x, 11 x y z + 20 z , 17 x y z + 19 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.4MB, alloc=32.3MB, time=0.35 memory used=47.7MB, alloc=32.3MB, time=0.52 memory used=68.4MB, alloc=32.3MB, time=0.70 memory used=87.8MB, alloc=32.3MB, time=0.86 memory used=106.1MB, alloc=56.3MB, time=1.03 memory used=144.7MB, alloc=60.3MB, time=1.37 memory used=181.4MB, alloc=60.3MB, time=1.68 memory used=216.3MB, alloc=84.3MB, time=2.00 memory used=272.1MB, alloc=84.3MB, time=2.49 memory used=326.0MB, alloc=108.3MB, time=2.97 memory used=400.3MB, alloc=116.3MB, time=3.67 memory used=478.9MB, alloc=140.3MB, time=4.42 memory used=582.1MB, alloc=164.3MB, time=5.28 memory used=694.2MB, alloc=188.3MB, time=6.52 memory used=823.6MB, alloc=212.3MB, time=7.92 memory used=977.3MB, alloc=236.3MB, time=9.33 memory used=1098.5MB, alloc=516.3MB, time=10.76 memory used=1255.8MB, alloc=540.3MB, time=13.16 memory used=1408.1MB, alloc=564.3MB, time=16.15 memory used=1569.7MB, alloc=588.3MB, time=19.66 memory used=1740.7MB, alloc=612.3MB, time=23.89 memory used=1931.6MB, alloc=636.3MB, time=28.71 memory used=2146.4MB, alloc=660.3MB, time=34.06 memory used=2385.1MB, alloc=684.3MB, time=39.97 memory used=2647.8MB, alloc=684.3MB, time=46.35 memory used=2910.4MB, alloc=684.3MB, time=52.74 memory used=3173.0MB, alloc=708.3MB, time=59.27 memory used=3459.6MB, alloc=708.3MB, time=66.17 memory used=3746.0MB, alloc=732.3MB, time=73.08 memory used=4056.5MB, alloc=732.3MB, time=80.46 memory used=4366.9MB, alloc=756.3MB, time=87.77 memory used=4701.2MB, alloc=756.3MB, time=95.43 N1 := 11251 > GB := Basis(F, plex(op(vars))); 4 3 GB := [27 x + 1000 x, 200 x y - 9 x, 9 x + 50 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5039.9MB, alloc=756.3MB, time=101.72 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)]; 3 3 3 H := [20 x y + 5 z, 12 x z + 10 z , -3 x z + 20 x, 6 x y + 9 x, 2 4 2 3 11 x y z + 20 z , 17 x y z + 19 z ] > J:=[op(GB),op(G)]; 4 3 J := [27 x + 1000 x, 200 x y - 9 x, 9 x + 50 z, 6 x y + 9 x, 2 4 2 3 11 x y z + 20 z , 17 x y z + 19 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, 15, 20, 4, 3, 1, 4, 1, 2/3, 5/6, 2/3, 1/3, 2/3, 6, 13, 19, 4, 4, 1, 4, 1, 2/3, 1/2, 3/4, 1/3, 5/12, 2, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=5193.2MB, alloc=756.3MB, time=103.64 |\^/| 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(); 1428352415 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 2 2 F := [10 y z - 3 x , -4 x y z + 17 y z, 19 x + 13 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 G := [15 x y + 8 y z , -16 y z, 15 x z - 2 x y z] > Problem := [F,G]; 3 2 2 4 2 2 Problem := [[10 y z - 3 x , -4 x y z + 17 y z, 19 x + 13 y z ], 2 2 2 2 2 3 [15 x y + 8 y z , -16 y z, 15 x z - 2 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.8MB, alloc=32.3MB, time=0.37 memory used=48.6MB, alloc=32.3MB, time=0.57 memory used=69.1MB, alloc=56.3MB, time=0.76 memory used=110.4MB, alloc=60.3MB, time=1.12 memory used=150.8MB, alloc=84.3MB, time=1.53 memory used=212.6MB, alloc=84.3MB, time=2.20 memory used=268.7MB, alloc=108.3MB, time=2.89 N1 := 1107 > GB := Basis(F, plex(op(vars))); 6 2 3 2 5 2 GB := [7488 x + 39672475 x , 1615 x + 78 x y, 1872 x + 2333675 x z, 4 -24 x + 1445 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 175 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 4 2 2 2 2 H := [10 y z - 3 x , -4 x y z + 17 y z, 13 z y + 19 x , 15 x y + 8 y z , 2 3 -16 y z, 15 x z - 2 x y z] > J:=[op(GB),op(G)]; 6 2 3 2 5 2 J := [7488 x + 39672475 x , 1615 x + 78 x y, 1872 x + 2333675 x z, 4 2 2 2 2 2 3 -24 x + 1445 y z, 15 x y + 8 y z , -16 y z, 15 x z - 2 x 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 := [6, 17, 23, 4, 4, 2, 3, 5/6, 1, 1, 6/13, 8/13, 8/13, 7, 16, 29, 6, 6, 2, 2, 6/7, 5/7, 5/7, 2/3, 2/5, 2/5, 1, -6, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=336.2MB, alloc=108.3MB, time=3.56 |\^/| 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(); 1428352419 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [z, 18 x y z + 3 x , -20 x z + 8] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 2 2 G := [9 x - 12 x y, -19 y z - 16 x , -8 y z + 19 x ] > Problem := [F,G]; 2 2 2 2 Problem := [[z, 18 x y z + 3 x , -20 x z + 8], 4 3 3 2 2 2 [9 x - 12 x y, -19 y z - 16 x , -8 y z + 19 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.8MB, alloc=32.3MB, time=0.36 memory used=47.7MB, alloc=32.3MB, time=0.54 memory used=68.0MB, alloc=56.3MB, time=0.72 memory used=110.1MB, alloc=60.3MB, time=1.08 memory used=150.7MB, alloc=84.3MB, time=1.44 memory used=213.1MB, alloc=92.3MB, time=1.99 memory used=277.1MB, alloc=116.3MB, time=2.62 memory used=373.2MB, alloc=116.3MB, time=3.27 memory used=460.5MB, alloc=140.3MB, time=4.01 memory used=556.3MB, alloc=140.3MB, time=5.03 memory used=649.8MB, alloc=164.3MB, time=5.98 memory used=765.6MB, alloc=188.3MB, time=7.11 memory used=888.1MB, alloc=468.3MB, time=8.46 memory used=1049.3MB, alloc=492.3MB, time=9.81 memory used=1195.6MB, alloc=516.3MB, time=13.22 memory used=1346.4MB, alloc=540.3MB, time=16.27 memory used=1503.6MB, alloc=564.3MB, time=20.04 memory used=1684.8MB, alloc=588.3MB, time=24.37 memory used=1890.0MB, alloc=588.3MB, time=29.17 memory used=2095.1MB, alloc=588.3MB, time=33.94 memory used=2300.2MB, alloc=612.3MB, time=38.72 memory used=2529.2MB, alloc=612.3MB, time=44.06 memory used=2758.3MB, alloc=636.3MB, time=49.31 memory used=3011.3MB, alloc=636.3MB, time=54.87 N1 := 8303 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 113 #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 2 4 3 3 2 H := [z, 18 x y z + 3 x , -20 x z + 8, 9 x - 12 x y, -19 y z - 16 x , 2 2 -8 z y + 19 x ] > J:=[op(GB),op(G)]; 4 3 3 2 2 2 J := [1, 9 x - 12 x y, -19 y z - 16 x , -8 z y + 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 := [6, 14, 20, 4, 4, 2, 3, 5/6, 2/3, 5/6, 7/11, 4/11, 5/11, 4, 8, 11, 4, 4, 2, 3, 3/4, 3/4, 1/2, 4/7, 3/7, 2/7, 6, 9, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3204.6MB, alloc=636.3MB, time=58.15 |\^/| 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(); 1428352476 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 3 3 2 F := [11 x y + 6 z , 20 x - 10 x , 4 x z + 6 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 G := [x + 19 z, -4 x z - 5 x y , -4 x y z - x y z ] > Problem := [F,G]; 2 2 2 4 3 3 2 Problem := [[11 x y + 6 z , 20 x - 10 x , 4 x z + 6 y z], 3 3 2 2 [x + 19 z, -4 x z - 5 x y , -4 x y z - x y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.4MB, alloc=32.3MB, time=0.36 memory used=47.9MB, alloc=32.3MB, time=0.54 memory used=67.9MB, alloc=32.3MB, time=0.71 memory used=87.2MB, alloc=56.3MB, time=0.89 memory used=126.0MB, alloc=60.3MB, time=1.23 memory used=162.8MB, alloc=60.3MB, time=1.55 memory used=197.6MB, alloc=84.3MB, time=1.87 memory used=252.3MB, alloc=84.3MB, time=2.36 memory used=310.2MB, alloc=116.3MB, time=2.99 memory used=386.4MB, alloc=140.3MB, time=3.80 memory used=481.7MB, alloc=164.3MB, time=4.78 memory used=585.7MB, alloc=188.3MB, time=6.45 memory used=695.7MB, alloc=212.3MB, time=8.62 memory used=829.8MB, alloc=212.3MB, time=10.88 N1 := 3243 > GB := Basis(F, plex(op(vars))); 4 3 4 2 2 2 2 2 GB := [2 x - x , y x , z y , 11 y x + 6 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 237 #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 4 3 3 2 H := [11 y x + 6 z , 20 x - 10 x , 4 x z + 6 y z, 19 z + x, 3 3 2 2 -4 x z - 5 x y , -4 x y z - x y z ] > J:=[op(GB),op(G)]; 4 3 4 2 2 2 2 2 3 3 J := [2 x - x , y x , z y , 11 y x + 6 z , 19 z + x, -4 x z - 5 x y , 2 2 -4 x y z - x 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 := [6, 15, 21, 4, 4, 3, 3, 1, 2/3, 5/6, 3/4, 5/12, 7/12, 7, 16, 26, 6, 4, 4, 2, 6/7, 5/7, 5/7, 9/14, 3/7, 3/7, -1, -5, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=920.1MB, alloc=212.3MB, time=11.74 |\^/| 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(); 1428352488 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 3 F := [18 x z + 6 x z , -7 x y z - 15 y, 2 x z + 3 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [10 y z + 2 y, -17 x y + 13 x, 13 x y - 20 z] > Problem := [F,G]; 3 2 2 2 3 3 Problem := [[18 x z + 6 x z , -7 x y z - 15 y, 2 x z + 3 x z ], 3 2 [10 y z + 2 y, -17 x y + 13 x, 13 x y - 20 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.34 memory used=47.4MB, alloc=32.3MB, time=0.52 memory used=67.7MB, alloc=32.3MB, time=0.69 memory used=87.2MB, alloc=56.3MB, time=0.89 memory used=129.2MB, alloc=56.3MB, time=1.44 memory used=165.9MB, alloc=84.3MB, time=1.89 N1 := 1197 > GB := Basis(F, plex(op(vars))); 4 3 2 2 3 3 GB := [y, z x , 3 x z + x z , 2 x z + 3 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=218.3MB, alloc=84.3MB, time=2.56 N2 := 417 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 3 H := [18 x z + 6 x z , -7 x y z - 15 y, 2 x z + 3 x z , 10 y z + 2 y, 3 2 -17 x y + 13 x, 13 y x - 20 z] > J:=[op(GB),op(G)]; 4 3 2 2 3 3 3 J := [y, z x , 3 x z + x z , 2 x z + 3 x z , 10 y z + 2 y, -17 x y + 13 x, 2 13 y x - 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 := [6, 14, 21, 4, 3, 1, 3, 5/6, 2/3, 5/6, 2/3, 1/2, 7/12, 7, 14, 23, 5, 4, 1, 3, 5/7, 4/7, 5/7, 8/13, 5/13, 7/13, 0, -2, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=269.0MB, alloc=84.3MB, time=3.04 |\^/| 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(); 1428352491 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 2 3 F := [9 x + 11 x , 11 y z + y z , 2 y z - 2 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 G := [19 x y z + 14 y , -13 y - 7 z, 8 y z + 11] > Problem := [F,G]; 4 3 3 2 2 3 Problem := [[9 x + 11 x , 11 y z + y z , 2 y z - 2 z], 2 3 3 2 2 [19 x y z + 14 y , -13 y - 7 z, 8 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=4.3MB, alloc=32.3MB, time=0.11 memory used=26.2MB, alloc=32.3MB, time=0.32 memory used=47.7MB, alloc=32.3MB, time=0.52 memory used=68.0MB, alloc=32.3MB, time=0.70 memory used=86.7MB, alloc=56.3MB, time=0.87 memory used=128.0MB, alloc=60.3MB, time=1.29 memory used=166.0MB, alloc=84.3MB, time=1.70 memory used=223.1MB, alloc=108.3MB, time=2.44 N1 := 1239 > GB := Basis(F, plex(op(vars))); 4 3 3 2 GB := [9 x + 11 x , y z - z, 11 y z + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=294.4MB, alloc=108.3MB, time=3.16 memory used=373.9MB, alloc=116.3MB, time=3.95 memory used=449.6MB, alloc=140.3MB, time=4.85 N2 := 1239 #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)]; 4 3 3 2 2 3 2 3 H := [9 x + 11 x , 11 y z + y z , 2 y z - 2 z, 19 x y z + 14 y , 3 2 2 -13 y - 7 z, 8 z y + 11] > J:=[op(GB),op(G)]; 4 3 3 2 2 3 3 J := [9 x + 11 x , y z - z, 11 y z + z , 19 x y z + 14 y , -13 y - 7 z, 2 2 8 z 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 := [6, 12, 23, 4, 4, 3, 2, 1/3, 5/6, 5/6, 1/4, 7/12, 7/12, 6, 12, 21, 4, 4, 3, 2, 1/3, 5/6, 5/6, 1/4, 1/2, 7/12, 0, 2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=483.6MB, alloc=140.3MB, time=5.33 |\^/| 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(); 1428352496 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [-20 x y z + 18 x z, 11 x y + 20 y z, -17 y z + 3 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 G := [11 y - 10 x , -8 x y - 7 z, 20 x z - 15 x] > Problem := [F,G]; 2 2 2 3 Problem := [[-20 x y z + 18 x z, 11 x y + 20 y z, -17 y z + 3 z], 4 3 2 2 [11 y - 10 x , -8 x y - 7 z, 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=4.2MB, alloc=32.3MB, time=0.14 memory used=26.0MB, alloc=32.3MB, time=0.34 memory used=47.3MB, alloc=32.3MB, time=0.50 memory used=68.0MB, alloc=32.3MB, time=0.68 memory used=87.4MB, alloc=56.3MB, time=0.86 memory used=127.2MB, alloc=60.3MB, time=1.23 memory used=166.6MB, alloc=84.3MB, time=1.66 memory used=223.2MB, alloc=108.3MB, time=2.27 memory used=297.4MB, alloc=140.3MB, time=3.07 memory used=385.5MB, alloc=164.3MB, time=4.03 memory used=485.1MB, alloc=188.3MB, time=5.17 memory used=590.5MB, alloc=212.3MB, time=6.93 memory used=706.9MB, alloc=236.3MB, time=9.16 memory used=835.7MB, alloc=260.3MB, time=12.03 memory used=981.9MB, alloc=284.3MB, time=15.46 memory used=1152.1MB, alloc=284.3MB, time=19.42 memory used=1322.1MB, alloc=308.3MB, time=23.39 memory used=1516.2MB, alloc=308.3MB, time=27.89 memory used=1710.2MB, alloc=308.3MB, time=32.34 memory used=1904.3MB, alloc=332.3MB, time=36.78 memory used=2122.2MB, alloc=332.3MB, time=41.65 memory used=2340.1MB, alloc=356.3MB, time=46.25 N1 := 7939 > GB := Basis(F, plex(op(vars))); 3 2 2 5 2 2 2 4 GB := [x y , 17 x y - 3 x y , 187 x y + 60 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2526.1MB, alloc=356.3MB, time=48.92 memory used=2816.2MB, alloc=636.3MB, time=53.02 N2 := 3193 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 4 3 H := [-20 x y z + 18 x z, 11 x y + 20 y z, -17 y z + 3 z, 11 y - 10 x , 2 2 -8 x y - 7 z, 20 x z - 15 x] > J:=[op(GB),op(G)]; 3 2 2 5 2 2 4 2 4 3 2 J := [x y , 17 x y - 3 x y , 187 y x + 60 z, 11 y - 10 x , -8 x y - 7 z, 2 20 x 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 := [6, 15, 22, 4, 3, 4, 2, 5/6, 5/6, 5/6, 7/12, 1/2, 7/12, 6, 14, 28, 7, 3, 5, 2, 1, 5/6, 1/2, 2/3, 1/2, 1/4, 1, -6, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3061.4MB, alloc=636.3MB, time=57.97 |\^/| 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(); 1428352554 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [11 y z - 6 x y , -17 x y + 10 x z, 12 x y + 8 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [-9 x y + 4 y, 17 x y z + 12 x y z, z + 5 x ] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[11 y z - 6 x y , -17 x y + 10 x z, 12 x y + 8 z ], 2 2 3 2 [-9 x y + 4 y, 17 x y z + 12 x y z, z + 5 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.12 memory used=26.3MB, alloc=32.3MB, time=0.30 memory used=47.8MB, alloc=32.3MB, time=0.49 memory used=68.1MB, alloc=32.3MB, time=0.71 memory used=87.3MB, alloc=56.3MB, time=0.90 memory used=129.0MB, alloc=60.3MB, time=1.27 memory used=167.7MB, alloc=60.3MB, time=1.61 memory used=204.5MB, alloc=84.3MB, time=1.94 memory used=262.9MB, alloc=116.3MB, time=2.54 memory used=342.9MB, alloc=116.3MB, time=3.40 memory used=416.2MB, alloc=140.3MB, time=4.19 memory used=506.8MB, alloc=164.3MB, time=5.18 memory used=611.6MB, alloc=188.3MB, time=6.40 memory used=722.6MB, alloc=212.3MB, time=8.27 memory used=841.3MB, alloc=236.3MB, time=10.75 memory used=973.6MB, alloc=260.3MB, time=13.83 memory used=1129.8MB, alloc=284.3MB, time=17.44 memory used=1310.0MB, alloc=284.3MB, time=21.53 memory used=1490.2MB, alloc=284.3MB, time=25.51 memory used=1670.5MB, alloc=308.3MB, time=29.35 N1 := 6105 > GB := Basis(F, plex(op(vars))); 7 4 4 2 2 2 2 GB := [4125 x y - 4913 x y, 150 x y + 289 x y , -17 x y + 10 x z, 5 2 3 2 2 2 -2250 x y + 4913 x y z, 11 y z - 6 x y , 3 y x + 2 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1873.2MB, alloc=308.3MB, time=32.24 memory used=2057.3MB, alloc=564.3MB, time=34.11 memory used=2218.7MB, alloc=588.3MB, time=35.72 memory used=2361.0MB, alloc=588.3MB, time=37.28 memory used=2505.9MB, alloc=612.3MB, time=38.80 memory used=2658.9MB, alloc=636.3MB, time=40.67 memory used=2835.5MB, alloc=660.3MB, time=42.90 memory used=3022.7MB, alloc=684.3MB, time=45.11 memory used=3197.1MB, alloc=708.3MB, time=47.38 memory used=3370.7MB, alloc=732.3MB, time=50.00 memory used=3671.1MB, alloc=756.3MB, time=56.73 memory used=3964.4MB, alloc=780.3MB, time=64.54 memory used=4265.8MB, alloc=804.3MB, time=72.89 memory used=4591.1MB, alloc=828.3MB, time=81.84 memory used=4940.4MB, alloc=852.3MB, time=91.35 memory used=5313.6MB, alloc=876.3MB, time=101.46 memory used=5710.8MB, alloc=900.3MB, time=112.05 memory used=6131.9MB, alloc=900.3MB, time=123.39 memory used=6553.0MB, alloc=924.3MB, time=134.48 memory used=6998.1MB, alloc=948.3MB, time=146.30 memory used=7467.5MB, alloc=972.3MB, time=157.31 N2 := 11683 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 2 H := [11 y z - 6 x y , -17 x y + 10 x z, 12 x y + 8 z , -9 x y + 4 y, 2 3 2 17 x y z + 12 x y z, z + 5 x ] > J:=[op(GB),op(G)]; 7 4 4 2 2 2 2 J := [4125 x y - 4913 x y, 150 x y + 289 x y , -17 x y + 10 x z, 5 2 3 2 2 2 2 -2250 x y + 4913 x y z, 11 y z - 6 x y , 3 y x + 2 z , -9 x y + 4 y, 2 3 2 17 x y z + 12 x y z, z + 5 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 16, 20, 4, 2, 3, 3, 1, 5/6, 5/6, 2/3, 2/3, 1/2, 9, 23, 39, 8, 7, 3, 3, 1, 8/9, 2/3, 7/9, 7/9, 7/18, -7, -19, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=7473.1MB, alloc=972.3MB, time=157.44 |\^/| 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(); 1428352708 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 2 3 F := [13 x y + 5 x z, 12 z - 5 z, -4 x y - 12 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [-20 y z + 19 x, -12 x z - 7 z , 5 x y - 8 y z ] > Problem := [F,G]; 2 2 2 4 2 2 3 Problem := [[13 x y + 5 x z, 12 z - 5 z, -4 x y - 12 z ], 2 2 3 2 2 [-20 y z + 19 x, -12 x z - 7 z , 5 x y - 8 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.8MB, alloc=32.3MB, time=0.38 memory used=48.0MB, alloc=32.3MB, time=0.56 memory used=68.3MB, alloc=32.3MB, time=0.73 memory used=87.9MB, alloc=56.3MB, time=0.91 memory used=128.8MB, alloc=60.3MB, time=1.27 memory used=166.7MB, alloc=84.3MB, time=1.61 memory used=211.4MB, alloc=84.3MB, time=2.01 memory used=268.8MB, alloc=116.3MB, time=2.57 memory used=348.9MB, alloc=372.3MB, time=3.28 memory used=428.5MB, alloc=396.3MB, time=3.99 memory used=538.3MB, alloc=420.3MB, time=4.90 memory used=662.4MB, alloc=444.3MB, time=6.02 memory used=805.2MB, alloc=468.3MB, time=7.29 memory used=950.1MB, alloc=492.3MB, time=8.65 memory used=1081.5MB, alloc=492.3MB, time=9.92 memory used=1201.9MB, alloc=516.3MB, time=11.14 memory used=1306.0MB, alloc=516.3MB, time=12.20 memory used=1404.5MB, alloc=516.3MB, time=13.24 memory used=1517.9MB, alloc=516.3MB, time=14.51 memory used=1606.4MB, alloc=540.3MB, time=15.54 memory used=1686.2MB, alloc=540.3MB, time=16.46 memory used=1767.5MB, alloc=540.3MB, time=17.47 memory used=1837.1MB, alloc=540.3MB, time=18.36 memory used=1890.9MB, alloc=540.3MB, time=19.10 memory used=1951.4MB, alloc=564.3MB, time=19.94 memory used=2008.0MB, alloc=564.3MB, time=20.73 memory used=2061.0MB, alloc=564.3MB, time=21.49 memory used=2288.1MB, alloc=588.3MB, time=24.31 memory used=2515.7MB, alloc=612.3MB, time=27.26 memory used=2740.4MB, alloc=636.3MB, time=30.21 memory used=2967.3MB, alloc=660.3MB, time=33.28 memory used=3195.9MB, alloc=684.3MB, time=36.36 memory used=3429.2MB, alloc=708.3MB, time=39.53 memory used=3666.7MB, alloc=732.3MB, time=42.80 memory used=3912.0MB, alloc=756.3MB, time=46.13 memory used=4153.5MB, alloc=780.3MB, time=49.54 memory used=4394.8MB, alloc=804.3MB, time=52.98 memory used=4635.4MB, alloc=828.3MB, time=56.51 memory used=4879.8MB, alloc=852.3MB, time=60.14 memory used=5127.2MB, alloc=876.3MB, time=63.83 memory used=5353.2MB, alloc=900.3MB, time=68.40 memory used=5560.7MB, alloc=924.3MB, time=73.62 memory used=5773.2MB, alloc=948.3MB, time=79.29 memory used=5994.6MB, alloc=972.3MB, time=85.38 memory used=6226.7MB, alloc=996.3MB, time=91.90 memory used=6470.8MB, alloc=1020.3MB, time=98.74 memory used=6728.3MB, alloc=1044.3MB, time=106.01 memory used=6999.2MB, alloc=1068.3MB, time=113.72 memory used=7284.0MB, alloc=1092.3MB, time=121.89 memory used=7582.2MB, alloc=1116.3MB, time=130.43 memory used=7894.3MB, alloc=1140.3MB, time=139.28 memory used=8220.8MB, alloc=1164.3MB, time=148.58 memory used=8562.1MB, alloc=1188.3MB, time=158.47 memory used=8917.9MB, alloc=1212.3MB, time=168.72 memory used=9288.8MB, alloc=1236.3MB, time=179.39 memory used=9674.6MB, alloc=1260.3MB, time=190.59 memory used=10075.7MB, alloc=1284.3MB, time=202.24 memory used=10491.3MB, alloc=1308.3MB, time=214.58 memory used=10921.7MB, alloc=1332.3MB, time=227.39 memory used=11367.1MB, alloc=1356.3MB, time=240.65 memory used=11827.4MB, alloc=1380.3MB, time=254.37 memory used=12301.7MB, alloc=1404.3MB, time=268.23 memory used=12786.4MB, alloc=1428.3MB, time=282.95 memory used=13295.1MB, alloc=1452.3MB, time=298.24 memory used=13827.6MB, alloc=1476.3MB, time=314.13 |\^/| 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(); 1428353008 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 F := [-7 x y z - 9, 9 x z + 12 y , 5 x + 16 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 3 G := [14 x z + 20 x z , 20 x y - 3 x y , 16 x z - 18 x] > Problem := [F,G]; 2 2 3 4 Problem := [[-7 x y z - 9, 9 x z + 12 y , 5 x + 16 y z], 2 2 3 2 2 3 [14 x z + 20 x z , 20 x y - 3 x y , 16 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=0.15 memory used=27.0MB, alloc=32.3MB, time=0.42 memory used=48.0MB, alloc=32.3MB, time=0.65 memory used=69.1MB, alloc=56.3MB, time=0.90 memory used=112.0MB, alloc=60.3MB, time=1.36 memory used=151.3MB, alloc=84.3MB, time=1.84 memory used=210.0MB, alloc=92.3MB, time=2.53 memory used=270.0MB, alloc=116.3MB, time=3.21 memory used=352.2MB, alloc=116.3MB, time=4.14 memory used=426.3MB, alloc=396.3MB, time=5.03 memory used=532.2MB, alloc=420.3MB, time=6.21 memory used=662.8MB, alloc=444.3MB, time=7.62 memory used=806.0MB, alloc=468.3MB, time=9.39 memory used=951.9MB, alloc=492.3MB, time=11.12 memory used=1073.7MB, alloc=492.3MB, time=12.41 memory used=1190.3MB, alloc=516.3MB, time=13.80 memory used=1282.7MB, alloc=516.3MB, time=14.98 memory used=1383.6MB, alloc=516.3MB, time=16.38 memory used=1520.2MB, alloc=540.3MB, time=18.59 memory used=1676.3MB, alloc=564.3MB, time=21.32 memory used=1839.1MB, alloc=588.3MB, time=23.39 memory used=1999.7MB, alloc=612.3MB, time=25.45 memory used=2155.3MB, alloc=636.3MB, time=27.32 memory used=2312.1MB, alloc=660.3MB, time=29.26 memory used=2451.3MB, alloc=684.3MB, time=31.15 memory used=2585.7MB, alloc=708.3MB, time=33.01 memory used=2698.2MB, alloc=732.3MB, time=34.62 memory used=2816.9MB, alloc=756.3MB, time=36.34 memory used=2936.8MB, alloc=780.3MB, time=38.05 memory used=3034.2MB, alloc=804.3MB, time=39.80 memory used=3214.3MB, alloc=828.3MB, time=43.79 memory used=3541.9MB, alloc=852.3MB, time=51.30 memory used=3870.3MB, alloc=876.3MB, time=59.37 memory used=4204.4MB, alloc=900.3MB, time=67.66 memory used=4546.8MB, alloc=924.3MB, time=76.34 memory used=4895.3MB, alloc=948.3MB, time=85.72 memory used=5255.1MB, alloc=972.3MB, time=95.59 memory used=5638.7MB, alloc=996.3MB, time=106.10 memory used=6046.3MB, alloc=1020.3MB, time=117.26 memory used=6477.9MB, alloc=1044.3MB, time=129.03 memory used=6933.4MB, alloc=1068.3MB, time=141.41 memory used=7412.8MB, alloc=1092.3MB, time=154.54 memory used=7916.2MB, alloc=1092.3MB, time=168.21 memory used=8419.5MB, alloc=1092.3MB, time=181.80 memory used=8922.8MB, alloc=1116.3MB, time=195.41 memory used=9450.0MB, alloc=1116.3MB, time=209.70 memory used=9977.2MB, alloc=1116.3MB, time=224.00 memory used=10504.3MB, alloc=1116.3MB, time=238.25 memory used=11031.4MB, alloc=1140.3MB, time=252.40 memory used=11582.3MB, alloc=1140.3MB, time=267.23 memory used=12133.0MB, alloc=1140.3MB, time=281.95 memory used=12683.6MB, alloc=1164.3MB, time=296.61 |\^/| 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(); 1428353308 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 3 F := [17 y z + 14 y z , -13 x y + 12 x z, 3 x z - 13 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 G := [z + 9 y, 16 x z - 5 y, 20 y z - 14 x ] > Problem := [F,G]; 2 2 2 3 3 2 3 Problem := [[17 y z + 14 y z , -13 x y + 12 x z, 3 x z - 13 z ], 3 2 2 2 3 [z + 9 y, 16 x z - 5 y, 20 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=0.15 memory used=26.4MB, alloc=32.3MB, time=0.42 memory used=48.0MB, alloc=32.3MB, time=0.67 memory used=68.5MB, alloc=32.3MB, time=0.92 memory used=88.0MB, alloc=56.3MB, time=1.18 memory used=127.1MB, alloc=60.3MB, time=1.65 memory used=165.0MB, alloc=60.3MB, time=2.09 memory used=202.1MB, alloc=84.3MB, time=2.51 memory used=258.8MB, alloc=92.3MB, time=3.21 memory used=314.6MB, alloc=116.3MB, time=3.91 memory used=392.5MB, alloc=116.3MB, time=4.81 memory used=469.1MB, alloc=140.3MB, time=5.74 memory used=564.6MB, alloc=164.3MB, time=6.94 memory used=657.4MB, alloc=420.3MB, time=8.20 memory used=771.2MB, alloc=444.3MB, time=9.32 memory used=907.3MB, alloc=468.3MB, time=10.68 memory used=1067.3MB, alloc=492.3MB, time=12.47 memory used=1231.2MB, alloc=516.3MB, time=14.32 memory used=1410.1MB, alloc=540.3MB, time=16.32 memory used=1598.0MB, alloc=564.3MB, time=18.52 memory used=1793.2MB, alloc=588.3MB, time=20.95 memory used=1997.0MB, alloc=612.3MB, time=23.47 memory used=2209.4MB, alloc=636.3MB, time=26.14 memory used=2423.7MB, alloc=660.3MB, time=28.96 memory used=2613.2MB, alloc=684.3MB, time=32.77 memory used=2804.7MB, alloc=708.3MB, time=37.01 memory used=3005.6MB, alloc=732.3MB, time=41.75 memory used=3217.5MB, alloc=756.3MB, time=46.89 memory used=3441.0MB, alloc=780.3MB, time=52.34 memory used=3677.6MB, alloc=804.3MB, time=58.20 memory used=3927.2MB, alloc=828.3MB, time=64.55 memory used=4183.8MB, alloc=852.3MB, time=71.55 memory used=4464.3MB, alloc=876.3MB, time=79.18 memory used=4768.8MB, alloc=900.3MB, time=87.56 memory used=5097.2MB, alloc=924.3MB, time=96.41 memory used=5449.6MB, alloc=948.3MB, time=105.87 memory used=5825.9MB, alloc=972.3MB, time=115.95 memory used=6226.3MB, alloc=996.3MB, time=126.69 memory used=6650.5MB, alloc=1020.3MB, time=138.00 memory used=7098.6MB, alloc=1044.3MB, time=150.00 memory used=7570.7MB, alloc=1068.3MB, time=162.58 memory used=8066.7MB, alloc=1092.3MB, time=175.75 memory used=8586.7MB, alloc=1092.3MB, time=189.72 memory used=9106.5MB, alloc=1092.3MB, time=203.46 memory used=9626.4MB, alloc=1092.3MB, time=217.28 memory used=10146.2MB, alloc=1116.3MB, time=231.06 memory used=10690.0MB, alloc=1116.3MB, time=246.10 memory used=11233.8MB, alloc=1116.3MB, time=260.57 memory used=11777.5MB, alloc=1140.3MB, time=275.07 memory used=12345.2MB, alloc=1140.3MB, time=290.09 memory used=12912.7MB, alloc=1140.3MB, time=305.08 |\^/| 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(); 1428353608 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [17 y z + 16 x z, 3 x y - 18 y z, 12 x z - 10 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 G := [9 x z + 14 x z, -14 x z - 11 y z , 7 z + 10] > Problem := [F,G]; 3 2 3 2 Problem := [[17 y z + 16 x z, 3 x y - 18 y z, 12 x z - 10 z], 3 3 3 2 [9 x z + 14 x z, -14 x z - 11 y z , 7 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=0.14 memory used=26.4MB, alloc=32.3MB, time=0.41 memory used=47.6MB, alloc=32.3MB, time=0.66 memory used=68.3MB, alloc=32.3MB, time=0.90 memory used=87.3MB, alloc=56.3MB, time=1.11 memory used=129.2MB, alloc=60.3MB, time=1.67 memory used=168.8MB, alloc=84.3MB, time=2.23 memory used=229.8MB, alloc=84.3MB, time=3.08 memory used=285.4MB, alloc=108.3MB, time=3.89 memory used=355.3MB, alloc=132.3MB, time=5.49 memory used=440.3MB, alloc=132.3MB, time=7.70 N1 := 2257 > GB := Basis(F, plex(op(vars))); 5 3 3 2 3 3 GB := [6 x y - 5 x y, 425 x y + 20736 x y, 425 x y + 124416 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=526.5MB, alloc=140.3MB, time=9.03 memory used=622.2MB, alloc=164.3MB, time=10.37 N2 := 773 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 3 H := [17 y z + 16 x z, 3 x y - 18 y z, 12 x z - 10 z, 9 x z + 14 x z, 3 3 2 -14 x z - 11 y z , 7 z + 10] > J:=[op(GB),op(G)]; 5 3 3 2 3 3 J := [6 x y - 5 x y, 425 x y + 20736 x y, 425 y x + 124416 z, 3 3 3 2 9 x z + 14 x z, -14 x z - 11 y z , 7 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 := [6, 14, 21, 4, 3, 1, 3, 5/6, 1/2, 1, 1/2, 1/3, 5/6, 6, 13, 25, 6, 5, 2, 3, 5/6, 2/3, 2/3, 2/3, 1/2, 1/2, 1, -4, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=663.3MB, alloc=164.3MB, time=11.14 |\^/| 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(); 1428353620 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 4 F := [12 x y z + 2 z , -5 x y z, -2 x y - 17 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [-6 y z - 19 y, -13 x y + 11 z , -5 x y - 15 x y z] > Problem := [F,G]; 2 3 2 3 4 Problem := [[12 x y z + 2 z , -5 x y z, -2 x y - 17 y ], 2 2 2 3 2 [-6 y z - 19 y, -13 x y + 11 z , -5 x y - 15 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.6MB, alloc=32.3MB, time=0.42 memory used=48.0MB, alloc=32.3MB, time=0.66 memory used=68.1MB, alloc=56.3MB, time=0.90 memory used=111.3MB, alloc=60.3MB, time=1.49 memory used=151.0MB, alloc=84.3MB, time=2.06 memory used=211.0MB, alloc=84.3MB, time=2.93 memory used=265.7MB, alloc=108.3MB, time=3.72 memory used=337.5MB, alloc=140.3MB, time=4.81 memory used=421.1MB, alloc=164.3MB, time=6.56 memory used=513.9MB, alloc=188.3MB, time=9.07 memory used=625.3MB, alloc=188.3MB, time=11.50 memory used=736.7MB, alloc=212.3MB, time=13.84 memory used=872.1MB, alloc=212.3MB, time=16.53 N1 := 4469 > GB := Basis(F, plex(op(vars))); 3 4 2 3 GB := [2 x y + 17 y , x y z, z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1010.1MB, alloc=212.3MB, time=18.71 N2 := 719 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 3 4 2 2 H := [12 x y z + 2 z , -5 x y z, -2 x y - 17 y , -6 y z - 19 y, 2 3 2 -13 x y + 11 z , -5 x y - 15 x y z] > J:=[op(GB),op(G)]; 3 4 2 3 2 2 2 J := [2 x y + 17 y , x y z, z , -6 y z - 19 y, -13 x y + 11 z , 3 2 -5 x y - 15 x 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 := [6, 16, 22, 4, 3, 4, 3, 5/6, 1, 5/6, 3/7, 9/14, 3/7, 6, 14, 21, 4, 3, 4, 3, 2/3, 5/6, 5/6, 5/13, 8/13, 5/13, 2, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1081.7MB, alloc=212.3MB, time=19.49 |\^/| 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(); 1428353640 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [15 y z - 8 x, -11 x y z + 11, -5 y z + 12] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [10 x y - 10 x z , 16 y z - 14 x y, -9 x z - 9 x y] > Problem := [F,G]; 2 2 Problem := [[15 y z - 8 x, -11 x y z + 11, -5 y z + 12], 2 2 2 2 3 2 [10 x y - 10 x z , 16 y z - 14 x y, -9 x z - 9 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.12 memory used=26.0MB, alloc=32.3MB, time=0.32 memory used=46.8MB, alloc=32.3MB, time=0.54 memory used=66.3MB, alloc=56.3MB, time=0.72 memory used=105.9MB, alloc=60.3MB, time=1.06 memory used=142.8MB, alloc=84.3MB, time=1.39 memory used=200.8MB, alloc=92.3MB, time=1.92 memory used=259.9MB, alloc=92.3MB, time=2.42 memory used=315.2MB, alloc=116.3MB, time=2.93 memory used=391.8MB, alloc=116.3MB, time=3.62 memory used=465.7MB, alloc=140.3MB, time=4.31 memory used=557.8MB, alloc=164.3MB, time=5.17 memory used=663.1MB, alloc=164.3MB, time=6.17 memory used=738.2MB, alloc=444.3MB, time=6.90 memory used=874.1MB, alloc=468.3MB, time=8.19 memory used=1040.6MB, alloc=492.3MB, time=9.66 memory used=1218.6MB, alloc=516.3MB, time=11.37 memory used=1412.5MB, alloc=540.3MB, time=13.28 memory used=1634.6MB, alloc=564.3MB, time=15.48 memory used=1861.2MB, alloc=588.3MB, time=17.85 memory used=2120.0MB, alloc=612.3MB, time=20.65 memory used=2395.6MB, alloc=636.3MB, time=23.74 memory used=2650.6MB, alloc=660.3MB, time=26.66 memory used=2838.2MB, alloc=684.3MB, time=28.89 memory used=3065.9MB, alloc=708.3MB, time=31.70 memory used=3260.3MB, alloc=732.3MB, time=34.28 memory used=3418.5MB, alloc=756.3MB, time=36.43 memory used=3645.9MB, alloc=780.3MB, time=39.66 memory used=3834.8MB, alloc=804.3MB, time=42.40 memory used=3975.2MB, alloc=804.3MB, time=44.45 memory used=4167.5MB, alloc=804.3MB, time=47.40 memory used=4308.1MB, alloc=828.3MB, time=49.68 memory used=4433.8MB, alloc=828.3MB, time=51.87 memory used=4877.5MB, alloc=852.3MB, time=57.01 memory used=5306.1MB, alloc=876.3MB, time=62.71 memory used=5727.7MB, alloc=900.3MB, time=68.38 memory used=6145.3MB, alloc=924.3MB, time=74.36 memory used=6518.8MB, alloc=948.3MB, time=79.97 memory used=6886.5MB, alloc=972.3MB, time=85.61 memory used=7247.8MB, alloc=996.3MB, time=91.24 memory used=7606.9MB, alloc=1020.3MB, time=96.86 memory used=7970.5MB, alloc=1044.3MB, time=102.53 memory used=8321.4MB, alloc=1068.3MB, time=108.22 memory used=8669.8MB, alloc=1092.3MB, time=113.91 memory used=9016.7MB, alloc=1116.3MB, time=119.71 memory used=9362.5MB, alloc=1140.3MB, time=125.48 memory used=9718.7MB, alloc=1164.3MB, time=131.30 memory used=10038.5MB, alloc=1188.3MB, time=139.13 memory used=10324.1MB, alloc=1212.3MB, time=147.68 memory used=10612.0MB, alloc=1236.3MB, time=156.63 memory used=10906.9MB, alloc=1260.3MB, time=165.86 memory used=11211.4MB, alloc=1284.3MB, time=175.60 memory used=11527.4MB, alloc=1308.3MB, time=185.86 memory used=11855.5MB, alloc=1332.3MB, time=196.53 memory used=12196.8MB, alloc=1356.3MB, time=207.64 memory used=12551.4MB, alloc=1380.3MB, time=219.13 memory used=12919.4MB, alloc=1404.3MB, time=231.01 memory used=13301.3MB, alloc=1428.3MB, time=243.39 memory used=13697.5MB, alloc=1452.3MB, time=256.37 memory used=14108.6MB, alloc=1476.3MB, time=269.69 memory used=14534.5MB, alloc=1500.3MB, time=283.64 memory used=14974.6MB, alloc=1524.3MB, time=298.08 memory used=15429.5MB, alloc=1548.3MB, time=313.16 |\^/| 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(); 1428353940 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 F := [-17 y z - 6 x y , -8 x y z + 15, -8 + 10 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 4 2 G := [6 y z + 15 x, -5 x y z - 20 x z , -5 y - 13 y ] > Problem := [F,G]; 3 2 Problem := [[-17 y z - 6 x y , -8 x y z + 15, -8 + 10 z], 2 2 2 2 4 2 [6 y z + 15 x, -5 x y z - 20 x z , -5 y - 13 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.2MB, alloc=32.3MB, time=0.38 memory used=47.8MB, alloc=32.3MB, time=0.61 memory used=68.4MB, alloc=32.3MB, time=0.87 memory used=87.8MB, alloc=56.3MB, time=1.11 memory used=125.5MB, alloc=60.3MB, time=1.57 memory used=162.3MB, alloc=60.3MB, time=1.98 memory used=198.4MB, alloc=84.3MB, time=2.44 memory used=257.1MB, alloc=92.3MB, time=3.16 memory used=311.4MB, alloc=116.3MB, time=3.80 memory used=387.1MB, alloc=116.3MB, time=4.72 memory used=460.8MB, alloc=140.3MB, time=5.62 memory used=556.3MB, alloc=164.3MB, time=6.89 memory used=670.0MB, alloc=188.3MB, time=8.71 memory used=773.7MB, alloc=468.3MB, time=10.14 memory used=916.1MB, alloc=492.3MB, time=11.72 memory used=1070.9MB, alloc=516.3MB, time=13.45 memory used=1228.4MB, alloc=540.3MB, time=15.92 memory used=1381.5MB, alloc=564.3MB, time=18.99 memory used=1541.3MB, alloc=588.3MB, time=22.75 memory used=1714.3MB, alloc=612.3MB, time=27.19 memory used=1911.2MB, alloc=636.3MB, time=32.16 memory used=2132.0MB, alloc=660.3MB, time=37.74 memory used=2376.8MB, alloc=684.3MB, time=43.82 memory used=2645.5MB, alloc=684.3MB, time=50.53 memory used=2914.2MB, alloc=684.3MB, time=57.11 memory used=3182.9MB, alloc=708.3MB, time=63.72 memory used=3475.5MB, alloc=708.3MB, time=70.89 memory used=3768.2MB, alloc=732.3MB, time=77.83 memory used=4085.0MB, alloc=756.3MB, time=84.36 N1 := 9875 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 181 #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)]; 3 2 2 2 H := [-17 y z - 6 x y , -8 x y z + 15, -8 + 10 z, 6 y z + 15 x, 2 2 4 2 -5 x y z - 20 x z , -5 y - 13 y ] > J:=[op(GB),op(G)]; 2 2 2 2 4 2 J := [1, 6 y z + 15 x, -5 x y z - 20 x z , -5 y - 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 := [6, 14, 20, 4, 2, 4, 3, 2/3, 5/6, 5/6, 5/12, 7/12, 1/2, 4, 7, 12, 4, 2, 4, 2, 1/2, 3/4, 1/2, 3/7, 4/7, 3/7, 7, 8, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=4126.4MB, alloc=756.3MB, time=84.88 |\^/| 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(); 1428354024 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 3 3 F := [20 x y - 12 x y z, 14 x z - 20 x z , 11 x z + 14 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [2 x + 5 x z , -2 x + 17 z, -6 x y + 20 z ] > Problem := [F,G]; 3 2 2 2 3 3 3 Problem := [[20 x y - 12 x y z, 14 x z - 20 x z , 11 x z + 14 y ], 3 2 3 2 [2 x + 5 x z , -2 x + 17 z, -6 x y + 20 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.9MB, alloc=32.3MB, time=0.37 memory used=48.4MB, alloc=32.3MB, time=0.56 memory used=68.3MB, alloc=60.3MB, time=0.74 memory used=110.2MB, alloc=60.3MB, time=1.10 memory used=150.7MB, alloc=84.3MB, time=1.45 memory used=212.7MB, alloc=92.3MB, time=2.03 memory used=270.9MB, alloc=116.3MB, time=2.56 memory used=351.3MB, alloc=116.3MB, time=3.29 memory used=426.8MB, alloc=396.3MB, time=4.06 memory used=525.4MB, alloc=420.3MB, time=5.03 memory used=643.6MB, alloc=444.3MB, time=6.33 memory used=777.0MB, alloc=468.3MB, time=7.79 memory used=924.7MB, alloc=492.3MB, time=9.42 memory used=1075.9MB, alloc=516.3MB, time=11.57 memory used=1218.3MB, alloc=540.3MB, time=14.38 memory used=1364.5MB, alloc=564.3MB, time=17.91 memory used=1534.6MB, alloc=588.3MB, time=21.99 memory used=1728.7MB, alloc=612.3MB, time=26.68 memory used=1946.7MB, alloc=636.3MB, time=31.77 memory used=2188.7MB, alloc=636.3MB, time=37.31 memory used=2430.7MB, alloc=660.3MB, time=42.62 N1 := 7283 > GB := Basis(F, plex(op(vars))); 5 3 3 4 4 3 2 3 3 GB := [x y, x y , 55 x y + 36 y , -5 x y + 3 x y z, -7 x y + 10 y z, 2 2 3 3 3 11 x z + 20 y , 11 z x + 14 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2708.5MB, alloc=660.3MB, time=47.19 memory used=2859.8MB, alloc=660.3MB, time=48.90 memory used=2991.5MB, alloc=660.3MB, time=50.40 memory used=3094.9MB, alloc=660.3MB, time=51.59 memory used=3186.8MB, alloc=660.3MB, time=52.63 memory used=3273.9MB, alloc=660.3MB, time=53.77 memory used=3343.7MB, alloc=660.3MB, time=54.74 memory used=3410.6MB, alloc=684.3MB, time=55.70 memory used=3467.0MB, alloc=684.3MB, time=56.64 memory used=3527.5MB, alloc=684.3MB, time=57.57 memory used=3578.5MB, alloc=684.3MB, time=58.44 memory used=3631.4MB, alloc=684.3MB, time=59.30 memory used=3677.9MB, alloc=684.3MB, time=60.18 memory used=3879.3MB, alloc=708.3MB, time=62.38 memory used=4082.1MB, alloc=732.3MB, time=64.67 memory used=4297.1MB, alloc=756.3MB, time=67.14 memory used=4460.6MB, alloc=780.3MB, time=69.15 memory used=4625.1MB, alloc=804.3MB, time=71.23 memory used=4772.1MB, alloc=828.3MB, time=73.26 memory used=4937.5MB, alloc=828.3MB, time=75.78 memory used=5197.3MB, alloc=852.3MB, time=79.67 memory used=5430.4MB, alloc=876.3MB, time=83.26 memory used=5685.8MB, alloc=900.3MB, time=87.20 memory used=5956.5MB, alloc=924.3MB, time=91.38 memory used=6191.5MB, alloc=948.3MB, time=95.10 memory used=6637.4MB, alloc=972.3MB, time=103.03 memory used=7019.3MB, alloc=996.3MB, time=112.73 memory used=7393.4MB, alloc=1020.3MB, time=122.96 memory used=7772.2MB, alloc=1044.3MB, time=133.25 memory used=8149.6MB, alloc=1068.3MB, time=144.19 memory used=8548.6MB, alloc=1092.3MB, time=155.90 memory used=8971.6MB, alloc=1116.3MB, time=168.10 memory used=9418.5MB, alloc=1140.3MB, time=180.97 memory used=9889.4MB, alloc=1164.3MB, time=194.47 memory used=10384.2MB, alloc=1188.3MB, time=208.61 memory used=10902.8MB, alloc=1212.3MB, time=223.46 memory used=11445.5MB, alloc=1236.3MB, time=238.79 memory used=12012.0MB, alloc=1260.3MB, time=254.74 memory used=12602.5MB, alloc=1284.3MB, time=271.31 memory used=13216.9MB, alloc=1308.3MB, time=288.69 memory used=13855.2MB, alloc=1332.3MB, time=306.55 |\^/| 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(); 1428354324 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 4 4 F := [-17 x y z - 3 x z, -4 x y z - 19 z , -13 x + 11 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 2 2 G := [2 x y z + 2 y z , -20 x z - y z , -13 y z - 2 x ] > Problem := [F,G]; 2 2 2 3 4 4 Problem := [[-17 x y z - 3 x z, -4 x y z - 19 z , -13 x + 11 z ], 2 3 3 2 2 2 2 [2 x y z + 2 y z , -20 x z - y z , -13 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=0.15 memory used=26.3MB, alloc=32.3MB, time=0.41 memory used=47.8MB, alloc=32.3MB, time=0.65 memory used=68.0MB, alloc=56.3MB, time=0.90 memory used=108.8MB, alloc=60.3MB, time=1.39 memory used=146.9MB, alloc=60.3MB, time=1.83 memory used=183.2MB, alloc=84.3MB, time=2.26 memory used=232.2MB, alloc=84.3MB, time=2.84 memory used=288.4MB, alloc=116.3MB, time=3.51 memory used=365.7MB, alloc=116.3MB, time=4.43 memory used=440.4MB, alloc=140.3MB, time=5.35 memory used=533.5MB, alloc=420.3MB, time=6.51 memory used=655.3MB, alloc=444.3MB, time=8.07 memory used=791.2MB, alloc=468.3MB, time=10.03 memory used=937.0MB, alloc=492.3MB, time=12.04 memory used=1094.7MB, alloc=516.3MB, time=14.28 memory used=1264.5MB, alloc=540.3MB, time=16.76 memory used=1446.2MB, alloc=564.3MB, time=19.16 memory used=1639.7MB, alloc=588.3MB, time=21.34 memory used=1844.0MB, alloc=612.3MB, time=23.65 memory used=2065.0MB, alloc=636.3MB, time=26.17 memory used=2305.2MB, alloc=660.3MB, time=28.62 memory used=2541.1MB, alloc=684.3MB, time=31.38 memory used=2778.5MB, alloc=708.3MB, time=34.27 memory used=3018.8MB, alloc=732.3MB, time=37.35 memory used=3240.6MB, alloc=756.3MB, time=41.44 memory used=3452.7MB, alloc=780.3MB, time=46.10 memory used=3672.3MB, alloc=804.3MB, time=51.26 memory used=3902.5MB, alloc=828.3MB, time=56.87 memory used=4144.0MB, alloc=852.3MB, time=62.76 memory used=4398.4MB, alloc=876.3MB, time=69.06 memory used=4665.7MB, alloc=900.3MB, time=75.82 memory used=4946.6MB, alloc=924.3MB, time=82.99 memory used=5241.6MB, alloc=948.3MB, time=90.75 memory used=5551.3MB, alloc=972.3MB, time=98.78 memory used=5874.8MB, alloc=996.3MB, time=107.14 memory used=6213.4MB, alloc=1020.3MB, time=115.94 memory used=6566.5MB, alloc=1044.3MB, time=125.22 memory used=6928.8MB, alloc=1068.3MB, time=135.16 memory used=7314.7MB, alloc=1092.3MB, time=145.68 memory used=7724.5MB, alloc=1116.3MB, time=156.95 memory used=8158.3MB, alloc=1140.3MB, time=168.73 memory used=8616.0MB, alloc=1164.3MB, time=181.16 memory used=9097.7MB, alloc=1188.3MB, time=194.19 memory used=9603.3MB, alloc=1212.3MB, time=207.82 memory used=10132.9MB, alloc=1236.3MB, time=222.29 memory used=10686.4MB, alloc=1260.3MB, time=237.43 memory used=11263.9MB, alloc=1284.3MB, time=253.04 memory used=11865.2MB, alloc=1308.3MB, time=269.18 memory used=12490.5MB, alloc=1332.3MB, time=286.06 memory used=13139.8MB, alloc=1356.3MB, time=303.36 |\^/| 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(); 1428354624 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 F := [10 x - 18 y z , y z + 9 x z , 13 x y z + 19 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 G := [-16 x + 3 x y , 19 x z - 5 x z, -20 y z + 3 y ] > Problem := [F,G]; 4 2 2 3 2 Problem := [[10 x - 18 y z , y z + 9 x z , 13 x y z + 19 x z], 3 2 2 2 2 2 2 [-16 x + 3 x y , 19 x z - 5 x z, -20 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=0.15 memory used=26.3MB, alloc=32.3MB, time=0.40 memory used=48.0MB, alloc=32.3MB, time=0.64 memory used=68.0MB, alloc=32.3MB, time=0.87 memory used=86.6MB, alloc=56.3MB, time=1.11 memory used=126.3MB, alloc=60.3MB, time=1.58 memory used=166.0MB, alloc=60.3MB, time=2.06 memory used=202.1MB, alloc=84.3MB, time=2.52 memory used=259.7MB, alloc=92.3MB, time=3.24 memory used=314.3MB, alloc=116.3MB, time=3.91 memory used=396.0MB, alloc=140.3MB, time=4.98 memory used=492.5MB, alloc=164.3MB, time=6.42 memory used=602.7MB, alloc=188.3MB, time=8.01 memory used=726.2MB, alloc=212.3MB, time=9.82 memory used=846.8MB, alloc=492.3MB, time=11.63 memory used=998.2MB, alloc=516.3MB, time=13.80 memory used=1158.0MB, alloc=540.3MB, time=16.20 memory used=1327.4MB, alloc=564.3MB, time=18.78 memory used=1497.8MB, alloc=588.3MB, time=21.73 memory used=1658.6MB, alloc=612.3MB, time=25.13 memory used=1828.9MB, alloc=636.3MB, time=28.91 memory used=2011.1MB, alloc=660.3MB, time=33.17 memory used=2207.4MB, alloc=684.3MB, time=37.88 memory used=2418.2MB, alloc=708.3MB, time=43.02 memory used=2642.4MB, alloc=732.3MB, time=48.64 memory used=2880.4MB, alloc=756.3MB, time=54.87 memory used=3142.3MB, alloc=780.3MB, time=61.83 memory used=3428.2MB, alloc=804.3MB, time=69.25 memory used=3738.0MB, alloc=828.3MB, time=77.26 memory used=4071.8MB, alloc=852.3MB, time=85.99 memory used=4429.4MB, alloc=876.3MB, time=95.21 memory used=4811.1MB, alloc=876.3MB, time=105.09 memory used=5192.6MB, alloc=876.3MB, time=115.00 memory used=5574.2MB, alloc=876.3MB, time=124.93 memory used=5955.7MB, alloc=900.3MB, time=135.05 memory used=6361.2MB, alloc=900.3MB, time=145.53 memory used=6766.6MB, alloc=900.3MB, time=156.08 memory used=7172.1MB, alloc=900.3MB, time=166.57 memory used=7577.5MB, alloc=924.3MB, time=176.98 memory used=8006.9MB, alloc=924.3MB, time=187.99 memory used=8436.1MB, alloc=924.3MB, time=198.94 memory used=8865.3MB, alloc=948.3MB, time=209.99 memory used=9318.3MB, alloc=948.3MB, time=221.46 memory used=9771.3MB, alloc=972.3MB, time=232.92 memory used=10248.2MB, alloc=972.3MB, time=244.94 memory used=10725.1MB, alloc=996.3MB, time=256.90 memory used=11225.8MB, alloc=996.3MB, time=269.49 memory used=11726.9MB, alloc=1020.3MB, time=281.73 memory used=12252.1MB, alloc=1044.3MB, time=293.79 N1 := 19091 > GB := Basis(F, plex(op(vars))); 11 5 10 4 GB := [36707882445 x - 16983563041 x , 2823683265 x + 893871739 x y, 6 5 3 4 2 2 -1856465 x + 2476099 x z, 845 x + 361 y z, -5 x + 9 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=12802.9MB, alloc=1044.3MB, time=300.62 |\^/| 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(); 1428354924 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 F := [-16 y z + 2 x , -5 y - 16 z , 8 y z + x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 G := [-2 z + 20, 19 x z - 2 x z , 4 y z - 18 y ] > Problem := [F,G]; 3 2 3 2 2 Problem := [[-16 y z + 2 x , -5 y - 16 z , 8 y z + x], 4 2 2 3 2 [-2 z + 20, 19 x z - 2 x z , 4 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=0.15 memory used=26.9MB, alloc=32.3MB, time=0.43 memory used=48.4MB, alloc=32.3MB, time=0.66 memory used=68.0MB, alloc=56.3MB, time=0.91 memory used=109.2MB, alloc=60.3MB, time=1.38 memory used=148.3MB, alloc=60.3MB, time=1.83 memory used=184.3MB, alloc=84.3MB, time=2.24 memory used=223.7MB, alloc=84.3MB, time=2.65 memory used=289.2MB, alloc=116.3MB, time=3.37 memory used=361.3MB, alloc=372.3MB, time=4.17 memory used=449.2MB, alloc=396.3MB, time=5.04 memory used=563.2MB, alloc=420.3MB, time=5.97 memory used=696.8MB, alloc=444.3MB, time=6.97 memory used=835.3MB, alloc=468.3MB, time=8.27 memory used=951.5MB, alloc=468.3MB, time=9.27 memory used=1066.8MB, alloc=492.3MB, time=10.30 memory used=1186.1MB, alloc=492.3MB, time=11.31 memory used=1294.6MB, alloc=516.3MB, time=12.30 memory used=1380.6MB, alloc=516.3MB, time=13.21 memory used=1450.3MB, alloc=516.3MB, time=13.91 memory used=1553.3MB, alloc=516.3MB, time=15.01 memory used=1639.0MB, alloc=516.3MB, time=15.91 memory used=1736.0MB, alloc=540.3MB, time=16.62 memory used=1833.7MB, alloc=540.3MB, time=17.45 memory used=1901.5MB, alloc=540.3MB, time=18.14 memory used=1992.6MB, alloc=564.3MB, time=19.19 memory used=2060.8MB, alloc=564.3MB, time=20.14 memory used=2105.9MB, alloc=564.3MB, time=20.80 memory used=2158.6MB, alloc=564.3MB, time=21.52 memory used=2205.4MB, alloc=564.3MB, time=22.28 memory used=2438.8MB, alloc=588.3MB, time=24.67 memory used=2653.0MB, alloc=612.3MB, time=26.63 memory used=2830.8MB, alloc=636.3MB, time=28.39 memory used=2988.6MB, alloc=660.3MB, time=30.09 memory used=3152.9MB, alloc=684.3MB, time=32.06 memory used=3285.6MB, alloc=684.3MB, time=33.64 memory used=3427.2MB, alloc=708.3MB, time=35.24 memory used=3567.4MB, alloc=708.3MB, time=36.88 memory used=3708.3MB, alloc=708.3MB, time=38.66 memory used=3827.8MB, alloc=732.3MB, time=40.08 memory used=3937.7MB, alloc=732.3MB, time=41.59 memory used=4307.1MB, alloc=756.3MB, time=46.19 memory used=4656.1MB, alloc=780.3MB, time=50.41 memory used=5055.1MB, alloc=804.3MB, time=54.56 memory used=5442.3MB, alloc=828.3MB, time=58.60 memory used=5854.9MB, alloc=852.3MB, time=62.93 memory used=6242.3MB, alloc=876.3MB, time=67.43 memory used=6677.8MB, alloc=900.3MB, time=71.39 memory used=7029.5MB, alloc=924.3MB, time=75.35 memory used=7300.8MB, alloc=948.3MB, time=79.43 memory used=7531.9MB, alloc=972.3MB, time=82.56 memory used=7806.0MB, alloc=996.3MB, time=86.90 memory used=8063.1MB, alloc=1020.3MB, time=90.73 memory used=8434.9MB, alloc=1044.3MB, time=97.69 memory used=8981.2MB, alloc=1068.3MB, time=105.55 memory used=9599.0MB, alloc=1092.3MB, time=110.99 memory used=10216.0MB, alloc=1116.3MB, time=118.36 memory used=10772.9MB, alloc=1140.3MB, time=126.55 memory used=11349.9MB, alloc=1164.3MB, time=134.75 memory used=11969.2MB, alloc=1188.3MB, time=143.53 memory used=12595.3MB, alloc=1212.3MB, time=151.91 memory used=13229.4MB, alloc=1236.3MB, time=160.37 memory used=13790.8MB, alloc=1260.3MB, time=168.21 memory used=14420.9MB, alloc=1284.3MB, time=176.87 memory used=14996.9MB, alloc=1308.3MB, time=185.69 memory used=15529.9MB, alloc=1332.3MB, time=194.62 memory used=16043.7MB, alloc=1356.3MB, time=203.70 memory used=16542.7MB, alloc=1380.3MB, time=212.88 memory used=17027.1MB, alloc=1404.3MB, time=222.06 memory used=17488.2MB, alloc=1428.3MB, time=231.22 memory used=17961.8MB, alloc=1452.3MB, time=240.46 memory used=18491.7MB, alloc=1476.3MB, time=249.48 memory used=19057.6MB, alloc=1500.3MB, time=258.49 memory used=19767.0MB, alloc=1524.3MB, time=266.64 memory used=20477.3MB, alloc=1548.3MB, time=275.81 memory used=21164.6MB, alloc=1572.3MB, time=286.30 memory used=21778.9MB, alloc=1596.3MB, time=298.64 memory used=22319.9MB, alloc=1620.3MB, time=309.64 memory used=22817.8MB, alloc=1644.3MB, time=320.32 memory used=23315.2MB, alloc=1668.3MB, time=330.90 |\^/| 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(); 1428355224 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [14 x + 16 y, -10 x , 17 x z + 8 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 3 G := [-x y z - 5 x z, 10 y z - 14 x z , -4 x z + 13 x ] > Problem := [F,G]; 2 2 2 2 Problem := [[14 x + 16 y, -10 x , 17 x z + 8 y ], 2 3 2 3 3 [-x y z - 5 x z, 10 y z - 14 x z , -4 x z + 13 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.2MB, alloc=40.3MB, time=0.55 memory used=61.1MB, alloc=44.3MB, time=0.92 memory used=89.0MB, alloc=44.3MB, time=1.23 memory used=116.5MB, alloc=68.3MB, time=1.55 memory used=167.5MB, alloc=68.3MB, time=2.26 memory used=213.1MB, alloc=92.3MB, time=2.94 memory used=273.1MB, alloc=116.3MB, time=3.69 memory used=346.1MB, alloc=140.3MB, time=4.99 N1 := 1653 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x , y, z x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 71 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 3 2 H := [14 x + 16 y, -10 x , 17 z x + 8 y , -x y z - 5 x z, 10 y z - 14 x z , 3 3 -4 x z + 13 x ] > J:=[op(GB),op(G)]; 2 2 2 3 2 3 3 J := [x , y, z x, -x y z - 5 x z, 10 y z - 14 x z , -4 x 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 := [6, 14, 19, 4, 3, 3, 3, 1, 2/3, 2/3, 2/3, 1/3, 1/2, 6, 12, 18, 4, 3, 3, 3, 5/6, 1/2, 2/3, 7/11, 3/11, 6/11, 2, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=370.2MB, alloc=140.3MB, 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(); 1428355230 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 3 F := [12 y z - 19 x z , -15 x y - 10 y z , 5 y z + 14 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 2 2 G := [-16 y z , 14 z - 2 z , -5 x z - 4 z ] > Problem := [F,G]; 3 2 2 2 2 2 3 Problem := [[12 y z - 19 x z , -15 x y - 10 y z , 5 y z + 14 z ], 3 4 3 2 2 [-16 y z , 14 z - 2 z , -5 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=0.14 memory used=26.8MB, alloc=32.3MB, time=0.37 memory used=48.1MB, alloc=32.3MB, time=0.58 memory used=68.3MB, alloc=56.3MB, time=0.79 memory used=108.9MB, alloc=60.3MB, time=1.18 memory used=147.9MB, alloc=84.3MB, time=1.53 memory used=210.2MB, alloc=92.3MB, time=2.08 memory used=273.0MB, alloc=116.3MB, time=2.63 memory used=355.4MB, alloc=116.3MB, time=3.36 memory used=427.2MB, alloc=396.3MB, time=4.03 memory used=528.1MB, alloc=420.3MB, time=4.96 memory used=651.9MB, alloc=444.3MB, time=6.16 memory used=784.1MB, alloc=468.3MB, time=7.66 memory used=920.3MB, alloc=492.3MB, time=9.93 memory used=1050.6MB, alloc=516.3MB, time=12.71 N1 := 3221 > GB := Basis(F, plex(op(vars))); 9 2 3 2 5 2 3 3 GB := [392073696 x y + 1128125 x y , -21 x y + 5 x y , 6 2 2 4 6 2 2 -441 x y + 25 x y , -111132 x y + 2375 x y z, 7 2 3 7 2 2 -2333772 x y + 11875 y z, -28005264 x y + 225625 x z , 2 2 2 2 3 3 x y + 2 y z , 5 y z + 14 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1211.5MB, alloc=516.3MB, time=15.21 memory used=1402.4MB, alloc=516.3MB, time=16.98 memory used=1583.4MB, alloc=540.3MB, time=18.77 memory used=1754.3MB, alloc=540.3MB, time=20.61 memory used=1905.9MB, alloc=564.3MB, time=22.21 memory used=2060.9MB, alloc=588.3MB, time=23.84 memory used=2194.9MB, alloc=588.3MB, time=25.31 memory used=2306.8MB, alloc=588.3MB, time=26.59 memory used=2407.4MB, alloc=612.3MB, time=27.77 memory used=2517.5MB, alloc=612.3MB, time=29.15 memory used=2626.2MB, alloc=612.3MB, time=30.50 memory used=2706.8MB, alloc=636.3MB, time=31.58 memory used=2789.4MB, alloc=636.3MB, time=32.72 memory used=2875.9MB, alloc=636.3MB, time=33.93 memory used=2960.1MB, alloc=636.3MB, time=35.16 memory used=3025.8MB, alloc=636.3MB, time=36.17 memory used=3085.1MB, alloc=636.3MB, time=37.05 memory used=3148.8MB, alloc=636.3MB, time=38.14 memory used=3399.8MB, alloc=660.3MB, time=40.86 memory used=3622.6MB, alloc=684.3MB, time=43.23 memory used=3858.1MB, alloc=708.3MB, time=45.83 memory used=4034.3MB, alloc=732.3MB, time=47.89 memory used=4235.4MB, alloc=756.3MB, time=50.16 memory used=4419.2MB, alloc=756.3MB, time=52.43 memory used=4586.4MB, alloc=780.3MB, time=54.51 memory used=4741.0MB, alloc=780.3MB, time=56.57 memory used=4872.2MB, alloc=780.3MB, time=58.41 memory used=5009.5MB, alloc=780.3MB, time=60.35 memory used=5133.9MB, alloc=780.3MB, time=62.31 memory used=5531.5MB, alloc=804.3MB, time=66.68 memory used=5948.9MB, alloc=828.3MB, time=71.20 memory used=6384.2MB, alloc=852.3MB, time=75.86 memory used=6763.0MB, alloc=876.3MB, time=80.11 memory used=7073.0MB, alloc=900.3MB, time=83.78 memory used=7371.5MB, alloc=924.3MB, time=87.51 memory used=7772.5MB, alloc=948.3MB, time=93.59 memory used=8153.6MB, alloc=972.3MB, time=99.55 memory used=8532.5MB, alloc=996.3MB, time=105.46 memory used=8895.1MB, alloc=1020.3MB, time=111.31 memory used=9238.7MB, alloc=1044.3MB, time=117.88 memory used=9520.7MB, alloc=1068.3MB, time=125.86 memory used=9797.1MB, alloc=1092.3MB, time=134.26 memory used=10077.6MB, alloc=1116.3MB, time=142.91 memory used=10365.9MB, alloc=1140.3MB, time=152.53 memory used=10664.2MB, alloc=1164.3MB, time=164.05 memory used=10974.6MB, alloc=1188.3MB, time=174.27 memory used=11296.8MB, alloc=1212.3MB, time=185.81 memory used=11623.4MB, alloc=1236.3MB, time=199.52 memory used=11974.1MB, alloc=1260.3MB, time=214.30 memory used=12348.7MB, alloc=1284.3MB, time=228.56 memory used=12747.2MB, alloc=1308.3MB, time=245.56 memory used=13169.7MB, alloc=1332.3MB, time=264.56 memory used=13616.0MB, alloc=1356.3MB, time=283.70 memory used=14086.3MB, alloc=1380.3MB, time=303.56 |\^/| 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(); 1428355530 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [-20 x y + 5 y , 16 x y + 17 x y z, 6 x y - 11 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [-8 x y z - 5 x y, 18 y z + 4 x z, -15 x z - 18 x y] > Problem := [F,G]; 2 2 2 3 Problem := [[-20 x y + 5 y , 16 x y + 17 x y z, 6 x y - 11 x y], 2 3 2 2 [-8 x y z - 5 x y, 18 y z + 4 x z, -15 x z - 18 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=47.4MB, alloc=32.3MB, time=0.82 memory used=68.0MB, alloc=32.3MB, time=1.15 memory used=87.6MB, alloc=56.3MB, time=1.41 memory used=126.5MB, alloc=60.3MB, time=1.93 memory used=163.0MB, alloc=84.3MB, time=2.44 memory used=216.4MB, alloc=108.3MB, time=3.27 memory used=292.7MB, alloc=116.3MB, time=4.51 memory used=362.2MB, alloc=140.3MB, time=5.85 memory used=449.7MB, alloc=164.3MB, time=7.28 memory used=553.0MB, alloc=188.3MB, time=8.91 memory used=671.0MB, alloc=212.3MB, time=11.11 memory used=795.2MB, alloc=236.3MB, time=14.55 memory used=928.3MB, alloc=260.3MB, time=17.96 memory used=1071.2MB, alloc=284.3MB, time=22.29 memory used=1235.9MB, alloc=308.3MB, time=27.19 memory used=1424.6MB, alloc=308.3MB, time=32.80 memory used=1613.2MB, alloc=308.3MB, time=39.00 memory used=1801.9MB, alloc=332.3MB, time=45.67 memory used=2014.5MB, alloc=332.3MB, time=52.88 memory used=2227.1MB, alloc=356.3MB, time=59.19 memory used=2463.6MB, alloc=380.3MB, time=66.18 N1 := 7769 > GB := Basis(F, plex(op(vars))); 5 2 2 3 GB := [96 x y - 11 x y, -4 x y + y , 64 x y + 17 x y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2639.2MB, alloc=380.3MB, time=69.82 memory used=2933.9MB, alloc=660.3MB, time=74.35 memory used=3221.6MB, alloc=684.3MB, time=83.26 N2 := 3743 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 H := [-20 x y + 5 y , 16 x y + 17 x y z, 6 x y - 11 x y, -8 x y z - 5 x y, 3 2 2 18 y z + 4 x z, -15 x z - 18 x y] > J:=[op(GB),op(G)]; 5 2 2 3 2 J := [96 x y - 11 x y, -4 x y + y , 64 x y + 17 x y z, -8 x y z - 5 x y, 3 2 2 18 y z + 4 x z, -15 x z - 18 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 := [6, 16, 21, 4, 2, 3, 3, 1, 1, 2/3, 5/6, 5/6, 5/12, 6, 16, 24, 6, 5, 2, 3, 1, 1, 2/3, 5/6, 5/6, 5/12, 0, -3, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3371.1MB, alloc=684.3MB, time=87.66 |\^/| 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(); 1428355620 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 4 2 2 F := [19 x y z - 20 y , 8 x - 16 z , -13 y z + 9 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 3 G := [-9 y z - 20 x y , 14 x z - 17 x y , 7 x y + 6 x] > Problem := [F,G]; 2 2 4 4 2 2 Problem := [[19 x y z - 20 y , 8 x - 16 z , -13 y z + 9 z], 3 2 2 2 3 3 [-9 y z - 20 x y , 14 x z - 17 x y , 7 x y + 6 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.47 memory used=48.2MB, alloc=32.3MB, time=0.82 memory used=68.4MB, alloc=56.3MB, time=1.18 memory used=111.9MB, alloc=60.3MB, time=1.72 memory used=152.9MB, alloc=60.3MB, time=2.18 memory used=191.7MB, alloc=84.3MB, time=2.73 memory used=238.6MB, alloc=84.3MB, time=3.21 memory used=297.7MB, alloc=92.3MB, time=3.82 memory used=353.6MB, alloc=116.3MB, time=4.41 memory used=433.0MB, alloc=116.3MB, time=5.22 memory used=502.9MB, alloc=396.3MB, time=5.96 memory used=610.7MB, alloc=420.3MB, time=7.01 memory used=742.6MB, alloc=420.3MB, time=8.35 memory used=873.9MB, alloc=444.3MB, time=10.13 memory used=1005.3MB, alloc=444.3MB, time=11.81 memory used=1148.0MB, alloc=468.3MB, time=13.35 memory used=1267.7MB, alloc=492.3MB, time=14.50 memory used=1400.7MB, alloc=492.3MB, time=15.94 memory used=1506.3MB, alloc=492.3MB, time=17.09 memory used=1616.9MB, alloc=516.3MB, time=18.48 memory used=1721.0MB, alloc=516.3MB, time=20.03 memory used=1804.9MB, alloc=516.3MB, time=21.26 memory used=1901.8MB, alloc=540.3MB, time=22.35 memory used=1983.5MB, alloc=540.3MB, time=23.36 memory used=2062.2MB, alloc=540.3MB, time=24.39 memory used=2123.1MB, alloc=540.3MB, time=25.17 memory used=2202.1MB, alloc=540.3MB, time=26.16 memory used=2268.5MB, alloc=540.3MB, time=27.07 memory used=2324.1MB, alloc=564.3MB, time=27.80 memory used=2384.1MB, alloc=564.3MB, time=28.63 memory used=2447.8MB, alloc=564.3MB, time=29.42 memory used=2514.7MB, alloc=564.3MB, time=30.61 memory used=2746.7MB, alloc=588.3MB, time=34.08 memory used=2973.8MB, alloc=612.3MB, time=37.04 memory used=3206.5MB, alloc=636.3MB, time=40.30 memory used=3443.0MB, alloc=660.3MB, time=44.14 memory used=3692.6MB, alloc=684.3MB, time=47.95 memory used=3955.8MB, alloc=708.3MB, time=52.25 memory used=4222.6MB, alloc=732.3MB, time=56.34 memory used=4495.4MB, alloc=756.3MB, time=61.34 memory used=4769.9MB, alloc=780.3MB, time=65.86 memory used=5055.8MB, alloc=804.3MB, time=70.01 memory used=5343.2MB, alloc=828.3MB, time=74.83 memory used=5583.6MB, alloc=852.3MB, time=82.15 memory used=5821.5MB, alloc=876.3MB, time=90.14 memory used=6067.0MB, alloc=900.3MB, time=98.80 memory used=6322.6MB, alloc=924.3MB, time=108.92 memory used=6589.4MB, alloc=948.3MB, time=119.82 memory used=6869.3MB, alloc=972.3MB, time=131.70 memory used=7163.2MB, alloc=996.3MB, time=143.68 memory used=7470.8MB, alloc=1020.3MB, time=156.78 memory used=7792.6MB, alloc=1044.3MB, time=168.57 memory used=8129.2MB, alloc=1068.3MB, time=181.39 memory used=8480.0MB, alloc=1092.3MB, time=194.98 memory used=8844.8MB, alloc=1116.3MB, time=207.31 memory used=9218.5MB, alloc=1140.3MB, time=222.55 