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moved tests
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‎M2/Macaulay2/packages/EngineTests.m2‎

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@@ -248,6 +248,7 @@ load "EngineTests/LinearAlgebra.Test.Driver.m2"
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load "EngineTests/MutableMatrix.Test.Driver.m2"
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load "EngineTests/Ring.Test.Driver.m2"
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load "EngineTests/GB.Test.Mathic.m2"
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load "EngineTests/GB.Test.LinearAlgebra.m2"
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load "EngineTests/Res.f4.m2"
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--check EngineTests

‎M2/Macaulay2/packages/EngineTests/GB.Test.LinearAlgebra.m2‎

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-- Tests for different variants
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TEST /// -- basics of Algorithm => LinearAlgebra
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I = ideal vars(QQ[x])
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assert try (elapsedTime gb(I, Algorithm => LinearAlgebra); false) else true
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R = ZZ/32003[x]
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I = ideal vars R
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elapsedTime result = gens (G = gb(I, Algorithm => LinearAlgebra));
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assert(result == vars R)
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assert try(getChangeMatrix G; false) else true
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assert try(mingens G; false) else true
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assert try(syz G; false) else true
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assert try(a // G; false) else true
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assert try(a % G; false) else true
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assert try(leadTerm G; false) else true
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leadTerm gens G
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assert(numcols gens G == 1)
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///
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TEST /// -- Algorithm => LinearAlgebra, over finite field.
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kk = ZZ/101;
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R1 = kk[a..f];
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J1 = ideal(a*b*c-d*e*f, a^2*c-b^2*e, b*e^4 - d*f^4 + e^5)
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elapsedTime gbC = flatten entries gens (G = gb(ideal J1_*, Algorithm => LinearAlgebra));
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elapsedTime gbB = flatten entries groebnerBasis(ideal J1_*, Strategy => "F4");
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assert(gbC == gbB)
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-- TODO: is it ok to check Msolve while we do this?
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needsPackage "Msolve"
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elapsedTime gbD = flatten entries msolveGB(ideal J1_*, Threads => 8); -- slowest, due to translation, or what?
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assert(gbD == gbB)
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assert try(getChangeMatrix G; false) else true
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assert try(mingens G; false) else true
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assert try(syz G; false) else true
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assert try(a // G; false) else true
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assert try(a % G; false) else true
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assert try(leadTerm G; false) else true
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assert(numcols gens G == 7)
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///
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TEST /// -- Algorithm => LinearAlgebra, over finite field.
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kk = ZZ/101;
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R1 = kk[a..g, MonomialSize=>8];
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setRandomSeed 42
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J1 = ideal random(R1^1, R1^{-2, -2, -2, -3});
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elapsedTime gbA = flatten entries gens gb(ideal J1_*);
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elapsedTime gbC = flatten entries gens (G = gb(ideal J1_*, Algorithm => LinearAlgebra));
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elapsedTime gbB = flatten entries groebnerBasis(ideal J1_*, Strategy => "F4");
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assert(gbA == gbB)
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assert(gbA == gbC)
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-- TODO: is it ok to check Msolve while we do this?
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needsPackage "Msolve"
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elapsedTime gbD = flatten entries msolveGB(ideal J1_*, Threads => 8); -- slowest, due to translation, or what?
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assert(gbD == gbB)
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assert try(getChangeMatrix G; false) else true
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assert try(mingens G; false) else true
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assert try(syz G; false) else true
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assert try(a // G; false) else true
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assert try(a % G; false) else true
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assert try(leadTerm G; false) else true
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assert(numcols gens G == 13)
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///
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TEST /// -- Algorithm => LinearAlgebra, over prime finite field.
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kk = ZZ/101;
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R1 = kk[a..g, MonomialSize=>8];
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setRandomSeed 42
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J1 = ideal random(R1^1, R1^{-4,-4,-5,-5});
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elapsedTime gbC = flatten entries gens (G = gb(ideal J1_*, Algorithm => LinearAlgebra));
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elapsedTime gbB = flatten entries groebnerBasis(ideal J1_*, Strategy => "F4");
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assert(gbC == gbB)
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-- TODO: is it ok to check Msolve while we do this?
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needsPackage "Msolve"
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elapsedTime gbD = flatten entries msolveGB(ideal J1_*, Threads => 8); -- slowest, due to translation, or what?
