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 0.0455416 seconds

             1       428
o8 : Matrix R  <--- R

i9 : time J1 = saturate(I);
     -- used 0.448459 seconds

o9 : Ideal of R

i10 : time J = saturate(I, MinimalGenerators => false);
     -- used 0.000134482 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 :

• "associatedPrimes(...,MinimalGenerators=>...)" -- see associatedPrimes -- find associated primes
• "intersect(...,MinimalGenerators=>...)" -- see intersect(List) -- compute an intersection 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 (missing documentation) -- saturation of ideal or submodule