memory used=9616.1MB, alloc=1164.3MB, time=239.97 memory used=10037.6MB, alloc=1188.3MB, time=256.83 memory used=10483.1MB, alloc=1212.3MB, time=274.27 memory used=10952.6MB, alloc=1236.3MB, time=291.26 |\^/| 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(); 1428355920 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 F := [17 x y + 19 x y, -9 x y z + 18 y z, -2 x z - 5 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 3 G := [13 y z - 16 y z, 17 y + 2 y z, 14 x y z - 7 y ] > Problem := [F,G]; 3 2 2 3 2 Problem := [[17 x y + 19 x y, -9 x y z + 18 y z, -2 x z - 5 z ], 3 4 2 3 [13 y z - 16 y z, 17 y + 2 y z, 14 x y z - 7 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=47.7MB, alloc=32.3MB, time=0.74 memory used=68.3MB, alloc=32.3MB, time=0.99 memory used=88.6MB, alloc=56.3MB, time=1.31 memory used=129.9MB, alloc=60.3MB, time=1.97 memory used=167.3MB, alloc=84.3MB, time=2.59 memory used=223.9MB, alloc=108.3MB, time=3.56 memory used=296.6MB, alloc=132.3MB, time=5.59 memory used=380.4MB, alloc=132.3MB, time=8.24 memory used=464.4MB, alloc=156.3MB, time=10.95 N1 := 2633 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 2 3 2 GB := [17 x y + 19 x y, -x y z + 2 y z, 17 x y z + 19 y z , 2 x z + 5 z , 2 3 -85 x y z + 38 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=568.7MB, alloc=164.3MB, time=12.55 memory used=679.8MB, alloc=420.3MB, time=14.26 memory used=791.7MB, alloc=444.3MB, time=16.06 memory used=924.2MB, alloc=468.3MB, time=18.14 memory used=1064.7MB, alloc=492.3MB, time=20.49 memory used=1211.9MB, alloc=516.3MB, time=24.28 memory used=1359.9MB, alloc=540.3MB, time=28.29 memory used=1517.1MB, alloc=564.3MB, time=32.98 memory used=1698.3MB, alloc=588.3MB, time=38.40 memory used=1903.5MB, alloc=612.3MB, time=44.42 memory used=2132.6MB, alloc=612.3MB, time=51.17 memory used=2361.8MB, alloc=636.3MB, time=58.24 memory used=2615.2MB, alloc=660.3MB, time=65.04 N2 := 6963 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 3 2 3 H := [17 x y + 19 x y, -9 x y z + 18 y z, -2 x z - 5 z , 13 y z - 16 y z, 4 2 3 17 y + 2 y z, 14 x y z - 7 y ] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 3 2 J := [17 x y + 19 x y, -x y z + 2 y z, 17 x y z + 19 y z , 2 x z + 5 z , 2 3 3 4 2 3 -85 x y z + 38 y z , 13 y z - 16 y z, 17 y + 2 y z, 14 x y z - 7 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 24, 4, 3, 4, 3, 2/3, 5/6, 5/6, 5/12, 5/6, 2/3, 8, 20, 33, 5, 3, 4, 3, 3/4, 7/8, 7/8, 7/16, 7/8, 3/4, -6, -9, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2634.7MB, alloc=660.3MB, time=65.39 |\^/| 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(); 1428355988 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 F := [-13 x z + 8 x z , -y z - 4 z, 13 z + 14 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 G := [-20 x z - 8, 14 x y - 11 x y , 10 x + 12 x y z] > Problem := [F,G]; 2 2 2 2 3 Problem := [[-13 x z + 8 x z , -y z - 4 z, 13 z + 14 z], 3 3 2 2 3 [-20 x z - 8, 14 x y - 11 x y , 10 x + 12 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.1MB, alloc=32.3MB, time=0.42 memory used=47.8MB, alloc=32.3MB, time=0.70 memory used=68.7MB, alloc=32.3MB, time=1.03 memory used=89.4MB, alloc=56.3MB, time=1.42 N1 := 521 > GB := Basis(F, plex(op(vars))); 2 2 3 GB := [13 x z - 8 x z, y z + 4 z, 13 z + 14 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=130.5MB, alloc=60.3MB, time=2.00 memory used=170.8MB, alloc=60.3MB, time=2.52 memory used=211.7MB, alloc=60.3MB, time=3.13 N2 := 521 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 3 H := [-13 x z + 8 x z , -y z - 4 z, 13 z + 14 z, -20 x z - 8, 3 2 2 3 14 x y - 11 x y , 10 x + 12 x y z] > J:=[op(GB),op(G)]; 2 2 3 3 J := [13 x z - 8 x z, y z + 4 z, 13 z + 14 z, -20 x z - 8, 3 2 2 3 14 x y - 11 x y , 10 x + 12 x 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 := [6, 12, 21, 4, 3, 2, 3, 2/3, 1/2, 5/6, 7/12, 1/3, 2/3, 6, 12, 20, 4, 3, 2, 3, 2/3, 1/2, 5/6, 7/12, 1/3, 2/3, 0, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=235.8MB, alloc=60.3MB, time=3.51 |\^/| 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(); 1428355992 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [-8 y z + 10 x y, -19 x z + 18 y z, -15 x z - 18 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 2 2 2 G := [-10 x y z - 2 x , -20 y z + 8 y , 7 y z + 14 x y ] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[-8 y z + 10 x y, -19 x z + 18 y z, -15 x z - 18 z ], 2 3 2 2 3 2 2 2 [-10 x y z - 2 x , -20 y z + 8 y , 7 y z + 14 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=26.8MB, alloc=32.3MB, time=0.51 memory used=48.0MB, alloc=32.3MB, time=0.89 memory used=68.0MB, alloc=56.3MB, time=1.24 memory used=109.0MB, alloc=60.3MB, time=1.95 memory used=147.1MB, alloc=84.3MB, time=2.57 memory used=206.4MB, alloc=92.3MB, time=3.41 memory used=264.3MB, alloc=116.3MB, time=4.25 memory used=342.4MB, alloc=140.3MB, time=5.50 memory used=429.1MB, alloc=396.3MB, time=6.55 memory used=528.8MB, alloc=420.3MB, time=7.79 memory used=653.8MB, alloc=444.3MB, time=8.99 memory used=792.6MB, alloc=468.3MB, time=10.57 memory used=945.9MB, alloc=492.3MB, time=12.34 memory used=1081.0MB, alloc=516.3MB, time=13.73 memory used=1233.2MB, alloc=540.3MB, time=15.52 memory used=1357.0MB, alloc=564.3MB, time=17.18 memory used=1466.9MB, alloc=564.3MB, time=18.81 memory used=1643.4MB, alloc=588.3MB, time=21.02 memory used=1835.3MB, alloc=612.3MB, time=23.45 memory used=2021.3MB, alloc=636.3MB, time=25.84 memory used=2194.5MB, alloc=660.3MB, time=28.46 memory used=2371.3MB, alloc=684.3MB, time=30.78 memory used=2545.2MB, alloc=708.3MB, time=33.39 memory used=2733.0MB, alloc=732.3MB, time=36.00 memory used=2866.4MB, alloc=756.3MB, time=38.17 memory used=3015.4MB, alloc=780.3MB, time=40.55 memory used=3147.4MB, alloc=804.3MB, time=42.65 memory used=3259.2MB, alloc=828.3MB, time=44.35 memory used=3358.7MB, alloc=852.3MB, time=46.19 memory used=3499.7MB, alloc=876.3MB, time=49.47 memory used=3850.3MB, alloc=900.3MB, time=58.03 memory used=4194.9MB, alloc=924.3MB, time=67.46 memory used=4540.6MB, alloc=948.3MB, time=77.48 memory used=4895.1MB, alloc=972.3MB, time=88.72 memory used=5261.5MB, alloc=996.3MB, time=100.07 memory used=5637.3MB, alloc=1020.3MB, time=111.63 memory used=6024.9MB, alloc=1044.3MB, time=123.43 memory used=6436.5MB, alloc=1068.3MB, time=135.60 memory used=6872.1MB, alloc=1092.3MB, time=149.96 memory used=7331.6MB, alloc=1116.3MB, time=165.47 memory used=7815.1MB, alloc=1140.3MB, time=182.66 memory used=8322.5MB, alloc=1164.3MB, time=199.14 memory used=8853.8MB, alloc=1188.3MB, time=216.17 memory used=9409.0MB, alloc=1212.3MB, time=233.26 memory used=9988.1MB, alloc=1212.3MB, time=254.53 memory used=10567.3MB, alloc=1212.3MB, time=274.16 memory used=11146.4MB, alloc=1236.3MB, time=294.29 |\^/| 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(); 1428356292 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 F := [-17 x y z + 12 z, 9 z + 20, -11 y - 8 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 G := [-14 z - 16, 20 z + 6 y, 3 z + 13 x] > Problem := [F,G]; 2 3 4 2 Problem := [[-17 x y z + 12 z, 9 z + 20, -11 y - 8 x y ], 2 4 2 [-14 z - 16, 20 z + 6 y, 3 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=26.4MB, alloc=32.3MB, time=0.46 memory used=48.0MB, alloc=32.3MB, time=0.73 memory used=68.8MB, alloc=32.3MB, time=1.00 memory used=88.9MB, alloc=56.3MB, time=1.29 memory used=129.1MB, alloc=60.3MB, time=1.86 memory used=170.6MB, alloc=92.3MB, time=2.44 memory used=232.5MB, alloc=92.3MB, time=3.26 memory used=291.4MB, alloc=116.3MB, time=4.07 memory used=370.4MB, alloc=372.3MB, time=5.17 memory used=448.0MB, alloc=396.3MB, time=6.32 memory used=548.2MB, alloc=420.3MB, time=8.04 memory used=666.3MB, alloc=444.3MB, time=10.05 memory used=795.1MB, alloc=468.3MB, time=12.25 memory used=936.9MB, alloc=492.3MB, time=14.79 memory used=1084.6MB, alloc=516.3MB, time=17.76 memory used=1228.2MB, alloc=540.3MB, time=22.11 memory used=1378.9MB, alloc=564.3MB, time=26.94 memory used=1538.2MB, alloc=588.3MB, time=33.19 memory used=1720.8MB, alloc=612.3MB, time=40.52 memory used=1927.4MB, alloc=636.3MB, time=48.03 memory used=2157.8MB, alloc=660.3MB, time=55.72 memory used=2412.3MB, alloc=660.3MB, time=63.05 memory used=2666.6MB, alloc=660.3MB, time=70.75 memory used=2920.9MB, alloc=684.3MB, time=79.36 memory used=3199.1MB, alloc=684.3MB, time=87.19 memory used=3477.5MB, alloc=708.3MB, time=94.89 N1 := 9017 > GB := Basis(F, plex(op(vars))); 9 5 3 GB := [1206878450 x + 78594219, 98260 x + 29403 y, -2890 x + 891 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3790.8MB, alloc=708.3MB, time=100.34 N2 := 1667 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 4 2 2 4 H := [-17 x y z + 12 z, 9 z + 20, -11 y - 8 x y , -14 z - 16, 20 z + 6 y, 2 3 z + 13 x] > J:=[op(GB),op(G)]; 9 5 3 J := [1206878450 x + 78594219, 98260 x + 29403 y, -2890 x + 891 z, 2 4 2 -14 z - 16, 20 z + 6 y, 3 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 := [6, 11, 19, 4, 1, 4, 4, 1/2, 1/2, 5/6, 1/4, 1/3, 1/2, 6, 10, 25, 9, 9, 1, 4, 2/3, 1/3, 2/3, 1/3, 1/6, 1/3, 1, -6, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3842.1MB, alloc=708.3MB, time=101.41 |\^/| 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(); 1428356398 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 F := [18 x y z + 17 x y z, -20 x z + 18 x z, -18 z + 10 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 G := [5 y z + 19 y, z + 6, -4 x y z + 10 y z ] > Problem := [F,G]; 2 3 2 3 2 Problem := [[18 x y z + 17 x y z, -20 x z + 18 x z, -18 z + 10 y ], 3 3 2 3 [5 y z + 19 y, z + 6, -4 x y z + 10 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.42 memory used=46.8MB, alloc=32.3MB, time=0.67 memory used=64.7MB, alloc=56.3MB, time=0.86 memory used=104.3MB, alloc=60.3MB, time=1.33 memory used=142.5MB, alloc=84.3MB, time=1.80 memory used=198.1MB, alloc=108.3MB, time=2.50 memory used=263.0MB, alloc=132.3MB, time=3.78 N1 := 1721 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 3 3 4 2 2 GB := [1458 x y - 1445 x y , 1458 x y - 1445 x y , 100 x y + 153 x y , 2 2 3 3 2 81 x z - 50 x y , -180 x y + 289 x y z, 9 z - 5 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=351.9MB, alloc=140.3MB, time=4.82 memory used=448.5MB, alloc=140.3MB, time=5.82 memory used=536.4MB, alloc=164.3MB, time=6.75 memory used=617.5MB, alloc=420.3MB, time=7.65 memory used=734.9MB, alloc=444.3MB, time=8.89 memory used=871.8MB, alloc=468.3MB, time=10.40 memory used=1026.0MB, alloc=492.3MB, time=12.15 memory used=1196.7MB, alloc=516.3MB, time=14.13 memory used=1386.0MB, alloc=540.3MB, time=16.36 memory used=1596.1MB, alloc=564.3MB, time=19.08 memory used=1813.7MB, alloc=588.3MB, time=22.00 memory used=2032.9MB, alloc=612.3MB, time=25.28 memory used=2254.2MB, alloc=636.3MB, time=28.37 memory used=2474.9MB, alloc=660.3MB, time=31.53 memory used=2673.4MB, alloc=684.3MB, time=36.05 memory used=2869.8MB, alloc=708.3MB, time=41.05 memory used=3075.0MB, alloc=732.3MB, time=46.49 memory used=3290.8MB, alloc=756.3MB, time=52.55 memory used=3518.8MB, alloc=780.3MB, time=58.86 memory used=3753.8MB, alloc=804.3MB, time=66.02 memory used=4012.7MB, alloc=828.3MB, time=73.77 memory used=4295.5MB, alloc=852.3MB, time=82.20 memory used=4602.3MB, alloc=876.3MB, time=91.32 memory used=4933.0MB, alloc=900.3MB, time=101.51 memory used=5287.7MB, alloc=924.3MB, time=110.77 memory used=5666.3MB, alloc=948.3MB, time=120.67 memory used=6068.8MB, alloc=972.3MB, time=131.10 memory used=6495.2MB, alloc=996.3MB, time=142.23 memory used=6945.5MB, alloc=1020.3MB, time=154.75 memory used=7419.6MB, alloc=1044.3MB, time=166.78 memory used=7917.7MB, alloc=1044.3MB, time=179.62 memory used=8415.6MB, alloc=1044.3MB, time=192.22 memory used=8913.3MB, alloc=1068.3MB, time=204.55 memory used=9434.9MB, alloc=1068.3MB, time=220.77 memory used=9956.4MB, alloc=1068.3MB, time=237.97 memory used=10477.7MB, alloc=1092.3MB, time=256.68 memory used=11022.9MB, alloc=1092.3MB, time=276.29 memory used=11568.1MB, alloc=1116.3MB, time=294.76 |\^/| 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(); 1428356698 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 3 F := [-12 y - 13 y z, x z - 6 x y z, 10 y z - 8 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [7 x y z - 16 z, -13 x z + z, -9 y z - 19 y z] > Problem := [F,G]; 4 2 3 2 3 Problem := [[-12 y - 13 y z, x z - 6 x y z, 10 y z - 8 y z], 2 2 2 [7 x y z - 16 z, -13 x z + z, -9 y z - 19 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.1MB, alloc=32.3MB, time=0.40 memory used=48.0MB, alloc=32.3MB, time=0.72 memory used=67.7MB, alloc=56.3MB, time=1.03 memory used=107.5MB, alloc=84.3MB, time=1.83 N1 := 1117 > GB := Basis(F, plex(op(vars))); 4 4 2 4 3 4 2 5 6 4 3 4 3 GB := [5 x y - 144 x y , -x y + 6 x y , 5 y - 4 y , 15 x y + 13 x z, 5 15 y + 13 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=164.4MB, alloc=84.3MB, time=3.35 memory used=223.0MB, alloc=84.3MB, time=4.38 memory used=279.7MB, alloc=108.3MB, time=6.01 N2 := 1117 #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)]; 4 2 3 2 3 2 H := [-12 y - 13 y z, x z - 6 x y z, 10 y z - 8 y z, 7 x y z - 16 z, 2 2 -13 x z + z, -9 y z - 19 y z] > J:=[op(GB),op(G)]; 4 4 2 4 3 4 2 5 6 4 3 4 3 J := [5 x y - 144 x y , -x y + 6 x y , 5 y - 4 y , 15 x y + 13 x z, 5 2 2 2 15 y + 13 y z, 7 x y z - 16 z, -13 x z + z, -9 y z - 19 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 := [6, 14, 22, 4, 3, 4, 1, 1/2, 5/6, 1, 1/3, 2/3, 11/12, 8, 17, 43, 8, 4, 6, 1, 5/8, 7/8, 5/8, 1/2, 3/4, 1/2, -3, -21, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=294.5MB, alloc=108.3MB, time=6.45 |\^/| 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(); 1428356706 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [2 y z + 14 x , x y z - 3 z , -14 x y + 20 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 4 2 G := [-17 x - 4 x y z, -16 y , -7 z - 9 y z ] > Problem := [F,G]; 3 2 2 3 Problem := [[2 y z + 14 x , x y z - 3 z , -14 x y + 20 y z], 4 2 3 4 2 [-17 x - 4 x y z, -16 y , -7 z - 9 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=68.4MB, alloc=56.3MB, time=1.07 memory used=109.4MB, alloc=60.3MB, time=1.64 memory used=147.2MB, alloc=60.3MB, time=2.16 memory used=185.5MB, alloc=84.3MB, time=2.70 memory used=226.2MB, alloc=84.3MB, time=3.26 memory used=286.7MB, alloc=92.3MB, time=4.20 memory used=346.5MB, alloc=116.3MB, time=5.01 memory used=417.2MB, alloc=116.3MB, time=5.91 memory used=494.1MB, alloc=140.3MB, time=7.08 memory used=569.5MB, alloc=140.3MB, time=8.23 memory used=635.0MB, alloc=420.3MB, time=9.28 memory used=752.9MB, alloc=444.3MB, time=11.04 memory used=888.6MB, alloc=468.3MB, time=13.22 memory used=1033.2MB, alloc=492.3MB, time=15.02 memory used=1188.7MB, alloc=516.3MB, time=16.83 memory used=1342.5MB, alloc=540.3MB, time=19.70 memory used=1496.0MB, alloc=564.3MB, time=23.35 memory used=1663.1MB, alloc=588.3MB, time=28.02 memory used=1854.1MB, alloc=612.3MB, time=34.66 memory used=2069.2MB, alloc=636.3MB, time=43.41 memory used=2308.2MB, alloc=636.3MB, time=52.91 memory used=2547.2MB, alloc=660.3MB, time=60.29 N1 := 7083 > GB := Basis(F, plex(op(vars))); 5 4 4 3 3 2 GB := [10000000 x + 3176523 x , 100000 x + 21609 x y, x y + 10 x , 3 2 4 3 -7 x + 10 x z, -7 x y + 10 y z, 10000 x + 9261 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2821.4MB, alloc=660.3MB, time=68.97 memory used=2956.9MB, alloc=660.3MB, time=71.19 memory used=3089.8MB, alloc=660.3MB, time=73.46 memory used=3295.3MB, alloc=660.3MB, time=77.32 memory used=3495.4MB, alloc=684.3MB, time=82.39 memory used=3767.9MB, alloc=708.3MB, time=93.58 memory used=4060.1MB, alloc=732.3MB, time=105.80 N2 := 4937 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 3 4 2 H := [2 y z + 14 x , x y z - 3 z , -14 x y + 20 y z, -17 x - 4 x y z, 3 4 2 -16 y , -7 z - 9 y z ] > J:=[op(GB),op(G)]; 5 4 4 3 3 2 J := [10000000 x + 3176523 x , 100000 x + 21609 x y, x y + 10 x , 3 2 4 3 4 2 -7 x + 10 x z, -7 x y + 10 y z, 10000 x + 9261 z , -17 x - 4 x y z, 3 4 2 -16 y , -7 z - 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 := [6, 15, 21, 4, 4, 3, 4, 2/3, 1, 5/6, 5/12, 7/12, 7/12, 9, 18, 33, 5, 5, 3, 4, 7/9, 2/3, 5/9, 2/3, 7/18, 1/3, -3, -12, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=4177.6MB, alloc=732.3MB, time=110.12 |\^/| 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(); 1428356821 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 F := [6 x y - 4 y , -19 x y + 3 y z, 14 x z + 4 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [-19 x y + y z, 12 z - 12 x y, -13 x + 15 x y ] > Problem := [F,G]; 3 2 3 2 3 Problem := [[6 x y - 4 y , -19 x y + 3 y z, 14 x z + 4 y z], 3 3 2 [-19 x y + y z, 12 z - 12 x y, -13 x + 15 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.20 memory used=26.2MB, alloc=32.3MB, time=0.57 memory used=47.5MB, alloc=32.3MB, time=0.89 memory used=67.9MB, alloc=32.3MB, time=1.18 memory used=87.7MB, alloc=56.3MB, time=1.46 memory used=127.7MB, alloc=60.3MB, time=2.01 memory used=170.5MB, alloc=84.3MB, time=2.71 memory used=232.8MB, alloc=84.3MB, time=3.69 memory used=288.1MB, alloc=108.3MB, time=4.65 memory used=372.4MB, alloc=116.3MB, time=5.80 memory used=450.5MB, alloc=140.3MB, time=6.96 memory used=540.5MB, alloc=164.3MB, time=8.48 memory used=640.6MB, alloc=188.3MB, time=11.28 memory used=750.2MB, alloc=212.3MB, time=14.42 memory used=870.4MB, alloc=236.3MB, time=18.71 memory used=1014.1MB, alloc=236.3MB, time=23.21 memory used=1157.8MB, alloc=260.3MB, time=27.67 memory used=1325.5MB, alloc=260.3MB, time=32.65 memory used=1493.2MB, alloc=284.3MB, time=38.69 N1 := 5691 > GB := Basis(F, plex(op(vars))); 7 3 3 2 6 3 3 GB := [21 x y + 4 x y, 7 x y + 2 y , 147 x z - 76 x y, 7 x z + 2 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1688.8MB, alloc=284.3MB, time=44.33 memory used=1799.1MB, alloc=540.3MB, time=46.13 memory used=2020.4MB, alloc=564.3MB, time=48.94 memory used=2243.8MB, alloc=588.3MB, time=55.68 memory used=2468.9MB, alloc=612.3MB, time=62.09 N2 := 3919 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 3 H := [6 x y - 4 y , -19 x y + 3 y z, 14 x z + 4 y z, -19 x y + y z, 3 3 2 12 z - 12 x y, -13 x + 15 x y ] > J:=[op(GB),op(G)]; 7 3 3 2 6 3 3 J := [21 x y + 4 x y, 7 x y + 2 y , 147 x z - 76 x y, 7 x z + 2 y z, 3 3 2 -19 x y + y z, 12 z - 12 x y, -13 x + 15 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 := [6, 16, 20, 4, 3, 3, 3, 1, 1, 2/3, 7/12, 3/4, 5/12, 7, 18, 31, 8, 7, 2, 3, 1, 1, 4/7, 5/7, 5/7, 5/14, -2, -11, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2558.5MB, alloc=612.3MB, time=63.90 |\^/| 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(); 1428356888 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 4 F := [5 x - 5 x y z, -18 x y - 3 x y z , -4 y + 11 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 G := [-5 x y - 5 y z, 10 y - 18 z, -16 x z + 15 y ] > Problem := [F,G]; 4 2 3 2 4 Problem := [[5 x - 5 x y z, -18 x y - 3 x y z , -4 y + 11 y z], 2 2 2 3 3 2 [-5 x y - 5 y z, 10 y - 18 z, -16 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=4.3MB, alloc=32.3MB, time=0.16 memory used=27.0MB, alloc=32.3MB, time=0.39 memory used=48.2MB, alloc=32.3MB, time=0.57 memory used=68.3MB, alloc=56.3MB, time=0.76 memory used=110.5MB, alloc=60.3MB, time=1.17 memory used=150.0MB, alloc=84.3MB, time=1.57 memory used=209.9MB, alloc=92.3MB, time=2.26 memory used=268.4MB, alloc=116.3MB, time=2.87 memory used=351.7MB, alloc=116.3MB, time=3.83 memory used=418.8MB, alloc=396.3MB, time=4.51 memory used=524.5MB, alloc=420.3MB, time=5.38 memory used=654.6MB, alloc=444.3MB, time=6.50 memory used=801.0MB, alloc=468.3MB, time=7.93 memory used=935.0MB, alloc=492.3MB, time=9.25 memory used=1046.2MB, alloc=492.3MB, time=10.33 memory used=1151.6MB, alloc=492.3MB, time=11.40 memory used=1248.9MB, alloc=516.3MB, time=12.42 memory used=1332.1MB, alloc=516.3MB, time=13.33 memory used=1401.1MB, alloc=516.3MB, time=14.13 memory used=1470.4MB, alloc=516.3MB, time=15.14 memory used=1533.7MB, alloc=516.3MB, time=16.37 memory used=1587.6MB, alloc=516.3MB, time=17.24 memory used=1664.2MB, alloc=516.3MB, time=18.44 memory used=1714.6MB, alloc=540.3MB, time=19.19 memory used=1770.2MB, alloc=540.3MB, time=20.06 memory used=1987.8MB, alloc=564.3MB, time=22.34 memory used=2185.1MB, alloc=588.3MB, time=24.41 memory used=2352.1MB, alloc=612.3MB, time=26.55 memory used=2513.1MB, alloc=636.3MB, time=28.62 memory used=2688.2MB, alloc=660.3MB, time=31.12 memory used=2842.4MB, alloc=684.3MB, time=33.43 memory used=2970.8MB, alloc=684.3MB, time=35.29 memory used=3180.5MB, alloc=708.3MB, time=38.82 memory used=3419.0MB, alloc=732.3MB, time=42.73 memory used=3642.6MB, alloc=756.3MB, time=46.65 memory used=3861.9MB, alloc=780.3MB, time=50.33 memory used=4020.1MB, alloc=804.3MB, time=53.05 memory used=4204.0MB, alloc=828.3MB, time=55.98 memory used=4469.5MB, alloc=852.3MB, time=62.65 memory used=4779.4MB, alloc=876.3MB, time=70.85 memory used=5093.1MB, alloc=900.3MB, time=79.62 memory used=5416.3MB, alloc=924.3MB, time=90.27 memory used=5744.9MB, alloc=948.3MB, time=102.72 memory used=6087.0MB, alloc=972.3MB, time=115.82 memory used=6453.0MB, alloc=996.3MB, time=128.35 memory used=6843.0MB, alloc=1020.3MB, time=141.69 memory used=7257.0MB, alloc=1044.3MB, time=155.47 memory used=7694.8MB, alloc=1068.3MB, time=170.35 memory used=8156.6MB, alloc=1092.3MB, time=185.83 memory used=8642.4MB, alloc=1116.3MB, time=204.36 memory used=9152.0MB, alloc=1140.3MB, time=221.74 memory used=9685.5MB, alloc=1164.3MB, time=239.92 memory used=10243.1MB, alloc=1188.3MB, time=259.16 memory used=10824.5MB, alloc=1188.3MB, time=278.37 memory used=11405.9MB, alloc=1212.3MB, time=297.60 |\^/| 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(); 1428357188 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 4 F := [13 x y - 7 x, 20 x - 11 x y z, 12 x z - 4 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 G := [-18 y z - 13 z, x y + x y , 18 x z + 14] > Problem := [F,G]; 4 2 2 2 4 Problem := [[13 x y - 7 x, 20 x - 11 x y z, 12 x z - 4 y ], 3 3 [-18 y z - 13 z, x y + x y , 18 x 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=0.15 memory used=26.2MB, alloc=32.3MB, time=0.42 memory used=47.6MB, alloc=32.3MB, time=0.68 memory used=68.3MB, alloc=32.3MB, time=0.94 memory used=88.0MB, alloc=56.3MB, time=1.20 memory used=131.1MB, alloc=60.3MB, time=1.91 memory used=169.4MB, alloc=84.3MB, time=2.51 memory used=227.9MB, alloc=84.3MB, time=3.44 memory used=281.3MB, alloc=108.3MB, time=4.30 memory used=350.9MB, alloc=132.3MB, time=6.05 memory used=430.1MB, alloc=156.3MB, time=8.94 memory used=532.3MB, alloc=156.3MB, time=12.59 N1 := 3167 > GB := Basis(F, plex(op(vars))); 9 8 4 GB := [978876865200 x - 697540921 x, 13 x y - 7 x, -34273200 x + 290521 y , 4 -3380 x + 539 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=635.4MB, alloc=156.3MB, time=15.20 memory used=747.1MB, alloc=188.3MB, time=16.79 N2 := 1043 #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)]; 4 2 2 2 4 H := [13 x y - 7 x, 20 x - 11 x y z, 12 x z - 4 y , -18 y z - 13 z, 3 3 x y + x y , 18 x z + 14] > J:=[op(GB),op(G)]; 9 8 4 J := [978876865200 x - 697540921 x, 13 x y - 7 x, -34273200 x + 290521 y , 4 3 3 -3380 x + 539 x z, -18 y z - 13 z, x y + x y , 18 x z + 14] > > 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, 18, 4, 4, 4, 2, 5/6, 5/6, 2/3, 2/3, 1/2, 5/12, 7, 13, 31, 9, 9, 4, 1, 6/7, 4/7, 3/7, 5/7, 5/14, 2/7, 1, -13, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=786.2MB, alloc=188.3MB, time=17.96 |\^/| 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(); 1428357207 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 F := [-15 x z + 5 y z , 4 x y - 16 y z, 20 y z - 14 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 4 2 G := [12 x y - 7 x y z, 12 x z - 10 y , -6 z + 19 x z ] > Problem := [F,G]; 3 2 2 2 2 2 2 Problem := [[-15 x z + 5 y z , 4 x y - 16 y z, 20 y z - 14 y ], 2 2 2 2 3 4 2 [12 x y - 7 x y z, 12 x z - 10 y , -6 z + 19 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.5MB, alloc=32.3MB, time=0.36 memory used=47.7MB, alloc=32.3MB, time=0.61 memory used=67.2MB, alloc=56.3MB, time=0.86 memory used=106.7MB, alloc=60.3MB, time=1.27 memory used=145.0MB, alloc=84.3MB, time=1.64 memory used=204.7MB, alloc=92.3MB, time=2.24 memory used=262.2MB, alloc=116.3MB, time=2.83 memory used=342.0MB, alloc=116.3MB, time=3.65 memory used=418.8MB, alloc=140.3MB, time=4.45 memory used=508.7MB, alloc=164.3MB, time=5.44 memory used=579.3MB, alloc=420.3MB, time=6.21 memory used=704.0MB, alloc=444.3MB, time=7.61 memory used=845.9MB, alloc=468.3MB, time=9.26 memory used=1010.4MB, alloc=492.3MB, time=11.16 memory used=1200.1MB, alloc=516.3MB, time=13.31 memory used=1417.4MB, alloc=540.3MB, time=15.75 memory used=1638.6MB, alloc=564.3MB, time=18.36 memory used=1882.6MB, alloc=588.3MB, time=21.13 memory used=2090.4MB, alloc=612.3MB, time=23.94 memory used=2278.3MB, alloc=636.3MB, time=26.44 memory used=2470.5MB, alloc=660.3MB, time=29.05 memory used=2614.2MB, alloc=684.3MB, time=31.31 memory used=2762.4MB, alloc=708.3MB, time=33.40 memory used=2908.2MB, alloc=732.3MB, time=35.77 memory used=3048.1MB, alloc=756.3MB, time=37.48 memory used=3163.1MB, alloc=756.3MB, time=39.49 memory used=3262.8MB, alloc=756.3MB, time=41.44 memory used=3354.1MB, alloc=756.3MB, time=43.37 memory used=3749.9MB, alloc=780.3MB, time=48.47 memory used=4114.4MB, alloc=804.3MB, time=53.66 memory used=4525.0MB, alloc=828.3MB, time=60.17 memory used=4971.1MB, alloc=852.3MB, time=65.12 memory used=5373.1MB, alloc=876.3MB, time=71.58 memory used=5719.5MB, alloc=900.3MB, time=78.09 memory used=6088.8MB, alloc=924.3MB, time=83.81 memory used=6524.1MB, alloc=948.3MB, time=89.35 memory used=6948.9MB, alloc=972.3MB, time=95.44 memory used=7335.6MB, alloc=996.3MB, time=101.54 memory used=7709.1MB, alloc=1020.3MB, time=107.52 memory used=8064.8MB, alloc=1044.3MB, time=113.39 memory used=8403.6MB, alloc=1068.3MB, time=119.43 memory used=8734.2MB, alloc=1092.3MB, time=125.12 memory used=9075.7MB, alloc=1116.3MB, time=130.85 memory used=9458.2MB, alloc=1140.3MB, time=137.12 memory used=9874.5MB, alloc=1164.3MB, time=143.48 memory used=10300.5MB, alloc=1188.3MB, time=150.51 memory used=10763.2MB, alloc=1212.3MB, time=157.20 memory used=11254.2MB, alloc=1236.3MB, time=163.52 memory used=11770.7MB, alloc=1260.3MB, time=170.97 memory used=12327.0MB, alloc=1284.3MB, time=176.91 memory used=12910.0MB, alloc=1308.3MB, time=183.27 memory used=13527.6MB, alloc=1332.3MB, time=189.16 memory used=13951.1MB, alloc=1356.3MB, time=201.99 memory used=14332.6MB, alloc=1380.3MB, time=216.07 memory used=14713.6MB, alloc=1404.3MB, time=229.42 memory used=15101.8MB, alloc=1428.3MB, time=244.41 memory used=15500.2MB, alloc=1452.3MB, time=259.21 memory used=15904.6MB, alloc=1476.3MB, time=274.59 memory used=16317.7MB, alloc=1500.3MB, time=289.34 memory used=16739.5MB, alloc=1524.3MB, time=304.51 |\^/| 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(); 1428357507 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 3 2 2 F := [17 y z + 8 x , -8 x z + 5 z , 12 x z - 15 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 3 2 G := [-11 x y z - 16 z , -13 x y z + 20, 15 x + 13 x z ] > Problem := [F,G]; 2 2 3 3 3 3 2 2 Problem := [[17 y z + 8 x , -8 x z + 5 z , 12 x z - 15 x y ], 2 4 2 3 2 [-11 x y z - 16 z , -13 x y z + 20, 15 x + 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=4.2MB, alloc=32.3MB, time=0.16 memory used=26.5MB, alloc=32.3MB, time=0.45 memory used=47.6MB, alloc=32.3MB, time=0.71 memory used=68.1MB, alloc=56.3MB, time=0.98 memory used=111.3MB, alloc=68.3MB, time=1.54 memory used=152.4MB, alloc=68.3MB, time=2.04 memory used=189.0MB, alloc=92.3MB, time=2.58 memory used=256.0MB, alloc=116.3MB, time=3.49 memory used=330.6MB, alloc=116.3MB, time=4.49 memory used=389.6MB, alloc=372.3MB, time=5.24 memory used=472.3MB, alloc=396.3MB, time=6.04 memory used=584.0MB, alloc=420.3MB, time=7.11 memory used=716.0MB, alloc=444.3MB, time=8.33 memory used=844.2MB, alloc=444.3MB, time=9.55 memory used=973.1MB, alloc=468.3MB, time=10.83 memory used=1083.5MB, alloc=468.3MB, time=12.02 memory used=1186.4MB, alloc=492.3MB, time=13.16 memory used=1283.8MB, alloc=492.3MB, time=14.41 memory used=1374.9MB, alloc=492.3MB, time=15.60 memory used=1463.3MB, alloc=516.3MB, time=16.80 memory used=1534.7MB, alloc=516.3MB, time=17.88 memory used=1593.9MB, alloc=516.3MB, time=18.83 memory used=1658.8MB, alloc=516.3MB, time=19.61 memory used=1719.3MB, alloc=516.3MB, time=20.46 memory used=1779.7MB, alloc=516.3MB, time=21.24 memory used=1839.0MB, alloc=516.3MB, time=21.99 memory used=1902.3MB, alloc=540.3MB, time=23.02 memory used=1966.6MB, alloc=540.3MB, time=24.03 memory used=2043.3MB, alloc=540.3MB, time=25.37 memory used=2130.0MB, alloc=564.3MB, time=26.90 memory used=2336.5MB, alloc=588.3MB, time=29.98 memory used=2542.3MB, alloc=612.3MB, time=34.52 memory used=2723.9MB, alloc=636.3MB, time=40.03 memory used=2929.6MB, alloc=660.3MB, time=46.16 memory used=3159.4MB, alloc=684.3MB, time=52.79 N1 := 5131 > GB := Basis(F, plex(op(vars))); 6 5 3 2 2 2 2 6 5 3 2 2 GB := [8 x - 5 x , 8 x y - 5 x y , 17 x y + 2 x , 4 x z - 5 x y , 2 4 2 2 2 2 3 5 3 -2 x y + x y z, 17 z y + 8 x , 1024 x + 425 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3446.3MB, alloc=684.3MB, time=57.69 memory used=3669.2MB, alloc=708.3MB, time=60.33 memory used=3871.9MB, alloc=708.3MB, time=62.86 memory used=4033.2MB, alloc=732.3MB, time=65.30 memory used=4179.1MB, alloc=732.3MB, time=67.61 memory used=4331.0MB, alloc=756.3MB, time=69.73 memory used=4484.7MB, alloc=756.3MB, time=72.01 memory used=4633.6MB, alloc=780.3MB, time=74.42 memory used=4753.8MB, alloc=780.3MB, time=76.28 memory used=4872.8MB, alloc=780.3MB, time=78.15 memory used=4980.7MB, alloc=804.3MB, time=80.23 memory used=5052.8MB, alloc=804.3MB, time=81.89 memory used=5483.7MB, alloc=828.3MB, time=87.35 memory used=5871.6MB, alloc=852.3MB, time=92.74 memory used=6202.8MB, alloc=876.3MB, time=97.48 memory used=6561.8MB, alloc=900.3MB, time=102.14 memory used=6861.1MB, alloc=924.3MB, time=106.08 memory used=7143.6MB, alloc=948.3MB, time=109.81 memory used=7388.6MB, alloc=972.3MB, time=113.49 memory used=7595.3MB, alloc=996.3MB, time=116.83 memory used=7800.8MB, alloc=1020.3MB, time=120.25 memory used=8382.7MB, alloc=1044.3MB, time=127.62 memory used=8973.7MB, alloc=1068.3MB, time=134.31 memory used=9583.0MB, alloc=1092.3MB, time=141.20 memory used=10193.2MB, alloc=1116.3MB, time=148.72 memory used=10784.7MB, alloc=1140.3MB, time=156.29 memory used=11366.8MB, alloc=1164.3MB, time=163.50 memory used=11933.0MB, alloc=1188.3MB, time=171.13 memory used=12416.5MB, alloc=1212.3MB, time=178.28 memory used=12978.0MB, alloc=1236.3MB, time=186.75 memory used=13349.6MB, alloc=1260.3MB, time=193.26 memory used=13823.2MB, alloc=1284.3MB, time=201.87 memory used=14149.7MB, alloc=1308.3MB, time=209.23 memory used=14485.3MB, alloc=1332.3MB, time=215.91 memory used=14841.5MB, alloc=1356.3MB, time=223.63 memory used=15178.9MB, alloc=1380.3MB, time=231.56 memory used=15419.0MB, alloc=1404.3MB, time=238.05 memory used=15599.4MB, alloc=1428.3MB, time=244.08 memory used=15827.7MB, alloc=1452.3MB, time=250.92 memory used=16038.1MB, alloc=1476.3MB, time=257.32 memory used=16249.4MB, alloc=1500.3MB, time=264.77 memory used=16396.4MB, alloc=1524.3MB, time=270.74 memory used=16557.2MB, alloc=1548.3MB, time=277.05 memory used=16730.5MB, alloc=1572.3MB, time=283.19 memory used=16953.4MB, alloc=1596.3MB, time=290.24 memory used=17062.2MB, alloc=1620.3MB, time=296.54 memory used=17184.8MB, alloc=1644.3MB, time=302.69 memory used=17310.5MB, alloc=1668.3MB, time=309.64 memory used=17409.2MB, alloc=1692.3MB, time=315.63 memory used=17465.4MB, alloc=1716.3MB, time=321.32 memory used=17546.2MB, alloc=1740.3MB, time=327.45 memory used=17667.8MB, alloc=1764.3MB, time=334.45 memory used=17739.3MB, alloc=1788.3MB, time=340.36 memory used=17817.6MB, alloc=1812.3MB, time=346.41 memory used=17872.8MB, alloc=1836.3MB, time=352.22 memory used=17917.2MB, alloc=1860.3MB, time=357.98 |\^/| 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(); 1428357807 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 F := [-13 y z - 12 x z, -3 x y z - 11 x y z, -9 x z + 12 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 2 G := [-8 z + x y, -x y + 13 x , 19 x y - 13 z] > Problem := [F,G]; 2 2 3 4 Problem := [[-13 y z - 12 x z, -3 x y z - 11 x y z, -9 x z + 12 z ], 4 2 3 2 2 2 [-8 z + x y, -x y + 13 x , 19 x 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=4.2MB, alloc=32.3MB, time=0.14 memory used=26.0MB, alloc=32.3MB, time=0.35 memory used=47.6MB, alloc=32.3MB, time=0.57 memory used=68.2MB, alloc=32.3MB, time=0.79 memory used=87.6MB, alloc=56.3MB, time=1.05 memory used=130.2MB, alloc=60.3MB, time=1.59 memory used=169.7MB, alloc=84.3MB, time=2.17 memory used=229.9MB, alloc=108.3MB, time=3.14 memory used=303.7MB, alloc=132.3MB, time=5.02 memory used=389.0MB, alloc=132.3MB, time=6.99 N1 := 2117 > GB := Basis(F, plex(op(vars))); 3 2 2 2 3 4 GB := [3 x z + 11 x z, 3 x y z + 11 x y z, 13 y z + 12 x z, -3 x z + 4 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=474.4MB, alloc=140.3MB, time=7.84 memory used=574.8MB, alloc=140.3MB, time=8.84 memory used=669.9MB, alloc=164.3MB, time=9.94 memory used=764.7MB, alloc=188.3MB, time=11.61 N2 := 2117 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 4 4 2 H := [-13 y z - 12 x z, -3 x y z - 11 x y z, -9 x z + 12 z , -8 z + y x , 3 2 2 2 -x y + 13 x , 19 y x - 13 z] > J:=[op(GB),op(G)]; 3 2 2 2 3 4 J := [3 x z + 11 x z, 3 x y z + 11 x y z, 13 y z + 12 x z, -3 x z + 4 z , 4 2 3 2 2 2 -8 z + y x , -x y + 13 x , 19 y x - 13 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, 16, 23, 4, 2, 3, 4, 1, 5/6, 5/6, 2/3, 1/2, 2/3, 7, 18, 27, 4, 3, 3, 4, 1, 5/7, 6/7, 5/7, 3/7, 5/7, -2, -4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=800.6MB, alloc=188.3MB, time=12.12 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428357820 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 4 F := [-2 x z - 4 z , 18 y , 8 x y z - 20 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 2 4 G := [-11 x z + 14 x y , -18 x y - 5 x y z, -13 x z - 15 z ] > Problem := [F,G]; 3 3 3 2 4 Problem := [[-2 x z - 4 z , 18 y , 8 x y z - 20 y ], 2 2 2 2 2 2 2 2 4 [-11 x z + 14 x y , -18 x y - 5 x y z, -13 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=0.14 memory used=26.7MB, alloc=32.3MB, time=0.36 memory used=48.0MB, alloc=32.3MB, time=0.56 memory used=68.1MB, alloc=56.3MB, time=0.75 memory used=109.5MB, alloc=60.3MB, time=1.10 memory used=148.1MB, alloc=84.3MB, time=1.44 memory used=207.6MB, alloc=92.3MB, time=1.99 memory used=265.7MB, alloc=116.3MB, time=2.57 memory used=342.0MB, alloc=140.3MB, time=3.43 memory used=437.7MB, alloc=164.3MB, time=4.47 memory used=545.2MB, alloc=188.3MB, time=5.88 memory used=652.7MB, alloc=212.3MB, time=8.09 memory used=779.8MB, alloc=236.3MB, time=10.80 N1 := 3455 > GB := Basis(F, plex(op(vars))); 3 4 2 3 3 GB := [y , x y z, y z x, x z + 2 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=940.4MB, alloc=236.3MB, time=13.18 N2 := 435 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 3 2 4 2 2 2 H := [-2 x z - 4 z , 18 y , 8 x y z - 20 y , -11 x z + 14 x y , 2 2 2 2 2 4 -18 x y - 5 x y z, -13 x z - 15 z ] > J:=[op(GB),op(G)]; 3 4 2 3 3 2 2 2 J := [y , x y z, y z x, x z + 2 z , -11 x z + 14 x y , 2 2 2 2 2 4 -18 x y - 5 x y z, -13 x z - 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, 23, 4, 3, 4, 4, 5/6, 2/3, 5/6, 7/12, 1/2, 7/12, 7, 17, 29, 6, 4, 3, 4, 6/7, 5/7, 6/7, 1/2, 3/8, 1/2, -3, -6, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=958.5MB, alloc=236.3MB, time=13.40 |\^/| 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(); 1428357833 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 F := [9 x z + 4 x y, -10 x z + y z, -10 x y + 13 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 2 G := [-15 x z - x z , 18 x y + 3 y , 14 x y + 9 x y ] > Problem := [F,G]; 2 2 2 3 3 2 Problem := [[9 x z + 4 x y, -10 x z + y z, -10 x y + 13 x z ], 2 2 2 2 2 2 2 2 [-15 x z - x z , 18 x y + 3 y , 14 x y + 9 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.5MB, alloc=32.3MB, time=0.34 memory used=48.7MB, alloc=32.3MB, time=0.57 memory used=70.2MB, alloc=56.3MB, time=0.80 N1 := 493 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 4 2 2 GB := [40 x y + 9 x y, 45 x y + 26 x y, 81 x y - 208 x y , 3 3 2 40 x y z + 9 y z, 45 y z + 26 y z, -10 x y + 13 x z , 2 2 2 6400 x y + 729 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.8MB, alloc=60.3MB, time=1.18 memory used=149.9MB, alloc=60.3MB, time=1.53 N2 := 511 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 3 2 2 2 2 H := [9 x z + 4 x y, -10 x z + y z, -10 x y + 13 x z , -15 x z - x z , 2 2 2 2 2 18 x y + 3 y , 14 x y + 9 x y ] > J:=[op(GB),op(G)]; 3 2 2 3 2 4 2 2 J := [40 x y + 9 x y, 45 x y + 26 x y, 81 x y - 208 x y , 3 3 2 40 x y z + 9 y z, 45 y z + 26 y z, -10 x y + 13 x z , 2 2 2 2 2 2 2 2 2 2 2 6400 x y + 729 y z , -15 x z - x z , 18 x y + 3 y , 14 x y + 9 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 := [6, 15, 23, 4, 2, 3, 3, 1, 5/6, 2/3, 5/6, 7/12, 1/2, 10, 23, 40, 5, 3, 4, 2, 9/10, 9/10, 1/2, 3/4, 17/20, 2/5, -8, -17, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=187.0MB, alloc=60.3MB, time=1.92 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428357835 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-15 x y z + 17 x , -14 x y z - 14 x y z , -19 y + y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 2 G := [-15 y , 9 x + 14 x z , 2 x y + 2 y z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-15 x y z + 17 x , -14 x y z - 14 x y z , -19 y + y z], 2 4 2 2 2 [-15 y , 9 x + 14 x z , 2 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=0.11 memory used=26.4MB, alloc=32.3MB, time=0.29 memory used=47.8MB, alloc=32.3MB, time=0.48 memory used=67.4MB, alloc=56.3MB, time=0.66 memory used=107.1MB, alloc=60.3MB, time=1.00 memory used=146.2MB, alloc=84.3MB, time=1.34 memory used=205.7MB, alloc=92.3MB, time=1.89 memory used=263.9MB, alloc=116.3MB, time=2.42 memory used=343.3MB, alloc=140.3MB, time=3.20 memory used=442.3MB, alloc=164.3MB, time=4.34 memory used=556.4MB, alloc=188.3MB, time=5.61 memory used=690.7MB, alloc=212.3MB, time=7.00 memory used=789.7MB, alloc=492.3MB, time=8.43 memory used=927.7MB, alloc=516.3MB, time=11.13 memory used=1071.3MB, alloc=540.3MB, time=14.50 memory used=1238.9MB, alloc=564.3MB, time=18.38 memory used=1430.5MB, alloc=564.3MB, time=22.74 memory used=1622.0MB, alloc=588.3MB, time=27.05 memory used=1837.6MB, alloc=612.3MB, time=31.58 N1 := 6239 > GB := Basis(F, plex(op(vars))); 2 3 2 GB := [x , x y , -19 y + y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 287 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 H := [-15 x y z + 17 x , -14 x y z - 14 x y z , -19 y + y z, -15 y , 4 2 2 2 9 x + 14 x z , 2 x y + 2 y z ] > J:=[op(GB),op(G)]; 2 3 2 2 4 2 2 2 J := [x , x y , -19 y + y z, -15 y , 9 x + 14 x z , 2 x y + 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 := [6, 14, 19, 4, 4, 2, 2, 2/3, 5/6, 5/6, 7/12, 2/3, 1/2, 6, 11, 17, 4, 4, 3, 2, 2/3, 2/3, 1/2, 5/12, 1/2, 1/4, 3, 2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1989.2MB, alloc=612.3MB, time=33.81 |\^/| 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(); 1428357868 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 4 2 3 F := [16 x z + 14 x, -20 y z - 14 z , -7 x y z + 7 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 4 G := [-13 x + 4 y , 9 y + 9, 16 x - 16 z] > Problem := [F,G]; 2 2 2 2 4 2 3 Problem := [[16 x z + 14 x, -20 y z - 14 z , -7 x y z + 7 x ], 3 3 4 4 [-13 x + 4 y , 9 y + 9, 16 x - 16 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.1MB, alloc=32.3MB, time=0.36 memory used=47.2MB, alloc=32.3MB, time=0.54 memory used=67.2MB, alloc=32.3MB, time=0.71 memory used=86.8MB, alloc=56.3MB, time=0.89 memory used=126.8MB, alloc=60.3MB, time=1.24 memory used=165.3MB, alloc=60.3MB, time=1.58 memory used=202.7MB, alloc=84.3MB, time=1.92 memory used=260.7MB, alloc=92.3MB, time=2.45 memory used=318.4MB, alloc=116.3MB, time=3.04 memory used=394.3MB, alloc=140.3MB, time=3.86 memory used=484.3MB, alloc=164.3MB, time=5.22 N1 := 1559 > GB := Basis(F, plex(op(vars))); 5 4 2 3 2 2 4 GB := [640 x + 343 x, 8 x + 7 x y , -80 x y + 49 x z, 10 y z + 7 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=588.6MB, alloc=164.3MB, time=6.17 N2 := 557 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 4 2 3 3 3 H := [16 x z + 14 x, -20 y z - 14 z , -7 x y z + 7 x , -13 x + 4 y , 4 4 9 y + 9, 16 x - 16 z] > J:=[op(GB),op(G)]; 5 4 2 3 2 2 4 J := [640 x + 343 x, 8 x + 7 x y , -80 x y + 49 x z, 10 y z + 7 z , 3 3 4 4 -13 x + 4 y , 9 y + 9, 16 x - 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 := [6, 12, 23, 4, 4, 4, 4, 2/3, 2/3, 2/3, 1/2, 1/3, 5/12, 7, 13, 28, 5, 5, 4, 4, 5/7, 5/7, 3/7, 4/7, 5/14, 2/7, -1, -5, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=671.6MB, alloc=164.3MB, 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(); 1428357875 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 F := [10 x , -9 x + 3 y, 8 y + x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 G := [-12 x y z + 18 z , -14 y, x z + 20 y z] > Problem := [F,G]; Problem := [ 2 3 4 2 2 [10 x , -9 x + 3 y, 8 y + x z ], [-12 x y z + 18 z , -14 y, x z + 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=0.12 memory used=26.9MB, alloc=32.3MB, time=0.37 memory used=50.3MB, alloc=32.3MB, time=0.60 N1 := 451 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x , y, z x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=69.9MB, alloc=56.3MB, time=0.82 N2 := 55 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 4 2 2 H := [10 x , -9 x + 3 y, 8 y + z x, -12 x y z + 18 z , -14 y, x z + 20 y z] > J:=[op(GB),op(G)]; 2 2 2 J := [x , y, z x, -12 x y z + 18 z , -14 y, x z + 20 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 := [6, 13, 15, 4, 3, 4, 2, 5/6, 5/6, 1/2, 5/12, 5/12, 5/12, 6, 11, 12, 3, 2, 1, 2, 2/3, 2/3, 1/2, 4/11, 4/11, 5/11, 2, 3, 1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=74.2MB, alloc=56.3MB, time=0.87 |\^/| 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(); 1428357876 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-20 x z - 3 x , 13 y z + 12, -14 y z - 13 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 2 G := [12 x y z + 16 z , 8 x z + 11 y , -3 x - 2 y ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-20 x z - 3 x , 13 y z + 12, -14 y z - 13 x], 2 3 3 3 2 2 [12 x y z + 16 z , 8 x z + 11 y , -3 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=0.11 memory used=26.5MB, alloc=32.3MB, time=0.30 memory used=47.8MB, alloc=32.3MB, time=0.48 memory used=68.4MB, alloc=56.3MB, time=0.68 memory used=110.0MB, alloc=60.3MB, time=1.04 memory used=149.2MB, alloc=84.3MB, time=1.39 memory used=207.7MB, alloc=92.3MB, time=1.93 memory used=268.8MB, alloc=116.3MB, time=2.46 memory used=341.6MB, alloc=116.3MB, time=3.11 memory used=416.6MB, alloc=396.3MB, time=3.86 memory used=526.9MB, alloc=420.3MB, time=4.78 memory used=656.7MB, alloc=444.3MB, time=5.95 memory used=797.4MB, alloc=468.3MB, time=7.29 memory used=938.7MB, alloc=492.3MB, time=8.53 memory used=1055.8MB, alloc=492.3MB, time=9.66 memory used=1162.7MB, alloc=492.3MB, time=10.76 memory used=1257.2MB, alloc=516.3MB, time=11.77 memory used=1352.7MB, alloc=516.3MB, time=12.76 memory used=1434.3MB, alloc=516.3MB, time=13.63 memory used=1532.6MB, alloc=540.3MB, time=14.94 memory used=1671.8MB, alloc=540.3MB, time=16.49 memory used=1888.6MB, alloc=564.3MB, time=18.04 memory used=2003.9MB, alloc=564.3MB, time=19.46 memory used=2128.9MB, alloc=588.3MB, time=21.10 memory used=2239.6MB, alloc=612.3MB, time=22.61 memory used=2361.4MB, alloc=636.3MB, time=24.30 memory used=2475.9MB, alloc=660.3MB, time=25.92 memory used=2581.4MB, alloc=684.3MB, time=27.46 memory used=2667.4MB, alloc=708.3MB, time=28.78 memory used=2744.4MB, alloc=708.3MB, time=30.01 memory used=2827.8MB, alloc=732.3MB, time=31.33 memory used=2905.4MB, alloc=732.3MB, time=32.55 memory used=2991.1MB, alloc=756.3MB, time=33.93 memory used=3303.5MB, alloc=780.3MB, time=37.85 memory used=3590.8MB, alloc=804.3MB, time=43.98 memory used=3867.4MB, alloc=828.3MB, time=50.63 memory used=4149.3MB, alloc=852.3MB, time=57.79 memory used=4439.8MB, alloc=876.3MB, time=65.20 memory used=4740.2MB, alloc=900.3MB, time=73.04 memory used=5050.7MB, alloc=924.3MB, time=81.49 memory used=5375.0MB, alloc=948.3MB, time=90.40 memory used=5709.5MB, alloc=972.3MB, time=100.02 memory used=6068.0MB, alloc=996.3MB, time=110.25 memory used=6450.4MB, alloc=1020.3MB, time=121.09 memory used=6856.8MB, alloc=1044.3MB, time=132.58 memory used=7287.1MB, alloc=1068.3MB, time=144.84 memory used=7741.4MB, alloc=1092.3MB, time=157.66 memory used=8219.6MB, alloc=1116.3MB, time=171.03 memory used=8721.7MB, alloc=1140.3MB, time=185.04 memory used=9247.7MB, alloc=1164.3MB, time=199.80 memory used=9797.7MB, alloc=1164.3MB, time=215.15 memory used=10347.7MB, alloc=1188.3MB, time=230.43 memory used=10921.5MB, alloc=1188.3MB, time=246.34 memory used=11495.3MB, alloc=1188.3MB, time=262.36 memory used=12069.1MB, alloc=1188.3MB, time=278.35 memory used=12642.6MB, alloc=1212.3MB, time=294.66 |\^/| 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(); 1428358176 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 3 F := [-12 x y - 20 x z, 15 x - 2 x y z, -18 x z + 9 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 G := [13 y z - 2 x y , -8 x y z + 14 y, -14 x y + 14 y z] > Problem := [F,G]; 2 2 4 2 3 Problem := [[-12 x y - 20 x z, 15 x - 2 x y z, -18 x z + 9 x z], 3 2 2 3 2 [13 y z - 2 x y , -8 x y z + 14 y, -14 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=0.15 memory used=26.0MB, alloc=32.3MB, time=0.39 memory used=46.7MB, alloc=32.3MB, time=0.60 memory used=67.5MB, alloc=32.3MB, time=0.84 memory used=86.7MB, alloc=56.3MB, time=1.09 memory used=125.6MB, alloc=60.3MB, time=1.52 memory used=162.8MB, alloc=60.3MB, time=1.94 memory used=201.1MB, alloc=84.3MB, time=2.44 memory used=258.9MB, alloc=92.3MB, time=3.30 memory used=311.7MB, alloc=116.3MB, time=4.06 memory used=381.6MB, alloc=140.3MB, time=4.96 memory used=458.1MB, alloc=164.3MB, time=6.51 memory used=557.0MB, alloc=188.3MB, time=8.30 N1 := 2715 > GB := Basis(F, plex(op(vars))); 6 4 4 2 2 2 2 4 4 2 2 GB := [2 x - x , 2 x y - x y , 2 x y + 25 x , 3 x y + 5 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=680.9MB, alloc=188.3MB, time=9.63 N2 := 1083 #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 4 2 3 3 2 H := [-12 x y - 20 x z, 15 x - 2 x y z, -18 x z + 9 x z, 13 y z - 2 x y , 2 3 2 -8 x y z + 14 y, -14 x y + 14 y z] > J:=[op(GB),op(G)]; 6 4 4 2 2 2 2 4 4 2 2 J := [2 x - x , 2 x y - x y , 2 x y + 25 x , 3 x y + 5 x z, 3 2 2 3 2 13 y z - 2 x y , -8 x y z + 14 y, -14 x 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 := [6, 17, 24, 4, 4, 3, 1, 1, 5/6, 1, 3/4, 2/3, 7/12, 7, 17, 34, 6, 6, 4, 1, 1, 6/7, 4/7, 11/14, 5/7, 2/7, 0, -10, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=778.1MB, alloc=188.3MB, time=10.80 |\^/| 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(); 1428358187 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 2 2 2 F := [-16 x y + 4 y , 2 x y - 4 x z, -15 x z + 13 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 G := [-6 y z - 1, 7 z - 2 x y , 6 x y z + 5 z] > Problem := [F,G]; 2 2 2 3 3 2 2 2 Problem := [[-16 x y + 4 y , 2 x y - 4 x z, -15 x z + 13 x z ], 2 4 2 [-6 y z - 1, 7 z - 2 x y , 6 x y z + 5 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.12 memory used=26.1MB, alloc=32.3MB, time=0.30 memory used=47.7MB, alloc=32.3MB, time=0.48 memory used=68.4MB, alloc=32.3MB, time=0.69 memory used=89.5MB, alloc=56.3MB, time=0.94 memory used=132.4MB, alloc=60.3MB, time=1.41 memory used=171.5MB, alloc=84.3MB, time=1.81 memory used=227.7MB, alloc=108.3MB, time=2.69 memory used=294.9MB, alloc=108.3MB, time=3.90 N1 := 2031 > GB := Basis(F, plex(op(vars))); 2 3 3 2 GB := [y , -x y + 2 x z, x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=364.1MB, alloc=108.3MB, time=4.74 memory used=442.5MB, alloc=140.3MB, time=5.58 N2 := 1325 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 3 2 2 2 2 H := [-16 x y + 4 y , 2 x y - 4 x z, -15 x z + 13 x z , -6 y z - 1, 4 2 7 z - 2 x y , 6 x y z + 5 z] > J:=[op(GB),op(G)]; 2 3 3 2 2 4 2 J := [y , -x y + 2 x z, x z , -6 y z - 1, 7 z - 2 x y , 6 x y z + 5 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 22, 4, 3, 2, 4, 5/6, 5/6, 5/6, 7/12, 1/2, 7/12, 6, 14, 19, 4, 3, 2, 4, 2/3, 5/6, 5/6, 5/12, 5/12, 1/2, 1, 3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=520.5MB, alloc=140.3MB, time=6.64 |\^/| 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(); 1428358194 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 2 F := [-15 y z + 7 y , -z - 7 y , -12 x y - 4 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 2 G := [17 x y , 9 y z - 10 y z , 17 x y z - 19 x y ] > Problem := [F,G]; 3 3 4 2 Problem := [[-15 y z + 7 y , -z - 7 y , -12 x y - 4 y], 2 2 2 2 3 2 2 [17 x y , 9 y z - 10 y z , 17 x y z - 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=4.3MB, alloc=32.3MB, time=0.13 memory used=26.3MB, alloc=32.3MB, time=0.34 memory used=48.7MB, alloc=32.3MB, time=0.56 memory used=69.2MB, alloc=56.3MB, time=0.79 N1 := 435 > GB := Basis(F, plex(op(vars))); 5 3 3 3 3 3 4 2 GB := [3 x y + y, 7 y + 50625 y , y z + 15 y , 15 y z - 7 y , z + 7 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=107.2MB, alloc=60.3MB, time=1.12 memory used=149.6MB, alloc=60.3MB, time=1.55 N2 := 645 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 4 2 2 2 2 2 3 H := [-15 y z + 7 y , -z - 7 y , -12 x y - 4 y, 17 x y , 9 y z - 10 y z , 2 2 17 x y z - 19 x y ] > J:=[op(GB),op(G)]; 5 3 3 3 3 3 4 2 J := [3 x y + y, 7 y + 50625 y , y z + 15 y , 15 y z - 7 y , z + 7 y , 2 2 2 2 3 2 2 17 x y , 9 y z - 10 y z , 17 x y z - 19 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 := [6, 13, 22, 4, 2, 3, 4, 1/2, 1, 2/3, 4/13, 10/13, 5/13, 8, 16, 31, 5, 2, 5, 4, 3/8, 1, 5/8, 4/17, 14/17, 6/17, -3, -9, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=168.9MB, alloc=60.3MB, time=1.81 |\^/| 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(); 1428358196 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 F := [-9 y z - 6 x, -17 x y z - x, 6 x y - 18 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 4 G := [19 x y - 19 x y z, -9 y + x z, -16 x ] > Problem := [F,G]; 3 2 3 3 Problem := [[-9 y z - 6 x, -17 x y z - x, 6 x y - 18 z ], 3 2 4 2 4 [19 x y - 19 x y z, -9 y + x z, -16 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.11 memory used=26.6MB, alloc=32.3MB, time=0.31 memory used=47.7MB, alloc=32.3MB, time=0.49 memory used=67.2MB, alloc=56.3MB, time=0.68 memory used=108.9MB, alloc=60.3MB, time=1.03 memory used=144.3MB, alloc=60.3MB, time=1.29 memory used=183.1MB, alloc=84.3MB, time=1.64 memory used=217.9MB, alloc=84.3MB, time=1.96 memory used=275.6MB, alloc=92.3MB, time=2.50 memory used=335.9MB, alloc=116.3MB, time=3.05 memory used=394.4MB, alloc=116.3MB, time=3.53 memory used=458.3MB, alloc=396.3MB, time=4.07 memory used=569.0MB, alloc=396.3MB, time=4.92 memory used=675.9MB, alloc=420.3MB, time=5.80 memory used=799.3MB, alloc=444.3MB, time=6.86 memory used=926.7MB, alloc=468.3MB, time=7.99 memory used=1034.8MB, alloc=492.3MB, time=8.83 memory used=1139.7MB, alloc=492.3MB, time=9.82 memory used=1254.1MB, alloc=492.3MB, time=10.89 memory used=1339.5MB, alloc=516.3MB, time=11.67 memory used=1447.6MB, alloc=516.3MB, time=12.61 memory used=1528.6MB, alloc=516.3MB, time=13.34 memory used=1606.9MB, alloc=516.3MB, time=14.12 memory used=1675.8MB, alloc=540.3MB, time=14.90 memory used=1832.2MB, alloc=540.3MB, time=16.42 memory used=1950.4MB, alloc=564.3MB, time=17.86 memory used=2088.9MB, alloc=588.3MB, time=19.43 memory used=2225.3MB, alloc=588.3MB, time=20.98 memory used=2346.2MB, alloc=612.3MB, time=22.48 memory used=2447.6MB, alloc=612.3MB, time=23.84 memory used=2562.1MB, alloc=636.3MB, time=25.76 memory used=2699.3MB, alloc=660.3MB, time=28.86 memory used=2925.7MB, alloc=684.3MB, time=34.55 memory used=3163.0MB, alloc=708.3MB, time=40.90 memory used=3424.3MB, alloc=732.3MB, time=47.58 memory used=3709.6MB, alloc=756.3MB, time=54.76 memory used=4018.9MB, alloc=756.3MB, time=62.55 N1 := 7481 > GB := Basis(F, plex(op(vars))); 3 2 2 3 GB := [19652 x + 3 x, 3 x y - 39304 x, -x y + 34 x z, 19652 z + x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4335.6MB, alloc=756.3MB, time=68.78 memory used=4775.8MB, alloc=756.3MB, time=72.42 memory used=5238.1MB, alloc=780.3MB, time=76.39 memory used=5697.6MB, alloc=804.3MB, time=82.25 N2 := 3451 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 3 3 2 H := [-9 y z - 6 x, -17 x y z - x, 6 x y - 18 z , 19 x y - 19 x y z, 4 2 4 -9 y + z x , -16 x ] > J:=[op(GB),op(G)]; 3 2 2 3 J := [19652 x + 3 x, 3 x y - 39304 x, -x y + 34 x z, 19652 z + y x, 3 2 4 2 4 19 x y - 19 x y z, -9 y + z 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 := [6, 16, 24, 4, 4, 4, 3, 1, 5/6, 5/6, 2/3, 1/2, 5/12, 7, 16, 24, 4, 4, 4, 3, 1, 5/7, 4/7, 11/14, 3/7, 2/7, 0, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=5965.2MB, alloc=804.3MB, time=87.84 |\^/| 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(); 1428358281 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 3 F := [13 y z - 5 z , -2 x y z - 19 y z , -10 x y - 14 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [-4 y z - 19 z, 9 x y - 9 z , -x y z + 9 z] > Problem := [F,G]; 3 4 2 2 3 Problem := [[13 y z - 5 z , -2 x y z - 19 y z , -10 x y - 14 x z], 2 2 2 3 2 [-4 y z - 19 z, 9 x y - 9 z , -x y z + 9 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.7MB, alloc=32.3MB, time=0.37 memory used=48.0MB, alloc=32.3MB, time=0.55 memory used=69.1MB, alloc=32.3MB, time=0.74 memory used=88.0MB, alloc=56.3MB, time=0.91 memory used=127.4MB, alloc=60.3MB, time=1.27 memory used=163.3MB, alloc=60.3MB, time=1.58 memory used=198.2MB, alloc=84.3MB, time=1.91 memory used=255.5MB, alloc=92.3MB, time=2.44 memory used=312.9MB, alloc=116.3MB, time=2.96 memory used=393.2MB, alloc=116.3MB, time=3.66 memory used=472.1MB, alloc=116.3MB, time=4.38 memory used=547.4MB, alloc=140.3MB, time=5.10 memory used=643.0MB, alloc=140.3MB, time=6.00 memory used=733.6MB, alloc=164.3MB, time=6.88 memory used=824.6MB, alloc=420.3MB, time=7.79 memory used=937.9MB, alloc=444.3MB, time=8.89 memory used=1072.1MB, alloc=468.3MB, time=10.16 memory used=1225.3MB, alloc=492.3MB, time=11.89 memory used=1384.4MB, alloc=516.3MB, time=13.70 memory used=1552.5MB, alloc=540.3MB, time=15.63 memory used=1728.8MB, alloc=564.3MB, time=17.75 memory used=1912.0MB, alloc=588.3MB, time=19.96 memory used=2090.4MB, alloc=612.3MB, time=23.01 memory used=2263.1MB, alloc=636.3MB, time=26.72 memory used=2444.6MB, alloc=660.3MB, time=31.04 memory used=2638.9MB, alloc=684.3MB, time=35.76 memory used=2846.7MB, alloc=708.3MB, time=40.94 memory used=3062.7MB, alloc=732.3MB, time=46.82 memory used=3301.7MB, alloc=756.3MB, time=53.32 memory used=3564.7MB, alloc=780.3MB, time=60.45 memory used=3851.7MB, alloc=804.3MB, time=68.22 memory used=4162.5MB, alloc=828.3MB, time=76.58 memory used=4497.3MB, alloc=852.3MB, time=85.58 memory used=4856.1MB, alloc=876.3MB, time=95.28 memory used=5238.8MB, alloc=876.3MB, time=105.52 memory used=5621.4MB, alloc=900.3MB, time=115.71 memory used=6028.0MB, alloc=900.3MB, time=126.56 memory used=6434.4MB, alloc=900.3MB, time=137.26 memory used=6840.9MB, alloc=924.3MB, time=147.94 memory used=7271.3MB, alloc=924.3MB, time=159.33 memory used=7701.6MB, alloc=924.3MB, time=170.50 memory used=8132.1MB, alloc=948.3MB, time=181.64 memory used=8586.4MB, alloc=948.3MB, time=193.51 memory used=9040.6MB, alloc=972.3MB, time=205.09 memory used=9518.9MB, alloc=996.3MB, time=217.07 N1 := 16259 > GB := Basis(F, plex(op(vars))); 9 4 5 4 6 4 4 5 7 3 4 GB := [2500 x y + 5551819 x y , 10 x y + 247 x y , 95 x y - 14 x y , 3 2 4 2 4 4 4 5 x y + 7 x z, -10 x y + 133 y z , 52 x y + 2527 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=10033.5MB, alloc=996.3MB, time=227.31 memory used=10361.2MB, alloc=996.3MB, time=231.33 memory used=10967.6MB, alloc=996.3MB, time=237.72 memory used=11567.7MB, alloc=1020.3MB, time=244.37 memory used=12120.8MB, alloc=1044.3MB, time=249.82 memory used=12764.4MB, alloc=1068.3MB, time=257.27 memory used=13373.0MB, alloc=1092.3MB, time=264.22 memory used=14036.5MB, alloc=1116.3MB, time=271.76 memory used=14683.6MB, alloc=1140.3MB, time=280.35 memory used=15238.1MB, alloc=1164.3MB, time=291.20 memory used=15676.4MB, alloc=1188.3MB, time=304.43 |\^/| 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(); 1428358581 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 F := [-5 x y + 15 x z, 19 x z + 17 y z , 9 x z - 1] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 4 3 2 G := [-18 x + 20 x z , 11 x y - 14 y , -7 x z + 10 x y] > Problem := [F,G]; 2 3 2 2 3 Problem := [[-5 x y + 15 x z, 19 x z + 17 y z , 9 x z - 1], 3 2 3 4 3 2 [-18 x + 20 x z , 11 x y - 14 y , -7 x z + 10 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.6MB, alloc=32.3MB, time=0.37 memory used=48.2MB, alloc=32.3MB, time=0.63 memory used=69.4MB, alloc=32.3MB, time=0.87 memory used=89.5MB, alloc=56.3MB, time=1.12 memory used=129.3MB, alloc=60.3MB, time=1.58 memory used=170.3MB, alloc=92.3MB, time=2.05 memory used=233.5MB, alloc=92.3MB, time=2.73 memory used=297.4MB, alloc=116.3MB, time=3.43 memory used=373.3MB, alloc=372.3MB, time=4.26 memory used=458.3MB, alloc=396.3MB, time=5.15 memory used=565.8MB, alloc=420.3MB, time=6.33 memory used=697.0MB, alloc=444.3MB, time=7.79 memory used=839.0MB, alloc=444.3MB, time=9.42 memory used=954.5MB, alloc=468.3MB, time=10.78 memory used=1069.5MB, alloc=492.3MB, time=12.17 memory used=1191.3MB, alloc=492.3MB, time=13.80 memory used=1311.7MB, alloc=516.3MB, time=15.12 memory used=1519.3MB, alloc=540.3MB, time=17.23 memory used=1736.4MB, alloc=564.3MB, time=19.55 memory used=1935.2MB, alloc=588.3MB, time=21.94 memory used=2120.1MB, alloc=612.3MB, time=24.26 memory used=2303.2MB, alloc=636.3MB, time=26.59 memory used=2487.2MB, alloc=660.3MB, time=28.81 memory used=2709.7MB, alloc=684.3MB, time=31.33 memory used=2868.1MB, alloc=708.3MB, time=33.52 memory used=3049.0MB, alloc=732.3MB, time=37.37 memory used=3275.8MB, alloc=756.3MB, time=42.72 memory used=3529.9MB, alloc=780.3MB, time=48.99 memory used=3793.4MB, alloc=804.3MB, time=55.68 memory used=4067.5MB, alloc=828.3MB, time=62.49 memory used=4346.8MB, alloc=852.3MB, time=69.94 memory used=4643.1MB, alloc=876.3MB, time=78.02 memory used=4963.3MB, alloc=900.3MB, time=86.74 memory used=5307.4MB, alloc=924.3MB, time=96.18 memory used=5675.5MB, alloc=948.3MB, time=106.12 memory used=6067.6MB, alloc=972.3MB, time=116.92 memory used=6483.6MB, alloc=996.3MB, time=128.09 memory used=6923.5MB, alloc=1020.3MB, time=139.89 memory used=7387.3MB, alloc=1044.3MB, time=152.41 memory used=7875.1MB, alloc=1044.3MB, time=165.44 memory used=8362.9MB, alloc=1044.3MB, time=178.43 memory used=8850.6MB, alloc=1044.3MB, time=191.48 memory used=9338.2MB, alloc=1068.3MB, time=204.49 memory used=9849.6MB, alloc=1068.3MB, time=218.21 memory used=10360.9MB, alloc=1068.3MB, time=232.00 memory used=10872.1MB, alloc=1092.3MB, time=245.62 memory used=11407.3MB, alloc=1092.3MB, time=259.85 memory used=11942.2MB, alloc=1092.3MB, time=274.14 memory used=12477.1MB, alloc=1116.3MB, time=288.35 memory used=13035.8MB, alloc=1116.3MB, time=303.22 |\^/| 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(); 1428358881 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 F := [-6 x y z - 10 x z , -10 y z + 2 x z, y z + 11 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 G := [-10 y z - 11 z, -8 x z + 8 x z, -3 x y - 3 y ] > Problem := [F,G]; 2 2 3 3 Problem := [[-6 x y z - 10 x z , -10 y z + 2 x z, y z + 11 y z], 3 3 3 3 [-10 y z - 11 z, -8 x z + 8 x z, -3 