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assert(gbD == gbB)
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assert try(getChangeMatrix G; false) else true
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assert try(mingens G; false) else true
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assert try(syz G; false) else true
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assert try(a // G; false) else true
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assert try(a % G; false) else true
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assert try(leadTerm G; false) else true
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assert(numcols gens G == 78)
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///
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TEST /// -- Algorithm => LinearAlgebra, over non-prime finite field.
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kk = GF 125;
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R1 = kk[a..g, MonomialSize=>8];
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setRandomSeed 42
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J1 = ideal random(R1^1, R1^{-4,-4,-5,-5});
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elapsedTime gbC = flatten entries gens gb(ideal J1_*, DegreeLimit => 10);
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elapsedTime gbB = flatten entries gens (G = gb(ideal J1_*, Algorithm => LinearAlgebra, DegreeLimit => 10));
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assert(gbC == gbB)
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-- the following appears to hang. BUG!! It should say it can't do it.
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--try(groebnerBasis(ideal J1_*, Strategy => "F4"); false) else true -- BUG: this should be disallowed...!
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needsPackage "Msolve"
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elapsedTime try(msolveGB(ideal J1_*, Threads => 8); false) else true -- correctly gives error
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///
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-*
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restart
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*-
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TEST /// -- hilbert driven gb computation, for default, Algorithm => LinearAlgebra
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setRandomSeed 42
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kk = ZZ/101
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R1 = kk[a..g, MonomialSize => 8];
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K1 = ideal (a^4, b^4, c^4, d^4)
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hfJ = poincare K1
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J1 = ideal random(R1^1, R1^{-4, -4, -4, -4});
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elapsedTime gbA = flatten entries gens gb(ideal J1_*, Hilbert => hfJ);
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elapsedTime gbB = flatten entries gens gb(ideal J1_*,
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Algorithm => LinearAlgebra,
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Hilbert => hfJ);
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elapsedTime gbB2 = flatten entries gens gb(ideal J1_*,
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Algorithm => LinearAlgebra);
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elapsedTime gbC = flatten entries groebnerBasis(ideal J1_*, Strategy => "F4");
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assert(gbA == gbB)
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assert(gbA == gbB2)
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assert(gbA == gbC)
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needsPackage "Msolve"
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elapsedTime gbD = flatten entries msolveGB(ideal J1_*, Threads => 8);
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assert(gbA == gbD)
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///
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-*
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restart
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*-
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TEST /// -- hilbert driven gb computation, quasi-degrees
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setRandomSeed 42
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kk = ZZ/101
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R1 = kk[a..g, Degrees => {1,2,3,3,4,4,5}];
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K1 = ideal (a^8, b^4, e^2, f^2)
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hfJ = poincare K1
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J1 = ideal random(R1^1, R1^{-8, -8, -8, -8});
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--elapsedTime gbA = flatten entries gens gb(ideal J1_*, Hilbert => hfJ);
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elapsedTime gbB = flatten entries gens gb(ideal J1_*,
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Algorithm => LinearAlgebra,
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Hilbert => hfJ);
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elapsedTime gbB2 = flatten entries gens gb(ideal J1_*,
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Algorithm => LinearAlgebra);
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elapsedTime gbC = flatten entries groebnerBasis(ideal J1_*, Strategy => "F4");
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assert(gbB == gbB2)
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assert(gbB == gbC)
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///
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-*
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restart
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*-
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TEST /// -- GB over quotient rings
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setRandomSeed 42
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kk = ZZ/101
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R1 = kk[a,b,c,d,e,f]/ideal(a^2 - b*c)
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J1 = ideal random(R1^1, R1^{-2,-2,-3,-3});
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elapsedTime gbA = flatten entries gens gb(ideal J1_*);
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assert try(gb(ideal J1_*, Algorithm => LinearAlgebra);false) else true
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elapsedTime gbC = flatten entries groebnerBasis(ideal J1_*, Strategy => "F4");
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assert(gbA == gbC) -- because it falls back to working version
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needsPackage "Msolve"
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assert try(msolveGB(ideal J1_*, Threads => 8); false) else true -- correctly gives error
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///
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-*
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restart
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*-
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TEST /// -- exterior algebra
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kk = ZZ/101
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R1 = kk[a,b,c,d,e,f, SkewCommutative=>true]
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setRandomSeed 42
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J1 = ideal random(R1^1, R1^{-2,-2,-2,-2});
