|\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428239471 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [15 x y z + 7 x z, -4 y z + 16 x , -x z + 19 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [20 x y + 10 x y z, 7 y , 19 y - 6 z] > Problem := [F,G]; 2 2 2 Problem := [[15 x y z + 7 x z, -4 y z + 16 x , -x z + 19 x z], 2 3 2 [20 x y + 10 x y z, 7 y , 19 y - 6 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.46 memory used=46.7MB, alloc=32.3MB, time=0.70 memory used=65.4MB, alloc=56.3MB, time=0.94 memory used=108.0MB, alloc=60.3MB, time=1.58 memory used=143.3MB, alloc=84.3MB, time=2.11 memory used=197.8MB, alloc=108.3MB, time=2.95 memory used=269.1MB, alloc=132.3MB, time=4.10 memory used=355.2MB, alloc=164.3MB, time=5.42 memory used=453.7MB, alloc=188.3MB, time=7.08 memory used=558.0MB, alloc=212.3MB, time=9.64 memory used=674.2MB, alloc=236.3MB, time=12.68 memory used=803.9MB, alloc=260.3MB, time=16.49 memory used=950.6MB, alloc=284.3MB, time=21.33 memory used=1121.4MB, alloc=284.3MB, time=26.76 memory used=1292.1MB, alloc=284.3MB, time=32.27 memory used=1462.8MB, alloc=284.3MB, time=37.79 memory used=1633.4MB, alloc=308.3MB, time=43.67 memory used=1828.0MB, alloc=308.3MB, time=51.43 memory used=2022.5MB, alloc=332.3MB, time=58.92 memory used=2240.8MB, alloc=332.3MB, time=67.26 memory used=2459.2MB, alloc=356.3MB, time=75.61 N1 := 8207 > GB := Basis(F, plex(op(vars))); 5 3 3 3 3 2 2 GB := [900 x - 931 x , 15 x y + 7 x , -900 x + 49 x z, y z - 4 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2633.8MB, alloc=356.3MB, time=80.26 memory used=2906.0MB, alloc=636.3MB, time=85.76 memory used=3172.7MB, alloc=660.3MB, time=96.15 memory used=3447.4MB, alloc=684.3MB, time=107.90 N2 := 4641 #save(Problem, "format.txt"); > if (GB=[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 := [15 x y z + 7 x z, -4 y z + 16 x , -x z + 19 x z, 20 x y + 10 x y z, 3 2 7 y , 19 y - 6 z] > J:=[op(GB),op(G)]; 5 3 3 3 3 2 2 J := [900 x - 931 x , 15 x y + 7 x , -900 x + 49 x z, y z - 4 x , 2 3 2 20 x y + 10 x y z, 7 y , 19 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, 17, 3, 2, 3, 2, 2/3, 5/6, 5/6, 7/12, 1/2, 7/12, 7, 14, 23, 5, 5, 3, 1, 5/7, 5/7, 4/7, 9/14, 3/7, 2/7, 0, -6, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=3601.5MB, alloc=684.3MB, time=114.23 |\^/| 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(); 1428239598 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-15 z , 7 x z , -12 y z + 13 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [6 x y, 8 y + 8 y , -x y + 4 x y z] > Problem := [F,G]; Problem := 2 2 3 2 2 [[-15 z , 7 x z , -12 y z + 13 y], [6 x y, 8 y + 8 y , -x y + 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=4.3MB, alloc=32.3MB, time=0.18 N1 := 135 > GB := Basis(F, plex(op(vars))); 2 GB := [y, z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=26.5MB, alloc=32.3MB, time=0.55 N2 := 69 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 H := [-15 z , 7 x z , -12 y z + 13 y, 6 x y, 8 y + 8 y , -x y + 4 x y z] > J:=[op(GB),op(G)]; 2 3 2 2 J := [y, z , 6 x y, 8 y + 8 y , -x y + 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, 11, 15, 3, 1, 3, 2, 1/2, 2/3, 2/3, 2/7, 1/2, 2/7, 5, 8, 11, 3, 1, 3, 2, 2/5, 4/5, 2/5, 3/10, 3/5, 1/5, 3, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=27.6MB, alloc=32.3MB, time=0.58 |\^/| 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(); 1428239598 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-15 z , 7 x z , -12 y z + 13 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [6 x y, 8 y + 8 y , -x y + 4 x y z] > Problem := [F,G]; Problem := 2 2 3 2 2 [[-15 z , 7 x z , -12 y z + 13 y], [6 x y, 8 y + 8 y , -x y + 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=4.3MB, alloc=32.3MB, time=0.17 N1 := 135 > GB := Basis(F, plex(op(vars))); 2 GB := [y, z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=26.5MB, alloc=32.3MB, time=0.54 N2 := 69 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 H := [-15 z , 7 x z , -12 y z + 13 y, 6 x y, 8 y + 8 y , -x y + 4 x y z] > J:=[op(GB),op(G)]; 2 3 2 2 J := [y, z , 6 x y, 8 y + 8 y , -x y + 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, 11, 15, 3, 1, 3, 2, 1/2, 2/3, 2/3, 2/7, 1/2, 2/7, 5, 8, 11, 3, 1, 3, 2, 2/5, 4/5, 2/5, 3/10, 3/5, 1/5, 3, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=27.6MB, alloc=32.3MB, time=0.56 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428239599 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [6 x y z + 10 y z, -14 x y - 11 x y, -18 z - 19 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [18 x y + y z, 11 y + 13, -8 x y - 12 x z] > Problem := [F,G]; 2 2 2 Problem := [[6 x y z + 10 y z, -14 x y - 11 x y, -18 z - 19 x], 2 2 2 2 [18 x y + y z, 11 y + 13, -8 x y - 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=26.0MB, alloc=32.3MB, time=0.47 memory used=47.3MB, alloc=32.3MB, time=0.78 memory used=68.4MB, alloc=56.3MB, time=1.15 memory used=112.0MB, alloc=60.3MB, time=1.93 memory used=148.6MB, alloc=84.3MB, time=2.68 memory used=199.7MB, alloc=108.3MB, time=4.43 N1 := 1403 > GB := Basis(F, plex(op(vars))); 2 2 2 2 GB := [42 x y - 55 x y, 14 x y + 11 x y, 3 x y z + 5 y z, 18 z + 19 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=272.0MB, alloc=116.3MB, time=5.65 memory used=354.1MB, alloc=140.3MB, time=7.24 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 := [6 x y z + 10 y z, -14 x y - 11 x y, -18 z - 19 x, 18 x y + y z, 2 2 11 y + 13, -8 x y - 12 x z] > J:=[op(GB),op(G)]; 2 2 2 2 J := [42 x y - 55 x y, 14 x y + 11 x y, 3 x y z + 5 y z, 18 z + 19 x, 2 2 2 2 18 x y + y z, 11 y + 13, -8 x y - 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, 16, 3, 2, 2, 2, 5/6, 5/6, 2/3, 7/12, 2/3, 5/12, 7, 16, 19, 3, 2, 2, 2, 6/7, 6/7, 4/7, 9/14, 5/7, 5/14, -2, -3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=408.8MB, alloc=140.3MB, time=9.09 |\^/| 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(); 1428239611 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [-2 x y + 20 z , -18 z - 18, -4 x + 10 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-10 x y + 20 x z , -5 x y + 4 y z , -20 x y + 6 x] > Problem := [F,G]; 2 2 2 3 Problem := [[-2 x y + 20 z , -18 z - 18, -4 x + 10 x y], 2 2 2 2 2 [-10 x y + 20 x z , -5 x y + 4 y z , -20 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=0.49 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=68.2MB, alloc=32.3MB, time=1.10 memory used=88.0MB, alloc=56.3MB, time=1.41 memory used=127.7MB, alloc=60.3MB, time=2.01 memory used=168.1MB, alloc=84.3MB, time=2.75 memory used=231.5MB, alloc=84.3MB, time=3.92 memory used=289.8MB, alloc=108.3MB, time=4.99 memory used=367.2MB, alloc=132.3MB, time=6.42 memory used=454.8MB, alloc=164.3MB, time=8.42 memory used=547.7MB, alloc=188.3MB, time=11.15 memory used=650.3MB, alloc=212.3MB, time=15.10 memory used=776.8MB, alloc=212.3MB, time=19.94 memory used=903.3MB, alloc=236.3MB, time=24.81 memory used=1053.9MB, alloc=236.3MB, time=30.52 N1 := 4907 > GB := Basis(F, plex(op(vars))); 4 2 2 GB := [x + 25, -2 x + 5 y, z + 1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1205.9MB, alloc=236.3MB, time=35.91 N2 := 995 #save(Problem, "format.txt"); > if (GB=[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 := [-2 x y + 20 z , -18 z - 18, -4 x + 10 x y, -10 x y + 20 x z , 2 2 2 -5 x y + 4 y z , -20 x y + 6 x] > J:=[op(GB),op(G)]; 4 2 2 2 2 2 2 J := [x + 25, -2 x + 5 y, z + 1, -10 x y + 20 x z , -5 x y + 4 y z , 2 -20 x 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, 14, 17, 3, 3, 2, 2, 5/6, 5/6, 2/3, 2/3, 1/2, 1/3, 6, 12, 17, 4, 4, 2, 2, 5/6, 2/3, 1/2, 7/12, 5/12, 1/4, 2, 0, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1336.8MB, alloc=236.3MB, time=38.74 |\^/| 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(); 1428239661 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [x y z + 12 y , 4 x z - 18 x y , 10 y z + 7 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-9 x z - 20 z , -6 x z - 8 y , 15 x + 9 y] > Problem := [F,G]; 3 2 2 2 2 Problem := [[x y z + 12 y , 4 x z - 18 x y , 10 y z + 7 y ], 2 2 2 2 2 [-9 x z - 20 z , -6 x z - 8 y , 15 x + 9 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=48.4MB, alloc=32.3MB, time=0.83 memory used=68.4MB, alloc=56.3MB, time=1.16 memory used=108.8MB, alloc=60.3MB, time=1.76 memory used=146.3MB, alloc=60.3MB, time=2.31 memory used=180.8MB, alloc=84.3MB, time=2.85 memory used=219.4MB, alloc=84.3MB, time=3.43 memory used=278.0MB, alloc=116.3MB, time=4.30 memory used=356.4MB, alloc=372.3MB, time=5.49 memory used=438.9MB, alloc=396.3MB, time=6.71 memory used=541.3MB, alloc=420.3MB, time=8.25 memory used=663.9MB, alloc=444.3MB, time=10.14 memory used=806.7MB, alloc=468.3MB, time=12.34 memory used=959.6MB, alloc=492.3MB, time=14.75 memory used=1103.5MB, alloc=516.3MB, time=17.29 memory used=1300.1MB, alloc=540.3MB, time=20.91 memory used=1494.8MB, alloc=564.3MB, time=24.72 memory used=1659.2MB, alloc=588.3MB, time=27.97 memory used=1844.8MB, alloc=612.3MB, time=31.70 memory used=2017.3MB, alloc=636.3MB, time=35.14 memory used=2200.7MB, alloc=660.3MB, time=38.65 memory used=2373.3MB, alloc=684.3MB, time=42.12 memory used=2493.2MB, alloc=708.3MB, time=44.77 memory used=2646.7MB, alloc=732.3MB, time=49.43 memory used=2904.1MB, alloc=756.3MB, time=58.50 memory used=3162.1MB, alloc=780.3MB, time=68.41 memory used=3427.4MB, alloc=804.3MB, time=79.18 memory used=3701.1MB, alloc=828.3MB, time=90.44 memory used=3985.6MB, alloc=852.3MB, time=102.44 memory used=4281.5MB, alloc=876.3MB, time=115.57 memory used=4593.8MB, alloc=900.3MB, time=129.87 memory used=4930.0MB, alloc=924.3MB, time=145.25 memory used=5290.2MB, alloc=948.3MB, time=161.60 memory used=5674.4MB, alloc=972.3MB, time=179.10 memory used=6082.4MB, alloc=996.3MB, time=197.62 memory used=6514.5MB, alloc=1020.3MB, time=217.06 |\^/| 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(); 1428239961 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [6 y z - 5 y , 11 x + 7 z , -x y z - 6 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [13 x y + 10 x y, 3 z , 2 x z - 9 y ] > Problem := [F,G]; 2 2 3 2 Problem := [[6 y z - 5 y , 11 x + 7 z , -x y z - 6 x y], 2 2 2 2 [13 x y + 10 x y, 3 z , 2 x z - 9 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=47.8MB, alloc=32.3MB, time=0.81 memory used=67.8MB, alloc=32.3MB, time=1.11 memory used=118.3MB, alloc=68.3MB, time=2.03 memory used=165.2MB, alloc=68.3MB, time=2.90 memory used=205.6MB, alloc=92.3MB, time=3.74 memory used=259.5MB, alloc=116.3MB, time=5.62 N1 := 1787 > GB := Basis(F, plex(op(vars))); 4 3 2 3 2 GB := [11 x y + 252 x y, 66 x y + 35 y , x y z + 6 x y, 11 x + 7 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=336.5MB, alloc=116.3MB, time=7.58 N2 := 783 #save(Problem, "format.txt"); > if (GB=[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 := [6 y z - 5 y , 11 x + 7 z , -x y z - 6 x y, 13 x y + 10 x y, 3 z , 2 2 2 z x - 9 y ] > J:=[op(GB),op(G)]; 4 3 2 3 2 J := [11 x y + 252 x y, 66 x y + 35 y , x y z + 6 x y, 11 x + 7 z , 2 2 2 2 13 x y + 10 x y, 3 z , 2 z 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, 13, 17, 3, 3, 2, 2, 2/3, 2/3, 5/6, 1/2, 7/12, 5/12, 7, 15, 23, 5, 4, 2, 2, 6/7, 5/7, 4/7, 9/14, 9/14, 2/7, -2, -6, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=421.8MB, alloc=124.3MB, time=9.38 |\^/| 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(); 1428239976 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [19 x y + 14 y, 7 x y + 15 z, -12 x y + 3 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 G := [-12 x - 20 y z , -10 x y - 18 y , 7 x - 20 y z] > Problem := [F,G]; 2 2 2 Problem := [[19 x y + 14 y, 7 x y + 15 z, -12 x y + 3 y z], 3 2 2 3 2 [-12 x - 20 y z , -10 x y - 18 y , 7 x - 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=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=47.7MB, alloc=32.3MB, time=0.82 memory used=67.9MB, alloc=56.3MB, time=1.13 memory used=108.3MB, alloc=60.3MB, time=1.75 memory used=146.8MB, alloc=84.3MB, time=2.34 memory used=208.4MB, alloc=116.3MB, time=3.45 memory used=291.1MB, alloc=116.3MB, time=4.87 memory used=365.7MB, alloc=140.3MB, time=6.22 memory used=466.7MB, alloc=164.3MB, time=7.86 memory used=595.6MB, alloc=164.3MB, time=9.61 memory used=700.6MB, alloc=188.3MB, time=11.67 memory used=812.9MB, alloc=212.3MB, time=14.98 memory used=934.0MB, alloc=236.3MB, time=19.27 memory used=1067.8MB, alloc=260.3MB, time=24.71 memory used=1225.5MB, alloc=284.3MB, time=31.09 memory used=1407.1MB, alloc=284.3MB, time=38.39 memory used=1588.8MB, alloc=284.3MB, time=45.70 memory used=1770.6MB, alloc=308.3MB, time=53.10 N1 := 5971 > GB := Basis(F, plex(op(vars))); 2 3 2 GB := [19 x y + 14 y, 7 y + 60 x y, 7 y x + 15 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1930.2MB, alloc=308.3MB, time=57.68 memory used=2181.3MB, alloc=588.3MB, time=63.98 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)]; 2 2 2 3 2 H := [19 x y + 14 y, 7 y x + 15 z, -12 x y + 3 y z, -12 x - 20 y z , 2 3 2 -10 x y - 18 y , -20 z y + 7 x ] > J:=[op(GB),op(G)]; 2 3 2 3 2 J := [19 x y + 14 y, 7 y + 60 x y, 7 y x + 15 z, -12 x - 20 y z , 2 3 2 -10 x y - 18 y , -20 z y + 7 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 16, 17, 3, 3, 3, 2, 1, 1, 2/3, 1/2, 3/4, 1/3, 6, 15, 17, 3, 3, 3, 2, 1, 1, 1/2, 1/2, 3/4, 1/4, 1, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2255.2MB, alloc=588.3MB, time=67.06 |\^/| 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(); 1428240081 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [-6 x - 5 y z, 11 x y - 13 z , 11 x z + 6 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-3 x z - 18 y , -6 x + 10 y z, -17 y z + 16 x] > Problem := [F,G]; 3 2 3 2 Problem := [[-6 x - 5 y z, 11 x y - 13 z , 11 x z + 6 x z], 2 3 2 [-3 x z - 18 y , -6 x + 10 y z, -17 y z + 16 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=48.4MB, alloc=32.3MB, time=0.84 memory used=69.3MB, alloc=56.3MB, time=1.16 memory used=110.5MB, alloc=60.3MB, time=1.77 memory used=150.5MB, alloc=84.3MB, time=2.39 memory used=211.4MB, alloc=92.3MB, time=3.32 memory used=268.5MB, alloc=116.3MB, time=4.21 memory used=346.6MB, alloc=116.3MB, time=5.43 memory used=422.5MB, alloc=396.3MB, time=6.49 memory used=531.5MB, alloc=420.3MB, time=8.01 memory used=658.6MB, alloc=444.3MB, time=9.86 memory used=782.9MB, alloc=468.3MB, time=11.67 memory used=891.7MB, alloc=468.3MB, time=13.30 memory used=991.4MB, alloc=492.3MB, time=14.92 memory used=1084.0MB, alloc=492.3MB, time=16.40 memory used=1179.2MB, alloc=492.3MB, time=17.98 memory used=1266.1MB, alloc=492.3MB, time=19.49 memory used=1343.6MB, alloc=492.3MB, time=20.78 memory used=1433.3MB, alloc=516.3MB, time=22.58 memory used=1509.3MB, alloc=516.3MB, time=24.00 memory used=1573.9MB, alloc=516.3MB, time=25.35 memory used=1623.8MB, alloc=516.3MB, time=26.32 memory used=1821.3MB, alloc=540.3MB, time=29.56 memory used=2003.7MB, alloc=564.3MB, time=32.69 memory used=2157.4MB, alloc=588.3MB, time=35.34 memory used=2331.2MB, alloc=612.3MB, time=38.60 memory used=2495.3MB, alloc=636.3MB, time=41.88 memory used=2644.7MB, alloc=660.3MB, time=44.73 memory used=2782.2MB, alloc=660.3MB, time=47.59 memory used=2900.0MB, alloc=684.3MB, time=50.10 memory used=3027.4MB, alloc=684.3MB, time=53.03 memory used=3118.8MB, alloc=684.3MB, time=55.22 memory used=3237.6MB, alloc=684.3MB, time=58.29 memory used=3564.3MB, alloc=708.3MB, time=64.24 memory used=3903.9MB, alloc=732.3MB, time=71.01 memory used=4250.2MB, alloc=756.3MB, time=78.15 memory used=4576.7MB, alloc=780.3MB, time=85.68 memory used=4869.4MB, alloc=804.3MB, time=93.06 memory used=5163.6MB, alloc=828.3MB, time=100.39 memory used=5473.2MB, alloc=852.3MB, time=107.87 memory used=5772.7MB, alloc=876.3MB, time=115.49 |\^/| 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(); 1428240381 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 F := [-4 x y + 10 y, 19 y z - 4 z, -10 x y - 10 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 G := [16 x y + 4 x, -13 z - 13 y, -18 x y + 18 y ] > Problem := [F,G]; 2 Problem := [[-4 x y + 10 y, 19 y z - 4 z, -10 x y - 10 z ], 2 3 2 3 [16 x y + 4 x, -13 z - 13 y, -18 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=0.18 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=47.5MB, alloc=32.3MB, time=0.82 memory used=69.2MB, alloc=56.3MB, time=1.23 N1 := 443 > GB := Basis(F, plex(op(vars))); 2 2 GB := [2 x y - 5 y, 19 y - 4 y, 2 x z - 5 z, 19 y z - 4 z, 2 z + 5 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=108.9MB, alloc=60.3MB, time=1.93 memory used=150.3MB, alloc=60.3MB, time=2.66 N2 := 463 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-4 x y + 10 y, 19 y z - 4 z, -10 x y - 10 z , 16 x y + 4 x, 3 2 3 -13 z - 13 y, -18 x y + 18 y ] > J:=[op(GB),op(G)]; 2 2 J := [2 x y - 5 y, 19 y - 4 y, 2 x z - 5 z, 19 y z - 4 z, 2 z + 5 y, 2 3 2 3 16 x y + 4 x, -13 z - 13 y, -18 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, 15, 3, 1, 3, 3, 2/3, 1, 1/2, 5/12, 2/3, 1/3, 8, 15, 19, 3, 1, 3, 3, 1/2, 7/8, 1/2, 5/16, 5/8, 3/8, -2, -4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=157.3MB, alloc=60.3MB, time=2.88 |\^/| 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(); 1428240390 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [17 x + 9 y, 12 x - 5 y z , -3 z - 14 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-17 x y + 14 z , -17 x z - 14 y , 12 y z ] > Problem := [F,G]; 2 3 2 2 Problem := [[17 x + 9 y, 12 x - 5 y z , -3 z - 14 x], 2 2 2 2 [-17 x y + 14 z , -17 x z - 14 y , 12 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.9MB, alloc=32.3MB, time=0.53 memory used=48.3MB, alloc=32.3MB, time=0.84 memory used=69.2MB, alloc=32.3MB, time=1.16 memory used=89.6MB, alloc=60.3MB, time=1.49 memory used=130.8MB, alloc=60.3MB, time=2.09 memory used=171.2MB, alloc=84.3MB, time=2.69 memory used=213.3MB, alloc=84.3MB, time=3.34 memory used=272.1MB, alloc=108.3MB, time=4.46 memory used=349.8MB, alloc=116.3MB, time=5.94 memory used=418.5MB, alloc=140.3MB, time=7.41 memory used=495.4MB, alloc=164.3MB, time=10.17 memory used=590.7MB, alloc=188.3MB, time=13.93 N1 := 2581 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [x , 17 x + 9 y, 3 z + 14 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 561 #save(Problem, "format.txt"); > if (GB=[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 + 9 y, -5 z y + 12 x , -3 z - 14 x, -17 x y + 14 z , 2 2 -17 x z - 14 y , 12 z y] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 2 J := [x , 17 x + 9 y, 3 z + 14 x, -17 x y + 14 z , -17 x z - 14 y , 12 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, 15, 3, 3, 2, 2, 5/6, 5/6, 5/6, 5/13, 5/13, 5/13, 6, 13, 15, 3, 3, 2, 2, 5/6, 2/3, 2/3, 5/13, 4/13, 4/13, 2, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=712.7MB, alloc=188.3MB, time=16.69 |\^/| 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(); 1428240440 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-4 x y - 4 y , 5 y z - y, 14 y z + 17 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 G := [-13 y - 19 z , -3 x + 5 x y , -x y z - 18 x z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-4 x y - 4 y , 5 y z - y, 14 y z + 17 y ], 3 3 3 2 [-13 y - 19 z , -3 x + 5 x y , -x 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=0.18 memory used=26.0MB, alloc=32.3MB, time=0.49 memory used=47.5MB, alloc=32.3MB, time=0.80 memory used=68.3MB, alloc=32.3MB, time=1.12 memory used=88.6MB, alloc=32.3MB, time=1.43 memory used=107.6MB, alloc=56.3MB, time=1.74 memory used=151.1MB, alloc=60.3MB, time=2.57 memory used=188.0MB, alloc=84.3MB, time=3.28 memory used=244.5MB, alloc=108.3MB, time=4.36 memory used=317.8MB, alloc=132.3MB, time=5.76 memory used=406.2MB, alloc=156.3MB, time=7.43 memory used=501.6MB, alloc=188.3MB, time=9.95 memory used=605.0MB, alloc=212.3MB, time=13.17 memory used=721.2MB, alloc=236.3MB, time=17.17 memory used=852.0MB, alloc=260.3MB, time=22.38 memory used=1006.7MB, alloc=260.3MB, time=28.51 memory used=1161.4MB, alloc=260.3MB, time=34.60 memory used=1316.0MB, alloc=260.3MB, time=40.69 memory used=1470.6MB, alloc=284.3MB, time=46.83 memory used=1649.0MB, alloc=284.3MB, time=53.83 memory used=1827.4MB, alloc=308.3MB, time=60.88 memory used=2029.7MB, alloc=308.3MB, time=68.82 memory used=2232.1MB, alloc=332.3MB, time=76.69 N1 := 7655 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [85 x y - 14 y, 85 y + 14 y, 5 y z - y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2381.0MB, alloc=332.3MB, time=80.04 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)]; 2 2 2 2 2 3 3 H := [-4 x y - 4 y , 5 y z - y, 14 y z + 17 y , -13 y - 19 z , 3 2 -3 x + 5 x y , -x y z - 18 x z] > J:=[op(GB),op(G)]; 2 2 2 3 3 3 2 J := [85 x y - 14 y, 85 y + 14 y, 5 y z - y, -13 y - 19 z , -3 x + 5 x y , -x 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, 13, 18, 3, 3, 3, 3, 1/2, 1, 2/3, 5/12, 3/4, 5/12, 6, 12, 17, 3, 3, 3, 3, 1/2, 1, 1/2, 5/12, 3/4, 1/3, 1, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2584.5MB, alloc=588.3MB, time=87.59 |\^/| 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(); 1428240708 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [17 z - x, y + 2 z , 6 x - 11] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 G := [-15 x - 20 x y, -11 y + 14 z, -8 - 17 y] > Problem := [F,G]; 2 3 2 2 Problem := [[17 z - x, y + 2 z , 6 x - 11], 3 3 [-15 x - 20 x y, -11 y + 14 z, -8 - 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=26.7MB, alloc=32.3MB, time=0.50 memory used=48.3MB, alloc=32.3MB, time=0.81 memory used=68.8MB, alloc=32.3MB, time=1.11 memory used=89.8MB, alloc=56.3MB, time=1.48 memory used=133.8MB, alloc=60.3MB, time=2.26 memory used=173.5MB, alloc=84.3MB, time=2.97 memory used=231.9MB, alloc=108.3MB, time=4.07 memory used=302.0MB, alloc=132.3MB, time=6.18 memory used=386.7MB, alloc=132.3MB, time=9.40 N1 := 2625 > GB := Basis(F, plex(op(vars))); 2 3 2 GB := [6 x - 11, 17 y + 2 x, 17 z - x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=472.4MB, alloc=132.3MB, time=12.40 memory used=568.9MB, alloc=164.3MB, time=14.08 N2 := 1133 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 3 2 2 3 3 17 z - x, y + 2 z , 6 x - 11, -15 x - 20 x y, -11 y + 14 z, -8 - 17 y] > J:=[op(GB),op(G)]; 2 3 2 3 3 J := [6 x - 11, 17 y + 2 x, 17 z - x, -15 x - 20 x y, -11 y + 14 z, -8 - 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, 10, 14, 3, 3, 3, 2, 1/2, 2/3, 1/2, 1/3, 1/3, 1/4, 6, 10, 14, 3, 3, 3, 2, 2/3, 2/3, 1/3, 5/12, 1/3, 1/6, 0, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=626.3MB, alloc=164.3MB, time=15.95 |\^/| 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(); 1428240758 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [-5 y z - 8 z , -3 x y - 9 y z, -7 x y + 12] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [20 x y + 2 z, -8 - 5 y, 8 x + 3 y ] > Problem := [F,G]; 2 3 2 2 Problem := [[-5 y z - 8 z , -3 x y - 9 y z, -7 x y + 12], 2 3 2 [20 x y + 2 z, -8 - 5 y, 8 x + 3 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.9MB, alloc=40.3MB, time=0.57 memory used=60.0MB, alloc=40.3MB, time=0.97 memory used=87.0MB, alloc=40.3MB, time=1.36 memory used=111.8MB, alloc=64.3MB, time=1.72 memory used=159.8MB, alloc=68.3MB, time=2.59 memory used=201.8MB, alloc=92.3MB, time=3.34 memory used=261.5MB, alloc=116.3MB, time=4.48 memory used=334.8MB, alloc=140.3MB, time=6.69 memory used=421.4MB, alloc=140.3MB, time=10.03 memory used=508.2MB, alloc=164.3MB, time=13.40 N1 := 2813 > GB := Basis(F, plex(op(vars))); 4 2 2 GB := [14 x - 45, -8 x + 15 y, x + 3 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 577 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 2 H := [-5 y z - 8 z , -3 x y - 9 y z, -7 x y + 12, 20 x y + 2 z, -8 - 5 y, 3 2 8 x + 3 y ] > J:=[op(GB),op(G)]; 4 2 2 2 3 2 J := [14 x - 45, -8 x + 15 y, x + 3 z, 20 x y + 2 z, -8 - 5 y, 8 x + 3 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 16, 3, 3, 2, 3, 2/3, 1, 1/2, 1/3, 7/12, 1/3, 6, 11, 15, 4, 4, 2, 1, 5/6, 2/3, 1/3, 5/12, 1/3, 1/6, 2, 1, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=616.3MB, alloc=172.3MB, time=15.76 |\^/| 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(); 1428240812 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [4 x z + z, -13 x z - 4 x z, 15 x y + 19 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-5 x z - 16 y , 20 x y - 7 x y z, -5 x z + 14 z ] > Problem := [F,G]; 2 2 2 Problem := [[4 x z + z, -13 x z - 4 x z, 15 x y + 19 x z], 2 2 2 2 [-5 x z - 16 y , 20 x y - 7 x y z, -5 x z + 14 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.1MB, alloc=32.3MB, time=0.78 memory used=66.5MB, alloc=56.3MB, time=1.07 memory used=105.7MB, alloc=60.3MB, time=1.65 memory used=142.3MB, alloc=84.3MB, time=2.21 memory used=197.3MB, alloc=84.3MB, time=3.05 memory used=251.0MB, alloc=108.3MB, time=3.89 memory used=325.9MB, alloc=116.3MB, time=5.04 memory used=396.3MB, alloc=140.3MB, time=6.14 memory used=487.0MB, alloc=164.3MB, time=7.61 memory used=590.5MB, alloc=444.3MB, time=9.39 memory used=723.4MB, alloc=468.3MB, time=11.83 memory used=864.7MB, alloc=492.3MB, time=14.52 memory used=1014.8MB, alloc=516.3MB, time=17.37 memory used=1174.0MB, alloc=540.3MB, time=20.40 memory used=1339.9MB, alloc=564.3MB, time=23.61 memory used=1512.2MB, alloc=588.3MB, time=27.02 memory used=1692.8MB, alloc=612.3MB, time=30.66 memory used=1879.4MB, alloc=636.3MB, time=34.52 memory used=2068.0MB, alloc=660.3MB, time=38.70 memory used=2243.5MB, alloc=684.3MB, time=44.46 memory used=2421.3MB, alloc=708.3MB, time=50.86 memory used=2608.5MB, alloc=732.3MB, time=57.99 memory used=2807.1MB, alloc=756.3MB, time=65.98 memory used=3018.2MB, alloc=780.3MB, time=74.65 memory used=3242.7MB, alloc=804.3MB, time=83.92 |\^/| 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(); 1428241112 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [18 y z - 17 z , 13 x z + 17 x, 20 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 G := [15 x + 14 x y, -2 x z - 18 z, 6 x - 2 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[18 y z - 17 z , 13 x z + 17 x, 20 x y], 3 2 3 3 [15 x + 14 x y, -2 x z - 18 z, 6 x - 2 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=48.4MB, alloc=32.3MB, time=0.87 N1 := 269 > GB := Basis(F, plex(op(vars))); 2 4 2 2 2 GB := [x , 4212 x y + 4913 x, -18 x y + 17 x z, -18 y z + 17 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=69.2MB, alloc=32.3MB, time=1.27 memory used=88.8MB, alloc=32.3MB, time=1.56 memory used=108.7MB, alloc=56.3MB, time=1.93 N2 := 269 #save(Problem, "format.txt"); > if (GB=[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 := [18 y z - 17 z , 13 x z + 17 x, 20 x y, 15 x + 14 x y, -2 x z - 18 z, 3 3 6 x - 2 z ] > J:=[op(GB),op(G)]; 2 4 2 2 2 J := [x , 4212 x y + 4913 x, -18 x y + 17 x z, -18 y z + 17 z , 3 2 3 3 15 x + 14 x y, -2 x z - 18 z, 6 x - 2 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 17, 3, 3, 2, 3, 5/6, 1/2, 2/3, 7/13, 3/13, 6/13, 7, 14, 21, 5, 3, 4, 3, 6/7, 4/7, 4/7, 9/14, 2/7, 3/7, -2, -4, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=116.6MB, alloc=56.3MB, time=2.09 |\^/| 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(); 1428241119 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 F := [18 x + 10 z , -6 y z + 7 x z, 17 x y - 18 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-13 y + 10 x, 16 - 16 y, 20 x y + 13 x ] > Problem := [F,G]; 3 2 2 2 3 Problem := [[18 x + 10 z , -6 y z + 7 x z, 17 x y - 18 z ], 3 2 2 [-13 y + 10 x, 16 - 16 y, 20 x y + 13 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.79 memory used=68.8MB, alloc=32.3MB, time=1.10 memory used=89.0MB, alloc=56.3MB, time=1.43 memory used=134.0MB, alloc=60.3MB, time=2.25 memory used=173.8MB, alloc=84.3MB, time=2.98 memory used=231.2MB, alloc=84.3MB, time=4.72 N1 := 1475 > GB := Basis(F, plex(op(vars))); 8 4 6 2 GB := [1417176 x + 252875 x , 1417176 x y + 252875 x y, 7 2 2 3 2 6 2 236196 x + 36125 x y , 162 x z + 85 x y, -1458 x + 425 x y z, 2 3 2 6 y z - 7 x z, 9 x + 5 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=282.9MB, alloc=84.3MB, time=6.25 memory used=335.4MB, alloc=108.3MB, time=7.04 memory used=411.4MB, alloc=116.3MB, time=8.25 memory used=489.7MB, alloc=140.3MB, time=9.66 memory used=585.8MB, alloc=164.3MB, time=12.61 N2 := 1839 #save(Problem, "format.txt"); > 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 := [18 x + 10 z , -6 y z + 7 x z, -18 z + 17 y x , -13 y + 10 x, 2 2 16 - 16 y, 20 x y + 13 x ] > J:=[op(GB),op(G)]; 8 4 6 2 J := [1417176 x + 252875 x , 1417176 x y + 252875 x y, 7 2 2 3 2 6 2 236196 x + 36125 x y , 162 x z + 85 x y, -1458 x + 425 x y z, 2 3 2 3 2 2 6 y z - 7 x z, 9 x + 5 z , -13 y + 10 x, 16 - 16 y, 20 x 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, 13, 16, 3, 3, 3, 3, 5/6, 5/6, 1/2, 1/2, 5/12, 1/3, 10, 21, 45, 8, 8, 3, 2, 9/10, 4/5, 2/5, 3/4, 9/20, 1/4, -8, -29, -5] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=642.5MB, alloc=164.3MB, time=14.92 |\^/| 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(); 1428241173 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [17 x + 13 y z, -15 z - 13 z, -8 y z - y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [-8 x z + 18 x , -y z + 12 x , -8 x z + 18 x z ] > Problem := [F,G]; 3 2 2 2 Problem := [[17 x + 13 y z, -15 z - 13 z, -8 y z - y], 2 2 2 2 2 2 [-8 x z + 18 x , -y z + 12 x , -8 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=0.18 memory used=26.3MB, alloc=32.3MB, time=0.51 memory used=47.7MB, alloc=32.3MB, time=0.83 memory used=67.5MB, alloc=56.3MB, time=1.14 memory used=106.0MB, alloc=60.3MB, time=1.76 memory used=142.4MB, alloc=60.3MB, time=2.32 memory used=177.1MB, alloc=84.3MB, time=2.88 memory used=227.8MB, alloc=84.3MB, time=3.68 memory used=282.3MB, alloc=116.3MB, time=4.56 memory used=356.7MB, alloc=116.3MB, time=5.77 memory used=428.9MB, alloc=140.3MB, time=6.96 memory used=520.0MB, alloc=164.3MB, time=8.49 memory used=617.3MB, alloc=164.3MB, time=10.14 memory used=716.6MB, alloc=444.3MB, time=12.05 memory used=840.8MB, alloc=468.3MB, time=14.29 memory used=985.8MB, alloc=492.3MB, time=16.60 memory used=1158.7MB, alloc=516.3MB, time=19.00 memory used=1351.4MB, alloc=540.3MB, time=21.73 memory used=1532.1MB, alloc=564.3MB, time=25.04 memory used=1725.6MB, alloc=588.3MB, time=28.45 memory used=1905.9MB, alloc=612.3MB, time=33.59 memory used=2083.5MB, alloc=636.3MB, time=39.48 memory used=2269.8MB, alloc=660.3MB, time=46.18 memory used=2467.7MB, alloc=684.3MB, time=53.54 memory used=2677.0MB, alloc=708.3MB, time=61.80 memory used=2897.1MB, alloc=732.3MB, time=71.16 memory used=3141.1MB, alloc=756.3MB, time=81.52 |\^/| 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(); 1428241472 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 F := [10 x z - 20 y z, 8 x y - 15 z , -6 y z + 14 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-16 x z - 16 y z , -3 y z - 19 y, -9 x z - 4 z ] > Problem := [F,G]; 2 2 2 3 2 2 Problem := [[10 x z - 20 y z, 8 x y - 15 z , -6 y z + 14 x ], 2 2 2 2 2 [-16 x z - 16 y z , -3 y z - 19 y, -9 x z - 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=48.3MB, alloc=32.3MB, time=0.81 memory used=68.9MB, alloc=56.3MB, time=1.12 memory used=112.6MB, alloc=60.3MB, time=1.83 memory used=153.2MB, alloc=84.3MB, time=2.56 memory used=214.5MB, alloc=92.3MB, time=3.64 memory used=270.2MB, alloc=116.3MB, time=4.62 memory used=341.3MB, alloc=140.3MB, time=6.38 memory used=421.6MB, alloc=164.3MB, time=9.36 memory used=524.6MB, alloc=164.3MB, time=13.21 N1 := 2847 > GB := Basis(F, plex(op(vars))); 5 2 4 2 2 4 2 2 2 GB := [9 x - 3430 x , -x + 2 x y , 18 x y - 1715 x , 3 x z - 14 x , 2 2 2 3 3 y z - 7 x , -8 x y + 15 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=628.7MB, alloc=164.3MB, time=15.57 memory used=737.3MB, alloc=188.3MB, time=17.30 memory used=837.1MB, alloc=444.3MB, time=18.87 memory used=970.2MB, alloc=468.3MB, time=21.11 memory used=1117.9MB, alloc=492.3MB, time=23.80 memory used=1277.6MB, alloc=516.3MB, time=26.72 memory used=1447.8MB, alloc=540.3MB, time=29.88 memory used=1615.2MB, alloc=564.3MB, time=34.95 memory used=1784.5MB, alloc=588.3MB, time=40.86 memory used=1963.2MB, alloc=612.3MB, time=47.75 memory used=2155.4MB, alloc=636.3MB, time=55.78 memory used=2371.5MB, alloc=660.3MB, time=64.73 memory used=2611.6MB, alloc=684.3MB, time=74.62 memory used=2875.7MB, alloc=708.3MB, time=85.72 |\^/| 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(); 1428241773 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [-6 y + 17 x, -x z + 9 y z, -10 x z - 13 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-17 y z - 5 y z, 10 x y - 10 y z, -13 x - 6 y ] > Problem := [F,G]; 3 2 2 3 Problem := [[-6 y + 17 x, -x z + 9 y z, -10 x z - 13 y ], 2 3 2 [-17 y z - 5 y z, 10 x y - 10 y z, -13 x - 6 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.48 memory used=46.9MB, alloc=32.3MB, time=0.78 memory used=67.7MB, alloc=32.3MB, time=1.09 memory used=87.6MB, alloc=56.3MB, time=1.43 memory used=129.8MB, alloc=60.3MB, time=2.21 memory used=169.9MB, alloc=84.3MB, time=2.91 memory used=227.1MB, alloc=108.3MB, time=4.38 N1 := 1581 > GB := Basis(F, plex(op(vars))); 6 3 3 2 2 GB := [2 x - 4131 x, -x + 9 x y, 6 y - 17 x, -x z + 9 y z, 60 x z + 221 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=299.0MB, alloc=108.3MB, time=6.67 memory used=374.5MB, alloc=116.3MB, time=7.92 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 2 2 3 2 H := [-6 y + 17 x, -x z + 9 y z, -10 x z - 13 y , -17 y z - 5 y z, 3 2 10 x y - 10 y z, -13 x - 6 y ] > J:=[op(GB),op(G)]; 6 3 3 2 2 J := [2 x - 4131 x, -x + 9 x y, 6 y - 17 x, -x z + 9 y z, 60 x z + 221 x, 2 3 2 -17 y z - 5 y z, 10 x y - 10 y z, -13 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, 15, 17, 3, 3, 3, 2, 5/6, 1, 2/3, 5/12, 2/3, 1/2, 8, 17, 26, 6, 6, 3, 2, 7/8, 3/4, 1/2, 5/8, 1/2, 3/8, -2, -9, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=403.3MB, alloc=116.3MB, time=8.66 |\^/| 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(); 1428241804 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 F := [12 x + 11, 15 x y - 5 y , 9 x - 11 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 G := [-14 x - 20 z, 19 x - 7 y, -13 x z - 14 z] > Problem := [F,G]; 2 2 3 3 2 Problem := [[12 x + 11, 15 x y - 5 y , 9 x - 11 y ], 3 [-14 x - 20 z, 19 x - 7 y, -13 x z - 14 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.51 memory used=47.9MB, alloc=56.3MB, time=0.91 N1 := 369 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 69 #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 3 3 2 3 H := [12 x + 11, 15 x y - 5 y , 9 x - 11 y , -14 x - 20 z, -7 y + 19 x, -13 x z - 14 z] > J:=[op(GB),op(G)]; 3 J := [1, -14 x - 20 z, -7 y + 19 x, -13 x z - 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, 11, 14, 3, 3, 3, 1, 1, 1/2, 1/3, 1/2, 1/3, 1/4, 4, 6, 6, 3, 3, 1, 1, 3/4, 1/4, 1/2, 3/7, 1/7, 3/7, 5, 8, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=60.2MB, alloc=56.3MB, time=1.14 |\^/| 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(); 1428241808 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-19 x y z - 16 y z, -8 x y - 13 y z , -7 x z + 14] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [2 x z - 7 y z, 3 y - 5 x, -4 y z - 16 y z] > Problem := [F,G]; 2 2 2 Problem := [[-19 x y z - 16 y z, -8 x y - 13 y z , -7 x z + 14], 2 2 3 2 [2 x z - 7 y z, 3 y - 5 x, -4 y z - 16 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=47.4MB, alloc=32.3MB, time=0.79 memory used=67.9MB, alloc=32.3MB, time=1.08 memory used=88.7MB, alloc=56.3MB, time=1.46 memory used=130.9MB, alloc=60.3MB, time=2.21 memory used=168.8MB, alloc=84.3MB, time=2.88 memory used=226.3MB, alloc=108.3MB, time=3.97 memory used=297.6MB, alloc=108.3MB, time=6.17 memory used=360.4MB, alloc=132.3MB, time=8.52 N1 := 2377 > GB := Basis(F, plex(op(vars))); 4 2 3 GB := [19 x y - 104 y, 19 x y + 16 y , z x - 2, -19 x y + 52 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=449.6MB, alloc=132.3MB, time=11.14 memory used=543.4MB, alloc=164.3MB, time=12.77 N2 := 1517 #save(Problem, "format.txt"); > if (GB=[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 := [-19 x y z - 16 y z, -8 x y - 13 y z , -7 x z + 14, 2 x z - 7 y z, 3 2 3 y - 5 x, -4 y z - 16 y z] > J:=[op(GB),op(G)]; 4 2 3 J := [19 x y - 104 y, 19 x y + 16 y , z x - 2, -19 x y + 52 y z, 2 2 3 2 2 x z - 7 y z, 3 y - 5 x, -4 y 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, 17, 3, 2, 3, 2, 5/6, 5/6, 5/6, 5/12, 2/3, 2/3, 7, 16, 22, 5, 4, 3, 1, 6/7, 6/7, 4/7, 3/7, 5/7, 3/7, -1, -5, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=647.2MB, alloc=164.3MB, time=16.07 |\^/| 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(); 1428241862 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 F := [9 x - 9 x y, -10 y z + 15 z, -2 x y - 18 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-6 y z - 18 z , 15 x + 11, -6 x y + 14 y z] > Problem := [F,G]; 3 2 2 2 3 Problem := [[9 x - 9 x y, -10 y z + 15 z, -2 x y - 18 y ], 2 3 2 [-6 y z - 18 z , 15 x + 11, -6 x y + 14 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.6MB, alloc=32.3MB, time=0.82 memory used=67.3MB, alloc=56.3MB, time=1.17 N1 := 527 > GB := Basis(F, plex(op(vars))); 5 3 2 2 3 GB := [x , -x + x y, x y + 9 y , z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 131 #save(Problem, "format.txt"); > 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 := [9 x - 9 x y, -10 y z + 15 z, -2 x y - 18 y , -6 y z - 18 z , 2 15 x + 11, -6 x y + 14 y z] > J:=[op(GB),op(G)]; 5 3 2 2 3 2 3 2 J := [x , -x + x y, x y + 9 y , z, -6 y z - 18 z , 15 x + 11, -6 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, 12, 16, 3, 3, 3, 3, 2/3, 5/6, 1/2, 5/12, 7/12, 5/12, 7, 12, 19, 5, 5, 3, 3, 5/7, 4/7, 3/7, 6/13, 6/13, 4/13, 0, -3, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=102.2MB, alloc=56.3MB, time=1.80 |\^/| 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(); 1428241868 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [y z + 13 y, -5 y z + 4 x, 9 y z + 6 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [10 x y - 19 y, -9 x y - 6 y, 10 x + 19 x] > Problem := [F,G]; 2 2 2 2 Problem := [[y z + 13 y, -5 y z + 4 x, 9 y z + 6 x ], 2 2 3 [10 x y - 19 y, -9 x y - 6 y, 10 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=26.6MB, alloc=32.3MB, time=0.50 memory used=48.5MB, alloc=32.3MB, time=0.82 memory used=69.3MB, alloc=32.3MB, time=1.13 memory used=90.0MB, alloc=56.3MB, time=1.53 N1 := 457 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x , 65 y + 4 x, x z + 13 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=131.7MB, alloc=60.3MB, time=2.35 N2 := 53 #save(Problem, "format.txt"); > if (GB=[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 := [y z + 13 y, -5 z y + 4 x, 9 y z + 6 x , 10 x y - 19 y, -9 x y - 6 y, 3 10 x + 19 x] > J:=[op(GB),op(G)]; 2 2 2 2 3 J := [x , 65 y + 4 x, x z + 13 x, 10 x y - 19 y, -9 x y - 6 y, 10 x + 19 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 18, 3, 3, 2, 2, 5/6, 5/6, 1/2, 1/2, 2/3, 1/4, 6, 10, 15, 3, 3, 2, 2, 1, 1/2, 1/6, 2/3, 5/12, 1/12, 3, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=144.8MB, alloc=60.3MB, time=2.55 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428241875 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 F := [-6 y z - 20 z , 19 x y - 16 y z, 2 z - 8 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-2 x y + 18 x, -16 x z + 12 y z, 3 x + 18 z] > Problem := [F,G]; 2 3 3 Problem := [[-6 y z - 20 z , 19 x y - 16 y z, 2 z - 8 z], 2 2 2 [-2 x y + 18 x, -16 x z + 12 y z, 3 x + 18 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.6MB, alloc=32.3MB, time=0.80 memory used=67.6MB, alloc=32.3MB, time=1.09 memory used=86.2MB, alloc=56.3MB, time=1.38 memory used=126.0MB, alloc=60.3MB, time=1.98 memory used=163.7MB, alloc=60.3MB, time=2.54 memory used=199.4MB, alloc=84.3MB, time=3.10 memory used=254.7MB, alloc=84.3MB, time=3.99 memory used=307.0MB, alloc=108.3MB, time=4.89 memory used=382.5MB, alloc=132.3MB, time=6.37 memory used=471.9MB, alloc=156.3MB, time=8.01 memory used=543.1MB, alloc=188.3MB, time=9.34 memory used=656.7MB, alloc=212.3MB, time=12.26 memory used=773.3MB, alloc=236.3MB, time=16.40 memory used=908.9MB, alloc=260.3MB, time=21.37 memory used=1068.4MB, alloc=260.3MB, time=27.29 memory used=1227.9MB, alloc=284.3MB, time=33.32 N1 := 5139 > GB := Basis(F, plex(op(vars))); 3 3 2 GB := [361 x y - 1024 x y, 3 x y + 40 x y, 57 x y + 640 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1413.0MB, alloc=284.3MB, time=39.58 N2 := 995 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 2 H := [-6 y z - 20 z , 19 x y - 16 y z, 2 z - 8 z, -2 x y + 18 x, 2 2 -16 x z + 12 y z, 3 x + 18 z] > J:=[op(GB),op(G)]; 3 3 2 2 J := [361 x y - 1024 x y, 3 x y + 40 x y, 57 y x + 640 z, -2 x y + 18 x, 2 2 -16 x z + 12 y z, 3 x + 18 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 15, 3, 2, 2, 3, 2/3, 2/3, 5/6, 5/12, 5/12, 2/3, 6, 14, 18, 4, 3, 3, 2, 1, 5/6, 1/2, 3/4, 7/12, 1/3, -1, -3, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1545.8MB, alloc=284.3MB, time=42.38 |\^/| 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(); 1428241998 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-2 x y z + 14 x, 13 y z - 16 x , -13 y z + 4 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [-9 z + z, 8 x z + 19, 18 x z + x] > Problem := [F,G]; 2 2 2 Problem := [[-2 x y z + 14 x, 13 y z - 16 x , -13 y z + 4 y z], 3 2 [-9 z + z, 8 x z + 19, 18 x z + x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=46.7MB, alloc=32.3MB, time=0.75 memory used=65.8MB, alloc=32.3MB, time=1.03 memory used=83.5MB, alloc=56.3MB, time=1.30 memory used=120.1MB, alloc=60.3MB, time=1.85 memory used=153.9MB, alloc=84.3MB, time=2.37 memory used=205.8MB, alloc=108.3MB, time=3.19 memory used=277.7MB, alloc=116.3MB, time=4.33 memory used=346.4MB, alloc=140.3MB, time=5.44 memory used=435.6MB, alloc=164.3MB, time=6.91 memory used=545.3MB, alloc=188.3MB, time=8.88 memory used=663.6MB, alloc=212.3MB, time=11.02 memory used=790.4MB, alloc=236.3MB, time=13.35 memory used=924.9MB, alloc=260.3MB, time=15.83 memory used=1058.7MB, alloc=540.3MB, time=18.97 memory used=1191.2MB, alloc=564.3MB, time=22.98 memory used=1332.5MB, alloc=588.3MB, time=27.63 memory used=1485.8MB, alloc=612.3MB, time=32.91 memory used=1650.4MB, alloc=636.3MB, time=39.15 memory used=1830.6MB, alloc=660.3MB, time=46.50 memory used=2034.7MB, alloc=684.3MB, time=54.77 memory used=2262.8MB, alloc=708.3MB, time=63.98 memory used=2514.9MB, alloc=732.3MB, time=74.04 memory used=2790.9MB, alloc=756.3MB, time=85.13 memory used=3090.8MB, alloc=756.3MB, time=97.16 |\^/| 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(); 1428242299 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 F := [-10 x y - 5 y , -20 x + 11 z , 9 x y + 13 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [12 y z, -12 x - 16 y, 12 y z + 5 y] > Problem := [F,G]; 2 2 3 3 2 Problem := [[-10 x y - 5 y , -20 x + 11 z , 9 x y + 13 y], 2 2 2 [12 y z, -12 x - 16 y, 12 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=0.18 N1 := 79 > GB := Basis(F, plex(op(vars))); 2 2 3 3 GB := [9 x y + 13 y, 9 y - 26 y, -20 x + 11 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=26.7MB, alloc=32.3MB, time=0.54 memory used=47.5MB, alloc=32.3MB, time=0.83 N2 := 85 #save(Problem, "format.txt"); > if (GB=[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 2 H := [-10 x y - 5 y , -20 x + 11 z , 9 x y + 13 y, 12 y z, -12 x - 16 y, 2 12 y z + 5 y] > J:=[op(GB),op(G)]; 2 2 3 3 2 2 J := [9 x y + 13 y, 9 y - 26 y, -20 x + 11 z , 12 y z, -12 x - 16 y, 2 12 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, 12, 17, 3, 3, 2, 3, 2/3, 5/6, 1/2, 4/13, 8/13, 3/13, 6, 11, 16, 3, 3, 2, 3, 1/2, 5/6, 1/2, 3/13, 8/13, 3/13, 1, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=53.3MB, alloc=32.3MB, time=0.93 |\^/| 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(); 1428242301 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [11 x y + 15 y , 10 z + 3, 15 x z + 2 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [11 x y - 8 x z, 2 x y - 6 y z, 2 x y + 18 y ] > Problem := [F,G]; 2 2 3 2 2 Problem := [[11 x y + 15 y , 10 z + 3, 15 x z + 2 z ], 2 2 [11 x y - 8 x z, 2 x y - 6 y z, 2 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=25.9MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.83 memory used=68.2MB, alloc=56.3MB, time=1.20 memory used=108.6MB, alloc=84.3MB, time=1.98 N1 := 1169 > GB := Basis(F, plex(op(vars))); 6 2 2 GB := [5625 x - 4, y , 15 x + 2 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=164.5MB, alloc=84.3MB, time=3.49 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 3 2 2 H := [11 x y + 15 y , 10 z + 3, 15 x z + 2 z , 11 x y - 8 x z, 2 x y - 6 y z, 2 2 2 x y + 18 y ] > J:=[op(GB),op(G)]; J := [ 6 2 2 2 2 5625 x - 4, y , 15 x + 2 z, 11 x y - 8 x z, 2 x y - 6 y z, 2 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, 16, 3, 2, 2, 3, 5/6, 2/3, 2/3, 1/2, 7/12, 5/12, 6, 12, 17, 6, 6, 2, 1, 5/6, 2/3, 1/2, 1/2, 1/2, 1/4, 1, -1, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=201.6MB, alloc=84.3MB, time=4.15 |\^/| 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(); 1428242313 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [4 x y + 8 y , -5 x y - 14 x z, -14 y + 14 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-16 x y z - 13 x, 7 x y - 8 x y z, -13 z - 18 z ] > Problem := [F,G]; 2 2 3 Problem := [[4 x y + 8 y , -5 x y - 14 x z, -14 y + 14 x z], 2 3 2 [-16 x y z - 13 x, 7 x y - 8 x y z, -13 z - 18 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=47.8MB, alloc=32.3MB, time=0.81 memory used=67.5MB, alloc=56.3MB, time=1.12 memory used=107.2MB, alloc=60.3MB, time=1.72 memory used=143.5MB, alloc=84.3MB, time=2.28 memory used=201.2MB, alloc=92.3MB, time=3.19 memory used=256.4MB, alloc=116.3MB, time=4.08 memory used=331.2MB, alloc=116.3MB, time=5.22 memory used=404.4MB, alloc=140.3MB, time=6.42 memory used=501.3MB, alloc=164.3MB, time=8.28 memory used=607.5MB, alloc=188.3MB, time=10.23 memory used=725.4MB, alloc=212.3MB, time=12.36 memory used=843.4MB, alloc=492.3MB, time=14.54 memory used=983.5MB, alloc=516.3MB, time=17.13 memory used=1133.1MB, alloc=540.3MB, time=19.90 memory used=1290.0MB, alloc=564.3MB, time=22.88 memory used=1451.0MB, alloc=588.3MB, time=26.50 memory used=1602.1MB, alloc=612.3MB, time=31.37 memory used=1761.8MB, alloc=636.3MB, time=36.92 memory used=1933.9MB, alloc=660.3MB, time=43.22 memory used=2120.0MB, alloc=684.3MB, time=50.20 memory used=2320.5MB, alloc=708.3MB, time=57.95 memory used=2535.9MB, alloc=732.3MB, time=66.52 memory used=2766.2MB, alloc=756.3MB, time=75.88 memory used=3009.1MB, alloc=780.3MB, time=86.20 memory used=3271.3MB, alloc=804.3MB, time=97.65 |\^/| 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(); 1428242613 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-7 x y - 2 x z, -14 y + 6 y z, 18 y z - 10 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [12 x + 7, 11 x y, -8 x y] > Problem := [F,G]; 2 2 2 2 Problem := [[-7 x y - 2 x z, -14 y + 6 y z, 18 y z - 10 y z], 3 2 [12 x + 7, 11 x y, -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=0.18 memory used=26.8MB, alloc=32.3MB, time=0.53 N1 := 275 > GB := Basis(F, plex(op(vars))); 2 2 3 2 2 2 2 GB := [x y , 21 y - 5 y , 7 x y + 2 x z, -7 y + 3 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=47.3MB, alloc=32.3MB, time=0.89 N2 := 115 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 2 H := [-7 x y - 2 x z, -14 y + 6 y z, 18 y z - 10 y z, 12 x + 7, 11 x y, -8 x y] > J:=[op(GB),op(G)]; 2 2 3 2 2 2 2 3 2 J := [x y , 21 y - 5 y , 7 x y + 2 x z, -7 y + 3 y z, 12 x + 7, 11 x y, -8 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, 16, 3, 3, 2, 2, 2/3, 5/6, 1/2, 5/14, 1/2, 2/7, 7, 13, 20, 4, 3, 3, 1, 5/7, 6/7, 2/7, 3/8, 1/2, 1/8, -1, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=47.8MB, alloc=32.3MB, time=0.90 |\^/| 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(); 1428242616 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 F := [-18 x y, 13 x + 10 y, -8 y + 3 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [-5 x - 15, -3 y - 7 x y, -6 y z + 18 y] > Problem := [F,G]; 3 2 Problem := [[-18 x y, 13 x + 10 y, -8 y + 3 y z], 3 3 2 [-5 x - 15, -3 y - 7 x y, -6 y z + 18 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.9MB, alloc=32.3MB, time=0.53 memory used=48.0MB, alloc=56.3MB, time=0.92 memory used=89.4MB, alloc=56.3MB, time=1.97 N1 := 935 > GB := Basis(F, plex(op(vars))); 4 3 3 GB := [x , 13 x + 10 y, x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=125.2MB, alloc=80.3MB, time=2.73 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)]; 3 2 3 3 H := [-18 x y, 13 x + 10 y, -8 y + 3 y z, -5 x - 15, -3 y - 7 x y, 2 -6 y z + 18 y] > J:=[op(GB),op(G)]; 4 3 3 3 3 2 J := [x , 13 x + 10 y, x z, -5 x - 15, -3 y - 7 x y, -6 y z + 18 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 11, 16, 3, 3, 3, 2, 2/3, 5/6, 1/3, 4/13, 8/13, 2/13, 6, 10, 20, 4, 4, 3, 2, 5/6, 1/2, 1/3, 5/12, 5/12, 1/6, 1, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=133.8MB, alloc=80.3MB, time=2.92 |\^/| 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(); 1428242625 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [-13 y + 18 y z, -5 x y + 4 z, -19 z - 8 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 G := [-18 z + 17 x z, -9 y - 20 y z , 16 z - 12 y ] > Problem := [F,G]; 3 2 2 2 Problem := [[-13 y + 18 y z, -5 x y + 4 z, -19 z - 8 x], 3 3 2 3 2 [-18 z + 17 x z, -9 y - 20 y z , 16 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=0.17 memory used=27.3MB, alloc=32.3MB, time=0.51 memory used=48.5MB, alloc=32.3MB, time=0.81 memory used=68.5MB, alloc=32.3MB, time=1.09 memory used=87.9MB, alloc=56.3MB, time=1.39 memory used=126.7MB, alloc=60.3MB, time=1.96 memory used=163.6MB, alloc=60.3MB, time=2.50 memory used=198.2MB, alloc=84.3MB, time=3.03 memory used=255.4MB, alloc=92.3MB, time=3.90 memory used=311.8MB, alloc=116.3MB, time=4.79 memory used=388.0MB, alloc=116.3MB, time=5.99 memory used=464.7MB, alloc=140.3MB, time=7.26 memory used=563.8MB, alloc=140.3MB, time=8.87 memory used=653.5MB, alloc=420.3MB, time=10.35 memory used=772.7MB, alloc=420.3MB, time=12.28 memory used=887.9MB, alloc=444.3MB, time=14.16 memory used=1021.2MB, alloc=468.3MB, time=16.45 memory used=1174.3MB, alloc=492.3MB, time=19.04 memory used=1345.4MB, alloc=516.3MB, time=22.06 memory used=1507.1MB, alloc=540.3MB, time=24.87 memory used=1647.0MB, alloc=564.3MB, time=27.23 memory used=1816.8MB, alloc=588.3MB, time=30.45 memory used=1968.0MB, alloc=612.3MB, time=33.44 memory used=2138.1MB, alloc=636.3MB, time=36.95 memory used=2315.0MB, alloc=660.3MB, time=40.71 memory used=2544.4MB, alloc=684.3MB, time=45.50 memory used=2758.3MB, alloc=708.3MB, time=49.89 memory used=2950.2MB, alloc=732.3MB, time=53.96 memory used=3116.2MB, alloc=756.3MB, time=57.51 memory used=3273.1MB, alloc=780.3MB, time=60.88 memory used=3415.6MB, alloc=804.3MB, time=64.02 memory used=3572.1MB, alloc=828.3MB, time=68.95 memory used=3824.0MB, alloc=852.3MB, time=78.00 memory used=4137.6MB, alloc=876.3MB, time=90.15 |\^/| 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(); 1428242925 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [14 x z - 3 x, 14 y + 11 x, 9 x - 9 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [17 x - 6 x z, -8 x y + 6 x z, -9 x y - 16 x] > Problem := [F,G]; 2 2 2 2 Problem := [[14 x z - 3 x, 14 y + 11 x, 9 x - 9 z ], 3 2 2 [17 x - 6 x z, -8 x y + 6 x z, -9 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=0.19 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=47.3MB, alloc=32.3MB, time=0.79 memory used=67.3MB, alloc=32.3MB, time=1.08 memory used=87.2MB, alloc=56.3MB, time=1.42 memory used=130.0MB, alloc=60.3MB, time=2.17 memory used=167.1MB, alloc=84.3MB, time=2.82 memory used=223.2MB, alloc=84.3MB, time=3.79 memory used=271.0MB, alloc=108.3MB, time=4.69 memory used=333.2MB, alloc=132.3MB, time=6.25 memory used=408.7MB, alloc=156.3MB, time=8.74 memory used=502.8MB, alloc=156.3MB, time=12.24 memory used=597.0MB, alloc=180.3MB, time=15.70 memory used=715.1MB, alloc=180.3MB, time=19.97 memory used=833.3MB, alloc=204.3MB, time=24.33 N1 := 4247 > GB := Basis(F, plex(op(vars))); 3 2 2 2 GB := [14 x - 3 x, 14 y + 11 x, -x + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=972.7MB, alloc=212.3MB, time=26.94 N2 := 1523 #save(Problem, "format.txt"); > if (GB=[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 := [14 x z - 3 x, 14 y + 11 x, 9 x - 9 z , 17 x - 6 x z, -8 x y + 6 x z, 2 -9 x y - 16 x] > J:=[op(GB),op(G)]; 3 2 2 2 3 2 J := [14 x - 3 x, 14 y + 11 x, -x + z , 17 x - 6 x z, -8 x y + 6 x z, 2 -9 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, 13, 16, 3, 3, 2, 2, 1, 1/2, 2/3, 5/6, 1/4, 1/3, 6, 12, 16, 3, 3, 2, 2, 1, 1/2, 1/2, 5/6, 1/4, 1/4, 1, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1065.8MB, alloc=212.3MB, time=30.15 |\^/| 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(); 1428243024 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [10 y z - 4 z , -17 z - 20 z , 15 x y - 18 x y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [-3 x y - 20 x z , 19 x y + 13 z , -3 x z + 4 x y] > Problem := [F,G]; 2 2 3 2 2 Problem := [[10 y z - 4 z , -17 z - 20 z , 15 x y - 18 x y z], 2 2 2 3 2 [-3 x y - 20 x z , 19 x y + 13 z , -3 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=0.18 memory used=26.3MB, alloc=32.3MB, time=0.52 memory used=47.2MB, alloc=32.3MB, time=0.82 memory used=66.6MB, alloc=32.3MB, time=1.11 memory used=85.2MB, alloc=56.3MB, time=1.40 memory used=123.3MB, alloc=60.3MB, time=1.97 memory used=158.9MB, alloc=84.3MB, time=2.51 memory used=212.6MB, alloc=84.3MB, time=3.32 memory used=263.5MB, alloc=108.3MB, time=4.12 memory used=338.9MB, alloc=116.3MB, time=5.32 memory used=413.1MB, alloc=140.3MB, time=6.53 memory used=509.7MB, alloc=140.3MB, time=8.08 memory used=602.6MB, alloc=140.3MB, time=9.60 memory used=694.9MB, alloc=164.3MB, time=11.26 memory used=802.6MB, alloc=164.3MB, time=13.18 memory used=904.3MB, alloc=444.3MB, time=15.06 memory used=1033.9MB, alloc=468.3MB, time=17.45 memory used=1183.5MB, alloc=492.3MB, time=20.23 memory used=1351.0MB, alloc=516.3MB, time=23.30 memory used=1537.1MB, alloc=540.3MB, time=26.62 memory used=1737.9MB, alloc=564.3MB, time=30.40 memory used=1953.7MB, alloc=588.3MB, time=34.46 memory used=2188.3MB, alloc=612.3MB, time=38.95 memory used=2437.8MB, alloc=636.3MB, time=43.79 memory used=2684.5MB, alloc=660.3MB, time=48.71 memory used=2938.6MB, alloc=684.3MB, time=53.69 memory used=3188.9MB, alloc=708.3MB, time=58.91 memory used=3430.0MB, alloc=732.3MB, time=65.21 memory used=3640.3MB, alloc=756.3MB, time=72.65 memory used=3855.6MB, alloc=780.3MB, time=80.82 memory used=4081.7MB, alloc=804.3MB, time=89.75 |\^/| 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(); 1428243324 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-11 x y + 4 z, 15 y z - 14, 7 y z - x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [12 y z + 11 x, 17 y - 16 y z, -15 y z + 14 z] > Problem := [F,G]; 2 2 2 Problem := [[-11 x y + 4 z, 15 y z - 14, 7 y z - x], 2 2 2 [12 y z + 11 x, 17 y - 16 y z, -15 y z + 14 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.6MB, alloc=32.3MB, time=0.82 memory used=67.4MB, alloc=56.3MB, time=1.13 memory used=107.7MB, alloc=60.3MB, time=1.76 memory used=145.6MB, alloc=60.3MB, time=2.34 memory used=182.0MB, alloc=84.3MB, time=2.93 memory used=234.3MB, alloc=84.3MB, time=3.76 memory used=288.2MB, alloc=116.3MB, time=4.67 memory used=363.1MB, alloc=116.3MB, time=5.83 memory used=437.6MB, alloc=140.3MB, time=6.96 memory used=522.5MB, alloc=396.3MB, time=8.32 memory used=619.0MB, alloc=420.3MB, time=9.81 memory used=734.9MB, alloc=420.3MB, time=11.64 memory used=844.6MB, alloc=444.3MB, time=13.51 memory used=978.3MB, alloc=468.3MB, time=15.69 memory used=1133.8MB, alloc=492.3MB, time=18.24 memory used=1298.0MB, alloc=516.3MB, time=21.02 memory used=1456.5MB, alloc=540.3MB, time=23.79 memory used=1602.2MB, alloc=564.3MB, time=26.29 memory used=1727.3MB, alloc=588.3MB, time=28.73 memory used=1862.3MB, alloc=612.3MB, time=31.52 memory used=2014.4MB, alloc=636.3MB, time=34.65 memory used=2135.2MB, alloc=636.3MB, time=37.18 memory used=2274.1MB, alloc=660.3MB, time=40.08 memory used=2414.1MB, alloc=684.3MB, time=43.07 memory used=2543.4MB, alloc=708.3MB, time=45.84 memory used=2688.1MB, alloc=732.3MB, time=48.93 memory used=2820.8MB, alloc=756.3MB, time=51.92 memory used=2949.1MB, alloc=780.3MB, time=54.87 memory used=3071.1MB, alloc=804.3MB, time=57.67 memory used=3192.1MB, alloc=828.3MB, time=60.50 memory used=3282.6MB, alloc=828.3MB, time=62.81 memory used=3399.2MB, alloc=852.3MB, time=65.65 memory used=3508.0MB, alloc=876.3MB, time=68.31 memory used=3607.5MB, alloc=900.3MB, time=70.86 memory used=3703.8MB, alloc=900.3MB, time=73.37 memory used=3793.4MB, alloc=924.3MB, time=75.71 memory used=3885.4MB, alloc=924.3MB, time=78.10 memory used=3963.7MB, alloc=948.3MB, time=80.24 memory used=4046.9MB, alloc=948.3MB, time=82.59 memory used=4415.3MB, alloc=972.3MB, time=90.13 memory used=4805.7MB, alloc=996.3MB, time=103.13 |\^/| 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(); 1428243625 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 F := [-16 x + 16 x y, -16 y + 18 x , 13 y - 16 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-13 y - 17 z , 16 x z - 2 z, 11 x y - 4 x] > Problem := [F,G]; 3 3 2 3 Problem := [[-16 x + 16 x y, -16 y + 18 x , 13 y - 16 y], 3 2 2 [-13 y - 17 z , 16 x z - 2 z, 11 x y - 4 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.50 memory used=47.0MB, alloc=32.3MB, time=0.82 memory used=68.9MB, alloc=56.3MB, time=1.22 memory used=111.0MB, alloc=56.3MB, time=1.96 memory used=147.7MB, alloc=80.3MB, time=2.85 N1 := 1261 > GB := Basis(F, plex(op(vars))); 2 GB := [x , y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=202.6MB, alloc=80.3MB, time=4.49 N2 := 97 #save(Problem, "format.txt"); > 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 := [-16 x + 16 x y, -16 y + 18 x , 13 y - 16 y, -13 y - 17 z , 2 16 x z - 2 z, 11 x y - 4 x] > J:=[op(GB),op(G)]; 2 3 2 2 J := [x , y, -13 y - 17 z , 16 x z - 2 z, 11 x y - 4 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 11, 17, 3, 3, 3, 2, 2/3, 5/6, 1/3, 1/2, 1/2, 1/4, 5, 8, 11, 3, 2, 3, 2, 3/5, 3/5, 2/5, 4/9, 1/3, 1/3, 3, 6, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=207.8MB, alloc=80.3MB, time=4.59 |\^/| 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(); 1428243641 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [4 x y - 5 y z, -y - 9 x , 12 x y - 19 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [19 x - 4 x y, -20 x z + 20 x, -4 x y + 13 x y z] > Problem := [F,G]; 3 2 2 Problem := [[4 x y - 5 y z, -y - 9 x , 12 x y - 19 x], 3 2 2 [19 x - 4 x y, -20 x z + 20 x, -4 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=48.9MB, alloc=32.3MB, time=0.86 memory used=69.4MB, alloc=56.3MB, time=1.22 N1 := 791 > GB := Basis(F, plex(op(vars))); 6 5 3 2 2 GB := [15552 x + 6859 x, 1296 x + 361 x y, y + 9 x , -4 x + 5 x z, 5 5184 x + 1805 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=111.3MB, alloc=56.3MB, time=2.21 memory used=148.8MB, alloc=60.3MB, time=2.75 memory used=185.3MB, alloc=84.3MB, time=3.30 memory used=246.5MB, alloc=84.3MB, time=4.34 memory used=303.5MB, alloc=108.3MB, time=5.34 memory used=377.7MB, alloc=132.3MB, time=7.18 memory used=459.9MB, alloc=156.3MB, time=10.29 N2 := 2147 #save(Problem, "format.txt"); > 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 := [4 x y - 5 y z, -y - 9 x , 12 x y - 19 x, 19 x - 4 x y, -20 x z + 20 x, 2 -4 x y + 13 x y z] > J:=[op(GB),op(G)]; 6 5 3 2 2 J := [15552 x + 6859 x, 1296 x + 361 x y, y + 9 x , -4 x + 5 x z, 5 3 2 2 5184 x + 1805 z y, 19 x - 4 x y, -20 x z + 20 x, -4 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, 17, 3, 3, 3, 1, 1, 5/6, 1/2, 5/6, 7/12, 1/4, 8, 17, 30, 6, 6, 3, 1, 1, 5/8, 1/2, 7/8, 3/8, 1/4, -3, -13, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=496.6MB, alloc=156.3MB, time=11.49 |\^/| 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(); 1428243676 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-16 x y - 13 y, -12 x - 8 y z, -17 x - 6 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [20 x y z + 16 y , 3 x y z + 9 x y, -11 x z + 17 x z] > Problem := [F,G]; 2 2 3 2 Problem := [[-16 x y - 13 y, -12 x - 8 y z, -17 x - 6 y z], 3 2 [20 x y z + 16 y , 3 x y z + 9 x y, -11 x 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=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=48.0MB, alloc=32.3MB, time=0.80 memory used=68.3MB, alloc=32.3MB, time=1.11 memory used=87.7MB, alloc=56.3MB, time=1.41 memory used=127.6MB, alloc=60.3MB, time=2.00 memory used=165.2MB, alloc=84.3MB, time=2.58 memory used=205.9MB, alloc=84.3MB, time=3.29 memory used=261.8MB, alloc=116.3MB, time=4.36 memory used=335.3MB, alloc=140.3MB, time=5.70 memory used=425.7MB, alloc=164.3MB, time=7.36 memory used=529.8MB, alloc=188.3MB, time=9.60 memory used=640.4MB, alloc=212.3MB, time=12.94 memory used=759.8MB, alloc=236.3MB, time=17.42 memory used=897.7MB, alloc=260.3MB, time=22.90 memory used=1059.6MB, alloc=260.3MB, time=29.42 memory used=1221.5MB, alloc=260.3MB, time=35.83 memory used=1383.2MB, alloc=284.3MB, time=42.30 memory used=1569.3MB, alloc=308.3MB, time=49.67 N1 := 5799 > GB := Basis(F, plex(op(vars))); 4 2 3 3 2 GB := [272 x + 117 x , 4624 x + 1053 y, 27 x + 34 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1665.9MB, alloc=308.3MB, time=51.70 N2 := 1099 #save(Problem, "format.txt"); > if (GB=[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 := [-16 x y - 13 y, -12 x - 8 y z, -17 x - 6 y z, 20 x y z + 16 y , 2 3 x y z + 9 x y, -11 x z + 17 x z] > J:=[op(GB),op(G)]; 4 2 3 3 2 3 J := [272 x + 117 x , 4624 x + 1053 y, 27 x + 34 x z, 20 x y z + 16 y , 2 3 x y z + 9 x y, -11 x 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, 16, 17, 3, 3, 3, 1, 1, 5/6, 5/6, 2/3, 2/3, 1/2, 6, 13, 19, 4, 4, 3, 1, 1, 1/2, 2/3, 5/6, 5/12, 5/12, 3, -2, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1718.2MB, alloc=564.3MB, time=53.39 |\^/| 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(); 1428243827 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 F := [-14 x y + x y, -7 x + 11 y, -5 x y z - 4] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [-12 x - 3 x , 16 z + 11, -3 y z - 7 x] > Problem := [F,G]; 2 Problem := [[-14 x y + x y, -7 x + 11 y, -5 x y z - 4], 3 2 3 2 [-12 x - 3 x , 16 z + 11, -3 y z - 7 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.51 memory used=48.4MB, alloc=32.3MB, time=0.87 memory used=69.4MB, alloc=56.3MB, time=1.30 memory used=112.1MB, alloc=60.3MB, time=2.06 memory used=149.8MB, alloc=84.3MB, time=3.14 N1 := 895 > GB := Basis(F, plex(op(vars))); GB := [14 x - 1, 22 y - 1, 5 z + 1232] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=207.4MB, alloc=84.3MB, time=4.10 N2 := 663 #save(Problem, "format.txt"); > if (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 H := [-14 x y + x y, -7 x + 11 y, -5 x y z - 4, -12 x - 3 x , 16 z + 11, 2 -3 y z - 7 x] > J:=[op(GB),op(G)]; 3 2 3 2 J := [14 x - 1, 22 y - 1, 5 z + 1232, -12 x - 3 x , 16 z + 11, -3 y z - 7 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 16, 3, 3, 1, 3, 5/6, 2/3, 1/2, 7/12, 5/12, 1/4, 6, 8, 12, 3, 3, 1, 3, 1/2, 1/3, 1/2, 1/3, 1/6, 1/4, 4, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=235.8MB, alloc=84.3MB, time=4.79 |\^/| 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(); 1428243840 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [9 x z + 6 y z, 6 x z + 8 y , 14 x z + 9 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 G := [x y + 8 x y z, 8 x y z - 19 y z, 6 x y + 18 z] > Problem := [F,G]; 2 2 2 3 2 Problem := [[9 x z + 6 y z, 6 x z + 8 y , 14 x z + 9 x], 2 [x y + 8 x y z, 8 x y z - 19 y z, 6 x y + 18 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.2MB, alloc=32.3MB, time=0.78 memory used=67.4MB, alloc=32.3MB, time=1.07 memory used=86.8MB, alloc=56.3MB, time=1.37 memory used=124.8MB, alloc=60.3MB, time=1.94 memory used=161.4MB, alloc=84.3MB, time=2.50 memory used=211.7MB, alloc=84.3MB, time=3.27 memory used=266.6MB, alloc=116.3MB, time=4.17 memory used=345.8MB, alloc=140.3MB, time=5.60 memory used=438.0MB, alloc=164.3MB, time=7.24 memory used=545.2MB, alloc=188.3MB, time=9.16 memory used=661.3MB, alloc=468.3MB, time=11.29 memory used=795.1MB, alloc=492.3MB, time=13.70 memory used=940.5MB, alloc=516.3MB, time=16.34 memory used=1095.4MB, alloc=540.3MB, time=19.43 memory used=1247.6MB, alloc=564.3MB, time=24.12 memory used=1406.3MB, alloc=588.3MB, time=29.55 memory used=1576.7MB, alloc=612.3MB, time=35.68 memory used=1760.0MB, alloc=636.3MB, time=42.54 memory used=1955.2MB, alloc=660.3MB, time=50.61 memory used=2168.3MB, alloc=684.3MB, time=59.75 memory used=2405.3MB, alloc=708.3MB, time=69.89 memory used=2666.2MB, alloc=732.3MB, time=81.00 memory used=2951.1MB, alloc=756.3MB, time=93.07 memory used=3260.0MB, alloc=756.3MB, time=106.11 |\^/| 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(); 1428244140 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-5 x y z + 20 z , 19 z, 5 x y + 10 y z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [-5 z + 15 x y, 2 x + 4 z, 7 x y - 5 x y] > Problem := [F,G]; 3 2 2 Problem := [[-5 x y z + 20 z , 19 z, 5 x y + 10 y z ], 3 3 2 [-5 z + 15 x y, 2 x + 4 z, 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=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.9MB, alloc=32.3MB, time=0.79 memory used=68.6MB, alloc=32.3MB, time=1.09 memory used=88.0MB, alloc=56.3MB, time=1.39 memory used=127.3MB, alloc=60.3MB, time=1.98 memory used=166.0MB, alloc=84.3MB, time=2.66 memory used=227.9MB, alloc=84.3MB, time=3.71 memory used=280.3MB, alloc=108.3MB, time=5.15 N1 := 1433 > GB := Basis(F, plex(op(vars))); 2 GB := [y x , z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 105 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 3 3 H := [-5 x y z + 20 z , 19 z, 5 x y + 10 y z , -5 z + 15 x y, 2 x + 4 z, 2 7 x y - 5 x y] > J:=[op(GB),op(G)]; 2 3 3 2 J := [y x , z, -5 z + 15 x y, 2 x + 4 z, 7 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, 14, 16, 3, 3, 2, 3, 5/6, 2/3, 5/6, 1/2, 1/2, 1/2, 5, 10, 13, 3, 3, 2, 3, 4/5, 3/5, 3/5, 5/9, 4/9, 1/3, 4, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=338.1MB, alloc=108.3MB, time=6.77 |\^/| 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(); 1428244161 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [5 x - 8 z, -9 y z - 11 x, -20 - 7 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-4 x z + 3 z , -6 y z - 9, 13 y z - 6 x z] > Problem := [F,G]; 2 2 Problem := [[5 x - 8 z, -9 y z - 11 x, -20 - 7 x], 2 3 2 [-4 x z + 3 z , -6 y z - 9, 13 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=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=46.9MB, alloc=32.3MB, time=0.76 memory used=66.7MB, alloc=56.3MB, time=1.06 memory used=105.6MB, alloc=60.3MB, time=1.64 memory used=142.6MB, alloc=60.3MB, time=2.18 memory used=180.0MB, alloc=84.3MB, time=2.86 memory used=236.5MB, alloc=108.3MB, time=3.88 memory used=310.9MB, alloc=140.3MB, time=5.23 memory used=399.1MB, alloc=164.3MB, time=7.03 memory used=494.3MB, alloc=188.3MB, time=10.02 memory used=601.6MB, alloc=212.3MB, time=14.15 memory used=732.9MB, alloc=212.3MB, time=19.13 memory used=864.3MB, alloc=236.3MB, time=24.12 N1 := 4153 > GB := Basis(F, plex(op(vars))); 2 GB := [7 x + 20, 225 y - 154, 49 z - 250] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1023.1MB, alloc=236.3MB, time=28.04 memory used=1202.0MB, alloc=260.3MB, time=33.54 N2 := 2297 #save(Problem, "format.txt"); > if (GB=[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 := [5 x - 8 z, -9 y z - 11 x, -20 - 7 x, -4 x z + 3 z , -6 y z - 9, 2 13 y z - 6 x z] > J:=[op(GB),op(G)]; 2 2 3 J := [7 x + 20, 225 y - 154, 49 z - 250, -4 x z + 3 z , -6 y z - 9, 2 13 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, 13, 14, 3, 2, 2, 3, 5/6, 1/2, 5/6, 5/12, 1/4, 7/12, 6, 10, 12, 3, 1, 2, 3, 1/2, 1/2, 2/3, 1/4, 1/4, 1/2, 3, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1269.7MB, alloc=260.3MB, time=36.09 |\^/| 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(); 1428244265 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-17 x y - 16 x z , 7 y z - 16 z, -18 y + 8 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 G := [-x - 16 y , -17 x - 16 z, 6 y - 1] > Problem := [F,G]; 2 2 3 2 Problem := [[-17 x y - 16 x z , 7 y z - 16 z, -18 y + 8 y z], 3 3 3 2 [-x - 16 y , -17 x - 16 z, 6 y - 1]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.46 memory used=47.5MB, alloc=32.3MB, time=0.77 memory used=68.1MB, alloc=32.3MB, time=1.07 memory used=87.9MB, alloc=32.3MB, time=1.35 memory used=106.4MB, alloc=56.3MB, time=1.63 memory used=147.8MB, alloc=60.3MB, time=2.33 memory used=186.4MB, alloc=84.3MB, time=3.04 memory used=244.3MB, alloc=108.3MB, time=4.09 memory used=320.1MB, alloc=132.3MB, time=5.47 memory used=409.8MB, alloc=164.3MB, time=7.16 memory used=508.5MB, alloc=188.3MB, time=9.90 memory used=617.4MB, alloc=212.3MB, time=13.49 memory used=739.5MB, alloc=236.3MB, time=18.31 memory used=885.5MB, alloc=236.3MB, time=24.00 memory used=1031.5MB, alloc=236.3MB, time=29.62 memory used=1177.6MB, alloc=260.3MB, time=35.23 memory used=1347.7MB, alloc=260.3MB, time=41.71 N1 := 5681 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 3 2 GB := [119 x y + 1296 x y, 7 x y - 16 x y, 567 x y + 272 x y, 4 3 3 7 y - 16 y , -441 y + 1024 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1521.2MB, alloc=260.3MB, time=46.84 memory used=1720.4MB, alloc=540.3MB, time=52.75 N2 := 1659 #save(Problem, "format.txt"); > if (GB=[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 := [-17 x y - 16 x z , 7 y z - 16 z, -18 y + 8 y z, -x - 16 y , 3 2 -17 x - 16 z, 6 y - 1] > J:=[op(GB),op(G)]; 3 2 2 2 2 3 2 J := [119 x y + 1296 x y, 7 x y - 16 x y, 567 x y + 272 x y, 4 3 3 3 3 3 2 7 y - 16 y , -441 y + 1024 z, -x - 16 y , -17 x - 16 z, 6 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, 12, 16, 3, 3, 3, 2, 1/2, 5/6, 2/3, 1/3, 1/2, 5/12, 8, 14, 27, 4, 3, 4, 1, 5/8, 7/8, 1/4, 1/2, 11/16, 1/8, -2, -11, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1721.3MB, alloc=540.3MB, time=52.82 |\^/| 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(); 1428244427 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-20 x , -11 x y + 17 z, 2 x z - 7 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [-4 x y - 6, -3 x y z + 12 y z , -20 x + 15 z] > Problem := [F,G]; 2 2 2 Problem := [[-20 x , -11 x y + 17 z, 2 x z - 7 y], 2 2 3 [-4 x y - 6, -3 x y z + 12 y z , -20 x + 15 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=47.5MB, alloc=32.3MB, time=0.79 memory used=98.3MB, alloc=68.3MB, time=1.65 memory used=145.1MB, alloc=68.3MB, time=2.44 memory used=188.4MB, alloc=92.3MB, time=3.18 memory used=248.9MB, alloc=116.3MB, time=4.34 memory used=322.4MB, alloc=140.3MB, time=6.49 memory used=408.4MB, alloc=140.3MB, time=9.71 memory used=494.5MB, alloc=164.3MB, time=12.97 N1 := 3187 > GB := Basis(F, plex(op(vars))); 2 GB := [x , y, z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); 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 H := [-20 x , -11 x y + 17 z, 2 z x - 7 y, -4 x y - 6, -3 x y z + 12 y z , 3 -20 x + 15 z] > J:=[op(GB),op(G)]; 2 2 2 3 J := [x , y, z, -4 x y - 6, -3 x y z + 12 y z , -20 x + 15 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 17, 3, 3, 2, 2, 1, 2/3, 2/3, 1/2, 5/12, 5/12, 6, 10, 13, 3, 3, 2, 2, 2/3, 1/2, 1/2, 2/5, 2/5, 2/5, 4, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=604.1MB, alloc=164.3MB, time=16.36 |\^/| 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(); 1428244480 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-3 y z - 14 y, 6 x z - 11 x z, -6 x + 16 y z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [20 x z - 19 y , -17 y - z, 7 x y + 4 x y ] > Problem := [F,G]; 2 2 3 2 Problem := [[-3 y z - 14 y, 6 x z - 11 x z, -6 x + 16 y z ], 2 2 3 2 2 [20 x z - 19 y , -17 y - z, 7 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=26.3MB, alloc=32.3MB, time=0.49 memory used=48.0MB, alloc=32.3MB, time=0.80 memory used=95.6MB, alloc=68.3MB, time=1.52 memory used=139.0MB, alloc=68.3MB, time=2.16 memory used=181.9MB, alloc=92.3MB, time=2.84 memory used=249.9MB, alloc=100.3MB, time=3.85 memory used=316.5MB, alloc=124.3MB, time=4.87 memory used=402.8MB, alloc=124.3MB, time=6.15 memory used=474.1MB, alloc=404.3MB, time=7.27 memory used=582.6MB, alloc=404.3MB, time=8.92 memory used=690.0MB, alloc=428.3MB, time=10.58 memory used=815.0MB, alloc=452.3MB, time=12.61 memory used=956.2MB, alloc=476.3MB, time=14.80 memory used=1098.7MB, alloc=500.3MB, time=17.03 memory used=1275.2MB, alloc=524.3MB, time=20.11 memory used=1470.9MB, alloc=548.3MB, time=23.55 memory used=1638.1MB, alloc=572.3MB, time=26.79 memory used=1806.1MB, alloc=596.3MB, time=30.18 memory used=1972.2MB, alloc=620.3MB, time=33.33 memory used=2145.7MB, alloc=644.3MB, time=36.50 memory used=2389.1MB, alloc=668.3MB, time=39.79 memory used=2551.9MB, alloc=692.3MB, time=43.03 memory used=2712.6MB, alloc=716.3MB, time=46.37 memory used=2873.0MB, alloc=740.3MB, time=49.77 memory used=3021.7MB, alloc=764.3MB, time=53.04 memory used=3143.6MB, alloc=788.3MB, time=55.83 memory used=3348.2MB, alloc=812.3MB, time=62.78 memory used=3634.2MB, alloc=836.3MB, time=73.45 memory used=3923.4MB, alloc=860.3MB, time=84.65 memory used=4220.2MB, alloc=884.3MB, time=96.62 |\^/| 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(); 1428244780 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-13 x z + 4 y , -10 z - 20 x, 20 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 G := [3 z - y, 18 x z - 3 z , -19 z - 18 z ] > Problem := [F,G]; 2 2 3 2 Problem := [[-13 x z + 4 y , -10 z - 20 x, 20 y z], 2 2 3 3 2 [3 z - y, 18 x z - 3 z , -19 z - 18 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=32.3MB, time=0.81 memory used=67.0MB, alloc=56.3MB, time=1.12 memory used=107.3MB, alloc=60.3MB, time=1.73 memory used=146.5MB, alloc=60.3MB, time=2.32 memory used=182.1MB, alloc=84.3MB, time=2.87 memory used=222.3MB, alloc=84.3MB, time=3.48 memory used=278.5MB, alloc=116.3MB, time=4.45 memory used=354.9MB, alloc=140.3MB, time=5.87 memory used=448.7MB, alloc=164.3MB, time=7.56 memory used=555.9MB, alloc=188.3MB, time=9.55 memory used=669.5MB, alloc=212.3MB, time=12.42 memory used=785.8MB, alloc=236.3MB, time=16.29 memory used=913.3MB, alloc=260.3MB, time=21.30 memory used=1064.8MB, alloc=284.3MB, time=27.21 memory used=1240.3MB, alloc=284.3MB, time=34.02 memory used=1415.8MB, alloc=308.3MB, time=40.84 memory used=1615.3MB, alloc=308.3MB, time=48.55 N1 := 6081 > GB := Basis(F, plex(op(vars))); 3 2 4 2 2 2 3 GB := [x , x y , y , 13 z x - 4 y , y z, z + 2 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1808.3MB, alloc=308.3MB, time=54.33 memory used=2038.2MB, alloc=588.3MB, time=58.29 memory used=2286.7MB, alloc=612.3MB, time=63.06 memory used=2532.5MB, alloc=636.3MB, time=71.06 memory used=2765.9MB, alloc=660.3MB, time=80.64 memory used=3023.3MB, alloc=684.3MB, time=91.14 |\^/| 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(); 1428245080 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-19 z , 12 x y - 13 y , -11 x - 2 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [11 y z - 20 x, 15 y z + 17 z , 6 x z + 17 z] > Problem := [F,G]; 2 2 3 2 Problem := [[-19 z , 12 x y - 13 y , -11 x - 2 z], 2 2 2 2 [11 y z - 20 x, 15 y z + 17 z , 6 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=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=48.6MB, alloc=32.3MB, time=0.86 memory used=68.0MB, alloc=56.3MB, time=1.21 N1 := 629 > GB := Basis(F, plex(op(vars))); 4 2 3 2 GB := [x , -12 x y + 13 y , 11 x + 2 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=106.4MB, alloc=60.3MB, time=1.93 memory used=147.7MB, alloc=84.3MB, time=2.66 N2 := 629 #save(Problem, "format.txt"); > if (GB=[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 := [-19 z , 12 x y - 13 y , -11 x - 2 z, 11 y z - 20 x, 15 y z + 17 z , 2 6 x z + 17 z] > J:=[op(GB),op(G)]; 4 2 3 2 2 2 2 J := [x , -12 x y + 13 y , 11 x + 2 z, 11 y z - 20 x, 15 y z + 17 z , 2 6 x 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, 16, 3, 2, 3, 2, 2/3, 1/2, 5/6, 1/3, 1/3, 7/12, 6, 12, 18, 4, 4, 3, 2, 5/6, 1/2, 2/3, 5/12, 1/3, 1/2, 0, -2, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=158.7MB, 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(); 1428245091 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [20 x z - x , -3 + 16 x, 12 x + 19] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 G := [14 x y + 12 x y, 9 x + 2 z , 12 x - 8 x ] > Problem := [F,G]; 2 2 3 Problem := [[20 x z - x , -3 + 16 x, 12 x + 19], 2 3 3 3 2 [14 x y + 12 x y, 9 x + 2 z , 12 x - 8 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.51 N1 := 295 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=48.4MB, 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: "Input concluded false after GB computation" > > H:=[op(F),op(G)]; 2 2 3 2 3 3 H := [20 x z - x , 16 x - 3, 12 x + 19, 14 x y + 12 x y, 2 z + 9 x , 3 2 12 x - 8 x ] > J:=[op(GB),op(G)]; 2 3 3 3 2 J := [1, 14 x y + 12 x y, 2 z + 9 x , 12 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, 9, 16, 3, 3, 2, 3, 1, 1/6, 1/3, 3/4, 1/6, 1/6, 4, 5, 9, 3, 3, 2, 3, 3/4, 1/4, 1/4, 5/7, 2/7, 1/7, 4, 7, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=54.2MB, alloc=32.3MB, time=0.98 |\^/| 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(); 1428245094 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [6 y + 17 x z, 16 x y + 7 x z , -15 x y z + 17 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [7 y + 3 y , 2 x y + 9 x z , -12 x y + y] > Problem := [F,G]; 3 2 2 2 Problem := [[6 y + 17 x z, 16 x y + 7 x z , -15 x y z + 17 z ], 3 2 2 2 2 [7 y + 3 y , 2 x y + 9 x z , -12 x y + y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.78 memory used=68.2MB, alloc=32.3MB, time=1.07 memory used=88.3MB, alloc=32.3MB, time=1.36 memory used=107.5MB, alloc=56.3MB, time=1.68 N1 := 181 > GB := Basis(F, plex(op(vars))); 3 2 2 4 2 2 3 5 GB := [1575 x y + 4624 x y , 315 x y - 2312 x y , 5 x y + 2 y , 3 3 2 4 2 6 y + 17 z x, 21 y z - 136 x y , 90 y + 289 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=146.6MB, alloc=60.3MB, time=2.29 memory used=186.9MB, alloc=60.3MB, time=2.87 memory used=226.2MB, alloc=60.3MB, time=3.44 memory used=263.2MB, alloc=84.3MB, time=4.01 memory used=319.4MB, alloc=92.3MB, time=4.87 memory used=373.7MB, alloc=92.3MB, time=5.68 memory used=427.7MB, alloc=116.3MB, time=6.49 memory used=503.8MB, alloc=116.3MB, time=7.68 memory used=577.2MB, alloc=140.3MB, time=9.03 N2 := 1157 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 2 H := [6 y + 17 z x, 16 x y + 7 x z , -15 x y z + 17 z , 7 y + 3 y , 2 2 2 2 x y + 9 x z , -12 x y + y] > J:=[op(GB),op(G)]; 3 2 2 4 2 2 3 5 J := [1575 x y + 4624 x y , 315 x y - 2312 x y , 5 x y + 2 y , 3 3 2 4 2 3 2 6 y + 17 z x, 21 y z - 136 x y , 90 y + 289 z , 7 y + 3 y , 2 2 2 2 x y + 9 x z , -12 x y + 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, 18, 3, 1, 3, 2, 5/6, 1, 2/3, 7/12, 2/3, 5/12, 9, 20, 35, 5, 3, 5, 2, 7/9, 1, 4/9, 5/9, 5/6, 2/9, -5, -17, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=663.2MB, alloc=140.3MB, time=11.35 |\^/| 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(); 1428245135 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-7 y z + y , 11 x z - 16 z, 2 x y z - z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 G := [16 x z + 4 x , 14 x - 12 x y , -9 y z - 6 y ] > Problem := [F,G]; 2 2 2 2 Problem := [[-7 y z + y , 11 x z - 16 z, 2 x y z - z ], 2 2 3 2 2 2 [16 x z + 4 x , 14 x - 12 x y , -9 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=26.3MB, alloc=32.3MB, time=0.49 memory used=47.4MB, alloc=32.3MB, time=0.78 memory used=67.6MB, alloc=32.3MB, time=1.07 memory used=87.2MB, alloc=56.3MB, time=1.37 memory used=127.5MB, alloc=60.3MB, time=1.97 memory used=165.8MB, alloc=60.3MB, time=2.53 memory used=202.0MB, alloc=84.3MB, time=3.08 memory used=257.1MB, alloc=108.3MB, time=3.95 memory used=335.8MB, alloc=140.3MB, time=5.34 memory used=430.5MB, alloc=164.3MB, time=6.98 memory used=537.1MB, alloc=188.3MB, time=8.87 memory used=656.8MB, alloc=212.3MB, time=10.99 memory used=788.4MB, alloc=236.3MB, time=13.34 memory used=924.7MB, alloc=260.3MB, time=15.88 memory used=1035.6MB, alloc=540.3MB, time=18.63 memory used=1182.9MB, alloc=564.3MB, time=23.06 memory used=1337.8MB, alloc=588.3MB, time=28.18 memory used=1503.3MB, alloc=612.3MB, time=34.05 memory used=1683.1MB, alloc=636.3MB, time=40.66 memory used=1874.9MB, alloc=660.3MB, time=48.54 memory used=2090.0MB, alloc=684.3MB, time=57.24 memory used=2329.1MB, alloc=708.3MB, time=67.02 memory used=2592.2MB, alloc=732.3MB, time=77.78 memory used=2879.2MB, alloc=732.3MB, time=89.59 |\^/| 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(); 1428245435 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 F := [-19 y + 7 z , -2 x y + 18, -18 x y - 18 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [12 x y - 13 x y , -11 x y - 20 x, 5 z] > Problem := [F,G]; 3 3 2 2 Problem := [[-19 y + 7 z , -2 x y + 18, -18 x y - 18 y], 2 2 2 [12 x y - 13 x y , -11 x y - 20 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=26.4MB, alloc=32.3MB, time=0.50 N1 := 251 > GB := Basis(F, plex(op(vars))); 2 3 GB := [x + 1, y + 9, 7 z + 13851] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=48.2MB, alloc=32.3MB, time=0.89 memory used=67.6MB, alloc=56.3MB, time=1.19 N2 := 275 #save(Problem, "format.txt"); > 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 H := [-19 y + 7 z , -2 x y + 18, -18 x y - 18 y, 12 x y - 13 x y , 2 -11 x y - 20 x, 5 z] > J:=[op(GB),op(G)]; 2 3 2 2 2 J := [x + 1, y + 9, 7 z + 13851, 12 x y - 13 x y , -11 x y - 20 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, 11, 16, 3, 2, 3, 3, 2/3, 5/6, 1/3, 1/2, 7/12, 1/6, 6, 8, 13, 3, 2, 2, 3, 1/2, 1/2, 1/3, 5/12, 1/3, 1/6, 3, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=79.7MB, alloc=56.3MB, 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(); 1428245440 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-7 x z + z, 16 x y - 14 x y, 12 x y - 2 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-2 x + 19 z, -7 x - 20 x y, -6 z - 14 x ] > Problem := [F,G]; 2 2 2 Problem := [[-7 x z + z, 16 x y - 14 x y, 12 x y - 2 z], 2 3 2 [-2 x + 19 z, -7 x - 20 x y, -6 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=47.6MB, alloc=32.3MB, time=0.78 memory used=69.6MB, alloc=56.3MB, time=1.17 memory used=113.4MB, alloc=60.3MB, time=1.93 memory used=150.3MB, alloc=84.3MB, time=2.86 N1 := 1229 > GB := Basis(F, plex(op(vars))); 4 2 2 2 GB := [7 x y - x y, 8 x y - 7 x y, -6 x y + z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=205.4MB, alloc=84.3MB, time=4.22 memory used=265.7MB, alloc=108.3MB, time=5.25 N2 := 965 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-7 x z + z, 16 x y - 14 x y, 12 x y - 2 z, -2 x + 19 z, -7 x - 20 x y, 3 2 -6 z - 14 x ] > J:=[op(GB),op(G)]; 4 2 2 2 2 J := [7 x y - x y, 8 x y - 7 x y, -6 x y + z, -2 x + 19 z, -7 x - 20 x y, 3 2 -6 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, 13, 15, 3, 2, 2, 3, 1, 1/2, 2/3, 2/3, 1/3, 5/12, 6, 13, 17, 5, 4, 2, 3, 1, 2/3, 1/2, 3/4, 1/2, 1/4, 0, -2, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=326.9MB, alloc=108.3MB, time=6.80 |\^/| 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(); 1428245461 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [6 z + 4 y, 10 x y + 3 x, -18 x z + 5 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-3 x + 7 y , 11 x y + 10, 2 y z + 17 z] > Problem := [F,G]; 2 2 2 Problem := [[6 z + 4 y, 10 x y + 3 x, -18 x z + 5 x z], 3 2 2 2 [-3 x + 7 y , 11 x y + 10, 2 y z + 17 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.82 memory used=68.8MB, alloc=56.3MB, time=1.23 N1 := 369 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [18 x - 5 x, 10 x y + 3 x, 3 z + 2 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=106.5MB, alloc=60.3MB, time=1.79 N2 := 369 #save(Problem, "format.txt"); > if (GB=[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 := [6 z + 4 y, 10 x y + 3 x, -18 x z + 5 x z, -3 x + 7 y , 11 y x + 10, 2 2 y z + 17 z] > J:=[op(GB),op(G)]; 2 2 2 3 2 2 J := [18 x - 5 x, 10 x y + 3 x, 3 z + 2 y, -3 x + 7 y , 11 y x + 10, 2 2 y 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, 17, 3, 3, 2, 2, 2/3, 5/6, 1/2, 1/2, 5/12, 5/12, 6, 11, 16, 3, 3, 2, 2, 2/3, 5/6, 1/3, 1/2, 5/12, 1/4, 1, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=136.6MB, alloc=60.3MB, 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(); 1428245468 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-3 x y, -7 y z - 3 y, 20 x z + 9 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [6 x y - 7, 6 x + x z, 10 x + 19 x z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-3 x y, -7 y z - 3 y, 20 x z + 9 z ], 3 2 3 2 [6 x y - 7, 6 x + x z, 10 x + 19 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.48 memory used=49.0MB, alloc=32.3MB, time=0.85 N1 := 415 > GB := Basis(F, plex(op(vars))); 2 2 GB := [y, 20 x z + 9 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=69.2MB, alloc=56.3MB, time=1.28 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 2 2 3 2 H := [-3 y x , -7 y z - 3 y, 20 x z + 9 z , 6 y x - 7, 6 x + x z, 3 2 10 x + 19 x z ] > J:=[op(GB),op(G)]; 2 2 3 2 3 2 J := [y, 20 x z + 9 z , 6 y x - 7, 6 x + x z, 10 x + 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, 12, 17, 3, 3, 2, 2, 5/6, 1/2, 2/3, 7/13, 4/13, 5/13, 5, 9, 12, 3, 3, 1, 2, 4/5, 2/5, 3/5, 2/3, 2/9, 4/9, 3, 5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=91.0MB, alloc=56.3MB, 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(); 1428245473 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-3 x z + 6 x y, -19 x y z - 13 x , -5 y + 10 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 G := [11 x z - 4 x , -11 x z + 19 y , 12 x y - 2 x z ] > Problem := [F,G]; 2 2 3 2 Problem := [[-3 x z + 6 x y, -19 x y z - 13 x , -5 y + 10 y ], 2 2 2 3 2 2 [11 x z - 4 x , -11 x z + 19 y , 12 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.49 memory used=48.1MB, alloc=32.3MB, time=0.81 memory used=67.4MB, alloc=56.3MB, time=1.10 memory used=108.4MB, alloc=60.3MB, time=1.70 memory used=147.1MB, alloc=60.3MB, time=2.28 memory used=184.3MB, alloc=84.3MB, time=2.84 memory used=222.3MB, alloc=84.3MB, time=3.39 memory used=278.0MB, alloc=116.3MB, time=4.24 memory used=357.8MB, alloc=116.3MB, time=5.44 memory used=434.4MB, alloc=116.3MB, time=6.60 memory used=512.1MB, alloc=140.3MB, time=7.77 memory used=587.8MB, alloc=140.3MB, time=8.85 memory used=664.3MB, alloc=396.3MB, time=9.99 memory used=765.2MB, alloc=420.3MB, time=11.36 memory used=888.0MB, alloc=444.3MB, time=13.06 memory used=1017.0MB, alloc=468.3MB, time=14.85 memory used=1144.6MB, alloc=492.3MB, time=16.86 memory used=1308.9MB, alloc=516.3MB, time=20.03 memory used=1489.3MB, alloc=540.3MB, time=23.41 memory used=1674.2MB, alloc=564.3MB, time=26.84 memory used=1864.7MB, alloc=588.3MB, time=30.54 memory used=2015.9MB, alloc=612.3MB, time=33.57 memory used=2172.7MB, alloc=636.3MB, time=36.70 memory used=2324.0MB, alloc=660.3MB, time=39.75 memory used=2547.1MB, alloc=684.3MB, time=47.06 memory used=2768.4MB, alloc=708.3MB, time=54.84 memory used=2967.5MB, alloc=732.3MB, time=62.59 memory used=3198.3MB, alloc=756.3MB, time=71.86 memory used=3447.5MB, alloc=780.3MB, time=81.74 |\^/| 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(); 1428245773 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [11 y z + 12 z , 7 x z - 13 z, 10 x y + 14 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-13 x y - 11 z , 7 x y + 11 z , 12 x z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[11 y z + 12 z , 7 x z - 13 z, 10 x y + 14 z ], 2 2 2 2 [-13 x y - 11 z , 7 x y + 11 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=27.0MB, alloc=32.3MB, time=0.51 memory used=48.3MB, alloc=32.3MB, time=0.81 memory used=68.9MB, alloc=32.3MB, time=1.11 memory used=88.1MB, alloc=56.3MB, time=1.41 memory used=129.6MB, alloc=60.3MB, time=2.01 memory used=168.2MB, alloc=60.3MB, time=2.58 memory used=206.2MB, alloc=84.3MB, time=3.15 memory used=266.7MB, alloc=92.3MB, time=4.07 memory used=324.5MB, alloc=116.3MB, time=4.94 memory used=404.8MB, alloc=116.3MB, time=6.10 memory used=480.6MB, alloc=140.3MB, time=7.27 memory used=556.7MB, alloc=164.3MB, time=8.50 memory used=649.0MB, alloc=420.3MB, time=10.24 memory used=759.2MB, alloc=444.3MB, time=12.28 memory used=884.6MB, alloc=468.3MB, time=14.62 memory used=1023.5MB, alloc=492.3MB, time=17.24 memory used=1172.3MB, alloc=516.3MB, time=20.09 memory used=1322.4MB, alloc=540.3MB, time=24.18 memory used=1471.9MB, alloc=564.3MB, time=29.06 memory used=1630.9MB, alloc=588.3MB, time=34.66 memory used=1798.1MB, alloc=612.3MB, time=41.45 memory used=1986.5MB, alloc=636.3MB, time=49.20 memory used=2198.8MB, alloc=660.3MB, time=57.95 memory used=2435.0MB, alloc=684.3MB, time=67.65 memory used=2695.2MB, alloc=708.3MB, time=78.25 |\^/| 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(); 1428246073 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [14 x z - 18 z, -3 x - 16, -20 x y + y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-5 x , 5 x y - 12 x y, 5 y z + 4 z ] > Problem := [F,G]; 2 3 2 Problem := [[14 x z - 18 z, -3 x - 16, -20 x y + y ], 2 2 2 2 [-5 x , 5 x y - 12 x y, 5 y z + 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=48.2MB, alloc=56.3MB, time=0.93 N1 := 383 > GB := Basis(F, plex(op(vars))); 3 2 2 2 GB := [3 x + 16, -20 x y + y , 27 x z + 112 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=88.6MB, alloc=60.3MB, time=1.64 N2 := 355 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 2 H := [14 x z - 18 z, -3 x - 16, -20 x y + y , -5 x , 5 x y - 12 x y, 2 2 5 y z + 4 z ] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 J := [3 x + 16, -20 x y + y , 27 x z + 112 z , -5 x , 5 x y - 12 x y, 2 2 5 y z + 4 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 10, 16, 3, 3, 2, 2, 5/6, 1/2, 1/3, 1/2, 5/12, 1/3, 6, 10, 16, 3, 3, 2, 2, 5/6, 1/2, 1/3, 1/2, 5/12, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=90.2MB, alloc=60.3MB, time=1.68 |\^/| 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(); 1428246079 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [-14 x - 4 y, -7 z + 13 x, 4 x z - 18 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-2 y z + 14 z , 14 x y + y z, 11 y z - 14 x ] > Problem := [F,G]; 2 2 2 3 Problem := [[-14 x - 4 y, -7 z + 13 x, 4 x z - 18 y ], 2 2 2 2 2 [-2 y z + 14 z , 14 x y + y z, 11 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=26.1MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.79 memory used=68.1MB, alloc=32.3MB, time=1.08 memory used=87.4MB, alloc=56.3MB, time=1.39 memory used=127.2MB, alloc=60.3MB, time=1.99 memory used=166.4MB, alloc=60.3MB, time=2.56 memory used=204.4MB, alloc=84.3MB, time=3.13 memory used=262.3MB, alloc=92.3MB, time=3.99 memory used=320.3MB, alloc=116.3MB, time=5.03 memory used=397.8MB, alloc=140.3MB, time=6.43 memory used=508.3MB, alloc=140.3MB, time=7.91 memory used=600.2MB, alloc=164.3MB, time=9.56 memory used=708.1MB, alloc=188.3MB, time=11.52 memory used=830.4MB, alloc=468.3MB, time=13.77 memory used=961.3MB, alloc=492.3MB, time=17.00 memory used=1091.7MB, alloc=516.3MB, time=20.98 memory used=1230.6MB, alloc=540.3MB, time=25.98 memory used=1382.5MB, alloc=564.3MB, time=32.03 memory used=1558.3MB, alloc=588.3MB, time=38.99 memory used=1758.1MB, alloc=612.3MB, time=46.96 memory used=1981.9MB, alloc=612.3MB, time=55.96 memory used=2205.6MB, alloc=612.3MB, time=64.71 memory used=2429.2MB, alloc=636.3MB, time=73.50 memory used=2676.9MB, alloc=636.3MB, time=83.33 memory used=2924.7MB, alloc=660.3MB, time=93.17 |\^/| 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(); 1428246379 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 F := [13 x y - 15 z, 4 y + 10 y z, 6 z + 4 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 3 G := [4 x - y , 13 x + 10 x z , -19 z - 3] > Problem := [F,G]; 2 3 3 2 Problem := [[13 x y - 15 z, 4 y + 10 y z, 6 z + 4 z ], 3 3 3 2 3 [4 x - y , 13 x + 10 x z , -19 z - 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=48.0MB, alloc=32.3MB, time=0.80 memory used=68.4MB, alloc=32.3MB, time=1.10 memory used=87.4MB, alloc=56.3MB, time=1.40 memory used=127.6MB, alloc=60.3MB, time=2.01 memory used=167.2MB, alloc=60.3MB, time=2.61 memory used=204.0MB, alloc=84.3MB, time=3.17 memory used=262.0MB, alloc=92.3MB, time=4.16 memory used=316.3MB, alloc=116.3MB, time=5.18 memory used=388.9MB, alloc=140.3MB, time=6.51 memory used=475.4MB, alloc=164.3MB, time=8.28 memory used=567.9MB, alloc=188.3MB, time=11.21 memory used=673.3MB, alloc=212.3MB, time=15.15 memory used=802.7MB, alloc=212.3MB, time=19.89 memory used=932.2MB, alloc=236.3MB, time=24.59 N1 := 3847 > GB := Basis(F, plex(op(vars))); 3 3 6 4 2 GB := [13 x y + 6 y , 3 y - 5 y , -13 x y + 15 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1060.8MB, alloc=236.3MB, time=27.06 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)]; 2 3 3 2 3 3 3 2 H := [13 y x - 15 z, 4 y + 10 y z, 6 z + 4 z , -y + 4 x , 13 x + 10 x z , 3 -19 z - 3] > J:=[op(GB),op(G)]; 3 3 6 4 2 3 3 3 2 J := [13 x y + 6 y , 3 y - 5 y , -13 x y + 15 z, -y + 4 x , 13 x + 10 x z , 3 -19 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, 11, 18, 3, 3, 3, 3, 1/2, 1/2, 5/6, 1/3, 1/3, 1/2, 6, 11, 22, 6, 3, 6, 3, 2/3, 2/3, 1/2, 5/12, 1/2, 1/4, 0, -4, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1065.5MB, alloc=492.3MB, time=27.25 |\^/| 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(); 1428246459 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [9 x y + 18 x y z, -7 + 8 x, -9 x - 20 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [-15 x y - 14 y z, 12 x - 8 y z, -x + 14 y] > Problem := [F,G]; 2 2 Problem := [[9 x y + 18 x y z, -7 + 8 x, -9 x - 20 x y], 2 2 3 [-15 x y - 14 y z, 12 x - 8 y z, -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=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.78 memory used=69.1MB, alloc=56.3MB, time=1.16 memory used=110.7MB, alloc=84.3MB, time=2.02 N1 := 809 > GB := Basis(F, plex(op(vars))); GB := [8 x - 7, 160 y + 63, 320 z - 63] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=167.9MB, alloc=84.3MB, time=3.09 N2 := 693 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [9 x y + 18 x y z, 8 x - 7, -9 x - 20 x y, -15 x y - 14 y z, 2 3 12 x - 8 y z, -x + 14 y] > J:=[op(GB),op(G)]; 2 2 J := [8 x - 7, 160 y + 63, 320 z - 63, -15 x y - 14 y z, 12 x - 8 y z, 3 -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, 14, 14, 3, 3, 2, 1, 1, 5/6, 1/2, 2/3, 7/12, 1/4, 6, 11, 11, 3, 3, 1, 1, 2/3, 2/3, 1/2, 1/3, 5/12, 1/4, 3, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=216.1MB, alloc=84.3MB, time=4.09 |\^/| 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(); 1428246471 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-9 y z - 11 z , 18 x y z - 11 x y, -3 x + 12 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; G := [-y z, -13 x y - 2 y, 14 x y] > Problem := [F,G]; 2 2 3 2 Problem := [[-9 y z - 11 z , 18 x y z - 11 x y, -3 x + 12 y z], [-y z, -13 x y - 2 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=4.2MB, alloc=32.3MB, time=0.17 memory used=27.1MB, alloc=32.3MB, time=0.53 N1 := 281 > GB := Basis(F, plex(op(vars))); 7 4 4 6 3 3 2 GB := [729 x - 2662 x , 81 x + 242 x y, -81 x + 484 x z, -x + 4 y z, 6 2 -6561 x + 234256 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=47.4MB, alloc=32.3MB, time=0.87 memory used=66.6MB, alloc=32.3MB, time=1.15 memory used=87.0MB, alloc=56.3MB, time=1.51 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 3 2 H := [-9 y z - 11 z , 18 x y z - 11 x y, -3 x + 12 y z, -y z, -13 x y - 2 y, 14 x y] > J:=[op(GB),op(G)]; 7 4 4 6 3 3 2 J := [729 x - 2662 x , 81 x + 242 x y, -81 x + 484 x z, -x + 4 y z, 6 2 -6561 x + 234256 z , -y z, -13 x y - 2 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, 15, 3, 3, 2, 2, 2/3, 1, 2/3, 5/14, 4/7, 5/14, 8, 16, 32, 7, 7, 2, 2, 7/8, 5/8, 1/2, 5/9, 1/3, 2/9, -2, -17, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=114.7MB, alloc=56.3MB, time=2.08 |\^/| 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(); 1428246477 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [y z, -7 x + 19 z, -14 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [18 x z + 19 y z, -18 x y - x z, -10 y z ] > Problem := [F,G]; Problem := [ 2 3 2 2 2 2 [y z, -7 x + 19 z, -14 y ], [18 x z + 19 y z, -18 x y - 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=0.17 N1 := 99 > GB := Basis(F, plex(op(vars))); 2 3 GB := [y , -7 x + 19 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=26.8MB, alloc=32.3MB, time=0.53 N2 := 99 #save(Problem, "format.txt"); > if (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 := [y z, -7 x + 19 z, -14 y , 18 x z + 19 y z, -18 x y - x z, -10 y z ] > J:=[op(GB),op(G)]; 2 3 2 2 2 J := [y , -7 x + 19 z, 18 x z + 19 y z, -18 x y - 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, 13, 17, 3, 3, 2, 2, 1/2, 5/6, 5/6, 4/13, 5/13, 6/13, 5, 11, 14, 3, 3, 2, 2, 3/5, 4/5, 4/5, 4/11, 4/11, 5/11, 2, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=29.5MB, alloc=32.3MB, time=0.58 |\^/| 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(); 1428246478 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [-13 x + 6 x y , -7 z - 18 z , -7 x + 20 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 G := [-4 y + 5 x z, 18 y z + 20 y z , 16 x - 17 y z] > Problem := [F,G]; 3 2 3 2 Problem := [[-13 x + 6 x y , -7 z - 18 z , -7 x + 20 z], 3 2 2 3 2 [-4 y + 5 x