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=4.3MB, alloc=32.3MB, time=0.14 memory used=26.0MB, alloc=32.3MB, time=0.38 memory used=46.1MB, alloc=32.3MB, time=0.59 memory used=66.7MB, alloc=32.3MB, time=0.82 memory used=86.1MB, alloc=32.3MB, time=1.02 memory used=104.6MB, alloc=56.3MB, time=1.25 memory used=145.3MB, alloc=60.3MB, time=1.80 memory used=180.8MB, alloc=84.3MB, time=2.26 memory used=233.8MB, alloc=108.3MB, time=3.15 memory used=298.8MB, alloc=132.3MB, time=4.94 N1 := 2201 > GB := Basis(F, plex(op(vars))); memory used=384.4MB, alloc=132.3MB, time=7.06 3 2 GB := [x z + 33275 x z, x z + 55 y z, x z + 363 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 675 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 3 H := [-6 x y z - 10 x z , -10 y z + 2 x z, y z + 11 y z, -10 y z - 11 z, 3 3 3 -8 x z + 8 x z, -3 x y - 3 y ] > J:=[op(GB),op(G)]; 3 2 3 J := [x z + 33275 x z, x z + 55 y z, x z + 363 x z, -10 y z - 11 z, 3 3 3 -8 x z + 8 x z, -3 x y - 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 := [6, 14, 24, 4, 3, 3, 3, 2/3, 5/6, 5/6, 1/2, 7/12, 5/6, 6, 13, 21, 4, 3, 3, 3, 5/6, 1/2, 5/6, 2/3, 1/3, 5/6, 1, 3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=470.9MB, alloc=140.3MB, time=8.20 |\^/| 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(); 1428358889 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 F := [6 y - 3 x z, -8 x y + 14 x z , 4 x y z + 7 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [-11 x z - 15 x y z, 2 x y + 6 z , -15 x y + 13 z] > Problem := [F,G]; 4 2 2 2 2 Problem := [[6 y - 3 x z, -8 x y + 14 x z , 4 x y z + 7 y z], 3 2 3 2 [-11 x z - 15 x y z, 2 x y + 6 z , -15 x 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=26.6MB, alloc=32.3MB, time=0.44 memory used=47.9MB, alloc=32.3MB, time=0.68 memory used=68.1MB, alloc=56.3MB, time=0.93 memory used=109.5MB, alloc=60.3MB, time=1.42 memory used=150.7MB, alloc=60.3MB, time=1.89 memory used=190.2MB, alloc=84.3MB, time=2.35 memory used=222.7MB, alloc=84.3MB, time=2.73 memory used=283.2MB, alloc=92.3MB, time=3.45 memory used=343.3MB, alloc=116.3MB, time=4.13 memory used=420.0MB, alloc=116.3MB, time=5.02 memory used=498.7MB, alloc=140.3MB, time=6.16 memory used=592.5MB, alloc=164.3MB, time=7.57 memory used=701.9MB, alloc=188.3MB, time=8.89 memory used=798.9MB, alloc=468.3MB, time=10.02 memory used=933.2MB, alloc=492.3MB, time=11.79 memory used=1064.3MB, alloc=516.3MB, time=14.29 memory used=1203.7MB, alloc=540.3MB, time=17.47 memory used=1354.8MB, alloc=564.3MB, time=21.40 memory used=1530.0MB, alloc=588.3MB, time=25.85 memory used=1729.0MB, alloc=612.3MB, time=30.88 memory used=1952.1MB, alloc=612.3MB, time=36.51 memory used=2175.1MB, alloc=612.3MB, time=42.09 memory used=2398.2MB, alloc=636.3MB, time=47.64 memory used=2645.2MB, alloc=660.3MB, time=53.28 N1 := 7947 > GB := Basis(F, plex(op(vars))); 11 2 2 3 2 3 8 2 6 GB := [4096 x y - 16807 x y , 4 x y + 7 x y , -256 x y + 2401 y , 4 7 2 2 -2 y + z x, -512 x y + 2401 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2923.7MB, alloc=660.3MB, time=57.81 memory used=3080.5MB, alloc=660.3MB, time=59.61 memory used=3238.5MB, alloc=660.3MB, time=61.35 memory used=3387.6MB, alloc=660.3MB, time=63.00 memory used=3582.4MB, alloc=684.3MB, time=65.61 memory used=3874.9MB, alloc=708.3MB, time=72.32 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)]; 4 2 2 2 2 3 H := [6 y - 3 x z, -8 x y + 14 x z , 4 x y z + 7 y z, -11 x z - 15 x y z, 2 3 2 2 x y + 6 z , -15 x y + 13 z] > J:=[op(GB),op(G)]; 11 2 2 3 2 3 8 2 6 J := [4096 x y - 16807 x y , 4 x y + 7 x y , -256 x y + 2401 y , 4 7 2 2 3 2 3 -2 y + z x, -512 x y + 2401 y z, -11 x z - 15 x y z, 2 x y + 6 z , 2 -15 x y + 13 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, 18, 21, 4, 3, 4, 3, 1, 1, 1, 2/3, 7/12, 2/3, 8, 21, 51, 13, 11, 6, 3, 1, 1, 5/8, 11/16, 3/4, 3/8, -3, -30, -9] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3949.5MB, alloc=708.3MB, time=73.62 |\^/| 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(); 1428358962 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [9 y - 12 z, -10 x - 12 x y, 7 x y z - 15 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 G := [-8 x y - 6 z, -9 x z - 9 x , 16 y z - y z] > Problem := [F,G]; 2 2 2 Problem := [[9 y - 12 z, -10 x - 12 x y, 7 x y z - 15 x], 3 2 3 [-8 x y - 6 z, -9 x z - 9 x , 16 y z - y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.4MB, alloc=32.3MB, time=0.36 memory used=47.6MB, alloc=32.3MB, time=0.53 memory used=67.2MB, alloc=32.3MB, time=0.71 memory used=85.9MB, alloc=56.3MB, time=0.89 memory used=124.7MB, alloc=60.3MB, time=1.23 memory used=160.9MB, alloc=60.3MB, time=1.54 memory used=195.0MB, alloc=84.3MB, time=1.86 memory used=248.3MB, alloc=84.3MB, time=2.36 memory used=298.3MB, alloc=108.3MB, time=2.83 memory used=370.7MB, alloc=116.3MB, time=3.51 memory used=441.9MB, alloc=116.3MB, time=4.16 memory used=512.3MB, alloc=140.3MB, time=4.82 memory used=605.0MB, alloc=140.3MB, time=5.68 memory used=695.9MB, alloc=164.3MB, time=6.55 memory used=804.4MB, alloc=164.3MB, time=7.68 memory used=896.5MB, alloc=444.3MB, time=8.62 memory used=1020.9MB, alloc=468.3MB, time=9.84 memory used=1167.7MB, alloc=492.3MB, time=11.49 memory used=1324.5MB, alloc=516.3MB, time=13.26 memory used=1486.3MB, alloc=540.3MB, time=15.14 memory used=1654.7MB, alloc=564.3MB, time=17.16 memory used=1829.1MB, alloc=588.3MB, time=19.27 memory used=2008.8MB, alloc=612.3MB, time=21.46 memory used=2193.5MB, alloc=636.3MB, time=23.76 memory used=2381.7MB, alloc=660.3MB, time=26.12 memory used=2571.8MB, alloc=684.3MB, time=28.56 memory used=2764.1MB, alloc=708.3MB, time=31.08 memory used=2933.5MB, alloc=732.3MB, time=34.59 memory used=3107.0MB, alloc=756.3MB, time=38.56 memory used=3290.5MB, alloc=780.3MB, time=43.02 memory used=3486.5MB, alloc=804.3MB, time=47.95 memory used=3695.8MB, alloc=828.3MB, time=53.27 memory used=3918.7MB, alloc=852.3MB, time=58.98 memory used=4156.0MB, alloc=876.3MB, time=65.16 memory used=4408.1MB, alloc=900.3MB, time=71.90 memory used=4674.6MB, alloc=924.3MB, time=79.04 memory used=4956.8MB, alloc=948.3MB, time=86.64 memory used=5254.2MB, alloc=972.3MB, time=94.68 memory used=5566.8MB, alloc=996.3MB, time=103.04 memory used=5894.3MB, alloc=1020.3MB, time=111.54 memory used=6236.8MB, alloc=1044.3MB, time=120.55 memory used=6590.0MB, alloc=1068.3MB, time=130.20 memory used=6967.1MB, alloc=1092.3MB, time=140.52 memory used=7368.2MB, alloc=1116.3MB, time=151.37 memory used=7793.2MB, alloc=1140.3MB, time=162.83 memory used=8242.2MB, alloc=1164.3MB, time=174.92 memory used=8715.1MB, alloc=1188.3MB, time=187.59 memory used=9212.0MB, alloc=1212.3MB, time=201.02 memory used=9732.8MB, alloc=1236.3MB, time=214.93 memory used=10277.6MB, alloc=1260.3MB, time=229.45 memory used=10846.2MB, alloc=1284.3MB, time=244.56 memory used=11438.9MB, alloc=1308.3MB, time=260.42 memory used=12055.5MB, alloc=1332.3MB, time=276.77 memory used=12696.0MB, alloc=1356.3MB, time=293.73 |\^/| 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(); 1428359262 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [-20 x y - 20 y z , -11 x + 17 x z, -2 x - y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [-15 x z - 17 x , -2 x y + 5 x z, 17 y z - 14 y ] > Problem := [F,G]; 3 2 3 2 Problem := [[-20 x y - 20 y z , -11 x + 17 x z, -2 x - y z], 2 2 2 2 3 2 [-15 x z - 17 x , -2 x y + 5 x z, 17 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=0.14 memory used=26.4MB, alloc=32.3MB, time=0.40 memory used=77.1MB, alloc=68.3MB, time=0.97 memory used=123.8MB, alloc=68.3MB, time=1.48 memory used=168.7MB, alloc=68.3MB, time=1.97 memory used=211.8MB, alloc=92.3MB, time=2.48 memory used=276.5MB, alloc=100.3MB, time=3.26 memory used=339.9MB, alloc=124.3MB, time=4.11 memory used=427.8MB, alloc=124.3MB, time=5.00 memory used=509.4MB, alloc=148.3MB, time=5.79 memory used=593.8MB, alloc=148.3MB, time=6.60 memory used=687.4MB, alloc=428.3MB, time=7.64 memory used=809.3MB, alloc=428.3MB, time=8.83 memory used=930.0MB, alloc=452.3MB, time=10.06 memory used=1071.4MB, alloc=476.3MB, time=11.51 memory used=1230.9MB, alloc=500.3MB, time=13.17 memory used=1387.6MB, alloc=524.3MB, time=14.82 memory used=1548.9MB, alloc=548.3MB, time=16.72 memory used=1752.0MB, alloc=572.3MB, time=19.15 memory used=1962.7MB, alloc=596.3MB, time=21.72 memory used=2156.1MB, alloc=620.3MB, time=24.18 memory used=2353.0MB, alloc=644.3MB, time=27.39 memory used=2556.3MB, alloc=668.3MB, time=31.82 memory used=2764.1MB, alloc=692.3MB, time=36.88 memory used=2980.7MB, alloc=716.3MB, time=42.61 memory used=3214.0MB, alloc=740.3MB, time=49.18 memory used=3471.2MB, alloc=764.3MB, time=56.14 memory used=3752.4MB, alloc=788.3MB, time=63.67 memory used=4057.5MB, alloc=812.3MB, time=71.95 memory used=4386.5MB, alloc=836.3MB, time=80.62 memory used=4739.5MB, alloc=860.3MB, time=89.86 memory used=5116.4MB, alloc=884.3MB, time=99.66 memory used=5517.3MB, alloc=908.3MB, time=110.05 memory used=5942.1MB, alloc=908.3MB, time=120.86 memory used=6366.8MB, alloc=932.3MB, time=131.56 N1 := 11925 > GB := Basis(F, plex(op(vars))); 4 3 3 3 3 2 GB := [121 x + 289 x , 11 x y + 34 x , -11 x + 17 x z, z y + 2 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6755.8MB, alloc=932.3MB, time=139.24 memory used=6882.7MB, alloc=932.3MB, time=141.33 memory used=7007.3MB, alloc=932.3MB, time=143.36 memory used=7123.1MB, alloc=932.3MB, time=145.34 memory used=7273.2MB, alloc=932.3MB, time=147.72 N2 := 2803 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 2 2 2 H := [-20 x y - 20 y z , -11 x + 17 x z, -2 x - y z, -15 x z - 17 x , 2 3 2 -2 x y + 5 x z, 17 y z - 14 y ] > J:=[op(GB),op(G)]; 4 3 3 3 3 2 J := [121 x + 289 x , 11 x y + 34 x , -11 x + 17 x z, z y + 2 x , 2 2 2 2 3 2 -15 x z - 17 x , -2 x y + 5 x z, 17 y z - 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 := [6, 15, 20, 4, 3, 2, 3, 5/6, 2/3, 1, 2/3, 1/2, 1/2, 7, 15, 24, 4, 4, 2, 3, 6/7, 4/7, 5/7, 11/14, 5/14, 5/14, 0, -4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=7562.5MB, alloc=932.3MB, time=153.75 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428359413 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 F := [10 x - 5 x y , 2 y z - 10 y, -6 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [-5 y z + 7 y, 14 x y z - 3 x y , -20 x y z - 5 y ] > Problem := [F,G]; 4 2 Problem := [[10 x - 5 x y , 2 y z - 10 y, -6 x z], 2 2 2 2 2 2 [-5 y z + 7 y, 14 x y z - 3 x y , -20 x y z - 5 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.1MB, alloc=40.3MB, time=0.37 memory used=59.8MB, alloc=40.3MB, time=0.64 memory used=85.2MB, alloc=64.3MB, time=0.91 memory used=133.4MB, alloc=68.3MB, time=1.43 memory used=175.4MB, alloc=92.3MB, time=1.88 memory used=236.8MB, alloc=116.3MB, time=2.52 memory used=311.6MB, alloc=140.3MB, time=3.59 memory used=394.9MB, alloc=164.3MB, time=5.24 memory used=502.3MB, alloc=164.3MB, time=7.20 N1 := 3167 > GB := Basis(F, plex(op(vars))); 4 GB := [x , y x, x z, y z - 5 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=612.1MB, alloc=164.3MB, time=8.72 memory used=741.7MB, alloc=196.3MB, time=10.38 N2 := 1291 #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)]; 4 2 2 2 2 2 H := [10 x - 5 x y , 2 y z - 10 y, -6 x z, -5 y z + 7 y, 14 x y z - 3 x y , 2 2 -20 x y z - 5 y ] > J:=[op(GB),op(G)]; 4 2 2 2 2 J := [x , y x, x z, y z - 5 y, -5 y z + 7 y, 14 x y z - 3 x y , 2 2 -20 x y 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 := [6, 14, 20, 4, 4, 2, 2, 2/3, 5/6, 5/6, 6/13, 9/13, 5/13, 7, 15, 22, 4, 4, 2, 2, 5/7, 5/7, 5/7, 3/7, 9/14, 5/14, -1, -2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=746.1MB, alloc=196.3MB, time=10.45 |\^/| 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(); 1428359423 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [-18 x y z - 7 y z, 16 x , 12 x z + 9 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 3 2 G := [-8 x y + 10 y , 9 x y + 10 y z , 10 x z - 15 x y] > Problem := [F,G]; 2 3 2 Problem := [[-18 x y z - 7 y z, 16 x , 12 x z + 9 x], 3 2 3 2 2 3 2 [-8 x y + 10 y , 9 x y + 10 y z , 10 x z - 15 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.8MB, alloc=32.3MB, time=0.34 memory used=48.0MB, alloc=32.3MB, time=0.52 memory used=69.5MB, alloc=32.3MB, time=0.77 N1 := 399 > GB := Basis(F, plex(op(vars))); 3 2 GB := [x , y x, y z, 4 x z + 3 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=88.4MB, alloc=56.3MB, time=0.99 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 3 2 3 2 H := [-18 x y z - 7 y z, 16 x , 12 x z + 9 x, -8 x y + 10 y , 3 2 2 3 2 9 x y + 10 y z , 10 x z - 15 x y] > J:=[op(GB),op(G)]; 3 2 3 2 3 2 2 J := [x , y x, y z, 4 x z + 3 x, -8 x y + 10 y , 9 x y + 10 y z , 3 2 10 x z - 15 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 := [6, 14, 22, 4, 3, 3, 2, 1, 2/3, 2/3, 2/3, 7/12, 5/12, 7, 15, 22, 4, 3, 3, 2, 6/7, 5/7, 4/7, 4/7, 1/2, 2/7, -1, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=121.3MB, alloc=60.3MB, time=1.27 |\^/| 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(); 1428359424 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [-8 x y + 13, -17 x y - 16 x z, 16 x y - z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 4 3 2 G := [-10 x y z + 7 y z , 5 x y - 13 y , -9 y z + 19 x y ] > Problem := [F,G]; 3 3 2 Problem := [[-8 x y + 13, -17 x y - 16 x z, 16 x y - z ], 2 3 2 2 4 3 2 [-10 x y z + 7 y z , 5 x y - 13 y , -9 y z + 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=4.3MB, alloc=32.3MB, time=0.11 memory used=26.4MB, alloc=32.3MB, time=0.29 memory used=47.7MB, alloc=32.3MB, time=0.46 memory used=67.7MB, alloc=32.3MB, time=0.63 memory used=87.1MB, alloc=56.3MB, time=0.80 memory used=127.1MB, alloc=60.3MB, time=1.16 memory used=165.2MB, alloc=60.3MB, time=1.49 memory used=201.6MB, alloc=84.3MB, time=1.81 memory used=258.3MB, alloc=84.3MB, time=2.31 memory used=314.3MB, alloc=116.3MB, time=2.89 memory used=390.1MB, alloc=140.3MB, time=3.73 memory used=480.7MB, alloc=164.3MB, time=4.78 memory used=585.9MB, alloc=188.3MB, time=5.93 memory used=707.1MB, alloc=212.3MB, time=7.25 memory used=824.2MB, alloc=492.3MB, time=8.61 memory used=966.9MB, alloc=516.3MB, time=10.32 memory used=1107.8MB, alloc=540.3MB, time=12.92 memory used=1256.4MB, alloc=564.3MB, time=16.02 memory used=1418.2MB, alloc=588.3MB, time=19.63 memory used=1593.1MB, alloc=612.3MB, time=23.80 memory used=1780.0MB, alloc=636.3MB, time=28.80 memory used=1990.9MB, alloc=660.3MB, time=34.27 memory used=2225.8MB, alloc=684.3MB, time=40.32 memory used=2484.5MB, alloc=708.3MB, time=46.99 memory used=2767.3MB, alloc=708.3MB, time=54.23 memory used=3050.0MB, alloc=708.3MB, time=61.48 memory used=3332.6MB, alloc=708.3MB, time=68.69 memory used=3615.1MB, alloc=732.3MB, time=75.80 memory used=3921.5MB, alloc=732.3MB, time=83.45 memory used=4227.8MB, alloc=732.3MB, time=91.15 memory used=4534.2MB, alloc=756.3MB, time=98.75 memory used=4864.5MB, alloc=756.3MB, time=106.75 memory used=5194.6MB, alloc=780.3MB, time=114.61 memory used=5548.9MB, alloc=804.3MB, time=122.41 N1 := 12333 > GB := Basis(F, plex(op(vars))); 6 3 3 GB := [32768 x - 3757, -4096 x + 289 y, 256 x + 17 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5790.6MB, alloc=804.3MB, time=125.79 N2 := 2307 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 2 3 H := [-8 x y + 13, -17 x y - 16 x z, 16 y x - z , -10 x y z + 7 y z , 2 2 4 3 2 5 x y - 13 y , -9 y z + 19 x y ] > J:=[op(GB),op(G)]; 6 3 3 2 3 J := [32768 x - 3757, -4096 x + 289 y, 256 x + 17 z, -10 x y z + 7 y z , 2 2 4 3 2 5 x y - 13 y , -9 y z + 19 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 := [6, 16, 22, 4, 3, 4, 3, 1, 1, 2/3, 7/12, 3/4, 5/12, 6, 13, 24, 6, 6, 4, 3, 1, 2/3, 1/2, 1/2, 7/12, 1/3, 3, -2, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=5995.2MB, alloc=804.3MB, time=129.40 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428359552 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 F := [7 y + 11 x z, 10 x - 3 x, 12 x y z + 16 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 3 G := [14 x y z + 19 y , -6 x z - 10 x z , -4 x z + 18 y z] > Problem := [F,G]; 4 3 2 2 Problem := [[7 y + 11 x z, 10 x - 3 x, 12 x y z + 16 x y], 2 2 2 2 3 3 [14 x y z + 19 y , -6 x z - 10 x z , -4 x z + 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=0.15 memory used=26.2MB, alloc=32.3MB, time=0.35 memory used=48.2MB, alloc=32.3MB, time=0.55 memory used=68.6MB, alloc=32.3MB, time=0.73 memory used=87.7MB, alloc=56.3MB, time=0.90 memory used=128.1MB, alloc=60.3MB, time=1.25 memory used=168.7MB, alloc=84.3MB, time=1.59 memory used=215.6MB, alloc=84.3MB, time=2.01 memory used=277.5MB, alloc=116.3MB, time=2.61 memory used=359.8MB, alloc=116.3MB, time=3.46 memory used=431.4MB, alloc=140.3MB, time=4.23 memory used=522.3MB, alloc=164.3MB, time=5.20 memory used=628.3MB, alloc=188.3MB, time=6.35 memory used=734.4MB, alloc=468.3MB, time=7.59 memory used=861.9MB, alloc=492.3MB, time=9.79 memory used=996.7MB, alloc=516.3MB, time=12.58 memory used=1142.5MB, alloc=540.3MB, time=16.01 memory used=1312.2MB, alloc=564.3MB, time=20.06 memory used=1505.9MB, alloc=564.3MB, time=24.51 memory used=1699.7MB, alloc=564.3MB, time=28.93 memory used=1893.4MB, alloc=588.3MB, time=33.28 memory used=2111.1MB, alloc=588.3MB, time=37.92 N1 := 6983 > GB := Basis(F, plex(op(vars))); 3 2 4 4 6 2 4 GB := [10 x - 3 x, 10 x y - 3 y , 21 y - 44 x y, 7 y + 11 z x, 4 3 3 y z + 4 x y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2335.6MB, alloc=588.3MB, time=41.46 memory used=2584.5MB, alloc=612.3MB, time=44.06 memory used=2847.3MB, alloc=636.3MB, time=47.05 memory used=3122.7MB, alloc=660.3MB, time=51.13 memory used=3371.7MB, alloc=684.3MB, time=56.90 memory used=3630.4MB, alloc=708.3MB, time=63.18 memory used=3913.1MB, alloc=732.3MB, time=69.98 memory used=4219.8MB, alloc=756.3MB, time=77.13 N2 := 6983 #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)]; 4 3 2 2 2 2 H := [7 y + 11 z x, 10 x - 3 x, 12 x y z + 16 x y, 14 x y z + 19 y , 2 2 3 3 -6 x z - 10 x z , -4 x z + 18 y z] > J:=[op(GB),op(G)]; 3 2 4 4 6 2 4 J := [10 x - 3 x, 10 x y - 3 y , 21 y - 44 x y, 7 y + 11 z x, 4 3 2 2 2 2 3 3 3 y z + 4 x y , 14 x y z + 19 y , -6 x z - 10 x z , -4 x z + 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 := [6, 15, 22, 4, 3, 4, 2, 1, 2/3, 5/6, 3/4, 1/2, 7/12, 8, 19, 35, 6, 3, 6, 2, 1, 3/4, 5/8, 5/8, 5/8, 7/16, -4, -13, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=4544.5MB, alloc=756.3MB, time=83.70 |\^/| 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(); 1428359634 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 3 F := [13 y z + 12 y z, 18 x y + 14 y , -4 x z + 10 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 2 2 G := [16 x y + 13 y z , 13 x z - 14 x z, 16 y z + x ] > Problem := [F,G]; 3 2 2 2 3 2 3 Problem := [[13 y z + 12 y z, 18 x y + 14 y , -4 x z + 10 z ], 2 2 2 2 3 2 2 2 [16 x y + 13 y z , 13 x z - 14 x z, 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=4.3MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.33 memory used=48.0MB, alloc=32.3MB, time=0.52 memory used=69.2MB, alloc=32.3MB, time=0.72 memory used=89.7MB, alloc=56.3MB, time=0.96 memory used=132.3MB, alloc=56.3MB, time=1.40 memory used=166.9MB, alloc=80.3MB, time=1.81 memory used=217.5MB, alloc=104.3MB, time=2.57 N1 := 1553 > GB := Basis(F, plex(op(vars))); 2 2 3 2 2 2 2 3 GB := [9 x y + 7 y , 39 x y z - 28 y z, -2 x z + 5 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=290.7MB, alloc=108.3MB, time=3.31 memory used=373.9MB, alloc=132.3MB, time=4.30 N2 := 1291 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 2 3 2 2 2 2 H := [13 y z + 12 y z, 18 x y + 14 y , -4 x z + 10 z , 16 x y + 13 y z , 3 2 2 2 13 x z - 14 x z, 16 z y + x ] > J:=[op(GB),op(G)]; 2 2 3 2 2 2 2 3 2 2 2 2 J := [9 x y + 7 y , 39 x y z - 28 y z, -2 x z + 5 z , 16 x y + 13 y z , 3 2 2 2 13 x z - 14 x z, 16 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 := [6, 14, 23, 4, 2, 3, 3, 5/6, 2/3, 5/6, 1/2, 7/12, 2/3, 6, 15, 24, 5, 2, 3, 3, 1, 2/3, 5/6, 7/12, 7/12, 2/3, -1, -1, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=406.2MB, alloc=132.3MB, time=4.74 |\^/| 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(); 1428359639 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [19 x y z - 11 y z , -6 x y - 10 x, -15 x y - 12 x y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 2 2 G := [-11 x z - 12 x y , -13 y z + 6 y z , -5 y z - 5 x y] > Problem := [F,G]; 2 2 2 3 2 Problem := [[19 x y z - 11 y z , -6 x y - 10 x, -15 x y - 12 x y z ], 3 2 2 2 2 2 2 2 2 [-11 x z - 12 x y , -13 y z + 6 y z , -5 y z - 5 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.12 memory used=26.2MB, alloc=32.3MB, time=0.33 memory used=48.1MB, alloc=32.3MB, time=0.53 memory used=68.4MB, alloc=32.3MB, time=0.70 memory used=87.2MB, alloc=56.3MB, time=0.87 memory used=126.4MB, alloc=60.3MB, time=1.22 memory used=164.6MB, alloc=60.3MB, time=1.55 memory used=201.5MB, alloc=84.3MB, time=1.89 memory used=260.4MB, alloc=92.3MB, time=2.42 memory used=315.8MB, alloc=116.3MB, time=2.92 memory used=393.8MB, alloc=140.3MB, time=3.75 memory used=487.4MB, alloc=140.3MB, time=4.76 memory used=573.6MB, alloc=164.3MB, time=5.70 memory used=672.1MB, alloc=188.3MB, time=7.31 memory used=776.4MB, alloc=212.3MB, time=9.55 memory used=904.8MB, alloc=236.3MB, time=12.24 N1 := 3381 > GB := Basis(F, plex(op(vars))); 7 6 3 GB := [12996 x + 15125 x, -4332 x + 3025 x y, -19 x + 11 x z, 3 2 1805 x + 363 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1060.9MB, alloc=236.3MB, time=14.13 memory used=1148.8MB, alloc=492.3MB, time=15.04 memory used=1323.9MB, alloc=492.3MB, time=16.80 memory used=1489.2MB, alloc=516.3MB, time=18.66 memory used=1670.1MB, alloc=540.3MB, time=21.29 memory used=1837.9MB, alloc=564.3MB, time=25.17 memory used=2021.1MB, alloc=588.3MB, time=29.56 memory used=2228.4MB, alloc=612.3MB, time=34.42 N2 := 5007 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 H := [19 x y z - 11 y z , -6 x y - 10 x, -15 x y - 12 x y z , 3 2 2 2 2 2 2 2 2 -11 x z - 12 x y , -13 y z + 6 y z , -5 y z - 5 x y] > J:=[op(GB),op(G)]; 7 6 3 J := [12996 x + 15125 x, -4332 x + 3025 x y, -19 x + 11 x z, 2 3 3 2 2 2 2 2 363 z y + 1805 x , -11 x z - 12 x y , -13 y z + 6 y z , 2 2 2 -5 y z - 5 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 := [6, 16, 23, 4, 3, 3, 2, 5/6, 1, 5/6, 2/3, 5/6, 7/12, 7, 16, 31, 7, 7, 2, 2, 6/7, 5/7, 5/7, 5/7, 1/2, 3/7, 0, -8, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2393.5MB, alloc=612.3MB, time=37.41 |\^/| 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(); 1428359676 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 3 4 F := [3 y z + 12 x z , 9 x y - 11 x z, -11 x z + 10 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 2 G := [-11 y z + 3 x, -11 y z - 19 y z , -10 x y + x z ] > Problem := [F,G]; 3 2 3 3 3 4 Problem := [[3 y z + 12 x z , 9 x y - 11 x z, -11 x z + 10 z ], 3 3 3 3 2 [-11 y z + 3 x, -11 y z - 19 y z , -10 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=4.2MB, alloc=32.3MB, time=0.14 memory used=26.7MB, alloc=32.3MB, time=0.36 memory used=48.1MB, alloc=32.3MB, time=0.54 memory used=67.8MB, alloc=56.3MB, time=0.71 memory used=107.6MB, alloc=60.3MB, time=1.06 memory used=145.0MB, alloc=60.3MB, time=1.39 memory used=181.6MB, alloc=84.3MB, time=1.71 memory used=221.3MB, alloc=84.3MB, time=2.06 memory used=277.2MB, alloc=116.3MB, time=2.57 memory used=353.4MB, alloc=116.3MB, time=3.26 memory used=428.0MB, alloc=140.3MB, time=3.93 memory used=502.3MB, alloc=396.3MB, time=4.66 memory used=597.0MB, alloc=420.3MB, time=5.55 memory used=721.3MB, alloc=444.3MB, time=6.66 memory used=868.0MB, alloc=468.3MB, time=7.90 memory used=1022.0MB, alloc=492.3MB, time=9.45 memory used=1166.2MB, alloc=516.3MB, time=10.87 memory used=1317.5MB, alloc=516.3MB, time=12.46 memory used=1445.6MB, alloc=540.3MB, time=13.74 memory used=1559.5MB, alloc=540.3MB, time=15.01 memory used=1663.7MB, alloc=540.3MB, time=16.18 memory used=1754.0MB, alloc=564.3MB, time=17.24 memory used=1824.0MB, alloc=564.3MB, time=18.12 memory used=1902.5MB, alloc=564.3MB, time=19.04 memory used=1970.0MB, alloc=564.3MB, time=19.92 memory used=2028.2MB, alloc=564.3MB, time=20.67 memory used=2085.5MB, alloc=564.3MB, time=21.56 memory used=2149.2MB, alloc=564.3MB, time=22.45 memory used=2179.2MB, alloc=564.3MB, time=23.11 memory used=2411.8MB, alloc=588.3MB, time=25.51 memory used=2638.1MB, alloc=612.3MB, time=28.02 memory used=2886.6MB, alloc=636.3MB, time=31.03 memory used=3084.6MB, alloc=660.3MB, time=33.33 memory used=3239.2MB, alloc=684.3MB, time=35.26 memory used=3424.1MB, alloc=708.3MB, time=37.62 memory used=3605.2MB, alloc=732.3MB, time=40.01 memory used=3750.6MB, alloc=756.3MB, time=41.96 memory used=3897.0MB, alloc=780.3MB, time=44.10 memory used=4017.7MB, alloc=780.3MB, time=45.87 memory used=4159.8MB, alloc=780.3MB, time=48.02 memory used=4281.5MB, alloc=780.3MB, time=50.01 memory used=4682.5MB, alloc=804.3MB, time=54.40 memory used=5098.8MB, alloc=828.3MB, time=59.24 memory used=5478.2MB, alloc=852.3MB, time=64.59 memory used=5832.0MB, alloc=876.3MB, time=69.82 memory used=6192.9MB, alloc=900.3MB, time=75.11 memory used=6548.7MB, alloc=924.3MB, time=80.52 memory used=6870.3MB, alloc=948.3MB, time=87.75 memory used=7156.0MB, alloc=972.3MB, time=95.57 memory used=7445.2MB, alloc=996.3MB, time=103.90 memory used=7743.0MB, alloc=1020.3MB, time=112.62 memory used=8047.7MB, alloc=1044.3MB, time=121.77 memory used=8361.8MB, alloc=1068.3MB, time=131.61 memory used=8699.8MB, alloc=1092.3MB, time=142.08 memory used=9061.9MB, alloc=1116.3MB, time=153.31 memory used=9447.7MB, alloc=1140.3MB, time=165.04 memory used=9857.6MB, alloc=1164.3MB, time=177.43 memory used=10291.4MB, alloc=1188.3MB, time=190.48 memory used=10749.2MB, alloc=1212.3MB, time=204.13 memory used=11230.8MB, alloc=1236.3MB, time=218.54 memory used=11736.4MB, alloc=1260.3MB, time=233.34 memory used=12265.9MB, alloc=1284.3MB, time=248.98 memory used=12819.3MB, alloc=1308.3MB, time=265.16 memory used=13396.8MB, alloc=1332.3MB, time=282.11 memory used=13998.0MB, alloc=1356.3MB, time=299.64 |\^/| 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(); 1428359976 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 3 F := [-14 x y + x z , -3 y z - 4 y z , 12 x z - 12 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 4 2 G := [-7 x z - 20 y , -17 y z + 18 y z, 18 x + 6 x ] > Problem := [F,G]; 2 2 3 2 3 3 Problem := [[-14 x y + x z , -3 y z - 4 y z , 12 x z - 12 y ], 2 2 3 2 4 2 [-7 x z - 20 y , -17 y z + 18 y z, 18 x + 6 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.4MB, alloc=32.3MB, time=0.42 memory used=47.9MB, alloc=32.3MB, time=0.67 memory used=68.0MB, alloc=56.3MB, time=0.92 memory used=107.4MB, alloc=60.3MB, time=1.37 memory used=143.8MB, alloc=84.3MB, time=1.75 memory used=203.6MB, alloc=92.3MB, time=2.48 memory used=263.6MB, alloc=92.3MB, time=3.25 memory used=320.1MB, alloc=116.3MB, time=3.98 memory used=397.7MB, alloc=116.3MB, time=4.66 memory used=475.8MB, alloc=140.3MB, time=5.36 memory used=556.8MB, alloc=396.3MB, time=6.10 memory used=657.0MB, alloc=420.3MB, time=7.12 memory used=770.6MB, alloc=444.3MB, time=8.35 memory used=894.8MB, alloc=468.3MB, time=9.74 memory used=1030.5MB, alloc=492.3MB, time=11.27 memory used=1177.7MB, alloc=516.3MB, time=12.99 memory used=1345.6MB, alloc=540.3MB, time=14.92 memory used=1523.5MB, alloc=564.3MB, time=16.92 memory used=1701.8MB, alloc=588.3MB, time=19.08 memory used=1892.7MB, alloc=612.3MB, time=21.31 memory used=2075.8MB, alloc=636.3MB, time=24.62 memory used=2253.6MB, alloc=660.3MB, time=28.50 memory used=2440.1MB, alloc=684.3MB, time=32.88 memory used=2637.6MB, alloc=708.3MB, time=37.73 memory used=2848.3MB, alloc=732.3MB, time=43.05 memory used=3072.3MB, alloc=756.3MB, time=48.72 memory used=3310.1MB, alloc=780.3MB, time=54.87 memory used=3560.8MB, alloc=804.3MB, time=61.65 memory used=3825.5MB, alloc=828.3MB, time=69.13 memory used=4114.1MB, alloc=852.3MB, time=77.35 memory used=4426.7MB, alloc=876.3MB, time=86.05 memory used=4763.2MB, alloc=900.3MB, time=95.40 memory used=5123.7MB, alloc=924.3MB, time=105.41 memory used=5508.1MB, alloc=948.3MB, time=116.04 memory used=5916.5MB, alloc=972.3MB, time=127.31 memory used=6348.7MB, alloc=996.3MB, time=139.38 memory used=6804.9MB, alloc=996.3MB, time=151.90 memory used=7261.1MB, alloc=996.3MB, time=164.48 memory used=7717.3MB, alloc=996.3MB, time=177.06 memory used=8173.5MB, alloc=1020.3MB, time=189.67 memory used=8653.5MB, alloc=1020.3MB, time=202.93 memory used=9133.5MB, alloc=1020.3MB, time=216.06 memory used=9613.5MB, alloc=1020.3MB, time=229.18 memory used=10093.4MB, alloc=1044.3MB, time=242.29 memory used=10597.2MB, alloc=1044.3MB, time=256.09 memory used=11101.0MB, alloc=1044.3MB, time=269.95 memory used=11604.6MB, alloc=1044.3MB, time=283.56 memory used=12108.2MB, alloc=1068.3MB, time=297.28 |\^/| 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(); 1428360276 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [-1 - 11 y, 17 x y z - 2 z , 19 x z + 19 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 G := [-19 y z - 19 x y, y + 17 y z , -14 x z] > Problem := [F,G]; 2 3 2 2 Problem := [[-1 - 11 y, 17 x y z - 2 z , 19 x z + 19 x ], 3 2 4 2 [-19 y z - 19 x y, y + 17 y z , -14 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.2MB, alloc=32.3MB, time=0.39 memory used=47.9MB, alloc=32.3MB, time=0.60 memory used=68.8MB, alloc=32.3MB, time=0.85 memory used=87.4MB, alloc=56.3MB, time=1.08 memory used=126.5MB, alloc=60.3MB, time=1.52 memory used=166.1MB, alloc=92.3MB, time=1.96 memory used=229.5MB, alloc=92.3MB, time=2.77 memory used=287.0MB, alloc=116.3MB, time=3.60 memory used=374.8MB, alloc=116.3MB, time=4.52 memory used=453.8MB, alloc=140.3MB, time=5.50 memory used=542.1MB, alloc=164.3MB, time=7.02 memory used=633.8MB, alloc=188.3MB, time=9.26 memory used=742.5MB, alloc=212.3MB, time=11.44 memory used=875.3MB, alloc=212.3MB, time=13.96 N1 := 3507 > GB := Basis(F, plex(op(vars))); 3 2 2 2 3 GB := [x , 11 y + 1, x z, x z + x , 242 z - 17 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=998.8MB, alloc=212.3MB, time=15.32 memory used=1166.1MB, alloc=492.3MB, time=17.06 memory used=1340.6MB, alloc=516.3MB, time=19.60 memory used=1500.7MB, alloc=540.3MB, time=22.91 N2 := 3233 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 3 2 H := [-1 - 11 y, 17 x y z - 2 z , 19 x z + 19 x , -19 y z - 19 x y, 4 2 y + 17 y z , -14 x z] > J:=[op(GB),op(G)]; 3 2 2 2 3 3 2 J := [x , 11 y + 1, x z, x z + x , 242 z - 17 x z, -19 y z - 19 x y, 4 2 y + 17 y z , -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 := [6, 13, 18, 4, 2, 4, 3, 2/3, 2/3, 5/6, 5/13, 6/13, 6/13, 8, 15, 23, 4, 3, 4, 3, 3/4, 3/8, 3/4, 7/17, 5/17, 7/17, -2, -5, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1598.6MB, alloc=540.3MB, time=24.47 |\^/| 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(); 1428360301 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 3 F := [13 x z, -16 z + 6 x y , 17 x z - 14 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 4 3 2 G := [-18 z - 10 x y, -20 x y - 10 y , 19 x y + 8 x ] > Problem := [F,G]; 2 4 2 3 Problem := [[13 x z, -16 z + 6 x y , 17 x z - 14 x y z], 4 2 2 4 3 2 [-18 z - 10 x y, -20 x y - 10 y , 19 x y + 8 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.5MB, alloc=32.3MB, time=0.36 memory used=48.1MB, alloc=32.3MB, time=0.55 memory used=71.1MB, alloc=32.3MB, time=0.78 memory used=91.3MB, alloc=56.3MB, time=0.99 N1 := 719 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 2 2 2 2 3 GB := [x y , x y , x z, y x z, -51 x y + 112 x y z , 17 x z - 14 x y z, 4 2 8 z - 3 x y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=130.7MB, alloc=56.3MB, time=1.42 memory used=169.0MB, alloc=60.3MB, time=1.75 memory used=206.5MB, alloc=84.3MB, time=2.11 memory used=272.1MB, alloc=92.3MB, time=2.80 memory used=325.1MB, alloc=116.3MB, time=3.55 N2 := 1149 #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 4 2 3 4 H := [13 x z, -16 z + 6 x y , 17 x z - 14 x y z, -18 z - 10 x y, 2 2 4 3 2 -20 x y - 10 y , 19 x y + 8 x ] > J:=[op(GB),op(G)]; 3 2 2 3 2 2 2 2 2 3 J := [x y , x y , x z, y x z, -51 x y + 112 x y z , 17 x z - 14 x y z, 4 2 4 2 2 4 3 2 8 z - 3 x y , -18 z - 10 x y, -20 x y - 10 y , 19 x y + 8 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 23, 4, 3, 4, 4, 1, 5/6, 2/3, 8/13, 6/13, 5/13, 10, 25, 41, 5, 3, 4, 4, 1, 9/10, 3/5, 13/21, 11/21, 1/3, -10, -18, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=326.5MB, alloc=116.3MB, time=3.58 |\^/| 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(); 1428360304 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 F := [-13 y z + 8, 11 x y - 6 x z , 7 x y z + 10 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 G := [-x - 13 x , -12 y z + 10 z, -x y z + 5 x z] > Problem := [F,G]; 3 2 2 3 2 Problem := [[-13 y z + 8, 11 x y - 6 x z , 7 x y z + 10 x], 4 2 3 [-x - 13 x , -12 y z + 10 z, -x y z + 5 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.12 memory used=26.0MB, alloc=32.3MB, time=0.32 memory used=47.9MB, alloc=32.3MB, time=0.54 memory used=68.4MB, alloc=56.3MB, time=0.74 memory used=110.2MB, alloc=60.3MB, time=1.15 memory used=148.2MB, alloc=84.3MB, time=1.55 memory used=206.7MB, alloc=108.3MB, time=2.19 N1 := 1219 > GB := Basis(F, plex(op(vars))); 14 8 GB := [957026143612 x + 163165869140625 x, -5176556 x + 102984375 x y, 6 3 -52822 x + 316875 x z, 13 z y - 8] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=277.8MB, alloc=108.3MB, time=3.03 memory used=357.2MB, alloc=140.3MB, time=3.87 N2 := 971 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 3 2 4 2 H := [-13 y z + 8, 11 x y - 6 x z , 7 x y z + 10 x, -x - 13 x , 3 -12 y z + 10 z, -x y z + 5 x z] > J:=[op(GB),op(G)]; 14 8 J := [957026143612 x + 163165869140625 x, -5176556 x + 102984375 x y, 6 3 4 2 3 -52822 x + 316875 x z, 13 z y - 8, -x - 13 x , -12 y z + 10 z, -x y z + 5 x z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 23, 4, 4, 3, 3, 2/3, 5/6, 5/6, 2/3, 5/12, 7/12, 7, 13, 43, 14, 14, 3, 1, 5/7, 4/7, 4/7, 5/7, 2/7, 3/7, 1, -20, -10] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=387.7MB, alloc=140.3MB, time=4.30 |\^/| 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(); 1428360309 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 2 F := [-7 x z + 20 z , 5 x + 2 y, -11 x y - 16 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 4 G := [6 y z + 15 x y z, -10 x z + 15 y z, -2 x + 10 z] > Problem := [F,G]; 2 2 4 2 2 2 Problem := [[-7 x z + 20 z , 5 x + 2 y, -11 x y - 16 z ], 3 3 2 4 [6 y z + 15 x y z, -10 x z + 15 y z, -2 x + 10 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.4MB, alloc=32.3MB, time=0.34 memory used=47.9MB, alloc=32.3MB, time=0.52 memory used=68.6MB, alloc=32.3MB, time=0.72 memory used=89.0MB, alloc=56.3MB, time=0.95 memory used=129.6MB, alloc=56.3MB, time=1.36 N1 := 859 > GB := Basis(F, plex(op(vars))); 11 10 4 10 2 GB := [7 x - 20 x , 5 x + 2 y, 275 x + 64 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=164.0MB, alloc=56.3MB, time=1.79 memory used=200.1MB, alloc=84.3MB, time=2.12 N2 := 439 #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 4 2 2 2 3 H := [-7 x z + 20 z , 5 x + 2 y, -11 x y - 16 z , 6 y z + 15 x y z, 3 2 4 -10 x z + 15 y z, -2 x + 10 z] > J:=[op(GB),op(G)]; 11 10 4 10 2 3 J := [7 x - 20 x , 5 x + 2 y, 275 x + 64 z , 6 y z + 15 x y z, 3 2 4 -10 x z + 15 y z, -2 x + 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, 15, 23, 4, 4, 2, 3, 1, 2/3, 5/6, 1/2, 5/12, 2/3, 6, 13, 37, 11, 11, 2, 3, 1, 1/2, 2/3, 7/12, 1/3, 1/2, 2, -14, -7] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=235.3MB, alloc=84.3MB, time=2.48 |\^/| 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(); 1428360311 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 4 F := [-8 x + 17 x y z, -18 x y + 4 x z , 5 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 2 G := [10 x y z - 7 y z, -4 x - 2 y z, -15 x y - 3 x z ] > Problem := [F,G]; 4 3 2 2 4 Problem := [[-8 x + 17 x y z, -18 x y + 4 x z , 5 y ], 2 3 2 3 2 2 [10 x y z - 7 y z, -4 x - 2 y z, -15 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=0.11 memory used=26.4MB, alloc=32.3MB, time=0.29 memory used=47.9MB, alloc=32.3MB, time=0.47 memory used=68.5MB, alloc=32.3MB, time=0.64 memory used=87.8MB, alloc=56.3MB, time=0.83 memory used=130.8MB, alloc=60.3MB, time=1.29 memory used=169.6MB, alloc=84.3MB, time=1.78 memory used=227.2MB, alloc=108.3MB, time=2.53 N1 := 1631 > GB := Basis(F, plex(op(vars))); 9 8 7 2 8 3 3 4 5 3 2 GB := [x , x y, x y , -128 x + 2601 x y , y , 16 x z - 153 x y , 4 3 2 2 -8 x + 17 x y z, -9 x y + 2 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=297.2MB, alloc=108.3MB, time=3.55 memory used=373.0MB, alloc=116.3MB, time=4.23 memory used=445.4MB, alloc=140.3MB, time=4.88 memory used=543.6MB, alloc=164.3MB, time=5.88 memory used=656.4MB, alloc=188.3MB, time=7.12 memory used=765.3MB, alloc=468.3MB, time=8.37 memory used=903.1MB, alloc=492.3MB, time=10.99 memory used=1046.5MB, alloc=516.3MB, time=14.24 memory used=1214.0MB, alloc=516.3MB, time=17.60 N2 := 3995 #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)]; 4 3 2 2 4 2 H := [-8 x + 17 x y z, -18 x y + 4 x z , 5 y , 10 x y z - 7 y z, 3 2 3 2 2 -4 x - 2 y z, -15 x y - 3 x z ] > J:=[op(GB),op(G)]; 9 8 7 2 8 3 3 4 5 3 2 J := [x , x y, x y , -128 x + 2601 x y , y , 16 x z - 153 x y , 4 3 2 2 2 3 2 -8 x + 17 x y z, -9 x y + 2 x z , 10 x y z - 7 y z, -4 x - 2 y z, 3 2 2 -15 x y - 3 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 := [6, 16, 23, 4, 4, 4, 2, 5/6, 1, 5/6, 2/3, 7/12, 1/2, 11, 26, 64, 9, 9, 4, 2, 10/11, 10/11, 6/11, 15/22, 1/2, 7/22, -10, -41, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1284.6MB, alloc=516.3MB, time=18.69 |\^/| 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(); 1428360330 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 2 F := [3 x z - 10 y z , -13 x z + 20 z , -2 x y - 14] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-11 x y, 6 y z + x , 2 x z + 19 y z] > Problem := [F,G]; 3 2 2 2 3 2 2 Problem := [[3 x z - 10 y z , -13 x z + 20 z , -2 x y - 14], 2 2 2 2 2 [-11 x y, 6 y z + x , 2 x z + 19 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.3MB, alloc=32.3MB, time=0.34 memory used=48.0MB, alloc=32.3MB, time=0.53 memory used=69.8MB, alloc=56.3MB, time=0.76 memory used=111.8MB, alloc=60.3MB, time=1.20 memory used=149.5MB, alloc=84.3MB, time=1.60 memory used=203.0MB, alloc=108.3MB, time=2.39 N1 := 1397 > GB := Basis(F, plex(op(vars))); 2 2 4 2 2 2 2 2 2 2 3 GB := [y x + 7, 39 x z + 1400 z , -39 x z + 200 y z , -13 x z + 20 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=277.7MB, alloc=116.3MB, time=3.17 N2 := 665 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 2 2 2 2 2 H := [3 x z - 10 y z , -13 x z + 20 z , -2 x y - 14, -11 x y, 6 z y + x , 2 2 2 x z + 19 y z] > J:=[op(GB),op(G)]; 2 2 4 2 2 2 2 2 2 2 3 J := [y x + 7, 39 x z + 1400 z , -39 x z + 200 y z , -13 x z + 20 z , 2 2 2 2 2 -11 x y, 6 z y + x , 2 x z + 19 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 := [6, 15, 20, 4, 2, 2, 3, 1, 5/6, 2/3, 6/13, 5/13, 7/13, 7, 17, 26, 6, 4, 2, 3, 1, 5/7, 5/7, 7/15, 1/3, 3/5, -2, -6, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=303.8MB, alloc=116.3MB, time=3.47 |\^/| 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(); 1428360333 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 4 2 F := [13 x y z - 19 x z, 4 x + 9 x y , 19 x - 6 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 2 2 2 2 G := [10 x y z - 11 y , 14 x y z + 13 y z, 15 x y - 15 y z ] > Problem := [F,G]; 2 4 3 4 2 Problem := [[13 x y z - 19 x z, 4 x + 9 x y , 19 x - 6 y z], 2 4 2 2 2 2 2 2 [10 x y z - 11 y , 14 x y z + 13 y z, 15 x 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=0.11 memory used=26.5MB, alloc=32.3MB, time=0.29 memory used=47.9MB, alloc=32.3MB, time=0.50 memory used=68.2MB, alloc=32.3MB, time=0.70 memory used=87.5MB, alloc=56.3MB, time=0.88 memory used=128.5MB, alloc=60.3MB, time=1.23 memory used=166.7MB, alloc=60.3MB, time=1.55 memory used=203.8MB, alloc=84.3MB, time=1.89 memory used=260.7MB, alloc=92.3MB, time=2.44 memory used=319.9MB, alloc=116.3MB, time=2.97 memory used=399.5MB, alloc=116.3MB, time=3.71 memory used=476.1MB, alloc=140.3MB, time=4.41 memory used=552.1MB, alloc=140.3MB, time=5.15 memory used=630.9MB, alloc=420.3MB, time=5.95 memory used=747.3MB, alloc=444.3MB, time=7.08 memory used=884.9MB, alloc=468.3MB, time=8.60 memory used=1026.5MB, alloc=492.3MB, time=10.17 memory used=1179.5MB, alloc=516.3MB, time=11.88 memory used=1342.0MB, alloc=540.3MB, time=13.73 memory used=1512.3MB, alloc=564.3MB, time=15.74 memory used=1690.7MB, alloc=588.3MB, time=18.07 memory used=1862.4MB, alloc=612.3MB, time=21.45 memory used=2038.3MB, alloc=636.3MB, time=25.37 memory used=2225.0MB, alloc=660.3MB, time=29.74 memory used=2424.9MB, alloc=684.3MB, time=34.60 memory used=2637.6MB, alloc=708.3MB, time=39.99 memory used=2860.7MB, alloc=732.3MB, time=46.08 memory used=3107.7MB, alloc=756.3MB, time=52.77 memory used=3378.6MB, alloc=780.3MB, time=60.06 memory used=3673.5MB, alloc=804.3MB, time=67.98 memory used=3992.3MB, alloc=828.3MB, time=76.52 memory used=4335.2MB, alloc=852.3MB, time=85.76 memory used=4701.9MB, alloc=852.3MB, time=95.49 memory used=5068.6MB, alloc=876.3MB, time=105.23 memory used=5459.1MB, alloc=876.3MB, time=115.55 memory used=5849.5MB, alloc=876.3MB, time=125.84 memory used=6239.8MB, alloc=900.3MB, time=136.12 memory used=6653.9MB, alloc=900.3MB, time=147.10 memory used=7067.9MB, alloc=900.3MB, time=157.90 memory used=7481.9MB, alloc=924.3MB, time=168.67 memory used=7919.7MB, alloc=924.3MB, time=179.91 memory used=8357.3MB, alloc=948.3MB, time=191.12 memory used=8818.8MB, alloc=948.3MB, time=202.95 memory used=9280.3MB, alloc=972.3MB, time=214.49 memory used=9766.2MB, alloc=996.3MB, time=226.22 N1 := 16581 > GB := Basis(F, plex(op(vars))); 11 5 10 5 4 3 GB := [8788 x + 61731 x , 676 x + 3249 x y, 4 x + 9 x y , 7 4 2 -169 x + 114 x z, -19 x + 6 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=10051.2MB, alloc=996.3MB, time=231.32 memory used=10389.0MB, alloc=996.3MB, time=235.70 memory used=10985.7MB, alloc=1020.3MB, time=242.42 memory used=11611.7MB, alloc=1044.3MB, time=249.74 memory used=12247.5MB, alloc=1068.3MB, time=257.21 memory used=12887.0MB, alloc=1092.3MB, time=265.28 memory used=13528.6MB, alloc=1116.3MB, time=273.86 memory used=14025.6MB, alloc=1140.3MB, time=281.55 memory used=14556.3MB, alloc=1164.3MB, time=289.17 memory used=15012.6MB, alloc=1188.3MB, time=296.47 memory used=15438.0MB, alloc=1212.3MB, time=303.31 |\^/| 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(); 1428360633 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 F := [-x y + 10, -19 x y + 17 x y z , -7 y z + 9 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [-6 y z - 11 x z, -20 x y z - 6 y z , -9 x - 5 y z] > Problem := [F,G]; 3 2 2 2 3 2 Problem := [[-x y + 10, -19 x y + 17 x y z , -7 y z + 9 y ], 3 2 3 2 [-6 y z - 11 x z, -20 x y z - 6 y z , -9 x - 5 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.5MB, alloc=32.3MB, time=0.36 memory used=47.8MB, alloc=32.3MB, time=0.57 memory used=69.0MB, alloc=32.3MB, time=0.81 memory used=89.2MB, alloc=56.3MB, time=1.08 memory used=130.4MB, alloc=60.3MB, time=1.55 memory used=170.5MB, alloc=60.3MB, time=1.89 memory used=209.5MB, alloc=84.3MB, time=2.24 memory used=268.3MB, alloc=92.3MB, time=2.76 memory used=326.1MB, alloc=116.3MB, time=3.29 memory used=406.8MB, alloc=116.3MB, time=4.18 memory used=480.1MB, alloc=140.3MB, time=4.99 memory used=570.2MB, alloc=164.3MB, time=6.00 memory used=669.8MB, alloc=188.3MB, time=7.66 memory used=775.6MB, alloc=212.3MB, time=9.92 memory used=905.4MB, alloc=236.3MB, time=12.55 N1 := 3623 > GB := Basis(F, plex(op(vars))); 8 GB := [379638849560015710 x - 63022459673442177, 5 -1129571602810 x + 158366590209 y, 7 -2854427440300870 x + 411911501133609 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1065.3MB, alloc=236.3MB, time=14.77 memory used=1174.7MB, alloc=492.3MB, time=15.99 memory used=1354.0MB, alloc=516.3MB, time=18.89 N2 := 2411 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 2 3 H := [-x y + 10, -19 x y + 17 x y z , -7 y z + 9 y , -6 y z - 11 x z, 2 3 2 -20 x y z - 6 y z , -9 x - 5 y z] > J:=[op(GB),op(G)]; 8 J := [379638849560015710 x - 63022459673442177, 5 -1129571602810 x + 158366590209 y, 7 3 -2854427440300870 x + 411911501133609 z, -6 y z - 11 x z, 2 3 2 -20 x y z - 6 y z , -9 x - 5 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 16, 22, 4, 2, 3, 3, 5/6, 1, 5/6, 1/2, 3/4, 7/12, 6, 14, 30, 8, 8, 3, 3, 1, 2/3, 2/3, 1/2, 5/12, 1/2, 2, -8, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1458.3MB, alloc=516.3MB, time=20.61 |\^/| 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(); 1428360654 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 2 2 F := [-6 y z - 19 x , -18 x y z - 14 z , -x y z + 10 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [5 x - 18 y z, 5 y z + 3 x, -9 x y z - 7 x y z] > Problem := [F,G]; 3 2 2 4 2 2 Problem := [[-6 y z - 19 x , -18 x y z - 14 z , -x y z + 10 x y ], 3 2 2 2 2 [5 x - 18 y z, 5 y z + 3 x, -9 x y z - 7 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.8MB, alloc=32.3MB, time=0.35 memory used=48.0MB, alloc=36.3MB, time=0.53 memory used=67.6MB, alloc=60.3MB, time=0.71 memory used=109.6MB, alloc=60.3MB, time=1.04 memory used=149.7MB, alloc=84.3MB, time=1.39 memory used=209.9MB, alloc=92.3MB, time=1.92 memory used=273.4MB, alloc=116.3MB, time=2.45 memory used=353.2MB, alloc=116.3MB, time=3.14 memory used=419.4MB, alloc=396.3MB, time=3.71 memory used=530.6MB, alloc=420.3MB, time=4.61 memory used=661.6MB, alloc=444.3MB, time=5.71 memory used=797.9MB, alloc=444.3MB, time=6.87 memory used=929.5MB, alloc=468.3MB, time=7.98 memory used=1061.8MB, alloc=492.3MB, time=9.20 memory used=1172.3MB, alloc=492.3MB, time=10.29 memory used=1285.4MB, alloc=516.3MB, time=11.40 memory used=1368.5MB, alloc=516.3MB, time=12.25 memory used=1466.3MB, alloc=516.3MB, time=13.28 memory used=1549.5MB, alloc=516.3MB, time=14.18 memory used=1628.8MB, alloc=516.3MB, time=15.01 memory used=1702.7MB, alloc=516.3MB, time=15.83 memory used=1766.1MB, alloc=540.3MB, time=16.58 memory used=1836.7MB, alloc=540.3MB, time=17.38 memory used=1902.1MB, alloc=540.3MB, time=18.05 memory used=1980.9MB, alloc=540.3MB, time=18.81 memory used=2022.7MB, alloc=540.3MB, time=19.41 memory used=2079.2MB, alloc=540.3MB, time=20.15 memory used=2136.3MB, alloc=564.3MB, time=20.99 memory used=2376.3MB, alloc=588.3MB, time=23.59 memory used=2613.1MB, alloc=612.3MB, time=26.33 memory used=2848.7MB, alloc=636.3MB, time=29.29 memory used=3090.6MB, alloc=660.3MB, time=32.44 memory used=3338.1MB, alloc=684.3MB, time=35.76 memory used=3591.7MB, alloc=708.3MB, time=39.09 memory used=3872.2MB, alloc=732.3MB, time=42.45 memory used=4129.1MB, alloc=756.3MB, time=46.77 memory used=4359.4MB, alloc=780.3MB, time=52.18 memory used=4592.3MB, alloc=804.3MB, time=58.13 memory used=4833.8MB, alloc=828.3MB, time=64.67 memory used=5085.8MB, alloc=852.3MB, time=71.42 memory used=5349.3MB, alloc=876.3MB, time=78.59 memory used=5623.0MB, alloc=900.3MB, time=86.31 memory used=5906.0MB, alloc=924.3MB, time=94.69 memory used=6211.3MB, alloc=948.3MB, time=103.74 memory used=6540.6MB, alloc=972.3MB, time=113.41 memory used=6893.8MB, alloc=996.3MB, time=123.86 memory used=7271.0MB, alloc=1020.3MB, time=134.86 memory used=7672.1MB, alloc=1044.3MB, time=146.45 memory used=8097.2MB, alloc=1068.3MB, time=158.70 memory used=8546.2MB, alloc=1092.3MB, time=171.56 memory used=9019.0MB, alloc=1116.3MB, time=185.17 memory used=9515.9MB, alloc=1140.3MB, time=199.41 memory used=10036.7MB, alloc=1164.3MB, time=214.28 memory used=10581.4MB, alloc=1188.3MB, time=229.69 memory used=11150.0MB, alloc=1212.3MB, time=245.92 memory used=11742.6MB, alloc=1236.3MB, time=262.57 memory used=12359.2MB, alloc=1236.3MB, time=279.97 memory used=12975.6MB, alloc=1236.3MB, time=297.22 |\^/| 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(); 1428360954 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 2 3 F := [17 x - 2 y z , 7 x z + y z , -7 x y - 17 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 2 G := [-8 x z + 5 y z , 20 z + 5 x , -5 y z + 4 x z] > Problem := [F,G]; 3 2 3 3 2 2 3 Problem := [[17 x - 2 y z , 7 x z + y z , -7 x y - 17 y z], 3 2 3 2 2 2 [-8 x z + 5 y z , 20 z + 5 x , -5 y z + 4 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.9MB, alloc=32.3MB, time=0.39 memory used=48.4MB, alloc=32.3MB, time=0.61 memory used=68.7MB, alloc=56.3MB, time=0.83 memory used=108.8MB, alloc=60.3MB, time=1.30 memory used=147.0MB, alloc=84.3MB, time=1.73 memory used=208.5MB, alloc=92.3MB, time=2.45 memory used=266.6MB, alloc=92.3MB, time=3.12 memory used=326.0MB, alloc=116.3MB, time=3.83 memory used=404.3MB, alloc=140.3MB, time=4.68 memory used=481.9MB, alloc=140.3MB, time=5.55 memory used=551.7MB, alloc=420.3MB, time=6.56 memory used=676.4MB, alloc=444.3MB, time=7.70 memory used=819.7MB, alloc=468.3MB, time=9.04 memory used=942.6MB, alloc=492.3MB, time=10.12 memory used=1063.5MB, alloc=516.3MB, time=11.24 memory used=1169.5MB, alloc=516.3MB, time=12.32 memory used=1264.8MB, alloc=516.3MB, time=13.29 memory used=1356.6MB, alloc=516.3MB, time=14.24 memory used=1442.2MB, alloc=516.3MB, time=15.21 memory used=1517.0MB, alloc=516.3MB, time=16.04 memory used=1591.0MB, alloc=516.3MB, time=16.93 memory used=1671.2MB, alloc=516.3MB, time=17.88 memory used=1731.0MB, alloc=516.3MB, time=18.69 memory used=1788.8MB, alloc=540.3MB, time=19.53 memory used=2005.0MB, alloc=564.3MB, time=21.71 memory used=2194.3MB, alloc=588.3MB, time=23.63 memory used=2407.3MB, alloc=612.3MB, time=25.93 memory used=2577.0MB, alloc=636.3MB, time=27.89 memory used=2734.8MB, alloc=660.3MB, time=29.74 memory used=2885.4MB, alloc=684.3MB, time=31.58 memory used=3024.4MB, alloc=708.3MB, time=33.37 memory used=3126.7MB, alloc=708.3MB, time=34.91 memory used=3219.6MB, alloc=708.3MB, time=36.38 memory used=3343.0MB, alloc=708.3MB, time=38.25 memory used=3685.3MB, alloc=732.3MB, time=42.04 memory used=4033.9MB, alloc=756.3MB, time=46.16 memory used=4393.4MB, alloc=780.3MB, time=50.48 memory used=4763.3MB, alloc=804.3MB, time=55.00 memory used=5141.9MB, alloc=828.3MB, time=60.12 memory used=5488.7MB, alloc=852.3MB, time=65.04 memory used=5802.3MB, alloc=876.3MB, time=70.01 memory used=6120.0MB, alloc=900.3MB, time=75.02 memory used=6441.4MB, alloc=924.3MB, time=80.13 memory used=6779.9MB, alloc=948.3MB, time=85.40 memory used=7203.5MB, alloc=972.3MB, time=90.24 memory used=7654.8MB, alloc=996.3MB, time=95.11 memory used=8150.7MB, alloc=1020.3MB, time=99.67 memory used=8689.0MB, alloc=1044.3MB, time=104.04 memory used=9266.7MB, alloc=1068.3MB, time=108.37 memory used=9833.0MB, alloc=1092.3MB, time=113.93 memory used=10395.3MB, alloc=1116.3MB, time=120.07 memory used=10863.1MB, alloc=1140.3MB, time=127.67 memory used=11345.7MB, alloc=1164.3MB, time=135.42 memory used=11732.8MB, alloc=1188.3MB, time=146.09 memory used=12104.3MB, alloc=1212.3MB, time=157.04 memory used=12477.3MB, alloc=1236.3MB, time=168.26 memory used=12856.6MB, alloc=1260.3MB, time=179.79 memory used=13245.4MB, alloc=1284.3MB, time=191.88 memory used=13645.5MB, alloc=1308.3MB, time=204.33 memory used=14057.2MB, alloc=1332.3MB, time=217.18 memory used=14480.8MB, alloc=1356.3MB, time=230.36 memory used=14917.3MB, alloc=1380.3MB, time=243.99 memory used=15367.1MB, alloc=1404.3MB, time=258.17 memory used=15830.4MB, alloc=1428.3MB, time=272.94 memory used=16305.6MB, alloc=1452.3MB, time=288.18 memory used=16789.9MB, alloc=1476.3MB, time=304.09 |\^/| 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(); 1428361254 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 F := [-9 x y + 2 y z, 5 y z + 14 x z, -14 x y z - 9 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [12 x z - 19 z, 16 x + 16 y, 11 x] > Problem := [F,G]; 3 3 2 2 3 Problem := [[-9 x y + 2 y z, 5 y z + 14 x z, -14 x y z - 9 x z ], 2 3 [12 x z - 19 z, 16 x + 16 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=4.3MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.44 memory used=48.3MB, alloc=32.3MB, time=0.67 memory used=69.8MB, alloc=56.3MB, time=1.03 memory used=113.3MB, alloc=60.3MB, time=1.63 memory used=151.5MB, alloc=84.3MB, time=2.04 memory used=204.6MB, alloc=108.3MB, time=2.87 N1 := 1647 > GB := Basis(F, plex(op(vars))); 14 5 10 5 2 9 2 GB := [295245 x y - 3136 x y, 729 x y + 56 x y , 3645 x y + 112 x z, 3 5 3 -9 x y + 2 y z, 7 x y + x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=279.1MB, alloc=108.3MB, time=3.72 memory used=359.2MB, alloc=116.3MB, time=4.55 memory used=436.4MB, alloc=140.3MB, time=5.62 N2 := 1423 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 2 3 2 H := [-9 x y + 2 y z, 5 y z + 14 x z, -14 x y z - 9 x z , 12 x z - 19 z, 3 16 x + 16 y, 11 x] > J:=[op(GB),op(G)]; 14 5 10 5 2 9 2 J := [295245 x y - 3136 x y, 729 x y + 56 x y , 3645 x y + 112 x z, 3 5 3 2 3 -9 x y + 2 y z, 7 x y + x z , 12 x z - 19 z, 16 x + 16 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 := [6, 14, 19, 4, 3, 1, 3, 1, 2/3, 2/3, 7/12, 5/12, 7/12, 8, 18, 53, 15, 14, 2, 3, 1, 3/4, 1/2, 3/4, 9/16, 5/16, -4, -34, -11] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=468.8MB, alloc=140.3MB, time=6.08 |\^/| 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(); 1428361260 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 4 F := [5 y z + 9 y z, 5 z - 3 y , 2 x + 20 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 3 2 G := [3 x z + 19 z , 7 x z - 3 x z , -18 x y + 16 y z] > Problem := [F,G]; 3 4 2 4 Problem := [[5 y z + 9 y z, 5 z - 3 y , 2 x + 20 y z], 3 3 3 2 3 2 [3 x z + 19 z , 7 x z - 3 x z , -18 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=0.12 memory used=26.1MB, alloc=32.3MB, time=0.30 memory used=47.6MB, alloc=32.3MB, time=0.48 memory used=67.8MB, alloc=32.3MB, time=0.65 memory used=86.8MB, alloc=56.3MB, time=0.84 memory used=125.4MB, alloc=60.3MB, time=1.22 memory used=163.6MB, alloc=84.3MB, time=1.60 memory used=212.9MB, alloc=84.3MB, time=2.04 memory used=270.1MB, alloc=116.3MB, time=2.57 memory used=350.9MB, alloc=116.3MB, time=3.27 memory used=430.6MB, alloc=140.3MB, time=4.00 memory used=505.7MB, alloc=420.3MB, time=4.75 memory used=628.6MB, alloc=444.3MB, time=5.91 memory used=776.6MB, alloc=468.3MB, time=7.39 memory used=930.1MB, alloc=492.3MB, time=9.05 memory used=1089.8MB, alloc=516.3MB, time=10.87 memory used=1260.5MB, alloc=540.3MB, time=12.82 memory used=1451.7MB, alloc=564.3MB, time=14.85 memory used=1647.1MB, alloc=588.3MB, time=17.09 memory used=1841.8MB, alloc=612.3MB, time=19.46 memory used=2029.2MB, alloc=636.3MB, time=22.87 memory used=2212.4MB, alloc=660.3MB, time=26.78 memory used=2403.5MB, alloc=684.3MB, time=31.16 memory used=2604.9MB, alloc=708.3MB, time=36.15 memory used=2820.5MB, alloc=732.3MB, time=41.52 memory used=3049.1MB, alloc=756.3MB, time=47.37 memory used=3289.1MB, alloc=780.3MB, time=53.97 memory used=3553.0MB, alloc=804.3MB, time=61.10 memory used=3840.8MB, alloc=828.3MB, time=68.88 memory used=4152.6MB, alloc=852.3MB, time=77.24 memory used=4488.3MB, alloc=876.3MB, time=86.18 memory used=4847.9MB, alloc=900.3MB, time=95.77 memory used=5231.5MB, alloc=924.3MB, time=105.91 memory used=5639.0MB, alloc=948.3MB, time=116.83 memory used=6070.5MB, alloc=948.3MB, time=128.27 memory used=6502.0MB, alloc=948.3MB, time=139.66 memory used=6933.4MB, alloc=948.3MB, time=151.10 memory used=7364.8MB, alloc=972.3MB, time=162.52 memory used=7820.1MB, alloc=972.3MB, time=174.63 memory used=8275.2MB, alloc=972.3MB, time=186.62 memory used=8730.1MB, alloc=996.3MB, time=198.63 memory used=9209.0MB, alloc=996.3MB, time=211.21 memory used=9687.8MB, alloc=996.3MB, time=223.78 memory used=10166.3MB, alloc=1020.3MB, time=236.56 memory used=10668.8MB, alloc=1020.3MB, time=249.84 memory used=11171.2MB, alloc=1044.3MB, time=262.96 memory used=11697.5MB, alloc=1044.3MB, time=276.67 memory used=12223.8MB, alloc=1068.3MB, time=290.27 memory used=12774.4MB, alloc=1092.3MB, time=304.33 |\^/| 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(); 1428361560 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 2 F := [6 z + 20 x y, 5 y , 11 x y z + y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 2 G := [-11 x y - 5 x z , 19 y - 14 z , -19 x z + 17 z ] > Problem := [F,G]; 3 4 2 2 Problem := [[6 z + 20 x y, 5 y , 11 x y z + y z], 3 2 3 2 3 2 [-11 x y - 5 x z , 19 y - 14 z , -19 x 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=0.14 memory used=26.8MB, alloc=32.3MB, time=0.40 memory used=48.1MB, alloc=32.3MB, time=0.64 memory used=68.2MB, alloc=32.3MB, time=0.87 memory used=87.2MB, alloc=56.3MB, time=1.12 memory used=126.0MB, alloc=60.3MB, time=1.61 memory used=162.8MB, alloc=84.3MB, time=2.06 memory used=211.5MB, alloc=84.3MB, time=2.61 memory used=269.1MB, alloc=92.3MB, time=3.28 memory used=324.8MB, alloc=116.3MB, time=3.99 memory used=402.8MB, alloc=116.3MB, time=4.94 memory used=478.2MB, alloc=140.3MB, time=5.89 memory used=573.7MB, alloc=140.3MB, time=7.08 memory used=663.1MB, alloc=420.3MB, time=8.21 memory used=778.2MB, alloc=444.3MB, time=9.70 memory used=910.6MB, alloc=468.3MB, time=11.63 memory used=1055.0MB, alloc=492.3MB, time=13.81 memory used=1216.7MB, alloc=516.3MB, time=16.12 memory used=1386.8MB, alloc=540.3MB, time=18.75 memory used=1562.4MB, alloc=564.3MB, time=21.33 memory used=1727.7MB, alloc=588.3MB, time=24.74 memory used=1901.5MB, alloc=612.3MB, time=28.59 memory used=2080.8MB, alloc=636.3MB, time=33.16 memory used=2281.7MB, alloc=660.3MB, time=38.33 memory used=2506.5MB, alloc=684.3MB, time=44.09 memory used=2755.2MB, alloc=708.3MB, time=50.54 memory used=3027.9MB, alloc=732.3MB, time=57.45 memory used=3324.4MB, alloc=732.3MB, time=65.20 memory used=3621.0MB, alloc=756.3MB, time=72.86 memory used=3941.5MB, alloc=756.3MB, time=80.89 memory used=4262.0MB, alloc=780.3MB, time=88.92 memory used=4606.5MB, alloc=780.3MB, time=97.36 memory used=4951.2MB, alloc=804.3MB, time=105.30 N1 := 10683 > GB := Basis(F, plex(op(vars))); 5 2 3 3 4 2 2 3 3 2 3 GB := [x y , x y , y , 11 x y z + x y , 1210 x y + 3 y z, 2 2 2 2 2 2 3 11 x y z + y z, -110 x y + 3 y z , 3 z + 10 y x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5116.2MB, alloc=804.3MB, time=107.45 memory used=5261.1MB, alloc=804.3MB, time=109.15 memory used=5400.3MB, alloc=804.3MB, time=111.05 memory used=5532.6MB, alloc=804.3MB, time=112.69 memory used=5644.5MB, alloc=804.3MB, time=114.06 memory used=5735.5MB, alloc=804.3MB, time=115.33 memory used=5843.2MB, alloc=804.3MB, time=116.68 memory used=5921.1MB, alloc=804.3MB, time=117.95 memory used=6007.1MB, alloc=804.3MB, time=119.29 memory used=6100.7MB, alloc=804.3MB, time=120.78 memory used=6180.5MB, alloc=804.3MB, time=121.96 memory used=6239.6MB, alloc=804.3MB, time=122.93 memory used=6314.6MB, alloc=804.3MB, time=124.16 memory used=6384.1MB, alloc=804.3MB, time=125.26 memory used=6443.5MB, alloc=804.3MB, time=126.50 memory used=6496.8MB, alloc=804.3MB, time=127.59 memory used=6577.9MB, alloc=804.3MB, time=129.01 memory used=6846.4MB, alloc=828.3MB, time=132.03 memory used=7072.1MB, alloc=852.3MB, time=134.75 memory used=7257.5MB, alloc=852.3MB, time=137.05 memory used=7457.1MB, alloc=876.3MB, time=139.47 memory used=7666.9MB, alloc=876.3MB, time=142.24 memory used=7832.3MB, alloc=900.3MB, time=144.50 memory used=8004.2MB, alloc=900.3MB, time=146.87 memory used=8155.9MB, alloc=900.3MB, time=149.24 memory used=8638.8MB, alloc=924.3MB, time=154.97 memory used=9143.8MB, alloc=948.3MB, time=160.95 memory used=9652.0MB, alloc=972.3MB, time=167.40 memory used=10178.8MB, alloc=996.3MB, time=174.00 memory used=10716.2MB, alloc=1020.3MB, time=181.42 memory used=11193.9MB, alloc=1044.3MB, time=188.52 memory used=11700.5MB, alloc=1068.3MB, time=195.39 memory used=12168.9MB, alloc=1092.3MB, time=202.60 memory used=12619.1MB, alloc=1116.3MB, time=209.62 memory used=13010.8MB, alloc=1140.3MB, time=219.57 memory used=13375.3MB, alloc=1164.3MB, time=229.93 