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elapsedTime gbA = flatten entries gens gb(J1);
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assert try(gb(ideal J1_*, Algorithm => LinearAlgebra); false) else true;
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elapsedTime gbC = flatten entries groebnerBasis(ideal J1_*, Strategy => "F4");
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assert(gbA == gbC)
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///
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-*
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restart
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*-
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TEST /// -- nonstandard grading
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kk = ZZ/101;
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R1 = kk[a..f, MonomialOrder => {GRevLex => {1,1,1,1,1,1}}, Degrees => {1,2,3,4,4,4}];
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setRandomSeed 42
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J1 = ideal random(R1^1, R1^{-5, -5, -5, -5});
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assert isHomogeneous J1
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elapsedTime gbA = flatten entries gens gb(J1);
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elapsedTime gbB = flatten entries gens gb(ideal J1_*, Algorithm => LinearAlgebra);
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elapsedTime gbC = flatten entries groebnerBasis(ideal J1_*, Strategy => "F4");
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needsPackage "Msolve"
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elapsedTime gbD = flatten entries msolveGB(ideal J1_*, Threads => 8);
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assert(gbA == gbB)
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assert(gbA == gbC)
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assert(gbA == gbD)
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///
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-*
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restart
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*-
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TEST /// -- GB's of modules
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-- default order: grevlex, followed by position up
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R1 = ZZ/101[vars(0..7)]
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assert(leadTerm matrix{{a},{a}} == matrix{{0},{a}})
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m1 = genericMatrix(R1, a, 2, 3)
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elapsedTime gbA = gens (gb m1);
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m1 = genericMatrix(R1, a, 2, 3)
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elapsedTime gbB = gens (G = gb(m1, Algorithm => LinearAlgebra));
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assert(gbA == gbB)
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m1 = genericMatrix(R1, a, 2, 3)
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elapsedTime gbC = groebnerBasis(m1, Strategy => "F4"); -- BUG: just wrong
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m1 = genericMatrix(R1, a, 2, 3)
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elapsedTime gbC = groebnerBasis(m1, Strategy => "MGB"); -- BUG: just wrong
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R2 = ZZ/101[vars(0..7), MonomialOrder => {Position => Up}]
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m2 = genericMatrix(R2, a, 2, 3)
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elapsedTime gbC = groebnerBasis(m2, Strategy => "MGB"); -- BUG: just wrong
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assert(leadTerm matrix{{a},{a}} == matrix{{0},{a}})
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-- note: msolveGB only works for ideals, doesn't take a matrix or Module, in any case.
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///
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TEST /// -- another module GB test
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R = ZZ/101[a..d]
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M = R^{0,-1,-2,-3}
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setRandomSeed 42
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mat = random(M,R^{-1,-2,-3,-4})
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gbA = gens gb mat;
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setRandomSeed 42
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mat = random(M,R^{-1,-2,-3,-4})
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gbB = gens gb(mat, Algorithm => LinearAlgebra);
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assert(gbA == gbB)
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///
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TEST /// -- another module GB test
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R = ZZ/101[a..d, MonomialOrder => {Position => Up, GRevLex => 2, GRevLex => 2 }]
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M = R^2
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setRandomSeed 42
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mat = matrix{{a,b},{a,c}}
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gbA = gens gb mat;
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-- to clear cache for mat
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mat = matrix{{a,b},{a,c}}
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assert try (gb(mat, Algorithm => LinearAlgebra); false) else true
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gens gb(ideal(a,b), Algorithm => LinearAlgebra)
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///
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TEST /// -- another module GB test
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R = ZZ/101[a..f, Degrees => {1,2,3,4,5,6}]
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M = koszul(3,vars R)
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gbA = gens gb M;
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M = koszul(3,vars R)
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gbB = gens gb(M, Algorithm => LinearAlgebra);
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assert(gbA == gbB)
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///
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-*
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restart
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*-
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TEST /// -- inhomgeneity. Algorithm => LinearAlgebra, over finite field. Need to implement still
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kk = ZZ/101;
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R1 = kk[a..g, MonomialSize=>8];
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setRandomSeed 42
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J1 = ideal (random(2, R1) + random(3, R1), random(2, R1) - 1)
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elapsedTime gbA = flatten entries gens gb(ideal J1_*);
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elapsedTime assert try(gb(ideal J1_*, Algorithm => LinearAlgebra); false) else true;
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elapsedTime gbB = flatten entries groebnerBasis(ideal J1_*, Strategy => "F4");
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assert(gbA == gbB)
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-- TODO: is it ok to check Msolve while we do this?