z, 18 y z + 20 y z , 16 x - 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=32.0MB, alloc=40.3MB, time=0.56 memory used=59.6MB, alloc=40.3MB, time=0.95 memory used=85.5MB, alloc=64.3MB, time=1.35 memory used=131.1MB, alloc=68.3MB, time=2.02 memory used=173.3MB, alloc=92.3MB, time=2.66 memory used=239.1MB, alloc=100.3MB, time=3.66 memory used=303.4MB, alloc=124.3MB, time=4.64 memory used=389.1MB, alloc=148.3MB, time=5.93 memory used=471.5MB, alloc=404.3MB, time=7.22 memory used=580.9MB, alloc=428.3MB, time=9.16 memory used=697.4MB, alloc=452.3MB, time=11.25 memory used=825.3MB, alloc=476.3MB, time=13.59 memory used=963.6MB, alloc=500.3MB, time=16.15 memory used=1111.4MB, alloc=524.3MB, time=18.95 memory used=1269.4MB, alloc=548.3MB, time=21.98 memory used=1435.2MB, alloc=572.3MB, time=25.16 memory used=1606.5MB, alloc=596.3MB, time=28.54 memory used=1773.4MB, alloc=620.3MB, time=33.62 memory used=1941.1MB, alloc=644.3MB, time=39.43 memory used=2118.9MB, alloc=668.3MB, time=46.00 memory used=2310.0MB, alloc=692.3MB, time=53.21 memory used=2515.0MB, alloc=716.3MB, time=61.15 memory used=2734.6MB, alloc=740.3MB, time=69.79 memory used=2968.8MB, alloc=764.3MB, time=79.23 memory used=3217.8MB, alloc=788.3MB, time=89.63 |\^/| 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(); 1428246778 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-17 y z + 17 x , 17 x y + 6, -2 x y z - x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 G := [x z + 8 y , 15 y - 18 x y, 4 x z + 17 x y] > Problem := [F,G]; 2 2 2 Problem := [[-17 y z + 17 x , 17 x y + 6, -2 x y z - x z], 2 3 3 2 [x z + 8 y , 15 y - 18 x y, 4 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=47.9MB, alloc=32.3MB, time=0.78 memory used=68.9MB, alloc=32.3MB, time=1.09 memory used=89.0MB, alloc=32.3MB, time=1.38 memory used=107.9MB, alloc=56.3MB, time=1.67 memory used=150.1MB, alloc=60.3MB, time=2.40 memory used=188.8MB, alloc=84.3MB, time=3.12 memory used=248.1MB, alloc=84.3MB, time=4.17 memory used=300.5MB, alloc=108.3MB, time=5.27 memory used=365.8MB, alloc=132.3MB, time=7.40 memory used=448.4MB, alloc=156.3MB, time=10.60 N1 := 2391 > GB := Basis(F, plex(op(vars))); 2 2 GB := [17 x - 12, 2 y + 1, 17 z + 24] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=526.8MB, alloc=156.3MB, time=12.50 memory used=651.9MB, alloc=164.3MB, time=14.97 N2 := 1105 #save(Problem, "format.txt"); > if (GB=[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 := [-17 y z + 17 x , 17 y x + 6, -2 x y z - x z, z x + 8 y , 3 2 15 y - 18 x y, 4 x z + 17 x y] > J:=[op(GB),op(G)]; 2 2 2 3 3 J := [17 x - 12, 2 y + 1, 17 z + 24, z x + 8 y , 15 y - 18 x y, 2 4 x z + 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, 16, 18, 3, 2, 3, 2, 1, 1, 2/3, 2/3, 7/12, 5/12, 6, 11, 14, 3, 2, 3, 2, 2/3, 2/3, 1/2, 5/12, 5/12, 1/4, 5, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=688.1MB, alloc=164.3MB, time=16.20 |\^/| 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(); 1428246826 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 F := [7 x + 14 x z, -9 x z + 13 y , -6 y + 20 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [-13 x y + 10 x y, -10 y z - 13 z , 11 z + 16 x ] > Problem := [F,G]; 3 2 3 3 Problem := [[7 x + 14 x z, -9 x z + 13 y , -6 y + 20 x z], 2 2 2 3 2 [-13 x y + 10 x y, -10 y z - 13 z , 11 z + 16 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.80 memory used=68.1MB, alloc=56.3MB, time=1.12 memory used=110.2MB, alloc=60.3MB, time=1.75 memory used=150.0MB, alloc=84.3MB, time=2.33 memory used=218.4MB, alloc=116.3MB, time=3.23 memory used=299.2MB, alloc=372.3MB, time=4.41 memory used=379.9MB, alloc=396.3MB, time=5.64 memory used=485.9MB, alloc=420.3MB, time=7.31 memory used=601.1MB, alloc=444.3MB, time=9.45 memory used=727.4MB, alloc=468.3MB, time=11.85 memory used=879.0MB, alloc=492.3MB, time=14.42 memory used=1032.4MB, alloc=516.3MB, time=17.32 memory used=1197.3MB, alloc=540.3MB, time=20.49 memory used=1361.9MB, alloc=564.3MB, time=25.19 memory used=1524.9MB, alloc=588.3MB, time=30.74 memory used=1698.5MB, alloc=612.3MB, time=37.04 memory used=1882.4MB, alloc=636.3MB, time=44.32 memory used=2078.4MB, alloc=660.3MB, time=52.73 memory used=2298.3MB, alloc=684.3MB, time=62.02 memory used=2542.2MB, alloc=708.3MB, time=72.55 memory used=2809.9MB, alloc=732.3MB, time=83.94 memory used=3101.7MB, alloc=756.3MB, time=96.44 |\^/| 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(); 1428247126 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [5 x y - 18 x, -3 x y + 12 x y , -15 x + 20 y z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-2 x z - 11 y , -16 y - 12 y z, -2 x y - 3 y] > Problem := [F,G]; 2 2 2 3 2 Problem := [[5 x y - 18 x, -3 x y + 12 x y , -15 x + 20 y z ], 2 2 [-2 x z - 11 y , -16 y - 12 y 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=0.18 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=48.0MB, alloc=32.3MB, time=0.82 memory used=69.0MB, alloc=56.3MB, time=1.20 memory used=113.0MB, alloc=60.3MB, time=1.99 memory used=152.4MB, alloc=84.3MB, time=2.74 memory used=211.3MB, alloc=116.3MB, time=3.90 memory used=285.6MB, alloc=116.3MB, time=6.44 memory used=351.2MB, alloc=140.3MB, time=9.04 N1 := 2109 > GB := Basis(F, plex(op(vars))); 3 2 2 2 GB := [5 x - 288 x, -x + 4 x y, 5 x z - 864 x, 5 y z - 216 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=439.9MB, alloc=140.3MB, time=10.88 memory used=538.6MB, alloc=164.3MB, time=12.65 memory used=656.7MB, alloc=188.3MB, time=14.98 memory used=787.4MB, alloc=468.3MB, time=17.57 memory used=927.2MB, alloc=492.3MB, time=21.43 memory used=1065.0MB, alloc=516.3MB, time=26.54 memory used=1215.6MB, alloc=540.3MB, time=32.86 memory used=1390.3MB, alloc=564.3MB, time=40.28 memory used=1588.9MB, alloc=564.3MB, time=48.29 memory used=1787.6MB, alloc=588.3MB, time=56.24 N2 := 6013 #save(Problem, "format.txt"); > if (GB=[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 := [5 x y - 18 x, -3 x y + 12 x y , -15 x + 20 y z , -2 x z - 11 y , 2 -16 y - 12 y z, -2 x y - 3 y] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [5 x - 288 x, -x + 4 x y, 5 x z - 864 x, 5 y z - 216 x, -2 x z - 11 y , 2 -16 y - 12 y z, -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, 15, 3, 3, 2, 2, 5/6, 1, 1/2, 7/12, 3/4, 1/4, 7, 15, 17, 3, 3, 2, 2, 6/7, 5/7, 4/7, 9/14, 1/2, 2/7, -1, -2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1980.7MB, alloc=588.3MB, time=63.47 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428247321 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 2 F := [20 y - 16 z , -17 y z + 11 z , 12 x y - 18 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-18 y z + 13, -18 y z - 11, -6 z + 18 y ] > Problem := [F,G]; 3 3 2 3 2 2 Problem := [[20 y - 16 z , -17 y z + 11 z , 12 x y - 18 x z], 2 3 2 [-18 y z + 13, -18 y z - 11, -6 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=0.18 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.8MB, alloc=32.3MB, time=0.80 memory used=66.8MB, alloc=32.3MB, time=1.07 memory used=86.7MB, alloc=56.3MB, time=1.43 memory used=129.3MB, alloc=60.3MB, time=2.19 memory used=166.9MB, alloc=84.3MB, time=2.85 memory used=220.9MB, alloc=84.3MB, time=4.49 N1 := 1665 > GB := Basis(F, plex(op(vars))); 2 3 5 2 2 3 2 3 3 GB := [x y , y , -2 x y + 3 x z, -55 y + 68 y z, -5 y + 4 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=269.7MB, alloc=84.3MB, time=6.08 memory used=320.3MB, alloc=108.3MB, time=6.86 memory used=401.0MB, alloc=140.3MB, time=8.34 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)]; 3 3 2 3 2 2 H := [20 y - 16 z , -17 y z + 11 z , 12 x y - 18 x z, -18 y z + 13, 2 3 2 -18 y z - 11, -6 z + 18 y ] > J:=[op(GB),op(G)]; 2 3 5 2 2 3 2 3 3 J := [x y , y , -2 x y + 3 x z, -55 y + 68 y z, -5 y + 4 z , -18 y z + 13, 2 3 2 -18 y z - 11, -6 z + 18 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 17, 3, 2, 3, 3, 1/6, 1, 1, 1/6, 1/2, 7/12, 8, 16, 27, 5, 2, 5, 3, 1/4, 1, 3/4, 3/16, 9/16, 3/8, -3, -10, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=449.9MB, alloc=140.3MB, time=9.93 |\^/| 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(); 1428247352 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 3 2 F := [10 x y - 16 z , 11 y - 20 z , -16 x - 6 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [1 + 18 x, -11 x y + 5 y z, -2 x z - 12 x ] > Problem := [F,G]; 2 3 2 2 3 2 Problem := [[10 x y - 16 z , 11 y - 20 z , -16 x - 6 y ], 2 2 2 2 [1 + 18 x, -11 x y + 5 y z, -2 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=26.7MB, alloc=32.3MB, time=0.50 memory used=48.5MB, alloc=32.3MB, time=0.82 memory used=69.5MB, alloc=32.3MB, time=1.13 memory used=89.8MB, alloc=56.3MB, time=1.44 memory used=130.2MB, alloc=60.3MB, time=2.05 memory used=169.1MB, alloc=84.3MB, time=2.65 memory used=219.5MB, alloc=84.3MB, time=3.50 memory used=279.4MB, alloc=116.3MB, time=4.64 memory used=358.5MB, alloc=140.3MB, time=6.06 memory used=454.9MB, alloc=164.3MB, time=7.79 memory used=568.3MB, alloc=188.3MB, time=9.86 memory used=696.0MB, alloc=212.3MB, time=12.20 memory used=797.7MB, alloc=492.3MB, time=14.16 memory used=948.6MB, alloc=516.3MB, time=17.44 memory used=1096.3MB, alloc=540.3MB, time=22.00 memory used=1251.2MB, alloc=564.3MB, time=27.22 memory used=1417.9MB, alloc=588.3MB, time=33.35 memory used=1598.0MB, alloc=612.3MB, time=40.61 memory used=1799.1MB, alloc=636.3MB, time=48.86 memory used=2024.0MB, alloc=660.3MB, time=58.15 memory used=2272.9MB, alloc=660.3MB, time=68.55 memory used=2521.7MB, alloc=660.3MB, time=78.76 memory used=2770.5MB, alloc=684.3MB, time=88.99 memory used=3043.3MB, alloc=684.3MB, time=100.25 |\^/| 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(); 1428247652 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-14 x z + 17 x, -8 y - 17 z, -12 x y z - 14 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [15 x y - 20 y z, 4 x z - 9 x, 12 x + x y] > Problem := [F,G]; 2 2 Problem := [[-14 x z + 17 x, -8 y - 17 z, -12 x y z - 14 x y], 2 2 3 [15 x y - 20 y z, 4 x z - 9 x, 12 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=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.5MB, alloc=32.3MB, time=0.80 memory used=67.3MB, alloc=32.3MB, time=1.09 memory used=86.4MB, alloc=56.3MB, time=1.39 memory used=125.0MB, alloc=60.3MB, time=1.99 memory used=160.8MB, alloc=60.3MB, time=2.52 memory used=195.0MB, alloc=84.3MB, time=3.05 memory used=249.4MB, alloc=84.3MB, time=3.87 memory used=301.7MB, alloc=108.3MB, time=4.69 memory used=373.8MB, alloc=116.3MB, time=5.80 memory used=446.2MB, alloc=140.3MB, time=7.11 memory used=532.8MB, alloc=164.3MB, time=8.69 memory used=632.7MB, alloc=188.3MB, time=10.53 memory used=744.7MB, alloc=212.3MB, time=12.61 memory used=867.0MB, alloc=236.3MB, time=14.87 memory used=997.8MB, alloc=260.3MB, time=17.26 memory used=1123.1MB, alloc=540.3MB, time=20.18 memory used=1257.1MB, alloc=564.3MB, time=24.43 memory used=1400.9MB, alloc=588.3MB, time=29.37 memory used=1557.6MB, alloc=612.3MB, time=35.28 memory used=1728.2MB, alloc=636.3MB, time=41.59 memory used=1914.0MB, alloc=660.3MB, time=48.51 memory used=2111.4MB, alloc=684.3MB, time=56.79 memory used=2330.6MB, alloc=708.3MB, time=66.21 memory used=2573.8MB, alloc=732.3MB, time=76.23 memory used=2840.9MB, alloc=756.3MB, time=87.65 |\^/| 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(); 1428247952 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [-17 x y z + 16 z , 3 z - 16 y z, 18 y - y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 G := [-6 z - 9 y z, 18 - 5 y, 6 x y z + 15 x y] > Problem := [F,G]; 3 3 2 Problem := [[-17 x y z + 16 z , 3 z - 16 y z, 18 y - y], 3 [-6 z - 9 y z, 18 - 5 y, 6 x y z + 15 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=48.5MB, alloc=32.3MB, time=0.85 memory used=69.5MB, alloc=56.3MB, time=1.24 memory used=111.3MB, alloc=84.3MB, time=2.00 memory used=168.0MB, alloc=84.3MB, time=3.82 N1 := 1333 > GB := Basis(F, plex(op(vars))); 2 3 GB := [18 y - y, 51 x y z - 256 y z, 3 z - 16 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=221.5MB, alloc=84.3MB, time=4.82 N2 := 455 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 3 H := [-17 x y z + 16 z , 3 z - 16 y z, 18 y - y, -6 z - 9 y z, 18 - 5 y, 6 x y z + 15 x y] > J:=[op(GB),op(G)]; 2 3 3 J := [18 y - y, 51 x y z - 256 y z, 3 z - 16 y z, -6 z - 9 y z, 18 - 5 y, 6 x y 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, 12, 15, 3, 1, 2, 3, 1/3, 1, 2/3, 1/4, 2/3, 7/12, 6, 12, 15, 3, 1, 2, 3, 1/3, 1, 2/3, 1/4, 3/4, 7/12, 0, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=229.2MB, alloc=84.3MB, time=5.06 |\^/| 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(); 1428247970 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [-19 x y z + x z , -10 x - 20 x y , -3 x z + 3 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-15 x y + 13 x z , 3 x z, 16 y z + 5 x z] > Problem := [F,G]; 2 3 2 2 Problem := [[-19 x y z + x z , -10 x - 20 x y , -3 x z + 3 x y], 2 2 2 [-15 x y + 13 x z , 3 x z, 16 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.7MB, alloc=32.3MB, time=0.83 memory used=67.9MB, alloc=32.3MB, time=1.13 memory used=86.8MB, alloc=56.3MB, time=1.43 memory used=129.9MB, alloc=60.3MB, time=2.18 memory used=168.4MB, alloc=84.3MB, time=2.86 memory used=225.1MB, alloc=108.3MB, time=3.86 memory used=297.8MB, alloc=132.3MB, time=6.25 N1 := 1903 > GB := Basis(F, plex(op(vars))); 4 3 3 2 3 2 2 3 GB := [19 x - x , 19 x y - x y, x + 2 x y , x z - x y, 19 x + 2 x y z, 3 2 361 x + 2 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=389.5MB, alloc=132.3MB, time=8.69 memory used=484.4MB, alloc=140.3MB, time=10.16 memory used=569.6MB, alloc=420.3MB, time=11.50 memory used=685.6MB, alloc=444.3MB, time=13.31 memory used=826.8MB, alloc=468.3MB, time=15.61 memory used=983.9MB, alloc=492.3MB, time=18.49 memory used=1146.6MB, alloc=516.3MB, time=22.44 memory used=1294.8MB, alloc=540.3MB, time=28.68 memory used=1465.4MB, alloc=564.3MB, time=35.83 N2 := 3591 #save(Problem, "format.txt"); > if (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 := [-19 x y z + x z , -10 x - 20 x y , -3 x z + 3 x y, -15 x y + 13 x z , 2 3 z x, 16 y z + 5 x z] > J:=[op(GB),op(G)]; 4 3 3 2 3 2 2 3 J := [19 x - x , 19 x y - x y, x + 2 x y , x z - x y, 19 x + 2 x y z, 3 2 2 2 2 361 x + 2 x z , -15 x y + 13 x z , 3 z x, 16 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, 16, 17, 3, 3, 2, 2, 1, 5/6, 5/6, 10/13, 5/13, 7/13, 9, 21, 28, 4, 4, 2, 2, 1, 2/3, 2/3, 16/19, 7/19, 7/19, -5, -11, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1504.4MB, alloc=564.3MB, time=37.15 |\^/| 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(); 1428248092 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 2 F := [-8 x z + 19 z , 7 y - 7 y z , 16 x - 13 y z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [10 x z + 16 y z, 14 y z + x , 13 x + 4 z] > Problem := [F,G]; 2 2 3 2 3 2 Problem := [[-8 x z + 19 z , 7 y - 7 y z , 16 x - 13 y z ], 2 2 [10 x z + 16 y z, 14 y z + x , 13 x + 4 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.78 memory used=67.8MB, alloc=56.3MB, time=1.09 memory used=107.8MB, alloc=60.3MB, time=1.68 memory used=145.2MB, alloc=60.3MB, time=2.23 memory used=179.9MB, alloc=84.3MB, time=2.76 memory used=234.2MB, alloc=84.3MB, time=3.58 memory used=287.1MB, alloc=116.3MB, time=4.39 memory used=361.7MB, alloc=116.3MB, time=5.51 memory used=433.5MB, alloc=140.3MB, time=6.62 memory used=525.8MB, alloc=164.3MB, time=8.13 memory used=623.3MB, alloc=188.3MB, time=9.88 memory used=738.3MB, alloc=468.3MB, time=12.01 memory used=879.0MB, alloc=492.3MB, time=14.58 memory used=1031.2MB, alloc=516.3MB, time=17.39 memory used=1205.0MB, alloc=540.3MB, time=20.39 memory used=1391.0MB, alloc=564.3MB, time=23.65 memory used=1576.0MB, alloc=588.3MB, time=27.20 memory used=1763.5MB, alloc=612.3MB, time=31.46 memory used=1937.4MB, alloc=636.3MB, time=37.13 memory used=2115.3MB, alloc=660.3MB, time=43.29 memory used=2303.3MB, alloc=684.3MB, time=50.21 memory used=2503.8MB, alloc=708.3MB, time=57.97 memory used=2718.0MB, alloc=732.3MB, time=66.28 memory used=2942.5MB, alloc=756.3MB, time=75.83 memory used=3184.2MB, alloc=780.3MB, time=86.34 |\^/| 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(); 1428248392 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [8 x z - 13 z , -17 x z - 14 z , -14 x y - 8 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [8 y z - 5 x , -5 x y z - 17 y , 9 x - 2 y z ] > Problem := [F,G]; 2 2 2 2 Problem := [[8 x z - 13 z , -17 x z - 14 z , -14 x y - 8 y ], 2 2 2 3 2 [8 y z - 5 x , -5 x y z - 17 y , 9 x - 2 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.6MB, alloc=32.3MB, time=0.80 memory used=67.4MB, alloc=56.3MB, time=1.10 memory used=107.4MB, alloc=60.3MB, time=1.70 memory used=147.1MB, alloc=84.3MB, time=2.29 memory used=206.7MB, alloc=92.3MB, time=3.18 memory used=265.1MB, alloc=116.3MB, time=4.04 memory used=345.3MB, alloc=140.3MB, time=5.28 memory used=442.0MB, alloc=396.3MB, time=6.88 memory used=538.0MB, alloc=420.3MB, time=8.43 memory used=654.3MB, alloc=444.3MB, time=10.40 memory used=786.9MB, alloc=468.3MB, time=12.91 memory used=929.1MB, alloc=492.3MB, time=15.57 memory used=1082.7MB, alloc=516.3MB, time=18.63 memory used=1247.9MB, alloc=540.3MB, time=21.78 memory used=1428.6MB, alloc=564.3MB, time=25.26 memory used=1614.1MB, alloc=588.3MB, time=28.95 memory used=1805.3MB, alloc=612.3MB, time=32.93 memory used=1985.2MB, alloc=636.3MB, time=38.89 memory used=2169.1MB, alloc=660.3MB, time=45.45 memory used=2363.6MB, alloc=684.3MB, time=52.66 memory used=2571.1MB, alloc=708.3MB, time=60.63 memory used=2792.2MB, alloc=732.3MB, time=69.40 memory used=3025.2MB, alloc=756.3MB, time=78.97 memory used=3270.6MB, alloc=780.3MB, time=89.76 memory used=3539.9MB, alloc=804.3MB, time=101.55 |\^/| 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(); 1428248692 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-8 x z - 11 x, 14 x y + 8 y z , -16 x z - 18 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [15 y + 14 x y, -13 z - 10 z, 12 x y z - 9 x ] > Problem := [F,G]; 2 2 2 2 Problem := [[-8 x z - 11 x, 14 x y + 8 y z , -16 x z - 18 y], 3 3 2 [15 y + 14 x y, -13 z - 10 z, 12 x 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=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.81 memory used=67.7MB, alloc=32.3MB, time=1.13 memory used=86.8MB, alloc=56.3MB, time=1.45 memory used=127.1MB, alloc=60.3MB, time=2.05 memory used=164.5MB, alloc=84.3MB, time=2.64 memory used=213.0MB, alloc=84.3MB, time=3.42 memory used=268.4MB, alloc=116.3MB, time=4.34 memory used=346.5MB, alloc=116.3MB, time=5.76 memory used=417.6MB, alloc=140.3MB, time=7.11 memory used=507.5MB, alloc=164.3MB, time=8.77 memory used=612.8MB, alloc=188.3MB, time=11.28 memory used=719.8MB, alloc=212.3MB, time=15.13 memory used=845.9MB, alloc=236.3MB, time=19.92 N1 := 3443 > GB := Basis(F, plex(op(vars))); 5 3 4 GB := [112 x + 121 x, -14 x + 9 y, -14 x + 11 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1000.3MB, alloc=236.3MB, time=24.78 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 3 H := [-8 x z - 11 x, 14 x y + 8 y z , -16 x z - 18 y, 15 y + 14 x y, 3 2 -13 z - 10 z, 12 x y z - 9 x ] > J:=[op(GB),op(G)]; 5 3 4 3 J := [112 x + 121 x, -14 x + 9 y, -14 x + 11 x z, 15 y + 14 x y, 3 2 -13 z - 10 z, 12 x 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, 14, 18, 3, 2, 3, 3, 5/6, 2/3, 5/6, 7/12, 1/2, 1/2, 6, 11, 21, 5, 5, 3, 3, 5/6, 1/2, 1/2, 2/3, 1/3, 1/3, 3, -3, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1063.4MB, alloc=236.3MB, time=25.98 |\^/| 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(); 1428248767 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [9 y z + 19 x, 15 x z + 13 y , 11 z - 16 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 2 G := [-15 x y + 11 y z , 5 x - y , -11 x y + 5 z ] > Problem := [F,G]; 2 3 2 Problem := [[9 y z + 19 x, 15 x z + 13 y , 11 z - 16 x], 2 2 3 3 2 2 [-15 x y + 11 y z , 5 x - y , -11 x y + 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=47.8MB, alloc=32.3MB, time=0.81 memory used=68.2MB, alloc=56.3MB, time=1.13 memory used=109.9MB, alloc=60.3MB, time=1.72 memory used=150.2MB, alloc=84.3MB, time=2.31 memory used=215.5MB, alloc=92.3MB, time=3.20 memory used=278.5MB, alloc=116.3MB, time=4.08 memory used=359.6MB, alloc=116.3MB, time=5.25 memory used=425.0MB, alloc=396.3MB, time=6.27 memory used=532.6MB, alloc=396.3MB, time=7.74 memory used=636.6MB, alloc=420.3MB, time=9.33 memory used=762.8MB, alloc=444.3MB, time=11.18 memory used=906.7MB, alloc=468.3MB, time=13.28 memory used=1043.3MB, alloc=492.3MB, time=15.20 memory used=1152.6MB, alloc=492.3MB, time=16.77 memory used=1263.0MB, alloc=492.3MB, time=18.39 memory used=1399.0MB, alloc=516.3MB, time=21.07 memory used=1568.4MB, alloc=540.3MB, time=24.41 memory used=1727.1MB, alloc=564.3MB, time=27.53 memory used=1895.2MB, alloc=588.3MB, time=31.00 memory used=2056.7MB, alloc=612.3MB, time=34.31 memory used=2208.1MB, alloc=636.3MB, time=37.49 memory used=2358.3MB, alloc=660.3MB, time=40.63 memory used=2476.0MB, alloc=684.3MB, time=43.21 memory used=2613.1MB, alloc=708.3MB, time=46.21 memory used=2716.0MB, alloc=732.3MB, time=48.87 memory used=2907.3MB, alloc=756.3MB, time=55.40 memory used=3106.1MB, alloc=780.3MB, time=62.78 memory used=3389.1MB, alloc=804.3MB, time=73.62 memory used=3678.1MB, alloc=828.3MB, time=85.23 memory used=3975.5MB, alloc=852.3MB, time=97.35 |\^/| 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(); 1428249067 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-9 x y - 5 x, 7 x - 4 z , 20 x y - 8 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [16 x y + z , 7 x z - 20 x y, -18 x y + y z] > Problem := [F,G]; 2 2 2 Problem := [[-9 x y - 5 x, 7 x - 4 z , 20 x y - 8 x z], 2 2 2 2 [16 x y + z , 7 x z - 20 x y, -18 x y + y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=47.9MB, alloc=32.3MB, time=0.80 memory used=68.1MB, alloc=32.3MB, time=1.10 memory used=87.1MB, alloc=56.3MB, time=1.39 memory used=126.3MB, alloc=60.3MB, time=1.98 memory used=163.4MB, alloc=84.3MB, time=2.55 memory used=216.8MB, alloc=84.3MB, time=3.36 memory used=275.8MB, alloc=92.3MB, time=4.21 memory used=332.2MB, alloc=116.3MB, time=5.10 memory used=408.9MB, alloc=116.3MB, time=6.26 memory used=484.6MB, alloc=140.3MB, time=7.42 memory used=574.8MB, alloc=140.3MB, time=8.83 memory used=657.6MB, alloc=420.3MB, time=10.18 memory used=775.0MB, alloc=444.3MB, time=12.37 memory used=905.0MB, alloc=468.3MB, time=14.72 memory used=1043.3MB, alloc=492.3MB, time=17.34 memory used=1191.8MB, alloc=516.3MB, time=20.26 memory used=1351.0MB, alloc=540.3MB, time=23.35 memory used=1520.7MB, alloc=564.3MB, time=26.67 memory used=1701.9MB, alloc=588.3MB, time=30.16 memory used=1893.1MB, alloc=612.3MB, time=33.83 memory used=2087.9MB, alloc=636.3MB, time=37.68 memory used=2286.7MB, alloc=660.3MB, time=41.69 memory used=2490.4MB, alloc=684.3MB, time=45.93 memory used=2678.7MB, alloc=708.3MB, time=51.85 memory used=2865.8MB, alloc=732.3MB, time=58.57 memory used=3062.5MB, alloc=756.3MB, time=65.93 memory used=3271.4MB, alloc=780.3MB, time=74.18 memory used=3493.8MB, alloc=804.3MB, time=83.17 memory used=3729.4MB, alloc=828.3MB, time=92.67 |\^/| 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(); 1428249367 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 F := [-8 x y z - 18 x, 0, -14 x + 7 x y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [6 y z + 4 x, -12 x y - 5 y z, 6 x y + 13 x y z] > Problem := [F,G]; 3 2 Problem := [[-8 x y z - 18 x, 0, -14 x + 7 x y ], 2 2 [6 y z + 4 x, -12 x y - 5 y z, 6 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=31.7MB, alloc=40.3MB, time=0.56 memory used=59.8MB, alloc=40.3MB, time=0.95 memory used=88.2MB, alloc=64.3MB, time=1.46 memory used=136.6MB, alloc=68.3MB, time=2.32 memory used=180.1MB, alloc=92.3MB, time=3.10 memory used=242.8MB, alloc=92.3MB, time=4.21 memory used=299.2MB, alloc=116.3MB, time=5.23 memory used=373.4MB, alloc=148.3MB, time=6.62 memory used=460.4MB, alloc=172.3MB, time=9.02 memory used=560.7MB, alloc=196.3MB, time=12.18 memory used=672.8MB, alloc=220.3MB, time=16.48 memory used=808.8MB, alloc=220.3MB, time=21.65 memory used=944.8MB, alloc=220.3MB, time=26.84 memory used=1080.9MB, alloc=244.3MB, time=32.05 memory used=1240.8MB, alloc=244.3MB, time=38.14 N1 := 5403 > GB := Basis(F, plex(op(vars))); 3 2 3 GB := [-2 x + x y , 8 x z + 9 x y, 4 x y z + 9 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1403.4MB, alloc=244.3MB, time=42.86 memory used=1490.6MB, alloc=500.3MB, time=44.34 memory used=1661.8MB, alloc=524.3MB, time=47.39 memory used=1840.2MB, alloc=548.3MB, time=50.70 memory used=2027.1MB, alloc=572.3MB, time=54.21 memory used=2221.8MB, alloc=596.3MB, time=57.99 memory used=2425.5MB, alloc=620.3MB, time=61.87 memory used=2641.4MB, alloc=644.3MB, time=68.40 memory used=2849.0MB, alloc=668.3MB, time=75.99 memory used=3066.5MB, alloc=692.3MB, time=84.26 memory used=3297.0MB, alloc=716.3MB, time=93.49 |\^/| 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(); 1428249667 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-18 y - 11 z, 5 - y, 19 x - 7 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [8 x y - 8 y z , 12 x - 19 z, -16 x y z + 17 z] > Problem := [F,G]; 2 2 Problem := [[-18 y - 11 z, 5 - y, 19 x - 7 y ], 2 2 2 [8 x y - 8 y z , 12 x - 19 z, -16 x y z + 17 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=47.3MB, alloc=32.3MB, time=0.75 memory used=68.3MB, alloc=32.3MB, time=1.04 memory used=88.2MB, alloc=32.3MB, time=1.32 memory used=106.7MB, alloc=56.3MB, time=1.60 memory used=148.7MB, alloc=60.3MB, time=2.34 memory used=184.5MB, alloc=84.3MB, time=2.99 memory used=239.5MB, alloc=108.3MB, time=3.96 memory used=310.5MB, alloc=132.3MB, time=5.22 memory used=395.1MB, alloc=164.3MB, time=7.29 memory used=488.2MB, alloc=188.3MB, time=10.15 memory used=594.5MB, alloc=212.3MB, time=14.19 memory used=724.7MB, alloc=212.3MB, time=19.04 memory used=855.0MB, alloc=212.3MB, time=23.87 memory used=985.1MB, alloc=236.3MB, time=28.73 memory used=1139.4MB, alloc=260.3MB, time=34.44 N1 := 5029 > GB := Basis(F, plex(op(vars))); 2 GB := [19 x - 175, y - 5, 11 z + 90] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); 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 2 2 2 H := [-18 y - 11 z, 5 - y, -7 y + 19 x , 8 x y - 8 y z , 12 x - 19 z, -16 x y z + 17 z] > J:=[op(GB),op(G)]; 2 2 2 2 J := [19 x - 175, y - 5, 11 z + 90, 8 x y - 8 y z , 12 x - 19 z, -16 x y 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, 13, 12, 3, 2, 2, 2, 2/3, 5/6, 2/3, 1/3, 1/2, 5/12, 6, 11, 12, 3, 2, 1, 2, 2/3, 1/2, 2/3, 1/3, 1/3, 5/12, 2, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1299.6MB, alloc=260.3MB, time=38.00 |\^/| 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(); 1428249779 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-x z + 15 y , -3 x - 20 x y, 7 x z - 7 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 G := [8 y - 10 z , 18 x y, 16 y z - 4 z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-x z + 15 y , -3 x - 20 x y, 7 x z - 7 x ], 3 3 2 2 3 [8 y - 10 z , 18 x y, 16 y z - 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=48.4MB, alloc=32.3MB, time=0.81 memory used=69.9MB, alloc=56.3MB, time=1.19 memory used=114.2MB, alloc=60.3MB, time=1.96 memory used=154.5MB, alloc=84.3MB, time=2.66 memory used=211.1MB, alloc=116.3MB, time=3.84 memory used=275.4MB, alloc=140.3MB, time=6.26 N1 := 2163 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 2 GB := [x , 3 x + 20 x y, -x + 15 y , x z - x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=366.0MB, alloc=140.3MB, time=8.88 memory used=466.7MB, alloc=164.3MB, time=10.68 memory used=579.8MB, alloc=188.3MB, time=14.61 N2 := 1767 #save(Problem, "format.txt"); > if (GB=[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 := [-x z + 15 y , -3 x - 20 x y, 7 x z - 7 x , 8 y - 10 z , 18 y x , 2 3 16 y z - 4 z ] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 3 3 2 J := [x , 3 x + 20 x y, -x + 15 y , x z - x , 8 y - 10 z , 18 y x , 2 3 16 y z - 4 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 17, 3, 2, 3, 3, 2/3, 5/6, 2/3, 6/13, 5/13, 5/13, 7, 13, 19, 3, 3, 3, 3, 5/7, 5/7, 3/7, 7/15, 1/3, 4/15, 0, -2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=584.5MB, alloc=188.3MB, time=14.73 |\^/| 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(); 1428249824 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [9 x y - 15 y , -5 x y z + 10 x z , -3 z - 2 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [5 z + 20 z, -11 x y + 6 x y, -2 x y - 20 y z] > Problem := [F,G]; 2 2 2 3 2 Problem := [[9 x y - 15 y , -5 x y z + 10 x z , -3 z - 2 x ], 3 2 [5 z + 20 z, -11 x y + 6 x y, -2 x y - 20 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.47 memory used=47.4MB, alloc=32.3MB, time=0.77 memory used=67.4MB, alloc=32.3MB, time=1.07 memory used=88.2MB, alloc=56.3MB, time=1.47 N1 := 565 > GB := Basis(F, plex(op(vars))); 7 3 5 3 2 2 5 3 GB := [81 x + 2000 x , -3 x + 5 x y, -3 x y + 5 y , -3 x + 10 x z, 2 3 2 -x y z + 2 x z , 3 z + 2 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=128.7MB, alloc=60.3MB, time=2.27 memory used=167.9MB, alloc=60.3MB, time=2.82 memory used=206.0MB, alloc=60.3MB, time=3.39 memory used=245.1MB, alloc=84.3MB, time=4.10 N2 := 673 #save(Problem, "format.txt"); > if (GB=[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 H := [9 x y - 15 y , -5 x y z + 10 x z , -3 z - 2 x , 5 z + 20 z, 2 -11 x y + 6 x y, -2 x y - 20 y z] > J:=[op(GB),op(G)]; 7 3 5 3 2 2 5 3 J := [81 x + 2000 x , -3 x + 5 x y, -3 x y + 5 y , -3 x + 10 x z, 2 3 2 3 2 -x y z + 2 x z , 3 z + 2 x , 5 z + 20 z, -11 x y + 6 x y, -2 x y - 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, 17, 3, 2, 2, 3, 5/6, 2/3, 2/3, 7/12, 7/12, 1/2, 9, 18, 34, 7, 7, 2, 3, 8/9, 5/9, 5/9, 13/18, 4/9, 7/18, -5, -17, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=260.4MB, alloc=84.3MB, time=4.51 |\^/| 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(); 1428249838 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 F := [20 y + 8 z, -10 x y + 6, 4 y z + 16] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [-8 x - 15 y , -12 z + 3 y , 10 x z + 12 y z] > Problem := [F,G]; 2 Problem := [[20 y + 8 z, -10 x y + 6, 4 y z + 16], 2 2 3 2 2 [-8 x - 15 y , -12 z + 3 y , 10 x 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.4MB, alloc=32.3MB, time=0.79 memory used=67.9MB, alloc=32.3MB, time=1.09 memory used=87.8MB, alloc=32.3MB, time=1.38 memory used=106.6MB, alloc=56.3MB, time=1.66 memory used=147.9MB, alloc=60.3MB, time=2.38 memory used=185.3MB, alloc=84.3MB, time=3.10 memory used=242.2MB, alloc=108.3MB, time=4.13 memory used=314.8MB, alloc=132.3MB, time=5.80 memory used=396.0MB, alloc=156.3MB, time=8.64 memory used=497.0MB, alloc=156.3MB, time=12.41 N1 := 2899 > GB := Basis(F, plex(op(vars))); 2 GB := [8 x - 3, 5 y - 8, 2 z + 5 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=599.4MB, alloc=156.3MB, time=15.30 N2 := 853 #save(Problem, "format.txt"); > if (GB=[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 y + 8 z, -10 x y + 6, 4 y z + 16, -8 x - 15 y , -12 z + 3 y , 2 10 x z + 12 y z] > J:=[op(GB),op(G)]; 2 2 2 3 2 J := [8 x - 3, 5 y - 8, 2 z + 5 y, -8 x - 15 y , -12 z + 3 y , 2 10 x z + 12 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, 14, 3, 2, 2, 3, 1/2, 1, 2/3, 1/4, 1/2, 5/12, 6, 11, 12, 3, 2, 2, 3, 1/2, 5/6, 1/2, 1/4, 5/12, 1/3, 2, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=686.9MB, alloc=156.3MB, time=17.12 |\^/| 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(); 1428249892 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-19 y z - 20, 17 x y + 2 x z, -8 x y z + 10] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-7 y + 17 z, -9 y z - 14 z , -9 y - 7 x] > Problem := [F,G]; 2 2 Problem := [[-19 y z - 20, 17 x y + 2 x z, -8 x y z + 10], 2 3 2 [-7 y + 17 z, -9 y z - 14 z , -9 y - 7 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.47 memory used=48.1MB, alloc=32.3MB, time=0.78 memory used=68.6MB, alloc=32.3MB, time=1.08 memory used=88.7MB, alloc=56.3MB, time=1.39 memory used=128.9MB, alloc=60.3MB, time=1.98 memory used=166.1MB, alloc=84.3MB, time=2.53 memory used=220.6MB, alloc=84.3MB, time=3.33 memory used=277.1MB, alloc=116.3MB, time=4.21 memory used=353.9MB, alloc=116.3MB, time=5.43 memory used=426.3MB, alloc=140.3MB, time=6.72 memory used=518.0MB, alloc=164.3MB, time=8.33 memory used=623.4MB, alloc=188.3MB, time=10.29 memory used=738.1MB, alloc=212.3MB, time=13.65 memory used=857.3MB, alloc=236.3MB, time=18.30 memory used=1000.6MB, alloc=260.3MB, time=23.90 memory used=1168.2MB, alloc=284.3MB, time=30.42 N1 := 4101 > GB := Basis(F, plex(op(vars))); 2 GB := [2048 x + 30685, 323 y - 32, 16 x + 19 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 627 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-19 y z - 20, 17 x y + 2 x z, -8 x y z + 10, -7 y + 17 z, 2 3 2 -9 y z - 14 z , -9 y - 7 x] > J:=[op(GB),op(G)]; 2 2 3 J := [2048 x + 30685, 323 y - 32, 19 z + 16 x, -7 y + 17 z, -9 y z - 14 z , 2 -9 y - 7 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 15, 3, 2, 2, 3, 1/2, 1, 5/6, 1/3, 1/2, 1/2, 6, 10, 10, 3, 2, 2, 3, 1/2, 2/3, 1/2, 1/4, 1/3, 1/3, 4, 5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1276.1MB, alloc=284.3MB, time=32.41 |\^/| 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(); 1428249990 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 F := [19 x - 10 y, -2 x y - 15 z, -10 x z - 14 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [-9 z - 11 x z, 17 x y - 17 x y, 11 y - 12 x ] > Problem := [F,G]; 3 2 Problem := [[19 x - 10 y, -2 x y - 15 z, -10 x z - 14 z ], 3 2 3 2 [-9 z - 11 x z, 17 x y - 17 x y, 11 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=0.17 memory used=26.1MB, alloc=32.3MB, time=0.47 memory used=47.3MB, alloc=32.3MB, time=0.76 memory used=67.9MB, alloc=32.3MB, time=1.05 memory used=87.8MB, alloc=56.3MB, time=1.36 memory used=131.7MB, alloc=60.3MB, time=2.15 memory used=170.5MB, alloc=84.3MB, time=2.82 memory used=226.7MB, alloc=108.3MB, time=3.84 memory used=297.9MB, alloc=132.3MB, time=5.90 memory used=382.6MB, alloc=132.3MB, time=9.04 memory used=467.4MB, alloc=156.3MB, time=12.04 N1 := 2633 > GB := Basis(F, plex(op(vars))); 8 5 3 4 GB := [133 x - 375 x , -19 x + 10 y, 19 x + 75 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=575.0MB, alloc=164.3MB, time=14.11 N2 := 759 #save(Problem, "format.txt"); > 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 H := [19 x - 10 y, -2 x y - 15 z, -10 x z - 14 z , -9 z - 11 x z, 2 3 2 17 x y - 17 x y, 11 y - 12 x ] > J:=[op(GB),op(G)]; 8 5 3 4 3 J := [133 x - 375 x , -19 x + 10 y, 19 x + 75 z, -9 z - 11 x z, 2 3 2 17 x y - 17 x y, 11 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, 13, 16, 3, 3, 3, 3, 1, 2/3, 1/2, 7/12, 5/12, 5/12, 6, 11, 24, 8, 8, 3, 3, 1, 1/2, 1/3, 2/3, 1/3, 1/4, 2, -8, -5] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=576.5MB, alloc=164.3MB, time=14.17 |\^/| 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(); 1428250031 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [6 z + 4, -14 y , 7 y z + 6 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-7 x y + 4 x, -17 y + 7 z, -4 x z - 13 x] > Problem := [F,G]; 3 2 2 Problem := [[6 z + 4, -14 y , 7 y z + 6 y z], 2 3 2 [-7 x y + 4 x, -17 y + 7 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.48 memory used=48.4MB, alloc=32.3MB, time=0.86 memory used=68.7MB, alloc=56.3MB, time=1.22 memory used=109.2MB, alloc=84.3MB, time=2.04 N1 := 1091 > GB := Basis(F, plex(op(vars))); 3 GB := [y, 3 z + 2] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=167.2MB, alloc=84.3MB, time=3.40 N2 := 569 #save(Problem, "format.txt"); > 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 := [6 z + 4, -14 y , 7 y z + 6 y z, -7 x y + 4 x, -17 y + 7 z, 2 -4 x z - 13 x] > J:=[op(GB),op(G)]; 3 2 3 2 J := [y, 3 z + 2, -7 x y + 4 x, -17 y + 7 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, 10, 17, 3, 2, 3, 3, 1/3, 2/3, 2/3, 1/3, 5/12, 5/12, 5, 8, 13, 3, 2, 3, 3, 2/5, 3/5, 3/5, 4/9, 1/3, 1/3, 2, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=209.3MB, alloc=84.3MB, time=4.22 |\^/| 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(); 1428250044 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-13 y z - 7 y z, -6 x + 10 x y, -6 x y + 10 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-3 x - 19 x, 13 x y z - 18, -14 x z - 9 x ] > Problem := [F,G]; 2 2 2 Problem := [[-13 y z - 7 y z, -6 x + 10 x y, -6 x y + 10 z], 3 2 2 [-3 x - 19 x, 13 x y z - 18, -14 x z - 9 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.79 memory used=67.8MB, alloc=32.3MB, time=1.07 memory used=86.6MB, alloc=56.3MB, time=1.36 memory used=128.5MB, alloc=60.3MB, time=2.09 memory used=166.2MB, alloc=84.3MB, time=2.76 memory used=222.1MB, alloc=108.3MB, time=3.77 memory used=293.0MB, alloc=132.3MB, time=5.68 memory used=375.1MB, alloc=132.3MB, time=8.74 memory used=457.2MB, alloc=156.3MB, time=11.72 N1 := 2643 > GB := Basis(F, plex(op(vars))); 7 4 2 3 GB := [351 x + 875 x , -3 x + 5 x y, -27 x + 125 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 431 #save(Problem, "format.txt"); > if (GB=[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 := [-13 y z - 7 y z, -6 x + 10 x y, -6 x y + 10 z, -3 x - 19 x, 2 2 13 z y x - 18, -14 x z - 9 x ] > J:=[op(GB),op(G)]; 7 4 2 3 3 J := [351 x + 875 x , -3 x + 5 x y, -27 x + 125 z, -3 x - 19 x, 2 2 13 z y x - 18, -14 x 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, 3, 3, 2, 2, 5/6, 2/3, 2/3, 2/3, 5/12, 5/12, 6, 11, 21, 7, 7, 1, 1, 1, 1/3, 1/2, 5/6, 1/6, 1/4, 2, -4, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=529.4MB, alloc=164.3MB, time=13.07 |\^/| 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(); 1428250085 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-16 x y z - 13 y z , 11 x z + 15 y , -6 y z - 4 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [11 x z - 4 z, -7 x z - 7 x z, -4 x y z + 7 z ] > Problem := [F,G]; 2 2 3 2 Problem := [[-16 x y z - 13 y z , 11 x z + 15 y , -6 y z - 4 y z], 2 2 3 [11 x z - 4 z, -7 x z - 7 x z, -4 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=26.1MB, alloc=32.3MB, time=0.48 memory used=47.4MB, alloc=32.3MB, time=0.77 memory used=67.9MB, alloc=56.3MB, time=1.09 memory used=108.6MB, alloc=60.3MB, time=1.68 memory used=146.9MB, alloc=60.3MB, time=2.23 memory used=182.6MB, alloc=84.3MB, time=2.76 memory used=228.5MB, alloc=84.3MB, time=3.54 memory used=282.5MB, alloc=108.3MB, time=4.50 memory used=354.9MB, alloc=140.3MB, time=5.80 memory used=445.0MB, alloc=164.3MB, time=7.37 memory used=548.4MB, alloc=188.3MB, time=9.21 memory used=661.4MB, alloc=212.3MB, time=12.12 memory used=777.8MB, alloc=236.3MB, time=15.57 memory used=902.4MB, alloc=260.3MB, time=20.19 memory used=1047.3MB, alloc=284.3MB, time=25.77 memory used=1216.0MB, alloc=284.3MB, time=32.27 memory used=1384.8MB, alloc=308.3MB, time=38.75 memory used=1577.5MB, alloc=308.3MB, time=46.11 memory used=1770.1MB, alloc=308.3MB, time=53.59 memory used=1962.9MB, alloc=332.3MB, time=61.08 memory used=2179.6MB, alloc=356.3MB, time=69.47 N1 := 7303 > GB := Basis(F, plex(op(vars))); GB := 4 4 7 4 2 3 4 [24 x y - 13 y , 12960 y - 1859 y , 11 z x + 15 y , 8640 y + 1859 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2305.7MB, alloc=356.3MB, time=72.67 memory used=2536.7MB, alloc=612.3MB, time=76.85 memory used=2804.2MB, alloc=636.3MB, time=85.81 |\^/| 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(); 1428250385 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [-15 x z - 6 x y, 7 x - 12 y z, -6 z - 11 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [-13 x z , 16 y z + 20 z , 17 z - 17 z ] > Problem := [F,G]; 2 3 2 2 Problem := [[-15 x z - 6 x y, 7 x - 12 y z, -6 z - 11 x], 2 2 2 3 2 [-13 x z , 16 y z + 20 z , 17 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=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.81 memory used=67.8MB, alloc=56.3MB, time=1.11 memory used=108.1MB, alloc=60.3MB, time=1.72 memory used=149.1MB, alloc=84.3MB, time=2.44 memory used=208.4MB, alloc=84.3MB, time=3.45 memory used=261.9MB, alloc=108.3MB, time=4.40 memory used=331.0MB, alloc=140.3MB, time=5.94 memory used=408.2MB, alloc=164.3MB, time=8.59 memory used=503.8MB, alloc=164.3MB, time=12.24 memory used=599.5MB, alloc=188.3MB, time=15.86 N1 := 3313 > GB := Basis(F, plex(op(vars))); 5 4 4 2 4 2 GB := [831875 x + 1176 x , 15125 x + 168 x y, 275 x + 24 x y , 2 3 3 2 2 5 x z + 2 x y, -55 x + 12 x y z, -7 x + 12 y z, 6 z + 11 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=721.6MB, alloc=188.3MB, time=18.89 memory used=814.0MB, alloc=444.3MB, time=20.36 memory used=938.9MB, alloc=468.3MB, time=22.27 memory used=1087.6MB, alloc=492.3MB, time=24.70 memory used=1262.0MB, alloc=516.3MB, time=27.82 memory used=1447.7MB, alloc=540.3MB, time=31.16 memory used=1634.4MB, alloc=564.3MB, time=35.41 memory used=1808.4MB, alloc=588.3MB, time=41.26 memory used=1985.8MB, alloc=612.3MB, time=48.36 memory used=2179.2MB, alloc=636.3MB, time=56.59 memory used=2396.6MB, alloc=660.3MB, time=65.76 memory used=2637.9MB, alloc=684.3MB, time=75.97 memory used=2903.2MB, alloc=708.3MB, time=87.03 memory used=3192.6MB, alloc=732.3MB, time=99.13 |\^/| 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(); 1428250685 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [2 x z + 14 z, 15 x z + 15 z , -z + 4] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-16 y - 10 x y, -4 x y + 10 x y , -5 x - 4 y] > Problem := [F,G]; 2 2 2 2 Problem := [[2 x z + 14 z, 15 x z + 15 z , -z + 4], 3 2 2 2 [-16 y - 10 x y, -4 x y + 10 x y , -5 x - 4 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.46 memory used=47.2MB, alloc=32.3MB, time=0.77 memory used=68.5MB, alloc=56.3MB, time=1.16 memory used=109.2MB, alloc=80.3MB, time=2.10 N1 := 1011 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 81 #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 H := [2 x z + 14 z, 15 x z + 15 z , -z + 4, -16 y - 10 x y, 2 2 2 -4 x y + 10 x y , -5 x - 4 y] > J:=[op(GB),op(G)]; 3 2 2 2 J := [1, -16 y - 10 x y, -4 x y + 10 x y , -5 x - 4 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 11, 16, 3, 2, 3, 2, 5/6, 1/2, 1/2, 1/2, 5/12, 5/12, 4, 6, 8, 3, 2, 3, 0, 3/4, 3/4, 0, 4/7, 5/7, 0, 5, 8, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=142.3MB, alloc=80.3MB, 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(); 1428250694 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 F := [-13 z + 1, 15 z + 2 z , -17 y - z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [10 x + 8 y , 3 x z - 11 y z , -15 x y z + 20] > Problem := [F,G]; 3 3 2 2 2 Problem := [[-13 z + 1, 15 z + 2 z , -17 y - z ], 2 2 2 2 [10 x + 8 y , 3 x z - 11 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=48.0MB, alloc=32.3MB, time=0.82 memory used=67.9MB, alloc=56.3MB, time=1.13 memory used=108.7MB, alloc=60.3MB, time=1.76 memory used=146.1MB, alloc=60.3MB, time=2.34 memory used=182.6MB, alloc=84.3MB, time=2.90 memory used=225.2MB, alloc=84.3MB, time=3.54 memory used=282.9MB, alloc=116.3MB, time=4.43 memory used=363.6MB, alloc=116.3MB, time=5.62 memory used=440.2MB, alloc=140.3MB, time=6.79 memory used=527.4MB, alloc=420.3MB, time=8.25 memory used=640.1MB, alloc=444.3MB, time=10.36 memory used=752.8MB, alloc=468.3MB, time=14.36 N1 := 1887 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 73 #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 2 2 2 2 H := [-13 z + 1, 15 z + 2 z , -17 y - z , 10 x + 8 y , 3 x z - 11 y z , -15 x y z + 20] > J:=[op(GB),op(G)]; 2 2 2 2 J := [1, 10 x + 8 y , 3 x z - 11 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, 12, 16, 3, 2, 2, 3, 1/2, 2/3, 5/6, 1/4, 1/3, 7/12, 4, 8, 8, 3, 2, 2, 2, 3/4, 3/4, 1/2, 3/7, 3/7, 3/7, 4, 8, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=772.5MB, alloc=468.3MB, time=14.74 |\^/| 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(); 1428250736 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 F := [12 x - 17, -20 x y z, 16 x - 2 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 G := [-6 x z - 18 z, -18 x + 20 z , -16 x + 13 z] > Problem := [F,G]; 3 Problem := [[12 x - 17, -20 x y z, 16 x - 2 z], 2 3 3 2 [-6 x z - 18 z, -18 x + 20 z , -16 x + 13 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.49 memory used=48.5MB, alloc=56.3MB, time=0.92 N1 := 321 > GB := Basis(F, plex(op(vars))); 3 GB := [12 x - 17, y, z - 8 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=88.8MB, alloc=60.3MB, time=1.55 N2 := 321 #save(Problem, "format.txt"); > 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 := [12 x - 17, -20 x y z, 16 x - 2 z, -6 x z - 18 z, -18 x + 20 z , 2 -16 x + 13 z] > J:=[op(GB),op(G)]; 3 2 3 3 2 J := [12 x - 17, y, z - 8 x, -6 x z - 18 z, -18 x + 20 z , -16 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, 12, 15, 3, 3, 1, 3, 1, 1/6, 5/6, 3/7, 1/14, 3/7, 6, 10, 13, 3, 3, 1, 3, 5/6, 1/6, 2/3, 5/11, 1/11, 5/11, 2, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=92.7MB, 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(); 1428250741 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [5 y - 9 x , -17 y + 17 y, 4 x y z - 9 x z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [8 x y - 9, 12 x y - 12 x y z, -7 x + 18 x z ] > Problem := [F,G]; 3 2 3 2 Problem := [[5 y - 9 x , -17 y + 17 y, 4 x y z - 9 x z ], 2 2 3 2 [8 x y - 9, 12 x y - 12 x y z, -7 x + 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=0.17 memory used=26.1MB, alloc=32.3MB, time=0.47 memory used=46.9MB, alloc=32.3MB, time=0.74 memory used=68.2MB, alloc=32.3MB, time=1.05 memory used=88.2MB, alloc=32.3MB, time=1.34 memory used=107.4MB, alloc=56.3MB, time=1.65 memory used=150.4MB, alloc=60.3MB, time=2.44 memory used=187.0MB, alloc=84.3MB, time=3.12 memory used=243.5MB, alloc=108.3MB, time=4.14 memory used=317.1MB, alloc=132.3MB, time=5.45 memory used=406.2MB, alloc=164.3MB, time=7.11 memory used=503.6MB, alloc=188.3MB, time=9.65 memory used=608.6MB, alloc=212.3MB, time=12.88 memory used=726.2MB, alloc=236.3MB, time=16.98 memory used=861.2MB, alloc=260.3MB, time=22.13 memory used=1020.2MB, alloc=260.3MB, time=28.12 memory used=1179.1MB, alloc=260.3MB, time=34.13 memory used=1338.1MB, alloc=260.3MB, time=40.13 memory used=1496.9MB, alloc=284.3MB, time=46.10 memory used=1679.7MB, alloc=284.3MB, time=52.95 memory used=1862.4MB, alloc=308.3MB, time=59.87 N1 := 7047 > GB := Basis(F, plex(op(vars))); 6 2 2 3 2 GB := [81 x - 25 x , -9 x + 5 y, -4 x z + 5 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2071.7MB, alloc=308.3MB, time=66.01 memory used=2235.3MB, alloc=588.3MB, time=69.27 memory used=2472.6MB, alloc=612.3MB, time=78.22 N2 := 3263 #save(Problem, "format.txt"); > 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 := [5 y - 9 x , -17 y + 17 y, 4 x y z - 9 x z , 8 y x - 9, 2 3 2 12 x y - 12 x y z, -7 x + 18 x z ] > J:=[op(GB),op(G)]; 6 2 2 3 2 2 J := [81 x - 25 x , -9 x + 5 y, -4 x z + 5 x z , 8 y x - 9, 2 3 2 12 x y - 12 x y z, -7 x + 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, 13, 18, 3, 3, 3, 2, 5/6, 5/6, 1/2, 2/3, 7/12, 1/3, 6, 12, 21, 6, 6, 2, 2, 1, 1/2, 1/2, 5/6, 1/3, 1/3, 1, -3, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2568.5MB, alloc=612.3MB, time=81.77 |\^/| 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(); 1428251001 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 F := [-3 z - 19 x y, -15 x z + 10, 19 y - 18 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-5 x y z + 20 x z , 5 y z - 5 x, 4 x y - 17 z] > Problem := [F,G]; 3 3 Problem := [[-3 z - 19 x y, -15 x z + 10, 19 y - 18 x z], 2 2 [-5 x y z + 20 x z , 5 y z - 5 x, 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=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=47.4MB, alloc=32.3MB, time=0.79 memory used=67.5MB, alloc=56.3MB, time=1.09 memory used=108.3MB, alloc=60.3MB, time=1.68 memory used=147.3MB, alloc=60.3MB, time=2.24 memory used=183.5MB, alloc=84.3MB, time=2.78 memory used=230.9MB, alloc=84.3MB, time=3.48 memory used=285.3MB, alloc=116.3MB, time=4.34 memory used=361.6MB, alloc=116.3MB, time=5.49 memory used=435.8MB, alloc=140.3MB, time=6.57 memory used=512.0MB, alloc=396.3MB, time=7.71 memory used=611.3MB, alloc=420.3MB, time=9.16 memory used=729.3MB, alloc=444.3MB, time=10.93 memory used=870.1MB, alloc=468.3MB, time=13.04 memory used=1006.8MB, alloc=492.3MB, time=15.14 memory used=1128.4MB, alloc=492.3MB, time=17.12 memory used=1223.6MB, alloc=516.3MB, time=18.64 memory used=1322.3MB, alloc=516.3MB, time=20.32 memory used=1421.0MB, alloc=516.3MB, time=22.04 memory used=1511.2MB, alloc=516.3MB, time=23.66 memory used=1584.0MB, alloc=516.3MB, time=25.06 memory used=1661.4MB, alloc=516.3MB, time=26.63 memory used=1744.3MB, alloc=540.3MB, time=28.25 memory used=1797.9MB, alloc=540.3MB, time=29.39 memory used=1871.1MB, alloc=540.3MB, time=30.90 memory used=1927.8MB, alloc=540.3MB, time=32.23 memory used=2127.6MB, alloc=564.3MB, time=35.61 memory used=2340.1MB, alloc=588.3MB, time=39.33 memory used=2539.3MB, alloc=612.3MB, time=42.90 memory used=2753.2MB, alloc=636.3MB, time=46.85 memory used=2927.5MB, alloc=660.3MB, time=50.19 memory used=3113.1MB, alloc=684.3MB, time=53.75 memory used=3279.1MB, alloc=708.3MB, time=56.91 memory used=3485.6MB, alloc=732.3MB, time=61.57 memory used=3721.4MB, alloc=756.3MB, time=66.51 memory used=3924.1MB, alloc=780.3MB, time=71.10 memory used=4122.2MB, alloc=804.3MB, time=75.81 memory used=4308.9MB, alloc=828.3MB, time=79.92 memory used=4572.7MB, alloc=852.3MB, time=83.97 memory used=4841.4MB, alloc=876.3MB, time=88.33 memory used=5030.1MB, alloc=900.3MB, time=92.84 memory used=5173.2MB, alloc=924.3MB, time=96.62 |\^/| 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(); 1428251301 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [20 x z + 6 x z, -9 y + 4 x , -y + 12] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 G := [-18 z - 12 x y, x z - 14 y z, -12 x + 15 x ] > Problem := [F,G]; 2 3 2 2 Problem := [[20 x z + 6 x z, -9 y + 4 x , -y + 12], 3 2 2 3 2 [-18 z - 12 x y, x z - 14 y z, -12 x + 15 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=48.9MB, alloc=32.3MB, time=0.87 memory used=70.1MB, alloc=56.3MB, time=1.25 memory used=111.9MB, alloc=84.3MB, time=2.04 N1 := 1075 > GB := Basis(F, plex(op(vars))); 4 2 GB := [x - 8748, -x + 27 y, z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=170.4MB, alloc=84.3MB, time=3.56 N2 := 505 #save(Problem, "format.txt"); > if (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 2 H := [20 x z + 6 x z, -9 y + 4 x , -y + 12, -18 z - 12 x y, x z - 14 y z, 3 2 -12 x + 15 x ] > J:=[op(GB),op(G)]; J := 4 2 3 2 2 3 2 [x - 8748, -x + 27 y, z, -18 z - 12 x y, x z - 14 y z, -12 x + 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, 12, 17, 3, 3, 3, 3, 5/6, 2/3, 1/2, 7/12, 1/3, 5/12, 6, 11, 16, 4, 4, 2, 3, 5/6, 1/2, 1/2, 6/11, 3/11, 4/11, 1, 1, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=216.9MB, alloc=84.3MB, time=4.43 |\^/| 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(); 1428251316 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-18 x y - 7 x y z, 19 x z + 2 z , 15 y - y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [-6 y + 15 x, 13 y z - y z , -8 x z - 10 z ] > Problem := [F,G]; 2 2 3 2 Problem := [[-18 x y - 7 x y z, 19 x z + 2 z , 15 y - y z], 2 2 2 2 3 [-6 y + 15 x, 13 y z - y z , -8 x z - 10 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.48 memory used=47.5MB, alloc=32.3MB, time=0.79 memory used=67.7MB, alloc=56.3MB, time=1.11 memory used=110.8MB, alloc=60.3MB, time=1.84 memory used=149.4MB, alloc=84.3MB, time=2.55 memory used=206.4MB, alloc=108.3MB, time=4.15 N1 := 1481 > GB := Basis(F, plex(op(vars))); 2 4 2 2 3 GB := [x y , y , -15 y + y z, 19 x z + 2 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=278.9MB, alloc=108.3MB, time=6.03 N2 := 711 #save(Problem, "format.txt"); > if (GB=[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 := [-18 x y - 7 x y z, 19 x z + 2 z , 15 y - y z, -6 y + 15 x, 2 2 2 3 13 y z - y z , -8 x z - 10 z ] > J:=[op(GB),op(G)]; 2 4 2 2 3 2 2 2 J := [x y , y , -15 y + y z, 19 x z + 2 z , -6 y + 15 x, 13 y z - y z , 2 3 -8 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, 13, 16, 3, 2, 2, 3, 2/3, 2/3, 5/6, 5/12, 7/12, 2/3, 7, 13, 20, 4, 2, 4, 3, 4/7, 5/7, 4/7, 2/7, 1/2, 1/2, 0, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=347.4MB, alloc=116.3MB, time=7.47 |\^/| 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(); 1428251339 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [13 x + 2 x y z, 14 z - 13 x y, 20 x y + 15 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [-x y z + 13 x y, 13 x y - 17 x y z, -11 x + 17] > Problem := [F,G]; 3 3 2 Problem := [[13 x + 2 x y z, 14 z - 13 x y, 20 x y + 15 z], 2 3 [-x y z + 13 x y, 13 x y - 17 x y z, -11 x + 17]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.4MB, alloc=32.3MB, time=0.77 memory used=66.9MB, alloc=56.3MB, time=1.07 memory used=107.3MB, alloc=60.3MB, time=1.67 memory used=145.7MB, alloc=60.3MB, time=2.25 memory used=183.1MB, alloc=84.3MB, time=2.84 memory used=237.5MB, alloc=84.3MB, time=3.67 memory used=293.7MB, alloc=116.3MB, time=4.59 memory used=370.7MB, alloc=116.3MB, time=5.81 memory used=447.2MB, alloc=140.3MB, time=7.03 memory used=558.0MB, alloc=140.3MB, time=8.50 memory used=666.1MB, alloc=164.3MB, time=9.89 memory used=783.9MB, alloc=188.3MB, time=11.97 memory used=904.5MB, alloc=468.3MB, time=14.04 memory used=1050.5MB, alloc=492.3MB, time=16.76 memory used=1192.0MB, alloc=516.3MB, time=20.93 memory used=1338.3MB, alloc=540.3MB, time=26.20 memory used=1497.7MB, alloc=564.3MB, time=32.57 memory used=1681.0MB, alloc=588.3MB, time=39.94 memory used=1888.4MB, alloc=588.3MB, time=48.24 memory used=2095.7MB, alloc=612.3MB, time=56.51 memory used=2327.1MB, alloc=636.3MB, time=65.77 N1 := 6727 > GB := Basis(F, plex(op(vars))); 14 3 5 9 GB := [3709888 x + 81 x , 182 x + 3 x y, 132496 x + 27 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 345 #save(Problem, "format.txt"); > 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 H := [13 x + 2 x y z, 14 z - 13 x y, 20 x y + 15 z, -x y z + 13 x y, 2 3 13 x y - 17 x y z, -11 x + 17] > J:=[op(GB),op(G)]; 14 3 5 9 J := [3709888 x + 81 x , 182 x + 3 x y, 132496 x + 27 z, -x y z + 13 x y, 2 3 13 x y - 17 x y z, -11 x + 17] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 16, 18, 3, 3, 2, 3, 1, 5/6, 5/6, 3/4, 7/12, 5/12, 6, 12, 37, 14, 14, 1, 1, 1, 1/2, 1/2, 5/6, 5/12, 1/4, 4, -19, -11] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2533.4MB, alloc=636.3MB, time=72.69 |\^/| 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(); 1428251553 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [9 x y - 12 y z, -16 x y - 7 y z, -19 y z - 19 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 G := [-5 x z + 20 y , 16 x z - 19 x y, -8 y + y z ] > Problem := [F,G]; 2 2 2 2 Problem := [[9 x y - 12 y z, -16 x y - 7 y z, -19 y z - 19 z ], 2 3 2 3 2 [-5 x z + 20 y , 16 x z - 19 x y, -8 y + y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.50 memory used=47.2MB, alloc=32.3MB, time=0.79 memory used=67.4MB, alloc=56.3MB, time=1.11 memory used=107.7MB, alloc=60.3MB, time=1.68 memory used=145.2MB, alloc=84.3MB, time=2.25 memory used=204.8MB, alloc=92.3MB, time=3.14 memory used=261.1MB, alloc=116.3MB, time=4.01 memory used=337.8MB, alloc=140.3MB, time=5.18 memory used=428.6MB, alloc=396.3MB, time=6.56 memory used=525.7MB, alloc=420.3MB, time=7.99 memory used=645.2MB, alloc=444.3MB, time=9.68 memory used=785.3MB, alloc=468.3MB, time=11.71 memory used=918.9MB, alloc=492.3MB, time=13.75 memory used=1051.2MB, alloc=516.3MB, time=15.95 memory used=1175.7MB, alloc=516.3MB, time=17.95 memory used=1296.6MB, alloc=540.3MB, time=19.73 memory used=1401.2MB, alloc=540.3MB, time=21.47 memory used=1476.4MB, alloc=540.3MB, time=22.74 memory used=1570.0MB, alloc=540.3MB, time=24.34 memory used=1646.9MB, alloc=564.3MB, time=25.79 memory used=1734.1MB, alloc=564.3MB, time=27.45 memory used=1801.5MB, alloc=564.3MB, time=28.79 memory used=1863.7MB, alloc=564.3MB, time=30.02 memory used=1927.2MB, alloc=564.3MB, time=31.38 memory used=1972.1MB, alloc=588.3MB, time=32.35 memory used=2213.0MB, alloc=612.3MB, time=36.53 memory used=2460.4MB, alloc=636.3MB, time=41.83 memory used=2691.2MB, alloc=660.3MB, time=46.72 memory used=2918.6MB, alloc=684.3MB, time=51.73 memory used=3146.6MB, alloc=708.3MB, time=57.03 memory used=3375.3MB, alloc=732.3MB, time=62.22 memory used=3612.3MB, alloc=756.3MB, time=67.34 memory used=3854.5MB, alloc=780.3MB, time=72.60 memory used=4086.5MB, alloc=804.3MB, time=77.79 memory used=4316.2MB, alloc=828.3MB, time=83.29 memory used=4545.0MB, alloc=852.3MB, time=88.85 memory used=4773.3MB, alloc=876.3MB, time=94.30 memory used=5006.6MB, alloc=900.3MB, time=99.73 |\^/| 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(); 1428251853 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 F := [13 x y - 5 y , 13 x y z + 3, -18 x - 5 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [20 + 4 x, 14 x + 5 y z, -2 y z - 20 y ] > Problem := [F,G]; 2 3 3 3 Problem := [[13 x y - 5 y , 13 x y z + 3, -18 x - 5 z ], 3 2 2 2 [20 + 4 x, 14 x + 5 y z, -2 y z - 20 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=48.2MB, alloc=32.3MB, time=0.84 memory used=68.7MB, alloc=56.3MB, time=1.17 memory used=110.7MB, alloc=60.3MB, time=1.83 memory used=152.4MB, alloc=84.3MB, time=2.62 memory used=213.7MB, alloc=84.3MB, time=3.74 memory used=269.7MB, alloc=108.3MB, time=4.80 memory used=348.3MB, alloc=116.3MB, time=6.13 memory used=419.2MB, alloc=140.3MB, time=7.64 memory used=498.4MB, alloc=164.3MB, time=10.11 memory used=589.9MB, alloc=188.3MB, time=13.77 memory used=705.4MB, alloc=188.3MB, time=18.29 memory used=821.1MB, alloc=212.3MB, time=22.79 N1 := 3691 > GB := Basis(F, plex(op(vars))); 9 7 GB := [9653618 x - 1875, 5 y - 13 x, 57122 x + 125 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=965.6MB, alloc=212.3MB, time=26.32 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)]; 2 3 3 3 2 3 H := [13 x y - 5 y , 13 z y x + 3, -18 x - 5 z , 20 + 4 x, 5 z y + 14 x , 2 2 -2 y z - 20 y ] > J:=[op(GB),op(G)]; 9 7 2 3 J := [9653618 x - 1875, 5 y - 13 x, 57122 x + 125 z, 20 + 4 x, 5 z y + 14 x , 2 2 -2 y 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, 13, 16, 3, 3, 3, 3, 5/6, 2/3, 2/3, 5/12, 1/2, 1/3, 6, 11, 24, 9, 9, 2, 1, 5/6, 1/2, 1/2, 5/12, 1/3, 1/4, 2, -8, -6] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=977.5MB, alloc=212.3MB, time=26.74 |\^/| 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(); 1428251929 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-13 x y - 2 y z, 15 x y - 15 x y, 16 x z + 4 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [-11 x - 11 x z , y z + 10 y , -13 x y - 18 x y z] > Problem := [F,G]; 2 2 2 2 Problem := [[-13 x y - 2 y z, 15 x y - 15 x y, 16 x z + 4 y z], 3 2 2 2 2 [-11 x - 11 x z , y z + 10 y , -13 x y - 18 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=26.2MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.81 memory used=67.3MB, alloc=32.3MB, time=1.10 memory used=85.9MB, alloc=56.3MB, time=1.39 memory used=123.9MB, alloc=60.3MB, time=1.97 memory used=159.7MB, alloc=84.3MB, time=2.51 memory used=215.0MB, alloc=84.3MB, time=3.36 memory used=268.7MB, alloc=116.3MB, time=4.22 memory used=344.8MB, alloc=140.3MB, time=5.51 memory used=439.2MB, alloc=164.3MB, time=7.22 memory used=546.7MB, alloc=188.3MB, time=9.76 memory used=652.4MB, alloc=212.3MB, time=13.83 N1 := 2787 > GB := Basis(F, plex(op(vars))); 2 4 3 2 3 2 GB := [x y - x y, x y - 26 x y , 13 x y + 2 y z, -13 x y + 8 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=786.3MB, alloc=212.3MB, time=18.01 memory used=904.4MB, alloc=468.3MB, time=19.86 memory used=1057.6MB, alloc=468.3MB, time=22.38 memory used=1206.1MB, alloc=492.3MB, time=25.20 memory used=1367.0MB, alloc=516.3MB, time=30.17 memory used=1523.5MB, alloc=540.3MB, time=36.73 N2 := 3413 #save(Problem, "format.txt"); > if (GB=[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 := [-13 x y - 2 y z, 15 x y - 15 x y, 16 x z + 4 y z, -11 x - 11 x z , 2 2 2 y z + 10 y , -13 x y - 18 x y z] > J:=[op(GB),op(G)]; 2 4 3 2 3 2 J := [x y - x y, x y - 26 x y , 13 x y + 2 y z, -13 x y + 8 x z , 3 2 2 2 2 -11 x - 11 x z , y z + 10 y , -13 x y - 18 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, 18, 3, 3, 2, 2, 5/6, 5/6, 5/6, 2/3, 3/4, 1/2, 7, 17, 24, 5, 3, 4, 2, 6/7, 6/7, 5/7, 11/14, 11/14, 5/14, -2, -6, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1648.2MB, alloc=540.3MB, time=41.60 |\^/| 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(); 1428252044 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 F := [11 - 11 y, 4 x z + 4 x, 7 + 7 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-18 z - 20 x z, -12 x y - 8 y , -16 y z + 19 x z] > Problem := [F,G]; 2 Problem := [[11 - 11 y, 4 x z + 4 x, 7 + 7 y], 3 2 2 2 [-18 z - 20 x z, -12 x y - 8 y , -16 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.46 memory used=47.8MB, alloc=32.3MB, time=0.79 memory used=68.6MB, alloc=32.3MB, time=1.15 memory used=86.9MB, alloc=56.3MB, time=1.48 N1 := 805 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=126.6MB, alloc=56.3MB, time=2.43 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)]; 2 3 2 2 H := [11 - 11 y, 4 x z + 4 x, 7 + 7 y, -18 z - 20 x z, -12 x y - 8 y , 2 -16 y z + 19 x z] > J:=[op(GB),op(G)]; 3 2 2 2 J := [1, -18 z - 20 x z, -12 x y - 8 y , -16 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, 11, 14, 3, 2, 2, 3, 2/3, 2/3, 1/2, 5/12, 5/12, 5/12, 4, 7, 9, 3, 2, 2, 3, 3/4, 1/2, 1/2, 3/7, 3/7, 4/7, 4, 5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=138.0MB, alloc=56.3MB, time=2.62 |\^/| 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(); 1428252051 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [9 z , -5 x y + 2 x , -8 y - 17] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-7 x y + x z , -11 x y z + 17 y z, -17 x y z - 11 z ] > Problem := [F,G]; 3 2 2 2 Problem := [[9 z , -5 x y + 2 x , -8 y - 17], 2 2 2 [-7 x y + x z , -11 x y z + 17 y z, -17 x y z - 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.8MB, alloc=32.3MB, time=0.53 N1 := 327 > GB := Basis(F, plex(op(vars))); 2 2 3 GB := [x , 8 y + 17, z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=48.0MB, alloc=32.3MB, time=0.91 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)]; 3 2 2 2 2 2 H := [9 z , -5 x y + 2 x , -8 y - 17, -7 x y + x z , -11 x y z + 17 y z, 2 -17 x y z - 11 z ] > J:=[op(GB),op(G)]; 2 2 3 2 2 2 J := [x , 8 y + 17, z , -7 x y + x z , -11 x y z + 17 y z, -17 x y z - 11 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 17, 3, 2, 2, 3, 2/3, 5/6, 2/3, 1/2, 1/2, 1/2, 6, 12, 16, 3, 2, 2, 3, 2/3, 2/3, 2/3, 5/12, 5/12, 1/2, 1, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=66.8MB, alloc=32.3MB, time=1.20 |\^/| 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(); 1428252054 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-18 x y + 5 z , -19 y z - 18 y z , -6 x y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [6 x y z + 14 x y, x z + 16 y z , -2 x y - 3 x] > Problem := [F,G]; 2 2 2 2 Problem := [[-18 x y + 5 z , -19 y z - 18 y z , -6 x y z], 2 2 2 [6 x y z + 14 x y, x z + 16 y z , -2 x y - 3 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=48.0MB, alloc=32.3MB, time=0.81 memory used=68.5MB, alloc=32.3MB, time=1.12 memory used=87.7MB, alloc=56.3MB, time=1.42 memory used=129.6MB, alloc=60.3MB, time=2.13 memory used=167.9MB, alloc=84.3MB, time=2.83 memory used=227.4MB, alloc=108.3MB, time=3.90 memory used=304.3MB, alloc=140.3MB, time=5.31 memory used=393.4MB, alloc=164.3MB, time=7.30 memory used=488.2MB, alloc=188.3MB, time=10.23 memory used=593.6MB, alloc=212.3MB, time=14.34 memory used=723.1MB, alloc=212.3MB, time=19.37 memory used=852.4MB, alloc=236.3MB, time=24.39 memory used=1005.9MB, alloc=236.3MB, time=30.30 N1 := 4739 > GB := Basis(F, plex(op(vars))); 2 3 4 3 2 2 2 GB := [x y , y x, x y z, 324 x y + 95 y z, -18 x y + 5 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1162.4MB, alloc=236.3MB, time=34.06 memory used=1262.3MB, alloc=492.3MB, time=35.94 memory used=1431.8MB, alloc=516.3MB, time=39.39 memory used=1593.1MB, alloc=540.3MB, time=45.52 memory used=1767.1MB, alloc=564.3MB, time=52.85 memory used=1965.6MB, alloc=588.3MB, time=61.26 N2 := 4213 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-18 x y + 5 z , -19 y z - 18 y z , -6 x y z, 6 x y z + 14 x y, 2 2 2 x z + 16 y z , -2 x y - 3 x] > J:=[op(GB),op(G)]; 2 3 4 3 2 2 2 J := [x y , y x, x y z, 324 x y + 95 y z, -18 x y + 5 z , 6 x y z + 14 x y, 2 2 2 x z + 16 y z , -2 x 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, 16, 18, 3, 2, 2, 2, 5/6, 1, 5/6, 1/2, 4/7, 1/2, 8, 21, 29, 5, 2, 4, 2, 1, 1, 5/8, 10/17, 10/17, 6/17, -5, -11, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1971.2MB, alloc=588.3MB, time=61.44 |\^/| 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(); 1428252235 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 3 F := [-10 z + 7 z , 19 y - 6 z , 19 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [2 y - 17 y , 7 x y z - 13 z, 18 x y - 4 y z] > Problem := [F,G]; 3 2 3 3 3 Problem := [[-10 z + 7 z , 19 y - 6 z , 19 x ], 3 2 [2 y - 17 y , 7 x y z - 13 z, 18 x y - 4 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.49 memory used=48.0MB, alloc=32.3MB, time=0.85 memory used=68.2MB, alloc=56.3MB, time=1.23 memory used=108.2MB, alloc=84.3MB, time=2.02 N1 := 1223 > GB := Basis(F, plex(op(vars))); 3 6 3 3 3 3 2 GB := [x , 9500 y - 1029 y , 10 y z - 7 y , -95 y + 21 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=164.2MB, alloc=84.3MB, time=3.61 memory used=222.1MB, alloc=84.3MB, time=4.54 memory used=280.0MB, alloc=108.3MB, time=5.65 memory used=347.2MB, alloc=132.3MB, time=7.98 N2 := 1587 #save(Problem, "format.txt"); > 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 3 2 H := [-10 z + 7 z , -6 z + 19 y , 19 x , 2 y - 17 y , 7 x y z - 13 z, 18 x y - 4 y z] > J:=[op(GB),op(G)]; 3 6 3 3 3 3 2 3 2 J := [x , 9500 y - 1029 y , 10 y z - 7 y , -95 y + 21 z , 2 y - 17 y , 7 x y z - 13 z, 18 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, 11, 17, 3, 3, 3, 3, 1/2, 2/3, 2/3, 1/4, 1/2, 1/2, 7, 13, 24, 6, 3, 6, 2, 3/7, 6/7, 4/7, 3/14, 5/7, 5/14, -2, -7, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=361.4MB, alloc=132.3MB, 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(); 1428252260 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [10 z + 19 y , -15 z + 6 x, -8 x y - 4 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-17 x y z + 17, 16 y z + 7 z, -9 x z - 3 x y ] > Problem := [F,G]; 3 2 3 2 Problem := [[10 z + 19 y , -15 z + 6 x, -8 x y - 4 x z], 2 2 [-17 x y z + 17, 16 y z + 7 z, -9 x z - 3 x y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=48.5MB, alloc=32.3MB, time=0.81 memory used=68.7MB, alloc=32.3MB, time=1.12 memory used=87.4MB, alloc=56.3MB, time=1.42 memory used=125.1MB, alloc=60.3MB, time=2.00 memory used=161.6MB, alloc=84.3MB, time=2.55 memory used=218.0MB, alloc=84.3MB, time=3.45 memory used=273.9MB, alloc=92.3MB, time=4.33 memory used=328.7MB, alloc=92.3MB, time=5.19 memory used=382.7MB, alloc=116.3MB, time=6.07 memory used=460.2MB, alloc=116.3MB, time=7.25 memory used=538.1MB, alloc=140.3MB, time=8.40 memory used=627.7MB, alloc=396.3MB, time=9.91 memory used=722.8MB, alloc=420.3MB, time=11.39 memory used=842.7MB, alloc=444.3MB, time=13.18 memory used=979.4MB, alloc=468.3MB, time=15.65 memory used=1120.8MB, alloc=492.3MB, time=18.29 memory used=1274.4MB, alloc=516.3MB, time=21.23 memory used=1441.2MB, alloc=540.3MB, time=24.35 memory used=1617.0MB, alloc=564.3MB, time=27.73 memory used=1792.6MB, alloc=588.3MB, time=32.61 memory used=1962.5MB, alloc=612.3MB, time=38.35 memory used=2141.7MB, alloc=636.3MB, time=44.80 memory used=2333.1MB, alloc=660.3MB, time=52.17 memory used=2531.6MB, alloc=684.3MB, time=60.86 memory used=2754.0MB, alloc=708.3MB, time=70.29 memory used=3000.4MB, alloc=732.3MB, time=80.64 memory used=3270.7MB, alloc=756.3MB, time=91.92 |\^/| 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(); 1428252560 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-2 x z + 10, -2 x + 18 x y, -20 z + 13 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-10 y - 16 y z, -2 x z + 15 y z , -7 x y - 2 x ] > Problem := [F,G]; 2 2 2 Problem := [[-2 x z + 10, -2 x + 18 x y, -20 z + 13 z], 2 2 2 2 2 [-10 y - 16 y z, -2 x z + 15 y z , -7 x y - 2 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=47.2MB, alloc=32.3MB, time=0.76 memory used=67.4MB, alloc=32.3MB, time=1.06 memory used=87.0MB, alloc=56.3MB, time=1.42 memory used=127.6MB, alloc=56.3MB, time=2.12 memory used=163.7MB, alloc=84.3MB, time=2.79 memory used=216.7MB, alloc=108.3MB, time=4.35 N1 := 1777 > GB := Basis(F, plex(op(vars))); GB := [169 x - 2000, 1521 y - 2000, 20 z - 13] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=288.5MB, alloc=108.3MB, time=6.57 memory used=365.7MB, alloc=140.3MB, time=7.87 N2 := 1053 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-2 x z + 10, -2 x + 18 x y, -20 z + 13 z, -10 y - 16 y z, 2 2 2 2 -2 x z + 15 y z , -7 x y - 2 x ] > J:=[op(GB),op(G)]; 2 J := [169 x - 2000, 1521 y - 2000, 20 z - 13, -10 y - 16 y z, 2 2 2 2 -2 x z + 15 y z , -7 x y - 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, 12, 15, 3, 2, 2, 2, 2/3, 2/3, 2/3, 1/2, 5/12, 1/2, 6, 10, 11, 3, 2, 2, 2, 1/2, 2/3, 1/2, 1/3, 5/12, 1/3, 2, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=408.1MB, alloc=140.3MB, 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(); 1428252589 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [-12 x y - 6 x , 19 x y z + 5 y, -19 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 G := [13 x y + 10 z , -4 x y z + 4, 11 x z + 3 z ] > Problem := [F,G]; 2 2 3 Problem := [[-12 x y - 6 x , 19 x y z + 5 y, -19 x ], 2 3 2 3 [13 x y + 10 z , -4 x y z + 4, 11 x z + 3 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.8MB, alloc=32.3MB, time=0.79 memory used=67.7MB, alloc=32.3MB, time=1.08 memory used=86.2MB, alloc=56.3MB, time=1.37 memory used=125.7MB, alloc=60.3MB, time=2.01 memory used=165.0MB, alloc=84.3MB, time=2.66 memory used=222.3MB, alloc=84.3MB, time=3.68 memory used=274.9MB, alloc=108.3MB, time=4.64 memory used=354.4MB, alloc=116.3MB, time=5.87 memory used=421.3MB, alloc=140.3MB, time=7.23 memory used=498.4MB, alloc=164.3MB, time=9.36 memory used=585.8MB, alloc=188.3MB, time=12.67 memory used=697.1MB, alloc=188.3MB, time=16.83 memory used=808.5MB, alloc=212.3MB, time=21.06 N1 := 4005 > GB := Basis(F, plex(op(vars))); 2 GB := [x , y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=946.3MB, alloc=212.3MB, time=25.77 N2 := 291 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 2 H := [-12 x y - 6 x , 19 x y z + 5 y, -19 x , 10 z + 13 y x , -4 x y z + 4, 2 3 11 x z + 3 z ] > J:=[op(GB),op(G)]; 2 3 2 2 3 J := [x , y, 10 z + 13 y x , -4 x y z + 4, 11 x 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, 14, 18, 3, 3, 2, 3, 1, 2/3, 2/3, 7/12, 5/12, 5/12, 5, 10, 12, 3, 2, 1, 3, 4/5, 3/5, 3/5, 4/9, 1/3, 4/9, 4, 6, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=972.6MB, alloc=212.3MB, time=26.24 |\^/| 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(); 1428252671 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 F := [19 x + 2 z, -6 z + 7 y, -20 x y - 6 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [15 x z + 7 z, -3 x z + y z, -8 x + 4 x z] > Problem := [F,G]; 3 2 3 Problem := [[19 x + 2 z, -6 z + 7 y, -20 x y - 6 z ], 2 2 2 3 2 [15 x z + 7 z, -3 x z + y z, -8 x + 4 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.80 memory used=68.3MB, alloc=32.3MB, time=1.09 memory used=87.8MB, alloc=56.3MB, time=1.39 memory used=130.5MB, alloc=60.3MB, time=2.12 memory used=169.8MB, alloc=84.3MB, time=2.84 memory used=229.7MB, alloc=84.3MB, time=3.91 memory used=283.1MB, alloc=108.3MB, time=4.88 memory used=351.0MB, alloc=132.3MB, time=6.51 memory used=429.4MB, alloc=156.3MB, time=9.25 memory used=526.5MB, alloc=156.3MB, time=12.96 memory used=623.5MB, alloc=180.3MB, time=16.67 N1 := 3559 > GB := Basis(F, plex(op(vars))); 7 3 3 GB := [102885 x - 49 x , 20577 x + 28 y, 2 z + 19 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=747.8MB, alloc=180.3MB, time=20.68 N2 := 471 #save(Problem, "format.txt"); > 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 := [2 z + 19 x, -6 z + 7 y, -20 x y - 6 z , 15 x z + 7 z, -3 x z + y z, 3 2 -8 x + 4 x z] > J:=[op(GB),op(G)]; 7 3 3 2 J := [102885 x - 49 x , 20577 x + 28 y, 2 z + 19 x, 15 x z + 7 z, 2 2 3 2 -3 x z + y z, -8 x + 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, 14, 16, 3, 3, 2, 3, 5/6, 1/2, 1, 1/2, 1/4, 2/3, 6, 12, 20, 7, 7, 2, 1, 1, 1/3, 2/3, 2/3, 1/6, 1/2, 2, -4, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=775.6MB, alloc=180.3MB, time=21.24 |\^/| 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(); 1428252734 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-10 y z + 3 x y, 4 x y - 3 y z, 10 x z + 6 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [18 x y - 15 z , 18 x y - 4 y, 18 x y + 2 x y z] > Problem := [F,G]; 2 2 2 2 Problem := [[-10 y z + 3 x y, 4 x y - 3 y z, 10 x z + 6 z], 2 2 2 [18 x y - 15 z , 18 x y - 4 y, 18 x y + 2 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=48.0MB, alloc=32.3MB, time=0.79 memory used=69.0MB, alloc=32.3MB, time=1.10 memory used=88.9MB, alloc=56.3MB, time=1.40 memory used=128.1MB, alloc=60.3MB, time=1.98 memory used=167.7MB, alloc=84.3MB, time=2.67 memory used=224.8MB, alloc=84.3MB, time=3.68 memory used=279.4MB, alloc=108.3MB, time=4.65 memory used=351.1MB, alloc=140.3MB, time=6.04 memory used=434.3MB, alloc=164.3MB, time=8.50 memory used=527.6MB, alloc=188.3MB, time=12.14 memory used=645.0MB, alloc=188.3MB, time=16.67 N1 := 3461 > GB := Basis(F, plex(op(vars))); 2 GB := [y x, 5 x z + 3 z, z y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=766.7MB, alloc=188.3MB, time=20.64 N2 := 283 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [-10 y z + 3 x y, 4 x y - 3 y z, 10 x z + 6 z, 18 x y - 15 z , 2 2 18 x y - 4 y, 18 x y + 2 x y z] > J:=[op(GB),op(G)]; 2 2 2 2 J := [y x, 5 x z + 3 z, z y, 18 x y - 15 z , 18 x y - 4 y, 18 x y + 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, 16, 17, 3, 2, 2, 2, 1, 5/6, 5/6, 7/12, 3/4, 1/2, 6, 14, 15, 3, 2, 2, 2, 5/6, 5/6, 2/3, 1/2, 7/12, 5/12, 2, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=776.3MB, alloc=188.3MB, time=20.85 |\^/| 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(); 1428252795 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [8 x y + 7 x y z, 13 y z - 3, 20 x + 4 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [-17 y + 3 z , -10 x y + 11 z , -12 x z - 16 x y] > Problem := [F,G]; 2 2 2 Problem := [[8 x y + 7 x y z, 13 y z - 3, 20 x + 4 y ], 3 2 2 2 2 [-17 y + 3 z , -10 x y + 11 z , -12 x 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=26.4MB, alloc=32.3MB, time=0.50 memory used=48.2MB, alloc=32.3MB, time=0.81 memory used=68.5MB, alloc=32.3MB, time=1.10 memory used=87.4MB, alloc=56.3MB, time=1.40 memory used=125.4MB, alloc=60.3MB, time=1.97 memory used=162.1MB, alloc=60.3MB, time=2.51 memory used=197.1MB, alloc=84.3MB, time=3.04 memory used=253.3MB, alloc=84.3MB, time=3.89 memory used=308.3MB, alloc=84.3MB, time=4.72 memory used=361.2MB, alloc=116.3MB, time=5.56 memory used=436.8MB, alloc=116.3MB, time=6.75 memory used=510.6MB, alloc=140.3MB, time=8.15 memory used=601.3MB, alloc=164.3MB, time=9.79 memory used=709.1MB, alloc=188.3MB, time=11.76 memory used=830.1MB, alloc=212.3MB, time=13.99 memory used=958.0MB, alloc=236.3MB, time=17.45 memory used=1090.9MB, alloc=260.3MB, time=21.74 memory used=1231.5MB, alloc=284.3MB, time=27.29 memory used=1395.7MB, alloc=308.3MB, time=33.76 memory used=1583.8MB, alloc=308.3MB, time=41.19 memory used=1771.9MB, alloc=308.3MB, time=48.55 memory used=1959.9MB, alloc=332.3MB, time=56.04 memory used=2171.8MB, alloc=332.3MB, time=64.31 memory used=2383.7MB, alloc=356.3MB, time=72.74 N1 := 7011 > GB := Basis(F, plex(op(vars))); 2 2 GB := [520 x - 21, 104 y + 21, 7 z + 8 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2494.8MB, alloc=356.3MB, time=75.33 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)]; 2 2 2 3 2 H := [8 x y + 7 x y z, 13 z y - 3, 20 x + 4 y , -17 y + 3 z , 2 2 2 -10 x y + 11 z , -12 x z - 16 x y] > J:=[op(GB),op(G)]; 2 2 3 2 2 2 J := [520 x - 21, 104 y + 21, 7 z + 8 y, -17 y + 3 z , -10 x y + 11 z , 2 -12 x 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, 15, 16, 3, 2, 3, 2, 2/3, 1, 5/6, 1/2, 7/12, 5/12, 6, 12, 14, 3, 2, 3, 2, 1/2, 5/6, 2/3, 1/3, 5/12, 1/3, 3, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2645.9MB, alloc=612.3MB, time=79.33 |\^/| 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(); 1428253040 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 F := [8 x z - 4 x , -3 x - 11 z , 5 x y + 18 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [15 x z + 13 y z, 10 y - 20 y z , 3 y + 19 y z] > Problem := [F,G]; 2 2 3 2 2 2 Problem := [[8 x z - 4 x , -3 x - 11 z , 5 x y + 18 x z], 2 3 2 2 [15 x z + 13 y z, 10 y - 20 y z , 3 y + 19 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.48 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=67.2MB, alloc=56.3MB, time=1.09 memory used=105.5MB, alloc=60.3MB, time=1.66 memory used=141.2MB, alloc=60.3MB, time=2.19 memory used=175.7MB, alloc=84.3MB, time=2.72 memory used=230.1MB, alloc=84.3MB, time=3.54 memory used=283.6MB, alloc=108.3MB, time=4.44 memory used=359.4MB, alloc=140.3MB, time=5.81 memory used=450.8MB, alloc=164.3MB, time=7.43 memory used=557.0MB, alloc=188.3MB, time=9.29 memory used=675.8MB, alloc=212.3MB, time=11.40 memory used=807.0MB, alloc=236.3MB, time=13.82 memory used=949.9MB, alloc=260.3MB, time=16.45 memory used=1062.2MB, alloc=540.3MB, time=18.71 memory used=1207.9MB, alloc=564.3MB, time=22.80 memory used=1356.1MB, alloc=588.3MB, time=27.74 memory used=1513.9MB, alloc=612.3MB, time=33.14 memory used=1683.7MB, alloc=636.3MB, time=39.20 memory used=1864.0MB, alloc=660.3MB, time=46.32 memory used=2060.2MB, alloc=684.3MB, time=54.64 memory used=2280.2MB, alloc=708.3MB, time=63.86 memory used=2524.3MB, alloc=732.3MB, time=73.96 memory used=2792.3MB, alloc=756.3MB, time=84.96 |\^/| 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(); 1428253340 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 F := [-12 y - 3 x , -y z - 16 z , -17 x z + 3] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 G := [-11 y z , -20 y - 4 z, -7 x y - 16 z] > Problem := [F,G]; 3 2 2 3 2 Problem := [[-12 y - 3 x , -y z - 16 z , -17 x z + 3], 2 [-11 y z , -20 y - 4 z, -7 x y - 16 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=78.8MB, alloc=68.3MB, time=1.41 N1 := 661 > GB := Basis(F, plex(op(vars))); 16 6 14 GB := [24137569 x + 47775744, -289 x + 576 y, 1419857 x + 15925248 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=126.3MB, alloc=68.3MB, time=2.43 memory used=174.2MB, alloc=92.3MB, time=3.28 N2 := 661 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 3 2 2 H := [-12 y - 3 x , -y z - 16 z , -17 x z + 3, -11 y z , -20 y - 4 z, -7 x y - 16 z] > J:=[op(GB),op(G)]; 16 6 14 J := [24137569 x + 47775744, -289 x + 576 y, 1419857 x + 15925248 z, 2 -11 y z , -20 y - 4 z, -7 x y - 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, 13, 15, 3, 2, 3, 3, 1/2, 5/6, 5/6, 3/13, 5/13, 6/13, 6, 12, 42, 16, 16, 1, 2, 2/3, 2/3, 2/3, 4/13, 4/13, 4/13, 1, -27, -13] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=195.1MB, alloc=92.3MB, time=3.84 |\^/| 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(); 1428253351 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [16 x z - 13 x z , 15 x z + 10 x, 9] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 G := [-2 z - 13 y z, -6 x y + 15 y z, -8 z + 8 x z] > Problem := [F,G]; 2 2 2 Problem := [[16 x z - 13 x z , 15 x z + 10 x, 9], 3 3 [-2 z - 13 y z, -6 x y + 15 y z, -8 z + 8 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=47.5MB, alloc=32.3MB, time=0.84 memory used=68.3MB, alloc=56.3MB, time=1.25 memory used=109.2MB, alloc=80.3MB, time=2.30 N1 := 897 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 255 #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 3 H := [16 x z - 13 x z , 15 x z + 10 x, 9, -2 z - 13 y z, -6 x y + 15 y z, 3 -8 z + 8 x z] > J:=[op(GB),op(G)]; 3 3 J := [1, -2 z - 13 y z, -6 x y + 15 y z, -8 z + 8 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, 11, 14, 3, 2, 1, 3, 2/3, 1/3, 5/6, 6/11, 3/11, 8/11, 4, 7, 8, 3, 1, 1, 3, 1/2, 1/2, 3/4, 2/7, 3/7, 5/7, 4, 6, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=142.5MB, alloc=80.3MB, time=2.98 |\^/| 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(); 1428253359 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 F := [15 x + 2 x y, -9 x y - 4 x z, 8 x + 7 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 G := [-14 y - 4 y z , 16 x y - 19 x, -5 x - 6] > Problem := [F,G]; 3 2 2 3 2 Problem := [[15 x + 2 x y, -9 x y - 4 x z, 8 x + 7 x z], 3 2 3 [-14 y - 4 y z , 16 x y - 19 x, -5 x - 6]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=48.0MB, alloc=32.3MB, time=0.83 memory used=68.7MB, alloc=56.3MB, time=1.24 N1 := 347 > GB := Basis(F, plex(op(vars))); 4 3 3 3 2 GB := [945 x + 64 x , 15 x + 2 x y, 8 x + 7 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 153 #save(Problem, "format.txt"); > 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 2 H := [15 x + 2 x y, -9 x y - 4 x z, 8 x + 7 x z, -14 y - 4 y z , 3 16 x y - 19 x, -5 x - 6] > J:=[op(GB),op(G)]; 4 3 3 3 2 3 2 J := [945 x + 64 x , 15 x + 2 x y, 8 x + 7 x z, -14 y - 4 y z , 3 16 x y - 19 x, -5 x - 6] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 17, 3, 3, 3, 2, 5/6, 2/3, 1/2, 3/4, 5/12, 1/4, 6, 10, 18, 4, 4, 3, 2, 5/6, 1/2, 1/3, 3/4, 1/3, 1/6, 2, -1, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=107.7MB, alloc=60.3MB, time=1.84 |\^/| 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(); 1428253364 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 F := [-12 x + 16 y , 10 z + 4 x y, -7 x y - 2 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-2 z - 18 x, -20 y z + 9 z , -5 y - 4] > Problem := [F,G]; 3 3 3 2 Problem := [[-12 x + 16 y , 10 z + 4 x y, -7 x y - 2 y ], 3 2 2 2 [-2 z - 18 x, -20 y z + 9 z , -5 y - 4]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.79 memory used=68.0MB, alloc=32.3MB, time=1.08 memory used=87.8MB, alloc=32.3MB, time=1.37 memory used=107.0MB, alloc=56.3MB, time=1.66 memory used=146.1MB, alloc=60.3MB, time=2.22 memory used=186.6MB, alloc=84.3MB, time=2.92 memory used=247.4MB, alloc=84.3MB, time=3.99 memory used=298.4MB, alloc=108.3MB, time=5.13 memory used=360.3MB, alloc=132.3MB, time=7.40 N1 := 1861 > GB := Basis(F, plex(op(vars))); 4 3 2 2 3 GB := [x , -3 x + 49 x y, 7 x y + 2 y , 5 z + 2 y x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=448.3MB, alloc=140.3MB, time=9.32 memory used=543.7MB, alloc=140.3MB, time=10.79 memory used=641.4MB, alloc=164.3MB, time=12.59 memory used=744.5MB, alloc=188.3MB, time=16.28 N2 := 1861 #save(Problem, "format.txt"); > 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 H := [-12 x + 16 y , 10 z + 4 x y, -7 x y - 2 y , -2 z - 18 x, 2 2 2 -20 y z + 9 z , -5 y - 4] > J:=[op(GB),op(G)]; 4 3 2 2 3 3 J := [x , -3 x + 49 x y, 7 x y + 2 y , 5 z + 2 y x, -2 z - 18 x, 2 2 2 -20 y z + 9 z , -5 y - 4] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 16, 3, 3, 3, 3, 2/3, 5/6, 1/2, 1/3, 1/2, 1/3, 7, 13, 20, 4, 4, 2, 3, 5/7, 5/7, 3/7, 3/7, 3/7, 2/7, -1, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=768.1MB, alloc=188.3MB, time=17.07 |\^/| 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(); 1428253412 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [-y - 7 z , -7 y z - 10 z, 10 x y + 10 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 G := [5 x - 9 x y z, 4 x - 5 z, -18 y + 4 y ] > Problem := [F,G]; 3 3 2 Problem := [[-y - 7 z , -7 y z - 10 z, 10 x y + 10 x y], 3 3 3 2 [5 x - 9 x y z, 4 x - 5 z, -18 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=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.9MB, alloc=32.3MB, time=0.80 memory used=68.3MB, alloc=32.3MB, time=1.09 memory used=88.8MB, alloc=56.3MB, time=1.46 memory used=130.6MB, alloc=84.3MB, time=2.22 N1 := 1053 > GB := Basis(F, plex(op(vars))); 2 4 3 2 3 3 GB := [x y + x y, 7 y + 10 y , x z + x z, 7 y z + 10 z, 7 z + y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=189.6MB, alloc=84.3MB, time=3.76 memory used=248.4MB, alloc=92.3MB, time=4.66 memory used=307.9MB, alloc=116.3MB, time=5.75 N2 := 1053 #save(Problem, "format.txt"); > 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 H := [-y - 7 z , -7 y z - 10 z, 10 x y + 10 x y, 5 x - 9 x y z, 4 x - 5 z, 3 2 -18 y + 4 y ] > J:=[op(GB),op(G)]; 2 4 3 2 3 3 J := [x y + x y, 7 y + 10 y , x z + x z, 7 y z + 10 z, 7 z + y , 3 3 3 2 5 x - 9 x y z, 4 x - 5 z, -18 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, 12, 17, 3, 3, 3, 3, 1/2, 5/6, 2/3, 5/12, 7/12, 5/12, 8, 15, 24, 4, 3, 4, 3, 1/2, 3/4, 5/8, 7/16, 9/16, 7/16, -3, -7, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=351.8MB, alloc=116.3MB, time=7.04 |\^/| 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(); 1428253430 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [9 z - 3, 18 x y - x y z, 8 x y + 11 x y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [6 x y - 4 x y z, 9 y z - 9 z, -14 y - 12 z] > Problem := [F,G]; 3 2 2 Problem := [[9 z - 3, 18 x y - x y z, 8 x y + 11 x y z], 2 2 3 [6 x y - 4 x y z, 9 y z - 9 z, -14 y - 12 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=31.7MB, alloc=40.3MB, time=0.54 memory used=59.2MB, alloc=40.3MB, time=0.92 memory used=85.4MB, alloc=40.3MB, time=1.29 memory used=108.8MB, alloc=64.3MB, time=1.64 memory used=150.3MB, alloc=68.3MB, time=2.26 memory used=190.7MB, alloc=92.3MB, time=2.87 memory used=251.1MB, alloc=92.3MB, time=3.76 memory used=311.5MB, alloc=116.3MB, time=4.87 memory used=386.8MB, alloc=140.3MB, time=6.23 memory used=477.3MB, alloc=172.3MB, time=7.88 memory used=581.5MB, alloc=196.3MB, time=9.77 memory used=694.6MB, alloc=220.3MB, time=12.05 memory used=808.7MB, alloc=244.3MB, time=15.32 memory used=933.1MB, alloc=268.3MB, time=19.33 memory used=1069.9MB, alloc=292.3MB, time=24.19 memory used=1221.2MB, alloc=316.3MB, time=30.21 memory used=1396.4MB, alloc=340.3MB, time=37.12 memory used=1595.4MB, alloc=364.3MB, time=45.01 memory used=1818.5MB, alloc=364.3MB, time=53.73 memory used=2041.5MB, alloc=364.3MB, time=62.46 memory used=2264.3MB, alloc=364.3MB, time=74.70 memory used=2487.2MB, alloc=388.3MB, time=88.23 memory used=2734.0MB, alloc=388.3MB, time=103.11 |\^/| 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(); 1428253731 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [-7 x y - 16 x, -2 z , y + 11 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [9 x y - 18 z , -6 z - 16 z , -6 x y + 5 x y] > Problem := [F,G]; 2 2 3 Problem := [[-7 x y - 16 x, -2 z , y + 11 x z], 2 2 3 2 2 [9 x y - 18 z , -6 z - 16 z , -6 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=26.3MB, alloc=32.3MB, time=0.85 memory used=47.8MB, alloc=32.3MB, time=1.41 memory used=67.8MB, alloc=32.3MB, time=1.92 memory used=88.3MB, alloc=56.3MB, time=2.56 memory used=131.7MB, alloc=60.3MB, time=3.86 memory used=169.8MB, alloc=84.3MB, time=5.04 memory used=225.8MB, alloc=108.3MB, time=6.96 memory used=291.7MB, alloc=132.3MB, time=10.62 N1 := 2237 > GB := Basis(F, plex(op(vars))); 3 2 GB := [x, y , z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=379.1MB, alloc=132.3MB, time=15.47 N2 := 251 #save(Problem, "format.txt"); > if (GB=[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 H := [-7 x y - 16 x, -2 z , y + 11 z x, 9 x y - 18 z , -6 z - 16 z , 2 -6 x y + 5 x y] > J:=[op(GB),op(G)]; 3 2 2 2 3 2 2 J := [x, y , z , 9 x y - 18 z , -6 z - 16 z , -6 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, 12, 17, 3, 2, 3, 3, 2/3, 2/3, 2/3, 1/2, 5/12, 5/12, 6, 9, 15, 3, 1, 3, 3, 1/2, 1/2, 1/2, 4/11, 4/11, 4/11, 3, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=402.4MB, alloc=132.3MB, time=16.15 |\^/| 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(); 1428253773 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 F := [4 y z + 2 z , 18 y + 20 x z, -15 y + 15 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [-5 x y - 7 x y z, -y z - 11 y, -16 y - y z] > Problem := [F,G]; 2 3 3 Problem := [[4 y z + 2 z , 18 y + 20 x z, -15 y + 15 x], 2 2 3 [-5 x y - 7 x y z, -y z - 11 y, -16 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=0.30 memory used=26.0MB, alloc=32.3MB, time=0.83 memory used=47.0MB, alloc=32.3MB, time=1.34 memory used=67.2MB, alloc=32.3MB, time=1.85 memory used=85.7MB, alloc=56.3MB, time=2.36 memory used=123.3MB, alloc=60.3MB, time=3.36 memory used=157.3MB, alloc=84.3MB, time=4.28 memory used=209.1MB, alloc=84.3MB, time=5.64 memory used=261.7MB, alloc=108.3MB, time=7.08 memory used=335.0MB, alloc=140.3MB, time=9.12 memory used=430.0MB, alloc=164.3MB, time=12.17 memory used=537.5MB, alloc=188.3MB, time=15.57 memory used=655.7MB, alloc=468.3MB, time=19.69 memory used=778.3MB, alloc=492.3MB, time=25.52 memory used=905.7MB, alloc=516.3MB, time=33.25 memory used=1055.9MB, alloc=540.3MB, time=42.41 memory used=1230.1MB, alloc=564.3MB, time=53.03 memory used=1428.4MB, alloc=564.3MB, time=65.09 N1 := 5271 > GB := Basis(F, plex(op(vars))); 2 3 2 GB := [8000 x - 729 x, 20 x y - 9 x, y - x, 10 x z + 9 x, 2 y z + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1630.0MB, alloc=564.3MB, time=74.09 memory used=1874.5MB, alloc=588.3MB, time=84.07 N2 := 2381 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 2 H := [4 y z + 2 z , 18 y + 20 x z, -15 y + 15 x, -5 x y - 7 x y z, 2 3 -y z - 11 y, -16 y - y z] > J:=[op(GB),op(G)]; 2 3 2 J := [8000 x - 729 x, 20 x y - 9 x, y - x, 10 x z + 9 x, 2 y z + z , 2 2 3 -5 x y - 7 x y z, -y z - 11 y, -16 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, 17, 3, 1, 3, 2, 1/2, 1, 5/6, 1/3, 3/4, 1/2, 8, 16, 20, 3, 2, 3, 2, 5/8, 3/4, 5/8, 9/16, 9/16, 3/8, -2, -3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1969.2MB, alloc=588.3MB, time=89.51 |\^/| 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(); 1428254015 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 F := [-16 y + 20, 2 y + 10 z, -15 x z + 19 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [-x z + 13 y, -5 x y + 18 y , 4 x + 7 y] > Problem := [F,G]; 3 3 Problem := [[-16 y + 20, 2 y + 10 z, -15 x z + 19 x], 2 2 3 2 [-x z + 13 y, -5 x y + 18 y , 4 x + 7 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.84 memory used=47.6MB, alloc=32.3MB, time=1.38 memory used=67.8MB, alloc=32.3MB, time=1.90 memory used=87.2MB, alloc=56.3MB, time=2.41 memory used=128.7MB, alloc=60.3MB, time=3.58 memory used=167.8MB, alloc=84.3MB, time=4.77 memory used=225.4MB, alloc=108.3MB, time=6.52 memory used=300.9MB, alloc=116.3MB, time=8.83 memory used=369.6MB, alloc=140.3MB, time=11.21 memory used=448.3MB, alloc=164.3MB, time=14.88 memory used=540.4MB, alloc=188.3MB, time=20.19 memory used=654.5MB, alloc=188.3MB, time=26.94 memory used=768.7MB, alloc=212.3MB, time=33.75 N1 := 3807 > GB := Basis(F, plex(op(vars))); 3 GB := [x, 4 y - 5, 4 z + 1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=912.5MB, alloc=212.3MB, time=40.27 N2 := 885 #save(Problem, "format.txt"); > 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 := [-16 y + 20, 2 y + 10 z, -15 x z + 19 x, -x z + 13 y, -5 x y + 18 y , 2 4 x + 7 y] > J:=[op(GB),op(G)]; 3 2 2 3 2 J := [x, 4 y - 5, 4 z + 1, -x z + 13 y, -5 x y + 18 y , 4 x + 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, 12, 16, 3, 2, 3, 2, 2/3, 5/6, 1/2, 5/12, 1/2, 1/4, 6, 10, 13, 3, 2, 3, 2, 2/3, 2/3, 1/3, 4/11, 5/11, 2/11, 2, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=980.8MB, alloc=212.3MB, time=42.94 |\^/| 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(); 1428254143 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [3 x y + 20 x z , -3 x y z - 18 x , -2 x y z + 19] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [11 y z + 13 x , -19 x + 12 y , -20 x z - 8 z] > Problem := [F,G]; 2 2 2 Problem := [[3 x y + 20 x z , -3 x y z - 18 x , -2 x y z + 19], 2 2 3 2 [11 y z + 13 x , -19 x + 12 y , -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=4.2MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.86 memory used=47.9MB, alloc=32.3MB, time=1.40 memory used=68.2MB, alloc=32.3MB, time=1.94 memory used=88.1MB, alloc=56.3MB, time=2.47 memory used=127.6MB, alloc=60.3MB, time=3.50 memory used=167.5MB, alloc=84.3MB, time=4.69 memory used=224.8MB, alloc=84.3MB, time=6.42 memory used=280.3MB, alloc=108.3MB, time=8.73 N1 := 1281 > GB := Basis(F, plex(op(vars))); 2 4 3 GB := [12 x + 19, y - 380, 3 x y + 190 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=351.7MB, alloc=108.3MB, time=11.50 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 H := [3 x y + 20 x z , -3 x y z - 18 x , -2 x y z + 19, 11 z y + 13 x , 3 2 -19 x + 12 y , -20 x z - 8 z] > J:=[op(GB),op(G)]; 2 4 3 2 2 3 2 J := [12 x + 19, y - 380, 3 y x + 190 z, 11 z y + 13 x , -19 x + 12 y , -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, 16, 17, 3, 3, 2, 2, 1, 5/6, 5/6, 2/3, 5/12, 1/2, 6, 12, 18, 4, 3, 4, 2, 5/6, 2/3, 1/2, 5/12, 1/3, 1/3, 4, -1, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=417.1MB, alloc=108.3MB, time=13.86 |\^/| 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(); 1428254183 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-7 x - 4 x z, 15 y z + 14, x z - 8 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 3 2 G := [20 x z + 10 y , -14 x + 11 y z, -19 x + 11 x z] > Problem := [F,G]; 3 2 2 Problem := [[-7 x - 4 x z, 15 y z + 14, x z - 8 y], 2 3 3 2 3 2 [20 x z + 10 y , -14 x + 11 y z, -19 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=0.30 memory used=26.7MB, alloc=32.3MB, time=0.87 memory used=47.5MB, alloc=32.3MB, time=1.40 memory used=67.4MB, alloc=56.3MB, time=1.94 memory used=109.1MB, alloc=68.3MB, time=3.05 memory used=146.5MB, alloc=92.3MB, time=4.03 memory used=207.1MB, alloc=92.3MB, time=5.57 memory used=265.0MB, alloc=116.3MB, time=7.08 memory used=335.4MB, alloc=116.3MB, time=8.78 memory used=404.8MB, alloc=396.3MB, time=10.55 memory used=512.9MB, alloc=420.3MB, time=13.17 memory used=640.5MB, alloc=444.3MB, time=16.52 memory used=771.0MB, alloc=468.3MB, time=19.63 memory used=869.7MB, alloc=468.3MB, time=22.18 memory used=978.5MB, alloc=492.3MB, time=25.12 memory used=1063.8MB, alloc=492.3MB, time=27.34 memory used=1142.3MB, alloc=492.3MB, time=29.62 memory used=1221.6MB, alloc=492.3MB, time=31.97 memory used=1282.9MB, alloc=516.3MB, time=33.69 memory used=1339.9MB, alloc=516.3MB, time=35.55 memory used=1396.8MB, alloc=516.3MB, time=37.48 memory used=1434.1MB, alloc=516.3MB, time=38.93 memory used=1637.6MB, alloc=540.3MB, time=44.09 memory used=1816.7MB, alloc=564.3MB, time=49.08 memory used=1971.7MB, alloc=588.3MB, time=53.52 memory used=2142.3MB, alloc=612.3MB, time=58.48 memory used=2269.9MB, alloc=636.3MB, time=62.47 memory used=2392.7MB, alloc=636.3MB, time=66.53 memory used=2515.4MB, alloc=660.3MB, time=70.94 memory used=2621.3MB, alloc=660.3MB, time=74.71 memory used=2712.7MB, alloc=660.3MB, time=77.95 memory used=2782.9MB, alloc=660.3MB, time=81.04 memory used=3079.6MB, alloc=684.3MB, time=89.99 memory used=3399.7MB, alloc=708.3MB, time=98.89 |\^/| 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(); 1428254484 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 F := [-8 x z - 16 z , -6 y z + 9 z , -7 y - 14 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [12 x z - 5 z, 11 y - 7 z , 11 z - 15 y] > Problem := [F,G]; 2 2 2 3 3 Problem := [[-8 x z - 16 z , -6 y z + 9 z , -7 y - 14 z ], 3 2 2 [12 x z - 5 z, 11 y - 7 z , 11 z - 15 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.84 memory used=47.8MB, alloc=32.3MB, time=1.37 memory used=68.5MB, alloc=32.3MB, time=1.90 memory used=88.6MB, alloc=32.3MB, time=2.43 memory used=107.0MB, alloc=56.3MB, time=2.93 memory used=145.1MB, alloc=60.3MB, time=3.92 memory used=183.6MB, alloc=84.3MB, time=5.11 memory used=241.9MB, alloc=108.3MB, time=6.93 memory used=317.9MB, alloc=132.3MB, time=9.32 memory used=409.1MB, alloc=164.3MB, time=12.21 memory used=510.3MB, alloc=188.3MB, time=15.62 memory used=614.8MB, alloc=212.3MB, time=20.27 memory used=730.1MB, alloc=236.3MB, time=26.09 memory used=856.2MB, alloc=260.3MB, time=33.68 memory used=1006.3MB, alloc=284.3MB, time=42.62 memory used=1180.2MB, alloc=284.3MB, time=52.93 memory used=1354.2MB, alloc=284.3MB, time=63.25 memory used=1528.1MB, alloc=308.3MB, time=73.56 memory used=1725.8MB, alloc=308.3MB, time=85.23 memory used=1923.6MB, alloc=332.3MB, time=96.98 |\^/| 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(); 1428254784 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-11 x z - 16 x y, 15 x y z, 15 x y - 20 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 G := [-10 y + 11 y z, 17 x - 7 x y , 3 x z - 18 x z ] > Problem := [F,G]; 2 2 2 Problem := [[-11 x z - 16 x y, 15 x y z, 15 x y - 20 y z], 3 3 2 2 2 [-10 y + 11 y z, 17 x - 7 x y , 3 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=26.4MB, alloc=32.3MB, time=0.85 memory used=47.6MB, alloc=32.3MB, time=1.39 memory used=67.8MB, alloc=32.3MB, time=1.90 memory used=86.8MB, alloc=56.3MB, time=2.41 memory used=126.4MB, alloc=60.3MB, time=3.43 memory used=166.1MB, alloc=84.3MB, time=4.67 memory used=223.9MB, alloc=108.3MB, time=6.42 memory used=301.0MB, alloc=116.3MB, time=8.72 memory used=369.5MB, alloc=140.3MB, time=10.79 memory used=452.1MB, alloc=164.3MB, time=14.13 memory used=543.8MB, alloc=188.3MB, time=18.89 memory used=650.3MB, alloc=212.3MB, time=25.27 