memory used=13736.2MB, alloc=1188.3MB, time=240.58 memory used=14101.4MB, alloc=1212.3MB, time=251.37 memory used=14473.9MB, alloc=1236.3MB, time=262.62 memory used=14855.8MB, alloc=1260.3MB, time=274.25 memory used=15239.3MB, alloc=1284.3MB, time=286.33 memory used=15638.4MB, alloc=1308.3MB, time=299.15 memory used=16061.5MB, alloc=1332.3MB, time=312.76 |\^/| 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(); 1428361860 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 F := [2 z + 2, -4 x y - 14 x z, 17 z - y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 4 2 G := [-16 x z , -8 y z + 16 z , -12 y + 16 y z] > Problem := [F,G]; 2 2 2 4 2 Problem := [[2 z + 2, -4 x y - 14 x z, 17 z - y z ], 3 2 2 4 4 2 [-16 x z , -8 y z + 16 z , -12 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=0.14 memory used=26.1MB, alloc=32.3MB, time=0.39 memory used=48.1MB, alloc=32.3MB, time=0.68 memory used=69.2MB, alloc=56.3MB, time=0.97 N1 := 603 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x , y + 17, z + 1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.0MB, alloc=60.3MB, time=1.50 N2 := 213 #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 4 2 3 2 2 4 H := [2 z + 2, -4 x y - 14 x z, 17 z - y z , -16 x z , -8 y z + 16 z , 4 2 -12 y + 16 y z] > J:=[op(GB),op(G)]; 2 2 3 2 2 4 4 2 J := [x , y + 17, z + 1, -16 x z , -8 y z + 16 z , -12 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 := [6, 12, 21, 4, 2, 4, 4, 1/3, 2/3, 1, 3/13, 5/13, 8/13, 6, 9, 17, 4, 2, 4, 4, 1/3, 1/2, 2/3, 2/13, 4/13, 5/13, 3, 4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=116.1MB, alloc=60.3MB, time=1.59 |\^/| 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(); 1428361862 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 F := [-y - 11 x , -6 y z - 16 y z, 3 x y z + x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 G := [-20 x z + 13 x , -8 x y z - 11 y , 20 y + 16 y] > Problem := [F,G]; 4 2 3 Problem := [[-y - 11 x , -6 y z - 16 y z, 3 x y z + x y], 3 2 2 2 3 [-20 x z + 13 x , -8 x y z - 11 y , 20 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=4.3MB, alloc=32.3MB, time=0.15 memory used=26.1MB, alloc=32.3MB, time=0.39 N1 := 165 > GB := Basis(F, plex(op(vars))); 3 4 2 2 3 2 3 GB := [x , x y, y + 11 x , 3 x z + 8 x z, 3 y z + 8 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 51 #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)]; 4 2 3 3 2 H := [-y - 11 x , -6 y z - 16 y z, 3 x y z + x y, -20 x z + 13 x , 2 2 3 -8 x y z - 11 y , 20 y + 16 y] > J:=[op(GB),op(G)]; 3 4 2 2 3 2 3 3 2 J := [x , x y, y + 11 x , 3 x z + 8 x z, 3 y z + 8 y z, -20 x z + 13 x , 2 2 3 -8 x y z - 11 y , 20 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 := [6, 13, 22, 4, 3, 4, 3, 2/3, 5/6, 2/3, 1/2, 3/4, 5/12, 8, 15, 29, 5, 3, 4, 3, 3/4, 5/8, 1/2, 1/2, 1/2, 3/8, -2, -7, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=71.3MB, alloc=68.3MB, time=0.95 |\^/| 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(); 1428361863 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 F := [-11 x + 12 y z , -20 x y + 10 x , -15 x z - 17 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 2 G := [-3 x y - 12 z , -10 y z + x , -y z - 11] > Problem := [F,G]; 4 2 3 2 2 Problem := [[-11 x + 12 y z , -20 x y + 10 x , -15 x z - 17 x z], 2 2 4 3 2 [-3 x y - 12 z , -10 y z + x , -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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.43 memory used=47.9MB, alloc=32.3MB, time=0.68 memory used=68.2MB, alloc=32.3MB, time=0.91 memory used=87.6MB, alloc=56.3MB, time=1.14 memory used=127.7MB, alloc=60.3MB, time=1.61 memory used=166.8MB, alloc=60.3MB, time=2.07 memory used=205.7MB, alloc=84.3MB, time=2.53 memory used=265.8MB, alloc=92.3MB, time=3.25 memory used=325.1MB, alloc=116.3MB, time=3.95 memory used=408.0MB, alloc=116.3MB, time=4.97 memory used=484.7MB, alloc=396.3MB, time=5.85 memory used=589.5MB, alloc=420.3MB, time=7.23 N1 := 1197 > GB := Basis(F, plex(op(vars))); 6 5 3 2 2 5 2 2 GB := [15 x + 17 x , 2 x y - x , 15 x z + 17 x z, 55 x y + 34 x z , 4 2 -11 x + 12 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=708.7MB, alloc=420.3MB, time=9.24 memory used=831.5MB, alloc=420.3MB, time=10.63 memory used=955.6MB, alloc=420.3MB, time=12.13 memory used=1078.2MB, alloc=444.3MB, time=13.62 memory used=1224.5MB, alloc=468.3MB, time=15.29 memory used=1356.3MB, alloc=492.3MB, time=16.40 memory used=1512.5MB, alloc=492.3MB, time=17.94 memory used=1637.5MB, alloc=516.3MB, time=19.18 memory used=1760.4MB, alloc=516.3MB, time=20.34 memory used=1884.5MB, alloc=516.3MB, time=21.66 memory used=1983.8MB, alloc=516.3MB, time=22.74 memory used=2080.9MB, alloc=516.3MB, time=23.78 memory used=2179.7MB, alloc=540.3MB, time=24.90 memory used=2276.6MB, alloc=540.3MB, time=26.03 memory used=2352.3MB, alloc=540.3MB, time=26.93 memory used=2427.4MB, alloc=540.3MB, time=27.89 memory used=2501.2MB, alloc=540.3MB, time=28.85 memory used=2575.3MB, alloc=540.3MB, time=29.83 memory used=2636.3MB, alloc=540.3MB, time=30.68 memory used=2696.9MB, alloc=564.3MB, time=31.54 memory used=2746.7MB, alloc=564.3MB, time=32.36 memory used=2785.4MB, alloc=564.3MB, time=33.04 memory used=3007.6MB, alloc=588.3MB, time=35.35 memory used=3233.1MB, alloc=612.3MB, time=37.68 memory used=3502.0MB, alloc=636.3MB, time=40.74 memory used=3762.7MB, alloc=660.3MB, time=44.26 memory used=3973.7MB, alloc=684.3MB, time=49.27 N2 := 2895 #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)]; 4 2 3 2 2 2 2 4 H := [-11 x + 12 y z , -20 x y + 10 x , -15 x z - 17 x z, -3 x y - 12 z , 3 2 -10 z y + x , -y z - 11] > J:=[op(GB),op(G)]; 6 5 3 2 2 5 2 2 J := [15 x + 17 x , 2 x y - x , 15 x z + 17 x z, 55 x y + 34 x z , 4 2 2 2 4 3 2 -11 x + 12 y z , -3 x y - 12 z , -10 z y + x , -y z - 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, 21, 4, 4, 3, 4, 5/6, 5/6, 5/6, 7/12, 5/12, 1/2, 8, 19, 34, 7, 6, 3, 4, 7/8, 3/4, 3/4, 11/16, 3/8, 7/16, -4, -13, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3996.7MB, alloc=684.3MB, time=49.63 |\^/| 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(); 1428361911 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 F := [6 y z, -8 x y + 16, -20 x y + 20 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 4 G := [20 x y + 11 y , -19 x y - 12 x y z, 19 z + 5 z] > Problem := [F,G]; 2 2 2 2 3 Problem := [[6 y z, -8 x y + 16, -20 x y + 20 z ], 3 4 3 4 [20 x y + 11 y , -19 x y - 12 x y z, 19 z + 5 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.4MB, alloc=32.3MB, time=0.36 memory used=48.2MB, alloc=32.3MB, time=0.54 memory used=68.5MB, alloc=32.3MB, time=0.71 memory used=88.3MB, alloc=56.3MB, time=0.90 memory used=131.9MB, alloc=60.3MB, time=1.37 memory used=170.5MB, alloc=84.3MB, time=1.79 memory used=229.0MB, alloc=108.3MB, time=2.43 memory used=302.7MB, alloc=140.3MB, time=3.38 memory used=385.6MB, alloc=164.3MB, time=4.91 memory used=483.7MB, alloc=164.3MB, time=6.98 memory used=581.9MB, alloc=188.3MB, time=9.08 N1 := 3427 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=708.9MB, alloc=188.3MB, time=10.95 N2 := 357 #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 2 3 3 4 H := [6 z y , -8 x y + 16, -20 x y + 20 z , 20 x y + 11 y , 3 4 -19 x y - 12 x y z, 19 z + 5 z] > J:=[op(GB),op(G)]; 3 4 3 4 J := [1, 20 x y + 11 y , -19 x y - 12 x y z, 19 z + 5 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 22, 4, 2, 4, 4, 2/3, 5/6, 2/3, 5/13, 7/13, 5/13, 4, 6, 12, 4, 1, 4, 4, 1/2, 1/2, 1/2, 3/7, 4/7, 3/7, 7, 10, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=711.1MB, alloc=188.3MB, time=10.98 |\^/| 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(); 1428361922 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 F := [-7 x y z - 6 x y , -6 x - 6 y z, -19 x z + 20 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 G := [-3 z + 10 x , 11 x y - 18 x z, -x z - 4 x z ] > Problem := [F,G]; 2 2 4 Problem := [[-7 x y z - 6 x y , -6 x - 6 y z, -19 x z + 20 y], 3 2 2 2 2 2 2 [-3 z + 10 x , 11 x y - 18 x z, -x z - 4 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.8MB, alloc=32.3MB, time=0.35 memory used=48.4MB, alloc=32.3MB, time=0.54 memory used=68.9MB, alloc=32.3MB, time=0.72 memory used=88.4MB, alloc=60.3MB, time=0.90 memory used=127.2MB, alloc=60.3MB, time=1.21 memory used=168.6MB, alloc=92.3MB, time=1.59 memory used=232.7MB, alloc=92.3MB, time=2.14 memory used=295.5MB, alloc=116.3MB, time=2.70 memory used=360.8MB, alloc=372.3MB, time=3.30 memory used=441.9MB, alloc=396.3MB, time=4.06 memory used=544.2MB, alloc=420.3MB, time=5.02 memory used=661.7MB, alloc=444.3MB, time=6.34 memory used=790.4MB, alloc=468.3MB, time=7.78 memory used=933.0MB, alloc=492.3MB, time=9.37 memory used=1087.0MB, alloc=516.3MB, time=11.22 memory used=1240.5MB, alloc=540.3MB, time=14.07 memory used=1397.9MB, alloc=564.3MB, time=17.64 memory used=1561.9MB, alloc=588.3MB, time=21.96 memory used=1749.8MB, alloc=612.3MB, time=26.86 memory used=1961.7MB, alloc=636.3MB, time=32.36 memory used=2197.6MB, alloc=660.3MB, time=38.43 memory used=2457.4MB, alloc=660.3MB, time=44.94 memory used=2717.2MB, alloc=684.3MB, time=51.45 memory used=3000.9MB, alloc=684.3MB, time=58.04 N1 := 8287 > GB := Basis(F, plex(op(vars))); 6 5 5 2 4 GB := [x , x y, 19 x + 20 y , 19 z x - 20 y, x + z y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3300.0MB, alloc=684.3MB, time=62.88 N2 := 1605 #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 4 3 2 H := [-7 x y z - 6 x y , -6 x - 6 y z, -19 x z + 20 y, -3 z + 10 x , 2 2 2 2 2 11 x y - 18 x z, -x z - 4 x z ] > J:=[op(GB),op(G)]; 6 5 5 2 4 3 2 J := [x , x y, 19 x + 20 y , 19 z x - 20 y, x + z y, -3 z + 10 x , 2 2 2 2 2 11 x y - 18 x z, -x z - 4 x z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 16, 21, 4, 4, 2, 3, 1, 2/3, 1, 3/4, 5/12, 7/12, 8, 18, 34, 6, 6, 2, 3, 1, 5/8, 5/8, 5/8, 5/16, 3/8, -2, -13, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3515.5MB, alloc=684.3MB, time=65.78 |\^/| 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(); 1428361987 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 F := [5 x - 12, -3 x y - 12 x , -18 y z - z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 2 G := [-13 x z , -9 x z + 7 y z , -9 x z + 19 y z] > Problem := [F,G]; 3 2 2 3 3 Problem := [[5 x - 12, -3 x y - 12 x , -18 y z - z ], 3 3 2 2 3 2 [-13 x z , -9 x z + 7 y z , -9 x z + 19 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.35 memory used=49.6MB, alloc=32.3MB, time=0.59 memory used=69.7MB, alloc=56.3MB, time=0.82 N1 := 465 > GB := Basis(F, plex(op(vars))); 3 2 3 GB := [5 x - 12, y + 4 x, -72 x y z + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=108.4MB, alloc=60.3MB, time=1.19 N2 := 461 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 3 3 3 3 2 2 H := [5 x - 12, -3 x y - 12 x , -18 y z - z , -13 x z , -9 x z + 7 y z , 3 2 -9 x z + 19 y z] > J:=[op(GB),op(G)]; 3 2 3 3 3 2 2 J := [5 x - 12, y + 4 x, -72 x y z + z , -13 x z , -9 x z + 7 y z , 3 2 -9 x z + 19 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 := [6, 13, 22, 4, 3, 3, 3, 5/6, 2/3, 2/3, 6/13, 4/13, 7/13, 6, 14, 20, 4, 3, 2, 3, 1, 2/3, 2/3, 6/13, 4/13, 7/13, -1, 2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=147.2MB, alloc=60.3MB, time=1.59 |\^/| 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(); 1428361988 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 2 2 F := [10 y z , -18 y z + 9 z , -9 x y - 8 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [-13 x y z - 5 y, 13 x y z + 8 x z , -19 y z + 3] > Problem := [F,G]; 3 2 2 3 2 2 2 Problem := [[10 y z , -18 y z + 9 z , -9 x y - 8 x y], 2 2 2 3 [-13 x y z - 5 y, 13 x y z + 8 x z , -19 y z + 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.11 memory used=26.3MB, alloc=32.3MB, time=0.29 memory used=47.7MB, alloc=32.3MB, time=0.47 memory used=68.1MB, alloc=56.3MB, time=0.66 memory used=110.8MB, alloc=60.3MB, time=1.10 memory used=148.8MB, alloc=84.3MB, time=1.51 memory used=205.7MB, alloc=108.3MB, time=2.12 memory used=277.6MB, alloc=132.3MB, time=3.36 memory used=364.5MB, alloc=132.3MB, time=4.82 N1 := 2269 > GB := Basis(F, plex(op(vars))); 2 2 2 2 2 3 2 2 2 3 GB := [9 x y + 8 x y, x y z , y z , -2 y z + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=451.5MB, alloc=140.3MB, time=5.73 memory used=547.2MB, alloc=164.3MB, time=6.78 memory used=660.3MB, alloc=188.3MB, time=8.53 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)]; 3 2 2 3 2 2 2 2 H := [10 y z , -18 y z + 9 z , -9 x y - 8 x y, -13 x y z - 5 y, 2 2 3 13 x y z + 8 x z , -19 y z + 3] > J:=[op(GB),op(G)]; 2 2 2 2 2 3 2 2 2 3 2 J := [9 x y + 8 x y, x y z , y z , -2 y z + z , -13 x y z - 5 y, 2 2 3 13 x y z + 8 x z , -19 y 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 := [6, 14, 24, 4, 2, 3, 3, 1/2, 1, 5/6, 5/13, 8/13, 7/13, 7, 17, 30, 5, 2, 3, 3, 4/7, 1, 6/7, 2/5, 3/5, 8/15, -3, -6, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=765.0MB, alloc=188.3MB, time=10.21 |\^/| 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(); 1428361999 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 2 F := [-19 x + 14 y , 7 x y + 5 y z, -17 x y z + 6 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [-6 x y + 20, -y z - 4 x z, -13 x z - 14 y] > Problem := [F,G]; 2 2 3 3 2 2 Problem := [[-19 x + 14 y , 7 x y + 5 y z, -17 x y z + 6 y ], 2 2 2 2 3 [-6 x y + 20, -y z - 4 x z, -13 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=4.3MB, alloc=32.3MB, time=0.13 memory used=26.4MB, alloc=32.3MB, time=0.35 memory used=48.6MB, alloc=32.3MB, time=0.54 memory used=68.9MB, alloc=32.3MB, time=0.72 memory used=87.9MB, alloc=56.3MB, time=0.90 memory used=130.0MB, alloc=60.3MB, time=1.26 memory used=171.7MB, alloc=92.3MB, time=1.63 memory used=239.9MB, alloc=92.3MB, time=2.18 memory used=305.0MB, alloc=116.3MB, time=2.72 memory used=376.7MB, alloc=372.3MB, time=3.31 memory used=463.7MB, alloc=396.3MB, time=4.03 memory used=573.6MB, alloc=420.3MB, time=4.93 memory used=704.0MB, alloc=444.3MB, time=6.23 memory used=845.9MB, alloc=468.3MB, time=7.66 memory used=992.2MB, alloc=492.3MB, time=9.29 memory used=1172.3MB, alloc=516.3MB, time=11.02 memory used=1356.6MB, alloc=540.3MB, time=13.01 memory used=1546.5MB, alloc=564.3MB, time=15.23 memory used=1758.7MB, alloc=588.3MB, time=18.11 memory used=1941.1MB, alloc=612.3MB, time=21.94 memory used=2131.5MB, alloc=636.3MB, time=26.27 memory used=2331.3MB, alloc=660.3MB, time=31.22 memory used=2540.4MB, alloc=684.3MB, time=36.99 memory used=2773.5MB, alloc=708.3MB, time=43.27 memory used=3030.6MB, alloc=732.3MB, time=50.11 memory used=3311.5MB, alloc=756.3MB, time=57.57 memory used=3616.5MB, alloc=780.3MB, time=65.64 memory used=3945.3MB, alloc=780.3MB, time=74.32 memory used=4274.2MB, alloc=804.3MB, time=82.94 memory used=4626.9MB, alloc=804.3MB, time=92.01 memory used=4979.7MB, alloc=804.3MB, time=101.16 memory used=5332.2MB, alloc=828.3MB, time=110.59 memory used=5708.5MB, alloc=852.3MB, time=121.18 memory used=6108.7MB, alloc=876.3MB, time=131.93 N1 := 12211 > GB := Basis(F, plex(op(vars))); 7 3 5 2 2 2 GB := [93297539384 x - 13928056875 x , -81634 x + 27075 x y, -19 x + 14 y , 4 3 2 2 98 x + 95 x z, 119 x y z - 57 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6396.1MB, alloc=876.3MB, time=137.03 memory used=6504.6MB, alloc=876.3MB, time=139.06 memory used=6621.7MB, alloc=876.3MB, time=141.15 memory used=6750.2MB, alloc=876.3MB, time=143.21 memory used=6855.1MB, alloc=876.3MB, time=144.87 memory used=6936.6MB, alloc=876.3MB, time=146.18 memory used=7019.5MB, alloc=876.3MB, time=147.80 memory used=7124.9MB, alloc=876.3MB, time=149.71 memory used=7245.7MB, alloc=876.3MB, time=152.15 memory used=7365.1MB, alloc=876.3MB, time=154.55 memory used=7472.4MB, alloc=876.3MB, time=156.86 memory used=7575.8MB, alloc=900.3MB, time=158.96 memory used=7687.5MB, alloc=900.3MB, time=161.12 memory used=7789.9MB, alloc=924.3MB, time=163.07 memory used=7887.2MB, alloc=948.3MB, time=164.96 memory used=7980.2MB, alloc=948.3MB, time=167.22 memory used=8062.8MB, alloc=972.3MB, time=169.38 memory used=8452.8MB, alloc=996.3MB, time=175.35 memory used=8916.3MB, alloc=1020.3MB, time=185.18 memory used=9366.4MB, alloc=1044.3MB, time=198.91 memory used=9814.8MB, alloc=1068.3MB, time=212.67 memory used=10267.7MB, alloc=1092.3MB, time=227.40 memory used=10728.9MB, alloc=1116.3MB, time=240.14 memory used=11189.5MB, alloc=1140.3MB, time=253.55 memory used=11673.7MB, alloc=1164.3MB, time=267.59 memory used=12181.7MB, alloc=1188.3MB, time=282.35 memory used=12713.7MB, alloc=1212.3MB, time=297.65 |\^/| 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(); 1428362299 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [3 x y - 14 x , x y z - 9 y , 11 x z + 3 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 2 G := [14 y z - 16 y , 13 x - 6 x y, 17 z + 13 z ] > Problem := [F,G]; 2 2 2 3 Problem := [[3 x y - 14 x , x y z - 9 y , 11 x z + 3 y z], 2 2 3 4 2 [14 y z - 16 y , 13 x - 6 x y, 17 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=4.3MB, alloc=32.3MB, time=0.14 memory used=26.2MB, alloc=32.3MB, time=0.38 memory used=48.0MB, alloc=32.3MB, time=0.63 memory used=68.7MB, alloc=32.3MB, time=0.87 memory used=88.3MB, alloc=56.3MB, time=1.10 memory used=127.9MB, alloc=60.3MB, time=1.59 memory used=167.0MB, alloc=84.3MB, time=2.17 memory used=225.2MB, alloc=84.3MB, time=2.99 memory used=276.4MB, alloc=108.3MB, time=3.94 memory used=340.0MB, alloc=132.3MB, time=5.55 N1 := 1721 > GB := Basis(F, plex(op(vars))); 4 3 3 2 2 2 3 3 GB := [121 x - 42 x , 11 x + 3 x y, 3 x y - 14 x , 1331 x + 27 y , 3 2 -14641 x + 42 x z, 11 x z + 3 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=426.7MB, alloc=140.3MB, time=6.55 memory used=525.7MB, alloc=140.3MB, time=7.52 memory used=618.1MB, alloc=164.3MB, time=8.80 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)]; 2 2 2 3 2 2 H := [3 x y - 14 x , x y z - 9 y , 11 x z + 3 y z, 14 y z - 16 y , 3 4 2 13 x - 6 x y, 17 z + 13 z ] > J:=[op(GB),op(G)]; 4 3 3 2 2 2 3 3 J := [121 x - 42 x , 11 x + 3 x y, 3 x y - 14 x , 1331 x + 27 y , 3 2 2 2 3 -14641 x + 42 x z, 11 x z + 3 y z, 14 y z - 16 y , 13 x - 6 x y, 4 2 17 z + 13 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, 19, 4, 3, 3, 4, 2/3, 5/6, 2/3, 1/2, 7/12, 1/2, 9, 17, 28, 4, 4, 3, 4, 7/9, 2/3, 4/9, 2/3, 7/18, 1/3, -4, -9, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=644.7MB, alloc=164.3MB, time=9.17 |\^/| 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(); 1428362308 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 3 F := [x + 15 y, 17 y z - 4 x z, -10 y - z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 2 3 G := [9 y z, -19 x - 13 y , -4 x y - 17 z ] > Problem := [F,G]; 4 3 2 3 Problem := [[x + 15 y, 17 y z - 4 x z, -10 y - z], 3 4 3 2 3 [9 y z, -19 x - 13 y , -4 x 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=0.13 memory used=26.1MB, alloc=32.3MB, time=0.33 memory used=47.9MB, alloc=32.3MB, time=0.54 memory used=70.0MB, alloc=32.3MB, time=0.75 memory used=90.9MB, alloc=56.3MB, time=0.98 memory used=134.1MB, alloc=60.3MB, time=1.43 memory used=171.0MB, alloc=84.3MB, time=1.85 memory used=222.8MB, alloc=108.3MB, time=2.63 N1 := 1395 > GB := Basis(F, plex(op(vars))); 24 14 4 12 GB := [17 x + 13500 x , x + 15 y, -2 x + 675 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=298.0MB, alloc=108.3MB, time=3.38 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)]; 4 3 2 3 3 4 3 H := [x + 15 y, 17 y z - 4 x z, -10 y - z, 9 z y , -19 x - 13 y , 2 3 -4 x y - 17 z ] > J:=[op(GB),op(G)]; 24 14 4 12 3 4 3 J := [17 x + 13500 x , x + 15 y, -2 x + 675 z, 9 z y , -19 x - 13 y , 2 3 -4 x y - 17 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, 22, 4, 4, 3, 3, 2/3, 1, 2/3, 4/13, 6/13, 5/13, 6, 12, 51, 24, 24, 3, 3, 5/6, 2/3, 1/2, 6/13, 4/13, 3/13, 2, -29, -20] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=332.1MB, alloc=108.3MB, time=3.78 |\^/| 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(); 1428362312 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 F := [8 z + 10 x, x y z - 9 y z , 9 x y + 3 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [6 y - 10 y z , -6 x z - 4 y z, 7 x y + 6 z ] > Problem := [F,G]; 2 2 2 2 3 2 Problem := [[8 z + 10 x, x y z - 9 y z , 9 x y + 3 y ], 3 2 2 [6 y - 10 y z , -6 x z - 4 y z, 7 x y + 6 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.11 memory used=26.3MB, alloc=32.3MB, time=0.29 memory used=48.0MB, alloc=32.3MB, time=0.47 memory used=68.0MB, alloc=32.3MB, time=0.64 memory used=87.7MB, alloc=56.3MB, time=0.82 memory used=127.9MB, alloc=60.3MB, time=1.18 memory used=166.3MB, alloc=60.3MB, time=1.57 memory used=203.7MB, alloc=84.3MB, time=1.91 memory used=262.2MB, alloc=92.3MB, time=2.44 memory used=322.1MB, alloc=116.3MB, time=3.10 memory used=400.3MB, alloc=140.3MB, time=3.94 memory used=494.2MB, alloc=164.3MB, time=4.96 memory used=603.0MB, alloc=188.3MB, time=6.14 memory used=724.9MB, alloc=212.3MB, time=7.50 memory used=842.8MB, alloc=492.3MB, time=8.86 memory used=983.4MB, alloc=516.3MB, time=10.61 memory used=1120.6MB, alloc=540.3MB, time=13.13 memory used=1264.8MB, alloc=564.3MB, time=16.12 memory used=1419.8MB, alloc=588.3MB, time=19.65 memory used=1587.1MB, alloc=612.3MB, time=23.64 memory used=1767.0MB, alloc=636.3MB, time=28.37 memory used=1970.9MB, alloc=660.3MB, time=33.69 memory used=2198.7MB, alloc=684.3MB, time=39.61 memory used=2450.5MB, alloc=708.3MB, time=46.14 memory used=2726.2MB, alloc=708.3MB, time=53.26 memory used=3001.9MB, alloc=708.3MB, time=60.36 memory used=3277.4MB, alloc=732.3MB, time=67.46 memory used=3577.0MB, alloc=732.3MB, time=75.22 memory used=3876.6MB, alloc=732.3MB, time=83.00 memory used=4176.1MB, alloc=756.3MB, time=90.69 memory used=4499.5MB, alloc=756.3MB, time=98.96 memory used=4822.9MB, alloc=756.3MB, time=107.21 memory used=5146.1MB, alloc=780.3MB, time=115.48 memory used=5493.3MB, alloc=780.3MB, time=124.32 memory used=5840.6MB, alloc=804.3MB, time=133.08 memory used=6211.8MB, alloc=828.3MB, time=142.15 N1 := 13473 > GB := Basis(F, plex(op(vars))); 6 3 3 2 4 2 2 GB := [3645 x y + 4 x y, 3 x y + y , -135 x y + 4 x y z, 4 z + 5 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6586.7MB, alloc=828.3MB, time=148.18 memory used=6829.0MB, alloc=828.3MB, time=151.73 memory used=7091.0MB, alloc=852.3MB, time=155.37 memory used=7338.5MB, alloc=876.3MB, time=160.46 memory used=7758.0MB, alloc=900.3MB, time=171.53 memory used=8181.4MB, alloc=924.3MB, time=183.40 memory used=8628.7MB, alloc=948.3MB, time=195.90 memory used=9099.9MB, alloc=972.3MB, time=209.17 memory used=9595.2MB, alloc=996.3MB, time=222.93 memory used=10114.4MB, alloc=1020.3MB, time=237.12 memory used=10657.8MB, alloc=1044.3MB, time=250.51 N2 := 10845 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 2 3 2 H := [8 z + 10 x, x y z - 9 y z , 9 x y + 3 y , 6 y - 10 y z , 2 -6 x z - 4 y z, 6 z + 7 y x] > J:=[op(GB),op(G)]; 6 3 3 2 4 2 2 J := [3645 x y + 4 x y, 3 x y + y , -135 x y + 4 x y z, 4 z + 5 x, 3 2 2 6 y - 10 y z , -6 x z - 4 y z, 6 z + 7 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 := [6, 15, 17, 4, 3, 3, 2, 5/6, 5/6, 5/6, 5/12, 2/3, 7/12, 7, 17, 25, 7, 6, 3, 2, 6/7, 6/7, 5/7, 4/7, 5/7, 3/7, -2, -8, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=10702.6MB, alloc=1044.3MB, time=251.32 |\^/| 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(); 1428362559 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [17 x z - 3, -2 y z + 2 y z , 20 x - 7 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 G := [5 x y z + 18 z , 18 x y z + 11, 14 x z + 2 z ] > Problem := [F,G]; 3 2 2 3 Problem := [[17 x z - 3, -2 y z + 2 y z , 20 x - 7 y], 2 3 2 2 2 2 [5 x y z + 18 z , 18 x y z + 11, 14 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=4.3MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.37 memory used=48.2MB, alloc=32.3MB, time=0.55 memory used=68.2MB, alloc=32.3MB, time=0.72 memory used=88.3MB, alloc=56.3MB, time=0.90 memory used=128.3MB, alloc=60.3MB, time=1.25 memory used=166.2MB, alloc=84.3MB, time=1.58 memory used=222.2MB, alloc=84.3MB, time=2.18 memory used=278.2MB, alloc=108.3MB, time=2.78 memory used=353.8MB, alloc=140.3MB, time=3.62 memory used=447.0MB, alloc=164.3MB, time=4.61 memory used=553.9MB, alloc=188.3MB, time=6.05 memory used=661.6MB, alloc=212.3MB, time=8.20 memory used=783.4MB, alloc=236.3MB, time=11.02 memory used=929.0MB, alloc=236.3MB, time=14.17 memory used=1074.8MB, alloc=260.3MB, time=17.15 N1 := 4729 > GB := Basis(F, plex(op(vars))); 4 3 3 GB := [340 x - 21, -20 x + 7 y, -20 x + 7 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1248.8MB, alloc=260.3MB, time=19.82 N2 := 1087 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 3 2 3 H := [17 z x - 3, -2 y z + 2 y z , 20 x - 7 y, 5 x y z + 18 z , 2 2 2 2 18 z y x + 11, 14 x z + 2 z ] > J:=[op(GB),op(G)]; 4 3 3 2 3 2 J := [340 x - 21, -20 x + 7 y, -20 x + 7 z, 5 x y z + 18 z , 18 z y x + 11, 2 2 2 14 x z + 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, 14, 21, 4, 3, 3, 3, 5/6, 2/3, 5/6, 5/12, 5/12, 2/3, 6, 13, 22, 4, 4, 1, 3, 1, 1/2, 2/3, 1/2, 1/4, 1/2, 1, -1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1382.4MB, alloc=260.3MB, time=21.37 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428362580 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [17 y + 5 y z, -10 y z - 4 y , 19 x y - 20 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [3 y z + 15, -8 x y - y, -18 x y z + 5 x y z] > Problem := [F,G]; 3 2 2 3 Problem := [[17 y + 5 y z, -10 y z - 4 y , 19 x y - 20 x y z], 2 2 2 [3 y z + 15, -8 x y - y, -18 x y z + 5 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.2MB, alloc=32.3MB, time=0.34 memory used=47.1MB, alloc=32.3MB, time=0.51 memory used=67.2MB, alloc=32.3MB, time=0.68 memory used=86.1MB, alloc=56.3MB, time=0.85 memory used=124.7MB, alloc=60.3MB, time=1.18 memory used=161.3MB, alloc=84.3MB, time=1.53 memory used=219.6MB, alloc=84.3MB, time=2.14 memory used=270.3MB, alloc=108.3MB, time=2.69 memory used=335.8MB, alloc=132.3MB, time=3.48 memory used=410.1MB, alloc=156.3MB, time=4.81 memory used=500.6MB, alloc=180.3MB, time=6.61 memory used=615.2MB, alloc=180.3MB, time=8.74 N1 := 3555 > GB := Basis(F, plex(op(vars))); 5 3 3 2 2 3 3 4 2 GB := [19 x y + 8 x y, 19 x y + 8 x y , 19 x y + 68 x y , 17 y - 2 y , 3 17 y + 5 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=731.2MB, alloc=180.3MB, time=10.55 memory used=861.0MB, alloc=188.3MB, time=11.84 N2 := 1545 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 3 H := [17 y + 5 y z, -10 y z - 4 y , 19 x y - 20 x y z, 3 y z + 15, 2 2 2 -8 x y - y, -18 x y z + 5 x y z] > J:=[op(GB),op(G)]; 5 3 3 2 2 3 3 4 2 J := [19 x y + 8 x y, 19 x y + 8 x y , 19 x y + 68 x y , 17 y - 2 y , 3 2 2 2 17 y + 5 y z, 3 y z + 15, -8 x y - y, -18 x y z + 5 x 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 := [6, 14, 20, 4, 3, 3, 2, 1/2, 1, 5/6, 5/12, 11/12, 1/2, 8, 16, 32, 6, 5, 4, 2, 5/8, 1, 3/8, 9/16, 15/16, 1/4, -2, -12, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=964.0MB, alloc=188.3MB, time=13.33 |\^/| 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(); 1428362593 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 F := [2 x y - 4 x y z, 8 z , 20 y z - 11] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 2 G := [11 x y + 17 x y z, 8 x + 12 z, 7 x y + 3 x y] > Problem := [F,G]; 3 2 4 2 Problem := [[2 x y - 4 x y z, 8 z , 20 y z - 11], 2 4 2 2 2 [11 x y + 17 x y z, 8 x + 12 z, 7 x y + 3 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=26.4MB, alloc=32.3MB, time=0.35 memory used=47.6MB, alloc=32.3MB, time=0.52 memory used=68.0MB, alloc=32.3MB, time=0.70 memory used=86.8MB, alloc=56.3MB, time=0.88 memory used=125.1MB, alloc=60.3MB, time=1.22 memory used=162.1MB, alloc=84.3MB, time=1.62 memory used=218.1MB, alloc=84.3MB, time=2.22 memory used=268.0MB, alloc=108.3MB, time=2.76 memory used=333.9MB, alloc=132.3MB, time=3.75 memory used=412.1MB, alloc=156.3MB, time=5.23 N1 := 2629 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=515.7MB, alloc=156.3MB, time=6.89 N2 := 89 #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)]; 3 2 4 2 2 4 H := [2 x y - 4 x y z, 8 z , 20 z y - 11, 11 x y + 17 x y z, 8 x + 12 z, 2 2 2 7 x y + 3 x y] > J:=[op(GB),op(G)]; 2 4 2 2 2 J := [1, 11 x y + 17 x y z, 8 x + 12 z, 7 x y + 3 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 := [6, 13, 22, 4, 4, 2, 4, 2/3, 2/3, 5/6, 7/12, 7/12, 5/12, 4, 7, 11, 4, 4, 2, 1, 3/4, 1/2, 1/2, 5/7, 4/7, 2/7, 6, 11, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=520.9MB, alloc=156.3MB, time=6.95 |\^/| 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(); 1428362600 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [4 y z - 18 x y z, -6 y z - 6, 20 x z + 15 x y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [10 x y z + 3 x z, 8 x y, 16 x z + z] > Problem := [F,G]; 3 2 2 2 2 Problem := [[4 y z - 18 x y z, -6 y z - 6, 20 x z + 15 x y z ], 2 2 2 2 [10 x y z + 3 x z, 8 x y, 16 x z + z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=26.2MB, alloc=32.3MB, time=0.35 memory used=48.2MB, alloc=32.3MB, time=0.56 memory used=68.4MB, alloc=56.3MB, time=0.78 memory used=110.9MB, alloc=56.3MB, time=1.21 memory used=147.4MB, alloc=84.3MB, time=1.61 memory used=199.9MB, alloc=108.3MB, time=2.46 N1 := 1869 > GB := Basis(F, plex(op(vars))); 2 2 GB := [6 x - 1, 3 y + 4 x, 2 z - 9 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=272.7MB, alloc=108.3MB, time=3.49 N2 := 529 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 2 H := [4 y z - 18 x y z, -6 y z - 6, 20 x z + 15 x y z , 10 x y z + 3 x z, 2 2 8 y x, 16 x z + z] > J:=[op(GB),op(G)]; 2 2 2 2 2 2 J := [6 x - 1, 3 y + 4 x, 2 z - 9 x, 10 x y z + 3 x z, 8 y x, 16 x z + z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 21, 4, 2, 1, 3, 5/6, 5/6, 5/6, 7/13, 6/13, 9/13, 6, 12, 15, 4, 2, 1, 2, 1, 1/2, 1/2, 7/13, 3/13, 5/13, 3, 6, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=325.4MB, alloc=108.3MB, time=4.00 |\^/| 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(); 1428362604 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 3 F := [-13 x y - 4 y z, -20 x z + 10 x y, -4 y z + 11 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 G := [-20 x y + 7 z , -2 y z + 19 z , -16 x z + 17 z] > Problem := [F,G]; 3 3 2 3 3 Problem := [[-13 x y - 4 y z, -20 x z + 10 x y, -4 y z + 11 x ], 3 2 2 3 3 [-20 x y + 7 z , -2 y z + 19 z , -16 x 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=0.13 memory used=27.0MB, alloc=32.3MB, time=0.36 memory used=50.5MB, alloc=60.3MB, time=0.54 memory used=92.0MB, alloc=60.3MB, time=0.88 memory used=138.1MB, alloc=68.3MB, time=1.18 memory used=178.3MB, alloc=92.3MB, time=1.53 memory used=246.0MB, alloc=92.3MB, time=1.99 memory used=314.1MB, alloc=116.3MB, time=2.38 memory used=387.1MB, alloc=140.3MB, time=3.02 memory used=459.9MB, alloc=396.3MB, time=3.57 memory used=567.2MB, alloc=396.3MB, time=4.12 memory used=676.3MB, alloc=420.3MB, time=4.67 memory used=797.6MB, alloc=444.3MB, time=5.67 memory used=917.2MB, alloc=468.3MB, time=6.70 memory used=1037.4MB, alloc=492.3MB, time=7.74 memory used=1154.9MB, alloc=492.3MB, time=8.82 memory used=1262.8MB, alloc=516.3MB, time=9.91 memory used=1371.3MB, alloc=516.3MB, time=10.99 memory used=1459.2MB, alloc=516.3MB, time=11.87 memory used=1542.4MB, alloc=540.3MB, time=12.72 memory used=1621.7MB, alloc=540.3MB, time=13.64 memory used=1696.6MB, alloc=540.3MB, time=14.54 memory used=1782.9MB, alloc=540.3MB, time=15.52 memory used=1849.1MB, alloc=564.3MB, time=16.15 memory used=1909.0MB, alloc=564.3MB, time=16.83 memory used=1968.0MB, alloc=564.3MB, time=17.52 memory used=2021.6MB, alloc=564.3MB, time=18.12 memory used=2218.8MB, alloc=588.3MB, time=19.82 memory used=2411.4MB, alloc=612.3MB, time=21.79 memory used=2595.7MB, alloc=636.3MB, time=23.65 memory used=2869.6MB, alloc=660.3MB, time=25.34 memory used=3069.7MB, alloc=684.3MB, time=26.86 memory used=3301.7MB, alloc=708.3MB, time=28.55 memory used=3625.2MB, alloc=732.3MB, time=30.46 memory used=3726.1MB, alloc=756.3MB, time=31.83 memory used=3837.1MB, alloc=780.3MB, time=33.44 memory used=3947.3MB, alloc=804.3MB, time=34.92 memory used=4058.1MB, alloc=804.3MB, time=36.51 memory used=4145.9MB, alloc=804.3MB, time=38.01 memory used=4572.6MB, alloc=828.3MB, time=41.82 memory used=4938.8MB, alloc=852.3MB, time=45.78 memory used=5299.8MB, alloc=876.3MB, time=49.79 memory used=5597.8MB, alloc=900.3MB, time=53.57 memory used=5893.4MB, alloc=924.3MB, time=57.39 memory used=6176.5MB, alloc=948.3MB, time=60.96 memory used=6423.3MB, alloc=972.3MB, time=64.53 memory used=6647.3MB, alloc=996.3MB, time=67.95 memory used=6839.1MB, alloc=1020.3MB, time=71.25 memory used=7090.3MB, alloc=1044.3MB, time=74.47 memory used=7675.8MB, alloc=1068.3MB, time=80.93 memory used=8237.1MB, alloc=1092.3MB, time=88.26 memory used=8833.2MB, alloc=1116.3MB, time=95.58 memory used=9436.9MB, alloc=1140.3MB, time=103.33 memory used=10065.5MB, alloc=1164.3MB, time=110.76 memory used=10669.4MB, alloc=1188.3MB, time=119.12 memory used=11222.2MB, alloc=1212.3MB, time=127.15 memory used=11806.9MB, alloc=1236.3MB, time=135.76 memory used=12318.0MB, alloc=1260.3MB, time=143.29 memory used=12824.8MB, alloc=1284.3MB, time=150.14 memory used=13301.0MB, alloc=1308.3MB, time=157.30 memory used=13733.5MB, alloc=1332.3MB, time=164.85 memory used=14090.9MB, alloc=1356.3MB, time=172.32 memory used=14478.1MB, alloc=1380.3MB, time=180.05 memory used=14723.4MB, alloc=1404.3MB, time=186.59 memory used=15038.0MB, alloc=1428.3MB, time=193.31 memory used=15291.9MB, alloc=1452.3MB, time=200.37 memory used=15586.2MB, alloc=1476.3MB, time=207.03 memory used=15870.9MB, alloc=1500.3MB, time=213.45 memory used=16098.9MB, alloc=1524.3MB, time=219.97 memory used=16335.1MB, alloc=1548.3MB, time=226.52 memory used=16524.5MB, alloc=1572.3MB, time=233.47 memory used=16675.9MB, alloc=1596.3MB, time=239.28 memory used=16837.4MB, alloc=1620.3MB, time=245.93 memory used=17007.8MB, alloc=1644.3MB, time=252.48 memory used=17166.2MB, alloc=1668.3MB, time=259.19 memory used=17332.8MB, alloc=1692.3MB, time=265.89 memory used=17444.4MB, alloc=1716.3MB, time=271.71 memory used=17543.1MB, alloc=1740.3MB, time=277.98 memory used=17651.6MB, alloc=1764.3MB, time=284.19 memory used=17745.2MB, alloc=1788.3MB, time=290.25 memory used=17880.3MB, alloc=1812.3MB, time=296.40 memory used=17988.4MB, alloc=1836.3MB, time=302.25 memory used=18113.0MB, alloc=1860.3MB, time=308.33 memory used=18267.9MB, alloc=1884.3MB, time=314.69 memory used=18318.6MB, alloc=1908.3MB, time=320.75 memory used=18355.5MB, alloc=1932.3MB, time=326.66 memory used=18421.4MB, alloc=1956.3MB, time=332.49 memory used=18492.3MB, alloc=1980.3MB, time=338.43 memory used=18549.0MB, alloc=2004.3MB, time=344.57 memory used=18613.1MB, alloc=2028.3MB, time=350.55 memory used=18644.2MB, alloc=2308.3MB, time=362.10 |\^/| 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(); 1428362904 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 4 2 F := [-16 x y + 12 y z, 12 y z - 3 x , 7 z - 2 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 G := [-20 z + 2, -20 x z - 2 y z, -20 x y z - 10 x z] > Problem := [F,G]; 2 2 3 2 4 2 Problem := [[-16 x y + 12 y z, 12 y z - 3 x , 7 z - 2 y z ], 3 3 3 2 2 [-20 z + 2, -20 x z - 2 y z, -20 x y z - 10 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.7MB, alloc=32.3MB, time=0.39 memory used=47.7MB, alloc=32.3MB, time=0.65 memory used=68.3MB, alloc=56.3MB, time=0.90 memory used=109.2MB, alloc=60.3MB, time=1.39 memory used=148.8MB, alloc=84.3MB, time=1.85 memory used=211.3MB, alloc=92.3MB, time=2.66 memory used=273.3MB, alloc=116.3MB, time=3.55 memory used=350.6MB, alloc=116.3MB, time=4.57 memory used=425.4MB, alloc=396.3MB, time=5.47 memory used=529.6MB, alloc=396.3MB, time=6.68 memory used=631.3MB, alloc=420.3MB, time=7.88 memory used=751.3MB, alloc=444.3MB, time=9.30 memory used=888.7MB, alloc=468.3MB, time=10.60 memory used=995.7MB, alloc=468.3MB, time=11.65 memory used=1117.6MB, alloc=492.3MB, time=12.89 memory used=1222.8MB, alloc=516.3MB, time=13.90 memory used=1303.2MB, alloc=516.3MB, time=14.73 memory used=1391.1MB, alloc=516.3MB, time=15.66 memory used=1463.5MB, alloc=516.3MB, time=16.45 memory used=1542.7MB, alloc=516.3MB, time=17.34 memory used=1616.4MB, alloc=516.3MB, time=18.28 memory used=1674.6MB, alloc=540.3MB, time=18.99 memory used=1738.7MB, alloc=540.3MB, time=19.87 memory used=1782.4MB, alloc=540.3MB, time=20.52 memory used=1822.1MB, alloc=540.3MB, time=21.11 memory used=2008.3MB, alloc=564.3MB, time=23.01 memory used=2204.3MB, alloc=588.3MB, time=25.02 memory used=2370.1MB, alloc=612.3MB, time=26.91 memory used=2557.9MB, alloc=636.3MB, time=29.12 memory used=2707.5MB, alloc=660.3MB, time=30.72 memory used=2839.0MB, alloc=660.3MB, time=32.25 memory used=2929.4MB, alloc=684.3MB, time=33.53 memory used=3035.0MB, alloc=684.3MB, time=35.13 memory used=3143.8MB, alloc=684.3MB, time=36.75 memory used=3485.7MB, alloc=708.3MB, time=40.33 memory used=3821.4MB, alloc=732.3MB, time=44.30 memory used=4137.9MB, alloc=756.3MB, time=47.93 memory used=4486.7MB, alloc=780.3MB, time=51.98 memory used=4775.7MB, alloc=804.3MB, time=55.56 memory used=5023.7MB, alloc=828.3MB, time=58.91 memory used=5250.2MB, alloc=852.3MB, time=62.22 memory used=5491.3MB, alloc=876.3MB, time=65.73 memory used=5715.5MB, alloc=900.3MB, time=69.29 memory used=5875.4MB, alloc=924.3MB, time=72.50 memory used=6390.1MB, alloc=948.3MB, time=78.81 memory used=6905.4MB, alloc=972.3MB, time=85.43 memory used=7425.3MB, alloc=996.3MB, time=92.34 memory used=7943.1MB, alloc=1020.3MB, time=99.73 memory used=8477.9MB, alloc=1044.3MB, time=107.18 memory used=9001.0MB, alloc=1068.3MB, time=115.30 memory used=9557.4MB, alloc=1092.3MB, time=122.62 memory used=10105.8MB, alloc=1116.3MB, time=130.43 memory used=10624.9MB, alloc=1140.3MB, time=137.82 memory used=11028.6MB, alloc=1164.3MB, time=144.66 memory used=11366.3MB, alloc=1188.3MB, time=151.21 memory used=11726.1MB, alloc=1212.3MB, time=157.91 memory used=12118.6MB, alloc=1236.3MB, time=165.20 memory used=12331.1MB, alloc=1260.3MB, time=170.90 memory used=12453.3MB, alloc=1284.3MB, time=175.72 memory used=12688.4MB, alloc=1308.3MB, time=181.78 memory used=12952.6MB, alloc=1332.3MB, time=188.04 memory used=13134.0MB, alloc=1356.3MB, time=193.38 memory used=13344.1MB, alloc=1380.3MB, time=199.25 memory used=13552.5MB, alloc=1404.3MB, time=204.67 memory used=13699.5MB, alloc=1428.3MB, time=209.84 memory used=13924.7MB, alloc=1452.3MB, time=216.45 memory used=14190.8MB, alloc=1476.3MB, time=223.62 memory used=14510.7MB, alloc=1500.3MB, time=230.37 memory used=15148.1MB, alloc=1524.3MB, time=238.29 memory used=15511.3MB, alloc=1548.3MB, time=246.09 memory used=15821.5MB, alloc=1572.3MB, time=254.27 memory used=16139.6MB, alloc=1596.3MB, time=262.86 memory used=16428.9MB, alloc=1620.3MB, time=271.08 memory used=16665.4MB, alloc=1644.3MB, time=278.66 memory used=16921.4MB, alloc=1668.3MB, time=286.54 memory used=17108.4MB, alloc=1692.3MB, time=293.47 memory used=17353.3MB, alloc=1716.3MB, time=301.33 memory used=17512.7MB, alloc=1740.3MB, time=308.06 memory used=17703.7MB, alloc=1764.3MB, time=315.15 memory used=17878.3MB, alloc=1788.3MB, time=322.22 memory used=18094.8MB, alloc=1812.3MB, time=329.82 memory used=18240.6MB, alloc=1836.3MB, time=336.44 memory used=18344.6MB, alloc=1860.3MB, time=342.52 memory used=18517.9MB, alloc=1884.3MB, time=349.62 memory used=18725.5MB, alloc=1908.3MB, time=357.25 |\^/| 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(); 1428363204 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 3 F := [-13 x + 7 x y , 14 x y - 3 x z, 17 x z - 11 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 G := [17 x y z - 6 y , -18 y z + 3 x y, -18 x y z + 7] > Problem := [F,G]; 4 3 3 3 Problem := [[-13 x + 7 x y , 14 x y - 3 x z, 17 x z - 11 y z], 2 3 2 2 2 [17 x y z - 6 y , -18 y z + 3 x y, -18 x 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=4.3MB, alloc=32.3MB, time=0.15 memory used=26.3MB, alloc=32.3MB, time=0.46 memory used=47.6MB, alloc=32.3MB, time=0.75 memory used=67.8MB, alloc=32.3MB, time=1.03 memory used=86.2MB, alloc=56.3MB, time=1.31 memory used=126.6MB, alloc=60.3MB, time=1.83 memory used=165.6MB, alloc=84.3MB, time=2.27 memory used=201.7MB, alloc=84.3MB, time=2.68 memory used=261.2MB, alloc=92.3MB, time=3.43 memory used=319.3MB, alloc=116.3MB, time=4.12 memory used=400.4MB, alloc=140.3MB, time=4.85 memory used=484.3MB, alloc=396.3MB, time=5.75 memory used=574.2MB, alloc=420.3MB, time=6.74 memory used=690.4MB, alloc=444.3MB, time=7.88 memory used=820.2MB, alloc=468.3MB, time=9.25 memory used=959.7MB, alloc=492.3MB, time=10.81 memory used=1112.4MB, alloc=516.3MB, time=12.53 memory used=1282.3MB, alloc=540.3MB, time=14.88 memory used=1436.3MB, alloc=564.3MB, time=18.02 memory used=1599.4MB, alloc=588.3MB, time=21.68 memory used=1771.8MB, alloc=612.3MB, time=26.15 memory used=1960.2MB, alloc=636.3MB, time=31.21 memory used=2172.5MB, alloc=660.3MB, time=36.86 memory used=2408.8MB, alloc=684.3MB, time=43.06 memory used=2669.1MB, alloc=708.3MB, time=49.78 memory used=2953.2MB, alloc=708.3MB, time=57.15 memory used=3237.3MB, alloc=708.3MB, time=64.45 memory used=3521.5MB, alloc=732.3MB, time=71.69 memory used=3829.5MB, alloc=732.3MB, time=79.42 memory used=4137.5MB, alloc=756.3MB, time=87.13 memory used=4469.1MB, alloc=780.3MB, time=95.07 N1 := 10751 > GB := Basis(F, plex(op(vars))); 7 4 4 3 3 3 GB := [x , y x , -13 x + 7 x y , -14 x y + 3 x z, -238 x y + 33 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4838.2MB, alloc=780.3MB, time=101.84 memory used=4980.5MB, alloc=780.3MB, time=103.80 memory used=5080.6MB, alloc=780.3MB, time=105.10 memory used=5184.2MB, alloc=780.3MB, time=106.53 memory used=5281.5MB, alloc=780.3MB, time=107.88 memory used=5353.2MB, alloc=780.3MB, time=108.91 memory used=5440.7MB, alloc=780.3MB, time=110.20 memory used=5524.4MB, alloc=780.3MB, time=111.45 memory used=5590.8MB, alloc=780.3MB, time=112.65 memory used=5646.7MB, alloc=780.3MB, time=113.68 memory used=5697.7MB, alloc=780.3MB, time=114.85 memory used=5747.9MB, alloc=780.3MB, time=115.97 memory used=5945.2MB, alloc=804.3MB, time=118.36 memory used=6163.7MB, alloc=828.3MB, time=121.00 memory used=6382.1MB, alloc=852.3MB, time=123.80 memory used=6645.3MB, alloc=876.3MB, time=127.56 memory used=6964.1MB, alloc=900.3MB, time=131.43 memory used=7400.0MB, alloc=924.3MB, time=135.23 memory used=7653.0MB, alloc=948.3MB, time=138.43 memory used=8142.9MB, alloc=972.3MB, time=144.97 memory used=8609.6MB, alloc=996.3MB, time=151.50 memory used=9122.3MB, alloc=1020.3MB, time=159.15 memory used=9544.5MB, alloc=1044.3MB, time=170.27 memory used=9959.7MB, alloc=1068.3MB, time=181.99 memory used=10378.3MB, alloc=1092.3MB, time=193.89 memory used=10804.3MB, alloc=1116.3MB, time=206.19 memory used=11237.9MB, alloc=1140.3MB, time=219.18 memory used=11676.3MB, alloc=1164.3MB, time=232.81 memory used=12138.8MB, alloc=1188.3MB, time=247.12 memory used=12625.1MB, alloc=1212.3MB, time=262.17 memory used=13135.4MB, alloc=1236.3MB, time=277.96 memory used=13669.6MB, alloc=1260.3MB, time=294.24 |\^/| 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(); 1428363504 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 F := [7 x z + 10 x y z, -16 x y - 8 x z , 15 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 2 G := [10 x y z + 12 x y z, 5 z + 12 x, -y z - 12 y ] > Problem := [F,G]; 3 3 3 Problem := [[7 x z + 10 x y z, -16 x y - 8 x z , 15 x z], 2 2 4 3 2 [10 x y z + 12 x y z, 5 z + 12 x, -y z - 12 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.5MB, alloc=32.3MB, time=0.38 memory used=48.1MB, alloc=32.3MB, time=0.70 memory used=68.9MB, alloc=32.3MB, time=0.97 memory used=89.1MB, alloc=56.3MB, time=1.26 memory used=129.6MB, alloc=60.3MB, time=1.69 memory used=166.9MB, alloc=84.3MB, time=2.03 memory used=221.7MB, alloc=84.3MB, time=2.53 memory used=278.3MB, alloc=116.3MB, time=3.14 memory used=361.3MB, alloc=140.3MB, time=3.96 memory used=460.1MB, alloc=164.3MB, time=4.99 memory used=574.4MB, alloc=188.3MB, time=6.22 memory used=698.7MB, alloc=212.3MB, time=7.64 memory used=822.4MB, alloc=236.3MB, time=9.76 memory used=952.0MB, alloc=260.3MB, time=12.50 memory used=1095.3MB, alloc=284.3MB, time=15.81 memory used=1262.5MB, alloc=308.3MB, time=19.62 memory used=1453.7MB, alloc=308.3MB, time=23.97 memory used=1644.9MB, alloc=308.3MB, time=28.38 memory used=1836.0MB, alloc=332.3MB, time=32.59 memory used=2051.2MB, alloc=356.3MB, time=37.09 N1 := 6965 > GB := Basis(F, plex(op(vars))); 3 GB := [y x, z x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 243 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 3 2 2 H := [7 x z + 10 x y z, -16 x y - 8 x z , 15 z x, 10 x y z + 12 x y z, 4 3 2 5 z + 12 x, -y z - 12 y ] > J:=[op(GB),op(G)]; 3 2 2 4 3 2 J := [y x, z x, 10 x y z + 12 x y z, 5 z + 12 x, -y 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, 15, 22, 4, 2, 3, 4, 5/6, 2/3, 1, 8/13, 6/13, 8/13, 5, 11, 18, 4, 2, 3, 4, 4/5, 3/5, 4/5, 1/2, 1/2, 1/2, 4, 4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2247.7MB, alloc=356.3MB, time=40.13 |\^/| 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(); 1428363544 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 3 3 F := [-14 x z + 15 z , -18 x y + 10 y , 5 x y - 16 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 G := [17 x - z, x y z - 13 x z , 18 x y + 11 x z ] > Problem := [F,G]; 2 2 3 3 2 3 3 Problem := [[-14 x z + 15 z , -18 x y + 10 y , 5 x y - 16 x ], 2 3 3 3 [17 x - z, x y z - 13 x z , 18 x y + 11 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=26.0MB, alloc=32.3MB, time=0.34 memory used=47.6MB, alloc=32.3MB, time=0.52 memory used=68.3MB, alloc=32.3MB, time=0.70 memory used=88.1MB, alloc=56.3MB, time=0.88 memory used=127.9MB, alloc=60.3MB, time=1.23 memory used=165.0MB, alloc=84.3MB, time=1.57 memory used=222.5MB, alloc=108.3MB, time=2.18 memory used=301.8MB, alloc=116.3MB, time=3.05 memory used=382.0MB, alloc=140.3MB, time=3.80 memory used=474.3MB, alloc=164.3MB, time=4.80 memory used=575.7MB, alloc=188.3MB, time=6.17 memory used=681.2MB, alloc=212.3MB, time=8.13 memory used=795.7MB, alloc=236.3MB, time=10.78 memory used=934.3MB, alloc=260.3MB, time=13.98 memory used=1096.8MB, alloc=260.3MB, time=17.58 memory used=1259.3MB, alloc=284.3MB, time=21.06 memory used=1446.0MB, alloc=284.3MB, time=24.68 N1 := 5489 > GB := Basis(F, plex(op(vars))); 6 3 3 3 3 2 2 2 3 GB := [9 x - 16 x , 5 x y - 16 x , -144 x + 25 y , -14 x z + 15 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1572.4MB, alloc=284.3MB, time=26.09 memory used=1788.3MB, alloc=540.3MB, time=28.33 memory used=2007.0MB, alloc=564.3MB, time=30.59 memory used=2233.2MB, alloc=588.3MB, time=34.01 memory used=2424.8MB, alloc=612.3MB, time=38.90 memory used=2633.8MB, alloc=636.3MB, time=44.33 memory used=2866.9MB, alloc=660.3MB, time=50.11 memory used=3124.3MB, alloc=684.3MB, time=55.83 N2 := 5681 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 2 3 3 H := [-14 x z + 15 z , -18 x y + 10 y , 5 x y - 16 x , -z + 17 x, 2 3 3 3 x y z - 13 x z , 18 x y + 11 x z ] > J:=[op(GB),op(G)]; 6 3 3 3 3 2 2 2 3 J := [9 x - 16 x , 5 x y - 16 x , -144 x + 25 y , -14 x z + 15 z , 2 3 3 3 -z + 17 x, x y z - 13 x z , 18 x y + 11 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 := [6, 14, 21, 4, 3, 2, 3, 1, 2/3, 2/3, 3/4, 5/12, 1/2, 7, 15, 26, 6, 6, 2, 3, 1, 4/7, 4/7, 11/14, 2/7, 3/7, -1, -5, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3143.8MB, alloc=684.3MB, time=56.14 |\^/| 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(); 1428363599 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 F := [20 y + 10 x z, -8 x z + 2 y z, -13 x y + 5 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 4 3 G := [15 y z - 19 y z , 6 y z - 7 z , -9 x y - 7 x y] > Problem := [F,G]; 3 3 2 3 Problem := [[20 y + 10 x z, -8 x z + 2 y z, -13 x y + 5 y], 3 2 2 2 4 3 [15 y z - 19 y z , 6 y z - 7 z , -9 x y - 7 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.1MB, alloc=32.3MB, time=0.32 memory used=47.7MB, alloc=32.3MB, time=0.52 memory used=68.6MB, alloc=32.3MB, time=0.70 memory used=88.3MB, alloc=56.3MB, time=0.88 memory used=129.2MB, alloc=60.3MB, time=1.26 memory used=169.2MB, alloc=84.3MB, time=1.70 memory used=227.1MB, alloc=108.3MB, time=2.33 memory used=301.7MB, alloc=140.3MB, time=3.16 memory used=390.8MB, alloc=164.3MB, time=4.15 memory used=488.1MB, alloc=188.3MB, time=5.74 memory used=595.6MB, alloc=212.3MB, time=7.92 memory used=717.9MB, alloc=236.3MB, time=10.72 memory used=864.2MB, alloc=236.3MB, time=14.03 memory used=1010.4MB, alloc=236.3MB, time=17.29 memory used=1156.7MB, alloc=260.3MB, time=20.44 memory used=1326.9MB, alloc=260.3MB, time=23.90 N1 := 5653 > GB := Basis(F, plex(op(vars))); 4 3 3 3 2 2 GB := [52 x y - 5 y, -4 x y + y , 8 x y + x z, 8 x y + y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1500.1MB, alloc=260.3MB, time=26.27 N2 := 1705 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 3 3 2 H := [20 y + 10 x z, -8 x z + 2 y z, -13 x y + 5 y, 15 y z - 19 y z , 2 2 4 3 6 y z - 7 z , -9 x y - 7 x y] > J:=[op(GB),op(G)]; 4 3 3 3 2 2 J := [52 x y - 5 y, -4 x y + y , 8 x y + x z, 8 x y + y z, 3 2 2 2 4 3 15 y z - 19 y z , 6 y z - 7 z , -9 x y - 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 := [6, 14, 23, 4, 3, 3, 4, 2/3, 1, 2/3, 5/12, 3/4, 7/12, 7, 16, 29, 5, 4, 3, 4, 5/7, 1, 4/7, 1/2, 6/7, 3/7, -2, -6, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1651.5MB, alloc=260.3MB, time=28.62 |\^/| 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(); 1428363628 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 F := [-2 x y + 10 x z, -8 x y + 15, -10 z - 8] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 G := [-17 y z + 10 z , -16 y z - 17 y z , -9 x y - 11 x z] > Problem := [F,G]; 3 3 3 2 Problem := [[-2 x y + 10 x z, -8 x y + 15, -10 z - 8], 2 3 3 2 2 [-17 y z + 10 z , -16 y z - 17 y z , -9 x y - 11 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.11 memory used=26.2MB, alloc=32.3MB, time=0.32 memory used=47.3MB, alloc=32.3MB, time=0.52 memory used=66.9MB, alloc=32.3MB, time=0.69 memory used=85.8MB, alloc=56.3MB, time=0.87 memory used=124.5MB, alloc=60.3MB, time=1.20 memory used=162.3MB, alloc=84.3MB, time=1.58 memory used=221.8MB, alloc=84.3MB, time=2.21 memory used=273.6MB, alloc=108.3MB, time=2.77 memory used=339.2MB, alloc=132.3MB, time=3.68 memory used=414.3MB, alloc=156.3MB, time=5.13 memory used=513.5MB, alloc=156.3MB, time=6.86 N1 := 2885 > GB := Basis(F, plex(op(vars))); 6 3 3 GB := [256 x + 45, 32 x + 3 y, 32 x + 15 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=605.5MB, alloc=156.3MB, time=8.00 memory used=721.0MB, alloc=188.3MB, time=9.24 memory used=855.0MB, alloc=212.3MB, time=10.77 memory used=986.4MB, alloc=236.3MB, time=13.26 memory used=1125.7MB, alloc=260.3MB, time=16.38 memory used=1289.0MB, alloc=284.3MB, time=19.89 memory used=1476.5MB, alloc=308.3MB, time=23.53 N2 := 4455 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 3 2 2 3 H := [-2 x y + 10 x z, -8 x y + 15, -10 z - 8, -17 y z + 10 z , 3 2 2 -16 y z - 17 y z , -9 x y - 11 x z] > J:=[op(GB),op(G)]; 6 3 3 2 3 J := [256 x + 45, 32 x + 3 y, 32 x + 15 z, -17 y z + 10 z , 3 2 2 -16 y z - 17 y z , -9 x y - 11 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 := [6, 13, 20, 4, 3, 2, 3, 1/2, 5/6, 5/6, 5/12, 1/2, 7/12, 6, 12, 22, 6, 6, 2, 3, 2/3, 2/3, 2/3, 5/12, 5/12, 1/2, 1, -2, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1480.5MB, alloc=308.3MB, time=23.60 |\^/| 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(); 1428363651 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [-3 x y - 13 y, -15 x y z + 16 x z, 15 x z - 17 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 2 G := [13 x z + 7 z , -6 x y + 5 y , -3 x - 13 z ] > Problem := [F,G]; 2 3 2 Problem := [[-3 x y - 13 y, -15 x y z + 16 x z, 15 x z - 17 z ], 3 2 3 3 2 2 [13 x z + 7 z , -6 x y + 5 y , -3 x - 13 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.1MB, alloc=32.3MB, time=0.34 memory used=48.7MB, alloc=32.3MB, time=0.56 N1 := 315 > GB := Basis(F, plex(op(vars))); 2 2 2 2 GB := [3 x y + 13 y, 3 x z + 13 x z, 65 y z + 16 x z, 3 x z + 13 z , 3 2 65 z + 17 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=67.5MB, alloc=32.3MB, time=0.74 memory used=87.2MB, alloc=56.3MB, time=0.94 N2 := 261 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 3 2 H := [-3 x y - 13 y, -15 x y z + 16 x z, 15 x z - 17 z , 13 x z + 7 z , 3 3 2 2 -6 x y + 5 y , -3 x - 13 z ] > J:=[op(GB),op(G)]; 2 2 2 2 J := [3 x y + 13 y, 3 x z + 13 x z, 65 y z + 16 x z, 3 x z + 13 z , 3 2 3 2 3 3 2 2 65 z + 17 z , 13 x z + 7 z , -6 x y + 5 y , -3 x - 13 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, 20, 4, 3, 3, 3, 1, 1/2, 2/3, 7/12, 5/12, 7/12, 8, 16, 24, 4, 3, 3, 3, 7/8, 3/8, 3/4, 1/2, 5/16, 11/16, -3, -4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=98.2MB, alloc=56.3MB, time=1.04 |\^/| 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(); 1428363652 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 3 3 F := [-6 x z + 13 z , 10 x + 2 x , -12 x + 6 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [-x z - 3 x, -6 x y z - 18 x z, -11 x z - 14 y ] > Problem := [F,G]; 2 3 4 3 3 Problem := [[-6 x z + 13 z , 10 x + 2 x , -12 x + 6 x y z], 2 2 2 2 3 [-x z - 3 x, -6 x y z - 18 x z, -11 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=4.3MB, alloc=32.3MB, time=0.11 memory used=26.5MB, alloc=32.3MB, time=0.30 memory used=47.7MB, alloc=32.3MB, time=0.47 memory used=67.8MB, alloc=32.3MB, time=0.64 memory used=86.5MB, alloc=56.3MB, time=0.81 memory used=126.9MB, alloc=60.3MB, time=1.16 memory used=165.5MB, alloc=84.3MB, time=1.50 memory used=203.4MB, alloc=84.3MB, time=1.83 memory used=264.2MB, alloc=116.3MB, time=2.45 memory used=344.0MB, alloc=116.3MB, time=3.17 memory used=421.5MB, alloc=140.3MB, time=3.98 memory used=517.6MB, alloc=164.3MB, time=5.01 memory used=626.2MB, alloc=188.3MB, time=6.20 memory used=744.7MB, alloc=468.3MB, time=7.51 memory used=885.2MB, alloc=492.3MB, time=9.01 memory used=1034.3MB, alloc=516.3MB, time=10.68 memory used=1200.9MB, alloc=540.3MB, time=12.48 memory used=1361.4MB, alloc=564.3MB, time=15.31 memory used=1523.7MB, alloc=588.3MB, time=18.64 memory used=1695.5MB, alloc=612.3MB, time=22.45 memory used=1877.8MB, alloc=636.3MB, time=26.85 memory used=2072.2MB, alloc=660.3MB, time=31.89 memory used=2290.6MB, alloc=684.3MB, time=37.55 memory used=2532.9MB, alloc=708.3MB, time=43.76 memory used=2799.2MB, alloc=732.3MB, time=50.59 memory used=3089.5MB, alloc=732.3MB, time=57.98 memory used=3379.7MB, alloc=756.3MB, time=65.50 memory used=3693.8MB, alloc=756.3MB, time=73.43 memory used=4007.9MB, alloc=756.3MB, time=81.35 memory used=4321.8MB, alloc=780.3MB, time=89.26 memory used=4659.6MB, alloc=780.3MB, time=97.69 memory used=4997.5MB, alloc=780.3MB, time=106.09 memory used=5335.2MB, alloc=804.3MB, time=114.43 memory used=5696.9MB, alloc=804.3MB, time=123.49 memory used=6058.7MB, alloc=828.3MB, time=132.31 memory used=6444.4MB, alloc=852.3MB, time=141.53 N1 := 13703 > GB := Basis(F, plex(op(vars))); 4 3 3 2 3 3 3 3 GB := [5 x + x , 75 x y - 26 x , -3 x y + 13 x z, -2 x + x y z, 2 3 -6 x z + 13 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6856.8MB, alloc=852.3MB, time=150.00 memory used=7273.0MB, alloc=852.3MB, time=154.65 memory used=7632.2MB, alloc=852.3MB, time=158.71 memory used=7947.0MB, alloc=876.3MB, time=162.20 memory used=8235.0MB, alloc=900.3MB, time=165.73 memory used=8481.2MB, alloc=924.3MB, time=168.93 memory used=8972.4MB, alloc=948.3MB, time=175.56 memory used=9435.2MB, alloc=972.3MB, time=181.98 memory used=9939.3MB, alloc=996.3MB, time=187.89 memory used=10389.1MB, alloc=1020.3MB, time=194.13 memory used=10830.3MB, alloc=1044.3MB, time=200.28 memory used=11278.5MB, alloc=1068.3MB, time=208.74 memory used=11653.4MB, alloc=1092.3MB, time=218.53 memory used=12025.3MB, alloc=1116.3MB, time=228.61 memory used=12400.1MB, alloc=1140.3MB, time=239.00 memory used=12782.3MB, alloc=1164.3MB, time=249.94 memory used=13173.1MB, alloc=1188.3MB, time=261.06 memory used=13574.2MB, alloc=1212.3MB, time=272.47 memory used=13986.3MB, alloc=1236.3MB, time=284.20 memory used=14410.8MB, alloc=1260.3MB, time=296.36 |\^/| 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(); 1428363952 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [-2 x z + 12 y z, -11 x y + 15 x y , x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 3 3 G := [-12 x y z + 20 y , -12 x + 20 x, -12 x y - 19 z ] > Problem := [F,G]; 2 2 3 2 2 Problem := [[-2 x z + 12 y z, -11 x y + 15 x y , x y ], 2 4 2 3 3 [-12 x y z + 20 y , -12 x + 20 x, -12 x y - 19 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.5MB, alloc=32.3MB, time=0.40 memory used=49.3MB, alloc=32.3MB, time=0.70 memory used=70.8MB, alloc=56.3MB, time=0.99 memory used=113.2MB, alloc=84.3MB, time=1.48 N1 := 821 > GB := Basis(F, plex(op(vars))); 2 3 2 2 GB := [x y , x z, -x z + 6 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 323 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 2 4 H := [-2 x z + 12 y z, -11 x y + 15 x y , x y , -12 x y z + 20 y , 2 3 3 -12 x + 20 x, -12 x y - 19 z ] > J:=[op(GB),op(G)]; 2 3 2 2 2 4 2 J := [x y , x z, -x z + 6 y z, -12 x y z + 20 y , -12 x + 20 x, 3 3 -12 x y - 19 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, 20, 4, 2, 4, 3, 1, 5/6, 1/2, 2/3, 7/12, 1/3, 6, 14, 20, 4, 3, 4, 3, 1, 2/3, 2/3, 7/12, 5/12, 5/12, 0, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=171.1MB, alloc=84.3MB, time=2.06 |\^/| 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(); 1428363954 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 2 2 F := [-17 x y + 12 z , 20 x y + 11 x y z , 11 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 G := [9 z - 9 y z, 16 x - 10 x, 13 x y z - 4 z] > Problem := [F,G]; 3 4 3 2 2 Problem := [[-17 x y + 12 z , 20 x y + 11 x y z , 11 x y z], 4 3 [9 z - 9 y z, 16 x - 10 x, 13 x y z - 4 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.6MB, alloc=32.3MB, time=0.34 memory used=48.4MB, alloc=32.3MB, time=0.53 memory used=69.0MB, alloc=56.3MB, time=0.73 memory used=114.3MB, alloc=60.3MB, time=1.23 memory used=153.7MB, alloc=84.3MB, time=1.66 N1 := 1147 > GB := Basis(F, plex(op(vars))); 4 2 3 2 3 4 GB := [y x , z y x , 20 x y + 11 x y z , -17 x y + 12 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=208.7MB, alloc=84.3MB, time=2.37 memory used=266.3MB, alloc=92.3MB, time=2.91 memory used=326.1MB, alloc=116.3MB, time=3.56 N2 := 1147 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 4 3 2 2 4 H := [-17 x y + 12 z , 20 x y + 11 x y z , 11 z y x , 9 z - 9 y z, 3 16 x - 10 x, 13 x y z - 4 z] > J:=[op(GB),op(G)]; 4 2 3 2 3 4 4 J := [y x , z y x , 20 x y + 11 x y z , -17 x y + 12 z , 9 z - 9 y z, 3 16 x - 10 x, 13 x 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, 15, 22, 4, 3, 1, 4, 5/6, 5/6, 5/6, 1/2, 3/7, 1/2, 7, 17, 27, 5, 4, 1, 4, 6/7, 6/7, 5/7, 8/15, 7/15, 7/15, -2, -5, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=385.5MB, alloc=116.3MB, time=4.32 |\^/| 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(); 1428363959 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-17 x y - 20 x y , 2 x y z + 6 y z, 11 x y + 4 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 3 2 G := [19 x y z - 15 z , 16 y z + 2 x z , 6 x - 5 y z ] > Problem := [F,G]; 2 2 3 2 Problem := [[-17 x y - 20 x y , 2 x y z + 6 y z, 11 x y + 4 x ], 2 3 3 2 3 2 [19 x y z - 15 z , 16 y z + 2 x z , 6 x - 5 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.0MB, alloc=32.3MB, time=0.33 memory used=47.8MB, alloc=32.3MB, time=0.52 memory used=68.4MB, alloc=32.3MB, time=0.69 memory used=88.5MB, alloc=56.3MB, time=0.91 memory used=130.6MB, alloc=60.3MB, time=1.34 memory used=168.1MB, alloc=84.3MB, time=1.78 N1 := 1005 > GB := Basis(F, plex(op(vars))); 4 2 3 2 3 2 2 GB := [54043 x - 32000 x , 17 x + 20 x y, -289 x + 400 x y , z x , z y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=222.3MB, alloc=84.3MB, time=2.37 