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needsPackage "Msolve"
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elapsedTime gbD = flatten entries msolveGB(ideal J1_*, Threads => 8); -- slowest, due to translation, or what?
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assert(gbD == gbB)
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///
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-*
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restart
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*-
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TEST /// -- different monomial orders
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kk = ZZ/101;
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R1 = kk[a..g, MonomialSize=>8];
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M = genericSymmetricMatrix(R1, 3)
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J1 = minors(2, M)
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-- grevlex
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elapsedTime gbA = flatten entries gens gb(ideal J1_*);
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elapsedTime gbC = flatten entries gens gb(ideal J1_*, Algorithm => LinearAlgebra);
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elapsedTime gbB = flatten entries groebnerBasis(ideal J1_*, Strategy => "F4");
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assert(gbA == gbB)
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assert(gbA == gbC)
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LT1 = leadTerm J1
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-- lex
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R1 = kk[a..g, MonomialOrder => Lex];
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J1 = sub(J1, R1)
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elapsedTime gbA = flatten entries gens gb(ideal J1_*);
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elapsedTime gbC = flatten entries gens gb(ideal J1_*, Algorithm => LinearAlgebra);
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elapsedTime gbB = flatten entries groebnerBasis(ideal J1_*, Strategy => "F4");
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assert(gbA == gbB)
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assert(gbA == gbC)
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LT2 = leadTerm J1
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assert(LT2 != sub(LT1, R1))
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-- product order
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R1 = kk[a..g, MonomialOrder => {3,4}];
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J1 = sub(J1, R1)
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elapsedTime gbA = flatten entries gens gb(ideal J1_*);
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elapsedTime gbC = flatten entries gens gb(ideal J1_*, Algorithm => LinearAlgebra);
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elapsedTime gbB = flatten entries groebnerBasis(ideal J1_*, Strategy => "F4");
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assert(gbA == gbB)
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assert(gbA == gbC)
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LT3 = leadTerm J1
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assert(LT3 != sub(LT1, R1))
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-- product order
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R1 = kk[a..g, MonomialOrder => {Lex => 3, GRevLex => {1,2,3,4}}];
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J1 = sub(J1, R1)
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elapsedTime gbA = flatten entries gens gb(ideal J1_*);
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elapsedTime gbC = flatten entries gens gb(ideal J1_*, Algorithm => LinearAlgebra);
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elapsedTime gbB = flatten entries groebnerBasis(ideal J1_*, Strategy => "F4");
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assert(gbA == gbB)
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assert(gbA == gbC)
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LT4 = leadTerm J1
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assert(LT4 != sub(LT1, R1))
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///
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-*
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restart
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*-
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TEST /// -- Weyl algebras
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R = QQ[x,dx, WeylAlgebra => {x=>dx}]
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I = ideal(x^3, x*dx)
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assert try (gb(I, Algorithm => LinearAlgebra); false) else true
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R = ZZ/32003[x,dx,h, WeylAlgebra => {x=>dx,h}]
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I = ideal(x^3, x*dx)
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assert try (gb(I, Algorithm => LinearAlgebra); false) else true -- this should error
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///
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-*
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restart
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*-
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TEST /// -- multigradings
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I = Grassmannian(2, 5, CoefficientRing => ZZ/32003)
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R = ring I
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es = entries id_(ZZ^6)
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degs = apply(subsets(0..5, 3), x -> sum apply(x, i -> es_i))
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S = newRing(R, Degrees => degs)
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J1 = sub(I, S)
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isHomogeneous J1
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elapsedTime gbA = flatten entries gens gb(ideal J1_*);
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elapsedTime gbC = flatten entries gens gb(ideal J1_*, Algorithm => LinearAlgebra);
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elapsedTime gbB = flatten entries groebnerBasis(ideal J1_*, Strategy => "F4");
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assert(gbA == gbB)
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assert(gbA == gbC)
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///
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-- todo:
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-- error for quotient rings (for LinearAlgebra)
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-- error for exterior algebra
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-- error for Weyl algebra
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-- error if module order is wrong (only if we are in a non-ideal situation).
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-- check
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-- Hilbert hint with quasi-gradings OK
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-- multi-gradings: OK
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-- check Weyl algebra (homogenized Weyl algebra): Need to error

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