memory used=780.7MB, alloc=212.3MB, time=32.99 memory used=911.1MB, alloc=236.3MB, time=40.77 memory used=1065.8MB, alloc=260.3MB, time=49.99 N1 := 4591 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 GB := [y x , y x, 11 x z + 16 x y, x y z, -3 x y + 4 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1164.5MB, alloc=260.3MB, time=53.11 memory used=1366.3MB, alloc=516.3MB, time=59.29 memory used=1551.5MB, alloc=540.3MB, time=66.52 memory used=1723.2MB, alloc=564.3MB, time=76.88 memory used=1914.1MB, alloc=588.3MB, time=88.75 memory used=2129.3MB, alloc=612.3MB, time=102.12 N2 := 4591 #save(Problem, "format.txt"); > if (GB=[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 := [-11 x z - 16 x y, 15 x y z, 15 x y - 20 y z, -10 y + 11 y z, 3 2 2 2 17 x - 7 x y , 3 x z - 18 x z ] > J:=[op(GB),op(G)]; 3 2 2 2 2 3 J := [y x , y x, 11 x z + 16 x y, x y z, -3 x y + 4 y z, -10 y + 11 y z, 3 2 2 2 17 x - 7 x y , 3 x 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, 18, 3, 3, 3, 2, 5/6, 5/6, 5/6, 4/7, 1/2, 3/7, 8, 19, 25, 4, 3, 3, 2, 7/8, 7/8, 5/8, 10/17, 9/17, 6/17, -4, -7, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2149.1MB, alloc=612.3MB, time=103.23 |\^/| 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(); 1428255075 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [15 y - 9 z, 18 x + 20 y, -6 y z - y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [7 y z - 17 x z, 15 y - 11 z, -18 x - 8 x z] > Problem := [F,G]; 2 2 2 2 Problem := [[15 y - 9 z, 18 x + 20 y, -6 y z - y ], 2 2 3 2 [7 y z - 17 x z, 15 y - 11 z, -18 x - 8 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.86 memory used=48.0MB, alloc=32.3MB, time=1.42 memory used=68.8MB, alloc=32.3MB, time=1.96 memory used=88.6MB, alloc=56.3MB, time=2.50 memory used=128.6MB, alloc=60.3MB, time=3.56 memory used=166.5MB, alloc=84.3MB, time=4.60 memory used=226.1MB, alloc=108.3MB, time=6.51 memory used=303.4MB, alloc=140.3MB, time=8.95 memory used=396.3MB, alloc=164.3MB, time=11.84 memory used=498.6MB, alloc=188.3MB, time=15.66 memory used=605.1MB, alloc=212.3MB, time=20.69 memory used=720.9MB, alloc=236.3MB, time=27.50 memory used=857.7MB, alloc=260.3MB, time=35.73 memory used=1018.4MB, alloc=260.3MB, time=45.32 memory used=1179.2MB, alloc=260.3MB, time=54.94 memory used=1339.9MB, alloc=284.3MB, time=64.56 memory used=1524.6MB, alloc=308.3MB, time=75.48 N1 := 5955 > GB := Basis(F, plex(op(vars))); 10 4 2 4 GB := [243 x - 20 x , 9 x + 10 y, -27 x + 20 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1681.9MB, alloc=308.3MB, time=81.69 N2 := 1417 #save(Problem, "format.txt"); > if (GB=[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 y - 9 z, 18 x + 20 y, -6 y z - y , 7 y z - 17 x z, 15 y - 11 z, 3 2 -18 x - 8 x z] > J:=[op(GB),op(G)]; 10 4 2 4 2 J := [243 x - 20 x , 9 x + 10 y, -27 x + 20 z, 7 y z - 17 x z, 2 3 2 15 y - 11 z, -18 x - 8 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, 15, 3, 3, 2, 2, 1/2, 5/6, 5/6, 1/3, 1/2, 1/2, 6, 12, 24, 10, 10, 2, 1, 5/6, 1/2, 2/3, 7/12, 1/4, 5/12, 1, -9, -7] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1765.4MB, alloc=564.3MB, time=86.06 |\^/| 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(); 1428255303 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [-13 x y z + 17 y , -12 x y - 19 x , -13 x y + 17 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [15 x y - 3 y, -14 x y - 19 x, -6 y z - x z] > Problem := [F,G]; 3 2 2 2 Problem := [[-13 x y z + 17 y , -12 x y - 19 x , -13 x y + 17 z ], 2 2 2 [15 x y - 3 y, -14 x y - 19 x, -6 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=0.30 memory used=26.2MB, alloc=32.3MB, time=0.84 memory used=47.7MB, alloc=32.3MB, time=1.39 memory used=68.3MB, alloc=32.3MB, time=1.91 memory used=88.0MB, alloc=56.3MB, time=2.45 memory used=127.6MB, alloc=60.3MB, time=3.50 memory used=165.0MB, alloc=60.3MB, time=4.45 memory used=203.3MB, alloc=84.3MB, time=5.65 memory used=261.7MB, alloc=116.3MB, time=7.50 memory used=337.8MB, alloc=140.3MB, time=9.79 memory used=428.0MB, alloc=164.3MB, time=13.74 memory used=525.0MB, alloc=164.3MB, time=19.51 memory used=622.0MB, alloc=188.3MB, time=25.31 N1 := 2845 > GB := Basis(F, plex(op(vars))); 5 2 2 2 4 3 GB := [3796416 x + 33698267 x , 12 x y + 19 x , -2197 x + 4913 x y , 5 3 4 2 3 707472 y - 793117 x , 2028 x + 5491 x z, 13 x y z - 17 y , 3 2 2 41616 y z - 61009 x , -13 x y + 17 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=738.6MB, alloc=188.3MB, time=28.60 memory used=843.5MB, alloc=444.3MB, time=31.45 memory used=978.6MB, alloc=444.3MB, time=35.01 memory used=1105.5MB, alloc=468.3MB, time=38.44 memory used=1257.4MB, alloc=492.3MB, time=42.57 memory used=1431.6MB, alloc=516.3MB, time=47.49 memory used=1620.6MB, alloc=540.3MB, time=52.86 memory used=1787.1MB, alloc=540.3MB, time=57.73 memory used=1926.5MB, alloc=564.3MB, time=61.78 memory used=2062.9MB, alloc=564.3MB, time=65.72 memory used=2193.1MB, alloc=564.3MB, time=69.60 memory used=2312.2MB, alloc=564.3MB, time=73.28 memory used=2424.5MB, alloc=564.3MB, time=76.81 memory used=2524.3MB, alloc=564.3MB, time=80.06 memory used=2624.5MB, alloc=564.3MB, time=83.38 memory used=2729.6MB, alloc=588.3MB, time=86.87 memory used=2833.9MB, alloc=588.3MB, time=90.31 memory used=2933.4MB, alloc=588.3MB, time=93.78 memory used=3011.3MB, alloc=588.3MB, time=96.59 memory used=3087.1MB, alloc=588.3MB, time=99.29 memory used=3167.4MB, alloc=612.3MB, time=102.16 memory used=3234.4MB, alloc=612.3MB, time=104.46 memory used=3289.6MB, alloc=612.3MB, time=106.64 memory used=3353.1MB, alloc=612.3MB, time=109.22 |\^/| 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(); 1428255603 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 3 F := [5 y - 10 x , -18 y + 12 z , -19 x + 16 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-3 x y - 14 x z, 13 x y z + 18 y z , -17 x - 8 y z ] > Problem := [F,G]; 3 2 3 2 3 Problem := [[5 y - 10 x , -18 y + 12 z , -19 x + 16 x z], 2 3 2 [-3 x y - 14 x z, 13 x y z + 18 y z , -17 x - 8 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.2MB, alloc=32.3MB, time=0.86 memory used=47.5MB, alloc=32.3MB, time=1.39 memory used=67.6MB, alloc=56.3MB, time=1.92 memory used=107.6MB, alloc=60.3MB, time=2.94 memory used=143.4MB, alloc=84.3MB, time=3.89 memory used=201.1MB, alloc=92.3MB, time=5.43 memory used=257.7MB, alloc=116.3MB, time=6.95 memory used=336.7MB, alloc=116.3MB, time=9.01 memory used=412.9MB, alloc=140.3MB, time=11.04 memory used=503.9MB, alloc=164.3MB, time=13.46 memory used=591.4MB, alloc=420.3MB, time=15.83 memory used=709.4MB, alloc=444.3MB, time=19.50 memory used=837.2MB, alloc=468.3MB, time=23.61 memory used=976.7MB, alloc=492.3MB, time=28.09 memory used=1132.4MB, alloc=516.3MB, time=32.95 memory used=1304.0MB, alloc=540.3MB, time=38.23 memory used=1479.6MB, alloc=564.3MB, time=43.94 memory used=1653.7MB, alloc=588.3MB, time=50.79 memory used=1813.6MB, alloc=612.3MB, time=59.01 memory used=1981.4MB, alloc=636.3MB, time=68.29 memory used=2160.7MB, alloc=660.3MB, time=78.66 memory used=2353.2MB, alloc=684.3MB, time=90.25 memory used=2558.5MB, alloc=708.3MB, 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(); 1428255903 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [17 y z + 17 x y, 14 x y + 7 y z, -20 y z - 9 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-16 x z + 11 z , -12 x + 12 z , -19 x z + 15 y z] > Problem := [F,G]; 2 2 2 2 Problem := [[17 y z + 17 x y, 14 x y + 7 y z, -20 y z - 9 x y], 2 2 2 2 2 [-16 x z + 11 z , -12 x + 12 z , -19 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=47.1MB, alloc=32.3MB, time=1.36 memory used=66.3MB, alloc=56.3MB, time=1.88 memory used=105.0MB, alloc=60.3MB, time=2.89 memory used=140.6MB, alloc=60.3MB, time=3.80 memory used=174.1MB, alloc=84.3MB, time=4.69 memory used=228.4MB, alloc=84.3MB, time=6.11 memory used=280.4MB, alloc=84.3MB, time=7.46 memory used=331.4MB, alloc=108.3MB, time=8.83 memory used=400.9MB, alloc=116.3MB, time=10.62 memory used=472.8MB, alloc=140.3MB, time=12.86 memory used=559.2MB, alloc=164.3MB, time=15.61 memory used=658.7MB, alloc=188.3MB, time=18.76 memory used=771.1MB, alloc=212.3MB, time=22.30 memory used=896.3MB, alloc=236.3MB, time=26.24 memory used=1029.1MB, alloc=260.3MB, time=30.49 memory used=1166.4MB, alloc=284.3MB, time=36.28 memory used=1304.3MB, alloc=308.3MB, time=43.10 memory used=1451.1MB, alloc=332.3MB, time=50.96 memory used=1609.7MB, alloc=356.3MB, time=60.07 memory used=1779.0MB, alloc=380.3MB, time=71.03 memory used=1972.2MB, alloc=404.3MB, time=83.45 memory used=2189.4MB, alloc=428.3MB, time=97.40 |\^/| 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(); 1428256203 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-8 y z - 18 y z, 13 y z + 19 x , 4 y + 4 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 G := [-16 x + 8, -20 y - x z, -10 z - 11 y ] > Problem := [F,G]; 2 2 2 2 Problem := [[-8 y z - 18 y z, 13 y z + 19 x , 4 y + 4 y], 2 3 3 2 [-16 x + 8, -20 y - x z, -10 z - 11 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.86 memory used=48.2MB, alloc=32.3MB, time=1.40 memory used=68.7MB, alloc=32.3MB, time=1.93 memory used=89.6MB, alloc=56.3MB, time=2.53 memory used=134.1MB, alloc=60.3MB, time=3.87 memory used=172.9MB, alloc=84.3MB, time=5.06 memory used=232.9MB, alloc=84.3MB, time=6.87 memory used=286.6MB, alloc=108.3MB, time=8.54 memory used=356.6MB, alloc=140.3MB, time=11.36 memory used=436.7MB, alloc=164.3MB, time=15.74 memory used=535.8MB, alloc=164.3MB, time=21.58 memory used=635.0MB, alloc=188.3MB, time=27.47 N1 := 3395 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x , y + y, y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); 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)]; 2 2 2 2 2 3 H := [-8 y z - 18 y z, 13 z y + 19 x , 4 y + 4 y, -16 x + 8, -20 y - x z, 3 2 -10 z - 11 y ] > J:=[op(GB),op(G)]; 2 2 2 3 3 2 J := [x , y + y, y z, -16 x + 8, -20 y - x z, -10 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, 12, 16, 3, 2, 3, 3, 1/2, 5/6, 2/3, 1/4, 7/12, 5/12, 6, 10, 14, 3, 2, 3, 3, 1/2, 2/3, 1/2, 1/4, 5/12, 1/4, 2, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=739.3MB, alloc=188.3MB, time=32.08 |\^/| 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(); 1428256305 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-16 x y z - 2 y , 9 x y - 20 y , 2 x z + 16 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 G := [6 y z - 13 y z, 2 z + 20 x z, -7 y - 19 z] > Problem := [F,G]; 3 2 2 Problem := [[-16 x y z - 2 y , 9 x y - 20 y , 2 x z + 16 z], 2 3 3 [6 y z - 13 y z, 2 z + 20 x z, -7 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=0.31 memory used=26.1MB, alloc=32.3MB, time=0.84 memory used=47.2MB, alloc=32.3MB, time=1.35 memory used=66.9MB, alloc=32.3MB, time=1.84 memory used=86.2MB, alloc=56.3MB, time=2.36 memory used=125.6MB, alloc=60.3MB, time=3.41 memory used=162.9MB, alloc=60.3MB, time=4.38 memory used=197.8MB, alloc=84.3MB, time=5.30 memory used=255.2MB, alloc=108.3MB, time=6.95 memory used=342.4MB, alloc=116.3MB, time=9.36 memory used=415.9MB, alloc=140.3MB, time=11.56 memory used=503.9MB, alloc=164.3MB, time=14.28 memory used=607.1MB, alloc=188.3MB, time=17.53 memory used=721.1MB, alloc=212.3MB, time=21.33 memory used=840.7MB, alloc=236.3MB, time=26.74 memory used=968.7MB, alloc=260.3MB, time=33.35 memory used=1108.6MB, alloc=284.3MB, time=41.58 memory used=1267.9MB, alloc=308.3MB, time=51.32 memory used=1451.2MB, alloc=332.3MB, time=62.51 memory used=1658.3MB, alloc=332.3MB, time=75.13 memory used=1865.5MB, alloc=332.3MB, time=87.84 memory used=2072.5MB, alloc=356.3MB, time=100.46 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428256605 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 F := [-20 x y z + 4 x z, 16 x y , -18 x y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 G := [-17 x z - 20 z , -11 x y z + 17 x, -19 x + 11 z ] > Problem := [F,G]; 2 Problem := [[-20 x y z + 4 x z, 16 x y , -18 x y z], 2 3 3 3 [-17 x z - 20 z , -11 x y z + 17 x, -19 x + 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.8MB, alloc=32.3MB, time=0.92 memory used=48.8MB, alloc=56.3MB, time=1.60 N1 := 437 > GB := Basis(F, plex(op(vars))); 2 GB := [x y , x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 127 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 H := [-20 x y z + 4 x z, 16 x y , -18 x y z, -17 x z - 20 z , -11 x y z + 17 x, 3 3 -19 x + 11 z ] > J:=[op(GB),op(G)]; 2 2 3 3 3 J := [x y , x z, -17 x z - 20 z , -11 x y z + 17 x, -19 x + 11 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 18, 3, 3, 2, 3, 1, 2/3, 5/6, 8/15, 4/15, 7/15, 5, 11, 14, 3, 3, 2, 3, 1, 2/5, 4/5, 3/5, 1/5, 1/2, 4, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=72.7MB, alloc=56.3MB, time=2.35 |\^/| 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(); 1428256611 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [-17 x z + z , 17 x z - 13 z, 20 x y - 2 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [-x y + 15 y, -18 x y z + 5, -16 x z + 10 z ] > Problem := [F,G]; 2 3 2 Problem := [[-17 x z + z , 17 x z - 13 z, 20 x y - 2 y z], 2 2 3 [-x y + 15 y, -18 x y z + 5, -16 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=0.31 memory used=26.1MB, alloc=32.3MB, time=0.84 memory used=48.0MB, alloc=32.3MB, time=1.44 memory used=69.4MB, alloc=56.3MB, time=2.10 memory used=112.5MB, alloc=56.3MB, time=3.35 memory used=149.2MB, alloc=84.3MB, time=4.63 memory used=200.9MB, alloc=108.3MB, time=7.41 N1 := 1653 > GB := Basis(F, plex(op(vars))); 2 3 2 GB := [y x , 17 x z - 13 z, y z, z - 13 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=276.1MB, alloc=108.3MB, time=10.33 N2 := 567 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 H := [-17 x z + z , 17 x z - 13 z, 20 x y - 2 y z, -x y + 15 y, 2 3 -18 x y z + 5, -16 x z + 10 z ] > J:=[op(GB),op(G)]; 2 3 2 2 J := [y x , 17 x z - 13 z, y z, z - 13 z , -x y + 15 y, -18 x y z + 5, 2 3 -16 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, 14, 17, 3, 2, 2, 3, 1, 1/2, 5/6, 1/2, 5/12, 2/3, 7, 14, 19, 3, 2, 2, 3, 5/7, 4/7, 5/7, 5/14, 5/14, 4/7, 0, -2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=297.7MB, alloc=108.3MB, time=11.20 |\^/| 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(); 1428256639 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 F := [4 z + 4 y, -3 y - 4 z, 10 x y + 5 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [4 y z - 18 x, -16 x z - 2 x y, -13 y z] > Problem := [F,G]; 3 3 2 2 Problem := [[4 z + 4 y, -3 y - 4 z, 10 x y + 5 x ], 2 2 [4 y z - 18 x, -16 x z - 2 x 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=0.30 memory used=26.2MB, alloc=32.3MB, time=0.85 memory used=47.3MB, alloc=32.3MB, time=1.38 memory used=67.7MB, alloc=32.3MB, time=1.92 memory used=87.1MB, alloc=56.3MB, time=2.45 memory used=126.2MB, alloc=60.3MB, time=3.48 memory used=162.8MB, alloc=84.3MB, time=4.46 memory used=221.9MB, alloc=84.3MB, time=6.27 memory used=275.4MB, alloc=108.3MB, time=7.95 memory used=347.8MB, alloc=140.3MB, time=10.26 memory used=436.6MB, alloc=164.3MB, time=13.07 memory used=537.9MB, alloc=188.3MB, time=17.31 memory used=644.9MB, alloc=212.3MB, time=23.17 memory used=767.4MB, alloc=236.3MB, time=30.60 memory used=913.9MB, alloc=236.3MB, time=39.45 memory used=1060.4MB, alloc=260.3MB, time=48.30 N1 := 4809 > GB := Basis(F, plex(op(vars))); 2 9 3 GB := [x , 27 y - 64 y, 3 y + 4 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1233.4MB, alloc=260.3MB, time=57.97 memory used=1349.2MB, alloc=516.3MB, time=61.84 N2 := 1385 #save(Problem, "format.txt"); > 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 := [4 z + 4 y, -3 y - 4 z, 10 x y + 5 x , 4 y z - 18 x, -16 x z - 2 x y, 2 -13 y z] > J:=[op(GB),op(G)]; 2 9 3 2 2 J := [x , 27 y - 64 y, 3 y + 4 z, 4 y z - 18 x, -16 x z - 2 x 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, 14, 17, 3, 2, 3, 3, 1/2, 1, 5/6, 5/13, 6/13, 5/13, 6, 12, 22, 9, 2, 9, 1, 1/2, 5/6, 2/3, 4/13, 6/13, 4/13, 2, -5, -6] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1409.3MB, alloc=516.3MB, time=65.30 |\^/| 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(); 1428256810 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [2 y z - 7 x z, 17 x y - 7 x z, 7 y z + 15] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-8 x z - 10 y , -2 y + 6 x, 20 y z + 3 z] > Problem := [F,G]; 2 2 2 Problem := [[2 y z - 7 x z, 17 x y - 7 x z, 7 y z + 15], 2 2 2 2 [-8 x z - 10 y , -2 y + 6 x, 20 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=0.31 memory used=26.0MB, alloc=32.3MB, time=0.85 memory used=47.7MB, alloc=32.3MB, time=1.42 memory used=67.8MB, alloc=32.3MB, time=1.94 memory used=87.3MB, alloc=56.3MB, time=2.49 memory used=125.2MB, alloc=60.3MB, time=3.51 memory used=162.6MB, alloc=84.3MB, time=4.51 memory used=214.0MB, alloc=84.3MB, time=5.88 memory used=272.1MB, alloc=92.3MB, time=7.45 memory used=327.9MB, alloc=116.3MB, time=8.95 memory used=407.6MB, alloc=140.3MB, time=11.25 memory used=501.3MB, alloc=164.3MB, time=14.19 memory used=605.7MB, alloc=188.3MB, time=17.45 memory used=711.4MB, alloc=468.3MB, time=20.86 memory used=850.0MB, alloc=492.3MB, time=25.37 memory used=993.4MB, alloc=516.3MB, time=32.06 memory used=1142.3MB, alloc=540.3MB, time=40.00 memory used=1298.5MB, alloc=564.3MB, time=49.80 memory used=1478.7MB, alloc=588.3MB, time=61.04 memory used=1682.8MB, alloc=612.3MB, time=73.72 memory used=1910.9MB, alloc=612.3MB, time=87.84 memory used=2138.9MB, alloc=612.3MB, time=101.97 |\^/| 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(); 1428257110 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [10 y z + 15 z, -20 y + 6 z, 11 y + 4 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 G := [17 x + 20, -7 x + 17 x z, 12 x z + 6 y ] > Problem := [F,G]; 2 2 3 Problem := [[10 y z + 15 z, -20 y + 6 z, 11 y + 4 y z], 3 3 2 2 [17 x + 20, -7 x + 17 x z, 12 x z + 6 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.31 memory used=26.5MB, alloc=32.3MB, time=0.88 memory used=48.2MB, alloc=32.3MB, time=1.43 memory used=68.4MB, alloc=56.3MB, time=2.00 memory used=111.1MB, alloc=60.3MB, time=3.12 memory used=152.2MB, alloc=60.3MB, time=4.16 memory used=190.9MB, alloc=84.3MB, time=5.18 memory used=246.6MB, alloc=84.3MB, time=6.65 memory used=302.2MB, alloc=116.3MB, time=8.20 memory used=380.2MB, alloc=116.3MB, time=10.25 memory used=456.4MB, alloc=140.3MB, time=12.59 memory used=548.7MB, alloc=164.3MB, time=15.46 memory used=655.4MB, alloc=188.3MB, time=18.82 memory used=776.2MB, alloc=212.3MB, time=22.60 memory used=893.6MB, alloc=492.3MB, time=26.34 memory used=1044.9MB, alloc=516.3MB, time=30.98 memory used=1196.7MB, alloc=540.3MB, time=36.98 memory used=1342.9MB, alloc=564.3MB, time=44.16 memory used=1497.7MB, alloc=588.3MB, time=52.42 memory used=1663.8MB, alloc=612.3MB, time=61.85 memory used=1840.5MB, alloc=636.3MB, time=73.15 memory used=2039.1MB, alloc=660.3MB, time=85.99 memory used=2261.6MB, alloc=684.3MB, time=100.14 |\^/| 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(); 1428257410 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [13 x y - 8 y z, 4 x - 7 y, 3 x z + 8 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [16 z + 8 z , -12 y z + 12 x , -11 y - 15 z] > Problem := [F,G]; 2 2 Problem := [[13 x y - 8 y z, 4 x - 7 y, 3 x z + 8 y z], 3 2 2 2 2 [16 z + 8 z , -12 y z + 12 x , -11 y - 15 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.84 memory used=47.5MB, alloc=32.3MB, time=1.37 memory used=67.6MB, alloc=32.3MB, time=1.89 memory used=87.1MB, alloc=56.3MB, time=2.43 memory used=126.4MB, alloc=60.3MB, time=3.45 memory used=163.6MB, alloc=84.3MB, time=4.42 memory used=215.8MB, alloc=84.3MB, time=5.79 memory used=270.1MB, alloc=116.3MB, time=7.30 memory used=345.8MB, alloc=116.3MB, time=9.33 memory used=419.3MB, alloc=140.3MB, time=11.54 memory used=509.8MB, alloc=164.3MB, time=14.39 memory used=613.6MB, alloc=188.3MB, time=17.62 memory used=732.2MB, alloc=212.3MB, time=21.28 memory used=858.5MB, alloc=492.3MB, time=25.35 memory used=999.8MB, alloc=516.3MB, time=29.92 memory used=1148.7MB, alloc=540.3MB, time=35.65 memory used=1289.7MB, alloc=564.3MB, time=42.67 memory used=1440.9MB, alloc=588.3MB, time=50.72 memory used=1604.3MB, alloc=612.3MB, time=59.72 memory used=1779.5MB, alloc=636.3MB, time=70.36 memory used=1969.8MB, alloc=660.3MB, time=82.52 memory used=2184.0MB, alloc=684.3MB, time=96.10 |\^/| 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(); 1428257710 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [-13 x z + 10 z , -17 x z + 3 z , 20 x z - 12] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [-4 x + 9 y z, 17 x y + 3 x , 19 x y - 16 z ] > Problem := [F,G]; 2 3 2 2 Problem := [[-13 x z + 10 z , -17 x z + 3 z , 20 x z - 12], 3 2 2 2 2 [-4 x + 9 y z, 17 x y + 3 x , 19 x y - 16 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=47.6MB, alloc=32.3MB, time=1.38 memory used=67.7MB, alloc=32.3MB, time=1.91 memory used=87.0MB, alloc=56.3MB, time=2.43 memory used=127.0MB, alloc=60.3MB, time=3.47 memory used=164.2MB, alloc=84.3MB, time=4.45 memory used=218.6MB, alloc=84.3MB, time=5.89 memory used=274.5MB, alloc=116.3MB, time=7.40 memory used=353.7MB, alloc=140.3MB, time=9.78 memory used=451.1MB, alloc=164.3MB, time=12.74 memory used=579.3MB, alloc=164.3MB, time=15.85 memory used=685.6MB, alloc=188.3MB, time=19.17 memory used=814.1MB, alloc=212.3MB, time=22.80 memory used=943.4MB, alloc=492.3MB, time=27.92 memory used=1072.7MB, alloc=516.3MB, time=34.07 memory used=1209.1MB, alloc=540.3MB, time=41.89 memory used=1362.3MB, alloc=564.3MB, time=51.22 memory used=1539.3MB, alloc=588.3MB, time=61.94 memory used=1740.4MB, alloc=588.3MB, time=74.08 memory used=1941.4MB, alloc=612.3MB, time=86.25 |\^/| 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(); 1428258010 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [-5 x y + 3 x, -20 y - 15 y, -18 x z - 9 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 G := [-x - 8 x z, -13 x y + 3 z , 16 z - x] > Problem := [F,G]; 2 3 2 Problem := [[-5 x y + 3 x, -20 y - 15 y, -18 x z - 9 y z], 3 2 2 3 2 [-x - 8 x z, -13 x y + 3 z , 16 z - x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.0MB, alloc=32.3MB, time=0.83 memory used=47.7MB, alloc=32.3MB, time=1.37 memory used=68.6MB, alloc=32.3MB, time=1.89 memory used=88.8MB, alloc=32.3MB, time=2.39 memory used=109.3MB, alloc=56.3MB, time=3.02 memory used=154.1MB, alloc=60.3MB, time=4.28 memory used=195.5MB, alloc=84.3MB, time=5.46 memory used=254.8MB, alloc=108.3MB, time=7.30 memory used=325.0MB, alloc=132.3MB, time=10.73 memory used=411.3MB, alloc=132.3MB, time=15.65 N1 := 2367 > GB := Basis(F, plex(op(vars))); 3 GB := [x, 4 y + 3 y, z y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 341 #save(Problem, "format.txt"); > if (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 := [-5 x y + 3 x, -20 y - 15 y, -18 x z - 9 y z, -x - 8 x z, 2 3 2 -13 x y + 3 z , 16 z - x] > J:=[op(GB),op(G)]; 3 3 2 2 3 2 J := [x, 4 y + 3 y, z y, -x - 8 x z, -13 x y + 3 z , 16 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, 17, 3, 3, 3, 3, 5/6, 2/3, 2/3, 7/12, 5/12, 5/12, 6, 11, 14, 3, 3, 3, 3, 2/3, 1/2, 2/3, 5/11, 4/11, 4/11, 2, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=496.1MB, alloc=140.3MB, time=18.77 |\^/| 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(); 1428258065 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [-17 x + 16 z , -9 x z - 7 x y, 17 z - 20 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-y z - 3 x z, 10 y - 16 x, -12 x y z + 20 y ] > Problem := [F,G]; 2 2 2 3 Problem := [[-17 x + 16 z , -9 x z - 7 x y, 17 z - 20 y z], 2 2 2 [-y z - 3 x z, 10 y - 16 x, -12 x y z + 20 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.2MB, alloc=40.3MB, time=1.00 memory used=60.5MB, alloc=40.3MB, time=1.69 memory used=87.9MB, alloc=40.3MB, time=2.38 memory used=114.1MB, alloc=40.3MB, time=3.05 memory used=138.8MB, alloc=64.3MB, time=3.71 memory used=188.6MB, alloc=68.3MB, time=5.24 memory used=234.0MB, alloc=92.3MB, time=6.68 memory used=299.1MB, alloc=116.3MB, time=8.71 memory used=382.8MB, alloc=124.3MB, time=11.35 memory used=453.0MB, alloc=148.3MB, time=13.95 memory used=533.7MB, alloc=172.3MB, time=17.70 memory used=625.7MB, alloc=196.3MB, time=23.18 memory used=741.7MB, alloc=196.3MB, time=29.98 memory used=857.6MB, alloc=220.3MB, time=36.81 memory used=997.7MB, alloc=220.3MB, time=45.04 N1 := 4655 > GB := Basis(F, plex(op(vars))); 4 3 3 2 2 2 GB := [x , 153 x + 112 x y, x z, -289 x z + 320 y z, -17 x + 16 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1139.9MB, alloc=220.3MB, time=52.28 memory used=1260.0MB, alloc=500.3MB, time=56.17 N2 := 1671 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 H := [-17 x + 16 z , -9 x z - 7 x y, 17 z - 20 y z, -y z - 3 x z, 2 2 10 y - 16 x, -12 x y z + 20 y ] > J:=[op(GB),op(G)]; 4 3 3 2 2 2 J := [x , 153 x + 112 x y, x z, -289 x z + 320 y z, -17 x + 16 z , 2 2 2 -y z - 3 x z, 10 y - 16 x, -12 x y 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, 16, 3, 2, 2, 3, 5/6, 5/6, 5/6, 1/2, 1/2, 7/12, 8, 18, 24, 4, 4, 2, 2, 1, 5/8, 5/8, 9/16, 3/8, 7/16, -3, -8, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1359.4MB, alloc=500.3MB, time=61.64 |\^/| 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(); 1428258236 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [10 x y + 2 x z , -11 x y + 11 y , 9 x + 16 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [-19 y z + 9, -15 z - 11 z, 5 x y - 8 x z] > Problem := [F,G]; 2 2 2 2 2 Problem := [[10 x y + 2 x z , -11 x y + 11 y , 9 x + 16 x y], 2 3 [-19 y z + 9, -15 z - 11 z, 5 x y - 8 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.85 memory used=47.9MB, alloc=32.3MB, time=1.39 memory used=68.0MB, alloc=32.3MB, time=1.89 memory used=87.3MB, alloc=56.3MB, time=2.42 memory used=126.4MB, alloc=60.3MB, time=3.45 memory used=163.8MB, alloc=60.3MB, time=4.41 memory used=199.2MB, alloc=84.3MB, time=5.35 memory used=257.9MB, alloc=108.3MB, time=7.19 memory used=334.5MB, alloc=116.3MB, time=9.57 memory used=404.2MB, alloc=140.3MB, time=11.75 memory used=488.6MB, alloc=164.3MB, time=14.89 memory used=579.8MB, alloc=188.3MB, time=19.57 memory used=684.1MB, alloc=212.3MB, time=25.96 memory used=812.4MB, alloc=212.3MB, time=33.72 memory used=940.8MB, alloc=236.3MB, time=41.39 N1 := 4043 > GB := Basis(F, plex(op(vars))); 4 3 2 3 2 3 2 GB := [16 x + 9 x , 9 x + 16 x y, 9 x + 16 y , -45 x + 16 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1090.5MB, alloc=236.3MB, time=47.16 memory used=1264.9MB, alloc=516.3MB, time=52.63 memory used=1457.9MB, alloc=540.3MB, time=59.37 memory used=1635.1MB, alloc=564.3MB, time=69.46 memory used=1821.8MB, alloc=588.3MB, time=81.44 memory used=2032.5MB, alloc=612.3MB, time=94.90 N2 := 4913 #save(Problem, "format.txt"); > if (GB=[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 := [10 x y + 2 x z , -11 x y + 11 y , 9 x + 16 x y, -19 y z + 9, 3 -15 z - 11 z, 5 x y - 8 x z] > J:=[op(GB),op(G)]; 4 3 2 3 2 3 2 2 J := [16 x + 9 x , 9 x + 16 x y, 9 x + 16 y , -45 x + 16 x z , -19 y z + 9, 3 -15 z - 11 z, 5 x y - 8 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, 16, 3, 2, 2, 3, 2/3, 5/6, 2/3, 7/12, 1/2, 5/12, 7, 13, 20, 4, 4, 2, 3, 5/7, 4/7, 4/7, 9/14, 2/7, 5/14, 0, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2200.8MB, alloc=612.3MB, time=105.10 |\^/| 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(); 1428258531 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [x y z - 16 y z , -14 x z + 14 y z, 18 x y z + 6 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 G := [17 y z , 7 x y + 5 y , -9 y - 5 z ] > Problem := [F,G]; 2 2 2 3 Problem := [[x y z - 16 y z , -14 x z + 14 y z, 18 x y z + 6 z ], 2 2 3 3 2 [17 y z , 7 x y + 5 y , -9 y - 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=47.7MB, alloc=32.3MB, time=1.41 memory used=68.9MB, alloc=56.3MB, time=2.06 memory used=113.8MB, alloc=60.3MB, time=3.40 memory used=150.8MB, alloc=84.3MB, time=4.69 N1 := 1311 > GB := Basis(F, plex(op(vars))); 4 3 2 2 2 3 2 2 GB := [x z, 768 x z + x y z, -x z + y z, -x z + 16 x z , 2 3 -x y z + 16 y z , 3 x y z + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=202.7MB, alloc=84.3MB, time=7.42 memory used=257.3MB, alloc=108.3MB, time=8.87 memory used=347.0MB, alloc=116.3MB, time=11.42 memory used=427.0MB, alloc=140.3MB, time=13.85 memory used=511.2MB, alloc=164.3MB, time=18.37 N2 := 2191 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 H := [x y z - 16 y z , -14 x z + 14 y z, 18 x y z + 6 z , 17 y z , 2 3 3 2 7 x y + 5 y , -9 y - 5 z ] > J:=[op(GB),op(G)]; 4 3 2 2 2 3 2 2 2 J := [x z, 768 x z + x y z, -x z + y z, -x z + 16 x z , -x y z + 16 y z , 3 2 2 3 3 2 3 x y z + z , 17 y z , 7 x y + 5 y , -9 y - 5 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 18, 3, 2, 3, 3, 2/3, 1, 5/6, 4/13, 8/13, 8/13, 9, 22, 31, 5, 4, 3, 3, 7/9, 7/9, 8/9, 9/19, 9/19, 13/19, -7, -13, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=593.1MB, alloc=164.3MB, time=22.94 |\^/| 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(); 1428258595 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-2 x + 9 y , 19 x y + 10 y z , 6 x y + 4 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [11 y - 8 z , -8 y z + y, -8 z + 5 y] > Problem := [F,G]; 2 2 2 2 Problem := [[-2 x + 9 y , 19 x y + 10 y z , 6 x y + 4 y], 3 2 2 2 [11 y - 8 z , -8 y z + y, -8 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=32.6MB, alloc=40.3MB, time=1.03 memory used=60.9MB, alloc=40.3MB, time=1.75 memory used=87.7MB, alloc=40.3MB, time=2.45 memory used=113.7MB, alloc=68.3MB, time=3.15 memory used=160.4MB, alloc=68.3MB, time=4.32 memory used=207.2MB, alloc=92.3MB, time=5.79 memory used=273.0MB, alloc=92.3MB, time=7.83 memory used=334.2MB, alloc=116.3MB, time=9.72 memory used=413.1MB, alloc=140.3MB, time=12.35 memory used=503.3MB, alloc=164.3MB, time=16.46 memory used=604.2MB, alloc=164.3MB, time=22.39 memory used=705.2MB, alloc=188.3MB, time=28.35 N1 := 3297 > GB := Basis(F, plex(op(vars))); GB := 3 2 2 2 2 2 2 2 [3 x + 2 x , 3 x y + 2 y, -2 x + 9 y , 45 x z + 38 x , 45 y z + 38 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=833.9MB, alloc=196.3MB, time=34.45 memory used=958.9MB, alloc=452.3MB, time=38.20 memory used=1099.2MB, alloc=476.3MB, time=42.74 memory used=1243.9MB, alloc=500.3MB, time=50.83 N2 := 2829 #save(Problem, "format.txt"); > if (GB=[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 x + 9 y , 19 x y + 10 y z , 6 x y + 4 y, 11 y - 8 z , -8 y z + y, 2 -8 z + 5 y] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 2 2 J := [3 x + 2 x , 3 x y + 2 y, -2 x + 9 y , 45 x z + 38 x , 45 y z + 38 y, 3 2 2 2 11 y - 8 z , -8 y z + y, -8 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, 15, 3, 2, 3, 2, 1/2, 1, 2/3, 1/4, 3/4, 1/3, 8, 15, 22, 4, 3, 3, 2, 1/2, 3/4, 5/8, 3/8, 9/16, 5/16, -2, -7, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1381.4MB, alloc=500.3MB, time=59.07 |\^/| 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(); 1428258771 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [-15 y , -10 y z + 2 x , 6 x z + 7 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 G := [-3 x + 13, -7 x + 20 y, 2 x + 19 y] > Problem := [F,G]; 3 2 2 2 2 Problem := [[-15 y , -10 y z + 2 x , 6 x z + 7 y z], 3 [-3 x + 13, -7 x + 20 y, 2 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=0.30 memory used=26.6MB, alloc=32.3MB, time=0.89 memory used=49.6MB, alloc=32.3MB, time=1.57 memory used=69.9MB, alloc=56.3MB, time=2.36 N1 := 461 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 2 2 2 GB := [x , x y , y , 6 x z + 7 y z, 5 y z - x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.5MB, alloc=60.3MB, time=3.46 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 2 2 3 H := [-15 y , -10 y z + 2 x , 6 x z + 7 y z, -3 x + 13, -7 x + 20 y, 19 y + 2 x] > J:=[op(GB),op(G)]; 3 2 2 3 2 2 2 2 3 J := [x , x y , y , 6 x z + 7 y z, 5 y z - x , -3 x + 13, -7 x + 20 y, 19 y + 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, 12, 14, 3, 3, 3, 2, 5/6, 5/6, 1/3, 5/12, 5/12, 1/4, 8, 15, 21, 4, 3, 3, 2, 7/8, 3/4, 1/4, 7/16, 3/8, 3/16, -3, -7, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=136.0MB, alloc=60.3MB, time=4.34 |\^/| 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(); 1428258783 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-15 x z + 17 y z , -18 y z - 4 z, -x y + 14 x z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [5 y z + 11 x, -14 x z, 9 x + 5 y z] > Problem := [F,G]; 2 2 2 2 Problem := [[-15 x z + 17 y z , -18 y z - 4 z, -x y + 14 x z ], 2 3 [5 y z + 11 x, -14 x 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=0.32 memory used=26.5MB, alloc=32.3MB, time=0.88 memory used=48.0MB, alloc=32.3MB, time=1.42 memory used=68.8MB, alloc=56.3MB, time=2.02 memory used=112.7MB, alloc=60.3MB, time=3.35 memory used=151.5MB, alloc=84.3MB, time=4.52 memory used=212.9MB, alloc=84.3MB, time=6.27 memory used=269.5MB, alloc=108.3MB, time=7.93 memory used=343.0MB, alloc=140.3MB, time=10.23 memory used=429.3MB, alloc=164.3MB, time=13.83 memory used=523.5MB, alloc=188.3MB, time=19.02 memory used=635.5MB, alloc=188.3MB, time=25.72 memory used=747.4MB, alloc=212.3MB, time=32.42 memory used=883.4MB, alloc=212.3MB, time=40.56 memory used=1019.4MB, alloc=236.3MB, time=48.76 N1 := 4657 > GB := Basis(F, plex(op(vars))); 5 2 2 3 2 3 2 GB := [10333575 x y - 2312 x y , 9 x y + 2 x y , 10935 x y + 136 x z, 4 2 2 9 y z + 2 z, -1476225 x y + 4624 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1150.9MB, alloc=236.3MB, time=53.27 memory used=1323.1MB, alloc=516.3MB, time=58.58 memory used=1512.9MB, alloc=540.3MB, time=64.95 memory used=1694.7MB, alloc=564.3MB, time=75.07 memory used=1882.2MB, alloc=588.3MB, time=87.11 memory used=2093.6MB, alloc=612.3MB, time=100.62 |\^/| 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(); 1428259083 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 F := [-2 x y - 12 y z, -8 x z - y z , -12 x + 15 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [-17 x z - 11 y , 6 x z - 19 x y, -13 y + 13 x ] > Problem := [F,G]; 2 2 2 2 3 Problem := [[-2 x y - 12 y z, -8 x z - y z , -12 x + 15 x], 2 2 3 2 [-17 x z - 11 y , 6 x z - 19 x y, -13 y + 13 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.86 memory used=47.8MB, alloc=32.3MB, time=1.41 memory used=68.1MB, alloc=56.3MB, time=1.95 memory used=113.0MB, alloc=60.3MB, time=3.33 memory used=152.2MB, alloc=84.3MB, time=4.53 memory used=210.9MB, alloc=116.3MB, time=6.41 memory used=284.7MB, alloc=140.3MB, time=9.89 memory used=371.8MB, alloc=140.3MB, time=15.02 N1 := 2391 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 2 GB := [4 x - 5 x, 8 x y + x y , -x y + 48 x y z, x y + 6 y z, 2 2 2 2 x y + 18432 x z , -x y + 2304 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=460.7MB, alloc=140.3MB, time=18.68 memory used=548.3MB, alloc=164.3MB, time=21.07 memory used=641.6MB, alloc=444.3MB, time=23.63 memory used=775.0MB, alloc=444.3MB, time=27.19 memory used=903.2MB, alloc=468.3MB, time=30.62 memory used=1058.4MB, alloc=492.3MB, time=34.71 memory used=1245.5MB, alloc=516.3MB, time=40.28 memory used=1443.3MB, alloc=540.3MB, time=46.49 memory used=1654.6MB, alloc=564.3MB, time=52.96 memory used=1866.7MB, alloc=588.3MB, time=59.82 memory used=2077.3MB, alloc=612.3MB, time=67.63 memory used=2266.4MB, alloc=636.3MB, time=77.61 memory used=2460.1MB, alloc=660.3MB, time=88.65 memory used=2664.9MB, alloc=684.3MB, time=101.05 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428259383 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-16 y - 16 y , -19 x z - 10 z, 10 x y z + 12 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [x y - 17 z , 18 x y + 12 x, 14 x z + 4 x z] > Problem := [F,G]; 3 2 2 Problem := [[-16 y - 16 y , -19 x z - 10 z, 10 x y z + 12 y], 2 3 2 2 [x y - 17 z , 18 x y + 12 x, 14 x z + 4 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.84 N1 := 363 > GB := Basis(F, plex(op(vars))); 2 GB := [y, 19 x z + 10 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=78.4MB, alloc=68.3MB, time=2.43 N2 := 141 #save(Problem, "format.txt"); > 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 := [-16 y - 16 y , -19 x z - 10 z, 10 x y z + 12 y, -17 z + y x, 2 2 18 x y + 12 x, 14 x z + 4 x z] > J:=[op(GB),op(G)]; 2 3 2 2 2 J := [y, 19 x z + 10 z, -17 z + y x, 18 x y + 12 x, 14 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, 13, 18, 3, 2, 3, 3, 5/6, 2/3, 2/3, 7/12, 1/2, 1/2, 5, 10, 13, 3, 2, 2, 3, 4/5, 3/5, 3/5, 2/3, 1/3, 5/9, 3, 5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=102.2MB, alloc=68.3MB, 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(); 1428259392 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-12 x z - 18 z, 16 x z - 2 y z, 6 y + 8 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [7 x z + 3 y, 6 z - 11 x , 15 x y z - 9 y ] > Problem := [F,G]; 2 2 Problem := [[-12 x z - 18 z, 16 x z - 2 y z, 6 y + 8 y], 3 2 2 [7 x z + 3 y, 6 z - 11 x , 15 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=0.30 memory used=26.0MB, alloc=32.3MB, time=0.83 memory used=47.6MB, alloc=32.3MB, time=1.37 memory used=67.8MB, alloc=32.3MB, time=1.89 memory used=86.3MB, alloc=56.3MB, time=2.39 memory used=128.1MB, alloc=60.3MB, time=3.67 memory used=165.2MB, alloc=84.3MB, time=4.81 memory used=222.3MB, alloc=84.3MB, time=6.56 memory used=274.6MB, alloc=108.3MB, time=8.20 memory used=342.5MB, alloc=140.3MB, time=10.98 memory used=420.2MB, alloc=164.3MB, time=15.51 memory used=521.2MB, alloc=164.3MB, time=21.35 N1 := 3121 > GB := Basis(F, plex(op(vars))); 2 2 GB := [3 y + 4 y, 6 x z + z, 3 y z + 4 z, z - 9 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=623.4MB, alloc=164.3MB, time=26.68 memory used=736.6MB, alloc=188.3MB, time=30.00 memory used=874.8MB, alloc=212.3MB, time=36.52 N2 := 1917 #save(Problem, "format.txt"); > if (GB=[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 := [-12 x z - 18 z, 16 x z - 2 y z, 6 y + 8 y, 7 z x + 3 y, 6 z - 11 x , 2 15 x y z - 9 y ] > J:=[op(GB),op(G)]; 2 2 3 2 J := [3 y + 4 y, 6 x z + z, 3 y z + 4 z, z - 9 z, 7 z x + 3 y, 6 z - 11 x , 2 15 x y z - 9 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 15, 3, 2, 2, 3, 5/6, 2/3, 5/6, 5/12, 1/2, 7/12, 7, 14, 16, 3, 2, 2, 3, 4/7, 4/7, 6/7, 2/7, 3/7, 9/14, 0, -1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=918.7MB, alloc=212.3MB, time=39.02 |\^/| 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(); 1428259493 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [13 x z, -4 z + 5 x , 9 x y + 10 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-5 x z + 20 y z, 9 x y - 16 y, -10 x z + 15 x] > Problem := [F,G]; 2 3 2 Problem := [[13 x z, -4 z + 5 x , 9 x y + 10 y], 2 2 [-5 x z + 20 y z, 9 x y - 16 y, -10 x z + 15 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.6MB, alloc=32.3MB, time=0.90 memory used=48.6MB, alloc=56.3MB, time=1.61 N1 := 349 > GB := Basis(F, plex(op(vars))); 4 2 3 2 GB := [x , y, x z, 4 z - 5 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 279 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 H := [13 x z, -4 z + 5 x , 9 x y + 10 y, -5 x z + 20 y z, 9 x y - 16 y, 2 -10 x z + 15 x] > J:=[op(GB),op(G)]; J := 4 2 3 2 2 2 [x , y, x z, 4 z - 5 x , -5 x z + 20 y z, 9 x y - 16 y, -10 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, 13, 16, 3, 2, 1, 3, 1, 1/2, 2/3, 7/13, 5/13, 5/13, 7, 13, 19, 4, 4, 1, 3, 6/7, 3/7, 4/7, 7/13, 4/13, 5/13, 0, -3, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=87.1MB, 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(); 1428259501 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [8 z + 18 y , -20 x y z + 15 x , 3 y z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 G := [11 x + 12 x, -14 z - y z, -19 y z - 19 x] > Problem := [F,G]; 3 2 2 2 Problem := [[8 z + 18 y , -20 x y z + 15 x , 3 y z ], 3 3 [11 x + 12 x, -14 z - y z, -19 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=0.31 memory used=26.7MB, alloc=32.3MB, time=0.89 memory used=48.7MB, alloc=32.3MB, time=1.47 memory used=69.0MB, alloc=56.3MB, time=2.01 memory used=112.3MB, alloc=60.3MB, time=3.24 memory used=155.1MB, alloc=84.3MB, time=4.50 memory used=220.4MB, alloc=92.3MB, time=6.41 memory used=275.0MB, alloc=116.3MB, time=8.63 memory used=341.7MB, alloc=140.3MB, time=12.50 N1 := 1747 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 2 2 3 2 GB := [x , x y , y , x z, 4 x y z - 3 x , y z , 4 z + 9 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=431.2MB, alloc=140.3MB, time=14.98 memory used=540.6MB, alloc=140.3MB, time=18.18 memory used=636.4MB, alloc=164.3MB, time=22.28 N2 := 1747 #save(Problem, "format.txt"); > 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 := [8 z + 18 y , -20 x y z + 15 x , 3 y z , 11 x + 12 x, -14 z - y z, -19 y z - 19 x] > J:=[op(GB),op(G)]; 3 2 2 3 2 2 2 3 2 3 J := [x , x y , y , x z, 4 x y z - 3 x , y z , 4 z + 9 y , 11 x + 12 x, 3 -14 z - y z, -19 y 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, 13, 17, 3, 3, 2, 3, 1/2, 5/6, 5/6, 5/13, 5/13, 6/13, 10, 19, 30, 4, 3, 3, 3, 3/5, 7/10, 3/5, 2/5, 7/20, 7/20, -6, -13, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=689.0MB, alloc=164.3MB, time=25.23 |\^/| 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(); 1428259569 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-17 y - 20 y z, 14 x y - 6 z, 5 x z - x y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [4 x y + 13, -8 x y z - 18 y , -13 x y + 11 z ] > Problem := [F,G]; 2 2 2 Problem := [[-17 y - 20 y z, 14 x y - 6 z, 5 x z - x y z], 2 3 2 [4 x y + 13, -8 x y z - 18 y , -13 x y + 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.84 memory used=47.7MB, alloc=32.3MB, time=1.38 memory used=68.3MB, alloc=32.3MB, time=1.91 memory used=88.1MB, alloc=56.3MB, time=2.44 memory used=128.7MB, alloc=60.3MB, time=3.49 memory used=167.1MB, alloc=84.3MB, time=4.54 memory used=218.2MB, alloc=84.3MB, time=6.11 memory used=274.0MB, alloc=108.3MB, time=7.85 memory used=348.4MB, alloc=140.3MB, time=10.17 memory used=440.1MB, alloc=164.3MB, time=12.99 memory used=543.1MB, alloc=188.3MB, time=17.06 memory used=650.7MB, alloc=212.3MB, time=22.47 memory used=769.2MB, alloc=236.3MB, time=29.67 memory used=911.6MB, alloc=236.3MB, time=38.24 memory used=1054.0MB, alloc=260.3MB, time=46.85 memory used=1220.4MB, alloc=260.3MB, time=56.85 memory used=1387.0MB, alloc=284.3MB, time=66.94 N1 := 5471 > GB := Basis(F, plex(op(vars))); 6 4 5 2 2 GB := [140 x y + 51 x y, -98000 x y + 2601 y , -7 x y + 3 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1521.6MB, alloc=284.3MB, time=72.10 memory used=1750.2MB, alloc=564.3MB, time=81.57 N2 := 1907 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-17 y - 20 y z, 14 x y - 6 z, 5 x z - x y z, 4 y x + 13, 3 2 -8 x y z - 18 y , -13 x y + 11 z ] > J:=[op(GB),op(G)]; 6 4 5 2 2 2 J := [140 x y + 51 x y, -98000 x y + 2601 y , -7 x y + 3 z, 4 y x + 13, 3 2 -8 x y z - 18 y , -13 x y + 11 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 16, 16, 3, 2, 3, 2, 5/6, 1, 5/6, 1/2, 2/3, 1/2, 6, 15, 24, 7, 6, 3, 2, 1, 1, 1/2, 7/12, 3/4, 1/4, 1, -8, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1799.2MB, alloc=564.3MB, time=84.44 |\^/| 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(); 1428259807 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [-11 x + 4 x z, 19 x - 5 z, 3 x z + 7] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [-7 y + 3 z, 17 y + 14 y , x y - 18 y ] > Problem := [F,G]; 2 3 2 Problem := [[-11 x + 4 x z, 19 x - 5 z, 3 x z + 7], 2 3 2 2 [-7 y + 3 z, 17 y + 14 y , 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=0.30 memory used=26.2MB, alloc=32.3MB, time=0.82 memory used=47.4MB, alloc=32.3MB, time=1.34 memory used=67.9MB, alloc=32.3MB, time=1.85 memory used=87.3MB, alloc=56.3MB, time=2.40 memory used=130.0MB, alloc=60.3MB, time=3.69 memory used=167.9MB, alloc=84.3MB, time=4.84 memory used=226.7MB, alloc=108.3MB, time=6.60 memory used=300.9MB, alloc=132.3MB, time=9.82 memory used=386.4MB, alloc=132.3MB, time=14.71 N1 := 2377 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 93 #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 H := [-11 x + 4 x z, 19 x - 5 z, 3 z x + 7, -7 y + 3 z, 17 y + 14 y , 2 x y - 18 y ] > J:=[op(GB),op(G)]; 2 3 2 2 J := [1, -7 y + 3 z, 17 y + 14 y , 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, 11, 15, 3, 3, 3, 2, 2/3, 1/2, 2/3, 5/12, 5/12, 1/3, 4, 5, 7, 3, 1, 3, 1, 1/4, 3/4, 1/4, 1/7, 5/7, 1/7, 6, 8, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=453.4MB, alloc=132.3MB, time=17.99 |\^/| 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(); 1428259856 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [11 x y, -13 y z - 6 y, 3 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [-15 y z , -5 z + 11 z , 9 y z - 17 x y] > Problem := [F,G]; Problem := [ 2 2 2 3 2 2 [11 x y, -13 y z - 6 y, 3 y], [-15 y z , -5 z + 11 z , 9 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=27.4MB, alloc=32.3MB, time=0.98 N1 := 227 > GB := Basis(F, plex(op(vars))); GB := [y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 77 #save(Problem, "format.txt"); > if (GB=[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, -13 y z - 6 y, 3 y, -15 y z , -5 z + 11 z , 9 y z - 17 x y] > J:=[op(GB),op(G)]; 2 3 2 2 J := [y, -15 y z , -5 z + 11 z , 9 y z - 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, 11, 16, 3, 2, 2, 3, 1/3, 5/6, 2/3, 1/7, 1/2, 5/14, 4, 7, 10, 3, 1, 2, 3, 1/4, 3/4, 3/4, 1/8, 1/2, 1/2, 4, 6, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=36.5MB, alloc=32.3MB, time=1.23 |\^/| 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(); 1428259859 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 F := [17 z - 17 z, 5 x + 6 z , 11 x z - 12 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [17 x z - 2 x , 5 x z - 9, x z + 17 x y] > Problem := [F,G]; 3 3 2 2 2 Problem := [[17 z - 17 z, 5 x + 6 z , 11 x z - 12 y z], 2 2 2 2 [17 x z - 2 x , 5 x z - 9, 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=0.30 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=47.2MB, alloc=32.3MB, time=1.41 memory used=66.6MB, alloc=56.3MB, time=1.94 memory used=104.9MB, alloc=60.3MB, time=2.96 memory used=140.8MB, alloc=84.3MB, time=3.88 memory used=196.3MB, alloc=92.3MB, time=5.35 memory used=248.3MB, alloc=116.3MB, time=6.73 memory used=321.2MB, alloc=116.3MB, time=8.63 memory used=393.3MB, alloc=140.3MB, time=10.48 memory used=484.0MB, alloc=140.3MB, time=12.80 memory used=580.5MB, alloc=164.3MB, time=15.73 memory used=686.3MB, alloc=188.3MB, time=19.08 memory used=812.1MB, alloc=212.3MB, time=22.78 memory used=967.7MB, alloc=236.3MB, time=26.58 memory used=1118.8MB, alloc=260.3MB, time=31.42 memory used=1273.8MB, alloc=540.3MB, time=36.36 memory used=1449.3MB, alloc=564.3MB, time=41.87 memory used=1616.0MB, alloc=588.3MB, time=49.50 memory used=1783.4MB, alloc=612.3MB, time=58.13 memory used=1959.4MB, alloc=636.3MB, time=67.68 memory used=2145.9MB, alloc=660.3MB, time=78.51 memory used=2342.1MB, alloc=684.3MB, time=91.08 memory used=2562.3MB, alloc=708.3MB, time=105.18 |\^/| 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(); 1428260159 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [7 x + 2 x z, 15 x y - 2 y z, 5 y + 11 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 2 G := [-11 x y + 14 z , -8 x + 2 y , 6 x z + 2 y z] > Problem := [F,G]; 3 2 2 Problem := [[7 x + 2 x z, 15 x y - 2 y z, 5 y + 11 y z], 2 3 3 3 2 [-11 x y + 14 z , -8 x + 2 y , 6 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=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=47.6MB, alloc=32.3MB, time=1.39 memory used=67.6MB, alloc=56.3MB, time=1.93 memory used=107.9MB, alloc=60.3MB, time=2.99 memory used=146.8MB, alloc=84.3MB, time=3.98 memory used=205.0MB, alloc=116.3MB, time=5.55 memory used=284.6MB, alloc=140.3MB, time=7.78 memory used=382.2MB, alloc=164.3MB, time=10.86 memory used=493.8MB, alloc=188.3MB, time=14.40 memory used=601.8MB, alloc=468.3MB, time=18.15 memory used=729.0MB, alloc=492.3MB, time=24.05 memory used=858.0MB, alloc=516.3MB, time=31.92 memory used=1009.9MB, alloc=540.3MB, time=41.21 memory used=1185.7MB, alloc=540.3MB, time=51.90 memory used=1361.5MB, alloc=564.3MB, time=62.62 memory used=1561.4MB, alloc=588.3MB, time=74.57 N1 := 5701 > GB := Basis(F, plex(op(vars))); 3 2 3 2 GB := [y x , 33 x y + 2 y , 7 x + 2 x z, -15 x y + 2 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1790.1MB, alloc=588.3MB, time=82.65 memory used=2048.3MB, alloc=612.3MB, time=92.90 memory used=2280.2MB, alloc=636.3MB, time=107.67 |\^/| 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(); 1428260459 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [17 y z - 20 z, -20 x - 6 y , -2 y z + 3 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 G := [-3 y - 13 x y, 9 y z - 10 z , -20 x - x z] > Problem := [F,G]; 3 2 2 Problem := [[17 y z - 20 z, -20 x - 6 y , -2 y z + 3 z ], 3 2 2 3 [-3 y - 13 x y, 9 y z - 10 z , -20 x - x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.83 memory used=47.2MB, alloc=32.3MB, time=1.33 memory used=68.2MB, alloc=56.3MB, time=1.92 memory used=110.5MB, alloc=60.3MB, time=3.18 memory used=147.8MB, alloc=84.3MB, time=4.30 memory used=202.6MB, alloc=108.3MB, time=6.71 memory used=272.7MB, alloc=108.3MB, time=10.60 N1 := 1823 > GB := Basis(F, plex(op(vars))); 3 2 3 2 GB := [10 x + 3 y , 289 x z + 120 z, 17 y z - 20 z, 51 z - 40 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=341.1MB, alloc=116.3MB, time=12.63 memory used=419.5MB, alloc=140.3MB, time=15.77 N2 := 1253 #save(Problem, "format.txt"); > 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 z - 20 z, -20 x - 6 y , -2 y z + 3 z , -3 y - 13 x y, 2 2 3 9 y z - 10 z , -20 x - x z] > J:=[op(GB),op(G)]; 3 2 3 2 J := [10 x + 3 y , 289 x z + 120 z, 17 y z - 20 z, 51 z - 40 z, 3 2 2 3 -3 y - 13 x y, 9 y z - 10 z , -20 x - 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, 12, 16, 3, 3, 3, 2, 1/2, 5/6, 2/3, 1/3, 1/2, 7/12, 7, 13, 20, 4, 3, 3, 2, 4/7, 4/7, 5/7, 5/14, 5/14, 9/14, -1, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=443.8MB, alloc=140.3MB, time=17.03 |\^/| 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(); 1428260504 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [-6 y z + 17 y z , -3 x z - 18 y, -11 z + 13 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 G := [-12 x z - 10 x, 14 x - 11 y z, 5 y - 9 y] > Problem := [F,G]; 2 2 3 Problem := [[-6 y z + 17 y z , -3 x z - 18 y, -11 z + 13 y], 3 3 [-12 x z - 10 x, 14 x - 11 y z, 5 y - 9 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=47.6MB, alloc=32.3MB, time=1.37 memory used=67.4MB, alloc=32.3MB, time=1.87 memory used=86.0MB, alloc=56.3MB, time=2.37 memory used=123.6MB, alloc=60.3MB, time=3.37 memory used=159.4MB, alloc=60.3MB, time=4.31 memory used=194.4MB, alloc=84.3MB, time=5.25 memory used=249.5MB, alloc=84.3MB, time=6.70 memory used=302.9MB, alloc=116.3MB, time=8.19 memory used=376.5MB, alloc=116.3MB, time=10.16 memory used=445.9MB, alloc=140.3MB, time=12.06 memory used=539.8MB, alloc=164.3MB, time=14.97 memory used=645.8MB, alloc=188.3MB, time=18.28 memory used=765.4MB, alloc=468.3MB, time=22.02 memory used=900.6MB, alloc=492.3MB, time=26.08 memory used=1044.7MB, alloc=516.3MB, time=30.65 memory used=1198.1MB, alloc=540.3MB, time=35.59 memory used=1349.7MB, alloc=564.3MB, time=42.69 memory used=1505.4MB, alloc=588.3MB, time=50.87 memory used=1672.2MB, alloc=612.3MB, time=60.17 memory used=1852.2MB, alloc=636.3MB, time=70.54 memory used=2042.1MB, alloc=660.3MB, time=82.75 memory used=2253.1MB, alloc=684.3MB, time=96.54 |\^/| 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(); 1428260804 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [12 y z + 18 z, 12 x y - 17 z, -8 x z - 17 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [-12 z - 17 z, -13 y + 8 y z , -9 x + 14 z] > Problem := [F,G]; 2 2 2 Problem := [[12 y z + 18 z, 12 x y - 17 z, -8 x z - 17 z ], 2 3 2 2 [-12 z - 17 z, -13 y + 8 y z , -9 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=0.31 memory used=26.2MB, alloc=32.3MB, time=0.85 memory used=47.3MB, alloc=32.3MB, time=1.38 memory used=67.9MB, alloc=32.3MB, time=1.92 memory used=87.1MB, alloc=56.3MB, time=2.45 memory used=125.7MB, alloc=60.3MB, time=3.47 memory used=162.0MB, alloc=84.3MB, time=4.51 memory used=220.1MB, alloc=108.3MB, time=6.36 memory used=294.8MB, alloc=132.3MB, time=8.73 memory used=384.5MB, alloc=164.3MB, time=11.61 memory used=486.8MB, alloc=188.3MB, time=14.86 memory used=598.4MB, alloc=212.3MB, time=18.57 memory used=712.3MB, alloc=236.3MB, time=23.66 memory used=834.6MB, alloc=260.3MB, time=29.67 memory used=968.8MB, alloc=284.3MB, time=36.98 memory used=1115.1MB, alloc=308.3MB, time=46.11 memory used=1285.4MB, alloc=332.3MB, time=56.68 memory used=1479.6MB, alloc=356.3MB, time=68.71 memory used=1697.7MB, alloc=356.3MB, time=82.11 memory used=1915.8MB, alloc=356.3MB, time=95.45 memory used=2133.9MB, alloc=356.3MB, time=108.75 |\^/| 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(); 1428261104 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 F := [-y z - z , -10 z - 11 x , -2 z - 14] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-5 y + y z, 9 z + y z, -14 x + 5 y] > Problem := [F,G]; 2 3 3 2 2 Problem := [[-y z - z , -10 z - 11 x , -2 z - 14], 2 3 2 [-5 y + y z, 9 z + y z, -14 x + 5 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.84 memory used=47.2MB, alloc=32.3MB, time=1.35 memory used=67.6MB, alloc=32.3MB, time=1.86 memory used=87.2MB, alloc=56.3MB, time=2.41 memory used=125.9MB, alloc=60.3MB, time=3.44 memory used=161.4MB, alloc=84.3MB, time=4.40 memory used=217.4MB, alloc=84.3MB, time=5.90 memory used=270.8MB, alloc=108.3MB, time=7.38 memory used=344.5MB, alloc=116.3MB, time=9.40 memory used=417.1MB, alloc=140.3MB, time=11.58 memory used=508.3MB, alloc=164.3MB, time=14.50 memory used=614.3MB, alloc=188.3MB, time=17.89 memory used=726.1MB, alloc=212.3MB, time=22.83 memory used=840.8MB, alloc=236.3MB, time=29.60 memory used=979.5MB, alloc=260.3MB, time=37.83 memory used=1142.3MB, alloc=260.3MB, time=47.50 N1 := 4313 > GB := Basis(F, plex(op(vars))); 4 2 2 GB := [121 x + 34300, 11 x + 70 y, -11 x + 70 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1312.4MB, alloc=260.3MB, time=54.94 N2 := 1455 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 2 2 2 3 H := [-y z - z , -10 z - 11 x , -2 z - 14, -5 y + y z, 9 z + y z, 2 -14 x + 5 y] > J:=[op(GB),op(G)]; 4 2 2 2 3 J := [121 x + 34300, 11 x + 70 y, -11 x + 70 z, -5 y + y z, 9 z + y z, 2 -14 x + 5 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 11, 15, 3, 2, 2, 3, 1/3, 2/3, 5/6, 1/6, 5/12, 7/12, 6, 11, 15, 4, 4, 2, 3, 2/3, 2/3, 1/2, 1/3, 5/12, 1/3, 0, 0, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1429.0MB, alloc=260.3MB, time=60.37 |\^/| 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(); 1428261278 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [x y + 18 x y, -6 x y z + 12 x z , -15 x y z - 18 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 G := [19 z - 20 y z, -19 x - 17 x z , -11 x y + 8 y z] > Problem := [F,G]; 2 2 3 Problem := [[x y + 18 x y, -6 x y z + 12 x z , -15 x y z - 18 y ], 3 3 2 2 2 [19 z - 20 y z, -19 x - 17 x z , -11 x y + 8 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.86 memory used=47.3MB, alloc=32.3MB, time=1.38 memory used=67.3MB, alloc=56.3MB, time=1.92 memory used=105.8MB, alloc=60.3MB, time=2.93 memory used=140.7MB, alloc=84.3MB, time=3.87 memory used=196.8MB, alloc=92.3MB, time=5.36 memory used=251.1MB, alloc=116.3MB, time=6.81 memory used=325.1MB, alloc=140.3MB, time=9.17 memory used=415.3MB, alloc=164.3MB, time=11.97 memory used=517.4MB, alloc=188.3MB, time=15.93 memory used=619.6MB, alloc=212.3MB, time=21.91 memory used=743.5MB, alloc=236.3MB, time=29.32 N1 := 3509 > GB := Basis(F, plex(op(vars))); 2 3 3 5 4 3 4 3 GB := [x y + 18 x y, x y + 18 y , 2 y - 15 y , 5 x y z + 6 y , -y + 2 y z, 2 3 5 x z + 3 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=895.3MB, alloc=236.3MB, time=37.12 memory used=996.8MB, alloc=492.3MB, time=39.94 memory used=1168.3MB, alloc=492.3MB, time=44.60 memory used=1332.3MB, alloc=516.3MB, time=49.06 memory used=1517.7MB, alloc=540.3MB, time=54.17 memory used=1699.5MB, alloc=564.3MB, time=59.21 memory used=1846.7MB, alloc=588.3MB, time=63.14 memory used=1992.1MB, alloc=588.3MB, time=67.26 memory used=2114.0MB, alloc=612.3MB, time=70.63 memory used=2270.1MB, alloc=636.3MB, time=76.04 memory used=2447.3MB, alloc=660.3MB, time=82.12 memory used=2634.2MB, alloc=684.3MB, time=88.49 memory used=2821.2MB, alloc=708.3MB, time=95.03 memory used=2977.8MB, alloc=732.3MB, time=100.80 |\^/| 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(); 1428261578 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [18 x z + 18 x , -11 y z + 5 x, 7 z - 14 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [-14 y z - 8, 17 z + 10, -13 z - 5 y ] > Problem := [F,G]; 2 2 2 Problem := [[18 x z + 18 x , -11 y z + 5 x, 7 z - 14 x], 2 2 3 2 [-14 y z - 8, 17 z + 10, -13 z - 5 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.7MB, alloc=32.3MB, time=0.88 memory used=47.8MB, alloc=32.3MB, time=1.42 memory used=68.3MB, alloc=32.3MB, time=1.94 memory used=87.5MB, alloc=56.3MB, time=2.45 memory used=126.9MB, alloc=60.3MB, time=3.47 memory used=162.8MB, alloc=60.3MB, time=4.41 memory used=199.1MB, alloc=84.3MB, time=5.35 memory used=256.2MB, alloc=92.3MB, time=6.92 memory used=312.3MB, alloc=116.3MB, time=8.44 memory used=392.3MB, alloc=116.3MB, time=10.61 memory used=469.4MB, alloc=116.3MB, time=12.76 memory used=545.8MB, alloc=140.3MB, time=14.78 memory used=633.8MB, alloc=396.3MB, time=17.22 memory used=728.5MB, alloc=420.3MB, time=19.82 memory used=842.6MB, alloc=444.3MB, time=23.02 memory used=978.0MB, alloc=468.3MB, time=26.93 memory used=1133.8MB, alloc=492.3MB, time=31.39 memory used=1290.5MB, alloc=516.3MB, time=35.66 memory used=1458.5MB, alloc=540.3MB, time=41.04 memory used=1653.6MB, alloc=564.3MB, time=47.72 memory used=1868.5MB, alloc=588.3MB, time=54.68 memory used=2085.4MB, alloc=612.3MB, time=61.96 memory used=2307.4MB, alloc=636.3MB, time=69.46 memory used=2510.1MB, alloc=660.3MB, time=76.40 memory used=2708.8MB, alloc=684.3MB, time=84.28 memory used=2916.5MB, alloc=708.3MB, time=95.53 memory used=3130.3MB, alloc=732.3MB, time=107.68 |\^/| 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(); 1428261878 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [2 y z - 10 y, -15 x y z - 15 y z, 6 x y z - 11 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 G := [2 y - 8 x y, 2 x - 11 x y , -x z - 20 y ] > Problem := [F,G]; 2 2 2 Problem := [[2 y z - 10 y, -15 x y z - 15 y z, 6 x y z - 11 y ], 3 3 2 2 [2 y - 8 x y, 2 x - 11 x y , -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=26.2MB, alloc=32.3MB, time=0.83 memory used=47.6MB, alloc=32.3MB, time=1.37 memory used=67.6MB, alloc=56.3MB, time=1.90 memory used=111.1MB, alloc=60.3MB, time=3.18 memory used=148.5MB, alloc=84.3MB, time=4.34 memory used=204.9MB, alloc=108.3MB, time=6.07 memory used=278.5MB, alloc=116.3MB, time=8.35 memory used=344.6MB, alloc=140.3MB, time=10.39 memory used=424.7MB, alloc=164.3MB, time=13.57 memory used=515.2MB, alloc=188.3MB, time=17.81 memory used=618.1MB, alloc=212.3MB, time=23.71 memory used=741.4MB, alloc=236.3MB, time=31.07 memory used=888.6MB, alloc=236.3MB, time=39.78 memory used=1035.7MB, alloc=236.3MB, time=48.46 memory used=1182.9MB, alloc=260.3MB, time=57.20 memory used=1354.0MB, alloc=260.3MB, time=67.30 N1 := 5859 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x y, y , y z - 5 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 655 #save(Problem, "format.txt"); > if (GB=[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 := [2 y z - 10 y, -15 x y z - 15 y z, 6 x y z - 11 y , 2 y - 8 x y, 3 2 2 2 x - 11 x y , -x z - 20 y ] > J:=[op(GB),op(G)]; 2 2 3 3 2 2 J := [x y, y , y z - 5 y, 2 y - 8 x y, 2 x - 11 x y , -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, 17, 3, 3, 3, 2, 5/6, 1, 2/3, 1/2, 5/6, 5/12, 6, 12, 15, 3, 3, 3, 2, 2/3, 1, 1/3, 5/12, 2/3, 1/6, 3, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1530.1MB, alloc=260.3MB, time=75.89 |\^/| 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(); 1428262074 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [12 x y - 19 y, -2 x y z + 16 y z , -14 y z + 17 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-6 x y - 2 x z, -12 y z - 18 y z, 8 x z - 11 z ] > Problem := [F,G]; 2 2 Problem := [[12 x y - 19 y, -2 x y z + 16 y z , -14 y z + 17 x], 2 2 2 [-6 x y - 2 x z, -12 y z - 18 y z, 8 x z - 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.82 memory used=46.7MB, alloc=32.3MB, time=1.33 memory used=65.8MB, alloc=56.3MB, time=1.84 memory used=107.9MB, alloc=60.3MB, time=3.07 memory used=145.4MB, alloc=84.3MB, time=4.23 memory used=202.6MB, alloc=108.3MB, time=5.94 memory used=280.7MB, alloc=108.3MB, time=8.19 memory used=345.6MB, alloc=140.3MB, time=10.34 memory used=422.2MB, alloc=164.3MB, time=13.61 memory used=510.8MB, alloc=188.3MB, time=18.23 memory used=615.6MB, alloc=212.3MB, time=24.45 memory used=744.5MB, alloc=212.3MB, time=31.97 memory used=873.3MB, alloc=212.3MB, time=39.47 memory used=1002.0MB, alloc=236.3MB, time=47.00 memory used=1154.7MB, alloc=236.3MB, time=55.83 N1 := 5311 > GB := Basis(F, plex(op(vars))); GB := 2 2 [12 x - 19 x, 12 x y - 19 y, 133 y - 816 x, 96 x z - 19 x, 96 y z - 19 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1309.2MB, alloc=236.3MB, time=62.39 N2 := 1637 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [12 x y - 19 y, -2 x y z + 16 y z , -14 z y + 17 x, -6 x y - 2 x z, 2 2 -12 y z - 18 y z, 8 x z - 11 z ] > J:=[op(GB),op(G)]; 2 2 J := [12 x - 19 x, 12 x y - 19 y, 133 y - 816 x, 96 x z - 19 x, 96 y z - 19 y, 2 2 2 -6 x y - 2 x z, -12 y z - 18 y z, 8 x z - 11 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 16, 3, 2, 2, 2, 5/6, 5/6, 5/6, 1/2, 2/3, 2/3, 8, 16, 18, 3, 2, 2, 2, 3/4, 5/8, 5/8, 9/16, 1/2, 7/16, -1, -2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1444.7MB, alloc=236.3MB, time=68.85 |\^/| 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(); 1428262252 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [18 x - 16 x y, 8 x y + 4 x y z, -6 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [-16 x - 10 z, -15 y + 19 y z, -15 y + 2 z] > Problem := [F,G]; 2 2 3 Problem := [[18 x - 16 x y, 8 x y + 4 x y z, -6 y ], 3 2 [-16 x - 10 z, -15 y + 19 y z, -15 y + 2 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.86 memory used=47.3MB, alloc=32.3MB, time=1.38 memory used=67.8MB, alloc=56.3MB, time=1.97 memory used=110.4MB, alloc=60.3MB, time=3.27 memory used=148.0MB, alloc=84.3MB, time=4.43 memory used=204.2MB, alloc=108.3MB, time=6.25 memory used=273.9MB, alloc=132.3MB, time=9.63 memory used=358.4MB, alloc=132.3MB, time=14.62 N1 := 2567 > GB := Basis(F, plex(op(vars))); 4 2 3 3 2 GB := [x , -9 x + 8 x y, y , 9 x + 4 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=444.9MB, alloc=132.3MB, time=19.09 memory used=539.8MB, alloc=164.3MB, time=21.95 N2 := 1527 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 3 H := [18 x - 16 x y, 8 x y + 4 x y z, -6 y , -16 x - 10 z, -15 y + 19 y z, 2 -15 y + 2 z] > J:=[op(GB),op(G)]; 4 2 3 3 2 3 J := [x , -9 x + 8 x y, y , 9 x + 4 x z, -16 x - 10 z, -15 y + 19 y z, 2 -15 y + 2 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 14, 3, 2, 3, 1, 1/2, 5/6, 2/3, 5/12, 7/12, 1/3, 7, 12, 18, 4, 4, 3, 1, 4/7, 4/7, 4/7, 3/7, 5/14, 2/7, 0, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=636.9MB, alloc=164.3MB, time=26.83 |\^/| 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(); 1428262325 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [-13 y z + 16 x, 9 z + 18 x , -5 y z - 9 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-9 x y z - 17 z, 8 x y + 17 z , 2 x y z + 14 y z] > Problem := [F,G]; 2 3 2 2 2 Problem := [[-13 y z + 16 x, 9 z + 18 x , -5 y z - 9 y ], 2 2 [-9 x y z - 17 z, 8 x y + 17 z , 2 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=0.30 memory used=26.5MB, alloc=32.3MB, time=0.85 memory used=48.7MB, alloc=32.3MB, time=1.43 memory used=69.7MB, alloc=32.3MB, time=1.97 memory used=89.9MB, alloc=56.3MB, time=2.52 memory used=129.9MB, alloc=60.3MB, time=3.57 memory used=168.7MB, alloc=84.3MB, time=4.61 memory used=221.8MB, alloc=84.3MB, time=6.31 memory used=280.4MB, alloc=108.3MB, time=8.21 memory used=359.3MB, alloc=140.3MB, time=10.71 memory used=452.5MB, alloc=164.3MB, time=13.73 memory used=552.3MB, alloc=188.3MB, time=18.34 memory used=660.3MB, alloc=212.3MB, time=24.73 memory used=792.3MB, alloc=212.3MB, time=32.59 memory used=924.4MB, alloc=236.3MB, time=40.40 N1 := 4037 > GB := Basis(F, plex(op(vars))); 7 2 4 2 GB := [274625 x + 186624 x , -325 x + 324 x y, 117 y + 80 x, 5 2 3 2 4225 x + 2592 x z, 13 y z - 16 x, z + 2 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1070.3MB, alloc=236.3MB, time=45.73 memory used=1239.9MB, alloc=492.3MB, time=50.23 memory used=1405.5MB, alloc=516.3MB, time=54.63 memory used=1601.5MB, alloc=540.3MB, time=60.82 memory used=1806.6MB, alloc=564.3MB, time=67.43 memory used=2017.7MB, alloc=588.3MB, time=75.66 memory used=2208.2MB, alloc=612.3MB, time=85.83 memory used=2398.3MB, alloc=636.3MB, time=97.94 |\^/| 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(); 1428262625 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 F := [-16 x + 11, -5 x z + x, 4 x y - 3 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-14, 11 x y + 3 x y z, 7 x z + 17 y z] > Problem := [F,G]; 3 2 Problem := [[-16 x + 11, -5 x z + x, 4 x y - 3 y z], 2 2 [-14, 11 x y + 3 x 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=4.2MB, alloc=32.3MB, time=0.31 memory used=26.7MB, alloc=32.3MB, time=0.90 N1 := 349 > GB := Basis(F, plex(op(vars))); 3 2 GB := [16 x - 11, y, -16 x + 55 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=48.1MB, alloc=32.3MB, time=1.57 memory used=68.4MB, alloc=56.3MB, time=2.16 N2 := 209 #save(Problem, "format.txt"); > 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 := [-16 x + 11, -5 x z + x, 4 x y - 3 y z, -14, 11 x y + 3 x y z, 2 7 x z + 17 y z] > J:=[op(GB),op(G)]; 3 2 2 2 J := [16 x - 11, y, -16 x + 55 z, -14, 11 x y + 3 x y z, 7 x z + 17 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, 14, 3, 3, 1, 1, 5/6, 1/2, 2/3, 7/11, 5/11, 5/11, 6, 10, 12, 3, 3, 1, 1, 2/3, 1/2, 1/2, 1/2, 2/5, 2/5, 2, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=69.2MB, alloc=56.3MB, time=2.20 |\^/| 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(); 1428262632 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [-x y - 15 z , -8 y z - 2 y , 18 x y + 10] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-4 x y z + 16 x , -20 y z + 2 z , -14 x z + 20 x ] > Problem := [F,G]; 2 3 2 2 2 Problem := [[-x y - 15 z , -8 y z - 2 y , 18 x y + 10], 2 2 2 2 2 [-4 x y z + 16 x , -20 y z + 2 z , -14 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=4.2MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.82 memory used=47.4MB, alloc=32.3MB, time=1.37 memory used=67.9MB, alloc=32.3MB, time=1.90 memory used=87.8MB, alloc=56.3MB, time=2.44 memory used=126.9MB, alloc=60.3MB, time=3.47 memory used=163.2MB, alloc=84.3MB, time=4.44 memory used=221.1MB, alloc=84.3MB, time=6.13 memory used=276.4MB, alloc=108.3MB, time=7.81 memory used=350.0MB, alloc=140.3MB, time=10.07 memory used=437.3MB, alloc=164.3MB, time=12.84 memory used=533.1MB, alloc=188.3MB, time=17.10 memory used=637.2MB, alloc=212.3MB, time=22.90 memory used=759.7MB, alloc=236.3MB, time=30.14 memory used=906.1MB, alloc=236.3MB, time=38.77 memory used=1052.5MB, alloc=260.3MB, time=47.52 N1 := 4877 > GB := Basis(F, plex(op(vars))); 3 GB := [243 x - 320, 27 x + 64 y, 4 z + 1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1224.9MB, alloc=260.3MB, time=56.94 N2 := 911 #save(Problem, "format.txt"); > if (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 := [-x y - 15 z , -8 y z - 2 y , 18 x y + 10, -4 x y z + 16 x , 2 2 2 2 -20 y z + 2 z , -14 x z + 20 x ] > J:=[op(GB),op(G)]; 3 2 2 2 J := [243 x - 320, 64 y + 27 x, 4 z + 1, -4 x y z + 16 x , -20 y z + 2 z , 2 2 -14 x 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, 14, 18, 3, 2, 2, 3, 2/3, 5/6, 5/6, 1/2, 1/2, 1/2, 6, 11, 14, 3, 3, 1, 2, 2/3, 1/2, 2/3, 1/2, 1/4, 5/12, 3, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1313.6MB, alloc=260.3MB, time=60.17 |\^/| 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(); 1428262810 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-18 x z + 10 y , -8 y z - 8, -19 x z - 8 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-18 x y z + 2 z, x z - 19 x z, y z - 18 x z] > Problem := [F,G]; 2 2 2 2 Problem := [[-18 x z + 10 y , -8 y z - 8, -19 x z - 8 y z], 2 2 [-18 x y z + 2 z, x z - 19 x z, 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=26.3MB, alloc=32.3MB, time=0.86 memory used=47.8MB, alloc=32.3MB, time=1.39 memory used=69.4MB, alloc=56.3MB, time=2.05 memory used=112.2MB, alloc=60.3MB, time=3.35 memory used=150.5MB, alloc=84.3MB, time=4.74 N1 := 1187 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [1805 x - 576, 8 y + 19 x , -95 x y + 72 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=204.7MB, alloc=84.3MB, time=7.10 N2 := 369 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-18 x z + 10 y , -8 y z - 8, -19 x z - 8 y z, -18 x y z + 2 z, 2 2 x z - 19 x z, y z - 18 x z] > J:=[op(GB),op(G)]; 3 2 2 J := [1805 x - 576, 8 y + 19 x , -95 x y + 72 z, -18 x y z + 2 z, 2 2 x z - 19 x z, 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, 17, 3, 2, 2, 2, 5/6, 5/6, 1, 1/2, 5/12, 5/6, 6, 14, 16, 3, 3, 2, 1, 1, 2/3, 2/3, 7/12, 1/3, 7/12, 2, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=241.3MB, alloc=84.3MB, 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(); 1428262836 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 F := [-x z + 8 y , 2 x y, 14 x + z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [11 x y + 20 x, 20 x + 14 x y z, 18 y z + 10 z] > Problem := [F,G]; 2 3 2 3 Problem := [[-x z + 8 y , 2 x y, 14 x + z], 2 3 [11 x y + 20 x, 20 x + 14 x y z, 18 y z + 10 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.31 memory used=26.3MB, alloc=32.3MB, time=0.87 memory used=48.0MB, alloc=32.3MB, time=1.42 memory used=68.7MB, alloc=56.3MB, time=2.03 N1 := 417 > GB := Basis(F, plex(op(vars))); 7 2 5 3 3 GB := [x , x y, 7 x + 4 y , 14 x + z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.3MB, alloc=60.3MB, time=3.28 memory used=150.2MB, alloc=60.3MB, time=4.42 N2 := 341 #save(Problem, "format.txt"); > if (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 := [-x z + 8 y , 2 x y, 14 x + z, 11 x y + 20 x, 20 x + 14 x y z, 18 y z + 10 z] > J:=[op(GB),op(G)]; 7 2 5 3 3 2 3 J := [x , x y, 7 x + 4 y , 14 x + z, 11 x y + 20 x, 20 x + 14 x y z, 18 y 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, 14, 17, 3, 3, 3, 1, 5/6, 5/6, 2/3, 7/13, 5/13, 5/13, 7, 14, 26, 7, 7, 3, 1, 6/7, 5/7, 3/7, 4/7, 5/14, 2/7, 0, -9, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=153.2MB, alloc=60.3MB, time=4.56 |\^/| 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(); 1428262849 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [-x - 15 y, 7 x y - 2 x z, 15 x y - 6 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [-8 x z + 20 y z, 13 x y z + 11 x z , 4 x - 20 x y z] > Problem := [F,G]; 2 2 3 Problem := [[-x - 15 y, 7 x y - 2 x z, 15 x y - 6 y ], 2 3 [-8 x z + 20 y z, 13 x y z + 11 x z , 4 x - 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.85 memory used=49.0MB, alloc=32.3MB, time=1.52 memory used=69.4MB, alloc=56.3MB, time=2.15 memory used=110.2MB, alloc=84.3MB, time=3.47 N1 := 1075 > GB := Basis(F, plex(op(vars))); 3 GB := [x , 15 y + x, x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 103 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 H := [-x - 15 y, 7 x y - 2 x z, 15 x y - 6 y , -8 x z + 20 y z, 2 3 13 x y z + 11 x z , 4 x - 20 x y z] > J:=[op(GB),op(G)]; 3 2 3 J := [x , 15 y + x, x z, -8 x z + 20 y z, 13 x y z + 11 x z , 4 x - 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, 16, 15, 3, 3, 3, 2, 1, 1, 2/3, 3/4, 7/12, 1/2, 6, 14, 14, 3, 3, 1, 2, 1, 2/3, 2/3, 2/3, 1/3, 1/2, 2, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=159.6MB, alloc=84.3MB, time=5.65 |\^/| 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(); 1428262865 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [-x - 14 z, 4 x - 18 x , 20 x z - 15 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [14 y z - 11 z, -4 y z + 12 x y, 12 x y z + y ] > Problem := [F,G]; 3 2 2 2 Problem := [[-x - 14 z, 4 x - 18 x , 20 x z - 15 y z], 2 2 [14 y z - 11 z, -4 y z + 12 x y, 12 x y z + y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.84 memory used=47.6MB, alloc=32.3MB, time=1.35 memory used=69.7MB, alloc=56.3MB, time=2.01 memory used=113.5MB, alloc=60.3MB, time=3.30 memory used=153.6MB, alloc=84.3MB, time=4.48 memory used=211.4MB, alloc=108.3MB, time=6.34 memory used=281.2MB, alloc=132.3MB, time=9.70 memory used=367.0MB, alloc=132.3MB, time=14.58 N1 := 2661 > GB := Basis(F, plex(op(vars))); 3 2 2 2 GB := [2 x - 9 x , x y - 6 x , 14 z + x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=453.8MB, alloc=132.3MB, time=19.02 memory used=549.2MB, alloc=164.3MB, time=21.85 memory used=668.6MB, alloc=188.3MB, time=26.21 memory used=784.3MB, alloc=212.3MB, time=33.27 N2 := 2403 #save(Problem, "format.txt"); > 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 := [-x - 14 z, 4 x - 18 x , 20 x z - 15 y z, 14 y z - 11 z, 2 2 -4 y z + 12 x y, 12 x y z + y ] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [2 x - 9 x , x y - 6 x , 14 z + x, 14 y z - 11 z, -4 y z + 12 x y, 2 12 x y 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, 15, 3, 3, 2, 2, 5/6, 2/3, 5/6, 1/2, 1/2, 7/12, 6, 13, 15, 3, 3, 2, 2, 5/6, 2/3, 2/3, 7/12, 1/2, 5/12, 1, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=817.1MB, alloc=212.3MB, time=35.08 |\^/| 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(); 1428262967 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 F := [16 y z + 14 z , 4 x y - 3 x y, 15 x + 20 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [3 x y + 20 x y, -4 x z + 9 x z, -8 x z - 4 z] > Problem := [F,G]; 2 3 2 3 Problem := [[16 y z + 14 z , 4 x y - 3 x y, 15 x + 20 y z], 2 2 2 [3 x y + 20 x y, -4 x z + 9 x 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=0.30 memory used=26.1MB, alloc=32.3MB, time=0.83 memory used=47.1MB, alloc=32.3MB, time=1.36 memory used=67.0MB, alloc=56.3MB, time=1.90 memory used=110.1MB, alloc=60.3MB, time=3.23 memory used=147.3MB, alloc=84.3MB, time=4.38 memory used=203.1MB, alloc=108.3MB, time=6.25 memory used=271.1MB, alloc=132.3MB, time=9.73 memory used=357.5MB, alloc=132.3MB, time=14.67 N1 := 2373 > GB := Basis(F, plex(op(vars))); 5 4 2 4 2 4 GB := [4 x - 3 x , 4 x y - 3 x y, -21 x + 32 x y , 56 x z + 27 x y, 3 3 2 4 3 3 3 x + 4 z y, 56 x z - 27 x , -6 x z + 7 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=443.5MB, alloc=140.3MB, time=17.58 memory used=532.7MB, alloc=164.3MB, time=20.00 memory used=634.9MB, alloc=420.3MB, time=22.77 memory used=743.0MB, alloc=444.3MB, time=25.66 memory used=872.2MB, alloc=468.3MB, time=29.14 memory used=1021.9MB, alloc=468.3MB, time=33.11 memory used=1171.5MB, alloc=492.3MB, time=37.15 memory used=1343.9MB, alloc=516.3MB, time=42.53 memory used=1535.9MB, alloc=540.3MB, time=48.53 memory used=1727.7MB, alloc=564.3MB, time=54.85 memory used=1926.2MB, alloc=588.3MB, time=61.27 memory used=2130.6MB, alloc=612.3MB, time=67.99 memory used=2332.7MB, alloc=636.3MB, time=75.54 memory used=2514.2MB, alloc=660.3MB, time=84.56 memory used=2697.5MB, alloc=684.3MB, time=94.52 memory used=2889.3MB, alloc=708.3MB, time=105.43 |\^/| 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(); 1428263267 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [-3 y - 20, -13 - 9 x, 4 y z - 14 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [20 y , 12 x y z + 10 z , 2 x z - 17 z ] > Problem := [F,G]; 2 2 3 Problem := [[-3 y - 20, -13 - 9 x, 4 y z - 14 z ], 3 3 2 [20 y , 12 x y z + 10 z , 2 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=0.30 memory used=26.4MB, alloc=32.3MB, time=0.84 memory used=49.7MB, alloc=32.3MB, time=1.51 memory used=70.0MB, alloc=56.3MB, time=2.25 N1 := 469 > GB := Basis(F, plex(op(vars))); 2 3 GB := [9 x + 13, 3 y + 20, 21 z + 40 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=108.1MB, alloc=60.3MB, time=3.29 N2 := 189 #save(Problem, "format.txt"); > if (GB=[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 := [-3 y - 20, -13 - 9 x, 4 y z - 14 z , 20 y , 12 x y z + 10 z , 2 2 x z - 17 z ] > J:=[op(GB),op(G)]; J := 2 3 3 3 2 [9 x + 13, 3 y + 20, 21 z + 40 z, 20 y , 12 x y z + 10 z , 2 x 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, 10, 14, 3, 1, 3, 3, 1/2, 2/3, 1/2, 1/4, 1/3, 1/2, 6, 9, 14, 3, 1, 3, 3, 1/2, 1/2, 1/2, 1/4, 1/4, 1/2, 1, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=111.9MB, alloc=60.3MB, time=3.42 |\^/| 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(); 1428263277 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [-6 x z + 13 x, z + 17 z, 10 x y + 17 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [-14 x + 8 y, 4 y z - 11 x, 9 x + 4 x ] > Problem := [F,G]; 2 3 2 2 Problem := [[-6 x z + 13 x, z + 17 z, 10 x y + 17 y z], 3 2 [-14 x + 8 y, 4 y z - 11 x, 9 x + 4 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.84 memory used=48.1MB, alloc=32.3MB, time=1.45 memory used=69.2MB, alloc=56.3MB, time=2.12 memory used=110.3MB, alloc=84.3MB, time=3.47 N1 := 1053 > GB := Basis(F, plex(op(vars))); 2 3 GB := [x, y z, z + 17 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)]; 2 3 2 2 H := [-6 x z + 13 x, z + 17 z, 10 x y + 17 y z, -14 x + 8 y, 4 y z - 11 x, 3 2 9 x + 4 x ] > J:=[op(GB),op(G)]; 2 3 3 2 J := [x, y z, z + 17 z, -14 x + 8 y, 4 y z - 11 x, 9 x + 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, 12, 15, 3, 3, 2, 3, 5/6, 1/2, 2/3, 7/12, 1/3, 5/12, 6, 10, 13, 3, 3, 2, 3, 2/3, 1/2, 1/2, 5/11, 3/11, 4/11, 2, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=158.5MB, alloc=84.3MB, time=5.42 |\^/| 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(); 1428263294 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-14 x y + 11 y z , 11 x + 2 x z, 9 x z + 9 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-20 y z - 19 x z, -14 x z - 8 x , 9 x y - x y ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-14 x y + 11 y z , 11 x + 2 x z, 9 x z + 9 y ], 2 2 2 2 2 [-20 y z - 19 x z, -14 x z - 8 x , 9 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=0.84 memory used=48.1MB, alloc=32.3MB, time=1.39 memory used=68.4MB, alloc=32.3MB, time=1.91 memory used=88.9MB, alloc=56.3MB, time=2.55 memory used=131.6MB, alloc=60.3MB, time=3.87 memory used=169.1MB, alloc=84.3MB, time=5.06 memory used=226.1MB, alloc=84.3MB, time=6.82 memory used=278.4MB, alloc=108.3MB, time=8.42 memory used=344.4MB, alloc=132.3MB, time=10.70 memory used=420.5MB, alloc=156.3MB, time=13.98 memory used=507.7MB, alloc=180.3MB, time=18.94 memory used=615.8MB, alloc=180.3MB, time=25.26 memory used=724.0MB, alloc=204.3MB, time=31.58 memory used=856.0MB, alloc=204.3MB, time=39.23 memory used=988.1MB, alloc=204.3MB, time=46.90 memory used=1120.1MB, alloc=228.3MB, time=54.59 N1 := 5115 > GB := Basis(F, plex(op(vars))); 5 3 3 2 2 2 2 GB := [x , x y, 121 x + 4 y , 11 x + 2 x z, -14 x y + 11 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1277.4MB, alloc=236.3MB, time=60.16 N2 := 1553 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 H := [-14 x y + 11 y z , 11 x + 2 x z, 9 x z + 9 y , -20 y z - 19 x z, 2 2 2 2 -14 x z - 8 x , 9 x y - x y ] > J:=[op(GB),op(G)]; 5 3 3 2 2 2 2 J := [x , x y, 121 x + 4 y , 11 x + 2 x z, -14 x y + 11 y z , 2 2 2 2 2 -20 y z - 19 x z, -14 x z - 8 x , 9 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, 15, 17, 3, 2, 2, 2, 1, 2/3, 5/6, 3/4, 1/2, 1/2, 8, 17, 26, 5, 5, 2, 2, 1, 5/8, 1/2, 11/16, 7/16, 5/16, -2, -9, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1345.7MB, alloc=236.3MB, time=64.01 |\^/| 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(); 1428263475 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-16 x z + 13 y , 8 x y - 5 z, 9 x z - 19 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [-17 x z - 2 z , -14 z + 10, 12 x y - 16 y z ] > Problem := [F,G]; 2 2 2 Problem := [[-16 x z + 13 y , 8 x y - 5 z, 9 x z - 19 x y], 2 2 3 2 2 [-17 x z - 2 z , -14 z + 10, 12 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=0.31 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=47.8MB, alloc=32.3MB, time=1.40 memory used=67.9MB, alloc=32.3MB, time=1.92 memory used=87.4MB, alloc=32.3MB, time=2.42 memory used=106.7MB, alloc=56.3MB, time=2.95 memory used=145.9MB, alloc=60.3MB, time=3.95 memory used=182.7MB, alloc=84.3MB, time=4.91 memory used=239.9MB, alloc=84.3MB, time=6.41 memory used=295.2MB, alloc=116.3MB, time=7.95 memory used=374.9MB, alloc=116.3MB, time=10.00 memory used=452.5MB, alloc=140.3MB, time=12.03 memory used=534.3MB, alloc=140.3MB, time=14.20 memory used=598.0MB, alloc=396.3MB, time=15.91 memory used=692.6MB, alloc=420.3MB, time=18.55 memory used=809.9MB, alloc=444.3MB, time=21.70 memory used=945.3MB, alloc=468.3MB, time=25.46 memory used=1100.7MB, alloc=492.3MB, time=29.88 memory used=1234.0MB, alloc=516.3MB, time=34.03 memory used=1426.2MB, alloc=540.3MB, time=40.12 memory used=1614.1MB, alloc=564.3MB, time=46.48 memory used=1810.4MB, alloc=588.3MB, time=53.20 memory used=2013.1MB, alloc=612.3MB, time=60.14 memory used=2217.7MB, alloc=636.3MB, time=67.20 memory used=2397.8MB, alloc=660.3MB, time=73.45 memory used=2593.4MB, alloc=684.3MB, time=80.31 memory used=2774.0MB, alloc=708.3MB, time=86.81 memory used=3010.2MB, alloc=732.3MB, time=95.42 memory used=3261.2MB, alloc=756.3MB, time=104.09 memory used=3494.1MB, alloc=780.3MB, time=114.64 |\^/| 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(); 1428263775 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [-9 y - 14 y z, -13 x z - 16 x, -15 z - 8 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [8 y z + 8 y z, -15 x - 12 y z, -4 x z - 2] > Problem := [F,G]; 3 2 2 2 Problem := [[-9 y - 14 y z, -13 x z - 16 x, -15 z - 8 x], 2 3 2 2 [8 y z + 8 y z, -15 x - 12 y z, -4 x z - 2]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.29 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=48.0MB, alloc=32.3MB, time=1.40 memory used=68.0MB, alloc=32.3MB, time=1.94 memory used=87.7MB, alloc=56.3MB, time=2.48 memory used=127.3MB, alloc=60.3MB, time=3.50 memory used=164.5MB, alloc=60.3MB, time=4.46 memory used=199.7MB, alloc=84.3MB, time=5.41 memory used=257.5MB, alloc=92.3MB, time=6.92 memory used=313.6MB, alloc=116.3MB, time=8.41 memory used=391.5MB, alloc=116.3MB, time=10.36 memory used=464.4MB, alloc=140.3MB, time=12.25 memory used=560.4MB, alloc=164.3MB, time=15.25 memory used=671.4MB, alloc=188.3MB, time=18.73 memory used=794.2MB, alloc=212.3MB, time=22.66 memory used=923.3MB, alloc=236.3MB, time=27.93 memory used=1051.2MB, alloc=260.3MB, time=34.90 memory used=1191.7MB, alloc=284.3MB, time=43.44 memory used=1356.2MB, alloc=308.3MB, time=53.40 memory used=1544.7MB, alloc=308.3MB, time=64.77 memory used=1733.1MB, alloc=332.3MB, time=76.21 memory used=1945.6MB, alloc=356.3MB, time=88.98 N1 := 6199 > GB := Basis(F, plex(op(vars))); 2 4 2 3 2 2 GB := [13 x - 30 x, 1215 y + 1568 x y , 9 y + 14 y z, 15 z + 8 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2106.1MB, alloc=356.3MB, time=96.38 memory used=2331.3MB, alloc=612.3MB, time=103.07 memory used=2605.6MB, alloc=636.3MB, time=113.61 |\^/| 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(); 1428264075 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 F := [-3 y z - 18 z , x , 9 x z - 3 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 G := [19 x y + 16 z, 19 x z - 15 y , 8 y - 14 x ] > Problem := [F,G]; 2 3 3 2 Problem := [[-3 y z - 18 z , x , 9 x z - 3 x], 2 2 3 3 2 [19 x y + 16 z, 19 x z - 15 y , 8 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=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.86 memory used=47.6MB, alloc=32.3MB, time=1.41 memory used=67.6MB, alloc=32.3MB, time=1.91 memory used=87.2MB, alloc=56.3MB, time=2.43 memory used=126.5MB, alloc=60.3MB, time=3.46 memory used=165.5MB, alloc=84.3MB, time=4.65 memory used=223.8MB, alloc=84.3MB, time=6.45 memory used=277.4MB, alloc=108.3MB, time=8.09 memory used=361.8MB, alloc=116.3MB, time=10.08 memory used=428.2MB, alloc=140.3MB, time=12.57 memory used=504.6MB, alloc=164.3MB, time=16.70 memory used=598.9MB, alloc=188.3MB, time=22.34 memory used=717.2MB, alloc=188.3MB, time=29.34 N1 := 3355 > GB := Basis(F, plex(op(vars))); 2 3 GB := [x, y z + 6 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=840.9MB, alloc=188.3MB, time=34.12 N2 := 711 #save(Problem, "format.txt"); > if (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 3 H := [-3 y z - 18 z , x , 9 x z - 3 x, 19 y x + 16 z, 19 z x - 15 y , 3 2 8 y - 14 x ] > J:=[op(GB),op(G)]; 2 3 2 2 3 3 2 J := [x, y z + 6 z , 19 y x + 16 z, 19 z x - 15 y , 8 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, 13, 18, 3, 3, 3, 3, 5/6, 2/3, 2/3, 1/2, 1/3, 5/12, 5, 11, 13, 3, 2, 3, 3, 4/5, 4/5, 3/5, 4/9, 4/9, 4/9, 2, 5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=860.2MB, alloc=188.3MB, time=35.07 |\^/| 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(); 1428264168 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [17 x z + 18 y z , -12 x y + 20 y z, -11 y z + 2 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 G := [-10 x y + 14 y , 12 x z + 11 x z , 11 x y - 18 x y ] > Problem := [F,G]; 2 2 2 2 Problem := [[17 x z + 18 y z , -12 x y + 20 y z, -11 y z + 2 z], 2 2 2 2 2 2 [-10 x y + 14 y , 12 x z + 11 x z , 11 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=0.31 memory used=26.1MB, alloc=32.3MB, time=0.83 memory used=48.1MB, alloc=32.3MB, time=1.43 memory used=69.0MB, alloc=56.3MB, time=2.06 memory used=110.8MB, alloc=56.3MB, time=3.30 memory used=147.3MB, alloc=84.3MB, time=4.56 memory used=199.1MB, alloc=108.3MB, time=7.35 N1 := 1669 > GB := Basis(F, plex(op(vars))); 4 2 3 2 2 2 GB := [x y, 11 x y - 2 x y, -33 x y + 10 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=274.1MB, alloc=108.3MB, time=10.26 N2 := 851 #save(Problem, "format.txt"); > if (GB=[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 := [17 x z + 18 y z , -12 x y + 20 y z, -11 y z + 2 z, -10 x y + 14 y , 2 2 2 2 12 x z + 11 x z , 11 x y - 18 x y ] > J:=[op(GB),op(G)]; 4 2 3 2 2 2 2 2 J := [x y, 11 x y - 2 x y, -33 x y + 10 z, -10 x y + 14 y , 2 2 2 2 12 x z + 11 x z , 11 x 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, 14, 18, 3, 2, 2, 2, 5/6, 5/6, 2/3, 7/12, 2/3, 7/12, 6, 13, 23, 5, 4, 3, 2, 1, 5/6, 1/3, 3/4, 2/3, 1/4, 1, -5, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=333.0MB, alloc=108.3MB, time=12.59 |\^/| 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(); 1428264201 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [-4 x - 6 x , -16 x - 16 x y z, -15 y z - 6 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [20 x z - 15 x, -2 x + 7 x y, 13 x z - 18 y z] > Problem := [F,G]; 3 2 3 2 Problem := [[-4 x - 6 x , -16 x - 16 x y z, -15 y z - 6 x], 2 2 2 [20 x z - 15 x, -2 x + 7 x y, 13 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=0.30 memory used=26.4MB, alloc=32.3MB, time=0.86 memory used=47.6MB, alloc=32.3MB, time=1.40 memory used=68.5MB, alloc=56.3MB, time=1.99 memory used=111.1MB, alloc=60.3MB, time=3.28 memory used=148.3MB, alloc=84.3MB, time=4.39 memory used=204.5MB, alloc=108.3MB, time=6.08 memory used=276.7MB, alloc=132.3MB, time=9.07 memory used=358.7MB, alloc=132.3MB, time=13.81 memory used=439.5MB, alloc=156.3MB, time=18.59 N1 := 2961 > GB := Basis(F, plex(op(vars))); GB := [ 3 2 2 2 2 2 2 2 2 x + 3 x , 15 x y + 4 x , 16 x z - 135 x , 2 x y z - 3 x , 5 z y + 2 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=545.9MB, alloc=156.3MB, time=23.80 memory used=656.6MB, alloc=188.3MB, time=26.94 memory used=788.0MB, alloc=212.3MB, time=31.06 memory used=911.7MB, alloc=492.3MB, time=35.59 memory used=1054.7MB, alloc=516.3MB, time=43.20 memory used=1207.4MB, alloc=540.3MB, time=52.60 memory used=1384.1MB, alloc=564.3MB, time=63.43 memory used=1584.9MB, alloc=588.3MB, time=75.71 N2 := 5109 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 H := [-4 x - 6 x , -16 x - 16 x y z, -15 y z - 6 x, 20 x z - 15 x, 2 2 2 -2 x + 7 x y, 13 x z - 18 y z] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 2 J := [2 x + 3 x , 15 x y + 4 x , 16 x z - 135 x , 2 x y z - 3 x , 2 2 2 2 5 z y + 2 x, 20 x z - 15 x, -2 x + 7 x y, 13 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, 14, 16, 3, 3, 2, 1, 1, 2/3, 2/3, 5/6, 1/3, 5/12, 8, 18, 22, 3, 3, 2, 1, 1, 5/8, 5/8, 7/8, 5/16, 3/8, -4, -6, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1710.1MB, alloc=588.3MB, time=83.06 |\^/| 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(); 1428264437 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 F := [-7 x y z + 8 y z, -10 x , -3 - 14 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [7 y + 2 x , 3 x y - 6 z , -12 y z - 15 y z] > Problem := [F,G]; 2 Problem := [[-7 x y z + 8 y z, -10 x , -3 - 14 y], 3 2 2 2 [7 y + 2 x , 3 x y - 6 z , -12 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=0.31 memory used=26.1MB, alloc=32.3MB, time=0.87 memory used=48.7MB, alloc=32.3MB, time=1.55 N1 := 473 > GB := Basis(F, plex(op(vars))); 2 GB := [x , 14 y + 3, z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=68.2MB, alloc=56.3MB, time=2.32 memory used=110.4MB, alloc=60.3MB, time=3.53 N2 := 411 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 H := [-7 x y z + 8 y z, -10 x , -3 - 14 y, 7 y + 2 x , 3 x y - 6 z , 2 -12 y z - 15 y z] > J:=[op(GB),op(G)]; 2 3 2 2 2 J := [x , 14 y + 3, z, 7 y + 2 x , 3 x y - 6 z , -12 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, 12, 14, 3, 2, 3, 2, 2/3, 5/6, 1/2, 1/3, 7/12, 5/12, 6, 10, 12, 3, 2, 3, 2, 1/2, 2/3, 1/2, 3/11, 5/11, 4/11, 2, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=117.5MB, alloc=60.3MB, time=3.87 |\^/| 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(); 1428264447 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-15 x z + 3 y z , 15 x z - 4, -13 y z - 13 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [10 x y - 19 y z, -14 x y - 14 y, 3 x z - 12 z ] > Problem := [F,G]; 2 2 Problem := [[-15 x z + 3 y z , 15 x z - 4, -13 y z - 13 x], 2 2 2 2 2 [10 x y - 19 y z, -14 x y - 14 y, 3 x z - 12 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.0MB, alloc=32.3MB, time=0.84 memory used=47.1MB, alloc=32.3MB, time=1.39 memory used=68.2MB, alloc=56.3MB, time=2.05 memory used=110.0MB, alloc=60.3MB, time=3.29 memory used=146.8MB, alloc=84.3MB, time=4.91 N1 := 1179 > GB := Basis(F, plex(op(vars))); GB := [3 x + 4, 3 y + 20, 5 z + 1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=201.8MB, alloc=84.3MB, time=6.97 memory used=263.3MB, alloc=108.3MB, time=9.31 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 2 2 2 H := [-15 x z + 3 y z , 15 z x - 4, -13 y z - 13 x, 10 x y - 19 y z, 2 2 2 -14 x y - 14 y, 3 x z - 12 z ] > J:=[op(GB),op(G)]; 2 2 2 J := [3 x + 4, 3 y + 20, 5 z + 1, 10 x y - 19 y z, -14 x y - 14 y, 2 2 3 x z - 12 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 16, 3, 2, 2, 2, 1, 2/3, 5/6, 1/2, 1/2, 7/12, 6, 10, 12, 3, 2, 2, 2, 2/3, 1/2, 1/2, 1/3, 5/12, 1/3, 5, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=264.6MB, alloc=108.3MB, time=9.40 |\^/| 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(); 1428264471 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 F := [-16 x y + 8 x, 17 y + 7 y, -12 x + 19] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 G := [16 z - 18 x, -4 x z - 15 y , 8 x + 9 z] > Problem := [F,G]; 2 3 Problem := [[-16 x y + 8 x, 17 y + 7 y, -12 x + 19], 3 2 3 [16 z - 18 x, -4 x z - 15 y , 8 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=0.30 memory used=26.2MB, alloc=32.3MB, time=0.86 memory used=47.9MB, alloc=32.3MB, time=1.41 memory used=70.3MB, alloc=32.3MB, time=2.08 memory used=89.6MB, alloc=56.3MB, time=2.70 memory used=130.4MB, alloc=80.3MB, time=4.40 N1 := 841 > 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)]; 2 3 3 2 H := [-16 x y + 8 x, 17 y + 7 y, -12 x + 19, 16 z - 18 x, -4 x z - 15 y , 3 8 x + 9 z] > J:=[op(GB),op(G)]; 3 2 3 J := [1, 16 z - 18 x, -4 x z - 15 y , 8 x + 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, 15, 3, 3, 2, 3, 5/6, 1/2, 1/2, 1/2, 1/3, 1/4, 4, 7, 8, 3, 3, 2, 3, 3/4, 1/4, 3/4, 3/7, 1/7, 3/7, 4, 7, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=148.3MB, alloc=80.3MB, time=4.98 |\^/| 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(); 1428264484 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-2 y z - 2 z, 7 x y + 15 x z, 11 y z - 17] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 G := [19 x z + 14 z , 10 x z - 3 y , -18 y - 10 z ] > Problem := [F,G]; 2 2 Problem := [[-2 y z - 2 z, 7 x y + 15 x z, 11 y z - 17], 2 2 2 3 3 [19 x z + 14 z , 10 x z - 3 y , -18 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=0.31 memory used=26.4MB, alloc=32.3MB, time=0.87 memory used=47.8MB, alloc=32.3MB, time=1.41 memory used=68.1MB, alloc=32.3MB, time=1.93 memory used=87.3MB, alloc=56.3MB, time=2.46 memory used=126.5MB, alloc=60.3MB, time=3.51 memory used=163.5MB, alloc=84.3MB, time=4.48 memory used=210.5MB, alloc=84.3MB, time=5.74 memory used=266.3MB, alloc=116.3MB, time=7.29 memory used=347.2MB, alloc=116.3MB, time=9.35 memory used=428.2MB, alloc=140.3MB, time=11.46 memory used=506.3MB, alloc=396.3MB, time=13.51 memory used=605.6MB, alloc=420.3MB, time=16.15 memory used=722.7MB, alloc=444.3MB, time=19.27 memory used=862.8MB, alloc=468.3MB, time=23.17 memory used=1014.2MB, alloc=492.3MB, time=28.10 memory used=1172.6MB, alloc=516.3MB, time=33.31 memory used=1340.2MB, alloc=540.3MB, time=38.96 memory used=1516.3MB, alloc=564.3MB, time=44.97 memory used=1697.3MB, alloc=588.3MB, time=51.45 memory used=1868.9MB, alloc=612.3MB, time=60.05 memory used=2044.4MB, alloc=636.3MB, time=69.71 memory used=2230.2MB, alloc=660.3MB, time=80.43 memory used=2428.4MB, alloc=684.3MB, time=92.32 memory used=2632.9MB, alloc=708.3MB, time=106.05 |\^/| 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(); 1428264784 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [-15 x y - 13 y z, -2 y - 2 z , -18 y z - 9 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-11 y z - 3 x z, -15 x y - 15 y , -4 y z + 7 z ] > Problem := [F,G]; 3 3 2 Problem := [[-15 x y - 13 y z, -2 y - 2 z , -18 y z - 9 y z], 2 2 2 2 [-11 y z - 3 x z, -15 x y - 15 y , -4 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=31.8MB, alloc=40.3MB, time=0.97 memory used=59.5MB, alloc=40.3MB, time=1.62 memory used=86.2MB, alloc=40.3MB, time=2.31 memory used=112.0MB, alloc=40.3MB, time=2.97 memory used=135.9MB, alloc=64.3MB, time=3.64 memory used=181.7MB, alloc=92.3MB, time=5.01 memory used=247.1MB, alloc=92.3MB, time=7.03 memory used=303.1MB, alloc=116.3MB, time=8.99 memory used=369.5MB, alloc=140.3MB, time=12.50 memory used=455.1MB, alloc=164.3MB, time=17.49 N1 := 2491 > GB := Basis(F, plex(op(vars))); 2 4 3 3 GB := [30 x y - 13 x y, 52 y - 15 x y, 15 x y + 13 y z, y + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=564.6MB, alloc=172.3MB, time=21.44 memory used=693.4MB, alloc=196.3MB, time=25.77 N2 := 1345 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 2 H := [-15 x y - 13 y z, -2 y - 2 z , -18 y z - 9 y z, -11 y z - 3 x z, 2 2 2 -15 x y - 15 y , -4 y z + 7 z ] > J:=[op(GB),op(G)]; 2 4 3 3 J := [30 x y - 13 x y, 52 y - 15 x y, 15 x y + 13 y z, y + z , 2 2 2 2 -11 y z - 3 x z, -15 x y - 15 y , -4 y z + 7 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 16, 3, 1, 3, 3, 1/2, 1, 5/6, 1/4, 3/4, 2/3, 7, 16, 20, 4, 2, 4, 3, 5/7, 1, 4/7, 3/7, 11/14, 3/7, -2, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=737.9MB, alloc=196.3MB, time=28.25 |\^/| 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(); 1428264864 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 F := [-8 y z + 5 y , 3 y + 17 z , 13 x y + 12 x z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [10 x - 13 x y , -20 x y + 9 x y z, -5 x z + 15] > Problem := [F,G]; 2 2 3 2 2 2 Problem := [[-8 y z + 5 y , 3 y + 17 z , 13 x y + 12 x z ], 3 2 2 2 [10 x - 13 x y , -20 x y + 9 x y z, -5 x z + 15]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.86 memory used=47.9MB, alloc=32.3MB, time=1.40 memory used=68.3MB, alloc=32.3MB, time=1.90 memory used=88.2MB, alloc=56.3MB, time=2.43 memory used=128.9MB, alloc=60.3MB, time=3.48 memory used=167.2MB, alloc=60.3MB, time=4.46 memory used=205.2MB, alloc=84.3MB, time=5.46 memory used=263.8MB, alloc=92.3MB, time=7.01 memory used=321.6MB, alloc=116.3MB, time=8.50 memory used=400.0MB, alloc=140.3MB, time=10.52 memory used=490.4MB, alloc=396.3MB, time=12.87 memory used=590.2MB, alloc=420.3MB, time=15.90 memory used=702.2MB, alloc=444.3MB, time=19.40 memory used=834.6MB, alloc=468.3MB, time=23.38 memory used=975.8MB, alloc=492.3MB, time=27.86 memory used=1127.9MB, alloc=516.3MB, time=32.95 memory used=1273.7MB, alloc=540.3MB, time=40.11 memory used=1427.1MB, alloc=564.3MB, time=48.28 memory used=1591.0MB, alloc=588.3MB, time=58.00 memory used=1769.9MB, alloc=612.3MB, time=69.16 memory used=1972.9MB, alloc=636.3MB, time=81.87 memory used=2199.7MB, alloc=660.3MB, time=96.00 |\^/| 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(); 1428265164 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-17 x z - 8 x , 18 x y + 17 x , x - 6 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [x y - 11 z , -17 x z + 8 x , -3 x y z + 2 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-17 x z - 8 x , 18 x y + 17 x , x - 6 y], 2 2 2 2 [x y - 11 z , -17 x z + 8 x , -3 x y z + 2 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.84 memory used=47.5MB, alloc=32.3MB, time=1.38 memory used=68.1MB, alloc=32.3MB, time=1.91 memory used=87.8MB, alloc=56.3MB, time=2.44 memory used=127.2MB, alloc=60.3MB, time=3.47 memory used=165.5MB, alloc=84.3MB, time=4.58 memory used=226.1MB, alloc=84.3MB, time=6.47 memory used=282.4MB, alloc=108.3MB, time=8.21 memory used=357.0MB, alloc=140.3MB, time=10.56 memory used=446.2MB, alloc=164.3MB, time=13.39 memory used=541.5MB, alloc=188.3MB, time=17.48 memory used=646.0MB, alloc=212.3MB, time=22.90 memory used=764.0MB, alloc=236.3MB, time=29.94 memory used=906.0MB, alloc=236.3MB, time=38.38 memory used=1047.9MB, alloc=260.3MB, time=46.80 memory used=1213.8MB, alloc=260.3MB, time=56.58 memory used=1379.8MB, alloc=284.3MB, time=66.44 N1 := 5803 > GB := Basis(F, plex(op(vars))); 3 2 2 2 GB := [3 x + 17 x , 6 y - x, 17 x z + 8 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1573.5MB, alloc=284.3MB, time=75.86 memory used=1688.2MB, alloc=540.3MB, time=79.62 memory used=1908.3MB, alloc=564.3MB, time=88.01 memory used=2103.2MB, alloc=588.3MB, time=100.47 N2 := 3899 #save(Problem, "format.txt"); > if (GB=[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 := [-17 x z - 8 x , 18 x y + 17 x , -6 y + x, -11 z + y x, -17 x z + 8 x , 2 -3 x y z + 2 z ] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 2 J := [3 x + 17 x , 6 y - x, 17 x z + 8 x , -11 z + y x, -17 x z + 8 x , 2 -3 x 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, 14, 15, 3, 2, 1, 2, 1, 2/3, 2/3, 3/4, 1/3, 5/12, 6, 13, 15, 3, 3, 1, 2, 1, 1/2, 2/3, 3/4, 1/4, 5/12, 1, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2310.7MB, alloc=588.3MB, time=113.26 |\^/| 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(); 1428265456 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 F := [16 x z + 12 x y , 18 x z + 19 x , 14 x - 17 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [-4 z - 17 y, 8 x z + 9 y z, 16 x + 14 x y] > Problem := [F,G]; 2 2 2 2 3 Problem := [[16 x z + 12 x y , 18 x z + 19 x , 14 x - 17 y z], 2 2 3 [-4 z - 17 y, 8 x z + 9 y z, 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=4.3MB, alloc=32.3MB, time=0.30 memory used=27.0MB, alloc=32.3MB, time=0.90 memory used=48.4MB, alloc=32.3MB, time=1.46 memory used=68.9MB, alloc=56.3MB, time=2.01 memory used=109.2MB, alloc=60.3MB, time=3.06 memory used=146.6MB, alloc=84.3MB, time=4.04 memory used=207.5MB, alloc=92.3MB, time=5.63 memory used=267.3MB, alloc=116.3MB, time=7.12 memory used=349.5MB, alloc=116.3MB, time=9.15 memory used=430.5MB, alloc=140.3MB, time=11.55 memory used=529.7MB, alloc=164.3MB, time=14.53 memory used=640.7MB, alloc=188.3MB, time=18.03 memory used=758.9MB, alloc=468.3MB, time=21.81 memory used=899.3MB, alloc=492.3MB, time=26.17 memory used=1044.8MB, alloc=516.3MB, time=31.14 memory used=1189.0MB, alloc=540.3MB, time=37.96 memory used=1339.4MB, alloc=564.3MB, time=45.78 memory used=1500.8MB, alloc=588.3MB, time=54.84 memory used=1671.0MB, alloc=612.3MB, time=65.63 memory used=1865.0MB, alloc=636.3MB, time=77.87 memory used=2083.0MB, alloc=660.3MB, time=91.58 memory used=2324.9MB, alloc=684.3MB, time=106.90 |\^/| 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(); 1428265756 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [18 y, 6 y z - 9 y , -13 x z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 G := [14 x + 9 x y z, 5 z + 6 x , 19 x z - 6 y ] > Problem := [F,G]; 2 2 2 Problem := [[18 y, 6 y z - 9 y , -13 x z ], 3 3 2 2 3 [14 x + 9 x y z, 5 z + 6 x , 19 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=27.0MB, alloc=32.3MB, time=0.89 memory used=48.2MB, alloc=32.3MB, time=1.42 memory used=68.4MB, alloc=56.3MB, time=2.01 memory used=111.3MB, alloc=60.3MB, time=3.29 memory used=148.7MB, alloc=84.3MB, time=4.78 N1 := 1017 > GB := Basis(F, plex(op(vars))); 2 GB := [y, x 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)]; H := [ 2 2 2 3 3 2 2 3 18 y, 6 y z - 9 y , -13 x z , 14 x + 9 x y z, 5 z + 6 x , 19 z x - 6 y ] > J:=[op(GB),op(G)]; 2 3 3 2 2 3 J := [y, x z , 14 x + 9 x y z, 5 z + 6 x , 19 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, 13, 16, 3, 3, 3, 3, 2/3, 2/3, 5/6, 5/13, 5/13, 5/13, 5, 11, 13, 3, 3, 3, 3, 4/5, 3/5, 4/5, 5/9, 1/3, 4/9, 2, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=192.1MB, alloc=84.3MB, time=6.32 |\^/| 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(); 1428265777 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-15 x z - 7 z, -15 x z + 6 y , -20 x z + 20 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [5 - 12 z, 18 y + 3, 15 x y - 12 y z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-15 x z - 7 z, -15 x z + 6 y , -20 x z + 20 x z], 2 2 2 [5 - 12 z, 18 y + 3, 15 x y - 12 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.84 memory used=47.5MB, alloc=32.3MB, time=1.35 memory used=69.0MB, alloc=56.3MB, time=2.01 memory used=112.0MB, alloc=56.3MB, time=3.30 memory used=150.3MB, alloc=84.3MB, time=4.49 memory used=205.2MB, alloc=108.3MB, time=6.77 memory used=274.2MB, alloc=108.3MB, time=10.60 N1 := 2055 > GB := Basis(F, plex(op(vars))); 2 2 4 2 2 GB := [x y - y , 90 y - 49 y , 6 y + 7 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=344.9MB, alloc=108.3MB, time=13.32 memory used=425.2MB, alloc=132.3MB, time=16.10 N2 := 1451 #save(Problem, "format.txt"); > if (GB=[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 := [-15 x z - 7 z, -15 x z + 6 y , -20 x z + 20 x z, 5 - 12 z, 18 y + 3, 2 2 15 x y - 12 y z ] > J:=[op(GB),op(G)]; 2 2 4 2 2 2 J := [x y - y , 90 y - 49 y , 6 y + 7 z, 5 - 12 z, 18 y + 3, 2 2 15 x y - 12 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, 15, 3, 2, 2, 2, 2/3, 1/2, 5/6, 5/12, 1/3, 7/12, 6, 10, 15, 4, 2, 4, 2, 1/3, 5/6, 1/2, 1/6, 2/3, 1/4, 2, 0, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=479.3MB, alloc=132.3MB, time=19.03 |\^/| 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(); 1428265839 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-3 x y - 15 x z , x z + 6 x z, 8 y - y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-3 x z - 3 x y, -14 y + 13 z, 4 y z + 7 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-3 x y - 15 x z , x z + 6 x z, 8 y - y], 2 2 2 2 [-3 x z - 3 x y, -14 y + 13 z, 4 y z + 7 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.1MB, alloc=32.3MB, time=0.84 memory used=47.4MB, alloc=32.3MB, time=1.40 memory used=68.2MB, alloc=56.3MB, time=2.04 N1 := 525 > GB := Basis(F, plex(op(vars))); 2 GB := [x y, 8 y - y, x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=107.6MB, alloc=60.3MB, time=3.32 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 2 2 2 2 H := [-3 x y - 15 x z , x z + 6 x z, 8 y - y, -3 x z - 3 x y, -14 y + 13 z, 2 2 4 y z + 7 z ] > J:=[op(GB),op(G)]; 2 2 2 2 2 J := [x y, 8 y - y, x z, -3 x z - 3 x y, -14 y + 13 z, 4 y z + 7 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 16, 3, 1, 2, 2, 1/2, 5/6, 5/6, 1/2, 1/2, 7/12, 6, 12, 14, 3, 1, 2, 2, 1/2, 5/6, 2/3, 1/3, 1/2, 5/12, 1, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=109.0MB, alloc=60.3MB, time=3.39 |\^/| 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(); 1428265851 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [2 y z + 10 y, 18 x z - 10 y z, -18 x z - 12 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-2 x y + 17 x z, 20 x z - 14 z , -2 x y - 11 x z] > Problem := [F,G]; 2 2 2 Problem := [[2 y z + 10 y, 18 x z - 10 y z, -18 x z - 12 y z], 2 2 2 [-2 x y + 17 x z, 20 x z - 14 z , -2 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=0.30 memory used=26.3MB, alloc=32.3MB, time=0.83 memory used=47.7MB, alloc=32.3MB, time=1.35 memory used=67.6MB, alloc=32.3MB, time=1.84 memory used=86.8MB, alloc=56.3MB, time=2.36 memory used=126.0MB, alloc=60.3MB, time=3.38 memory used=162.0MB, alloc=84.3MB, time=4.31 memory used=215.3MB, alloc=84.3MB, time=5.71 memory used=268.4MB, alloc=108.3MB, time=7.14 memory used=343.5MB, alloc=140.3MB, time=9.49 memory used=433.8MB, alloc=164.3MB, time=12.28 memory used=535.8MB, alloc=188.3MB, time=17.16 memory used=647.0MB, alloc=212.3MB, time=23.70 N1 := 2765 > GB := Basis(F, plex(op(vars))); 2 2 GB := [2916 x y + 3125 y, -9 x y + 5 y , 6 x y + 5 x z, 54 x y + 25 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=783.4MB, alloc=212.3MB, time=28.99 memory used=907.4MB, alloc=468.3MB, time=32.73 memory used=1052.4MB, alloc=492.3MB, time=37.32 memory used=1205.6MB, alloc=516.3MB, time=44.47 memory used=1356.1MB, alloc=540.3MB, time=53.88 memory used=1530.7MB, alloc=564.3MB, time=64.80 memory used=1729.3MB, alloc=588.3MB, time=77.19 N2 := 4977 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [2 y z + 10 y, 18 x z - 10 y z, -18 x z - 12 y z, -2 x y + 17 x z, 2 2 20 x z - 14 z , -2 x y - 11 x z] > J:=[op(GB),op(G)]; 2 2 J := [2916 x y + 3125 y, -9 x y + 5 y , 6 x y + 5 x z, 54 x y + 25 y z, 2 2 2 -2 x y + 17 x z, 20 x z - 14 z , -2 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, 16, 16, 3, 2, 2, 2, 5/6, 5/6, 1, 7/12, 1/2, 3/4, 7, 18, 17, 3, 2, 2, 2, 1, 6/7, 5/7, 5/7, 9/14, 3/7, -2, -1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1857.7MB, alloc=588.3MB, time=84.76 |\^/| 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(); 1428266125 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [-12 x y z + 13 x, -19 x + 13 x y , -13 x - 10 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [11 y z - 9 y, -2 x z - 9 x, 11 x z + 15 z] > Problem := [F,G]; 3 2 3 2 Problem := [[-12 x y z + 13 x, -19 x + 13 x y , -13 x - 10 z ], 2 2 [11 y z - 9 y, -2 x z - 9 x, 11 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=0.30 memory used=26.2MB, alloc=32.3MB, time=0.85 memory used=47.6MB, alloc=32.3MB, time=1.39 memory used=70.0MB, alloc=56.3MB, time=2.12 memory used=113.3MB, alloc=56.3MB, time=3.46 memory used=150.2MB, alloc=84.3MB, time=4.64 memory used=204.0MB, alloc=108.3MB, time=7.18 memory used=275.3MB, alloc=108.3MB, time=11.11 N1 := 1955 > GB := Basis(F, plex(op(vars))); 6 3 2 4 3 2 GB := [1368 x + 845 x, -19 x + 13 x y , 6 x y + 5 x z, 13 x + 10 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=343.7MB, alloc=116.3MB, time=13.12 memory used=424.1MB, alloc=140.3MB, time=15.73 memory used=518.8MB, alloc=164.3MB, time=20.48 N2 := 1919 #save(Problem, "format.txt"); > 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 := [-12 x y z + 13 x, -19 x + 13 x y , -13 x - 10 z , 11 y z - 9 y, 2 -2 x z - 9 x, 11 x z + 15 z] > J:=[op(GB),op(G)]; 6 3 2 4 3 2 J := [1368 x + 845 x, -19 x + 13 x y , 6 x y + 5 x z, 13 x + 10 z , 2 2 11 y z - 9 y, -2 x z - 9 x, 11 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, 13, 17, 3, 3, 2, 2, 5/6, 1/2, 5/6, 2/3, 1/3, 1/2, 7, 14, 25, 6, 6, 2, 2, 6/7, 3/7, 5/7, 5/7, 2/7, 3/7, -1, -8, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=571.0MB, alloc=164.3MB, time=23.45 |\^/| 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(); 1428266185 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [20 x y - 13 y z, 12 y - 17 y z, 13 x y z - 11 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 G := [-14 x + 9 z , 2 y z, 17 y z] > Problem := [F,G]; 2 2 2 Problem := [[20 x y - 13 y z, 12 y - 17 y z, 13 x y z - 11 z], 3 3 2 2 [-14 x + 9 z , 2 y 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=26.9MB, alloc=32.3MB, time=0.91 memory used=49.6MB, alloc=32.3MB, time=1.60 memory used=69.9MB, alloc=56.3MB, time=2.26 memory used=111.7MB, alloc=60.3MB, time=3.57 memory used=147.2MB, alloc=84.3MB, time=5.13 N1 := 1375 > GB := Basis(F, plex(op(vars))); 6 2 3 2 4 GB := [1105 x y - 363 x y, -85 x y + 33 y , -260 x y + 121 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=202.5MB, alloc=84.3MB, time=7.77 N2 := 431 #save(Problem, "format.txt"); > if (GB=[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 := [20 x y - 13 y z, 12 y - 17 y z, 13 x y z - 11 z, -14 x + 9 z , 2 y z, 2 17 y z] > J:=[op(GB),op(G)]; 6 2 3 2 4 3 3 J := [1105 x y - 363 x y, -85 x y + 33 y , -260 x y + 121 z, -14 x + 9 z , 2 2 2 y z, 17 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, 3, 3, 2, 3, 1/2, 5/6, 1, 3/14, 1/2, 1/2, 6, 13, 25, 7, 6, 2, 3, 2/3, 5/6, 2/3, 5/14, 1/2, 2/7, 1, -8, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=241.1MB, alloc=84.3MB, time=9.03 |\^/| 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(); 1428266208 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-13 x z + 11 z , 8 x z - 18 y , 6 x - 6] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [-10 z - 7 y, -17 x y + 16 x z, -9 x y z - 13 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-13 x z + 11 z , 8 x z - 18 y , 6 x - 6], 2 2 3 [-10 z - 7 y, -17 x y + 16 x z, -9 x 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=0.30 memory used=26.1MB, alloc=32.3MB, time=0.85 memory used=47.8MB, alloc=32.3MB, time=1.41 memory used=67.7MB, alloc=56.3MB, time=1.94 memory used=107.9MB, alloc=60.3MB, time=2.98 memory used=146.9MB, alloc=60.3MB, time=3.96 memory used=184.5MB, alloc=84.3MB, time=4.91 memory used=226.3MB, alloc=84.3MB, time=5.95 memory used=284.2MB, alloc=92.3MB, time=7.48 memory used=339.8MB, alloc=116.3MB, time=8.90 memory used=415.1MB, alloc=116.3MB, time=10.83 memory used=492.1MB, alloc=140.3MB, time=13.21 memory used=583.9MB, alloc=164.3MB, time=16.13 memory used=694.7MB, alloc=188.3MB, time=19.61 memory used=801.9MB, alloc=468.3MB, time=23.08 memory used=939.6MB, alloc=492.3MB, time=27.47 memory used=1089.8MB, alloc=516.3MB, time=32.37 memory used=1237.5MB, alloc=540.3MB, time=38.77 memory used=1385.9MB, alloc=564.3MB, time=46.16 memory used=1543.6MB, alloc=588.3MB, time=54.59 memory used=1712.8MB, alloc=612.3MB, time=64.23 memory used=1892.5MB, alloc=636.3MB, time=75.75 memory used=2096.2MB, alloc=660.3MB, time=88.92 memory used=2323.9MB, alloc=684.3MB, time=103.63 |\^/| 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(); 1428266508 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-20 x , -10 y z + 10 y , -13 x y z - 10 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 G := [19 - 12 y, 18 x y z + 10 x y, -11 x + 9 y z] > Problem := [F,G]; 3 2 2 Problem := [[-20 x , -10 y z + 10 y , -13 x y z - 10 y z], 3 [19 - 12 y, 18 x y z + 10 x y, -11 x + 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.1MB, alloc=32.3MB, time=0.84 memory used=48.5MB, alloc=32.3MB, time=1.47 memory used=68.7MB, alloc=56.3MB, time=2.11 memory used=108.9MB, alloc=84.3MB, time=3.41 memory used=164.4MB, alloc=84.3MB, time=6.34 N1 := 1353 > GB := Basis(F, plex(op(vars))); 3 2 GB := [x , y , z y] > 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)]; 3 2 2 H := [-20 x , -10 y z + 10 y , -13 x y z - 10 y z, 19 - 12 y, 3 18 x y z + 10 x y, -11 x + 9 y z] > J:=[op(GB),op(G)]; 3 2 3 J := [x , y , z y, 19 - 12 y, 18 x y z + 10 x y, -11 x + 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, 13, 16, 3, 3, 2, 2, 2/3, 5/6, 2/3, 5/12, 2/3, 5/12, 6, 11, 14, 3, 3, 2, 1, 1/2, 5/6, 1/2, 1/3, 1/2, 1/4, 2, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=191.8MB, alloc=84.3MB, 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(); 1428266532 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 F := [20 x - 18 x y, -13 z - 19, 14 y z + 10 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-2 y z + z, -3 x z + 15 x, 3 z + 13 y] > Problem := [F,G]; 3 3 2 2 Problem := [[20 x - 18 x y, -13 z - 19, 14 y z + 10 y ], 2 2 [-2 y z + z, -3 x z + 15 x, 3 z + 13 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.1MB, alloc=32.3MB, time=0.86 memory used=47.5MB, alloc=32.3MB, time=1.39 memory used=68.0MB, alloc=32.3MB, time=1.91 memory used=87.8MB, alloc=56.3MB, time=2.45 memory used=129.0MB, alloc=60.3MB, time=3.63 memory used=167.9MB, alloc=84.3MB, time=4.83 memory used=227.1MB, alloc=84.3MB, time=6.66 memory used=278.2MB, alloc=108.3MB, time=8.34 memory used=342.1MB, alloc=132.3MB, time=11.38 memory used=421.2MB, alloc=132.3MB, time=15.91 memory used=500.4MB, alloc=156.3MB, time=20.49 N1 := 2837 > GB := Basis(F, plex(op(vars))); 9 3 3 4 GB := [21125000 x + 90266967 x , -10 x + 9 x y, 21125 y + 123823 y, 7 3 3 3 32500 x + 75411 x z, 325 y + 931 y z, 13 z + 19] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=585.9MB, alloc=156.3MB, time=23.75 memory used=698.4MB, alloc=164.3MB, time=26.75 memory used=806.2MB, alloc=188.3MB, time=29.66 memory used=915.8MB, alloc=468.3MB, time=32.71 memory used=1064.6MB, alloc=492.3MB, time=36.63 memory used=1252.4MB, alloc=516.3MB, time=41.90 memory used=1434.8MB, alloc=540.3MB, time=47.85 memory used=1622.4MB, alloc=564.3MB, time=54.09 memory used=1811.5MB, alloc=588.3MB, time=60.79 memory used=1984.9MB, alloc=612.3MB, time=69.50 memory used=2163.8MB, alloc=636.3MB, time=79.25 memory used=2353.4MB, alloc=660.3MB, time=90.00 memory used=2550.4MB, alloc=684.3MB, time=102.74 |\^/| 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(); 1428266832 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-14 y - 6, 9 x y + 13 x z, -12 x y z - 13 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [-14 y + 6, z , -9 x z + 3 z ] > Problem := [F,G]; 2 2 2 Problem := [[-14 y - 6, 9 x y + 13 x z, -12 x y z - 13 x], 3 3 2 [-14 y + 6, z , -9 x z + 3 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.31 memory used=26.0MB, alloc=32.3MB, time=0.86 memory used=47.5MB, alloc=32.3MB, time=1.46 memory used=67.6MB, alloc=56.3MB, time=2.10 memory used=107.9MB, alloc=84.3MB, time=3.58 N1 := 1001 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x , 7 y + 3, -91 x y + 36 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 189 #save(Problem, "format.txt"); > if (GB=[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 := [-14 y - 6, 9 x y + 13 x z, -12 x y z - 13 x, -14 y + 6, z , 2 -9 x z + 3 z ] > J:=[op(GB),op(G)]; 2 2 3 3 2 J := [x , 7 y + 3, -91 x y + 36 x z, -14 y + 6, z , -9 x 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, 11, 16, 3, 2, 3, 3, 1/2, 2/3, 2/3, 5/12, 1/3, 5/12, 6, 9, 14, 3, 2, 3, 3, 1/2, 1/2, 1/2, 1/3, 1/4, 1/3, 2, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=157.4MB, alloc=84.3MB, time=5.50 |\^/| 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(); 1428266847 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [18 z + 8 y z, -4 x y + 14 z , 18 x y + 10 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [5 y z + 11 x, -9 x y - 16 x y, 20 x y z - 9 y z] > Problem := [F,G]; 3 2 3 2 Problem := [[18 z + 8 y z, -4 x y + 14 z , 18 x y + 10 x], 2 2 [5 y z + 11 x, -9 x y - 16 x y, 20 x y z - 9 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=48.3MB, alloc=32.3MB, time=1.43 memory used=69.3MB, alloc=32.3MB, time=1.97 memory used=89.3MB, alloc=56.3MB, time=2.50 memory used=131.6MB, alloc=60.3MB, time=3.70 memory used=171.9MB, alloc=84.3MB, time=4.97 memory used=229.8MB, alloc=84.3MB, time=6.74 memory used=282.5MB, alloc=108.3MB, time=8.70 memory used=346.1MB, alloc=132.3MB, time=12.40 N1 := 2137 > GB := Basis(F, plex(op(vars))); 2 GB := [405 x - 784 x, 784 x y + 225 x, 14 x z - 5 x, 8605184 y z + 455625 x, 3 2151296 z - 50625 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=433.6MB, alloc=132.3MB, time=16.82 memory used=526.7MB, alloc=164.3MB, time=19.40 memory used=649.7MB, alloc=188.3MB, time=23.18 memory used=781.2MB, alloc=468.3MB, time=27.86 memory used=908.3MB, alloc=492.3MB, time=35.37 memory used=1054.5MB, alloc=516.3MB, time=44.34 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 3 2 H := [18 z + 8 y z, -4 x y + 14 z , 18 x y + 10 x, 5 z y + 11 x, 2 2 -9 x y - 16 x y, 20 x y z - 9 y z] > J:=[op(GB),op(G)]; 2 J := [405 x - 784 x, 784 x y + 225 x, 14 x z - 5 x, 8605184 z y + 455625 x, 3 2 2 2151296 z - 50625 x, 5 z y + 11 x, -9 x y - 16 x y, 20 x 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, 15, 17, 3, 2, 2, 3, 5/6, 1, 2/3, 7/12, 2/3, 1/2, 8, 18, 19, 3, 2, 2, 3, 1, 5/8, 5/8, 3/4, 7/16, 3/8, -3, -2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1123.2MB, alloc=516.3MB, time=48.26 |\^/| 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(); 1428266975 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-15 - 15 y, -15 y z + 16 y z, 8 x z - 14] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [-3 x y z + 3 x z, -12 x z + 14 z , -5 x z + 8 y ] > Problem := [F,G]; 2 2 Problem := [[-15 - 15 y, -15 y z + 16 y z, 8 x z - 14], 2 2 3 [-3 x y z + 3 x z, -12 x z + 14 z , -5 x z + 8 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.30 memory used=26.2MB, alloc=32.3MB, time=0.85 memory used=47.4MB, alloc=32.3MB, time=1.39 memory used=67.6MB, alloc=56.3MB, time=1.97 memory used=109.9MB, alloc=56.3MB, time=3.30 memory used=148.3MB, alloc=80.3MB, time=4.49 memory used=204.5MB, alloc=108.3MB, time=6.37 memory used=272.8MB, alloc=108.3MB, time=9.81 memory used=335.2MB, alloc=132.3MB, time=13.46 N1 := 2445 > GB := Basis(F, plex(op(vars))); GB := [1024 x - 1575, y + 1, 15 z - 16] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=423.3MB, alloc=132.3MB, time=17.44 memory used=522.1MB, alloc=164.3MB, time=20.63 N2 := 1503 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-15 - 15 y, -15 y z + 16 y z, 8 x z - 14, -3 x y z + 3 x z, 2 2 3 -12 x z + 14 z , -5 x z + 8 y ] > J:=[op(GB),op(G)]; 2 J := [1024 x - 1575, y + 1, 15 z - 16, -3 x y z + 3 x z, -12 x z + 14 z , 2 3 -5 x z + 8 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 15, 3, 1, 3, 2, 2/3, 2/3, 5/6, 5/12, 5/12, 2/3, 6, 11, 11, 3, 1, 3, 2, 2/3, 1/2, 2/3, 5/12, 1/4, 1/2, 2, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=590.7MB, alloc=164.3MB, time=24.39 |\^/| 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(); 1428267042 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 F := [12 z + 5, -7 x y z - 8 x z , 20 x z + 20 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 3 G := [17 z + 10 z , -3 x z + 12 z , -2 x y - 11 z ] > Problem := [F,G]; 3 2 Problem := [[12 z + 5, -7 x y z - 8 x z , 20 x z + 20 z], 3 2 2 3 2 3 [17 z + 10 z , -3 x z + 12 z , -2 x y - 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.32 memory used=26.1MB, alloc=32.3MB, time=0.86 memory used=47.0MB, alloc=32.3MB, time=1.39 memory used=66.5MB, alloc=56.3MB, time=1.92 memory used=106.6MB, alloc=60.3MB, time=2.97 memory used=143.0MB, alloc=84.3MB, time=3.95 memory used=203.4MB, alloc=84.3MB, time=5.85 memory used=256.8MB, alloc=108.3MB, time=7.55 memory used=326.0MB, alloc=132.3MB, time=9.78 memory used=405.7MB, alloc=156.3MB, time=13.40 memory used=495.9MB, alloc=180.3MB, time=18.75 memory used=610.1MB, alloc=180.3MB, time=25.40 memory used=724.4MB, alloc=204.3MB, time=32.11 N1 := 3637 > GB := Basis(F, plex(op(vars))); 3 GB := [x + 1, 1029 y - 640, 8 z + 7 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=851.0MB, alloc=212.3MB, time=36.31 memory used=1012.3MB, alloc=492.3MB, time=42.82 N2 := 2013 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 3 2 H := [12 z + 5, -7 x y z - 8 x z , 20 x z + 20 z, 17 z + 10 z , 2 3 2 3 -3 x z + 12 z , -2 x y - 11 z ] > J:=[op(GB),op(G)]; 3 3 2 2 3 J := [x + 1, 1029 y - 640, 8 z + 7 y, 17 z + 10 z , -3 x z + 12 z , 2 3 -2 x y - 11 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 17, 3, 1, 2, 3, 2/3, 1/3, 1, 5/12, 1/6, 5/6, 6, 10, 14, 3, 1, 3, 3, 1/2, 1/2, 2/3, 1/4, 1/4, 1/2, 2, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1088.2MB, alloc=492.3MB, time=47.36 |\^/| 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(); 1428267166 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 F := [-12 x z + 14 z , -x y + z , -17 x z - 4 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-12 x z - 6 y, -6 x y z + 10 x , -18 x y + 7 x y z] > Problem := [F,G]; 2 3 2 3 2 Problem := [[-12 x z + 14 z , -x y + z , -17 x z - 4 y], 2 2 [-12 x z - 6 y, -6 x y z + 10 x , -18 x y + 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=0.30 memory used=26.5MB, alloc=32.3MB, time=0.87 memory used=47.8MB, alloc=32.3MB, time=1.42 memory used=67.8MB, alloc=56.3MB, time=1.98 memory used=106.5MB, alloc=60.3MB, time=3.02 memory used=142.7MB, alloc=84.3MB, time=4.00 memory used=198.9MB, alloc=92.3MB, time=5.53 memory used=252.6MB, alloc=116.3MB, time=7.00 memory used=327.2MB, alloc=140.3MB, time=9.01 memory used=422.3MB, alloc=396.3MB, time=11.60 memory used=518.2MB, alloc=420.3MB, time=14.22 memory used=634.5MB, alloc=444.3MB, time=17.44 memory used=772.9MB, alloc=468.3MB, time=21.34 memory used=934.2MB, alloc=492.3MB, time=25.93 memory used=1081.3MB, alloc=516.3MB, time=30.02 memory used=1215.7MB, alloc=516.3MB, time=33.93 memory used=1358.0MB, alloc=540.3MB, time=38.34 memory used=1505.5MB, alloc=540.3MB, time=43.06 memory used=1636.1MB, alloc=564.3MB, time=47.20 memory used=1722.6MB, alloc=564.3MB, time=50.06 memory used=1813.6MB, alloc=564.3MB, time=53.24 memory used=1897.9MB, alloc=564.3MB, time=56.22 memory used=1992.8MB, alloc=588.3MB, time=59.55 memory used=2082.9MB, alloc=588.3MB, time=62.91 memory used=2152.5MB, alloc=588.3MB, time=65.45 memory used=2235.0MB, alloc=588.3MB, time=68.66 memory used=2283.6MB, alloc=588.3MB, time=70.67 memory used=2338.2MB, alloc=588.3MB, time=72.82 memory used=2572.2MB, alloc=612.3MB, time=79.85 memory used=2807.2MB, alloc=636.3MB, time=87.58 memory used=3046.1MB, alloc=660.3MB, time=95.86 memory used=3295.9MB, alloc=684.3MB, time=104.77 memory used=3547.2MB, alloc=708.3MB, time=114.02 |\^/| 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(); 1428267466 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [2 x y - 7 x y z, 17 x y + 6 y, -18 x + 3 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [-x z + 2 x y , -15 z , 15 x z + 14 z ] > Problem := [F,G]; 2 2 3 Problem := [[2 x y - 7 x y z, 17 x y + 6 y, -18 x + 3 x], 2 2 3 2 2 [-x z + 2 x y , -15 z , 15 x z + 14 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.30 memory used=26.3MB, alloc=32.3MB, time=0.86 memory used=49.0MB, alloc=32.3MB, time=1.54 memory used=68.9MB, alloc=56.3MB, time=2.15 memory used=109.1MB, alloc=84.3MB, time=3.46 N1 := 1243 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [6 x - x, 6 x y - y, 36 x y + 17 y , -2 x y + 7 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=165.5MB, alloc=84.3MB, time=6.08 memory used=225.2MB, alloc=108.3MB, time=7.82 N2 := 915 #save(Problem, "format.txt"); > if (GB=[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 := [2 x y - 7 x y z, 17 x y + 6 y, -18 x + 3 x, -x z + 2 x y , -15 z , 2 2 15 x z + 14 z ] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [6 x - x, 6 x y - y, 36 x y + 17 y , -2 x y + 7 y z, -x z + 2 x y , 3 2 2 -15 z , 15 x z + 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, 12, 18, 3, 3, 2, 3, 5/6, 1/2, 2/3, 2/3, 5/12, 5/12, 7, 14, 19, 3, 3, 2, 3, 6/7, 4/7, 4/7, 4/7, 1/2, 5/14, -2, -1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=263.5MB, alloc=108.3MB, time=9.53 |\^/| 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(); 1428314097 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 F := [15 y + 11 y z, 12 x z + 2 z, 6 z - y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [20 z + 12, -3 x z + 8 z , 12 z + 9] > Problem := [F,G]; 3 2 3 Problem := [[15 y + 11 y z, 12 x z + 2 z, 6 z - y], 3 2 3 2 [20 z + 12, -3 x z + 8 z , 12 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=0.13 memory used=26.5MB, 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=86.6MB, alloc=56.3MB, time=1.09 memory used=124.9MB, alloc=60.3MB, time=1.57 memory used=162.2MB, alloc=84.3MB, time=2.06 memory used=219.8MB, alloc=84.3MB, time=2.78 memory used=274.3MB, alloc=92.3MB, time=3.54 memory used=326.1MB, alloc=116.3MB, time=4.19 memory used=401.0MB, alloc=140.3MB, time=5.08 memory used=498.0MB, alloc=140.3MB, time=6.42 memory used=585.5MB, alloc=164.3MB, time=7.65 memory used=689.5MB, alloc=188.3MB, time=9.18 memory used=804.8MB, alloc=212.3MB, time=10.93 memory used=922.4MB, alloc=236.3MB, time=13.59 memory used=1046.7MB, alloc=260.3MB, time=17.06 memory used=1187.8MB, alloc=284.3MB, time=21.31 memory used=1352.7MB, alloc=308.3MB, time=26.27 memory used=1541.7MB, alloc=308.3MB, time=31.85 memory used=1730.6MB, alloc=332.3MB, time=37.41 memory used=1943.4MB, alloc=356.3MB, time=44.01 N1 := 6393 > GB := Basis(F, plex(op(vars))); 5 2 2 2 GB := [792 x y - 5 y, 22 x y + 5 y , -6 x y + z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2135.5MB, alloc=356.3MB, time=49.72 N2 := 831 #save(Problem, "format.txt"); > 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 := [15 y + 11 y z, 12 x z + 2 z, 6 z - y, 20 z + 12, -3 x z + 8 z , 2 12 z + 9] > J:=[op(GB),op(G)]; 5 2 2 2 3 2 3 J := [792 x y - 5 y, 22 x y + 5 y , -6 x y + z, 20 z + 12, -3 x z + 8 z , 2 12 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, 10, 17, 3, 1, 3, 3, 1/3, 1/3, 1, 1/6, 1/4, 2/3, 6, 11, 20, 6, 5, 2, 3, 2/3, 1/2, 2/3, 1/3, 5/12, 5/12, -1, -3, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2208.7MB, alloc=612.3MB, time=51.47 |\^/| 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(); 1428314153 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 F := [-12 x y - 8 y , -7 y - 2 y z , -15 x y + 20 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [11 z , 18 y - 11 y z, -6 x y z - 6 z ] > Problem := [F,G]; 2 3 3 2 Problem := [[-12 x y - 8 y , -7 y - 2 y z , -15 x y + 20 z], 2 3 2 2 [11 z , 18 y - 11 y z, -6 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=0.18 memory used=26.4MB, alloc=32.3MB, time=0.54 N1 := 231 > GB := Basis(F, plex(op(vars))); 3 2 2 2 3 GB := [9 x y + 56 x y , 3 x y + 2 y , -3 x y + 4 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=47.9MB, alloc=32.3MB, time=0.93 memory used=67.9MB, alloc=56.3MB, time=1.27 N2 := 231 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 2 2 3 2 H := [-12 x y - 8 y , -7 y - 2 y z , -15 x y + 20 z, 11 z , 18 y - 11 y z, 2 -6 x y z - 6 z ] > J:=[op(GB),op(G)]; 3 2 2 2 3 2 3 2 J := [9 x y + 56 x y , 3 x y + 2 y , -3 x y + 4 z, 11 z , 18 y - 11 y z, 2 -6 x y z - 6 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 16, 3, 1, 3, 2, 1/2, 5/6, 5/6, 1/4, 2/3, 1/2, 6, 13, 18, 5, 3, 3, 2, 2/3, 5/6, 2/3, 5/12, 2/3, 5/12, 0, -2, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=71.6MB, alloc=56.3MB, time=1.35 |\^/| 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(); 1428314155 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 F := [3 z + 20 x, -8 y z + 4 z, -19 y z - 7 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 G := [-19 x + 16 y , -9 y z + 3 z , 4 x z - 15 z ] > Problem := [F,G]; 3 2 Problem := [[3 z + 20 x, -8 y z + 4 z, -19 y z - 7 x y], 3 3 2 2 2 [-19 x + 16 y , -9 y z + 3 z , 4 x z - 15 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=47.5MB, alloc=32.3MB, time=0.82 memory used=68.0MB, alloc=32.3MB, time=1.15 memory used=88.7MB, alloc=56.3MB, time=1.55 memory used=131.1MB, alloc=60.3MB, time=2.31 memory used=168.8MB, alloc=84.3MB, time=3.03 memory used=223.9MB, alloc=108.3MB, time=4.58 memory used=294.2MB, alloc=108.3MB, time=7.06 N1 := 1875 > GB := Basis(F, plex(op(vars))); 3 GB := [2058 x - 34295 x, 2 x y - x, 14 x + 19 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 2 3 3 H := [3 z + 20 x, -8 y z + 4 z, -19 y z - 7 x y, -19 x + 16 y , 2 2 2 -9 y z + 3 z , 4 x z - 15 z ] > J:=[op(GB),op(G)]; 3 3 3 2 2 J := [2058 x - 34295 x, 2 x y - x, 19 z + 14 x, -19 x + 16 y , -9 y z + 3 z , 2 4 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, 13, 16, 3, 3, 3, 3, 2/3, 2/3, 5/6, 1/3, 5/12, 2/3, 6, 11, 14, 3, 3, 3, 2, 5/6, 1/2, 1/2, 7/12, 1/4, 5/12, 2, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=363.0MB, alloc=108.3MB, time=8.31 |\^/| 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(); 1428314164 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 F := [8 z - 4, -9 x y - 4 x y z, -4 x + x y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-9 x z + 19 x, -13 y z - 19, -5 x y - 19 x ] > Problem := [F,G]; 3 2 3 Problem := [[8 z - 4, -9 x y - 4 x y z, -4 x + x y z], 2 2 2 2 [-9 x z + 19 x, -13 y z - 19, -5 x y - 19 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=32.3MB, time=0.83 memory used=67.5MB, alloc=56.3MB, time=1.13 memory used=107.3MB, alloc=60.3MB, time=1.72 memory used=145.8MB, alloc=60.3MB, time=2.31 memory used=182.8MB, alloc=84.3MB, time=2.89 memory used=238.6MB, alloc=84.3MB, time=3.74 memory used=294.6MB, alloc=108.3MB, time=4.80 memory used=366.3MB, alloc=140.3MB, time=6.16 memory used=454.3MB, alloc=164.3MB, time=7.77 memory used=557.4MB, alloc=188.3MB, time=9.66 memory used=672.8MB, alloc=212.3MB, time=11.79 memory used=800.3MB, alloc=236.3MB, time=14.13 memory used=931.2MB, alloc=260.3MB, time=17.62 memory used=1066.3MB, alloc=284.3MB, time=21.80 memory used=1212.7MB, alloc=308.3MB, time=26.66 memory used=1371.7MB, alloc=332.3MB, time=32.64 memory used=1543.9MB, alloc=356.3MB, time=39.65 memory used=1740.1MB, alloc=380.3MB, time=47.67 memory used=1960.2MB, alloc=404.3MB, time=56.65 memory used=2204.3MB, alloc=404.3MB, time=66.42 memory used=2448.3MB, alloc=404.3MB, time=76.46 memory used=2692.3MB, alloc=428.3MB, time=86.86 memory used=2960.2MB, alloc=428.3MB, time=98.00 memory used=3228.1MB, alloc=428.3MB, time=108.38 memory used=3496.0MB, alloc=452.3MB, time=118.81 memory used=3787.7MB, alloc=452.3MB, time=130.69 memory used=4079.3MB, alloc=452.3MB, time=142.65 memory used=4370.9MB, alloc=476.3MB, time=154.42 memory used=4686.3MB, alloc=476.3MB, time=167.77 memory used=5001.7MB, alloc=500.3MB, time=180.27 N1 := 12005 > GB := Basis(F, plex(op(vars))); 6 3 5 4 3 3 GB := [729 x + 32 x , -81 x + 2 x y, 9 x + 4 x z, 2 z - 1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5235.4MB, alloc=500.3MB, time=188.15 N2 := 1917 #save(Problem, "format.txt"); > 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 := [8 z - 4, -9 x y - 4 x y z, -4 x + x y z, -9 x z + 19 x, -13 y z - 19, 2 2 -5 x y - 19 x ] > J:=[op(GB),op(G)]; 6 3 5 4 3 3 2 J := [729 x + 32 x , -81 x + 2 x y, 9 x + 4 x z, 2 z - 1, -9 x z + 19 x, 2 2 2 -13 y z - 19, -5 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, 13, 18, 3, 3, 1, 3, 2/3, 2/3, 5/6, 2/3, 5/12, 5/12, 7, 12, 27, 6, 6, 1, 3, 5/7, 3/7, 4/7, 5/7, 3/14, 2/7, 1, -9, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=5485.4MB, alloc=756.3MB, time=194.91 |\^/| 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(); 1428314385 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-10 x z - 5 x y z, -6 x y - 13 z , 5 y z - 6 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [14 y z - 9 y, -4 - y, 4 x z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-10 x z - 5 x y z, -6 x y - 13 z , 5 y z - 6 x z], 2 2 [14 y z - 9 y, -4 - y, 4 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.5MB, alloc=32.3MB, time=0.79 memory used=68.7MB, alloc=56.3MB, time=1.19 memory used=110.9MB, alloc=60.3MB, time=1.92 memory used=148.4MB, alloc=84.3MB, time=2.59 memory used=203.9MB, alloc=108.3MB, time=3.74 memory used=272.7MB, alloc=132.3MB, time=5.75 memory used=354.7MB, alloc=132.3MB, time=8.72 memory used=436.7MB, alloc=156.3MB, time=11.71 N1 := 3037 > GB := Basis(F, plex(op(vars))); 6 3 4 3 2 4 2 3 2 2 GB := [100 x y - 39 x y, 2 x y + x y , -4 x y + x y , 5 x y + 13 x z, 2 2 6 y x + 13 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=544.4MB, alloc=156.3MB, time=14.54 memory used=657.0MB, alloc=188.3MB, time=16.47 memory used=790.9MB, alloc=212.3MB, time=18.90 memory used=932.1MB, alloc=236.3MB, time=22.65 memory used=1069.1MB, alloc=260.3MB, time=27.76 memory used=1224.9MB, alloc=284.3MB, time=33.80 memory used=1404.6MB, alloc=308.3MB, time=41.01 memory used=1608.4MB, alloc=332.3MB, time=49.22 N2 := 5137 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [-10 x z - 5 x y z, -6 x y - 13 z , 5 y z - 6 x z, 14 y z - 9 y, 2 -4 - y, 4 x z ] > J:=[op(GB),op(G)]; 6 3 4 3 2 4 2 3 2 2 J := [100 x y - 39 x y, 2 x y + x y , -4 x y + x y , 5 x y + 13 x z, 2 2 2 2 6 y x + 13 z , 14 y z - 9 y, -4 - y, 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, 14, 16, 3, 2, 1, 2, 2/3, 5/6, 5/6, 5/13, 6/13, 7/13, 8, 17, 31, 7, 6, 3, 2, 3/4, 7/8, 1/2, 10/17, 11/17, 4/17, -3, -15, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1677.5MB, alloc=332.3MB, time=51.65 |\^/| 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(); 1428314440 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 F := [-10 x z + 4 z , -16 x y z + 9 x z , -7 y + x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-20 z + 16, -16 x y z + 9 x y, -18 y - 14 y z] > Problem := [F,G]; 2 3 2 3 Problem := [[-10 x z + 4 z , -16 x y z + 9 x z , -7 y + x y], 2 3 2 [-20 z + 16, -16 x y z + 9 x y, -18 y - 14 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.46 memory used=47.3MB, alloc=32.3MB, time=0.76 memory used=67.6MB, alloc=32.3MB, time=1.05 memory used=86.4MB, alloc=56.3MB, time=1.34 memory used=125.1MB, alloc=60.3MB, time=1.95 memory used=163.2MB, alloc=84.3MB, time=2.66 memory used=218.4MB, alloc=108.3MB, time=3.70 memory used=290.3MB, alloc=132.3MB, time=5.00 memory used=377.5MB, alloc=156.3MB, time=6.59 memory used=457.0MB, alloc=188.3MB, time=8.10 memory used=568.1MB, alloc=212.3MB, time=10.14 memory used=683.8MB, alloc=236.3MB, time=12.47 memory used=798.3MB, alloc=260.3MB, time=15.66 memory used=922.1MB, alloc=284.3MB, time=19.43 memory used=1058.1MB, alloc=308.3MB, time=23.89 memory used=1207.5MB, alloc=332.3MB, time=28.94 memory used=1368.3MB, alloc=356.3MB, time=35.15 memory used=1550.6MB, alloc=380.3MB, time=42.24 memory used=1756.8MB, alloc=404.3MB, time=50.22 memory used=1987.0MB, alloc=428.3MB, time=59.13 memory used=2241.1MB, alloc=428.3MB, time=68.86 memory used=2495.1MB, alloc=428.3MB, time=78.57 memory used=2749.2MB, alloc=452.3MB, time=88.37 memory used=3027.2MB, alloc=452.3MB, time=99.28 memory used=3305.1MB, alloc=452.3MB, time=110.04 memory used=3583.0MB, alloc=452.3MB, time=120.71 memory used=3860.9MB, alloc=476.3MB, time=131.44 memory used=4162.7MB, alloc=476.3MB, time=143.19 memory used=4464.5MB, alloc=476.3MB, time=155.01 memory used=4766.0MB, alloc=476.3MB, time=167.30 memory used=5067.6MB, alloc=500.3MB, time=179.36 memory used=5393.0MB, alloc=500.3MB, time=192.18 memory used=5718.3MB, alloc=524.3MB, time=204.89 memory used=6067.5MB, alloc=524.3MB, time=218.56 memory used=6416.7MB, alloc=548.3MB, time=231.91 memory used=6790.1MB, alloc=572.3MB, time=246.19 N1 := 14473 > GB := Basis(F, plex(op(vars))); 3 5 4 3 2 GB := [7 y - x y, 2835 x z - 512 x z, 2835 x y z - 512 x y z, 3 2 2 2 3 -405 x z + 512 x y z, -16 x y z + 9 x z , -5 x z + 2 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6873.9MB, alloc=572.3MB, time=249.00 memory used=7319.6MB, alloc=828.3MB, time=257.51 memory used=7740.0MB, alloc=852.3MB, time=268.18 memory used=8107.8MB, alloc=876.3MB, time=281.00 |\^/| 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(); 1428314740 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 F := [-11 x z - 18, -9 - 9 y, -9 x y z + 7 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-7 x , -12 y z - 20 z, 8 x y - 11 x z ] > Problem := [F,G]; 2 Problem := [[-11 x z - 18, -9 - 9 y, -9 x y z + 7 x z], 3 2 2 2 [-7 x , -12 y z - 20 z, 8 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=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=48.0MB, alloc=32.3MB, time=0.83 memory used=68.4MB, alloc=56.3MB, time=1.22 memory used=109.9MB, alloc=60.3MB, time=1.96 memory used=147.0MB, alloc=84.3MB, time=2.63 memory used=202.2MB, alloc=108.3MB, time=3.71 memory used=270.5MB, alloc=132.3MB, time=5.77 memory used=354.4MB, alloc=132.3MB, time=8.85 memory used=438.4MB, alloc=156.3MB, time=11.83 N1 := 2907 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 159 #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 H := [-11 x z - 18, -9 - 9 y, -9 x y z + 7 x z, -7 x , -12 y z - 20 z, 2 2 8 x y - 11 x z ] > J:=[op(GB),op(G)]; 3 2 2 2 J := [1, -7 x , -12 y z - 20 z, 8 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, 12, 16, 3, 3, 2, 2, 2/3, 2/3, 2/3, 1/2, 1/3, 1/2, 4, 6, 9, 3, 3, 2, 2, 1/2, 1/2, 1/2, 3/7, 2/7, 3/7, 6, 7, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=490.9MB, alloc=156.3MB, time=13.15 |\^/| 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(); 1428314755 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [18 x y - 11 x, -6 x - 14 y , 18 x - y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [-20 x + 16 x y z, -18 y z - 2 z, -19 x - 15 x] > Problem := [F,G]; 2 2 2 Problem := [[18 x y - 11 x, -6 x - 14 y , 18 x - y], 3 2 [-20 x + 16 x y z, -18 y z - 2 z, -19 x - 15 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=48.0MB, alloc=32.3MB, time=0.83 N1 := 345 > GB := Basis(F, plex(op(vars))); GB := [x, y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=67.9MB, alloc=32.3MB, time=1.21 N2 := 107 #save(Problem, "format.txt"); > if (GB=[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 := [18 x y - 11 x, -6 x - 14 y , 18 x - y, -20 x + 16 x y z, -18 y z - 2 z, 2 -19 x - 15 x] > J:=[op(GB),op(G)]; 3 2 J := [x, y, -20 x + 16 x y z, -18 y z - 2 z, -19 x - 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, 12, 13, 3, 3, 2, 1, 5/6, 5/6, 1/3, 2/3, 5/12, 1/4, 5, 8, 9, 3, 3, 1, 1, 3/5, 3/5, 2/5, 5/8, 3/8, 3/8, 4, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=78.3MB, alloc=32.3MB, time=1.37 |\^/| 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(); 1428314757 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 2 F := [14 x z - 18 x , -3 x y + 2 z , 10 y - 9 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-14 x z - 17 z , 17 x y - 3, 17 z + 8 y] > Problem := [F,G]; 2 2 2 3 2 2 Problem := [[14 x z - 18 x , -3 x y + 2 z , 10 y - 9 z ], 2 2 2 2 [-14 x z - 17 z , 17 x y - 3, 17 z + 8 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=48.0MB, alloc=32.3MB, time=0.80 memory used=68.6MB, alloc=32.3MB, time=1.11 memory used=88.6MB, alloc=32.3MB, time=1.41 memory used=107.9MB, alloc=56.3MB, time=1.72 memory used=147.4MB, alloc=60.3MB, time=2.33 memory used=183.4MB, alloc=84.3MB, time=2.89 memory used=244.2MB, alloc=108.3MB, time=3.98 memory used=322.4MB, alloc=140.3MB, time=5.38 memory used=416.9MB, alloc=164.3MB, time=7.04 memory used=525.6MB, alloc=188.3MB, time=9.02 memory used=641.2MB, alloc=212.3MB, time=11.38 memory used=755.7MB, alloc=236.3MB, time=14.67 memory used=881.2MB, alloc=260.3MB, time=18.60 memory used=1017.3MB, alloc=284.3MB, time=23.71 memory used=1173.7MB, alloc=308.3MB, time=29.80 memory used=1353.9MB, alloc=332.3MB, time=36.78 memory used=1558.2MB, alloc=332.3MB, time=44.74 memory used=1762.4MB, alloc=332.3MB, time=52.57 memory used=1966.5MB, alloc=356.3MB, time=60.49 memory used=2194.6MB, alloc=356.3MB, time=69.19 memory used=2422.7MB, alloc=356.3MB, time=77.96 memory used=2650.6MB, alloc=380.3MB, time=86.68 memory used=2902.7MB, alloc=404.3MB, time=96.13 N1 := 8725 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 4 2 GB := [21 x - 20 x , 490 x y - 729 x , 1960000 y - 4782969 x , 2 2 2 2 2 2 7 x z - 9 x , -27 x y + 20 y z, -10 y + 9 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3028.5MB, alloc=404.3MB, time=99.18 memory used=3337.0MB, alloc=660.3MB, time=104.48 memory used=3639.5MB, alloc=684.3MB, time=110.14 memory used=3931.8MB, alloc=708.3MB, time=118.27 memory used=4193.0MB, alloc=732.3MB, time=127.56 memory used=4454.7MB, alloc=756.3MB, time=138.12 memory used=4736.5MB, alloc=780.3MB, time=149.64 memory used=5042.1MB, alloc=804.3MB, time=162.80 memory used=5371.7MB, alloc=828.3MB, time=176.46 memory used=5725.2MB, alloc=852.3MB, time=191.15 memory used=6102.7MB, alloc=876.3MB, time=207.66 memory used=6504.1MB, alloc=900.3MB, time=226.02 memory used=6929.6MB, alloc=924.3MB, time=245.14 memory used=7378.9MB, alloc=948.3MB, time=263.76 |\^/| 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(); 1428315057 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [-10 y + 18 x , -6 x - 9 x y, -17 x z - 19 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 G := [2 x y + 8 x z, 18 y z + 2 x y, -13 x y + 6 y ] > Problem := [F,G]; 3 2 2 2 2 Problem := [[-10 y + 18 x , -6 x - 9 x y, -17 x z - 19 y z], 2 2 2 2 3 [2 x y + 8 x z, 18 y z + 2 x y, -13 x y + 6 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.80 memory used=68.3MB, alloc=56.3MB, time=1.12 memory used=110.9MB, alloc=60.3MB, time=1.85 memory used=148.8MB, alloc=84.3MB, time=2.51 memory used=206.8MB, alloc=108.3MB, time=3.53 memory used=281.4MB, alloc=140.3MB, time=5.38 memory used=363.9MB, alloc=140.3MB, time=8.30 N1 := 2455 > GB := Basis(F, plex(op(vars))); 4 3 2 3 2 3 2 GB := [40 x + 243 x , 2 x + 3 x y, 5 y - 9 x , 40 x z + 243 x z, 2 2 17 x z + 19 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=447.9MB, alloc=140.3MB, time=10.91 memory used=539.4MB, alloc=164.3MB, time=12.30 memory used=654.6MB, alloc=188.3MB, time=14.29 memory used=782.0MB, alloc=212.3MB, time=18.34 N2 := 2455 #save(Problem, "format.txt"); > 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 := [-10 y + 18 x , -6 x - 9 x y, -17 x z - 19 y z, 2 x y + 8 x z, 2 2 3 18 y z + 2 x y, -13 x y + 6 y ] > J:=[op(GB),op(G)]; 4 3 2 3 2 3 2 J := [40 x + 243 x , 2 x + 3 x y, 5 y - 9 x , 40 x z + 243 x z, 2 2 2 2 2 2 3 17 x z + 19 y z, 2 x y + 8 x z, 18 y z + 2 x y, -13 x y + 6 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 17, 3, 2, 3, 2, 1, 1, 1/2, 2/3, 2/3, 1/3, 8, 18, 25, 4, 4, 3, 2, 1, 3/4, 1/2, 3/4, 1/2, 3/8, -3, -8, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=874.4MB, alloc=212.3MB, time=21.57 |\^/| 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(); 1428315081 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [4 y z + 20 y z, -10 x y + 14 y , -15 x + 5 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [8 y z + 19 z, -9 y z + 18 z, 18 x y ] > Problem := [F,G]; 2 2 3 2 Problem := [[4 y z + 20 y z, -10 x y + 14 y , -15 x + 5 y z], 2 2 [8 y z + 19 z, -9 y z + 18 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.48 memory used=47.1MB, alloc=32.3MB, time=0.80 memory used=67.5MB, alloc=56.3MB, time=1.18 memory used=108.4MB, alloc=60.3MB, time=1.91 memory used=143.4MB, alloc=84.3MB, time=2.68 memory used=193.7MB, alloc=108.3MB, time=4.45 N1 := 1483 > GB := Basis(F, plex(op(vars))); 5 4 4 3 2 3 3 GB := [147 x + 125 x , -5 x + 7 x y, -5 x y + 7 y , x z + 5 x , 3 2 -21 x + 5 x y z, y z + 5 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=266.9MB, alloc=116.3MB, time=5.76 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 3 2 2 H := [4 y z + 20 y z, -10 x y + 14 y , -15 x + 5 y z, 8 y z + 19 z, 2 -9 y z + 18 z, 18 x y ] > J:=[op(GB),op(G)]; 5 4 4 3 2 3 3 J := [147 x + 125 x , -5 x + 7 x y, -5 x y + 7 y , x z + 5 x , 3 2 2 2 -21 x + 5 x y z, y z + 5 y z, 8 y z + 19 z, -9 y z + 18 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, 13, 16, 3, 3, 2, 2, 1/2, 1, 2/3, 3/13, 8/13, 7/13, 9, 18, 29, 5, 5, 2, 2, 2/3, 7/9, 5/9, 10/19, 9/19, 8/19, -5, -13, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=296.1MB, alloc=116.3MB, time=6.48 |\^/| 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(); 1428315089 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [-20 x + 6 x z, -20 y z + 4 x, -3 x z + 3 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [6 x - 3 y z, 13 x y - 7 x y, 8 x z + 11 z ] > Problem := [F,G]; 3 2 2 2 2 Problem := [[-20 x + 6 x z, -20 y z + 4 x, -3 x z + 3 y z], 2 2 2 3 [6 x - 3 y z, 13 x y - 7 x y, 8 x z + 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.46 memory used=47.8MB, alloc=32.3MB, time=0.78 memory used=68.4MB, alloc=32.3MB, time=1.07 memory used=88.0MB, alloc=56.3MB, time=1.37 memory used=126.7MB, alloc=60.3MB, time=1.96 memory used=161.1MB, alloc=84.3MB, time=2.48 memory used=218.1MB, alloc=108.3MB, time=3.51 memory used=291.7MB, alloc=116.3MB, time=4.82 memory used=359.1MB, alloc=140.3MB, time=5.99 memory used=444.5MB, alloc=164.3MB, time=7.41 memory used=545.0MB, alloc=188.3MB, time=9.13 memory used=656.9MB, alloc=212.3MB, time=11.77 memory used=771.4MB, alloc=236.3MB, time=15.29 memory used=897.5MB, alloc=260.3MB, time=19.55 memory used=1036.3MB, alloc=284.3MB, time=24.95 memory used=1199.1MB, alloc=308.3MB, time=31.26 memory used=1385.9MB, alloc=308.3MB, time=38.22 memory used=1572.6MB, alloc=332.3MB, time=45.19 memory used=1783.2MB, alloc=332.3MB, time=53.04 memory used=1993.9MB, alloc=332.3MB, time=60.90 memory used=2204.6MB, alloc=356.3MB, time=68.70 memory used=2439.3MB, alloc=380.3MB, time=77.41 N1 := 7793 > GB := Basis(F, plex(op(vars))); 6 2 4 3 2 3 2 GB := [250000 x - 81 x , -500 x + 9 x y, -10 x + 3 x z, -10 x + 3 y z, 2 5 y z - x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2565.6MB, alloc=380.3MB, time=80.43 memory used=2853.4MB, alloc=636.3MB, time=84.96 memory used=3140.3MB, alloc=660.3MB, time=89.62 memory used=3439.7MB, alloc=684.3MB, time=95.26 memory used=3733.7MB, alloc=708.3MB, time=100.84 memory used=4029.6MB, alloc=732.3MB, time=106.35 memory used=4320.6MB, alloc=756.3MB, time=112.08 memory used=4614.3MB, alloc=780.3MB, time=120.21 memory used=4873.9MB, alloc=804.3MB, time=129.72 memory used=5138.5MB, alloc=828.3MB, time=140.07 memory used=5411.9MB, alloc=852.3MB, time=150.98 memory used=5695.1MB, alloc=876.3MB, time=162.49 memory used=5985.6MB, alloc=900.3MB, time=175.12 memory used=6292.4MB, alloc=924.3MB, time=188.75 memory used=6623.1MB, alloc=948.3MB, time=203.59 memory used=6977.7MB, alloc=972.3MB, time=219.50 memory used=7356.3MB, alloc=996.3MB, time=236.50 memory used=7758.8MB, alloc=1020.3MB, time=254.08 memory used=8185.3MB, alloc=1044.3MB, time=272.82 |\^/| 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(); 1428315389 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-3 x + 4 x y z, -2 x y + 2, -8 x y + 4 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [7 y z - 2, 16 x y z - 11 y , 16 x - 20 y ] > Problem := [F,G]; 3 2 2 Problem := [[-3 x + 4 x y z, -2 x y + 2, -8 x y + 4 x z], 2 3 2 2 [7 y z - 2, 16 x y z - 11 y , 16 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=0.22 memory used=26.3MB, alloc=32.3MB, time=0.62 memory used=47.8MB, alloc=32.3MB, time=1.04 memory used=67.9MB, alloc=32.3MB, time=1.42 memory used=87.1MB, alloc=56.3MB, time=1.72 memory used=127.6MB, alloc=60.3MB, time=2.48 memory used=166.6MB, alloc=84.3MB, time=3.32 memory used=207.2MB, alloc=84.3MB, time=3.99 memory used=270.6MB, alloc=92.3MB, time=4.92 memory used=327.7MB, alloc=116.3MB, time=6.08 memory used=404.1MB, alloc=140.3MB, time=8.05 memory used=495.0MB, alloc=164.3MB, time=9.82 memory used=599.0MB, alloc=188.3MB, time=11.83 memory used=699.5MB, alloc=468.3MB, time=13.71 memory used=836.7MB, alloc=492.3MB, time=16.50 memory used=977.7MB, alloc=516.3MB, time=21.14 memory used=1127.9MB, alloc=540.3MB, time=26.31 memory used=1285.5MB, alloc=564.3MB, time=32.66 memory used=1465.3MB, alloc=588.3MB, time=40.44 memory used=1669.1MB, alloc=588.3MB, time=48.83 memory used=1872.9MB, alloc=612.3MB, time=57.06 memory used=2100.6MB, alloc=612.3MB, time=66.10 memory used=2328.3MB, alloc=636.3MB, time=75.16 memory used=2580.0MB, alloc=636.3MB, time=85.08 N1 := 7919 > GB := Basis(F, plex(op(vars))); 7 3 6 GB := [9 x - 64, -3 x + 8 y, -9 x + 32 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2833.0MB, alloc=636.3MB, time=94.70 memory used=3119.9MB, alloc=660.3MB, time=100.24 N2 := 2879 #save(Problem, "format.txt"); > 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 := [-3 x + 4 x y z, -2 x y + 2, -8 x y + 4 x z, 7 z y - 2, 3 2 2 16 x y z - 11 y , 16 x - 20 y ] > J:=[op(GB),op(G)]; 7 3 6 2 3 J := [9 x - 64, -3 x + 8 y, -9 x + 32 z, 7 z y - 2, 16 x y z - 11 y , 2 2 16 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, 15, 17, 3, 3, 3, 2, 5/6, 1, 2/3, 7/12, 7/12, 1/3, 6, 12, 24, 7, 7, 3, 2, 5/6, 2/3, 1/2, 5/12, 5/12, 1/4, 3, -7, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=3399.8MB, alloc=660.3MB, time=110.96 |\^/| 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(); 1428315510 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 F := [-13 y z - 19 x , 3 y - 20 x, 20 x - 11 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-12 x y z - 10 y z, -14 z - 10 z , 17 + 18 x] > Problem := [F,G]; 2 2 3 3 Problem := [[-13 y z - 19 x , 3 y - 20 x, 20 x - 11 z], 2 3 2 [-12 x y z - 10 y z, -14 z - 10 z , 17 + 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.46 memory used=78.6MB, alloc=68.3MB, time=1.35 memory used=127.4MB, alloc=68.3MB, time=2.19 memory used=168.8MB, alloc=92.3MB, time=3.29 N1 := 1483 > GB := Basis(F, plex(op(vars))); 15 2 11 2 GB := [2812160000000 x + 36453410697 x , -540800000 x + 15856203 x y, 3 3 3 y - 20 x, -20 x + 11 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=228.6MB, alloc=92.3MB, time=4.89 memory used=294.5MB, alloc=116.3MB, time=6.05 N2 := 599 #save(Problem, "format.txt"); > if (GB=[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 := [-13 y z - 19 x , 3 y - 20 x, 20 x - 11 z, -12 x y z - 10 y z, 3 2 -14 z - 10 z , 18 x + 17] > J:=[op(GB),op(G)]; 15 2 11 2 J := [2812160000000 x + 36453410697 x , -540800000 x + 15856203 x y, 3 3 2 3 2 3 y - 20 x, -20 x + 11 z, -12 x y z - 10 y z, -14 z - 10 z , 18 x + 17] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 16, 3, 3, 3, 3, 5/6, 1/2, 2/3, 5/12, 1/3, 1/2, 7, 12, 39, 15, 15, 3, 3, 6/7, 3/7, 3/7, 4/7, 2/7, 5/14, 0, -23, -12] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=298.5MB, alloc=116.3MB, time=6.15 |\^/| 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(); 1428315516 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 F := [-19 y + 9 x , -15 y z - 19 x y, 3 x - 19 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-20 x y + 6 y , -9 y z + 3, 16 x y - 17 x z] > Problem := [F,G]; 3 2 2 3 2 Problem := [[-19 y + 9 x , -15 y z - 19 x y, 3 x - 19 x y], 2 2 [-20 x y + 6 y , -9 y z + 3, 16 x y - 17 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.81 memory used=68.0MB, alloc=56.3MB, time=1.15 memory used=109.9MB, alloc=60.3MB, time=1.80 memory used=151.1MB, alloc=84.3MB, time=2.54 memory used=212.3MB, alloc=92.3MB, time=3.59 memory used=265.7MB, alloc=116.3MB, time=4.60 memory used=333.5MB, alloc=140.3MB, time=6.62 memory used=416.7MB, alloc=140.3MB, time=9.69 N1 := 2363 > GB := Basis(F, plex(op(vars))); 5 4 3 2 3 2 2 2 3 GB := [3 x - 361 x , -3 x + 19 x y, 19 y - 9 x , 15 x z + 19 x , 2 15 y z + 19 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=502.6MB, alloc=140.3MB, time=11.94 memory used=597.0MB, alloc=164.3MB, time=13.48 memory used=714.5MB, alloc=188.3MB, time=15.60 memory used=841.1MB, alloc=212.3MB, time=19.99 N2 := 2363 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 3 2 2 H := [-19 y + 9 x , -15 y z - 19 x y, 3 x - 19 x y, -20 x y + 6 y , 2 -9 y z + 3, 16 x y - 17 x z] > J:=[op(GB),op(G)]; 5 4 3 2 3 2 2 2 3 J := [3 x - 361 x , -3 x + 19 x y, 19 y - 9 x , 15 x z + 19 x , 2 2 2 15 y z + 19 x y, -20 x y + 6 y , -9 y z + 3, 16 x y - 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, 16, 3, 3, 3, 2, 5/6, 1, 1/2, 7/12, 2/3, 1/4, 8, 17, 25, 5, 5, 3, 2, 7/8, 3/4, 1/2, 11/16, 1/2, 1/4, -3, -9, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=927.1MB, alloc=212.3MB, time=23.12 |\^/| 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(); 1428315541 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-3 x y + 18 x , 11 x - 13 y , -3 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [13 x + 16 x z, 18 x z + 9 y , 12 x y + 8 x y] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-3 x y + 18 x , 11 x - 13 y , -3 x y], 3 2 3 2 [13 x + 16 x z, 18 x z + 9 y , 12 x y + 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 memory used=48.9MB, alloc=32.3MB, time=0.86 memory used=68.9MB, alloc=56.3MB, time=1.24 memory used=110.4MB, alloc=60.3MB, time=1.98 memory used=147.8MB, alloc=84.3MB, time=2.78 N1 := 1223 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x , y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=202.6MB, alloc=84.3MB, time=4.28 N2 := 157 #save(Problem, "format.txt"); > if (GB=[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 3 H := [-3 x y + 18 x , -13 y + 11 x , -3 y x , 13 x + 16 x z, 18 x z + 9 y , 2 12 x y + 8 x y] > J:=[op(GB),op(G)]; 2 2 3 2 3 2 J := [x , y , 13 x + 16 x z, 18 x z + 9 y , 12 x y + 8 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, 3, 3, 3, 2, 1, 5/6, 1/3, 9/13, 6/13, 2/13, 5, 9, 13, 3, 3, 3, 2, 4/5, 3/5, 2/5, 3/5, 2/5, 1/5, 4, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=210.1MB, alloc=84.3MB, time=4.42 |\^/| 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(); 1428315546 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 F := [-17 y z - 8 z , -2 x y - 6 y, 12 y + 7 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [18 x y - 12 x , 8 x z - 5 y, 16 x z + 5] > Problem := [F,G]; 2 3 3 2 Problem := [[-17 y z - 8 z , -2 x y - 6 y, 12 y + 7 z ], 2 2 2 2 [18 x y - 12 x , 8 x z - 5 y, 16 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=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=68.2MB, alloc=32.3MB, time=1.11 memory used=87.9MB, alloc=56.3MB, time=1.41 memory used=126.8MB, alloc=60.3MB, time=1.97 memory used=165.7MB, alloc=84.3MB, time=2.61 memory used=225.8MB, alloc=84.3MB, time=3.66 memory used=280.2MB, alloc=108.3MB, time=4.64 memory used=352.6MB, alloc=132.3MB, time=5.93 memory used=440.4MB, alloc=164.3MB, time=7.75 memory used=534.3MB, alloc=188.3MB, time=10.65 memory used=640.9MB, alloc=212.3MB, time=14.65 memory used=771.6MB, alloc=212.3MB, time=19.56 memory used=902.3MB, alloc=236.3MB, time=24.44 N1 := 4311 > GB := Basis(F, plex(op(vars))); 6 5 4 3 3 2 GB := [x y + 3 y, 768 y + 2023 y , 17 y + 8 y z, 12 y + 7 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1060.6MB, alloc=236.3MB, time=29.03 memory used=1170.2MB, alloc=492.3MB, time=30.91 memory used=1341.6MB, alloc=516.3MB, time=34.01 memory used=1528.2MB, alloc=540.3MB, time=39.96 memory used=1713.4MB, alloc=564.3MB, time=47.33 N2 := 3583 #save(Problem, "format.txt"); > if (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 := [-17 y z - 8 z , -2 x y - 6 y, 12 y + 7 z , 18 x y - 12 x , 2 2 8 z x - 5 y, 16 z x + 5] > J:=[op(GB),op(G)]; 6 5 4 3 3 2 J := [x y + 3 y, 768 y + 2023 y , 17 y + 8 y z, 12 y + 7 z , 2 2 2 2 18 x y - 12 x , 8 z x - 5 y, 16 z 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, 13, 17, 3, 2, 3, 3, 2/3, 5/6, 2/3, 5/12, 1/2, 5/12, 7, 14, 24, 6, 2, 6, 2, 4/7, 6/7, 4/7, 5/14, 9/14, 2/7, -1, -7, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1813.2MB, alloc=564.3MB, time=51.01 |\^/| 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(); 1428315599 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [15 x - 16 y , -19 x + 7 x y z, 16 x y + 14 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-19 x z - 6 y z , 18 x y + 18 z , -15 y z - 16] > Problem := [F,G]; 3 2 3 2 Problem := [[15 x - 16 y , -19 x + 7 x y z, 16 x y + 14 x], 2 2 2 2 2 [-19 x z - 6 y z , 18 x y + 18 z , -15 y z - 16]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=68.3MB, alloc=32.3MB, time=1.12 memory used=88.1MB, alloc=32.3MB, time=1.41 memory used=107.2MB, alloc=56.3MB, time=1.71 memory used=145.9MB, alloc=60.3MB, time=2.29 memory used=184.6MB, alloc=84.3MB, time=2.95 memory used=243.7MB, alloc=84.3MB, time=3.97 memory used=297.6MB, alloc=108.3MB, time=4.94 memory used=367.6MB, alloc=140.3MB, time=6.58 memory used=445.0MB, alloc=164.3MB, time=9.41 memory used=544.8MB, alloc=188.3MB, time=13.13 N1 := 2613 > GB := Basis(F, plex(op(vars))); 4 3 2 3 GB := [15 x + 14 x, -15 x + 16 y , 152 x y + 49 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=668.0MB, alloc=188.3MB, time=15.20 memory used=785.3MB, alloc=444.3MB, time=17.30 memory used=915.3MB, alloc=468.3MB, time=21.44 N2 := 2405 #save(Problem, "format.txt"); > 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 := [15 x - 16 y , -19 x + 7 x y z, 16 x y + 14 x, -19 x z - 6 y z , 2 2 2 18 x y + 18 z , -15 y z - 16] > J:=[op(GB),op(G)]; 4 3 2 3 2 2 J := [15 x + 14 x, -15 x + 16 y , 152 x y + 49 x z, -19 x z - 6 y z , 2 2 2 18 x y + 18 z , -15 y z - 16] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 18, 3, 3, 2, 2, 5/6, 1, 2/3, 7/12, 1/2, 5/12, 6, 14, 20, 4, 4, 2, 2, 5/6, 5/6, 2/3, 7/12, 5/12, 5/12, 1, -2, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1016.3MB, alloc=468.3MB, time=24.87 |\^/| 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(); 1428315625 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 2 F := [18 x y + 9 y, -10 x - 20 x , 6 x - 5 y z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 G := [9 x + 4 x z, 2 x y - 17 y, -13 x y + 4 z ] > Problem := [F,G]; 2 3 2 3 2 Problem := [[18 x y + 9 y, -10 x - 20 x , 6 x - 5 y z ], 3 2 2 3 [9 x + 4 x z, 2 x y - 17 y, -13 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=0.17 memory used=26.6MB, alloc=32.3MB, time=0.48 memory used=49.0MB, alloc=32.3MB, time=0.83 memory used=70.1MB, alloc=56.3MB, time=1.20 memory used=112.4MB, alloc=84.3MB, time=2.05 N1 := 721 > GB := Basis(F, plex(op(vars))); 2 GB := [x , y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 147 #save(Problem, "format.txt"); > if (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 H := [18 x y + 9 y, -10 x - 20 x , -5 z y + 6 x , 9 x + 4 x z, 2 2 3 2 x y - 17 y, -13 x y + 4 z ] > J:=[op(GB),op(G)]; 2 3 2 2 3 J := [x , y, 9 x + 4 x z, 2 x y - 17 y, -13 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, 13, 18, 3, 3, 1, 3, 1, 2/3, 1/2, 2/3, 1/2, 1/4, 5, 9, 12, 3, 3, 1, 3, 4/5, 3/5, 2/5, 5/9, 4/9, 2/9, 4, 6, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=135.0MB, alloc=84.3MB, time=2.43 |\^/| 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(); 1428315628 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 F := [-11 y z + 5, -17 y z - 11 z, -7 x + 7 x y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 3 2 G := [-4 y z - 9 z , 17 x + 17 y , -15 x - 4 z ] > Problem := [F,G]; 2 3 Problem := [[-11 y z + 5, -17 y z - 11 z, -7 x + 7 x y z], 2 2 3 3 3 2 [-4 y z - 9 z , 17 x + 17 y , -15 x - 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=48.0MB, alloc=32.3MB, time=0.80 memory used=68.6MB, alloc=32.3MB, time=1.10 memory used=87.8MB, alloc=56.3MB, time=1.39 memory used=126.9MB, alloc=60.3MB, time=1.93 memory used=162.9MB, alloc=84.3MB, time=2.46 memory used=216.6MB, alloc=84.3MB, time=3.25 memory used=272.0MB, alloc=116.3MB, time=4.11 memory used=351.0MB, alloc=116.3MB, time=5.25 memory used=426.6MB, alloc=140.3MB, time=6.44 memory used=525.4MB, alloc=420.3MB, time=8.06 memory used=640.3MB, alloc=444.3MB, time=10.10 memory used=766.3MB, alloc=468.3MB, time=12.41 memory used=909.4MB, alloc=492.3MB, time=14.88 memory used=1055.6MB, alloc=516.3MB, time=17.88 memory used=1200.4MB, alloc=540.3MB, time=22.13 memory used=1352.1MB, alloc=564.3MB, time=27.19 memory used=1513.7MB, alloc=588.3MB, time=33.28 memory used=1694.7MB, alloc=612.3MB, time=40.30 memory used=1899.7MB, alloc=636.3MB, time=48.47 memory used=2128.6MB, alloc=660.3MB, time=57.52 memory used=2381.5MB, alloc=660.3MB, time=67.31 memory used=2634.4MB, alloc=660.3MB, time=77.09 memory used=2887.2MB, alloc=684.3MB, time=87.09 memory used=3163.9MB, alloc=684.3MB, time=97.98 memory used=3440.8MB, alloc=708.3MB, time=108.80 memory used=3741.8MB, alloc=732.3MB, time=120.63 N1 := 9375 > GB := Basis(F, plex(op(vars))); 5 3 2 GB := [17 x + 5 x, 17 y + 11, 17 x + 11 x z, 121 z + 85] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3967.5MB, alloc=732.3MB, time=125.10 N2 := 1759 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 H := [-11 y z + 5, -17 y z - 11 z, -7 x + 7 x y z, -4 y z - 9 z , 3 3 3 2 17 x + 17 y , -15 x - 4 z ] > J:=[op(GB),op(G)]; 5 3 2 2 2 J := [17 x + 5 x, 17 y + 11, 17 x + 11 x z, 121 z + 85, -4 y z - 9 z , 3 3 3 2 17 x + 17 y , -15 x - 4 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 17, 3, 3, 3, 2, 1/2, 5/6, 5/6, 1/3, 5/12, 7/12, 7, 11, 20, 5, 5, 3, 2, 4/7, 3/7, 4/7, 3/7, 3/14, 5/14, 2, -3, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=4123.9MB, alloc=732.3MB, time=129.98 |\^/| 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(); 1428315764 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-5 x y + 4 x z, x y - 3 y z, -14 x y - x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-15 x z - 18 z , -y z + 4 y , -2 x y - 10 x] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-5 x y + 4 x z, x y - 3 y z, -14 x y - x z], 2 2 2 2 2 [-15 x z - 18 z , -y z + 4 y , -2 x y - 10 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.47 memory used=47.2MB, alloc=32.3MB, time=0.75 memory used=67.0MB, alloc=32.3MB, time=1.06 memory used=85.9MB, alloc=56.3MB, time=1.35 memory used=124.9MB, alloc=60.3MB, time=1.91 memory used=161.0MB, alloc=84.3MB, time=2.45 memory used=217.0MB, alloc=84.3MB, time=3.28 memory used=272.5MB, alloc=108.3MB, time=4.20 memory used=348.6MB, alloc=140.3MB, time=5.51 memory used=437.9MB, alloc=164.3MB, time=7.07 memory used=540.8MB, alloc=188.3MB, time=8.82 memory used=656.0MB, alloc=212.3MB, time=10.87 memory used=771.1MB, alloc=492.3MB, time=13.02 memory used=901.2MB, alloc=516.3MB, time=16.58 memory used=1036.9MB, alloc=540.3MB, time=20.89 memory used=1184.6MB, alloc=564.3MB, time=25.80 memory used=1344.6MB, alloc=588.3MB, time=31.60 memory used=1520.0MB, alloc=612.3MB, time=38.50 memory used=1719.5MB, alloc=636.3MB, time=46.31 memory used=1942.9MB, alloc=660.3MB, time=55.10 memory used=2190.2MB, alloc=660.3MB, time=64.89 memory used=2437.5MB, alloc=660.3MB, time=74.69 memory used=2684.7MB, alloc=684.3MB, time=84.43 memory used=2955.9MB, alloc=684.3MB, time=95.18 memory used=3227.1MB, alloc=684.3MB, time=105.91 memory used=3498.2MB, alloc=708.3MB, time=116.58 memory used=3793.3MB, alloc=708.3MB, time=128.01 memory used=4088.3MB, alloc=732.3MB, time=139.49 memory used=4407.3MB, alloc=732.3MB, time=151.89 memory used=4726.3MB, alloc=756.3MB, time=164.43 N1 := 11457 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 2 2 2 GB := [56 x y + 5 x y, 2352 x y - 5 x y, 14 x y + x z, -x y + 3 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5063.7MB, alloc=756.3MB, time=171.70 memory used=5449.1MB, alloc=780.3MB, time=183.33 memory used=5797.2MB, alloc=804.3MB, time=197.98 memory used=6169.5MB, alloc=828.3MB, time=213.56 N2 := 5981 #save(Problem, "format.txt"); > if (GB=[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 := [-5 x y + 4 x z, x y - 3 y z, -14 x y - x z, -15 x z - 18 z , 2 2 2 -y z + 4 y , -2 x y - 10 x] > J:=[op(GB),op(G)]; 3 2 2 3 2 2 2 2 J := [56 x y + 5 x y, 2352 x y - 5 x y, 14 x y + x z, -x y + 3 y z, 2 2 2 2 2 -15 x z - 18 z , -y z + 4 y , -2 x y - 10 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 18, 3, 2, 2, 2, 5/6, 5/6, 5/6, 2/3, 7/12, 1/2, 7, 16, 24, 5, 3, 3, 2, 6/7, 6/7, 4/7, 5/7, 5/7, 5/14, -1, -6, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=6350.9MB, alloc=828.3MB, time=220.73 |\^/| 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(); 1428315994 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 F := [-15 x - 2 x y z, -15 + 7 z, 12 z - 15 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [14 x y + 8 z , 20 y - 19 x, -13 - 7 z] > Problem := [F,G]; 3 3 Problem := [[-15 x - 2 x y z, -15 + 7 z, 12 z - 15 y z], 2 2 2 [14 x y + 8 z , 20 y - 19 x, -13 - 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=26.6MB, alloc=32.3MB, time=0.50 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=67.4MB, alloc=56.3MB, time=1.10 memory used=107.0MB, alloc=60.3MB, time=1.69 memory used=143.8MB, alloc=60.3MB, time=2.23 memory used=180.0MB, alloc=84.3MB, time=2.77 memory used=236.2MB, alloc=84.3MB, time=3.61 memory used=291.4MB, alloc=108.3MB, time=4.44 memory used=368.7MB, alloc=116.3MB, time=5.57 memory used=443.1MB, alloc=140.3MB, time=6.74 memory used=532.0MB, alloc=396.3MB, time=8.17 memory used=623.9MB, alloc=420.3MB, time=9.62 memory used=738.1MB, alloc=444.3MB, time=11.54 memory used=867.0MB, alloc=468.3MB, time=13.88 memory used=1005.3MB, alloc=492.3MB, time=16.37 memory used=1152.9MB, alloc=516.3MB, time=19.04 memory used=1307.2MB, alloc=540.3MB, time=21.91 memory used=1464.9MB, alloc=564.3MB, time=25.05 memory used=1614.5MB, alloc=588.3MB, time=29.40 memory used=1768.9MB, alloc=612.3MB, time=34.45 memory used=1933.8MB, alloc=636.3MB, time=40.08 memory used=2110.9MB, alloc=660.3MB, time=46.65 memory used=2302.6MB, alloc=684.3MB, time=54.93 memory used=2506.8MB, alloc=708.3MB, time=64.85 memory used=2731.0MB, alloc=732.3MB, time=74.86 memory used=2979.2MB, alloc=756.3MB, time=85.92 memory used=3251.4MB, alloc=780.3MB, time=98.00 memory used=3547.4MB, alloc=804.3MB, time=111.24 memory used=3867.5MB, alloc=828.3MB, time=125.30 memory used=4211.4MB, alloc=852.3MB, time=140.85 memory used=4579.3MB, alloc=852.3MB, time=157.37 memory used=4947.1MB, alloc=852.3MB, time=173.71 memory used=5315.0MB, alloc=876.3MB, time=189.85 memory used=5706.7MB, alloc=876.3MB, time=206.80 memory used=6098.3MB, alloc=876.3MB, time=223.75 memory used=6489.8MB, alloc=876.3MB, time=239.91 memory used=6881.1MB, alloc=900.3MB, time=257.27 |\^/| 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(); 1428316294 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 3 F := [11 y - 18 x , -4 x y - 18, 13 x - 6 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [11 y z - 6 x y, -15 x - 6 x z, 16 y z + 20 z ] > Problem := [F,G]; 3 2 2 3 3 Problem := [[11 y - 18 x , -4 x y - 18, 13 x - 6 z ], 2 3 2 2 [11 y z - 6 x y, -15 x - 6 x z, 16 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.52 memory used=47.4MB, alloc=32.3MB, time=0.83 memory used=68.6MB, alloc=32.3MB, time=1.18 memory used=89.7MB, alloc=56.3MB, time=1.63 memory used=131.9MB, alloc=56.3MB, time=2.57 N1 := 861 > GB := Basis(F, plex(op(vars))); 7 3 3 3 GB := [32 x + 1089, 4 x + 11 y, -13 x + 6 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=166.4MB, alloc=56.3MB, time=3.32 memory used=204.0MB, alloc=84.3MB, time=3.96 N2 := 735 #save(Problem, "format.txt"); > 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 H := [11 y - 18 x , -4 x y - 18, -6 z + 13 x , 11 y z - 6 x y, 3 2 2 -15 x - 6 x z, 16 y z + 20 z ] > J:=[op(GB),op(G)]; 7 3 3 3 2 3 J := [32 x + 1089, 4 x + 11 y, -13 x + 6 z , 11 y z - 6 x y, -15 x - 6 x z, 2 2 16 y z + 20 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 18, 3, 3, 3, 3, 5/6, 2/3, 2/3, 1/2, 5/12, 5/12, 6, 12, 22, 7, 7, 1, 3, 5/6, 1/2, 2/3, 1/2, 1/3, 5/12, 1, -4, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=251.7MB, alloc=84.3MB, time=5.07 |\^/| 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(); 1428316301 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 2 F := [9 x + 6 y , 7 x y - 20 y , -14 y - 20 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 G := [-14 y - 17 x , 2 x z + 8 y z, -7 y - 3] > Problem := [F,G]; 3 2 2 3 2 Problem := [[9 x + 6 y , 7 x y - 20 y , -14 y - 20 y z], 3 2 2 2 3 [-14 y - 17 x , 2 x z + 8 y z, -7 y - 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.51 memory used=45.6MB, alloc=32.3MB, time=0.77 memory used=65.1MB, alloc=32.3MB, time=1.06 memory used=85.0MB, alloc=56.3MB, time=1.44 memory used=124.8MB, alloc=60.3MB, time=2.13 memory used=159.5MB, alloc=84.3MB, time=3.05 memory used=211.2MB, alloc=108.3MB, time=4.94 N1 := 1349 > GB := Basis(F, plex(op(vars))); 6 5 3 2 3 2 3 2 GB := [30 x + 7 x , 30 x y + 7 x y, 3 x + 2 y , 300 x z - 49 x y, 3 -21 x + 20 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=282.4MB, alloc=116.3MB, time=6.06 memory used=363.2MB, alloc=116.3MB, time=7.47 memory used=438.2MB, alloc=140.3MB, time=9.12 memory used=521.6MB, alloc=164.3MB, time=12.45 N2 := 1757 #save(Problem, "format.txt"); > 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 2 H := [9 x + 6 y , 7 x y - 20 y , -14 y - 20 y z, -14 y - 17 x , 2 2 3 2 x z + 8 y z, -7 y - 3] > J:=[op(GB),op(G)]; 6 5 3 2 3 2 3 2 J := [30 x + 7 x , 30 x y + 7 x y, 3 x + 2 y , 300 x z - 49 x y, 3 3 2 2 2 3 -21 x + 20 y z, -14 y - 17 x , 2 x z + 8 y z, -7 y - 3] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 17, 3, 3, 3, 1, 2/3, 1, 1/3, 1/3, 2/3, 1/4, 8, 17, 29, 6, 6, 3, 1, 7/8, 7/8, 3/8, 5/8, 1/2, 1/4, -5, -12, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=536.8MB, alloc=164.3MB, time=13.11 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428316317 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [-5 x y - 14 x , -16 z , 3 x - 9 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [9 x z + 5 y , 3 y z - 14 y, 17 x z - 7 y z ] > Problem := [F,G]; 2 2 3 Problem := [[-5 x y - 14 x , -16 z , 3 x - 9 z], 2 2 2 2 [9 x z + 5 y , 3 y z - 14 y, 17 x z - 7 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.52 memory used=48.1MB, alloc=32.3MB, time=0.92 memory used=68.9MB, alloc=56.3MB, time=1.35 memory used=111.1MB, alloc=60.3MB, time=2.19 memory used=147.4MB, alloc=84.3MB, time=2.93 memory used=200.5MB, alloc=108.3MB, time=4.55 memory used=271.1MB, alloc=108.3MB, time=7.18 N1 := 1951 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [x , 5 x y + 14 x , 3 z - x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=341.4MB, alloc=116.3MB, time=8.52 memory used=419.2MB, alloc=140.3MB, time=9.91 memory used=508.9MB, alloc=164.3MB, time=12.95 N2 := 1951 #save(Problem, "format.txt"); > if (GB=[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 := [-5 x y - 14 x , -16 z , 3 x - 9 z, 9 z x + 5 y , 3 y z - 14 y, 2 2 17 x z - 7 y z ] > J:=[op(GB),op(G)]; J := [ 3 2 2 2 2 2 2 x , 5 x y + 14 x , 3 z - x, 9 z x + 5 y , 3 y z - 14 y, 17 x z - 7 y z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 15, 3, 2, 2, 3, 2/3, 2/3, 5/6, 5/12, 5/12, 1/2, 6, 13, 15, 3, 3, 2, 2, 5/6, 2/3, 2/3, 1/2, 5/12, 5/12, 0, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=556.6MB, alloc=164.3MB, time=14.70 |\^/| 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(); 1428316334 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [-2 x y - 6 x , 12 y + 2 y , 17 x z - 8 x y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 G := [10 y + 7 y, -5 x y + 20 y , -12 x + 2 x y] > Problem := [F,G]; 2 2 3 2 2 Problem := [[-2 x y - 6 x , 12 y + 2 y , 17 x z - 8 x y z], 3 2 3 3 [10 y + 7 y, -5 x y + 20 y , -12 x + 2 x y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.49 memory used=45.1MB, alloc=32.3MB, time=0.77 memory used=63.4MB, alloc=56.3MB, time=1.11 memory used=103.7MB, alloc=60.3MB, time=1.80 memory used=138.7MB, alloc=84.3MB, time=2.63 N1 := 1065 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 2 3 2 2 GB := [108 x + x , 6 x y + x , x y + 3 x , 6 y + y , x z, x z y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=192.2MB, alloc=84.3MB, time=4.08 memory used=247.5MB, alloc=84.3MB, time=4.96 N2 := 693 #save(Problem, "format.txt"); > if (GB=[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 := [-2 x y - 6 x , 12 y + 2 y , 17 x z - 8 x y z, 10 y + 7 y, 2 3 3 -5 x y + 20 y , -12 x + 2 x y] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 3 2 2 J := [108 x + x , 6 x y + x , x y + 3 x , 6 y + y , x z, x z y, 3 2 3 3 10 y + 7 y, -5 x y + 20 y , -12 x + 2 x y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 11, 18, 3, 3, 3, 1, 2/3, 1, 1/6, 7/12, 3/4, 1/6, 9, 16, 27, 3, 3, 3, 1, 7/9, 7/9, 2/9, 11/19, 10/19, 2/19, -5, -9, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=283.5MB, alloc=84.3MB, time=5.88 |\^/| 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(); 1428316341 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [-8 y - 2 z , 6 x - 8 x z , 4 x + 13 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 G := [4 x z + y , -17 x + 18 x, -20 y + 14 y z] > Problem := [F,G]; 2 2 3 2 2 Problem := [[-8 y - 2 z , 6 x - 8 x z , 4 x + 13 z], 2 2 3 3 [4 x z + y , -17 x + 18 x, -20 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=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=48.0MB, alloc=32.3MB, time=0.89 memory used=68.2MB, alloc=32.3MB, time=1.25 memory used=87.7MB, alloc=56.3MB, time=1.61 memory used=127.3MB, alloc=60.3MB, time=2.24 memory used=164.4MB, alloc=84.3MB, time=2.84 memory used=217.4MB, alloc=84.3MB, time=3.75 memory used=278.0MB, alloc=108.3MB, time=4.93 memory used=354.8MB, alloc=116.3MB, time=6.34 memory used=425.5MB, alloc=140.3MB, time=7.78 memory used=518.2MB, alloc=164.3MB, time=9.41 memory used=624.9MB, alloc=188.3MB, time=11.50 memory used=744.8MB, alloc=212.3MB, time=13.95 memory used=868.4MB, alloc=236.3MB, time=17.72 memory used=1001.1MB, alloc=260.3MB, time=21.96 memory used=1144.5MB, alloc=284.3MB, time=27.60 memory used=1308.5MB, alloc=308.3MB, time=34.19 memory used=1496.5MB, alloc=308.3MB, time=41.77 memory used=1684.4MB, alloc=308.3MB, time=49.41 memory used=1872.4MB, alloc=332.3MB, time=56.74 memory used=2084.2MB, alloc=332.3MB, time=65.15 memory used=2296.0MB, alloc=332.3MB, time=73.76 memory used=2507.5MB, alloc=356.3MB, time=82.26 N1 := 7867 > GB := Basis(F, plex(op(vars))); 5 3 4 2 2 GB := [64 x - 507 x , 4 x + 169 y , 4 x + 13 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2750.7MB, alloc=356.3MB, time=90.96 N2 := 615 #save(Problem, "format.txt"); > if (GB=[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 3 H := [-8 y - 2 z , 6 x - 8 x z , 4 x + 13 z, 4 z x + y , -17 x + 18 x, 3 -20 y + 14 y z] > J:=[op(GB),op(G)]; 5 3 4 2 2 2 2 3 J := [64 x - 507 x , 4 x + 169 y , 4 x + 13 z, 4 z x + y , -17 x + 18 x, 3 -20 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, 12, 16, 3, 3, 3, 2, 2/3, 1/2, 5/6, 1/2, 1/3, 5/12, 6, 11, 20, 5, 5, 3, 1, 5/6, 1/2, 1/2, 7/12, 1/3, 1/4, 1, -4, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2772.2MB, alloc=356.3MB, time=91.57 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428316451 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-x y + z, -7 x z + 13 x, -7 x y + y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [18 x z + 14 x z, 5 y z + 6 z , 14 x y + 16 z ] > Problem := [F,G]; 2 2 2 Problem := [[-x y + z, -7 x z + 13 x, -7 x y + y z], 2 2 3 2 [18 x z + 14 x z, 5 y z + 6 z , 14 x y + 16 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.50 memory used=46.9MB, alloc=32.3MB, time=0.79 memory used=66.3MB, alloc=32.3MB, time=1.07 memory used=85.0MB, alloc=56.3MB, time=1.37 memory used=123.2MB, alloc=60.3MB, time=1.95 memory used=158.6MB, alloc=84.3MB, time=2.49 memory used=214.0MB, alloc=84.3MB, time=3.28 memory used=267.7MB, alloc=108.3MB, time=4.12 memory used=341.6MB, alloc=140.3MB, time=5.29 memory used=434.3MB, alloc=140.3MB, time=6.74 memory used=522.3MB, alloc=164.3MB, time=8.08 memory used=614.9MB, alloc=188.3MB, time=9.77 memory used=727.8MB, alloc=468.3MB, time=11.88 memory used=860.6MB, alloc=492.3MB, time=14.25 memory used=1002.8MB, alloc=516.3MB, time=16.84 memory used=1152.7MB, alloc=540.3MB, time=19.64 memory used=1311.1MB, alloc=564.3MB, time=22.64 memory used=1477.8MB, alloc=588.3MB, time=25.77 memory used=1648.1MB, alloc=612.3MB, time=29.07 memory used=1823.6MB, alloc=636.3MB, time=32.48 memory used=2003.9MB, alloc=660.3MB, time=36.03 memory used=2175.1MB, alloc=684.3MB, time=40.98 memory used=2344.4MB, alloc=708.3MB, time=46.80 memory used=2522.1MB, alloc=732.3MB, time=53.12 memory used=2711.2MB, alloc=756.3MB, time=60.20 memory used=2913.2MB, alloc=780.3MB, time=67.83 memory used=3128.1MB, alloc=804.3MB, time=76.05 memory used=3356.6MB, alloc=828.3MB, time=85.06 memory used=3599.6MB, alloc=852.3MB, time=94.73 memory used=3857.3MB, alloc=876.3MB, time=105.10 memory used=4130.1MB, alloc=900.3MB, time=116.25 memory used=4418.0MB, alloc=924.3MB, time=128.38 memory used=4719.6MB, alloc=948.3MB, time=140.94 memory used=5034.8MB, alloc=972.3MB, time=154.77 memory used=5374.0MB, alloc=996.3MB, time=169.49 memory used=5737.1MB, alloc=1020.3MB, time=185.43 memory used=6124.2MB, alloc=1044.3MB, time=202.49 memory used=6535.2MB, alloc=1068.3MB, time=220.24 memory used=6970.2MB, alloc=1092.3MB, time=239.46 memory used=7429.0MB, alloc=1116.3MB, time=259.46 memory used=7911.9MB, alloc=1140.3MB, time=280.42 |\^/| 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(); 1428316751 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 3 F := [13 x z + 20 y , 10 x z + 6 x y, -18 x - 9 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [20 x y + 3 x, 9 x z - 16 z , 15 x z - 9 x] > Problem := [F,G]; 2 3 2 3 3 Problem := [[13 x z + 20 y , 10 x z + 6 x y, -18 x - 9 y ], 2 2 3 [20 x y + 3 x, 9 x z - 16 z , 15 x 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=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=48.0MB, alloc=32.3MB, time=0.80 memory used=68.4MB, alloc=32.3MB, time=1.10 memory used=88.2MB, alloc=56.3MB, time=1.40 memory used=128.3MB, alloc=60.3MB, time=1.99 memory used=166.3MB, alloc=60.3MB, time=2.55 memory used=201.8MB, alloc=84.3MB, time=3.09 memory used=261.0MB, alloc=116.3MB, time=4.17 memory used=336.2MB, alloc=140.3MB, time=5.50 memory used=428.7MB, alloc=164.3MB, time=7.16 memory used=534.2MB, alloc=188.3MB, time=9.07 memory used=647.9MB, alloc=212.3MB, time=11.65 memory used=763.0MB, alloc=236.3MB, time=15.06 memory used=889.0MB, alloc=260.3MB, time=19.21 memory used=1027.4MB, alloc=284.3MB, time=24.59 memory used=1189.8MB, alloc=308.3MB, time=30.94 memory used=1376.0MB, alloc=308.3MB, time=38.18 memory used=1562.3MB, alloc=332.3MB, time=45.43 memory used=1772.5MB, alloc=332.3MB, time=53.54 memory used=1982.8MB, alloc=332.3MB, time=61.65 memory used=2193.0MB, alloc=356.3MB, time=69.67 memory used=2427.1MB, alloc=380.3MB, time=78.58 N1 := 7917 > GB := Basis(F, plex(op(vars))); 8 5 4 2 3 3 GB := [256000000000 x - 130323843 x , 8000 x + 507 x y, y + 2 x , 3 2 2 -40 x + 13 x z, 5 x z + 3 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2593.7MB, alloc=380.3MB, time=83.54 memory used=2899.8MB, alloc=660.3MB, time=90.25 memory used=3177.2MB, alloc=684.3MB, time=101.23 N2 := 3609 #save(Problem, "format.txt"); > if (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 2 H := [13 z x + 20 y , 10 x z + 6 x y, -18 x - 9 y , 20 x y + 3 x, 2 3 9 x z - 16 z , 15 x z - 9 x] > J:=[op(GB),op(G)]; 8 5 4 2 3 3 J := [256000000000 x - 130323843 x , 8000 x + 507 x y, y + 2 x , 3 2 2 2 2 3 -40 x + 13 x z, 5 x z + 3 x y, 20 x y + 3 x, 9 x z - 16 z , 15 x 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, 17, 3, 3, 3, 3, 1, 2/3, 2/3, 3/4, 1/3, 5/12, 8, 16, 29, 8, 8, 3, 3, 1, 1/2, 1/2, 7/8, 1/4, 5/16, -2, -12, -5] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=3228.7MB, alloc=684.3MB, time=102.82 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428316861 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-10 x z + 4 y z, 10 z - 7 x, -z - 13 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [15 x y - 7 x , 19 x y - 3 y z, 9 x y + 6 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-10 x z + 4 y z, 10 z - 7 x, -z - 13 y], 2 2 2 2 [15 x y - 7 x , 19 x y - 3 y z, 9 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=0.17 memory used=26.2MB, alloc=32.3MB, time=0.46 memory used=47.9MB, alloc=32.3MB, time=0.76 memory used=68.5MB, alloc=32.3MB, time=1.05 memory used=88.0MB, alloc=56.3MB, time=1.34 memory used=128.1MB, alloc=60.3MB, time=1.99 memory used=168.3MB, alloc=84.3MB, time=2.67 memory used=228.9MB, alloc=84.3MB, time=3.74 memory used=284.3MB, alloc=108.3MB, time=4.65 memory used=358.5MB, alloc=132.3MB, time=5.92 memory used=451.1MB, alloc=164.3MB, time=7.55 memory used=548.4MB, alloc=188.3MB, time=9.73 memory used=652.1MB, alloc=212.3MB, time=12.69 memory used=765.7MB, alloc=236.3MB, time=16.93 memory used=898.2MB, alloc=260.3MB, time=21.94 memory used=1054.6MB, alloc=260.3MB, time=27.80 memory used=1211.0MB, alloc=260.3MB, time=33.53 memory used=1367.4MB, alloc=284.3MB, time=39.99 memory used=1547.7MB, alloc=284.3MB, time=47.10 memory used=1728.1MB, alloc=308.3MB, time=53.88 memory used=1932.5MB, alloc=308.3MB, time=61.48 N1 := 7065 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [x , 130 y + 7 x, z x , 10 z - 7 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2119.8MB, alloc=308.3MB, time=66.40 N2 := 1899 #save(Problem, "format.txt"); > if (GB=[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 := [-10 x z + 4 y z, 10 z - 7 x, -z - 13 y, 15 x y - 7 x , 2 2 19 x y - 3 y z, 9 x y + 6 z ] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [x , 130 y + 7 x, z x , 10 z - 7 x, 15 x y - 7 x , 19 x y - 3 y z, 2 2 9 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, 15, 15, 3, 2, 2, 2, 5/6, 5/6, 5/6, 1/2, 1/2, 1/2, 7, 15, 17, 3, 3, 2, 2, 1, 4/7, 4/7, 4/7, 5/14, 2/7, 0, -2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2299.5MB, alloc=564.3MB, time=71.84 |\^/| 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(); 1428316938 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 2 F := [4 x z + 12 x z , 19 x + 7 y z , -10 y z - 13 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-19 y z + 20 x, -16 z + 18, -19 x + y] > Problem := [F,G]; 2 2 3 2 2 2 Problem := [[4 x z + 12 x z , 19 x + 7 y z , -10 y z - 13 x ], 2 2 [-19 y z + 20 x, -16 z + 18, -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=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=48.2MB, alloc=32.3MB, time=0.80 memory used=68.3MB, alloc=56.3MB, time=1.10 memory used=109.3MB, alloc=60.3MB, time=1.70 memory used=148.7MB, alloc=60.3MB, time=2.25 memory used=186.5MB, alloc=84.3MB, time=2.77 memory used=235.7MB, alloc=84.3MB, time=3.51 memory used=291.8MB, alloc=116.3MB, time=4.29 memory used=370.4MB, alloc=116.3MB, time=5.43 memory used=445.1MB, alloc=140.3MB, time=6.76 memory used=535.9MB, alloc=164.3MB, time=8.38 memory used=652.0MB, alloc=188.3MB, time=10.31 memory used=778.6MB, alloc=468.3MB, time=12.56 memory used=916.9MB, alloc=492.3MB, time=15.06 memory used=1058.6MB, alloc=516.3MB, time=18.64 memory used=1198.4MB, alloc=540.3MB, time=22.94 memory used=1346.3MB, alloc=564.3MB, time=28.11 memory used=1507.2MB, alloc=588.3MB, time=34.58 memory used=1692.1MB, alloc=612.3MB, time=42.33 memory used=1900.8MB, alloc=636.3MB, time=51.67 memory used=2133.6MB, alloc=636.3MB, time=61.10 memory used=2366.3MB, alloc=660.3MB, time=70.60 memory used=2622.9MB, alloc=660.3MB, time=80.79 memory used=2879.4MB, alloc=660.3MB, time=91.04 memory used=3135.8MB, alloc=684.3MB, time=101.20 memory used=3416.2MB, alloc=684.3MB, time=112.66 memory used=3696.6MB, alloc=708.3MB, time=124.40 N1 := 9595 > GB := Basis(F, plex(op(vars))); 5 4 4 4 3 2 4 GB := [97470 x - 637 x , 570 x y + 91 x , 10 x y - 39 x , 3 2 2 2 3 2 2 3 -190 x y + 91 x z, 10 z y + 13 x , 190 x y + 273 x z , 7 z y + 19 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4001.8MB, alloc=708.3MB, time=131.63 memory used=4357.4MB, alloc=732.3MB, time=137.92 memory used=4663.5MB, alloc=756.3MB, time=143.31 memory used=4962.7MB, alloc=780.3MB, time=148.89 memory used=5194.3MB, alloc=804.3MB, time=153.05 memory used=5467.6MB, alloc=828.3MB, time=158.37 memory used=5727.0MB, alloc=852.3MB, time=163.49 memory used=5979.5MB, alloc=852.3MB, time=168.45 memory used=6190.9MB, alloc=852.3MB, time=172.75 memory used=6426.7MB, alloc=876.3MB, time=177.44 memory used=6651.0MB, alloc=900.3MB, time=182.64 memory used=6919.9MB, alloc=924.3MB, time=189.03 memory used=7395.8MB, alloc=948.3MB, time=200.22 memory used=7862.4MB, alloc=972.3MB, time=210.53 memory used=8366.0MB, alloc=996.3MB, time=220.03 memory used=8826.5MB, alloc=1020.3MB, time=230.31 memory used=9263.7MB, alloc=1044.3MB, time=240.48 memory used=9683.1MB, alloc=1068.3MB, time=253.28 |\^/| 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(); 1428317238 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 F := [7 y - 9 x , 7 z + 8 y , 3 y z - 17 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 3 2 G := [-13 y - 4 z , 5 y z - 20 z, 14 z - 18 x ] > Problem := [F,G]; 3 2 3 2 2 Problem := [[7 y - 9 x , 7 z + 8 y , 3 y z - 17 x z], 3 3 2 3 2 [-13 y - 4 z , 5 y z - 20 z, 14 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=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=48.2MB, alloc=32.3MB, time=0.84 memory used=69.0MB, alloc=32.3MB, time=1.17 memory used=89.1MB, alloc=60.3MB, time=1.48 memory used=129.8MB, alloc=60.3MB, time=2.10 memory used=169.7MB, alloc=92.3MB, time=2.76 memory used=226.9MB, alloc=92.3MB, time=3.72 memory used=287.2MB, alloc=116.3MB, time=4.69 memory used=366.4MB, alloc=372.3MB, time=5.86 memory used=454.5MB, alloc=396.3MB, time=7.15 memory used=566.2MB, alloc=420.3MB, time=8.77 memory used=687.3MB, alloc=444.3MB, time=10.74 memory used=830.7MB, alloc=468.3MB, time=13.06 memory used=955.5MB, alloc=492.3MB, time=14.92 memory used=1085.5MB, alloc=492.3MB, time=17.10 memory used=1264.9MB, alloc=516.3MB, time=20.46 memory used=1444.4MB, alloc=540.3MB, time=24.13 memory used=1630.3MB, alloc=564.3MB, time=27.94 memory used=1816.5MB, alloc=588.3MB, time=32.05 memory used=1995.5MB, alloc=612.3MB, time=38.06 memory used=2178.7MB, alloc=636.3MB, time=44.82 memory used=2363.0MB, alloc=660.3MB, time=52.83 memory used=2570.9MB, alloc=684.3MB, time=61.89 memory used=2802.7MB, alloc=708.3MB, time=71.99 memory used=3058.5MB, alloc=732.3MB, time=83.06 memory used=3338.2MB, alloc=756.3MB, time=95.03 memory used=3641.9MB, alloc=780.3MB, time=108.05 memory used=3969.5MB, alloc=804.3MB, time=122.07 memory used=4321.1MB, alloc=804.3MB, time=137.40 memory used=4672.7MB, alloc=828.3MB, time=152.68 memory used=5048.5MB, alloc=852.3MB, time=169.21 N1 := 10383 > GB := Basis(F, plex(op(vars))); 4 3 3 3 GB := [595077871104 x + 683635509017782097 x , 34012224 x y - 405680122183 x , 2 2 3 2 2 2 17496 x y + 1685159 x y , 7 y - 9 x , 648 x y + 14161 x z, 2 2 2 3 2 833 x z + 216 x , 3 y z - 17 x z, 7 z + 8 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5182.0MB, alloc=852.3MB, time=172.59 memory used=5300.2MB, alloc=852.3MB, time=175.00 memory used=5405.4MB, alloc=852.3MB, time=177.24 memory used=5521.2MB, alloc=852.3MB, time=179.73 memory used=5624.4MB, alloc=852.3MB, time=181.98 memory used=5715.6MB, alloc=852.3MB, time=184.03 memory used=5806.3MB, alloc=852.3MB, time=186.10 memory used=5872.8MB, alloc=852.3MB, time=187.73 memory used=5952.5MB, alloc=852.3MB, time=189.61 memory used=6032.8MB, alloc=852.3MB, time=191.75 memory used=6110.2MB, alloc=852.3MB, time=193.68 memory used=6188.1MB, alloc=852.3MB, time=195.72 memory used=6260.1MB, alloc=852.3MB, time=197.71 memory used=6321.8MB, alloc=852.3MB, time=199.52 memory used=6578.5MB, alloc=852.3MB, time=204.45 memory used=6805.6MB, alloc=852.3MB, time=208.67 memory used=7002.8MB, alloc=876.3MB, time=212.40 memory used=7210.4MB, alloc=900.3MB, time=216.42 memory used=7382.8MB, alloc=924.3MB, time=219.87 memory used=7567.2MB, alloc=924.3MB, time=223.67 memory used=8094.1MB, alloc=948.3MB, time=233.37 memory used=8615.9MB, alloc=972.3MB, time=242.22 memory used=9109.9MB, alloc=996.3MB, time=251.63 memory used=9567.2MB, alloc=1020.3MB, time=260.29 memory used=10010.0MB, alloc=1044.3MB, time=268.81 |\^/| 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(); 1428317538 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 F := [-17 y + 11 z, 15 y z + 11 z, -18 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 G := [19 - 9 y, -9 x y + 7 x y, 6 x z + 4 y] > Problem := [F,G]; 2 3 Problem := [[-17 y + 11 z, 15 y z + 11 z, -18 z ], 2 [19 - 9 y, -9 x y + 7 x y, 6 x z + 4 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.67 memory used=48.6MB, alloc=56.3MB, time=1.12 N1 := 461 > GB := Basis(F, plex(op(vars))); 2 GB := [y , z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 107 #save(Problem, "format.txt"); > if (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 H := [-17 y + 11 z, 15 y z + 11 z, -18 z , 19 - 9 y, -9 x y + 7 x y, 6 x z + 4 y] > J:=[op(GB),op(G)]; 2 2 J := [y , z, 19 - 9 y, -9 x y + 7 x y, 6 x z + 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, 11, 13, 3, 2, 2, 3, 1/3, 5/6, 2/3, 1/4, 1/2, 5/12, 5, 8, 9, 3, 2, 2, 1, 2/5, 4/5, 2/5, 1/3, 5/9, 2/9, 3, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=73.7MB, alloc=56.3MB, time=1.62 |\^/| 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(); 1428317541 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 3 F := [8 x y - 5 x y z, -6 x + 5 x, 20 x + 10 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-17 z + 2 y, -4 x y z, -11 x z + 15 x y z] > Problem := [F,G]; 2 3 3 3 Problem := [[8 x y - 5 x y z, -6 x + 5 x, 20 x + 10 y ], 2 2 [-17 z + 2 y, -4 x y z, -11 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.55 memory used=48.9MB, alloc=32.3MB, time=0.95 memory used=67.6MB, alloc=56.3MB, time=1.41 N1 := 607 > GB := Basis(F, plex(op(vars))); 3 3 2 GB := [6 x - 5 x, 3 y + 5 x, -8 x + 5 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=105.4MB, alloc=60.3MB, time=2.09 memory used=146.3MB, alloc=84.3MB, time=3.03 N2 := 607 #save(Problem, "format.txt"); > if (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 H := [8 x y - 5 x y z, -6 x + 5 x, 20 x + 10 y , -17 z + 2 y, -4 x y z, 2 -11 x z + 15 x y z] > J:=[op(GB),op(G)]; 3 3 2 2 J := [6 x - 5 x, 3 y + 5 x, -8 x + 5 x z, -17 z + 2 y, -4 x y z, 2 -11 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, 14, 17, 3, 3, 3, 2, 5/6, 5/6, 2/3, 4/7, 3/7, 5/14, 6, 13, 16, 3, 3, 3, 2, 5/6, 2/3, 2/3, 4/7, 2/7, 5/14, 1, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=146.8MB, alloc=84.3MB, time=3.06 |\^/| 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(); 1428317545 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [20 y - 15 y z, 14 x y z - 20 y , -16 x z - 18] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [17 + 7 z, 15 y z - 3 x z, x - 11 y] > Problem := [F,G]; 3 2 2 2 Problem := [[20 y - 15 y z, 14 x y z - 20 y , -16 x z - 18], 2 3 [17 + 7 z, 15 y z - 3 x z, x - 11 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.52 memory used=47.2MB, alloc=32.3MB, time=0.84 memory used=67.6MB, alloc=32.3MB, time=1.16 memory used=86.6MB, alloc=56.3MB, time=1.51 memory used=127.6MB, alloc=60.3MB, time=2.26 memory used=164.9MB, alloc=84.3MB, time=3.00 memory used=221.4MB, alloc=108.3MB, time=4.14 memory used=295.0MB, alloc=140.3MB, time=5.62 memory used=382.1MB, alloc=164.3MB, time=7.97 memory used=476.7MB, alloc=188.3MB, time=11.61 memory used=592.0MB, alloc=188.3MB, time=16.32 memory used=707.2MB, alloc=212.3MB, time=21.10 N1 := 3887 > GB := Basis(F, plex(op(vars))); 2 2 GB := [14 x y - 15 y, 200 y + 147 y, 8 z x + 9, 50 y z + 49 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=847.4MB, alloc=212.3MB, time=25.85 N2 := 1241 #save(Problem, "format.txt"); > 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 := [20 y - 15 y z, 14 x y z - 20 y , -16 x z - 18, 7 z + 17, 2 3 15 y z - 3 x z, x - 11 y] > J:=[op(GB),op(G)]; 2 2 J := [14 x y - 15 y, 200 y + 147 y, 8 z x + 9, 50 y z + 49 y, 7 z + 17, 2 3 15 y z - 3 x z, x - 11 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 16, 3, 3, 3, 1, 2/3, 2/3, 5/6, 1/3, 1/2, 1/2, 7, 13, 16, 3, 3, 2, 1, 4/7, 5/7, 4/7, 2/7, 4/7, 5/14, 0, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=968.0MB, alloc=212.3MB, time=29.32 |\^/| 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(); 1428317581 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 2 F := [16 y z + 18 y z , -17 x y + 12 x , -7 y z + 17 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 G := [16 y + 19 z, -16 z + 15 y, -13 y z + 17 z] > Problem := [F,G]; 2 2 2 2 2 2 Problem := [[16 y z + 18 y z , -17 x y + 12 x , -7 y z + 17 z ], 3 [16 y + 19 z, -16 z + 15 y, -13 y z + 17 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.46 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=69.3MB, alloc=56.3MB, time=1.20 N1 := 771 > GB := Basis(F, plex(op(vars))); 2 2 3 2 2 2 GB := [17 x y - 12 x , 588 x z - 4913 x z, 7 x y z - 17 x z, 3 2 2 2 7 y z - 17 y z, 56 y z + 153 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=139.5MB, alloc=92.3MB, time=3.04 memory used=210.2MB, alloc=92.3MB, time=4.35 memory used=275.7MB, alloc=116.3MB, time=6.04 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 H := [16 y z + 18 y z , -17 x y + 12 x , -7 y z + 17 z , 19 z + 16 y, 3 -16 z + 15 y, -13 y z + 17 z] > J:=[op(GB),op(G)]; 2 2 3 2 2 2 J := [17 x y - 12 x , 588 x z - 4913 x z, 7 x y z - 17 x z, 3 2 2 2 3 7 y z - 17 y z, 56 y z + 153 z , 19 z + 16 y, -16 z + 15 y, -13 y 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, 15, 3, 2, 2, 3, 1/6, 1, 5/6, 1/6, 7/12, 2/3, 8, 17, 24, 4, 3, 3, 3, 3/8, 7/8, 7/8, 3/8, 1/2, 3/4, -5, -9, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=318.2MB, alloc=116.3MB, time=7.53 |\^/| 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(); 1428317591 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [7 x z - 6 z , -16 x z + 15 x , 16 x y + 13] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [5 x y + 15 x z, -12 x + 20 z , 14 x y + 11 y ] > Problem := [F,G]; 2 3 2 2 2 Problem := [[7 x z - 6 z , -16 x z + 15 x , 16 x y + 13], 2 3 2 2 [5 x y + 15 x z, -12 x + 20 z , 14 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=0.19 memory used=26.2MB, alloc=32.3MB, time=0.54 memory used=47.5MB, alloc=32.3MB, time=0.88 memory used=67.9MB, alloc=32.3MB, time=1.19 memory used=87.6MB, alloc=32.3MB, time=1.51 memory used=106.8MB, alloc=56.3MB, time=1.87 memory used=148.8MB, alloc=60.3MB, time=2.72 memory used=187.4MB, alloc=84.3MB, time=3.44 memory used=246.3MB, alloc=108.3MB, time=4.50 memory used=322.0MB, alloc=132.3MB, time=5.87 memory used=407.4MB, alloc=164.3MB, time=7.81 memory used=499.3MB, alloc=188.3MB, time=10.36 memory used=600.7MB, alloc=212.3MB, time=14.08 memory used=724.4MB, alloc=212.3MB, time=18.82 memory used=848.0MB, alloc=236.3MB, time=23.41 memory used=995.6MB, alloc=236.3MB, time=28.80 memory used=1143.0MB, alloc=236.3MB, time=34.35 memory used=1290.4MB, alloc=260.3MB, time=40.31 N1 := 5791 > GB := Basis(F, plex(op(vars))); 2 GB := [896 x - 675, 675 y + 728, 16 z - 15] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1464.9MB, alloc=260.3MB, time=45.84 N2 := 1767 #save(Problem, "format.txt"); > if (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 := [7 x z - 6 z , -16 x z + 15 x , 16 y x + 13, 5 x y + 15 x z, 3 2 2 -12 x + 20 z , 14 x y + 11 y ] > J:=[op(GB),op(G)]; 2 2 3 2 J := [896 x - 675, 675 y + 728, 16 z - 15, 5 x y + 15 x z, -12 x + 20 z , 2 14 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, 13, 17, 3, 3, 2, 3, 1, 1/2, 2/3, 2/3, 1/3, 5/12, 6, 10, 12, 3, 3, 2, 2, 2/3, 1/2, 1/2, 5/12, 1/3, 1/4, 3, 