memory used=282.3MB, alloc=92.3MB, time=2.98 memory used=339.3MB, alloc=116.3MB, time=3.58 memory used=414.9MB, alloc=140.3MB, time=4.72 N2 := 1623 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 3 H := [-17 x y - 20 x y , 2 x y z + 6 y z, 11 x y + 4 x , 19 x y z - 15 z , 3 2 2 3 16 y z + 2 x z , -5 z y + 6 x ] > J:=[op(GB),op(G)]; 4 2 3 2 3 2 2 J := [54043 x - 32000 x , 17 x + 20 x y, -289 x + 400 x y , z x , z y, 2 3 3 2 2 3 19 x y z - 15 z , 16 y z + 2 x z , -5 z 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 := [6, 16, 21, 4, 3, 3, 3, 1, 1, 2/3, 2/3, 2/3, 7/12, 8, 18, 26, 4, 4, 2, 3, 7/8, 3/4, 5/8, 5/8, 3/8, 7/16, -2, -5, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=452.5MB, alloc=140.3MB, time=5.25 |\^/| 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(); 1428363964 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 F := [7 x - 3 x y z , 16 x z + 13 y z, -7 y z - x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 G := [-10 x y - 5 x y , -19 x y - 18 x , -20 x - 8 x y z] > Problem := [F,G]; 4 2 2 2 2 2 Problem := [[7 x - 3 x y z , 16 x z + 13 y z, -7 y z - x], 3 2 3 2 3 [-10 x y - 5 x y , -19 x y - 18 x , -20 x - 8 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.2MB, alloc=32.3MB, time=0.34 memory used=47.7MB, alloc=32.3MB, time=0.51 memory used=68.5MB, alloc=32.3MB, time=0.68 memory used=89.1MB, alloc=56.3MB, time=0.89 memory used=132.7MB, alloc=60.3MB, time=1.35 memory used=171.4MB, alloc=84.3MB, time=1.76 N1 := 1139 > GB := Basis(F, plex(op(vars))); 7 5 2 2 6 2 GB := [38416 x + 117 x, -784 x + 39 x y, 16 x z + 13 y z, 343 x + 9 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=227.3MB, alloc=84.3MB, time=2.49 memory used=282.8MB, alloc=84.3MB, time=2.95 memory used=340.1MB, alloc=108.3MB, time=3.56 N2 := 1147 #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)]; 4 2 2 2 2 2 3 2 H := [7 x - 3 x y z , 16 x z + 13 y z, -7 y z - x, -10 x y - 5 x y , 3 2 3 -19 x y - 18 x , -20 x - 8 x y z] > J:=[op(GB),op(G)]; 7 5 2 2 6 2 J := [38416 x + 117 x, -784 x + 39 x y, 16 x z + 13 y z, 343 x + 9 x z , 3 2 3 2 3 -10 x y - 5 x y , -19 x y - 18 x , -20 x - 8 x 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 := [6, 16, 22, 4, 4, 3, 2, 1, 1, 2/3, 5/6, 7/12, 5/12, 7, 15, 32, 7, 7, 3, 2, 1, 5/7, 3/7, 13/14, 3/7, 2/7, 1, -10, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=415.9MB, alloc=108.3MB, time=4.53 |\^/| 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(); 1428363969 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 4 F := [4 x y z - 14 x y, 15 x y - 14 x , -4 x z - 5 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 G := [2 y z - 4 z, -8 x y z - 8, 2 x y + 14 x ] > Problem := [F,G]; 2 2 3 3 3 4 Problem := [[4 x y z - 14 x y, 15 x y - 14 x , -4 x z - 5 y ], 2 3 3 [2 y z - 4 z, -8 x y z - 8, 2 x y + 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=0.13 memory used=26.1MB, alloc=32.3MB, time=0.34 memory used=47.5MB, alloc=32.3MB, time=0.52 memory used=68.1MB, alloc=32.3MB, time=0.70 memory used=87.9MB, alloc=56.3MB, time=0.88 memory used=127.3MB, alloc=60.3MB, time=1.23 memory used=164.3MB, alloc=84.3MB, time=1.57 memory used=210.6MB, alloc=84.3MB, time=1.98 memory used=270.5MB, alloc=116.3MB, time=2.57 memory used=351.3MB, alloc=116.3MB, time=3.37 memory used=423.6MB, alloc=140.3MB, time=4.12 memory used=510.9MB, alloc=164.3MB, time=5.06 memory used=614.2MB, alloc=188.3MB, time=6.18 memory used=736.8MB, alloc=212.3MB, time=7.54 memory used=859.9MB, alloc=236.3MB, time=9.70 memory used=990.3MB, alloc=260.3MB, time=12.44 memory used=1129.6MB, alloc=284.3MB, time=16.00 memory used=1292.9MB, alloc=308.3MB, time=20.12 memory used=1480.1MB, alloc=308.3MB, time=24.83 memory used=1667.3MB, alloc=332.3MB, time=29.52 memory used=1878.4MB, alloc=332.3MB, time=34.75 memory used=2089.6MB, alloc=356.3MB, time=39.83 memory used=2324.8MB, alloc=356.3MB, time=45.30 N1 := 7603 > GB := Basis(F, plex(op(vars))); 10 3 3 3 7 4 GB := [102515625 x - 26353376 x , 15 x y - 14 x , -2025 x + 686 y , 7 3 2 2 10125 x + 2744 x z, 2 x y z - 7 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2564.5MB, alloc=356.3MB, time=49.51 memory used=2662.2MB, alloc=612.3MB, time=50.67 memory used=2927.1MB, alloc=636.3MB, time=53.45 memory used=3195.2MB, alloc=660.3MB, time=56.65 memory used=3473.7MB, alloc=684.3MB, time=61.94 memory used=3729.9MB, alloc=708.3MB, time=68.53 memory used=4000.0MB, alloc=732.3MB, time=75.83 memory used=4294.0MB, alloc=756.3MB, time=83.76 memory used=4612.0MB, alloc=780.3MB, time=92.13 memory used=4954.0MB, alloc=804.3MB, time=100.88 memory used=5319.7MB, alloc=828.3MB, time=109.95 N2 := 8825 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 3 4 2 H := [4 x y z - 14 x y, 15 x y - 14 x , -4 x z - 5 y , 2 y z - 4 z, 3 3 -8 x y z - 8, 2 x y + 14 x ] > J:=[op(GB),op(G)]; 10 3 3 3 7 4 J := [102515625 x - 26353376 x , 15 x y - 14 x , -2025 x + 686 y , 7 3 2 2 2 10125 x + 2744 x z, 2 x y z - 7 x y, 2 y z - 4 z, -8 x y z - 8, 3 3 2 x y + 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 := [6, 15, 22, 4, 3, 4, 2, 5/6, 1, 2/3, 2/3, 7/12, 5/12, 8, 17, 42, 10, 10, 4, 2, 7/8, 3/4, 1/2, 3/4, 7/16, 5/16, -2, -20, -6] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=5648.8MB, alloc=828.3MB, time=116.78 |\^/| 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(); 1428364084 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 F := [8 x z, 14 y + 9 z, -18 x + 8 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 3 4 3 G := [-10 x y + 10 z , 5 x y + 3 y z , -2 z - 6 x ] > Problem := [F,G]; 2 4 3 Problem := [[8 x z, 14 y + 9 z, -18 x + 8 y ], 2 2 4 3 3 4 3 [-10 x y + 10 z , 5 x y + 3 y z , -2 z - 6 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.6MB, alloc=32.3MB, time=0.36 memory used=48.8MB, alloc=32.3MB, time=0.54 memory used=69.4MB, alloc=32.3MB, time=0.72 memory used=89.5MB, alloc=56.3MB, time=0.91 memory used=130.4MB, alloc=60.3MB, time=1.28 memory used=169.4MB, alloc=84.3MB, time=1.63 memory used=220.7MB, alloc=84.3MB, time=2.06 memory used=277.2MB, alloc=116.3MB, time=2.60 memory used=355.6MB, alloc=116.3MB, time=3.32 memory used=431.4MB, alloc=140.3MB, time=4.08 memory used=530.2MB, alloc=164.3MB, time=5.16 memory used=645.9MB, alloc=188.3MB, time=6.41 memory used=777.1MB, alloc=212.3MB, time=7.86 memory used=923.0MB, alloc=236.3MB, time=9.46 memory used=1032.9MB, alloc=516.3MB, time=11.04 memory used=1182.0MB, alloc=540.3MB, time=13.84 memory used=1336.3MB, alloc=564.3MB, time=17.34 memory used=1503.1MB, alloc=588.3MB, time=21.49 memory used=1693.8MB, alloc=612.3MB, time=26.26 memory used=1908.5MB, alloc=636.3MB, time=31.50 memory used=2147.1MB, alloc=636.3MB, time=37.26 memory used=2385.7MB, alloc=636.3MB, time=43.02 memory used=2624.2MB, alloc=660.3MB, time=48.81 memory used=2886.7MB, alloc=660.3MB, time=54.92 memory used=3149.3MB, alloc=684.3MB, time=60.83 N1 := 8889 > GB := Basis(F, plex(op(vars))); 6 2 4 3 GB := [x , y x , -9 x + 4 y , 9 z + 14 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3441.9MB, alloc=684.3MB, time=65.98 memory used=3769.0MB, alloc=684.3MB, time=69.40 memory used=4106.3MB, alloc=708.3MB, time=73.44 memory used=4450.2MB, alloc=732.3MB, time=78.48 memory used=4742.8MB, alloc=756.3MB, time=85.60 memory used=5044.6MB, alloc=780.3MB, time=93.16 memory used=5370.4MB, alloc=804.3MB, time=101.23 memory used=5720.1MB, alloc=828.3MB, time=109.84 memory used=6094.3MB, alloc=852.3MB, time=117.93 N2 := 7593 #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 4 3 2 2 4 3 3 H := [8 x z, 9 z + 14 y, -18 x + 8 y , -10 x y + 10 z , 5 x y + 3 y z , 4 3 -2 z - 6 x ] > J:=[op(GB),op(G)]; 6 2 4 3 2 2 4 3 3 J := [x , y x , -9 x + 4 y , 9 z + 14 y, -10 x y + 10 z , 5 x y + 3 y z , 4 3 -2 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 := [6, 14, 20, 4, 4, 3, 4, 5/6, 2/3, 5/6, 5/13, 5/13, 5/13, 7, 15, 26, 6, 6, 3, 4, 6/7, 5/7, 4/7, 3/7, 3/7, 2/7, -1, -6, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=6117.6MB, alloc=852.3MB, time=118.31 |\^/| 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(); 1428364200 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 F := [-2 x - 12 y z , -18 x y z - 18 x , 14 y z + 1] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 G := [14 x + 19 y, -x y - 9 y z , 4 x y + 7 z ] > Problem := [F,G]; 3 2 2 2 3 Problem := [[-2 x - 12 y z , -18 x y z - 18 x , 14 y z + 1], 3 2 2 3 3 [14 x + 19 y, -x y - 9 y z , 4 x 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=0.13 memory used=27.0MB, alloc=32.3MB, time=0.33 memory used=48.5MB, alloc=32.3MB, time=0.51 memory used=68.5MB, alloc=56.3MB, time=0.72 memory used=110.7MB, alloc=60.3MB, time=1.10 memory used=149.6MB, alloc=60.3MB, time=1.43 memory used=185.7MB, alloc=84.3MB, time=1.75 memory used=230.6MB, alloc=84.3MB, time=2.15 memory used=288.9MB, alloc=92.3MB, time=2.68 memory used=349.2MB, alloc=116.3MB, time=3.22 memory used=426.6MB, alloc=116.3MB, time=3.88 memory used=505.4MB, alloc=140.3MB, time=4.62 memory used=577.6MB, alloc=140.3MB, time=5.27 memory used=650.5MB, alloc=396.3MB, time=6.01 memory used=748.9MB, alloc=420.3MB, time=6.96 memory used=873.4MB, alloc=444.3MB, time=8.10 memory used=1011.8MB, alloc=468.3MB, time=9.38 memory used=1154.7MB, alloc=468.3MB, time=10.73 memory used=1276.1MB, alloc=492.3MB, time=12.00 memory used=1405.7MB, alloc=492.3MB, time=13.37 memory used=1519.6MB, alloc=516.3MB, time=14.50 memory used=1627.2MB, alloc=516.3MB, time=15.56 memory used=1711.6MB, alloc=540.3MB, time=16.47 memory used=1808.8MB, alloc=540.3MB, time=17.59 memory used=1887.5MB, alloc=540.3MB, time=18.47 memory used=1957.6MB, alloc=540.3MB, time=19.17 memory used=2043.9MB, alloc=540.3MB, time=20.08 memory used=2116.8MB, alloc=540.3MB, time=21.01 memory used=2183.0MB, alloc=564.3MB, time=21.91 memory used=2270.5MB, alloc=564.3MB, time=23.07 memory used=2377.7MB, alloc=564.3MB, time=24.31 memory used=2466.8MB, alloc=564.3MB, time=25.34 memory used=2580.8MB, alloc=588.3MB, time=26.51 memory used=2667.7MB, alloc=588.3MB, time=27.57 memory used=2788.8MB, alloc=588.3MB, time=28.83 memory used=2877.7MB, alloc=612.3MB, time=29.97 memory used=2968.4MB, alloc=612.3MB, time=31.31 memory used=3212.0MB, alloc=636.3MB, time=34.21 memory used=3463.5MB, alloc=660.3MB, time=37.27 memory used=3730.1MB, alloc=684.3MB, time=40.42 memory used=4031.8MB, alloc=708.3MB, time=43.25 memory used=4331.3MB, alloc=732.3MB, time=46.69 memory used=4637.9MB, alloc=756.3MB, time=50.32 memory used=4953.7MB, alloc=780.3MB, time=54.13 memory used=5282.8MB, alloc=804.3MB, time=57.96 memory used=5615.4MB, alloc=828.3MB, time=61.96 memory used=5907.7MB, alloc=852.3MB, time=65.60 memory used=6291.2MB, alloc=876.3MB, time=69.56 memory used=6722.0MB, alloc=900.3MB, time=72.19 memory used=7123.1MB, alloc=924.3MB, time=76.84 memory used=7436.5MB, alloc=948.3MB, time=84.43 memory used=7749.2MB, alloc=972.3MB, time=92.61 memory used=8067.9MB, alloc=996.3MB, time=101.14 memory used=8396.0MB, alloc=1020.3MB, time=110.07 memory used=8735.8MB, alloc=1044.3MB, time=119.57 memory used=9088.9MB, alloc=1068.3MB, time=129.41 memory used=9455.9MB, alloc=1092.3MB, time=139.81 memory used=9836.9MB, alloc=1116.3MB, time=150.68 memory used=10232.5MB, alloc=1140.3MB, time=161.85 memory used=10643.0MB, alloc=1164.3MB, time=173.50 memory used=11068.3MB, alloc=1188.3MB, time=185.69 memory used=11509.6MB, alloc=1212.3MB, time=198.29 memory used=11958.8MB, alloc=1236.3MB, time=211.54 memory used=12427.9MB, alloc=1260.3MB, time=225.50 memory used=12921.1MB, alloc=1284.3MB, time=240.19 memory used=13438.1MB, alloc=1308.3MB, time=255.48 memory used=13979.1MB, alloc=1332.3MB, time=271.40 memory used=14544.1MB, alloc=1356.3MB, time=287.98 memory used=15133.0MB, alloc=1380.3MB, time=305.44 |\^/| 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(); 1428364500 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 2 F := [6 x z + 13, 19 y + 9 z , 12 x y z - 13 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 4 4 G := [-11 x + 10 z, 7 z + 4 x z, 11 x - 14 y ] > Problem := [F,G]; 4 4 2 Problem := [[6 x z + 13, 19 y + 9 z , 12 x y z - 13 x z], 3 4 2 4 4 [-11 x + 10 z, 7 z + 4 x z, 11 x - 14 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.2MB, alloc=32.3MB, time=0.36 memory used=48.1MB, alloc=32.3MB, time=0.63 memory used=68.7MB, alloc=32.3MB, time=0.87 memory used=88.4MB, alloc=56.3MB, time=1.12 memory used=128.8MB, alloc=60.3MB, time=1.62 memory used=167.0MB, alloc=84.3MB, time=2.08 memory used=228.3MB, alloc=84.3MB, time=2.99 memory used=282.3MB, alloc=108.3MB, time=3.76 memory used=350.4MB, alloc=132.3MB, time=5.32 N1 := 1687 > GB := Basis(F, plex(op(vars))); 4 2 3 GB := [19 x + 169, 12 y - 13, -19 x + 78 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=439.8MB, alloc=132.3MB, time=6.74 N2 := 723 #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)]; 4 4 2 3 H := [6 z x + 13, 9 z + 19 y , 12 x y z - 13 x z, -11 x + 10 z, 4 2 4 4 7 z + 4 x z, -14 y + 11 x ] > J:=[op(GB),op(G)]; 4 2 3 3 4 2 J := [19 x + 169, 12 y - 13, -19 x + 78 z, -11 x + 10 z, 7 z + 4 x z, 4 4 -14 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 := [6, 13, 21, 4, 4, 4, 4, 5/6, 1/2, 5/6, 1/2, 1/4, 7/12, 6, 10, 20, 4, 4, 4, 4, 5/6, 1/3, 1/2, 5/12, 1/6, 1/3, 3, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=470.1MB, alloc=132.3MB, time=7.25 |\^/| 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(); 1428364508 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 2 F := [-2 z + 11 y z, -y + 17 z , 14 x y - 4 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 G := [13 x y z + 15 y z , 9 y z + 2 x z, -x z + 19 y] > Problem := [F,G]; 4 2 3 2 2 2 Problem := [[-2 z + 11 y z, -y + 17 z , 14 x y - 4 y z ], 2 3 3 3 [13 x y z + 15 y z , 9 y z + 2 x z, -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=4.2MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.43 memory used=47.3MB, alloc=32.3MB, time=0.70 memory used=67.5MB, alloc=32.3MB, time=0.93 memory used=87.2MB, alloc=56.3MB, time=1.17 memory used=128.1MB, alloc=60.3MB, time=1.62 memory used=165.7MB, alloc=84.3MB, time=2.06 memory used=217.6MB, alloc=84.3MB, time=2.67 memory used=276.4MB, alloc=116.3MB, time=3.34 memory used=356.3MB, alloc=116.3MB, time=4.33 memory used=435.0MB, alloc=140.3MB, time=5.28 memory used=515.5MB, alloc=396.3MB, time=6.27 memory used=616.9MB, alloc=420.3MB, time=7.44 memory used=741.6MB, alloc=444.3MB, time=8.92 memory used=883.5MB, alloc=468.3MB, time=10.27 memory used=1045.1MB, alloc=492.3MB, time=11.84 memory used=1180.2MB, alloc=492.3MB, time=13.20 memory used=1323.8MB, alloc=516.3MB, time=14.67 memory used=1457.2MB, alloc=540.3MB, time=16.05 memory used=1579.9MB, alloc=540.3MB, time=17.41 memory used=1709.8MB, alloc=564.3MB, time=18.94 memory used=1875.1MB, alloc=564.3MB, time=20.66 memory used=2027.9MB, alloc=588.3MB, time=22.62 memory used=2170.2MB, alloc=612.3MB, time=24.50 memory used=2308.1MB, alloc=636.3MB, time=26.30 memory used=2510.3MB, alloc=660.3MB, time=28.23 memory used=2853.9MB, alloc=660.3MB, time=30.35 memory used=3048.6MB, alloc=684.3MB, time=31.89 memory used=3159.8MB, alloc=684.3MB, time=33.49 memory used=3258.6MB, alloc=708.3MB, time=34.99 memory used=3362.5MB, alloc=732.3MB, time=36.53 memory used=3475.4MB, alloc=756.3MB, time=38.21 memory used=3556.5MB, alloc=756.3MB, time=39.54 memory used=3638.7MB, alloc=756.3MB, time=40.73 memory used=3735.6MB, alloc=780.3MB, time=42.03 memory used=3855.8MB, alloc=804.3MB, time=44.72 memory used=4177.2MB, alloc=828.3MB, time=52.05 memory used=4496.1MB, alloc=852.3MB, time=59.87 memory used=4819.1MB, alloc=876.3MB, time=68.05 memory used=5150.0MB, alloc=900.3MB, time=76.52 memory used=5480.9MB, alloc=924.3MB, time=85.64 memory used=5835.8MB, alloc=948.3MB, time=95.37 memory used=6214.6MB, alloc=972.3MB, time=105.81 memory used=6617.3MB, alloc=996.3MB, time=116.79 memory used=7044.0MB, alloc=1020.3MB, time=128.36 memory used=7494.6MB, alloc=1044.3MB, time=140.59 memory used=7969.2MB, alloc=1044.3MB, time=153.40 memory used=8443.7MB, alloc=1068.3MB, time=166.20 memory used=8942.2MB, alloc=1068.3MB, time=179.75 memory used=9440.6MB, alloc=1068.3MB, time=193.17 memory used=9939.0MB, alloc=1068.3MB, time=206.59 memory used=10437.3MB, alloc=1092.3MB, time=220.01 memory used=10959.6MB, alloc=1092.3MB, time=234.16 memory used=11481.8MB, alloc=1092.3MB, time=248.16 memory used=12003.9MB, alloc=1116.3MB, time=262.20 memory used=12549.9MB, alloc=1116.3MB, time=276.82 memory used=13095.7MB, alloc=1140.3MB, time=291.63 memory used=13665.5MB, alloc=1140.3MB, time=306.88 |\^/| 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(); 1428364808 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 2 F := [-8 x z - 15 x y z, -4 x + 2 x , 19 x - z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 G := [-13 x z - 7 y, 18 x y z + 11 y , 16 x y z - 13 x y z] > Problem := [F,G]; 2 4 3 2 Problem := [[-8 x z - 15 x y z, -4 x + 2 x , 19 x - z], 3 2 4 2 [-13 x z - 7 y, 18 x y z + 11 y , 16 x y z - 13 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.1MB, alloc=32.3MB, time=0.36 memory used=47.8MB, alloc=32.3MB, time=0.62 memory used=68.3MB, alloc=56.3MB, time=0.88 memory used=109.7MB, alloc=60.3MB, time=1.36 memory used=148.1MB, alloc=84.3MB, time=1.83 memory used=210.7MB, alloc=92.3MB, time=2.73 memory used=265.5MB, alloc=116.3MB, time=3.51 memory used=342.2MB, alloc=140.3MB, time=4.54 memory used=436.7MB, alloc=164.3MB, time=5.84 memory used=543.5MB, alloc=188.3MB, time=7.32 memory used=658.2MB, alloc=212.3MB, time=9.69 memory used=779.0MB, alloc=236.3MB, time=12.69 memory used=907.5MB, alloc=260.3MB, time=16.57 memory used=1059.6MB, alloc=284.3MB, time=20.98 memory used=1235.5MB, alloc=284.3MB, time=25.02 memory used=1411.5MB, alloc=284.3MB, time=28.99 memory used=1587.4MB, alloc=308.3MB, time=32.93 memory used=1787.3MB, alloc=308.3MB, time=37.31 memory used=1987.3MB, alloc=332.3MB, time=41.60 N1 := 7011 > GB := Basis(F, plex(op(vars))); 4 3 3 3 2 GB := [2 x - x , 15 x y + 4 x , -19 x + z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2175.2MB, alloc=332.3MB, time=44.40 memory used=2426.0MB, alloc=612.3MB, time=47.22 memory used=2691.8MB, alloc=636.3MB, time=51.36 memory used=2925.6MB, alloc=660.3MB, time=57.06 memory used=3183.7MB, alloc=684.3MB, time=63.16 N2 := 5313 #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 4 3 2 3 H := [-8 x z - 15 x y z, -4 x + 2 x , 19 x - z, -13 x z - 7 y, 2 4 2 18 x y z + 11 y , 16 x y z - 13 x y z] > J:=[op(GB),op(G)]; 4 3 3 3 2 3 2 4 J := [2 x - x , 15 x y + 4 x , -19 x + z, -13 x z - 7 y, 18 x y z + 11 y , 2 16 x y z - 13 x 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 := [6, 15, 21, 4, 4, 4, 2, 1, 2/3, 5/6, 3/4, 1/2, 7/12, 6, 14, 22, 4, 4, 4, 2, 1, 2/3, 2/3, 3/4, 1/2, 5/12, 1, -1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3445.8MB, alloc=684.3MB, time=68.22 |\^/| 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(); 1428364876 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 2 F := [7 x y z + 15 y z , -2 y z - 20 x, -12 x y - 18 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 G := [2 y z - 17 x, -x z + 15 y z, 9 x + 3 y z] > Problem := [F,G]; 2 2 2 2 2 2 2 Problem := [[7 x y z + 15 y z , -2 y z - 20 x, -12 x y - 18 y z ], 3 2 2 4 [2 y z - 17 x, -x z + 15 y z, 9 x + 3 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.7MB, alloc=32.3MB, time=0.37 memory used=48.1MB, alloc=32.3MB, time=0.54 memory used=68.0MB, alloc=56.3MB, time=0.73 memory used=109.9MB, alloc=60.3MB, time=1.09 memory used=150.3MB, alloc=84.3MB, time=1.44 memory used=214.7MB, alloc=92.3MB, time=1.98 memory used=276.5MB, alloc=116.3MB, time=2.52 memory used=352.4MB, alloc=116.3MB, time=3.17 memory used=421.8MB, alloc=372.3MB, time=3.81 memory used=500.5MB, alloc=396.3MB, time=4.56 memory used=599.0MB, alloc=396.3MB, time=5.45 memory used=697.2MB, alloc=420.3MB, time=6.39 memory used=817.4MB, alloc=444.3MB, time=7.51 memory used=954.3MB, alloc=468.3MB, time=8.83 memory used=1069.0MB, alloc=492.3MB, time=9.87 memory used=1189.6MB, alloc=492.3MB, time=11.05 memory used=1291.7MB, alloc=492.3MB, time=12.07 memory used=1370.7MB, alloc=516.3MB, time=12.85 memory used=1444.5MB, alloc=516.3MB, time=13.70 memory used=1517.0MB, alloc=516.3MB, time=14.56 memory used=1581.4MB, alloc=516.3MB, time=15.37 memory used=1632.9MB, alloc=516.3MB, time=16.01 memory used=1695.3MB, alloc=516.3MB, time=16.82 memory used=1751.7MB, alloc=516.3MB, time=17.68 memory used=1957.4MB, alloc=540.3MB, time=19.53 memory used=2155.4MB, alloc=564.3MB, time=21.52 memory used=2340.6MB, alloc=588.3MB, time=23.51 memory used=2518.6MB, alloc=612.3MB, time=25.48 memory used=2671.6MB, alloc=636.3MB, time=27.21 memory used=2832.8MB, alloc=660.3MB, time=29.21 memory used=2954.5MB, alloc=660.3MB, time=30.79 memory used=3085.1MB, alloc=660.3MB, time=32.57 memory used=3218.0MB, alloc=660.3MB, time=34.37 memory used=3300.2MB, alloc=684.3MB, time=35.71 memory used=3641.6MB, alloc=708.3MB, time=39.44 memory used=3977.4MB, alloc=732.3MB, time=43.40 memory used=4322.6MB, alloc=756.3MB, time=47.68 memory used=4641.9MB, alloc=780.3MB, time=51.64 memory used=4984.5MB, alloc=804.3MB, time=56.18 memory used=5322.1MB, alloc=828.3MB, time=60.51 memory used=5586.1MB, alloc=852.3MB, time=64.19 memory used=5861.3MB, alloc=876.3MB, time=68.38 memory used=6253.8MB, alloc=900.3MB, time=73.92 memory used=6608.2MB, alloc=924.3MB, time=79.43 memory used=6938.5MB, alloc=948.3MB, time=84.75 memory used=7300.4MB, alloc=972.3MB, time=90.65 memory used=7583.4MB, alloc=996.3MB, time=95.64 memory used=7826.6MB, alloc=1020.3MB, time=100.13 memory used=8145.5MB, alloc=1044.3MB, time=105.84 memory used=8601.6MB, alloc=1068.3MB, time=111.62 memory used=9105.4MB, alloc=1092.3MB, time=116.67 memory used=9507.3MB, alloc=1116.3MB, time=123.39 memory used=9914.8MB, alloc=1140.3MB, time=132.17 memory used=10245.4MB, alloc=1164.3MB, time=141.91 memory used=10571.9MB, alloc=1188.3MB, time=151.98 memory used=10902.6MB, alloc=1212.3MB, time=162.31 memory used=11241.0MB, alloc=1236.3MB, time=173.27 memory used=11589.6MB, alloc=1260.3MB, time=184.48 memory used=11948.7MB, alloc=1284.3MB, time=196.12 memory used=12319.8MB, alloc=1308.3MB, time=207.98 memory used=12703.1MB, alloc=1332.3MB, time=220.35 memory used=13097.4MB, alloc=1356.3MB, time=233.28 memory used=13505.9MB, alloc=1380.3MB, time=246.66 memory used=13930.1MB, alloc=1404.3MB, time=260.47 memory used=14370.3MB, alloc=1428.3MB, time=274.80 memory used=14822.3MB, alloc=1452.3MB, time=289.72 memory used=15289.8MB, alloc=1476.3MB, time=305.46 memory used=15781.4MB, alloc=1500.3MB, time=321.73 |\^/| 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(); 1428365176 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 2 F := [-4 x z - z, 7 x z - 9 x , -3 x - 15 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 4 G := [3 x z + x, 6 x z + 9 y z, 4 x y - z ] > Problem := [F,G]; 3 2 4 2 2 Problem := [[-4 x z - z, 7 x z - 9 x , -3 x - 15 y z ], 3 3 3 4 [3 x z + x, 6 x z + 9 y z, 4 x y - z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=26.4MB, alloc=32.3MB, time=0.40 memory used=47.8MB, alloc=32.3MB, time=0.65 memory used=68.7MB, alloc=56.3MB, time=0.92 memory used=110.8MB, alloc=60.3MB, time=1.41 memory used=150.0MB, alloc=60.3MB, time=1.85 memory used=189.3MB, alloc=84.3MB, time=2.33 memory used=230.9MB, alloc=84.3MB, time=2.79 memory used=291.5MB, alloc=116.3MB, time=3.59 memory used=370.0MB, alloc=140.3MB, time=4.73 memory used=460.6MB, alloc=164.3MB, time=6.62 N1 := 1483 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 2 GB := [4 x + x , 1658880 x y + 49 x , 576 x + 7 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=567.6MB, alloc=164.3MB, time=7.96 N2 := 579 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 4 2 2 3 3 H := [-4 x z - z, 7 x z - 9 x , -3 x - 15 y z , 3 x z + x, 6 x z + 9 y z, 4 3 -z + 4 y x ] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 3 J := [4 x + x , 1658880 x y + 49 x , 576 x + 7 z, 3 x z + x, 3 4 3 6 x z + 9 y z, -z + 4 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 := [6, 15, 22, 4, 4, 2, 4, 1, 1/2, 1, 2/3, 1/4, 2/3, 6, 13, 21, 4, 3, 2, 4, 1, 1/2, 2/3, 3/4, 1/4, 5/12, 2, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=586.3MB, alloc=164.3MB, time=8.28 |\^/| 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(); 1428365185 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 F := [-4 x z + 17 y z, z + 3 y , -12 y z - 18 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 3 G := [y z + 11 x y, 11 x y z + 18 y z, -7 x z + 6 y z] > Problem := [F,G]; 3 3 3 2 2 Problem := [[-4 x z + 17 y z, z + 3 y , -12 y z - 18 x y], 3 2 3 2 2 3 [y z + 11 x y, 11 x y z + 18 y z, -7 x z + 6 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.6MB, alloc=32.3MB, time=0.42 memory used=47.9MB, alloc=32.3MB, time=0.67 memory used=68.1MB, alloc=56.3MB, time=0.91 memory used=109.5MB, alloc=60.3MB, time=1.39 memory used=148.2MB, alloc=84.3MB, time=1.77 memory used=212.8MB, alloc=92.3MB, time=2.49 memory used=274.4MB, alloc=116.3MB, time=3.21 memory used=351.7MB, alloc=140.3MB, time=4.09 memory used=425.7MB, alloc=396.3MB, time=4.95 memory used=530.7MB, alloc=396.3MB, time=6.20 memory used=640.6MB, alloc=420.3MB, time=7.35 memory used=769.5MB, alloc=444.3MB, time=8.82 memory used=900.3MB, alloc=468.3MB, time=10.17 memory used=1013.3MB, alloc=492.3MB, time=11.72 memory used=1121.8MB, alloc=492.3MB, time=12.67 memory used=1221.2MB, alloc=492.3MB, time=13.62 memory used=1309.7MB, alloc=492.3MB, time=14.48 memory used=1377.1MB, alloc=516.3MB, time=15.20 memory used=1456.8MB, alloc=516.3MB, time=16.02 memory used=1528.1MB, alloc=516.3MB, time=16.84 memory used=1591.8MB, alloc=516.3MB, time=17.54 memory used=1651.3MB, alloc=516.3MB, time=18.34 memory used=1719.6MB, alloc=516.3MB, time=19.20 memory used=1766.0MB, alloc=516.3MB, time=19.86 memory used=1963.2MB, alloc=540.3MB, time=21.64 memory used=2162.6MB, alloc=564.3MB, time=23.64 memory used=2372.9MB, alloc=588.3MB, time=25.74 memory used=2541.9MB, alloc=612.3MB, time=27.52 memory used=2750.4MB, alloc=636.3MB, time=29.38 memory used=2894.1MB, alloc=660.3MB, time=31.20 memory used=3013.4MB, alloc=684.3MB, time=32.77 memory used=3130.8MB, alloc=708.3MB, time=34.23 memory used=3276.9MB, alloc=732.3MB, time=35.64 memory used=3385.8MB, alloc=756.3MB, time=37.19 memory used=3474.2MB, alloc=756.3MB, time=38.53 memory used=3570.1MB, alloc=756.3MB, time=40.07 memory used=3937.4MB, alloc=780.3MB, time=44.60 memory used=4267.4MB, alloc=804.3MB, time=49.20 memory used=4591.3MB, alloc=828.3MB, time=53.89 memory used=4917.1MB, alloc=852.3MB, time=58.56 memory used=5236.8MB, alloc=876.3MB, time=63.31 memory used=5551.4MB, alloc=900.3MB, time=69.37 memory used=5824.2MB, alloc=924.3MB, time=76.44 memory used=6098.5MB, alloc=948.3MB, time=84.00 memory used=6380.5MB, alloc=972.3MB, time=92.03 memory used=6668.8MB, alloc=996.3MB, time=100.50 memory used=6972.4MB, alloc=1020.3MB, time=109.48 memory used=7288.6MB, alloc=1044.3MB, time=119.05 memory used=7619.0MB, alloc=1068.3MB, time=129.37 memory used=7973.3MB, alloc=1092.3MB, time=140.32 memory used=8351.5MB, alloc=1116.3MB, time=152.04 memory used=8753.7MB, alloc=1140.3MB, time=164.49 memory used=9179.9MB, alloc=1164.3MB, time=177.70 memory used=9630.0MB, alloc=1188.3MB, time=191.39 memory used=10103.9MB, alloc=1212.3MB, time=205.58 memory used=10601.9MB, alloc=1236.3MB, time=220.52 memory used=11123.8MB, alloc=1260.3MB, time=236.03 memory used=11669.6MB, alloc=1284.3MB, time=252.15 memory used=12239.3MB, alloc=1308.3MB, time=268.91 memory used=12832.9MB, alloc=1332.3MB, time=286.30 memory used=13450.3MB, alloc=1356.3MB, time=304.32 |\^/| 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(); 1428365485 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [10 y z + 3 z , x y z - 14 x y, 20 x z + 6 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 4 G := [2 y + x y, 10 x y - 5, 4 y z - 9 z ] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[10 y z + 3 z , x y z - 14 x y, 20 x z + 6 x z], 4 2 3 2 2 4 [2 y + x y, 10 x y - 5, 4 y z - 9 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.1MB, alloc=32.3MB, time=0.38 memory used=47.3MB, alloc=32.3MB, time=0.62 memory used=67.4MB, alloc=32.3MB, time=0.87 memory used=86.5MB, alloc=56.3MB, time=1.08 memory used=126.2MB, alloc=60.3MB, time=1.52 memory used=162.5MB, alloc=60.3MB, time=1.95 memory used=196.7MB, alloc=84.3MB, time=2.39 memory used=252.8MB, alloc=84.3MB, time=3.03 memory used=307.8MB, alloc=84.3MB, time=3.71 memory used=360.6MB, alloc=108.3MB, time=4.36 memory used=435.1MB, alloc=140.3MB, time=5.35 memory used=528.6MB, alloc=164.3MB, time=6.66 memory used=640.2MB, alloc=188.3MB, time=8.22 memory used=762.9MB, alloc=212.3MB, time=9.99 memory used=895.5MB, alloc=236.3MB, time=12.01 memory used=1012.7MB, alloc=516.3MB, time=13.76 memory used=1155.9MB, alloc=540.3MB, time=16.32 memory used=1305.6MB, alloc=564.3MB, time=19.35 memory used=1465.9MB, alloc=588.3MB, time=22.84 memory used=1633.5MB, alloc=612.3MB, time=27.25 memory used=1824.6MB, alloc=636.3MB, time=32.06 memory used=2039.7MB, alloc=660.3MB, time=37.45 memory used=2278.7MB, alloc=684.3MB, time=43.43 memory used=2541.7MB, alloc=684.3MB, time=49.90 memory used=2804.6MB, alloc=684.3MB, time=56.41 memory used=3067.4MB, alloc=708.3MB, time=62.91 memory used=3354.2MB, alloc=708.3MB, time=69.91 memory used=3640.8MB, alloc=708.3MB, time=76.87 memory used=3927.4MB, alloc=732.3MB, time=83.76 memory used=4238.0MB, alloc=732.3MB, time=91.26 memory used=4548.5MB, alloc=756.3MB, time=98.51 memory used=4882.9MB, alloc=780.3MB, time=106.09 N1 := 11767 > GB := Basis(F, plex(op(vars))); 5 2 3 2 2 2 3 2 GB := [1400 x y - 9 x y, -x y + x y , 140 x y + 3 x z, 10 y z + 3 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5244.0MB, alloc=780.3MB, time=112.41 memory used=5452.7MB, alloc=780.3MB, time=115.20 memory used=5683.1MB, alloc=804.3MB, time=119.02 memory used=6072.6MB, alloc=828.3MB, time=128.57 N2 := 4551 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 4 2 H := [10 y z + 3 z , x y z - 14 x y, 20 x z + 6 x z, 2 y + x y, 3 2 2 4 10 x y - 5, 4 y z - 9 z ] > J:=[op(GB),op(G)]; 5 2 3 2 2 2 3 2 J := [1400 x y - 9 x y, -x y + x y , 140 x y + 3 x z, 10 y z + 3 z , 4 2 3 2 2 4 2 y + x y, 10 x y - 5, 4 y z - 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 := [6, 13, 24, 4, 2, 4, 4, 2/3, 5/6, 2/3, 1/2, 7/12, 7/12, 7, 15, 29, 6, 5, 4, 4, 5/7, 1, 3/7, 4/7, 5/7, 5/14, -2, -5, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=6243.7MB, alloc=828.3MB, time=131.83 |\^/| 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(); 1428365616 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 F := [18 y z - 11 y z , -2 x z + 11 y z, 18 x y + 15 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 3 2 G := [16 x + 19 y z, -10 y + 16 y z , -18 x y + 13 y ] > Problem := [F,G]; 3 2 3 2 3 Problem := [[18 y z - 11 y z , -2 x z + 11 y z, 18 x y + 15 x z], 3 2 4 3 3 2 [16 x + 19 y z, -10 y + 16 y z , -18 x y + 13 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.7MB, alloc=32.3MB, time=0.37 memory used=77.2MB, alloc=68.3MB, time=0.83 memory used=126.3MB, alloc=68.3MB, time=1.26 memory used=172.8MB, alloc=76.3MB, time=1.68 memory used=217.5MB, alloc=100.3MB, time=2.09 memory used=285.4MB, alloc=124.3MB, time=2.69 memory used=369.9MB, alloc=380.3MB, time=3.44 memory used=458.5MB, alloc=404.3MB, time=4.22 memory used=567.9MB, alloc=404.3MB, time=5.21 memory used=677.2MB, alloc=428.3MB, time=6.21 memory used=807.3MB, alloc=452.3MB, time=7.39 memory used=939.2MB, alloc=476.3MB, time=8.55 memory used=1107.5MB, alloc=500.3MB, time=10.22 memory used=1286.7MB, alloc=524.3MB, time=12.32 memory used=1517.1MB, alloc=548.3MB, time=14.13 memory used=1697.4MB, alloc=572.3MB, time=16.46 memory used=1884.6MB, alloc=596.3MB, time=18.98 memory used=2028.4MB, alloc=620.3MB, time=21.02 memory used=2242.3MB, alloc=644.3MB, time=25.51 memory used=2450.8MB, alloc=668.3MB, time=30.40 memory used=2665.6MB, alloc=692.3MB, time=35.56 memory used=2882.5MB, alloc=716.3MB, time=41.48 memory used=3119.8MB, alloc=740.3MB, time=48.04 memory used=3381.0MB, alloc=764.3MB, time=55.22 memory used=3666.1MB, alloc=788.3MB, time=63.03 memory used=3975.2MB, alloc=812.3MB, time=71.45 memory used=4308.3MB, alloc=836.3MB, time=80.58 memory used=4665.2MB, alloc=860.3MB, time=90.21 memory used=5046.1MB, alloc=860.3MB, time=100.44 memory used=5427.0MB, alloc=860.3MB, time=110.60 memory used=5807.7MB, alloc=884.3MB, time=120.66 memory used=6212.6MB, alloc=884.3MB, time=131.34 memory used=6617.2MB, alloc=908.3MB, time=142.04 memory used=7045.9MB, alloc=908.3MB, time=153.13 memory used=7474.6MB, alloc=932.3MB, time=164.14 memory used=7927.4MB, alloc=956.3MB, time=175.33 N1 := 14131 > GB := Basis(F, plex(op(vars))); 4 5 5 3 5 6 3 GB := [22 x y - 18225 x y , 11 x y + 1215 x y , 6 x y + 5 x z, 3 5 2 3 2 44 x y + 30375 y z, 18 y z - 11 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=8124.5MB, alloc=956.3MB, time=178.77 memory used=8220.4MB, alloc=956.3MB, time=180.62 memory used=8328.2MB, alloc=956.3MB, time=182.35 memory used=8412.4MB, alloc=956.3MB, time=183.79 memory used=8493.3MB, alloc=956.3MB, time=185.28 memory used=8566.7MB, alloc=956.3MB, time=186.68 memory used=8629.5MB, alloc=956.3MB, time=187.86 memory used=8699.4MB, alloc=956.3MB, time=189.20 memory used=8762.1MB, alloc=956.3MB, time=190.52 memory used=9052.2MB, alloc=956.3MB, time=194.03 memory used=9301.7MB, alloc=956.3MB, time=197.19 memory used=9906.2MB, alloc=956.3MB, time=203.28 memory used=10432.6MB, alloc=980.3MB, time=210.21 memory used=10948.6MB, alloc=1004.3MB, time=219.52 memory used=11382.3MB, alloc=1028.3MB, time=230.85 memory used=11796.9MB, alloc=1052.3MB, time=243.04 memory used=12231.7MB, alloc=1076.3MB, time=255.88 memory used=12690.4MB, alloc=1100.3MB, time=269.46 memory used=13173.1MB, alloc=1124.3MB, time=283.57 memory used=13679.6MB, alloc=1148.3MB, time=298.29 |\^/| 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(); 1428365916 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 F := [-19 x y z - 13 y, -5 y + 7 y, 2 x y - 8 x y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 4 G := [-10 x - 7 y, -7 x z + 10 y , -18 x y z + 11 y ] > Problem := [F,G]; 2 3 3 2 Problem := [[-19 x y z - 13 y, -5 y + 7 y, 2 x y - 8 x y z ], 2 3 4 2 4 [-10 x - 7 y, -7 x z + 10 y , -18 x y z + 11 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.4MB, alloc=32.3MB, time=0.37 memory used=47.9MB, alloc=32.3MB, time=0.61 memory used=67.7MB, alloc=32.3MB, time=0.83 memory used=86.1MB, alloc=56.3MB, time=1.08 memory used=125.6MB, alloc=60.3MB, time=1.55 memory used=165.3MB, alloc=84.3MB, time=2.03 memory used=211.9MB, alloc=84.3MB, time=2.58 memory used=268.9MB, alloc=92.3MB, time=3.31 memory used=324.2MB, alloc=116.3MB, time=4.00 memory used=403.3MB, alloc=116.3MB, time=4.93 memory used=482.1MB, alloc=140.3MB, time=5.92 memory used=580.9MB, alloc=164.3MB, time=7.25 memory used=689.9MB, alloc=188.3MB, time=8.44 memory used=814.3MB, alloc=212.3MB, time=9.82 memory used=950.6MB, alloc=492.3MB, time=11.35 memory used=1101.7MB, alloc=516.3MB, time=13.05 memory used=1261.4MB, alloc=540.3MB, time=15.54 memory used=1414.9MB, alloc=564.3MB, time=18.59 memory used=1578.4MB, alloc=588.3MB, time=22.10 memory used=1753.8MB, alloc=612.3MB, time=26.20 memory used=1943.5MB, alloc=636.3MB, time=30.90 memory used=2157.2MB, alloc=660.3MB, time=36.15 memory used=2394.8MB, alloc=684.3MB, time=41.96 memory used=2656.3MB, alloc=684.3MB, time=48.31 memory used=2917.8MB, alloc=708.3MB, time=54.69 memory used=3203.2MB, alloc=708.3MB, time=61.55 memory used=3488.7MB, alloc=708.3MB, time=68.39 memory used=3774.0MB, alloc=732.3MB, time=75.32 memory used=4083.5MB, alloc=732.3MB, time=82.61 memory used=4392.8MB, alloc=756.3MB, time=89.75 memory used=4726.2MB, alloc=780.3MB, time=96.87 N1 := 10827 > GB := Basis(F, plex(op(vars))); 6 3 4 GB := [361 x y - 676 y, 5 y - 7 y, 19 x y + 52 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5095.5MB, alloc=780.3MB, time=101.73 N2 := 2473 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 2 2 H := [-19 x y z - 13 y, -5 y + 7 y, 2 x y - 8 x y z , -10 x - 7 y, 3 4 2 4 -7 x z + 10 y , -18 x y z + 11 y ] > J:=[op(GB),op(G)]; 6 3 4 2 J := [361 x y - 676 y, 5 y - 7 y, 19 x y + 52 y z, -10 x - 7 y, 3 4 2 4 -7 x z + 10 y , -18 x 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 := [6, 15, 21, 4, 3, 4, 3, 5/6, 1, 2/3, 1/2, 5/6, 1/3, 6, 14, 25, 7, 6, 4, 3, 5/6, 1, 1/2, 5/12, 5/6, 1/4, 1, -4, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=5334.3MB, alloc=780.3MB, 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(); 1428366021 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-17 x y z + 8 y , 5 x y - 5 y z, 12 x y - 3 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 2 2 2 G := [-19 x z + 13 z , 8 z + 10 x y, -3 x z - 4 y z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-17 x y z + 8 y , 5 x y - 5 y z, 12 x y - 3 y z ], 3 3 4 2 2 2 [-19 x z + 13 z , 8 z + 10 x y, -3 x z - 4 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.6MB, alloc=32.3MB, time=0.37 memory used=48.0MB, alloc=32.3MB, time=0.54 memory used=68.8MB, alloc=32.3MB, time=0.72 memory used=88.4MB, alloc=56.3MB, time=0.91 memory used=128.9MB, alloc=60.3MB, time=1.26 memory used=167.8MB, alloc=84.3MB, time=1.60 memory used=211.1MB, alloc=84.3MB, time=1.99 memory used=272.3MB, alloc=116.3MB, time=2.51 memory used=356.4MB, alloc=140.3MB, time=3.32 memory used=454.4MB, alloc=164.3MB, time=4.35 memory used=569.2MB, alloc=188.3MB, time=5.59 memory used=674.5MB, alloc=444.3MB, time=6.76 memory used=791.6MB, alloc=468.3MB, time=8.49 memory used=910.3MB, alloc=492.3MB, time=10.91 memory used=1039.0MB, alloc=516.3MB, time=13.95 memory used=1191.7MB, alloc=540.3MB, time=17.55 memory used=1368.3MB, alloc=540.3MB, time=21.59 memory used=1544.9MB, alloc=564.3MB, time=25.48 N1 := 5545 > GB := Basis(F, plex(op(vars))); 5 2 4 2 3 3 GB := [4913 x y - 32 x y, -289 x y + 16 x y , -17 x y + 8 y , 2 2 2 4 2 17 x y z - 8 y , -x y + y z, -289 x y + 4 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1750.9MB, alloc=564.3MB, time=28.90 memory used=1976.3MB, alloc=564.3MB, time=31.21 memory used=2166.7MB, alloc=588.3MB, time=33.21 memory used=2406.7MB, alloc=612.3MB, time=35.91 memory used=2652.1MB, alloc=636.3MB, time=38.72 memory used=2888.2MB, alloc=660.3MB, time=41.34 memory used=3143.2MB, alloc=684.3MB, time=46.39 memory used=3389.4MB, alloc=708.3MB, time=52.18 memory used=3633.2MB, alloc=732.3MB, time=58.81 memory used=3900.9MB, alloc=756.3MB, time=66.11 memory used=4192.5MB, alloc=780.3MB, time=73.95 memory used=4508.1MB, alloc=804.3MB, time=82.38 memory used=4847.6MB, alloc=828.3MB, time=91.55 memory used=5211.1MB, alloc=852.3MB, time=101.15 memory used=5598.4MB, alloc=876.3MB, time=111.25 memory used=6009.6MB, alloc=900.3MB, time=121.90 memory used=6444.7MB, alloc=924.3MB, time=132.81 memory used=6904.1MB, alloc=948.3MB, time=143.25 N2 := 11505 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 3 3 H := [-17 x y z + 8 y , 5 x y - 5 y z, 12 x y - 3 y z , -19 x z + 13 z , 4 2 2 2 8 z + 10 x y, -3 x z - 4 y z ] > J:=[op(GB),op(G)]; 5 2 4 2 3 3 J := [4913 x y - 32 x y, -289 x y + 16 x y , -17 x y + 8 y , 2 2 2 4 2 3 3 17 x y z - 8 y , -x y + y z, -289 x y + 4 y z , -19 x z + 13 z , 4 2 2 2 8 z + 10 x y, -3 x z - 4 y z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 17, 21, 4, 2, 2, 4, 1, 5/6, 1, 1/2, 2/3, 2/3, 9, 23, 38, 6, 5, 3, 4, 1, 8/9, 2/3, 11/18, 7/9, 4/9, -6, -17, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=6936.7MB, alloc=948.3MB, time=143.80 |\^/| 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(); 1428366162 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-8 x z - 20 y, -17 x y z + 15 y z, -8 y z + 5 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 G := [2 x z + 18 y, 13 x y z - 12 y , 12 x z - 9 z] > Problem := [F,G]; 2 2 3 2 Problem := [[-8 x z - 20 y, -17 x y z + 15 y z, -8 y z + 5 y z], 3 2 2 3 [2 x z + 18 y, 13 x y z - 12 y , 12 x z - 9 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=26.0MB, alloc=32.3MB, time=0.31 memory used=47.7MB, alloc=32.3MB, time=0.54 memory used=68.0MB, alloc=32.3MB, time=0.72 memory used=88.2MB, alloc=56.3MB, time=0.95 memory used=129.6MB, alloc=60.3MB, time=1.39 memory used=167.8MB, alloc=84.3MB, time=1.79 memory used=225.1MB, alloc=108.3MB, time=2.59 N1 := 1655 > GB := Basis(F, plex(op(vars))); 2 2 3 2 2 GB := [136 x y - 75 y , 8 y - 5 y , 136 x y z - 75 y z, 8 y z - 5 y z, 2 2 2 2 z x + 5 y, 15 y z + 68 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=296.5MB, alloc=108.3MB, time=3.64 memory used=372.0MB, alloc=116.3MB, time=4.31 memory used=447.4MB, alloc=140.3MB, time=5.09 memory used=545.1MB, alloc=164.3MB, time=6.15 memory used=656.9MB, alloc=188.3MB, time=7.97 memory used=769.9MB, alloc=212.3MB, time=10.24 N2 := 2785 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 3 H := [-8 x z - 20 y, -17 x y z + 15 y z, -8 y z + 5 y z, 2 x z + 18 y, 2 2 3 13 x y z - 12 y , 12 x z - 9 z] > J:=[op(GB),op(G)]; 2 2 3 2 2 J := [136 x y - 75 y , 8 y - 5 y , 136 x y z - 75 y z, 8 y z - 5 y z, 2 2 2 3 2 2 2 z x + 5 y, 15 y z + 68 y , 2 x z + 18 y, 13 x y z - 12 y , 3 12 x z - 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 := [6, 16, 22, 4, 3, 3, 3, 5/6, 5/6, 1, 5/12, 2/3, 3/4, 9, 21, 30, 4, 3, 3, 3, 2/3, 8/9, 7/9, 1/3, 7/9, 5/9, -5, -8, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=844.1MB, alloc=212.3MB, time=11.36 |\^/| 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(); 1428366174 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 2 F := [12 y - 20 y z , 11 x y - 18 x y z, 15 x y - 20 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-18 y z - 2 y z, 19 y z - 11 z , 9 x ] > Problem := [F,G]; 4 2 2 2 2 2 2 Problem := [[12 y - 20 y z , 11 x y - 18 x y z, 15 x y - 20 y ], 3 2 2 [-18 y z - 2 y z, 19 y z - 11 z , 9 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.0MB, alloc=32.3MB, time=0.33 memory used=47.1MB, alloc=32.3MB, time=0.51 memory used=68.3MB, alloc=56.3MB, time=0.74 memory used=110.1MB, alloc=60.3MB, time=1.20 N1 := 739 > GB := Basis(F, plex(op(vars))); 2 2 2 4 3 2 3 2 GB := [3 x y - 4 y , 729 y - 605 y , 27 x y z - 22 y , -11 x y + 18 y z, 3 2 -121 y + 243 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=144.2MB, alloc=60.3MB, time=1.53 memory used=181.3MB, alloc=60.3MB, time=1.86 memory used=218.3MB, alloc=84.3MB, time=2.24 N2 := 761 #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)]; 4 2 2 2 2 2 2 3 H := [12 y - 20 y z , 11 x y - 18 x y z, 15 x y - 20 y , -18 y z - 2 y z, 2 2 19 y z - 11 z , 9 x ] > J:=[op(GB),op(G)]; 2 2 2 4 3 2 3 2 J := [3 x y - 4 y , 729 y - 605 y , 27 x y z - 22 y , -11 x y + 18 y z, 3 2 3 2 2 -121 y + 243 y z , -18 y z - 2 y z, 19 y z - 11 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, 20, 4, 2, 4, 3, 1/2, 5/6, 2/3, 1/3, 3/4, 1/2, 8, 16, 26, 4, 2, 4, 3, 1/2, 7/8, 5/8, 1/4, 13/16, 7/16, -4, -6, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=266.2MB, alloc=84.3MB, time=2.77 |\^/| 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(); 1428366176 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 F := [16 x z + y z , -11 x y - 6 x y z, 8 y z + 8 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 G := [-5 x , -19 z - 10 y, -8 x z - 10 y ] > Problem := [F,G]; 2 2 3 2 3 Problem := [[16 x z + y z , -11 x y - 6 x y z, 8 y z + 8 z], 3 2 2 3 [-5 x , -19 z - 10 y, -8 x z - 10 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.11 memory used=26.7MB, alloc=32.3MB, time=0.30 memory used=48.5MB, alloc=32.3MB, time=0.48 memory used=69.0MB, alloc=32.3MB, time=0.66 memory used=88.4MB, alloc=56.3MB, time=0.84 memory used=128.9MB, alloc=60.3MB, time=1.19 memory used=169.5MB, alloc=84.3MB, time=1.57 memory used=207.9MB, alloc=84.3MB, time=1.90 memory used=271.5MB, alloc=116.3MB, time=2.48 memory used=352.0MB, alloc=140.3MB, time=3.35 memory used=446.5MB, alloc=164.3MB, time=4.42 memory used=571.5MB, alloc=164.3MB, time=5.54 memory used=679.2MB, alloc=444.3MB, time=6.68 memory used=799.9MB, alloc=468.3MB, time=7.99 memory used=944.9MB, alloc=492.3MB, time=9.44 memory used=1082.4MB, alloc=516.3MB, time=11.89 memory used=1226.8MB, alloc=540.3MB, time=14.82 memory used=1380.9MB, alloc=564.3MB, time=18.45 memory used=1551.0MB, alloc=588.3MB, time=22.64 memory used=1745.0MB, alloc=612.3MB, time=27.42 memory used=1963.0MB, alloc=612.3MB, time=32.72 memory used=2181.0MB, alloc=636.3MB, time=38.02 memory used=2422.9MB, alloc=636.3MB, time=43.90 memory used=2664.7MB, alloc=636.3MB, time=49.75 memory used=2906.5MB, alloc=660.3MB, time=55.70 memory used=3172.4MB, alloc=660.3MB, time=61.96 memory used=3438.2MB, alloc=684.3MB, time=67.93 N1 := 9307 > GB := Basis(F, plex(op(vars))); 6 3 4 3 2 3 GB := [121 x y - 576 x y, 16 x y + x y , 1331 x y + 884736 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3757.1MB, alloc=684.3MB, time=72.43 N2 := 1085 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 3 3 2 H := [16 x z + y z , -11 x y - 6 x y z, 8 y z + 8 z, -5 x , -19 z - 10 y, 2 3 -8 x z - 10 y ] > J:=[op(GB),op(G)]; 6 3 4 3 2 3 3 J := [121 x y - 576 x y, 16 x y + x y , 1331 y x + 884736 z, -5 x , 2 2 3 -19 z - 10 y, -8 x z - 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 := [6, 14, 19, 4, 3, 3, 3, 2/3, 5/6, 5/6, 5/12, 1/2, 7/12, 6, 13, 24, 7, 6, 3, 2, 5/6, 5/6, 1/2, 7/12, 7/12, 1/4, 1, -5, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=4006.9MB, alloc=684.3MB, time=74.23 |\^/| 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(); 1428366250 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 4 3 F := [-19 x y z - 3 x y, -17 x - 6 y z , -3 y - 20 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 4 G := [9 x y - 12 x y, 16 y - 12 x y z, 8 y z + 20 z ] > Problem := [F,G]; 2 4 2 4 3 Problem := [[-19 x y z - 3 x y, -17 x - 6 y z , -3 y - 20 z ], 3 4 3 4 [9 x y - 12 x y, 16 y - 12 x y z, 8 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=0.14 memory used=26.6MB, alloc=32.3MB, time=0.36 memory used=48.3MB, alloc=32.3MB, time=0.55 memory used=68.7MB, alloc=56.3MB, time=0.74 memory used=109.0MB, alloc=60.3MB, time=1.10 memory used=145.4MB, alloc=84.3MB, time=1.44 memory used=205.3MB, alloc=92.3MB, time=2.01 memory used=269.2MB, alloc=116.3MB, time=2.56 memory used=350.9MB, alloc=116.3MB, time=3.31 memory used=428.2MB, alloc=372.3MB, time=4.03 memory used=514.5MB, alloc=396.3MB, time=4.75 memory used=617.1MB, alloc=420.3MB, time=5.69 memory used=739.6MB, alloc=444.3MB, time=6.85 memory used=887.4MB, alloc=468.3MB, time=8.23 memory used=1042.8MB, alloc=492.3MB, time=9.74 memory used=1178.2MB, alloc=492.3MB, time=11.05 memory used=1318.4MB, alloc=516.3MB, time=12.45 memory used=1481.1MB, alloc=540.3MB, time=14.09 memory used=1664.9MB, alloc=564.3MB, time=16.24 memory used=1854.4MB, alloc=588.3MB, time=18.50 memory used=2061.0MB, alloc=612.3MB, time=20.83 memory used=2237.9MB, alloc=636.3MB, time=23.03 memory used=2398.1MB, alloc=660.3MB, time=25.11 memory used=2541.6MB, alloc=684.3MB, time=26.96 memory used=2692.2MB, alloc=708.3MB, time=29.81 memory used=2929.7MB, alloc=732.3MB, time=35.14 memory used=3115.3MB, alloc=756.3MB, time=39.77 memory used=3383.8MB, alloc=780.3MB, time=46.68 memory used=3657.8MB, alloc=804.3MB, time=54.08 memory used=3942.2MB, alloc=828.3MB, time=62.05 memory used=4250.4MB, alloc=852.3MB, time=70.64 memory used=4582.6MB, alloc=876.3MB, time=79.87 memory used=4938.7MB, alloc=900.3MB, time=89.74 memory used=5318.9MB, alloc=924.3MB, time=100.28 memory used=5722.8MB, alloc=948.3MB, time=111.58 memory used=6150.7MB, alloc=948.3MB, time=123.39 memory used=6578.7MB, alloc=948.3MB, time=135.22 memory used=7006.6MB, alloc=972.3MB, time=147.05 memory used=7458.3MB, alloc=972.3MB, time=159.47 memory used=7909.9MB, alloc=972.3MB, time=171.84 memory used=8361.3MB, alloc=996.3MB, time=184.16 memory used=8836.7MB, alloc=996.3MB, time=197.11 memory used=9311.9MB, alloc=1020.3MB, time=209.83 memory used=9810.9MB, alloc=1020.3MB, time=223.12 memory used=10309.9MB, alloc=1044.3MB, time=236.47 memory used=10832.9MB, alloc=1068.3MB, time=250.18 memory used=11380.2MB, alloc=1092.3MB, time=264.06 N1 := 17309 > GB := Basis(F, plex(op(vars))); 32 5 7 GB := [9729382913438149099 x - 1530550080 x , 6137 x + 54 x y, 9 6 4 5 4 2 4 3 -27455 x + 81 y , 170 z x - 9 y , 17 x + 6 z y, 3 y + 20 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=11983.9MB, alloc=1092.3MB, time=272.78 memory used=12576.2MB, alloc=1116.3MB, time=278.83 memory used=13260.3MB, alloc=1140.3MB, time=285.50 memory used=13960.6MB, alloc=1164.3MB, time=292.81 memory used=14623.9MB, alloc=1188.3MB, time=298.52 memory used=15349.3MB, alloc=1212.3MB, time=306.04 |\^/| 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(); 1428366550 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 F := [-3 y z - 14 y, 20 x z - 15 y, -8 x z - 17 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 2 2 G := [-8 y z - 16 y, 2 y z + 2 y , -6 y + 19 y z ] > Problem := [F,G]; 2 3 Problem := [[-3 y z - 14 y, 20 x z - 15 y, -8 x z - 17 x y], 3 2 2 4 2 2 [-8 y z - 16 y, 2 y z + 2 y , -6 y + 19 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.6MB, alloc=32.3MB, time=0.41 memory used=47.8MB, alloc=32.3MB, time=0.66 memory used=67.6MB, alloc=56.3MB, time=0.90 memory used=107.1MB, alloc=60.3MB, time=1.35 memory used=144.5MB, alloc=60.3MB, time=1.80 memory used=179.9MB, alloc=84.3MB, time=2.22 memory used=222.8MB, alloc=84.3MB, time=2.71 memory used=282.0MB, alloc=116.3MB, time=3.47 memory used=359.2MB, alloc=116.3MB, time=4.43 memory used=434.8MB, alloc=140.3MB, time=5.45 memory used=521.9MB, alloc=420.3MB, time=6.57 memory used=639.0MB, alloc=444.3MB, time=8.09 memory used=778.1MB, alloc=468.3MB, time=10.00 memory used=921.8MB, alloc=492.3MB, time=11.63 memory used=1076.7MB, alloc=516.3MB, time=13.37 memory used=1241.1MB, alloc=540.3MB, time=15.26 memory used=1414.0MB, alloc=564.3MB, time=17.34 memory used=1594.9MB, alloc=588.3MB, time=19.47 memory used=1782.3MB, alloc=612.3MB, time=21.73 memory used=1977.2MB, alloc=636.3MB, time=24.13 memory used=2177.7MB, alloc=660.3MB, time=26.63 memory used=2384.6MB, alloc=684.3MB, time=29.23 memory used=2592.5MB, alloc=708.3MB, time=32.12 memory used=2780.0MB, alloc=732.3MB, time=35.97 memory used=2971.4MB, alloc=756.3MB, time=40.34 memory used=3172.6MB, alloc=780.3MB, time=45.32 memory used=3385.5MB, alloc=804.3MB, time=50.66 memory used=3611.8MB, alloc=828.3MB, time=56.26 memory used=3851.3MB, alloc=852.3MB, time=62.31 memory used=4104.8MB, alloc=876.3MB, time=68.78 memory used=4372.7MB, alloc=900.3MB, time=75.72 memory used=4655.4MB, alloc=924.3MB, time=83.13 memory used=4953.3MB, alloc=948.3MB, time=90.98 memory used=5266.4MB, alloc=972.3MB, time=99.23 memory used=5594.4MB, alloc=996.3MB, time=107.99 memory used=5936.7MB, alloc=1020.3MB, time=117.16 memory used=6290.6MB, alloc=1044.3MB, time=126.99 memory used=6668.5MB, alloc=1068.3MB, time=137.47 memory used=7070.2MB, alloc=1092.3MB, time=148.58 memory used=7496.0MB, alloc=1116.3MB, time=160.34 memory used=7945.6MB, alloc=1140.3MB, time=172.81 memory used=8419.3MB, alloc=1164.3MB, time=185.82 memory used=8916.8MB, alloc=1188.3MB, time=199.47 memory used=9438.4MB, alloc=1212.3MB, time=213.72 memory used=9983.9MB, alloc=1236.3MB, time=228.72 memory used=10553.2MB, alloc=1260.3MB, time=244.21 memory used=11146.6MB, alloc=1284.3MB, time=260.34 memory used=11763.8MB, alloc=1308.3MB, time=277.10 memory used=12405.1MB, alloc=1308.3MB, time=294.61 |\^/| 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(); 1428366850 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 F := [8 x - 7 x y, 4 x y + 2 z, -20 y - 16 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 G := [17 y z - 17 y z , 8 x - 5 x y, -14 x z - 19 y] > Problem := [F,G]; 2 3 3 Problem := [[8 x - 7 x y, 4 x y + 2 z, -20 y - 16 z ], 3 2 2 3 3 [17 y z - 17 y z , 8 x - 5 x y, -14 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=0.15 memory used=26.1MB, alloc=32.3MB, time=0.40 memory used=48.0MB, alloc=32.3MB, time=0.66 memory used=69.3MB, alloc=56.3MB, time=0.96 memory used=110.8MB, alloc=84.3MB, time=1.63 N1 := 1027 > GB := Basis(F, plex(op(vars))); 7 4 2 6 3 2 GB := [32 x - 5 x , -8 x + 7 x y, -16384 x + 1715 y , 16 x + 7 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=168.0MB, alloc=84.3MB, time=2.50 memory used=226.8MB, alloc=84.3MB, time=3.24 memory used=281.8MB, alloc=108.3MB, time=4.00 memory used=356.0MB, alloc=132.3MB, time=5.86 N2 := 1813 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 3 2 2 H := [8 x - 7 x y, 4 x y + 2 z, -20 y - 16 z , 17 y z - 17 y z , 3 3 8 x - 5 x y, -14 x z - 19 y] > J:=[op(GB),op(G)]; 7 4 2 6 3 2 J := [32 x - 5 x , -8 x + 7 x y, -16384 x + 1715 y , 16 x + 7 z, 3 2 2 3 3 17 y z - 17 y z , 8 x - 5 x y, -14 x z - 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 := [6, 14, 18, 4, 3, 3, 3, 2/3, 1, 2/3, 1/2, 7/12, 5/12, 7, 14, 28, 7, 7, 3, 2, 6/7, 5/7, 3/7, 9/14, 3/7, 2/7, 0, -10, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=414.7MB, alloc=132.3MB, time=7.10 |\^/| 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(); 1428366857 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 3 2 F := [17 x y z - 9 x , -8 x + 19 y , 8 x - 9 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 3 4 G := [2 x z + 12 x y z, 2 y - 16 x , -7 x z - y ] > Problem := [F,G]; 2 2 4 2 3 2 Problem := [[17 x y z - 9 x , -8 x + 19 y , 8 x - 9 x ], 2 2 4 3 3 4 [2 x z + 12 x y z, 2 y - 16 x , -7 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=0.13 memory used=26.1MB, alloc=32.3MB, time=0.34 memory used=47.6MB, alloc=32.3MB, time=0.52 memory used=68.4MB, alloc=32.3MB, time=0.70 memory used=89.2MB, alloc=60.3MB, time=0.89 memory used=131.1MB, alloc=60.3MB, time=1.28 memory used=172.2MB, alloc=84.3MB, time=1.71 memory used=231.4MB, alloc=84.3MB, time=2.33 memory used=286.3MB, alloc=108.3MB, time=2.92 memory used=369.4MB, alloc=116.3MB, time=3.68 memory used=439.6MB, alloc=140.3MB, time=4.51 memory used=519.1MB, alloc=164.3MB, time=5.89 memory used=610.5MB, alloc=188.3MB, time=7.83 memory used=726.1MB, alloc=188.3MB, time=10.19 memory used=841.7MB, alloc=212.3MB, time=12.23 N1 := 3607 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 2 2 2 2 GB := [8 x - 9 x , -81 x + 152 y , 1377 x z - 1216 x y, 17 x y z - 9 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=955.1MB, alloc=212.3MB, time=13.36 memory used=1116.5MB, alloc=468.3MB, time=14.83 memory used=1278.4MB, alloc=492.3MB, time=16.29 memory used=1458.7MB, alloc=516.3MB, time=17.66 memory used=1663.6MB, alloc=540.3MB, time=19.06 memory used=1882.8MB, alloc=564.3MB, time=21.34 memory used=2106.0MB, alloc=588.3MB, time=23.81 memory used=2337.1MB, alloc=612.3MB, time=26.44 memory used=2581.5MB, alloc=636.3MB, time=29.23 memory used=2794.4MB, alloc=660.3MB, time=33.65 memory used=3006.4MB, alloc=684.3MB, time=38.61 memory used=3224.5MB, alloc=708.3MB, time=44.07 memory used=3447.6MB, alloc=732.3MB, time=50.21 memory used=3694.7MB, alloc=756.3MB, time=56.94 memory used=3965.7MB, alloc=780.3MB, time=64.25 memory used=4260.6MB, alloc=804.3MB, time=72.23 memory used=4579.5MB, alloc=828.3MB, time=80.80 memory used=4922.3MB, alloc=852.3MB, time=89.98 memory used=5289.2MB, alloc=876.3MB, time=99.87 memory used=5679.9MB, alloc=900.3MB, time=110.27 memory used=6094.5MB, alloc=900.3MB, time=121.09 memory used=6509.2MB, alloc=924.3MB, time=131.68 memory used=6947.9MB, alloc=948.3MB, time=142.70 memory used=7410.7MB, alloc=972.3MB, time=153.69 N2 := 12761 #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 4 2 3 2 2 2 H := [17 x y z - 9 x , -8 x + 19 y , 8 x - 9 x , 2 x z + 12 x y z, 4 3 3 4 2 y - 16 x , -7 x z - y ] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 2 2 2 J := [8 x - 9 x , -81 x + 152 y , 1377 x z - 1216 x y, 17 x y z - 9 x , 2 2 4 3 3 4 2 x z + 12 x y z, 2 y - 16 x , -7 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 := [6, 14, 23, 4, 4, 4, 2, 1, 5/6, 1/2, 3/4, 5/12, 1/3, 7, 17, 25, 4, 3, 4, 2, 1, 6/7, 4/7, 11/14, 3/7, 5/14, -3, -2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=7550.0MB, alloc=972.3MB, time=156.37 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428367011 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 4 2 F := [8 x - 13 x y, 20 x y - 9 x, -18 x - 2 x y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [-4 x y z + 9 z, 13 x z - 19 z , -8 x z + 4 z] > Problem := [F,G]; 4 3 2 4 2 Problem := [[8 x - 13 x y, 20 x y - 9 x, -18 x - 2 x y z], 3 3 2 [-4 x y z + 9 z, 13 x z - 19 z , -8 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=0.15 memory used=26.4MB, alloc=32.3MB, time=0.37 memory used=48.4MB, alloc=32.3MB, time=0.58 memory used=68.4MB, alloc=56.3MB, time=0.80 N1 := 685 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [160 x - 117 x, -8 x + 13 x y, 1521 x + 64 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.8MB, alloc=60.3MB, time=1.27 memory used=150.3MB, alloc=84.3MB, time=1.67 N2 := 401 #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)]; 4 3 2 4 2 H := [8 x - 13 x y, 20 x y - 9 x, -18 x - 2 x y z, -4 x y z + 9 z, 3 3 2 13 x z - 19 z , -8 x z + 4 z] > J:=[op(GB),op(G)]; 3 2 2 J := [160 x - 117 x, -8 x + 13 x y, 1521 x + 64 x z, -4 x y z + 9 z, 3 3 2 13 x z - 19 z , -8 x 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, 14, 21, 4, 4, 2, 3, 1, 2/3, 2/3, 3/4, 1/3, 7/12, 6, 12, 17, 4, 3, 1, 3, 1, 1/3, 2/3, 3/4, 1/6, 7/12, 2, 4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=152.0MB, alloc=84.3MB, time=1.70 |\^/| 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(); 1428367012 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 F := [-20 x z + 18 x z, 11 x y - 4 x y, -16 x y + 12 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 3 2 G := [-2 z - 11 y z , 5 x y + 5, -20 x y + 6 x y z ] > Problem := [F,G]; 3 3 3 2 2 Problem := [[-20 x z + 18 x z, 11 x y - 4 x y, -16 x y + 12 y z ], 4 2 3 3 2 [-2 z - 11 y z , 5 x y + 5, -20 x y + 6 x y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.11 memory used=26.3MB, alloc=32.3MB, time=0.29 memory used=47.7MB, alloc=32.3MB, time=0.46 memory used=68.2MB, alloc=32.3MB, time=0.63 memory used=88.1MB, alloc=32.3MB, time=0.79 memory used=106.9MB, alloc=56.3MB, time=0.96 memory used=147.6MB, alloc=60.3MB, time=1.36 memory used=187.3MB, alloc=84.3MB, time=1.79 memory used=246.3MB, alloc=108.3MB, time=2.44 memory used=322.7MB, alloc=132.3MB, time=3.32 memory used=412.3MB, alloc=164.3MB, time=4.32 memory used=507.3MB, alloc=188.3MB, time=5.64 memory used=609.2MB, alloc=212.3MB, time=7.42 memory used=722.1MB, alloc=236.3MB, time=9.86 memory used=854.4MB, alloc=260.3MB, time=12.85 memory used=1010.7MB, alloc=260.3MB, time=16.36 memory used=1166.9MB, alloc=260.3MB, time=19.86 memory used=1323.1MB, alloc=284.3MB, time=23.35 memory used=1503.3MB, alloc=284.3MB, time=27.32 memory used=1683.4MB, alloc=284.3MB, time=31.18 memory used=1863.4MB, alloc=308.3MB, time=34.90 memory used=2067.6MB, alloc=332.3MB, time=38.54 N1 := 7295 > GB := Basis(F, plex(op(vars))); 4 2 3 2 2 3 GB := [6400 x y - 8019 x y, -160 x y + 297 x y , 11 x y - 4 x y, 3 2 2 3 2 6400 x y z - 8019 x y z, -160 x y z + 297 x y z, -640 x y + 891 x y z , 2 2 3 33 y z - 16 x y, 10 x z - 9 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2158.0MB, alloc=332.3MB, time=39.57 memory used=2391.5MB, alloc=588.3MB, time=41.79 memory used=2645.6MB, alloc=612.3MB, time=44.77 memory used=2894.4MB, alloc=636.3MB, time=47.72 memory used=3138.4MB, alloc=660.3MB, time=50.75 memory used=3370.2MB, alloc=684.3MB, time=54.79 memory used=3586.1MB, alloc=708.3MB, time=59.59 memory used=3806.4MB, alloc=732.3MB, time=64.76 memory used=4035.8MB, alloc=756.3MB, time=70.33 memory used=4272.5MB, alloc=780.3MB, time=76.60 memory used=4533.3MB, alloc=804.3MB, time=83.48 memory used=4818.0MB, alloc=828.3MB, time=90.96 memory used=5126.6MB, alloc=852.3MB, time=99.03 memory used=5459.1MB, alloc=876.3MB, time=107.73 memory used=5815.6MB, alloc=900.3MB, time=117.06 memory