MinimalGenerators -- whether to compute minimal generators and return a trimmed set of generators

Description

i1 : S = ZZ/101[a,b]

o1 = S

o1 : PolynomialRing

i2 : i = ideal(a^4,b^4)

             4   4
o2 = ideal (a , b )

o2 : Ideal of S

i3 : quotient(i, a^3+b^3)

                  3    3
o3 = ideal (a*b, a  - b )

o3 : Ideal of S

i4 : quotient(i, a^3+b^3, MinimalGenerators => false)

                  3    3
o4 = ideal (a*b, a  - b )

o4 : Ideal of S

i5 : needsPackage "Truncations"

o5 = Truncations

o5 : Package

i6 : R = ZZ/101[x_0..x_4]

o6 = R

o6 : PolynomialRing

i7 : I = truncate(8, monomialCurveIdeal(R,{1,4,5,9}));

o7 : Ideal of R

i8 : time gens gb I;
     -- used 0.0236064 seconds

             1      428
o8 : Matrix R  <-- R

i9 : time J1 = saturate(I);
     -- used 0.188839 seconds

o9 : Ideal of R

i10 : time J = saturate(I, MinimalGenerators => false);
     -- used 0.000064136 seconds

o10 : Ideal of R

i11 : numgens J

o11 = 7

i12 : numgens J1

o12 = 7

See also

• quotient(Ideal,Ideal) -- ideal or submodule quotient
• saturate(Ideal,Ideal) -- saturation of ideal or submodule
• monomialCurveIdeal -- make the ideal of a monomial curve
• truncate(ZZ,Ideal) -- truncation of the graded ring, ideal or module at a specified degree or set of degrees

Functions with optional argument named MinimalGenerators :

• adjoint(...,MinimalGenerators=>...) (missing documentation)
• associatedPrimes(...,MinimalGenerators=>...) -- see associatedPrimes -- find associated primes
• canonicalBundle(...,MinimalGenerators=>...) (missing documentation)
• compose(Module,Module,Module,MinimalGenerators=>...) -- see compose -- composition as a pairing on Hom-modules
• cotangentSheaf(...,MinimalGenerators=>...) -- see cotangentSheaf(ProjectiveVariety) -- cotangent sheaf of a projective variety
• dual(ChainComplex,MinimalGenerators=>...) (missing documentation)
• dual(Matrix,MinimalGenerators=>...) (missing documentation)
• dual(SheafMap,MinimalGenerators=>...) (missing documentation)
• End(...,MinimalGenerators=>...) -- see End -- module of endomorphisms
• Hom(...,MinimalGenerators=>...) -- see Hom -- module of homomorphisms
• homomorphism'(...,MinimalGenerators=>...) -- see homomorphism' -- get the element of Hom from a homomorphism
• intersect(Ideal,Ideal,MinimalGenerators=>...) -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
• intersect(Module,Module,MinimalGenerators=>...) -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
• intersectInP(...,MinimalGenerators=>...) -- see intersectInP(...,BasisElementLimit=>...) -- Option for intersectInP
• decompose(Ideal,MinimalGenerators=>...) -- see minimalPrimes -- minimal primes of an ideal
• minimalPrimes(...,MinimalGenerators=>...) -- see minimalPrimes -- minimal primes of an ideal
• primaryDecomposition(...,MinimalGenerators=>...) -- see primaryDecomposition -- irredundant primary decomposition of an ideal
• quotient(...,MinimalGenerators=>...) -- see quotient(Module,Module) -- ideal or submodule quotient
• analyticSpread(...,MinimalGenerators=>...) -- see reesIdeal(...,MinimalGenerators=>...) -- Whether the saturation step returns minimal generators
• distinguished(...,MinimalGenerators=>...) -- see reesIdeal(...,MinimalGenerators=>...) -- Whether the saturation step returns minimal generators
• isLinearType(...,MinimalGenerators=>...) -- see reesIdeal(...,MinimalGenerators=>...) -- Whether the saturation step returns minimal generators
• isReduction(...,MinimalGenerators=>...) -- see reesIdeal(...,MinimalGenerators=>...) -- Whether the saturation step returns minimal generators
• minimalReduction(...,MinimalGenerators=>...) -- see reesIdeal(...,MinimalGenerators=>...) -- Whether the saturation step returns minimal generators
• multiplicity(...,MinimalGenerators=>...) -- see reesIdeal(...,MinimalGenerators=>...) -- Whether the saturation step returns minimal generators
• normalCone(...,MinimalGenerators=>...) -- see reesIdeal(...,MinimalGenerators=>...) -- Whether the saturation step returns minimal generators
• reesAlgebra(...,MinimalGenerators=>...) -- see reesIdeal(...,MinimalGenerators=>...) -- Whether the saturation step returns minimal generators
• reesIdeal(...,MinimalGenerators=>...) -- Whether the saturation step returns minimal generators
• specialFiber(...,MinimalGenerators=>...) -- see reesIdeal(...,MinimalGenerators=>...) -- Whether the saturation step returns minimal generators
• specialFiberIdeal(...,MinimalGenerators=>...) -- see reesIdeal(...,MinimalGenerators=>...) -- Whether the saturation step returns minimal generators
• saturate(...,MinimalGenerators=>...) -- see saturate -- saturation of ideal or submodule
• sheafExt(ZZ,CoherentSheaf,CoherentSheaf,MinimalGenerators=>...) (missing documentation)
• sheafExt(ZZ,CoherentSheaf,SheafOfRings,MinimalGenerators=>...) (missing documentation)
• sheafExt(ZZ,SheafOfRings,CoherentSheaf,MinimalGenerators=>...) (missing documentation)
• sheafExt(ZZ,SheafOfRings,SheafOfRings,MinimalGenerators=>...) (missing documentation)
• sheafHom(...,MinimalGenerators=>...) (missing documentation)
• tangentSheaf(...,MinimalGenerators=>...) -- see tangentSheaf(ProjectiveVariety) -- tangent sheaf of a projective variety
• truncate(InfiniteNumber,Thing,MinimalGenerators=>...) (missing documentation)
• truncate(List,Ideal,MinimalGenerators=>...) (missing documentation)
• truncate(List,Matrix,MinimalGenerators=>...) -- see truncate(List,Matrix) -- truncation of a map of free modules
• truncate(List,Module,MinimalGenerators=>...) -- see truncate(List,Module) -- truncation of the graded ring, ideal or module at a specified degree or set of degrees
• truncate(List,Ring,MinimalGenerators=>...) (missing documentation)
• truncate(ZZ,Ideal,MinimalGenerators=>...) (missing documentation)
• truncate(ZZ,Matrix,MinimalGenerators=>...) (missing documentation)
• truncate(ZZ,Module,MinimalGenerators=>...) (missing documentation)
• truncate(ZZ,Ring,MinimalGenerators=>...) (missing documentation)