5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1663.7MB, alloc=260.3MB, time=51.82 |\^/| 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(); 1428317650 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-5 x y - x y z, 6 y z - 20 x, 5 x y z + 12 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [17 x y z + 16 y, -13 y - 13 y, -11 x y - 20 y ] > Problem := [F,G]; 2 2 Problem := [[-5 x y - x y z, 6 y z - 20 x, 5 x y z + 12 y z], 3 2 2 [17 x y z + 16 y, -13 y - 13 y, -11 x y - 20 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.82 memory used=68.2MB, alloc=32.3MB, time=1.15 memory used=88.1MB, alloc=56.3MB, time=1.53 memory used=128.6MB, alloc=84.3MB, time=2.30 N1 := 853 > GB := Basis(F, plex(op(vars))); 2 3 2 GB := [5 x + 12 x, 5 x y - 8 x, 5 x y + x z, -25 x y + 12 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=185.3MB, alloc=84.3MB, time=3.59 memory used=245.2MB, alloc=84.3MB, time=4.63 N2 := 791 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 H := [-5 x y - x y z, 6 y z - 20 x, 5 x y z + 12 y z, 17 x y z + 16 y, 3 2 2 -13 y - 13 y, -11 x y - 20 y ] > J:=[op(GB),op(G)]; 2 3 2 J := [5 x + 12 x, 5 x y - 8 x, 5 x y + x z, -25 x y + 12 y z, 3 2 2 17 x y z + 16 y, -13 y - 13 y, -11 x y - 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, 18, 3, 2, 3, 1, 5/6, 1, 2/3, 1/2, 11/12, 5/12, 7, 15, 20, 4, 2, 3, 1, 6/7, 6/7, 3/7, 9/14, 5/7, 3/14, 0, -2, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=296.5MB, alloc=84.3MB, time=5.85 |\^/| 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(); 1428317657 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-9 x y + 14 z , -11 x y - 6 x z, -18 x y - 4 x y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [-8 x + 8 x , 9 x y z + 9 z , -16 x z + 5 x ] > Problem := [F,G]; 2 2 Problem := [[-9 x y + 14 z , -11 x y - 6 x z, -18 x y - 4 x y z], 3 2 2 2 2 [-8 x + 8 x , 9 x y z + 9 z , -16 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=0.17 memory used=26.0MB, alloc=32.3MB, time=0.48 memory used=47.0MB, alloc=32.3MB, time=0.79 memory used=67.3MB, alloc=32.3MB, time=1.08 memory used=86.1MB, alloc=56.3MB, time=1.39 memory used=124.1MB, alloc=60.3MB, time=1.97 memory used=158.7MB, alloc=84.3MB, time=2.53 memory used=214.7MB, alloc=108.3MB, time=3.58 memory used=289.2MB, alloc=140.3MB, time=4.98 memory used=380.6MB, alloc=164.3MB, time=6.66 memory used=483.6MB, alloc=188.3MB, time=8.74 memory used=594.6MB, alloc=212.3MB, time=11.61 memory used=707.9MB, alloc=236.3MB, time=15.24 memory used=831.6MB, alloc=260.3MB, time=19.80 memory used=969.0MB, alloc=284.3MB, time=25.37 memory used=1130.3MB, alloc=308.3MB, time=32.12 memory used=1315.6MB, alloc=308.3MB, time=39.74 memory used=1500.9MB, alloc=332.3MB, time=47.20 memory used=1710.1MB, alloc=332.3MB, time=55.52 memory used=1919.3MB, alloc=332.3MB, time=63.81 memory used=2128.5MB, alloc=356.3MB, time=72.07 memory used=2361.5MB, alloc=380.3MB, time=81.13 N1 := 8029 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [y x , x y , 11 x y + 6 x z, -9 x y + 14 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2591.4MB, alloc=380.3MB, time=88.43 N2 := 1737 #save(Problem, "format.txt"); > if (GB=[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 := [-9 x y + 14 z , -11 x y - 6 x z, -18 x y - 4 x y z, -8 x + 8 x , 2 2 2 9 x y z + 9 z , -16 x z + 5 x ] > J:=[op(GB),op(G)]; 2 2 2 3 2 2 J := [y x , x y , 11 x y + 6 x z, -9 x y + 14 z , -8 x + 8 x , 9 x y z + 9 z , 2 2 -16 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, 15, 16, 3, 3, 1, 2, 1, 2/3, 5/6, 5/6, 5/12, 1/2, 7, 16, 19, 3, 3, 2, 2, 1, 5/7, 4/7, 5/7, 5/14, 5/14, -1, -3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2757.0MB, alloc=636.3MB, time=93.47 |\^/| 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(); 1428317762 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [2 z + 3, 3 x + 2 x z, -7 x y + 5 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [15 y , 10 x z - 19 z , x z + 5 x z] > Problem := [F,G]; 3 2 2 2 Problem := [[2 z + 3, 3 x + 2 x z, -7 x y + 5 z ], 3 2 2 2 [15 y , 10 x z - 19 z , 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=49.0MB, alloc=32.3MB, time=0.90 memory used=68.1MB, alloc=56.3MB, time=1.30 N1 := 613 > GB := Basis(F, plex(op(vars))); 3 GB := [9 x - 4, 28 y - 45, 2 z + 3 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 215 #save(Problem, "format.txt"); > 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 H := [2 z + 3, 3 x + 2 x z, -7 x y + 5 z , 15 y , 10 x z - 19 z , 2 x z + 5 x z] > J:=[op(GB),op(G)]; 3 3 2 2 2 J := [9 x - 4, 28 y - 45, 2 z + 3 x, 15 y , 10 x z - 19 z , 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, 11, 17, 3, 2, 3, 3, 2/3, 1/3, 5/6, 1/2, 1/6, 7/12, 6, 9, 14, 3, 3, 3, 2, 2/3, 1/3, 1/2, 5/12, 1/6, 5/12, 2, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=102.1MB, alloc=56.3MB, 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(); 1428317765 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [-y + 11 z, -16 x y + 8 z , 4 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [6 y - 20 y, -16 x z + 13 z , 12 x y + 19] > Problem := [F,G]; 3 2 3 2 Problem := [[-y + 11 z, -16 x y + 8 z , 4 z ], 2 2 2 2 [6 y - 20 y, -16 x z + 13 z , 12 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=0.17 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.79 memory used=68.1MB, alloc=32.3MB, time=1.08 memory used=87.8MB, alloc=56.3MB, time=1.40 memory used=131.3MB, alloc=60.3MB, time=2.17 memory used=169.7MB, alloc=84.3MB, time=2.89 memory used=225.9MB, alloc=108.3MB, time=4.23 memory used=293.1MB, alloc=132.3MB, time=6.67 N1 := 1789 > GB := Basis(F, plex(op(vars))); 2 6 3 GB := [y x, y , -y + 11 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 613 #save(Problem, "format.txt"); > 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 := [-y + 11 z, -16 x y + 8 z , 4 z , 6 y - 20 y, -16 x z + 13 z , 2 12 y x + 19] > J:=[op(GB),op(G)]; 2 6 3 2 2 2 2 J := [y x, y , -y + 11 z, 6 y - 20 y, -16 x z + 13 z , 12 y x + 19] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 11, 16, 3, 2, 3, 3, 1/2, 2/3, 2/3, 1/4, 5/12, 5/12, 6, 10, 20, 6, 2, 6, 2, 1/2, 5/6, 1/3, 1/4, 1/2, 1/4, 1, -4, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=376.9MB, alloc=140.3MB, time=8.37 |\^/| 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(); 1428317774 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 F := [8 x z + 14 y , -8 x y + 2 z , 11 x + 15 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 3 G := [12 x z + 11 z, -9 x y + 9 y , -12 x z - 16 z ] > Problem := [F,G]; 2 2 3 3 2 Problem := [[8 x z + 14 y , -8 x y + 2 z , 11 x + 15 z ], 2 2 3 2 3 [12 x z + 11 z, -9 x y + 9 y , -12 x z - 16 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=48.1MB, alloc=32.3MB, time=0.81 memory used=69.2MB, alloc=56.3MB, time=1.15 memory used=111.2MB, alloc=60.3MB, time=1.77 memory used=153.1MB, alloc=84.3MB, time=2.50 memory used=214.8MB, alloc=84.3MB, time=3.62 memory used=271.2MB, alloc=108.3MB, time=4.61 memory used=341.5MB, alloc=132.3MB, time=6.37 memory used=420.0MB, alloc=156.3MB, time=9.20 memory used=522.8MB, alloc=180.3MB, time=12.78 N1 := 2663 > GB := Basis(F, plex(op(vars))); 6 5 2 2 2 5 4 2 GB := [77 x - 240 x , 77 x y - 240 x y , 176 x + 735 y , 4 z x + 7 y , 4 2 3 2 -44 x + 105 y z, 11 x + 15 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=644.0MB, alloc=188.3MB, time=14.81 N2 := 1469 #save(Problem, "format.txt"); > if (GB=[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 z + 14 y , -8 x y + 2 z , 11 x + 15 z , 12 x z + 11 z, 2 3 2 3 -9 x y + 9 y , -12 x z - 16 z ] > J:=[op(GB),op(G)]; 6 5 2 2 2 5 4 2 J := [77 x - 240 x , 77 x y - 240 x y , 176 x + 735 y , 4 z x + 7 y , 4 2 3 2 2 2 3 -44 x + 105 y z, 11 x + 15 z , 12 x z + 11 z, -9 x y + 9 y , 2 3 -12 x 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, 17, 3, 3, 3, 3, 1, 1/2, 5/6, 1/2, 1/3, 7/12, 9, 19, 33, 6, 6, 4, 3, 1, 5/9, 5/9, 11/18, 7/18, 7/18, -5, -16, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=765.4MB, alloc=444.3MB, time=18.30 |\^/| 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(); 1428317793 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 F := [-4 x - y, -11 y - 18, -18 x - x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 G := [-3 z - 18, -8 x y z + 2 y, -10 x - 14 z ] > Problem := [F,G]; 3 3 3 2 Problem := [[-4 x - y, -11 y - 18, -18 x - x y], 3 3 2 [-3 z - 18, -8 x y z + 2 y, -10 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=48.0MB, alloc=32.3MB, time=0.84 memory used=69.7MB, alloc=32.3MB, time=1.23 memory used=89.3MB, alloc=56.3MB, time=1.60 memory used=129.5MB, alloc=80.3MB, time=2.57 N1 := 967 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 201 #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 3 2 3 H := [-4 x - y, -11 y - 18, -18 x - x y, -3 z - 18, -8 x y z + 2 y, 3 2 -10 x - 14 z ] > J:=[op(GB),op(G)]; 3 3 2 J := [1, -3 z - 18, -8 x y z + 2 y, -10 x - 14 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 11, 18, 3, 3, 3, 3, 2/3, 2/3, 1/2, 5/12, 5/12, 1/4, 4, 6, 9, 3, 3, 1, 3, 1/2, 1/4, 3/4, 2/7, 2/7, 3/7, 5, 9, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=172.0MB, alloc=80.3MB, time=3.48 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428317797 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [8 y z + 6, -8 x y z, -15 y z - 17 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [13 x y - 16 x , -7 x z + 18 y , 19 x y z - 11 x z ] > Problem := [F,G]; 2 2 Problem := [[8 y z + 6, -8 x y z, -15 y z - 17 z], 2 2 2 2 2 [13 x y - 16 x , -7 x z + 18 y , 19 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=0.17 memory used=26.4MB, alloc=32.3MB, time=0.52 memory used=47.9MB, alloc=32.3MB, time=0.85 memory used=68.0MB, alloc=32.3MB, time=1.16 memory used=86.8MB, alloc=56.3MB, time=1.46 memory used=128.4MB, alloc=60.3MB, time=2.22 memory used=166.5MB, alloc=84.3MB, time=2.93 memory used=224.9MB, alloc=84.3MB, time=3.96 memory used=278.2MB, alloc=108.3MB, time=4.92 memory used=346.7MB, alloc=140.3MB, time=6.59 memory used=423.3MB, alloc=164.3MB, time=9.44 memory used=522.9MB, alloc=164.3MB, time=13.20 memory used=622.8MB, alloc=188.3MB, time=16.85 N1 := 3165 > GB := Basis(F, plex(op(vars))); GB := [x, 675 y + 1156, 68 z - 45] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=743.8MB, alloc=188.3MB, time=19.03 N2 := 1357 #save(Problem, "format.txt"); > if (GB=[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 := [8 y z + 6, -8 x y z, -15 y z - 17 z, 13 x y - 16 x , -7 x z + 18 y , 2 19 x y z - 11 x z ] > J:=[op(GB),op(G)]; 2 2 2 2 J := [x, 675 y + 1156, 68 z - 45, 13 x y - 16 x , -7 x z + 18 y , 2 19 x y z - 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, 15, 18, 3, 2, 2, 2, 2/3, 1, 5/6, 3/7, 3/7, 1/2, 6, 11, 12, 3, 2, 2, 2, 2/3, 2/3, 1/2, 6/11, 4/11, 4/11, 4, 6, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=797.1MB, alloc=188.3MB, time=20.85 |\^/| 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(); 1428317819 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [13 x z - 11 x y, x , -x z - 15 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [5 x, -20 y z + 10 x y, 10 z + 17 y] > Problem := [F,G]; 2 3 2 Problem := [[13 x z - 11 x y, x , -x z - 15 y z], 2 2 [5 x, -20 y z + 10 x y, 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.6MB, alloc=32.3MB, time=0.49 memory used=50.2MB, alloc=32.3MB, time=0.90 memory used=71.6MB, alloc=56.3MB, time=1.29 memory used=113.2MB, alloc=80.3MB, time=2.32 N1 := 959 > GB := Basis(F, plex(op(vars))); 3 2 2 2 GB := [x , y x , y x, 13 x z - 11 x y, 11 x y + 195 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=144.3MB, alloc=80.3MB, time=2.91 memory used=209.8MB, alloc=84.3MB, time=4.10 memory used=270.4MB, alloc=108.3MB, time=5.44 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)]; H := [ 2 3 2 2 2 13 x z - 11 x y, x , -x z - 15 y z, 5 x, -20 y z + 10 x y, 10 z + 17 y] > J:=[op(GB),op(G)]; 3 2 2 2 J := [x , y x , y x, 13 x z - 11 x y, 11 x y + 195 y z, 5 x, 2 2 -20 y z + 10 x y, 10 z + 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, 13, 15, 3, 3, 1, 2, 5/6, 2/3, 2/3, 1/2, 5/12, 5/12, 8, 17, 20, 3, 3, 2, 2, 7/8, 3/4, 1/2, 1/2, 1/2, 1/4, -4, -5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=320.9MB, alloc=108.3MB, time=7.33 |\^/| 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(); 1428317828 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 3 2 F := [8 x y - 17 z , -8 z - 6 y , 5 x + 8 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-6 x y + 16 x , -9 x y + 14 x, 15 y z + 11 y z] > Problem := [F,G]; 2 3 3 2 3 2 Problem := [[8 x y - 17 z , -8 z - 6 y , 5 x + 8 x y], 2 2 2 [-6 x y + 16 x , -9 x y + 14 x, 15 y z + 11 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.52 memory used=48.6MB, alloc=32.3MB, time=0.92 memory used=70.5MB, alloc=56.3MB, time=1.36 N1 := 711 > GB := Basis(F, plex(op(vars))); 5 4 3 2 4 2 4 3 GB := [32 x + 51 x , 5 x + 8 x y, -400 x + 2601 y , 100 x + 867 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=111.8MB, alloc=60.3MB, time=2.32 memory used=148.6MB, alloc=60.3MB, time=2.85 memory used=185.8MB, alloc=84.3MB, time=3.47 memory used=246.8MB, alloc=84.3MB, time=4.60 memory used=299.2MB, alloc=108.3MB, time=5.95 memory used=365.5MB, alloc=132.3MB, time=8.35 N2 := 1717 #save(Problem, "format.txt"); > 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 2 2 2 H := [-17 z + 8 y x, -8 z - 6 y , 5 x + 8 x y, -6 x y + 16 x , 2 -9 x y + 14 x, 15 y z + 11 y z] > J:=[op(GB),op(G)]; 5 4 3 2 4 2 4 3 J := [32 x + 51 x , 5 x + 8 x y, -400 x + 2601 y , 100 x + 867 z , 2 2 2 -6 x y + 16 x , -9 x y + 14 x, 15 y z + 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, 13, 17, 3, 3, 2, 3, 2/3, 1, 1/2, 7/12, 7/12, 1/3, 7, 13, 24, 5, 5, 2, 3, 6/7, 5/7, 2/7, 5/7, 3/7, 3/14, 0, -7, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=383.5MB, alloc=132.3MB, time=8.88 |\^/| 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(); 1428317839 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 F := [-10 x + 17 y , -19 x + 8 x y z, -19 x - 14 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [-7 x z + 11 z, 8 y z + 9, 8 y - 3 y z] > Problem := [F,G]; 3 2 3 3 2 Problem := [[-10 x + 17 y , -19 x + 8 x y z, -19 x - 14 x y], 2 3 [-7 x z + 11 z, 8 y z + 9, 8 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=26.4MB, alloc=32.3MB, time=0.50 memory used=47.8MB, alloc=32.3MB, time=0.82 memory used=67.8MB, alloc=32.3MB, time=1.13 memory used=86.4MB, alloc=56.3MB, time=1.44 memory used=124.8MB, alloc=60.3MB, time=2.06 memory used=162.8MB, alloc=60.3MB, time=2.66 memory used=198.8MB, alloc=84.3MB, time=3.23 memory used=255.4MB, alloc=84.3MB, time=4.16 memory used=312.1MB, alloc=108.3MB, time=5.27 memory used=384.6MB, alloc=140.3MB, time=6.70 memory used=472.9MB, alloc=164.3MB, time=8.41 memory used=575.8MB, alloc=188.3MB, time=10.62 memory used=685.4MB, alloc=212.3MB, time=13.91 memory used=802.6MB, alloc=236.3MB, time=18.48 memory used=941.2MB, alloc=260.3MB, time=24.07 memory used=1103.8MB, alloc=260.3MB, time=30.66 memory used=1266.4MB, alloc=284.3MB, time=37.38 memory used=1453.3MB, alloc=308.3MB, time=44.87 N1 := 5315 > GB := Basis(F, plex(op(vars))); 5 4 3 2 3 2 4 3 GB := [1960 x - 6137 x , 19 x + 14 x y, -10 x + 17 y , 7 x + 4 x z, 3 -19 x + 8 x y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1543.0MB, alloc=308.3MB, time=46.62 memory used=1776.4MB, alloc=564.3MB, time=50.69 memory used=2001.0MB, alloc=564.3MB, time=54.51 memory used=2222.3MB, alloc=588.3MB, time=58.78 memory used=2444.1MB, alloc=612.3MB, time=63.38 memory used=2675.5MB, alloc=636.3MB, time=69.12 memory used=2887.5MB, alloc=660.3MB, time=76.90 memory used=3102.6MB, alloc=684.3MB, time=85.78 memory used=3322.7MB, alloc=708.3MB, time=95.98 memory used=3566.7MB, alloc=732.3MB, time=107.24 memory used=3834.7MB, alloc=756.3MB, time=119.34 memory used=4126.6MB, alloc=780.3MB, time=132.84 memory used=4442.5MB, alloc=804.3MB, time=146.83 memory used=4782.4MB, alloc=828.3MB, time=162.26 memory used=5146.2MB, alloc=852.3MB, time=178.57 memory used=5534.0MB, alloc=876.3MB, time=195.72 memory used=5945.7MB, alloc=900.3MB, time=213.48 memory used=6381.5MB, alloc=924.3MB, time=232.32 N2 := 11219 #save(Problem, "format.txt"); > 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 := [-10 x + 17 y , -19 x + 8 x y z, -19 x - 14 x y, -7 x z + 11 z, 3 8 z y + 9, 8 y - 3 y z] > J:=[op(GB),op(G)]; 5 4 3 2 3 2 4 3 J := [1960 x - 6137 x , 19 x + 14 x y, -10 x + 17 y , 7 x + 4 x z, 3 2 3 -19 x + 8 x y z, -7 x z + 11 z, 8 z y + 9, 8 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, 13, 17, 3, 3, 3, 2, 2/3, 5/6, 2/3, 1/2, 1/2, 5/12, 8, 16, 26, 5, 5, 3, 2, 3/4, 5/8, 5/8, 5/8, 3/8, 3/8, -3, -9, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=6447.6MB, alloc=924.3MB, time=234.91 |\^/| 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(); 1428318118 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [15 y z - 10 y , -3 y z + 5 x z, -9 y + 10 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [15 x y - 8 y z, -19 x z - 12 x , x z - 5 x y z] > Problem := [F,G]; 2 2 2 3 Problem := [[15 y z - 10 y , -3 y z + 5 x z, -9 y + 10 z], 2 2 2 2 2 [15 x y - 8 y z, -19 x z - 12 x , x z - 5 x y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=47.5MB, alloc=32.3MB, time=0.82 memory used=67.5MB, alloc=32.3MB, time=1.12 memory used=86.6MB, alloc=56.3MB, time=1.41 memory used=124.7MB, alloc=60.3MB, time=1.98 memory used=161.7MB, alloc=84.3MB, time=2.54 memory used=214.3MB, alloc=84.3MB, time=3.36 memory used=270.9MB, alloc=92.3MB, time=4.25 memory used=325.7MB, alloc=116.3MB, time=5.12 memory used=402.0MB, alloc=116.3MB, time=6.31 memory used=477.2MB, alloc=140.3MB, time=7.47 memory used=566.4MB, alloc=164.3MB, time=9.04 memory used=682.3MB, alloc=444.3MB, time=11.13 memory used=810.3MB, alloc=468.3MB, time=13.51 memory used=948.2MB, alloc=492.3MB, time=16.14 memory used=1097.6MB, alloc=516.3MB, time=19.04 memory used=1254.5MB, alloc=540.3MB, time=22.21 memory used=1416.6MB, alloc=564.3MB, time=25.74 memory used=1571.6MB, alloc=588.3MB, time=30.65 memory used=1732.0MB, alloc=612.3MB, time=36.31 memory used=1902.8MB, alloc=636.3MB, time=42.72 memory used=2086.1MB, alloc=660.3MB, time=49.92 memory used=2285.5MB, alloc=684.3MB, time=57.90 memory used=2495.7MB, alloc=708.3MB, time=67.12 memory used=2729.8MB, alloc=732.3MB, time=77.28 memory used=2987.8MB, alloc=756.3MB, time=88.53 memory used=3269.7MB, alloc=780.3MB, time=100.78 memory used=3575.5MB, alloc=804.3MB, time=113.99 memory used=3905.4MB, alloc=828.3MB, time=128.15 memory used=4259.2MB, alloc=828.3MB, time=143.40 memory used=4612.9MB, alloc=828.3MB, time=158.64 memory used=4966.6MB, alloc=852.3MB, time=174.03 memory used=5344.2MB, alloc=852.3MB, time=190.85 memory used=5721.8MB, alloc=852.3MB, time=207.42 memory used=6099.4MB, alloc=876.3MB, time=223.76 memory used=6500.6MB, alloc=876.3MB, time=241.12 memory used=6901.8MB, alloc=876.3MB, 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(); 1428318418 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 F := [14 x + 4 x y z, x z - 10 y z, 3 x y - 9 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [14 x y + 16 z , -4 y + 11 x, 8 z - 16] > Problem := [F,G]; 3 2 3 Problem := [[14 x + 4 x y z, x z - 10 y z, 3 x y - 9 z ], 2 2 2 3 [14 x y + 16 z , -4 y + 11 x, 8 z - 16]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.3MB, alloc=40.3MB, time=0.60 memory used=61.1MB, alloc=44.3MB, time=1.07 memory used=87.8MB, alloc=68.3MB, time=1.52 memory used=133.5MB, alloc=68.3MB, time=2.23 memory used=178.4MB, alloc=92.3MB, time=2.91 memory used=247.5MB, alloc=100.3MB, time=3.96 memory used=312.9MB, alloc=124.3MB, time=5.09 memory used=400.8MB, alloc=124.3MB, time=6.47 memory used=487.3MB, alloc=404.3MB, time=7.97 memory used=597.5MB, alloc=428.3MB, time=10.24 memory used=725.2MB, alloc=452.3MB, time=12.79 memory used=867.1MB, alloc=476.3MB, time=15.53 memory used=1019.7MB, alloc=500.3MB, time=18.62 memory used=1185.2MB, alloc=524.3MB, time=22.04 memory used=1345.3MB, alloc=548.3MB, time=26.93 memory used=1505.4MB, alloc=572.3MB, time=32.65 memory used=1675.4MB, alloc=596.3MB, time=39.12 memory used=1853.5MB, alloc=620.3MB, time=46.73 memory used=2055.7MB, alloc=644.3MB, time=56.33 memory used=2281.7MB, alloc=668.3MB, time=66.35 memory used=2531.8MB, alloc=692.3MB, time=77.93 memory used=2805.7MB, alloc=692.3MB, time=89.43 memory used=3079.6MB, alloc=716.3MB, time=101.73 memory used=3377.5MB, alloc=716.3MB, time=114.58 memory used=3675.3MB, alloc=740.3MB, time=127.43 memory used=3997.2MB, alloc=740.3MB, time=141.23 memory used=4319.1MB, alloc=764.3MB, time=155.58 N1 := 10149 > GB := Basis(F, plex(op(vars))); 5 4 3 2 2 3 3 2 GB := [x , -x + 10 x y, -x y + 10 x y , 35 x + x z, -x z + 10 y z, 2 3 -x y + 3 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4539.2MB, alloc=764.3MB, time=161.86 memory used=4702.8MB, alloc=764.3MB, time=165.21 memory used=4933.1MB, alloc=764.3MB, time=169.74 memory used=5135.0MB, alloc=788.3MB, time=174.76 memory used=5509.7MB, alloc=812.3MB, time=190.56 memory used=5886.8MB, alloc=836.3MB, time=207.40 N2 := 5979 #save(Problem, "format.txt"); > 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 := [14 x + 4 x y z, x z - 10 y z, 3 x y - 9 z , 14 x y + 16 z , 2 3 -4 y + 11 x, 8 z - 16] > J:=[op(GB),op(G)]; 5 4 3 2 2 3 3 2 J := [x , -x + 10 x y, -x y + 10 x y , 35 x + x z, -x z + 10 y z, 2 3 2 2 2 3 -x y + 3 z , 14 x y + 16 z , -4 y + 11 x, 8 z - 16] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 16, 3, 3, 2, 3, 5/6, 5/6, 5/6, 1/2, 5/12, 1/2, 9, 19, 29, 5, 5, 3, 3, 8/9, 2/3, 5/9, 11/18, 7/18, 1/3, -4, -13, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=6228.4MB, alloc=836.3MB, time=222.62 |\^/| 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(); 1428318678 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [20 - 2 z, -8 x z + 5 x y z, -19 x y z + 15 y z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 G := [-20 z - 6, -10 z - 18 x, -18 x y] > Problem := [F,G]; 2 2 Problem := [[20 - 2 z, -8 x z + 5 x y z, -19 x y z + 15 y z ], 3 3 [-20 z - 6, -10 z - 18 x, -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=26.2MB, alloc=32.3MB, time=0.49 memory used=48.8MB, alloc=32.3MB, time=0.88 N1 := 531 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [19 x - 150 x , -76 x + 375 y, z - 10] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=67.5MB, alloc=56.3MB, time=1.33 N2 := 281 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 H := [20 - 2 z, -8 x z + 5 x y z, -19 x y z + 15 y z , -20 z - 6, 3 -10 z - 18 x, -18 x y] > J:=[op(GB),op(G)]; J := [ 3 2 2 3 3 19 x - 150 x , -76 x + 375 y, z - 10, -20 z - 6, -10 z - 18 x, -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, 12, 15, 3, 2, 1, 3, 2/3, 1/2, 5/6, 5/13, 4/13, 7/13, 6, 9, 14, 3, 3, 1, 3, 2/3, 1/3, 1/2, 5/13, 2/13, 3/13, 3, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=97.1MB, alloc=56.3MB, time=1.86 |\^/| 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(); 1428318680 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [13 x - 7 x y, 4 y + 20 x , -8 x z - 13 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 3 3 G := [-13 y z + 14 z , 9 y + y z , -14 y + 6 z ] > Problem := [F,G]; 2 3 2 2 2 Problem := [[13 x - 7 x y, 4 y + 20 x , -8 x z - 13 z ], 2 3 3 2 3 3 [-13 y z + 14 z , 9 y + y z , -14 y + 6 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.9MB, alloc=32.3MB, time=0.80 memory used=68.9MB, alloc=32.3MB, time=1.11 memory used=88.9MB, alloc=56.3MB, time=1.42 memory used=133.0MB, alloc=60.3MB, time=2.22 memory used=172.4MB, alloc=84.3MB, time=2.96 memory used=229.3MB, alloc=108.3MB, time=4.84 N1 := 1347 > GB := Basis(F, plex(op(vars))); 4 3 2 3 2 2 2 GB := [2197 x + 1715 x , -13 x + 7 x y, y + 5 x , 8 x z + 13 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=302.6MB, alloc=108.3MB, time=6.42 memory used=385.0MB, alloc=116.3MB, time=8.04 memory used=463.0MB, alloc=140.3MB, time=10.28 N2 := 1347 #save(Problem, "format.txt"); > if (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 3 H := [13 x - 7 x y, 4 y + 20 x , -8 x z - 13 z , -13 y z + 14 z , 3 2 3 3 9 y + y z , -14 y + 6 z ] > J:=[op(GB),op(G)]; 4 3 2 3 2 2 2 J := [2197 x + 1715 x , -13 x + 7 x y, y + 5 x , 8 x z + 13 z , 2 3 3 2 3 3 -13 y z + 14 z , 9 y + y z , -14 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, 17, 3, 2, 3, 3, 1/2, 5/6, 2/3, 1/3, 1/2, 1/2, 7, 13, 21, 4, 4, 3, 3, 4/7, 5/7, 4/7, 3/7, 3/7, 3/7, -1, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=488.5MB, alloc=140.3MB, time=11.13 |\^/| 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(); 1428318693 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-12 x y - 7 y z, -3 y z - y , -y z + 14 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-8 x - 4 x y z, 6 x z + 4 y , -7 x z - 3 x z] > Problem := [F,G]; 2 2 2 Problem := [[-12 x y - 7 y z, -3 y z - y , -y z + 14 x y], 3 2 2 2 [-8 x - 4 x y z, 6 x z + 4 y , -7 x z - 3 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.53 memory used=47.4MB, alloc=32.3MB, time=0.86 memory used=67.0MB, alloc=56.3MB, time=1.20 memory used=106.5MB, alloc=60.3MB, time=1.84 memory used=144.1MB, alloc=84.3MB, time=2.43 memory used=200.0MB, alloc=92.3MB, time=3.34 memory used=256.4MB, alloc=116.3MB, time=4.21 memory used=333.6MB, alloc=116.3MB, time=5.58 memory used=409.6MB, alloc=140.3MB, time=6.89 memory used=487.7MB, alloc=140.3MB, time=8.21 memory used=573.8MB, alloc=420.3MB, time=9.77 memory used=690.1MB, alloc=444.3MB, time=11.62 memory used=823.2MB, alloc=468.3MB, time=14.11 memory used=975.2MB, alloc=492.3MB, time=17.11 memory used=1142.9MB, alloc=516.3MB, time=20.68 memory used=1319.7MB, alloc=540.3MB, time=24.32 memory used=1463.4MB, alloc=564.3MB, time=27.45 memory used=1633.2MB, alloc=588.3MB, time=30.80 memory used=1804.5MB, alloc=612.3MB, time=34.36 memory used=1962.7MB, alloc=636.3MB, time=37.79 memory used=2129.5MB, alloc=660.3MB, time=41.45 memory used=2302.2MB, alloc=684.3MB, time=45.35 memory used=2471.6MB, alloc=708.3MB, time=48.99 memory used=2618.9MB, alloc=732.3MB, time=52.40 memory used=2753.5MB, alloc=756.3MB, time=55.65 memory used=2900.9MB, alloc=780.3MB, time=59.38 memory used=3188.7MB, alloc=804.3MB, time=66.25 memory used=3480.5MB, alloc=828.3MB, time=72.84 memory used=3767.2MB, alloc=852.3MB, time=80.24 memory used=4007.7MB, alloc=876.3MB, time=89.58 memory used=4250.9MB, alloc=900.3MB, time=99.67 memory used=4502.8MB, alloc=924.3MB, time=110.72 memory used=4764.4MB, alloc=948.3MB, time=121.99 memory used=5038.0MB, alloc=972.3MB, time=134.30 memory used=5323.9MB, alloc=996.3MB, time=146.97 memory used=5622.7MB, alloc=1020.3MB, time=160.70 memory used=5935.6MB, alloc=1044.3MB, time=175.33 memory used=6262.2MB, alloc=1068.3MB, time=190.32 memory used=6602.9MB, alloc=1092.3MB, time=205.39 memory used=6957.8MB, alloc=1116.3MB, time=222.11 memory used=7327.8MB, alloc=1140.3MB, time=239.62 |\^/| 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(); 1428318994 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [-15 y z - 11 y z, 18 x y - 5 x z, 19 y + 19 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [11 y + 3 y , -20 x z - 2, 3 y + 12 x] > Problem := [F,G]; 2 2 2 3 2 Problem := [[-15 y z - 11 y z, 18 x y - 5 x z, 19 y + 19 x ], 3 2 2 2 [11 y + 3 y , -20 x z - 2, 3 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=0.21 memory used=26.1MB, alloc=32.3MB, time=0.54 memory used=47.2MB, alloc=32.3MB, time=0.87 memory used=67.5MB, alloc=32.3MB, time=1.19 memory used=87.7MB, alloc=56.3MB, time=1.59 memory used=128.4MB, alloc=60.3MB, time=2.42 memory used=164.5MB, alloc=84.3MB, time=3.16 memory used=219.7MB, alloc=84.3MB, time=4.22 memory used=268.0MB, alloc=108.3MB, time=5.27 memory used=330.5MB, alloc=132.3MB, time=7.03 memory used=406.3MB, alloc=156.3MB, time=9.91 memory used=505.6MB, alloc=156.3MB, time=13.71 memory used=604.8MB, alloc=180.3MB, time=17.55 N1 := 3583 > GB := Basis(F, plex(op(vars))); 6 4 4 2 3 2 4 2 GB := [157464 x - 1331 x , 2916 x + 121 x y, y + x , 52488 x + 605 x z, 2 15 y z + 11 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=728.1MB, alloc=188.3MB, time=21.11 memory used=860.8MB, alloc=188.3MB, time=23.46 memory used=991.6MB, alloc=212.3MB, time=27.36 memory used=1125.1MB, alloc=236.3MB, time=32.62 N2 := 2635 #save(Problem, "format.txt"); > if (GB=[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 := [-15 y z - 11 y z, 18 x y - 5 x z, 19 y + 19 x , 11 y + 3 y , 2 2 -20 x z - 2, 3 y + 12 x] > J:=[op(GB),op(G)]; 6 4 4 2 3 2 4 2 J := [157464 x - 1331 x , 2916 x + 121 x y, y + x , 52488 x + 605 x z, 2 3 2 2 2 15 y z + 11 y z, 11 y + 3 y , -20 x z - 2, 3 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, 12, 17, 3, 2, 3, 2, 2/3, 5/6, 1/2, 5/12, 7/12, 1/3, 8, 14, 28, 6, 6, 3, 2, 3/4, 5/8, 3/8, 9/16, 7/16, 1/4, -2, -11, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1140.1MB, alloc=236.3MB, time=33.09 |\^/| 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(); 1428319036 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-x + 18 y, 13 x + 4 y , -17 x - 18 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 G := [17 y , 18 x z - 16 y z, 5 x y + 12 y ] > Problem := [F,G]; 2 2 2 Problem := [[-x + 18 y, 13 x + 4 y , -17 x - 18 y], 3 2 2 3 [17 y , 18 x z - 16 y z, 5 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.52 N1 := 131 > GB := Basis(F, plex(op(vars))); GB := [x, y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 35 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 H := [-x + 18 y, 4 y + 13 x , -17 x - 18 y, 17 y , 18 x z - 16 y z, 2 3 5 x y + 12 y ] > J:=[op(GB),op(G)]; 3 2 2 3 J := [x, y, 17 y , 18 x z - 16 y z, 5 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, 14, 3, 2, 3, 2, 5/6, 1, 1/6, 5/12, 7/12, 1/6, 5, 8, 11, 3, 2, 3, 2, 3/5, 4/5, 1/5, 3/8, 5/8, 1/4, 4, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=40.5MB, alloc=32.3MB, time=0.75 |\^/| 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(); 1428319036 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-x + 18 y, 13 x + 4 y , -17 x - 18 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 G := [17 y , 18 x z - 16 y z, 5 x y + 12 y ] > Problem := [F,G]; 2 2 2 Problem := [[-x + 18 y, 13 x + 4 y , -17 x - 18 y], 3 2 2 3 [17 y , 18 x z - 16 y z, 5 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.52 N1 := 131 > GB := Basis(F, plex(op(vars))); GB := [x, y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 35 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 3 2 H := [-x + 18 y, 4 y + 13 x , -17 x - 18 y, 17 y , 18 x z - 16 y z, 2 3 5 x y + 12 y ] > J:=[op(GB),op(G)]; 3 2 2 3 J := [x, y, 17 y , 18 x z - 16 y z, 5 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, 14, 3, 2, 3, 2, 5/6, 1, 1/6, 5/12, 7/12, 1/6, 5, 8, 11, 3, 2, 3, 2, 3/5, 4/5, 1/5, 3/8, 5/8, 1/4, 4, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=40.5MB, alloc=32.3MB, time=0.75 |\^/| 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(); 1428319037 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 2 F := [16 y z - 14 x , -20 x + 14 y , -15 y z + 7 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [12 x z - 9 y z , 14 x z - y , x z + 3 y z] > Problem := [F,G]; 2 2 3 3 2 Problem := [[16 y z - 14 x , -20 x + 14 y , -15 y z + 7 y], 2 2 2 3 2 [12 x z - 9 y z , 14 x z - y , 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=0.18 memory used=26.5MB, alloc=32.3MB, time=0.52 memory used=47.5MB, alloc=32.3MB, time=0.84 memory used=68.3MB, alloc=32.3MB, time=1.15 memory used=87.3MB, alloc=56.3MB, time=1.46 memory used=127.2MB, alloc=60.3MB, time=2.08 memory used=165.5MB, alloc=84.3MB, time=2.67 memory used=201.6MB, alloc=84.3MB, time=3.17 memory used=262.9MB, alloc=116.3MB, time=4.11 memory used=343.1MB, alloc=372.3MB, time=5.40 memory used=428.6MB, alloc=396.3MB, time=6.58 memory used=532.3MB, alloc=420.3MB, time=8.17 memory used=658.1MB, alloc=444.3MB, time=10.07 memory used=793.7MB, alloc=468.3MB, time=12.17 memory used=931.8MB, alloc=492.3MB, time=14.60 memory used=1097.3MB, alloc=516.3MB, time=17.81 memory used=1261.9MB, alloc=540.3MB, time=21.14 memory used=1419.5MB, alloc=564.3MB, time=24.35 memory used=1551.9MB, alloc=588.3MB, time=27.00 memory used=1712.4MB, alloc=612.3MB, time=30.32 memory used=1862.2MB, alloc=636.3MB, time=33.57 memory used=1997.8MB, alloc=660.3MB, time=36.42 memory used=2137.0MB, alloc=684.3MB, time=39.43 memory used=2258.2MB, alloc=708.3MB, time=42.14 memory used=2450.5MB, alloc=732.3MB, time=48.53 memory used=2709.6MB, alloc=756.3MB, time=58.38 memory used=2942.5MB, alloc=780.3MB, time=67.81 memory used=3217.6MB, alloc=804.3MB, time=79.29 memory used=3503.2MB, alloc=828.3MB, time=92.48 memory used=3801.0MB, alloc=852.3MB, time=105.90 memory used=4108.2MB, alloc=876.3MB, time=120.36 memory used=4429.8MB, alloc=900.3MB, time=135.28 memory used=4775.4MB, alloc=924.3MB, time=151.39 memory used=5144.9MB, alloc=948.3MB, time=168.52 memory used=5538.3MB, alloc=972.3MB, time=186.63 memory used=5955.7MB, alloc=996.3MB, time=205.56 memory used=6397.0MB, alloc=1020.3MB, time=225.61 memory used=6862.3MB, alloc=1020.3MB, time=246.68 memory used=7327.5MB, alloc=1044.3MB, time=268.06 |\^/| 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(); 1428319337 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [16 z + 11 x, 20 y z + 4 x y, -17 x - 5 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 3 G := [8 y + 3 x z, -5 y + 4 y z, -3 x z + 11 z ] > Problem := [F,G]; 2 2 3 Problem := [[16 z + 11 x, 20 y z + 4 x y, -17 x - 5 y z], 3 3 2 2 3 [8 y + 3 x z, -5 y + 4 y z, -3 x z + 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=27.0MB, alloc=32.3MB, time=0.53 memory used=48.0MB, alloc=32.3MB, time=0.84 memory used=68.2MB, alloc=56.3MB, time=1.17 memory used=108.6MB, alloc=60.3MB, time=1.79 memory used=147.4MB, alloc=84.3MB, time=2.39 memory used=209.2MB, alloc=92.3MB, time=3.35 memory used=266.3MB, alloc=116.3MB, time=4.26 memory used=345.3MB, alloc=140.3MB, time=5.46 memory used=433.5MB, alloc=396.3MB, time=6.85 memory used=531.4MB, alloc=420.3MB, time=8.37 memory used=650.6MB, alloc=444.3MB, time=10.27 memory used=792.5MB, alloc=444.3MB, time=12.49 memory used=931.6MB, alloc=468.3MB, time=14.66 memory used=1088.4MB, alloc=492.3MB, time=17.22 memory used=1245.7MB, alloc=516.3MB, time=19.98 memory used=1383.3MB, alloc=540.3MB, time=22.34 memory used=1493.7MB, alloc=540.3MB, time=24.29 memory used=1630.3MB, alloc=564.3MB, time=26.96 memory used=1776.0MB, alloc=588.3MB, time=29.96 memory used=1981.8MB, alloc=612.3MB, time=33.68 memory used=2149.2MB, alloc=636.3MB, time=37.06 memory used=2303.7MB, alloc=660.3MB, time=40.31 memory used=2493.6MB, alloc=684.3MB, time=44.16 memory used=2660.2MB, alloc=708.3MB, time=47.62 memory used=2813.2MB, alloc=732.3MB, time=50.85 memory used=2970.9MB, alloc=756.3MB, time=54.28 memory used=3115.2MB, alloc=780.3MB, time=57.41 memory used=3257.5MB, alloc=804.3MB, time=60.50 memory used=3569.6MB, alloc=828.3MB, time=66.95 memory used=3876.1MB, alloc=852.3MB, time=73.37 memory used=4177.5MB, alloc=876.3MB, time=79.64 memory used=4487.2MB, alloc=900.3MB, time=85.97 memory used=4772.0MB, alloc=924.3MB, time=92.15 memory used=5050.3MB, alloc=948.3MB, time=98.46 memory used=5298.1MB, alloc=972.3MB, time=107.32 memory used=5539.5MB, alloc=996.3MB, time=116.72 memory used=5785.6MB, alloc=1020.3MB, time=126.65 memory used=6038.3MB, alloc=1044.3MB, time=137.34 memory used=6300.3MB, alloc=1068.3MB, time=148.48 memory used=6572.9MB, alloc=1092.3MB, time=160.71 memory used=6856.7MB, alloc=1116.3MB, time=173.56 memory used=7152.5MB, alloc=1140.3MB, time=186.45 memory used=7460.1MB, alloc=1164.3MB, time=200.08 memory used=7780.7MB, alloc=1188.3MB, time=214.35 memory used=8114.4MB, alloc=1212.3MB, time=229.10 memory used=8461.5MB, alloc=1236.3MB, time=244.51 memory used=8822.1MB, alloc=1260.3MB, time=260.83 |\^/| 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(); 1428319637 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 2 2 F := [15 x + 10 y z , 20 y + 20 z , 10 y z + 9 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 G := [10 y + 19 y z, -19 + 14 x, -14 x y - 15 x] > Problem := [F,G]; 3 2 3 3 2 2 Problem := [[15 x + 10 y z , 20 y + 20 z , 10 y z + 9 x ], 2 [10 y + 19 y z, -19 + 14 x, -14 x y - 15 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=48.0MB, alloc=32.3MB, time=0.84 memory used=68.9MB, alloc=32.3MB, time=1.16 memory used=88.4MB, alloc=56.3MB, time=1.47 memory used=128.4MB, alloc=60.3MB, time=2.10 memory used=166.0MB, alloc=60.3MB, time=2.69 memory used=203.0MB, alloc=84.3MB, time=3.33 memory used=263.0MB, alloc=84.3MB, time=4.47 memory used=318.2MB, alloc=108.3MB, time=5.52 memory used=392.3MB, alloc=140.3MB, time=7.04 memory used=478.3MB, alloc=164.3MB, time=9.90 memory used=576.8MB, alloc=188.3MB, time=13.88 N1 := 2709 > GB := Basis(F, plex(op(vars))); 3 2 4 4 9 2 4 2 GB := [5 x - 3 x , 5 x y - 3 y , 625000 y + 59049 x , -10 y + 9 x z, 8 4 2 2 3 3 -250 y + 81 y z, 10 z y + 9 x , y + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=700.3MB, alloc=188.3MB, time=17.19 memory used=806.9MB, alloc=444.3MB, time=19.07 memory used=936.4MB, alloc=444.3MB, time=21.10 memory used=1063.6MB, alloc=468.3MB, time=23.23 memory used=1219.0MB, alloc=492.3MB, time=26.08 memory used=1389.5MB, alloc=516.3MB, time=29.37 memory used=1571.5MB, alloc=540.3MB, time=33.11 memory used=1759.8MB, alloc=564.3MB, time=38.41 memory used=1935.3MB, alloc=588.3MB, time=45.03 memory used=2113.2MB, alloc=612.3MB, time=53.07 memory used=2315.0MB, alloc=636.3MB, time=62.38 memory used=2540.8MB, alloc=660.3MB, time=72.46 memory used=2790.5MB, alloc=684.3MB, time=83.68 memory used=3064.2MB, alloc=708.3MB, time=95.88 memory used=3362.0MB, alloc=732.3MB, time=108.78 N2 := 7863 #save(Problem, "format.txt"); > 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 2 H := [15 x + 10 y z , 20 y + 20 z , 10 z y + 9 x , 10 y + 19 y z, 14 x - 19, -14 x y - 15 x] > J:=[op(GB),op(G)]; 3 2 4 4 9 2 4 2 J := [5 x - 3 x , 5 x y - 3 y , 625000 y + 59049 x , -10 y + 9 z x , 8 4 2 2 3 3 2 -250 y + 81 y z, 10 z y + 9 x , y + z , 10 y + 19 y z, 14 x - 19, -14 x y - 15 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 14, 3, 3, 3, 3, 2/3, 5/6, 2/3, 5/12, 1/2, 1/3, 10, 20, 40, 9, 3, 9, 3, 7/10, 4/5, 1/2, 9/20, 11/20, 1/4, -7, -26, -6] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=3586.2MB, alloc=732.3MB, time=118.01 |\^/| 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(); 1428319789 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [14 y + 13, 18 x + y , -10 y z + 4] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-16 x y z + y , 14 - 11 x, 7 y z + 19 y ] > Problem := [F,G]; 3 2 2 2 Problem := [[14 y + 13, 18 x + y , -10 y z + 4], 3 2 2 [-16 x y z + y , 14 - 11 x, 7 y z + 19 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.52 memory used=47.8MB, alloc=32.3MB, time=0.84 memory used=68.0MB, alloc=32.3MB, time=1.16 memory used=88.0MB, alloc=56.3MB, time=1.48 memory used=131.7MB, alloc=60.3MB, time=2.38 memory used=170.7MB, alloc=84.3MB, time=3.12 memory used=227.5MB, alloc=108.3MB, time=4.86 N1 := 1269 > GB := Basis(F, plex(op(vars))); 6 4 4 GB := [1143072 x + 169, 4536 x + 13 y, -127008 x + 845 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=301.7MB, alloc=116.3MB, time=6.25 memory used=384.4MB, alloc=140.3MB, time=7.90 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 2 2 3 H := [14 y + 13, y + 18 x , -10 y z + 4, -16 x y z + y , 14 - 11 x, 2 2 7 y z + 19 y ] > J:=[op(GB),op(G)]; 6 4 4 3 J := [1143072 x + 169, 4536 x + 13 y, -127008 x + 845 z, -16 x y z + y , 2 2 14 - 11 x, 7 y 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, 11, 15, 3, 2, 3, 2, 1/2, 5/6, 1/2, 1/4, 7/12, 1/4, 6, 11, 21, 6, 6, 3, 2, 5/6, 1/2, 1/2, 5/12, 5/12, 1/4, 0, -6, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=451.0MB, alloc=140.3MB, time=10.36 |\^/| 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(); 1428319802 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 3 F := [19 y z, 5 y - 10 z , -13 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [-4 x y + 18 x z , 16 x - 4 y, -16 x y - 2 y z] > Problem := [F,G]; 3 3 3 Problem := [[19 y z, 5 y - 10 z , -13 x ], 2 2 3 2 [-4 x y + 18 x z , 16 x - 4 y, -16 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.7MB, alloc=32.3MB, time=0.51 memory used=49.0MB, alloc=32.3MB, time=0.90 memory used=70.5MB, alloc=56.3MB, time=1.30 memory used=113.1MB, alloc=84.3MB, time=2.12 N1 := 1103 > GB := Basis(F, plex(op(vars))); 3 4 3 3 GB := [x , y , z y, -y + 2 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=171.4MB, alloc=84.3MB, time=3.73 memory used=233.8MB, alloc=84.3MB, time=4.82 memory used=292.4MB, alloc=108.3MB, time=6.51 N2 := 1103 #save(Problem, "format.txt"); > 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 := [19 z y, 5 y - 10 z , -13 x , -4 x y + 18 x z , 16 x - 4 y, 2 -16 x y - 2 y z] > J:=[op(GB),op(G)]; J := 3 4 3 3 2 2 3 2 [x , y , z y, -y + 2 z , -4 x y + 18 x z , 16 x - 4 y, -16 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, 13, 17, 3, 3, 3, 3, 2/3, 5/6, 2/3, 5/13, 6/13, 4/13, 7, 14, 21, 4, 3, 4, 3, 4/7, 6/7, 4/7, 5/14, 1/2, 2/7, -1, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=307.3MB, alloc=108.3MB, time=7.03 |\^/| 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(); 1428319810 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [4 x y + 15 x y , -9 x z + 16 y z, 11 x z + 15 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-2 x z + x , 19 x + 15 x z, -15 x y z - 8 x z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[4 x y + 15 x y , -9 x z + 16 y z, 11 x z + 15 x z], 2 2 2 2 [-2 x z + x , 19 x + 15 x z, -15 x y 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=0.18 memory used=26.3MB, alloc=32.3MB, time=0.50 memory used=48.2MB, alloc=32.3MB, time=0.86 memory used=69.1MB, alloc=56.3MB, time=1.25 memory used=109.8MB, alloc=84.3MB, time=2.06 N1 := 1219 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [4 x y + 15 x y , x z, y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=165.9MB, alloc=84.3MB, time=3.66 N2 := 563 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 2 2 H := [4 x y + 15 x y , -9 x z + 16 y z, 11 x z + 15 x z, -2 x z + x , 2 2 19 x + 15 x z, -15 x y z - 8 x z ] > J:=[op(GB),op(G)]; 2 2 2 2 2 2 J := [4 x y + 15 x y , x z, y z, -2 x z + x , 19 x + 15 x z, 2 -15 x y z - 8 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, 17, 3, 2, 2, 2, 1, 1/2, 5/6, 11/12, 1/3, 2/3, 6, 13, 16, 3, 2, 2, 2, 5/6, 1/2, 5/6, 3/4, 1/3, 1/2, 1, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=214.0MB, alloc=84.3MB, time=4.61 |\^/| 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(); 1428319815 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [-7 z + 16 z, 13 x y + 3 y , 10 y z + 12 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 3 3 G := [-4 x - 14, 20 x + 2 y , -15 z + 18 x] > Problem := [F,G]; 3 2 2 2 Problem := [[-7 z + 16 z, 13 x y + 3 y , 10 y z + 12 y], 3 3 3 3 [-4 x - 14, 20 x + 2 y , -15 z + 18 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=49.7MB, alloc=32.3MB, time=0.92 N1 := 451 > GB := Basis(F, plex(op(vars))); 3 GB := [y, 7 z - 16 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=69.1MB, alloc=56.3MB, time=1.33 N2 := 361 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 3 3 H := [-7 z + 16 z, 13 x y + 3 y , 10 y z + 12 y, -4 x - 14, 20 x + 2 y , 3 -15 z + 18 x] > J:=[op(GB),op(G)]; 3 3 3 3 3 J := [y, 7 z - 16 z, -4 x - 14, 20 x + 2 y , -15 z + 18 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 10, 18, 3, 3, 3, 3, 2/3, 1/2, 1/2, 1/3, 5/12, 1/3, 5, 7, 13, 3, 3, 3, 3, 3/5, 2/5, 2/5, 1/3, 2/9, 1/3, 3, 5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=102.2MB, alloc=56.3MB, time=1.94 |\^/| 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(); 1428319817 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [2 x + 8 y z, 18 x z - 6 z, -16 x y z + 20 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 2 G := [5 y + 9 y , -6 z - 20 x , 5 y z + 16 z ] > Problem := [F,G]; 2 2 Problem := [[2 x + 8 y z, 18 x z - 6 z, -16 x y z + 20 y], 3 2 3 2 2 2 [5 y + 9 y , -6 z - 20 x , 5 y z + 16 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.51 memory used=47.8MB, alloc=32.3MB, time=0.89 memory used=68.4MB, alloc=32.3MB, time=1.24 memory used=87.9MB, alloc=56.3MB, time=1.59 memory used=127.6MB, alloc=60.3MB, time=2.22 memory used=166.6MB, alloc=84.3MB, time=2.93 memory used=225.9MB, alloc=84.3MB, time=4.00 memory used=280.0MB, alloc=108.3MB, time=5.01 memory used=353.2MB, alloc=132.3MB, time=6.36 memory used=441.1MB, alloc=164.3MB, time=8.33 memory used=536.8MB, alloc=188.3MB, time=11.45 memory used=641.4MB, alloc=212.3MB, time=15.70 memory used=770.0MB, alloc=212.3MB, time=20.81 memory used=898.6MB, alloc=236.3MB, time=25.89 memory used=1051.2MB, alloc=236.3MB, time=31.84 N1 := 4565 > GB := Basis(F, plex(op(vars))); 4 2 3 3 GB := [3 x - x , x + 5 y, -45 x + 4 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1204.7MB, alloc=236.3MB, time=35.31 memory used=1383.2MB, alloc=516.3MB, time=40.64 N2 := 2305 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 3 2 H := [2 x + 8 y z, 18 x z - 6 z, -16 x y z + 20 y, 5 y + 9 y , -6 z - 20 x , 2 2 5 y z + 16 z ] > J:=[op(GB),op(G)]; 4 2 3 3 3 2 3 2 J := [3 x - x , x + 5 y, -45 x + 4 z, 5 y + 9 y , -6 z - 20 x , 2 2 5 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, 13, 17, 3, 2, 3, 3, 2/3, 2/3, 5/6, 1/3, 1/2, 7/12, 6, 10, 19, 4, 4, 3, 3, 2/3, 1/2, 1/2, 5/12, 1/3, 1/3, 3, -2, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1470.7MB, alloc=516.3MB, time=44.07 |\^/| 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(); 1428319867 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [14 x z - 17, -18 x z - 8 z , -3 z + 5 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [12 y + 13 z, 7 x y z + 6 y z, 10 x z - 17 y z] > Problem := [F,G]; 2 2 2 3 Problem := [[14 x z - 17, -18 x z - 8 z , -3 z + 5 y z], 2 2 2 [12 y + 13 z, 7 x y z + 6 y z, 10 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.51 memory used=48.2MB, alloc=32.3MB, time=0.85 memory used=69.0MB, alloc=32.3MB, time=1.17 memory used=88.7MB, alloc=56.3MB, time=1.53 memory used=130.7MB, alloc=60.3MB, time=2.38 memory used=169.0MB, alloc=84.3MB, time=3.13 memory used=225.4MB, alloc=108.3MB, time=4.32 memory used=294.6MB, alloc=132.3MB, time=6.63 memory used=381.5MB, alloc=132.3MB, time=9.89 N1 := 2293 > GB := Basis(F, plex(op(vars))); 2 GB := [9 x + 4, 280 y + 459, 56 z + 153] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 347 #save(Problem, "format.txt"); > if (GB=[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 := [14 z x - 17, -18 x z - 8 z , -3 z + 5 y z, 12 y + 13 z, 2 2 7 x y z + 6 y z, 10 x z - 17 y z] > J:=[op(GB),op(G)]; 2 2 2 J := [9 x + 4, 280 y + 459, 56 z + 153, 12 y + 13 z, 7 x y z + 6 y z, 2 10 x z - 17 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, 3, 2, 2, 3, 2/3, 2/3, 1, 1/3, 5/12, 5/6, 6, 11, 12, 3, 2, 2, 2, 1/2, 2/3, 2/3, 1/4, 5/12, 1/2, 3, 5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=463.2MB, alloc=140.3MB, time=11.42 |\^/| 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(); 1428319880 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 F := [18 x z - 14 y , -20 x y z - 19 y, 19 x + 10] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [5 x z - 7, 7 + 20 x, 19 x - 8] > Problem := [F,G]; 2 3 3 Problem := [[18 x z - 14 y , -20 x y z - 19 y, 19 x + 10], 2 2 [5 x z - 7, 7 + 20 x, 19 x - 8]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.4MB, alloc=32.3MB, time=0.56 memory used=48.6MB, alloc=32.3MB, time=0.99 memory used=68.8MB, alloc=56.3MB, time=1.36 N1 := 509 > GB := Basis(F, plex(op(vars))); 3 4 3 GB := [19 x + 10, 140 y + 171 x y, 133 x y + 90 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=108.8MB, alloc=60.3MB, time=2.15 N2 := 395 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 3 2 H := [18 x z - 14 y , -20 x y z - 19 y, 19 x + 10, 5 z x - 7, 20 x + 7, 2 19 x - 8] > J:=[op(GB),op(G)]; 3 4 3 2 J := [19 x + 10, 140 y + 171 x y, 133 y x + 90 z, 5 z x - 7, 20 x + 7, 2 19 x - 8] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 11, 15, 3, 3, 3, 2, 1, 1/3, 1/2, 1/2, 1/4, 1/4, 6, 10, 17, 4, 3, 4, 2, 1, 1/3, 1/3, 1/2, 1/4, 1/6, 1, -2, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=136.9MB, alloc=60.3MB, 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(); 1428319883 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [3 y z - 2 y, 7 y + 4 y, 5 x z + 12 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [13 x y - 16 x z, -20 x y + 20 y z, 17 x z + 14 y z ] > Problem := [F,G]; 2 3 2 Problem := [[3 y z - 2 y, 7 y + 4 y, 5 x z + 12 x], 2 2 2 2 2 [13 x y - 16 x z, -20 x y + 20 y z, 17 x z + 14 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=47.3MB, alloc=32.3MB, time=0.80 memory used=67.1MB, alloc=32.3MB, time=1.09 memory used=85.5MB, alloc=56.3MB, time=1.39 memory used=123.6MB, alloc=60.3MB, time=1.98 memory used=161.9MB, alloc=84.3MB, time=2.71 memory used=218.6MB, alloc=84.3MB, time=3.79 memory used=269.4MB, alloc=108.3MB, time=4.75 memory used=336.4MB, alloc=132.3MB, time=6.17 memory used=412.8MB, alloc=156.3MB, time=8.52 memory used=503.3MB, alloc=180.3MB, time=11.95 memory used=617.7MB, alloc=180.3MB, time=16.34 memory used=732.2MB, alloc=204.3MB, time=20.80 N1 := 3751 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [x y, 7 y + 4 y, 5 x z + 12 x, 3 y z - 2 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=868.0MB, alloc=212.3MB, time=23.64 memory used=1022.6MB, alloc=212.3MB, time=26.51 memory used=1165.4MB, alloc=236.3MB, time=30.21 memory used=1300.4MB, alloc=260.3MB, time=35.73 memory used=1459.5MB, alloc=284.3MB, time=42.23 N2 := 3751 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 2 H := [3 y z - 2 y, 7 y + 4 y, 5 x z + 12 x, 13 x y - 16 x z, 2 2 2 -20 x y + 20 y z, 17 x z + 14 y z ] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [x y, 7 y + 4 y, 5 x z + 12 x, 3 y z - 2 y, 13 x y - 16 x z, 2 2 2 -20 x y + 20 y z, 17 x 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, 18, 3, 2, 3, 2, 2/3, 5/6, 5/6, 1/2, 2/3, 1/2, 7, 16, 20, 3, 2, 3, 2, 5/7, 6/7, 5/7, 1/2, 9/14, 3/7, -2, -2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1535.7MB, alloc=284.3MB, time=45.09 |\^/| 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(); 1428319937 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [-12 y + 10 y , -18 y z + 7 y z , 7 x y + 4 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [2 y + y z , 11 x y, -20 x z] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[-12 y + 10 y , -18 y z + 7 y z , 7 x y + 4 y ], 3 2 [2 y + y z , 11 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=4.2MB, alloc=32.3MB, time=0.18 N1 := 89 > GB := Basis(F, plex(op(vars))); 4 2 2 2 2 2 GB := [21 x y + 10 x y, 7 x y + 4 y , 9 x y z + 2 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=26.7MB, alloc=32.3MB, time=0.55 N2 := 59 #save(Problem, "format.txt"); > 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 2 H := [-12 y + 10 y , -18 y z + 7 y z , 7 x y + 4 y , 2 y + y z , 11 x y, -20 x z] > J:=[op(GB),op(G)]; 4 2 2 2 2 2 3 2 J := [21 x y + 10 x y, 7 x y + 4 y , 9 x y z + 2 y z , 2 y + y z , 11 x y, -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, 11, 16, 3, 2, 3, 2, 1/2, 5/6, 1/2, 3/14, 9/14, 2/7, 6, 13, 19, 5, 4, 3, 2, 5/6, 5/6, 1/2, 3/7, 9/14, 2/7, -2, -3, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=37.4MB, alloc=32.3MB, time=0.72 |\^/| 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(); 1428319937 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 2 F := [-12 y + 10 y , -18 y z + 7 y z , 7 x y + 4 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [2 y + y z , 11 x y, -20 x z] > Problem := [F,G]; 3 2 2 2 2 2 Problem := [[-12 y + 10 y , -18 y z + 7 y z , 7 x y + 4 y ], 3 2 [2 y + y z , 11 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=4.2MB, alloc=32.3MB, time=0.18 N1 := 89 > GB := Basis(F, plex(op(vars))); 4 2 2 2 2 2 GB := [21 x y + 10 x y, 7 x y + 4 y , 9 x y z + 2 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=26.7MB, alloc=32.3MB, time=0.55 N2 := 59 #save(Problem, "format.txt"); > 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 2 H := [-12 y + 10 y , -18 y z + 7 y z , 7 x y + 4 y , 2 y + y z , 11 x y, -20 x z] > J:=[op(GB),op(G)]; 4 2 2 2 2 2 3 2 J := [21 x y + 10 x y, 7 x y + 4 y , 9 x y z + 2 y z , 2 y + y z , 11 x y, -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, 11, 16, 3, 2, 3, 2, 1/2, 5/6, 1/2, 3/14, 9/14, 2/7, 6, 13, 19, 5, 4, 3, 2, 5/6, 5/6, 1/2, 3/7, 9/14, 2/7, -2, -3, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=37.5MB, alloc=32.3MB, time=0.71 |\^/| 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(); 1428319938 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 F := [-14 z - 6 x z, 15 x - 11 x y , 18 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 G := [-20 x y - 14 y , -2 x y + x z, -9 z - 15] > Problem := [F,G]; 3 3 2 Problem := [[-14 z - 6 x z, 15 x - 11 x y , 18 y z], 2 3 2 3 [-20 x y - 14 y , -2 x y + x z, -9 z - 15]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.51 memory used=48.0MB, alloc=32.3MB, time=0.86 memory used=69.7MB, alloc=56.3MB, time=1.27 memory used=111.6MB, alloc=84.3MB, time=2.12 N1 := 947 > GB := Basis(F, plex(op(vars))); 3 2 3 3 GB := [-15 x + 11 x y , x z, y z, 7 z + 3 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=168.7MB, alloc=84.3MB, time=3.41 memory used=231.6MB, alloc=108.3MB, time=4.58 N2 := 947 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 3 2 2 3 2 H := [-14 z - 6 x z, 15 x - 11 x y , 18 y z, -20 x y - 14 y , -2 x y + x z, 3 -9 z - 15] > J:=[op(GB),op(G)]; 3 2 3 3 2 3 J := [-15 x + 11 x y , x z, y z, 7 z + 3 x z, -20 x y - 14 y , 2 3 -2 x y + x z, -9 z - 15] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 17, 3, 3, 3, 3, 2/3, 2/3, 2/3, 6/13, 5/13, 5/13, 7, 14, 21, 4, 3, 3, 3, 5/7, 4/7, 5/7, 1/2, 5/14, 3/7, -2, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=265.0MB, alloc=108.3MB, time=5.61 |\^/| 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(); 1428319945 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 F := [12 x y z - z , 9 y z + 4 x, -17 x y - 2 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [-2 x y - 20, -x y z - 19 y , -4 x z - 7 x z ] > Problem := [F,G]; 2 Problem := [[12 x y z - z , 9 y z + 4 x, -17 x y - 2 y z], 2 3 2 2 [-2 x y - 20, -x y z - 19 y , -4 x z - 7 x z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.80 memory used=67.6MB, alloc=32.3MB, time=1.13 memory used=85.9MB, alloc=56.3MB, time=1.45 memory used=122.8MB, alloc=60.3MB, time=2.07 memory used=157.8MB, alloc=60.3MB, time=2.62 memory used=191.1MB, alloc=84.3MB, time=3.16 memory used=244.3MB, alloc=84.3MB, time=4.00 memory used=295.5MB, alloc=108.3MB, time=4.85 memory used=371.0MB, alloc=140.3MB, time=6.28 memory used=462.1MB, alloc=164.3MB, time=8.08 memory used=567.0MB, alloc=188.3MB, time=10.06 memory used=690.8MB, alloc=212.3MB, time=12.38 memory used=842.4MB, alloc=236.3MB, time=14.91 memory used=986.3MB, alloc=516.3MB, time=17.65 memory used=1144.4MB, alloc=540.3MB, time=20.80 memory used=1308.1MB, alloc=564.3MB, time=25.21 memory used=1464.7MB, alloc=588.3MB, time=30.64 memory used=1630.9MB, alloc=612.3MB, time=36.83 memory used=1809.8MB, alloc=636.3MB, time=43.74 memory used=2001.9MB, alloc=660.3MB, time=51.38 memory used=2204.2MB, alloc=684.3MB, time=60.34 memory used=2429.3MB, alloc=708.3MB, time=70.33 memory used=2678.3MB, alloc=732.3MB, time=81.47 memory used=2951.2MB, alloc=756.3MB, time=94.16 memory used=3248.1MB, alloc=780.3MB, time=107.83 memory used=3569.0MB, alloc=780.3MB, time=122.66 memory used=3889.7MB, alloc=804.3MB, time=137.78 memory used=4234.4MB, alloc=804.3MB, time=153.03 memory used=4579.2MB, alloc=804.3MB, time=167.37 memory used=4923.7MB, alloc=804.3MB, time=181.28 memory used=5268.0MB, alloc=828.3MB, time=195.15 memory used=5636.5MB, alloc=828.3MB, time=209.95 memory used=6004.6MB, alloc=852.3MB, time=225.78 memory used=6396.5MB, alloc=852.3MB, time=242.65 |\^/| 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(); 1428320245 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-11 x y + 8 x y, 6 x y - 18 y, 13 y z + 3 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-11 y z , 18 z + 20 x z, 15 z - 2 y] > Problem := [F,G]; 2 2 Problem := [[-11 x y + 8 x y, 6 x y - 18 y, 13 y z + 3 y], 2 3 2 [-11 y z , 18 z + 20 x z, 15 z - 2 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.9MB, alloc=32.3MB, time=0.52 memory used=48.9MB, alloc=32.3MB, time=0.95 N1 := 437 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x y - 3 y, 11 y - 8 y, 13 y z + 3 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=68.2MB, alloc=32.3MB, time=1.37 memory used=86.8MB, alloc=56.3MB, time=1.68 N2 := 437 #save(Problem, "format.txt"); > if (GB=[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 := [-11 x y + 8 x y, 6 x y - 18 y, 13 y z + 3 y, -11 y z , 18 z + 20 x z, 2 15 z - 2 y] > J:=[op(GB),op(G)]; 2 2 2 3 J := [x y - 3 y, 11 y - 8 y, 13 y z + 3 y, -11 y z , 18 z + 20 x z, 2 15 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, 12, 16, 3, 1, 2, 3, 1/2, 5/6, 2/3, 4/13, 8/13, 5/13, 6, 11, 15, 3, 1, 2, 3, 1/3, 5/6, 2/3, 2/13, 8/13, 5/13, 1, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=119.6MB, alloc=56.3MB, 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(); 1428320248 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [-3 x z , -16 x + 9 y z, -5 x y + 10 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [6 x z + 11 x z, 8 x z - 19 y , 15 y z - 5 x] > Problem := [F,G]; 2 3 2 2 Problem := [[-3 x z , -16 x + 9 y z, -5 x y + 10 y z], 2 2 2 [6 x z + 11 x z, 8 x z - 19 y , 15 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=0.18 memory used=26.8MB, alloc=32.3MB, time=0.53 memory used=47.7MB, alloc=32.3MB, time=0.86 memory used=67.3MB, alloc=56.3MB, time=1.21 memory used=107.5MB, alloc=60.3MB, time=1.86 memory used=144.6MB, alloc=84.3MB, time=2.47 memory used=204.1MB, alloc=92.3MB, time=3.46 memory used=260.9MB, alloc=116.3MB, time=4.45 memory used=338.6MB, alloc=116.3MB, time=5.79 memory used=416.8MB, alloc=140.3MB, time=7.21 memory used=512.5MB, alloc=164.3MB, time=8.93 memory used=629.5MB, alloc=188.3MB, time=10.94 memory used=787.2MB, alloc=188.3MB, time=12.85 memory used=901.0MB, alloc=468.3MB, time=15.04 memory used=1037.7MB, alloc=492.3MB, time=17.68 memory used=1189.6MB, alloc=516.3MB, time=20.54 memory used=1382.9MB, alloc=540.3MB, time=23.05 memory used=1550.7MB, alloc=564.3MB, time=28.16 memory used=1719.1MB, alloc=588.3MB, time=33.96 memory used=1896.5MB, alloc=612.3MB, time=40.53 memory used=2080.4MB, alloc=636.3MB, time=48.37 memory used=2284.5MB, alloc=660.3MB, time=57.35 memory used=2512.6MB, alloc=684.3MB, time=67.21 memory used=2764.6MB, alloc=708.3MB, time=78.21 memory used=3040.5MB, alloc=732.3MB, time=90.14 memory used=3340.5MB, alloc=732.3MB, time=102.96 memory used=3640.3MB, alloc=732.3MB, time=115.71 memory used=3940.1MB, alloc=756.3MB, time=128.63 memory used=4263.9MB, alloc=756.3MB, time=142.57 memory used=4587.6MB, alloc=756.3MB, time=156.58 memory used=4911.5MB, alloc=780.3MB, time=170.93 memory used=5259.1MB, alloc=780.3MB, time=185.79 memory used=5606.7MB, alloc=804.3MB, time=200.53 memory used=5978.2MB, alloc=828.3MB, time=216.40 N1 := 12523 > GB := Basis(F, plex(op(vars))); 5 3 3 4 3 2 2 GB := [x , 9 x y - 32 x , -x y + 2 x z, -x y + 2 y z, z x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=6379.7MB, alloc=828.3MB, time=228.82 memory used=6843.9MB, alloc=852.3MB, time=245.87 |\^/| 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(); 1428320548 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [11 z + 5 z, 10 x + 17 y, -z - 15 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [6 x y z + 10 z, -14 z - 16 x, -y - 15 x] > Problem := [F,G]; 3 2 3 2 Problem := [[11 z + 5 z, 10 x + 17 y, -z - 15 x ], 3 2 [6 x y z + 10 z, -14 z - 16 x, -y - 15 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.80 memory used=71.0MB, alloc=32.3MB, time=1.23 N1 := 447 > GB := Basis(F, plex(op(vars))); 6 2 2 2 GB := [11979 x + 5 x , 10 x + 17 y, -33 x + z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=119.3MB, alloc=68.3MB, time=2.16 N2 := 495 #save(Problem, "format.txt"); > 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 := [11 z + 5 z, 10 x + 17 y, -z - 15 x , 6 x y z + 10 z, -14 z - 16 x, 2 -y - 15 x] > J:=[op(GB),op(G)]; 6 2 2 2 3 J := [11979 x + 5 x , 10 x + 17 y, -33 x + z, 6 x y z + 10 z, -14 z - 16 x, 2 -y - 15 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 16, 3, 2, 2, 3, 5/6, 1/2, 2/3, 5/12, 1/4, 1/2, 6, 12, 18, 6, 6, 2, 3, 1, 1/2, 1/2, 7/12, 1/4, 1/3, 0, -2, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=162.3MB, alloc=68.3MB, time=2.95 |\^/| 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(); 1428320554 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [-2 z + 12 x z, -14 x y + 18 x z , -11 x z - 14 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 G := [-x z + 5 y z, -10, -11 x - y] > Problem := [F,G]; 3 2 2 2 2 Problem := [[-2 z + 12 x z, -14 x y + 18 x z , -11 x z - 14 y ], 2 [-x z + 5 y z, -10, -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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.7MB, alloc=32.3MB, time=0.50 memory used=48.2MB, alloc=32.3MB, time=0.81 memory used=70.6MB, alloc=56.3MB, time=1.23 memory used=115.2MB, alloc=60.3MB, time=2.01 memory used=153.6MB, alloc=84.3MB, time=2.82 N1 := 1311 > GB := Basis(F, plex(op(vars))); 2 2 4 2 3 2 2 2 GB := [11 x y + 18 y , 77 y + 972 y , 11 x z + 18 x z, 33 x z + 7 y z, 2 2 3 11 z x + 14 y , z - 6 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=206.9MB, alloc=84.3MB, time=4.49 memory used=262.3MB, alloc=84.3MB, time=5.43 N2 := 631 #save(Problem, "format.txt"); > 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 := [-2 z + 12 x z, -14 x y + 18 x z , -11 x z - 14 y , -x z + 5 y z, -10, -11 x - y] > J:=[op(GB),op(G)]; 2 2 4 2 3 2 2 2 J := [11 x y + 18 y , 77 y + 972 y , 11 x z + 18 x z, 33 x z + 7 y z, 2 2 3 2 11 z x + 14 y , z - 6 x z, -x z + 5 y z, -10, -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, 13, 13, 3, 1, 2, 3, 5/6, 2/3, 2/3, 6/11, 4/11, 6/11, 9, 18, 24, 4, 3, 4, 3, 7/9, 2/3, 5/9, 8/17, 8/17, 9/17, -5, -11, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=321.9MB, alloc=84.3MB, time=6.71 |\^/| 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(); 1428320568 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [8 x + 2 x, 18 x z - 11 z , -9 x - 12 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [x y z + 8 x z , -3 x, -16 x z - 17 z] > Problem := [F,G]; 2 2 3 Problem := [[8 x + 2 x, 18 x z - 11 z , -9 x - 12 z], 2 2 [x y z + 8 x z , -3 x, -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=0.17 memory used=26.7MB, alloc=32.3MB, time=0.54 memory used=48.5MB, alloc=56.3MB, time=0.93 N1 := 673 > GB := Basis(F, plex(op(vars))); GB := [x, z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); 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 2 3 2 H := [8 x + 2 x, 18 x z - 11 z , -9 x - 12 z, x y z + 8 x z , -3 x, 2 -16 x z - 17 z] > J:=[op(GB),op(G)]; 2 2 J := [x, z, x y z + 8 x z , -3 x, -16 x 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, 11, 13, 3, 2, 1, 3, 1, 1/6, 2/3, 2/3, 1/12, 7/12, 5, 8, 9, 3, 1, 1, 2, 4/5, 1/5, 3/5, 5/8, 1/8, 5/8, 3, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=82.2MB, alloc=56.3MB, time=1.67 |\^/| 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(); 1428320571 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-14 y z + 11 y, -15 x z - 2 x, 13 x y - 17] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-16 y z - 6 x, -15 z , -20 x y - 17 y] > Problem := [F,G]; 2 2 2 Problem := [[-14 y z + 11 y, -15 x z - 2 x, 13 x y - 17], 2 3 2 [-16 y z - 6 x, -15 z , -20 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=26.4MB, alloc=32.3MB, time=0.50 memory used=48.9MB, alloc=32.3MB, time=0.88 memory used=69.3MB, alloc=56.3MB, time=1.27 memory used=109.7MB, alloc=84.3MB, time=2.16 N1 := 1091 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 63 #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 H := [-14 y z + 11 y, -15 x z - 2 x, 13 y x - 17, -16 y z - 6 x, -15 z , 2 -20 x y - 17 y] > J:=[op(GB),op(G)]; 2 3 2 J := [1, -16 y z - 6 x, -15 z , -20 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, 12, 18, 3, 2, 2, 3, 2/3, 2/3, 2/3, 5/12, 1/2, 1/3, 4, 6, 9, 3, 1, 2, 3, 1/2, 1/2, 1/2, 2/7, 3/7, 2/7, 6, 9, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=146.9MB, alloc=84.3MB, time=3.18 |\^/| 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(); 1428320576 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [8 z - 17 z, -20 y z - 17 y, -19 x z + 19 x y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [19 y + 8 x y, -x y z - 14 x z , -6 x z + 10 x] > Problem := [F,G]; 3 2 2 2 Problem := [[8 z - 17 z, -20 y z - 17 y, -19 x z + 19 x y ], 3 2 [19 y + 8 x y, -x y z - 14 x z , -6 x z + 10 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.48 memory used=47.0MB, alloc=32.3MB, time=0.78 memory used=66.9MB, alloc=56.3MB, time=1.09 memory used=106.0MB, alloc=60.3MB, time=1.68 memory used=140.3MB, alloc=84.3MB, time=2.21 memory used=195.5MB, alloc=92.3MB, time=3.08 memory used=248.1MB, alloc=116.3MB, time=3.91 memory used=324.9MB, alloc=140.3MB, time=5.25 memory used=419.4MB, alloc=164.3MB, time=6.93 memory used=525.0MB, alloc=188.3MB, time=8.82 memory used=642.3MB, alloc=212.3MB, time=10.93 memory used=765.6MB, alloc=492.3MB, time=13.22 memory used=900.9MB, alloc=516.3MB, time=15.71 memory used=1045.5MB, alloc=540.3MB, time=18.47 memory used=1199.9MB, alloc=564.3MB, time=21.48 memory used=1354.4MB, alloc=588.3MB, time=25.35 memory used=1498.4MB, alloc=612.3MB, time=30.18 memory used=1651.4MB, alloc=636.3MB, time=35.75 memory used=1816.1MB, alloc=660.3MB, time=41.59 memory used=1994.8MB, alloc=684.3MB, time=48.35 memory used=2187.6MB, alloc=708.3MB, time=56.02 memory used=2394.6MB, alloc=732.3MB, time=64.42 memory used=2616.4MB, alloc=756.3MB, time=73.57 memory used=2851.7MB, alloc=780.3MB, time=83.68 memory used=3104.1MB, alloc=804.3MB, time=94.90 memory used=3380.3MB, alloc=828.3MB, time=107.16 memory used=3680.6MB, alloc=852.3MB, time=120.35 memory used=4004.8MB, alloc=876.3MB, time=134.98 memory used=4352.9MB, alloc=900.3MB, time=150.59 memory used=4725.0MB, alloc=924.3MB, time=167.09 memory used=5121.1MB, alloc=948.3MB, time=184.61 memory used=5541.0MB, alloc=948.3MB, time=202.80 memory used=5960.9MB, alloc=948.3MB, time=221.15 memory used=6380.7MB, alloc=948.3MB, time=239.22 memory used=6800.5MB, alloc=972.3MB, time=258.12 |\^/| 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(); 1428320876 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [4 x z + 16 y z, 9 y z + 6 x y, -4 x z + 16 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-17 x z + 7 x y z, 20 y z + 15 z , 4 x y - 17 y] > Problem := [F,G]; 2 2 2 2 Problem := [[4 x z + 16 y z, 9 y z + 6 x y, -4 x z + 16 y z], 2 2 [-17 x z + 7 x y z, 20 y z + 15 z , 4 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=26.1MB, alloc=32.3MB, time=0.50 memory used=47.7MB, alloc=32.3MB, time=0.83 memory used=67.9MB, alloc=56.3MB, time=1.17 memory used=111.7MB, alloc=60.3MB, time=2.04 memory used=151.8MB, alloc=84.3MB, time=2.82 memory used=208.2MB, alloc=108.3MB, time=4.05 memory used=276.9MB, alloc=132.3MB, time=6.54 N1 := 2135 > GB := Basis(F, plex(op(vars))); GB := [ 6 3 2 4 3 2 5 2 3 x y + 32 x y, -x y + 4 x y , x y + x z, -x z + 4 y z, -x y + 4 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=366.9MB, alloc=132.3MB, time=9.71 memory used=465.9MB, alloc=164.3MB, time=11.56 N2 := 1037 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [4 x z + 16 y z, 9 y z + 6 x y, -4 x z + 16 y z, -17 x z + 7 x y z, 2 20 y z + 15 z , 4 x y - 17 y] > J:=[op(GB),op(G)]; 6 3 2 4 3 2 J := [3 x y + 32 x y, -x y + 4 x y , x y + x z, -x z + 4 y z, 5 2 2 2 -x y + 4 x z , -17 x z + 7 x y z, 20 y z + 15 z , 4 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, 16, 16, 3, 2, 2, 2, 5/6, 1, 5/6, 1/2, 2/3, 3/4, 8, 20, 32, 7, 6, 2, 2, 7/8, 1, 5/8, 3/4, 11/16, 1/2, -4, -16, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=498.0MB, alloc=164.3MB, time=12.72 |\^/| 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(); 1428320894 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [2 x z + 17 x, 19 x y z - 16 x z, 14 y z - 4] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 G := [19 x y + 3 x z , -20 x - 6 x y, 20 x - 19] > Problem := [F,G]; 2 2 Problem := [[2 x z + 17 x, 19 x y z - 16 x z, 14 y z - 4], 2 2 3 3 [19 x y + 3 x z , -20 x - 6 x y, 20 x - 19]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.51 memory used=47.9MB, alloc=32.3MB, time=0.84 memory used=68.6MB, alloc=32.3MB, time=1.15 memory used=88.9MB, alloc=56.3MB, time=1.53 memory used=131.0MB, alloc=60.3MB, time=2.32 N1 := 819 > GB := Basis(F, plex(op(vars))); 2 GB := [x, 7 z y - 2] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=167.3MB, alloc=60.3MB, time=3.34 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 2 2 H := [2 x z + 17 x, 19 x y z - 16 x z, 14 y z - 4, 19 x y + 3 x z , 3 3 -20 x - 6 x y, 20 x - 19] > J:=[op(GB),op(G)]; 2 2 2 3 3 J := [x, 7 z y - 2, 19 x y + 3 x z , -20 x - 6 x y, 20 x - 19] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 18, 3, 3, 2, 2, 5/6, 2/3, 2/3, 3/4, 1/3, 5/12, 5, 9, 13, 3, 3, 2, 2, 4/5, 3/5, 2/5, 2/3, 1/3, 2/9, 4, 5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=194.1MB, alloc=60.3MB, time=3.79 |\^/| 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(); 1428320899 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [10 x y + 15 y z, -7 y z - 19 y z , 5 x z - 14 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 G := [6 x + 8 x, 14 x, -2 x y z + 19 x z] > Problem := [F,G]; 2 2 2 2 Problem := [[10 x y + 15 y z, -7 y z - 19 y z , 5 x z - 14 x y], 3 [6 x + 8 x, 14 x, -2 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=0.17 memory used=26.0MB, alloc=32.3MB, time=0.45 memory used=48.6MB, alloc=32.3MB, time=0.83 memory used=68.5MB, alloc=56.3MB, time=1.21 memory used=108.3MB, alloc=84.3MB, time=2.03 memory used=162.6MB, alloc=84.3MB, time=3.81 N1 := 1349 > GB := Basis(F, plex(op(vars))); 6 4 5 2 2 2 GB := [5 x y - 57 x y, -10 x y + 63 x y , 2 x y + 3 y z, 5 x z - 14 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=214.5MB, alloc=84.3MB, time=4.70 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 H := [10 x y + 15 y z, -7 y z - 19 y z , 5 x z - 14 x y, 6 x + 8 x, 14 x, -2 x y z + 19 x z] > J:=[op(GB),op(G)]; 6 4 5 2 2 2 J := [5 x y - 57 x y, -10 x y + 63 x y , 2 x y + 3 y z, 5 x z - 14 x y, 3 6 x + 8 x, 14 x, -2 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, 13, 16, 3, 3, 2, 2, 5/6, 2/3, 2/3, 2/3, 1/2, 1/2, 7, 15, 26, 7, 6, 2, 2, 1, 5/7, 3/7, 6/7, 4/7, 2/7, -2, -10, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=225.1MB, alloc=84.3MB, time=4.98 |\^/| 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(); 1428320905 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-7 x y + 20 x z, 2 y z + 12 z , 10 y z - 7 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [-4 y z + x, -x z + x z , -y + 9] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-7 x y + 20 x z, 2 y z + 12 z , 10 y z - 7 z ], 2 2 3 [-4 y z + x, -x z + x z , -y + 9]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.50 memory used=47.6MB, alloc=32.3MB, time=0.83 memory used=67.8MB, alloc=32.3MB, time=1.15 memory used=87.4MB, alloc=56.3MB, time=1.47 memory used=126.8MB, alloc=60.3MB, time=2.11 memory used=162.4MB, alloc=84.3MB, time=2.68 memory used=218.2MB, alloc=84.3MB, time=3.64 memory used=272.0MB, alloc=108.3MB, time=4.64 memory used=344.9MB, alloc=140.3MB, time=6.01 memory used=432.4MB, alloc=164.3MB, time=7.60 memory used=532.7MB, alloc=188.3MB, time=9.52 memory used=640.8MB, alloc=212.3MB, time=12.58 memory used=756.7MB, alloc=236.3MB, time=16.45 memory used=881.3MB, alloc=260.3MB, time=21.58 memory used=1028.9MB, alloc=284.3MB, time=27.66 memory used=1200.5MB, alloc=284.3MB, time=34.80 memory used=1372.1MB, alloc=308.3MB, time=41.78 memory used=1567.6MB, alloc=308.3MB, time=49.26 memory used=1763.1MB, alloc=332.3MB, time=56.62 memory used=1982.7MB, alloc=332.3MB, time=64.56 N1 := 7017 > GB := Basis(F, plex(op(vars))); 4 2 2 2 GB := [x y , -7 x y + 20 x z, z y , z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2154.1MB, alloc=332.3MB, time=69.04 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)]; 2 2 2 2 2 H := [-7 x y + 20 x z, 2 y z + 12 z , 10 y z - 7 z , -4 z y + x, 2 2 3 -x z + x z , -y + 9] > J:=[op(GB),op(G)]; 4 2 2 2 2 2 3 J := [x y , -7 x y + 20 x z, z y , z , -4 z y + x, -x z + x z , -y + 9] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 17, 3, 2, 3, 2, 1/2, 5/6, 5/6, 5/12, 5/12, 2/3, 7, 14, 21, 5, 2, 4, 2, 4/7, 5/7, 5/7, 3/7, 5/14, 3/7, -1, -4, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2177.0MB, alloc=588.3MB, time=69.65 |\^/| 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(); 1428320982 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [5 y + 9 y , 7 z - 3 z, 5 x y + 8] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-17 x - 3, -7 y z - 2 z, -11 x y + 11 x z ] > Problem := [F,G]; 3 2 2 2 Problem := [[5 y + 9 y , 7 z - 3 z, 5 x y + 8], 3 2 2 2 [-17 x - 3, -7 y z - 2 z, -11 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=0.17 memory used=25.9MB, alloc=32.3MB, time=0.45 memory used=47.4MB, alloc=32.3MB, time=0.73 memory used=67.7MB, alloc=56.3MB, time=1.04 memory used=111.7MB, alloc=60.3MB, time=1.80 memory used=151.0MB, alloc=84.3MB, time=2.45 memory used=207.5MB, alloc=108.3MB, time=3.47 memory used=277.6MB, alloc=132.3MB, time=5.42 memory used=361.7MB, alloc=132.3MB, time=8.32 memory used=446.1MB, alloc=156.3MB, time=11.32 N1 := 2701 > GB := Basis(F, plex(op(vars))); 2 2 GB := [9 x - 8, 5 y + 9, 7 z - 3 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=503.3MB, alloc=156.3MB, time=12.34 memory used=628.5MB, alloc=188.3MB, time=15.54 N2 := 1537 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 2 H := [5 y + 9 y , 7 z - 3 z, 5 y x + 8, -17 x - 3, -7 y z - 2 z, 2 2 -11 x y + 11 x z ] > J:=[op(GB),op(G)]; 2 2 3 2 J := [9 x - 8, 5 y + 9, 7 z - 3 z, -17 x - 3, -7 y z - 2 z, 2 2 -11 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, 10, 17, 3, 3, 3, 2, 1/2, 2/3, 1/2, 1/3, 5/12, 5/12, 6, 9, 14, 3, 3, 1, 2, 1/2, 1/2, 1/2, 1/3, 1/4, 5/12, 1, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=660.9MB, alloc=188.3MB, time=16.72 |\^/| 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(); 1428321000 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-3 y - 7 z , -14 y z + 8 z, 13 x y - 7 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-8 x z - 2 x y, 10 x + 6 y z , -14 x y z + 17 y] > Problem := [F,G]; 3 2 2 Problem := [[-3 y - 7 z , -14 y z + 8 z, 13 x y - 7 y z], 2 3 2 [-8 x z - 2 x y, 10 x + 6 y z , -14 x y z + 17 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.49 memory used=47.8MB, alloc=32.3MB, time=0.81 memory used=67.9MB, alloc=56.3MB, time=1.14 memory used=107.0MB, alloc=60.3MB, time=1.80 memory used=144.2MB, alloc=84.3MB, time=2.43 memory used=202.3MB, alloc=84.3MB, time=3.41 memory used=259.2MB, alloc=116.3MB, time=4.38 memory used=336.1MB, alloc=116.3MB, time=5.69 memory used=409.9MB, alloc=140.3MB, time=6.99 memory used=505.1MB, alloc=164.3MB, time=8.66 memory used=592.3MB, alloc=420.3MB, time=10.27 memory used=705.2MB, alloc=444.3MB, time=12.50 memory used=828.8MB, alloc=468.3MB, time=14.90 memory used=968.4MB, alloc=492.3MB, time=17.61 memory used=1123.6MB, alloc=516.3MB, time=20.89 memory used=1287.8MB, alloc=540.3MB, time=24.36 memory used=1461.5MB, alloc=564.3MB, time=27.94 memory used=1651.5MB, alloc=588.3MB, time=31.63 memory used=1828.4MB, alloc=612.3MB, time=37.76 memory used=2008.0MB, alloc=636.3MB, time=44.40 memory used=2197.0MB, alloc=660.3MB, time=51.70 memory used=2398.4MB, alloc=684.3MB, time=59.84 memory used=2611.2MB, alloc=708.3MB, time=68.95 memory used=2833.7MB, alloc=732.3MB, time=79.03 memory used=3080.2MB, alloc=756.3MB, time=89.84 memory used=3350.6MB, alloc=780.3MB, time=101.25 memory used=3644.9MB, alloc=804.3MB, time=113.52 memory used=3963.1MB, alloc=828.3MB, time=126.58 memory used=4305.4MB, alloc=852.3MB, time=141.12 memory used=4671.5MB, alloc=876.3MB, time=156.47 memory used=5061.6MB, alloc=876.3MB, time=173.33 memory used=5451.7MB, alloc=876.3MB, time=189.81 memory used=5841.7MB, alloc=876.3MB, time=206.58 memory used=6231.6MB, alloc=900.3MB, time=222.59 memory used=6645.5MB, alloc=900.3MB, time=239.81 memory used=7059.4MB, alloc=900.3MB, time=256.87 |\^/| 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(); 1428321300 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 F := [2 x z - 6 y z, 12 x y z + 3 x z , -16 y + 16 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-12 y z - 10 x, 16 x y z + 7 x z, -15 y + 12 z ] > Problem := [F,G]; 2 3 Problem := [[2 x z - 6 y z, 12 x y z + 3 x z , -16 y + 16 x z], 2 2 [-12 y z - 10 x, 16 x y z + 7 x z, -15 y + 12 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=47.6MB, alloc=32.3MB, time=0.78 memory used=67.5MB, alloc=32.3MB, time=1.07 memory used=86.7MB, alloc=56.3MB, time=1.37 memory used=126.0MB, alloc=60.3MB, time=1.95 memory used=163.5MB, alloc=84.3MB, time=2.57 memory used=223.3MB, alloc=108.3MB, time=3.64 memory used=299.7MB, alloc=140.3MB, time=5.02 memory used=391.3MB, alloc=164.3MB, time=6.64 memory used=495.3MB, alloc=188.3MB, time=8.82 memory used=603.8MB, alloc=212.3MB, time=11.89 memory used=720.2MB, alloc=236.3MB, time=16.15 memory used=856.7MB, alloc=260.3MB, time=21.31 memory used=1017.2MB, alloc=260.3MB, time=27.32 memory used=1177.8MB, alloc=284.3MB, time=33.36 memory used=1362.2MB, alloc=284.3MB, time=40.28 memory used=1546.9MB, alloc=308.3MB, time=47.12 N1 := 6001 > GB := Basis(F, plex(op(vars))); 2 3 3 3 4 3 3 GB := [x y + 36 x y , -x y + 3 y , -y + z x, -y + 3 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1672.3MB, alloc=308.3MB, time=49.85 memory used=1906.3MB, alloc=564.3MB, time=53.94 memory used=2121.5MB, alloc=588.3MB, time=57.88 memory used=2339.4MB, alloc=612.3MB, time=64.52 memory used=2548.0MB, alloc=636.3MB, time=72.99 memory used=2776.3MB, alloc=660.3MB, time=82.43 memory used=3028.5MB, alloc=684.3MB, time=92.82 memory used=3304.8MB, alloc=708.3MB, time=104.12 memory used=3605.1MB, alloc=732.3MB, time=116.32 N2 := 7411 #save(Problem, "format.txt"); > if (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 := [2 x z - 6 y z, 12 x y z + 3 x z , -16 y + 16 x z, -12 y z - 10 x, 2 2 16 x y z + 7 x z, -15 y + 12 z ] > J:=[op(GB),op(G)]; 2 3 3 3 4 3 3 J := [x y + 36 x y , -x y + 3 y , -y + z x, -y + 3 y z, -12 y z - 10 x, 2 2 16 x y z + 7 x z, -15 y + 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, 17, 15, 3, 1, 3, 2, 5/6, 1, 1, 7/12, 1/2, 3/4, 7, 17, 22, 5, 2, 4, 2, 5/7, 1, 5/7, 1/2, 5/7, 3/7, 0, -7, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=3847.4MB, alloc=732.3MB, time=125.37 |\^/| 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(); 1428321432 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [19 x y + 3 x , -10 x z + 19 x z, -15 x + 8 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-x y - x y, 20 x - 5 y , 7 x + 14 y ] > Problem := [F,G]; 2 2 2 3 2 Problem := [[19 x y + 3 x , -10 x z + 19 x z, -15 x + 8 y ], 2 2 2 2 2 [-x y - x y, 20 x - 5 y , 7 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=0.17 memory used=26.2MB, alloc=32.3MB, time=0.47 memory used=46.0MB, alloc=32.3MB, time=0.72 memory used=65.7MB, alloc=32.3MB, time=1.01 memory used=85.2MB, alloc=56.3MB, time=1.38 memory used=124.1MB, alloc=80.3MB, time=2.14 N1 := 1115 > GB := Basis(F, plex(op(vars))); 4 2 3 2 2 GB := [95 x + 8 x , -15 x + 8 y , 10 x z - 19 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=180.4MB, alloc=80.3MB, time=3.60 memory used=208.3MB, alloc=84.3MB, time=4.02 N2 := 655 #save(Problem, "format.txt"); > if (GB=[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 := [19 x y + 3 x , -10 x z + 19 x z, -15 x + 8 y , -x y - x y, 2 2 2 2 20 x - 5 y , 7 x + 14 y ] > J:=[op(GB),op(G)]; 4 2 3 2 2 2 2 2 J := [95 x + 8 x , -15 x + 8 y , 10 x z - 19 x z, -x y - x y, 20 x - 5 y , 2 2 7 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, 12, 16, 3, 3, 2, 2, 1, 5/6, 1/6, 3/4, 1/2, 1/6, 6, 11, 17, 4, 4, 2, 2, 1, 2/3, 1/6, 3/4, 5/12, 1/6, 1, -1, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=258.7MB, alloc=84.3MB, time=5.02 |\^/| 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(); 1428321437 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [-7 x y + 16 y z , 10 x + 3 y , -2 x - z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 G := [-3 y + 19 z , 13 z + 2 x, 4 y z - 18 z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[-7 x y + 16 y z , 10 x + 3 y , -2 x - z], 3 3 2 2 2 [-3 y + 19 z , 13 z + 2 x, 4 y z - 18 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.48 memory used=48.0MB, alloc=32.3MB, time=0.79 memory used=69.0MB, alloc=32.3MB, time=1.10 memory used=89.1MB, alloc=56.3MB, time=1.42 memory used=130.0MB, alloc=60.3MB, time=2.06 memory used=170.7MB, alloc=84.3MB, time=2.74 memory used=233.0MB, alloc=84.3MB, time=3.80 memory used=287.8MB, alloc=108.3MB, time=4.75 memory used=356.2MB, alloc=132.3MB, time=6.31 memory used=432.4MB, alloc=156.3MB, time=8.92 memory used=532.6MB, alloc=156.3MB, time=12.18 N1 := 2829 > GB := Basis(F, plex(op(vars))); 6 4 4 2 2 2 2 GB := [64 x - 7 x , 64 x y - 7 x y, 3 y + 10 x , 2 x + z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=614.1MB, alloc=156.3MB, time=13.86 memory used=736.6MB, alloc=188.3MB, time=16.33 N2 := 979 #save(Problem, "format.txt"); > if (GB=[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 := [-7 x y + 16 y z , 3 y + 10 x , -2 x - z, -3 y + 19 z , 13 z + 2 x, 2 2 4 y z - 18 z ] > J:=[op(GB),op(G)]; 6 4 4 2 2 2 2 3 3 J := [64 x - 7 x , 64 x y - 7 x y, 3 y + 10 x , 2 x + z, -3 y + 19 z , 2 2 2 13 z + 2 x, 4 y z - 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, 15, 3, 2, 3, 3, 2/3, 2/3, 5/6, 1/3, 5/12, 1/2, 7, 13, 23, 6, 6, 3, 3, 5/7, 4/7, 4/7, 1/2, 5/14, 5/14, 0, -8, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=739.4MB, alloc=188.3MB, time=16.40 |\^/| 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(); 1428321454 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-8 x z - 4 y z , -13 x z - 9 y z, -x - 6 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [-5 z, 12 x z + 4 x , 19 x - 13 x] > Problem := [F,G]; 2 2 2 2 Problem := [[-8 x z - 4 y z , -13 x z - 9 y z, -x - 6 y], 2 2 3 [-5 z, 12 x z + 4 x , 19 x - 13 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 N1 := 159 > GB := Basis(F, plex(op(vars))); 2 2 GB := [6 y + x, z x , z x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=27.3MB, alloc=32.3MB, time=0.54 N2 := 99 #save(Problem, "format.txt"); > if (GB=[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 := [-8 x z - 4 y z , -13 x z - 9 y z, -x - 6 y, -5 z, 12 x z + 4 x , 3 19 x - 13 x] > J:=[op(GB),op(G)]; 2 2 2 2 3 J := [6 y + x, z x , z x, -5 z, 12 x z + 4 x , 19 x - 13 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 14, 3, 3, 2, 2, 5/6, 1/2, 2/3, 7/12, 1/4, 1/2, 6, 10, 14, 3, 3, 1, 2, 5/6, 1/6, 2/3, 7/12, 1/12, 1/3, 2, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=38.0MB, alloc=32.3MB, time=0.70 |\^/| 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(); 1428321455 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [-8 x y z + 15 y , 20 y z - 8 y z, -9 x y + 6 y z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [2 x y - y , -5 x y + 10 x z, -20 x + 17 y] > Problem := [F,G]; 3 2 2 2 Problem := [[-8 x y z + 15 y , 20 y z - 8 y z, -9 x y + 6 y z ], 2 2 2 3 [2 x y - y , -5 x y + 10 x z, -20 x + 17 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.45 memory used=47.7MB, alloc=32.3MB, time=0.75 memory used=68.5MB, alloc=32.3MB, time=1.06 memory used=87.9MB, alloc=56.3MB, time=1.34 memory used=130.3MB, alloc=60.3MB, time=2.06 memory used=168.3MB, alloc=84.3MB, time=2.72 memory used=225.7MB, alloc=108.3MB, time=3.71 memory used=302.9MB, alloc=116.3MB, time=5.05 memory used=371.7MB, alloc=140.3MB, time=6.26 memory used=457.2MB, alloc=164.3MB, time=7.79 memory used=554.2MB, alloc=188.3MB, time=10.14 memory used=658.3MB, alloc=212.3MB, time=13.24 memory used=775.4MB, alloc=236.3MB, time=17.14 memory used=906.5MB, alloc=260.3MB, time=22.26 memory used=1061.6MB, alloc=260.3MB, time=28.24 memory used=1216.7MB, alloc=284.3MB, time=34.19 memory used=1395.8MB, alloc=284.3MB, time=41.02 memory used=1574.7MB, alloc=284.3MB, time=47.81 memory used=1753.7MB, alloc=308.3MB, time=54.65 memory used=1956.7MB, alloc=308.3MB, time=62.31 memory used=2159.8MB, alloc=332.3MB, time=69.67 N1 := 7313 > GB := Basis(F, plex(op(vars))); 6 2 2 2 2 4 3 3 GB := [50 x y - 3 x y, 5 x y - 2 x y, -8 x y + 3 y , -5 x y + y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2261.9MB, alloc=332.3MB, time=71.84 N2 := 1657 #save(Problem, "format.txt"); > 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 := [-8 x y z + 15 y , 20 y z - 8 y z, -9 x y + 6 y z , 2 x y - y , 2 3 -5 x y + 10 x z, -20 x + 17 y] > J:=[op(GB),op(G)]; 6 2 2 2 2 4 3 3 J := [50 x y - 3 x y, 5 x y - 2 x y, -8 x y + 3 y , -5 x y + y z, 2 2 2 3 2 x y - y , -5 x y + 10 x z, -20 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, 15, 18, 3, 3, 3, 2, 5/6, 1, 2/3, 1/2, 5/6, 5/12, 7, 16, 29, 7, 6, 3, 1, 1, 1, 2/7, 5/7, 6/7, 1/7, -1, -11, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2441.3MB, alloc=588.3MB, time=76.93 |\^/| 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(); 1428321536 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [4 x z - 18 y z , 4 x z + 6 x y, -3 x y z - 19 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 G := [-7 x - 7 x z , -2 y - 8 y z , 8 x y z - x ] > Problem := [F,G]; 2 2 2 2 Problem := [[4 x z - 18 y z , 4 x z + 6 x y, -3 x y z - 19 y ], 3 2 3 2 2 [-7 x - 7 x z , -2 y - 8 y z , 8 x y z - x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.8MB, alloc=32.3MB, time=0.51 memory used=47.7MB, alloc=32.3MB, time=0.81 memory used=67.2MB, alloc=56.3MB, time=1.13 memory used=107.0MB, alloc=60.3MB, time=1.72 memory used=143.8MB, alloc=84.3MB, time=2.29 memory used=201.0MB, alloc=92.3MB, time=3.18 memory used=257.0MB, alloc=116.3MB, time=4.01 memory used=334.8MB, alloc=116.3MB, time=5.16 memory used=408.7MB, alloc=140.3MB, time=6.32 memory used=485.3MB, alloc=140.3MB, time=7.49 memory used=569.6MB, alloc=420.3MB, time=8.79 memory used=685.8MB, alloc=444.3MB, time=10.61 memory used=827.0MB, alloc=468.3MB, time=12.58 memory used=980.2MB, alloc=492.3MB, time=15.02 memory used=1111.8MB, alloc=516.3MB, time=16.96 memory used=1252.0MB, alloc=516.3MB, time=19.30 memory used=1384.0MB, alloc=540.3MB, time=21.49 memory used=1484.4MB, alloc=540.3MB, time=23.09 memory used=1587.5MB, alloc=540.3MB, time=24.75 memory used=1679.7MB, alloc=564.3MB, time=26.42 memory used=1768.9MB, alloc=564.3MB, time=28.11 memory used=1842.5MB, alloc=564.3MB, time=29.66 memory used=1911.0MB, alloc=564.3MB, time=30.93 memory used=1971.4MB, alloc=564.3MB, time=32.13 memory used=2038.6MB, alloc=564.3MB, time=33.62 memory used=2099.8MB, alloc=564.3MB, time=35.03 memory used=2153.5MB, alloc=588.3MB, time=36.29 memory used=2393.3MB, alloc=612.3MB, time=40.29 memory used=2599.2MB, alloc=636.3MB, time=43.56 memory used=2851.0MB, alloc=660.3MB, time=48.77 memory used=3095.3MB, alloc=684.3MB, time=53.99 memory used=3341.0MB, alloc=708.3MB, time=60.50 memory used=3563.2MB, alloc=732.3MB, time=68.75 memory used=3779.3MB, alloc=756.3MB, time=78.05 memory used=4014.1MB, alloc=780.3MB, time=88.39 memory used=4272.8MB, alloc=804.3MB, time=99.62 memory used=4555.5MB, alloc=828.3MB, time=111.66 memory used=4862.1MB, alloc=852.3MB, time=124.67 memory used=5192.7MB, alloc=876.3MB, time=138.61 memory used=5547.3MB, alloc=900.3MB, time=153.45 N1 := 9055 > GB := Basis(F, plex(op(vars))); 4 3 3 2 3 3 GB := [2187 x y + 54872 x y, 27 x y + 722 x y , 2 x y + 57 y , 3 3 2 3 2 -729 x y + 2888 x z, 3 x y z + 19 y , 243 x y + 27436 y z, 2 2 2 2 x z + 3 x y, -2 x z + 9 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=5953.5MB, alloc=900.3MB, time=166.19 memory used=6233.4MB, alloc=900.3MB, time=171.67 memory used=6443.4MB, alloc=900.3MB, time=175.86 memory used=6640.6MB, alloc=900.3MB, time=180.09 memory used=6798.3MB, alloc=900.3MB, time=183.55 memory used=6945.8MB, alloc=900.3MB, time=186.86 memory used=7121.3MB, alloc=924.3MB, time=190.99 memory used=7293.7MB, alloc=924.3MB, time=194.83 memory used=7419.4MB, alloc=924.3MB, time=197.61 memory used=7538.2MB, alloc=924.3MB, time=200.45 memory used=7649.0MB, alloc=948.3MB, time=203.42 memory used=8130.7MB, alloc=972.3MB, time=212.32 memory used=8588.6MB, alloc=996.3MB, time=220.91 memory used=9025.3MB, alloc=1020.3MB, time=229.23 memory used=9425.5MB, alloc=1044.3MB, time=237.03 memory used=10018.0MB, alloc=1068.3MB, time=248.55 memory used=10623.2MB, alloc=1092.3MB, time=260.01 memory used=11225.7MB, alloc=1116.3MB, time=272.13 memory used=11852.0MB, alloc=1140.3MB, time=283.77 |\^/| 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(); 1428321836 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-12 x + 8 x y z, 17 x y z + 8 x z , 17 y z - 3] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-14 x + 5 z, 8 y z - 8 x, 5 y z + z ] > Problem := [F,G]; 3 2 2 Problem := [[-12 x + 8 x y z, 17 x y z + 8 x z , 17 y z - 3], 2 2 2 [-14 x + 5 z, 8 y z - 8 x, 5 y z + z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.49 memory used=47.3MB, alloc=32.3MB, time=0.79 memory used=67.0MB, alloc=32.3MB, time=1.06 memory used=85.9MB, alloc=56.3MB, time=1.33 memory used=123.4MB, alloc=60.3MB, time=1.87 memory used=158.5MB, alloc=84.3MB, time=2.37 memory used=210.1MB, alloc=84.3MB, time=3.10 memory used=264.6MB, alloc=108.3MB, time=3.94 memory used=340.6MB, alloc=116.3MB, time=5.11 memory used=414.8MB, alloc=140.3MB, time=6.45 memory used=503.7MB, alloc=164.3MB, time=8.02 memory used=606.9MB, alloc=188.3MB, time=9.91 memory used=719.7MB, alloc=468.3MB, time=11.95 memory used=849.6MB, alloc=492.3MB, time=14.25 memory used=987.6MB, alloc=516.3MB, time=17.57 memory used=1123.6MB, alloc=540.3MB, time=21.73 memory used=1270.1MB, alloc=564.3MB, time=26.58 memory used=1427.6MB, alloc=588.3MB, time=32.67 memory used=1602.2MB, alloc=612.3MB, time=39.75 memory used=1800.8MB, alloc=636.3MB, time=47.73 memory used=2023.3MB, alloc=660.3MB, time=55.63 memory used=2269.7MB, alloc=660.3MB, time=63.72 memory used=2516.1MB, alloc=684.3MB, time=72.02 memory used=2786.4MB, alloc=684.3MB, time=80.96 memory used=3056.8MB, alloc=684.3MB, time=89.88 memory used=3327.1MB, alloc=708.3MB, time=98.70 memory used=3621.4MB, alloc=708.3MB, time=108.24 memory used=3915.7MB, alloc=732.3MB, time=117.74 memory used=4234.0MB, alloc=756.3MB, time=128.00 N1 := 10529 > GB := Basis(F, plex(op(vars))); 7 5 5 2 GB := [51 x + x, 6 x + x y, -51 x + 4 x z, 17 z y - 3] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4573.2MB, alloc=756.3MB, time=133.87 memory used=4945.3MB, alloc=780.3MB, time=140.00 memory used=5322.7MB, alloc=804.3MB, time=150.31 memory used=5669.1MB, alloc=828.3MB, time=162.10 memory used=6027.3MB, alloc=852.3MB, time=174.55 memory used=6409.5MB, alloc=876.3MB, time=187.72 memory used=6815.7MB, alloc=900.3MB, time=201.84 memory used=7245.8MB, alloc=924.3MB, time=216.78 memory used=7699.7MB, alloc=948.3MB, time=232.31 N2 := 9969 #save(Problem, "format.txt"); > 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 := [-12 x + 8 x y z, 17 x y z + 8 x z , 17 z y - 3, -14 x + 5 z, 2 2 8 y z - 8 x, 5 y z + z ] > J:=[op(GB),op(G)]; 7 5 5 2 2 J := [51 x + x, 6 x + x y, -51 x + 4 x z, 17 z y - 3, -14 x + 5 z, 2 2 8 y z - 8 x, 5 y z + z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 16, 3, 3, 2, 2, 2/3, 5/6, 1, 1/2, 5/12, 2/3, 7, 14, 27, 7, 7, 2, 2, 5/7, 4/7, 5/7, 4/7, 2/7, 3/7, 1, -11, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=8118.3MB, alloc=948.3MB, time=244.78 |\^/| 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(); 1428322090 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-4 y z - z, 20 z - 15 y, -11 x z + 15 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [4 x z + 16 y, -11 x z + 16 z , 14 x z + 3 y z ] > Problem := [F,G]; 2 2 Problem := [[-4 y z - z, 20 z - 15 y, -11 x z + 15 z], 2 2 2 2 [4 x z + 16 y, -11 x z + 16 z , 14 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.43 memory used=47.6MB, alloc=32.3MB, time=0.67 memory used=67.9MB, alloc=32.3MB, time=0.90 memory used=87.6MB, alloc=56.3MB, time=1.13 memory used=127.3MB, alloc=60.3MB, time=1.62 memory used=166.6MB, alloc=84.3MB, time=2.17 memory used=225.3MB, alloc=84.3MB, time=3.01 memory used=278.0MB, alloc=108.3MB, time=3.74 memory used=348.7MB, alloc=132.3MB, time=4.75 memory used=434.0MB, alloc=164.3MB, time=6.44 memory used=526.0MB, alloc=188.3MB, time=8.90 memory used=632.8MB, alloc=212.3MB, time=12.20 memory used=763.5MB, alloc=212.3MB, time=16.21 memory used=894.3MB, alloc=212.3MB, time=20.17 memory used=1025.2MB, alloc=236.3MB, time=24.02 N1 := 4639 > GB := Basis(F, plex(op(vars))); 2 2 GB := [121 x y + 1200 y, 4 y + y, -11 x y + 20 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1177.3MB, alloc=236.3MB, time=26.59 memory used=1356.4MB, alloc=516.3MB, time=30.41 N2 := 2393 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-4 y z - z, 20 z - 15 y, -11 x z + 15 z, 4 x z + 16 y, -11 x z + 16 z , 2 2 14 x z + 3 y z ] > J:=[op(GB),op(G)]; 2 2 2 J := [121 x y + 1200 y, 4 y + y, -11 x y + 20 z, 4 x z + 16 y, 2 2 2 -11 x z + 16 z , 14 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, 15, 3, 1, 1, 2, 2/3, 2/3, 1, 1/3, 1/3, 5/6, 6, 14, 15, 3, 2, 2, 2, 5/6, 5/6, 2/3, 5/12, 7/12, 1/2, 0, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1463.9MB, alloc=516.3MB, time=33.09 |\^/| 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(); 1428322125 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-6 x z, -7 x y z + 20 x z, 11 x z - 15 x y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 3 G := [8 x y + 4 y z , 15 y z + 9, 18 x + 4 y ] > Problem := [F,G]; 2 2 2 Problem := [[-6 x z, -7 x y z + 20 x z, 11 x z - 15 x y ], 2 2 2 3 3 [8 x y + 4 y z , 15 y z + 9, 18 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=0.15 memory used=26.2MB, alloc=32.3MB, time=0.42 memory used=48.2MB, alloc=32.3MB, time=0.70 memory used=68.6MB, alloc=32.3MB, time=0.92 memory used=89.2MB, alloc=56.3MB, time=1.22 memory used=131.2MB, alloc=60.3MB, time=1.80 memory used=169.6MB, alloc=84.3MB, time=2.37 memory used=226.3MB, alloc=108.3MB, time=3.66 N1 := 1549 > GB := Basis(F, plex(op(vars))); 2 GB := [y x, z x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 211 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [-6 x z, -7 x y z + 20 x z, 11 x z - 15 x y , 8 x y + 4 y z , 2 3 3 15 y z + 9, 18 x + 4 y ] > J:=[op(GB),op(G)]; 2 2 2 2 3 3 J := [y x, z x, 8 x y + 4 y z , 15 y z + 9, 18 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, 15, 18, 3, 3, 3, 2, 5/6, 5/6, 5/6, 7/13, 6/13, 6/13, 5, 11, 14, 3, 3, 3, 2, 4/5, 4/5, 3/5, 2/5, 1/2, 3/10, 4, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=295.0MB, alloc=108.3MB, time=4.91 |\^/| 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(); 1428322130 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [14 z + 20 x, -9 x y + 9 y z, 17 y z - 12 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [10 x + 14 y , 11 x - 6 z , -7 y z + 3 x] > Problem := [F,G]; 2 2 2 2 2 Problem := [[14 z + 20 x, -9 x y + 9 y z, 17 y z - 12 y ], 3 2 3 2 [10 x + 14 y , 11 x - 6 z , -7 y z + 3 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.44 memory used=47.6MB, alloc=32.3MB, time=0.67 memory used=68.4MB, alloc=32.3MB, time=0.91 memory used=87.7MB, alloc=56.3MB, time=1.14 memory used=126.7MB, alloc=60.3MB, time=1.57 memory used=165.3MB, alloc=84.3MB, time=1.99 memory used=217.6MB, alloc=84.3MB, time=2.59 memory used=273.4MB, alloc=116.3MB, time=3.29 memory used=353.3MB, alloc=140.3MB, time=4.37 memory used=449.0MB, alloc=164.3MB, time=5.76 memory used=561.5MB, alloc=188.3MB, time=7.42 memory used=688.3MB, alloc=212.3MB, time=9.24 memory used=821.2MB, alloc=236.3MB, time=11.82 memory used=952.8MB, alloc=260.3MB, time=15.14 memory used=1094.2MB, alloc=284.3MB, time=19.33 memory used=1250.1MB, alloc=308.3MB, time=24.57 memory used=1430.0MB, alloc=332.3MB, time=30.33 memory used=1633.9MB, alloc=332.3MB, time=36.98 memory used=1837.7MB, alloc=356.3MB, time=43.40 memory used=2065.5MB, alloc=356.3MB, time=50.72 memory used=2293.3MB, alloc=380.3MB, time=57.98 memory used=2545.0MB, alloc=404.3MB, time=66.41 N1 := 7771 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 GB := [7 x y + 10 x y, 85 x y + 42 y , -x y + x y z, 7 z + 10 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2714.9MB, alloc=404.3MB, time=70.20 N2 := 2095 #save(Problem, "format.txt"); > if (GB=[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 z + 20 x, -9 x y + 9 y z, 17 y z - 12 y , 10 x + 14 y , 3 2 11 x - 6 z , -7 z y + 3 x] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [7 x y + 10 x y, 85 x y + 42 y , -x y + x y z, 7 z + 10 x, 3 2 3 2 10 x + 14 y , 11 x - 6 z , -7 z 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, 14, 16, 3, 3, 2, 2, 5/6, 2/3, 5/6, 5/12, 1/2, 5/12, 7, 16, 19, 4, 3, 2, 2, 1, 5/7, 4/7, 9/14, 4/7, 2/7, -2, -3, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=3034.3MB, alloc=660.3MB, time=77.05 |\^/| 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(); 1428322210 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [-3 x z - 6 x z, -11 x y - 19, 16 x y + 18 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-14 x + 19 z , -14 x + 14 z, 19 + 8 z] > Problem := [F,G]; 2 2 2 3 Problem := [[-3 x z - 6 x z, -11 x y - 19, 16 x y + 18 y ], 3 2 2 [-14 x + 19 z , -14 x + 14 z, 19 + 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=26.4MB, alloc=32.3MB, time=0.39 memory used=48.3MB, alloc=32.3MB, time=0.70 memory used=68.8MB, alloc=56.3MB, time=0.98 N1 := 671 > GB := Basis(F, plex(op(vars))); 3 2 GB := [704 x + 1539, 9 y + 8 x, z + 2 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=108.3MB, alloc=56.3MB, time=1.57 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 2 3 3 2 H := [-3 x z - 6 x z, -11 x y - 19, 16 x y + 18 y , -14 x + 19 z , 2 -14 x + 14 z, 8 z + 19] > J:=[op(GB),op(G)]; J := [ 3 2 3 2 2 704 x + 1539, 9 y + 8 x, z + 2 z, -14 x + 19 z , -14 x + 14 z, 8 z + 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, 11, 15, 3, 3, 3, 2, 5/6, 1/3, 2/3, 1/2, 1/4, 5/12, 6, 9, 12, 3, 3, 1, 2, 2/3, 1/6, 2/3, 1/3, 1/12, 5/12, 2, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=133.0MB, alloc=56.3MB, 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(); 1428322212 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-5 y z - 15 x y, 15 y z - 19 y, -11 x z + 8 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 G := [16 x + 9 y , -10 z - 4 z, 2 x y + 13 x] > Problem := [F,G]; 2 2 2 2 Problem := [[-5 y z - 15 x y, 15 y z - 19 y, -11 x z + 8 y z], 3 2 3 2 [16 x + 9 y , -10 z - 4 z, 2 x y + 13 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.40 memory used=47.6MB, alloc=32.3MB, time=0.65 memory used=68.0MB, alloc=32.3MB, time=0.89 memory used=88.4MB, alloc=56.3MB, time=1.23 memory used=129.0MB, alloc=60.3MB, time=1.83 memory used=165.6MB, alloc=84.3MB, time=2.38 N1 := 1233 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [45 x y + 19 y, 16200 y - 3971 y, 165 x z - 152 y, -1080 y + 209 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=218.5MB, alloc=84.3MB, time=3.48 memory used=273.7MB, alloc=84.3MB, time=4.08 memory used=330.2MB, alloc=108.3MB, time=4.87 memory used=408.5MB, alloc=140.3MB, time=6.30 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 2 2 2 3 2 H := [-5 y z - 15 x y, 15 y z - 19 y, -11 x z + 8 y z, 16 x + 9 y , 3 2 -10 z - 4 z, 2 x y + 13 x] > J:=[op(GB),op(G)]; 3 2 2 J := [45 x y + 19 y, 16200 y - 3971 y, 165 z x - 152 y, -1080 y + 209 y z, 3 2 3 2 16 x + 9 y , -10 z - 4 z, 2 x 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, 13, 18, 3, 3, 2, 3, 2/3, 5/6, 2/3, 5/12, 7/12, 1/2, 7, 13, 19, 3, 3, 3, 3, 4/7, 6/7, 3/7, 5/14, 9/14, 2/7, 0, -1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=436.9MB, alloc=140.3MB, time=6.94 |\^/| 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(); 1428322220 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [16 y z + 4, 10 x y z - 13 x z , -7 x y - 11 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [-19 x - 6 x, -13 x y - 12 z , 15 x ] > Problem := [F,G]; 2 2 Problem := [[16 y z + 4, 10 x y z - 13 x z , -7 x y - 11 y], 2 2 3 [-19 x - 6 x, -13 x y - 12 z , 15 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.1MB, alloc=32.3MB, time=0.44 memory used=49.1MB, alloc=32.3MB, time=0.72 memory used=69.4MB, alloc=56.3MB, time=1.01 N1 := 719 > GB := Basis(F, plex(op(vars))); 3 GB := [7 x + 11, 40 y + 13, 13 z - 10 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.3MB, alloc=56.3MB, time=1.69 N2 := 281 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [16 y z + 4, 10 x y z - 13 x z , -7 x y - 11 y, -19 x - 6 x, 2 3 -13 x y - 12 z , 15 x ] > J:=[op(GB),op(G)]; 3 2 2 3 J := [7 x + 11, 40 y + 13, 13 z - 10 y, -19 x - 6 x, -13 x y - 12 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, 12, 15, 3, 3, 2, 2, 5/6, 2/3, 1/2, 7/12, 5/12, 1/3, 6, 9, 12, 3, 3, 3, 2, 2/3, 1/2, 1/3, 5/12, 1/4, 1/6, 3, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=134.4MB, alloc=56.3MB, time=2.01 |\^/| 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(); 1428322222 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 F := [6 x y + 5 x y, z + 6 z, 8 x y z - 11 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-18 x y - 9, -11 x z - 7 y z, -19 x z - 15 z] > Problem := [F,G]; 2 3 Problem := [[6 x y + 5 x y, z + 6 z, 8 x y z - 11 y z], 2 2 2 [-18 x y - 9, -11 x z - 7 y z, -19 x z - 15 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=25.9MB, alloc=32.3MB, time=0.39 N1 := 219 > GB := Basis(F, plex(op(vars))); 2 2 3 GB := [6 x y + 5 x y, 8 x y z - 11 y z, 6 y z + 5 y z, z + 6 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=48.5MB, alloc=32.3MB, time=0.70 memory used=68.1MB, alloc=32.3MB, time=0.92 memory used=88.1MB, alloc=56.3MB, time=1.18 N2 := 219 #save(Problem, "format.txt"); > if (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 H := [6 x y + 5 x y, z + 6 z, 8 x y z - 11 y z, -18 x y - 9, 2 2 -11 x z - 7 y z, -19 x z - 15 z] > J:=[op(GB),op(G)]; 2 2 3 2 J := [6 x y + 5 x y, 8 x y z - 11 y z, 6 y z + 5 y z, z + 6 z, -18 x y - 9, 2 2 -11 x z - 7 y z, -19 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, 13, 17, 3, 2, 2, 3, 5/6, 2/3, 2/3, 1/2, 1/2, 2/3, 7, 15, 20, 3, 2, 2, 3, 5/7, 5/7, 5/7, 3/7, 4/7, 5/7, -2, -3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=90.9MB, alloc=56.3MB, time=1.23 |\^/| 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(); 1428322223 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-7 y z - 17 y, -16 x z - 10 x , 17 y z + 18 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-7 x y + 7 x , -7 y z + 18, 5 y z - 13 x z] > Problem := [F,G]; 2 2 2 Problem := [[-7 y z - 17 y, -16 x z - 10 x , 17 y z + 18 x], 2 2 2 [-7 x y + 7 x , -7 y z + 18, 5 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=0.15 memory used=26.3MB, alloc=32.3MB, time=0.38 memory used=47.9MB, alloc=32.3MB, time=0.64 memory used=68.1MB, alloc=32.3MB, time=0.88 memory used=87.7MB, alloc=56.3MB, time=1.16 memory used=129.2MB, alloc=60.3MB, time=1.68 memory used=166.8MB, alloc=84.3MB, time=2.20 memory used=223.0MB, alloc=108.3MB, time=2.99 memory used=294.6MB, alloc=132.3MB, time=4.64 memory used=379.0MB, alloc=132.3MB, time=6.87 N1 := 2553 > GB := Basis(F, plex(op(vars))); 2 2 GB := [126 x - 289 x, 126 x y - 289 y, 1445 y + 2592 x, 18144 x z - 24565 y, 17 z y + 18 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=465.5MB, alloc=132.3MB, time=8.73 memory used=558.2MB, alloc=164.3MB, time=10.12 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 2 2 2 H := [-7 y z - 17 y, -16 x z - 10 x , 17 z y + 18 x, -7 x y + 7 x , 2 -7 y z + 18, 5 y z - 13 x z] > J:=[op(GB),op(G)]; 2 2 J := [126 x - 289 x, 126 x y - 289 y, 1445 y + 2592 x, 18144 z x - 24565 y, 2 2 2 17 z y + 18 x, -7 x y + 7 x , -7 y z + 18, 5 y 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, 14, 16, 3, 2, 2, 2, 2/3, 5/6, 5/6, 1/2, 1/2, 1/2, 8, 18, 18, 3, 2, 2, 1, 7/8, 7/8, 1/2, 9/16, 1/2, 5/16, -4, -2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=642.3MB, alloc=164.3MB, time=11.81 |\^/| 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(); 1428322235 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [10 x + 15 x y z, 2 x z - 14 x , -6 y z - 20 y z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [2 x y - 14 x z , -x z + 18, 17 x z - 5 x z] > Problem := [F,G]; 3 2 2 2 2 Problem := [[10 x + 15 x y z, 2 x z - 14 x , -6 y z - 20 y z ], 2 2 2 [2 x y - 14 x z , -x z + 18, 17 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=0.15 memory used=26.3MB, alloc=32.3MB, time=0.41 memory used=47.5MB, alloc=32.3MB, time=0.66 memory used=67.0MB, alloc=56.3MB, time=0.89 memory used=106.1MB, alloc=60.3MB, time=1.34 memory used=143.4MB, alloc=60.3MB, time=1.78 memory used=178.2MB, alloc=84.3MB, time=2.19 memory used=233.5MB, alloc=84.3MB, time=2.92 memory used=286.7MB, alloc=116.3MB, time=3.59 memory used=360.1MB, alloc=140.3MB, time=4.47 memory used=451.4MB, alloc=140.3MB, time=5.60 memory used=543.1MB, alloc=164.3MB, time=6.93 memory used=646.6MB, alloc=188.3MB, time=8.52 memory used=761.7MB, alloc=212.3MB, time=10.16 memory used=868.4MB, alloc=492.3MB, time=11.78 memory used=1006.2MB, alloc=516.3MB, time=13.75 memory used=1153.4MB, alloc=540.3MB, time=15.92 memory used=1306.9MB, alloc=564.3MB, time=18.36 memory used=1468.3MB, alloc=588.3MB, time=20.89 memory used=1636.8MB, alloc=612.3MB, time=23.59 memory used=1810.2MB, alloc=636.3MB, time=26.44 memory used=1987.2MB, alloc=660.3MB, time=29.37 memory used=2169.5MB, alloc=684.3MB, time=32.36 memory used=2356.7MB, alloc=708.3MB, time=35.50 memory used=2548.7MB, alloc=732.3MB, time=38.94 memory used=2728.8MB, alloc=756.3MB, time=43.20 memory used=2899.9MB, alloc=780.3MB, time=47.98 memory used=3078.7MB, alloc=804.3MB, time=53.54 memory used=3268.5MB, alloc=828.3MB, time=59.62 memory used=3470.9MB, alloc=852.3MB, time=66.22 memory used=3686.1MB, alloc=876.3MB, time=73.30 memory used=3915.0MB, alloc=900.3MB, time=81.15 memory used=4158.1MB, alloc=924.3MB, time=89.50 memory used=4415.1MB, alloc=948.3MB, time=98.20 memory used=4686.7MB, alloc=972.3MB, time=107.68 memory used=4972.8MB, alloc=996.3MB, time=117.71 memory used=5273.7MB, alloc=1020.3MB, time=128.04 memory used=5588.7MB, alloc=1044.3MB, time=139.22 memory used=5918.8MB, alloc=1068.3MB, time=150.59 memory used=6263.7MB, alloc=1092.3MB, time=162.80 memory used=6623.9MB, alloc=1116.3MB, time=175.57 memory used=6998.9MB, alloc=1140.3MB, time=188.88 memory used=7388.9MB, alloc=1164.3MB, time=202.71 memory used=7793.9MB, alloc=1188.3MB, time=217.25 memory used=8209.7MB, alloc=1212.3MB, time=232.75 memory used=8649.3MB, alloc=1236.3MB, time=249.27 memory used=9113.0MB, alloc=1260.3MB, time=266.50 memory used=9600.6MB, alloc=1284.3MB, time=284.74 |\^/| 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(); 1428322535 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [6 x + 18 y, 9 x z + 13 z , 20 x + 15 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 G := [14 y - 8 x, 11 y + 6 y z, -3 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[6 x + 18 y, 9 x z + 13 z , 20 x + 15 y], 3 2 3 [14 y - 8 x, 11 y + 6 y z, -3 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.6MB, alloc=32.3MB, time=0.50 N1 := 337 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x , y, z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=48.2MB, alloc=32.3MB, time=0.88 N2 := 59 #save(Problem, "format.txt"); > if (GB=[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 := [6 x + 18 y, 9 x z + 13 z , 20 x + 15 y, 14 y - 8 x, 11 y + 6 y z, 3 -3 z ] > J:=[op(GB),op(G)]; 2 2 3 2 3 J := [x , y, z , 14 y - 8 x, 11 y + 6 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, 11, 15, 3, 2, 3, 3, 2/3, 2/3, 1/2, 1/3, 5/12, 1/3, 6, 8, 13, 3, 2, 3, 3, 1/3, 1/2, 1/2, 2/11, 4/11, 3/11, 3, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=54.2MB, alloc=32.3MB, time=0.97 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428322537 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [18 y z + y , -9 x - 3 y z, 12 z + 15] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 3 2 G := [2 x z - 9 y , -17 y - 13 y , -6 x - 11 y z] > Problem := [F,G]; 2 2 3 2 Problem := [[18 y z + y , -9 x - 3 y z, 12 z + 15], 2 3 3 2 3 2 [2 x z - 9 y , -17 y - 13 y , -6 x - 11 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=47.4MB, alloc=32.3MB, time=0.77 memory used=67.7MB, alloc=56.3MB, time=1.07 memory used=107.2MB, alloc=60.3MB, time=1.66 memory used=143.9MB, alloc=60.3MB, time=2.22 memory used=178.6MB, alloc=84.3MB, time=2.76 memory used=228.0MB, alloc=84.3MB, time=3.49 memory used=285.0MB, alloc=92.3MB, time=4.38 memory used=347.4MB, alloc=116.3MB, time=5.24 memory used=427.7MB, alloc=116.3MB, time=6.42 memory used=504.5MB, alloc=140.3MB, time=7.65 memory used=592.0MB, alloc=140.3MB, time=9.01 memory used=649.5MB, alloc=420.3MB, time=9.84 memory used=781.6MB, alloc=420.3MB, time=11.26 memory used=909.0MB, alloc=444.3MB, time=12.58 memory used=1052.0MB, alloc=468.3MB, time=14.19 memory used=1188.9MB, alloc=492.3MB, time=15.83 memory used=1337.8MB, alloc=516.3MB, time=18.06 memory used=1521.4MB, alloc=540.3MB, time=20.86 memory used=1717.6MB, alloc=564.3MB, time=23.83 memory used=1892.0MB, alloc=588.3MB, time=26.62 memory used=2095.5MB, alloc=612.3MB, time=32.12 memory used=2297.0MB, alloc=636.3MB, time=38.38 memory used=2504.9MB, alloc=660.3MB, time=45.38 memory used=2736.7MB, alloc=684.3MB, time=53.35 memory used=2992.6MB, alloc=708.3MB, time=61.94 memory used=3272.3MB, alloc=732.3MB, time=71.35 memory used=3576.1MB, alloc=756.3MB, time=81.94 memory used=3904.1MB, alloc=780.3MB, time=92.91 N1 := 7907 > GB := Basis(F, plex(op(vars))); 9 3 6 6 3 2 GB := [16 x + 1125 x , 8 x + 25 y, 2 x + 15 x z, 4 z + 5] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4040.8MB, alloc=780.3MB, time=95.64 memory used=4163.9MB, alloc=780.3MB, time=97.69 memory used=4341.0MB, alloc=780.3MB, time=100.95 memory used=4760.1MB, alloc=780.3MB, time=117.30 N2 := 3201 #save(Problem, "format.txt"); > if (GB=[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 2 H := [18 y z + y , -9 x - 3 y z, 12 z + 15, 2 z x - 9 y , -17 y - 13 y , 3 2 -6 x - 11 y z] > J:=[op(GB),op(G)]; 9 3 6 6 3 2 2 3 J := [16 x + 1125 x , 8 x + 25 y, 2 x + 15 x z, 4 z + 5, 2 z x - 9 y , 3 2 3 2 -17 y - 13 y , -6 x - 11 y z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 17, 3, 3, 3, 2, 1/2, 5/6, 5/6, 1/4, 7/12, 5/12, 7, 13, 32, 9, 9, 3, 2, 5/7, 4/7, 4/7, 1/2, 5/14, 2/7, 0, -15, -6] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=4825.4MB, alloc=780.3MB, time=120.48 |\^/| 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(); 1428322667 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 F := [17 x + 11 z, -15 x z + 7 y, -13] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [18 x - 9 z , -16 y - 11 y z, 20 y z - 19 x] > Problem := [F,G]; 2 Problem := [[17 x + 11 z, -15 x z + 7 y, -13], 2 2 3 2 2 [18 x - 9 z , -16 y - 11 y z, 20 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=0.20 memory used=26.7MB, alloc=32.3MB, time=0.58 memory used=48.0MB, alloc=32.3MB, time=0.92 memory used=68.7MB, alloc=60.3MB, time=1.26 memory used=110.8MB, alloc=60.3MB, time=1.97 memory used=150.7MB, alloc=84.3MB, time=2.63 memory used=209.0MB, alloc=92.3MB, time=3.61 memory used=267.3MB, alloc=116.3MB, time=4.86 memory used=341.5MB, alloc=140.3MB, time=6.31 memory used=431.9MB, alloc=164.3MB, time=8.00 memory used=538.5MB, alloc=188.3MB, time=9.86 memory used=658.4MB, alloc=212.3MB, time=11.85 memory used=772.6MB, alloc=492.3MB, time=13.92 memory used=908.9MB, alloc=516.3MB, time=17.20 memory used=1052.0MB, alloc=540.3MB, time=20.99 memory used=1205.3MB, alloc=564.3MB, time=25.62 memory used=1373.8MB, alloc=588.3MB, time=31.10 memory used=1566.2MB, alloc=612.3MB, time=37.24 memory used=1782.5MB, alloc=612.3MB, time=44.06 memory used=1998.8MB, alloc=636.3MB, time=50.99 memory used=2239.1MB, alloc=636.3MB, time=58.55 memory used=2479.3MB, alloc=636.3MB, time=66.21 memory used=2719.6MB, alloc=660.3MB, time=73.90 memory used=2983.7MB, alloc=660.3MB, time=82.23 memory used=3247.9MB, alloc=684.3MB, time=90.35 memory used=3536.2MB, alloc=684.3MB, time=99.18 N1 := 9743 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 539 #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 3 2 H := [11 z + 17 x, -15 x z + 7 y, -13, 18 x - 9 z , -16 y - 11 y z, 2 20 y z - 19 x] > J:=[op(GB),op(G)]; 2 2 3 2 2 J := [1, 18 x - 9 z , -16 y - 11 y z, 20 y 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, 12, 12, 3, 2, 3, 2, 2/3, 1/2, 5/6, 4/11, 4/11, 5/11, 4, 7, 8, 3, 2, 3, 2, 1/2, 1/2, 3/4, 2/7, 3/7, 3/7, 5, 4, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=3736.8MB, alloc=684.3MB, time=103.52 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428322778 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [6 x y - 19 z , 9 x z - 3 y z, -16 y z - 16 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [15 x + 6 y, -7 x y + 16 y, -8 x ] > Problem := [F,G]; 2 3 2 2 2 Problem := [[6 x y - 19 z , 9 x z - 3 y z, -16 y z - 16 y], 2 3 [15 x + 6 y, -7 x y + 16 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=0.16 memory used=26.2MB, alloc=32.3MB, time=0.43 memory used=49.3MB, alloc=32.3MB, time=0.74 N1 := 267 > GB := Basis(F, plex(op(vars))); 6 2 3 3 2 2 3 GB := [324 x y + 361 y, -3 x y + y , 6 x y + 19 x z, 18 x y + 19 y z, 2 3 -6 x y + 19 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=67.8MB, alloc=32.3MB, time=0.98 memory used=87.1MB, alloc=32.3MB, time=1.22 memory used=107.4MB, alloc=56.3MB, time=1.52 N2 := 351 #save(Problem, "format.txt"); > 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 := [-19 z + 6 y x, 9 x z - 3 y z, -16 y z - 16 y, 15 x + 6 y, 2 3 -7 x y + 16 y, -8 x ] > J:=[op(GB),op(G)]; 6 2 3 3 2 2 3 J := [324 x y + 361 y, -3 x y + y , 6 x y + 19 x z, 18 x y + 19 y z, 2 3 2 3 -6 x y + 19 z , 15 x + 6 y, -7 x y + 16 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, 13, 16, 3, 3, 2, 3, 5/6, 5/6, 1/2, 5/12, 7/12, 1/3, 8, 18, 29, 7, 6, 3, 3, 1, 7/8, 3/8, 9/16, 11/16, 3/16, -5, -13, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=123.0MB, alloc=56.3MB, time=1.75 |\^/| 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(); 1428322780 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-13 x y z + 5 x z, -9 y + 2 x, -5 x z - 3 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-14 y z - 9 x , 6 y - 13 z, -11 x y ] > Problem := [F,G]; 2 2 2 Problem := [[-13 x y z + 5 x z, -9 y + 2 x, -5 x z - 3 x ], 2 2 2 2 [-14 y z - 9 x , 6 y - 13 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=4.2MB, 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=67.6MB, alloc=56.3MB, time=0.88 memory used=112.2MB, alloc=60.3MB, time=1.56 memory used=151.7MB, alloc=84.3MB, time=2.12 memory used=208.7MB, alloc=108.3MB, time=3.26 N1 := 1657 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 2 GB := [338 x - 225 x , 13 x y - 5 x , 9 y - 2 x, 338 x z - 225 x z, 2 2 13 x y z - 5 x z, 5 x z + 3 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=279.7MB, alloc=108.3MB, time=4.85 memory used=357.5MB, alloc=116.3MB, time=5.85 memory used=435.4MB, alloc=140.3MB, time=6.94 memory used=524.3MB, alloc=164.3MB, time=8.99 N2 := 1657 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [-13 x y z + 5 x z, -9 y + 2 x, -5 x z - 3 x , -14 y z - 9 x , 2 2 6 y - 13 z, -11 x y ] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 J := [338 x - 225 x , 13 x y - 5 x , 9 y - 2 x, 338 x z - 225 x z, 2 2 2 2 2 2 13 x y z - 5 x z, 5 x z + 3 x , -14 y z - 9 x , 6 y - 13 z, -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, 16, 3, 2, 2, 2, 5/6, 5/6, 2/3, 7/13, 5/13, 5/13, 9, 19, 25, 3, 3, 2, 2, 8/9, 2/3, 5/9, 13/19, 6/19, 7/19, -5, -9, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=535.9MB, alloc=164.3MB, time=9.22 |\^/| 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(); 1428322790 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [-11 x z - 2 y z, 8 x z + 16 z , -12 x y z - 14 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-14 x z, -18 x y + 4 z, 4 x y + 7 y ] > Problem := [F,G]; 2 2 2 3 Problem := [[-11 x z - 2 y z, 8 x z + 16 z , -12 x y z - 14 x z], 2 2 2 2 [-14 x z, -18 x y + 4 z, 4 x y + 7 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.1MB, alloc=32.3MB, time=0.40 memory used=48.0MB, alloc=32.3MB, time=0.68 N1 := 193 > GB := Basis(F, plex(op(vars))); 3 2 2 2 3 GB := [198 x z + 49 x z, 6 x y z + 7 x z, 11 x z + 2 y z, x z + 2 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=67.8MB, alloc=32.3MB, time=0.93 memory used=87.3MB, alloc=32.3MB, time=1.14 memory used=107.3MB, alloc=56.3MB, time=1.43 N2 := 193 #save(Problem, "format.txt"); > if (GB=[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 := [-11 x z - 2 y z, 8 x z + 16 z , -12 x y z - 14 x z, -14 x z, 2 2 2 -18 x y + 4 z, 4 x y + 7 y ] > J:=[op(GB),op(G)]; 3 2 2 2 3 J := [198 x z + 49 x z, 6 x y z + 7 x z, 11 x z + 2 y z, x z + 2 z , 2 2 2 2 -14 x z, -18 x y + 4 z, 4 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, 15, 18, 3, 2, 2, 3, 1, 2/3, 5/6, 7/13, 5/13, 8/13, 7, 17, 22, 4, 3, 2, 3, 1, 4/7, 6/7, 3/5, 1/3, 2/3, -2, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=110.2MB, alloc=56.3MB, time=1.47 |\^/| 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(); 1428322792 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 F := [x y z, -12 y, -12 x z - 18 x y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-3 x y - 5 y z, -x z - y , 19 x y z + 6] > Problem := [F,G]; 2 Problem := [[x y z, -12 y, -12 x z - 18 x y z], 2 2 [-3 x y - 5 y z, -x z - y , 19 x y z + 6]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.13 memory used=26.5MB, alloc=32.3MB, time=0.39 memory used=48.7MB, alloc=32.3MB, time=0.70 memory used=68.6MB, alloc=56.3MB, time=1.02 N1 := 683 > GB := Basis(F, plex(op(vars))); 2 GB := [y, z x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=108.8MB, alloc=60.3MB, time=1.63 N2 := 291 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; H := [ 2 2 2 z y x, -12 y, -12 x z - 18 x y z, -3 x y - 5 y z, -x z - y , 19 z y x + 6 ] > J:=[op(GB),op(G)]; 2 2 2 J := [y, z x , -3 x y - 5 y z, -x z - y , 19 z y x + 6] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 16, 15, 3, 2, 2, 1, 5/6, 1, 5/6, 6/13, 7/13, 6/13, 5, 12, 12, 3, 2, 2, 1, 4/5, 4/5, 4/5, 4/9, 5/9, 4/9, 4, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=129.1MB, alloc=60.3MB, 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(); 1428322794 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [6 x y - 6 y , 5 x y z - 16 y z , 19 x z + 10 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [12 x z - 6 y , 14 x z , 4 y z + 9 x y] > Problem := [F,G]; 2 2 2 2 Problem := [[6 x y - 6 y , 5 x y z - 16 y z , 19 x z + 10 x], 2 3 2 2 [12 x z - 6 y , 14 x z , 4 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=4.2MB, alloc=32.3MB, time=0.14 memory used=26.5MB, alloc=32.3MB, time=0.40 memory used=47.9MB, alloc=32.3MB, time=0.65 memory used=69.8MB, alloc=56.3MB, time=0.98 memory used=112.3MB, alloc=60.3MB, time=1.61 N1 := 851 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 GB := [95 x y + 512 x y, -x y + y , -5 x y + 16 x y z, 19 x z + 10 x, 2 2 -25 x y + 256 y z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=147.8MB, alloc=60.3MB, time=2.19 memory used=184.1MB, alloc=84.3MB, time=2.63 memory used=248.0MB, alloc=84.3MB, time=3.54 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)]; 2 2 2 2 2 3 2 H := [6 x y - 6 y , 5 x y z - 16 y z , 19 x z + 10 x, 12 x z - 6 y , 14 z x, 2 4 y z + 9 x y] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [95 x y + 512 x y, -x y + y , -5 x y + 16 x y z, 19 x z + 10 x, 2 2 2 3 2 2 -25 x y + 256 y z , 12 x z - 6 y , 14 z x, 4 y z + 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, 18, 3, 2, 3, 2, 1, 2/3, 5/6, 7/13, 7/13, 6/13, 8, 20, 25, 4, 3, 3, 2, 1, 3/4, 3/4, 11/17, 11/17, 6/17, -5, -7, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=298.2MB, alloc=84.3MB, time=4.42 |\^/| 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(); 1428322798 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-y - 15 x z, -16 x - 16, -x z - y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 G := [20 y z , -14 x z + 16 x, 2 x] > Problem := [F,G]; Problem := 3 2 2 2 [[-y - 15 x z, -16 x - 16, -x z - y z], [20 y z , -14 x z + 16 x, 2 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.7MB, alloc=32.3MB, time=0.48 N1 := 181 > GB := Basis(F, plex(op(vars))); 2 4 3 3 GB := [x + 1, y - y , -x y + 15 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=46.6MB, alloc=32.3MB, time=0.73 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)]; 3 2 2 2 H := [-y - 15 x z, -16 x - 16, -x z - y z, 20 y z , -14 x z + 16 x, 2 x] > J:=[op(GB),op(G)]; 2 4 3 3 2 J := [x + 1, y - y , -x y + 15 z, 20 y z , -14 x z + 16 x, 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, 12, 14, 3, 2, 3, 2, 5/6, 1/2, 2/3, 6/13, 3/13, 5/13, 6, 10, 16, 4, 2, 4, 2, 2/3, 1/2, 1/2, 5/13, 4/13, 3/13, 2, -2, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=53.3MB, alloc=32.3MB, time=0.83 |\^/| 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(); 1428322799 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-4 x y z + 13, -7 x y , -8 z + 14 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [13 x z - 7 x, -10 x y + 19 x y, -20 x - 10] > Problem := [F,G]; 2 2 Problem := [[-4 x y z + 13, -7 x y , -8 z + 14 y], 2 2 [13 x z - 7 x, -10 x y + 19 x y, -20 x - 10]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.39 memory used=48.8MB, alloc=32.3MB, time=0.70 N1 := 487 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=67.9MB, alloc=56.3MB, time=1.04 N2 := 45 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Input concluded false after GB computation" > > H:=[op(F),op(G)]; 2 2 2 H := [-4 x y z + 13, -7 x y , -8 z + 14 y, 13 x z - 7 x, -10 x y + 19 x y, 2 -20 x - 10] > J:=[op(GB),op(G)]; 2 2 J := [1, 13 x z - 7 x, -10 x y + 19 x y, -20 x - 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, 12, 15, 3, 2, 2, 2, 5/6, 2/3, 1/2, 7/13, 5/13, 3/13, 4, 5, 7, 3, 2, 1, 1, 3/4, 1/4, 1/4, 5/7, 2/7, 1/7, 7, 8, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=72.9MB, 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(); 1428322801 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [17 y + 7 z , z + 5, 5 y z + 2] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 G := [7 x z - 20 z , 13 x - 6 z, -y + 2] > Problem := [F,G]; Problem := [ 3 2 3 2 2 3 2 3 [17 y + 7 z , z + 5, 5 y z + 2], [7 x z - 20 z , 13 x - 6 z, -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=26.5MB, alloc=32.3MB, time=0.41 memory used=47.8MB, alloc=32.3MB, time=0.66 memory used=68.1MB, alloc=56.3MB, time=0.90 memory used=111.0MB, alloc=60.3MB, time=1.43 memory used=148.6MB, alloc=60.3MB, time=1.86 memory used=183.4MB, alloc=84.3MB, time=2.31 memory used=223.2MB, alloc=84.3MB, time=2.77 memory used=283.3MB, alloc=92.3MB, time=3.43 memory used=344.5MB, alloc=116.3MB, time=4.10 memory used=421.6MB, alloc=116.3MB, time=5.04 memory used=498.7MB, alloc=140.3MB, time=6.16 memory used=591.0MB, alloc=164.3MB, time=7.53 memory used=698.8MB, alloc=188.3MB, time=9.14 memory used=819.0MB, alloc=212.3MB, time=10.94 memory used=944.0MB, alloc=236.3MB, time=13.39 memory used=1068.6MB, alloc=260.3MB, time=16.49 memory used=1203.0MB, alloc=284.3MB, time=20.53 memory used=1351.9MB, alloc=308.3MB, time=25.18 memory used=1524.9MB, alloc=332.3MB, time=30.71 memory used=1721.8MB, alloc=356.3MB, time=36.88 memory used=1942.6MB, alloc=356.3MB, time=43.78 memory used=2163.3MB, alloc=356.3MB, time=50.76 memory used=2384.1MB, alloc=380.3MB, time=57.78 memory used=2628.9MB, alloc=380.3MB, time=65.41 memory used=2873.5MB, alloc=404.3MB, time=73.13 N1 := 8295 > GB := Basis(F, plex(op(vars))); 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 2 3 2 2 3 2 3 H := [17 y + 7 z , z + 5, 5 z y + 2, 7 x z - 20 z , 13 x - 6 z, -y + 2] > J:=[op(GB),op(G)]; 2 3 2 3 J := [1, 7 x z - 20 z , 13 x - 6 z, -y + 2] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 10, 17, 3, 2, 3, 3, 1/3, 1/2, 5/6, 1/6, 1/4, 1/2, 4, 5, 8, 3, 2, 3, 3, 1/2, 1/4, 1/2, 2/7, 1/7, 3/7, 5, 9, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2998.8MB, alloc=404.3MB, time=76.33 |\^/| 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(); 1428322880 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [17 x - 17 x y, -14 z , -2 x y - 18 x y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [9 x + 10 x y, 3 x y - 15 z, 12 y z - 6] > Problem := [F,G]; 3 2 2 2 Problem := [[17 x - 17 x y, -14 z , -2 x y - 18 x y z], 2 2 2 [9 x + 10 x y, 3 x y - 15 z, 12 y z - 6]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.4MB, alloc=32.3MB, time=0.43 memory used=48.5MB, alloc=32.3MB, time=0.75 memory used=68.4MB, alloc=56.3MB, time=1.03 N1 := 847 > GB := Basis(F, plex(op(vars))); 5 3 2 3 4 3 2 2 GB := [x , -x + x y, x y , x + 9 x z, x y + 9 x y z, z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=109.4MB, alloc=56.3MB, time=1.73 memory used=146.4MB, alloc=84.3MB, time=2.17 memory used=207.5MB, alloc=92.3MB, time=2.93 memory used=265.4MB, alloc=116.3MB, time=3.75 memory used=339.5MB, alloc=140.3MB, time=4.87 memory used=422.7MB, alloc=164.3MB, time=7.00 memory used=520.9MB, alloc=188.3MB, time=9.98 N2 := 2811 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 2 2 H := [17 x - 17 x y, -14 z , -2 x y - 18 x y z, 9 x + 10 x y, 3 x y - 15 z, 2 12 y z - 6] > J:=[op(GB),op(G)]; 5 3 2 3 4 3 2 2 2 J := [x , -x + x y, x y , x + 9 x z, x y + 9 x y z, z , 9 x + 10 x y, 2 2 3 x y - 15 z, 12 y 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, 13, 16, 3, 3, 2, 2, 2/3, 5/6, 2/3, 7/12, 1/2, 1/3, 9, 18, 29, 5, 5, 3, 2, 7/9, 2/3, 5/9, 11/18, 7/18, 5/18, -5, -13, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=599.1MB, alloc=188.3MB, time=11.79 |\^/| Maple 17 (APPLE UNIVERSAL OSX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2013 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > restart: > randomize(); 1428322892 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [7 x z + 6 x , -z - 6, 18 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [16 x z + 14 y , 15 x y - 15 x, -5 x + 19 y ] > Problem := [F,G]; 2 2 3 2 Problem := [[7 x z + 6 x , -z - 6, 18 z ], 2 2 3 2 [16 x z + 14 y , 15 x y - 15 x, -5 x + 19 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=32.1MB, alloc=40.3MB, time=0.47 memory used=62.2MB, alloc=44.3MB, time=0.87 memory used=89.0MB, alloc=68.3MB, time=1.24 memory used=135.9MB, alloc=68.3MB, time=1.90 memory used=175.5MB, alloc=92.3MB, time=2.61 memory used=230.2MB, alloc=116.3MB, time=4.17 N1 := 1981 > 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)]; 2 2 3 2 2 2 H := [7 x z + 6 x , -z - 6, 18 z , 16 x z + 14 y , 15 x y - 15 x, 3 2 -5 x + 19 y ] > J:=[op(GB),op(G)]; 2 2 3 2 J := [1, 16 x z + 14 y , 15 x y - 15 x, -5 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, 11, 16, 3, 3, 2, 3, 2/3, 1/2, 2/3, 1/2, 1/4, 1/3, 4, 7, 8, 3, 3, 2, 1, 3/4, 3/4, 1/4, 4/7, 3/7, 1/7, 4, 8, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=296.7MB, alloc=116.3MB, 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(); 1428322898 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [3 y - 2 y z, -9 z + 13 z , -16 x y + 10 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [9 x + 9 x, 11 x + 1, -3 y - 4 z ] > Problem := [F,G]; 2 3 2 2 2 Problem := [[3 y - 2 y z, -9 z + 13 z , -16 x y + 10 z ], 2 3 2 2 [9 x + 9 x, 11 x + 1, -3 y - 4 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=26.0MB, alloc=32.3MB, time=0.38 memory used=48.1MB, alloc=32.3MB, time=0.66 memory used=68.5MB, alloc=56.3MB, time=0.93 N1 := 477 > GB := Basis(F, plex(op(vars))); 2 2 2 2 3 2 2 2 GB := [32 x y - 45 x y , -832 x y + 1215 y , -3 y + 2 y z, -8 x y + 5 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=107.6MB, alloc=60.3MB, time=1.49 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)]; 2 3 2 2 2 2 3 H := [3 y - 2 y z, -9 z + 13 z , -16 x y + 10 z , 9 x + 9 x, 11 x + 1, 2 2 -3 y - 4 z ] > J:=[op(GB),op(G)]; 2 2 2 2 3 2 2 2 J := [32 x y - 45 x y , -832 x y + 1215 y , -3 y + 2 y z, -8 x y + 5 z , 2 3 2 2 9 x + 9 x, 11 x + 1, -3 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, 10, 15, 3, 3, 2, 3, 1/2, 1/2, 2/3, 1/3, 1/3, 5/12, 7, 13, 19, 4, 3, 3, 2, 5/7, 5/7, 3/7, 1/2, 4/7, 3/14, -3, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=115.0MB, 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(); 1428322900 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-19 x z - 6 x, -2 x y z - 13 y z, 13 y z - 15 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [-9 x y z + 19 y z, -17 z + 10, 17 x y + 8 z] > Problem := [F,G]; 2 2 Problem := [[-19 x z - 6 x, -2 x y z - 13 y z, 13 y z - 15 x ], 2 3 [-9 x y z + 19 y z, -17 z + 10, 17 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=0.16 memory used=26.1MB, alloc=32.3MB, time=0.39 memory used=47.6MB, alloc=32.3MB, time=0.64 memory used=67.5MB, alloc=56.3MB, time=0.90 memory used=108.0MB, alloc=60.3MB, time=1.38 memory used=148.3MB, alloc=84.3MB, time=1.97 memory used=207.7MB, alloc=84.3MB, time=2.88 memory used=261.3MB, alloc=108.3MB, time=3.66 memory used=331.4MB, alloc=140.3MB, time=4.78 memory used=413.1MB, alloc=164.3MB, time=6.52 memory used=502.8MB, alloc=188.3MB, time=9.26 memory used=616.6MB, alloc=188.3MB, time=12.73 memory used=730.4MB, alloc=212.3MB, time=16.09 N1 := 3949 > GB := Basis(F, plex(op(vars))); 3 2 2 2 GB := [2 x + 13 x , 1805 x + 24 x y, 19 x z + 6 x, 95 x + 26 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=871.5MB, alloc=212.3MB, time=19.32 memory used=969.5MB, alloc=468.3MB, time=20.63 memory used=1122.6MB, alloc=492.3MB, time=22.82 memory used=1288.7MB, alloc=516.3MB, time=25.85 memory used=1442.7MB, alloc=540.3MB, time=30.45 memory used=1611.4MB, alloc=564.3MB, time=36.12 memory used=1804.1MB, alloc=588.3MB, time=42.40 N2 := 4637 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 H := [-19 x z - 6 x, -2 x y z - 13 y z, 13 y z - 15 x , -9 x y z + 19 y z, 3 -17 z + 10, 17 y x + 8 z] > J:=[op(GB),op(G)]; 3 2 2 2 J := [2 x + 13 x , 1805 x + 24 x y, 19 x z + 6 x, 26 z y + 95 x , 2 3 -9 x y z + 19 y z, -17 z + 10, 17 y x + 8 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 16, 3, 2, 2, 3, 5/6, 2/3, 1, 1/2, 1/2, 2/3, 7, 15, 17, 3, 3, 2, 3, 6/7, 4/7, 5/7, 9/14, 5/14, 3/7, 0, -1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1926.9MB, alloc=588.3MB, time=45.70 |\^/| 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(); 1428322948 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 F := [14 x - 2 z , -12 x y + 18 y z, -18 x z - 3 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 G := [16 x - 5 z , 10 z + 18 x y, 13 y + 15 x z] > Problem := [F,G]; 3 3 2 2 Problem := [[14 x - 2 z , -12 x y + 18 y z, -18 x z - 3 x y], 3 2 3 3 [16 x - 5 z , 10 z + 18 x y, 13 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=0.16 memory used=26.9MB, alloc=32.3MB, time=0.45 memory used=48.6MB, alloc=32.3MB, time=0.71 memory used=69.3MB, alloc=56.3MB, time=0.95 memory used=110.8MB, alloc=60.3MB, time=1.44 memory used=151.2MB, alloc=60.3MB, time=1.89 memory used=190.4MB, alloc=84.3MB, time=2.33 memory used=228.0MB, alloc=84.3MB, time=2.74 memory used=290.0MB, alloc=92.3MB, time=3.52 memory used=351.7MB, alloc=116.3MB, time=4.24 memory used=432.7MB, alloc=116.3MB, time=5.21 memory used=501.7MB, alloc=396.3MB, time=5.94 memory used=616.9MB, alloc=420.3MB, time=6.88 memory used=738.9MB, alloc=444.3MB, time=8.37 memory used=870.4MB, alloc=468.3MB, time=9.75 memory used=975.0MB, alloc=492.3MB, time=10.80 memory used=1078.9MB, alloc=492.3MB, time=11.99 memory used=1176.3MB, alloc=516.3MB, time=13.02 memory used=1258.1MB, alloc=516.3MB, time=14.15 memory used=1328.1MB, alloc=516.3MB, time=15.02 memory used=1408.5MB, alloc=516.3MB, time=16.21 memory used=1476.0MB, alloc=516.3MB, time=17.22 memory used=1544.2MB, alloc=516.3MB, time=18.25 memory used=1597.8MB, alloc=516.3MB, time=19.20 memory used=1633.9MB, alloc=516.3MB, time=19.88 memory used=1825.2MB, alloc=540.3MB, time=21.90 memory used=2000.2MB, alloc=564.3MB, time=24.04 memory used=2165.1MB, alloc=588.3MB, time=26.05 memory used=2333.8MB, alloc=612.3MB, time=28.18 memory used=2475.0MB, alloc=636.3MB, time=29.89 memory used=2606.9MB, alloc=660.3MB, time=31.86 memory used=2717.7MB, alloc=684.3MB, time=33.61 memory used=2805.4MB, alloc=684.3MB, time=35.22 memory used=2887.6MB, alloc=684.3MB, time=36.88 memory used=3226.0MB, alloc=708.3MB, time=41.21 memory used=3563.9MB, alloc=732.3MB, time=46.08 memory used=3898.1MB, alloc=756.3MB, time=50.87 memory used=4207.8MB, alloc=780.3MB, time=55.78 memory used=4443.7MB, alloc=804.3MB, time=59.88 memory used=4741.0MB, alloc=828.3MB, time=64.55 memory used=4950.1MB, alloc=852.3MB, time=68.52 memory used=5187.7MB, alloc=876.3MB, time=72.65 memory used=5376.0MB, alloc=900.3MB, time=76.36 memory used=5554.7MB, alloc=924.3MB, time=80.19 memory used=6070.1MB, alloc=948.3MB, time=86.93 memory used=6566.0MB, alloc=972.3MB, time=93.51 memory used=7053.2MB, alloc=996.3MB, time=101.92 memory used=7495.2MB, alloc=1020.3MB, time=110.17 memory used=7898.6MB, alloc=1044.3MB, time=118.57 memory used=8372.4MB, alloc=1068.3MB, time=126.74 memory used=8813.3MB, alloc=1092.3MB, time=135.53 memory used=9234.0MB, alloc=1116.3MB, time=144.40 memory used=9666.4MB, alloc=1140.3MB, time=153.18 memory used=10114.7MB, alloc=1164.3MB, time=162.15 memory used=10565.9MB, alloc=1188.3MB, time=171.10 memory used=11055.0MB, alloc=1212.3MB, time=179.87 memory used=11569.7MB, alloc=1236.3MB, time=188.41 memory used=12125.0MB, alloc=1260.3MB, time=196.52 memory used=12493.2MB, alloc=1284.3MB, time=209.96 memory used=12833.7MB, alloc=1308.3MB, time=223.65 memory used=13177.1MB, alloc=1332.3MB, time=238.03 memory used=13523.8MB, alloc=1356.3MB, time=252.61 memory used=13878.6MB, alloc=1380.3MB, time=267.48 memory used=14243.4MB, alloc=1404.3MB, time=283.22 memory used=14619.1MB, alloc=1428.3MB, time=299.60 |\^/| 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(); 1428323248 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [7 y - 4, -7 x z + 16 x, -2 x z + 4 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 G := [17 x z + 3 y , -3 y + 3 x, 12 x - 17 z ] > Problem := [F,G]; 3 2 2 Problem := [[7 y - 4, -7 x z + 16 x, -2 x z + 4 y], 2 3 2 2 2 [17 x z + 3 y , -3 y + 3 x, 12 x - 17 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=67.7MB, alloc=56.3MB, time=1.09 memory used=107.7MB, alloc=60.3MB, time=1.76 memory used=146.4MB, alloc=60.3MB, time=2.36 memory used=184.1MB, alloc=84.3MB, time=2.91 memory used=229.0MB, alloc=84.3MB, time=3.59 memory used=290.9MB, alloc=116.3MB, time=4.59 memory used=369.0MB, alloc=116.3MB, time=5.96 memory used=444.1MB, alloc=140.3MB, time=7.25 memory used=541.6MB, alloc=164.3MB, time=8.70 memory used=650.5MB, alloc=188.3MB, time=10.33 memory used=775.0MB, alloc=212.3MB, time=12.13 memory used=910.3MB, alloc=492.3MB, time=14.86 memory used=1044.0MB, alloc=516.3MB, time=18.45 memory used=1187.5MB, alloc=540.3MB, time=23.33 memory used=1342.2MB, alloc=564.3MB, time=29.17 memory used=1521.0MB, alloc=588.3MB, time=34.92 memory used=1723.6MB, alloc=588.3MB, time=41.35 memory used=1926.3MB, alloc=612.3MB, time=48.00 memory used=2152.9MB, alloc=612.3MB, time=55.13 memory used=2379.5MB, alloc=612.3MB, time=62.28 memory used=2606.0MB, alloc=636.3MB, time=69.46 memory used=2856.7MB, alloc=660.3MB, time=78.07 N1 := 8223 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [16807 x - 524288, -343 x + 4096 y, -2401 x + 32768 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3143.2MB, alloc=660.3MB, time=84.51 N2 := 1651 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 3 2 H := [7 y - 4, -7 x z + 16 x, -2 x z + 4 y, 17 z x + 3 y , -3 y + 3 x, 2 2 -17 z + 12 x ] > J:=[op(GB),op(G)]; 3 2 2 2 3 J := [16807 x - 524288, -343 x + 4096 y, -2401 x + 32768 z, 17 z x + 3 y , 2 2 2 -3 y + 3 x, -17 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, 13, 16, 3, 2, 3, 2, 5/6, 2/3, 2/3, 1/2, 1/3, 1/3, 6, 12, 14, 3, 3, 3, 2, 1, 1/2, 1/2, 1/2, 1/4, 1/4, 1, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=3234.0MB, alloc=660.3MB, time=88.09 |\^/| 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(); 1428323342 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [9 x z + 7 z , -10 x y + 17 x, -4 x - 14 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [11 x z + 6 y z, -16 y z + 11 z , -7 x - 14] > Problem := [F,G]; 2 2 3 2 Problem := [[9 x z + 7 z , -10 x y + 17 x, -4 x - 14 y ], 2 2 2 3 2 [11 x z + 6 y z, -16 y z + 11 z , -7 x - 14]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.0MB, alloc=32.3MB, time=0.51 memory used=47.3MB, alloc=32.3MB, time=0.84 memory used=67.6MB, alloc=32.3MB, time=1.18 memory used=88.2MB, alloc=56.3MB, time=1.61 memory used=128.9MB, alloc=60.3MB, time=2.40 memory used=164.6MB, alloc=84.3MB, time=3.21 memory used=215.1MB, alloc=108.3MB, time=4.97 N1 := 1405 > GB := Basis(F, plex(op(vars))); 4 3 2 2 2 GB := [200 x + 2023 x, 10 x y - 17 x, 2 x + 7 y , 9 x z + 7 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=286.2MB, alloc=116.3MB, time=6.25 memory used=367.7MB, alloc=140.3MB, time=7.88 N2 := 1405 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 2 2 H := [9 x z + 7 z , -10 x y + 17 x, -4 x - 14 y , 11 x z + 6 y z, 2 3 2 -16 y z + 11 z , -7 x - 14] > J:=[op(GB),op(G)]; 4 3 2 2 2 J := [200 x + 2023 x, 10 x y - 17 x, 2 x + 7 y , 9 x z + 7 z , 2 2 2 3 2 11 x z + 6 y z, -16 y z + 11 z , -7 x - 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, 12, 16, 3, 3, 2, 3, 5/6, 2/3, 1/2, 1/2, 1/3, 1/2, 7, 13, 20, 4, 4, 2, 3, 6/7, 4/7, 3/7, 4/7, 2/7, 3/7, -1, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=437.1MB, alloc=140.3MB, time=10.30 |\^/| 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(); 1428323353 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [18 x z + 9 y z , -9 x z, -4 x z - 9 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 G := [-10 y z + 12 x, -x z + 2 y z, 5 z + 2 z] > Problem := [F,G]; 2 2 2 2 Problem := [[18 x z + 9 y z , -9 x z, -4 x z - 9 x], 2 [-10 y z + 12 x, -x z + 2 y z, 5 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=0.18 memory used=26.4MB, alloc=32.3MB, time=0.52 memory used=47.6MB, alloc=32.3MB, time=0.85 memory used=68.9MB, alloc=56.3MB, time=1.29 memory used=109.8MB, alloc=60.3MB, time=2.08 memory used=145.6MB, alloc=84.3MB, time=2.82 memory used=196.2MB, alloc=108.3MB, time=4.60 N1 := 1647 > GB := Basis(F, plex(op(vars))); 2 GB := [x, z y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 105 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [18 x z + 9 y z , -9 x z, -4 x z - 9 x, -10 y z + 12 x, -x z + 2 y z, 2 5 z + 2 z] > J:=[op(GB),op(G)]; 2 2 J := [x, z y, -10 y z + 12 x, -x z + 2 y z, 5 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, 15, 3, 2, 1, 2, 5/6, 1/2, 1, 6/13, 3/13, 9/13, 5, 10, 10, 3, 1, 1, 2, 3/5, 3/5, 4/5, 1/3, 1/3, 2/3, 4, 5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=240.8MB, alloc=108.3MB, time=5.77 |\^/| 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(); 1428323359 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 2 F := [8 y - 17 x y, -17 x - 11 y , 15 x + 10 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [19 z , -20 y z + 3 x y, 15 y - 9 x] > Problem := [F,G]; 3 3 2 2 2 Problem := [[8 y - 17 x y, -17 x - 11 y , 15 x + 10 y ], 2 2 3 [19 z , -20 y z + 3 x y, 15 y - 9 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.42 memory used=47.8MB, alloc=32.3MB, time=0.70 memory used=68.0MB, alloc=56.3MB, time=0.97 N1 := 419 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x , y x, y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); 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)]; 3 3 2 2 2 2 2 H := [8 y - 17 x y, -17 x - 11 y , 15 x + 10 y , 19 z , -20 y z + 3 x y, 3 15 y - 9 x] > J:=[op(GB),op(G)]; 2 2 2 2 3 J := [x , y x, y , 19 z , -20 y z + 3 x y, 15 y - 9 x] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 16, 3, 3, 3, 2, 5/6, 5/6, 1/3, 5/12, 7/12, 1/6, 6, 10, 14, 3, 2, 3, 2, 2/3, 2/3, 1/3, 1/3, 5/12, 1/6, 2, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=84.4MB, alloc=56.3MB, time=1.20 |\^/| 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(); 1428323361 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [9 z - 19 y z, 11 y z - 9 x , -11 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-9 x - 17, 19 x z , 9 x + 18 x z] > Problem := [F,G]; 3 2 2 3 Problem := [[9 z - 19 y z, 11 y z - 9 x , -11 x ], 2 2 2 [-9 x - 17, 19 x z , 9 x + 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=0.15 memory used=27.3MB, alloc=32.3MB, time=0.46 memory used=49.1MB, alloc=56.3MB, time=0.77 N1 := 531 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 2 2 2 2 2 GB := [x , y x , -81 x z + 209 y z, 9 x z - 19 x y, 11 y z - 9 x , 3 9 z - 19 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=89.3MB, alloc=60.3MB, time=1.32 N2 := 531 #save(Problem, "format.txt"); > 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 2 3 2 2 2 [9 z - 19 y z, 11 y z - 9 x , -11 x , -9 x - 17, 19 x z , 9 x + 18 x z] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 2 2 2 2 J := [x , y x , -81 x z + 209 y z, 9 x z - 19 x y, 11 y z - 9 x , 3 2 2 2 9 z - 19 y z, -9 x - 17, 19 x z , 9 x + 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, 11, 16, 3, 3, 1, 3, 5/6, 1/3, 2/3, 6/13, 2/13, 5/13, 9, 19, 27, 4, 3, 2, 3, 8/9, 5/9, 2/3, 10/19, 5/19, 8/19, -8, -11, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=128.2MB, alloc=60.3MB, 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(); 1428323363 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [3 y z + 14 x, -7 x z + 18 y z, 20 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 2 G := [17 x y - 3 z , 7 z - 15 x , 9 x - 17 z ] > Problem := [F,G]; 2 2 3 Problem := [[3 y z + 14 x, -7 x z + 18 y z, 20 y ], 2 3 3 2 2 2 [17 x y - 3 z , 7 z - 15 x , 9 x - 17 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=27.0MB, alloc=32.3MB, time=0.44 memory used=48.3MB, alloc=32.3MB, time=0.71 memory used=68.9MB, alloc=56.3MB, time=0.97 memory used=110.4MB, alloc=60.3MB, time=1.44 memory used=150.4MB, alloc=84.3MB, time=1.94 memory used=214.6MB, alloc=92.3MB, time=2.65 memory used=272.5MB, alloc=116.3MB, time=3.40 memory used=351.4MB, alloc=116.3MB, time=4.33 memory used=415.5MB, alloc=396.3MB, time=5.09 memory used=520.9MB, alloc=396.3MB, time=6.32 memory used=625.6MB, alloc=420.3MB, time=7.54 memory used=748.6MB, alloc=444.3MB, time=9.05 memory used=882.6MB, alloc=468.3MB, time=10.64 memory used=998.4MB, alloc=468.3MB, time=12.06 memory used=1109.9MB, alloc=492.3MB, time=13.48 memory used=1284.7MB, alloc=516.3MB, time=16.24 memory used=1460.2MB, alloc=540.3MB, time=19.07 memory used=1649.5MB, alloc=564.3MB, time=22.09 memory used=1832.8MB, alloc=588.3MB, time=25.15 memory used=2031.4MB, alloc=612.3MB, time=28.50 memory used=2218.2MB, alloc=636.3MB, time=31.71 memory used=2362.2MB, alloc=660.3MB, time=34.49 memory used=2575.5MB, alloc=684.3MB, time=40.31 memory used=2786.7MB, alloc=708.3MB, time=46.73 memory used=3005.7MB, alloc=732.3MB, time=53.74 memory used=3235.1MB, alloc=756.3MB, time=61.35 memory used=3473.5MB, alloc=780.3MB, time=69.52 memory used=3721.5MB, alloc=804.3MB, time=78.55 memory used=3993.5MB, alloc=828.3MB, time=88.51 memory used=4289.4MB, alloc=852.3MB, time=99.26 memory used=4609.2MB, alloc=876.3MB, time=110.66 memory used=4953.0MB, alloc=900.3MB, time=123.02 memory used=5320.7MB, alloc=924.3MB, time=136.15 memory used=5712.4MB, alloc=948.3MB, time=150.00 memory used=6128.0MB, alloc=972.3MB, time=165.00 memory used=6567.5MB, alloc=972.3MB, time=180.99 memory used=7007.0MB, alloc=996.3MB, time=196.83 memory used=7470.4MB, alloc=996.3MB, time=213.69 memory used=7933.7MB, alloc=996.3MB, time=230.17 memory used=8396.9MB, alloc=1020.3MB, time=246.76 memory used=8883.9MB, alloc=1020.3MB, time=264.10 memory used=9370.9MB, alloc=1020.3MB, time=281.40 |\^/| 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(); 1428323663 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-18 x - 11 y z, 17 x - 12 x z, 7 z + 20] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 G := [10 y - 6 y, -16 x y - 3 y , 15 x - 10 y ] > Problem := [F,G]; 3 2 2 Problem := [[-18 x - 11 y z, 17 x - 12 x z, 7 z + 20], 2 2 3 2 2 [10 y - 6 y, -16 x y - 3 y , 15 x - 10 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.2MB, alloc=32.3MB, time=0.44 memory used=47.2MB, alloc=32.3MB, time=0.71 memory used=68.2MB, alloc=56.3MB, time=1.06 memory used=110.4MB, alloc=60.3MB, time=1.78 memory used=148.2MB, alloc=84.3MB, time=2.72 N1 := 809 > GB := Basis(F, plex(op(vars))); 3 2 2 2 GB := [2023 x + 2880 x, 216 x + 187 y, -17 x + 12 x z, 7 z + 20] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=203.4MB, alloc=84.3MB, time=3.60 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)]; 3 2 2 2 2 3 H := [-18 x - 11 y z, 17 x - 12 x z, 7 z + 20, 10 y - 6 y, -16 x y - 3 y , 2 2 15 x - 10 y ] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [2023 x + 2880 x, 216 x + 187 y, -17 x + 12 x z, 7 z + 20, 10 y - 6 y, 2 3 2 2 -16 x y - 3 y , 15 x - 10 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 11, 14, 3, 3, 3, 2, 2/3, 2/3, 1/2, 5/12, 1/2, 1/4, 7, 11, 16, 3, 3, 3, 2, 5/7, 4/7, 2/7, 1/2, 3/7, 1/7, 0, -2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=238.2MB, alloc=84.3MB, 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(); 1428323667 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [16 x y - 4 x , -19 x y z - 10 y z, -y + 2 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [9 z - 11 z , -17 y z + 12, 10 x z + 2 z ] > Problem := [F,G]; 2 2 2 3 Problem := [[16 x y - 4 x , -19 x y z - 10 y z, -y + 2 x y], 3 2 2 2 2 [9 z - 11 z , -17 y z + 12, 10 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=26.0MB, alloc=32.3MB, time=0.48 memory used=47.9MB, alloc=32.3MB, time=0.81 memory used=67.6MB, alloc=56.3MB, time=1.15 memory used=107.4MB, alloc=84.3MB, time=1.90 memory used=163.8MB, alloc=84.3MB, time=3.55 N1 := 1347 > GB := Basis(F, plex(op(vars))); 3 2 2 2 3 2 2 GB := [32 x - x , 4 x y - x , y - 2 x y, z x , y z x, z y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=216.9MB, alloc=84.3MB, time=4.48 N2 := 611 #save(Problem, "format.txt"); > if (GB=[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 := [16 x y - 4 x , -19 x y z - 10 y z, -y + 2 x y, 9 z - 11 z , 2 2 2 -17 y z + 12, 10 x z + 2 z ] > J:=[op(GB),op(G)]; 3 2 2 2 3 2 2 3 2 J := [32 x - x , 4 x y - x , y - 2 x y, z x , y z x, z y , 9 z - 11 z , 2 2 2 -17 y z + 12, 10 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, 12, 18, 3, 2, 3, 3, 2/3, 2/3, 2/3, 5/12, 1/2, 7/12, 9, 17, 27, 3, 3, 3, 3, 2/3, 5/9, 2/3, 8/19, 6/19, 8/19, -5, -9, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=239.5MB, alloc=84.3MB, time=4.87 |\^/| 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(); 1428323672 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 3 F := [5 y - 2, -4 y + 7 x y, -6 z - 12] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [15 x z - 9 y , -y z - 5 z, 3 y z - 12 x ] > Problem := [F,G]; 3 3 3 Problem := [[5 y - 2, -4 y + 7 x y, -6 z - 12], 2 2 2 2 [15 x z - 9 y , -y z - 5 z, 3 y 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=0.16 memory used=26.0MB, alloc=32.3MB, time=0.40 memory used=47.4MB, alloc=32.3MB, time=0.65 memory used=67.2MB, alloc=56.3MB, time=0.90 memory used=106.7MB, alloc=60.3MB, time=1.38 memory used=145.9MB, alloc=60.3MB, time=1.83 memory used=182.1MB, alloc=84.3MB, time=2.25 memory used=232.8MB, alloc=84.3MB, time=2.83 memory used=289.3MB, alloc=116.3MB, time=3.50 memory used=367.4MB, alloc=140.3MB, time=4.61 memory used=459.6MB, alloc=164.3MB, time=5.97 memory used=567.2MB, alloc=188.3MB, time=7.49 memory used=683.6MB, alloc=212.3MB, time=10.13 memory used=803.3MB, alloc=236.3MB, time=13.59 memory used=939.9MB, alloc=260.3MB, time=17.88 memory used=1100.5MB, alloc=260.3MB, time=22.71 memory used=1261.0MB, alloc=284.3MB, time=27.65 N1 := 5025 > GB := Basis(F, plex(op(vars))); 3 2 3 GB := [8575 x - 256, -245 x + 32 y, z + 2] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1451.2MB, alloc=284.3MB, time=32.01 memory used=1510.8MB, alloc=540.3MB, time=32.90 memory used=1672.2MB, alloc=540.3MB, time=35.03 memory used=1883.3MB, alloc=564.3MB, time=38.53 memory used=2077.9MB, alloc=588.3MB, time=44.97 N2 := 3369 #save(Problem, "format.txt"); > 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 := [5 y - 2, -4 y + 7 x y, -6 z - 12, 15 x z - 9 y , -y z - 5 z, 2 2 3 y z - 12 x ] > J:=[op(GB),op(G)]; 3 2 3 2 2 J := [8575 x - 256, -245 x + 32 y, z + 2, 15 x z - 9 y , -y z - 5 z, 2 2 3 y 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, 17, 3, 2, 3, 3, 1/2, 5/6, 2/3, 1/4, 1/2, 5/12, 6, 12, 16, 3, 3, 2, 3, 2/3, 2/3, 2/3, 1/3, 1/3, 5/12, 0, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2221.7MB, alloc=588.3MB, time=49.16 |\^/| 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(); 1428323724 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [12 x y , 14 x y + 5, -11 x y + 9 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 G := [-18 x z - 2 x, x y - y, 17 x + 2 y ] > Problem := [F,G]; 2 2 Problem := [[12 x y , 14 x y + 5, -11 x y + 9 z], 3 3 [-18 x z - 2 x, x y - y, 17 x + 2 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.9MB, alloc=32.3MB, time=0.45 memory used=48.6MB, alloc=32.3MB, time=0.74 memory used=67.5MB, alloc=56.3MB, time=1.09 N1 := 511 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 69 #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 [12 y x, 14 y x + 5, -11 x y + 9 z, -18 x z - 2 x, x y - y, 2 y + 17 x ] > J:=[op(GB),op(G)]; 3 3 J := [1, -18 x z - 2 x, x y - y, 2 y + 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, 13, 15, 3, 3, 3, 1, 1, 5/6, 1/3, 7/13, 6/13, 2/13, 4, 6, 7, 3, 3, 3, 1, 3/4, 1/2, 1/4, 4/7, 3/7, 1/7, 7, 8, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=77.6MB, alloc=56.3MB, time=1.22 |\^/| 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(); 1428323725 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [14 y z + 17 y z, -19 x y + 17 x y, -8 x - 2 x y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [20 x y + x z, 12 x y - 3 z , -6 x + 14] > Problem := [F,G]; 2 2 3 Problem := [[14 y z + 17 y z, -19 x y + 17 x y, -8 x - 2 x y z], 2 2 2 3 [20 x y + x z, 12 x y - 3 z , -6 x + 14]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.1MB, alloc=32.3MB, time=0.36 memory used=47.7MB, alloc=32.3MB, time=0.60 memory used=68.0MB, alloc=32.3MB, time=0.83 memory used=87.7MB, alloc=56.3MB, time=1.07 memory used=129.6MB, alloc=60.3MB, time=1.65 memory used=170.5MB, alloc=84.3MB, time=2.20 memory used=232.8MB, alloc=108.3MB, time=3.03 memory used=310.5MB, alloc=140.3MB, time=4.15 memory used=400.5MB, alloc=164.3MB, time=5.83 memory used=496.3MB, alloc=188.3MB, time=8.21 memory used=602.3MB, alloc=212.3MB, time=11.50 memory used=732.3MB, alloc=212.3MB, time=15.41 memory used=862.3MB, alloc=236.3MB, time=19.34 memory used=1016.4MB, alloc=236.3MB, time=24.15 N1 := 4645 > GB := Basis(F, plex(op(vars))); 4 3 3 3 3 2 GB := [19 x - 17 x , -56 x + 17 x y, 14 x z + 17 x , 14 y z + 17 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1170.1MB, alloc=236.3MB, time=27.36 memory used=1347.7MB, alloc=516.3MB, time=32.94 N2 := 2361 #save(Problem, "format.txt"); > if (GB=[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 := [14 y z + 17 y z, -19 x y + 17 x y, -8 x - 2 x y z, 20 x y + x z, 2 2 3 12 x y - 3 z , -6 x + 14] > J:=[op(GB),op(G)]; 4 3 3 3 3 2 J := [19 x - 17 x , -56 x + 17 x y, 14 x z + 17 x , 14 y z + 17 y z, 2 2 2 3 20 x y + x z, 12 x y - 3 z , -6 x + 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, 3, 3, 2, 2, 5/6, 5/6, 2/3, 2/3, 7/12, 5/12, 7, 14, 23, 4, 4, 2, 2, 6/7, 4/7, 4/7, 5/7, 5/14, 5/14, 0, -5, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1417.1MB, alloc=516.3MB, time=35.40 |\^/| 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(); 1428323762 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [15 x y + 7, -13 y + 14 z, 12 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [-7 x + 11 x z, -5 x y - 18 x, -y + y] > Problem := [F,G]; 2 2 Problem := [[15 x y + 7, -13 y + 14 z, 12 x y], 3 2 2 2 [-7 x + 11 x z, -5 x y - 18 x, -y + y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.3MB, alloc=32.3MB, time=0.47 memory used=47.4MB, alloc=56.3MB, time=0.82 N1 := 423 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 45 #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 3 2 2 H := [15 y x + 7, -13 y + 14 z, 12 x y, -7 x + 11 x z, -5 x y - 18 x, 2 -y + y] > J:=[op(GB),op(G)]; 3 2 2 2 J := [1, -7 x + 11 x z, -5 x y - 18 x, -y + 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, 15, 3, 3, 2, 1, 2/3, 5/6, 1/3, 6/13, 6/13, 2/13, 4, 5, 8, 3, 3, 2, 1, 1/2, 1/2, 1/4, 4/7, 3/7, 1/7, 6, 7, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=65.3MB, alloc=56.3MB, time=1.15 |\^/| 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(); 1428323763 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [-17 x z + 8 x, -5 x + 7 x z , -18 x - 8 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [13 y + 11 y , 10 x y z + 4 y z, -20 y z - 5 z ] > Problem := [F,G]; 3 2 3 2 Problem := [[-17 x z + 8 x, -5 x + 7 x z , -18 x - 8 x z], 3 2 2 2 2 [13 y + 11 y , 10 x y z + 4 y z, -20 y z - 5 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.0MB, alloc=32.3MB, time=0.46 memory used=48.7MB, alloc=32.3MB, time=0.83 memory used=69.8MB, alloc=56.3MB, time=1.19 memory used=110.1MB, alloc=80.3MB, time=2.08 N1 := 1125 > GB := Basis(F, plex(op(vars))); GB := [x] > 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)]; 3 2 3 2 3 2 H := [-17 x z + 8 x, -5 x + 7 x z , -18 x - 8 x z, 13 y + 11 y , 2 2 2 10 x y z + 4 y z, -20 y z - 5 z ] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [x, 13 y + 11 y , 10 x y z + 4 y z, -20 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, 12, 17, 3, 3, 3, 2, 2/3, 1/2, 5/6, 7/12, 5/12, 7/12, 4, 7, 10, 3, 1, 3, 2, 1/2, 3/4, 1/2, 2/7, 5/7, 4/7, 5, 7, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=153.5MB, alloc=80.3MB, time=2.97 |\^/| 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(); 1428323766 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [12 x - z, -14 x y - 2 y , -4 y + 15 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-3 x y - 13 y, 16 x z - 15 x , 3 x y + 17 x y] > Problem := [F,G]; 2 2 3 2 Problem := [[12 x - z, -14 x y - 2 y , -4 y + 15 z], 2 2 2 2 [-3 x y - 13 y, 16 x z - 15 x , 3 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=26.2MB, alloc=32.3MB, time=0.46 memory used=47.8MB, alloc=32.3MB, time=0.76 memory used=69.6MB, alloc=56.3MB, time=1.14 memory used=113.2MB, alloc=56.3MB, time=1.87 memory used=149.0MB, alloc=84.3MB, time=2.70 memory used=201.2MB, alloc=108.3MB, time=4.48 N1 := 1437 > GB := Basis(F, plex(op(vars))); 4 3 2 2 2 2 GB := [x , 7 x + x y, -45 x + y , -12 x + z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 597 #save(Problem, "format.txt"); > if (GB=[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 := [12 x - z, -14 x y - 2 y , -4 y + 15 z, -3 x y - 13 y, 16 x z - 15 x , 2 3 x y + 17 x y] > J:=[op(GB),op(G)]; 4 3 2 2 2 2 2 2 2 J := [x , 7 x + x y, -45 x + y , -12 x + z, -3 x y - 13 y, 16 x z - 15 x , 2 3 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, 12, 16, 3, 2, 3, 2, 5/6, 2/3, 1/2, 7/12, 7/12, 1/4, 7, 13, 20, 4, 4, 2, 2, 1, 4/7, 2/7, 5/7, 3/7, 1/7, -1, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=275.2MB, alloc=108.3MB, 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(); 1428323772 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [17 x + 14 x y, -8 x y - 20 x z, 14 x z + 7 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [-4 x y - 11 x , 19 x y + 2 y , -17 z - 11 z] > Problem := [F,G]; 3 2 2 Problem := [[17 x + 14 x y, -8 x y - 20 x z, 14 x z + 7 x y], 2 2 2 3 2 [-4 x y - 11 x , 19 x y + 2 y , -17 z - 11 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.0MB, alloc=32.3MB, time=0.37 memory used=77.4MB, alloc=68.3MB, time=1.12 memory used=124.5MB, alloc=92.3MB, time=1.83 memory used=186.2MB, alloc=92.3MB, time=3.24 N1 := 1445 > GB := Basis(F, plex(op(vars))); 4 3 3 3 GB := [4 x - 5 x , 34 x + 35 x y, -68 x + 175 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=245.2MB, alloc=92.3MB, time=4.08 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)]; 3 2 2 2 2 H := [17 x + 14 x y, -8 x y - 20 x z, 14 x z + 7 x y, -4 x y - 11 x , 2 3 2 19 x y + 2 y , -17 z - 11 z] > J:=[op(GB),op(G)]; 4 3 3 3 2 2 J := [4 x - 5 x , 34 x + 35 x y, -68 x + 175 x z, -4 x y - 11 x , 2 3 2 19 x y + 2 y , -17 z - 11 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 16, 3, 3, 3, 2, 5/6, 5/6, 1/2, 3/4, 1/2, 1/3, 6, 10, 18, 4, 4, 3, 2, 5/6, 1/2, 1/3, 3/4, 1/3, 1/4, 3, -2, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=279.7MB, alloc=92.3MB, time=4.67 |\^/| 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(); 1428323777 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 F := [-14 x y + 8 y , -8 z - 12 x , -13 y + 4 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [15 y + 7, 8 x y z + 14 x, -12 y + 13 x ] > Problem := [F,G]; 2 3 3 2 2 Problem := [[-14 x y + 8 y , -8 z - 12 x , -13 y + 4 x], 2 3 2 [15 y + 7, 8 x y z + 14 x, -12 y + 13 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.4MB, alloc=32.3MB, time=0.41 memory used=47.9MB, alloc=32.3MB, time=0.67 memory used=68.4MB, alloc=32.3MB, time=0.94 memory used=89.3MB, alloc=56.3MB, time=1.33 memory used=131.2MB, alloc=60.3MB, time=2.01 memory used=169.1MB, alloc=84.3MB, time=2.57 memory used=223.6MB, alloc=108.3MB, time=4.03 N1 := 1295 > GB := Basis(F, plex(op(vars))); 3 2 2 2 3 2 GB := [91 x - 16 x , 91 x y - 16 x y, 13 y - 4 x, 2 z + 3 x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=298.5MB, alloc=116.3MB, time=5.11 N2 := 587 #save(Problem, "format.txt"); > if (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 := [-14 x y + 8 y , -8 z - 12 x , -13 y + 4 x, 15 y + 7, 8 x y z + 14 x, 3 2 -12 y + 13 x ] > J:=[op(GB),op(G)]; 3 2 2 2 3 2 2 J := [91 x - 16 x , 91 x y - 16 x y, 13 y - 4 x, 2 z + 3 x , 15 y + 7, 3 2 8 x y z + 14 x, -12 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, 12, 16, 3, 2, 3, 3, 5/6, 5/6, 1/3, 1/2, 1/2, 1/6, 7, 13, 19, 3, 3, 3, 3, 6/7, 5/7, 2/7, 9/14, 3/7, 1/7, -1, -3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=339.3MB, alloc=116.3MB, 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(); 1428323783 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-18 x z - 4, 20 x z + 15 x, 14 x y + 6 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 2 G := [2 x y - 4 z , -15 y - 2 y, -9 x y + 20 y z ] > Problem := [F,G]; 2 2 2 Problem := [[-18 x z - 4, 20 x z + 15 x, 14 x y + 6 x y], 2 3 3 2 2 [2 x y - 4 z , -15 y - 2 y, -9 x y + 20 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.1MB, alloc=32.3MB, time=0.41 memory used=47.8MB, alloc=32.3MB, time=0.69 memory used=68.4MB, alloc=32.3MB, time=0.94 memory used=88.1MB, alloc=56.3MB, time=1.20 memory used=128.3MB, alloc=60.3MB, time=1.69 memory used=167.3MB, alloc=84.3MB, time=2.17 memory used=228.6MB, alloc=84.3MB, time=3.10 memory used=285.2MB, alloc=108.3MB, time=3.92 memory used=358.1MB, alloc=140.3MB, time=5.29 memory used=437.5MB, alloc=164.3MB, time=7.58 N1 := 2263 > GB := Basis(F, plex(op(vars))); GB := [32 x + 81, y, 27 z - 8] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=545.9MB, alloc=164.3MB, time=9.66 N2 := 545 #save(Problem, "format.txt"); > if (GB=[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 := [-18 x z - 4, 20 x z + 15 x, 14 x y + 6 x y, 2 x y - 4 z , 3 2 2 -15 y - 2 y, -9 x y + 20 y z ] > J:=[op(GB),op(G)]; 2 3 3 2 2 J := [32 x + 81, y, 27 z - 8, 2 x y - 4 z , -15 y - 2 y, -9 x y + 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, 18, 3, 2, 3, 3, 5/6, 2/3, 2/3, 7/12, 7/12, 1/3, 6, 10, 12, 3, 1, 3, 3, 1/2, 2/3, 1/2, 3/11, 6/11, 3/11, 3, 6, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=582.3MB, alloc=164.3MB, 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(); 1428323794 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [10 y z - 19 z, 18 x z - 8, 2 x - 8 x y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [10 y z - 13 y z , -4 y z - 1, 19 z + 15] > Problem := [F,G]; 2 2 3 2 Problem := [[10 y z - 19 z, 18 x z - 8, 2 x - 8 x y ], 2 2 2 2 [10 y z - 13 y z , -4 y z - 1, 19 z + 15]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.1MB, alloc=32.3MB, time=0.42 memory used=47.3MB, alloc=32.3MB, time=0.67 memory used=67.5MB, alloc=32.3MB, time=0.92 memory used=86.5MB, alloc=56.3MB, time=1.16 memory used=124.3MB, alloc=60.3MB, time=1.58 memory used=158.6MB, alloc=84.3MB, time=2.04 memory used=214.3MB, alloc=84.3MB, time=2.77 memory used=267.9MB, alloc=84.3MB, time=3.41 memory used=319.3MB, alloc=108.3MB, time=4.02 memory used=391.1MB, alloc=116.3MB, time=4.89 memory used=459.9MB, alloc=140.3MB, time=5.80 memory used=551.3MB, alloc=164.3MB, time=7.08 memory used=657.1MB, alloc=188.3MB, time=8.55 memory used=777.0MB, alloc=212.3MB, time=10.43 memory used=910.9MB, alloc=236.3MB, time=12.44 memory used=1051.0MB, alloc=516.3MB, time=14.59 memory used=1208.1MB, alloc=540.3MB, time=17.05 memory used=1365.0MB, alloc=564.3MB, time=20.85 memory used=1527.6MB, alloc=588.3MB, time=25.36 memory used=1702.5MB, alloc=612.3MB, time=30.43 memory used=1890.0MB, alloc=636.3MB, time=36.27 memory used=2093.1MB, alloc=660.3MB, time=42.88 memory used=2320.1MB, alloc=684.3MB, time=50.21 memory used=2571.0MB, alloc=708.3MB, time=58.41 memory used=2845.9MB, alloc=708.3MB, time=67.33 memory used=3120.8MB, alloc=708.3MB, time=76.29 memory used=3395.6MB, alloc=732.3MB, time=85.27 memory used=3694.4MB, alloc=732.3MB, time=94.72 memory used=3993.1MB, alloc=732.3MB, time=104.39 memory used=4291.8MB, alloc=756.3MB, time=114.01 memory used=4614.4MB, alloc=756.3MB, time=124.38 memory used=4936.8MB, alloc=780.3MB, time=134.93 memory used=5283.2MB, alloc=780.3MB, time=146.08 memory used=5629.6MB, alloc=804.3MB, time=156.86 N1 := 12041 > GB := Basis(F, plex(op(vars))); 2 GB := [29241 x - 400, 171 y - 10, 100 z - 3249] > 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 2 3 2 2 2 H := [10 y z - 19 z, 18 x z - 8, 2 x - 8 x y , 10 y z - 13 y z , 2 2 -4 y z - 1, 19 z + 15] > J:=[op(GB),op(G)]; 2 2 2 2 J := [29241 x - 400, 171 y - 10, 100 z - 3249, 10 y z - 13 y z , -4 y z - 1, 2 19 z + 15] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 11, 17, 3, 3, 2, 2, 1/3, 2/3, 5/6, 1/4, 5/12, 7/12, 6, 8, 12, 3, 2, 2, 2, 1/6, 1/2, 2/3, 1/12, 1/3, 5/12, 3, 5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=5763.1MB, alloc=804.3MB, time=159.32 |\^/| 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(); 1428323959 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 F := [16 x y z + 17, 11 x z, -15 y + 4 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 G := [20 x y z + 3, 9 x, -18 x - 14 y] > Problem := [F,G]; Problem := [ 2 3 3 2 [16 x y z + 17, 11 x z, -15 y + 4 z ], [20 x y z + 3, 9 x, -18 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=0.16 memory used=27.1MB, alloc=32.3MB, time=0.47 memory used=50.0MB, alloc=32.3MB, time=0.77 memory used=70.3MB, alloc=56.3MB, time=1.07 N1 := 531 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 29 #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 3 2 H := [16 z y x + 17, 11 x z, -15 y + 4 z , 20 z y x + 3, 9 x, -18 x - 14 y] > J:=[op(GB),op(G)]; 2 J := [1, 20 z y x + 3, 9 x, -18 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, 15, 3, 2, 3, 3, 5/6, 2/3, 2/3, 5/13, 4/13, 4/13, 4, 6, 6, 3, 2, 1, 1, 3/4, 1/2, 1/4, 3/7, 2/7, 1/7, 7, 9, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=85.8MB, alloc=56.3MB, time=1.33 |\^/| 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(); 1428323961 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 F := [7 x z + 17 x z, -2 x z - 3 x , -16 x + 8 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [-10 z + 6 y , 6 z + 5 x, 10 x z - 2 z ] > Problem := [F,G]; 2 2 2 2 2 Problem := [[7 x z + 17 x z, -2 x z - 3 x , -16 x + 8 z ], 3 2 2 2 2 [-10 z + 6 y , 6 z + 5 x, 10 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=0.14 memory used=26.2MB, alloc=32.3MB, time=0.39 memory used=47.5MB, alloc=32.3MB, time=0.61 memory used=67.4MB, alloc=56.3MB, time=0.84 memory used=109.7MB, alloc=60.3MB, time=1.40 memory used=149.8MB, alloc=84.3MB, time=2.00 memory used=210.0MB, alloc=108.3MB, time=2.91 memory used=287.4MB, alloc=132.3MB, time=3.97 memory used=373.4MB, alloc=164.3MB, time=5.55 memory used=464.0MB, alloc=188.3MB, time=8.17 memory used=577.4MB, alloc=188.3MB, time=11.57 memory used=690.8MB, alloc=188.3MB, time=14.84 memory used=804.1MB, alloc=212.3MB, time=17.83 N1 := 4181 > GB := Basis(F, plex(op(vars))); 2 2 GB := [x , z x, z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 335 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 3 2 2 H := [7 x z + 17 x z, -2 x z - 3 x , -16 x + 8 z , -10 z + 6 y , 6 z + 5 x, 2 2 10 x z - 2 z ] > J:=[op(GB),op(G)]; 2 2 3 2 2 2 2 J := [x , z x, z , -10 z + 6 y , 6 z + 5 x, 10 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, 12, 16, 3, 2, 2, 3, 5/6, 1/6, 1, 7/12, 1/12, 2/3, 6, 10, 14, 3, 2, 2, 3, 2/3, 1/6, 5/6, 1/3, 1/12, 1/2, 2, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=890.6MB, alloc=212.3MB, 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(); 1428323981 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 F := [10 z - 16 y , -11 x y - z , 19 x z + 18 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 G := [16 x - 4 x , 16 x - 20 y , 13 x z - 11 x] > Problem := [F,G]; 3 2 2 2 2 Problem := [[10 z - 16 y , -11 x y - z , 19 x z + 18 y z], 3 2 3 2 2 [16 x - 4 x , 16 x - 20 y , 13 x z - 11 x]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.44 memory used=47.8MB, alloc=32.3MB, time=0.68 memory used=68.6MB, alloc=32.3MB, time=0.90 memory used=88.4MB, alloc=56.3MB, time=1.14 memory used=128.5MB, alloc=60.3MB, time=1.64 memory used=167.0MB, alloc=84.3MB, time=2.16 memory used=227.1MB, alloc=84.3MB, time=3.05 memory used=280.4MB, alloc=108.3MB, time=3.84 memory used=352.1MB, alloc=140.3MB, time=4.92 memory used=438.7MB, alloc=164.3MB, time=6.11 memory used=535.8MB, alloc=188.3MB, time=8.22 memory used=640.2MB, alloc=212.3MB, time=11.11 memory used=760.6MB, alloc=236.3MB, time=14.80 memory used=904.9MB, alloc=236.3MB, time=19.22 memory used=1049.3MB, alloc=236.3MB, time=23.64 memory used=1193.6MB, alloc=260.3MB, time=28.09 memory used=1362.0MB, alloc=284.3MB, time=32.91 N1 := 5431 > GB := Basis(F, plex(op(vars))); 3 2 2 3 2 2 2 2 2 GB := [3971 x y + 324 y , 495 y - 76 y , -209 x y + 18 y z, 11 y x + z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1480.9MB, alloc=284.3MB, time=34.74 N2 := 1551 #save(Problem, "format.txt"); > 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 := [10 z - 16 y , -11 x y - z , 19 x z + 18 y z, 16 x - 4 x , 3 2 2 16 x - 20 y , 13 x z - 11 x] > J:=[op(GB),op(G)]; 3 2 2 3 2 2 2 2 2 J := [3971 x y + 324 y , 495 y - 76 y , -209 x y + 18 y z, 11 y x + z , 3 2 3 2 2 16 x - 4 x , 16 x - 20 y , 13 x 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, 13, 18, 3, 3, 2, 3, 5/6, 2/3, 2/3, 7/12, 1/3, 5/12, 7, 14, 24, 5, 3, 3, 2, 6/7, 5/7, 3/7, 4/7, 4/7, 3/14, -1, -6, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1613.0MB, alloc=540.3MB, time=37.54 |\^/| 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(); 1428324020 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-16 y - 5 z, -16 x y z + 5, -13 x z + 8 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [16 y , 14 x - 7 y z, -19 x - z] > Problem := [F,G]; 2 2 Problem := [[-16 y - 5 z, -16 x y z + 5, -13 x z + 8 x ], 2 3 2 [16 y , 14 x - 7 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=0.16 memory used=26.9MB, alloc=32.3MB, time=0.43 memory used=48.0MB, alloc=32.3MB, time=0.66 memory used=67.8MB, alloc=32.3MB, time=0.92 memory used=87.0MB, alloc=56.3MB, time=1.16 memory used=128.1MB, alloc=60.3MB, time=1.64 memory used=167.2MB, alloc=84.3MB, time=2.11 memory used=209.6MB, alloc=84.3MB, time=2.64 memory used=267.4MB, alloc=92.3MB, time=3.34 memory used=323.9MB, alloc=116.3MB, time=4.01 memory used=401.5MB, alloc=140.3MB, time=5.16 memory used=500.5MB, alloc=164.3MB, time=6.56 memory used=612.2MB, alloc=188.3MB, time=8.16 memory used=726.8MB, alloc=468.3MB, time=9.81 memory used=887.7MB, alloc=492.3MB, time=11.61 memory used=1035.2MB, alloc=516.3MB, time=15.01 memory used=1184.6MB, alloc=540.3MB, time=19.33 memory used=1346.6MB, alloc=564.3MB, time=24.42 memory used=1532.6MB, alloc=588.3MB, time=30.23 memory used=1742.5MB, alloc=588.3MB, time=37.57 memory used=1952.4MB, alloc=588.3MB, time=45.86 memory used=2162.4MB, alloc=612.3MB, time=53.03 memory used=2396.5MB, alloc=636.3MB, time=60.46 N1 := 7081 > GB := Basis(F, plex(op(vars))); 2 2 GB := [8 x + 13, 416 y - 25 x, 5 z + 16 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 469 #save(Problem, "format.txt"); > if (GB=[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 := [-16 y - 5 z, -16 x y z + 5, -13 x z + 8 x , 16 y , 14 x - 7 y z, -19 x - z] > J:=[op(GB),op(G)]; 2 2 2 3 2 J := [8 x + 13, 416 y - 25 x, 5 z + 16 y, 16 y , 14 x - 7 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, 13, 13, 3, 3, 2, 2, 2/3, 2/3, 5/6, 5/12, 1/3, 5/12, 6, 11, 11, 3, 3, 2, 1, 2/3, 2/3, 1/2, 1/3, 1/3, 1/4, 2, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2528.8MB, alloc=636.3MB, time=62.95 |\^/| 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(); 1428324086 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 F := [13 x y + 3 z , 14 y z + 15 y, -18 x y + 3 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [8 z + 17, 5 y + 1, 2 x y + 17] > Problem := [F,G]; 2 3 2 2 2 Problem := [[13 x y + 3 z , 14 y z + 15 y, -18 x y + 3 z ], 2 2 [8 z + 17, 5 y + 1, 2 x y + 17]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.45 memory used=47.8MB, alloc=32.3MB, time=0.73 memory used=68.5MB, alloc=32.3MB, time=0.99 memory used=88.8MB, alloc=56.3MB, time=1.24 memory used=129.4MB, alloc=60.3MB, time=1.74 memory used=170.0MB, alloc=60.3MB, time=2.29 memory used=210.0MB, alloc=84.3MB, time=2.92 N1 := 727 > GB := Basis(F, plex(op(vars))); 2 GB := [y, z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 39 #save(Problem, "format.txt"); > 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 := [3 z + 13 y x , 14 y z + 15 y, -18 x y + 3 z , 8 z + 17, 5 y + 1, 2 y x + 17] > J:=[op(GB),op(G)]; 2 2 2 J := [y, z , 8 z + 17, 5 y + 1, 2 y x + 17] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 15, 3, 2, 2, 3, 1/2, 5/6, 2/3, 1/4, 1/2, 1/3, 5, 6, 9, 2, 1, 2, 2, 1/5, 3/5, 2/5, 1/9, 1/3, 2/9, 6, 6, 1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=263.0MB, alloc=84.3MB, time=3.80 |\^/| 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(); 1428324090 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-2 x z - 1, -9 y z - 8 x z, 11 y - 3 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 G := [-17 x y - 17 y, -20 x , 17 x - 9 y z ] > Problem := [F,G]; 2 2 3 2 Problem := [[-2 x z - 1, -9 y z - 8 x z, 11 y - 3 x ], 2 3 3 2 [-17 x y - 17 y, -20 x , 17 x - 9 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.6MB, alloc=32.3MB, time=0.45 memory used=47.7MB, alloc=32.3MB, time=0.71 memory used=68.9MB, alloc=56.3MB, time=1.04 memory used=110.8MB, alloc=60.3MB, time=1.69 memory used=148.0MB, alloc=84.3MB, time=2.52 N1 := 1095 > GB := Basis(F, plex(op(vars))); 7 3 5 GB := [45056 x - 2187, -16 x + 9 y, 22528 x + 2187 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); 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 H := [-2 x z - 1, -9 y z - 8 x z, 11 y - 3 x , -17 x y - 17 y, -20 x , 2 3 -9 z y + 17 x ] > J:=[op(GB),op(G)]; 7 3 5 2 3 J := [45056 x - 2187, -16 x + 9 y, 22528 x + 2187 z, -17 x y - 17 y, -20 x , 2 3 -9 z y + 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, 13, 18, 3, 3, 3, 2, 1, 2/3, 1/2, 1/2, 5/12, 1/3, 6, 11, 24, 7, 7, 1, 2, 1, 1/2, 1/3, 1/2, 1/3, 1/6, 2, -6, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=203.9MB, alloc=84.3MB, time=3.42 |\^/| 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(); 1428324093 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 F := [14 x - 13 x y, 2 x z + 10 y , -11 x z + 18 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 G := [19 x z , -7 y, 2 x y z + 10 y] > Problem := [F,G]; 3 2 3 2 2 Problem := [[14 x - 13 x y, 2 x z + 10 y , -11 x z + 18 y ], 2 [19 x z , -7 y, 2 x 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=0.16 memory used=26.8MB, alloc=32.3MB, time=0.47 memory used=48.8MB, alloc=32.3MB, time=0.80 memory used=69.0MB, alloc=56.3MB, time=1.13 memory used=110.4MB, alloc=60.3MB, time=1.76 memory used=147.3MB, alloc=84.3MB, time=2.63 N1 := 1163 > GB := Basis(F, plex(op(vars))); 8 7 3 6 3 2 2 GB := [7865 x + 4536 x , -14 x + 13 x y, -2744 x + 2197 y , 11 z x - 18 y , 7 2 6 2 75460 x + 19773 y z, 13720 x + 2197 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=202.7MB, alloc=84.3MB, time=3.62 memory used=259.9MB, alloc=92.3MB, time=4.37 memory used=315.1MB, alloc=116.3MB, time=5.18 memory used=394.4MB, alloc=140.3MB, time=6.44 memory used=485.3MB, alloc=164.3MB, time=9.17 N2 := 1827 #save(Problem, "format.txt"); > 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 := [14 x - 13 x y, 2 x z + 10 y , -11 x z + 18 y , 19 z x, -7 y, 2 x y z + 10 y] > J:=[op(GB),op(G)]; 8 7 3 6 3 2 2 J := [7865 x + 4536 x , -14 x + 13 x y, -2744 x + 2197 y , 11 z x - 18 y , 7 2 6 2 2 75460 x + 19773 z y , 13720 x + 2197 x z , 19 z x, -7 y, 2 x y 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, 16, 3, 3, 3, 2, 5/6, 5/6, 2/3, 6/13, 6/13, 4/13, 9, 19, 40, 8, 8, 3, 2, 8/9, 2/3, 5/9, 11/19, 7/19, 5/19, -5, -24, -5] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=517.0MB, alloc=164.3MB, time=10.03 |\^/| 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(); 1428324104 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [-5 x y - 12 x , 12 x z + 3 x, -17 x + 2] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-18 x z - 10 y , -19 y z + 9 y z, 6 x + 5 y z] > Problem := [F,G]; 2 2 3 Problem := [[-5 x y - 12 x , 12 x z + 3 x, -17 x + 2], 2 2 2 2 [-18 x z - 10 y , -19 y z + 9 y 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=0.17 memory used=26.4MB, alloc=32.3MB, time=0.46 memory used=47.9MB, alloc=32.3MB, time=0.73 memory used=68.0MB, alloc=32.3MB, time=1.00 memory used=86.9MB, alloc=56.3MB, time=1.27 memory used=129.7MB, alloc=60.3MB, time=1.97 memory used=166.4MB, alloc=84.3MB, time=2.55 memory used=221.9MB, alloc=108.3MB, time=3.44 memory used=292.7MB, alloc=132.3MB, time=5.09 memory used=374.3MB, alloc=132.3MB, time=7.73 memory used=456.0MB, alloc=156.3MB, time=10.40 N1 := 2839 > GB := Basis(F, plex(op(vars))); 3 GB := [17 x - 2, 5 y + 12, 4 z + 1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=561.4MB, alloc=164.3MB, time=12.48 memory used=677.6MB, alloc=188.3MB, time=14.29 memory used=810.3MB, alloc=212.3MB, time=17.52 memory used=943.0MB, alloc=236.3MB, time=22.02 N2 := 2839 #save(Problem, "format.txt"); > if (GB=[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 := [-5 x y - 12 x , 12 x z + 3 x, -17 x + 2, -18 x z - 10 y , 2 2 -19 y z + 9 y z, 5 z y + 6 x ] > J:=[op(GB),op(G)]; 3 2 2 2 J := [17 x - 2, 5 y + 12, 4 z + 1, -18 x z - 10 y , -19 y z + 9 y z, 2 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, 13, 16, 3, 3, 2, 2, 5/6, 2/3, 2/3, 7/12, 5/12, 5/12, 6, 11, 13, 3, 3, 2, 2, 1/2, 2/3, 2/3, 1/4, 5/12, 5/12, 2, 3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=994.4MB, alloc=236.3MB, time=23.49 |\^/| 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(); 1428324129 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [15 x z - 4 z , 15 x y z + 18 y z , x - 19 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 G := [-20 x z - 13 y , -9 x y + 17 y z, 8 x y] > Problem := [F,G]; 2 2 2 3 2 Problem := [[15 x z - 4 z , 15 x y z + 18 y z , x - 19 x z], 2 3 2 2 2 [-20 x z - 13 y , -9 x y + 17 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=4.2MB, alloc=32.3MB, time=0.14 memory used=26.4MB, alloc=32.3MB, time=0.42 memory used=49.1MB, alloc=32.3MB, time=0.78 N1 := 445 > GB := Basis(F, plex(op(vars))); 5 4 3 3 2 4 2 GB := [15 x - 4 x , y x , -x + 19 x z, z y x, -225 x + 5776 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=68.3MB, alloc=56.3MB, time=1.10 memory used=108.4MB, alloc=60.3MB, time=1.63 memory used=146.1MB, alloc=60.3MB, time=2.10 memory used=185.3MB, alloc=84.3MB, time=2.71 memory used=244.5MB, alloc=108.3MB, time=3.66 memory used=320.6MB, alloc=140.3MB, time=4.87 memory used=407.0MB, alloc=164.3MB, time=7.29 memory used=507.0MB, alloc=164.3MB, time=10.59 N2 := 2883 #save(Problem, "format.txt"); > if (GB=[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 H := [15 x z - 4 z , 15 x y z + 18 y z , x - 19 x z, -20 x z - 13 y , 2 2 2 -9 x y + 17 y z, 8 x y] > J:=[op(GB),op(G)]; 5 4 3 3 2 4 2 J := [15 x - 4 x , y x , -x + 19 x z, z y x, -225 x + 5776 z , 2 3 2 2 2 -20 x z - 13 y , -9 x y + 17 y z, 8 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, 18, 3, 3, 3, 2, 1, 2/3, 5/6, 7/13, 6/13, 7/13, 8, 18, 28, 5, 5, 3, 2, 1, 5/8, 5/8, 5/9, 1/3, 5/18, -3, -10, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=594.3MB, alloc=164.3MB, time=13.17 |\^/| 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(); 1428324143 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [15 + 16 z, 8 x + 12, -2 x y + 9 x z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [19 x z + 13 y z, -5 x z + 16 y z , -19 x z - 10 y] > Problem := [F,G]; 3 2 2 Problem := [[15 + 16 z, 8 x + 12, -2 x y + 9 x z ], 2 2 2 2 [19 x z + 13 y z, -5 x z + 16 y z , -19 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=26.5MB, alloc=32.3MB, time=0.42 memory used=48.0MB, alloc=32.3MB, time=0.71 memory used=68.0MB, alloc=56.3MB, time=0.99 memory used=106.6MB, alloc=60.3MB, time=1.49 memory used=144.5MB, alloc=84.3MB, time=1.98 memory used=204.3MB, alloc=92.3MB, time=2.77 memory used=262.2MB, alloc=116.3MB, time=3.54 memory used=339.5MB, alloc=116.3MB, time=4.53 memory used=415.5MB, alloc=140.3MB, time=5.68 memory used=509.1MB, alloc=164.3MB, time=7.16 memory used=618.8MB, alloc=188.3MB, time=8.93 memory used=734.4MB, alloc=468.3MB, time=10.85 memory used=871.7MB, alloc=492.3MB, time=13.06 memory used=1012.7MB, alloc=516.3MB, time=16.64 memory used=1157.9MB, alloc=540.3MB, time=20.90 memory used=1308.8MB, alloc=564.3MB, time=26.26 memory used=1483.6MB, alloc=588.3MB, time=32.52 memory used=1682.3MB, alloc=612.3MB, time=39.67 memory used=1905.0MB, alloc=612.3MB, time=47.75 memory used=2127.6MB, alloc=636.3MB, time=55.79 memory used=2374.3MB, alloc=636.3MB, time=64.53 memory used=2620.9MB, alloc=660.3MB, time=73.28 N1 := 8047 > GB := Basis(F, plex(op(vars))); 3 2 GB := [2 x + 3, 675 x + 256 y, 16 z + 15] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2929.0MB, alloc=692.3MB, time=83.15 memory used=3134.8MB, alloc=692.3MB, time=86.52 memory used=3378.4MB, alloc=716.3MB, time=91.51 memory used=3700.6MB, alloc=740.3MB, time=103.50 N2 := 4643 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 3 2 2 2 H := [16 z + 15, 8 x + 12, -2 x y + 9 x z , 19 x z + 13 y z, 2 2 2 -5 x z + 16 y z , -19 x z - 10 y] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [2 x + 3, 675 x + 256 y, 16 z + 15, 19 x z + 13 y z, -5 x z + 16 y z , 2 -19 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, 16, 3, 3, 1, 2, 5/6, 2/3, 5/6, 1/2, 1/3, 7/12, 6, 13, 15, 3, 3, 1, 2, 5/6, 2/3, 2/3, 5/12, 1/3, 1/2, 1, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=4000.9MB, alloc=740.3MB, time=114.43 |\^/| 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(); 1428324263 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [5 y z - 20 z, -6 x z + 15 x z , 19 x y z - 15 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-6 x + 7 x y, -4 x y + 4 x y z, -9 x y - 9 x z ] > Problem := [F,G]; 2 2 2 2 Problem := [[5 y z - 20 z, -6 x z + 15 x z , 19 x y z - 15 y ], 2 2 2 2 [-6 x + 7 x y, -4 x y + 4 x y z, -9 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=0.18 memory used=26.0MB, alloc=32.3MB, time=0.43 memory used=47.5MB, alloc=32.3MB, time=0.67 memory used=67.4MB, alloc=32.3MB, time=0.92 memory used=86.7MB, alloc=56.3MB, time=1.17 memory used=126.5MB, alloc=60.3MB, time=1.72 memory used=163.7MB, alloc=84.3MB, time=2.20 memory used=221.0MB, alloc=108.3MB, time=3.05 memory used=297.3MB, alloc=140.3MB, time=4.25 memory used=388.7MB, alloc=164.3MB, time=5.72 memory used=493.6MB, alloc=188.3MB, time=7.42 memory used=610.1MB, alloc=212.3MB, time=9.45 memory used=729.9MB, alloc=236.3MB, time=12.56 memory used=859.4MB, alloc=260.3MB, time=16.26 memory used=999.4MB, alloc=284.3MB, time=20.96 memory used=1160.3MB, alloc=308.3MB, time=26.72 memory used=1345.2MB, alloc=308.3MB, time=33.26 memory used=1530.0MB, alloc=332.3MB, time=39.65 memory used=1738.8MB, alloc=332.3MB, time=46.82 memory used=1947.6MB, alloc=332.3MB, time=53.99 memory used=2156.2MB, alloc=356.3MB, time=61.16 memory used=2388.8MB, alloc=356.3MB, time=69.11 N1 := 8027 > GB := Basis(F, plex(op(vars))); 4 2 2 2 2 3 2 GB := [361 x y - 5625 y , -38 x y + 75 y , -x y + 10 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=2623.2MB, alloc=356.3MB, time=76.88 memory used=2708.7MB, alloc=612.3MB, time=78.44 memory used=2994.1MB, alloc=636.3MB, time=86.63 N2 := 2231 #save(Problem, "format.txt"); > if (GB=[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 := [5 y z - 20 z, -6 x z + 15 x z , 19 x y z - 15 y , -6 x + 7 x y, 2 2 2 -4 x y + 4 x y z, -9 x y - 9 x z ] > J:=[op(GB),op(G)]; 4 2 2 2 2 3 2 2 J := [361 x y - 5625 y , -38 x y + 75 y , -x y + 10 z, -6 x + 7 x y, 2 2 2 -4 x y + 4 x y z, -9 x y - 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, 15, 17, 3, 2, 2, 2, 5/6, 5/6, 5/6, 3/4, 7/12, 7/12, 6, 15, 21, 6, 4, 3, 2, 1, 1, 1/2, 3/4, 3/4, 1/4, 0, -4, -3] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=3010.9MB, alloc=636.3MB, time=87.14 |\^/| 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(); 1428324353 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-4 x z + 2 y , 16 y z - 6 x y, -20 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 G := [2 x z - 15 x y, 2 y z, -8 y - 15 z] > Problem := [F,G]; 2 2 2 Problem := [[-4 x z + 2 y , 16 y z - 6 x y, -20 x z], 2 [2 x z - 15 x y, 2 y z, -8 y - 15 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.9MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.77 memory used=67.6MB, alloc=56.3MB, time=1.02 memory used=109.6MB, alloc=60.3MB, time=1.59 memory used=149.1MB, alloc=84.3MB, time=2.21 memory used=208.2MB, alloc=108.3MB, time=3.16 memory used=284.2MB, alloc=140.3MB, time=4.57 memory used=367.7MB, alloc=164.3MB, time=7.07 memory used=468.3MB, alloc=164.3MB, time=10.43 N1 := 2835 > GB := Basis(F, plex(op(vars))); 2 GB := [y x, y , x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 99 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-4 x z + 2 y , 16 y z - 6 x y, -20 x z, 2 x z - 15 x y, 2 z y, -8 y - 15 z] > J:=[op(GB),op(G)]; 2 2 J := [y x, y , x z, 2 x z - 15 x y, 2 z y, -8 y - 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, 14, 3, 2, 2, 2, 2/3, 5/6, 1, 5/14, 3/7, 3/7, 6, 12, 12, 3, 1, 2, 2, 1/2, 5/6, 2/3, 4/13, 5/13, 4/13, 3, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=546.8MB, alloc=164.3MB, time=12.64 |\^/| 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(); 1428324367 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-7 x y + 20 y z, -y + 10 y z, -10 x y - 4 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 3 2 G := [17 x - 13 x z, 18 x z + 3 y z, 10 x - 8 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-7 x y + 20 y z, -y + 10 y z, -10 x y - 4 z], 3 2 2 2 3 2 [17 x - 13 x z, 18 x z + 3 y z, 10 x - 8 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.45 memory used=47.5MB, alloc=32.3MB, time=0.74 memory used=66.6MB, alloc=32.3MB, time=0.95 memory used=85.7MB, alloc=56.3MB, time=1.21 memory used=125.8MB, alloc=60.3MB, time=1.72 memory used=163.1MB, alloc=84.3MB, time=2.19 memory used=219.3MB, alloc=84.3MB, time=2.94 memory used=272.9MB, alloc=116.3MB, time=3.65 memory used=349.5MB, alloc=140.3MB, time=4.91 memory used=443.2MB, alloc=164.3MB, time=6.45 memory used=566.1MB, alloc=188.3MB, time=8.06 memory used=696.7MB, alloc=212.3MB, time=10.06 memory used=827.0MB, alloc=492.3MB, time=12.28 memory used=971.5MB, alloc=516.3MB, time=15.31 memory used=1112.4MB, alloc=540.3MB, time=18.83 memory used=1261.4MB, alloc=564.3MB, time=23.07 memory used=1419.3MB, alloc=588.3MB, time=28.30 memory used=1601.1MB, alloc=612.3MB, time=34.22 memory used=1806.9MB, alloc=636.3MB, time=40.92 memory used=2036.6MB, alloc=660.3MB, time=48.37 memory used=2290.3MB, alloc=660.3MB, time=56.59 memory used=2543.9MB, alloc=660.3MB, time=64.73 memory used=2797.5MB, alloc=684.3MB, time=73.01 memory used=3075.1MB, alloc=684.3MB, time=82.10 memory used=3352.6MB, alloc=708.3MB, time=90.94 memory used=3654.1MB, alloc=732.3MB, time=100.29 N1 := 9757 > GB := Basis(F, plex(op(vars))); 4 2 2 2 2 2 3 2 GB := [25 x y + x y, 25 x y + y , -7 x y + 2 y , 5 y x + 2 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 1127 #save(Problem, "format.txt"); > if (GB=[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 x y + 20 y z, -y + 10 y z, -10 x y - 4 z, 17 x - 13 x z, 2 2 3 2 18 x z + 3 y z, 10 x - 8 z ] > J:=[op(GB),op(G)]; 4 2 2 2 2 2 3 2 J := [25 x y + x y, 25 x y + y , -7 x y + 2 y , 5 y x + 2 z, 3 2 2 2 3 2 17 x - 13 x z, 18 x z + 3 y z, 10 x - 8 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 17, 3, 3, 2, 2, 5/6, 2/3, 1, 1/2, 1/2, 7/12, 7, 16, 24, 5, 4, 3, 2, 1, 5/7, 4/7, 9/14, 4/7, 5/14, -1, -7, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=3953.9MB, alloc=732.3MB, time=106.26 |\^/| 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(); 1428324477 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 F := [-14 y + 10 y, -17 x z + 5 y z, 12 y + 11] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-8 z + 13 x y, 7 x y + 2 x z, 8 x z + 12] > Problem := [F,G]; 2 2 3 Problem := [[-14 y + 10 y, -17 x z + 5 y z, 12 y + 11], 3 2 2 [-8 z + 13 x y, 7 x y + 2 x z, 8 x z + 12]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.2MB, alloc=32.3MB, time=0.40 memory used=47.8MB, alloc=32.3MB, time=0.64 memory used=68.5MB, alloc=32.3MB, time=0.90 memory used=88.3MB, alloc=56.3MB, time=1.14 memory used=128.1MB, alloc=60.3MB, time=1.61 memory used=168.3MB, alloc=84.3MB, time=2.16 memory used=227.7MB, alloc=84.3MB, time=3.03 memory used=281.5MB, alloc=108.3MB, time=3.84 memory used=354.6MB, alloc=140.3MB, time=4.96 memory used=443.4MB, alloc=164.3MB, time=6.49 memory used=538.3MB, alloc=188.3MB, time=8.78 memory used=643.5MB, alloc=212.3MB, time=11.91 memory used=772.1MB, alloc=212.3MB, time=15.90 memory used=900.6MB, alloc=236.3MB, time=19.99 memory used=1053.1MB, alloc=236.3MB, time=24.84 N1 := 4507 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 363 #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 3 3 H := [-14 y + 10 y, -17 x z + 5 y z, 12 y + 11, -8 z + 13 y x, 2 2 7 x y + 2 x z, 8 x z + 12] > J:=[op(GB),op(G)]; 3 2 2 J := [1, -8 z + 13 y x, 7 x y + 2 x z, 8 x z + 12] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 17, 3, 2, 3, 3, 2/3, 5/6, 2/3, 5/12, 1/2, 5/12, 4, 8, 9, 3, 2, 2, 3, 3/4, 1/2, 3/4, 4/7, 2/7, 3/7, 5, 8, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1141.2MB, alloc=236.3MB, time=26.47 |\^/| 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(); 1428324504 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [15 y - 19 z, 10 x y + x z, 15 y z - 13 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [8 x y - 4 y, -18 y z - 7 z , -10 x y + 18 y z] > Problem := [F,G]; 2 2 2 Problem := [[15 y - 19 z, 10 x y + x z, 15 y z - 13 x ], 2 2 2 [8 x y - 4 y, -18 y z - 7 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=4.2MB, alloc=32.3MB, time=0.16 memory used=26.3MB, alloc=32.3MB, time=0.45 memory used=47.8MB, alloc=32.3MB, time=0.68 memory used=67.1MB, alloc=56.3MB, time=0.93 memory used=105.4MB, alloc=60.3MB, time=1.41 memory used=142.3MB, alloc=84.3MB, time=1.90 memory used=199.7MB, alloc=92.3MB, time=2.65 memory used=255.4MB, alloc=92.3MB, time=3.32 memory used=311.1MB, alloc=116.3MB, time=4.01 memory used=387.1MB, alloc=116.3MB, time=5.03 memory used=460.3MB, alloc=140.3MB, time=6.02 memory used=553.6MB, alloc=164.3MB, time=7.29 memory used=652.7MB, alloc=188.3MB, time=8.79 memory used=768.6MB, alloc=468.3MB, time=10.54 memory used=910.3MB, alloc=492.3MB, time=12.64 memory used=1063.2MB, alloc=516.3MB, time=14.98 memory used=1223.0MB, alloc=540.3MB, time=17.57 memory used=1387.6MB, alloc=564.3MB, time=20.72 memory used=1543.3MB, alloc=588.3MB, time=24.89 memory used=1706.8MB, alloc=612.3MB, time=29.60 memory used=1882.0MB, alloc=636.3MB, time=34.89 memory used=2069.6MB, alloc=660.3MB, time=41.02 memory used=2267.3MB, alloc=684.3MB, time=47.98 memory used=2488.8MB, alloc=708.3MB, time=55.77 memory used=2734.3MB, alloc=732.3MB, time=64.21 memory used=3003.8MB, alloc=756.3MB, time=73.45 memory used=3297.3MB, alloc=780.3MB, time=83.64 memory used=3614.6MB, alloc=804.3MB, time=94.63 memory used=3955.9MB, alloc=804.3MB, time=106.32 memory used=4297.2MB, alloc=804.3MB, time=117.96 memory used=4638.4MB, alloc=828.3MB, time=130.10 memory used=5003.5MB, alloc=828.3MB, time=142.84 memory used=5368.6MB, alloc=828.3MB, time=155.34 memory used=5733.7MB, alloc=852.3MB, time=167.90 memory used=6122.7MB, alloc=852.3MB, time=181.39 memory used=6511.8MB, alloc=876.3MB, time=194.65 memory used=6924.8MB, alloc=876.3MB, time=208.63 memory used=7337.9MB, alloc=900.3MB, time=222.46 N1 := 14475 > GB := Basis(F, plex(op(vars))); 5 3 3 3 2 GB := [257514296 x + 91125 x , -6776692 x + 30375 x y, 3375 y - 4693 x , 19 z - 15 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7786.4MB, alloc=900.3MB, time=235.70 N2 := 1835 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-19 z + 15 y, 10 x y + x z, 15 y z - 13 x , 8 x y - 4 y, 2 2 -18 y z - 7 z , -10 x y + 18 y z] > J:=[op(GB),op(G)]; 5 3 3 3 2 J := [257514296 x + 91125 x , -6776692 x + 30375 x y, 3375 y - 4693 x , 2 2 2 19 z - 15 y, 8 x y - 4 y, -18 y z - 7 z , -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, 15, 15, 3, 2, 2, 2, 2/3, 1, 5/6, 5/12, 2/3, 1/2, 7, 14, 20, 5, 5, 3, 2, 5/7, 6/7, 3/7, 1/2, 4/7, 2/7, 1, -5, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=7946.8MB, alloc=900.3MB, time=241.04 |\^/| 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(); 1428324754 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [7 y z - 13 y z , 18 x y + 12 x y, -20 x z + 7 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [16 y z - 8 y z, -3 x z - 4 x y, 14 x z + 7 y] > Problem := [F,G]; 2 2 2 2 Problem := [[7 y z - 13 y z , 18 x y + 12 x y, -20 x z + 7 z ], 2 2 2 [16 y z - 8 y z, -3 x z - 4 x y, 14 x z + 7 y]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.44 memory used=46.9MB, alloc=32.3MB, time=0.66 memory used=67.1MB, alloc=32.3MB, time=0.88 memory used=86.0MB, alloc=56.3MB, time=1.10 memory used=123.9MB, alloc=60.3MB, time=1.58 memory used=160.9MB, alloc=84.3MB, time=2.13 memory used=216.9MB, alloc=108.3MB, time=2.99 memory used=290.5MB, alloc=140.3MB, time=4.12 memory used=379.8MB, alloc=164.3MB, time=5.41 memory used=480.9MB, alloc=188.3MB, time=7.45 memory used=587.7MB, alloc=212.3MB, time=10.12 memory used=703.4MB, alloc=236.3MB, time=13.88 memory used=843.2MB, alloc=236.3MB, time=18.36 memory used=982.9MB, alloc=260.3MB, time=22.79 memory used=1146.6MB, alloc=260.3MB, time=27.94 memory used=1310.3MB, alloc=284.3MB, time=33.18 memory used=1498.2MB, alloc=308.3MB, time=38.62 N1 := 5835 > GB := Basis(F, plex(op(vars))); GB := [ 2 2 2 2 3 x y + 2 x y, 390 x y z + 49 x y z, -260 x y z + 49 y z, -20 x z + 7 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1598.9MB, alloc=308.3MB, time=40.05 memory used=1842.3MB, alloc=588.3MB, time=44.72 memory used=2066.0MB, alloc=612.3MB, time=51.68 N2 := 3223 #save(Problem, "format.txt"); > if (GB=[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 := [7 y z - 13 y z , 18 x y + 12 x y, -20 x z + 7 z , 16 y z - 8 y z, 2 2 -3 x z - 4 x y, 14 x z + 7 y] > J:=[op(GB),op(G)]; 2 2 2 J := [3 x y + 2 x y, 390 x y z + 49 x y z, -260 x y z + 49 y z, 2 2 2 2 -20 x z + 7 z , 16 y z - 8 y z, -3 x z - 4 x y, 14 x z + 7 y] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 17, 3, 2, 2, 2, 2/3, 5/6, 5/6, 1/2, 2/3, 2/3, 7, 18, 21, 4, 2, 2, 2, 6/7, 6/7, 6/7, 9/14, 5/7, 5/7, -4, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2112.9MB, alloc=612.3MB, time=52.72 |\^/| 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(); 1428324809 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 2 2 F := [7 y , -3 x + 19 z , 10 y + y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [10 y + 12 y, 15 y z - y z, 3 x y - 18 x y z] > Problem := [F,G]; 3 3 2 2 Problem := [[7 y , -3 x + 19 z , 10 y + y z], 3 2 2 [10 y + 12 y, 15 y z - y z, 3 x y - 18 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=0.37 memory used=48.8MB, alloc=32.3MB, time=0.70 memory used=68.9MB, alloc=56.3MB, time=1.00 N1 := 797 > GB := Basis(F, plex(op(vars))); 3 3 2 3 2 GB := [x y, y , 10 y + y z, -3 x + 19 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=108.6MB, alloc=56.3MB, time=1.68 memory used=148.1MB, alloc=84.3MB, time=2.24 N2 := 797 #save(Problem, "format.txt"); > 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 := [7 y , -3 x + 19 z , 10 y + y z, 10 y + 12 y, 15 y z - y z, 2 3 x y - 18 x y z] > J:=[op(GB),op(G)]; 3 3 2 3 2 3 2 J := [x y, y , 10 y + y z, -3 x + 19 z , 10 y + 12 y, 15 y z - y z, 2 3 x y - 18 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, 11, 17, 3, 3, 3, 2, 1/3, 5/6, 2/3, 1/4, 3/4, 5/12, 7, 13, 21, 4, 3, 3, 2, 3/7, 6/7, 4/7, 2/7, 5/7, 5/14, -2, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=195.4MB, alloc=84.3MB, 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(); 1428324812 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [3 y z - 10 y , -6 x y + x y z, 3 y z - 17 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 G := [-10 x y z + 18 z , -13 x y z + 6 z, 16 x z - 7 z] > Problem := [F,G]; 2 2 2 2 Problem := [[3 y z - 10 y , -6 x y + x y z, 3 y z - 17 y], 3 2 [-10 x y z + 18 z , -13 x y z + 6 z, 16 x z - 7 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.1MB, alloc=32.3MB, time=0.37 memory used=47.6MB, alloc=32.3MB, time=0.62 memory used=68.3MB, alloc=32.3MB, time=0.85 memory used=88.0MB, alloc=56.3MB, time=1.10 memory used=131.7MB, alloc=60.3MB, time=1.73 memory used=169.5MB, alloc=84.3MB, time=2.24 memory used=228.0MB, alloc=108.3MB, time=3.06 memory used=303.1MB, alloc=140.3MB, time=4.21 memory used=386.9MB, alloc=164.3MB, time=5.80 memory used=479.3MB, alloc=188.3MB, time=8.02 memory used=583.2MB, alloc=212.3MB, time=11.25 memory used=711.2MB, alloc=212.3MB, time=15.12 memory used=839.1MB, alloc=212.3MB, time=19.05 memory used=967.0MB, alloc=236.3MB, time=23.02 memory used=1118.8MB, alloc=236.3MB, time=27.55 memory used=1270.9MB, alloc=260.3MB, time=31.69 