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# reesIdeal(...,MinimalGenerators=>...) -- Whether the saturation step returns minimal generators

- Usage:
    `reesIdeal(...,MinimalGenerators => X)`

## Description

Here X is of type boolean. Each of these functions involves the computation of a Rees algebra, which may involve a saturation step. This optional argument determines whether or not the output of the saturation step will be forced to have a minimal generating set. This is described in the documentation node for saturate.

## See also

- reesIdeal -- Compute the defining ideal of the Rees Algebra
- reesAlgebra -- Compute the defining ideal of the Rees Algebra
- isLinearType -- Determine whether module has linear type
- isReduction -- Determine whether an ideal is a reduction
- associatedGradedRing -- The normal cone of a subscheme
- multiplicity -- Compute the Hilbert-Samuel multiplicity of an ideal
- specialFiberIdeal -- Special fiber of a blowup
- specialFiber -- Special fiber of a blowup
- analyticSpread -- Compute the analytic spread of a module or ideal
- distinguished -- Compute the distinguished subvarieties of a pullback, intersection or cone
- minimalReduction -- Find a minimal reduction of an ideal
- saturate

## 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
- `intersectInP(...,MinimalGenerators=>...)` -- see intersectInP(...,BasisElementLimit=>...) -- Option for intersectInP
- quotient'(...,MinimalGenerators=>...) (missing documentation)
- quotient(...,MinimalGenerators=>...)
- `analyticSpread(...,MinimalGenerators=>...)`
- `associatedGradedRing(...,MinimalGenerators=>...)`
- `distinguished(...,MinimalGenerators=>...)`
- `isLinearType(...,MinimalGenerators=>...)`
- `isReduction(...,MinimalGenerators=>...)`
- `minimalReduction(...,MinimalGenerators=>...)`
- `multiplicity(...,MinimalGenerators=>...)`
- `normalCone(Ideal,MinimalGenerators=>...)`
- `normalCone(Ideal,RingElement,MinimalGenerators=>...)`
- `reesAlgebra(...,MinimalGenerators=>...)`
- reesIdeal(...,MinimalGenerators=>...) -- Whether the saturation step returns minimal generators
- `specialFiber(...,MinimalGenerators=>...)`
- `specialFiberIdeal(...,MinimalGenerators=>...)`
- saturate(...,MinimalGenerators=>...)
- truncate(InfiniteNumber,InfiniteNumber,Matrix,MinimalGenerators=>...) (missing documentation)
- truncate(InfiniteNumber,Thing,MinimalGenerators=>...) (missing documentation)
- truncate(List,Ideal,MinimalGenerators=>...) (missing documentation)
- truncate(List,List,Matrix,MinimalGenerators=>...) (missing documentation)
- truncate(List,Matrix,MinimalGenerators=>...) (missing documentation)
- truncate(List,Module,MinimalGenerators=>...) (missing documentation)
- truncate(List,Ring,MinimalGenerators=>...) (missing documentation)
- 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=>...) (missing documentation)
- truncate(ZZ,Matrix,MinimalGenerators=>...) (missing documentation)
- truncate(ZZ,Module,MinimalGenerators=>...) (missing documentation)
- truncate(ZZ,Ring,MinimalGenerators=>...) (missing documentation)
- truncate(ZZ,ZZ,Matrix,MinimalGenerators=>...) (missing documentation)

## Further information

- Default value: true
- Function: reesIdeal -- Compute the defining ideal of the Rees Algebra
- Option key: MinimalGenerators -- whether to compute minimal generators and return a trimmed set of generators

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/ReesAlgebra.m2:2102:0.