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

Description

The following returns two minimal generators (Serre's Theorem: a codim 2 Gorenstein ideal is a complete intersection.)

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

Without trimming we would get 4 generators instead.

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

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

o4 : Ideal of S

Sometimes the extra time to find the minimal generators is too large. This allows one to bypass this part of the computation.

i5 : needsPackage "Truncations"

o5 = Truncations

o5 : Package

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

o6 = R

o6 : PolynomialRing

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

o7 : Ideal of R

i8 : time J = truncate(8, I, MinimalGenerators => false);
 -- used 0.00419647s (cpu); 0.00419569s (thread); 0s (gc)

o8 : Ideal of R

i9 : time K = truncate(8, I, MinimalGenerators => true);
 -- used 0.176723s (cpu); 0.176726s (thread); 0s (gc)

o9 : Ideal of R

i10 : numgens J

o10 = 1067

i11 : numgens K

o11 = 428

Functions with optional argument named MinimalGenerators:

compose(Module,Module,Module,MinimalGenerators=>...) -- see compose -- composition as a pairing on Hom-modules
decompose(Ideal,MinimalGenerators=>...)
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
normalCone(Ideal,MinimalGenerators=>...)
normalCone(Ideal,RingElement,MinimalGenerators=>...)
quotient'(...,MinimalGenerators=>...) (missing documentation)
quotient(...,MinimalGenerators=>...)
saturate(...,MinimalGenerators=>...) -- see saturate -- saturation of ideal or submodule
truncate(InfiniteNumber,InfiniteNumber,Matrix,MinimalGenerators=>...) (missing documentation)
truncate(InfiniteNumber,Thing,MinimalGenerators=>...) (missing documentation)
truncate(List,Ideal,MinimalGenerators=>...)
truncate(List,List,Matrix,MinimalGenerators=>...) (missing documentation)
truncate(List,Matrix,MinimalGenerators=>...)
truncate(List,Module,MinimalGenerators=>...)
truncate(List,Ring,MinimalGenerators=>...)
truncate(Nothing,InfiniteNumber,Matrix,MinimalGenerators=>...) (missing documentation)
truncate(Nothing,List,Matrix,MinimalGenerators=>...) (missing documentation)
truncate(Nothing,ZZ,Matrix,MinimalGenerators=>...) (missing documentation)
truncate(ZZ,Ideal,MinimalGenerators=>...)
truncate(ZZ,Matrix,MinimalGenerators=>...)
truncate(ZZ,Module,MinimalGenerators=>...)
truncate(ZZ,Ring,MinimalGenerators=>...)
truncate(ZZ,ZZ,Matrix,MinimalGenerators=>...) (missing documentation)

For the programmer

The object MinimalGenerators is a symbol.

The source of this document is in Macaulay2Doc/functions/trim-doc.m2:84:0.

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

Description

See also

Functions with optional argument named MinimalGenerators:

For the programmer