used=6196.1MB, alloc=924.3MB, time=127.07 memory used=6600.4MB, alloc=948.3MB, time=137.55 memory used=7028.8MB, alloc=972.3MB, time=148.65 memory used=7481.0MB, alloc=996.3MB, time=160.30 memory used=7957.1MB, alloc=996.3MB, time=172.60 memory used=8433.3MB, alloc=1020.3MB, time=184.85 memory used=8933.4MB, alloc=1020.3MB, time=197.58 memory used=9433.4MB, alloc=1020.3MB, time=210.27 memory used=9933.2MB, alloc=1044.3MB, time=222.90 memory used=10456.9MB, alloc=1044.3MB, time=236.10 memory used=10980.4MB, alloc=1068.3MB, time=249.58 memory used=11528.0MB, alloc=1068.3MB, time=263.27 memory used=12075.5MB, alloc=1092.3MB, time=276.83 memory used=12647.3MB, alloc=1116.3MB, time=290.45 N2 := 18413 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 3 2 2 4 2 H := [-20 x z + 18 x z, 11 x y - 4 x y, -16 x y + 12 y z , -2 z - 11 y z , 3 3 2 5 x y + 5, -20 x y + 6 x y z ] > J:=[op(GB),op(G)]; 4 2 3 2 2 3 J := [6400 x y - 8019 x y, -160 x y + 297 x y , 11 x y - 4 x y, 3 2 2 3 2 6400 x y z - 8019 x y z, -160 x y z + 297 x y z, -640 x y + 891 x y z , 2 2 3 4 2 3 33 y z - 16 x y, 10 x z - 9 x z, -2 z - 11 y z , 5 x y + 5, 3 2 -20 x y + 6 x 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 := [6, 14, 24, 4, 3, 3, 4, 5/6, 5/6, 2/3, 2/3, 2/3, 1/2, 11, 27, 46, 5, 4, 3, 4, 10/11, 10/11, 7/11, 9/11, 9/11, 1/2, -13, -22, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=13073.1MB, alloc=1116.3MB, time=299.02 |\^/| 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(); 1428367307 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 F := [-2 y z + 17 y z , 16 z + 14 x z, -19 + 12 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 G := [-9 x y - 15 x z, -15 x y z - 20 y, x y - 5 x z ] > Problem := [F,G]; 2 2 4 Problem := [[-2 y z + 17 y z , 16 z + 14 x z, -19 + 12 x], 3 3 2 2 2 [-9 x y - 15 x z, -15 x y z - 20 y, x y - 5 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.38 memory used=47.7MB, alloc=32.3MB, time=0.56 memory used=67.5MB, alloc=56.3MB, time=0.74 memory used=107.8MB, alloc=60.3MB, time=1.09 memory used=146.5MB, alloc=60.3MB, time=1.42 memory used=183.5MB, alloc=84.3MB, time=1.75 memory used=240.3MB, alloc=84.3MB, time=2.26 memory used=296.0MB, alloc=116.3MB, time=2.79 memory used=373.2MB, alloc=140.3MB, time=3.68 memory used=473.4MB, alloc=164.3MB, time=4.77 memory used=589.2MB, alloc=188.3MB, time=6.02 memory used=717.6MB, alloc=212.3MB, time=7.45 memory used=846.4MB, alloc=492.3MB, time=8.91 memory used=994.5MB, alloc=516.3MB, time=10.87 memory used=1137.7MB, alloc=540.3MB, time=13.56 memory used=1287.9MB, alloc=564.3MB, time=16.80 memory used=1446.1MB, alloc=588.3MB, time=20.83 memory used=1626.5MB, alloc=612.3MB, time=25.44 memory used=1830.9MB, alloc=636.3MB, time=30.65 memory used=2059.2MB, alloc=660.3MB, time=36.45 memory used=2311.5MB, alloc=660.3MB, time=42.82 memory used=2563.7MB, alloc=660.3MB, time=49.17 memory used=2815.9MB, alloc=684.3MB, time=55.55 memory used=3092.1MB, alloc=684.3MB, time=62.51 memory used=3368.2MB, alloc=708.3MB, time=69.57 memory used=3668.4MB, alloc=708.3MB, time=76.73 memory used=3968.8MB, alloc=732.3MB, time=82.99 N1 := 9997 > GB := Basis(F, plex(op(vars))); 4 2 2 4 GB := [12 x - 19, 768 y z + 653429 y z, -2 y z + 17 y z , 96 z + 133 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4278.8MB, alloc=732.3MB, time=86.45 memory used=4652.3MB, alloc=756.3MB, time=91.02 memory used=5019.7MB, alloc=780.3MB, time=97.22 memory used=5337.1MB, alloc=804.3MB, time=105.24 memory used=5660.4MB, alloc=828.3MB, time=113.89 memory used=6007.7MB, alloc=852.3MB, time=123.06 memory used=6378.9MB, alloc=876.3MB, time=133.00 memory used=6774.0MB, alloc=900.3MB, time=143.40 memory used=7193.1MB, alloc=924.3MB, time=154.36 memory used=7636.4MB, alloc=948.3MB, time=165.58 N2 := 10035 #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 4 3 3 H := [-2 y z + 17 y z , 16 z + 14 x z, 12 x - 19, -9 x y - 15 x z, 2 2 2 -15 x y z - 20 y, x y - 5 x z ] > J:=[op(GB),op(G)]; 4 2 2 4 J := [12 x - 19, 768 y z + 653429 y z, -2 y z + 17 y z , 96 z + 133 z, 3 3 2 2 2 -9 x y - 15 x z, -15 x y z - 20 y, x y - 5 x z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 19, 4, 3, 2, 4, 5/6, 2/3, 5/6, 7/12, 1/2, 7/12, 7, 15, 24, 5, 3, 4, 4, 4/7, 5/7, 6/7, 3/7, 4/7, 9/14, -1, -5, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=7888.6MB, alloc=948.3MB, time=170.81 |\^/| 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(); 1428367475 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 F := [-16 x y - 2 y , -9 y z + 3 z , 11 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 G := [-6 x y - 16 y , 7 y z + 4 x, -13 x y z + 13 x y z] > Problem := [F,G]; 2 2 2 4 2 Problem := [[-16 x y - 2 y , -9 y z + 3 z , 11 z ], 3 4 2 [-6 x y - 16 y , 7 y z + 4 x, -13 x y z + 13 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.37 memory used=48.7MB, alloc=32.3MB, time=0.59 memory used=69.3MB, alloc=56.3MB, time=0.83 memory used=111.0MB, alloc=60.3MB, time=1.27 memory used=146.7MB, alloc=84.3MB, time=1.67 memory used=198.0MB, alloc=108.3MB, time=2.49 N1 := 1813 > GB := Basis(F, plex(op(vars))); 2 2 GB := [8 x y + y , z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=271.8MB, alloc=108.3MB, time=3.46 N2 := 253 #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 4 2 3 4 H := [-16 x y - 2 y , -9 y z + 3 z , 11 z , -6 x y - 16 y , 7 z y + 4 x, 2 -13 x y z + 13 x y z] > J:=[op(GB),op(G)]; 2 2 3 4 2 J := [8 x y + y , z , -6 x y - 16 y , 7 z y + 4 x, -13 x y z + 13 x 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 := [6, 13, 18, 4, 1, 4, 4, 2/3, 5/6, 2/3, 5/12, 2/3, 1/2, 5, 11, 14, 4, 1, 4, 2, 4/5, 4/5, 3/5, 1/2, 7/10, 2/5, 2, 4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=282.3MB, alloc=108.3MB, time=3.58 |\^/| 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(); 1428367478 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 3 2 F := [-16 y z + 3 y , -12 x y - 17 y z , -5 y + 7 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 4 G := [12 y z + 20 y , -9 x z + 5 x y z , -9 y - 16 y z] > Problem := [F,G]; 3 3 3 2 2 3 2 Problem := [[-16 y z + 3 y , -12 x y - 17 y z , -5 y + 7 y z], 3 2 3 2 4 [12 y z + 20 y , -9 x z + 5 x y z , -9 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=0.11 memory used=26.0MB, alloc=32.3MB, time=0.28 memory used=46.9MB, alloc=32.3MB, time=0.47 memory used=65.7MB, alloc=56.3MB, time=0.70 memory used=104.1MB, alloc=60.3MB, time=1.03 memory used=138.3MB, alloc=60.3MB, time=1.32 memory used=171.0MB, alloc=84.3MB, time=1.62 memory used=224.0MB, alloc=84.3MB, time=2.09 memory used=278.2MB, alloc=92.3MB, time=2.59 memory used=330.5MB, alloc=116.3MB, time=3.08 memory used=405.1MB, alloc=116.3MB, time=3.75 memory used=478.0MB, alloc=116.3MB, time=4.43 memory used=550.9MB, alloc=140.3MB, time=5.12 memory used=643.9MB, alloc=140.3MB, time=5.99 memory used=734.0MB, alloc=164.3MB, time=6.87 memory used=836.6MB, alloc=420.3MB, time=7.89 memory used=943.9MB, alloc=444.3MB, time=8.94 memory used=1071.0MB, alloc=468.3MB, time=10.19 memory used=1217.2MB, alloc=492.3MB, time=11.74 memory used=1381.2MB, alloc=516.3MB, time=13.51 memory used=1563.3MB, alloc=540.3MB, time=15.41 memory used=1761.0MB, alloc=564.3MB, time=17.58 memory used=1982.1MB, alloc=588.3MB, time=20.14 memory used=2196.0MB, alloc=612.3MB, time=22.71 memory used=2412.1MB, alloc=636.3MB, time=25.38 memory used=2632.0MB, alloc=660.3MB, time=28.12 memory used=2855.7MB, alloc=684.3MB, time=30.90 memory used=3088.6MB, alloc=708.3MB, time=33.74 memory used=3318.2MB, alloc=732.3MB, time=36.69 memory used=3546.6MB, alloc=756.3MB, time=39.70 memory used=3778.2MB, alloc=780.3MB, time=42.80 memory used=4019.5MB, alloc=804.3MB, time=45.92 memory used=4223.1MB, alloc=828.3MB, time=50.33 memory used=4426.4MB, alloc=852.3MB, time=55.23 memory used=4638.8MB, alloc=876.3MB, time=60.63 memory used=4862.6MB, alloc=900.3MB, time=66.45 memory used=5097.9MB, alloc=924.3MB, time=72.63 memory used=5346.1MB, alloc=948.3MB, time=79.36 memory used=5608.1MB, alloc=972.3MB, time=86.44 memory used=5883.8MB, alloc=996.3MB, time=93.96 memory used=6173.9MB, alloc=1020.3MB, time=101.99 memory used=6478.8MB, alloc=1044.3MB, time=110.49 memory used=6798.0MB, alloc=1068.3MB, time=119.28 memory used=7131.9MB, alloc=1092.3MB, time=128.52 memory used=7481.0MB, alloc=1116.3MB, time=138.35 memory used=7845.3MB, alloc=1140.3MB, time=148.57 memory used=8224.7MB, alloc=1164.3MB, time=159.27 memory used=8613.9MB, alloc=1188.3MB, time=170.67 memory used=9023.5MB, alloc=1212.3MB, time=182.70 memory used=9457.0MB, alloc=1236.3MB, time=195.45 memory used=9914.5MB, alloc=1260.3MB, time=208.95 memory used=10396.0MB, alloc=1284.3MB, time=223.01 memory used=10901.3MB, alloc=1308.3MB, time=237.73 memory used=11430.6MB, alloc=1332.3MB, time=253.09 memory used=11983.8MB, alloc=1356.3MB, time=269.22 memory used=12561.0MB, alloc=1380.3MB, time=285.86 memory used=13162.2MB, alloc=1404.3MB, time=303.20 |\^/| 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(); 1428367778 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 2 3 2 F := [19 z - 18 x , -14 y - 8 x z , -13 y z - 17 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 4 G := [y z - 20 x y , -15 x z + 14 x z , -4 y - 17 y z] > Problem := [F,G]; 3 2 4 2 3 2 Problem := [[19 z - 18 x , -14 y - 8 x z , -13 y z - 17 x y], 3 2 3 3 4 [y z - 20 x y , -15 x z + 14 x z , -4 y - 17 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.4MB, alloc=32.3MB, time=0.40 memory used=47.5MB, alloc=32.3MB, time=0.63 memory used=67.9MB, alloc=56.3MB, time=0.87 memory used=109.8MB, alloc=60.3MB, time=1.36 memory used=148.5MB, alloc=84.3MB, time=1.80 memory used=207.5MB, alloc=92.3MB, time=2.53 memory used=270.6MB, alloc=116.3MB, time=3.22 memory used=351.8MB, alloc=116.3MB, time=4.16 memory used=430.0MB, alloc=396.3MB, time=5.10 memory used=537.7MB, alloc=420.3MB, time=6.19 memory used=661.0MB, alloc=444.3MB, time=7.71 memory used=804.9MB, alloc=468.3MB, time=9.48 memory used=946.8MB, alloc=468.3MB, time=11.38 memory used=1083.3MB, alloc=492.3MB, time=13.04 memory used=1212.9MB, alloc=516.3MB, time=14.49 memory used=1332.1MB, alloc=516.3MB, time=16.03 memory used=1443.6MB, alloc=516.3MB, time=17.21 memory used=1566.9MB, alloc=516.3MB, time=18.54 memory used=1661.4MB, alloc=540.3MB, time=19.42 memory used=1745.0MB, alloc=540.3MB, time=20.12 memory used=1820.6MB, alloc=564.3MB, time=20.85 memory used=1902.3MB, alloc=564.3MB, time=21.72 memory used=1975.9MB, alloc=564.3MB, time=22.64 memory used=2046.3MB, alloc=564.3MB, time=23.59 memory used=2094.1MB, alloc=564.3MB, time=24.26 memory used=2156.2MB, alloc=564.3MB, time=25.17 memory used=2360.2MB, alloc=588.3MB, time=27.34 memory used=2558.7MB, alloc=612.3MB, time=29.30 memory used=2745.5MB, alloc=636.3MB, time=31.44 memory used=2932.8MB, alloc=660.3MB, time=33.47 memory used=3110.3MB, alloc=684.3MB, time=35.61 memory used=3261.5MB, alloc=684.3MB, time=37.41 memory used=3428.7MB, alloc=684.3MB, time=39.45 memory used=3551.9MB, alloc=684.3MB, time=41.12 memory used=3673.1MB, alloc=708.3MB, time=42.57 memory used=3777.6MB, alloc=708.3MB, time=44.05 memory used=3879.5MB, alloc=708.3MB, time=45.69 memory used=3980.6MB, alloc=732.3MB, time=47.14 memory used=4365.7MB, alloc=756.3MB, time=50.95 memory used=4749.3MB, alloc=780.3MB, time=55.23 memory used=5152.8MB, alloc=804.3MB, time=58.95 memory used=5507.2MB, alloc=828.3MB, time=63.03 memory used=5791.1MB, alloc=852.3MB, time=66.57 memory used=6098.3MB, alloc=876.3MB, time=70.01 memory used=6404.2MB, alloc=900.3MB, time=73.38 memory used=6684.8MB, alloc=924.3MB, time=77.36 memory used=6933.5MB, alloc=948.3MB, time=80.73 memory used=7136.9MB, alloc=972.3MB, time=83.79 memory used=7343.2MB, alloc=996.3MB, time=87.09 memory used=7537.6MB, alloc=1020.3MB, time=90.24 memory used=8128.5MB, alloc=1044.3MB, time=97.57 memory used=8736.9MB, alloc=1068.3MB, time=103.88 memory used=9307.3MB, alloc=1092.3MB, time=111.11 memory used=9845.5MB, alloc=1116.3MB, time=118.74 memory used=10337.4MB, alloc=1140.3MB, time=126.66 memory used=10802.8MB, alloc=1164.3MB, time=134.50 memory used=11250.4MB, alloc=1188.3MB, time=142.26 memory used=11683.3MB, alloc=1212.3MB, time=150.03 memory used=12101.4MB, alloc=1236.3MB, time=157.59 memory used=12508.4MB, alloc=1260.3MB, time=165.08 memory used=12961.4MB, alloc=1284.3MB, time=172.38 memory used=13520.0MB, alloc=1308.3MB, time=178.47 memory used=14110.5MB, alloc=1332.3MB, time=184.10 memory used=14717.1MB, alloc=1356.3MB, time=190.90 memory used=15176.2MB, alloc=1380.3MB, time=199.38 memory used=15738.7MB, alloc=1404.3MB, time=207.08 memory used=16116.3MB, alloc=1428.3MB, time=218.45 memory used=16472.6MB, alloc=1452.3MB, time=229.92 memory used=16826.8MB, alloc=1476.3MB, time=241.60 memory used=17185.6MB, alloc=1500.3MB, time=253.59 memory used=17552.3MB, alloc=1524.3MB, time=265.99 memory used=17928.9MB, alloc=1548.3MB, time=278.82 memory used=18315.3MB, alloc=1572.3MB, time=292.01 memory used=18713.3MB, alloc=1596.3MB, time=305.61 memory used=19122.8MB, alloc=1620.3MB, time=319.57 |\^/| 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(); 1428368078 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [-10 x y + 16 y z , -13 x y z - 12 y, -20 x y z - 16 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 G := [2 x - 19 y z , -5 y z, -10 y z - 11 x] > Problem := [F,G]; 3 2 2 2 2 Problem := [[-10 x y + 16 y z , -13 x y z - 12 y, -20 x y z - 16 x ], 3 2 3 3 [2 x - 19 y z , -5 y z, -10 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=0.15 memory used=26.7MB, alloc=32.3MB, time=0.39 memory used=48.2MB, alloc=32.3MB, time=0.64 memory used=68.2MB, alloc=32.3MB, time=0.88 memory used=87.5MB, alloc=56.3MB, time=1.12 memory used=127.8MB, alloc=60.3MB, time=1.59 memory used=166.7MB, alloc=60.3MB, time=2.10 memory used=204.1MB, alloc=84.3MB, time=2.64 memory used=262.6MB, alloc=92.3MB, time=3.34 memory used=319.3MB, alloc=116.3MB, time=4.01 memory used=396.3MB, alloc=116.3MB, time=4.80 memory used=471.2MB, alloc=140.3MB, time=5.51 memory used=566.4MB, alloc=164.3MB, time=6.49 memory used=665.2MB, alloc=444.3MB, time=7.63 memory used=806.4MB, alloc=468.3MB, time=8.96 memory used=955.4MB, alloc=492.3MB, time=10.58 memory used=1115.1MB, alloc=516.3MB, time=12.49 memory used=1286.4MB, alloc=540.3MB, time=14.48 memory used=1468.3MB, alloc=564.3MB, time=16.64 memory used=1662.2MB, alloc=588.3MB, time=19.07 memory used=1836.8MB, alloc=612.3MB, time=22.48 memory used=2015.4MB, alloc=636.3MB, time=26.33 memory used=2204.0MB, alloc=660.3MB, time=30.67 memory used=2404.3MB, alloc=684.3MB, time=35.54 memory used=2612.4MB, alloc=708.3MB, time=41.22 memory used=2844.5MB, alloc=732.3MB, time=47.50 memory used=3100.5MB, alloc=756.3MB, time=54.41 memory used=3380.5MB, alloc=780.3MB, time=61.92 memory used=3684.4MB, alloc=804.3MB, time=70.05 memory used=4012.3MB, alloc=828.3MB, time=78.92 memory used=4364.1MB, alloc=828.3MB, time=88.25 memory used=4715.8MB, alloc=852.3MB, time=97.60 memory used=5091.5MB, alloc=852.3MB, time=107.55 memory used=5467.2MB, alloc=852.3MB, time=117.49 memory used=5842.8MB, alloc=876.3MB, time=127.42 memory used=6242.3MB, alloc=876.3MB, time=138.08 memory used=6641.6MB, alloc=876.3MB, time=148.58 memory used=7040.7MB, alloc=900.3MB, time=159.06 memory used=7463.7MB, alloc=900.3MB, time=170.13 memory used=7886.5MB, alloc=924.3MB, time=181.19 memory used=8333.3MB, alloc=924.3MB, time=192.77 memory used=8780.1MB, alloc=948.3MB, time=204.31 memory used=9251.3MB, alloc=972.3MB, time=215.56 N1 := 16135 > GB := Basis(F, plex(op(vars))); 9 2 2 7 2 GB := [845 x - 1152 x , -13 x + 15 y, 65 x + 96 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 1465 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 H := [-10 x y + 16 y z , -13 x y z - 12 y, -20 x y z - 16 x , 2 3 3 3 -19 z y + 2 x , -5 y z, -10 y z - 11 x] > J:=[op(GB),op(G)]; 9 2 2 7 2 2 3 J := [845 x - 1152 x , -13 x + 15 y, 65 x + 96 x z, -19 z y + 2 x , 3 3 -5 y z, -10 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 := [6, 17, 23, 4, 3, 3, 3, 5/6, 1, 1, 6/13, 8/13, 6/13, 6, 13, 29, 9, 9, 3, 3, 5/6, 2/3, 2/3, 7/13, 4/13, 4/13, 4, -6, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=9581.8MB, alloc=972.3MB, time=220.41 |\^/| 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(); 1428368296 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [12 y z - 16 y z , 14 x z + 11 y, -14 x - 16 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 G := [5 y z + 13 x y, 15 z - 2 y, -18 y z + 12 y z] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[12 y z - 16 y z , 14 x z + 11 y, -14 x - 16 z ], 2 2 3 3 [5 y z + 13 x y, 15 z - 2 y, -18 y z + 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=0.16 memory used=26.6MB, alloc=32.3MB, time=0.37 memory used=48.3MB, alloc=32.3MB, time=0.56 memory used=68.7MB, alloc=32.3MB, time=0.73 memory used=88.2MB, alloc=56.3MB, time=0.92 memory used=128.3MB, alloc=60.3MB, time=1.27 memory used=165.9MB, alloc=84.3MB, time=1.61 memory used=218.6MB, alloc=84.3MB, time=2.09 memory used=276.4MB, alloc=92.3MB, time=2.64 memory used=333.7MB, alloc=116.3MB, time=3.17 memory used=412.6MB, alloc=116.3MB, time=3.89 memory used=489.0MB, alloc=140.3MB, time=4.61 memory used=577.4MB, alloc=140.3MB, time=5.44 memory used=660.1MB, alloc=420.3MB, time=6.25 memory used=780.0MB, alloc=444.3MB, time=7.38 memory used=916.9MB, alloc=468.3MB, time=8.74 memory used=1067.5MB, alloc=492.3MB, time=10.45 memory used=1228.5MB, alloc=516.3MB, time=12.29 memory used=1399.8MB, alloc=540.3MB, time=14.28 memory used=1580.0MB, alloc=564.3MB, time=16.49 memory used=1751.6MB, alloc=588.3MB, time=19.69 memory used=1925.3MB, alloc=612.3MB, time=23.43 memory used=2107.2MB, alloc=636.3MB, time=27.76 memory used=2301.3MB, alloc=660.3MB, time=32.74 memory used=2519.4MB, alloc=684.3MB, time=38.43 memory used=2761.4MB, alloc=708.3MB, time=44.51 memory used=3027.3MB, alloc=732.3MB, time=51.24 memory used=3317.1MB, alloc=756.3MB, time=58.44 memory used=3630.9MB, alloc=756.3MB, time=66.21 memory used=3944.6MB, alloc=780.3MB, time=73.96 memory used=4282.0MB, alloc=780.3MB, time=82.19 memory used=4619.6MB, alloc=804.3MB, time=90.37 memory used=4981.1MB, alloc=804.3MB, time=99.12 memory used=5342.6MB, alloc=828.3MB, time=107.09 N1 := 11237 > GB := Basis(F, plex(op(vars))); 12 6 8 2 6 2 2 GB := [3087 x + 3872 x , 1029 x + 968 x y, 343 x + 242 y , 14 z x + 11 y, 4 2 2 -49 x + 44 y z, 8 z + 7 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5548.1MB, alloc=828.3MB, time=109.90 memory used=5683.9MB, alloc=828.3MB, time=111.73 memory used=5803.1MB, alloc=828.3MB, time=113.40 memory used=5906.6MB, alloc=828.3MB, time=114.83 memory used=5999.1MB, alloc=828.3MB, time=116.16 memory used=6089.6MB, alloc=828.3MB, time=117.39 memory used=6172.5MB, alloc=828.3MB, time=118.54 memory used=6261.2MB, alloc=828.3MB, time=119.89 memory used=6331.8MB, alloc=828.3MB, time=121.15 memory used=6396.8MB, alloc=828.3MB, time=122.29 memory used=6444.6MB, alloc=828.3MB, time=123.28 memory used=6510.7MB, alloc=828.3MB, time=124.42 memory used=6569.0MB, alloc=828.3MB, time=125.55 memory used=6628.2MB, alloc=828.3MB, time=126.73 memory used=6852.2MB, alloc=828.3MB, time=129.39 memory used=7050.8MB, alloc=828.3MB, time=131.81 memory used=7264.0MB, alloc=828.3MB, time=134.43 memory used=7432.2MB, alloc=852.3MB, time=136.83 memory used=7621.3MB, alloc=852.3MB, time=139.53 memory used=7779.4MB, alloc=876.3MB, time=141.72 memory used=7925.1MB, alloc=876.3MB, time=143.83 memory used=8026.6MB, alloc=876.3MB, time=145.71 memory used=8153.1MB, alloc=876.3MB, time=147.84 memory used=8268.1MB, alloc=900.3MB, time=149.81 memory used=8370.1MB, alloc=900.3MB, time=151.67 memory used=8459.5MB, alloc=900.3MB, time=153.48 memory used=8895.0MB, alloc=924.3MB, time=158.44 memory used=9332.0MB, alloc=948.3MB, time=163.89 memory used=9729.8MB, alloc=972.3MB, time=168.91 memory used=10210.2MB, alloc=996.3MB, time=176.01 memory used=10651.4MB, alloc=1020.3MB, time=182.82 memory used=11081.5MB, alloc=1044.3MB, time=189.53 memory used=11499.0MB, alloc=1068.3MB, time=196.22 memory used=11907.6MB, alloc=1092.3MB, time=202.82 memory used=12308.5MB, alloc=1116.3MB, time=209.41 memory used=12709.4MB, alloc=1140.3MB, time=217.16 memory used=13034.9MB, alloc=1164.3MB, time=226.56 memory used=13356.1MB, alloc=1188.3MB, time=236.49 memory used=13681.9MB, alloc=1212.3MB, time=246.50 memory used=14015.8MB, alloc=1236.3MB, time=256.97 memory used=14360.3MB, alloc=1260.3MB, time=267.99 memory used=14716.3MB, alloc=1284.3MB, time=279.25 memory used=15085.2MB, alloc=1308.3MB, time=291.00 memory used=15465.8MB, alloc=1332.3MB, time=303.13 memory used=15859.9MB, alloc=1356.3MB, time=315.57 |\^/| 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(); 1428368596 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 F := [-2 y - 6 y z, -14 x z , -11 x y - 20] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 4 2 2 G := [-20 x y z + 5 x z , 15 x y z + 5 z, -9 x - 17 x z ] > Problem := [F,G]; 4 3 2 2 Problem := [[-2 y - 6 y z, -14 x z , -11 x y - 20], 2 3 2 4 2 2 [-20 x y z + 5 x z , 15 x y z + 5 z, -9 x - 17 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.4MB, alloc=32.3MB, time=0.37 memory used=48.0MB, alloc=32.3MB, time=0.62 memory used=68.7MB, alloc=56.3MB, time=0.89 memory used=111.5MB, alloc=60.3MB, time=1.48 N1 := 711 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=149.3MB, alloc=60.3MB, time=2.08 N2 := 85 #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)]; 4 3 2 2 2 3 H := [-2 y - 6 y z, -14 x z , -11 x y - 20, -20 x y z + 5 x z , 2 4 2 2 15 x y z + 5 z, -9 x - 17 x z ] > J:=[op(GB),op(G)]; 2 3 2 4 2 2 J := [1, -20 x y z + 5 x z , 15 x y z + 5 z, -9 x - 17 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 := [6, 14, 24, 4, 4, 4, 3, 5/6, 2/3, 5/6, 7/13, 5/13, 7/13, 4, 8, 12, 4, 4, 2, 3, 3/4, 1/2, 3/4, 5/7, 2/7, 5/7, 6, 12, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=154.7MB, alloc=60.3MB, time=2.17 |\^/| 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(); 1428368598 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 F := [-8 z + 2 x y, -2 y z - 19 x, 18 x y z + 7 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 G := [5 y - 4 x z , 16 x z, -8 x y z + 17 x z] > Problem := [F,G]; 4 2 3 2 2 Problem := [[-8 z + 2 x y, -2 y z - 19 x, 18 x y z + 7 x ], 4 2 2 2 [5 y - 4 x z , 16 x z, -8 x y z + 17 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=27.1MB, alloc=32.3MB, time=0.44 memory used=48.5MB, alloc=32.3MB, time=0.70 memory used=69.9MB, alloc=60.3MB, time=0.96 memory used=111.0MB, alloc=60.3MB, time=1.41 memory used=151.5MB, alloc=84.3MB, time=1.85 memory used=216.3MB, alloc=92.3MB, time=2.49 memory used=276.0MB, alloc=116.3MB, time=3.19 memory used=360.2MB, alloc=116.3MB, time=4.14 memory used=441.0MB, alloc=140.3MB, time=5.14 memory used=512.5MB, alloc=140.3MB, time=5.94 memory used=587.7MB, alloc=396.3MB, time=6.79 memory used=700.5MB, alloc=420.3MB, time=7.85 memory used=838.6MB, alloc=444.3MB, time=9.09 memory used=974.0MB, alloc=468.3MB, time=10.51 memory used=1105.4MB, alloc=492.3MB, time=11.67 memory used=1247.6MB, alloc=492.3MB, time=12.99 memory used=1370.4MB, alloc=516.3MB, time=14.19 memory used=1484.5MB, alloc=516.3MB, time=15.35 memory used=1585.0MB, alloc=540.3MB, time=16.27 memory used=1703.5MB, alloc=540.3MB, time=17.41 memory used=1781.9MB, alloc=540.3MB, time=18.15 memory used=1861.8MB, alloc=564.3MB, time=19.07 memory used=1949.3MB, alloc=564.3MB, time=20.07 memory used=2026.0MB, alloc=564.3MB, time=21.00 memory used=2094.1MB, alloc=564.3MB, time=21.87 memory used=2157.7MB, alloc=564.3MB, time=22.55 memory used=2232.9MB, alloc=564.3MB, time=23.44 memory used=2278.2MB, alloc=588.3MB, time=24.17 memory used=2342.5MB, alloc=588.3MB, time=25.02 memory used=2444.0MB, alloc=588.3MB, time=26.19 memory used=2512.8MB, alloc=588.3MB, time=27.19 memory used=2624.2MB, alloc=612.3MB, time=28.44 memory used=2872.9MB, alloc=636.3MB, time=31.31 memory used=3141.9MB, alloc=660.3MB, time=34.41 memory used=3441.2MB, alloc=684.3MB, time=37.29 memory used=3733.5MB, alloc=708.3MB, time=40.73 memory used=4029.6MB, alloc=732.3MB, time=44.41 memory used=4337.7MB, alloc=756.3MB, time=48.40 memory used=4596.3MB, alloc=780.3MB, time=54.18 memory used=4853.4MB, alloc=804.3MB, time=60.50 memory used=5116.3MB, alloc=828.3MB, time=67.32 memory used=5383.8MB, alloc=852.3MB, time=74.69 memory used=5661.1MB, alloc=876.3MB, time=82.61 memory used=5962.3MB, alloc=900.3MB, time=91.17 memory used=6287.5MB, alloc=924.3MB, time=100.46 memory used=6636.5MB, alloc=948.3MB, time=110.29 memory used=7009.6MB, alloc=972.3MB, time=120.78 memory used=7406.5MB, alloc=996.3MB, time=131.95 memory used=7827.4MB, alloc=1020.3MB, time=143.75 memory used=8272.3MB, alloc=1044.3MB, time=156.18 memory used=8741.0MB, alloc=1068.3MB, time=169.36 memory used=9233.6MB, alloc=1092.3MB, time=183.04 memory used=9750.1MB, alloc=1116.3MB, time=197.30 memory used=10290.3MB, alloc=1116.3MB, time=212.09 memory used=10830.3MB, alloc=1140.3MB, time=227.05 memory used=11394.3MB, alloc=1140.3MB, time=242.39 memory used=11958.1MB, alloc=1164.3MB, time=257.82 memory used=12545.9MB, alloc=1188.3MB, time=273.64 memory used=13157.7MB, alloc=1212.3MB, time=289.91 N1 := 17719 > GB := Basis(F, plex(op(vars))); 5 2 3 2 GB := [823543 x + 1800151923205512 x , 343 x + 526338 x y, 4 3 4 3 117649 x + 10527204229272 x z, 2 z y + 19 x, 2105352 z + 343 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=13838.6MB, alloc=1212.3MB, time=304.06 |\^/| 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(); 1428368898 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 3 F := [-15 x y + 11 y , 20 y z + 10 z , 15 x y + z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [18 x y z + 2 x y, 10 x - 4 y z, 4 y + 14 z ] > Problem := [F,G]; 3 3 2 2 3 3 Problem := [[-15 x y + 11 y , 20 y z + 10 z , 15 x y + z], 2 2 2 2 [18 x y z + 2 x y, 10 x - 4 y z, 4 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=0.16 memory used=26.4MB, alloc=32.3MB, time=0.42 memory used=48.2MB, alloc=32.3MB, time=0.68 memory used=68.2MB, alloc=56.3MB, time=0.92 memory used=108.7MB, alloc=60.3MB, time=1.40 memory used=147.4MB, alloc=84.3MB, time=1.82 memory used=205.8MB, alloc=92.3MB, time=2.51 memory used=264.7MB, alloc=92.3MB, time=3.23 memory used=321.0MB, alloc=116.3MB, time=3.90 memory used=397.3MB, alloc=140.3MB, time=4.94 memory used=492.7MB, alloc=164.3MB, time=6.31 memory used=601.8MB, alloc=188.3MB, time=7.88 memory used=710.9MB, alloc=212.3MB, time=9.94 N1 := 2621 > GB := Basis(F, plex(op(vars))); 3 3 4 3 3 GB := [15 x y - 11 y , 450 y - 1331 y , 15 y x + z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=847.2MB, alloc=212.3MB, time=11.76 memory used=978.8MB, alloc=468.3MB, time=13.23 N2 := 625 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 2 3 3 2 H := [-15 x y + 11 y , 20 y z + 10 z , 15 y x + z, 18 x y z + 2 x y, 2 2 2 10 x - 4 y z, 4 y + 14 z ] > J:=[op(GB),op(G)]; 3 3 4 3 3 2 J := [15 x y - 11 y , 450 y - 1331 y , 15 y x + z, 18 x y z + 2 x y, 2 2 2 10 x - 4 y z, 4 y + 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 := [6, 15, 20, 4, 3, 3, 3, 2/3, 1, 5/6, 5/12, 2/3, 1/2, 6, 14, 20, 4, 3, 4, 2, 2/3, 1, 2/3, 5/12, 3/4, 1/3, 1, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=979.0MB, alloc=468.3MB, time=13.24 |\^/| 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(); 1428368912 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 3 F := [10 y + 18 x y, 14 y z + 19 z , -13 y z + 6 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 G := [-20 x y + 8 y, 10 x y z - 12 z , x z + x ] > Problem := [F,G]; 3 3 4 3 Problem := [[10 y + 18 x y, 14 y z + 19 z , -13 y z + 6 x], 3 2 3 3 2 [-20 x y + 8 y, 10 x y z - 12 z , 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=0.15 memory used=26.6MB, alloc=32.3MB, time=0.37 memory used=48.4MB, alloc=32.3MB, time=0.56 memory used=69.5MB, alloc=32.3MB, time=0.74 memory used=89.6MB, alloc=56.3MB, time=0.93 memory used=130.0MB, alloc=60.3MB, time=1.29 memory used=170.0MB, alloc=92.3MB, time=1.65 memory used=232.4MB, alloc=92.3MB, time=2.19 memory used=292.7MB, alloc=92.3MB, time=2.72 memory used=352.7MB, alloc=116.3MB, time=3.27 memory used=433.0MB, alloc=116.3MB, time=4.00 memory used=512.4MB, alloc=396.3MB, time=4.71 memory used=614.7MB, alloc=420.3MB, time=5.75 memory used=732.8MB, alloc=444.3MB, time=7.05 memory used=866.3MB, alloc=468.3MB, time=8.53 memory used=1013.6MB, alloc=492.3MB, time=10.20 memory used=1167.6MB, alloc=516.3MB, time=12.21 memory used=1314.5MB, alloc=540.3MB, time=15.11 memory used=1469.4MB, alloc=564.3MB, time=18.51 memory used=1632.9MB, alloc=588.3MB, time=22.68 memory used=1820.4MB, alloc=612.3MB, time=27.29 memory used=2031.8MB, alloc=636.3MB, time=32.65 memory used=2267.3MB, alloc=660.3MB, time=38.33 memory used=2526.6MB, alloc=660.3MB, time=44.76 memory used=2785.9MB, alloc=660.3MB, time=50.95 memory used=3045.3MB, alloc=684.3MB, time=56.81 N1 := 8295 > GB := Basis(F, plex(op(vars))); 3 2 2 2 3 2 GB := [2457 x + 475 x , 5 x y + 9 x , 5 y + 9 x y, 2457 x z + 475 x z, 3 2 3 4 95 x z - 126 x y, 13 y z - 6 x, 95 z - 126 x y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3337.5MB, alloc=684.3MB, time=61.82 memory used=3524.6MB, alloc=684.3MB, time=63.96 memory used=3666.1MB, alloc=684.3MB, time=65.60 memory used=3856.8MB, alloc=684.3MB, time=68.19 memory used=4048.6MB, alloc=708.3MB, time=70.75 memory used=4231.6MB, alloc=732.3MB, time=73.33 memory used=4563.8MB, alloc=756.3MB, time=80.60 memory used=4874.1MB, alloc=780.3MB, time=89.08 memory used=5205.8MB, alloc=804.3MB, time=98.16 memory used=5561.5MB, alloc=828.3MB, time=107.77 memory used=5941.2MB, alloc=852.3MB, time=117.76 memory used=6345.0MB, alloc=876.3MB, time=127.94 N2 := 8467 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 4 3 3 H := [10 y + 18 x y, 14 y z + 19 z , -13 z y + 6 x, -20 x y + 8 y, 2 3 3 2 10 x y z - 12 z , x z + x ] > J:=[op(GB),op(G)]; 3 2 2 2 3 2 J := [2457 x + 475 x , 5 x y + 9 x , 5 y + 9 x y, 2457 x z + 475 x z, 3 2 3 4 3 95 x z - 126 x y, 13 y z - 6 x, 95 z - 126 x y z, -20 x y + 8 y, 2 3 3 2 10 x y z - 12 z , x z + x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 23, 4, 2, 3, 4, 5/6, 5/6, 2/3, 1/2, 7/12, 1/2, 10, 23, 36, 4, 3, 3, 4, 1, 7/10, 3/5, 3/4, 9/20, 9/20, -9, -13, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=6512.4MB, alloc=876.3MB, time=131.18 |\^/| 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(); 1428369040 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 2 F := [13 x y + 13 x y z, -20 x y + 18 x y z, -13 y z + 11 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [7 x - 13 x z, -6 x y + 16 z, -11 x z + 19] > Problem := [F,G]; 3 2 2 2 2 2 2 Problem := [[13 x y + 13 x y z, -20 x y + 18 x y z, -13 y z + 11 x y], 2 2 [7 x - 13 x z, -6 x y + 16 z, -11 x 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=0.12 memory used=27.0MB, alloc=32.3MB, time=0.33 memory used=48.0MB, alloc=32.3MB, time=0.54 memory used=68.3MB, alloc=32.3MB, time=0.73 memory used=87.5MB, alloc=56.3MB, time=0.91 memory used=126.7MB, alloc=60.3MB, time=1.25 memory used=162.1MB, alloc=84.3MB, time=1.57 memory used=211.2MB, alloc=84.3MB, time=2.00 memory used=268.7MB, alloc=92.3MB, time=2.54 memory used=324.6MB, alloc=116.3MB, time=3.05 memory used=403.6MB, alloc=116.3MB, time=3.77 memory used=480.1MB, alloc=140.3MB, time=4.48 memory used=573.7MB, alloc=140.3MB, time=5.37 memory used=665.0MB, alloc=420.3MB, time=6.28 memory used=781.1MB, alloc=444.3MB, time=7.39 memory used=917.4MB, alloc=468.3MB, time=8.74 memory used=1071.5MB, alloc=492.3MB, time=10.36 memory used=1243.3MB, alloc=516.3MB, time=12.10 memory used=1430.7MB, alloc=540.3MB, time=14.27 memory used=1620.5MB, alloc=564.3MB, time=16.49 memory used=1817.6MB, alloc=588.3MB, time=18.84 memory used=2020.1MB, alloc=612.3MB, time=21.30 memory used=2231.0MB, alloc=636.3MB, time=23.90 memory used=2437.0MB, alloc=660.3MB, time=26.43 memory used=2641.2MB, alloc=684.3MB, time=28.97 memory used=2844.0MB, alloc=708.3MB, time=31.58 memory used=3005.7MB, alloc=732.3MB, time=33.74 memory used=3232.5MB, alloc=756.3MB, time=38.45 memory used=3455.2MB, alloc=780.3MB, time=43.76 memory used=3686.9MB, alloc=804.3MB, time=49.55 memory used=3929.4MB, alloc=828.3MB, time=55.85 memory used=4184.9MB, alloc=852.3MB, time=62.53 memory used=4453.3MB, alloc=876.3MB, time=69.61 memory used=4736.5MB, alloc=900.3MB, time=77.25 memory used=5033.3MB, alloc=924.3MB, time=85.00 memory used=5344.2MB, alloc=948.3MB, time=93.19 memory used=5669.7MB, alloc=972.3MB, time=101.88 memory used=6002.2MB, alloc=996.3MB, time=111.28 memory used=6358.6MB, alloc=1020.3MB, time=121.33 memory used=6739.1MB, alloc=1044.3MB, time=132.05 memory used=7143.4MB, alloc=1068.3MB, time=143.50 memory used=7571.7MB, alloc=1092.3MB, time=155.44 memory used=8024.0MB, alloc=1116.3MB, time=168.02 memory used=8500.2MB, alloc=1140.3MB, time=181.24 memory used=9000.4MB, alloc=1164.3MB, time=195.15 memory used=9524.4MB, alloc=1188.3MB, time=209.64 memory used=10072.4MB, alloc=1212.3MB, time=224.78 memory used=10644.3MB, alloc=1236.3MB, time=240.52 memory used=11240.2MB, alloc=1260.3MB, time=257.03 memory used=11860.0MB, alloc=1260.3MB, time=273.92 memory used=12479.8MB, alloc=1260.3MB, time=290.87 |\^/| 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(); 1428369340 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [7 y z + 6 x y, 20 x y z + 9 z , -13 x y + 20 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [-18 x y z + 11 y , 6 x y z - 12 x y, -20 x y - 9 x y z] > Problem := [F,G]; 2 2 3 2 Problem := [[7 y z + 6 x y, 20 x y z + 9 z , -13 x y + 20 x], 2 2 2 2 3 [-18 x y z + 11 y , 6 x y z - 12 x y, -20 x y - 9 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.48 memory used=48.2MB, alloc=32.3MB, time=0.66 memory used=69.0MB, alloc=32.3MB, time=0.84 memory used=88.3MB, alloc=56.3MB, time=1.01 memory used=128.1MB, alloc=60.3MB, time=1.36 memory used=165.1MB, alloc=60.3MB, time=1.67 memory used=201.0MB, alloc=84.3MB, time=1.99 memory used=258.3MB, alloc=92.3MB, time=2.51 memory used=313.7MB, alloc=116.3MB, time=3.02 memory used=391.6MB, alloc=116.3MB, time=3.72 memory used=467.5MB, alloc=140.3MB, time=4.43 memory used=563.5MB, alloc=140.3MB, time=5.32 memory used=640.1MB, alloc=420.3MB, time=6.06 memory used=755.7MB, alloc=444.3MB, time=7.26 memory used=886.7MB, alloc=468.3MB, time=8.73 memory used=1031.1MB, alloc=492.3MB, time=10.47 memory used=1188.1MB, alloc=516.3MB, time=12.25 memory used=1357.2MB, alloc=540.3MB, time=14.20 memory used=1535.7MB, alloc=564.3MB, time=16.34 memory used=1720.9MB, alloc=588.3MB, time=18.64 memory used=1895.0MB, alloc=612.3MB, time=22.01 memory used=2072.4MB, alloc=636.3MB, time=25.86 memory used=2259.5MB, alloc=660.3MB, time=30.20 memory used=2458.8MB, alloc=684.3MB, time=35.00 memory used=2668.4MB, alloc=708.3MB, time=40.48 memory used=2891.3MB, alloc=732.3MB, time=46.63 memory used=3138.2MB, alloc=756.3MB, time=53.37 memory used=3409.1MB, alloc=780.3MB, time=60.75 memory used=3703.8MB, alloc=804.3MB, time=68.72 memory used=4022.5MB, alloc=828.3MB, time=77.45 memory used=4365.2MB, alloc=852.3MB, time=86.70 memory used=4731.8MB, alloc=876.3MB, time=96.54 memory used=5122.3MB, alloc=876.3MB, time=106.98 memory used=5512.8MB, alloc=876.3MB, time=117.41 memory used=5903.2MB, alloc=876.3MB, time=127.79 memory used=6293.5MB, alloc=900.3MB, time=138.29 memory used=6707.7MB, alloc=900.3MB, time=149.23 memory used=7121.8MB, alloc=900.3MB, time=160.15 memory used=7535.9MB, alloc=924.3MB, time=171.01 memory used=7974.0MB, alloc=924.3MB, time=182.36 memory used=8412.0MB, alloc=948.3MB, time=193.77 memory used=8873.9MB, alloc=948.3MB, time=205.58 memory used=9335.8MB, alloc=972.3MB, time=217.21 memory used=9821.7MB, alloc=996.3MB, time=229.09 N1 := 16807 > GB := Basis(F, plex(op(vars))); 4 3 3 GB := [177957 x + 1960000 x, 13689 x + 98000 x y, 39 x + 70 x z, 3 2 3 3 -41067 x + 343000 y z, -40 x + 21 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=10214.3MB, alloc=996.3MB, time=236.67 memory used=10513.0MB, alloc=996.3MB, time=240.44 memory used=11095.1MB, alloc=1020.3MB, time=246.70 memory used=11718.2MB, alloc=1044.3MB, time=253.65 memory used=12354.6MB, alloc=1068.3MB, time=260.21 memory used=13004.8MB, alloc=1092.3MB, time=267.53 memory used=13660.0MB, alloc=1116.3MB, time=274.23 memory used=14295.9MB, alloc=1140.3MB, time=280.85 memory used=14950.6MB, alloc=1164.3MB, time=287.80 memory used=15614.2MB, alloc=1188.3MB, time=295.63 memory used=16283.7MB, alloc=1212.3MB, time=303.56 |\^/| 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(); 1428369640 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 3 F := [-15 z + 15 y z , x z + 7 y z , -8 x z - 9 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 2 3 G := [-19 x z + 9 y z, -16 x z + 13 y z , 18 x y + 4 x y ] > Problem := [F,G]; 4 2 3 2 2 3 Problem := [[-15 z + 15 y z , x z + 7 y z , -8 x z - 9 z], 3 2 2 2 3 2 2 3 [-19 x z + 9 y z, -16 x z + 13 y z , 18 x y + 4 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.47 memory used=47.8MB, alloc=32.3MB, time=0.70 memory used=68.1MB, alloc=32.3MB, time=0.92 memory used=87.7MB, alloc=56.3MB, time=1.16 memory used=127.6MB, alloc=60.3MB, time=1.61 memory used=167.0MB, alloc=84.3MB, time=2.07 memory used=210.1MB, alloc=84.3MB, time=2.54 memory used=269.1MB, alloc=116.3MB, time=3.20 memory used=348.3MB, alloc=116.3MB, time=3.99 memory used=418.1MB, alloc=140.3MB, time=4.75 memory used=507.7MB, alloc=164.3MB, time=5.73 memory used=609.7MB, alloc=188.3MB, time=7.19 memory used=714.9MB, alloc=212.3MB, time=9.36 memory used=834.4MB, alloc=236.3MB, time=12.20 memory used=977.7MB, alloc=236.3MB, time=15.40 memory used=1121.2MB, alloc=260.3MB, time=18.48 memory used=1288.8MB, alloc=284.3MB, time=21.73 N1 := 4891 > GB := Basis(F, plex(op(vars))); 3 4 2 2 2 2 2 2 3 GB := [8 x z + 9 z, 49 y z - x y z , -56 x y z + 9 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1394.0MB, alloc=284.3MB, time=22.90 memory used=1629.5MB, alloc=540.3MB, time=25.43 memory used=1821.9MB, alloc=564.3MB, time=29.04 N2 := 2503 #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)]; 4 2 3 2 2 3 3 2 H := [-15 z + 15 y z , x z + 7 y z , -8 x z - 9 z, -19 x z + 9 y z, 2 2 3 2 2 3 -16 x z + 13 y z , 18 x y + 4 x y ] > J:=[op(GB),op(G)]; 3 4 2 2 2 2 2 2 3 3 2 J := [8 x z + 9 z, 49 y z - x y z , -56 x y z + 9 z , -19 x z + 9 y z, 2 2 3 2 2 3 -16 x z + 13 y z , 18 x y + 4 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 := [6, 15, 24, 4, 3, 3, 4, 5/6, 5/6, 5/6, 1/2, 1/2, 5/6, 6, 16, 28, 6, 3, 4, 3, 1, 5/6, 5/6, 7/12, 7/12, 5/6, -1, -4, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1831.0MB, alloc=564.3MB, time=29.19 |\^/| 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(); 1428369669 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [-14 y - 12 y z, 14 x y + 7 y z, -18 y z + 2 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 G := [-x y - 8 x y z, 15 x z - 19 z , -6 x y z + 9 z] > Problem := [F,G]; 2 2 2 3 2 Problem := [[-14 y - 12 y z, 14 x y + 7 y z, -18 y z + 2 y z], 3 2 3 2 2 [-x y - 8 x y z, 15 x z - 19 z , -6 x y z + 9 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.2MB, alloc=32.3MB, time=0.35 memory used=47.2MB, alloc=32.3MB, time=0.53 memory used=67.4MB, alloc=32.3MB, time=0.70 memory used=86.0MB, alloc=56.3MB, time=0.87 memory used=123.1MB, alloc=60.3MB, time=1.19 memory used=158.9MB, alloc=84.3MB, time=1.51 memory used=215.7MB, alloc=84.3MB, time=2.00 memory used=270.4MB, alloc=108.3MB, time=2.51 memory used=345.3MB, alloc=116.3MB, time=3.22 memory used=418.9MB, alloc=140.3MB, time=4.00 memory used=507.6MB, alloc=164.3MB, time=4.98 memory used=611.1MB, alloc=188.3MB, time=6.09 memory used=728.0MB, alloc=212.3MB, time=7.37 memory used=844.7MB, alloc=492.3MB, time=8.72 memory used=979.9MB, alloc=516.3MB, time=10.31 memory used=1124.4MB, alloc=540.3MB, time=11.98 memory used=1267.4MB, alloc=564.3MB, time=14.39 memory used=1412.2MB, alloc=588.3MB, time=17.43 memory used=1568.4MB, alloc=612.3MB, time=20.90 memory used=1738.1MB, alloc=636.3MB, time=24.82 memory used=1922.3MB, alloc=660.3MB, time=29.24 memory used=2121.6MB, alloc=684.3MB, time=34.09 memory used=2332.0MB, alloc=708.3MB, time=39.57 memory used=2563.3MB, alloc=732.3MB, time=45.76 memory used=2818.5MB, alloc=756.3MB, time=52.44 memory used=3097.7MB, alloc=780.3MB, time=59.74 memory used=3400.8MB, alloc=804.3MB, time=67.62 memory used=3727.8MB, alloc=828.3MB, time=76.09 memory used=4078.8MB, alloc=828.3MB, time=85.16 memory used=4429.7MB, alloc=828.3MB, time=94.22 memory used=4780.6MB, alloc=852.3MB, time=103.41 memory used=5155.3MB, alloc=852.3MB, time=113.12 memory used=5529.9MB, alloc=852.3MB, time=122.84 memory used=5904.5MB, alloc=852.3MB, time=132.56 memory used=6279.0MB, alloc=876.3MB, time=142.30 memory used=6677.6MB, alloc=876.3MB, time=152.61 memory used=7076.0MB, alloc=876.3MB, time=162.90 memory used=7474.5MB, alloc=900.3MB, time=173.27 memory used=7896.8MB, alloc=900.3MB, time=184.11 memory used=8319.0MB, alloc=924.3MB, time=194.90 memory used=8765.0MB, alloc=924.3MB, time=206.29 memory used=9211.1MB, alloc=948.3MB, time=217.72 memory used=9681.0MB, alloc=948.3MB, time=229.55 memory used=10151.3MB, alloc=972.3MB, time=240.78 N1 := 17533 > GB := Basis(F, plex(op(vars))); 2 2 2 3 2 2 GB := [189 x y - y , 21 y + 2 y , 7 y + 6 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 1577 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 3 2 H := [-14 y - 12 y z, 14 x y + 7 y z, -18 y z + 2 y z, -x y - 8 x y z, 3 2 2 15 x z - 19 z , -6 x y z + 9 z] > J:=[op(GB),op(G)]; 2 2 2 3 2 2 3 2 J := [189 x y - y , 21 y + 2 y , 7 y + 6 y z, -x y - 8 x y z, 3 2 2 15 x z - 19 z , -6 x y z + 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 := [6, 15, 21, 4, 3, 3, 2, 2/3, 5/6, 1, 5/12, 3/4, 3/4, 6, 13, 21, 4, 3, 3, 2, 2/3, 5/6, 2/3, 5/12, 3/4, 1/2, 2, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=10614.3MB, alloc=972.3MB, time=248.63 |\^/| 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(); 1428369914 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [-16 x y + 10 x z, -20 x y z + 16 x z, -3 x y z - 19 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 G := [10 y + 18 z, 8 x y z - 18 x z , -17 x z + 5 y z ] > Problem := [F,G]; 3 2 2 2 2 Problem := [[-16 x y + 10 x z, -20 x y z + 16 x z, -3 x y z - 19 x z], 2 2 3 3 3 [10 y + 18 z, 8 x y z - 18 x z , -17 x z + 5 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.6MB, alloc=32.3MB, time=0.37 memory used=48.2MB, alloc=32.3MB, time=0.55 memory used=68.6MB, alloc=32.3MB, time=0.72 memory used=87.2MB, alloc=56.3MB, time=0.90 memory used=127.4MB, alloc=60.3MB, time=1.25 memory used=165.9MB, alloc=84.3MB, time=1.61 memory used=222.1MB, alloc=84.3MB, time=2.10 memory used=278.8MB, alloc=116.3MB, time=2.64 memory used=359.3MB, alloc=140.3MB, time=3.45 memory used=457.8MB, alloc=164.3MB, time=4.53 memory used=571.2MB, alloc=188.3MB, time=5.77 memory used=688.0MB, alloc=468.3MB, time=7.08 memory used=838.1MB, alloc=492.3MB, time=8.61 memory used=994.7MB, alloc=516.3MB, time=10.37 memory used=1153.5MB, alloc=540.3MB, time=12.83 memory used=1306.9MB, alloc=564.3MB, time=15.97 memory used=1470.5MB, alloc=588.3MB, time=19.58 memory used=1646.3MB, alloc=612.3MB, time=23.76 memory used=1832.6MB, alloc=636.3MB, time=28.59 memory used=2042.9MB, alloc=660.3MB, time=34.04 memory used=2277.2MB, alloc=684.3MB, time=40.15 memory used=2535.3MB, alloc=708.3MB, time=46.70 memory used=2817.5MB, alloc=708.3MB, time=53.91 memory used=3099.6MB, alloc=708.3MB, time=60.96 memory used=3381.6MB, alloc=732.3MB, time=68.00 memory used=3687.6MB, alloc=732.3MB, time=75.66 memory used=3993.6MB, alloc=732.3MB, time=83.23 memory used=4299.6MB, alloc=756.3MB, time=90.81 memory used=4629.5MB, alloc=756.3MB, time=99.02 memory used=4959.4MB, alloc=780.3MB, time=107.01 memory used=5313.2MB, alloc=804.3MB, time=115.13 N1 := 11993 > GB := Basis(F, plex(op(vars))); 6 3 5 3 2 5 GB := [475 x y + 48 x y, 95 x y + 12 x y , 95 x y + 6 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5600.6MB, alloc=804.3MB, time=119.37 memory used=5745.2MB, alloc=804.3MB, time=121.26 memory used=5920.2MB, alloc=804.3MB, time=123.84 memory used=6105.3MB, alloc=804.3MB, time=126.44 memory used=6264.0MB, alloc=828.3MB, time=129.09 memory used=6672.5MB, alloc=852.3MB, time=139.28 memory used=7069.1MB, alloc=876.3MB, time=150.03 memory used=7489.8MB, alloc=900.3MB, time=161.45 memory used=7934.5MB, alloc=924.3MB, time=173.06 N2 := 8037 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 H := [-16 x y + 10 x z, -20 x y z + 16 x z, -3 x y z - 19 x z, 2 2 3 3 3 10 y + 18 z, 8 x y z - 18 x z , -17 x z + 5 y z ] > J:=[op(GB),op(G)]; 6 3 5 3 2 5 2 J := [475 x y + 48 x y, 95 x y + 12 x y , 95 x y + 6 x z, 10 y + 18 z, 2 3 3 3 8 x y z - 18 x z , -17 x z + 5 y z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 17, 22, 4, 3, 2, 3, 5/6, 1, 1, 3/4, 1/2, 5/6, 6, 15, 29, 7, 6, 2, 3, 5/6, 1, 2/3, 3/4, 2/3, 1/2, 2, -7, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=8243.7MB, alloc=924.3MB, time=179.65 |\^/| 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(); 1428370091 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 4 3 2 2 F := [6 x z + 5 x y z , 12 x + 14 y z , 17 x y + 4] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 2 4 G := [6 x z + 3 y , 12 x z + 11 x z , x y z + 19 z ] > Problem := [F,G]; 3 2 4 3 2 2 Problem := [[6 x z + 5 x y z , 12 x + 14 y z , 17 x y + 4], 3 3 2 2 3 2 4 [6 x z + 3 y , 12 x z + 11 x z , x y z + 19 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.7MB, alloc=32.3MB, time=0.38 memory used=47.9MB, alloc=32.3MB, time=0.57 memory used=67.7MB, alloc=56.3MB, time=0.74 memory used=108.9MB, alloc=60.3MB, time=1.10 memory used=148.9MB, alloc=60.3MB, time=1.44 memory used=187.3MB, alloc=84.3MB, time=1.77 memory used=229.0MB, alloc=84.3MB, time=2.14 memory used=289.6MB, alloc=116.3MB, time=2.66 memory used=360.6MB, alloc=372.3MB, time=3.24 memory used=442.7MB, alloc=396.3MB, time=3.97 memory used=552.1MB, alloc=420.3MB, time=4.89 memory used=682.4MB, alloc=444.3MB, time=6.01 memory used=815.4MB, alloc=468.3MB, time=7.16 memory used=930.6MB, alloc=468.3MB, time=8.13 memory used=1036.1MB, alloc=492.3MB, time=9.05 memory used=1134.1MB, alloc=492.3MB, time=9.97 memory used=1233.1MB, alloc=492.3MB, time=10.94 memory used=1311.1MB, alloc=492.3MB, time=11.76 memory used=1387.3MB, alloc=516.3MB, time=12.55 memory used=1463.5MB, alloc=516.3MB, time=13.40 memory used=1533.2MB, alloc=516.3MB, time=14.23 memory used=1592.5MB, alloc=516.3MB, time=14.96 memory used=1651.1MB, alloc=516.3MB, time=15.62 memory used=1696.1MB, alloc=516.3MB, time=16.24 memory used=1747.3MB, alloc=516.3MB, time=16.94 memory used=1793.5MB, alloc=516.3MB, time=17.60 memory used=1838.9MB, alloc=540.3MB, time=18.32 memory used=2018.2MB, alloc=564.3MB, time=19.96 memory used=2238.1MB, alloc=588.3MB, time=22.67 memory used=2451.9MB, alloc=612.3MB, time=25.40 memory used=2671.3MB, alloc=636.3MB, time=28.26 memory used=2901.7MB, alloc=660.3MB, time=31.33 memory used=3140.5MB, alloc=684.3MB, time=34.78 memory used=3347.5MB, alloc=708.3MB, time=39.48 memory used=3556.2MB, alloc=732.3MB, time=44.81 memory used=3774.3MB, alloc=756.3MB, time=50.51 memory used=3996.0MB, alloc=780.3MB, time=56.87 memory used=4237.6MB, alloc=804.3MB, time=63.88 memory used=4503.2MB, alloc=828.3MB, time=71.52 memory used=4792.7MB, alloc=852.3MB, time=79.82 memory used=5106.1MB, alloc=876.3MB, time=88.71 memory used=5443.5MB, alloc=900.3MB, time=98.21 memory used=5804.8MB, alloc=924.3MB, time=108.47 memory used=6190.2MB, alloc=948.3MB, time=119.22 memory used=6599.3MB, alloc=972.3MB, time=130.56 memory used=7032.4MB, alloc=996.3MB, time=142.46 memory used=7489.5MB, alloc=1020.3MB, time=154.89 memory used=7970.6MB, alloc=1044.3MB, time=167.93 memory used=8475.7MB, alloc=1044.3MB, time=181.33 memory used=8980.9MB, alloc=1068.3MB, time=194.37 N1 := 14385 > GB := Basis(F, plex(op(vars))); 4 2 2 GB := [1071 x + 125, -252 x + 125 y , 25 y + 42 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=9542.5MB, alloc=1068.3MB, time=205.33 memory used=10202.7MB, alloc=1092.3MB, time=218.81 N2 := 4873 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 4 3 2 2 3 3 H := [6 x z + 5 x y z , 12 x + 14 y z , 17 y x + 4, 6 x z + 3 y , 2 2 3 2 4 12 x z + 11 x z , x y z + 19 z ] > J:=[op(GB),op(G)]; 4 2 2 3 3 J := [1071 x + 125, -252 x + 125 y , 42 z + 25 y, 6 x z + 3 y , 2 2 3 2 4 12 x z + 11 x z , x y z + 19 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, 16, 24, 4, 4, 3, 4, 1, 5/6, 5/6, 2/3, 5/12, 2/3, 6, 13, 19, 4, 4, 3, 4, 5/6, 2/3, 2/3, 1/2, 1/3, 1/2, 3, 5, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=10589.2MB, alloc=1092.3MB, 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(); 1428370312 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 2 F := [-2 x y + 7 y z , -6 x z - 6 z, -19 x y - 14 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 3 G := [-10 y z - 5 x z , y - 15 y z, 15 x y] > Problem := [F,G]; 2 2 3 2 2 2 2 Problem := [[-2 x y + 7 y z , -6 x z - 6 z, -19 x y - 14 y z ], 2 2 2 4 2 3 [-10 y z - 5 x z , y - 15 y z, 15 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.2MB, alloc=40.3MB, time=0.45 memory used=60.5MB, alloc=40.3MB, time=0.69 memory used=87.3MB, alloc=40.3MB, time=0.93 memory used=113.5MB, alloc=68.3MB, time=1.17 memory used=159.0MB, alloc=68.3MB, time=1.57 memory used=204.6MB, alloc=100.3MB, time=1.99 memory used=270.5MB, alloc=100.3MB, time=2.57 memory used=338.0MB, alloc=124.3MB, time=3.26 memory used=434.3MB, alloc=124.3MB, time=4.05 memory used=514.0MB, alloc=148.3MB, time=4.92 memory used=613.2MB, alloc=172.3MB, time=5.96 memory used=746.1MB, alloc=196.3MB, time=6.97 memory used=860.0MB, alloc=476.3MB, time=8.44 memory used=990.8MB, alloc=500.3MB, time=10.84 memory used=1126.2MB, alloc=524.3MB, time=13.92 memory used=1283.6MB, alloc=548.3MB, time=17.54 memory used=1464.9MB, alloc=548.3MB, time=21.65 memory used=1646.2MB, alloc=572.3MB, time=25.71 memory used=1851.6MB, alloc=572.3MB, time=30.07 N1 := 6039 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 3 2 2 2 2 GB := [4 x y - 19 x y , 2476099 x y + 3584 x y , -361 x y + 56 y z, 2 x z + z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2066.3MB, alloc=572.3MB, time=33.15 memory used=2326.2MB, alloc=596.3MB, time=36.92 N2 := 2061 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 2 2 2 2 2 H := [-2 x y + 7 y z , -6 x z - 6 z, -19 x y - 14 y z , -10 y z - 5 x z , 4 2 3 y - 15 y z, 15 y x ] > J:=[op(GB),op(G)]; 3 2 2 2 2 3 2 2 2 2 J := [4 x y - 19 x y , 2476099 x y + 3584 x y , -361 x y + 56 y z, 2 2 2 2 4 2 3 x z + z, -10 y z - 5 x z , y - 15 y z, 15 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 := [6, 15, 23, 4, 3, 4, 3, 5/6, 5/6, 5/6, 5/13, 8/13, 7/13, 7, 16, 29, 5, 3, 4, 2, 6/7, 6/7, 4/7, 8/15, 2/3, 2/5, -1, -6, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2364.1MB, alloc=596.3MB, time=37.51 |\^/| 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(); 1428370349 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 F := [2 y z - 13 z, -10 y z + 6 y , 11 x z - 16 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 3 G := [-13 x y z + x y , 18 y - 9 x y z, 5 x z - 4 z ] > Problem := [F,G]; 2 2 2 2 3 Problem := [[2 y z - 13 z, -10 y z + 6 y , 11 x z - 16 z], 2 2 4 3 3 [-13 x y z + x y , 18 y - 9 x y z, 5 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=0.14 memory used=26.2MB, alloc=32.3MB, time=0.33 memory used=47.7MB, alloc=32.3MB, time=0.53 memory used=69.4MB, alloc=56.3MB, time=0.75 memory used=113.4MB, alloc=60.3MB, time=1.20 memory used=151.0MB, alloc=84.3MB, time=1.59 memory used=208.3MB, alloc=84.3MB, time=2.19 memory used=257.1MB, alloc=108.3MB, time=2.78 memory used=320.3MB, alloc=132.3MB, time=3.82 memory used=397.6MB, alloc=156.3MB, time=5.36 memory used=499.0MB, alloc=156.3MB, time=7.31 memory used=600.4MB, alloc=156.3MB, time=9.09 N1 := 3551 > GB := Basis(F, plex(op(vars))); 3 2 2 4 2 2 GB := [11 x y - 16 y , 6 y - 65 y , -18 y + 325 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=694.0MB, alloc=156.3MB, time=10.25 memory used=809.1MB, alloc=188.3MB, time=11.50 memory used=934.1MB, alloc=212.3MB, time=13.66 N2 := 2145 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 2 2 H := [2 y z - 13 z, -10 y z + 6 y , 11 x z - 16 z, -13 x y z + x y , 4 3 3 18 y - 9 x y z, 5 x z - 4 z ] > J:=[op(GB),op(G)]; 3 2 2 4 2 2 2 2 J := [11 x y - 16 y , 6 y - 65 y , -18 y + 325 z, -13 x y z + x y , 4 3 3 18 y - 9 x y z, 5 x 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, 14, 23, 4, 3, 4, 3, 2/3, 2/3, 1, 5/12, 7/12, 3/4, 6, 13, 23, 5, 3, 4, 3, 2/3, 5/6, 2/3, 5/12, 3/4, 5/12, 1, 0, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=969.4MB, alloc=212.3MB, time=14.18 |\^/| 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(); 1428370363 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 F := [-2 x y - 15 y, 15 x z + 20 y , -11 x y - x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 2 2 2 2 G := [-15 y z - 9 z , -3 x y + 8 x z , 19 x z + 19 y z] > Problem := [F,G]; 3 2 2 3 2 Problem := [[-2 x y - 15 y, 15 x z + 20 y , -11 x y - x z ], 2 2 4 2 2 2 2 [-15 y z - 9 z , -3 x y + 8 x z , 19 x z + 19 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.4MB, alloc=32.3MB, time=0.34 memory used=48.3MB, alloc=32.3MB, time=0.53 memory used=68.7MB, alloc=32.3MB, time=0.70 memory used=88.2MB, alloc=32.3MB, time=0.86 memory used=107.4MB, alloc=56.3MB, time=1.04 memory used=147.3MB, alloc=60.3MB, time=1.39 memory used=188.5MB, alloc=84.3MB, time=1.81 memory used=250.3MB, alloc=92.3MB, time=2.49 memory used=307.2MB, alloc=116.3MB, time=3.12 memory used=382.3MB, alloc=140.3MB, time=3.92 memory used=470.4MB, alloc=164.3MB, time=5.21 memory used=563.2MB, alloc=188.3MB, time=7.22 memory used=679.0MB, alloc=188.3MB, time=9.77 memory used=794.8MB, alloc=212.3MB, time=12.07 N1 := 3729 > GB := Basis(F, plex(op(vars))); 3 4 2 2 3 GB := [2 x y + 15 y, 64 y + 22275 y, 3 z x + 4 y , -8 x y + 45 y z, 2 2 x z - 165 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=935.3MB, alloc=212.3MB, time=13.71 memory used=1051.9MB, alloc=468.3MB, time=14.83 memory used=1200.2MB, alloc=492.3MB, time=16.20 memory used=1373.6MB, alloc=516.3MB, time=17.79 memory used=1539.0MB, alloc=516.3MB, time=19.38 memory used=1703.8MB, alloc=540.3MB, time=21.00 memory used=1853.1MB, alloc=564.3MB, time=22.55 memory used=2009.5MB, alloc=564.3MB, time=24.22 memory used=2151.9MB, alloc=588.3MB, time=25.73 memory used=2275.8MB, alloc=588.3MB, time=27.09 memory used=2403.3MB, alloc=612.3MB, time=28.57 memory used=2531.7MB, alloc=636.3MB, time=30.29 memory used=2679.4MB, alloc=636.3MB, time=32.12 memory used=2816.3MB, alloc=660.3MB, time=33.92 memory used=2939.1MB, alloc=684.3MB, time=35.64 memory used=3073.9MB, alloc=708.3MB, time=37.52 memory used=3199.8MB, alloc=708.3MB, time=39.26 memory used=3331.9MB, alloc=732.3MB, time=41.10 memory used=3472.7MB, alloc=756.3MB, time=42.81 memory used=3613.4MB, alloc=756.3MB, time=44.55 memory used=3719.8MB, alloc=780.3MB, time=46.18 memory used=3818.3MB, alloc=780.3MB, time=47.77 memory used=3911.1MB, alloc=804.3MB, time=49.27 memory used=4023.8MB, alloc=828.3MB, time=51.05 memory used=4111.6MB, alloc=828.3MB, time=52.49 memory used=4197.9MB, alloc=852.3MB, time=53.96 memory used=4273.4MB, alloc=852.3MB, time=55.27 memory used=4372.4MB, alloc=876.3MB, time=56.78 memory used=4475.9MB, alloc=900.3MB, time=58.91 memory used=4860.5MB, alloc=924.3MB, time=67.74 memory used=5233.0MB, alloc=948.3MB, time=77.26 memory used=5607.3MB, alloc=972.3MB, time=86.86 memory used=5987.6MB, alloc=996.3MB, time=96.90 memory used=6377.5MB, alloc=1020.3MB, time=107.40 memory used=6766.5MB, alloc=1044.3MB, time=118.72 memory used=7179.0MB, alloc=1068.3MB, time=130.70 memory used=7615.4MB, alloc=1092.3MB, time=143.46 memory used=8075.8MB, alloc=1116.3MB, time=156.84 memory used=8560.0MB, alloc=1140.3MB, time=170.81 memory used=9068.2MB, alloc=1164.3MB, time=185.37 memory used=9600.4MB, alloc=1188.3MB, time=200.72 memory used=10156.5MB, alloc=1212.3MB, time=216.57 memory used=10736.4MB, alloc=1212.3MB, time=233.11 memory used=11316.5MB, alloc=1212.3MB, time=249.61 memory used=11896.4MB, alloc=1236.3MB, time=266.29 memory used=12500.2MB, alloc=1236.3MB, time=283.42 memory used=13104.1MB, alloc=1236.3MB, time=300.56 |\^/| 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(); 1428370663 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [15 x y z - 11 x y z, 18 x y z + 11 z , 4 x y z + 14 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 G := [7 x z + 17, 20 x - 5 x y, -16 x y - 16 x z] > Problem := [F,G]; 2 2 3 2 2 Problem := [[15 x y z - 11 x y z, 18 x y z + 11 z , 4 x y z + 14 x ], 3 3 2 3 2 [7 x z + 17, 20 x - 5 x y, -16 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=0.14 memory used=26.3MB, alloc=32.3MB, time=0.38 memory used=47.9MB, alloc=32.3MB, time=0.62 memory used=68.7MB, alloc=32.3MB, time=0.88 memory used=88.5MB, alloc=56.3MB, time=1.11 memory used=128.6MB, alloc=60.3MB, time=1.62 memory used=165.7MB, alloc=84.3MB, time=2.06 memory used=215.0MB, alloc=84.3MB, time=2.66 memory used=272.9MB, alloc=116.3MB, time=3.49 memory used=348.4MB, alloc=140.3MB, time=4.60 memory used=442.9MB, alloc=164.3MB, time=5.92 memory used=552.8MB, alloc=188.3MB, time=7.63 memory used=674.7MB, alloc=212.3MB, time=9.87 memory used=799.1MB, alloc=236.3MB, time=12.89 memory used=930.4MB, alloc=260.3MB, time=15.92 memory used=1081.8MB, alloc=284.3MB, time=19.45 memory used=1257.1MB, alloc=284.3MB, time=23.53 memory used=1432.4MB, alloc=308.3MB, time=27.51 memory used=1631.7MB, alloc=308.3MB, time=31.86 memory used=1831.2MB, alloc=332.3MB, time=35.65 N1 := 6141 > GB := Basis(F, plex(op(vars))); 3 2 2 5 2 2 3 2 GB := [15 x - 11 x , 72 x y + 539 x , -12 x y + 35 x z, 2 4 2 4 3 -36 x y + 77 x y z, 216 x y + 385 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1917.9MB, alloc=332.3MB, time=36.69 memory used=2112.0MB, alloc=588.3MB, time=38.60 memory used=2268.7MB, alloc=588.3MB, time=40.21 memory used=2418.3MB, alloc=588.3MB, time=41.75 memory used=2567.9MB, alloc=588.3MB, time=43.36 memory used=2708.7MB, alloc=612.3MB, time=44.85 memory used=2828.6MB, alloc=612.3MB, time=46.22 memory used=2920.9MB, alloc=612.3MB, time=47.27 memory used=3024.2MB, alloc=636.3MB, time=48.49 memory used=3134.0MB, alloc=636.3MB, time=49.90 memory used=3218.1MB, alloc=636.3MB, time=50.96 memory used=3282.8MB, alloc=636.3MB, time=51.83 memory used=3347.8MB, alloc=636.3MB, time=52.66 memory used=3427.4MB, alloc=636.3MB, time=53.77 memory used=3494.3MB, alloc=660.3MB, time=54.78 memory used=3566.9MB, alloc=660.3MB, time=55.90 memory used=3629.3MB, alloc=660.3MB, time=56.98 memory used=3735.3MB, alloc=684.3MB, time=58.55 memory used=3831.5MB, alloc=684.3MB, time=60.06 memory used=3919.7MB, alloc=708.3MB, time=61.48 memory used=4001.3MB, alloc=708.3MB, time=62.83 memory used=4306.5MB, alloc=732.3MB, time=66.78 memory used=4609.1MB, alloc=756.3MB, time=72.27 memory used=4882.0MB, alloc=780.3MB, time=79.06 memory used=5159.9MB, alloc=804.3MB, time=86.33 memory used=5436.2MB, alloc=828.3MB, time=94.47 memory used=5736.4MB, alloc=852.3MB, time=103.27 memory used=6060.5MB, alloc=876.3MB, time=112.73 memory used=6408.5MB, alloc=900.3MB, time=122.81 memory used=6780.5MB, alloc=924.3MB, time=133.61 memory used=7176.4MB, alloc=948.3MB, time=144.85 memory used=7596.3MB, alloc=972.3MB, time=156.68 memory used=8040.0MB, alloc=996.3MB, time=168.91 memory used=8507.8MB, alloc=1020.3MB, time=181.59 memory used=8999.4MB, alloc=1044.3MB, time=194.79 memory used=9514.9MB, alloc=1068.3MB, time=208.01 N2 := 13117 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 3 H := [15 x y z - 11 x y z, 18 x y z + 11 z , 4 x y z + 14 x , 7 z x + 17, 3 2 3 2 20 x - 5 x y, -16 x y - 16 x z] > J:=[op(GB),op(G)]; 3 2 2 5 2 2 3 2 J := [15 x - 11 x , 72 x y + 539 x , -12 x y + 35 x z, 2 4 4 2 3 3 3 2 -36 x y + 77 x y z, 216 y x + 385 z , 