N1 := 5499 > GB := Basis(F, plex(op(vars))); 2 2 GB := [y x, 10 y - 17 y, 3 y z - 17 y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); 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)]; 2 2 2 2 3 H := [3 y z - 10 y , -6 x y + x y z, 3 y z - 17 y, -10 x y z + 18 z , 2 -13 x y z + 6 z, 16 x z - 7 z] > J:=[op(GB),op(G)]; 2 2 3 J := [y x, 10 y - 17 y, 3 y z - 17 y, -10 x y z + 18 z , -13 x y z + 6 z, 2 16 x z - 7 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 18, 3, 2, 2, 3, 2/3, 5/6, 1, 5/12, 2/3, 3/4, 6, 13, 16, 3, 2, 2, 3, 2/3, 5/6, 2/3, 1/3, 7/12, 7/12, 2, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1362.2MB, alloc=260.3MB, time=33.07 |\^/| 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(); 1428324846 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [20 x z - 18 y, -9 y z - 20 y , -5 x y + 2 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [13 x z + 2 x y , 20 x - 16 x z, -12 x y - 6 x z] > Problem := [F,G]; 2 2 2 2 Problem := [[20 x z - 18 y, -9 y z - 20 y , -5 x y + 2 x z], 2 2 3 2 [13 x z + 2 x y , 20 x - 16 x z, -12 x y - 6 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.13 memory used=26.1MB, alloc=32.3MB, time=0.37 memory used=47.2MB, alloc=32.3MB, time=0.64 memory used=67.1MB, alloc=32.3MB, time=0.90 memory used=85.5MB, alloc=56.3MB, time=1.12 memory used=123.0MB, alloc=60.3MB, time=1.56 memory used=158.3MB, alloc=84.3MB, time=1.99 memory used=213.2MB, alloc=84.3MB, time=2.64 memory used=267.2MB, alloc=84.3MB, time=3.33 memory used=321.1MB, alloc=108.3MB, time=4.04 memory used=396.5MB, alloc=116.3MB, time=5.02 memory used=472.5MB, alloc=140.3MB, time=5.95 memory used=567.3MB, alloc=164.3MB, time=7.22 memory used=676.5MB, alloc=420.3MB, time=8.63 memory used=787.4MB, alloc=444.3MB, time=10.18 memory used=918.4MB, alloc=468.3MB, time=11.93 memory used=1067.7MB, alloc=492.3MB, time=14.20 memory used=1234.0MB, alloc=516.3MB, time=16.53 memory used=1417.8MB, alloc=540.3MB, time=19.16 memory used=1619.3MB, alloc=564.3MB, time=22.72 memory used=1820.5MB, alloc=588.3MB, time=25.83 memory used=2028.2MB, alloc=612.3MB, time=29.32 memory used=2267.6MB, alloc=636.3MB, time=32.85 memory used=2498.7MB, alloc=660.3MB, time=37.20 memory used=2727.3MB, alloc=684.3MB, time=41.01 memory used=2960.9MB, alloc=708.3MB, time=44.99 memory used=3204.9MB, alloc=732.3MB, time=48.95 memory used=3450.0MB, alloc=756.3MB, time=54.33 memory used=3661.8MB, alloc=780.3MB, time=60.81 memory used=3880.4MB, alloc=804.3MB, time=68.25 memory used=4109.7MB, alloc=828.3MB, time=76.63 memory used=4351.5MB, alloc=852.3MB, time=85.01 memory used=4606.4MB, alloc=876.3MB, time=93.76 memory used=4875.3MB, alloc=900.3MB, time=103.47 memory used=5158.4MB, alloc=924.3MB, time=114.77 memory used=5456.1MB, alloc=948.3MB, time=126.56 memory used=5769.1MB, alloc=972.3MB, time=138.89 memory used=6097.3MB, alloc=996.3MB, time=150.94 memory used=6436.4MB, alloc=1020.3MB, time=163.42 memory used=6792.6MB, alloc=1044.3MB, time=176.81 memory used=7172.8MB, alloc=1068.3MB, time=191.23 memory used=7576.9MB, alloc=1092.3MB, time=207.16 memory used=8005.0MB, alloc=1116.3MB, time=222.92 memory used=8457.1MB, alloc=1140.3MB, time=239.41 memory used=8933.0MB, alloc=1164.3MB, time=256.87 memory used=9432.9MB, alloc=1188.3MB, time=275.00 |\^/| 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(); 1428325147 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 F := [8 y z + 9 z, -x z - 19 x, -9 x y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 G := [-20 y z + 8 y , 12 x y - 13 x, 12 y - 13 x ] > Problem := [F,G]; 2 Problem := [[8 y z + 9 z, -x z - 19 x, -9 x y z], 2 2 2 3 2 [-20 y z + 8 y , 12 x y - 13 x, 12 y - 13 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.2MB, alloc=32.3MB, time=0.46 memory used=48.7MB, alloc=32.3MB, time=0.84 memory used=68.0MB, alloc=56.3MB, time=1.26 N1 := 611 > GB := Basis(F, plex(op(vars))); GB := [x, 8 y z + 9 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=106.1MB, alloc=60.3MB, time=1.93 N2 := 355 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [8 y z + 9 z, -x z - 19 x, -9 x y z, -20 y z + 8 y , 12 x y - 13 x, 3 2 12 y - 13 x ] > J:=[op(GB),op(G)]; 2 2 2 3 2 J := [x, 8 y z + 9 z, -20 y z + 8 y , 12 x y - 13 x, 12 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, 13, 17, 3, 2, 3, 1, 2/3, 5/6, 2/3, 3/7, 3/7, 5/14, 5, 9, 12, 3, 2, 3, 1, 3/5, 4/5, 2/5, 4/9, 5/9, 1/3, 4, 5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=112.3MB, alloc=60.3MB, time=2.07 |\^/| 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(); 1428325149 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [-3 z + 20 y , 7 x y + 2 x y z, -18 x z + 7 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [7 z - 8 z , 5 x z + 11 y z, 2 x z - 13 x y] > Problem := [F,G]; 3 2 2 2 Problem := [[-3 z + 20 y , 7 x y + 2 x y z, -18 x z + 7 x z], 3 2 2 2 2 [7 z - 8 z , 5 x z + 11 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=0.18 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=47.5MB, alloc=32.3MB, time=0.79 memory used=67.1MB, alloc=56.3MB, time=1.09 memory used=106.4MB, alloc=60.3MB, time=1.70 memory used=142.8MB, alloc=60.3MB, time=2.17 memory used=176.9MB, alloc=84.3MB, time=2.59 memory used=231.5MB, alloc=84.3MB, time=3.26 memory used=283.6MB, alloc=116.3MB, time=3.96 memory used=355.8MB, alloc=140.3MB, time=4.87 memory used=451.0MB, alloc=164.3MB, time=6.16 memory used=561.6MB, alloc=188.3MB, time=7.78 memory used=684.3MB, alloc=212.3MB, time=9.66 memory used=818.3MB, alloc=236.3MB, time=11.76 memory used=957.5MB, alloc=516.3MB, time=13.96 memory used=1108.8MB, alloc=540.3MB, time=16.48 memory used=1254.6MB, alloc=564.3MB, time=20.22 memory used=1407.3MB, alloc=588.3MB, time=24.38 memory used=1572.0MB, alloc=612.3MB, time=29.27 memory used=1749.9MB, alloc=636.3MB, time=34.62 memory used=1936.7MB, alloc=660.3MB, time=41.03 memory used=2147.2MB, alloc=684.3MB, time=48.11 memory used=2381.8MB, alloc=708.3MB, time=56.03 memory used=2640.2MB, alloc=732.3MB, time=64.76 memory used=2922.6MB, alloc=756.3MB, time=74.40 memory used=3228.9MB, alloc=756.3MB, time=84.65 memory used=3535.2MB, alloc=780.3MB, time=94.89 memory used=3865.4MB, alloc=780.3MB, time=105.80 memory used=4195.7MB, alloc=780.3MB, time=116.76 memory used=4525.9MB, alloc=780.3MB, time=127.80 memory used=4856.0MB, alloc=804.3MB, time=138.74 memory used=5210.2MB, alloc=804.3MB, time=150.47 memory used=5564.2MB, alloc=828.3MB, time=162.03 memory used=5942.2MB, alloc=828.3MB, time=174.43 memory used=6320.0MB, alloc=852.3MB, time=186.99 memory used=6722.0MB, alloc=876.3MB, time=199.94 N1 := 13853 > GB := Basis(F, plex(op(vars))); 2 2 2 4 3 2 GB := [18 x y - 7 x y , 1029 x y + 160 x y , 18 x z - 7 x z, 2 3 2 7 x y + 2 x y z, 3 z - 20 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=7053.1MB, alloc=876.3MB, time=207.31 memory used=7255.1MB, alloc=876.3MB, time=210.46 memory used=7454.3MB, alloc=876.3MB, time=214.16 memory used=7663.0MB, alloc=876.3MB, time=218.08 memory used=7900.6MB, alloc=900.3MB, time=222.62 memory used=8157.4MB, alloc=924.3MB, time=229.03 memory used=8604.3MB, alloc=948.3MB, time=242.75 memory used=9035.8MB, alloc=972.3MB, time=257.82 memory used=9488.7MB, alloc=996.3MB, time=273.93 |\^/| 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(); 1428325449 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 2 F := [4 y z + 9 x z, -18 x y - 7 x z , 18 x - 20 x z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [7 y z - 13 y z, -9 x y + 8 z , -10 y z + 4] > Problem := [F,G]; 2 2 2 3 2 Problem := [[4 y z + 9 x z, -18 x y - 7 x z , 18 x - 20 x z ], 2 2 2 [7 y z - 13 y z, -9 x y + 8 z , -10 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=0.16 memory used=26.3MB, alloc=32.3MB, time=0.46 memory used=47.8MB, alloc=32.3MB, time=0.77 memory used=68.2MB, alloc=32.3MB, time=1.06 memory used=87.1MB, alloc=56.3MB, time=1.34 memory used=126.0MB, alloc=60.3MB, time=1.91 memory used=162.8MB, alloc=60.3MB, time=2.46 memory used=197.8MB, alloc=84.3MB, time=3.00 memory used=256.1MB, alloc=92.3MB, time=3.77 memory used=312.0MB, alloc=116.3MB, time=4.45 memory used=387.4MB, alloc=116.3MB, time=5.34 memory used=461.4MB, alloc=140.3MB, time=6.27 memory used=556.1MB, alloc=164.3MB, time=7.45 memory used=658.1MB, alloc=420.3MB, time=8.94 memory used=769.6MB, alloc=444.3MB, time=10.62 memory used=895.1MB, alloc=468.3MB, time=12.50 memory used=1039.6MB, alloc=492.3MB, time=14.57 memory used=1199.6MB, alloc=516.3MB, time=16.94 memory used=1366.7MB, alloc=540.3MB, time=19.50 memory used=1543.4MB, alloc=564.3MB, time=22.31 memory used=1727.0MB, alloc=588.3MB, time=25.23 memory used=1918.3MB, alloc=612.3MB, time=28.31 memory used=2116.4MB, alloc=636.3MB, time=31.52 memory used=2304.6MB, alloc=660.3MB, time=35.80 memory used=2482.4MB, alloc=684.3MB, time=40.77 memory used=2667.3MB, alloc=708.3MB, time=46.12 memory used=2862.5MB, alloc=732.3MB, time=52.24 memory used=3069.4MB, alloc=756.3MB, time=58.96 memory used=3288.5MB, alloc=780.3MB, time=66.08 memory used=3521.1MB, alloc=804.3MB, time=73.77 memory used=3767.3MB, alloc=828.3MB, time=82.47 memory used=4027.5MB, alloc=852.3MB, time=92.40 memory used=4298.2MB, alloc=876.3MB, time=102.30 memory used=4586.7MB, alloc=900.3MB, time=112.98 memory used=4899.1MB, alloc=924.3MB, time=124.47 memory used=5235.5MB, alloc=948.3MB, time=136.65 memory used=5595.8MB, alloc=972.3MB, time=149.62 memory used=5980.1MB, alloc=996.3MB, time=163.64 memory used=6388.2MB, alloc=1020.3MB, time=179.89 memory used=6820.4MB, alloc=1044.3MB, time=197.86 memory used=7276.5MB, alloc=1068.3MB, time=215.76 memory used=7756.4MB, alloc=1092.3MB, time=234.66 memory used=8260.4MB, alloc=1116.3MB, time=253.30 memory used=8788.2MB, alloc=1116.3MB, time=271.99 |\^/| 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(); 1428325749 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 F := [18 x y + 17 y , -10 y z + 19 z , -19 y - 15] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 G := [-15 y , -9 y + 6 z, -12 x - 3] > Problem := [F,G]; 2 2 2 3 Problem := [[18 x y + 17 y , -10 y z + 19 z , -19 y - 15], 2 3 2 [-15 y , -9 y + 6 z, -12 x - 3]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.18 memory used=25.8MB, alloc=32.3MB, time=0.51 memory used=48.1MB, alloc=32.3MB, time=0.88 N1 := 357 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [36936 x - 24565, 17 y + 18 x, -3240 x z + 5491 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=66.0MB, alloc=32.3MB, time=1.17 memory used=86.3MB, alloc=56.3MB, time=1.53 N2 := 269 #save(Problem, "format.txt"); > if (GB=[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 H := [18 x y + 17 y , -10 y z + 19 z , -19 y - 15, -15 y , -9 y + 6 z, 2 -12 x - 3] > J:=[op(GB),op(G)]; 3 2 2 2 3 J := [36936 x - 24565, 17 y + 18 x, -3240 x z + 5491 z , -15 y , -9 y + 6 z, 2 -12 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, 9, 15, 3, 2, 3, 2, 1/3, 5/6, 1/3, 1/6, 1/2, 1/4, 6, 9, 14, 3, 3, 3, 2, 2/3, 1/2, 1/3, 1/3, 1/4, 1/4, 0, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=87.6MB, alloc=56.3MB, time=1.56 |\^/| 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(); 1428325751 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 F := [-13 x z , 18 x - 7 x z, 11 x y - 3 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [-4 x y + 8, 9 x z - 5 z , -5 y - 5] > Problem := [F,G]; 2 3 Problem := [[-13 x z , 18 x - 7 x z, 11 x y - 3 z], 2 2 2 3 [-4 x y + 8, 9 x z - 5 z , -5 y - 5]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.6MB, alloc=32.3MB, time=0.79 memory used=68.1MB, alloc=56.3MB, time=1.13 memory used=110.3MB, alloc=60.3MB, time=1.94 memory used=146.0MB, alloc=84.3MB, time=2.94 N1 := 1071 > GB := Basis(F, plex(op(vars))); 5 3 2 GB := [x , -54 x + 77 x y, -11 x y + 3 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=199.5MB, alloc=84.3MB, time=3.96 memory used=257.7MB, alloc=108.3MB, time=5.00 N2 := 849 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 2 H := [-13 x z , 18 x - 7 x z, 11 y x - 3 z, -4 x y + 8, 9 x z - 5 z , 3 -5 y - 5] > J:=[op(GB),op(G)]; J := [ 5 3 2 2 2 2 3 x , -54 x + 77 x y, -11 x y + 3 z, -4 x y + 8, 9 x z - 5 z , -5 y - 5] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 17, 3, 3, 3, 2, 5/6, 1/2, 2/3, 6/13, 3/13, 5/13, 6, 11, 19, 5, 5, 3, 2, 5/6, 2/3, 1/3, 1/2, 1/3, 1/4, 1, -2, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=295.6MB, alloc=108.3MB, time=6.11 |\^/| 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(); 1428325758 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 2 F := [-14 x z - 6 z , 5 y + 16 y , 11 x z + 13 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [5 x y + 5 y z , 4 x y - 13 y z, 7 x y - 15 x ] > Problem := [F,G]; 2 3 3 2 Problem := [[-14 x z - 6 z , 5 y + 16 y , 11 x z + 13 y], 2 2 2 2 2 [5 x y + 5 y z , 4 x y - 13 y z, 7 x y - 15 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.52 memory used=47.4MB, alloc=32.3MB, time=0.81 memory used=68.0MB, alloc=32.3MB, time=1.15 memory used=87.8MB, alloc=56.3MB, time=1.63 N1 := 347 > GB := Basis(F, plex(op(vars))); 7 3 4 2 GB := [21175 x y + 129792 x y, -4235 x y + 8112 y , 11 z x + 13 y, 2 2 3 7 x y + 3 y z , 33 z - 91 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=129.4MB, alloc=60.3MB, time=2.51 memory used=169.6MB, alloc=60.3MB, time=3.20 memory used=208.5MB, alloc=60.3MB, time=3.79 memory used=245.8MB, alloc=60.3MB, time=4.46 memory used=282.5MB, alloc=84.3MB, time=5.09 memory used=339.2MB, alloc=84.3MB, time=5.94 memory used=394.8MB, alloc=116.3MB, time=6.88 memory used=473.2MB, alloc=116.3MB, time=8.42 memory used=547.0MB, alloc=140.3MB, time=10.24 N2 := 925 #save(Problem, "format.txt"); > if (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 := [-14 x z - 6 z , 5 y + 16 y , 11 z x + 13 y, 5 x y + 5 y z , 2 2 2 4 x y - 13 y z, 7 x y - 15 x ] > J:=[op(GB),op(G)]; 7 3 4 2 J := [21175 x y + 129792 x y, -4235 x y + 8112 y , 11 z x + 13 y, 2 2 3 2 2 2 7 x y + 3 y z , 33 z - 91 x y, 5 x y + 5 y z , 4 x y - 13 y z, 2 2 7 x y - 15 x ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 17, 3, 2, 3, 3, 5/6, 5/6, 2/3, 1/2, 2/3, 5/12, 8, 21, 30, 8, 7, 2, 3, 1, 1, 5/8, 5/8, 13/16, 5/16, -7, -13, -5] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=550.4MB, alloc=140.3MB, time=10.37 |\^/| 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(); 1428325770 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 F := [-15 y z + 9 x z, 9 x - 9 x y z, -3 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [-10 x - 13 y z, -20 z + 3 x, -6 x y + 6 y ] > Problem := [F,G]; 2 3 3 Problem := [[-15 y z + 9 x z, 9 x - 9 x y z, -3 x ], 2 2 2 3 [-10 x - 13 y z, -20 z + 3 x, -6 x y + 6 y ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=48.2MB, alloc=32.3MB, time=0.80 memory used=69.1MB, alloc=56.3MB, time=1.14 memory used=112.2MB, alloc=60.3MB, time=1.89 memory used=151.7MB, alloc=84.3MB, time=2.65 memory used=210.9MB, alloc=116.3MB, time=3.79 memory used=284.9MB, alloc=140.3MB, time=5.92 memory used=371.3MB, alloc=140.3MB, time=8.70 N1 := 2517 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [x , z x , x z y, 5 y z - 3 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=459.8MB, alloc=140.3MB, time=10.91 memory used=564.1MB, alloc=164.3MB, time=13.00 N2 := 1071 #save(Problem, "format.txt"); > if (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 := [-15 y z + 9 x z, 9 x - 9 x y z, -3 x , -10 x - 13 y z, -20 z + 3 x, 2 3 -6 x y + 6 y ] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [x , z x , x z y, 5 y z - 3 x z, -10 x - 13 y z, -20 z + 3 x, 2 3 -6 x y + 6 y ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 16, 3, 3, 3, 2, 1, 2/3, 2/3, 7/12, 5/12, 5/12, 7, 16, 19, 3, 3, 3, 2, 1, 4/7, 5/7, 7/15, 1/3, 2/5, -2, -3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=567.9MB, alloc=164.3MB, time=13.10 |\^/| 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(); 1428325784 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-11 y z + 14 x y, 6 y + 18 y, -2 x y - 11 y z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [5 x z + 10 x y z, 4 y z - 15 y, -13 y - 18 y z] > Problem := [F,G]; 2 2 2 2 Problem := [[-11 y z + 14 x y, 6 y + 18 y, -2 x y - 11 y z ], 2 2 3 [5 x z + 10 x y z, 4 y z - 15 y, -13 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=0.15 memory used=26.0MB, alloc=32.3MB, time=0.44 memory used=47.5MB, alloc=32.3MB, time=0.74 memory used=67.2MB, alloc=32.3MB, time=0.98 memory used=86.5MB, alloc=56.3MB, time=1.21 memory used=126.2MB, alloc=60.3MB, time=1.71 memory used=164.1MB, alloc=84.3MB, time=2.29 memory used=224.1MB, alloc=84.3MB, time=3.29 memory used=277.4MB, alloc=108.3MB, time=4.17 memory used=347.4MB, alloc=140.3MB, time=5.49 memory used=428.5MB, alloc=164.3MB, time=7.50 memory used=520.0MB, alloc=188.3MB, time=10.95 memory used=635.6MB, alloc=188.3MB, time=14.99 memory used=751.3MB, alloc=212.3MB, time=18.83 N1 := 3577 > GB := Basis(F, plex(op(vars))); 2 2 GB := [y x , y + 3 y, 14 x y + 33 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=891.9MB, alloc=212.3MB, time=21.28 memory used=1035.7MB, alloc=236.3MB, time=26.29 N2 := 2161 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [-11 y z + 14 x y, 6 y + 18 y, -2 x y - 11 y z , 5 x z + 10 x y z, 2 3 4 y z - 15 y, -13 y - 18 y z] > J:=[op(GB),op(G)]; 2 2 2 2 J := [y x , y + 3 y, 14 x y + 33 y z, 5 x z + 10 x y z, 4 y z - 15 y, 3 -13 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, 14, 17, 3, 2, 3, 2, 1/2, 1, 5/6, 1/3, 11/12, 1/2, 6, 13, 16, 3, 2, 3, 2, 1/2, 1, 2/3, 1/3, 5/6, 5/12, 1, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1052.8MB, alloc=236.3MB, time=26.99 |\^/| 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(); 1428325814 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [17 x - 8 x z, -9 y - 12 z , 3 x z - 17 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 G := [-6 - 18 y, -2 x y z + 19 x y, 12 x y + 3 x y] > Problem := [F,G]; 3 2 2 2 Problem := [[17 x - 8 x z, -9 y - 12 z , 3 x z - 17 x z], 2 [-6 - 18 y, -2 x y z + 19 x y, 12 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=4.3MB, alloc=32.3MB, time=0.18 memory used=26.1MB, alloc=32.3MB, time=0.46 memory used=48.2MB, alloc=32.3MB, time=0.80 N1 := 355 > GB := Basis(F, plex(op(vars))); 4 3 3 2 3 2 2 GB := [3 x - 17 x , 83521 x + 432 x y , -17 x + 8 x z, 4 z + 3 y ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=67.6MB, alloc=32.3MB, time=1.14 memory used=85.9MB, alloc=56.3MB, time=1.44 memory used=127.4MB, alloc=60.3MB, time=2.14 N2 := 437 #save(Problem, "format.txt"); > 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 := [17 x - 8 x z, -9 y - 12 z , 3 x z - 17 x z, -6 - 18 y, 2 -2 x y z + 19 x y, 12 x y + 3 x y] > J:=[op(GB),op(G)]; 4 3 3 2 3 2 2 J := [3 x - 17 x , 83521 x + 432 x y , -17 x + 8 x z, 4 z + 3 y , -6 - 18 y, 2 -2 x y z + 19 x y, 12 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, 12, 15, 3, 3, 2, 2, 2/3, 2/3, 2/3, 2/3, 1/2, 5/12, 7, 13, 19, 4, 4, 2, 2, 5/7, 5/7, 3/7, 5/7, 1/2, 3/14, -1, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=144.4MB, alloc=60.3MB, time=2.46 |\^/| 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(); 1428325817 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 F := [-11 y z + 13 y, -9 x + z, 2 x + 11 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [-12 x y + 4 y z, -11 y z + 15, -20 y z - 11 x ] > Problem := [F,G]; 2 Problem := [[-11 y z + 13 y, -9 x + z, 2 x + 11 z], 2 2 2 2 2 [-12 x y + 4 y z, -11 y z + 15, -20 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=4.3MB, alloc=32.3MB, time=0.16 memory used=26.1MB, alloc=32.3MB, time=0.42 memory used=47.1MB, alloc=32.3MB, time=0.69 memory used=67.0MB, alloc=32.3MB, time=0.95 memory used=85.6MB, alloc=56.3MB, time=1.21 memory used=123.7MB, alloc=60.3MB, time=1.76 memory used=159.7MB, alloc=84.3MB, time=2.26 memory used=216.0MB, alloc=84.3MB, time=3.01 memory used=269.7MB, alloc=108.3MB, time=3.77 memory used=344.2MB, alloc=116.3MB, time=4.81 memory used=416.6MB, alloc=140.3MB, time=5.95 memory used=515.5MB, alloc=164.3MB, time=7.33 memory used=626.5MB, alloc=188.3MB, time=9.07 memory used=749.7MB, alloc=212.3MB, time=11.07 memory used=883.6MB, alloc=236.3MB, time=13.44 memory used=1013.1MB, alloc=516.3MB, time=16.25 memory used=1152.6MB, alloc=540.3MB, time=20.36 memory used=1300.6MB, alloc=564.3MB, time=24.78 memory used=1457.8MB, alloc=588.3MB, time=30.97 memory used=1632.7MB, alloc=612.3MB, time=37.48 memory used=1831.5MB, alloc=636.3MB, time=44.67 memory used=2054.3MB, alloc=660.3MB, time=53.55 memory used=2301.0MB, alloc=660.3MB, time=62.75 memory used=2547.6MB, alloc=684.3MB, time=73.13 memory used=2818.1MB, alloc=684.3MB, time=83.54 memory used=3088.8MB, alloc=684.3MB, time=94.38 memory used=3359.3MB, alloc=708.3MB, time=105.16 memory used=3653.7MB, alloc=708.3MB, time=118.00 memory used=3948.1MB, alloc=732.3MB, time=129.42 N1 := 10241 > GB := Basis(F, plex(op(vars))); 2 GB := [99 x + 2 x, y, 11 z + 2 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4279.7MB, alloc=732.3MB, time=138.87 N2 := 1681 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-11 y z + 13 y, -9 x + z, 11 z + 2 x, -12 x y + 4 y z, -11 y z + 15, 2 2 -20 y z - 11 x ] > J:=[op(GB),op(G)]; 2 2 2 2 J := [99 x + 2 x, y, 11 z + 2 x, -12 x y + 4 y z, -11 y z + 15, 2 2 -20 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, 14, 14, 3, 2, 2, 2, 2/3, 2/3, 1, 1/3, 1/2, 1/2, 6, 12, 13, 3, 2, 2, 2, 2/3, 2/3, 2/3, 5/11, 5/11, 4/11, 2, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=4428.9MB, alloc=732.3MB, time=143.04 |\^/| 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(); 1428325973 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [17 x - 8 x , z + 19 x z, 9 x y z - 5 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [9 x y + 14 y , -2 y z - 2 z , 13 + 20 x] > Problem := [F,G]; 3 2 3 2 Problem := [[17 x - 8 x , z + 19 x z, 9 x y z - 5 x ], 2 2 [9 x y + 14 y , -2 y z - 2 z , 13 + 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=0.15 memory used=26.1MB, alloc=32.3MB, time=0.43 memory used=47.9MB, alloc=32.3MB, time=0.74 memory used=69.7MB, alloc=56.3MB, time=1.10 memory used=112.1MB, alloc=60.3MB, time=1.77 memory used=148.4MB, alloc=84.3MB, time=2.42 memory used=199.3MB, alloc=108.3MB, time=3.98 N1 := 1579 > GB := Basis(F, plex(op(vars))); 3 2 2 2 2 2 2 2 GB := [17 x - 8 x , 26163 x y + 200 x , 171 x y + 5 x z, 9 x y z - 5 x , 3 z + 19 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=271.9MB, alloc=108.3MB, time=5.20 memory used=351.2MB, alloc=116.3MB, time=6.37 memory used=426.9MB, alloc=140.3MB, time=7.65 memory used=509.4MB, alloc=164.3MB, time=10.34 N2 := 2003 #save(Problem, "format.txt"); > 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 := [17 x - 8 x , z + 19 x z, 9 x y z - 5 x , 9 x y + 14 y , -2 y z - 2 z , 20 x + 13] > J:=[op(GB),op(G)]; 3 2 2 2 2 2 2 2 J := [17 x - 8 x , 26163 x y + 200 x , 171 x y + 5 x z, 9 x y z - 5 x , 3 2 2 z + 19 x z, 9 x y + 14 y , -2 y z - 2 z , 20 x + 13] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 11, 14, 3, 3, 2, 3, 5/6, 1/2, 1/2, 7/12, 1/3, 5/12, 8, 16, 21, 4, 3, 2, 3, 7/8, 5/8, 1/2, 11/16, 3/8, 3/8, -5, -7, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=554.1MB, alloc=164.3MB, time=11.63 |\^/| 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(); 1428325985 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [5 x z, 3 x y - 9, -2 x y - 2 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [x y - 2 y, -3 y - y z, 6 x z - 5 y z ] > Problem := [F,G]; 2 2 2 Problem := [[5 x z, 3 x y - 9, -2 x y - 2 x y], 2 2 2 2 [x y - 2 y, -3 y - y z, 6 x z - 5 y z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.8MB, alloc=32.3MB, time=0.48 N1 := 333 > GB := Basis(F, plex(op(vars))); 2 GB := [x + 1, y + 3, z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=47.6MB, alloc=32.3MB, time=0.81 memory used=66.4MB, alloc=56.3MB, time=1.12 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 H := [5 x z, 3 x y - 9, -2 x y - 2 x y, x y - 2 y, -3 y - y z, 2 2 6 x z - 5 y z ] > J:=[op(GB),op(G)]; 2 2 2 2 2 J := [x + 1, y + 3, z, x y - 2 y, -3 y - y z, 6 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, 13, 17, 3, 2, 2, 2, 5/6, 5/6, 1/2, 6/13, 8/13, 4/13, 6, 10, 12, 3, 2, 2, 2, 1/2, 2/3, 1/2, 3/11, 6/11, 4/11, 3, 5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=70.1MB, alloc=56.3MB, time=1.21 |\^/| 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(); 1428325987 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 F := [-12 y - 19 y , -3 y + 11 x , -15 y z - 13 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 3 G := [2 x z + 14 y z, -11 x z + 3 y , 13 x y - 16 z] > Problem := [F,G]; 3 2 3 2 Problem := [[-12 y - 19 y , -3 y + 11 x , -15 y z - 13 x], 2 2 2 3 [2 x z + 14 y z, -11 x z + 3 y , 13 x y - 16 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.21 memory used=26.0MB, alloc=32.3MB, time=0.52 memory used=47.3MB, alloc=32.3MB, time=0.81 memory used=68.0MB, alloc=32.3MB, time=1.09 memory used=87.8MB, alloc=32.3MB, time=1.36 memory used=106.8MB, alloc=56.3MB, time=1.68 memory used=147.9MB, alloc=60.3MB, time=2.35 memory used=185.7MB, alloc=84.3MB, time=2.98 memory used=243.1MB, alloc=116.3MB, time=3.96 memory used=315.0MB, alloc=140.3MB, time=6.16 N1 := 1723 > GB := Basis(F, plex(op(vars))); 4 2 3 2 2 3 2 GB := [6336 x + 6859 x , -528 x + 361 x y, 44 x + 19 y , -52 x + 95 x z, 15 z y + 13 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=405.1MB, alloc=140.3MB, time=7.99 memory used=499.7MB, alloc=140.3MB, time=9.26 memory used=591.2MB, alloc=164.3MB, time=10.55 memory used=699.7MB, alloc=444.3MB, time=12.17 memory used=836.3MB, alloc=468.3MB, time=14.37 memory used=982.0MB, alloc=492.3MB, time=16.91 memory used=1128.1MB, alloc=516.3MB, time=21.31 memory used=1276.3MB, alloc=540.3MB, time=27.05 memory used=1448.6MB, alloc=564.3MB, time=33.23 memory used=1645.0MB, alloc=588.3MB, time=40.52 N2 := 4837 #save(Problem, "format.txt"); > 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 := [-12 y - 19 y , -3 y + 11 x , -15 y z - 13 x, 2 x z + 14 y z, 2 3 -11 x z + 3 y , 13 y x - 16 z] > J:=[op(GB),op(G)]; 4 2 3 2 2 3 2 J := [6336 x + 6859 x , -528 x + 361 x y, 19 y + 44 x , -52 x + 95 x z, 2 2 2 3 15 z y + 13 x, 2 x z + 14 y z, -11 x z + 3 y , 13 y 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, 15, 16, 3, 2, 3, 1, 5/6, 1, 2/3, 5/12, 7/12, 5/12, 8, 19, 22, 4, 4, 3, 1, 1, 3/4, 5/8, 11/16, 3/8, 3/8, -4, -6, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1738.1MB, alloc=588.3MB, time=43.48 |\^/| 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(); 1428326033 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-6 y - 9 y, -x z - 17 z , 18 x y - 14 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [-18 x z - 20 x y z, -5 x y z + 3 y , -14 x y - 19 x z] > Problem := [F,G]; 3 2 2 Problem := [[-6 y - 9 y, -x z - 17 z , 18 x y - 14 x], 2 3 [-18 x z - 20 x y z, -5 x y z + 3 y , -14 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=0.17 memory used=26.2MB, alloc=32.3MB, time=0.45 memory used=48.2MB, alloc=32.3MB, time=0.79 memory used=68.3MB, alloc=56.3MB, time=1.14 N1 := 451 > GB := Basis(F, plex(op(vars))); 3 2 GB := [x, 2 y + 3 y, z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 99 #save(Problem, "format.txt"); > 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 := [-6 y - 9 y, -x z - 17 z , 18 x y - 14 x, -18 x z - 20 x y z, 3 -5 x y z + 3 y , -14 x y - 19 x z] > J:=[op(GB),op(G)]; J := 3 2 2 3 [x, 2 y + 3 y, z , -18 x z - 20 x y z, -5 x y z + 3 y , -14 x y - 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, 14, 16, 3, 2, 3, 2, 5/6, 5/6, 2/3, 2/3, 7/12, 1/2, 6, 12, 14, 3, 2, 3, 2, 2/3, 2/3, 2/3, 6/11, 6/11, 5/11, 2, 2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=95.5MB, alloc=56.3MB, time=1.53 |\^/| 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(); 1428326034 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 F := [-6 x , -13 x + 11 y , -13 y z + 16 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [12 x y - y z , 3 y z - 15 x, -10 x - 19 z ] > Problem := [F,G]; 3 3 3 2 Problem := [[-6 x , -13 x + 11 y , -13 y z + 16 y z], 2 2 3 2 [12 x y - y z , 3 y z - 15 x, -10 x - 19 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=54.7MB, alloc=68.3MB, time=0.85 memory used=102.5MB, alloc=68.3MB, time=1.49 memory used=151.5MB, alloc=92.3MB, time=2.35 memory used=220.3MB, alloc=92.3MB, time=4.00 memory used=283.1MB, alloc=116.3MB, time=4.97 memory used=361.9MB, alloc=148.3MB, time=6.41 memory used=449.3MB, alloc=172.3MB, time=8.94 memory used=544.2MB, alloc=196.3MB, time=12.12 memory used=658.8MB, alloc=196.3MB, time=15.91 memory used=773.4MB, alloc=220.3MB, time=20.11 memory used=912.0MB, alloc=220.3MB, time=24.87 memory used=1050.7MB, alloc=244.3MB, time=29.31 N1 := 4621 > GB := Basis(F, plex(op(vars))); 3 3 2 GB := [x , y , 13 y z - 16 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1152.8MB, alloc=244.3MB, time=30.80 memory used=1344.3MB, alloc=524.3MB, time=36.73 N2 := 2133 #save(Problem, "format.txt"); > 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 H := [-6 x , -13 x + 11 y , -13 y z + 16 y z, 12 x y - y z , 3 y z - 15 x, 3 2 -10 x - 19 z ] > J:=[op(GB),op(G)]; 3 3 2 2 2 3 2 J := [x , y , 13 y z - 16 y z, 12 x y - y z , 3 y z - 15 x, -10 x - 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, 17, 3, 3, 3, 2, 5/6, 2/3, 2/3, 5/12, 1/2, 5/12, 6, 12, 17, 3, 3, 3, 2, 2/3, 2/3, 2/3, 1/3, 1/2, 5/12, 1, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1384.7MB, alloc=524.3MB, time=37.64 |\^/| 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(); 1428326075 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-12 x y + 10 y, -8 x z - 18 z , 2 y + 16 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [15 x z + 12 y z , 10 x y - 6 x , 3 y z] > Problem := [F,G]; 2 2 2 2 Problem := [[-12 x y + 10 y, -8 x z - 18 z , 2 y + 16 y], 2 2 2 2 [15 x z + 12 y z , 10 x y - 6 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.46 memory used=48.4MB, alloc=32.3MB, time=0.77 memory used=68.5MB, alloc=56.3MB, time=1.16 memory used=114.6MB, alloc=60.3MB, time=1.57 memory used=164.4MB, alloc=60.3MB, time=1.81 memory used=198.6MB, alloc=60.3MB, time=1.96 memory used=239.5MB, alloc=60.3MB, time=2.09 memory used=286.8MB, alloc=60.3MB, time=2.25 memory used=339.4MB, alloc=60.3MB, time=2.42 memory used=389.2MB, alloc=60.3MB, time=2.56 memory used=419.8MB, alloc=60.3MB, time=2.66 memory used=450.7MB, alloc=84.3MB, time=2.79 memory used=511.3MB, alloc=84.3MB, time=2.97 memory used=575.9MB, alloc=84.3MB, time=3.14 memory used=644.8MB, alloc=84.3MB, time=3.32 memory used=718.1MB, alloc=84.3MB, time=3.51 memory used=795.7MB, alloc=84.3MB, time=3.67 memory used=877.7MB, alloc=84.3MB, time=3.83 memory used=964.0MB, alloc=84.3MB, time=4.03 memory used=1054.8MB, alloc=84.3MB, time=4.23 memory used=1149.7MB, alloc=84.3MB, time=4.42 memory used=1224.5MB, alloc=97.3MB, time=4.57 memory used=1297.6MB, alloc=104.9MB, time=4.73 memory used=1370.8MB, alloc=104.9MB, time=4.87 memory used=1445.2MB, alloc=104.9MB, time=5.01 memory used=1521.7MB, alloc=104.9MB, time=5.14 memory used=1600.0MB, alloc=104.9MB, time=5.28 memory used=1680.4MB, alloc=104.9MB, time=5.49 memory used=1762.8MB, alloc=104.9MB, time=5.63 memory used=1847.3MB, alloc=104.9MB, time=5.78 memory used=1933.9MB, alloc=104.9MB, time=5.92 memory used=2022.5MB, alloc=104.9MB, time=6.06 memory used=2113.1MB, alloc=104.9MB, time=6.20 memory used=2205.8MB, alloc=104.9MB, time=6.37 memory used=2300.6MB, alloc=104.9MB, time=6.58 memory used=2397.4MB, alloc=104.9MB, time=6.81 memory used=2496.3MB, alloc=104.9MB, time=7.03 memory used=2597.2MB, alloc=104.9MB, time=7.19 memory used=2700.2MB, alloc=104.9MB, time=7.33 memory used=2805.3MB, alloc=104.9MB, time=7.47 memory used=2912.4MB, alloc=104.9MB, time=7.62 memory used=3021.6MB, alloc=104.9MB, time=7.75 memory used=3132.8MB, alloc=104.9MB, time=7.92 memory used=3246.0MB, alloc=104.9MB, time=8.07 memory used=3361.3MB, alloc=104.9MB, time=8.23 memory used=3478.7MB, alloc=104.9MB, time=8.39 memory used=3598.1MB, alloc=104.9MB, time=8.60 memory used=3719.5MB, alloc=104.9MB, time=8.80 memory used=3843.0MB, alloc=104.9MB, time=8.99 memory used=3968.6MB, alloc=104.9MB, time=9.16 memory used=4096.2MB, alloc=104.9MB, time=9.32 memory used=4194.2MB, alloc=107.8MB, time=9.46 memory used=4220.3MB, alloc=107.8MB, time=9.52 memory used=4244.1MB, alloc=107.8MB, time=9.59 memory used=4267.0MB, alloc=107.8MB, time=9.64 memory used=4289.2MB, alloc=107.8MB, time=9.70 memory used=4310.8MB, alloc=107.8MB, time=9.75 memory used=4331.7MB, alloc=107.8MB, time=9.82 memory used=4352.1MB, alloc=107.8MB, time=9.88 memory used=4371.9MB, alloc=107.8MB, time=9.93 memory used=4391.3MB, alloc=107.8MB, time=9.99 memory used=4410.4MB, alloc=107.8MB, time=10.04 memory used=4429.1MB, alloc=107.8MB, time=10.09 memory used=4447.5MB, alloc=107.8MB, time=10.14 memory used=4465.7MB, alloc=107.8MB, time=10.20 memory used=4483.7MB, alloc=107.8MB, time=10.25 memory used=4501.6MB, alloc=107.8MB, time=10.30 memory used=4519.1MB, alloc=107.8MB, time=10.35 memory used=4536.8MB, alloc=107.8MB, time=10.41 memory used=4554.2MB, alloc=107.8MB, time=10.46 memory used=4571.5MB, alloc=107.8MB, time=10.52 memory used=4588.8MB, alloc=107.8MB, time=10.57 memory used=4606.2MB, alloc=107.8MB, time=10.62 memory used=4623.6MB, alloc=107.8MB, time=10.67 memory used=4641.0MB, alloc=107.8MB, time=10.72 memory used=4658.4MB, alloc=107.8MB, time=10.77 memory used=4675.7MB, alloc=107.8MB, time=10.84 memory used=4693.0MB, alloc=107.8MB, time=10.89 memory used=4710.3MB, alloc=107.8MB, time=10.94 memory used=4727.6MB, alloc=107.8MB, time=11.00 memory used=4744.8MB, alloc=107.8MB, time=11.05 memory used=4762.2MB, alloc=107.8MB, time=11.11 memory used=4779.5MB, alloc=107.8MB, time=11.17 memory used=4797.0MB, alloc=107.8MB, time=11.22 memory used=4814.4MB, alloc=107.8MB, time=11.27 memory used=4831.9MB, alloc=107.8MB, time=11.33 memory used=4849.3MB, alloc=107.8MB, time=11.38 memory used=4866.7MB, alloc=107.8MB, time=11.44 memory used=4884.3MB, alloc=107.8MB, time=11.49 memory used=4901.8MB, alloc=107.8MB, time=11.55 memory used=4919.4MB, alloc=107.8MB, time=11.60 memory used=4937.0MB, alloc=107.8MB, time=11.65 memory used=4954.7MB, alloc=107.8MB, time=11.70 memory used=4972.3MB, alloc=107.8MB, time=11.75 memory used=4990.0MB, alloc=107.8MB, time=11.82 memory used=5007.6MB, alloc=107.8MB, time=11.88 memory used=5025.3MB, alloc=107.8MB, time=11.94 memory used=5043.1MB, alloc=107.8MB, time=12.00 memory used=5060.9MB, alloc=107.8MB, time=12.05 memory used=5078.7MB, alloc=107.8MB, time=12.12 memory used=5096.6MB, alloc=107.8MB, time=12.17 memory used=5114.4MB, alloc=107.8MB, time=12.23 memory used=5132.3MB, alloc=107.8MB, time=12.29 memory used=5150.1MB, alloc=107.8MB, time=12.35 memory used=5168.1MB, alloc=107.8MB, time=12.41 memory used=5186.1MB, alloc=107.8MB, time=12.47 memory used=5204.1MB, alloc=107.8MB, time=12.55 memory used=5222.2MB, alloc=107.8MB, time=12.62 memory used=5240.3MB, alloc=107.8MB, time=12.69 memory used=5258.2MB, alloc=107.8MB, time=12.74 memory used=5276.4MB, alloc=107.8MB, time=12.80 memory used=5294.5MB, alloc=107.8MB, time=12.87 memory used=5312.8MB, alloc=107.8MB, time=12.93 memory used=5331.0MB, alloc=107.8MB, time=12.99 memory used=5349.2MB, alloc=107.8MB, time=13.04 memory used=5367.4MB, alloc=107.8MB, time=13.09 memory used=5385.7MB, alloc=107.8MB, time=13.15 memory used=5404.0MB, alloc=107.8MB, time=13.20 memory used=5422.3MB, alloc=107.8MB, time=13.25 memory used=5440.7MB, alloc=107.8MB, time=13.31 memory used=5459.2MB, alloc=107.8MB, time=13.37 memory used=5477.6MB, alloc=107.8MB, time=13.43 memory used=5496.2MB, alloc=107.8MB, time=13.49 memory used=5514.6MB, alloc=107.8MB, time=13.54 memory used=5533.2MB, alloc=107.8MB, time=13.59 memory used=5551.9MB, alloc=107.8MB, time=13.63 memory used=5570.5MB, alloc=107.8MB, time=13.68 memory used=5589.1MB, alloc=107.8MB, time=13.73 memory used=5607.8MB, alloc=107.8MB, time=13.78 memory used=5626.5MB, alloc=107.8MB, time=13.84 memory used=5645.3MB, alloc=107.8MB, time=13.89 memory used=5664.0MB, alloc=107.8MB, time=13.94 memory used=5682.9MB, alloc=107.8MB, time=13.99 memory used=5701.7MB, alloc=107.8MB, time=14.04 memory used=5720.5MB, alloc=107.8MB, time=14.09 memory used=5739.4MB, alloc=107.8MB, time=14.14 memory used=5758.1MB, alloc=107.8MB, time=14.19 memory used=5777.1MB, alloc=107.8MB, time=14.24 memory used=5796.0MB, alloc=107.8MB, time=14.29 memory used=5815.0MB, alloc=107.8MB, time=14.35 memory used=5834.0MB, alloc=107.8MB, time=14.40 memory used=5853.0MB, alloc=107.8MB, time=14.45 memory used=5872.0MB, alloc=107.8MB, time=14.51 memory used=5891.1MB, alloc=107.8MB, time=14.56 memory used=5910.2MB, alloc=107.8MB, time=14.62 memory used=5929.4MB, alloc=107.8MB, time=14.67 memory used=5948.5MB, alloc=107.8MB, time=14.72 memory used=5967.7MB, alloc=107.8MB, time=14.78 memory used=5986.8MB, alloc=107.8MB, time=14.83 memory used=6006.2MB, alloc=107.8MB, time=14.88 memory used=6025.5MB, alloc=107.8MB, time=14.94 memory used=6044.8MB, alloc=107.8MB, time=14.99 memory used=6064.3MB, alloc=107.8MB, time=15.04 memory used=6083.6MB, alloc=107.8MB, time=15.10 memory used=6103.3MB, alloc=107.8MB, time=15.14 memory used=6122.8MB, alloc=107.8MB, time=15.19 memory used=6142.5MB, alloc=107.8MB, time=15.25 memory used=6162.2MB, alloc=107.8MB, time=15.29 memory used=6181.9MB, alloc=107.8MB, time=15.35 memory used=6201.5MB, alloc=107.8MB, time=15.40 memory used=6221.2MB, alloc=107.8MB, time=15.45 memory used=6241.0MB, alloc=107.8MB, time=15.51 memory used=6260.9MB, alloc=107.8MB, time=15.55 memory used=6280.8MB, alloc=107.8MB, time=15.59 memory used=6300.7MB, alloc=107.8MB, time=15.66 memory used=6320.6MB, alloc=107.8MB, time=15.71 memory used=6340.7MB, alloc=107.8MB, time=15.77 memory used=6360.7MB, alloc=107.8MB, time=15.82 memory used=6380.7MB, alloc=107.8MB, time=15.87 memory used=6400.8MB, alloc=107.8MB, time=15.93 memory used=6420.8MB, alloc=107.8MB, time=15.98 memory used=6440.9MB, alloc=107.8MB, time=16.03 memory used=6461.0MB, alloc=107.8MB, time=16.08 memory used=6481.2MB, alloc=107.8MB, time=16.13 memory used=6501.4MB, alloc=107.8MB, time=16.19 memory used=6521.7MB, alloc=107.8MB, time=16.24 memory used=6541.9MB, alloc=107.8MB, time=16.29 memory used=6562.1MB, alloc=107.8MB, time=16.35 memory used=6582.3MB, alloc=107.8MB, time=16.41 memory used=6602.5MB, alloc=107.8MB, time=16.46 memory used=6623.0MB, alloc=107.8MB, time=16.51 memory used=6643.3MB, alloc=107.8MB, time=16.56 memory used=6663.8MB, alloc=107.8MB, time=16.61 memory used=6684.2MB, alloc=107.8MB, time=16.65 memory used=6704.6MB, alloc=107.8MB, time=16.71 memory used=6725.2MB, alloc=107.8MB, time=16.76 memory used=6745.6MB, alloc=107.8MB, time=16.81 memory used=6766.2MB, alloc=107.8MB, time=16.86 memory used=6786.9MB, alloc=107.8MB, time=16.91 memory used=6807.4MB, alloc=107.8MB, time=16.97 memory used=6828.2MB, alloc=107.8MB, time=17.03 memory used=6848.8MB, alloc=107.8MB, time=17.09 memory used=6869.5MB, alloc=107.8MB, time=17.15 memory used=6890.2MB, alloc=107.8MB, time=17.21 memory used=6911.0MB, alloc=107.8MB, time=17.26 memory used=6931.8MB, alloc=107.8MB, time=17.31 memory used=6952.6MB, alloc=107.8MB, time=17.37 memory used=6973.4MB, alloc=107.8MB, time=17.43 memory used=6994.3MB, alloc=107.8MB, time=17.48 memory used=7015.2MB, alloc=107.8MB, time=17.54 memory used=7036.2MB, alloc=107.8MB, time=17.59 memory used=7057.2MB, alloc=107.8MB, time=17.64 memory used=7078.2MB, alloc=107.8MB, time=17.70 memory used=7099.4MB, alloc=107.8MB, time=17.78 memory used=7120.5MB, alloc=107.8MB, time=17.83 memory used=7141.6MB, alloc=107.8MB, time=17.88 memory used=7162.9MB, alloc=107.8MB, time=17.94 memory used=7184.2MB, alloc=107.8MB, time=17.99 memory used=7205.5MB, alloc=107.8MB, time=18.04 memory used=7226.9MB, alloc=107.8MB, time=18.09 memory used=7248.3MB, alloc=107.8MB, time=18.14 memory used=7269.6MB, alloc=107.8MB, time=18.19 memory used=7291.0MB, alloc=107.8MB, time=18.25 memory used=7312.3MB, alloc=107.8MB, time=18.30 memory used=7333.8MB, alloc=107.8MB, time=18.35 memory used=7355.1MB, alloc=107.8MB, time=18.40 memory used=7376.5MB, alloc=107.8MB, time=18.46 memory used=7398.0MB, alloc=107.8MB, time=18.52 memory used=7419.6MB, alloc=107.8MB, time=18.57 memory used=7441.1MB, alloc=107.8MB, time=18.62 memory used=7462.6MB, alloc=107.8MB, time=18.68 memory used=7484.3MB, alloc=107.8MB, time=18.74 memory used=7506.0MB, alloc=107.8MB, time=18.80 memory used=7527.7MB, alloc=107.8MB, time=18.86 memory used=7549.5MB, alloc=107.8MB, time=18.91 memory used=7571.2MB, alloc=107.8MB, time=18.96 memory used=7592.9MB, alloc=107.8MB, time=19.01 memory used=7614.8MB, alloc=107.8MB, time=19.06 memory used=7636.6MB, alloc=107.8MB, time=19.12 memory used=7658.5MB, alloc=107.8MB, time=19.18 memory used=7680.4MB, alloc=107.8MB, time=19.24 memory used=7702.3MB, alloc=107.8MB, time=19.29 memory used=7724.2MB, alloc=107.8MB, time=19.35 memory used=7746.1MB, alloc=107.8MB, time=19.44 memory used=7768.2MB, alloc=107.8MB, time=19.51 memory used=7790.3MB, alloc=107.8MB, time=19.58 memory used=7812.3MB, alloc=107.8MB, time=19.64 memory used=7834.4MB, alloc=107.8MB, time=19.69 memory used=7856.6MB, alloc=107.8MB, time=19.75 memory used=7878.8MB, alloc=107.8MB, time=19.81 memory used=7901.1MB, alloc=107.8MB, time=19.86 memory used=7923.4MB, alloc=107.8MB, time=19.93 memory used=7945.8MB, alloc=107.8MB, time=19.98 memory used=7968.1MB, alloc=107.8MB, time=20.04 memory used=7990.4MB, alloc=107.8MB, time=20.09 memory used=8012.7MB, alloc=107.8MB, time=20.14 memory used=8035.1MB, alloc=107.8MB, time=20.19 memory used=8057.5MB, alloc=107.8MB, time=20.24 memory used=8079.7MB, alloc=107.8MB, time=20.29 memory used=8102.1MB, alloc=107.8MB, time=20.34 memory used=8124.5MB, alloc=107.8MB, time=20.42 memory used=8147.0MB, alloc=107.8MB, time=20.49 memory used=8169.4MB, alloc=107.8MB, time=20.55 memory used=8192.0MB, alloc=107.8MB, time=20.62 memory used=8214.4MB, alloc=107.8MB, time=20.67 memory used=8237.0MB, alloc=107.8MB, time=20.72 memory used=8259.6MB, alloc=107.8MB, time=20.77 memory used=8282.3MB, alloc=107.8MB, time=20.84 memory used=8305.0MB, alloc=107.8MB, time=20.90 memory used=8327.7MB, alloc=107.8MB, time=20.96 memory used=8350.5MB, alloc=107.8MB, time=21.01 memory used=8373.3MB, alloc=107.8MB, time=21.06 memory used=8396.1MB, alloc=107.8MB, time=21.13 memory used=8418.9MB, alloc=107.8MB, time=21.19 memory used=8441.7MB, alloc=107.8MB, time=21.24 memory used=8464.7MB, alloc=107.8MB, time=21.30 memory used=8487.6MB, alloc=107.8MB, time=21.35 memory used=8510.7MB, alloc=107.8MB, time=21.41 memory used=8533.7MB, alloc=107.8MB, time=21.46 memory used=8556.7MB, alloc=107.8MB, time=21.52 memory used=8579.8MB, alloc=107.8MB, time=21.58 memory used=8602.8MB, alloc=107.8MB, time=21.63 memory used=8626.0MB, alloc=107.8MB, time=21.69 memory used=8649.1MB, alloc=107.8MB, time=21.74 memory used=8672.5MB, alloc=107.8MB, time=21.79 memory used=8695.7MB, alloc=107.8MB, time=21.84 memory used=8719.0MB, alloc=107.8MB, time=21.89 memory used=8742.3MB, alloc=107.8MB, time=21.95 memory used=8765.8MB, alloc=107.8MB, time=22.00 memory used=8789.4MB, alloc=107.8MB, time=22.08 memory used=8812.8MB, alloc=107.8MB, time=22.14 memory used=8836.4MB, alloc=107.8MB, time=22.20 memory used=8859.9MB, alloc=107.8MB, time=22.26 memory used=8883.4MB, alloc=107.8MB, time=22.33 memory used=8907.1MB, alloc=107.8MB, time=22.39 memory used=8930.7MB, alloc=107.8MB, time=22.46 memory used=8954.4MB, alloc=107.8MB, time=22.52 memory used=8978.1MB, alloc=107.8MB, time=22.59 memory used=9001.8MB, alloc=107.8MB, time=22.66 memory used=9025.7MB, alloc=107.8MB, time=22.73 memory used=9049.5MB, alloc=107.8MB, time=22.79 memory used=9073.3MB, alloc=107.8MB, time=22.85 memory used=9097.3MB, alloc=107.8MB, time=22.92 memory used=9121.2MB, alloc=107.8MB, time=22.98 memory used=9145.2MB, alloc=107.8MB, time=23.05 memory used=9168.6MB, alloc=107.8MB, time=23.10 memory used=9191.4MB, alloc=107.8MB, time=23.17 memory used=9214.0MB, alloc=107.8MB, time=23.22 memory used=9236.7MB, alloc=107.8MB, time=23.28 memory used=9259.4MB, alloc=107.8MB, time=23.34 memory used=9282.1MB, alloc=107.8MB, time=23.40 memory used=9304.8MB, alloc=107.8MB, time=23.46 memory used=9327.5MB, alloc=107.8MB, time=23.51 memory used=9350.1MB, alloc=107.8MB, time=23.57 memory used=9372.9MB, alloc=107.8MB, time=23.63 memory used=9395.6MB, alloc=107.8MB, time=23.68 memory used=9418.3MB, alloc=107.8MB, time=23.74 memory used=9441.0MB, alloc=107.8MB, time=23.79 memory used=9463.7MB, alloc=107.8MB, time=23.86 memory used=9486.4MB, alloc=107.8MB, time=23.92 memory used=9509.2MB, alloc=107.8MB, time=23.97 memory used=9532.0MB, alloc=107.8MB, time=24.02 memory used=9554.8MB, alloc=107.8MB, time=24.07 memory used=9577.6MB, alloc=107.8MB, time=24.13 memory used=9600.3MB, alloc=107.8MB, time=24.18 memory used=9623.0MB, alloc=107.8MB, time=24.23 memory used=9646.0MB, alloc=107.8MB, time=24.28 memory used=9668.8MB, alloc=107.8MB, time=24.33 memory used=9691.7MB, alloc=107.8MB, time=24.39 memory used=9714.7MB, alloc=107.8MB, time=24.44 memory used=9737.7MB, alloc=107.8MB, time=24.51 memory used=9760.8MB, alloc=107.8MB, time=24.56 memory used=9783.9MB, alloc=107.8MB, time=24.61 memory used=9807.1MB, alloc=107.8MB, time=24.68 memory used=9830.3MB, alloc=107.8MB, time=24.73 memory used=9853.5MB, alloc=107.8MB, time=24.78 memory used=9876.8MB, alloc=107.8MB, time=24.84 memory used=9900.1MB, alloc=107.8MB, time=24.89 memory used=9923.6MB, alloc=107.8MB, time=24.94 memory used=9946.9MB, alloc=107.8MB, time=25.00 memory used=9970.4MB, alloc=107.8MB, time=25.06 memory used=9993.8MB, alloc=107.8MB, time=25.11 memory used=10017.2MB, alloc=107.8MB, time=25.19 memory used=10040.8MB, alloc=107.8MB, time=25.27 memory used=10064.2MB, alloc=107.8MB, time=25.35 memory used=10087.8MB, alloc=107.8MB, time=25.42 memory used=10111.3MB, alloc=107.8MB, time=25.50 memory used=10134.9MB, alloc=107.8MB, time=25.58 memory used=10158.5MB, alloc=107.8MB, time=25.66 memory used=10182.2MB, alloc=107.8MB, time=25.74 memory used=10205.8MB, alloc=107.8MB, time=25.81 memory used=10229.4MB, alloc=107.8MB, time=25.87 memory used=10253.1MB, alloc=107.8MB, time=25.93 memory used=10276.8MB, alloc=107.8MB, time=26.00 memory used=10300.5MB, alloc=107.8MB, time=26.05 memory used=10324.3MB, alloc=107.8MB, time=26.11 memory used=10348.0MB, alloc=107.8MB, time=26.17 memory used=10371.9MB, alloc=107.8MB, time=26.22 memory used=10395.8MB, alloc=107.8MB, time=26.28 memory used=10419.7MB, alloc=107.8MB, time=26.33 memory used=10443.7MB, alloc=107.8MB, time=26.38 memory used=10467.6MB, alloc=107.8MB, time=26.44 memory used=10491.6MB, alloc=107.8MB, time=26.49 memory used=10515.6MB, alloc=107.8MB, time=26.55 memory used=10539.7MB, alloc=107.8MB, time=26.61 memory used=10563.8MB, alloc=107.8MB, time=26.66 memory used=10588.0MB, alloc=107.8MB, time=26.72 memory used=10612.1MB, alloc=107.8MB, time=26.77 memory used=10636.3MB, alloc=107.8MB, time=26.83 memory used=10660.5MB, alloc=107.8MB, time=26.89 memory used=10684.7MB, alloc=107.8MB, time=26.95 memory used=10709.0MB, alloc=107.8MB, time=27.00 memory used=10733.4MB, alloc=107.8MB, time=27.06 memory used=10757.9MB, alloc=107.8MB, time=27.11 memory used=10782.3MB, alloc=107.8MB, time=27.17 memory used=10806.8MB, alloc=107.8MB, time=27.22 memory used=10831.3MB, alloc=107.8MB, time=27.28 memory used=10855.9MB, alloc=107.8MB, time=27.33 memory used=10880.5MB, alloc=107.8MB, time=27.38 memory used=10905.2MB, alloc=107.8MB, time=27.44 memory used=10929.8MB, alloc=107.8MB, time=27.49 memory used=10954.6MB, alloc=107.8MB, time=27.54 memory used=10979.4MB, alloc=107.8MB, time=27.60 memory used=11004.2MB, alloc=107.8MB, time=27.65 memory used=11029.0MB, alloc=107.8MB, time=27.70 memory used=11053.9MB, alloc=107.8MB, time=27.76 memory used=11078.8MB, alloc=107.8MB, time=27.82 memory used=11103.8MB, alloc=107.8MB, time=27.87 memory used=11128.9MB, alloc=107.8MB, time=27.93 memory used=11154.0MB, alloc=107.8MB, time=27.98 memory used=11179.0MB, alloc=107.8MB, time=28.03 memory used=11204.1MB, alloc=107.8MB, time=28.08 memory used=11229.4MB, alloc=107.8MB, time=28.13 memory used=11254.6MB, alloc=107.8MB, time=28.18 memory used=11279.8MB, alloc=107.8MB, time=28.23 memory used=11305.0MB, alloc=107.8MB, time=28.28 memory used=11330.3MB, alloc=107.8MB, time=28.34 memory used=11355.6MB, alloc=107.8MB, time=28.38 memory used=11380.8MB, alloc=107.8MB, time=28.43 memory used=11406.1MB, alloc=107.8MB, time=28.49 memory used=11431.5MB, alloc=107.8MB, time=28.55 memory used=11456.8MB, alloc=107.8MB, time=28.60 memory used=11482.2MB, alloc=107.8MB, time=28.66 memory used=11507.7MB, alloc=107.8MB, time=28.71 memory used=11533.1MB, alloc=107.8MB, time=28.76 memory used=11558.6MB, alloc=107.8MB, time=28.82 memory used=11584.1MB, alloc=107.8MB, time=28.87 memory used=11609.8MB, alloc=107.8MB, time=28.93 memory used=11635.3MB, alloc=107.8MB, time=28.98 memory used=11660.9MB, alloc=107.8MB, time=29.03 memory used=11686.6MB, alloc=107.8MB, time=29.08 memory used=11712.3MB, alloc=107.8MB, time=29.13 memory used=11737.9MB, alloc=107.8MB, time=29.19 memory used=11763.6MB, alloc=107.8MB, time=29.24 memory used=11789.5MB, alloc=107.8MB, time=29.29 memory used=11815.3MB, alloc=107.8MB, time=29.34 memory used=11841.2MB, alloc=107.8MB, time=29.40 memory used=11867.1MB, alloc=107.8MB, time=29.45 memory used=11893.0MB, alloc=107.8MB, time=29.51 memory used=11919.0MB, alloc=107.8MB, time=29.56 memory used=11944.9MB, alloc=107.8MB, time=29.61 memory used=11971.0MB, alloc=107.8MB, time=29.67 memory used=11997.1MB, alloc=107.8MB, time=29.72 memory used=12023.3MB, alloc=107.8MB, time=29.77 memory used=12049.4MB, alloc=107.8MB, time=29.82 memory used=12075.5MB, alloc=107.8MB, time=29.87 memory used=12101.6MB, alloc=107.8MB, time=29.93 memory used=12127.8MB, alloc=107.8MB, time=29.98 memory used=12154.0MB, alloc=107.8MB, time=30.04 memory used=12180.1MB, alloc=107.8MB, time=30.09 memory used=12206.3MB, alloc=107.8MB, time=30.14 memory used=12232.6MB, alloc=107.8MB, time=30.20 memory used=12258.9MB, alloc=107.8MB, time=30.25 memory used=12285.2MB, alloc=107.8MB, time=30.30 memory used=12311.5MB, alloc=107.8MB, time=30.35 memory used=12337.9MB, alloc=107.8MB, time=30.41 memory used=12364.4MB, alloc=107.8MB, time=30.46 memory used=12390.8MB, alloc=107.8MB, time=30.51 memory used=12417.2MB, alloc=107.8MB, time=30.56 memory used=12443.8MB, alloc=107.8MB, time=30.61 memory used=12470.4MB, alloc=107.8MB, time=30.67 memory used=12497.0MB, alloc=107.8MB, time=30.73 memory used=12523.6MB, alloc=107.8MB, time=30.79 memory used=12550.3MB, alloc=107.8MB, time=30.86 memory used=12577.1MB, alloc=107.8MB, time=30.91 memory used=12603.9MB, alloc=107.8MB, time=30.96 memory used=12630.5MB, alloc=107.8MB, time=31.03 memory used=12657.3MB, alloc=107.8MB, time=31.08 memory used=12684.2MB, alloc=107.8MB, time=31.13 memory used=12711.0MB, alloc=107.8MB, time=31.18 memory used=12737.8MB, alloc=107.8MB, time=31.24 memory used=12764.8MB, alloc=107.8MB, time=31.29 memory used=12791.8MB, alloc=107.8MB, time=31.34 memory used=12819.0MB, alloc=107.8MB, time=31.40 memory used=12846.1MB, alloc=107.8MB, time=31.45 memory used=12873.2MB, alloc=107.8MB, time=31.50 memory used=12900.2MB, alloc=107.8MB, time=31.55 memory used=12927.2MB, alloc=107.8MB, time=31.61 memory used=12954.4MB, alloc=107.8MB, time=31.66 memory used=12981.5MB, alloc=107.8MB, time=31.71 memory used=13008.7MB, alloc=107.8MB, time=31.77 memory used=13035.8MB, alloc=107.8MB, time=31.82 memory used=13063.0MB, alloc=107.8MB, time=31.87 memory used=13090.2MB, alloc=107.8MB, time=31.92 memory used=13117.6MB, alloc=107.8MB, time=31.97 memory used=13145.0MB, alloc=107.8MB, time=32.03 memory used=13172.2MB, alloc=107.8MB, time=32.08 memory used=13199.6MB, alloc=107.8MB, time=32.14 memory used=13227.1MB, alloc=107.8MB, time=32.19 memory used=13254.7MB, alloc=107.8MB, time=32.25 memory used=13282.4MB, alloc=107.8MB, time=32.30 memory used=13310.0MB, alloc=107.8MB, time=32.35 memory used=13337.6MB, alloc=107.8MB, time=32.40 memory used=13365.2MB, alloc=107.8MB, time=32.45 memory used=13392.8MB, alloc=107.8MB, time=32.51 memory used=13420.5MB, alloc=107.8MB, time=32.56 memory used=13448.3MB, alloc=107.8MB, time=32.61 memory used=13476.0MB, alloc=107.8MB, time=32.67 memory used=13503.7MB, alloc=107.8MB, time=32.72 memory used=13531.4MB, alloc=107.8MB, time=32.77 memory used=13559.3MB, alloc=107.8MB, time=32.83 memory used=13587.1MB, alloc=107.8MB, time=32.89 memory used=13615.1MB, alloc=107.8MB, time=32.95 memory used=13643.0MB, alloc=107.8MB, time=33.00 memory used=13670.8MB, alloc=107.8MB, time=33.05 memory used=13698.7MB, alloc=107.8MB, time=33.11 memory used=13726.6MB, alloc=107.8MB, time=33.16 memory used=13754.5MB, alloc=107.8MB, time=33.22 memory used=13782.4MB, alloc=107.8MB, time=33.27 memory used=13810.2MB, alloc=107.8MB, time=33.32 memory used=13838.1MB, alloc=107.8MB, time=33.37 memory used=13866.2MB, alloc=107.8MB, time=33.42 memory used=13894.2MB, alloc=107.8MB, time=33.46 memory used=13922.2MB, alloc=107.8MB, time=33.52 memory used=13950.3MB, alloc=107.8MB, time=33.57 memory used=13978.5MB, alloc=107.8MB, time=33.62 memory used=14006.7MB, alloc=107.8MB, time=33.70 memory used=14034.9MB, alloc=107.8MB, time=33.78 memory used=14063.1MB, alloc=107.8MB, time=33.86 memory used=14091.5MB, alloc=107.8MB, time=33.93 memory used=14120.0MB, alloc=107.8MB, time=33.98 memory used=14148.5MB, alloc=107.8MB, time=34.04 memory used=14177.1MB, alloc=107.8MB, time=34.11 memory used=14205.5MB, alloc=107.8MB, time=34.16 memory used=14234.0MB, alloc=107.8MB, time=34.22 memory used=14262.5MB, alloc=107.8MB, time=34.28 memory used=14291.2MB, alloc=107.8MB, time=34.34 memory used=14319.9MB, alloc=107.8MB, time=34.40 memory used=14348.6MB, alloc=107.8MB, time=34.46 memory used=14377.3MB, alloc=107.8MB, time=34.52 memory used=14406.1MB, alloc=107.8MB, time=34.59 memory used=14434.7MB, alloc=107.8MB, time=34.67 memory used=14463.4MB, alloc=107.8MB, time=34.73 memory used=14492.3MB, alloc=107.8MB, time=34.79 memory used=14521.1MB, alloc=107.8MB, time=34.85 memory used=14550.0MB, alloc=107.8MB, time=34.91 memory used=14578.9MB, alloc=107.8MB, time=34.96 memory used=14607.6MB, alloc=107.8MB, time=35.03 memory used=14636.4MB, alloc=107.8MB, time=35.09 memory used=14665.3MB, alloc=107.8MB, time=35.15 memory used=14694.2MB, alloc=107.8MB, time=35.21 memory used=14723.2MB, alloc=107.8MB, time=35.27 memory used=14752.0MB, alloc=107.8MB, time=35.33 memory used=14781.0MB, alloc=107.8MB, time=35.39 memory used=14810.1MB, alloc=107.8MB, time=35.45 memory used=14839.2MB, alloc=107.8MB, time=35.50 memory used=14868.2MB, alloc=107.8MB, time=35.56 memory used=14897.2MB, alloc=107.8MB, time=35.61 memory used=14926.4MB, alloc=107.8MB, time=35.66 memory used=14955.7MB, alloc=107.8MB, time=35.71 memory used=14984.9MB, alloc=107.8MB, time=35.76 memory used=15014.2MB, alloc=107.8MB, time=35.81 memory used=15043.5MB, alloc=107.8MB, time=35.86 memory used=15072.8MB, alloc=107.8MB, time=35.91 memory used=15102.1MB, alloc=107.8MB, time=35.97 memory used=15131.5MB, alloc=107.8MB, time=36.03 memory used=15160.9MB, alloc=107.8MB, time=36.08 memory used=15190.4MB, alloc=107.8MB, time=36.13 memory used=15219.8MB, alloc=107.8MB, time=36.19 memory used=15249.3MB, alloc=107.8MB, time=36.25 memory used=15279.0MB, alloc=107.8MB, time=36.31 memory used=15308.7MB, alloc=107.8MB, time=36.37 memory used=15338.5MB, alloc=107.8MB, time=36.42 memory used=15368.2MB, alloc=107.8MB, time=36.48 memory used=15398.1MB, alloc=107.8MB, time=36.53 memory used=15428.0MB, alloc=107.8MB, time=36.59 memory used=15457.9MB, alloc=107.8MB, time=36.64 memory used=15487.7MB, alloc=107.8MB, time=36.69 memory used=15517.3MB, alloc=107.8MB, time=36.74 memory used=15547.1MB, alloc=107.8MB, time=36.84 memory used=15577.0MB, alloc=107.8MB, time=36.92 memory used=15607.0MB, alloc=107.8MB, time=37.00 memory used=15637.0MB, alloc=107.8MB, time=37.08 memory used=15667.0MB, alloc=107.8MB, time=37.17 memory used=15697.0MB, alloc=107.8MB, time=37.26 memory used=15727.0MB, alloc=107.8MB, time=37.32 memory used=15757.1MB, alloc=107.8MB, time=37.38 memory used=15787.2MB, alloc=107.8MB, time=37.44 memory used=15817.4MB, alloc=107.8MB, time=37.49 memory used=15847.5MB, alloc=107.8MB, time=37.55 memory used=15877.8MB, alloc=107.8MB, time=37.60 memory used=15908.0MB, alloc=107.8MB, time=37.65 memory used=15937.9MB, alloc=107.8MB, time=37.71 memory used=15965.8MB, alloc=107.8MB, time=37.76 memory used=15990.4MB, alloc=107.8MB, time=37.82 memory used=16010.2MB, alloc=107.8MB, time=37.86 memory used=16027.6MB, alloc=107.8MB, time=37.91 memory used=16044.2MB, alloc=107.8MB, time=37.95 memory used=16060.6MB, alloc=107.8MB, time=38.00 memory used=16076.9MB, alloc=107.8MB, time=38.04 memory used=16093.0MB, alloc=107.8MB, time=38.09 memory used=16109.1MB, alloc=107.8MB, time=38.13 memory used=16125.2MB, alloc=107.8MB, time=38.17 memory used=16140.9MB, alloc=107.8MB, time=38.21 memory used=16156.7MB, alloc=107.8MB, time=38.26 memory used=16172.5MB, alloc=107.8MB, time=38.31 memory used=16188.1MB, alloc=107.8MB, time=38.35 memory used=16203.3MB, alloc=107.8MB, time=38.39 memory used=16218.5MB, alloc=107.8MB, time=38.44 memory used=16233.4MB, alloc=107.8MB, time=38.48 memory used=16248.6MB, alloc=107.8MB, time=38.52 memory used=16263.4MB, alloc=107.8MB, time=38.56 memory used=16277.9MB, alloc=107.8MB, time=38.61 memory used=16292.5MB, alloc=107.8MB, time=38.65 memory used=16306.7MB, alloc=107.8MB, time=38.69 memory used=16321.1MB, alloc=107.8MB, time=38.73 memory used=16335.2MB, alloc=107.8MB, time=38.78 memory used=16349.2MB, alloc=107.8MB, time=38.82 memory used=16363.5MB, alloc=107.8MB, time=38.86 memory used=16377.2MB, alloc=107.8MB, time=38.90 memory used=16390.9MB, alloc=107.8MB, time=38.95 memory used=16404.7MB, alloc=107.8MB, time=38.99 memory used=16418.4MB, alloc=107.8MB, time=39.03 memory used=16432.2MB, alloc=107.8MB, time=39.07 memory used=16446.0MB, alloc=107.8MB, time=39.11 memory used=16459.6MB, alloc=107.8MB, time=39.16 memory used=16473.1MB, alloc=107.8MB, time=39.20 memory used=16486.6MB, alloc=107.8MB, time=39.24 memory used=16500.2MB, alloc=107.8MB, time=39.28 memory used=16513.7MB, alloc=107.8MB, time=39.32 memory used=16527.0MB, alloc=107.8MB, time=39.37 memory used=16540.4MB, alloc=107.8MB, time=39.41 memory used=16553.5MB, alloc=107.8MB, time=39.45 memory used=16566.6MB, alloc=107.8MB, time=39.49 memory used=16579.6MB, alloc=107.8MB, time=39.53 memory used=16592.7MB, alloc=107.8MB, time=39.57 memory used=16605.7MB, alloc=107.8MB, time=39.61 memory used=16618.9MB, alloc=107.8MB, time=39.65 memory used=16631.9MB, alloc=107.8MB, time=39.69 memory used=16645.0MB, alloc=107.8MB, time=39.72 memory used=16657.9MB, alloc=107.8MB, time=39.76 memory used=16670.9MB, alloc=107.8MB, time=39.80 memory used=16683.9MB, alloc=107.8MB, time=39.84 memory used=16696.8MB, alloc=107.8MB, time=39.88 memory used=16709.8MB, alloc=107.8MB, time=39.92 memory used=16722.6MB, alloc=107.8MB, time=39.96 memory used=16735.5MB, alloc=107.8MB, time=40.00 memory used=16748.5MB, alloc=107.8MB, time=40.04 memory used=16761.4MB, alloc=107.8MB, time=40.08 memory used=16774.2MB, alloc=107.8MB, time=40.12 memory used=16786.9MB, alloc=107.8MB, time=40.16 memory used=16799.9MB, alloc=107.8MB, time=40.20 memory used=16812.7MB, alloc=107.8MB, time=40.24 memory used=16825.5MB, alloc=107.8MB, time=40.28 memory used=16838.4MB, alloc=107.8MB, time=40.32 memory used=16851.1MB, alloc=107.8MB, time=40.37 memory used=16864.1MB, alloc=107.8MB, time=40.41 memory used=16876.9MB, alloc=107.8MB, time=40.45 memory used=16889.6MB, alloc=107.8MB, time=40.49 memory used=16902.3MB, alloc=107.8MB, time=40.57 memory used=16915.3MB, alloc=107.8MB, time=40.61 memory used=16928.0MB, alloc=107.8MB, time=40.67 memory used=16940.8MB, alloc=107.8MB, time=40.71 memory used=16953.5MB, alloc=107.8MB, time=40.77 memory used=16966.3MB, alloc=107.8MB, time=40.82 memory used=16979.0MB, alloc=107.8MB, time=40.86 memory used=16991.9MB, alloc=107.8MB, time=40.90 memory used=17004.8MB, alloc=107.8MB, time=40.95 memory used=17017.5MB, alloc=107.8MB, time=40.99 memory used=17030.2MB, alloc=107.8MB, time=41.03 memory used=17042.9MB, alloc=107.8MB, time=41.07 memory used=17055.5MB, alloc=107.8MB, time=41.11 memory used=17068.5MB, alloc=107.8MB, time=41.17 memory used=17081.2MB, alloc=107.8MB, time=41.21 memory used=17094.1MB, alloc=107.8MB, time=41.25 memory used=17106.6MB, alloc=107.8MB, time=41.29 memory used=17119.3MB, alloc=107.8MB, time=41.33 memory used=17131.9MB, alloc=107.8MB, time=41.38 memory used=17144.4MB, alloc=107.8MB, time=41.42 memory used=17157.1MB, alloc=107.8MB, time=41.46 memory used=17169.7MB, alloc=107.8MB, time=41.51 memory used=17182.1MB, alloc=107.8MB, time=41.55 memory used=17194.8MB, alloc=107.8MB, time=41.59 memory used=17207.3MB, alloc=107.8MB, time=41.63 memory used=17219.8MB, alloc=107.8MB, time=41.67 memory used=17232.6MB, alloc=107.8MB, time=41.71 memory used=17245.1MB, alloc=107.8MB, time=41.75 memory used=17257.8MB, alloc=107.8MB, time=41.79 memory used=17270.5MB, alloc=107.8MB, time=41.83 memory used=17283.1MB, alloc=107.8MB, time=41.88 memory used=17295.9MB, alloc=107.8MB, time=41.92 memory used=17308.5MB, alloc=107.8MB, time=41.96 memory used=17321.1MB, alloc=107.8MB, time=42.00 memory used=17334.1MB, alloc=107.8MB, time=42.05 memory used=17346.7MB, alloc=107.8MB, time=42.09 memory used=17359.7MB, alloc=107.8MB, time=42.13 memory used=17372.4MB, alloc=107.8MB, time=42.18 memory used=17385.3MB, alloc=107.8MB, time=42.22 memory used=17398.0MB, alloc=107.8MB, time=42.26 memory used=17410.7MB, alloc=107.8MB, time=42.30 memory used=17423.6MB, alloc=107.8MB, time=42.35 memory used=17436.2MB, alloc=107.8MB, time=42.39 memory used=17449.0MB, alloc=107.8MB, time=42.43 memory used=17461.8MB, alloc=107.8MB, time=42.48 memory used=17474.5MB, alloc=107.8MB, time=42.52 memory used=17487.4MB, alloc=107.8MB, time=42.57 memory used=17499.9MB, alloc=107.8MB, time=42.62 memory used=17512.6MB, alloc=107.8MB, time=42.66 memory used=17525.3MB, alloc=107.8MB, time=42.71 memory used=17537.9MB, alloc=107.8MB, time=42.76 memory used=17550.5MB, alloc=107.8MB, time=42.80 memory used=17563.3MB, alloc=107.8MB, time=42.84 memory used=17575.9MB, alloc=107.8MB, time=42.88 memory used=17588.5MB, alloc=107.8MB, time=42.92 memory used=17601.4MB, alloc=107.8MB, time=42.96 memory used=17614.1MB, alloc=107.8MB, time=43.00 memory used=17627.0MB, alloc=107.8MB, time=43.05 memory used=17639.9MB, alloc=107.8MB, time=43.09 memory used=17652.7MB, alloc=107.8MB, time=43.13 memory used=17665.6MB, alloc=107.8MB, time=43.17 memory used=17678.2MB, alloc=107.8MB, time=43.22 memory used=17691.0MB, alloc=107.8MB, time=43.26 memory used=17703.9MB, alloc=107.8MB, time=43.30 memory used=17716.5MB, alloc=107.8MB, time=43.34 memory used=17729.3MB, alloc=107.8MB, time=43.38 memory used=17742.1MB, alloc=107.8MB, time=43.42 memory used=17754.7MB, alloc=107.8MB, time=43.46 memory used=17767.5MB, alloc=107.8MB, time=43.50 memory used=17780.3MB, alloc=107.8MB, time=43.54 memory used=17793.0MB, alloc=107.8MB, time=43.58 memory used=17805.7MB, alloc=107.8MB, time=43.62 memory used=17818.6MB, alloc=107.8MB, time=43.66 memory used=17831.3MB, alloc=107.8MB, time=43.70 memory used=17843.9MB, alloc=107.8MB, time=43.74 memory used=17856.7MB, alloc=107.8MB, time=43.77 memory used=17869.3MB, alloc=107.8MB, time=43.82 memory 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alloc=107.8MB, time=44.69 memory used=18150.8MB, alloc=107.8MB, time=44.74 memory used=18163.6MB, alloc=107.8MB, time=44.78 memory used=18176.6MB, alloc=107.8MB, time=44.82 memory used=18189.6MB, alloc=107.8MB, time=44.86 memory used=18202.3MB, alloc=107.8MB, time=44.90 memory used=18215.3MB, alloc=107.8MB, time=44.95 memory used=18228.3MB, alloc=107.8MB, time=44.99 memory used=18241.1MB, alloc=107.8MB, time=45.03 memory used=18254.1MB, alloc=107.8MB, time=45.07 memory used=18267.1MB, alloc=107.8MB, time=45.11 memory used=18279.9MB, alloc=107.8MB, time=45.15 memory used=18292.8MB, alloc=107.8MB, time=45.19 memory used=18305.9MB, alloc=107.8MB, time=45.23 memory used=18318.8MB, alloc=107.8MB, time=45.27 memory used=18332.0MB, alloc=107.8MB, time=45.31 memory used=18344.9MB, alloc=107.8MB, time=45.35 memory used=18358.0MB, alloc=107.8MB, time=45.39 memory used=18371.1MB, alloc=107.8MB, time=45.44 memory used=18384.1MB, alloc=107.8MB, time=45.48 memory used=18397.2MB, alloc=107.8MB, time=45.52 memory used=18410.3MB, alloc=107.8MB, time=45.57 memory used=18423.3MB, alloc=107.8MB, time=45.61 memory used=18436.5MB, alloc=107.8MB, time=45.65 memory used=18449.5MB, alloc=107.8MB, time=45.70 memory used=18462.5MB, alloc=107.8MB, time=45.74 memory used=18475.8MB, alloc=107.8MB, time=45.78 memory used=18488.8MB, alloc=107.8MB, time=45.82 memory used=18502.0MB, alloc=107.8MB, time=45.86 memory used=18515.1MB, alloc=107.8MB, time=45.91 memory used=18528.1MB, alloc=107.8MB, time=45.95 memory used=18541.3MB, alloc=107.8MB, time=46.00 memory used=18554.3MB, alloc=107.8MB, time=46.04 memory used=18567.1MB, alloc=107.8MB, time=46.08 memory used=18580.3MB, alloc=107.8MB, time=46.13 memory used=18593.3MB, alloc=107.8MB, time=46.17 memory used=18606.3MB, alloc=107.8MB, time=46.21 memory used=18619.6MB, alloc=107.8MB, time=46.25 memory used=18632.7MB, alloc=107.8MB, time=46.30 memory used=18646.0MB, alloc=107.8MB, time=46.34 memory used=18659.3MB, alloc=107.8MB, time=46.41 memory used=18672.4MB, alloc=107.8MB, time=46.48 memory used=18685.7MB, alloc=107.8MB, time=46.56 memory used=18698.8MB, alloc=107.8MB, time=46.63 memory used=18712.2MB, alloc=107.8MB, time=46.70 memory used=18725.5MB, alloc=107.8MB, time=46.76 memory used=18738.6MB, alloc=107.8MB, time=46.83 memory used=18751.9MB, alloc=107.8MB, time=46.89 memory used=18764.9MB, alloc=107.8MB, time=46.96 memory used=18778.2MB, alloc=107.8MB, time=47.02 memory used=18791.4MB, alloc=107.8MB, time=47.09 memory used=18804.4MB, alloc=107.8MB, time=47.16 memory used=18817.5MB, alloc=107.8MB, time=47.21 memory used=18830.8MB, alloc=107.8MB, time=47.28 memory used=18843.8MB, alloc=107.8MB, time=47.33 memory used=18857.1MB, alloc=107.8MB, time=47.40 memory used=18870.3MB, alloc=107.8MB, time=47.45 memory used=18883.2MB, alloc=107.8MB, time=47.49 memory used=18896.6MB, alloc=107.8MB, time=47.53 memory used=18909.7MB, alloc=107.8MB, time=47.58 memory used=18922.7MB, alloc=107.8MB, time=47.62 memory used=18936.1MB, alloc=107.8MB, time=47.67 memory used=18949.2MB, alloc=107.8MB, time=47.71 memory used=18962.2MB, alloc=107.8MB, time=47.78 memory used=18975.6MB, alloc=107.8MB, time=47.85 memory used=18988.6MB, alloc=107.8MB, time=47.92 memory used=19001.7MB, alloc=107.8MB, time=47.99 memory used=19015.0MB, alloc=107.8MB, time=48.06 memory used=19028.2MB, alloc=107.8MB, time=48.12 memory used=19041.3MB, alloc=107.8MB, time=48.18 memory used=19054.7MB, alloc=107.8MB, time=48.24 memory used=19067.9MB, alloc=107.8MB, time=48.28 memory used=19081.0MB, alloc=107.8MB, time=48.32 memory used=19094.5MB, alloc=107.8MB, time=48.36 memory used=19107.7MB, alloc=107.8MB, time=48.40 memory used=19121.0MB, alloc=107.8MB, time=48.44 memory used=19134.5MB, alloc=107.8MB, time=48.48 memory used=19147.7MB, alloc=107.8MB, time=48.52 memory used=19161.1MB, alloc=107.8MB, time=48.57 memory used=19174.4MB, alloc=107.8MB, time=48.62 memory used=19187.6MB, alloc=107.8MB, time=48.67 memory used=19201.2MB, alloc=107.8MB, time=48.72 memory used=19214.6MB, alloc=107.8MB, time=48.77 memory used=19228.1MB, alloc=107.8MB, time=48.82 memory used=19241.5MB, alloc=107.8MB, time=48.87 memory used=19254.6MB, alloc=107.8MB, time=48.91 memory used=19268.0MB, alloc=107.8MB, time=48.95 memory used=19281.4MB, alloc=107.8MB, time=49.00 memory used=19294.5MB, alloc=107.8MB, time=49.04 memory used=19307.9MB, alloc=107.8MB, time=49.08 memory used=19321.1MB, alloc=107.8MB, time=49.12 memory used=19334.3MB, alloc=107.8MB, time=49.16 memory used=19347.6MB, alloc=107.8MB, time=49.20 memory used=19361.1MB, alloc=107.8MB, time=49.24 memory used=19374.3MB, alloc=107.8MB, time=49.28 memory used=19387.7MB, alloc=107.8MB, time=49.32 memory used=19401.0MB, alloc=107.8MB, time=49.36 memory used=19414.1MB, alloc=107.8MB, time=49.40 memory used=19427.4MB, alloc=107.8MB, time=49.45 memory used=19440.8MB, alloc=107.8MB, time=49.49 memory used=19454.1MB, alloc=107.8MB, time=49.53 memory used=19467.5MB, alloc=107.8MB, time=49.58 memory used=19480.9MB, alloc=107.8MB, time=49.62 memory used=19494.1MB, alloc=107.8MB, time=49.66 memory used=19507.4MB, alloc=107.8MB, time=49.70 memory used=19520.8MB, alloc=107.8MB, time=49.75 memory used=19534.0MB, alloc=107.8MB, time=49.79 memory used=19547.2MB, alloc=107.8MB, time=49.83 memory used=19560.6MB, alloc=107.8MB, time=49.87 memory used=19573.9MB, alloc=107.8MB, time=49.91 memory used=19587.1MB, alloc=107.8MB, time=49.95 memory used=19600.6MB, alloc=107.8MB, time=50.00 memory used=19614.0MB, alloc=107.8MB, time=50.04 memory used=19627.3MB, alloc=107.8MB, time=50.08 memory used=19640.8MB, alloc=107.8MB, time=50.12 memory used=19654.2MB, alloc=107.8MB, time=50.16 memory used=19667.5MB, alloc=107.8MB, time=50.21 memory used=19680.9MB, alloc=107.8MB, time=50.25 memory used=19694.4MB, alloc=107.8MB, time=50.29 memory used=19707.6MB, alloc=107.8MB, time=50.33 memory used=19720.7MB, alloc=107.8MB, time=50.37 memory used=19734.3MB, alloc=107.8MB, time=50.41 memory used=19747.7MB, alloc=107.8MB, time=50.45 memory used=19761.1MB, alloc=107.8MB, time=50.48 memory used=19774.6MB, alloc=107.8MB, time=50.53 memory used=19788.0MB, alloc=107.8MB, time=50.57 memory used=19801.2MB, alloc=107.8MB, time=50.61 memory used=19814.7MB, alloc=107.8MB, time=50.65 memory used=19828.1MB, alloc=107.8MB, time=50.69 memory used=19841.5MB, alloc=107.8MB, time=50.73 memory used=19855.1MB, alloc=107.8MB, time=50.77 memory used=19868.6MB, alloc=107.8MB, time=50.81 memory used=19882.0MB, alloc=107.8MB, time=50.85 memory used=19895.5MB, alloc=107.8MB, time=50.89 memory used=19909.1MB, alloc=107.8MB, time=50.93 memory used=19922.5MB, alloc=107.8MB, time=50.97 memory used=19936.1MB, alloc=107.8MB, time=51.01 memory used=19949.8MB, alloc=107.8MB, time=51.05 memory used=19963.2MB, alloc=107.8MB, time=51.09 memory used=19976.7MB, alloc=107.8MB, time=51.14 memory used=19990.2MB, alloc=107.8MB, time=51.18 memory used=20003.7MB, alloc=107.8MB, time=51.22 memory used=20017.3MB, alloc=107.8MB, time=51.27 memory used=20030.8MB, alloc=107.8MB, time=51.31 memory used=20044.3MB, alloc=107.8MB, time=51.35 memory used=20058.1MB, alloc=107.8MB, time=51.39 memory used=20071.7MB, alloc=107.8MB, time=51.43 memory used=20085.4MB, alloc=107.8MB, time=51.47 memory used=20099.3MB, alloc=107.8MB, time=51.51 memory used=20113.0MB, alloc=107.8MB, time=51.55 memory used=20126.9MB, alloc=107.8MB, time=51.60 memory used=20140.6MB, alloc=107.8MB, time=51.64 memory used=20154.5MB, alloc=107.8MB, time=51.68 memory used=20168.2MB, alloc=107.8MB, time=51.72 memory used=20181.9MB, alloc=107.8MB, time=51.76 memory used=20195.8MB, alloc=107.8MB, time=51.80 memory used=20209.3MB, alloc=107.8MB, time=51.85 memory used=20223.1MB, alloc=107.8MB, time=51.88 memory used=20236.9MB, alloc=107.8MB, time=51.92 memory used=20250.4MB, alloc=107.8MB, time=51.96 memory used=20264.3MB, alloc=107.8MB, time=52.01 memory used=20277.7MB, alloc=107.8MB, time=52.05 memory used=20291.3MB, alloc=107.8MB, time=52.09 memory used=20304.9MB, alloc=107.8MB, time=52.14 memory used=20318.5MB, alloc=107.8MB, time=52.18 memory used=20331.9MB, alloc=107.8MB, time=52.22 memory used=20345.7MB, alloc=107.8MB, time=52.26 memory used=20359.3MB, alloc=107.8MB, time=52.30 memory used=20372.9MB, alloc=107.8MB, time=52.34 memory used=20386.7MB, alloc=107.8MB, time=52.38 memory used=20400.4MB, alloc=107.8MB, time=52.42 memory used=20414.0MB, alloc=107.8MB, time=52.48 memory used=20427.7MB, alloc=107.8MB, time=52.52 memory used=20441.4MB, alloc=107.8MB, time=52.56 memory used=20455.0MB, alloc=107.8MB, time=52.60 memory used=20468.7MB, alloc=107.8MB, time=52.65 memory used=20482.2MB, alloc=107.8MB, time=52.69 memory used=20495.6MB, alloc=107.8MB, time=52.73 memory used=20509.1MB, alloc=107.8MB, time=52.77 memory used=20522.8MB, alloc=107.8MB, time=52.82 memory used=20536.5MB, alloc=107.8MB, time=52.89 memory used=20550.0MB, alloc=107.8MB, time=52.93 memory used=20563.8MB, alloc=107.8MB, time=52.98 memory used=20577.6MB, alloc=107.8MB, time=53.02 memory used=20591.2MB, alloc=107.8MB, time=53.07 memory used=20605.2MB, alloc=107.8MB, time=53.11 memory used=20619.1MB, alloc=107.8MB, time=53.16 memory used=20632.8MB, alloc=107.8MB, time=53.21 memory used=20646.8MB, alloc=107.8MB, time=53.26 memory used=20660.4MB, alloc=107.8MB, time=53.30 memory used=20674.0MB, alloc=107.8MB, time=53.35 memory used=20688.0MB, alloc=107.8MB, time=53.39 memory used=20701.8MB, alloc=107.8MB, time=53.44 memory used=20715.4MB, alloc=107.8MB, time=53.49 memory used=20729.3MB, alloc=107.8MB, time=53.57 memory used=20743.0MB, alloc=107.8MB, time=53.63 memory used=20756.6MB, alloc=107.8MB, time=53.69 memory used=20770.6MB, alloc=107.8MB, time=53.77 memory used=20784.2MB, alloc=107.8MB, time=53.83 memory used=20797.8MB, alloc=107.8MB, time=53.90 memory used=20811.7MB, alloc=107.8MB, time=53.97 memory used=20825.6MB, alloc=107.8MB, time=54.04 memory used=20839.4MB, alloc=107.8MB, time=54.12 memory used=20853.4MB, alloc=107.8MB, time=54.18 memory used=20867.2MB, alloc=107.8MB, time=54.24 memory used=20881.1MB, alloc=107.8MB, time=54.28 memory used=20895.1MB, alloc=107.8MB, time=54.32 memory used=20909.0MB, alloc=107.8MB, time=54.37 memory used=20923.1MB, alloc=107.8MB, time=54.40 memory used=20937.1MB, alloc=107.8MB, time=54.46 memory used=20951.0MB, alloc=107.8MB, time=54.53 memory used=20965.0MB, alloc=107.8MB, time=54.59 memory used=20978.9MB, alloc=107.8MB, time=54.66 memory used=20993.0MB, alloc=107.8MB, time=54.73 memory used=21007.0MB, alloc=107.8MB, time=54.79 memory used=21020.8MB, alloc=107.8MB, time=54.87 memory used=21034.9MB, alloc=107.8MB, time=54.94 memory used=21048.8MB, alloc=107.8MB, time=55.01 memory used=21062.6MB, alloc=107.8MB, time=55.08 memory used=21076.6MB, alloc=107.8MB, time=55.14 memory used=21090.5MB, alloc=107.8MB, time=55.22 memory used=21104.4MB, alloc=107.8MB, time=55.29 memory used=21118.5MB, alloc=107.8MB, time=55.36 memory used=21132.4MB, alloc=107.8MB, time=55.43 memory used=21146.5MB, alloc=107.8MB, time=55.49 memory used=21160.5MB, alloc=107.8MB, time=55.55 memory used=21174.4MB, alloc=107.8MB, time=55.59 memory used=21188.5MB, alloc=107.8MB, time=55.64 memory used=21202.5MB, alloc=107.8MB, time=55.68 memory used=21216.4MB, alloc=107.8MB, time=55.75 memory used=21230.6MB, alloc=107.8MB, time=55.81 memory used=21244.5MB, alloc=107.8MB, time=55.89 memory used=21258.5MB, alloc=107.8MB, time=55.95 memory used=21272.5MB, alloc=107.8MB, time=56.00 memory used=21286.4MB, alloc=107.8MB, time=56.05 memory used=21300.4MB, alloc=107.8MB, time=56.09 memory used=21314.5MB, alloc=107.8MB, time=56.14 memory used=21328.5MB, alloc=107.8MB, time=56.19 memory used=21342.6MB, alloc=107.8MB, time=56.23 memory used=21356.6MB, alloc=107.8MB, time=56.27 memory used=21370.5MB, alloc=107.8MB, time=56.32 memory used=21384.6MB, alloc=107.8MB, time=56.36 memory used=21398.8MB, alloc=107.8MB, time=56.40 memory used=21412.8MB, alloc=107.8MB, time=56.45 memory used=21427.0MB, alloc=107.8MB, time=56.49 memory used=21441.0MB, alloc=107.8MB, time=56.54 memory used=21455.4MB, alloc=107.8MB, time=56.58 memory used=21469.7MB, alloc=107.8MB, time=56.63 memory used=21483.9MB, alloc=107.8MB, time=56.67 memory used=21498.2MB, alloc=107.8MB, time=56.71 memory used=21512.3MB, alloc=107.8MB, time=56.76 memory used=21526.7MB, alloc=107.8MB, time=56.80 memory used=21540.7MB, alloc=107.8MB, time=56.85 memory used=21554.9MB, alloc=107.8MB, time=56.89 memory used=21569.1MB, alloc=107.8MB, time=56.93 memory used=21583.3MB, alloc=107.8MB, time=56.97 memory used=21597.5MB, alloc=107.8MB, time=57.02 memory used=21611.6MB, alloc=107.8MB, time=57.06 memory used=21625.6MB, alloc=107.8MB, time=57.10 memory used=21640.0MB, alloc=107.8MB, time=57.14 memory used=21654.0MB, alloc=107.8MB, time=57.19 memory used=21668.4MB, alloc=107.8MB, time=57.23 memory used=21682.6MB, alloc=107.8MB, time=57.27 memory used=21696.7MB, alloc=107.8MB, time=57.31 memory used=21711.1MB, alloc=107.8MB, time=57.35 memory used=21725.2MB, alloc=107.8MB, time=57.40 memory used=21739.6MB, alloc=107.8MB, time=57.44 memory used=21753.8MB, alloc=107.8MB, time=57.48 memory used=21768.0MB, alloc=107.8MB, time=57.52 memory used=21782.4MB, alloc=107.8MB, time=57.57 memory used=21796.6MB, alloc=107.8MB, time=57.61 memory used=21811.1MB, alloc=107.8MB, time=57.66 memory used=21825.3MB, alloc=107.8MB, time=57.70 memory used=21839.5MB, alloc=107.8MB, time=57.74 memory used=21853.8MB, alloc=107.8MB, time=57.78 memory used=21868.0MB, alloc=107.8MB, time=57.82 memory used=21882.3MB, alloc=107.8MB, time=57.87 memory used=21896.6MB, alloc=107.8MB, time=57.91 memory used=21910.8MB, alloc=107.8MB, time=57.96 memory used=21925.3MB, alloc=107.8MB, time=58.00 memory used=21939.6MB, alloc=107.8MB, time=58.04 memory used=21953.9MB, alloc=107.8MB, time=58.08 memory used=21968.1MB, alloc=107.8MB, time=58.12 memory used=21982.2MB, alloc=107.8MB, time=58.17 memory used=21996.5MB, alloc=107.8MB, time=58.21 memory used=22010.6MB, alloc=107.8MB, time=58.25 memory used=22024.6MB, alloc=107.8MB, time=58.30 memory used=22039.1MB, alloc=107.8MB, time=58.34 memory used=22053.4MB, alloc=107.8MB, time=58.38 memory used=22067.5MB, alloc=107.8MB, time=58.42 memory used=22082.0MB, alloc=107.8MB, time=58.46 memory used=22096.2MB, alloc=107.8MB, time=58.51 memory used=22110.3MB, alloc=107.8MB, time=58.55 memory used=22124.7MB, alloc=107.8MB, time=58.59 memory used=22138.9MB, alloc=107.8MB, time=58.63 memory used=22152.8MB, alloc=107.8MB, time=58.67 memory used=22167.2MB, alloc=107.8MB, time=58.72 memory used=22181.3MB, alloc=107.8MB, time=58.76 memory used=22195.6MB, alloc=107.8MB, time=58.81 memory used=22210.0MB, alloc=107.8MB, time=58.85 memory used=22224.2MB, alloc=107.8MB, time=58.89 memory used=22238.5MB, alloc=107.8MB, time=58.93 memory used=22252.9MB, alloc=107.8MB, time=58.97 memory used=22267.3MB, alloc=107.8MB, time=59.02 memory used=22281.4MB, alloc=107.8MB, time=59.06 memory used=22295.9MB, alloc=107.8MB, time=59.10 memory used=22310.1MB, alloc=107.8MB, time=59.14 memory used=22324.3MB, alloc=107.8MB, time=59.18 memory used=22338.8MB, alloc=107.8MB, time=59.22 memory used=22352.9MB, alloc=107.8MB, time=59.27 memory used=22366.9MB, alloc=107.8MB, time=59.32 memory used=22381.3MB, alloc=107.8MB, time=59.36 memory used=22395.5MB, alloc=107.8MB, time=59.41 memory used=22409.5MB, alloc=107.8MB, time=59.45 memory used=22423.4MB, alloc=107.8MB, time=59.50 memory used=22437.7MB, alloc=107.8MB, time=59.54 memory used=22451.9MB, alloc=107.8MB, time=59.58 memory used=22465.9MB, alloc=107.8MB, time=59.62 memory used=22480.0MB, alloc=107.8MB, time=59.67 memory used=22494.4MB, alloc=107.8MB, time=59.71 memory used=22508.7MB, alloc=107.8MB, time=59.75 memory used=22522.9MB, alloc=107.8MB, time=59.79 memory used=22537.3MB, alloc=107.8MB, time=59.83 memory used=22551.8MB, alloc=107.8MB, time=59.87 memory used=22566.1MB, alloc=107.8MB, time=59.92 memory used=22580.6MB, alloc=107.8MB, time=59.96 memory used=22595.1MB, alloc=107.8MB, time=60.00 memory used=22609.4MB, alloc=107.8MB, time=60.05 memory used=22624.0MB, alloc=107.8MB, time=60.09 memory used=22638.4MB, alloc=107.8MB, time=60.13 memory used=22652.7MB, alloc=107.8MB, time=60.17 memory used=22667.3MB, alloc=107.8MB, time=60.21 memory used=22681.7MB, alloc=107.8MB, time=60.25 memory used=22695.9MB, alloc=107.8MB, time=60.29 memory used=22710.6MB, alloc=107.8MB, time=60.33 memory used=22725.0MB, alloc=107.8MB, time=60.38 memory used=22739.2MB, alloc=107.8MB, time=60.42 memory used=22753.9MB, alloc=107.8MB, time=60.46 memory used=22768.3MB, alloc=107.8MB, time=60.51 memory used=22782.3MB, alloc=107.8MB, time=60.55 memory used=22796.8MB, alloc=107.8MB, time=60.60 memory used=22811.2MB, alloc=107.8MB, time=60.64 memory used=22825.4MB, alloc=107.8MB, time=60.68 memory used=22839.6MB, alloc=107.8MB, time=60.73 memory used=22854.0MB, alloc=107.8MB, time=60.77 memory used=22868.3MB, alloc=107.8MB, time=60.81 memory used=22882.5MB, alloc=107.8MB, time=60.85 memory used=22896.9MB, alloc=107.8MB, time=60.89 memory used=22911.3MB, alloc=107.8MB, time=60.93 memory used=22925.7MB, alloc=107.8MB, time=60.97 memory used=22939.9MB, alloc=107.8MB, time=61.01 memory used=22954.4MB, alloc=107.8MB, time=61.05 memory used=22968.8MB, alloc=107.8MB, time=61.09 memory used=22983.1MB, alloc=107.8MB, time=61.13 memory used=22997.2MB, alloc=107.8MB, time=61.18 memory used=23011.8MB, alloc=107.8MB, time=61.22 memory used=23026.2MB, alloc=107.8MB, time=61.26 memory used=23040.5MB, alloc=107.8MB, time=61.30 memory used=23054.7MB, alloc=107.8MB, time=61.34 memory used=23069.2MB, alloc=107.8MB, time=61.38 memory used=23083.6MB, alloc=107.8MB, time=61.42 memory used=23097.8MB, alloc=107.8MB, time=61.46 memory used=23111.9MB, alloc=107.8MB, time=61.51 memory used=23126.4MB, alloc=107.8MB, time=61.55 memory used=23140.8MB, alloc=107.8MB, time=61.59 memory used=23155.1MB, alloc=107.8MB, time=61.63 memory used=23169.3MB, alloc=107.8MB, time=61.68 memory used=23184.0MB, alloc=107.8MB, time=61.72 memory used=23198.3MB, alloc=107.8MB, time=61.77 memory used=23212.6MB, alloc=107.8MB, time=61.82 memory used=23226.8MB, alloc=107.8MB, time=61.88 memory used=23241.3MB, alloc=107.8MB, time=61.95 memory used=23255.8MB, alloc=107.8MB, time=62.01 memory used=23270.1MB, alloc=107.8MB, time=62.08 memory used=23284.6MB, alloc=107.8MB, time=62.15 memory used=23299.2MB, alloc=107.8MB, time=62.22 memory used=23313.7MB, alloc=107.8MB, time=62.29 memory used=23328.0MB, alloc=107.8MB, time=62.35 memory used=23342.6MB, alloc=107.8MB, time=62.42 memory used=23357.2MB, alloc=107.8MB, time=62.49 memory used=23371.7MB, alloc=107.8MB, time=62.55 memory used=23386.0MB, alloc=107.8MB, time=62.61 memory used=23400.8MB, alloc=107.8MB, time=62.66 memory used=23415.5MB, alloc=107.8MB, time=62.70 memory used=23429.9MB, alloc=107.8MB, time=62.75 memory used=23444.8MB, alloc=107.8MB, time=62.79 memory used=23459.4MB, alloc=107.8MB, time=62.84 memory used=23473.9MB, alloc=107.8MB, time=62.89 memory used=23488.5MB, alloc=107.8MB, time=62.93 memory used=23503.4MB, alloc=107.8MB, time=62.97 memory used=23517.9MB, alloc=107.8MB, time=63.02 memory used=23532.6MB, alloc=107.8MB, time=63.06 memory used=23547.5MB, alloc=107.8MB, time=63.10 memory used=23562.0MB, alloc=107.8MB, time=63.15 memory used=23576.9MB, alloc=107.8MB, time=63.19 memory used=23591.8MB, alloc=107.8MB, time=63.23 memory used=23606.4MB, alloc=107.8MB, time=63.28 memory used=23621.4MB, alloc=107.8MB, time=63.32 memory used=23636.2MB, alloc=107.8MB, time=63.37 memory used=23651.1MB, alloc=107.8MB, time=63.41 memory used=23665.7MB, alloc=107.8MB, time=63.46 memory used=23680.4MB, alloc=107.8MB, time=63.50 memory used=23695.4MB, alloc=107.8MB, time=63.54 memory used=23710.2MB, alloc=107.8MB, time=63.58 memory used=23725.0MB, alloc=107.8MB, time=63.62 memory used=23739.9MB, alloc=107.8MB, time=63.67 memory used=23754.7MB, alloc=107.8MB, time=63.71 memory 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alloc=107.8MB, time=64.62 memory used=24081.3MB, alloc=107.8MB, time=64.66 memory used=24096.0MB, alloc=107.8MB, time=64.71 memory used=24110.9MB, alloc=107.8MB, time=64.75 memory used=24125.9MB, alloc=107.8MB, time=64.80 memory used=24140.6MB, alloc=107.8MB, time=64.84 memory used=24155.5MB, alloc=107.8MB, time=64.88 memory used=24170.3MB, alloc=107.8MB, time=64.93 memory used=24185.1MB, alloc=107.8MB, time=64.97 memory used=24199.9MB, alloc=107.8MB, time=65.01 memory used=24214.9MB, alloc=107.8MB, time=65.05 memory used=24229.7MB, alloc=107.8MB, time=65.09 memory used=24244.5MB, alloc=107.8MB, time=65.14 memory used=24259.6MB, alloc=107.8MB, time=65.18 memory used=24274.3MB, alloc=107.8MB, time=65.22 memory used=24289.1MB, alloc=107.8MB, time=65.26 memory used=24304.0MB, alloc=107.8MB, time=65.31 memory used=24318.8MB, alloc=107.8MB, time=65.35 memory used=24333.6MB, alloc=107.8MB, time=65.39 memory used=24348.5MB, alloc=107.8MB, time=65.43 memory used=24363.4MB, alloc=107.8MB, 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used=28777.5MB, alloc=107.8MB, time=80.00 memory used=28791.9MB, alloc=107.8MB, time=80.04 memory used=28806.2MB, alloc=107.8MB, time=80.09 memory used=28820.7MB, alloc=107.8MB, time=80.13 memory used=28835.0MB, alloc=107.8MB, time=80.17 memory used=28849.4MB, alloc=107.8MB, time=80.21 memory used=28863.8MB, alloc=107.8MB, time=80.25 memory used=28878.0MB, alloc=107.8MB, time=80.29 memory used=28892.5MB, alloc=107.8MB, time=80.34 memory used=28906.7MB, alloc=107.8MB, time=80.39 memory used=28921.0MB, alloc=107.8MB, time=80.43 memory used=28935.1MB, alloc=107.8MB, time=80.47 memory used=28949.3MB, alloc=107.8MB, time=80.51 memory used=28963.3MB, alloc=107.8MB, time=80.56 memory used=28977.6MB, alloc=107.8MB, time=80.60 memory used=28991.8MB, alloc=107.8MB, time=80.64 memory used=29006.1MB, alloc=107.8MB, time=80.69 memory used=29020.5MB, alloc=107.8MB, time=80.74 memory used=29034.7MB, alloc=107.8MB, time=80.78 memory used=29049.1MB, alloc=107.8MB, time=80.83 memory used=29063.4MB, alloc=107.8MB, time=80.87 memory used=29077.8MB, alloc=107.8MB, time=80.92 memory used=29092.1MB, alloc=107.8MB, time=80.96 memory used=29106.4MB, alloc=107.8MB, time=81.00 memory used=29120.7MB, alloc=107.8MB, time=81.04 memory used=29135.0MB, alloc=107.8MB, time=81.09 memory used=29149.5MB, alloc=107.8MB, time=81.14 memory used=29163.7MB, alloc=107.8MB, time=81.18 memory used=29178.1MB, alloc=107.8MB, time=81.22 memory used=29192.4MB, alloc=107.8MB, time=81.27 memory used=29206.9MB, alloc=107.8MB, time=81.31 memory used=29221.1MB, alloc=107.8MB, time=81.35 memory used=29235.5MB, alloc=107.8MB, time=81.40 memory used=29249.8MB, alloc=107.8MB, time=81.44 memory used=29264.2MB, alloc=107.8MB, time=81.48 memory used=29278.9MB, alloc=107.8MB, time=81.53 memory used=29293.3MB, alloc=107.8MB, time=81.57 memory used=29307.9MB, alloc=107.8MB, time=81.61 memory used=29322.4MB, alloc=107.8MB, time=81.66 memory used=29336.9MB, alloc=107.8MB, time=81.71 memory used=29351.4MB, alloc=107.8MB, time=81.75 memory used=29366.0MB, alloc=107.8MB, time=81.79 memory used=29380.6MB, alloc=107.8MB, time=81.84 memory used=29395.2MB, alloc=107.8MB, time=81.88 memory used=29409.7MB, alloc=107.8MB, time=81.92 memory used=29424.4MB, alloc=107.8MB, time=81.96 memory used=29438.8MB, alloc=107.8MB, time=82.00 memory used=29453.4MB, alloc=107.8MB, time=82.05 memory used=29468.1MB, alloc=107.8MB, time=82.09 memory used=29482.7MB, alloc=107.8MB, time=82.13 memory used=29497.3MB, alloc=107.8MB, time=82.17 memory used=29512.1MB, alloc=107.8MB, time=82.21 memory used=29526.7MB, alloc=107.8MB, time=82.26 memory used=29541.5MB, alloc=107.8MB, time=82.30 memory used=29556.2MB, alloc=107.8MB, time=82.34 memory used=29570.9MB, alloc=107.8MB, time=82.38 memory used=29585.7MB, alloc=107.8MB, time=82.42 memory used=29600.4MB, alloc=107.8MB, time=82.46 memory used=29615.1MB, alloc=107.8MB, time=82.50 memory used=29629.9MB, alloc=107.8MB, time=82.55 memory used=29644.7MB, alloc=107.8MB, time=82.59 memory used=29659.3MB, alloc=107.8MB, time=82.63 memory used=29674.1MB, alloc=107.8MB, time=82.67 memory used=29688.9MB, alloc=107.8MB, time=82.72 memory used=29703.6MB, alloc=107.8MB, time=82.76 memory used=29718.3MB, alloc=107.8MB, time=82.80 memory used=29733.0MB, alloc=107.8MB, time=82.84 memory used=29747.6MB, alloc=107.8MB, time=82.89 memory used=29762.3MB, alloc=107.8MB, time=82.94 memory used=29776.8MB, alloc=107.8MB, time=82.98 memory used=29791.4MB, alloc=107.8MB, time=83.02 memory used=29806.1MB, alloc=107.8MB, time=83.06 memory used=29820.6MB, alloc=107.8MB, time=83.11 memory used=29835.3MB, alloc=107.8MB, time=83.15 memory used=29849.8MB, alloc=107.8MB, time=83.19 memory used=29864.4MB, alloc=107.8MB, time=83.24 memory used=29879.1MB, alloc=107.8MB, time=83.28 memory used=29893.5MB, alloc=107.8MB, time=83.33 memory used=29908.2MB, alloc=107.8MB, time=83.37 memory used=29922.8MB, alloc=107.8MB, time=83.42 memory used=29937.5MB, alloc=107.8MB, time=83.46 memory used=29952.0MB, alloc=107.8MB, time=83.50 memory used=29966.5MB, alloc=107.8MB, time=83.54 memory used=29981.3MB, alloc=107.8MB, time=83.58 memory used=29996.1MB, alloc=107.8MB, time=83.63 memory used=30010.9MB, alloc=107.8MB, time=83.68 memory used=30025.7MB, alloc=107.8MB, time=83.72 memory used=30040.4MB, alloc=107.8MB, time=83.77 memory used=30055.2MB, alloc=107.8MB, time=83.81 memory used=30069.8MB, alloc=107.8MB, time=83.85 memory used=30084.5MB, alloc=107.8MB, time=83.89 memory used=30099.4MB, alloc=107.8MB, time=83.94 memory used=30114.1MB, alloc=107.8MB, time=83.98 memory used=30128.9MB, alloc=107.8MB, time=84.02 memory used=30143.8MB, alloc=107.8MB, time=84.06 memory used=30158.6MB, alloc=107.8MB, time=84.10 memory used=30173.6MB, alloc=107.8MB, time=84.15 memory used=30188.5MB, alloc=107.8MB, time=84.20 memory used=30203.2MB, alloc=107.8MB, time=84.24 memory used=30218.1MB, alloc=107.8MB, time=84.28 memory used=30233.1MB, alloc=107.8MB, time=84.32 memory used=30248.0MB, alloc=107.8MB, time=84.37 memory used=30262.9MB, alloc=107.8MB, time=84.42 memory used=30278.0MB, alloc=107.8MB, time=84.46 memory used=30292.8MB, alloc=107.8MB, time=84.51 memory used=30307.8MB, alloc=107.8MB, time=84.55 memory used=30322.8MB, alloc=107.8MB, time=84.59 memory used=30337.6MB, alloc=107.8MB, time=84.63 memory used=30352.5MB, alloc=107.8MB, time=84.67 memory used=30367.5MB, alloc=107.8MB, time=84.72 memory used=30382.3MB, alloc=107.8MB, time=84.76 memory used=30397.1MB, alloc=107.8MB, time=84.80 memory used=30412.1MB, alloc=107.8MB, time=84.84 memory used=30426.9MB, alloc=107.8MB, time=84.89 memory used=30441.9MB, alloc=107.8MB, time=84.93 memory used=30456.8MB, alloc=107.8MB, time=84.97 memory used=30471.7MB, alloc=107.8MB, time=85.01 memory used=30486.7MB, alloc=107.8MB, time=85.05 memory used=30501.7MB, alloc=107.8MB, time=85.09 memory used=30516.6MB, alloc=107.8MB, time=85.13 memory used=30531.6MB, alloc=107.8MB, time=85.18 memory used=30546.6MB, alloc=107.8MB, time=85.22 memory used=30561.3MB, alloc=107.8MB, time=85.26 memory used=30576.3MB, alloc=107.8MB, time=85.31 memory used=30591.1MB, alloc=107.8MB, time=85.35 memory used=30606.0MB, alloc=107.8MB, time=85.39 memory used=30621.0MB, alloc=107.8MB, time=85.44 memory used=30635.8MB, alloc=107.8MB, time=85.48 memory used=30650.6MB, alloc=107.8MB, time=85.52 memory used=30665.6MB, alloc=107.8MB, time=85.57 memory used=30680.5MB, alloc=107.8MB, time=85.61 memory used=30695.4MB, alloc=107.8MB, time=85.65 memory used=30710.2MB, alloc=107.8MB, time=85.70 memory used=30725.1MB, alloc=107.8MB, time=85.74 memory used=30740.2MB, alloc=107.8MB, time=85.78 memory used=30755.0MB, alloc=107.8MB, time=85.83 memory used=30770.0MB, alloc=107.8MB, time=85.87 memory used=30785.0MB, alloc=107.8MB, time=85.92 memory used=30800.0MB, alloc=107.8MB, time=85.97 memory used=30815.1MB, alloc=107.8MB, time=86.01 memory used=30830.3MB, alloc=107.8MB, time=86.06 memory used=30845.3MB, alloc=107.8MB, time=86.10 memory used=30860.4MB, alloc=107.8MB, time=86.15 memory used=30875.6MB, alloc=107.8MB, time=86.19 memory used=30890.5MB, alloc=107.8MB, time=86.23 memory used=30905.4MB, alloc=107.8MB, time=86.27 memory used=30920.5MB, alloc=107.8MB, time=86.31 memory used=30935.4MB, alloc=107.8MB, time=86.35 memory used=30950.3MB, alloc=107.8MB, time=86.39 memory used=30965.4MB, alloc=107.8MB, time=86.43 memory used=30980.4MB, alloc=107.8MB, time=86.47 memory used=30995.5MB, alloc=107.8MB, time=86.52 memory used=31010.6MB, alloc=107.8MB, time=86.56 memory used=31025.4MB, alloc=107.8MB, time=86.62 memory used=31040.5MB, alloc=107.8MB, time=86.68 memory used=31055.3MB, alloc=107.8MB, time=86.74 memory used=31070.3MB, alloc=107.8MB, time=86.80 memory used=31085.4MB, alloc=107.8MB, time=86.87 memory used=31100.4MB, alloc=107.8MB, time=86.92 memory used=31115.4MB, alloc=107.8MB, time=86.99 memory used=31130.5MB, alloc=107.8MB, time=87.05 memory used=31145.4MB, alloc=107.8MB, time=87.11 memory used=31160.6MB, alloc=107.8MB, time=87.17 memory used=31175.5MB, alloc=107.8MB, time=87.24 memory used=31190.6MB, alloc=107.8MB, time=87.30 memory used=31205.9MB, alloc=107.8MB, time=87.34 memory used=31220.8MB, alloc=107.8MB, time=87.38 memory used=31235.8MB, alloc=107.8MB, time=87.43 memory used=31251.0MB, alloc=107.8MB, time=87.50 memory used=31266.1MB, alloc=107.8MB, time=87.57 memory used=31281.3MB, alloc=107.8MB, time=87.63 memory used=31296.5MB, alloc=107.8MB, time=87.69 memory used=31311.5MB, alloc=107.8MB, time=87.75 memory used=31326.7MB, alloc=107.8MB, time=87.82 memory used=31342.0MB, alloc=107.8MB, time=87.88 memory used=31357.1MB, alloc=107.8MB, time=87.93 memory used=31372.3MB, alloc=107.8MB, time=87.97 memory used=31387.6MB, alloc=107.8MB, time=88.01 memory used=31402.8MB, alloc=107.8MB, time=88.06 memory used=31418.0MB, alloc=107.8MB, time=88.11 memory used=31433.5MB, alloc=107.8MB, time=88.15 memory used=31448.9MB, alloc=107.8MB, time=88.19 memory used=31464.3MB, alloc=107.8MB, time=88.24 memory used=31479.7MB, alloc=107.8MB, time=88.28 memory used=31495.2MB, alloc=107.8MB, time=88.33 memory used=31510.7MB, alloc=107.8MB, time=88.36 memory used=31526.0MB, alloc=107.8MB, time=88.41 memory used=31541.3MB, alloc=107.8MB, time=88.45 memory used=31556.7MB, alloc=107.8MB, time=88.50 memory used=31571.7MB, alloc=107.8MB, time=88.54 memory used=31587.1MB, alloc=107.8MB, time=88.58 memory used=31602.6MB, alloc=107.8MB, time=88.63 memory used=31617.9MB, alloc=107.8MB, time=88.68 memory used=31633.2MB, alloc=107.8MB, time=88.72 memory used=31648.6MB, alloc=107.8MB, time=88.76 memory used=31664.0MB, alloc=107.8MB, time=88.81 memory used=31679.2MB, alloc=107.8MB, time=88.85 memory used=31694.6MB, alloc=107.8MB, time=88.90 memory used=31710.2MB, alloc=107.8MB, time=88.94 memory used=31725.7MB, alloc=107.8MB, time=88.98 memory used=31741.0MB, alloc=107.8MB, time=89.02 memory used=31756.5MB, alloc=107.8MB, time=89.06 memory used=31772.1MB, alloc=107.8MB, time=89.11 memory used=31787.6MB, alloc=107.8MB, time=89.15 memory used=31802.9MB, alloc=107.8MB, time=89.19 memory used=31818.4MB, alloc=107.8MB, time=89.23 memory used=31833.9MB, alloc=107.8MB, time=89.28 memory used=31849.1MB, alloc=107.8MB, time=89.32 memory used=31864.4MB, alloc=107.8MB, time=89.36 memory used=31879.9MB, alloc=107.8MB, time=89.42 memory used=31895.4MB, alloc=107.8MB, time=89.47 memory used=31910.6MB, alloc=107.8MB, time=89.52 memory used=31926.0MB, alloc=107.8MB, time=89.58 memory used=31941.6MB, alloc=107.8MB, time=89.63 memory used=31957.0MB, alloc=107.8MB, time=89.68 memory used=31972.4MB, alloc=107.8MB, time=89.73 memory used=31987.9MB, alloc=107.8MB, time=89.80 memory used=32003.4MB, alloc=107.8MB, time=89.87 memory used=32018.7MB, alloc=107.8MB, time=89.94 memory used=32034.0MB, alloc=107.8MB, time=90.01 memory used=32049.4MB, alloc=107.8MB, time=90.07 memory used=32064.7MB, alloc=107.8MB, time=90.14 memory used=32080.0MB, alloc=107.8MB, time=90.21 memory used=32095.4MB, alloc=107.8MB, time=90.28 memory used=32110.7MB, alloc=107.8MB, time=90.34 memory used=32126.1MB, alloc=107.8MB, time=90.40 memory used=32141.5MB, alloc=107.8MB, time=90.47 memory used=32156.7MB, alloc=107.8MB, time=90.53 memory used=32172.1MB, alloc=107.8MB, time=90.58 memory used=32187.6MB, alloc=107.8MB, time=90.64 memory used=32202.8MB, alloc=107.8MB, time=90.69 memory used=32218.2MB, alloc=107.8MB, time=90.73 memory used=32233.7MB, alloc=107.8MB, time=90.78 memory used=32249.0MB, alloc=107.8MB, time=90.83 memory used=32264.4MB, alloc=107.8MB, time=90.87 memory used=32280.0MB, alloc=107.8MB, time=90.92 memory used=32295.3MB, alloc=107.8MB, time=90.96 memory used=32310.7MB, alloc=107.8MB, time=91.01 memory used=32326.2MB, alloc=107.8MB, time=91.05 memory used=32341.5MB, alloc=107.8MB, time=91.09 memory used=32357.0MB, alloc=107.8MB, time=91.13 memory used=32372.5MB, alloc=107.8MB, time=91.17 memory used=32387.8MB, alloc=107.8MB, time=91.21 memory used=32403.2MB, alloc=107.8MB, time=91.25 memory used=32418.6MB, alloc=107.8MB, time=91.30 memory used=32434.0MB, alloc=107.8MB, time=91.34 memory used=32449.3MB, alloc=107.8MB, time=91.38 memory used=32464.8MB, alloc=107.8MB, time=91.42 memory used=32480.1MB, alloc=107.8MB, time=91.47 memory used=32495.6MB, alloc=107.8MB, time=91.51 memory used=32511.0MB, alloc=107.8MB, time=91.55 memory used=32526.4MB, alloc=107.8MB, time=91.59 memory used=32541.9MB, alloc=107.8MB, time=91.63 memory used=32557.4MB, alloc=107.8MB, time=91.67 memory used=32572.7MB, alloc=107.8MB, time=91.71 memory used=32588.2MB, alloc=107.8MB, time=91.76 memory used=32603.7MB, alloc=107.8MB, time=91.80 memory used=32619.0MB, alloc=107.8MB, time=91.84 memory used=32634.4MB, alloc=107.8MB, time=91.88 memory used=32649.6MB, alloc=107.8MB, time=91.92 memory used=32664.9MB, alloc=107.8MB, time=91.96 memory used=32680.4MB, alloc=107.8MB, time=92.01 memory used=32695.8MB, alloc=107.8MB, time=92.06 memory used=32711.2MB, alloc=107.8MB, time=92.12 memory used=32726.6MB, alloc=107.8MB, time=92.17 memory used=32741.9MB, alloc=107.8MB, time=92.24 memory used=32757.3MB, alloc=107.8MB, time=92.31 memory used=32772.5MB, alloc=107.8MB, time=92.37 