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# minimalReduction(...,BasisElementLimit=>...) -- Bound the number of Groebner basis elements to compute in the saturation step

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

## Description

Here X is a positive integer. Each of these functions computes the Rees Algebra using a saturation step, and the optional argument causes the saturation process to stop after that number of s-pairs is found. 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 BasisElementLimit:

- `gb(...,BasisElementLimit=>...)` -- see gb -- compute a Gröbner basis
- intersectInP(...,BasisElementLimit=>...) -- Option for intersectInP
- `analyticSpread(...,BasisElementLimit=>...)`
- `associatedGradedRing(...,BasisElementLimit=>...)`
- `distinguished(...,BasisElementLimit=>...)`
- `isLinearType(...,BasisElementLimit=>...)`
- `isReduction(...,BasisElementLimit=>...)`
- minimalReduction(...,BasisElementLimit=>...) -- Bound the number of Groebner basis elements to compute in the saturation step
- `multiplicity(...,BasisElementLimit=>...)`
- `normalCone(Ideal,BasisElementLimit=>...)`
- `normalCone(Ideal,RingElement,BasisElementLimit=>...)`
- `reesAlgebra(...,BasisElementLimit=>...)`
- `reesIdeal(...,BasisElementLimit=>...)`
- `specialFiber(...,BasisElementLimit=>...)`
- `specialFiberIdeal(...,BasisElementLimit=>...)`
- quotient(...,BasisElementLimit=>...)
- saturate(...,BasisElementLimit=>...)
- `syz(...,BasisElementLimit=>...)` -- see syz(Matrix) -- compute the syzygy matrix

## Further information

- Default value: infinity
- Function: minimalReduction -- Find a minimal reduction of an ideal
- Option key: BasisElementLimit -- an optional argument

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/ReesAlgebra.m2:2141:0.