7 z x + 17, 20 x - 5 x y, 3 2 -16 x y - 16 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 := [6, 16, 23, 4, 3, 2, 3, 1, 5/6, 5/6, 5/6, 1/2, 7/12, 8, 19, 38, 7, 3, 5, 3, 1, 3/4, 5/8, 7/8, 7/16, 5/16, -3, -15, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=9773.9MB, alloc=1068.3MB, time=213.26 |\^/| 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(); 1428370871 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 2 F := [-17 x y z - z , 18 x z - 11 z , 12 y z + 20 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-20 x y + 20 x y , 13 x + 10 z , 14 y z - 10 x] > Problem := [F,G]; 3 3 3 2 2 2 Problem := [[-17 x y z - z , 18 x z - 11 z , 12 y z + 20 y ], 3 2 2 2 [-20 x y + 20 x y , 13 x + 10 z , 14 y z - 10 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.36 memory used=47.6MB, alloc=32.3MB, time=0.55 memory used=68.0MB, alloc=32.3MB, time=0.73 memory used=87.7MB, alloc=56.3MB, time=0.90 memory used=128.6MB, alloc=60.3MB, time=1.25 memory used=168.0MB, alloc=60.3MB, time=1.58 memory used=205.3MB, alloc=84.3MB, time=1.92 memory used=263.5MB, alloc=92.3MB, time=2.44 memory used=319.0MB, alloc=116.3MB, time=2.99 memory used=397.3MB, alloc=116.3MB, time=3.84 memory used=470.5MB, alloc=140.3MB, time=4.66 memory used=558.2MB, alloc=164.3MB, time=5.71 memory used=651.1MB, alloc=188.3MB, time=7.48 memory used=760.2MB, alloc=212.3MB, time=9.63 N1 := 3067 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 3 8 5 GB := [54 x y + 55 y , 18 x y + 187 y , 54 x z + 55 x z, 3 7 2 5 2 2 18 x z + 187 x y z, 17496 x z + 1923295 y z, 972 x z + 174845 x y , 3 3 -18 x z + 11 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=898.0MB, alloc=212.3MB, time=11.57 memory used=998.6MB, alloc=468.3MB, time=12.54 memory used=1155.2MB, alloc=468.3MB, time=14.09 memory used=1311.2MB, alloc=492.3MB, time=15.93 N2 := 2063 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 3 2 2 2 3 2 H := [-17 x y z - z , 18 x z - 11 z , 12 y z + 20 y , -20 x y + 20 x y , 2 2 10 z + 13 x , 14 y z - 10 x] > J:=[op(GB),op(G)]; 3 2 2 2 2 3 8 5 J := [54 x y + 55 y , 18 x y + 187 y , 54 x z + 55 x z, 3 7 2 5 2 2 18 x z + 187 x y z, 17496 x z + 1923295 y z, 972 x z + 174845 x y , 3 3 3 2 2 2 -18 x z + 11 z , -20 x y + 20 x y , 10 z + 13 x , 14 y 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, 14, 19, 4, 3, 2, 3, 5/6, 2/3, 5/6, 1/2, 1/2, 7/12, 10, 24, 49, 9, 8, 3, 3, 1, 7/10, 7/10, 7/10, 1/2, 11/20, -10, -30, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1443.1MB, alloc=492.3MB, time=18.17 |\^/| 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(); 1428370889 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 F := [6 z , 2 x y - 2 z , -13 y z + 7 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 3 G := [10 y z - 8 z, 12 y z - 15 z , 18 x y z - 12 y ] > Problem := [F,G]; 3 3 3 3 Problem := [[6 z , 2 x y - 2 z , -13 y z + 7 z], 3 2 2 4 3 [10 y z - 8 z, 12 y z - 15 z , 18 x y z - 12 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.7MB, alloc=32.3MB, time=0.36 memory used=48.4MB, alloc=32.3MB, time=0.55 memory used=69.9MB, alloc=32.3MB, time=0.74 memory used=90.3MB, alloc=32.3MB, time=0.91 memory used=140.9MB, alloc=68.3MB, time=1.45 memory used=187.3MB, alloc=92.3MB, time=1.95 memory used=252.9MB, alloc=92.3MB, time=2.64 memory used=313.3MB, alloc=124.3MB, time=3.31 memory used=391.1MB, alloc=148.3MB, time=4.16 memory used=480.1MB, alloc=172.3MB, time=5.59 memory used=578.6MB, alloc=196.3MB, time=7.62 memory used=695.1MB, alloc=196.3MB, time=10.12 memory used=811.5MB, alloc=220.3MB, time=12.58 memory used=951.9MB, alloc=220.3MB, time=15.41 memory used=1092.3MB, alloc=244.3MB, time=17.93 N1 := 4723 > GB := Basis(F, plex(op(vars))); 3 3 3 3 GB := [y x , x z, 13 y z - 7 z, z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 863 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 3 3 3 2 2 4 H := [6 z , 2 x y - 2 z , -13 y z + 7 z, 10 y z - 8 z, 12 y z - 15 z , 3 18 x y z - 12 y ] > J:=[op(GB),op(G)]; 3 3 3 3 3 2 2 4 J := [y x , x z, 13 y z - 7 z, z , 10 y z - 8 z, 12 y z - 15 z , 3 18 x y 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, 13, 22, 4, 3, 3, 4, 1/3, 5/6, 1, 1/6, 1/2, 3/4, 7, 14, 26, 4, 3, 3, 4, 3/7, 5/7, 6/7, 3/14, 3/7, 9/14, -1, -4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1219.1MB, alloc=244.3MB, time=19.41 |\^/| 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(); 1428370908 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [8 z, 17 y + 12, -16 x y z + 11 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [-2 y z - 4 y , -4 x y z - 10, -20 x z - 4 x y] > Problem := [F,G]; 2 2 Problem := [[8 z, 17 y + 12, -16 x y z + 11 x], 2 2 3 2 [-2 y z - 4 y , -4 x y z - 10, -20 x z - 4 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.3MB, alloc=32.3MB, time=0.33 memory used=48.2MB, alloc=32.3MB, time=0.54 memory used=68.7MB, alloc=32.3MB, time=0.71 memory used=87.6MB, alloc=56.3MB, time=0.90 memory used=126.5MB, alloc=60.3MB, time=1.25 memory used=164.9MB, alloc=84.3MB, time=1.66 memory used=223.4MB, alloc=84.3MB, time=2.39 memory used=275.0MB, alloc=108.3MB, time=2.98 memory used=338.6MB, alloc=132.3MB, time=4.05 N1 := 1993 > GB := Basis(F, plex(op(vars))); 2 GB := [x, 17 y + 12, z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=424.1MB, alloc=132.3MB, time=5.19 N2 := 537 #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 z, 17 y + 12, -16 x y z + 11 x, -2 y z - 4 y , -4 x y z - 10, 3 2 -20 x z - 4 x y] > J:=[op(GB),op(G)]; 2 2 2 3 2 J := [x, 17 y + 12, z, -2 y z - 4 y , -4 x y z - 10, -20 x z - 4 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 := [6, 13, 17, 4, 2, 2, 3, 1/2, 5/6, 5/6, 5/12, 1/2, 5/12, 6, 11, 14, 4, 2, 2, 3, 1/2, 2/3, 2/3, 2/5, 1/2, 2/5, 2, 3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=474.8MB, alloc=132.3MB, time=5.71 |\^/| 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(); 1428370914 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-15 x y z - 14, 19 x y - 8 y z , 7 y - 3 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 2 2 2 2 2 G := [-10 x + 18 x y , -9 x z + 10 x z , -15 x y - 3 x y] > Problem := [F,G]; 2 2 2 2 Problem := [[-15 x y z - 14, 19 x y - 8 y z , 7 y - 3 x], 4 3 2 2 2 2 2 [-10 x + 18 x y , -9 x z + 10 x z , -15 x y - 3 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=26.0MB, alloc=32.3MB, time=0.34 memory used=47.7MB, alloc=32.3MB, time=0.53 memory used=69.1MB, alloc=56.3MB, time=0.74 memory used=112.4MB, alloc=60.3MB, time=1.20 memory used=151.0MB, alloc=84.3MB, time=1.64 N1 := 1089 > GB := Basis(F, plex(op(vars))); 11 6 4 GB := [493441875 x - 843308032, -38475 x + 76832 y, 855 x + 784 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=205.3MB, alloc=84.3MB, time=2.30 N2 := 439 #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 4 3 H := [-15 x y z - 14, 19 x y - 8 y z , 7 y - 3 x, -10 x + 18 x y , 2 2 2 2 2 -9 x z + 10 x z , -15 x y - 3 x y] > J:=[op(GB),op(G)]; 11 6 4 J := [493441875 x - 843308032, -38475 x + 76832 y, 855 x + 784 z, 4 3 2 2 2 2 2 -10 x + 18 x y , -9 x z + 10 x z , -15 x y - 3 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 := [6, 14, 21, 4, 4, 3, 2, 1, 5/6, 1/2, 3/4, 7/12, 1/3, 6, 11, 33, 11, 11, 3, 2, 1, 1/2, 1/3, 3/4, 1/3, 1/4, 3, -12, -7] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=244.2MB, alloc=84.3MB, time=2.68 |\^/| 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(); 1428370917 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 2 2 F := [18 x y - 9 y z , 18 x - 18 y z , -20 x y z - 20] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 4 3 G := [-11 y z - 3 z, -15 x z - 15 y z, -18 z - 16 z ] > Problem := [F,G]; 3 3 4 2 2 Problem := [[18 x y - 9 y z , 18 x - 18 y z , -20 x y z - 20], 3 3 3 4 3 [-11 y z - 3 z, -15 x z - 15 y z, -18 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=0.11 memory used=26.2MB, alloc=32.3MB, time=0.29 memory used=47.1MB, alloc=32.3MB, time=0.46 memory used=67.7MB, alloc=32.3MB, time=0.63 memory used=86.9MB, alloc=32.3MB, time=0.79 memory used=105.4MB, alloc=56.3MB, time=0.97 memory used=143.6MB, alloc=60.3MB, time=1.37 memory used=181.6MB, alloc=60.3MB, time=1.71 memory used=218.7MB, alloc=84.3MB, time=2.05 memory used=268.9MB, alloc=84.3MB, time=2.50 memory used=325.3MB, alloc=116.3MB, time=3.04 memory used=403.2MB, alloc=116.3MB, time=3.75 memory used=478.4MB, alloc=140.3MB, time=4.46 memory used=577.0MB, alloc=420.3MB, time=5.39 memory used=694.4MB, alloc=444.3MB, time=6.66 memory used=822.8MB, alloc=468.3MB, time=8.08 memory used=965.0MB, alloc=492.3MB, time=9.67 memory used=1111.4MB, alloc=516.3MB, time=11.95 memory used=1254.9MB, alloc=540.3MB, time=14.92 memory used=1406.7MB, alloc=564.3MB, time=18.49 memory used=1582.5MB, alloc=588.3MB, time=22.60 memory used=1782.2MB, alloc=612.3MB, time=27.21 memory used=2005.9MB, alloc=612.3MB, time=32.26 memory used=2229.7MB, alloc=636.3MB, time=37.20 memory used=2477.9MB, alloc=660.3MB, time=42.02 N1 := 6833 > GB := Basis(F, plex(op(vars))); 5 7 3 2 GB := [x + 1, 4 y - 1, 2 y x + z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 987 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 4 2 2 3 H := [18 x y - 9 y z , 18 x - 18 y z , -20 x y z - 20, -11 y z - 3 z, 3 3 4 3 -15 x z - 15 y z, -18 z - 16 z ] > J:=[op(GB),op(G)]; 5 7 3 2 3 3 3 J := [x + 1, 4 y - 1, 2 y x + z, -11 y z - 3 z, -15 x z - 15 y z, 4 3 -18 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 := [6, 15, 24, 4, 4, 3, 4, 2/3, 5/6, 1, 1/3, 1/2, 3/4, 6, 11, 29, 7, 5, 7, 4, 1/2, 2/3, 2/3, 1/4, 1/3, 7/12, 4, -5, -3] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=2637.3MB, alloc=660.3MB, time=43.71 |\^/| 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(); 1428370960 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 3 3 3 F := [10 x y + 19 z , -8 x y + 3 y , -5 x + 3 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 2 G := [-7 y + 19 y z , 11 x y z - 18 y z, -15 x z + 10 y z] > Problem := [F,G]; 3 4 3 3 3 Problem := [[10 x y + 19 z , -8 x y + 3 y , -5 x + 3 x y], 4 2 2 2 3 2 [-7 y + 19 y z , 11 x y z - 18 y z, -15 x z + 10 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.4MB, alloc=32.3MB, time=0.37 memory used=48.3MB, alloc=32.3MB, time=0.55 memory used=69.3MB, alloc=32.3MB, time=0.75 memory used=90.6MB, alloc=56.3MB, time=0.99 memory used=133.8MB, alloc=60.3MB, time=1.44 memory used=173.2MB, alloc=84.3MB, time=1.85 memory used=230.6MB, alloc=108.3MB, time=2.48 memory used=300.1MB, alloc=132.3MB, time=3.65 memory used=385.9MB, alloc=132.3MB, time=5.15 N1 := 2529 > GB := Basis(F, plex(op(vars))); 8 7 3 7 3 5 4 GB := [8 x - 3 x , -5 x + 3 x y, -1000 x + 81 y , 50 x + 57 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=473.8MB, alloc=132.3MB, time=6.27 memory used=564.8MB, alloc=420.3MB, time=7.19 memory used=685.4MB, alloc=444.3MB, time=8.49 memory used=822.8MB, alloc=468.3MB, time=9.90 memory used=962.6MB, alloc=492.3MB, time=12.21 memory used=1098.3MB, alloc=516.3MB, time=15.28 memory used=1256.1MB, alloc=540.3MB, time=18.85 memory used=1438.0MB, alloc=564.3MB, time=22.74 N2 := 4795 #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)]; 4 3 3 3 3 4 2 2 H := [19 z + 10 y x , -8 x y + 3 y , -5 x + 3 x y, -7 y + 19 y z , 2 3 2 11 x y z - 18 y z, -15 x z + 10 y z] > J:=[op(GB),op(G)]; 8 7 3 7 3 5 4 J := [8 x - 3 x , -5 x + 3 x y, -1000 x + 81 y , 50 x + 57 z , 4 2 2 2 3 2 -7 y + 19 y z , 11 x y z - 18 y z, -15 x z + 10 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 := [6, 15, 22, 4, 3, 4, 4, 5/6, 1, 2/3, 1/2, 3/4, 1/2, 7, 15, 34, 8, 8, 4, 4, 6/7, 5/7, 4/7, 4/7, 1/2, 3/7, 0, -12, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1598.0MB, alloc=564.3MB, time=25.42 |\^/| 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(); 1428370985 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 F := [7 x y, -16 y z - 13 y z, 10 x + 9 y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 4 3 G := [4 x y - 14 z, 5 y z + 20 x y, -10 y + 9 z ] > Problem := [F,G]; 2 Problem := [[7 x y, -16 y z - 13 y z, 10 x + 9 y], 3 3 4 3 [4 x y - 14 z, 5 y z + 20 x y, -10 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=0.14 memory used=26.5MB, alloc=32.3MB, time=0.36 memory used=48.3MB, alloc=32.3MB, time=0.55 memory used=69.1MB, alloc=32.3MB, time=0.74 memory used=88.5MB, alloc=56.3MB, time=0.92 memory used=143.6MB, alloc=92.3MB, time=1.47 memory used=213.6MB, alloc=92.3MB, time=2.22 memory used=272.5MB, alloc=116.3MB, time=2.95 memory used=339.3MB, alloc=140.3MB, time=4.08 N1 := 1965 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x , 9 y + 10 x, 16 x z + 13 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=434.3MB, alloc=148.3MB, time=5.15 memory used=539.8MB, alloc=148.3MB, time=6.20 memory used=641.3MB, alloc=172.3MB, time=7.39 memory used=740.4MB, alloc=196.3MB, time=9.06 N2 := 1965 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 H := [7 y x, -16 y z - 13 y z, 9 y + 10 x, 4 x y - 14 z, 5 y z + 20 x y, 4 3 -10 y + 9 z ] > J:=[op(GB),op(G)]; 2 2 3 3 J := [x , 9 y + 10 x, 16 x z + 13 x z, 4 x y - 14 z, 5 y z + 20 x y, 4 3 -10 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 := [6, 14, 18, 4, 3, 4, 3, 2/3, 1, 2/3, 4/13, 8/13, 5/13, 6, 13, 18, 4, 3, 4, 3, 5/6, 2/3, 2/3, 1/2, 5/12, 5/12, 1, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=746.0MB, alloc=196.3MB, time=9.15 |\^/| 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(); 1428370994 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 3 F := [19 x y z + y , -15 x z - 17 x y , 10 x y + 3 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 G := [10 y z - 10 x , -2 z + 3 x , 9 x z + 20 x] > Problem := [F,G]; 2 2 2 2 3 3 Problem := [[19 x y z + y , -15 x z - 17 x y , 10 x y + 3 x z], 2 2 2 3 2 3 [10 y z - 10 x , -2 z + 3 x , 9 x z + 20 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.5MB, alloc=32.3MB, time=0.35 memory used=48.0MB, alloc=32.3MB, time=0.52 memory used=68.8MB, alloc=56.3MB, time=0.72 memory used=109.5MB, alloc=60.3MB, time=1.09 memory used=149.3MB, alloc=84.3MB, time=1.45 memory used=211.8MB, alloc=116.3MB, time=2.03 memory used=289.6MB, alloc=372.3MB, time=2.76 memory used=373.0MB, alloc=396.3MB, time=3.48 memory used=471.5MB, alloc=420.3MB, time=4.42 memory used=589.8MB, alloc=444.3MB, time=5.53 memory used=735.0MB, alloc=468.3MB, time=6.84 memory used=859.9MB, alloc=492.3MB, time=7.76 memory used=1005.9MB, alloc=516.3MB, time=9.23 memory used=1126.8MB, alloc=516.3MB, time=10.42 memory used=1220.0MB, alloc=540.3MB, time=11.21 memory used=1306.7MB, alloc=540.3MB, time=12.20 memory used=1398.2MB, alloc=540.3MB, time=13.15 memory used=1483.2MB, alloc=540.3MB, time=14.06 memory used=1568.2MB, alloc=540.3MB, time=15.13 memory used=1654.3MB, alloc=540.3MB, time=16.25 memory used=1716.6MB, alloc=540.3MB, time=17.12 memory used=1780.1MB, alloc=540.3MB, time=17.99 memory used=1825.3MB, alloc=540.3MB, time=18.66 memory used=1881.4MB, alloc=540.3MB, time=19.46 memory used=1922.3MB, alloc=540.3MB, time=20.09 memory used=2139.1MB, alloc=564.3MB, time=22.19 memory used=2326.0MB, alloc=588.3MB, time=24.08 memory used=2508.5MB, alloc=612.3MB, time=26.06 memory used=2692.9MB, alloc=636.3MB, time=28.04 memory used=2835.5MB, alloc=660.3MB, time=29.78 memory used=3009.3MB, alloc=684.3MB, time=31.96 memory used=3158.8MB, alloc=708.3MB, time=33.77 memory used=3302.1MB, alloc=708.3MB, time=35.67 memory used=3427.9MB, alloc=732.3MB, time=37.28 memory used=3587.6MB, alloc=732.3MB, time=39.57 memory used=3674.2MB, alloc=732.3MB, time=41.07 memory used=3789.1MB, alloc=756.3MB, time=42.65 memory used=3899.2MB, alloc=756.3MB, time=44.46 memory used=4290.0MB, alloc=780.3MB, time=48.79 memory used=4639.8MB, alloc=804.3MB, time=53.45 memory used=4973.9MB, alloc=828.3MB, time=58.15 memory used=5306.1MB, alloc=852.3MB, time=62.89 memory used=5639.7MB, alloc=876.3MB, time=67.69 memory used=5996.1MB, alloc=900.3MB, time=72.43 memory used=6392.7MB, alloc=924.3MB, time=76.99 memory used=6793.9MB, alloc=948.3MB, time=81.70 memory used=7146.2MB, alloc=972.3MB, time=86.97 memory used=7494.6MB, alloc=996.3MB, time=93.50 memory used=7792.0MB, alloc=1020.3MB, time=101.32 memory used=8086.1MB, alloc=1044.3MB, time=109.73 memory used=8385.9MB, alloc=1068.3MB, time=118.13 memory used=8693.5MB, alloc=1092.3MB, time=127.03 memory used=9011.0MB, alloc=1116.3MB, time=136.34 memory used=9339.7MB, alloc=1140.3MB, time=146.07 memory used=9681.3MB, alloc=1164.3MB, time=156.22 memory used=10034.9MB, alloc=1188.3MB, time=166.64 memory used=10399.1MB, alloc=1212.3MB, time=177.70 memory used=10778.2MB, alloc=1236.3MB, time=189.21 memory used=11173.7MB, alloc=1260.3MB, time=201.20 memory used=11585.4MB, alloc=1284.3MB, time=213.71 memory used=12009.7MB, alloc=1308.3MB, time=226.88 memory used=12451.0MB, alloc=1332.3MB, time=240.83 memory used=12916.2MB, alloc=1356.3MB, time=255.35 memory used=13405.4MB, alloc=1380.3MB, time=270.57 memory used=13918.5MB, alloc=1404.3MB, time=286.42 memory used=14455.6MB, alloc=1428.3MB, time=303.10 |\^/| 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(); 1428371294 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 F := [-20 z - 17 z , 3 x y z + 8 x z, -17 y z - 16 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 G := [-x y z + 12 x z , -12 x y + 13 x z , 16 y z] > Problem := [F,G]; 3 2 2 2 3 2 Problem := [[-20 z - 17 z , 3 x y z + 8 x z, -17 y z - 16 x z], 2 3 3 3 [-x y z + 12 x z , -12 x y + 13 x z , 16 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.42 memory used=47.8MB, alloc=32.3MB, time=0.66 memory used=67.5MB, alloc=56.3MB, time=0.87 memory used=108.3MB, alloc=60.3MB, time=1.33 memory used=146.7MB, alloc=60.3MB, time=1.76 memory used=183.4MB, alloc=84.3MB, time=2.22 memory used=237.9MB, alloc=84.3MB, time=2.86 memory used=296.9MB, alloc=116.3MB, time=3.84 memory used=373.9MB, alloc=140.3MB, time=4.99 memory used=469.1MB, alloc=164.3MB, time=6.00 memory used=598.8MB, alloc=164.3MB, time=6.93 memory used=707.1MB, alloc=188.3MB, time=8.08 memory used=817.5MB, alloc=212.3MB, time=9.87 memory used=934.8MB, alloc=236.3MB, time=12.28 memory used=1063.8MB, alloc=260.3MB, time=15.31 memory used=1216.7MB, alloc=284.3MB, time=18.84 memory used=1393.5MB, alloc=284.3MB, time=22.86 memory used=1570.4MB, alloc=308.3MB, time=26.85 memory used=1771.3MB, alloc=308.3MB, time=31.17 N1 := 6225 > GB := Basis(F, plex(op(vars))); 4 3 3 2 3 2 GB := [256000 x z + 7803 x z, -160 x z + 51 x y z, 17 y z + 16 x z, 2 2 2 2 2 3 2 20 x z + 17 x z, 3 x y z + 8 x z, 20 z + 17 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1976.8MB, alloc=308.3MB, time=34.61 memory used=2067.3MB, alloc=564.3MB, time=35.69 memory used=2299.0MB, alloc=588.3MB, time=38.37 memory used=2569.5MB, alloc=612.3MB, time=40.91 memory used=2828.4MB, alloc=636.3MB, time=45.19 memory used=3055.6MB, alloc=660.3MB, time=50.62 memory used=3304.9MB, alloc=684.3MB, time=56.53 memory used=3578.3MB, alloc=708.3MB, time=62.81 memory used=3875.9MB, alloc=732.3MB, time=68.83 N2 := 6225 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 2 2 3 H := [-20 z - 17 z , 3 x y z + 8 x z, -17 y z - 16 x z, -x y z + 12 x z , 3 3 -12 x y + 13 x z , 16 z y] > J:=[op(GB),op(G)]; 4 3 3 2 3 2 J := [256000 x z + 7803 x z, -160 x z + 51 x y z, 17 y z + 16 x z, 2 2 2 2 2 3 2 2 3 20 x z + 17 x z, 3 x y z + 8 x z, 20 z + 17 z , -x y z + 12 x z , 3 3 -12 x y + 13 x z , 16 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 := [6, 15, 21, 4, 3, 3, 3, 2/3, 5/6, 1, 7/13, 5/13, 10/13, 9, 22, 34, 5, 4, 3, 3, 7/9, 2/3, 1, 13/19, 6/19, 16/19, -7, -13, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3885.3MB, alloc=732.3MB, time=68.99 |\^/| 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(); 1428371362 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 2 F := [20 x + 15 y , 6 x y + 6 x z , 14 x y - 7 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 4 3 G := [3 x y + 16 z , 10 x z + 12 z , -4 x y ] > Problem := [F,G]; 4 2 3 2 2 2 Problem := [[20 x + 15 y , 6 x y + 6 x z , 14 x y - 7 z], 2 2 2 3 4 3 [3 x y + 16 z , 10 x z + 12 z , -4 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.6MB, alloc=32.3MB, time=0.37 memory used=47.8MB, alloc=32.3MB, time=0.56 memory used=67.8MB, alloc=32.3MB, time=0.74 memory used=87.2MB, alloc=56.3MB, time=0.92 memory used=128.2MB, alloc=60.3MB, time=1.29 memory used=166.9MB, alloc=60.3MB, time=1.63 memory used=203.5MB, alloc=84.3MB, time=1.97 memory used=261.0MB, alloc=92.3MB, time=2.53 memory used=317.8MB, alloc=116.3MB, time=3.15 memory used=391.7MB, alloc=140.3MB, time=4.10 N1 := 1351 > GB := Basis(F, plex(op(vars))); 21 7 12 3 4 2 5 GB := [1024 x + 27 x , 64 x + 9 x y, 4 x + 3 y , 8 x + 3 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=478.0MB, alloc=140.3MB, time=5.04 N2 := 479 #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)]; 4 2 3 2 2 2 2 2 2 H := [20 x + 15 y , 6 x y + 6 x z , 14 x y - 7 z, 3 y x + 16 z , 3 4 3 10 x z + 12 z , -4 y x] > J:=[op(GB),op(G)]; 21 7 12 3 4 2 5 J := [1024 x + 27 x , 64 x + 9 x y, 4 x + 3 y , 8 x + 3 z, 2 2 2 3 4 3 3 y x + 16 z , 10 x z + 12 z , -4 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 := [6, 15, 23, 4, 4, 3, 4, 1, 5/6, 2/3, 7/13, 5/13, 5/13, 7, 14, 54, 21, 21, 3, 4, 1, 4/7, 3/7, 3/5, 4/15, 4/15, 1, -31, -17] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=549.5MB, alloc=140.3MB, time=5.72 |\^/| 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(); 1428371368 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 F := [7 x - 16 y , 8 x y + 13 y , -6 x z - 14 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 3 G := [9 x z - 2 x z, -7 y z - 16 y, 12 x - 5 x y ] > Problem := [F,G]; 2 2 3 3 3 Problem := [[7 x - 16 y , 8 x y + 13 y , -6 x z - 14 x z], 2 2 2 4 3 [9 x z - 2 x z, -7 y z - 16 y, 12 x - 5 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.11 memory used=27.0MB, alloc=32.3MB, time=0.32 N1 := 273 > GB := Basis(F, plex(op(vars))); 5 4 3 2 2 2 3 GB := [8 x + 13 x , 8 x y + 13 x y, -7 x + 16 y , 3 x z + 7 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=47.8MB, alloc=32.3MB, time=0.54 memory used=68.3MB, alloc=56.3MB, time=0.78 N2 := 273 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 3 2 2 2 H := [-16 y + 7 x , 8 x y + 13 y , -6 x z - 14 x z, 9 x z - 2 x z, 4 3 -7 y z - 16 y, 12 x - 5 x y ] > J:=[op(GB),op(G)]; 5 4 3 2 2 2 3 J := [8 x + 13 x , 8 x y + 13 x y, -7 x + 16 y , 3 x z + 7 x z, 2 2 2 4 3 9 x z - 2 x z, -7 y z - 16 y, 12 x - 5 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 := [6, 12, 20, 4, 4, 3, 3, 5/6, 2/3, 1/2, 2/3, 1/2, 5/12, 7, 13, 25, 5, 5, 3, 3, 6/7, 4/7, 3/7, 11/14, 3/7, 5/14, -1, -5, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=70.5MB, alloc=56.3MB, time=0.82 |\^/| 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(); 1428371369 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 3 F := [-20 z + 13 z , 13 x z + 6 x z, -2 x z - 7 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 2 2 2 G := [18 x y + 5 x y z , -2 z + 7 y , -8 x y z + 13 x y z] > Problem := [F,G]; 4 2 2 3 3 Problem := [[-20 z + 13 z , 13 x z + 6 x z, -2 x z - 7 y z], 2 2 2 4 2 2 2 [18 x y + 5 x y z , -2 z + 7 y , -8 x y z + 13 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.11 memory used=26.3MB, alloc=32.3MB, time=0.29 memory used=47.5MB, alloc=32.3MB, time=0.47 memory used=67.9MB, alloc=32.3MB, time=0.65 memory used=86.9MB, alloc=56.3MB, time=0.83 memory used=127.5MB, alloc=60.3MB, time=1.23 memory used=166.5MB, alloc=84.3MB, time=1.66 memory used=224.1MB, alloc=108.3MB, time=2.28 memory used=298.6MB, alloc=140.3MB, time=3.12 memory used=387.0MB, alloc=164.3MB, time=4.16 memory used=484.8MB, alloc=188.3MB, time=5.26 memory used=586.2MB, alloc=212.3MB, time=6.84 memory used=696.8MB, alloc=236.3MB, time=8.87 memory used=819.7MB, alloc=260.3MB, time=11.35 memory used=954.2MB, alloc=284.3MB, time=14.51 memory used=1112.6MB, alloc=308.3MB, time=18.19 memory used=1294.9MB, alloc=308.3MB, time=22.50 memory used=1477.2MB, alloc=308.3MB, time=26.72 memory used=1659.5MB, alloc=332.3MB, time=30.92 memory used=1865.7MB, alloc=332.3MB, time=35.63 memory used=2071.8MB, alloc=332.3MB, time=40.32 memory used=2277.8MB, alloc=356.3MB, time=45.02 memory used=2507.8MB, alloc=356.3MB, time=50.21 memory used=2737.7MB, alloc=356.3MB, time=55.34 memory used=2967.6MB, alloc=380.3MB, time=60.39 memory used=3221.3MB, alloc=404.3MB, time=65.52 N1 := 9657 > GB := Basis(F, plex(op(vars))); 3 4 2 GB := [x z, z y , 20 z - 13 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3388.6MB, alloc=404.3MB, time=67.91 N2 := 1195 #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)]; 4 2 2 3 3 2 2 2 H := [-20 z + 13 z , 13 x z + 6 x z, -2 x z - 7 y z, 18 x y + 5 x y z , 4 2 2 2 -2 z + 7 y , -8 x y z + 13 x y z] > J:=[op(GB),op(G)]; 3 4 2 2 2 2 4 2 J := [x z, z y , 20 z - 13 z , 18 x y + 5 x y z , -2 z + 7 y , 2 2 -8 x y z + 13 x 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 := [6, 14, 23, 4, 3, 3, 4, 2/3, 2/3, 1, 7/12, 1/2, 5/6, 6, 13, 22, 4, 2, 3, 4, 1/2, 2/3, 1, 5/12, 1/2, 2/3, 1, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3439.1MB, alloc=660.3MB, time=68.68 |\^/| 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(); 1428371436 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [10 x y + 19 x z, -19 x z - 18 x z, 18 x z - 18 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 3 2 G := [-9 y z + 8 x y, 20 x + 18 x z, -18 y + 13 y ] > Problem := [F,G]; 3 2 3 2 Problem := [[10 x y + 19 x z, -19 x z - 18 x z, 18 x z - 18 x z ], 2 4 3 2 [-9 y z + 8 x y, 20 x + 18 x z, -18 y + 13 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.2MB, alloc=32.3MB, time=0.34 memory used=47.3MB, alloc=32.3MB, time=0.51 memory used=67.4MB, alloc=32.3MB, time=0.68 memory used=87.6MB, alloc=56.3MB, time=0.90 memory used=130.4MB, alloc=56.3MB, time=1.34 memory used=166.5MB, alloc=80.3MB, time=1.73 memory used=196.0MB, alloc=108.3MB, time=2.07 memory used=267.2MB, alloc=132.3MB, time=3.15 memory used=351.6MB, alloc=132.3MB, time=4.67 memory used=436.2MB, alloc=132.3MB, time=6.03 N1 := 2869 > GB := Basis(F, plex(op(vars))); 3 GB := [x y , x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 165 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 2 H := [10 x y + 19 x z, -19 x z - 18 x z, 18 x z - 18 x z , -9 y z + 8 x y, 4 3 2 20 x + 18 x z, -18 y + 13 y ] > J:=[op(GB),op(G)]; 3 2 4 3 2 J := [x y , x z, -9 y z + 8 x y, 20 x + 18 x z, -18 y + 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 := [6, 13, 21, 4, 4, 3, 3, 5/6, 1/2, 5/6, 3/4, 5/12, 7/12, 5, 10, 16, 4, 4, 3, 2, 4/5, 3/5, 3/5, 1/2, 1/2, 3/10, 3, 5, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=486.3MB, alloc=132.3MB, time=6.63 |\^/| 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(); 1428371443 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [-6 y z - 3 x, -11 x y z + 11 y z , 10 y z - 2 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 2 G := [17 x y + 16 x y z, -x y z - 18 z , -9 x y z + x y] > Problem := [F,G]; 3 2 3 2 Problem := [[-6 y z - 3 x, -11 x y z + 11 y z , 10 y z - 2 z], 3 2 2 3 2 2 [17 x y + 16 x y z, -x y z - 18 z , -9 x y z + x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.11 memory used=26.3MB, alloc=32.3MB, time=0.29 memory used=48.0MB, alloc=32.3MB, time=0.50 memory used=68.1MB, alloc=32.3MB, time=0.71 memory used=87.0MB, alloc=56.3MB, time=0.89 memory used=124.5MB, alloc=60.3MB, time=1.22 memory used=160.2MB, alloc=84.3MB, time=1.54 memory used=214.5MB, alloc=84.3MB, time=2.02 memory used=270.4MB, alloc=116.3MB, time=2.53 memory used=352.8MB, alloc=116.3MB, time=3.19 memory used=428.8MB, alloc=140.3MB, time=3.88 memory used=496.0MB, alloc=396.3MB, time=4.45 memory used=587.4MB, alloc=420.3MB, time=5.29 memory used=703.3MB, alloc=444.3MB, time=6.32 memory used=845.1MB, alloc=468.3MB, time=7.92 memory used=997.6MB, alloc=492.3MB, time=9.62 memory used=1160.5MB, alloc=516.3MB, time=11.45 memory used=1332.9MB, alloc=540.3MB, time=13.43 memory used=1516.0MB, alloc=564.3MB, time=15.57 memory used=1710.3MB, alloc=588.3MB, time=17.84 memory used=1876.1MB, alloc=612.3MB, time=19.87 memory used=2067.4MB, alloc=636.3MB, time=23.53 memory used=2254.9MB, alloc=660.3MB, time=27.71 memory used=2451.0MB, alloc=684.3MB, time=32.42 memory used=2657.6MB, alloc=708.3MB, time=37.68 memory used=2876.6MB, alloc=732.3MB, time=43.42 memory used=3108.0MB, alloc=756.3MB, time=49.62 memory used=3354.9MB, alloc=780.3MB, time=56.47 memory used=3625.9MB, alloc=804.3MB, time=63.92 memory used=3920.7MB, alloc=828.3MB, time=72.12 memory used=4239.5MB, alloc=852.3MB, time=80.81 memory used=4582.3MB, alloc=876.3MB, time=90.12 memory used=4949.0MB, alloc=900.3MB, time=100.08 memory used=5339.7MB, alloc=924.3MB, time=110.67 memory used=5754.2MB, alloc=924.3MB, time=121.85 memory used=6168.8MB, alloc=948.3MB, time=133.18 memory used=6607.3MB, alloc=948.3MB, time=145.02 memory used=7045.7MB, alloc=948.3MB, time=156.81 memory used=7484.0MB, alloc=948.3MB, time=168.61 memory used=7922.2MB, alloc=972.3MB, time=180.38 memory used=8384.2MB, alloc=972.3MB, time=192.89 memory used=8846.1MB, alloc=972.3MB, time=205.26 memory used=9307.9MB, alloc=996.3MB, time=217.61 memory used=9793.5MB, alloc=996.3MB, time=230.56 memory used=10279.1MB, alloc=1020.3MB, time=243.52 memory used=10788.5MB, alloc=1020.3MB, time=257.12 memory used=11297.9MB, alloc=1044.3MB, time=270.52 memory used=11831.6MB, alloc=1068.3MB, time=284.36 memory used=12389.4MB, alloc=1092.3MB, time=298.16 N1 := 18811 > GB := Basis(F, plex(op(vars))); 4 2 3 2 2 GB := [78125 x - 16 x , -125 x + 4 x y, 5 x y - x, 25 x y + 2 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428371743 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 3 3 2 2 3 F := [6 y + 7 z, -7 y z + 18 z , -18 x z + 10 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 2 G := [2 x y + 2 y z, y z - 6 z , 12 z - 9 z] > Problem := [F,G]; 4 3 3 2 2 3 Problem := [[6 y + 7 z, -7 y z + 18 z , -18 x z + 10 x ], 2 2 2 2 3 2 [2 x y + 2 y z, y z - 6 z , 12 z - 9 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.0MB, alloc=32.3MB, time=0.40 memory used=47.0MB, alloc=32.3MB, time=0.62 memory used=66.6MB, alloc=32.3MB, time=0.82 memory used=85.8MB, alloc=56.3MB, time=1.04 memory used=123.7MB, alloc=60.3MB, time=1.50 memory used=159.3MB, alloc=84.3MB, time=1.92 memory used=217.8MB, alloc=84.3MB, time=2.76 memory used=271.2MB, alloc=108.3MB, time=3.47 memory used=342.0MB, alloc=132.3MB, time=4.50 memory used=429.1MB, alloc=164.3MB, time=5.65 memory used=525.5MB, alloc=188.3MB, time=6.90 memory used=624.9MB, alloc=212.3MB, time=8.66 memory used=733.9MB, alloc=236.3MB, time=10.96 memory used=861.7MB, alloc=260.3MB, time=13.83 memory used=1013.5MB, alloc=260.3MB, time=17.15 memory used=1165.2MB, alloc=284.3MB, time=20.45 memory used=1340.9MB, alloc=284.3MB, time=24.24 memory used=1516.6MB, alloc=308.3MB, time=27.92 memory used=1716.2MB, alloc=308.3MB, time=31.85 N1 := 6655 > GB := Basis(F, plex(op(vars))); 5 4 4 4 GB := [1412376245 x - 3570467226624 x , 7 x y - 18 x , 3 4 4 2 8 3 13 12 4 34012224 x y - 588245 x , 324 x y - 245 x , 7 y - 18 y , 6 y + 7 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1917.4MB, alloc=308.3MB, time=34.65 memory used=2012.2MB, alloc=564.3MB, time=35.70 memory used=2237.0MB, alloc=588.3MB, time=38.14 memory used=2467.3MB, alloc=612.3MB, time=42.09 memory used=2678.0MB, alloc=636.3MB, time=47.23 memory used=2910.8MB, alloc=660.3MB, time=52.88 memory used=3167.7MB, alloc=684.3MB, time=58.99 memory used=3448.8MB, alloc=708.3MB, time=64.98 N2 := 6121 #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)]; 4 3 3 2 2 3 2 2 H := [6 y + 7 z, -7 y z + 18 z , -18 x z + 10 x , 2 x y + 2 y z, 2 2 3 2 y z - 6 z , 12 z - 9 z] > J:=[op(GB),op(G)]; 5 4 4 4 J := [1412376245 x - 3570467226624 x , 7 x y - 18 x , 3 4 4 2 8 3 13 12 4 34012224 x y - 588245 x , 324 x y - 245 x , 7 y - 18 y , 6 y + 7 z, 2 2 2 2 3 2 2 x y + 2 y z, y z - 6 z , 12 z - 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 := [6, 12, 21, 4, 3, 4, 3, 1/3, 2/3, 1, 1/4, 5/12, 3/4, 9, 16, 53, 13, 5, 13, 3, 5/9, 7/9, 4/9, 1/2, 1/2, 1/3, -4, -32, -9] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3490.1MB, alloc=708.3MB, time=65.61 |\^/| 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(); 1428371808 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 F := [2 x y - 14 x, 2 x - x z , -11 x - 7] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 3 2 G := [19 x z + x y z, 10 x - 13 x z, -8 x z - 15 x y z] > Problem := [F,G]; 4 2 4 Problem := [[2 x y - 14 x, 2 x - x z , -11 x - 7], 2 2 2 3 2 3 2 [19 x z + x y z, 10 x - 13 x z, -8 x z - 15 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.2MB, alloc=32.3MB, time=0.35 memory used=47.8MB, alloc=32.3MB, time=0.54 memory used=69.8MB, alloc=56.3MB, time=0.77 memory used=113.6MB, alloc=60.3MB, time=1.20 N1 := 881 > GB := Basis(F, plex(op(vars))); 4 3 2 GB := [11 x + 7, y - 7, -2 x + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=148.2MB, alloc=60.3MB, time=1.64 memory used=184.3MB, alloc=84.3MB, time=1.94 memory used=248.6MB, alloc=84.3MB, time=2.69 N2 := 881 #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)]; 4 2 4 2 2 2 3 2 H := [2 x y - 14 x, 2 x - x z , -11 x - 7, 19 x z + x y z, 10 x - 13 x z, 3 2 -8 x z - 15 x y z] > J:=[op(GB),op(G)]; 4 3 2 2 2 2 3 2 J := [11 x + 7, y - 7, -2 x + z , 19 x z + x y z, 10 x - 13 x z, 3 2 -8 x z - 15 x 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 := [6, 13, 21, 4, 4, 2, 2, 1, 1/2, 2/3, 11/12, 1/4, 1/2, 6, 12, 19, 4, 4, 2, 2, 5/6, 1/2, 2/3, 2/3, 1/4, 1/2, 1, 2, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=276.7MB, alloc=84.3MB, time=3.05 |\^/| 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(); 1428371811 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 2 2 3 2 F := [-14 x z + 7 y , -4 x + 8 x z , 19 x z - 2 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 G := [14 x y z - 20 y z , -3 z - 2 x, 2 x z + 7 y z] > Problem := [F,G]; 2 4 2 2 3 2 Problem := [[-14 x z + 7 y , -4 x + 8 x z , 19 x z - 2 x z], 2 2 2 2 2 3 [14 x y z - 20 y z , -3 z - 2 x, 2 x z + 7 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.12 memory used=26.8MB, alloc=32.3MB, time=0.32 memory used=48.2MB, alloc=32.3MB, time=0.50 memory used=68.4MB, alloc=56.3MB, time=0.69 memory used=109.1MB, alloc=60.3MB, time=1.04 memory used=149.0MB, alloc=84.3MB, time=1.38 memory used=210.3MB, alloc=92.3MB, time=1.97 memory used=268.7MB, alloc=116.3MB, time=2.52 memory used=349.6MB, alloc=116.3MB, time=3.18 memory used=427.0MB, alloc=396.3MB, time=3.87 memory used=527.3MB, alloc=396.3MB, time=4.77 memory used=625.8MB, alloc=420.3MB, time=5.62 memory used=749.9MB, alloc=444.3MB, time=6.65 memory used=896.5MB, alloc=468.3MB, time=8.12 memory used=1049.4MB, alloc=492.3MB, time=9.79 memory used=1205.8MB, alloc=516.3MB, time=11.59 memory used=1390.3MB, alloc=540.3MB, time=13.57 memory used=1579.8MB, alloc=564.3MB, time=15.74 memory used=1771.3MB, alloc=588.3MB, time=18.11 memory used=1972.5MB, alloc=612.3MB, time=20.56 memory used=2153.6MB, alloc=636.3MB, time=24.03 memory used=2334.6MB, alloc=660.3MB, time=27.98 memory used=2524.4MB, alloc=684.3MB, time=32.41 memory used=2725.5MB, alloc=708.3MB, time=37.28 memory used=2936.0MB, alloc=732.3MB, time=42.57 memory used=3157.6MB, alloc=756.3MB, time=48.52 memory used=3403.0MB, alloc=780.3MB, time=55.03 memory used=3672.4MB, alloc=804.3MB, time=62.29 memory used=3965.7MB, alloc=828.3MB, time=70.04 memory used=4283.0MB, alloc=852.3MB, time=78.41 memory used=4624.2MB, alloc=876.3MB, time=87.35 memory used=4989.4MB, alloc=900.3MB, time=96.86 memory used=5378.5MB, alloc=924.3MB, time=107.00 memory used=5791.5MB, alloc=924.3MB, time=117.70 memory used=6204.5MB, alloc=924.3MB, time=128.59 memory used=6617.5MB, alloc=948.3MB, time=139.24 memory used=7054.4MB, alloc=948.3MB, time=150.52 memory used=7491.1MB, alloc=948.3MB, time=161.71 memory used=7927.7MB, alloc=972.3MB, time=172.87 memory used=8388.3MB, alloc=972.3MB, time=184.71 memory used=8848.7MB, alloc=972.3MB, time=196.41 memory used=9309.0MB, alloc=996.3MB, time=208.10 memory used=9793.1MB, alloc=996.3MB, time=220.33 memory used=10277.2MB, alloc=1020.3MB, time=232.54 memory used=10785.3MB, alloc=1044.3MB, time=245.40 memory used=11317.4MB, alloc=1044.3MB, time=258.41 memory used=11849.9MB, alloc=1068.3MB, time=270.81 N1 := 18461 > GB := Basis(F, plex(op(vars))); GB := [ 6 5 3 2 2 2 4 4 2 2 2 2 19 x - 4 x , 19 x y - 4 x y , -2 x + y , 2 z x - y , 19 y z - 2 x y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=12421.0MB, alloc=1068.3MB, time=278.42 memory used=13081.1MB, alloc=1092.3MB, time=286.82 memory used=13697.7MB, alloc=1116.3MB, time=301.74 |\^/| 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(); 1428372111 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [-11 y z - 9 x y, 12 x z - 3 x y z, 7 x y z - x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [20 x y z + 8 y , -15 x y + 16 z, 19 y z + 13 z ] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[-11 y z - 9 x y, 12 x z - 3 x y z, 7 x y z - x y], 2 2 2 2 [20 x y z + 8 y , -15 x y + 16 z, 19 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=4.3MB, alloc=32.3MB, time=0.13 memory used=26.7MB, alloc=32.3MB, time=0.37 memory used=47.8MB, alloc=32.3MB, time=0.58 memory used=68.4MB, alloc=56.3MB, time=0.84 memory used=109.8MB, alloc=60.3MB, time=1.31 memory used=148.3MB, alloc=84.3MB, time=1.77 memory used=207.4MB, alloc=92.3MB, time=2.48 memory used=264.3MB, alloc=116.3MB, time=3.16 memory used=341.8MB, alloc=116.3MB, time=4.19 memory used=420.0MB, alloc=396.3MB, time=5.16 memory used=521.8MB, alloc=420.3MB, time=6.37 memory used=646.1MB, alloc=444.3MB, time=7.85 memory used=792.9MB, alloc=468.3MB, time=9.65 memory used=920.4MB, alloc=468.3MB, time=11.17 memory used=1048.6MB, alloc=492.3MB, time=12.94 memory used=1159.5MB, alloc=492.3MB, time=14.54 memory used=1292.6MB, alloc=516.3MB, time=16.21 memory used=1399.1MB, alloc=516.3MB, time=17.35 memory used=1502.6MB, alloc=516.3MB, time=18.48 memory used=1601.2MB, alloc=540.3MB, time=19.61 memory used=1696.0MB, alloc=540.3MB, time=20.74 memory used=1784.2MB, alloc=540.3MB, time=21.83 memory used=1849.3MB, alloc=540.3MB, time=22.69 memory used=1922.3MB, alloc=540.3MB, time=23.63 memory used=1984.4MB, alloc=564.3MB, time=24.51 memory used=2053.7MB, alloc=564.3MB, time=25.53 memory used=2276.2MB, alloc=588.3MB, time=28.15 memory used=2485.8MB, alloc=612.3MB, time=30.80 memory used=2748.0MB, alloc=636.3MB, time=33.27 memory used=2985.4MB, alloc=660.3MB, time=36.28 memory used=3224.7MB, alloc=684.3MB, time=39.37 memory used=3465.0MB, alloc=708.3MB, time=42.51 memory used=3707.7MB, alloc=732.3MB, time=45.74 memory used=3952.8MB, alloc=756.3MB, time=49.03 memory used=4215.8MB, alloc=780.3MB, time=52.34 memory used=4494.1MB, alloc=804.3MB, time=56.12 memory used=4718.5MB, alloc=828.3MB, time=61.51 memory used=4944.7MB, alloc=852.3MB, time=67.25 memory used=5178.2MB, alloc=876.3MB, time=73.47 memory used=5421.6MB, alloc=900.3MB, time=79.97 memory used=5675.4MB, alloc=924.3MB, time=86.85 memory used=5941.6MB, alloc=948.3MB, time=94.22 memory used=6220.5MB, alloc=972.3MB, time=101.99 memory used=6512.7MB, alloc=996.3MB, time=110.20 memory used=6819.0MB, alloc=1020.3MB, time=118.84 memory used=7139.0MB, alloc=1044.3MB, time=128.01 memory used=7468.8MB, alloc=1068.3MB, time=137.60 memory used=7814.1MB, alloc=1092.3MB, time=147.84 memory used=8183.4MB, alloc=1116.3MB, time=158.78 memory used=8576.7MB, alloc=1140.3MB, time=170.32 memory used=8993.9MB, alloc=1164.3MB, time=182.54 memory used=9435.0MB, alloc=1188.3MB, time=195.51 memory used=9900.1MB, alloc=1212.3MB, time=209.00 memory used=10389.1MB, alloc=1236.3MB, time=223.14 memory used=10902.1MB, alloc=1260.3MB, time=237.91 memory used=11439.1MB, alloc=1284.3MB, time=253.49 memory used=12000.0MB, alloc=1308.3MB, time=269.61 memory used=12584.8MB, alloc=1332.3MB, time=286.37 memory used=13193.5MB, alloc=1356.3MB, time=303.78 |\^/| 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(); 1428372411 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [6 x y z - 2 x z, 4 x z - 20 y z, 16 x y z - 3 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 4 2 G := [-14 y + 16 y z , 13 x y z - 13 z, 12 z + 15 z ] > Problem := [F,G]; 2 2 2 Problem := [[6 x y z - 2 x z, 4 x z - 20 y z, 16 x y z - 3 x y], 3 2 2 4 2 [-14 y + 16 y z , 13 x y z - 13 z, 12 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=0.14 memory used=26.1MB, alloc=32.3MB, time=0.37 memory used=47.4MB, alloc=32.3MB, time=0.61 memory used=67.8MB, alloc=32.3MB, time=0.86 memory used=87.3MB, alloc=56.3MB, time=1.09 memory used=126.2MB, alloc=60.3MB, time=1.53 memory used=164.3MB, alloc=84.3MB, time=2.03 memory used=224.2MB, alloc=84.3MB, time=2.87 memory used=278.0MB, alloc=108.3MB, time=3.68 memory used=350.7MB, alloc=132.3MB, time=4.71 memory used=440.2MB, alloc=164.3MB, time=6.02 memory used=540.5MB, alloc=188.3MB, time=8.05 memory used=648.2MB, alloc=212.3MB, time=10.83 memory used=770.2MB, alloc=236.3MB, time=14.47 memory used=916.1MB, alloc=236.3MB, time=18.05 memory used=1062.1MB, alloc=236.3MB, time=21.10 memory used=1208.1MB, alloc=260.3MB, time=24.10 N1 := 5329 > GB := Basis(F, plex(op(vars))); 2 GB := [x y, z x, z y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1378.9MB, alloc=260.3MB, time=26.96 N2 := 79 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 H := [6 x y z - 2 x z, 4 x z - 20 y z, 16 x y z - 3 x y, -14 y + 16 y z , 2 4 2 13 x y z - 13 z, 12 z + 15 z ] > J:=[op(GB),op(G)]; 2 3 2 2 4 2 J := [x y, z x, z y , -14 y + 16 y z , 13 x y z - 13 z, 12 z + 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, 15, 21, 4, 2, 3, 4, 2/3, 5/6, 1, 1/2, 7/12, 5/6, 6, 12, 18, 4, 2, 3, 4, 1/2, 2/3, 5/6, 1/4, 5/12, 7/12, 3, 3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1391.4MB, alloc=260.3MB, time=27.09 |\^/| 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(); 1428372439 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 F := [-18 x y - 17 y z, 5 x y z - 6 y , 15 x z + 13 x z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 4 3 2 2 G := [19 x y - 2 y , 20 x - 20 x z, 18 x y z - 14 x y z] > Problem := [F,G]; 2 2 2 3 3 Problem := [[-18 x y - 17 y z, 5 x y z - 6 y , 15 x z + 13 x z ], 2 2 2 4 3 2 2 [19 x y - 2 y , 20 x - 20 x z, 18 x y z - 14 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.2MB, alloc=32.3MB, time=0.31 memory used=48.3MB, alloc=32.3MB, time=0.54 memory used=69.1MB, alloc=56.3MB, time=0.79 N1 := 723 > GB := Basis(F, plex(op(vars))); 2 2 3 2 2 2 3 3 GB := [y x , y , 5 x y z - 6 y , 18 x y + 17 y z, 15 x z + 13 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=111.0MB, alloc=56.3MB, time=1.28 memory used=149.8MB, alloc=60.3MB, time=1.63 memory used=189.0MB, alloc=84.3MB, time=2.03 N2 := 723 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 3 2 2 2 H := [-18 x y - 17 y z, 5 x y z - 6 y , 15 x z + 13 x z , 19 x y - 2 y , 4 3 2 2 20 x - 20 x z, 18 x y z - 14 x y z] > J:=[op(GB),op(G)]; 2 2 3 2 2 2 3 3 J := [y x , y , 5 x y z - 6 y , 18 x y + 17 y z, 15 x z + 13 x z , 2 2 2 4 3 2 2 19 x y - 2 y , 20 x - 20 x z, 18 x y z - 14 x 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 := [6, 15, 22, 4, 4, 2, 3, 1, 2/3, 5/6, 3/4, 2/3, 7/12, 8, 18, 29, 4, 4, 3, 3, 7/8, 3/4, 5/8, 5/8, 5/8, 7/16, -3, -7, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=210.2MB, alloc=84.3MB, time=2.31 |\^/| 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(); 1428372441 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [-8 x + 18, 8 x z - 14 y, -10 x y z + 17] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 2 G := [-16 x y + 5 z, 12 x y - 3 x z , 17 x z - 12 x y z ] > Problem := [F,G]; 3 2 2 2 Problem := [[-8 x + 18, 8 x z - 14 y, -10 x y z + 17], 2 3 3 2 2 2 [-16 x y + 5 z, 12 x y - 3 x z , 17 x z - 12 x y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.12 memory used=26.4MB, alloc=32.3MB, time=0.30 memory used=48.3MB, alloc=32.3MB, time=0.49 memory used=68.6MB, alloc=32.3MB, time=0.67 memory used=88.2MB, alloc=56.3MB, time=0.85 memory used=129.5MB, alloc=60.3MB, time=1.22 memory used=171.1MB, alloc=68.3MB, time=1.59 memory used=210.2MB, alloc=92.3MB, time=1.94 memory used=272.0MB, alloc=92.3MB, time=2.48 memory used=331.7MB, alloc=116.3MB, time=3.10 memory used=415.3MB, alloc=140.3MB, time=4.00 memory used=514.5MB, alloc=140.3MB, time=5.09 memory used=608.0MB, alloc=164.3MB, time=6.11 memory used=720.4MB, alloc=188.3MB, time=7.32 memory used=833.5MB, alloc=468.3MB, time=8.61 memory used=968.1MB, alloc=492.3MB, time=10.57 memory used=1102.4MB, alloc=516.3MB, time=13.15 memory used=1241.0MB, alloc=540.3MB, time=16.46 memory used=1401.7MB, alloc=564.3MB, time=20.33 memory used=1586.2MB, alloc=588.3MB, time=24.72 memory used=1794.8MB, alloc=588.3MB, time=29.77 memory used=2003.3MB, alloc=612.3MB, time=34.70 memory used=2235.9MB, alloc=612.3MB, time=40.00 memory used=2468.6MB, alloc=636.3MB, time=44.91 N1 := 7343 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [4 x - 9, 35 y - 34 x, -7 x y + 9 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2734.9MB, alloc=636.3MB, time=48.33 memory used=3039.5MB, alloc=660.3MB, time=53.98 N2 := 2837 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 H := [-8 x + 18, 8 x z - 14 y, -10 x y z + 17, -16 x y + 5 z, 3 3 2 2 2 12 x y - 3 x z , 17 x z - 12 x y z ] > J:=[op(GB),op(G)]; 3 2 2 2 3 3 J := [4 x - 9, 35 y - 34 x, -7 x y + 9 z , -16 x y + 5 z, 12 x y - 3 x z , 2 2 2 17 x z - 12 x 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 := [6, 16, 22, 4, 3, 3, 3, 1, 5/6, 5/6, 2/3, 5/12, 1/2, 6, 15, 18, 4, 3, 3, 3, 1, 5/6, 2/3, 2/3, 5/12, 5/12, 1, 4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3120.4MB, alloc=660.3MB, time=55.49 |\^/| 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(); 1428372496 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 F := [-16 x + 2 x y z, 5 x y z + 2 y , 8 y z - 10 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 G := [-8 x z + 20 z , 10 x y + 9 z , 9 x y - 19 x z] > Problem := [F,G]; 4 2 3 Problem := [[-16 x + 2 x y z, 5 x y z + 2 y , 8 y z - 10 z], 2 3 3 2 [-8 x z + 20 z , 10 x y + 9 z , 9 x y - 19 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.5MB, alloc=32.3MB, time=0.35 memory used=48.0MB, alloc=32.3MB, time=0.54 memory used=68.4MB, alloc=56.3MB, time=0.73 memory used=107.8MB, alloc=60.3MB, time=1.07 memory used=144.2MB, alloc=84.3MB, time=1.40 memory used=204.1MB, alloc=92.3MB, time=1.94 memory used=261.7MB, alloc=116.3MB, time=2.47 memory used=341.1MB, alloc=116.3MB, time=3.19 memory used=414.7MB, alloc=396.3MB, time=3.84 memory used=515.3MB, alloc=420.3MB, time=4.72 memory used=635.6MB, alloc=444.3MB, time=5.83 memory used=776.1MB, alloc=468.3MB, time=7.08 memory used=916.1MB, alloc=492.3MB, time=8.44 memory used=1087.9MB, alloc=516.3MB, time=10.42 memory used=1265.3MB, alloc=540.3MB, time=12.48 memory used=1450.3MB, alloc=564.3MB, time=14.66 memory used=1643.3MB, alloc=588.3MB, time=16.99 memory used=1833.0MB, alloc=612.3MB, time=19.28 memory used=2024.7MB, alloc=636.3MB, time=21.65 memory used=2194.5MB, alloc=660.3MB, time=23.79 memory used=2369.8MB, alloc=684.3MB, time=25.96 memory used=2540.4MB, alloc=708.3MB, time=28.09 memory used=2699.1MB, alloc=732.3MB, time=30.18 memory used=2954.8MB, alloc=756.3MB, time=33.49 memory used=3212.0MB, alloc=780.3MB, time=36.88 memory used=3470.2MB, alloc=804.3MB, time=40.23 memory used=3706.7MB, alloc=828.3MB, time=44.97 memory used=3931.2MB, alloc=852.3MB, time=50.32 memory used=4162.4MB, alloc=876.3MB, time=56.13 memory used=4403.8MB, alloc=900.3MB, time=62.65 memory used=4655.9MB, alloc=924.3MB, time=69.34 memory used=4920.1MB, alloc=948.3MB, time=76.32 memory used=5197.6MB, alloc=972.3MB, time=83.77 memory used=5488.6MB, alloc=996.3MB, time=91.70 memory used=5793.6MB, alloc=1020.3MB, time=100.18 memory used=6112.8MB, alloc=1044.3MB, time=108.95 memory used=6446.2MB, alloc=1068.3MB, time=118.06 memory used=6794.5MB, alloc=1092.3MB, time=127.63 memory used=7157.5MB, alloc=1116.3MB, time=137.81 memory used=7535.7MB, alloc=1140.3MB, time=148.33 memory used=7929.0MB, alloc=1164.3MB, time=159.40 memory used=8337.7MB, alloc=1188.3MB, time=171.09 memory used=8760.2MB, alloc=1212.3MB, time=183.20 memory used=9193.3MB, alloc=1236.3MB, time=196.01 memory used=9650.4MB, alloc=1260.3MB, time=209.45 memory used=10131.5MB, alloc=1284.3MB, time=223.67 memory used=10636.5MB, alloc=1308.3MB, time=238.51 memory used=11165.4MB, alloc=1332.3MB, time=253.98 memory used=11718.3MB, alloc=1356.3MB, time=270.13 memory used=12295.1MB, alloc=1380.3MB, time=287.03 memory used=12895.8MB, alloc=1404.3MB, time=304.52 |\^/| 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(); 1428372796 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [8 x y, -13 x y + 20 y z, 9 x z - 20 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-7 x z + 12 x, -13 x y z, -17 x z - 6] > Problem := [F,G]; 3 2 2 Problem := [[8 x y, -13 x y + 20 y z, 9 x z - 20 x z], 2 2 [-7 x z + 12 x, -13 x y z, -17 x 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=0.15 memory used=27.0MB, alloc=32.3MB, time=0.45 memory used=49.3MB, alloc=32.3MB, time=0.76 memory used=68.0MB, alloc=56.3MB, time=1.04 N1 := 891 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 GB := [x y, y x , -13 x y + 20 y z, 9 x z - 20 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=106.3MB, alloc=56.3MB, time=1.72 memory used=146.0MB, alloc=84.3MB, time=2.28 N2 := 891 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 H := [8 x y, -13 x y + 20 y z, 9 x z - 20 x z, -7 x z + 12 x, -13 x y z, 2 -17 x z - 6] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 J := [x y, y x , -13 x y + 20 y z, 9 x z - 20 x z, -7 x z + 12 x, 2 -13 x y z, -17 x 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 := [6, 14, 19, 4, 3, 2, 2, 1, 1/2, 5/6, 8/15, 4/15, 2/5, 7, 16, 23, 4, 3, 2, 2, 1, 4/7, 5/7, 9/16, 5/16, 3/8, -2, -4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=188.4MB, alloc=84.3MB, time=2.96 |\^/| 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(); 1428372799 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 2 2 F := [x y z + 5 x , 8 x y - 11 x y z, -10 x y z - 7 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [14 x y - 17 x z, 17 x - 17 y, 13 x y z - 7 z ] > Problem := [F,G]; 2 3 2 2 2 2 2 Problem := [[x y z + 5 x , 8 x y - 11 x y z, -10 x y z - 7 x y], 2 2 3 [14 x y - 17 x z, 17 x - 17 y, 13 x y z - 7 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.43 memory used=48.2MB, alloc=32.3MB, time=0.70 memory used=68.4MB, alloc=32.3MB, time=0.93 memory used=87.3MB, alloc=56.3MB, time=1.16 memory used=125.7MB, alloc=60.3MB, time=1.60 memory used=161.1MB, alloc=84.3MB, time=2.04 memory used=217.5MB, alloc=84.3MB, time=2.70 memory used=272.8MB, alloc=92.3MB, time=3.37 memory used=325.8MB, alloc=116.3MB, time=4.02 memory used=399.6MB, alloc=116.3MB, time=4.89 memory used=471.7MB, alloc=140.3MB, time=5.85 memory used=564.1MB, alloc=164.3MB, time=7.17 memory used=672.5MB, alloc=188.3MB, time=8.75 memory used=794.6MB, alloc=468.3MB, time=10.52 memory used=929.4MB, alloc=492.3MB, time=12.72 memory used=1064.4MB, alloc=516.3MB, time=15.48 memory used=1204.6MB, alloc=540.3MB, time=18.60 memory used=1359.0MB, alloc=564.3MB, time=22.31 memory used=1537.4MB, alloc=588.3MB, time=26.57 memory used=1739.8MB, alloc=612.3MB, time=31.49 memory used=1966.1MB, alloc=612.3MB, time=36.77 memory used=2192.5MB, alloc=636.3MB, time=41.92 memory used=2443.0MB, alloc=660.3MB, time=47.14 N1 := 7181 > GB := Basis(F, plex(op(vars))); 5 4 4 3 4 2 2 GB := [34375 x + 343 x , -275 x + 28 x y, -75625 x + 784 x y , 4 4 4 2 2 2 2 3 1375 x z + 98 x , -6875 x + 98 x y z, 10 x y z + 7 x y, x y z + 5 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2699.7MB, alloc=660.3MB, time=50.17 memory used=2899.9MB, alloc=660.3MB, time=52.31 memory used=3124.2MB, alloc=660.3MB, time=54.68 memory used=3310.7MB, alloc=660.3MB, time=56.76 memory used=3491.1MB, alloc=660.3MB, time=58.68 memory used=3673.6MB, alloc=684.3MB, time=60.71 memory used=3836.5MB, alloc=684.3MB, time=62.55 memory used=3983.1MB, alloc=708.3MB, time=64.30 memory used=4134.1MB, alloc=708.3MB, time=66.06 memory used=4267.1MB, alloc=732.3MB, time=67.79 memory used=4387.8MB, alloc=756.3MB, time=69.52 memory used=4524.5MB, alloc=756.3MB, time=71.43 memory used=4680.0MB, alloc=780.3MB, time=73.67 memory used=4821.7MB, alloc=804.3MB, time=75.71 memory used=4967.5MB, alloc=828.3MB, time=77.69 memory used=5105.2MB, alloc=852.3MB, time=79.75 memory used=5233.2MB, alloc=876.3MB, time=81.69 memory used=5357.3MB, alloc=876.3MB, time=83.59 memory used=5476.6MB, alloc=900.3MB, time=85.53 memory used=5587.6MB, alloc=924.3MB, time=87.34 memory used=5695.0MB, alloc=948.3MB, time=89.11 memory used=5809.4MB, alloc=948.3MB, time=90.73 memory used=5938.0MB, alloc=948.3MB, time=92.41 memory used=6080.0MB, alloc=972.3MB, time=95.53 memory used=6258.0MB, alloc=996.3MB, time=99.94 memory used=6706.7MB, alloc=1020.3MB, time=111.02 memory used=7149.3MB, alloc=1044.3MB, time=122.32 memory used=7594.5MB, alloc=1068.3MB, time=134.00 memory used=8036.7MB, alloc=1092.3MB, time=146.39 memory used=8497.9MB, alloc=1116.3MB, time=159.57 memory used=8983.1MB, alloc=1140.3MB, time=173.26 memory used=9492.2MB, alloc=1164.3MB, time=187.57 memory used=10025.2MB, alloc=1188.3MB, time=202.51 memory used=10582.2MB, alloc=1212.3MB, time=218.26 memory used=11163.1MB, alloc=1236.3MB, time=234.47 memory used=11767.9MB, alloc=1260.3MB, time=251.33 memory used=12396.7MB, alloc=1260.3MB, time=268.75 memory used=13025.4MB, alloc=1260.3MB, time=286.26 memory used=13654.0MB, alloc=1284.3MB, time=303.67 |\^/| 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(); 1428373099 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 2 2 F := [-18 x - 7 x z , 5 x y z - 20 y z, -3 x y z + 13 x ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [-x y + 16 z, 3 y z + 5 x z, -5 x y - 16 x] > Problem := [F,G]; 4 2 2 2 2 2 2 Problem := [[-18 x - 7 x z , 5 x y z - 20 y z, -3 x y z + 13 x ], 2 2 2 2 3 [-x y + 16 z, 3 y z + 5 x z, -5 x 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=0.15 memory used=26.6MB, alloc=32.3MB, time=0.41 memory used=48.2MB, alloc=32.3MB, time=0.65 memory used=68.6MB, alloc=32.3MB, time=0.89 memory used=88.0MB, alloc=56.3MB, time=1.11 memory used=128.2MB, alloc=60.3MB, time=1.58 memory used=167.0MB, alloc=60.3MB, time=2.02 memory used=204.4MB, alloc=84.3MB, time=2.47 memory used=264.4MB, alloc=92.3MB, time=3.17 memory used=323.6MB, alloc=116.3MB, time=4.01 memory used=400.7MB, alloc=140.3MB, time=5.12 memory used=494.6MB, alloc=164.3MB, time=6.71 memory used=590.4MB, alloc=188.3MB, time=9.44 N1 := 2329 > GB := Basis(F, plex(op(vars))); 4 3 3 2 3 2 2 2 3 GB := [x - 4 x , 91 x + 864 x y, -8281 x z + 2985984 y z, 7 x z + 72 x , 2 2 3 x y z - 13 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=713.6MB, alloc=188.3MB, time=11.64 memory used=805.5MB, alloc=444.3MB, time=12.79 memory used=942.9MB, alloc=468.3MB, time=14.45 memory used=1106.1MB, alloc=492.3MB, time=16.43 memory used=1245.8MB, alloc=492.3MB, time=18.18 memory used=1376.6MB, alloc=516.3MB, time=19.70 memory used=1494.8MB, alloc=540.3MB, time=20.93 memory used=1734.1MB, alloc=564.3MB, time=23.08 memory used=1932.1MB, alloc=588.3MB, time=25.31 memory used=2118.2MB, alloc=612.3MB, time=27.54 memory used=2285.0MB, alloc=636.3MB, time=29.63 memory used=2484.1MB, alloc=660.3MB, time=32.02 memory used=2633.7MB, alloc=684.3MB, time=34.33 memory used=2888.5MB, alloc=708.3MB, time=39.83 memory used=3141.9MB, alloc=732.3MB, time=45.99 memory used=3398.5MB, alloc=756.3MB, time=52.82 memory used=3667.8MB, alloc=780.3MB, time=60.29 memory used=3961.0MB, alloc=804.3MB, time=68.41 memory used=4278.2MB, alloc=828.3MB, time=77.12 memory used=4619.3MB, alloc=852.3MB, time=86.45 memory used=4984.3MB, alloc=876.3MB, time=96.50 memory used=5373.2MB, alloc=876.3MB, time=107.00 memory used=5762.2MB, alloc=900.3MB, time=117.46 memory used=6175.0MB, alloc=900.3MB, time=128.44 memory used=6587.9MB, alloc=924.3MB, time=139.33 memory used=7024.6MB, alloc=924.3MB, time=150.80 memory used=7461.5MB, alloc=948.3MB, time=162.32 memory used=7922.3MB, alloc=972.3MB, time=174.02 N2 := 13755 #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)]; 4 2 2 2 2 2 2 2 H := [-18 x - 7 x z , 5 x y z - 20 y z, -3 x y z + 13 x , -x y + 16 z, 2 2 2 3 3 y z + 5 x z, -5 x y - 16 x] > J:=[op(GB),op(G)]; 4 3 3 2 3 2 2 2 3 J := [x - 4 x , 91 x + 864 x y, -8281 x z + 2985984 y z, 7 x z + 72 x , 2 2 2 2 2 2 3 3 x y z - 13 x , -x y + 16 z, 3 y z + 5 x z, -5 x 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 := [6, 16, 23, 4, 4, 2, 2, 1, 5/6, 5/6, 3/4, 1/2, 7/12, 8, 19, 30, 4, 4, 2, 2, 1, 3/4, 5/8, 13/16, 3/8, 7/16, -3, -7, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=8369.3MB, alloc=972.3MB, time=183.76 |\^/| 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(); 1428373281 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 F := [16 x y + 3 x y , -16 x z + 13 x y z, 13 z - 16] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 G := [-x z + 4 x y , x y z - 7 y z , 13 z + 9 x] > Problem := [F,G]; 2 2 3 3 2 Problem := [[16 x y + 3 x y , -16 x z + 13 x y z, 13 z - 16], 3 3 2 3 [-x z + 4 x y , x y z - 7 y z , 13 z + 9 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.7MB, alloc=32.3MB, time=0.36 memory used=47.9MB, alloc=32.3MB, time=0.58 memory used=68.7MB, alloc=60.3MB, time=0.78 memory used=109.8MB, alloc=60.3MB, time=1.11 memory used=147.2MB, alloc=84.3MB, time=1.45 memory used=208.1MB, alloc=92.3MB, time=1.97 memory used=265.6MB, alloc=92.3MB, time=2.46 memory used=325.5MB, alloc=116.3MB, time=2.97 memory used=403.7MB, alloc=396.3MB, time=3.69 memory used=505.7MB, alloc=420.3MB, time=4.60 memory used=639.7MB, alloc=444.3MB, time=5.87 memory used=776.8MB, alloc=468.3MB, time=7.33 memory used=926.6MB, alloc=492.3MB, time=8.91 memory used=1100.4MB, alloc=516.3MB, time=10.52 memory used=1276.7MB, alloc=540.3MB, time=12.39 memory used=1452.1MB, alloc=564.3MB, time=14.55 memory used=1612.7MB, alloc=588.3MB, time=17.52 memory used=1777.8MB, alloc=612.3MB, time=20.95 memory used=1952.4MB, alloc=636.3MB, time=24.87 memory used=2139.8MB, alloc=660.3MB, time=29.23 memory used=2333.4MB, alloc=684.3MB, time=34.43 memory used=2551.0MB, alloc=708.3MB, time=40.10 memory used=2792.4MB, alloc=732.3MB, time=46.36 memory used=3057.9MB, alloc=756.3MB, time=53.19 memory used=3347.2MB, alloc=780.3MB, time=60.63 memory used=3660.5MB, alloc=804.3MB, time=68.65 memory used=3997.8MB, alloc=804.3MB, time=77.24 memory used=4334.9MB, alloc=804.3MB, time=85.83 memory used=4672.1MB, alloc=828.3MB, time=94.53 memory used=5033.2MB, alloc=828.3MB, time=103.66 memory used=5394.3MB, alloc=828.3MB, time=112.80 memory used=5755.4MB, alloc=852.3MB, time=121.89 memory used=6140.2MB, alloc=852.3MB, time=131.47 memory used=6524.9MB, alloc=852.3MB, time=140.98 memory used=6909.7MB, alloc=876.3MB, time=150.43 memory used=7318.4MB, alloc=876.3MB, time=160.54 memory used=7727.0MB, alloc=900.3MB, time=170.39 memory used=8159.6MB, alloc=924.3MB, time=180.68 N1 := 15525 > GB := Basis(F, plex(op(vars))); 2 2 GB := [169 x + 48 x, 169 x y - 256 x, 13 z - 16] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=8620.3MB, alloc=924.3MB, time=189.97 memory used=8840.9MB, alloc=924.3MB, time=193.36 N2 := 2927 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 2 3 3 H := [16 x y + 3 x y , -16 x z + 13 x y z, 13 z - 16, -x z + 4 x y , 2 3 x y z - 7 y z , 13 z + 9 x] > J:=[op(GB),op(G)]; 2 2 3 3 J := [169 x + 48 x, 169 x y - 256 x, 13 z - 16, -x z + 4 x y , 2 3 x y z - 7 y z , 13 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, 14, 20, 4, 3, 3, 3, 5/6, 2/3, 5/6, 2/3, 1/2, 7/12, 6, 12, 16, 4, 3, 3, 3, 5/6, 1/2, 2/3, 2/3, 1/3, 5/12, 2, 4, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=9115.6MB, alloc=924.3MB, time=198.57 |\^/| 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(); 1428373476 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 F := [-10 x z - 7 x y , -13 x y - 8 x, -16 x y - 5 