memory used=32787.8MB, alloc=107.8MB, time=92.43 memory used=32803.2MB, alloc=107.8MB, time=92.49 memory used=32818.6MB, alloc=107.8MB, time=92.56 memory used=32834.2MB, alloc=107.8MB, time=92.63 memory used=32849.9MB, alloc=107.8MB, time=92.70 memory used=32865.4MB, alloc=107.8MB, time=92.78 memory used=32880.9MB, alloc=107.8MB, time=92.84 memory used=32896.5MB, alloc=107.8MB, time=92.90 memory used=32912.0MB, alloc=107.8MB, time=92.96 memory used=32927.6MB, alloc=107.8MB, time=93.02 memory used=32943.3MB, alloc=107.8MB, time=93.06 memory used=32958.8MB, alloc=107.8MB, time=93.11 memory used=32974.4MB, alloc=107.8MB, time=93.16 memory used=32990.1MB, alloc=107.8MB, time=93.22 memory used=33005.5MB, alloc=107.8MB, time=93.28 memory used=33021.0MB, alloc=107.8MB, time=93.34 memory used=33036.7MB, alloc=107.8MB, time=93.41 memory used=33052.2MB, alloc=107.8MB, time=93.48 memory used=33067.8MB, alloc=107.8MB, time=93.54 memory used=33083.4MB, alloc=107.8MB, time=93.61 memory used=33098.9MB, alloc=107.8MB, time=93.68 memory used=33114.6MB, alloc=107.8MB, time=93.75 memory used=33130.3MB, alloc=107.8MB, time=93.81 memory used=33145.8MB, alloc=107.8MB, time=93.88 memory used=33161.5MB, alloc=107.8MB, time=93.95 memory used=33177.3MB, alloc=107.8MB, time=94.01 memory used=33192.8MB, alloc=107.8MB, time=94.08 memory used=33208.5MB, alloc=107.8MB, time=94.13 memory used=33224.4MB, alloc=107.8MB, time=94.19 memory used=33240.2MB, alloc=107.8MB, time=94.23 memory used=33255.7MB, alloc=107.8MB, time=94.28 memory used=33271.4MB, alloc=107.8MB, time=94.32 memory used=33287.3MB, alloc=107.8MB, time=94.37 memory used=33302.9MB, alloc=107.8MB, time=94.41 memory used=33318.7MB, alloc=107.8MB, time=94.46 memory used=33334.7MB, alloc=107.8MB, time=94.50 memory used=33350.6MB, alloc=107.8MB, time=94.54 memory used=33366.4MB, alloc=107.8MB, time=94.62 memory used=33382.2MB, alloc=107.8MB, time=94.68 memory used=33398.2MB, alloc=107.8MB, time=94.73 memory used=33414.0MB, alloc=107.8MB, time=94.80 memory used=33429.6MB, alloc=107.8MB, time=94.87 memory used=33445.3MB, alloc=107.8MB, time=94.93 memory used=33461.1MB, alloc=107.8MB, time=95.00 memory used=33476.8MB, alloc=107.8MB, time=95.04 memory used=33492.5MB, alloc=107.8MB, time=95.08 memory used=33508.3MB, alloc=107.8MB, time=95.13 memory used=33524.0MB, alloc=107.8MB, time=95.18 memory used=33539.7MB, alloc=107.8MB, time=95.22 memory used=33555.6MB, alloc=107.8MB, time=95.27 memory used=33571.3MB, alloc=107.8MB, time=95.31 memory used=33587.2MB, alloc=107.8MB, time=95.35 memory used=33603.3MB, alloc=107.8MB, time=95.40 memory used=33619.2MB, alloc=107.8MB, time=95.44 memory used=33635.0MB, alloc=107.8MB, time=95.49 memory used=33651.1MB, alloc=107.8MB, time=95.53 memory used=33667.0MB, alloc=107.8MB, time=95.58 memory used=33683.0MB, alloc=107.8MB, time=95.62 memory used=33698.9MB, alloc=107.8MB, time=95.66 memory used=33714.9MB, alloc=107.8MB, time=95.71 memory used=33730.9MB, alloc=107.8MB, time=95.75 memory used=33746.9MB, alloc=107.8MB, time=95.79 memory used=33762.8MB, alloc=107.8MB, time=95.83 memory used=33778.7MB, alloc=107.8MB, time=95.88 memory used=33794.8MB, alloc=107.8MB, time=95.92 memory used=33810.9MB, alloc=107.8MB, time=95.96 memory used=33826.7MB, alloc=107.8MB, time=96.04 memory used=33842.6MB, alloc=107.8MB, time=96.10 memory used=33858.8MB, alloc=107.8MB, time=96.17 memory used=33875.1MB, alloc=107.8MB, time=96.24 memory used=33891.2MB, alloc=107.8MB, time=96.31 memory used=33907.1MB, alloc=107.8MB, time=96.38 memory used=33923.3MB, alloc=107.8MB, time=96.44 memory used=33939.4MB, alloc=107.8MB, time=96.51 memory used=33955.5MB, alloc=107.8MB, time=96.58 memory used=33971.4MB, alloc=107.8MB, time=96.64 memory used=33987.4MB, alloc=107.8MB, time=96.71 memory used=34003.5MB, alloc=107.8MB, time=96.78 memory used=34019.6MB, alloc=107.8MB, time=96.85 memory used=34035.4MB, alloc=107.8MB, time=96.92 memory used=34051.5MB, alloc=107.8MB, time=96.99 memory used=34067.6MB, alloc=107.8MB, time=97.04 memory used=34083.6MB, alloc=107.8MB, time=97.08 memory used=34099.5MB, alloc=107.8MB, time=97.13 memory used=34115.5MB, alloc=107.8MB, time=97.17 memory used=34131.6MB, alloc=107.8MB, time=97.24 memory used=34147.6MB, alloc=107.8MB, time=97.33 memory used=34163.6MB, alloc=107.8MB, time=97.40 memory used=34179.6MB, alloc=107.8MB, time=97.46 memory used=34195.8MB, alloc=107.8MB, time=97.52 memory used=34211.9MB, alloc=107.8MB, time=97.58 memory used=34227.8MB, alloc=107.8MB, time=97.65 memory used=34243.9MB, alloc=107.8MB, time=97.71 memory used=34260.1MB, alloc=107.8MB, time=97.77 memory used=34276.2MB, alloc=107.8MB, time=97.81 memory used=34292.1MB, alloc=107.8MB, time=97.88 memory used=34308.0MB, alloc=107.8MB, time=97.93 memory used=34324.0MB, alloc=107.8MB, time=97.98 memory used=34339.9MB, alloc=107.8MB, time=98.02 memory used=34355.9MB, alloc=107.8MB, time=98.07 memory used=34372.1MB, alloc=107.8MB, time=98.11 memory used=34388.2MB, alloc=107.8MB, time=98.18 memory used=34404.2MB, alloc=107.8MB, time=98.23 memory used=34420.4MB, alloc=107.8MB, time=98.28 memory used=34436.6MB, alloc=107.8MB, time=98.34 memory used=34452.9MB, alloc=107.8MB, time=98.39 memory used=34468.8MB, alloc=107.8MB, time=98.43 memory used=34484.9MB, alloc=107.8MB, time=98.47 memory used=34501.2MB, alloc=107.8MB, time=98.52 memory used=34517.4MB, alloc=107.8MB, time=98.56 memory used=34533.4MB, alloc=107.8MB, time=98.63 memory used=34549.5MB, alloc=107.8MB, time=98.69 memory used=34565.8MB, alloc=107.8MB, time=98.75 memory used=34582.1MB, alloc=107.8MB, time=98.82 memory used=34598.2MB, alloc=107.8MB, time=98.88 memory used=34614.3MB, alloc=107.8MB, time=98.94 memory used=34630.5MB, alloc=107.8MB, time=99.02 memory used=34646.6MB, alloc=107.8MB, time=99.08 memory used=34662.7MB, alloc=107.8MB, time=99.14 memory used=34678.9MB, alloc=107.8MB, time=99.21 memory used=34695.2MB, alloc=107.8MB, time=99.27 memory used=34711.4MB, alloc=107.8MB, time=99.34 memory used=34727.5MB, alloc=107.8MB, time=99.41 memory used=34743.7MB, alloc=107.8MB, time=99.48 memory used=34760.0MB, alloc=107.8MB, time=99.54 memory used=34776.2MB, alloc=107.8MB, time=99.60 memory used=34792.3MB, alloc=107.8MB, time=99.66 memory used=34808.3MB, alloc=107.8MB, time=99.71 memory used=34824.6MB, alloc=107.8MB, time=99.76 memory used=34840.7MB, alloc=107.8MB, time=99.80 memory used=34856.9MB, alloc=107.8MB, time=99.86 memory used=34873.1MB, alloc=107.8MB, time=99.93 memory used=34889.5MB, alloc=107.8MB, time=100.00 memory used=34905.6MB, alloc=107.8MB, time=100.06 memory used=34921.9MB, alloc=107.8MB, time=100.13 memory used=34938.4MB, alloc=107.8MB, time=100.20 memory used=34954.8MB, alloc=107.8MB, time=100.26 memory used=34971.2MB, alloc=107.8MB, time=100.34 memory used=34987.3MB, alloc=107.8MB, time=100.40 memory used=35003.4MB, alloc=107.8MB, time=100.47 memory used=35019.7MB, alloc=107.8MB, time=100.53 memory used=35036.1MB, alloc=107.8MB, time=100.59 memory used=35052.3MB, alloc=107.8MB, time=100.66 memory used=35068.7MB, alloc=107.8MB, time=100.73 memory used=35085.1MB, alloc=107.8MB, time=100.79 memory used=35101.5MB, alloc=107.8MB, time=100.84 memory used=35117.6MB, alloc=107.8MB, time=100.89 memory used=35133.9MB, alloc=107.8MB, time=100.95 memory used=35150.3MB, alloc=107.8MB, time=101.03 memory used=35166.6MB, alloc=107.8MB, time=101.10 memory used=35182.8MB, alloc=107.8MB, time=101.15 memory used=35199.2MB, alloc=107.8MB, time=101.22 memory used=35215.5MB, alloc=107.8MB, time=101.29 memory used=35232.0MB, alloc=107.8MB, time=101.35 memory used=35248.2MB, alloc=107.8MB, time=101.42 memory used=35264.5MB, alloc=107.8MB, time=101.49 memory used=35280.8MB, alloc=107.8MB, time=101.55 memory used=35297.1MB, alloc=107.8MB, time=101.61 memory used=35313.2MB, alloc=107.8MB, time=101.68 memory used=35329.6MB, alloc=107.8MB, time=101.75 memory used=35345.9MB, alloc=107.8MB, time=101.81 memory used=35362.3MB, alloc=107.8MB, time=101.88 memory used=35378.5MB, alloc=107.8MB, time=101.94 memory used=35394.4MB, alloc=107.8MB, time=101.98 memory used=35410.2MB, alloc=107.8MB, time=102.02 memory used=35425.5MB, alloc=107.8MB, time=102.07 memory used=35440.8MB, alloc=107.8MB, time=102.13 memory used=35454.9MB, alloc=107.8MB, time=102.17 memory used=35468.8MB, alloc=107.8MB, time=102.21 memory used=35482.4MB, alloc=107.8MB, time=102.26 memory used=35491.6MB, alloc=107.8MB, time=102.32 memory used=35500.7MB, alloc=107.8MB, time=102.36 memory used=35509.6MB, alloc=107.8MB, time=102.40 memory used=35518.5MB, alloc=107.8MB, time=102.45 memory used=35527.1MB, alloc=107.8MB, time=102.49 memory used=35535.1MB, alloc=107.8MB, time=102.53 memory used=35542.9MB, alloc=107.8MB, time=102.57 memory used=35550.8MB, alloc=107.8MB, time=102.61 memory used=35558.6MB, alloc=107.8MB, time=102.65 memory used=35566.3MB, alloc=107.8MB, time=102.69 memory used=35573.9MB, alloc=107.8MB, time=102.73 memory used=35581.6MB, alloc=107.8MB, time=102.80 memory used=35588.9MB, alloc=107.8MB, time=102.86 memory used=35596.2MB, alloc=107.8MB, time=102.90 memory used=35603.4MB, alloc=107.8MB, time=102.95 memory used=35610.5MB, alloc=107.8MB, time=102.99 memory used=35617.4MB, alloc=107.8MB, time=103.03 memory used=35624.4MB, alloc=107.8MB, time=103.07 memory used=35631.1MB, alloc=107.8MB, time=103.11 memory used=35638.1MB, alloc=107.8MB, time=103.14 memory used=35644.7MB, alloc=107.8MB, time=103.18 memory used=35651.3MB, alloc=107.8MB, time=103.22 memory used=35658.0MB, alloc=107.8MB, time=103.26 memory used=35664.4MB, alloc=107.8MB, time=103.29 memory used=35670.7MB, alloc=107.8MB, time=103.33 memory used=35677.2MB, alloc=107.8MB, time=103.36 memory used=35683.7MB, alloc=107.8MB, time=103.40 memory used=35690.0MB, alloc=107.8MB, time=103.44 memory used=35696.2MB, alloc=107.8MB, time=103.47 memory used=35702.6MB, alloc=107.8MB, time=103.51 memory used=35708.9MB, alloc=107.8MB, time=103.54 memory used=35715.1MB, alloc=107.8MB, time=103.58 memory used=35721.0MB, alloc=107.8MB, time=103.61 memory used=35726.9MB, alloc=107.8MB, time=103.65 memory used=35732.8MB, alloc=107.8MB, time=103.68 memory used=35738.6MB, alloc=107.8MB, time=103.72 memory used=35744.3MB, alloc=107.8MB, time=103.75 memory used=35750.0MB, alloc=107.8MB, time=103.80 memory used=35755.6MB, alloc=107.8MB, time=103.83 memory used=35761.4MB, alloc=107.8MB, time=103.87 memory used=35767.2MB, alloc=107.8MB, time=103.90 memory used=35773.0MB, alloc=107.8MB, time=103.95 memory used=35778.7MB, alloc=107.8MB, time=104.01 memory used=35784.4MB, alloc=107.8MB, time=104.06 memory used=35790.1MB, alloc=107.8MB, time=104.11 memory used=35795.7MB, alloc=107.8MB, time=104.17 memory used=35801.3MB, alloc=107.8MB, time=104.22 memory used=35806.8MB, alloc=107.8MB, time=104.28 memory used=35812.3MB, alloc=107.8MB, time=104.33 memory used=35817.9MB, alloc=107.8MB, time=104.38 memory used=35823.4MB, alloc=107.8MB, time=104.44 memory used=35828.8MB, alloc=107.8MB, time=104.49 memory used=35834.2MB, alloc=107.8MB, time=104.55 memory used=35839.6MB, alloc=107.8MB, time=104.60 memory used=35844.8MB, alloc=107.8MB, time=104.66 memory used=35849.7MB, alloc=107.8MB, time=104.72 memory used=35854.8MB, alloc=107.8MB, time=104.77 memory used=35860.0MB, alloc=107.8MB, time=104.82 memory used=35865.2MB, alloc=107.8MB, time=104.87 memory used=35870.3MB, alloc=107.8MB, time=104.93 memory used=35875.1MB, alloc=107.8MB, time=104.99 memory used=35879.9MB, alloc=107.8MB, time=105.02 memory used=35884.9MB, alloc=107.8MB, time=105.08 memory used=35889.5MB, alloc=107.8MB, time=105.12 memory used=35894.3MB, alloc=107.8MB, time=105.16 memory used=35899.1MB, alloc=107.8MB, time=105.21 memory used=35903.6MB, alloc=107.8MB, time=105.25 memory used=35908.2MB, alloc=107.8MB, time=105.28 memory used=35912.7MB, alloc=107.8MB, time=105.32 memory used=35917.0MB, alloc=107.8MB, time=105.36 memory used=35921.4MB, alloc=107.8MB, time=105.39 memory used=35925.6MB, alloc=107.8MB, time=105.44 memory used=35930.0MB, alloc=107.8MB, time=105.48 memory used=35934.2MB, alloc=107.8MB, time=105.52 memory used=35938.6MB, alloc=107.8MB, time=105.56 memory used=35942.7MB, alloc=107.8MB, time=105.59 memory used=35947.1MB, alloc=107.8MB, time=105.63 memory used=35951.2MB, alloc=107.8MB, time=105.66 memory used=35955.5MB, alloc=107.8MB, time=105.70 memory used=35959.7MB, alloc=107.8MB, time=105.74 memory used=35963.9MB, alloc=107.8MB, time=105.77 memory used=35967.9MB, alloc=107.8MB, time=105.81 memory used=35971.8MB, alloc=107.8MB, time=105.84 memory used=35975.9MB, alloc=107.8MB, time=105.87 memory used=35979.8MB, alloc=107.8MB, time=105.93 memory used=35983.8MB, alloc=107.8MB, time=105.97 memory used=35987.8MB, alloc=107.8MB, time=106.03 memory used=35991.6MB, alloc=107.8MB, time=106.09 memory used=35995.6MB, alloc=107.8MB, time=106.14 memory used=35999.4MB, alloc=107.8MB, time=106.19 memory used=36003.1MB, alloc=107.8MB, time=106.24 memory used=36007.0MB, alloc=107.8MB, time=106.29 memory used=36010.8MB, alloc=107.8MB, time=106.34 memory used=36014.5MB, alloc=107.8MB, time=106.37 memory used=36018.5MB, alloc=107.8MB, time=106.41 memory used=36022.4MB, alloc=107.8MB, time=106.44 memory used=36026.1MB, alloc=107.8MB, time=106.47 memory used=36030.0MB, alloc=107.8MB, time=106.51 memory used=36033.8MB, alloc=107.8MB, time=106.54 memory used=36037.5MB, alloc=107.8MB, time=106.57 memory used=36041.4MB, alloc=107.8MB, time=106.61 memory used=36045.1MB, alloc=107.8MB, time=106.64 memory used=36048.8MB, alloc=107.8MB, time=106.67 memory used=36052.6MB, alloc=107.8MB, time=106.70 memory used=36056.3MB, alloc=107.8MB, time=106.73 memory used=36059.7MB, alloc=107.8MB, time=106.76 memory used=36062.9MB, alloc=107.8MB, time=106.79 memory used=36066.2MB, alloc=107.8MB, time=106.82 memory used=36069.8MB, alloc=107.8MB, time=106.85 memory used=36073.2MB, alloc=107.8MB, time=106.88 memory used=36076.6MB, alloc=107.8MB, time=106.91 memory used=36079.9MB, alloc=107.8MB, time=106.95 memory used=36083.2MB, alloc=107.8MB, time=106.98 memory used=36086.7MB, alloc=107.8MB, time=107.01 memory used=36090.3MB, alloc=107.8MB, time=107.04 memory used=36093.3MB, alloc=107.8MB, time=107.07 memory used=36096.7MB, alloc=107.8MB, time=107.10 memory used=36099.7MB, alloc=107.8MB, time=107.14 memory used=36102.9MB, alloc=107.8MB, time=107.17 memory used=36106.1MB, alloc=107.8MB, time=107.20 memory used=36109.5MB, alloc=107.8MB, time=107.24 memory used=36113.0MB, alloc=107.8MB, time=107.27 memory used=36116.3MB, alloc=107.8MB, time=107.31 memory used=36119.6MB, alloc=107.8MB, time=107.34 memory used=36122.9MB, alloc=107.8MB, time=107.37 memory used=36125.6MB, alloc=107.8MB, time=107.41 memory used=36128.7MB, alloc=107.8MB, time=107.44 memory used=36131.8MB, alloc=107.8MB, time=107.47 memory used=36134.9MB, alloc=107.8MB, time=107.51 memory used=36138.1MB, alloc=107.8MB, time=107.54 memory used=36141.5MB, alloc=107.8MB, time=107.58 memory used=36144.8MB, alloc=107.8MB, time=107.61 memory used=36147.9MB, alloc=107.8MB, time=107.64 memory used=36151.0MB, alloc=107.8MB, time=107.68 memory used=36154.0MB, alloc=107.8MB, time=107.71 memory used=36157.0MB, alloc=107.8MB, time=107.74 memory used=36160.0MB, alloc=107.8MB, time=107.78 memory used=36162.9MB, alloc=107.8MB, time=107.81 memory used=36165.9MB, alloc=107.8MB, time=107.85 memory used=36168.8MB, alloc=107.8MB, time=107.88 memory used=36171.7MB, alloc=107.8MB, time=107.91 memory used=36174.6MB, alloc=107.8MB, time=107.95 memory used=36177.4MB, alloc=107.8MB, time=107.98 memory used=36180.3MB, alloc=107.8MB, time=108.02 memory used=36183.2MB, alloc=107.8MB, time=108.05 memory used=36186.0MB, alloc=107.8MB, time=108.09 memory used=36188.9MB, alloc=107.8MB, time=108.12 memory used=36191.7MB, alloc=107.8MB, time=108.16 memory used=36194.5MB, alloc=107.8MB, time=108.19 memory used=36197.4MB, alloc=107.8MB, time=108.23 memory used=36200.1MB, alloc=107.8MB, time=108.26 memory used=36202.9MB, alloc=107.8MB, time=108.29 memory used=36205.5MB, alloc=107.8MB, time=108.32 memory used=36208.4MB, alloc=107.8MB, time=108.36 memory used=36211.3MB, alloc=107.8MB, time=108.39 memory used=36214.1MB, alloc=107.8MB, time=108.43 memory used=36216.9MB, alloc=107.8MB, time=108.46 memory used=36219.7MB, alloc=107.8MB, time=108.49 memory used=36222.5MB, alloc=107.8MB, time=108.53 memory used=36225.4MB, alloc=107.8MB, time=108.56 memory used=36228.2MB, alloc=107.8MB, time=108.59 memory used=36231.1MB, alloc=107.8MB, time=108.63 memory used=36234.0MB, alloc=107.8MB, time=108.66 memory used=36236.9MB, alloc=107.8MB, time=108.70 memory used=36239.7MB, alloc=107.8MB, time=108.73 memory used=36242.6MB, alloc=107.8MB, time=108.76 memory used=36245.5MB, alloc=107.8MB, time=108.80 memory used=36248.4MB, alloc=107.8MB, time=108.83 memory used=36251.3MB, alloc=107.8MB, time=108.87 memory used=36254.2MB, alloc=107.8MB, time=108.90 memory used=36257.0MB, alloc=107.8MB, time=108.93 memory used=36259.9MB, alloc=107.8MB, time=108.97 memory used=36262.8MB, alloc=107.8MB, time=109.00 memory used=36265.7MB, alloc=107.8MB, time=109.03 memory used=36268.6MB, alloc=107.8MB, time=109.07 memory used=36271.4MB, alloc=107.8MB, time=109.10 memory used=36274.3MB, alloc=107.8MB, time=109.14 memory used=36277.2MB, alloc=107.8MB, time=109.17 memory used=36280.1MB, alloc=107.8MB, time=109.20 memory used=36282.9MB, alloc=107.8MB, time=109.24 memory used=36285.6MB, alloc=107.8MB, time=109.27 memory used=36288.5MB, alloc=107.8MB, time=109.30 memory used=36291.4MB, alloc=107.8MB, time=109.34 memory used=36294.3MB, alloc=107.8MB, time=109.37 memory used=36297.2MB, alloc=107.8MB, time=109.40 memory used=36300.0MB, alloc=107.8MB, time=109.44 memory used=36302.9MB, alloc=107.8MB, time=109.47 memory used=36305.8MB, alloc=107.8MB, time=109.51 memory used=36308.7MB, alloc=107.8MB, time=109.54 memory used=36311.5MB, alloc=107.8MB, time=109.58 memory used=36314.4MB, alloc=107.8MB, time=109.61 memory used=36317.3MB, alloc=107.8MB, time=109.65 memory used=36320.2MB, alloc=107.8MB, time=109.68 memory used=36323.1MB, alloc=107.8MB, time=109.73 memory used=36325.9MB, alloc=107.8MB, time=109.76 memory used=36328.7MB, alloc=107.8MB, time=109.81 memory used=36331.4MB, alloc=107.8MB, time=109.87 memory used=36334.1MB, alloc=107.8MB, time=109.91 memory used=36336.9MB, alloc=107.8MB, time=109.96 memory used=36339.6MB, alloc=107.8MB, time=110.01 memory used=36342.4MB, alloc=107.8MB, time=110.06 memory used=36345.1MB, alloc=107.8MB, time=110.11 memory used=36347.4MB, alloc=107.8MB, time=110.17 memory used=36349.9MB, alloc=107.8MB, time=110.22 memory used=36352.3MB, alloc=107.8MB, time=110.27 memory used=36354.9MB, alloc=107.8MB, time=110.32 memory used=36357.5MB, alloc=107.8MB, time=110.37 memory used=36360.3MB, alloc=107.8MB, time=110.42 memory used=36363.0MB, alloc=107.8MB, time=110.47 memory used=36365.7MB, alloc=107.8MB, time=110.53 memory used=36368.3MB, alloc=107.8MB, time=110.58 memory used=36371.0MB, alloc=107.8MB, time=110.63 memory used=36373.4MB, alloc=107.8MB, time=110.67 memory used=36375.9MB, alloc=107.8MB, time=110.70 memory used=36378.5MB, alloc=107.8MB, time=110.74 memory used=36381.1MB, alloc=107.8MB, time=110.78 memory used=36383.8MB, alloc=107.8MB, time=110.81 memory used=36386.5MB, alloc=107.8MB, time=110.85 memory used=36389.2MB, alloc=107.8MB, time=110.88 memory used=36392.0MB, alloc=107.8MB, time=110.92 memory used=36394.9MB, alloc=107.8MB, time=110.96 memory used=36397.7MB, alloc=107.8MB, time=110.99 memory used=36400.4MB, alloc=107.8MB, time=111.02 memory used=36403.1MB, alloc=107.8MB, time=111.06 memory used=36405.8MB, alloc=107.8MB, time=111.09 memory used=36408.5MB, alloc=107.8MB, time=111.12 memory used=36411.0MB, alloc=107.8MB, time=111.16 memory used=36413.4MB, alloc=107.8MB, time=111.19 memory used=36415.8MB, alloc=107.8MB, 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time=138.53 memory used=38072.8MB, alloc=107.8MB, time=138.56 memory used=38075.0MB, alloc=107.8MB, time=138.59 memory used=38077.4MB, alloc=107.8MB, time=138.63 memory used=38079.5MB, alloc=107.8MB, time=138.66 memory used=38081.6MB, alloc=107.8MB, time=138.70 memory used=38083.9MB, alloc=107.8MB, time=138.73 memory used=38086.2MB, alloc=107.8MB, time=138.77 memory used=38088.6MB, alloc=107.8MB, time=138.80 memory used=38090.6MB, alloc=107.8MB, time=138.84 memory used=38092.7MB, alloc=107.8MB, time=138.87 memory used=38095.1MB, alloc=107.8MB, time=138.90 memory used=38097.3MB, alloc=107.8MB, time=138.94 memory used=38099.4MB, alloc=107.8MB, time=138.97 memory used=38101.6MB, alloc=107.8MB, time=139.00 memory used=38103.9MB, alloc=107.8MB, time=139.04 memory used=38106.2MB, alloc=107.8MB, time=139.07 memory used=38108.3MB, alloc=107.8MB, time=139.10 memory used=38110.5MB, alloc=107.8MB, time=139.14 memory used=38112.8MB, alloc=107.8MB, time=139.17 memory used=38115.2MB, alloc=107.8MB, 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time=307.44 memory used=88282.0MB, alloc=363.8MB, time=307.80 memory used=88755.6MB, alloc=363.8MB, time=308.16 memory used=89230.4MB, alloc=363.8MB, time=308.54 memory used=89706.3MB, alloc=363.8MB, time=308.93 memory used=90184.0MB, alloc=363.8MB, time=309.32 memory used=90662.6MB, alloc=363.8MB, time=309.70 memory used=91142.6MB, alloc=363.8MB, time=310.09 memory used=91624.4MB, alloc=363.8MB, time=310.48 memory used=92107.2MB, alloc=363.8MB, time=310.86 memory used=92591.3MB, alloc=363.8MB, time=311.22 memory used=93077.0MB, alloc=363.8MB, time=311.57 memory used=93563.6MB, alloc=363.8MB, time=311.94 memory used=94051.2MB, alloc=363.8MB, time=312.29 memory used=94540.8MB, alloc=363.8MB, time=312.66 memory used=95031.0MB, alloc=363.8MB, time=313.02 memory used=95522.6MB, alloc=363.8MB, time=313.39 memory used=96016.2MB, alloc=363.8MB, time=313.74 memory used=96510.6MB, alloc=363.8MB, time=314.10 memory used=97006.5MB, alloc=363.8MB, time=314.46 memory used=97493.3MB, alloc=363.8MB, time=314.82 memory used=97884.3MB, alloc=363.8MB, time=315.11 memory used=98271.6MB, alloc=363.8MB, time=315.40 memory used=98660.2MB, alloc=363.8MB, time=315.70 memory used=99048.8MB, alloc=363.8MB, time=316.01 memory used=99438.1MB, alloc=363.8MB, time=316.32 memory used=99827.9MB, alloc=363.8MB, time=316.63 memory used=100219.0MB, alloc=363.8MB, time=316.93 memory used=100610.3MB, alloc=363.8MB, time=317.23 memory used=101001.4MB, alloc=363.8MB, time=317.54 memory used=101394.6MB, alloc=363.8MB, time=317.85 memory used=101788.8MB, alloc=363.8MB, time=318.16 memory used=102183.6MB, alloc=363.8MB, time=318.46 memory used=102579.4MB, alloc=363.8MB, time=318.77 memory used=102976.0MB, alloc=363.8MB, time=319.09 memory used=103373.0MB, alloc=363.8MB, time=319.40 memory used=103770.2MB, alloc=363.8MB, time=319.70 memory used=104169.4MB, alloc=363.8MB, time=320.00 memory used=104567.9MB, alloc=363.8MB, time=320.34 memory used=104967.3MB, alloc=363.8MB, time=320.68 memory used=105367.8MB, alloc=363.8MB, time=321.02 memory used=105769.4MB, alloc=363.8MB, time=321.36 memory used=106171.3MB, alloc=363.8MB, time=321.70 memory used=106573.6MB, alloc=363.8MB, time=322.04 memory used=106976.9MB, alloc=363.8MB, time=322.39 memory used=107381.6MB, alloc=363.8MB, time=322.72 memory used=107787.3MB, alloc=363.8MB, time=323.06 memory used=108192.5MB, alloc=363.8MB, time=323.39 memory used=108598.8MB, alloc=363.8MB, time=323.74 memory used=109006.4MB, alloc=363.8MB, time=324.19 memory used=109415.4MB, alloc=363.8MB, time=324.61 memory used=109824.0MB, alloc=363.8MB, time=325.01 memory used=110234.3MB, alloc=363.8MB, time=325.36 memory used=110645.4MB, alloc=363.8MB, time=325.71 memory used=111056.3MB, alloc=363.8MB, time=326.07 memory used=111468.2MB, alloc=363.8MB, time=326.42 memory used=111881.2MB, alloc=363.8MB, time=326.76 memory used=112295.4MB, alloc=363.8MB, time=327.19 memory used=112709.3MB, alloc=363.8MB, time=327.58 memory used=113125.2MB, alloc=363.8MB, time=327.92 memory used=113541.5MB, alloc=363.8MB, time=328.26 memory used=113957.9MB, alloc=363.8MB, time=328.60 memory used=114374.4MB, alloc=363.8MB, time=328.94 memory used=114792.6MB, alloc=363.8MB, time=329.27 memory used=115211.5MB, alloc=363.8MB, time=329.61 memory used=115630.8MB, alloc=363.8MB, time=329.96 memory used=116051.4MB, alloc=363.8MB, time=330.29 memory used=116472.2MB, alloc=363.8MB, time=330.64 memory used=116894.0MB, alloc=363.8MB, time=330.99 memory used=117316.9MB, alloc=363.8MB, time=331.33 memory used=117740.3MB, alloc=363.8MB, time=331.68 memory used=118177.7MB, alloc=363.8MB, time=332.03 memory used=118619.2MB, alloc=363.8MB, time=332.38 memory used=119062.9MB, alloc=363.8MB, time=332.74 memory used=119508.6MB, alloc=363.8MB, time=333.10 memory used=119956.8MB, alloc=363.8MB, time=333.46 memory used=120405.8MB, alloc=363.8MB, time=333.82 memory used=120856.5MB, alloc=363.8MB, time=334.18 memory used=121308.3MB, alloc=363.8MB, time=334.54 memory used=121760.8MB, alloc=363.8MB, time=334.91 memory used=122214.7MB, alloc=363.8MB, time=335.29 memory used=122669.6MB, alloc=363.8MB, time=335.67 memory used=123125.5MB, alloc=363.8MB, time=336.04 memory used=123582.3MB, alloc=363.8MB, time=336.38 memory used=124040.2MB, alloc=363.8MB, time=336.72 memory used=124499.2MB, alloc=363.8MB, time=337.05 memory used=124958.8MB, alloc=363.8MB, time=337.38 memory used=125419.4MB, alloc=363.8MB, time=337.71 memory used=125881.0MB, alloc=363.8MB, time=338.04 memory used=126344.0MB, alloc=363.8MB, time=338.38 memory used=126808.0MB, alloc=363.8MB, time=338.72 memory used=127272.6MB, alloc=363.8MB, time=339.05 memory used=127737.9MB, alloc=363.8MB, time=339.39 memory used=128204.1MB, alloc=363.8MB, time=339.75 memory used=128671.6MB, alloc=363.8MB, time=340.08 memory used=129139.8MB, alloc=363.8MB, time=340.41 memory used=129608.7MB, alloc=363.8MB, time=340.75 memory used=130078.0MB, alloc=363.8MB, time=341.08 memory used=130548.3MB, alloc=363.8MB, time=341.41 memory used=131019.3MB, alloc=363.8MB, time=341.74 memory used=131492.2MB, alloc=363.8MB, time=342.08 memory used=131965.7MB, alloc=363.8MB, time=342.42 memory used=132439.6MB, alloc=363.8MB, time=342.76 memory used=132914.6MB, alloc=363.8MB, time=343.11 memory used=133391.1MB, alloc=363.8MB, time=343.44 memory used=133868.3MB, alloc=363.8MB, time=343.81 memory used=134345.8MB, alloc=363.8MB, time=344.15 memory used=134824.3MB, alloc=363.8MB, time=344.50 memory used=135304.1MB, alloc=363.8MB, time=344.83 memory used=135784.8MB, alloc=363.8MB, time=345.19 memory used=136266.0MB, alloc=363.8MB, time=345.55 memory used=136748.6MB, alloc=363.8MB, time=345.91 memory used=137231.9MB, alloc=363.8MB, time=346.26 memory used=137715.8MB, alloc=363.8MB, time=346.61 memory used=138201.0MB, alloc=363.8MB, time=346.95 memory used=138687.0MB, alloc=363.8MB, time=347.30 memory used=139173.4MB, alloc=363.8MB, time=347.65 memory used=139661.3MB, alloc=363.8MB, time=347.98 memory used=140117.0MB, alloc=363.8MB, time=348.31 memory used=140502.5MB, alloc=363.8MB, time=348.60 memory used=140890.6MB, alloc=363.8MB, time=348.89 memory used=141279.2MB, alloc=363.8MB, time=349.17 memory used=141668.6MB, alloc=363.8MB, time=349.47 memory used=142058.4MB, alloc=363.8MB, time=349.76 memory used=142447.7MB, alloc=363.8MB, time=350.04 memory used=142838.4MB, alloc=363.8MB, time=350.33 memory used=143230.0MB, alloc=363.8MB, time=350.61 memory used=143621.5MB, alloc=363.8MB, time=350.89 memory used=144013.1MB, alloc=363.8MB, time=351.18 memory used=144406.2MB, alloc=363.8MB, time=351.46 memory used=144799.1MB, alloc=363.8MB, time=351.76 memory used=145192.7MB, alloc=363.8MB, time=352.05 memory used=145586.3MB, alloc=363.8MB, time=352.34 memory used=145981.1MB, alloc=363.8MB, time=352.62 memory used=146375.8MB, alloc=363.8MB, time=352.90 memory used=146770.7MB, alloc=363.8MB, time=353.21 memory used=147167.7MB, alloc=363.8MB, time=353.49 memory used=147564.5MB, alloc=363.8MB, time=353.78 memory used=147961.4MB, alloc=363.8MB, time=354.06 memory used=148358.7MB, alloc=363.8MB, time=354.34 memory used=148757.1MB, alloc=363.8MB, time=354.64 |\^/| 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(); 1428326375 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; F := [17 x y z - x, -12 y z - 8, -14 x y z - 17 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [12 y z + 8 z, -16 x y + 19 y , 11 x z - 14 y z] > Problem := [F,G]; Problem := [[17 x y z - x, -12 y z - 8, -14 x y z - 17 z], 2 2 2 [12 y z + 8 z, -16 x y + 19 y , 11 x z - 14 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.46 memory used=47.4MB, alloc=32.3MB, time=0.70 memory used=67.6MB, alloc=32.3MB, time=0.95 memory used=87.9MB, alloc=56.3MB, time=1.29 memory used=128.1MB, alloc=60.3MB, time=1.90 memory used=164.9MB, alloc=84.3MB, time=2.45 memory used=220.7MB, alloc=108.3MB, time=3.75 memory used=290.5MB, alloc=108.3MB, time=5.65 N1 := 1813 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 81 #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 := [17 x y z - x, -12 y z - 8, -14 x y z - 17 z, 12 y z + 8 z, 2 2 2 -16 x y + 19 y , 11 x z - 14 y z] > J:=[op(GB),op(G)]; 2 2 2 J := [1, 12 y z + 8 z, -16 x y + 19 y , 11 x 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, 15, 16, 3, 2, 2, 2, 2/3, 1, 5/6, 5/12, 7/12, 2/3, 4, 7, 8, 3, 2, 2, 2, 1/2, 3/4, 1/2, 2/7, 4/7, 4/7, 8, 8, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=311.1MB, alloc=108.3MB, time=5.99 |\^/| 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(); 1428326381 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [-16 x z - x y, -5 x z - 4, 20 x y + 5 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [5 y + 6 y z , x y + 17 z , -11 y z - 11 z ] > Problem := [F,G]; 2 2 2 2 Problem := [[-16 x z - x y, -5 x z - 4, 20 x y + 5 y ], 3 2 2 2 [5 y + 6 y z , x y + 17 z , -11 y z - 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.1MB, alloc=32.3MB, time=0.49 memory used=47.6MB, alloc=32.3MB, time=0.78 memory used=67.5MB, alloc=32.3MB, time=1.04 memory used=86.5MB, alloc=56.3MB, time=1.28 memory used=125.9MB, alloc=60.3MB, time=1.78 memory used=162.6MB, alloc=84.3MB, time=2.25 memory used=222.5MB, alloc=84.3MB, time=3.17 memory used=277.4MB, alloc=108.3MB, time=4.04 memory used=351.3MB, alloc=140.3MB, time=5.38 memory used=440.6MB, alloc=164.3MB, time=7.33 memory used=533.7MB, alloc=188.3MB, time=10.39 memory used=645.7MB, alloc=188.3MB, time=14.34 memory used=757.7MB, alloc=212.3MB, time=18.29 N1 := 3399 > GB := Basis(F, plex(op(vars))); GB := [4 x + 1, 5 y + 256, 5 z + 64] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=890.0MB, alloc=212.3MB, time=20.56 N2 := 1685 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 3 2 2 H := [-16 x z - x y, -5 x z - 4, 20 x y + 5 y , 5 y + 6 y z , 17 z + y x, 2 -11 y z - 11 z ] > J:=[op(GB),op(G)]; J := 3 2 2 2 [4 x + 1, 5 y + 256, 5 z + 64, 5 y + 6 y z , 17 z + y x, -11 y z - 11 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 16, 3, 2, 3, 2, 2/3, 5/6, 5/6, 5/12, 7/12, 1/2, 6, 10, 10, 3, 1, 3, 2, 1/3, 2/3, 2/3, 1/6, 5/12, 5/12, 4, 6, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1048.7MB, alloc=468.3MB, time=24.65 |\^/| 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(); 1428326407 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [14 x + 19 y, 19 z - 10 x, 5 x y z + 13 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [14 x z + 14, -4 x z - 17 x y z, -3 x y - 2 x z] > Problem := [F,G]; 2 2 2 Problem := [[14 x + 19 y, 19 z - 10 x, 5 x y z + 13 y ], 2 2 2 [14 x z + 14, -4 x z - 17 x y z, -3 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=4.2MB, alloc=32.3MB, time=0.16 memory used=26.1MB, alloc=32.3MB, time=0.46 memory used=47.3MB, alloc=32.3MB, time=0.71 memory used=67.4MB, alloc=32.3MB, time=0.96 memory used=86.9MB, alloc=56.3MB, time=1.21 memory used=126.5MB, alloc=60.3MB, time=1.70 memory used=165.6MB, alloc=84.3MB, time=2.27 memory used=224.6MB, alloc=84.3MB, time=3.20 memory used=279.9MB, alloc=108.3MB, time=4.09 memory used=353.8MB, alloc=140.3MB, time=5.23 memory used=441.3MB, alloc=164.3MB, time=7.29 memory used=535.1MB, alloc=188.3MB, time=10.44 memory used=653.0MB, alloc=188.3MB, time=14.71 N1 := 3363 > GB := Basis(F, plex(op(vars))); 5 4 2 4 3 2 GB := [16562 x - 2375 x , 14 x + 19 y, -182 x + 95 x z, 19 z - 10 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=773.6MB, alloc=188.3MB, time=18.19 memory used=904.3MB, alloc=188.3MB, time=19.99 memory used=1039.2MB, alloc=212.3MB, time=22.33 memory used=1166.9MB, alloc=236.3MB, time=26.91 N2 := 2719 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [14 x + 19 y, 19 z - 10 x, 5 x y z + 13 y , 14 x z + 14, 2 2 -4 x z - 17 x y z, -3 x y - 2 x z] > J:=[op(GB),op(G)]; 5 4 2 4 3 2 J := [16562 x - 2375 x , 14 x + 19 y, -182 x + 95 x z, 19 z - 10 x, 2 2 2 14 x z + 14, -4 x z - 17 x y z, -3 x y - 2 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, 16, 3, 2, 2, 2, 1, 2/3, 5/6, 2/3, 5/12, 1/2, 7, 15, 22, 5, 5, 1, 2, 1, 3/7, 5/7, 11/14, 3/14, 3/7, 0, -6, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1247.2MB, alloc=236.3MB, time=29.20 |\^/| 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(); 1428326439 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [7 x y z - z , 16 y z - 17 y , -6 x y z - 18 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 G := [5 z - 16 y, 6 z - y z, 19 x y z - 16 x] > Problem := [F,G]; 3 2 2 2 Problem := [[7 x y z - z , 16 y z - 17 y , -6 x y z - 18 z ], 2 3 [5 z - 16 y, 6 z - y z, 19 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=0.15 memory used=26.9MB, alloc=32.3MB, time=0.44 memory used=48.1MB, alloc=32.3MB, time=0.67 memory used=68.0MB, alloc=32.3MB, time=0.92 memory used=87.0MB, alloc=56.3MB, time=1.15 memory used=126.8MB, alloc=60.3MB, time=1.61 memory used=163.9MB, alloc=60.3MB, time=2.16 memory used=198.6MB, alloc=60.3MB, time=2.59 memory used=232.5MB, alloc=84.3MB, time=3.00 memory used=286.9MB, alloc=84.3MB, time=3.60 memory used=340.1MB, alloc=84.3MB, time=4.22 memory used=393.4MB, alloc=84.3MB, time=4.85 memory used=444.6MB, alloc=108.3MB, time=5.45 memory used=513.2MB, alloc=116.3MB, time=6.29 memory used=585.3MB, alloc=140.3MB, time=7.32 memory used=677.1MB, alloc=164.3MB, time=8.66 memory used=783.6MB, alloc=188.3MB, time=10.27 memory used=904.0MB, alloc=212.3MB, time=12.07 memory used=1016.6MB, alloc=492.3MB, time=13.79 memory used=1165.1MB, alloc=516.3MB, time=15.98 memory used=1322.3MB, alloc=540.3MB, time=18.62 memory used=1489.7MB, alloc=564.3MB, time=21.31 memory used=1649.9MB, alloc=588.3MB, time=25.22 memory used=1802.3MB, alloc=612.3MB, time=29.27 memory used=1963.2MB, alloc=636.3MB, time=34.23 memory used=2133.2MB, alloc=660.3MB, time=39.45 memory used=2314.5MB, alloc=684.3MB, time=45.53 memory used=2507.3MB, alloc=708.3MB, time=52.65 memory used=2706.5MB, alloc=732.3MB, time=61.42 memory used=2929.5MB, alloc=756.3MB, time=70.24 memory used=3176.6MB, alloc=780.3MB, time=79.24 memory used=3447.5MB, alloc=804.3MB, time=88.85 memory used=3742.4MB, alloc=828.3MB, time=99.31 memory used=4061.2MB, alloc=852.3MB, time=110.15 memory used=4404.0MB, alloc=876.3MB, time=121.67 memory used=4770.7MB, alloc=900.3MB, time=133.96 memory used=5161.3MB, alloc=900.3MB, time=146.97 memory used=5551.9MB, alloc=924.3MB, time=160.23 memory used=5966.5MB, alloc=924.3MB, time=174.24 memory used=6381.0MB, alloc=924.3MB, time=187.93 memory used=6795.5MB, alloc=924.3MB, time=201.71 memory used=7210.0MB, alloc=948.3MB, time=215.58 memory used=7648.4MB, alloc=948.3MB, time=230.07 memory used=8086.6MB, alloc=948.3MB, time=244.76 memory used=8524.6MB, alloc=948.3MB, time=259.66 memory used=8962.6MB, alloc=972.3MB, time=274.51 |\^/| 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(); 1428326739 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-2 x + 14 x z, -12 y z + 13 x, 4 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [-19 x y - 20 z, 7 y - 5 z, -17 y z + 10 x ] > Problem := [F,G]; 3 2 2 Problem := [[-2 x + 14 x z, -12 y z + 13 x, 4 y z], 2 3 2 2 [-19 x y - 20 z, 7 y - 5 z, -17 y z + 10 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=26.9MB, alloc=32.3MB, time=0.50 memory used=47.9MB, alloc=32.3MB, time=0.80 memory used=67.7MB, alloc=56.3MB, time=1.09 memory used=107.7MB, alloc=60.3MB, time=1.67 memory used=147.2MB, alloc=84.3MB, time=2.23 memory used=206.8MB, alloc=92.3MB, time=3.09 memory used=264.8MB, alloc=116.3MB, time=3.95 memory used=342.6MB, alloc=116.3MB, time=5.16 memory used=420.0MB, alloc=140.3MB, time=6.42 memory used=518.0MB, alloc=164.3MB, time=8.16 memory used=628.5MB, alloc=188.3MB, time=10.07 memory used=742.8MB, alloc=468.3MB, time=12.13 memory used=879.0MB, alloc=492.3MB, time=14.21 memory used=1019.1MB, alloc=516.3MB, time=17.42 memory used=1162.3MB, alloc=540.3MB, time=21.25 memory used=1314.6MB, alloc=564.3MB, time=25.90 memory used=1483.1MB, alloc=588.3MB, time=31.60 memory used=1675.6MB, alloc=612.3MB, time=38.41 memory used=1892.0MB, alloc=636.3MB, time=46.36 memory used=2132.3MB, alloc=636.3MB, time=54.72 memory used=2372.6MB, alloc=636.3MB, time=63.18 memory used=2613.0MB, alloc=660.3MB, time=72.52 memory used=2877.2MB, alloc=660.3MB, time=81.51 memory used=3141.6MB, alloc=684.3MB, time=91.41 N1 := 8885 > GB := Basis(F, plex(op(vars))); 2 GB := [x, z y ] > 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)]; 3 2 2 2 3 H := [-2 x + 14 x z, -12 z y + 13 x, 4 z y , -19 x y - 20 z, 7 y - 5 z, 2 2 -17 z y + 10 x ] > J:=[op(GB),op(G)]; 2 2 3 2 2 J := [x, z y , -19 x y - 20 z, 7 y - 5 z, -17 z 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, 15, 18, 3, 3, 3, 1, 2/3, 5/6, 1, 5/13, 5/13, 6/13, 5, 11, 13, 3, 2, 3, 1, 3/5, 4/5, 4/5, 1/3, 4/9, 4/9, 4, 5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=3376.8MB, alloc=684.3MB, time=99.30 |\^/| 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(); 1428326845 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 F := [9 z + 12 x z, 17 x z - 6, -3 z + 10 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [-8 y z - 20 z, -14 x y + 11 x , -3 x - 4 x y] > Problem := [F,G]; 3 3 Problem := [[9 z + 12 x z, 17 x z - 6, -3 z + 10 x y], 2 2 3 [-8 y z - 20 z, -14 x y + 11 x , -3 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=4.2MB, alloc=32.3MB, time=0.16 memory used=26.2MB, alloc=32.3MB, time=0.40 memory used=47.7MB, alloc=32.3MB, time=0.64 memory used=68.4MB, alloc=32.3MB, time=0.90 memory used=88.1MB, alloc=56.3MB, time=1.19 memory used=131.9MB, alloc=60.3MB, time=1.86 memory used=170.6MB, alloc=84.3MB, time=2.55 memory used=227.5MB, alloc=108.3MB, time=3.55 memory used=296.7MB, alloc=108.3MB, time=5.63 memory used=360.2MB, alloc=132.3MB, time=7.66 N1 := 2243 > GB := Basis(F, plex(op(vars))); 3 2 2 GB := [289 x + 27, -68 x + 45 y, 34 x + 9 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=449.7MB, alloc=140.3MB, time=9.41 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)]; 3 3 H := [9 z + 12 x z, 17 z x - 6, -3 z + 10 y x, -8 y z - 20 z, 2 2 3 -14 x y + 11 x , -3 x - 4 x y] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [289 x + 27, -68 x + 45 y, 34 x + 9 z, -8 y z - 20 z, -14 x y + 11 x , 3 -3 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, 16, 3, 3, 1, 3, 5/6, 2/3, 2/3, 7/12, 1/3, 1/2, 6, 11, 15, 3, 3, 1, 1, 5/6, 2/3, 1/3, 7/12, 1/3, 1/4, 2, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=456.6MB, alloc=140.3MB, time=9.56 |\^/| 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(); 1428326856 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 F := [-20 x - 5 z, 19 x y - 8 x y , 20 y - 19 y z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 3 G := [-4 x + 12 y , -20 x - 6 x y z, -10 x - 8] > Problem := [F,G]; 2 2 3 2 Problem := [[-20 x - 5 z, 19 x y - 8 x y , 20 y - 19 y z ], 3 2 3 3 [-4 x + 12 y , -20 x - 6 x y z, -10 x - 8]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.19 memory used=26.5MB, alloc=32.3MB, time=0.49 memory used=47.7MB, alloc=32.3MB, time=0.77 memory used=69.8MB, alloc=56.3MB, time=1.35 memory used=112.5MB, alloc=60.3MB, time=2.10 memory used=151.0MB, alloc=84.3MB, time=3.16 memory used=206.3MB, alloc=108.3MB, time=4.81 memory used=276.0MB, alloc=108.3MB, time=7.99 N1 := 1927 > GB := Basis(F, plex(op(vars))); 3 2 2 2 3 GB := [x y, -19 x y + 8 x y , -76 x y + 5 y , z + 4 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=347.1MB, alloc=116.3MB, time=9.20 N2 := 619 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 3 2 3 2 H := [-20 x - 5 z, 19 x y - 8 x y , 20 y - 19 y z , -4 x + 12 y , 3 3 -20 x - 6 x y z, -10 x - 8] > J:=[op(GB),op(G)]; 3 2 2 2 3 3 2 J := [x y, -19 x y + 8 x y , -76 x y + 5 y , z + 4 x, -4 x + 12 y , 3 3 -20 x - 6 x y z, -10 x - 8] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 12, 16, 3, 3, 3, 2, 5/6, 2/3, 1/2, 7/12, 1/2, 1/4, 7, 14, 20, 4, 3, 3, 1, 1, 5/7, 2/7, 9/14, 1/2, 1/7, -2, -4, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=378.1MB, alloc=116.3MB, time=10.14 |\^/| 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(); 1428326868 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 F := [6 x z - 1, 7 x z + 19 x, -6 x - 19] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [-16 x z - 14 x z , 19 x y + 6 z, -9 x y + 11 z] > Problem := [F,G]; 3 Problem := [[6 x z - 1, 7 x z + 19 x, -6 x - 19], 2 2 2 [-16 x z - 14 x z , 19 x y + 6 z, -9 x y + 11 z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.17 memory used=25.9MB, alloc=32.3MB, time=0.42 memory used=46.7MB, alloc=32.3MB, time=0.66 memory used=66.5MB, alloc=32.3MB, time=0.88 memory used=85.8MB, alloc=56.3MB, time=1.16 memory used=126.6MB, alloc=60.3MB, time=1.92 memory used=163.9MB, alloc=84.3MB, time=2.53 memory used=218.6MB, alloc=108.3MB, time=3.86 memory used=288.5MB, alloc=132.3MB, time=6.20 memory used=370.4MB, alloc=132.3MB, time=8.78 memory used=452.4MB, alloc=156.3MB, time=12.17 N1 := 2895 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 199 #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 H := [6 z x - 1, 7 x z + 19 x, -6 x - 19, -16 x z - 14 x z , 19 y x + 6 z, 2 -9 x y + 11 z] > J:=[op(GB),op(G)]; 2 2 2 J := [1, -16 x z - 14 x z , 19 y x + 6 z, -9 x y + 11 z] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 13, 15, 3, 3, 1, 2, 1, 1/3, 5/6, 2/3, 1/6, 1/2, 4, 8, 8, 3, 2, 1, 2, 3/4, 1/2, 3/4, 4/7, 2/7, 4/7, 5, 7, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=520.2MB, alloc=156.3MB, time=13.91 |\^/| 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(); 1428326884 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [14 y z + 19 z , -x z - 16 x, 16 x + 9 x z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [2 x + 9 x y, -17 x y z - 12 y, 2 x y + 12 x z] > Problem := [F,G]; 2 3 2 2 Problem := [[14 y z + 19 z , -x z - 16 x, 16 x + 9 x z], 2 2 [2 x + 9 x y, -17 x y z - 12 y, 2 x y + 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=4.2MB, alloc=32.3MB, time=0.22 memory used=26.3MB, alloc=32.3MB, time=0.65 memory used=47.4MB, alloc=32.3MB, time=1.05 memory used=67.3MB, alloc=32.3MB, time=1.50 memory used=86.1MB, alloc=56.3MB, time=1.89 memory used=124.4MB, alloc=60.3MB, time=2.44 memory used=160.6MB, alloc=84.3MB, time=2.89 memory used=216.4MB, alloc=84.3MB, time=3.59 memory used=271.3MB, alloc=108.3MB, time=4.46 memory used=344.9MB, alloc=132.3MB, time=5.74 memory used=435.5MB, alloc=164.3MB, time=7.13 memory used=537.3MB, alloc=188.3MB, time=9.58 memory used=645.5MB, alloc=212.3MB, time=12.59 memory used=777.7MB, alloc=212.3MB, time=16.22 N1 := 3271 > GB := Basis(F, plex(op(vars))); 3 2 2 2 3 GB := [16 x + 81 x, 7 x y - 152 x, 16 x + 9 x z, 14 y z + 19 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=910.0MB, alloc=212.3MB, time=18.21 memory used=1039.9MB, alloc=468.3MB, time=20.10 memory used=1190.4MB, alloc=492.3MB, time=23.05 memory used=1337.3MB, alloc=516.3MB, time=27.49 memory used=1499.8MB, alloc=540.3MB, time=32.15 N2 := 3271 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 2 H := [14 y z + 19 z , -x z - 16 x, 16 x + 9 x z, 2 x + 9 x y, 2 -17 x y z - 12 y, 2 x y + 12 x z] > J:=[op(GB),op(G)]; 3 2 2 2 3 J := [16 x + 81 x, 7 x y - 152 x, 16 x + 9 x z, 14 y z + 19 z , 2 2 2 x + 9 x y, -17 x y z - 12 y, 2 x y + 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, 16, 3, 2, 2, 3, 5/6, 2/3, 5/6, 3/4, 5/12, 1/2, 7, 15, 19, 3, 3, 2, 3, 6/7, 5/7, 4/7, 11/14, 3/7, 5/14, -1, -3, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1530.7MB, alloc=540.3MB, time=32.71 |\^/| 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(); 1428326919 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [11 y - 10 y z, -15 x y z + 12 x z , -10 z + 18 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [2 y z + 20 y z, 19 x y z - 7 x z , 8 x z - 15 z ] > Problem := [F,G]; 3 2 2 3 Problem := [[11 y - 10 y z, -15 x y z + 12 x z , -10 z + 18 z], 2 2 2 2 [2 y z + 20 y z, 19 x y z - 7 x z , 8 x z - 15 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.2MB, alloc=32.3MB, time=0.39 memory used=47.4MB, alloc=32.3MB, time=0.64 memory used=67.1MB, alloc=56.3MB, time=0.85 memory used=107.3MB, alloc=60.3MB, time=1.37 memory used=144.1MB, alloc=84.3MB, time=1.87 memory used=199.4MB, alloc=108.3MB, time=2.72 memory used=271.5MB, alloc=132.3MB, time=3.71 memory used=358.1MB, alloc=156.3MB, time=5.00 memory used=456.1MB, alloc=188.3MB, time=6.46 memory used=561.5MB, alloc=212.3MB, time=8.59 memory used=674.5MB, alloc=236.3MB, time=11.34 memory used=799.4MB, alloc=260.3MB, time=14.70 memory used=937.8MB, alloc=284.3MB, time=18.89 memory used=1100.2MB, alloc=308.3MB, time=23.90 memory used=1286.5MB, alloc=308.3MB, time=29.60 memory used=1472.8MB, alloc=308.3MB, time=35.07 memory used=1659.1MB, alloc=308.3MB, time=40.50 memory used=1845.2MB, alloc=332.3MB, time=46.04 memory used=2055.3MB, alloc=332.3MB, time=52.22 memory used=2265.3MB, alloc=332.3MB, time=58.31 memory used=2475.2MB, alloc=356.3MB, time=64.42 memory used=2709.0MB, alloc=356.3MB, time=71.17 memory used=2942.7MB, alloc=380.3MB, time=77.67 N1 := 9237 > GB := Basis(F, plex(op(vars))); 3 5 3 3 2 3 GB := [x y , 121 y - 180 y , x z, -11 y + 10 y z, 5 z - 9 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3134.8MB, alloc=380.3MB, time=81.47 memory used=3438.6MB, alloc=660.3MB, time=89.00 N2 := 2749 #save(Problem, "format.txt"); > 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 := [11 y - 10 y z, -15 x y z + 12 x z , -10 z + 18 z, 2 y z + 20 y z, 2 2 2 19 x y z - 7 x z , 8 x z - 15 z ] > J:=[op(GB),op(G)]; 3 5 3 3 2 3 2 J := [x y , 121 y - 180 y , x z, -11 y + 10 y z, 5 z - 9 z, 2 y z + 20 y z, 2 2 2 19 x y z - 7 x z , 8 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, 13, 18, 3, 2, 3, 3, 1/2, 2/3, 1, 5/12, 1/2, 11/12, 8, 15, 26, 5, 2, 5, 3, 1/2, 5/8, 3/4, 5/16, 1/2, 5/8, -2, -8, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=3477.3MB, alloc=660.3MB, time=89.90 |\^/| 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(); 1428327016 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-8 x y , -14 x - 15 x, 15 x z - 10 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 2 G := [6 y - 4 x , 13 x z + 3, 12 y z - 12 y z ] > Problem := [F,G]; 2 2 2 Problem := [[-8 x y , -14 x - 15 x, 15 x z - 10 x y], 3 2 2 2 2 [6 y - 4 x , 13 x z + 3, 12 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=4.2MB, alloc=32.3MB, time=0.15 memory used=26.4MB, alloc=32.3MB, time=0.39 memory used=47.6MB, alloc=32.3MB, time=0.68 memory used=69.1MB, alloc=56.3MB, time=1.03 memory used=110.7MB, alloc=56.3MB, time=1.60 memory used=147.0MB, alloc=84.3MB, time=2.15 memory used=198.0MB, alloc=108.3MB, time=3.22 N1 := 1453 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [14 x + 15 x, x y , 3 x z - 2 x y] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=271.5MB, alloc=116.3MB, time=4.19 memory used=351.2MB, alloc=140.3MB, time=5.37 N2 := 1453 #save(Problem, "format.txt"); > if (GB=[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 := [-8 x y , -14 x - 15 x, 15 x z - 10 x y, 6 y - 4 x , 13 z x + 3, 2 2 12 y z - 12 y z ] > J:=[op(GB),op(G)]; 2 2 2 3 2 2 J := [14 x + 15 x, x y , 3 x z - 2 x y, 6 y - 4 x , 13 z x + 3, 2 2 12 y z - 12 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, 17, 3, 2, 3, 2, 5/6, 2/3, 1/2, 7/13, 5/13, 4/13, 6, 12, 17, 3, 2, 3, 2, 5/6, 2/3, 1/2, 7/12, 5/12, 1/3, 0, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=407.9MB, alloc=140.3MB, time=6.49 |\^/| 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(); 1428327023 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 F := [13 x z - 10 x y, -15 x z + 19 x y , 13 x z + 16 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [y z - 3 y z, 11 x y z - 10 y z , 20 y z - 7 x ] > Problem := [F,G]; 2 2 2 2 Problem := [[13 x z - 10 x y, -15 x z + 19 x y , 13 x z + 16 y], 2 2 2 2 [y z - 3 y z, 11 x y z - 10 y z , 20 y z - 7 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.4MB, alloc=32.3MB, time=0.41 memory used=47.6MB, alloc=32.3MB, time=0.67 memory used=66.9MB, alloc=56.3MB, time=0.89 memory used=107.5MB, alloc=60.3MB, time=1.36 memory used=145.6MB, alloc=84.3MB, time=1.81 memory used=204.1MB, alloc=92.3MB, time=2.53 memory used=260.5MB, alloc=116.3MB, time=3.15 memory used=336.3MB, alloc=140.3MB, time=4.05 memory used=429.8MB, alloc=396.3MB, time=5.18 memory used=525.0MB, alloc=420.3MB, time=6.35 memory used=643.0MB, alloc=444.3MB, time=7.79 memory used=782.3MB, alloc=468.3MB, time=9.51 memory used=932.8MB, alloc=492.3MB, time=11.41 memory used=1087.5MB, alloc=516.3MB, time=13.43 memory used=1235.3MB, alloc=516.3MB, time=15.38 memory used=1351.9MB, alloc=540.3MB, time=16.89 memory used=1469.1MB, alloc=540.3MB, time=18.62 memory used=1561.4MB, alloc=540.3MB, time=19.86 memory used=1682.6MB, alloc=564.3MB, time=21.61 memory used=1757.0MB, alloc=564.3MB, time=22.80 memory used=1850.7MB, alloc=564.3MB, time=24.29 memory used=1930.8MB, alloc=588.3MB, time=25.64 memory used=2014.7MB, alloc=588.3MB, time=27.03 memory used=2091.8MB, alloc=588.3MB, time=28.31 memory used=2174.3MB, alloc=588.3MB, time=29.72 memory used=2232.1MB, alloc=588.3MB, time=30.91 memory used=2283.7MB, alloc=588.3MB, time=31.82 memory used=2336.0MB, alloc=612.3MB, time=32.88 memory used=2581.9MB, alloc=636.3MB, time=36.41 memory used=2839.0MB, alloc=660.3MB, time=40.57 memory used=3091.2MB, alloc=684.3MB, time=44.65 memory used=3341.9MB, alloc=708.3MB, time=48.87 memory used=3592.8MB, alloc=732.3MB, time=53.19 memory used=3843.8MB, alloc=756.3MB, time=57.71 memory used=4096.0MB, alloc=780.3MB, time=62.20 memory used=4348.6MB, alloc=804.3MB, time=66.64 memory used=4610.6MB, alloc=828.3MB, time=71.29 memory used=4873.7MB, alloc=852.3MB, time=75.92 memory used=5132.6MB, alloc=876.3MB, time=80.69 memory used=5392.2MB, alloc=900.3MB, time=85.53 memory used=5653.6MB, alloc=924.3MB, time=90.37 memory used=5916.5MB, alloc=948.3MB, time=95.24 memory used=6181.5MB, alloc=972.3MB, time=100.26 memory used=6453.5MB, alloc=996.3MB, time=105.36 memory used=6735.3MB, alloc=1020.3MB, time=110.67 memory used=6967.9MB, alloc=1044.3MB, time=117.55 memory used=7191.1MB, alloc=1068.3MB, time=125.10 memory used=7421.4MB, alloc=1092.3MB, time=133.14 memory used=7661.3MB, alloc=1116.3MB, time=141.69 memory used=7912.0MB, alloc=1140.3MB, time=150.72 memory used=8174.3MB, alloc=1164.3MB, time=160.23 memory used=8449.9MB, alloc=1188.3MB, time=170.46 memory used=8738.6MB, alloc=1212.3MB, time=181.29 memory used=9041.6MB, alloc=1236.3MB, time=192.60 memory used=9357.5MB, alloc=1260.3MB, time=204.25 memory used=9687.8MB, alloc=1284.3MB, time=216.58 memory used=10032.1MB, alloc=1308.3MB, time=229.74 memory used=10390.5MB, alloc=1332.3MB, time=243.35 memory used=10763.1MB, alloc=1356.3MB, time=257.54 memory used=11151.4MB, alloc=1380.3MB, time=272.26 memory used=11554.9MB, alloc=1404.3MB, time=287.70 |\^/| 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(); 1428327323 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [6 x y - 11 x, -12 y z - 20 x , 12 y - 18 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [18 x y + 17 y, -10 y z + 12 x, 6 x + 7 x z] > Problem := [F,G]; 2 2 2 Problem := [[6 x y - 11 x, -12 y z - 20 x , 12 y - 18 y z], 2 2 [18 x y + 17 y, -10 y z + 12 x, 6 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=0.16 memory used=26.2MB, alloc=32.3MB, time=0.46 memory used=47.4MB, alloc=32.3MB, time=0.74 memory used=67.2MB, alloc=32.3MB, time=1.05 memory used=86.3MB, alloc=56.3MB, time=1.32 memory used=124.8MB, alloc=60.3MB, time=1.87 memory used=160.4MB, alloc=84.3MB, time=2.40 memory used=211.7MB, alloc=84.3MB, time=3.26 memory used=265.2MB, alloc=108.3MB, time=4.19 memory used=336.4MB, alloc=140.3MB, time=5.45 memory used=424.1MB, alloc=164.3MB, time=7.02 memory used=527.5MB, alloc=188.3MB, time=8.86 memory used=641.2MB, alloc=212.3MB, time=12.01 memory used=765.1MB, alloc=236.3MB, time=15.69 memory used=898.7MB, alloc=260.3MB, time=19.82 memory used=1055.5MB, alloc=260.3MB, time=24.77 memory used=1212.2MB, alloc=284.3MB, time=29.56 memory used=1393.1MB, alloc=284.3MB, time=35.22 memory used=1573.8MB, alloc=308.3MB, time=40.78 memory used=1778.8MB, alloc=332.3MB, time=46.66 N1 := 6265 > GB := Basis(F, plex(op(vars))); 3 3 2 2 GB := [540 x + 1331 x, 6 x y - 11 x, 2 y + 5 x , 9 x z - 11 x, -2 y + 3 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1898.1MB, alloc=332.3MB, time=48.65 memory used=2151.3MB, alloc=588.3MB, time=52.36 memory used=2385.0MB, alloc=612.3MB, time=59.19 memory used=2621.6MB, alloc=636.3MB, time=66.49 N2 := 4069 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [6 x y - 11 x, -12 y z - 20 x , 12 y - 18 y z, 18 x y + 17 y, 2 -10 y z + 12 x, 6 x + 7 x z] > J:=[op(GB),op(G)]; 3 3 2 2 J := [540 x + 1331 x, 6 x y - 11 x, 2 y + 5 x , 9 x z - 11 x, -2 y + 3 y z, 2 2 18 x y + 17 y, -10 y z + 12 x, 6 x + 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, 14, 14, 3, 2, 2, 1, 5/6, 5/6, 2/3, 7/12, 7/12, 1/3, 8, 16, 19, 3, 3, 3, 1, 7/8, 5/8, 1/2, 11/16, 7/16, 1/4, -2, -5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=2721.1MB, alloc=636.3MB, time=69.00 |\^/| 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(); 1428327397 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 F := [18 x y z + 9 x z , -9 x z - 15 z , -8 z - 13 y z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 G := [-14 y + 20 y, -15 x y - 15 y , 3 x y - 17 x z] > Problem := [F,G]; 2 2 3 3 Problem := [[18 x y z + 9 x z , -9 x z - 15 z , -8 z - 13 y z], 3 2 2 [-14 y + 20 y, -15 x y - 15 y , 3 x y - 17 x z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.14 memory used=26.3MB, alloc=32.3MB, time=0.38 memory used=47.6MB, alloc=32.3MB, time=0.58 memory used=67.0MB, alloc=32.3MB, time=0.79 memory used=85.4MB, alloc=56.3MB, time=1.00 memory used=124.1MB, alloc=60.3MB, time=1.47 memory used=159.8MB, alloc=84.3MB, time=1.89 memory used=218.7MB, alloc=108.3MB, time=2.69 memory used=295.8MB, alloc=132.3MB, time=3.78 memory used=388.6MB, alloc=164.3MB, time=5.07 memory used=494.5MB, alloc=188.3MB, time=6.50 memory used=611.0MB, alloc=212.3MB, time=8.09 memory used=730.2MB, alloc=236.3MB, time=10.82 memory used=857.0MB, alloc=260.3MB, time=14.05 memory used=996.8MB, alloc=284.3MB, time=17.82 memory used=1147.7MB, alloc=308.3MB, time=22.51 memory used=1321.1MB, alloc=332.3MB, time=27.81 memory used=1518.5MB, alloc=356.3MB, time=33.88 memory used=1739.9MB, alloc=356.3MB, time=40.66 memory used=1961.2MB, alloc=356.3MB, time=47.40 memory used=2182.5MB, alloc=356.3MB, time=54.27 memory used=2403.7MB, alloc=380.3MB, time=61.16 memory used=2648.9MB, alloc=380.3MB, time=68.93 memory used=2894.1MB, alloc=404.3MB, time=76.79 memory used=3163.1MB, alloc=404.3MB, time=85.18 memory used=3432.2MB, alloc=428.3MB, time=93.38 N1 := 9621 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [48 x y z + 65 y z, 32 y z + 13 y z, 24 x z - 65 y z, 16 y z - 13 y z, 3 8 z + 13 y z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3553.5MB, alloc=428.3MB, time=95.83 memory used=3880.7MB, alloc=684.3MB, time=100.60 memory used=4185.9MB, alloc=708.3MB, time=105.33 memory used=4488.2MB, alloc=732.3MB, time=113.26 memory used=4774.9MB, alloc=756.3MB, time=122.18 memory used=5063.6MB, alloc=780.3MB, time=132.39 memory used=5376.4MB, alloc=804.3MB, time=144.60 memory used=5713.0MB, alloc=828.3MB, time=156.73 memory used=6073.5MB, alloc=852.3MB, time=169.23 memory used=6458.0MB, alloc=876.3MB, time=182.31 memory used=6866.5MB, alloc=900.3MB, time=195.91 memory used=7298.7MB, alloc=924.3MB, time=210.41 memory used=7755.0MB, alloc=948.3MB, time=225.00 N2 := 11237 #save(Problem, "format.txt"); > if (GB=[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 := [18 x y z + 9 x z , -9 x z - 15 z , -8 z - 13 y z, -14 y + 20 y, 2 2 -15 x y - 15 y , 3 x y - 17 x z] > J:=[op(GB),op(G)]; 2 2 2 J := [48 x y z + 65 y z, 32 y z + 13 y z, 24 x z - 65 y z, 16 y z - 13 y z, 3 3 2 2 8 z + 13 y z, -14 y + 20 y, -15 x y - 15 y , 3 x y - 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, 13, 17, 3, 1, 3, 3, 2/3, 5/6, 2/3, 1/2, 7/12, 7/12, 8, 18, 23, 3, 1, 3, 3, 1/2, 1, 3/4, 5/16, 13/16, 11/16, -5, -6, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=8131.1MB, alloc=948.3MB, time=236.13 |\^/| 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(); 1428327651 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 F := [4 x y + 19 y, 10 x + 9 x z , 7 x z - 9 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 G := [4 x y z - 13, -13 y - 11 x , -x z + 20 y z] > Problem := [F,G]; 2 3 2 2 Problem := [[4 x y + 19 y, 10 x + 9 x z , 7 x z - 9 y], 3 2 2 2 [4 x y z - 13, -13 y - 11 x , -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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.4MB, alloc=32.3MB, time=0.42 memory used=47.8MB, alloc=32.3MB, time=0.65 memory used=68.3MB, alloc=32.3MB, time=0.88 memory used=88.1MB, alloc=56.3MB, time=1.13 memory used=128.6MB, alloc=60.3MB, time=1.61 memory used=167.5MB, alloc=84.3MB, time=2.08 memory used=217.4MB, alloc=84.3MB, time=2.57 memory used=276.1MB, alloc=92.3MB, time=3.26 memory used=332.4MB, alloc=116.3MB, time=3.97 memory used=409.4MB, alloc=140.3MB, time=5.03 memory used=502.3MB, alloc=164.3MB, time=6.41 memory used=601.6MB, alloc=188.3MB, time=9.14 N1 := 1839 > GB := Basis(F, plex(op(vars))); 12 4 7 7 2 GB := [7840 x + 263169 x , -1960 x + 13851 y, -280 x + 1539 x z, 3 2 10 x + 9 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=693.4MB, alloc=188.3MB, time=10.31 memory used=838.0MB, alloc=444.3MB, time=12.05 memory used=979.8MB, alloc=444.3MB, time=13.90 memory used=1109.7MB, alloc=468.3MB, time=15.99 memory used=1236.0MB, alloc=492.3MB, time=19.75 N2 := 2275 #save(Problem, "format.txt"); > if (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 := [4 x y + 19 y, 10 x + 9 x z , 7 z x - 9 y, 4 z y x - 13, -13 y - 11 x , 2 2 -x z + 20 y z] > J:=[op(GB),op(G)]; 12 4 7 7 2 J := [7840 x + 263169 x , -1960 x + 13851 y, -280 x + 1539 x z, 3 2 3 2 2 2 10 x + 9 x z , 4 z y x - 13, -13 y - 11 x , -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, 15, 18, 3, 3, 3, 2, 1, 5/6, 2/3, 7/12, 1/2, 5/12, 7, 15, 38, 12, 12, 3, 2, 1, 4/7, 4/7, 5/7, 2/7, 5/14, 0, -20, -9] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1264.6MB, alloc=492.3MB, time=20.42 |\^/| 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(); 1428327673 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 3 2 2 F := [-x - 18 x z , -11 y + 8 y z, 5 y z + 14 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [17 x y - 12 y z, 8 x z - 17 x, -6 x y + 11 z ] > Problem := [F,G]; 3 2 3 2 2 Problem := [[-x - 18 x z , -11 y + 8 y z, 5 y z + 14 x ], 2 2 2 2 [17 x y - 12 y z, 8 x z - 17 x, -6 x y + 11 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.16 memory used=26.6MB, alloc=32.3MB, time=0.43 memory used=47.9MB, alloc=32.3MB, time=0.68 memory used=68.1MB, alloc=56.3MB, time=0.95 memory used=108.1MB, alloc=60.3MB, time=1.40 memory used=146.7MB, alloc=60.3MB, time=1.85 memory used=184.1MB, alloc=84.3MB, time=2.27 memory used=231.5MB, alloc=84.3MB, time=2.82 memory used=290.8MB, alloc=116.3MB, time=3.54 memory used=371.5MB, alloc=116.3MB, time=4.50 memory used=450.2MB, alloc=140.3MB, time=5.46 memory used=534.6MB, alloc=396.3MB, time=6.50 memory used=628.6MB, alloc=420.3MB, time=7.69 memory used=746.2MB, alloc=444.3MB, time=9.17 memory used=878.9MB, alloc=468.3MB, time=10.88 memory used=1037.2MB, alloc=492.3MB, time=13.15 memory used=1197.9MB, alloc=516.3MB, time=15.55 memory used=1376.2MB, alloc=540.3MB, time=18.23 memory used=1566.4MB, alloc=564.3MB, time=21.10 memory used=1754.7MB, alloc=588.3MB, time=25.30 memory used=1936.9MB, alloc=612.3MB, time=30.19 memory used=2123.1MB, alloc=636.3MB, time=35.93 memory used=2323.6MB, alloc=660.3MB, time=42.51 memory used=2548.0MB, alloc=684.3MB, time=49.75 memory used=2796.4MB, alloc=708.3MB, time=57.83 memory used=3068.8MB, alloc=732.3MB, time=66.54 memory used=3365.0MB, alloc=756.3MB, time=75.94 memory used=3685.1MB, alloc=756.3MB, time=86.19 memory used=4005.1MB, alloc=780.3MB, time=96.41 memory used=4349.3MB, alloc=804.3MB, time=107.34 N1 := 9767 > GB := Basis(F, plex(op(vars))); GB := [ 4 3 4 2 2 2 2 3 3 2 x , x y, 55 y + 112 x , -11 x y + 8 x z, -11 y + 8 y z, x + 18 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4697.3MB, alloc=804.3MB, time=115.01 memory used=4887.3MB, alloc=804.3MB, time=118.21 N2 := 2941 #save(Problem, "format.txt"); > 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 := [-x - 18 x z , -11 y + 8 y z, 5 z y + 14 x , 17 x y - 12 y z, 2 2 2 8 x z - 17 x, -6 x y + 11 z ] > J:=[op(GB),op(G)]; 4 3 4 2 2 2 2 3 J := [x , x y, 55 y + 112 x , -11 x y + 8 x z, -11 y + 8 y z, 3 2 2 2 2 2 x + 18 x z , 17 x y - 12 y z, 8 x z - 17 x, -6 x y + 11 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 15, 18, 3, 3, 3, 2, 5/6, 2/3, 1, 7/12, 1/2, 1/2, 9, 20, 31, 4, 4, 4, 2, 8/9, 2/3, 2/3, 11/18, 4/9, 1/3, -5, -13, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=5316.8MB, alloc=804.3MB, time=128.86 |\^/| 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(); 1428327811 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-7 x y z - 14 y, 20 y z, -7 x z - 14 x y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 3 G := [20 x z + 13 y, 11 z + 12, -8 y + 2 z ] > Problem := [F,G]; 2 2 2 Problem := [[-7 x y z - 14 y, 20 y z, -7 x z - 14 x y ], 2 2 3 3 [20 x z + 13 y, 11 z + 12, -8 y + 2 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.15 memory used=26.4MB, alloc=32.3MB, time=0.40 memory used=47.2MB, alloc=32.3MB, time=0.67 memory used=66.3MB, alloc=56.3MB, time=0.90 memory used=107.0MB, alloc=60.3MB, time=1.36 memory used=145.8MB, alloc=60.3MB, time=1.81 memory used=182.8MB, alloc=84.3MB, time=2.23 memory used=221.7MB, alloc=84.3MB, time=2.67 memory used=278.3MB, alloc=116.3MB, time=3.35 memory used=354.6MB, alloc=140.3MB, time=4.37 memory used=445.9MB, alloc=164.3MB, time=5.79 memory used=541.1MB, alloc=188.3MB, time=8.19 N1 := 1903 > GB := Basis(F, plex(op(vars))); 2 GB := [y, z x ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 115 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 2 H := [-7 x y z - 14 y, 20 y z, -7 x z - 14 x y , 20 z x + 13 y, 11 z + 12, 3 3 -8 y + 2 z ] > J:=[op(GB),op(G)]; 2 2 2 3 3 J := [y, z x , 20 z x + 13 y, 11 z + 12, -8 y + 2 z ] > > NoOfPolysWithVar:=proc(H,v) > local tot,f: > tot := 0: > for f in H do > if degree(f,v)>0 then > tot := tot+1; > end if: > end do: > return tot: > end proc: > > NoOfMonosWithVar:=proc(H,v) > local tot,f,m: > tot := 0: > for f in H do > for m in f do > if degree(m,v)>0 then > tot := tot+1; > end if: > end do: > end do: > return tot: > end proc: > > NoOfPossMonosD:=proc(deg,vars) > local tot,n,l,T,v: > tot := 0: > n:=nops(vars): > > l:=[seq(i,i=0..deg)]: > T:=combinat:-cartprod([seq(l,i=1..n)]): > > while not T[finished] do > v := T[nextvalue](): > if (add(i,i in v)=deg) then > tot := tot + 1: > end if: > end do: > > return tot: > end proc: > > NoOfPossMonos:=proc(deg,vars) > local tot,i: > tot:=0: > for i from 0 to deg do > tot := tot + NoOfPossMonosD(i,vars): > end do: > return tot: > end proc: > #TNoI := proc(F::list(polynom)) #local f: #return( add( nops(indets(f)), f in F)); #end proc: > > > FeatureComputation:=proc(H,vars) > local Features: > > Features:=[]: > > #Number of Input Polys > Features := [op(Features), nops(H)]: > > #TNoI > Features := [op(Features), add( nops(indets(f)), f in H)]: > > #sotd > Features := [op(Features), add( degree(f), f in H)]: > > #Max Total Degree > Features := [op(Features), max(seq(degree(f),f in H))]: > > #Max Degree in x > Features := [op(Features), max(seq(degree(f,x),f in H))]: > > #Max Degree in y > Features := [op(Features), max(seq(degree(f,y),f in H))]: > > #Max Degree in z > Features := [op(Features), max(seq(degree(f,z),f in H))]: > > #Proportion of polynomials in which x occurs > Features := [op(Features), NoOfPolysWithVar(H,x)/nops(H)]: > > #Proportion of polynomials in which y occurs > Features := [op(Features), NoOfPolysWithVar(H,y)/nops(H)]: > > #Proportion of polynomials in which z occurs > Features := [op(Features), NoOfPolysWithVar(H,z)/nops(H)]: > > #Max Norm of the polynomials > #Features := [op(Features), max(seq(max({seq(abs(c),c in coeffs(expand(f),vars))}),f in H))]: > > #Proportion of monomials in which x occur > Features := [op(Features), NoOfMonosWithVar(H,x)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,y)/add(nops(f),f in H)]: > > #Proportion of monomials in which certain variables occur > Features := [op(Features), NoOfMonosWithVar(H,z)/add(nops(f),f in H)]: > > return Features: > > end proc: > > BF:=FeatureComputation(H,vars): > AF:=FeatureComputation(J,vars): > > df := [BF[2] - AF[2], BF[3] - AF[3], BF[4] - AF[4]]: > featureList := [op(BF), op(AF), op(df)]; featureList := [6, 14, 17, 3, 2, 3, 3, 1/2, 5/6, 1, 4/13, 6/13, 6/13, 5, 9, 12, 3, 2, 3, 3, 2/5, 3/5, 4/5, 2/9, 1/3, 4/9, 5, 5, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=574.4MB, alloc=188.3MB, time=8.63 |\^/| 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(); 1428327820 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 3 F := [13 x z + 7 y z, -x z + 8 y, 5 x y + 9 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [16 x z + 13 x z, 10 x y z + 13 x y, -4 x z - 14 x z] > Problem := [F,G]; 2 2 2 2 3 Problem := [[13 x z + 7 y z, -x z + 8 y, 5 x y + 9 y ], 2 2 [16 x z + 13 x z, 10 x y z + 13 x y, -4 x 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=0.16 memory used=26.2MB, alloc=32.3MB, time=0.41 memory used=48.0MB, alloc=32.3MB, time=0.72 memory used=68.6MB, alloc=56.3MB, time=1.03 memory used=109.9MB, alloc=60.3MB, time=1.57 memory used=145.9MB, alloc=84.3MB, time=2.24 N1 := 1365 > GB := Basis(F, plex(op(vars))); 2 2 2 2 3 2 2 GB := [35 x y - 936 y , 5 x y + 9 y , z x - 8 y, -35 y + 117 y z, 2 2 -1225 x y + 13689 x z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=199.9MB, alloc=84.3MB, time=3.27 memory used=255.0MB, alloc=84.3MB, time=3.88 memory used=311.0MB, alloc=108.3MB, time=4.64 memory used=386.5MB, alloc=132.3MB, time=6.36 N2 := 1661 #save(Problem, "format.txt"); > if (GB=[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 := [13 x z + 7 y z, -x z + 8 y, 5 x y + 9 y , 16 x z + 13 x z, 2 10 x y z + 13 x y, -4 x z - 14 x z] > J:=[op(GB),op(G)]; 2 2 2 2 3 2 2 J := [35 x y - 936 y , 5 x y + 9 y , z x - 8 y, -35 y + 117 y z, 2 2 2 -1225 x y + 13689 x z , 16 x z + 13 x z, 10 x y z + 13 x y, 2 -4 x 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, 15, 18, 3, 2, 3, 2, 1, 2/3, 5/6, 3/4, 1/2, 2/3, 8, 19, 24, 4, 2, 3, 2, 7/8, 3/4, 3/4, 11/16, 5/8, 1/2, -4, -6, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=427.5MB, alloc=132.3MB, 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(); 1428327828 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 3 2 F := [-13 z - 12, 4 x - 18 x z, -8 z + 17 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [9 x y + 18 z , 11 y - 18 x , 17 x y z - 15 z] > Problem := [F,G]; 3 3 3 2 Problem := [[-13 z - 12, 4 x - 18 x z, -8 z + 17 z ], 2 2 3 2 [9 x y + 18 z , 11 y - 18 x , 17 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=0.17 memory used=26.3MB, alloc=32.3MB, time=0.42 memory used=47.6MB, alloc=32.3MB, time=0.66 memory used=67.7MB, alloc=32.3MB, time=0.87 memory used=86.9MB, alloc=56.3MB, time=1.08 memory used=127.5MB, alloc=60.3MB, time=1.54 memory used=170.0MB, alloc=84.3MB, time=2.17 memory used=231.7MB, alloc=84.3MB, time=3.03 memory used=286.9MB, alloc=108.3MB, time=3.81 memory used=355.7MB, alloc=132.3MB, time=4.89 memory used=433.8MB, alloc=156.3MB, time=6.67 memory used=523.7MB, alloc=180.3MB, time=9.36 memory used=637.7MB, alloc=180.3MB, time=12.79 memory used=751.6MB, alloc=204.3MB, time=15.86 N1 := 4071 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); 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 3 2 2 2 3 2 H := [-13 z - 12, 4 x - 18 x z, -8 z + 17 z , 9 x y + 18 z , 11 y - 18 x , 17 x y z - 15 z] > J:=[op(GB),op(G)]; 2 2 3 2 J := [1, 9 x y + 18 z , 11 y - 18 x , 17 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, 12, 18, 3, 3, 3, 3, 2/3, 1/2, 5/6, 5/12, 1/4, 7/12, 4, 8, 9, 3, 2, 3, 2, 3/4, 3/4, 1/2, 3/7, 3/7, 3/7, 4, 9, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=890.1MB, alloc=204.3MB, time=18.93 |\^/| 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(); 1428327849 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 2 F := [9 z + 12 y, 4 y z + 17 x, 7 y z + 16 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 G := [-8 x + 15 z , y + 14 z, -4 x y - 20 z] > Problem := [F,G]; 3 2 2 2 Problem := [[9 z + 12 y, 4 y z + 17 x, 7 y z + 16 x ], 2 2 2 2 [-8 x + 15 z , y + 14 z, -4 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=4.2MB, alloc=32.3MB, time=0.16 memory used=26.8MB, alloc=32.3MB, time=0.44 memory used=47.9MB, alloc=32.3MB, time=0.68 memory used=67.7MB, alloc=32.3MB, time=0.88 memory used=86.8MB, alloc=56.3MB, time=1.12 memory used=128.9MB, alloc=60.3MB, time=1.56 memory used=169.7MB, alloc=92.3MB, time=2.05 memory used=230.3MB, alloc=92.3MB, time=2.74 memory used=290.4MB, alloc=116.3MB, time=3.42 memory used=369.5MB, alloc=116.3MB, time=4.34 memory used=445.2MB, alloc=140.3MB, time=5.26 memory used=508.8MB, alloc=396.3MB, time=6.09 memory used=612.0MB, alloc=420.3MB, time=7.23 memory used=738.1MB, alloc=444.3MB, time=8.67 memory used=879.9MB, alloc=468.3MB, time=10.61 memory used=1007.5MB, alloc=492.3MB, time=12.08 memory used=1123.0MB, alloc=492.3MB, time=13.72 memory used=1213.2MB, alloc=492.3MB, time=15.22 memory used=1305.4MB, alloc=492.3MB, time=16.76 memory used=1400.5MB, alloc=492.3MB, time=18.34 memory used=1498.0MB, alloc=516.3MB, time=20.24 memory used=1581.2MB, alloc=516.3MB, time=21.90 memory used=1659.3MB, alloc=516.3MB, time=23.51 memory used=1740.1MB, alloc=516.3MB, time=25.19 memory used=1820.5MB, alloc=516.3MB, time=26.79 memory used=1894.2MB, alloc=516.3MB, time=28.24 memory used=1952.1MB, alloc=516.3MB, time=29.46 memory used=2002.6MB, alloc=516.3MB, time=30.65 memory used=2052.6MB, alloc=516.3MB, time=31.81 memory used=2247.0MB, alloc=540.3MB, time=35.04 memory used=2461.3MB, alloc=564.3MB, time=37.96 memory used=2675.2MB, alloc=588.3MB, time=41.06 memory used=2886.9MB, alloc=612.3MB, time=44.26 memory used=3068.0MB, alloc=636.3MB, time=47.11 memory used=3230.9MB, alloc=660.3MB, time=49.64 memory used=3395.9MB, alloc=684.3MB, time=52.23 memory used=3548.6MB, alloc=708.3MB, time=54.87 memory used=3683.0MB, alloc=708.3MB, time=57.07 memory used=3793.1MB, alloc=708.3MB, time=59.12 memory used=3901.5MB, alloc=708.3MB, time=61.41 memory used=3996.4MB, alloc=708.3MB, time=63.23 memory used=4090.2MB, alloc=732.3MB, time=64.81 memory used=4459.2MB, alloc=756.3MB, time=70.04 memory used=4850.7MB, alloc=780.3MB, time=75.21 memory used=5263.2MB, alloc=804.3MB, time=80.55 memory used=5662.4MB, alloc=828.3MB, time=86.61 memory used=6033.2MB, alloc=852.3MB, time=93.19 memory used=6368.4MB, alloc=876.3MB, time=99.40 memory used=6693.2MB, alloc=900.3MB, time=105.77 memory used=7014.8MB, alloc=924.3MB, time=112.00 memory used=7335.2MB, alloc=948.3MB, time=118.51 memory used=7652.4MB, alloc=972.3MB, time=124.92 memory used=7968.1MB, alloc=996.3MB, time=131.39 memory used=8285.5MB, alloc=1020.3MB, time=137.93 memory used=8659.1MB, alloc=1044.3MB, time=144.14 memory used=9104.2MB, alloc=1068.3MB, time=149.03 memory used=9565.5MB, alloc=1092.3MB, time=154.92 memory used=10061.7MB, alloc=1116.3MB, time=160.37 memory used=10505.2MB, alloc=1140.3MB, time=167.97 memory used=10896.7MB, alloc=1164.3MB, time=175.98 memory used=11277.4MB, alloc=1188.3MB, time=183.93 memory used=11649.5MB, alloc=1212.3MB, time=191.89 memory used=12018.0MB, alloc=1236.3MB, time=199.85 memory used=12380.2MB, alloc=1260.3MB, time=207.69 memory used=12737.0MB, alloc=1284.3MB, time=215.52 memory used=13080.5MB, alloc=1308.3MB, time=223.32 memory used=13432.9MB, alloc=1332.3MB, time=231.46 memory used=13799.9MB, alloc=1356.3MB, time=239.20 memory used=14112.8MB, alloc=1380.3MB, time=248.70 memory used=14379.5MB, alloc=1404.3MB, time=259.27 memory used=14650.9MB, alloc=1428.3MB, time=270.38 memory used=14931.1MB, alloc=1452.3MB, time=281.85 memory used=15222.4MB, alloc=1476.3MB, time=293.88 |\^/| 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(); 1428328149 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 3 F := [-3 x - 18 y z , -2 y - 18 x, -4 x + 5] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [10 x z + 12 z, 14 x y + 4, -2 x y + 16 x ] > Problem := [F,G]; 3 2 2 3 Problem := [[-3 x - 18 y z , -2 y - 18 x, -4 x + 5], 2 2 2 [10 x z + 12 z, 14 x y + 4, -2 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=4.2MB, alloc=32.3MB, time=0.18 memory used=26.3MB, alloc=32.3MB, time=0.48 memory used=49.7MB, alloc=32.3MB, time=0.89 memory used=71.0MB, alloc=56.3MB, time=1.25 N1 := 665 > GB := Basis(F, plex(op(vars))); 3 2 2 2 GB := [4 x - 5, y + 9 x, -x y + 54 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=112.0MB, alloc=60.3MB, time=2.10 memory used=152.4MB, alloc=60.3MB, time=2.72 memory used=192.6MB, alloc=84.3MB, time=3.53 N2 := 705 #save(Problem, "format.txt"); > 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 := [-3 x - 18 y z , -2 y - 18 x, -4 x + 5, 10 x z + 12 z, 14 x y + 4, 2 2 -2 x y + 16 x ] > J:=[op(GB),op(G)]; 3 2 2 2 2 J := [4 x - 5, y + 9 x, -x y + 54 z , 10 x z + 12 z, 14 x y + 4, 2 2 -2 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, 12, 16, 3, 3, 2, 2, 1, 2/3, 1/3, 7/12, 1/3, 1/4, 6, 12, 16, 3, 3, 2, 2, 1, 2/3, 1/3, 7/12, 1/3, 1/4, 0, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=199.1MB, alloc=84.3MB, time=3.70 |\^/| 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(); 1428328153 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [-2 x y z + 14 y , -9 x z + 15 x, 20 y - 11 y ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [2 x z + 19 z , 3 x y z - 20 z , -4 x y - 15 x y z] > Problem := [F,G]; 2 3 2 Problem := [[-2 x y z + 14 y , -9 x z + 15 x, 20 y - 11 y ], 2 3 2 2 [2 x z + 19 z , 3 x y z - 20 z , -4 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=26.0MB, alloc=32.3MB, time=0.45 memory used=47.2MB, alloc=32.3MB, time=0.73 memory used=67.0MB, alloc=32.3MB, time=1.01 memory used=85.3MB, alloc=56.3MB, time=1.30 memory used=124.9MB, alloc=84.3MB, time=1.96 memory used=185.1MB, alloc=84.3MB, time=2.79 memory used=239.0MB, alloc=108.3MB, time=3.51 memory used=310.1MB, alloc=132.3MB, time=4.48 memory used=394.9MB, alloc=164.3MB, time=5.84 memory used=487.6MB, alloc=188.3MB, time=7.88 memory used=590.3MB, alloc=212.3MB, time=11.13 memory used=712.5MB, alloc=236.3MB, time=15.66 memory used=858.6MB, alloc=236.3MB, time=20.69 memory used=1004.6MB, alloc=236.3MB, time=25.10 memory used=1150.5MB, alloc=260.3MB, time=29.45 memory used=1320.5MB, alloc=284.3MB, time=34.24 N1 := 5583 > GB := Basis(F, plex(op(vars))); 2 2 GB := [100 x y - 231 x y, -5 x y + 21 y , 3 x z - 5 x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=1468.5MB, alloc=284.3MB, time=36.58 N2 := 1659 #save(Problem, "format.txt"); > if (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 := [-2 x y z + 14 y , -9 x z + 15 x, 20 y - 11 y , 2 x z + 19 z , 2 2 3 x y z - 20 z , -4 x y - 15 x y z] > J:=[op(GB),op(G)]; 2 2 2 3 J := [100 x y - 231 x y, -5 x y + 21 y , 3 x z - 5 x, 2 x z + 19 z , 2 2 3 x y z - 20 z , -4 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, 14, 17, 3, 2, 3, 3, 5/6, 2/3, 5/6, 7/12, 7/12, 7/12, 6, 14, 16, 3, 2, 2, 3, 1, 2/3, 2/3, 3/4, 7/12, 1/2, 0, 1, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1572.5MB, alloc=540.3MB, time=38.97 |\^/| 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(); 1428328194 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 3 F := [17 x y - 11 y z, -18 x - 15 y, 2 x y - 18 z ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 3 G := [-12 x + 7 x z, -6 z + 15 x z, 11 x + 13 z] > Problem := [F,G]; 2 3 2 3 Problem := [[17 x y - 11 y z, -18 x - 15 y, 2 x y - 18 z ], 3 3 [-12 x + 7 x z, -6 z + 15 x z, 11 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=0.17 memory used=26.1MB, alloc=32.3MB, time=0.42 memory used=47.9MB, alloc=32.3MB, time=0.66 memory used=68.5MB, alloc=32.3MB, time=0.88 memory used=87.9MB, alloc=56.3MB, time=1.12 memory used=128.2MB, alloc=60.3MB, time=1.60 memory used=167.1MB, alloc=84.3MB, time=2.16 memory used=227.7MB, alloc=84.3MB, time=3.00 memory used=282.6MB, alloc=108.3MB, time=3.73 memory used=351.9MB, alloc=140.3MB, time=4.86 memory used=427.6MB, alloc=164.3MB, time=7.01 memory used=523.2MB, alloc=164.3MB, time=9.59 memory used=618.8MB, alloc=188.3MB, time=11.92 N1 := 3099 > GB := Basis(F, plex(op(vars))); 10 9 3 5 3 7 3 GB := [5324 x - 122825 x , 6 x + 5 y, -17 x + 11 x z, -4 x + 25 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 711 #save(Problem, "format.txt"); > if (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 := [17 x y - 11 y z, -18 x - 15 y, 2 x y - 18 z , -12 x + 7 x z, 3 -6 z + 15 x z, 13 z + 11 x] > J:=[op(GB),op(G)]; 10 9 3 5 3 7 3 J := [5324 x - 122825 x , 6 x + 5 y, -17 x + 11 x z, -4 x + 25 z , 3 3 -12 x + 7 x z, -6 z + 15 x z, 13 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, 14, 16, 3, 3, 2, 3, 1, 1/2, 5/6, 7/12, 1/3, 1/2, 7, 13, 32, 10, 10, 1, 3, 1, 1/7, 5/7, 5/7, 1/14, 3/7, 1, -16, -7] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=730.0MB, alloc=188.3MB, time=13.45 |\^/| 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(); 1428328209 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 F := [-14 + 13 z, 5 x y + 7 x y, 8 x z + 11 y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 G := [-7 x y - 6 y , -4 y z + 19, -7 x y z - 18 y z] > Problem := [F,G]; 2 2 Problem := [[-14 + 13 z, 5 x y + 7 x y, 8 x z + 11 y], 2 3 2 2 [-7 x y - 6 y , -4 y z + 19, -7 x 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=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.43 memory used=47.7MB, alloc=32.3MB, time=0.67 memory used=68.4MB, alloc=56.3MB, time=0.92 memory used=110.8MB, alloc=60.3MB, time=1.54 memory used=148.7MB, alloc=84.3MB, time=2.11 memory used=205.0MB, alloc=108.3MB, time=2.95 memory used=272.9MB, alloc=108.3MB, time=4.63 memory used=337.6MB, alloc=132.3MB, time=6.11 N1 := 2143 > GB := Basis(F, plex(op(vars))); 4 3 2 GB := [5 x + 7 x , 112 x + 143 y, 13 z - 14] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=426.8MB, alloc=140.3MB, time=7.32 N2 := 871 #save(Problem, "format.txt"); > if (GB=[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 := [13 z - 14, 5 x y + 7 x y, 8 z x + 11 y, -7 x y - 6 y , -4 y z + 19, 2 -7 x y z - 18 y z] > J:=[op(GB),op(G)]; 4 3 2 2 3 2 J := [5 x + 7 x , 112 x + 143 y, 13 z - 14, -7 x y - 6 y , -4 y z + 19, 2 -7 x y 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, 13, 16, 3, 2, 3, 2, 2/3, 5/6, 2/3, 5/12, 2/3, 5/12, 6, 11, 16, 4, 4, 3, 2, 2/3, 2/3, 1/2, 5/12, 1/2, 1/3, 2, 0, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=456.6MB, alloc=140.3MB, time=7.87 |\^/| 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(); 1428328217 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-12 y z + 11 y z, 18 y - 7 z, 17 x y - 18 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 2 2 G := [17 x + 14 z , 19 x y + 14 z , 20 x z - 14 y] > Problem := [F,G]; 2 2 2 Problem := [[-12 y z + 11 y z, 18 y - 7 z, 17 x y - 18 x], 2 2 2 2 2 [17 x + 14 z , 19 x y + 14 z , 20 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=0.14 memory used=26.4MB, alloc=32.3MB, time=0.38 memory used=47.8MB, alloc=32.3MB, time=0.61 memory used=67.8MB, alloc=32.3MB, time=0.82 memory used=86.8MB, alloc=56.3MB, time=1.05 memory used=125.1MB, alloc=60.3MB, time=1.55 memory used=161.5MB, alloc=60.3MB, time=1.98 memory used=196.6MB, alloc=84.3MB, time=2.40 memory used=253.0MB, alloc=92.3MB, time=3.07 memory used=307.0MB, alloc=116.3MB, time=3.70 memory used=381.8MB, alloc=116.3MB, time=4.61 memory used=454.3MB, alloc=140.3MB, time=5.46 memory used=548.9MB, alloc=164.3MB, time=6.67 memory used=664.0MB, alloc=444.3MB, time=8.39 memory used=791.6MB, alloc=468.3MB, time=10.29 memory used=931.9MB, alloc=492.3MB, time=12.35 memory used=1084.5MB, alloc=516.3MB, time=14.60 memory used=1244.7MB, alloc=540.3MB, time=17.03 memory used=1414.6MB, alloc=564.3MB, time=19.76 memory used=1588.2MB, alloc=588.3MB, time=23.48 memory used=1757.3MB, alloc=612.3MB, time=27.98 memory used=1935.9MB, alloc=636.3MB, time=33.22 memory used=2126.7MB, alloc=660.3MB, time=38.97 memory used=2333.6MB, alloc=684.3MB, time=45.57 memory used=2553.0MB, alloc=708.3MB, time=52.63 memory used=2792.7MB, alloc=732.3MB, time=60.64 memory used=3056.4MB, alloc=756.3MB, time=69.31 memory used=3344.0MB, alloc=780.3MB, time=78.66 memory used=3655.6MB, alloc=804.3MB, time=88.94 memory used=3991.1MB, alloc=804.3MB, time=99.88 memory used=4326.6MB, alloc=828.3MB, time=110.94 memory used=4685.9MB, alloc=828.3MB, time=122.75 memory used=5045.3MB, alloc=828.3MB, time=134.43 memory used=5404.7MB, alloc=828.3MB, time=146.01 memory used=5763.9MB, alloc=852.3MB, time=157.62 memory used=6147.2MB, alloc=852.3MB, time=169.99 memory used=6530.4MB, alloc=876.3MB, time=182.42 memory used=6937.6MB, alloc=876.3MB, time=195.62 memory used=7344.8MB, alloc=900.3MB, time=208.78 memory used=7775.9MB, alloc=900.3MB, time=222.87 memory used=8207.0MB, alloc=924.3MB, time=238.77 memory used=8662.3MB, alloc=948.3MB, time=253.41 N1 := 15327 > GB := Basis(F, plex(op(vars))); 5 3 2 GB := [x, 216 y - 77 y , -18 y + 7 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=9145.9MB, alloc=948.3MB, time=262.76 N2 := 2645 #save(Problem, "format.txt"); > if (GB=[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 := [-12 y z + 11 y z, 18 y - 7 z, 17 x y - 18 x, 14 z + 17 x , 2 2 2 19 y x + 14 z , 20 x z - 14 y] > J:=[op(GB),op(G)]; 5 3 2 2 2 2 2 J := [x, 216 y - 77 y , -18 y + 7 z, 14 z + 17 x , 19 y x + 14 z , 2 20 x 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, 16, 3, 2, 2, 2, 2/3, 5/6, 5/6, 5/12, 1/2, 1/2, 6, 12, 16, 5, 2, 5, 2, 2/3, 2/3, 2/3, 4/11, 5/11, 4/11, 2, 0, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=9301.2MB, alloc=948.3MB, time=267.33 |\^/| 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(); 1428328504 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 3 F := [-15 x y + 7 y , -15 x - 6, -17 - 6 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 G := [-20 y z + 12 x, 13 x z + 18 z , 15 x + 16 x z] > Problem := [F,G]; 2 3 3 Problem := [[-15 x y + 7 y , -15 x - 6, -17 - 6 x], 2 2 3 [-20 y z + 12 x, 13 x z + 18 z , 15 x + 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=4.2MB, alloc=32.3MB, time=0.18 memory used=25.9MB, alloc=32.3MB, time=0.40 memory used=48.7MB, alloc=32.3MB, time=0.75 memory used=69.3MB, alloc=56.3MB, time=1.04 N1 := 793 > GB := Basis(F, plex(op(vars))); GB := [1] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=110.5MB, alloc=56.3MB, time=1.72 N2 := 135 #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 3 2 2 H := [-15 x y + 7 y , -15 x - 6, -17 - 6 x, -20 y z + 12 x, 13 x z + 18 z , 3 15 x + 16 x z] > J:=[op(GB),op(G)]; 2 2 3 J := [1, -20 y z + 12 x, 13 x z + 18 z , 15 x + 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, 11, 15, 3, 3, 3, 2, 1, 1/3, 1/2, 7/12, 1/4, 1/3, 4, 7, 8, 3, 3, 2, 2, 3/4, 1/4, 3/4, 4/7, 1/7, 4/7, 4, 7, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=121.8MB, alloc=56.3MB, 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(); 1428328506 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 3 2 2 F := [-6 z - 15 x z, 19 x y - 11 z, 16 y z - 10 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [-5 x z - 6 z, -14 x - 7 y, 19 x y z + 14 z ] > Problem := [F,G]; 3 2 2 Problem := [[-6 z - 15 x z, 19 x y - 11 z, 16 y z - 10 x], 2 2 [-5 x z - 6 z, -14 x - 7 y, 19 x y z + 14 z ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.15 memory used=26.4MB, alloc=32.3MB, time=0.40 memory used=47.7MB, alloc=32.3MB, time=0.65 memory used=67.8MB, alloc=32.3MB, time=0.87 memory used=86.9MB, alloc=56.3MB, time=1.09 memory used=125.7MB, alloc=60.3MB, time=1.51 memory used=161.9MB, alloc=84.3MB, time=2.00 memory used=216.3MB, alloc=84.3MB, time=2.74 memory used=270.2MB, alloc=108.3MB, time=3.50 memory used=343.2MB, alloc=140.3MB, time=4.54 memory used=433.2MB, alloc=164.3MB, time=5.80 memory used=538.3MB, alloc=188.3MB, time=7.26 memory used=653.7MB, alloc=212.3MB, time=8.98 memory used=775.1MB, alloc=236.3MB, time=11.73 memory used=905.0MB, alloc=260.3MB, time=15.19 memory used=1045.5MB, alloc=284.3MB, time=19.40 memory used=1204.0MB, alloc=308.3MB, time=24.49 memory used=1386.4MB, alloc=332.3MB, time=30.25 memory used=1592.8MB, alloc=332.3MB, time=36.84 memory used=1799.2MB, alloc=332.3MB, time=43.46 memory used=2005.6MB, alloc=356.3MB, time=49.98 memory used=2235.9MB, alloc=356.3MB, time=57.35 memory used=2466.2MB, alloc=356.3MB, time=64.68 memory used=2696.3MB, alloc=380.3MB, time=72.02 memory used=2950.4MB, alloc=404.3MB, time=79.88 N1 := 8649 > GB := Basis(F, plex(op(vars))); 3 2 4 2 GB := [19 x + 44 x , 152 x y - 55 x, -19 x y + 11 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=3036.5MB, alloc=404.3MB, time=81.58 N2 := 959 #save(Problem, "format.txt"); > 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 := [-6 z - 15 x z, 19 y x - 11 z, 16 y z - 10 x, -5 x z - 6 z, 2 2 -14 x - 7 y, 19 x y z + 14 z ] > J:=[op(GB),op(G)]; 3 2 4 2 J := [19 x + 44 x , 152 x y - 55 x, -19 x y + 11 z, -5 x z - 6 z, 2 2 -14 x - 7 y, 19 x y z + 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, 16, 3, 2, 2, 3, 1, 2/3, 5/6, 1/2, 1/3, 2/3, 6, 13, 18, 5, 3, 4, 2, 1, 2/3, 1/2, 2/3, 1/3, 5/12, 2, -2, -2] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=3103.3MB, alloc=660.3MB, time=82.76 |\^/| 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(); 1428328595 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-11 x y - 20 z , 6 y z - 19 y z, -11 y z + 17 x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 G := [12 x y + 20, -7 x y z - 8 y, 13 y z + 10 x] > Problem := [F,G]; 2 2 2 Problem := [[-11 x y - 20 z , 6 y z - 19 y z, -11 y z + 17 x y], 2 2 [12 x y + 20, -7 x y z - 8 y, 13 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=26.1MB, alloc=32.3MB, time=0.44 memory used=47.7MB, alloc=32.3MB, time=0.67 memory used=68.1MB, alloc=32.3MB, time=0.90 memory used=87.0MB, alloc=56.3MB, time=1.12 memory used=126.7MB, alloc=60.3MB, time=1.54 memory used=165.1MB, alloc=60.3MB, time=1.94 memory used=202.7MB, alloc=84.3MB, time=2.38 memory used=259.5MB, alloc=92.3MB, time=3.06 memory used=316.4MB, alloc=116.3MB, time=3.80 memory used=392.9MB, alloc=140.3MB, time=4.88 memory used=486.4MB, alloc=164.3MB, time=6.18 memory used=596.0MB, alloc=188.3MB, time=7.73 memory used=717.0MB, alloc=468.3MB, time=9.46 memory used=856.6MB, alloc=492.3MB, time=11.36 memory used=1006.0MB, alloc=516.3MB, time=13.67 memory used=1154.2MB, alloc=540.3MB, time=17.15 memory used=1309.3MB, alloc=564.3MB, time=21.35 memory used=1476.5MB, alloc=588.3MB, time=25.90 memory used=1651.3MB, alloc=612.3MB, time=31.57 memory used=1849.8MB, alloc=636.3MB, time=38.13 memory used=2072.2MB, alloc=660.3MB, time=45.31 memory used=2318.6MB, alloc=660.3MB, time=53.15 memory used=2565.0MB, alloc=684.3MB, time=61.16 memory used=2835.2MB, alloc=684.3MB, time=69.88 memory used=3105.4MB, alloc=684.3MB, time=78.65 memory used=3375.5MB, alloc=708.3MB, time=87.32 memory used=3669.5MB, alloc=708.3MB, time=96.72 memory used=3963.5MB, alloc=732.3MB, time=106.15 memory used=4281.5MB, alloc=732.3MB, time=116.24 memory used=4599.4MB, alloc=756.3MB, time=126.59 N1 := 11263 > GB := Basis(F, plex(op(vars))); 2 2 GB := [1248480 x y + 9129329 x y, 6 x y - 19 x y, -102 x y + 209 y z, 2 20 z + 11 y x] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4948.1MB, alloc=756.3MB, time=136.21 memory used=5337.3MB, alloc=756.3MB, time=142.34 memory used=5718.4MB, alloc=780.3MB, time=151.17 memory used=6052.5MB, alloc=804.3MB, time=162.64 memory used=6410.1MB, alloc=828.3MB, time=174.93 memory used=6791.7MB, alloc=852.3MB, time=188.04 N2 := 7039 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 2 2 2 H := [-11 x y - 20 z , 6 y z - 19 y z, -11 y z + 17 x y, 12 x y + 20, 2 -7 x y z - 8 y, 13 z y + 10 x] > J:=[op(GB),op(G)]; 2 2 J := [1248480 x y + 9129329 x y, 6 x y - 19 x y, -102 x y + 209 y z, 2 2 2 20 z + 11 y x, 12 x y + 20, -7 x y z - 8 y, 13 z 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, 17, 3, 1, 2, 2, 5/6, 1, 5/6, 5/12, 3/4, 1/2, 7, 18, 19, 3, 2, 2, 2, 1, 1, 4/7, 9/14, 11/14, 2/7, -2, -2, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=7056.7MB, alloc=852.3MB, time=196.45 |\^/| 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(); 1428328807 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 F := [15 x y z - 2 x , -17 y - 19, -19 x z - x y] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 G := [17 x z + 19 z , -15 y - 9 y , 15 x y z - 13 x z] > Problem := [F,G]; 2 3 2 Problem := [[15 x y z - 2 x , -17 y - 19, -19 x z - x y], 2 2 3 2 [17 x z + 19 z , -15 y - 9 y , 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=0.15 memory used=26.1MB, alloc=32.3MB, time=0.39 memory used=48.4MB, alloc=32.3MB, time=0.74 N1 := 263 > GB := Basis(F, plex(op(vars))); 7 5 3 4 GB := [43928 x + 3375 x, 1292 x + 225 x y, 17 y + 19, -68 x + 225 x z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=66.5MB, alloc=32.3MB, time=0.94 memory used=85.6MB, alloc=56.3MB, time=1.19 memory used=127.7MB, alloc=56.3MB, time=1.77 N2 := 647 #save(Problem, "format.txt"); > if (GB=[1]) then > print ("Input concluded false after GB computation") > else > print ("Nothing found") > end if: "Nothing found" > > H:=[op(F),op(G)]; 2 3 2 2 2 H := [15 x y z - 2 x , -17 y - 19, -19 x z - x y, 17 x z + 19 z , 3 2 -15 y - 9 y , 15 x y z - 13 x z] > J:=[op(GB),op(G)]; 7 5 3 4 J := [43928 x + 3375 x, 1292 x + 225 x y, 17 y + 19, -68 x + 225 x z, 2 2 3 2 17 x z + 19 z , -15 y - 9 y , 15 x y 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, 13, 18, 3, 2, 3, 2, 2/3, 5/6, 2/3, 7/12, 1/2, 1/2, 7, 12, 28, 7, 7, 3, 2, 5/7, 4/7, 3/7, 9/14, 5/14, 5/14, 1, -10, -4] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=134.8MB, alloc=56.3MB, time=1.91 |\^/| 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(); 1428328809 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [2 x z, 14 x z - 3 x , 2 y - 20 z] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 3 2 2 2 G := [-11 x y - 7 z , -7 y - 9 y z, 9 x y - 3 x ] > Problem := [F,G]; 2 2 2 Problem := [[2 x z, 14 x z - 3 x , 2 y - 20 z], 2 3 2 2 2 [-11 x y - 7 z , -7 y - 9 y z, 9 x y - 3 x ]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.14 memory used=26.1MB, alloc=32.3MB, time=0.37 memory used=47.0MB, alloc=32.3MB, time=0.59 memory used=66.4MB, alloc=56.3MB, time=0.83 memory used=106.8MB, alloc=60.3MB, time=1.35 memory used=144.7MB, alloc=84.3MB, time=1.93 memory used=202.3MB, alloc=108.3MB, time=2.77 memory used=278.8MB, alloc=108.3MB, time=3.79 memory used=346.6MB, alloc=140.3MB, time=4.74 memory used=427.4MB, alloc=164.3MB, time=6.09 memory used=515.2MB, alloc=188.3MB, time=8.06 memory used=616.3MB, alloc=212.3MB, time=10.93 memory used=734.3MB, alloc=236.3MB, time=15.30 memory used=876.3MB, alloc=236.3MB, time=20.53 memory used=1018.3MB, alloc=236.3MB, time=25.74 memory used=1160.2MB, alloc=260.3MB, time=30.98 memory used=1325.9MB, alloc=260.3MB, time=36.24 memory used=1491.7MB, alloc=284.3MB, time=40.77 N1 := 5903 > GB := Basis(F, plex(op(vars))); 2 2 2 GB := [x , y x, -y + 10 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); N2 := 753 #save(Problem, "format.txt"); > if (GB=[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 := [2 x z, 14 x z - 3 x , 2 y - 20 z, -11 x y - 7 z , -7 y - 9 y z, 2 2 9 x y - 3 x ] > J:=[op(GB),op(G)]; 2 2 2 2 3 2 2 2 J := [x , y x, -y + 10 z, -11 x y - 7 z , -7 y - 9 y z, 9 x 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, 15, 3, 2, 2, 3, 2/3, 2/3, 5/6, 6/13, 5/13, 5/13, 6, 12, 15, 3, 2, 2, 3, 2/3, 5/6, 1/2, 5/12, 1/2, 1/4, 1, 0, 0] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=1610.2MB, alloc=284.3MB, time=42.55 |\^/| 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(); 1428328854 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 3 2 2 F := [8 x y - 18 x y , -7 x + 3 z , 7 x y z - 18 x ] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [11 y z - 11 z, 9 y z - 8 x y, -8 x z + 2 y z] > Problem := [F,G]; 2 2 3 2 2 Problem := [[8 x y - 18 x y , -7 x + 3 z , 7 x y z - 18 x ], 2 2 2 [11 y z - 11 z, 9 y z - 8 x y, -8 x z + 2 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.3MB, alloc=32.3MB, time=0.16 memory used=26.1MB, alloc=32.3MB, time=0.40 memory used=48.0MB, alloc=32.3MB, time=0.69 memory used=68.0MB, alloc=56.3MB, time=0.95 memory used=108.3MB, alloc=60.3MB, time=1.43 memory used=146.2MB, alloc=60.3MB, time=1.88 memory used=182.1MB, alloc=84.3MB, time=2.28 memory used=232.6MB, alloc=84.3MB, time=2.91 memory used=290.6MB, alloc=116.3MB, time=3.71 memory used=370.9MB, alloc=140.3MB, time=4.73 memory used=464.8MB, alloc=164.3MB, time=6.01 memory used=572.4MB, alloc=188.3MB, time=7.47 memory used=694.8MB, alloc=212.3MB, time=9.16 memory used=822.6MB, alloc=492.3MB, time=11.08 memory used=956.3MB, alloc=516.3MB, time=13.98 memory used=1094.9MB, alloc=540.3MB, time=17.45 memory used=1244.4MB, alloc=564.3MB, time=21.46 memory used=1401.6MB, alloc=588.3MB, time=26.43 memory used=1582.7MB, alloc=612.3MB, time=32.11 memory used=1787.8MB, alloc=636.3MB, time=38.62 memory used=2016.7MB, alloc=660.3MB, time=45.82 memory used=2269.7MB, alloc=660.3MB, time=53.65 memory used=2522.6MB, alloc=660.3MB, time=61.51 memory used=2775.5MB, alloc=660.3MB, time=69.24 memory used=3028.2MB, alloc=684.3MB, time=76.93 memory used=3304.8MB, alloc=684.3MB, time=85.42 memory used=3581.3MB, alloc=684.3MB, time=93.88 memory used=3857.7MB, alloc=708.3MB, time=102.16 memory used=4158.0MB, alloc=732.3MB, time=111.12 memory used=4482.4MB, alloc=756.3MB, time=120.37 N1 := 11129 > GB := Basis(F, plex(op(vars))); 6 3 3 2 3 2 5 2 GB := [1372 x - 19683 x , -4 x + 9 x y, -16 x + 81 x y , -98 x + 243 x z, 2 3 2 7 x y z - 18 x , -7 x + 3 z ] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=4819.9MB, alloc=756.3MB, time=125.78 memory used=5190.1MB, alloc=756.3MB, time=130.72 memory used=5575.0MB, alloc=780.3MB, time=136.60 memory used=5959.4MB, alloc=804.3MB, time=142.73 memory used=6318.9MB, alloc=828.3MB, time=148.67 memory used=6673.1MB, alloc=852.3MB, time=154.59 memory used=7021.0MB, alloc=876.3MB, time=163.23 memory used=7335.0MB, alloc=900.3MB, time=172.80 memory used=7649.6MB, alloc=924.3MB, time=182.76 memory used=7969.5MB, alloc=948.3MB, time=193.08 memory used=8297.7MB, alloc=972.3MB, time=203.92 memory used=8635.5MB, alloc=996.3MB, time=215.34 memory used=8976.5MB, alloc=1020.3MB, time=227.84 memory used=9341.3MB, alloc=1044.3MB, time=240.94 memory used=9730.1MB, alloc=1068.3MB, time=254.90 memory used=10142.9MB, alloc=1092.3MB, time=269.60 |\^/| 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(); 1428329154 > libname := "/Library/Frameworks/Maple.framework/Versions/17", libname: > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > F := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 F := [-19 x z - 17, -4 x y + 18 y z, -9 y - 16 x] > G := [ randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)), > randpoly([x,y,z], terms=2, degree=3, coeffs=rand(-20 .. 20)) > ]; 2 2 2 G := [16 x y - 12 x , 5 y z - 16 x, 2 x y z - 2 y z] > Problem := [F,G]; 2 2 2 Problem := [[-19 x z - 17, -4 x y + 18 y z, -9 y - 16 x], 2 2 2 [16 x y - 12 x , 5 y z - 16 x, 2 x y z - 2 y z]] > with(RegularChains): with(SemiAlgebraicSetTools): with(Groebner): > vars := [z,y,x]; R:=PolynomialRing(vars): vars := [z, y, x] > cad1 := CylindricalAlgebraicDecompose( [op(F), op(G)], R, output=list): N1 := nops(cad1); memory used=4.2MB, alloc=32.3MB, time=0.17 memory used=26.2MB, alloc=32.3MB, time=0.48 memory used=47.7MB, alloc=32.3MB, time=0.78 memory used=67.5MB, alloc=56.3MB, time=1.08 memory used=111.1MB, alloc=60.3MB, time=1.81 memory used=150.5MB, alloc=84.3MB, time=2.47 memory used=209.7MB, alloc=108.3MB, time=3.50 memory used=284.2MB, alloc=108.3MB, time=5.63 memory used=349.5MB, alloc=132.3MB, time=7.35 N1 := 2123 > GB := Basis(F, plex(op(vars))); 4 2 GB := [1216 x - 12393, 9 y + 16 x, -2 x y + 9 z] > cad2 := CylindricalAlgebraicDecompose( [op(GB), op(G)], R, output=list): N2 := nops(cad2); memory used=439.8MB, alloc=140.3MB, time=8.66 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)]; 2 2 2 2 2 H := [-19 x z - 17, -4 x y + 18 y z, -9 y - 16 x, 16 x y - 12 x , 2 5 y z - 16 x, 2 x y z - 2 y z] > J:=[op(GB),op(G)]; 4 2 2 2 J := [1216 x - 12393, 9 y + 16 x, -2 x y + 9 z, 16 x y - 12 x , 2 5 y z - 16 x, 2 x 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, 15, 17, 3, 2, 2, 2, 1, 5/6, 2/3, 7/12, 7/12, 5/12, 6, 14, 17, 4, 4, 2, 1, 1, 5/6, 1/2, 7/12, 1/2, 1/3, 1, 0, -1] > save(F, G, cat("ranSet/23", convert(F, string),".txt")); > quit memory used=460.5MB, alloc=140.3MB, time=9.02