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 4 G := [-4 x y - 6 z , -5 z - 19 y , 4 z + 5 x z] > Problem := [F,G]; 3 2 2 3 3 Problem := [[-10 x z - 7 x y , -13 x y - 8 x, -16 x y - 5 y z ], 3 2 3 2 4 [-4 x y - 6 z , -5 z - 19 y , 4 z + 5 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.8MB, alloc=32.3MB, time=0.38 memory used=48.7MB, alloc=32.3MB, time=0.57 memory used=69.3MB, alloc=32.3MB, time=0.75 memory used=87.8MB, alloc=56.3MB, time=0.93 memory used=128.2MB, alloc=60.3MB, time=1.28 memory used=167.0MB, alloc=60.3MB, time=1.62 memory used=204.8MB, alloc=84.3MB, time=1.96 memory used=264.0MB, alloc=92.3MB, time=2.50 memory used=322.9MB, alloc=116.3MB, time=3.02 memory used=402.9MB, alloc=116.3MB, time=3.70 memory used=480.8MB, alloc=140.3MB, time=4.40 memory used=562.0MB, alloc=140.3MB, time=5.11 memory used=628.3MB, alloc=396.3MB, time=5.71 memory used=728.9MB, alloc=420.3MB, time=6.60 memory used=850.8MB, alloc=444.3MB, time=7.73 memory used=994.9MB, alloc=468.3MB, time=9.09 memory used=1102.3MB, alloc=468.3MB, time=10.07 memory used=1249.6MB, alloc=492.3MB, time=11.56 memory used=1385.2MB, alloc=492.3MB, time=12.91 memory used=1501.2MB, alloc=516.3MB, time=14.13 memory used=1609.9MB, alloc=516.3MB, time=15.43 memory used=1697.1MB, alloc=516.3MB, time=16.36 memory used=1798.4MB, alloc=516.3MB, time=17.49 memory used=1865.5MB, alloc=516.3MB, time=18.32 memory used=1940.2MB, alloc=540.3MB, time=19.22 memory used=1996.6MB, alloc=540.3MB, time=20.00 memory used=2055.6MB, alloc=540.3MB, time=20.79 memory used=2117.1MB, alloc=540.3MB, time=21.62 memory used=2166.3MB, alloc=540.3MB, time=22.36 memory used=2237.6MB, alloc=564.3MB, time=23.45 memory used=2291.0MB, alloc=564.3MB, time=24.39 memory used=2501.0MB, alloc=588.3MB, time=27.04 memory used=2720.8MB, alloc=612.3MB, time=29.82 memory used=2967.1MB, alloc=636.3MB, time=32.58 memory used=3234.0MB, alloc=660.3MB, time=35.36 memory used=3498.3MB, alloc=684.3MB, time=38.58 memory used=3759.6MB, alloc=708.3MB, time=42.06 memory used=4024.2MB, alloc=732.3MB, time=45.65 memory used=4293.7MB, alloc=756.3MB, time=49.37 memory used=4555.4MB, alloc=780.3MB, time=53.51 memory used=4782.3MB, alloc=804.3MB, time=58.86 memory used=5012.6MB, alloc=828.3MB, time=64.77 memory used=5252.6MB, alloc=852.3MB, time=71.21 memory used=5504.3MB, alloc=876.3MB, time=78.09 memory used=5768.1MB, alloc=900.3MB, time=85.28 memory used=6045.1MB, alloc=924.3MB, time=92.90 memory used=6336.4MB, alloc=948.3MB, time=101.00 memory used=6642.2MB, alloc=972.3MB, time=109.58 memory used=6962.7MB, alloc=996.3MB, time=118.62 memory used=7298.5MB, alloc=1020.3MB, time=128.18 memory used=7642.8MB, alloc=1044.3MB, time=138.25 memory used=8006.9MB, alloc=1068.3MB, time=149.06 memory used=8394.9MB, alloc=1092.3MB, time=160.38 memory used=8806.8MB, alloc=1116.3MB, time=172.38 memory used=9242.7MB, alloc=1140.3MB, time=185.02 memory used=9702.6MB, alloc=1164.3MB, time=198.28 memory used=10186.3MB, alloc=1188.3MB, time=212.35 memory used=10694.1MB, alloc=1212.3MB, time=226.94 memory used=11225.8MB, alloc=1236.3MB, time=242.22 memory used=11781.4MB, alloc=1260.3MB, time=258.13 memory used=12360.9MB, alloc=1284.3MB, time=274.87 memory used=12964.5MB, alloc=1308.3MB, time=292.08 memory used=13591.9MB, alloc=1332.3MB, time=309.97 |\^/| 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(); 1428373776 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 F := [-9 z - 20 x z , -7 x y - 14 y z, 20 x y + 6 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 G := [4 x + 17 z, -19 x y z - 20 x, -10 z + 7 x] > Problem := [F,G]; 4 2 2 3 2 Problem := [[-9 z - 20 x z , -7 x y - 14 y z, 20 x y + 6 z ], 2 2 4 [4 x + 17 z, -19 x y z - 20 x, -10 z + 7 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=26.2MB, alloc=32.3MB, time=0.37 memory used=47.9MB, alloc=32.3MB, time=0.61 memory used=68.4MB, alloc=32.3MB, time=0.84 memory used=87.7MB, alloc=56.3MB, time=1.08 memory used=127.0MB, alloc=60.3MB, time=1.55 memory used=164.0MB, alloc=60.3MB, time=1.98 memory used=199.1MB, alloc=84.3MB, time=2.39 memory used=255.4MB, alloc=92.3MB, time=3.02 memory used=312.3MB, alloc=92.3MB, time=3.59 memory used=367.4MB, alloc=92.3MB, time=4.21 memory used=422.1MB, alloc=116.3MB, time=4.85 memory used=495.4MB, alloc=116.3MB, time=5.68 memory used=567.9MB, alloc=140.3MB, time=6.62 memory used=661.6MB, alloc=164.3MB, time=8.00 memory used=778.5MB, alloc=188.3MB, time=9.59 memory used=903.7MB, alloc=212.3MB, time=11.43 memory used=1044.1MB, alloc=236.3MB, time=13.62 memory used=1197.0MB, alloc=260.3MB, time=15.94 memory used=1322.0MB, alloc=540.3MB, time=17.83 memory used=1481.9MB, alloc=564.3MB, time=21.40 memory used=1643.2MB, alloc=588.3MB, time=25.22 memory used=1814.2MB, alloc=612.3MB, time=28.93 memory used=1991.7MB, alloc=636.3MB, time=33.34 memory used=2190.8MB, alloc=660.3MB, time=38.31 memory used=2413.9MB, alloc=684.3MB, time=43.86 memory used=2660.8MB, alloc=708.3MB, time=49.98 memory used=2931.8MB, alloc=732.3MB, time=56.66 memory used=3226.7MB, alloc=732.3MB, time=63.87 memory used=3521.5MB, alloc=732.3MB, time=71.01 memory used=3816.3MB, alloc=732.3MB, time=78.23 memory used=4111.1MB, alloc=756.3MB, time=85.34 memory used=4429.8MB, alloc=756.3MB, time=92.93 memory used=4748.4MB, alloc=756.3MB, time=100.50 memory used=5067.0MB, alloc=780.3MB, time=108.02 memory used=5409.4MB, alloc=780.3MB, time=115.98 memory used=5751.8MB, alloc=804.3MB, time=123.78 memory used=6118.4MB, alloc=828.3MB, time=131.44 N1 := 12739 > GB := Basis(F, plex(op(vars))); 8 5 5 3 2 3 4 4 2 GB := [9 x y + 80 x y, 9 x y + 80 x y , 3 x y + 40 x y , x y + 2 y z, 3 2 10 y x + 3 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6512.9MB, alloc=828.3MB, time=136.43 memory used=6979.8MB, alloc=852.3MB, time=143.16 memory used=7377.7MB, alloc=876.3MB, time=153.24 memory used=7792.4MB, alloc=900.3MB, time=163.72 memory used=8231.5MB, alloc=924.3MB, time=174.10 N2 := 6925 #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)]; 4 2 2 3 2 2 H := [-9 z - 20 x z , -7 x y - 14 y z, 20 x y + 6 z , 4 x + 17 z, 2 4 -19 x y z - 20 x, -10 z + 7 x] > J:=[op(GB),op(G)]; 8 5 5 3 2 3 4 4 2 J := [9 x y + 80 x y, 9 x y + 80 x y , 3 x y + 40 x y , x y + 2 y z, 3 2 2 2 4 10 y x + 3 z , 4 x + 17 z, -19 x y z - 20 x, -10 z + 7 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 21, 4, 2, 3, 4, 1, 1/2, 1, 7/12, 1/3, 7/12, 8, 19, 39, 9, 8, 4, 4, 1, 3/4, 5/8, 3/4, 5/8, 5/16, -4, -18, -5] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=8312.2MB, alloc=924.3MB, time=175.48 |\^/| 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(); 1428373950 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [-10 x z + 15 z , -4 x y z - 10 x z, -9 x + 11 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 G := [-6 x z - 16 x, -7 x z + 13 y z, -20 x y z - 13 y z] > Problem := [F,G]; 2 2 2 3 Problem := [[-10 x z + 15 z , -4 x y z - 10 x z, -9 x + 11 x z], 3 3 2 3 [-6 x z - 16 x, -7 x z + 13 y z, -20 x y z - 13 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.33 memory used=47.6MB, alloc=32.3MB, time=0.54 memory used=67.9MB, alloc=56.3MB, time=0.75 memory used=108.3MB, alloc=60.3MB, time=1.11 memory used=146.4MB, alloc=84.3MB, time=1.47 memory used=205.9MB, alloc=84.3MB, time=2.11 memory used=258.9MB, alloc=108.3MB, time=2.69 memory used=329.2MB, alloc=140.3MB, time=3.50 memory used=409.7MB, alloc=164.3MB, time=4.87 memory used=503.8MB, alloc=188.3MB, time=6.70 memory used=622.0MB, alloc=188.3MB, time=8.76 N1 := 3143 > GB := Basis(F, plex(op(vars))); 6 5 3 2 3 3 5 2 GB := [2 x - 3 x , 2 x y + 5 x , -9 x + 11 x z, -54 x + 121 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=739.9MB, alloc=188.3MB, time=9.95 memory used=822.6MB, alloc=444.3MB, time=10.79 memory used=955.8MB, alloc=468.3MB, time=12.02 memory used=1113.7MB, alloc=492.3MB, time=13.60 memory used=1288.2MB, alloc=516.3MB, time=15.48 memory used=1467.2MB, alloc=540.3MB, time=17.50 memory used=1648.4MB, alloc=564.3MB, time=20.28 memory used=1815.9MB, alloc=588.3MB, time=23.84 memory used=1983.5MB, alloc=612.3MB, time=28.06 memory used=2175.1MB, alloc=636.3MB, time=32.85 memory used=2390.7MB, alloc=660.3MB, time=38.19 memory used=2630.2MB, alloc=684.3MB, time=44.03 memory used=2893.6MB, alloc=708.3MB, time=50.36 memory used=3181.1MB, alloc=732.3MB, time=57.07 memory used=3492.6MB, alloc=756.3MB, time=64.01 N2 := 8395 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 H := [-10 x z + 15 z , -4 x y z - 10 x z, -9 x + 11 x z, -6 x z - 16 x, 3 3 2 3 -7 x z + 13 y z, -20 x y z - 13 y z] > J:=[op(GB),op(G)]; 6 5 3 2 3 3 5 2 J := [2 x - 3 x , 2 x y + 5 x , -9 x + 11 x z, -54 x + 121 z , 3 3 2 3 -6 x z - 16 x, -7 x z + 13 y z, -20 x y z - 13 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 := [6, 15, 20, 4, 3, 3, 3, 1, 1/2, 1, 3/4, 1/3, 5/6, 7, 15, 29, 6, 6, 3, 3, 1, 3/7, 5/7, 11/14, 2/7, 1/2, 0, -9, -2] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3698.9MB, alloc=756.3MB, time=67.63 |\^/| 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(); 1428374017 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 3 2 2 F := [11 x + 12 x z, -15 x y z - 9 y z , 6 x y - 17 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-5 x y - 17 x, 7 x z - 10, -16 x - 8 x] > Problem := [F,G]; 4 2 2 2 3 2 2 Problem := [[11 x + 12 x z, -15 x y z - 9 y z , 6 x y - 17 y z ], 2 2 2 2 [-5 x y - 17 x, 7 x z - 10, -16 x - 8 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.35 memory used=47.9MB, alloc=32.3MB, time=0.54 memory used=69.3MB, alloc=56.3MB, time=0.77 memory used=111.9MB, alloc=56.3MB, time=1.21 memory used=152.7MB, alloc=80.3MB, time=1.64 memory used=209.9MB, alloc=108.3MB, time=2.29 memory used=278.2MB, alloc=108.3MB, time=3.42 memory used=342.6MB, alloc=132.3MB, time=4.45 N1 := 2253 > GB := Basis(F, plex(op(vars))); 3 4 2 2 GB := [x y, 11 x + 12 x z, z y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 177 #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)]; 4 2 2 2 3 2 2 2 2 H := [11 x + 12 x z, -15 x y z - 9 y z , 6 x y - 17 y z , -5 x y - 17 x, 2 2 7 z x - 10, -16 x - 8 x] > J:=[op(GB),op(G)]; 3 4 2 2 2 2 2 2 J := [x y, 11 x + 12 x z, z y, -5 x y - 17 x, 7 z x - 10, -16 x - 8 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 21, 4, 4, 2, 2, 1, 1/2, 2/3, 3/4, 5/12, 5/12, 6, 11, 20, 4, 4, 2, 2, 5/6, 1/2, 1/2, 2/3, 1/4, 1/4, 2, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=388.8MB, alloc=132.3MB, 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(); 1428374022 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-7 x y z - 16 x y z, 14 x y z + 18 x z, -17 y z + 11 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-11 x z , 13 x + 4 x, 20 y z - 9 y z ] > Problem := [F,G]; 2 2 2 Problem := [[-7 x y z - 16 x y z, 14 x y z + 18 x z, -17 y z + 11 x], 2 2 2 2 [-11 x z , 13 x + 4 x, 20 y z - 9 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=26.1MB, alloc=32.3MB, time=0.34 memory used=48.5MB, alloc=32.3MB, time=0.56 memory used=69.0MB, alloc=56.3MB, time=0.79 memory used=109.5MB, alloc=84.3MB, time=1.23 N1 := 1115 > GB := Basis(F, plex(op(vars))); GB := 3 2 2 2 2 2 2 [26411 x - 352512 x , 7 x y + 9 x , 3773 x + 22032 x z, 17 y z - 11 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=164.9MB, alloc=84.3MB, time=1.87 memory used=225.5MB, alloc=108.3MB, time=2.50 memory used=307.6MB, alloc=132.3MB, time=3.58 N2 := 1369 #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 y z - 16 x y z, 14 x y z + 18 x z, -17 z y + 11 x, -11 x z , 2 2 2 13 x + 4 x, 20 y z - 9 y z ] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 2 J := [26411 x - 352512 x , 7 x y + 9 x , 3773 x + 22032 x z, 17 y z - 11 x, 2 2 2 2 -11 x z , 13 x + 4 x, 20 y z - 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 := [6, 14, 19, 4, 2, 2, 2, 5/6, 2/3, 5/6, 8/13, 6/13, 8/13, 7, 13, 20, 4, 3, 2, 2, 6/7, 3/7, 4/7, 2/3, 4/15, 1/3, 1, -1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=332.3MB, alloc=132.3MB, time=3.94 |\^/| 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(); 1428374026 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 F := [-3 x - 8 x , -20 y - y, 19 y z + 12 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 4 4 2 2 2 G := [-5 x y z - 12 y , -6 z + 13 x z, 12 x y - 7 y z] > Problem := [F,G]; 4 2 2 2 2 Problem := [[-3 x - 8 x , -20 y - y, 19 y z + 12 z], 2 4 4 2 2 2 [-5 x y z - 12 y , -6 z + 13 x z, 12 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=4.3MB, alloc=32.3MB, time=0.14 memory used=26.1MB, alloc=32.3MB, time=0.34 memory used=48.0MB, alloc=32.3MB, time=0.53 memory used=68.6MB, alloc=32.3MB, time=0.71 memory used=87.9MB, alloc=56.3MB, time=0.88 memory used=127.7MB, alloc=60.3MB, time=1.23 memory used=168.8MB, alloc=92.3MB, time=1.57 memory used=236.9MB, alloc=92.3MB, time=2.19 memory used=296.5MB, alloc=116.3MB, time=2.80 memory used=371.8MB, alloc=140.3MB, time=3.65 memory used=451.0MB, alloc=164.3MB, time=5.12 N1 := 1969 > GB := Basis(F, plex(op(vars))); 4 2 2 2 GB := [3 x + 8 x , 20 y + y, 20 y z + z, 19 z + 4800 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=559.5MB, alloc=164.3MB, time=6.26 N2 := 1239 #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)]; 4 2 2 2 2 2 4 H := [-3 x - 8 x , -20 y - y, 19 y z + 12 z, -5 x y z - 12 y , 4 2 2 2 -6 z + 13 x z, 12 x y - 7 y z] > J:=[op(GB),op(G)]; 4 2 2 2 2 4 J := [3 x + 8 x , 20 y + y, 20 y z + z, 19 z + 4800 z, -5 x y z - 12 y , 4 2 2 2 -6 z + 13 x z, 12 x y - 7 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 22, 4, 4, 4, 4, 2/3, 2/3, 2/3, 5/12, 7/12, 1/2, 7, 13, 22, 4, 4, 4, 4, 4/7, 4/7, 5/7, 5/14, 1/2, 4/7, -1, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=680.5MB, alloc=164.3MB, time=7.67 |\^/| 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(); 1428374034 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 3 2 F := [-2 x z + 9 z , -15 x z + 11 x y , y z + 20] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 4 4 2 G := [-15 x z - 6 z , 14 x - 15 x y z, -19 y + 16 x ] > Problem := [F,G]; 2 2 2 2 2 3 2 Problem := [[-2 x z + 9 z , -15 x z + 11 x y , y z + 20], 2 2 3 4 4 2 [-15 x z - 6 z , 14 x - 15 x y z, -19 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=0.13 memory used=26.6MB, alloc=32.3MB, time=0.35 memory used=48.7MB, alloc=32.3MB, time=0.54 memory used=69.0MB, alloc=32.3MB, time=0.71 memory used=88.5MB, alloc=56.3MB, time=0.90 memory used=130.2MB, alloc=60.3MB, time=1.24 memory used=169.8MB, alloc=84.3MB, time=1.55 memory used=213.7MB, alloc=84.3MB, time=1.93 memory used=270.5MB, alloc=92.3MB, time=2.45 memory used=328.3MB, alloc=116.3MB, time=3.03 memory used=408.9MB, alloc=140.3MB, time=3.85 memory used=503.2MB, alloc=164.3MB, time=4.87 memory used=612.4MB, alloc=188.3MB, time=6.07 memory used=741.5MB, alloc=212.3MB, time=7.45 memory used=864.3MB, alloc=492.3MB, time=8.80 memory used=1016.1MB, alloc=516.3MB, time=10.94 memory used=1163.0MB, alloc=540.3MB, time=13.81 memory used=1319.3MB, alloc=564.3MB, time=17.19 memory used=1484.4MB, alloc=588.3MB, time=21.23 memory used=1673.5MB, alloc=612.3MB, time=25.84 memory used=1886.6MB, alloc=636.3MB, time=31.02 memory used=2123.6MB, alloc=636.3MB, time=36.72 memory used=2360.6MB, alloc=636.3MB, time=42.41 memory used=2597.4MB, alloc=660.3MB, time=48.08 memory used=2858.4MB, alloc=660.3MB, time=54.32 memory used=3119.3MB, alloc=684.3MB, time=60.58 memory used=3404.3MB, alloc=708.3MB, time=66.88 N1 := 9133 > GB := Basis(F, plex(op(vars))); 2 4 3 2 GB := [2 x - 9, 11 y + 300 x, -22 x y + 135 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3710.6MB, alloc=708.3MB, time=71.32 memory used=4078.8MB, alloc=732.3MB, time=78.15 N2 := 3297 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 3 2 2 2 3 H := [-2 x z + 9 z , -15 x z + 11 x y , z y + 20, -15 x z - 6 z , 4 4 2 14 x - 15 x y z, -19 y + 16 x ] > J:=[op(GB),op(G)]; 2 4 3 2 2 2 3 J := [2 x - 9, 11 y + 300 x, -22 x y + 135 z , -15 x z - 6 z , 4 4 2 14 x - 15 x y z, -19 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 := [6, 14, 23, 4, 4, 4, 3, 5/6, 2/3, 5/6, 7/12, 1/3, 7/12, 6, 13, 22, 4, 4, 4, 3, 1, 2/3, 1/2, 7/12, 1/3, 1/3, 1, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=4229.0MB, alloc=732.3MB, time=80.86 |\^/| 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(); 1428374113 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 4 3 2 F := [16 y - 15 x z , 19 x y - 17 y , -4 x - 10 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [-8 x z - 7 x, -15 x y - 8 y , 3 x z - 3 y z] > Problem := [F,G]; 4 2 2 2 4 3 2 Problem := [[16 y - 15 x z , 19 x y - 17 y , -4 x - 10 x y ], 2 2 3 2 2 [-8 x z - 7 x, -15 x y - 8 y , 3 x z - 3 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.12 memory used=26.1MB, alloc=32.3MB, time=0.33 memory used=47.6MB, alloc=32.3MB, time=0.53 memory used=67.9MB, alloc=32.3MB, time=0.70 memory used=87.4MB, alloc=56.3MB, time=0.88 memory used=128.6MB, alloc=60.3MB, time=1.26 memory used=167.9MB, alloc=60.3MB, time=1.67 memory used=204.3MB, alloc=84.3MB, time=2.06 memory used=260.8MB, alloc=108.3MB, time=2.68 memory used=332.1MB, alloc=108.3MB, time=3.78 N1 := 1827 > GB := Basis(F, plex(op(vars))); 5 3 2 4 4 4 2 GB := [x , 2 x + 5 x y , 38 x + 85 y , 608 x + 1275 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=400.1MB, alloc=108.3MB, time=4.64 memory used=473.0MB, alloc=140.3MB, time=5.32 memory used=575.5MB, alloc=164.3MB, time=6.53 N2 := 1147 #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)]; 4 2 2 2 4 3 2 2 2 H := [16 y - 15 x z , 19 x y - 17 y , -4 x - 10 x y , -8 x z - 7 x, 3 2 2 -15 x y - 8 y , 3 x z - 3 y z] > J:=[op(GB),op(G)]; 5 3 2 4 4 4 2 2 2 J := [x , 2 x + 5 x y , 85 y + 38 x , 608 x + 1275 x z , -8 x z - 7 x, 3 2 2 -15 x y - 8 y , 3 x z - 3 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 := [6, 14, 22, 4, 3, 4, 2, 1, 5/6, 1/2, 2/3, 7/12, 1/3, 7, 14, 27, 5, 5, 4, 2, 1, 4/7, 3/7, 5/7, 5/14, 2/7, 0, -5, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=590.7MB, alloc=164.3MB, time=6.75 |\^/| 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(); 1428374120 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 2 2 F := [16 x - 3 x z, 3 x y + 17 y z , 4 x y - 7 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [8 x z + 13 x z , 8 x y, -3 x y z] > Problem := [F,G]; 4 2 3 2 2 2 Problem := [[16 x - 3 x z, 3 x y + 17 y z , 4 x y - 7 x], 2 2 2 3 2 [8 x z + 13 x z , 8 x y, -3 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=27.0MB, alloc=32.3MB, time=0.38 N1 := 189 > GB := Basis(F, plex(op(vars))); 5 4 3 2 2 2 GB := [17408 x + 189 x, 4352 x + 27 x y, -16 x + 3 x z, 9 y z - 784 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=46.7MB, alloc=32.3MB, time=0.56 memory used=67.3MB, alloc=56.3MB, time=0.77 N2 := 557 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 4 2 3 2 2 2 2 2 2 H := [16 x - 3 x z, 3 x y + 17 y z , 4 x y - 7 x, 8 x z + 13 x z , 3 2 8 x y, -3 x y z] > J:=[op(GB),op(G)]; 5 4 3 2 2 2 J := [17408 x + 189 x, 4352 x + 27 x y, -16 x + 3 x z, 9 y z - 784 x , 2 2 2 3 2 8 x z + 13 x z , 8 x y, -3 x 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 := [6, 14, 23, 4, 4, 3, 2, 1, 2/3, 2/3, 3/5, 1/3, 1/3, 7, 15, 28, 5, 5, 2, 2, 1, 4/7, 4/7, 11/17, 4/17, 5/17, -1, -5, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=100.7MB, alloc=56.3MB, time=1.12 |\^/| 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(); 1428374121 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 F := [-5 x z - x z , 10 z , 4 x y - 17 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 2 G := [-17 x y - 12 x z, -5 x - 9 x z, -5 x z + 5] > Problem := [F,G]; 3 3 2 3 2 Problem := [[-5 x z - x z , 10 z , 4 x y - 17 x y ], 3 4 2 [-17 x y - 12 x z, -5 x - 9 x z, -5 x 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=0.11 memory used=26.5MB, alloc=32.3MB, time=0.29 memory used=48.1MB, alloc=32.3MB, time=0.47 memory used=69.0MB, alloc=32.3MB, time=0.66 memory used=89.4MB, alloc=56.3MB, time=0.89 N1 := 679 > GB := Basis(F, plex(op(vars))); 3 2 3 2 GB := [-4 x y + 17 x y , x z, z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=131.1MB, alloc=56.3MB, time=1.37 memory used=171.1MB, alloc=60.3MB, time=1.76 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)]; 3 3 2 3 2 3 H := [-5 x z - x z , 10 z , 4 x y - 17 x y , -17 x y - 12 x z, 4 2 -5 x - 9 x z, -5 x z + 5] > J:=[op(GB),op(G)]; J := [ 3 2 3 2 3 4 2 -4 x y + 17 x y , x z, z , -17 x y - 12 x z, -5 x - 9 x z, -5 x 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 := [6, 12, 20, 4, 4, 3, 3, 5/6, 1/3, 5/6, 3/4, 1/4, 1/2, 6, 12, 20, 4, 4, 3, 2, 5/6, 1/3, 5/6, 2/3, 1/4, 5/12, 0, 0, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=206.1MB, alloc=60.3MB, time=2.17 |\^/| 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(); 1428374123 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 F := [-x y + 15 x z , -12 y + 2 y , -14 y z + 18 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 2 G := [-16 x y z - 7 x z, -20 y z - z , 13 y z - 13 z] > Problem := [F,G]; 2 2 3 2 2 2 Problem := [[-x y + 15 x z , -12 y + 2 y , -14 y z + 18 z ], 2 3 4 2 2 [-16 x y z - 7 x z, -20 y z - z , 13 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=4.3MB, alloc=32.3MB, time=0.13 memory used=26.0MB, alloc=32.3MB, time=0.30 memory used=47.4MB, alloc=32.3MB, time=0.49 memory used=69.1MB, alloc=56.3MB, time=0.72 memory used=111.7MB, alloc=56.3MB, time=1.16 memory used=148.0MB, alloc=84.3MB, time=1.56 memory used=199.3MB, alloc=108.3MB, time=2.38 N1 := 1831 > GB := Basis(F, plex(op(vars))); 2 3 2 2 GB := [x y , 6 y - y , z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=272.0MB, alloc=108.3MB, time=3.42 N2 := 357 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 2 2 H := [-x y + 15 x z , -12 y + 2 y , -14 y z + 18 z , -16 x y z - 7 x z, 3 4 2 2 -20 y z - z , 13 y z - 13 z] > J:=[op(GB),op(G)]; 2 3 2 2 2 3 4 2 2 J := [x y , 6 y - y , z , -16 x y z - 7 x z, -20 y z - z , 13 y z - 13 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, 21, 4, 2, 3, 4, 1/3, 1, 5/6, 1/3, 7/12, 3/4, 6, 11, 20, 4, 2, 3, 4, 1/3, 5/6, 2/3, 1/4, 1/2, 7/12, 2, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=295.1MB, alloc=108.3MB, time=3.66 |\^/| 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(); 1428374127 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 3 F := [-13 x z + 5 z, -18 x y - 7 y z , -11 x z + 3 y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 4 3 G := [14 y z, 13 x y z - 14 x, 6 x - 17 z ] > Problem := [F,G]; 2 2 3 3 2 3 Problem := [[-13 x z + 5 z, -18 x y - 7 y z , -11 x z + 3 y ], 2 2 4 3 [14 y z, 13 x y z - 14 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=4.2MB, alloc=32.3MB, time=0.11 memory used=27.1MB, alloc=32.3MB, time=0.31 memory used=48.1MB, alloc=32.3MB, time=0.49 memory used=69.4MB, alloc=60.3MB, time=0.69 memory used=111.9MB, alloc=60.3MB, time=1.04 memory used=151.9MB, alloc=60.3MB, time=1.37 memory used=191.0MB, alloc=84.3MB, time=1.73 memory used=229.5MB, alloc=84.3MB, time=2.08 memory used=296.4MB, alloc=92.3MB, time=2.58 memory used=361.5MB, alloc=372.3MB, time=3.10 memory used=449.5MB, alloc=396.3MB, time=3.84 memory used=558.8MB, alloc=420.3MB, time=4.77 memory used=696.3MB, alloc=444.3MB, time=5.83 memory used=822.9MB, alloc=468.3MB, time=6.93 memory used=964.1MB, alloc=468.3MB, time=7.78 memory used=1124.6MB, alloc=492.3MB, time=8.81 memory used=1227.8MB, alloc=492.3MB, time=9.75 memory used=1335.4MB, alloc=492.3MB, time=10.67 memory used=1436.5MB, alloc=516.3MB, time=11.51 memory used=1529.8MB, alloc=516.3MB, time=12.38 memory used=1681.8MB, alloc=540.3MB, time=14.09 memory used=1913.1MB, alloc=564.3MB, time=16.08 memory used=2130.6MB, alloc=588.3MB, time=18.39 memory used=2297.5MB, alloc=612.3MB, time=20.53 memory used=2443.9MB, alloc=636.3MB, time=22.47 memory used=2613.8MB, alloc=660.3MB, time=24.74 memory used=2781.4MB, alloc=684.3MB, time=27.00 memory used=2895.7MB, alloc=708.3MB, time=28.82 memory used=3150.4MB, alloc=732.3MB, time=34.30 memory used=3288.6MB, alloc=756.3MB, time=37.79 memory used=3562.9MB, alloc=780.3MB, time=44.42 memory used=3841.3MB, alloc=804.3MB, time=51.62 memory used=4128.1MB, alloc=828.3MB, time=59.44 memory used=4438.8MB, alloc=852.3MB, time=67.88 memory used=4773.4MB, alloc=876.3MB, time=76.92 memory used=5132.0MB, alloc=900.3MB, time=86.67 memory used=5514.5MB, alloc=924.3MB, time=96.92 memory used=5921.0MB, alloc=924.3MB, time=107.77 memory used=6327.4MB, alloc=948.3MB, time=118.60 memory used=6757.8MB, alloc=948.3MB, time=129.96 memory used=7188.0MB, alloc=948.3MB, time=141.34 memory used=7618.3MB, alloc=972.3MB, time=152.81 memory used=8072.3MB, alloc=972.3MB, time=164.94 memory used=8526.1MB, alloc=996.3MB, time=176.77 memory used=9004.1MB, alloc=996.3MB, time=189.20 memory used=9481.9MB, alloc=1020.3MB, time=201.50 memory used=9983.7MB, alloc=1044.3MB, time=214.43 memory used=10509.7MB, alloc=1068.3MB, time=227.14 N1 := 16103 > GB := Basis(F, plex(op(vars))); 21 3 3 7 3 4 GB := [4919985720936 x y + 26796875 y , 11154 x y + 175 y , 19 3 1341814287528 x y + 26796875 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 1937 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 2 3 2 H := [-13 x z + 5 z, -18 x y - 7 y z , -11 x z + 3 y , 14 z y , 2 4 3 13 x y z - 14 x, 6 x - 17 z ] > J:=[op(GB),op(G)]; 21 3 3 7 3 4 J := [4919985720936 x y + 26796875 y , 11154 x y + 175 y , 3 19 2 2 4 3 1341814287528 y x + 26796875 z, 14 z y , 13 x y z - 14 x, 6 x - 17 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, 15, 22, 4, 4, 3, 3, 5/6, 2/3, 1, 6/13, 5/13, 7/13, 6, 14, 67, 24, 21, 4, 3, 5/6, 5/6, 2/3, 6/13, 7/13, 4/13, 1, -45, -20] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=11078.8MB, alloc=1068.3MB, time=236.02 |\^/| 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(); 1428374358 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 F := [2 z + 9 z, -3 x, -10 y z + 9 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [14 x y + 18 x y , 3 x y - x y z, 18 z + 2 x y] > Problem := [F,G]; 4 2 2 2 Problem := [[2 z + 9 z, -3 x, -10 y z + 9 z ], 2 2 2 3 [14 x y + 18 x y , 3 x y - x y z, 18 z + 2 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.2MB, alloc=32.3MB, time=0.32 memory used=47.7MB, alloc=32.3MB, time=0.53 memory used=68.5MB, alloc=56.3MB, time=0.75 memory used=112.9MB, alloc=60.3MB, time=1.25 memory used=152.2MB, alloc=84.3MB, time=1.67 memory used=209.0MB, alloc=108.3MB, time=2.35 memory used=276.6MB, alloc=108.3MB, time=3.56 memory used=341.1MB, alloc=132.3MB, time=4.59 N1 := 2195 > GB := Basis(F, plex(op(vars))); 2 4 GB := [x, 10 y z - 9 z, 2 z + 9 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=429.6MB, alloc=140.3MB, time=5.49 memory used=531.7MB, alloc=164.3MB, time=6.58 memory used=639.7MB, alloc=188.3MB, time=8.46 N2 := 2195 #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)]; 4 2 2 2 2 2 2 H := [2 z + 9 z, -3 x, -10 y z + 9 z , 14 x y + 18 x y , 3 x y - x y z, 3 18 z + 2 x y] > J:=[op(GB),op(G)]; 2 4 2 2 2 J := [x, 10 y z - 9 z, 2 z + 9 z, 14 x y + 18 x y , 3 x y - x y z, 3 18 z + 2 x y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 18, 4, 2, 2, 4, 2/3, 2/3, 2/3, 1/2, 1/2, 1/2, 6, 12, 17, 4, 2, 2, 4, 2/3, 2/3, 2/3, 6/11, 6/11, 6/11, 0, 1, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=705.8MB, alloc=188.3MB, time=9.44 |\^/| 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(); 1428374367 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 4 2 2 2 F := [-6 x z + 16 y , -2 y + 20 x z , 20 y z - 17] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-5 z + 18 x , 17 - 12 x, 20 x - 12 y] > Problem := [F,G]; 2 3 4 2 2 2 Problem := [[-6 x z + 16 y , -2 y + 20 x z , 20 y z - 17], 3 2 2 [-5 z + 18 x , 17 - 12 x, 20 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=4.3MB, alloc=32.3MB, time=0.13 memory used=55.8MB, alloc=68.3MB, time=0.63 memory used=106.8MB, alloc=76.3MB, time=1.07 memory used=157.2MB, alloc=76.3MB, time=1.50 memory used=206.7MB, alloc=100.3MB, time=1.93 memory used=276.7MB, alloc=100.3MB, time=2.54 memory used=347.8MB, alloc=124.3MB, time=3.14 memory used=413.2MB, alloc=380.3MB, time=3.64 memory used=503.5MB, alloc=404.3MB, time=4.50 memory used=611.4MB, alloc=428.3MB, time=5.65 memory used=742.8MB, alloc=452.3MB, time=6.91 memory used=881.8MB, alloc=476.3MB, time=8.43 memory used=1038.5MB, alloc=500.3MB, time=10.13 memory used=1228.1MB, alloc=524.3MB, time=11.83 memory used=1401.1MB, alloc=548.3MB, time=14.73 memory used=1570.9MB, alloc=572.3MB, time=18.21 memory used=1741.2MB, alloc=596.3MB, time=22.53 memory used=1935.5MB, alloc=620.3MB, time=27.54 memory used=2153.6MB, alloc=644.3MB, time=33.05 memory used=2395.7MB, alloc=644.3MB, time=39.09 memory used=2637.7MB, alloc=668.3MB, time=45.05 memory used=2903.9MB, alloc=668.3MB, time=51.49 memory used=3169.8MB, alloc=692.3MB, time=57.82 memory used=3460.0MB, alloc=716.3MB, time=64.32 N1 := 8629 > GB := Basis(F, plex(op(vars))); 2 GB := [12393 x - 524288000000, 3 y - 80, 128000 z - 153] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 477 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 4 2 2 2 3 2 H := [-6 x z + 16 y , -2 y + 20 x z , 20 z y - 17, -5 z + 18 x , 17 - 12 x, 2 20 x - 12 y] > J:=[op(GB),op(G)]; 2 3 2 J := [12393 x - 524288000000, 3 y - 80, 128000 z - 153, -5 z + 18 x , 2 17 - 12 x, 20 x - 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, 13, 17, 4, 2, 4, 3, 5/6, 2/3, 2/3, 5/12, 1/3, 1/3, 6, 8, 10, 3, 2, 1, 3, 2/3, 1/3, 1/3, 1/3, 1/6, 1/6, 5, 7, 1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=3626.1MB, alloc=716.3MB, time=66.75 |\^/| 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(); 1428374433 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 4 2 F := [20 x y + 20 z , 11 y - 5 y, -18 x z + 2 x] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [-5 y z + y , -6 x z + 14 x y, 18 x z - 3 x] > Problem := [F,G]; 3 4 4 2 Problem := [[20 x y + 20 z , 11 y - 5 y, -18 x z + 2 x], 3 2 3 2 [-5 y z + y , -6 x z + 14 x y, 18 x z - 3 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.12 memory used=26.4MB, alloc=32.3MB, time=0.30 memory used=47.8MB, alloc=32.3MB, time=0.49 memory used=68.3MB, alloc=32.3MB, time=0.68 memory used=86.9MB, alloc=56.3MB, time=0.89 memory used=124.4MB, alloc=60.3MB, time=1.23 memory used=159.4MB, alloc=84.3MB, time=1.54 memory used=214.1MB, alloc=84.3MB, time=2.03 memory used=267.1MB, alloc=84.3MB, time=2.51 memory used=319.1MB, alloc=108.3MB, time=3.02 memory used=391.7MB, alloc=116.3MB, time=3.72 memory used=460.8MB, alloc=140.3MB, time=4.38 memory used=549.2MB, alloc=164.3MB, time=5.24 memory used=657.1MB, alloc=164.3MB, time=6.28 memory used=764.7MB, alloc=444.3MB, time=7.48 memory used=891.8MB, alloc=468.3MB, time=8.73 memory used=1030.7MB, alloc=492.3MB, time=10.20 memory used=1179.0MB, alloc=516.3MB, time=11.85 memory used=1335.4MB, alloc=540.3MB, time=13.66 memory used=1501.0MB, alloc=564.3MB, time=15.55 memory used=1676.0MB, alloc=588.3MB, time=17.53 memory used=1848.3MB, alloc=612.3MB, time=19.86 memory used=2003.0MB, alloc=636.3MB, time=22.79 memory used=2163.9MB, alloc=660.3MB, time=26.18 memory used=2336.0MB, alloc=684.3MB, time=30.04 memory used=2520.8MB, alloc=708.3MB, time=34.38 memory used=2719.6MB, alloc=732.3MB, time=39.05 memory used=2931.6MB, alloc=756.3MB, time=44.08 memory used=3158.4MB, alloc=780.3MB, time=49.55 memory used=3397.9MB, alloc=804.3MB, time=55.66 memory used=3655.3MB, alloc=828.3MB, time=62.39 memory used=3936.5MB, alloc=852.3MB, time=69.72 memory used=4241.7MB, alloc=876.3MB, time=77.63 memory used=4570.9MB, alloc=900.3MB, time=86.20 memory used=4924.0MB, alloc=924.3MB, time=95.26 memory used=5301.0MB, alloc=948.3MB, time=104.89 memory used=5702.0MB, alloc=972.3MB, time=115.14 memory used=6126.9MB, alloc=996.3MB, time=125.98 memory used=6575.7MB, alloc=996.3MB, time=137.38 memory used=7024.5MB, alloc=996.3MB, time=148.87 memory used=7473.2MB, alloc=996.3MB, time=160.25 memory used=7921.7MB, alloc=1020.3MB, time=171.65 memory used=8394.2MB, alloc=1020.3MB, time=183.65 memory used=8866.6MB, alloc=1020.3MB, time=195.63 memory used=9339.2MB, alloc=1020.3MB, time=207.72 memory used=9811.5MB, alloc=1044.3MB, time=219.67 memory used=10307.8MB, alloc=1044.3MB, time=232.22 memory used=10804.1MB, alloc=1044.3MB, time=244.74 memory used=11300.3MB, alloc=1068.3MB, time=257.27 memory used=11820.3MB, alloc=1068.3MB, time=270.47 memory used=12340.2MB, alloc=1068.3MB, time=283.53 memory used=12860.1MB, alloc=1092.3MB, time=296.62 |\^/| 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(); 1428374733 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 2 F := [-9 x y + 16 x z , 18 y + 10 y , -15 x y - 6 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [y z - 17 y, -13 x y z + 5 x y, 3 x y z + 7 x y z ] > Problem := [F,G]; 3 2 3 2 2 2 Problem := [[-9 x y + 16 x z , 18 y + 10 y , -15 x y - 6 x z], 3 2 2 2 2 [y z - 17 y, -13 x y z + 5 x y, 3 x y z + 7 x y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.1MB, alloc=32.3MB, time=0.39 memory used=47.1MB, alloc=32.3MB, time=0.64 memory used=66.3MB, alloc=56.3MB, time=0.87 memory used=104.9MB, alloc=60.3MB, time=1.33 memory used=140.7MB, alloc=84.3MB, time=1.75 memory used=199.6MB, alloc=92.3MB, time=2.47 memory used=254.8MB, alloc=116.3MB, time=3.12 memory used=332.0MB, alloc=116.3MB, time=4.10 memory used=406.1MB, alloc=140.3MB, time=5.01 memory used=496.6MB, alloc=164.3MB, time=6.22 memory used=581.9MB, alloc=420.3MB, time=7.17 memory used=695.7MB, alloc=444.3MB, time=8.41 memory used=819.1MB, alloc=468.3MB, time=9.79 memory used=955.2MB, alloc=492.3MB, time=11.30 memory used=1103.8MB, alloc=516.3MB, time=13.00 memory used=1260.8MB, alloc=540.3MB, time=14.84 memory used=1422.6MB, alloc=564.3MB, time=17.25 memory used=1573.1MB, alloc=588.3MB, time=20.25 memory used=1732.7MB, alloc=612.3MB, time=23.72 memory used=1905.0MB, alloc=636.3MB, time=27.68 memory used=2090.3MB, alloc=660.3MB, time=32.13 memory used=2285.0MB, alloc=684.3MB, time=37.28 memory used=2503.6MB, alloc=708.3MB, time=43.02 memory used=2746.2MB, alloc=732.3MB, time=49.39 memory used=3012.7MB, alloc=756.3MB, time=56.36 memory used=3303.2MB, alloc=780.3MB, time=63.93 memory used=3617.6MB, alloc=804.3MB, time=72.06 memory used=3955.9MB, alloc=804.3MB, time=80.95 memory used=4294.2MB, alloc=828.3MB, time=89.75 memory used=4656.5MB, alloc=828.3MB, time=99.06 memory used=5018.7MB, alloc=828.3MB, time=108.34 memory used=5380.8MB, alloc=852.3MB, time=117.56 memory used=5766.7MB, alloc=852.3MB, time=127.38 memory used=6152.5MB, alloc=852.3MB, time=137.10 memory used=6538.5MB, alloc=876.3MB, time=146.84 memory used=6948.3MB, alloc=900.3MB, time=156.85 memory used=7382.1MB, alloc=924.3MB, time=167.07 N1 := 14439 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 2 2 GB := [500 x y + 81 x y , 9 y + 5 y , 5 x y + 2 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7854.0MB, alloc=924.3MB, time=175.07 N2 := 2723 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 2 2 3 H := [-9 x y + 16 x z , 18 y + 10 y , -15 x y - 6 x z, y z - 17 y, 2 2 2 2 -13 x y z + 5 x y, 3 x y z + 7 x y z ] > J:=[op(GB),op(G)]; 3 2 2 3 2 2 2 3 J := [500 x y + 81 x y , 9 y + 5 y , 5 x y + 2 x z, y z - 17 y, 2 2 2 2 -13 x y z + 5 x y, 3 x y z + 7 x 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 := [6, 15, 23, 4, 2, 3, 3, 2/3, 1, 5/6, 2/3, 5/6, 1/2, 6, 14, 24, 5, 3, 3, 3, 2/3, 1, 2/3, 2/3, 11/12, 5/12, 1, -1, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=8119.0MB, alloc=924.3MB, time=179.99 |\^/| 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(); 1428374911 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 4 4 2 2 F := [-2 x z - 18 y , 10 x - 19 y , x y z - 20 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 4 2 2 G := [-18 x z - 13 y , 12 x y + 19 z , -12 x + 14 x z ] > Problem := [F,G]; 3 4 4 2 2 Problem := [[-2 x z - 18 y , 10 x - 19 y , x y z - 20 x z], 2 2 3 2 2 4 2 2 [-18 x z - 13 y , 12 x y + 19 z , -12 x + 14 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=27.0MB, alloc=32.3MB, time=0.38 memory used=48.4MB, alloc=32.3MB, time=0.57 memory used=69.0MB, alloc=32.3MB, time=0.74 memory used=89.2MB, alloc=60.3MB, time=0.93 memory used=129.5MB, alloc=60.3MB, time=1.26 memory used=166.6MB, alloc=60.3MB, time=1.58 memory used=200.3MB, alloc=84.3MB, time=1.86 memory used=266.2MB, alloc=92.3MB, time=2.40 memory used=327.1MB, alloc=116.3MB, time=2.92 memory used=404.7MB, alloc=116.3MB, time=3.58 memory used=472.9MB, alloc=396.3MB, time=4.17 memory used=577.7MB, alloc=420.3MB, time=5.07 memory used=711.1MB, alloc=444.3MB, time=6.37 memory used=849.2MB, alloc=468.3MB, time=7.85 memory used=998.5MB, alloc=492.3MB, time=9.50 memory used=1165.3MB, alloc=516.3MB, time=11.31 memory used=1358.3MB, alloc=540.3MB, time=13.19 memory used=1575.7MB, alloc=564.3MB, time=15.10 memory used=1805.5MB, alloc=588.3MB, time=17.35 memory used=2013.1MB, alloc=612.3MB, time=19.79 memory used=2236.4MB, alloc=636.3MB, time=22.67 memory used=2448.9MB, alloc=660.3MB, time=26.51 memory used=2653.3MB, alloc=684.3MB, time=30.98 memory used=2865.6MB, alloc=708.3MB, time=35.99 memory used=3088.7MB, alloc=732.3MB, time=41.44 memory used=3324.7MB, alloc=756.3MB, time=47.28 memory used=3574.2MB, alloc=780.3MB, time=53.52 memory used=3833.7MB, alloc=804.3MB, time=60.45 memory used=4110.1MB, alloc=828.3MB, time=68.04 memory used=4410.4MB, alloc=852.3MB, time=76.22 memory used=4734.7MB, alloc=876.3MB, time=85.17 memory used=5082.8MB, alloc=900.3MB, time=94.62 memory used=5455.0MB, alloc=924.3MB, time=104.70 memory used=5851.0MB, alloc=948.3MB, time=115.39 memory used=6271.0MB, alloc=972.3MB, time=126.71 memory used=6714.9MB, alloc=972.3MB, time=138.63 memory used=7158.8MB, alloc=972.3MB, time=150.65 memory used=7602.7MB, alloc=972.3MB, time=162.57 memory used=8046.5MB, alloc=996.3MB, time=174.49 memory used=8514.2MB, alloc=996.3MB, time=186.98 memory used=8982.0MB, alloc=996.3MB, time=199.53 memory used=9449.5MB, alloc=1020.3MB, time=212.19 memory used=9940.9MB, alloc=1020.3MB, time=225.36 memory used=10432.2MB, alloc=1020.3MB, time=238.49 memory used=10923.3MB, alloc=1020.3MB, time=251.61 memory used=11414.4MB, alloc=1044.3MB, time=264.76 memory used=11929.4MB, alloc=1044.3MB, time=278.29 memory used=12444.3MB, alloc=1068.3MB, time=291.87 |\^/| 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(); 1428375211 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [x z + 4 x, 20 x y - 12 x y, -13 x y z + 2 y z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 G := [15 x z - 15, 14 x + 6 x y z, 18 y z + 2 y ] > Problem := [F,G]; 3 2 2 2 Problem := [[x z + 4 x, 20 x y - 12 x y, -13 x y z + 2 y z], 3 3 2 2 2 [15 x z - 15, 14 x + 6 x y z, 18 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=4.3MB, alloc=32.3MB, time=0.14 memory used=26.4MB, alloc=32.3MB, time=0.40 memory used=48.1MB, alloc=32.3MB, time=0.71 memory used=68.0MB, alloc=56.3MB, time=0.96 memory used=108.3MB, alloc=60.3MB, time=1.31 memory used=146.1MB, alloc=60.3MB, time=1.64 memory used=183.5MB, alloc=60.3MB, time=1.96 memory used=220.2MB, alloc=84.3MB, time=2.29 memory used=276.7MB, alloc=92.3MB, time=2.81 memory used=331.4MB, alloc=116.3MB, time=3.33 memory used=408.3MB, alloc=140.3MB, time=4.15 memory used=501.7MB, alloc=164.3MB, time=5.16 memory used=613.1MB, alloc=188.3MB, time=6.36 memory used=734.1MB, alloc=212.3MB, time=8.22 memory used=854.6MB, alloc=236.3MB, time=10.79 memory used=996.4MB, alloc=260.3MB, time=13.85 memory used=1162.2MB, alloc=260.3MB, time=17.16 N1 := 4393 > GB := Basis(F, plex(op(vars))); 2 2 3 GB := [3 x y + 130 x y, 5 x y - 3 x y, x z + 4 x, 4225 x y z + 9 x y, 2 2746250 y z - 81 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1332.8MB, alloc=260.3MB, time=19.46 memory used=1432.5MB, alloc=516.3MB, time=20.62 memory used=1620.0MB, alloc=540.3MB, time=22.48 memory used=1818.4MB, alloc=564.3MB, time=24.41 memory used=2095.9MB, alloc=588.3MB, time=26.71 memory used=2374.0MB, alloc=612.3MB, time=29.53 memory used=2690.4MB, alloc=636.3MB, time=32.07 memory used=3004.2MB, alloc=660.3MB, time=35.09 memory used=3275.5MB, alloc=684.3MB, time=40.61 memory used=3528.5MB, alloc=708.3MB, time=46.93 memory used=3803.3MB, alloc=732.3MB, time=53.76 memory used=4102.1MB, alloc=756.3MB, time=61.09 memory used=4425.1MB, alloc=780.3MB, time=68.73 memory used=4772.3MB, alloc=804.3MB, time=76.02 N2 := 7495 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 H := [x z + 4 x, 20 x y - 12 x y, -13 x y z + 2 y z, 15 x z - 15, 3 2 2 2 14 x + 6 x y z, 18 y z + 2 y ] > J:=[op(GB),op(G)]; 2 2 3 J := [3 x y + 130 x y, 5 x y - 3 x y, x z + 4 x, 4225 x y z + 9 x y, 2 3 3 2 2 2 2746250 y z - 81 x y, 15 x z - 15, 14 x + 6 x y z, 18 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 := [6, 14, 22, 4, 3, 2, 3, 5/6, 2/3, 5/6, 2/3, 7/12, 1/2, 8, 19, 27, 4, 3, 2, 3, 7/8, 3/4, 3/4, 3/4, 11/16, 3/8, -5, -5, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=4802.8MB, alloc=804.3MB, time=76.52 |\^/| 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(); 1428375286 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 2 2 F := [-4 y z - 7, -4 x z - y z, -20 x z - 12 x y ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-4 x y - 12 x y, -5 x z - 18 z, -15 x y - 7 x y] > Problem := [F,G]; 3 3 3 2 2 2 Problem := [[-4 y z - 7, -4 x z - y z, -20 x z - 12 x y ], 2 3 2 [-4 x y - 12 x y, -5 x z - 18 z, -15 x y - 7 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.4MB, alloc=32.3MB, time=0.36 memory used=48.5MB, alloc=32.3MB, time=0.54 memory used=68.6MB, alloc=56.3MB, time=0.73 memory used=109.4MB, alloc=60.3MB, time=1.09 memory used=146.2MB, alloc=84.3MB, time=1.42 memory used=207.4MB, alloc=84.3MB, time=2.05 memory used=262.0MB, alloc=108.3MB, time=2.63 memory used=336.4MB, alloc=132.3MB, time=3.42 memory used=431.1MB, alloc=140.3MB, time=4.52 memory used=517.7MB, alloc=164.3MB, time=5.45 memory used=617.8MB, alloc=188.3MB, time=6.60 memory used=725.6MB, alloc=212.3MB, time=8.37 memory used=839.3MB, alloc=236.3MB, time=10.91 memory used=971.7MB, alloc=260.3MB, time=13.93 memory used=1128.2MB, alloc=260.3MB, time=17.50 memory used=1284.6MB, alloc=284.3MB, time=21.03 memory used=1464.9MB, alloc=284.3MB, time=24.99 memory used=1645.4MB, alloc=308.3MB, time=28.75 N1 := 6141 > GB := Basis(F, plex(op(vars))); 3 GB := [2392578125 x + 185752092672, 5 y - 12, -4375 x + 20736 z] > 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)]; 3 3 3 2 2 2 2 H := [-4 y z - 7, -4 x z - y z, -20 x z - 12 x y , -4 x y - 12 x y, 3 2 -5 x z - 18 z, -15 x y - 7 x y] > J:=[op(GB),op(G)]; 3 J := [2392578125 x + 185752092672, 5 y - 12, -4375 x + 20736 z, 2 3 2 -4 x y - 12 x y, -5 x z - 18 z, -15 x y - 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 := [6, 14, 22, 4, 2, 3, 3, 5/6, 5/6, 2/3, 2/3, 7/12, 1/2, 6, 10, 15, 4, 3, 2, 3, 5/6, 1/2, 1/3, 7/12, 5/12, 1/4, 4, 7, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=1845.3MB, alloc=308.3MB, time=31.62 |\^/| 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(); 1428375317 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 2 2 3 F := [-13 z - 20 x y, -18 x y z + 4 x, -5 x y + 5 y z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 G := [-16 x y - 11 z, 16 x y + 2, 19 x y z + 5] > Problem := [F,G]; 4 2 2 2 2 3 Problem := [[-13 z - 20 x y, -18 x y z + 4 x, -5 x y + 5 y z ], 2 [-16 x y - 11 z, 16 x y + 2, 19 x y z + 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.11 memory used=26.7MB, alloc=32.3MB, time=0.33 memory used=48.4MB, alloc=32.3MB, time=0.55 memory used=69.1MB, alloc=56.3MB, time=0.74 memory used=109.6MB, alloc=60.3MB, time=1.10 memory used=163.2MB, alloc=84.3MB, time=1.46 memory used=223.9MB, alloc=92.3MB, time=2.01 memory used=284.1MB, alloc=92.3MB, time=2.55 memory used=344.1MB, alloc=116.3MB, time=3.10 memory used=415.6MB, alloc=372.3MB, time=3.67 memory used=501.0MB, alloc=396.3MB, time=4.41 memory used=649.3MB, alloc=396.3MB, time=5.25 memory used=736.2MB, alloc=396.3MB, time=5.80 memory used=858.0MB, alloc=420.3MB, time=6.66 memory used=1006.1MB, alloc=420.3MB, time=7.38 memory used=1127.9MB, alloc=444.3MB, time=8.42 memory used=1261.9MB, alloc=468.3MB, time=9.71 memory used=1389.4MB, alloc=468.3MB, time=10.95 memory used=1517.4MB, alloc=492.3MB, time=12.04 memory used=1641.6MB, alloc=516.3MB, time=13.16 memory used=1755.0MB, alloc=516.3MB, time=14.23 memory used=1866.3MB, alloc=516.3MB, time=15.23 memory used=1965.6MB, alloc=516.3MB, time=16.13 memory used=2071.7MB, alloc=540.3MB, time=17.06 memory used=2177.4MB, alloc=540.3MB, time=18.24 memory used=2292.4MB, alloc=564.3MB, time=19.54 memory used=2409.7MB, alloc=588.3MB, time=21.03 memory used=2556.1MB, alloc=588.3MB, time=22.73 memory used=2687.6MB, alloc=612.3MB, time=24.39 memory used=2803.9MB, alloc=636.3MB, time=25.95 memory used=2932.4MB, alloc=660.3MB, time=27.64 memory used=3069.4MB, alloc=660.3MB, time=29.30 memory used=3186.8MB, alloc=684.3MB, time=30.80 memory used=3269.6MB, alloc=684.3MB, time=32.03 memory used=3357.7MB, alloc=708.3MB, time=33.31 memory used=3472.7MB, alloc=708.3MB, time=34.88 memory used=3590.4MB, alloc=732.3MB, time=36.47 memory used=3729.4MB, alloc=756.3MB, time=39.22 memory used=3929.9MB, alloc=780.3MB, time=44.01 memory used=4232.2MB, alloc=804.3MB, time=51.41 memory used=4539.2MB, alloc=828.3MB, time=59.35 memory used=4844.2MB, alloc=852.3MB, time=68.10 memory used=5173.2MB, alloc=876.3MB, time=77.52 memory used=5526.1MB, alloc=900.3MB, time=87.58 memory used=5903.0MB, alloc=924.3MB, time=98.40 memory used=6303.8MB, alloc=924.3MB, time=109.76 memory used=6704.6MB, alloc=948.3MB, time=121.12 memory used=7129.3MB, alloc=948.3MB, time=133.07 memory used=7553.9MB, alloc=948.3MB, time=145.02 memory used=7978.6MB, alloc=972.3MB, time=156.96 memory used=8426.9MB, alloc=972.3MB, time=169.59 memory used=8875.1MB, alloc=996.3MB, time=181.97 memory used=9347.4MB, alloc=1020.3MB, time=194.81 memory used=9843.5MB, alloc=1020.3MB, time=207.95 memory used=10339.8MB, alloc=1044.3MB, time=220.90 N1 := 15029 > GB := Basis(F, plex(op(vars))); 5 3 GB := [62748517 x + 5760000000 x, -28561 x + 720000 x y, 13 x z + 20 x, 3 2 4 4 90 y z + 13 x , 2197 x + 36000 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=10880.6MB, alloc=1044.3MB, time=229.64 memory used=11515.8MB, alloc=1068.3MB, time=236.87 memory used=12158.6MB, alloc=1092.3MB, time=248.96 N2 := 3891 #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)]; 4 2 2 2 2 3 H := [-13 z - 20 x y, -18 x y z + 4 x, -5 x y + 5 y z , -16 x y - 11 z, 2 16 x y + 2, 19 z y x + 5] > J:=[op(GB),op(G)]; 5 3 J := [62748517 x + 5760000000 x, -28561 x + 720000 x y, 13 x z + 20 x, 3 2 4 4 90 z y + 13 x , 36000 z + 2197 x , -16 x y - 11 z, 16 x y + 2, 2 19 z y 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 := [6, 17, 20, 4, 2, 2, 4, 1, 1, 5/6, 7/12, 7/12, 5/12, 8, 18, 26, 5, 5, 2, 4, 1, 5/8, 5/8, 11/16, 5/16, 5/16, -1, -6, -1] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=12383.6MB, alloc=1092.3MB, time=253.77 |\^/| 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(); 1428375565 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 3 4 F := [-10 x y - 10 x y, 11 x z - x z , 2 x y + 17 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 3 2 4 G := [9 x + 7 x z, 10 x y - 2 x y z, -16 y - 11 x y z] > Problem := [F,G]; 3 2 3 3 3 4 Problem := [[-10 x y - 10 x y, 11 x z - x z , 2 x y + 17 z ], 4 2 3 2 4 [9 x + 7 x z, 10 x y - 2 x y z, -16 y - 11 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.38 memory used=47.8MB, alloc=32.3MB, time=0.57 memory used=68.2MB, alloc=32.3MB, time=0.75 memory used=88.1MB, alloc=56.3MB, time=0.93 memory used=129.5MB, alloc=60.3MB, time=1.29 memory used=168.9MB, alloc=84.3MB, time=1.63 memory used=202.4MB, alloc=84.3MB, time=1.91 memory used=263.5MB, alloc=116.3MB, time=2.47 memory used=344.4MB, alloc=116.3MB, time=3.18 memory used=416.1MB, alloc=140.3MB, time=3.83 memory used=469.5MB, alloc=396.3MB, time=4.34 memory used=573.6MB, alloc=420.3MB, time=5.31 memory used=698.0MB, alloc=444.3MB, time=6.53 memory used=825.8MB, alloc=468.3MB, time=7.96 memory used=979.9MB, alloc=492.3MB, time=9.49 memory used=1165.4MB, alloc=516.3MB, time=10.99 memory used=1375.2MB, alloc=540.3MB, time=12.57 memory used=1609.1MB, alloc=540.3MB, time=14.36 memory used=1802.4MB, alloc=564.3MB, time=16.52 memory used=1980.1MB, alloc=588.3MB, time=19.54 memory used=2154.5MB, alloc=612.3MB, time=23.12 memory used=2337.6MB, alloc=636.3MB, time=27.25 memory used=2528.5MB, alloc=660.3MB, time=31.96 memory used=2734.0MB, alloc=684.3MB, time=37.26 memory used=2963.4MB, alloc=708.3MB, time=43.17 memory used=3216.7MB, alloc=732.3MB, time=49.64 memory used=3494.0MB, alloc=756.3MB, time=56.69 memory used=3795.2MB, alloc=780.3MB, time=64.33 memory used=4120.4MB, alloc=780.3MB, time=72.52 memory used=4445.5MB, alloc=780.3MB, time=80.68 memory used=4770.6MB, alloc=804.3MB, time=88.92 memory used=5119.6MB, alloc=804.3MB, time=97.58 memory used=5468.5MB, alloc=804.3MB, time=106.17 memory used=5817.5MB, alloc=828.3MB, time=114.76 memory used=6190.4MB, alloc=828.3MB, time=123.92 memory used=6563.4MB, alloc=852.3MB, time=132.94 memory used=6960.2MB, alloc=852.3MB, time=142.37 memory used=7357.2MB, alloc=876.3MB, time=151.69 N1 := 13849 > GB := Basis(F, plex(op(vars))); 7 4 5 3 2 3 2 GB := [4231249 x y + 4 x y, -2057 x y + 2 x y , x y + x y, 9 6 5 3 3 2 3 4231249 x z + 4 x z, -2057 x z + 2 x y z, 187 x z - 2 x y, 3 3 4 2 -11 x z + x z , 17 z - 2 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7675.4MB, alloc=876.3MB, time=156.81 memory used=7792.6MB, alloc=876.3MB, time=158.76 memory used=7917.4MB, alloc=876.3MB, time=160.73 memory used=8029.2MB, alloc=876.3MB, time=162.41 memory used=8114.5MB, alloc=876.3MB, time=163.72 memory used=8203.1MB, alloc=876.3MB, time=165.06 memory used=8279.1MB, alloc=876.3MB, time=166.37 memory used=8360.6MB, alloc=876.3MB, time=167.65 memory used=8434.0MB, alloc=876.3MB, time=168.87 memory used=8496.6MB, alloc=876.3MB, time=169.91 memory used=8558.8MB, alloc=876.3MB, time=171.42 memory used=8621.4MB, alloc=876.3MB, time=172.84 memory used=8671.6MB, alloc=876.3MB, time=174.11 memory used=8901.6MB, alloc=876.3MB, time=176.79 memory used=9089.5MB, alloc=900.3MB, time=179.28 memory used=9294.2MB, alloc=924.3MB, time=181.59 memory used=9519.5MB, alloc=948.3MB, time=184.83 memory used=10083.3MB, alloc=972.3MB, time=191.04 memory used=10667.9MB, alloc=996.3MB, time=196.77 memory used=11222.4MB, alloc=1020.3MB, time=203.63 memory used=11810.9MB, alloc=1044.3MB, time=209.62 memory used=12420.3MB, alloc=1068.3MB, time=215.34 memory used=13045.0MB, alloc=1092.3MB, time=221.12 memory used=13697.3MB, alloc=1116.3MB, time=226.57 memory used=14371.1MB, alloc=1140.3MB, time=232.18 memory used=15060.2MB, alloc=1164.3MB, time=238.13 memory used=15763.5MB, alloc=1188.3MB, time=244.53 memory used=16460.7MB, alloc=1212.3MB, time=251.75 memory used=17100.5MB, alloc=1236.3MB, time=261.11 memory used=17599.1MB, alloc=1260.3MB, time=274.06 memory used=18078.7MB, alloc=1284.3MB, time=287.22 memory used=18553.8MB, alloc=1308.3MB, time=300.51 |\^/| 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(); 1428375865 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 4 2 2 3 2 F := [-10 y - 5 x, -19 x - 7 x z , 7 x z + 12 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 G := [-3 z + 16 x , -4 x y z + 12 x, 5 y z ] > Problem := [F,G]; 4 4 2 2 3 2 Problem := [[-10 y - 5 x, -19 x - 7 x z , 7 x z + 12 z ], 3 2 2 3 [-3 z + 16 x , -4 x y z + 12 x, 5 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.5MB, alloc=40.3MB, time=0.52 memory used=61.0MB, alloc=40.3MB, time=0.88 memory used=88.9MB, alloc=40.3MB, time=1.23 memory used=116.0MB, alloc=64.3MB, time=1.54 memory used=163.7MB, alloc=92.3MB, time=2.07 N1 := 1163 > GB := Basis(F, plex(op(vars))); 8 4 4 7 4 6 2 GB := [133 x + 144 x , 2 y + x, -19 x + 12 x z, -361 x + 144 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=228.3MB, alloc=92.3MB, time=2.86 memory used=295.5MB, alloc=100.3MB, time=3.53 N2 := 963 #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)]; 4 4 2 2 3 2 3 2 H := [-10 y - 5 x, -19 x - 7 x z , 7 x z + 12 z , -3 z + 16 x , 2 3 -4 x y z + 12 x, 5 y z ] > J:=[op(GB),op(G)]; 8 4 4 7 4 6 2 J := [133 x + 144 x , 2 y + x, -19 x + 12 x z, -361 x + 144 z , 3 2 2 3 -3 z + 16 x , -4 x y z + 12 x, 5 y z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 23, 4, 4, 4, 3, 5/6, 1/2, 5/6, 7/13, 3/13, 6/13, 7, 14, 36, 8, 8, 4, 3, 6/7, 3/7, 5/7, 3/5, 1/5, 1/3, -1, -13, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=356.7MB, alloc=100.3MB, time=4.23 |\^/| 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(); 1428375869 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 3 3 F := [-3 y z + 14 z , -13 x y z + 15 x, -2 y z + 20 x z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 3 2 G := [-5 x - 14 x y z , 16 x y z + 14 x y, -3 x y - 15 x y z ] > Problem := [F,G]; 2 3 3 Problem := [[-3 y z + 14 z , -13 x y z + 15 x, -2 y z + 20 x z], 4 2 2 3 2 [-5 x - 14 x y z , 16 x y z + 14 x y, -3 x y - 15 x y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.0MB, alloc=32.3MB, time=0.35 memory used=47.3MB, alloc=32.3MB, time=0.55 memory used=67.7MB, alloc=32.3MB, time=0.72 memory used=86.7MB, alloc=56.3MB, time=0.90 memory used=126.9MB, alloc=60.3MB, time=1.26 memory used=163.5MB, alloc=84.3MB, time=1.59 memory used=220.4MB, alloc=84.3MB, time=2.09 memory used=274.9MB, alloc=84.3MB, time=2.58 memory used=327.4MB, alloc=108.3MB, time=3.07 memory used=401.1MB, alloc=116.3MB, time=3.76 memory used=471.5MB, alloc=140.3MB, time=4.44 memory used=565.2MB, alloc=164.3MB, time=5.49 memory used=673.3MB, alloc=188.3MB, time=6.70 memory used=797.0MB, alloc=212.3MB, time=8.08 memory used=930.4MB, alloc=492.3MB, time=9.60 memory used=1075.2MB, alloc=516.3MB, time=12.03 memory used=1225.0MB, alloc=540.3MB, time=15.03 memory used=1382.0MB, alloc=564.3MB, time=18.71 memory used=1563.0MB, alloc=588.3MB, time=23.03 memory used=1768.0MB, alloc=588.3MB, time=27.79 memory used=1972.9MB, alloc=612.3MB, time=32.48 memory used=2201.9MB, alloc=612.3MB, time=37.52 memory used=2430.8MB, alloc=636.3MB, time=42.11 N1 := 6855 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 GB := [2197 x - 3430 x, -13 x + 7 x y, -39 x + 98 x z, 49 y z - 195 x , 2 3 -3 y z + 14 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2686.2MB, alloc=636.3MB, time=45.05 memory used=2984.4MB, alloc=660.3MB, time=48.05 memory used=3303.9MB, alloc=684.3MB, time=51.23 memory used=3608.7MB, alloc=708.3MB, time=54.03 memory used=3873.8MB, alloc=732.3MB, time=56.73 memory used=4141.9MB, alloc=756.3MB, time=59.50 memory used=4370.3MB, alloc=780.3MB, time=61.94 memory used=4550.6MB, alloc=804.3MB, time=63.99 memory used=4725.5MB, alloc=828.3MB, time=66.08 memory used=4896.3MB, alloc=852.3MB, time=68.19 memory used=5042.9MB, alloc=876.3MB, time=70.16 memory used=5275.5MB, alloc=900.3MB, time=73.70 memory used=5553.2MB, alloc=924.3MB, time=77.81 memory used=6007.6MB, alloc=948.3MB, time=84.24 memory used=6448.5MB, alloc=972.3MB, time=90.92 memory used=6826.5MB, alloc=996.3MB, time=100.57 memory used=7196.7MB, alloc=1020.3MB, time=110.77 memory used=7572.3MB, alloc=1044.3MB, time=121.34 memory used=7953.6MB, alloc=1068.3MB, time=132.24 memory used=8342.8MB, alloc=1092.3MB, time=143.87 memory used=8756.1MB, alloc=1116.3MB, time=156.20 memory used=9193.2MB, alloc=1140.3MB, time=169.06 memory used=9654.3MB, alloc=1164.3MB, time=182.60 memory used=10139.4MB, alloc=1188.3MB, time=196.74 memory used=10648.3MB, alloc=1212.3MB, time=211.58 memory used=11181.3MB, alloc=1236.3MB, time=226.95 memory used=11738.1MB, alloc=1260.3MB, time=242.96 memory used=12318.7MB, alloc=1284.3MB, time=259.57 memory used=12923.4MB, alloc=1308.3MB, time=277.02 memory used=13552.0MB, alloc=1332.3MB, time=294.94 |\^/| 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(); 1428376169 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 2 4 4 F := [-8 y - 17 x y , 6 x y z - 8 y , -16 y + 6 z] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 4 2 G := [2 x y + 7 y , -19 x y - 10 y , -13 z - 17 z ] > Problem := [F,G]; 4 2 2 4 4 Problem := [[-8 y - 17 x y , 6 x y z - 8 y , -16 y + 6 z], 2 2 3 3 4 2 [2 x y + 7 y , -19 x y - 10 y , -13 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=0.16 memory used=26.2MB, alloc=32.3MB, time=0.40 memory used=47.9MB, alloc=32.3MB, time=0.65 memory used=68.3MB, alloc=32.3MB, time=0.89 memory used=87.9MB, alloc=56.3MB, time=1.12 memory used=131.1MB, alloc=60.3MB, time=1.76 N1 := 611 > GB := Basis(F, plex(op(vars))); 6 2 2 4 2 3 4 2 2 GB := [17 x y + 2 x y , 17 x y + 4 x y , 8 y + 17 x y , 17 x y + 3 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=168.3MB, alloc=60.3MB, time=2.31 memory used=205.9MB, alloc=84.3MB, time=2.73 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)]; 4 2 2 4 4 2 2 H := [-8 y - 17 x y , 6 x y z - 8 y , -16 y + 6 z, 2 x y + 7 y , 3 3 4 2 -19 x y - 10 y , -13 z - 17 z ] > J:=[op(GB),op(G)]; 6 2 2 4 2 3 4 2 2 J := [17 x y + 2 x y , 17 x y + 4 x y , 8 y + 17 x y , 17 y x + 3 z, 2 2 3 3 4 2 2 x y + 7 y , -19 x y - 10 y , -13 z - 17 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, 12, 23, 4, 2, 4, 4, 2/3, 5/6, 1/2, 1/3, 3/4, 1/3, 7, 14, 32, 8, 6, 4, 4, 6/7, 6/7, 2/7, 4/7, 11/14, 3/14, -2, -9, -4] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=244.9MB, alloc=84.3MB, time=3.24 |\^/| 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(); 1428376173 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [2 x y - 10 x y z, 5 x y z - 11, 20 x y + 11 x y] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [17 y z + y z , -4 x y + 9 x z, -9 y z - 9] > Problem := [F,G]; 2 2 2 2 Problem := [[2 x y - 10 x y z, 5 x y z - 11, 20 x y + 11 x y], 2 2 2 2 2 2 [17 y z + y z , -4 x y + 9 x z, -9 y z - 9]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.2MB, alloc=32.3MB, time=0.42 memory used=47.3MB, alloc=32.3MB, time=0.72 memory used=67.8MB, alloc=32.3MB, time=0.97 memory used=87.0MB, alloc=56.3MB, time=1.27 memory used=145.2MB, alloc=92.3MB, time=1.92 N1 := 299 > GB := Basis(F, plex(op(vars))); 3 GB := [20 x + 11, 11 y - 400, 100 z + 11 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=207.4MB, alloc=92.3MB, time=2.52 N2 := 381 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 H := [2 x y - 10 x y z, 5 z y x - 11, 20 x y + 11 x y, 17 y z + y z , 2 2 2 -4 x y + 9 x z, -9 y z - 9] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [20 x + 11, 11 y - 400, 100 z + 11 y, 17 y z + y z , -4 x y + 9 x z, 2 2 -9 y z - 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 := [6, 15, 22, 4, 2, 2, 2, 2/3, 1, 5/6, 7/12, 3/4, 1/2, 6, 11, 16, 4, 2, 3, 2, 1/3, 5/6, 2/3, 1/4, 1/2, 5/12, 4, 6, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=220.2MB, alloc=92.3MB, time=2.66 |\^/| 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(); 1428376176 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-19 x y - 4 x, -20 y z , -16 z - 10 z ] > G := [ randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=4, coeffs=rand(-20 .. 20)) > ]; 4 2 4 G := [11 y + 16 x y , -16 z + 11, -16 x z - 19 y z] > Problem := [F,G]; 2 2 3 2 Problem := [[-19 x y - 4 x, -20 y z , -16 z - 10 z ], 4 2 4 [11 y + 16 x y , -16 z + 11, -16 x z - 19 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.11 memory used=25.9MB, alloc=32.3MB, time=0.28 memory used=48.4MB, alloc=56.3MB, time=0.52 N1 := 387 > GB := Basis(F, plex(op(vars))); 2 2 2 3 2 GB := [19 x y + 4 x, x z , y z , 8 z + 5 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=87.7MB, alloc=60.3MB, time=0.88 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 3 2 4 2 4 H := [-19 x y - 4 x, -20 y z , -16 z - 10 z , 11 y + 16 x y , -16 z + 11, -16 x z - 19 y z] > J:=[op(GB),op(G)]; 2 2 2 3 2 4 2 4 J := [19 x y + 4 x, x z , y z , 8 z + 5 z , 11 y + 16 x y , -16 z + 11, -16 x z - 19 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 := [6, 11, 19, 4, 1, 4, 4, 1/2, 2/3, 2/3, 4/13, 5/13, 6/13, 7, 13, 22, 4, 1, 4, 4, 4/7, 4/7, 5/7, 5/14, 5/14, 1/2, -2, -3, 0] > save(F, G, cat("ranSet/24", convert(F, string),".txt")); > quit memory used=95.2MB, alloc=60.3MB, time=0.97