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# reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step

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

## Description

where X is is one of Iterate, Linear, Bayer, Eliminate. These are described in the documentation node for saturate.

The Rees algebra S(M) of a submodule M of a free module (most importantly, an ideal in the ring), is equal to the symmetric algebra Sym_k(M) mod torsion. computing this torsion is the slow link in most of the programs in this package. The fastest way to compute it is usually by saturating the ideal defining the symmetric algebra with respect to an element in that ideal.

## 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 Strategy:

- `addHook(...,Strategy=>...)` -- see addHook -- add a hook function to an object for later processing
- `annihilator(...,Strategy=>...)` -- see annihilator -- the annihilator ideal
- `basis(...,Strategy=>...)` -- see basis -- basis or generating set of all or part of a ring, ideal or module
- `mingens(...,Strategy=>...)` -- see Complement -- a Strategy option value
- `trim(...,Strategy=>...)` -- see Complement -- a Strategy option value
- `compose(Module,Module,Module,Strategy=>...)` -- see compose -- composition as a pairing on Hom-modules
- decompose(Ideal,Strategy=>...)
- determinant(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
- `dual(MonomialIdeal,List,Strategy=>...)` -- see dual(MonomialIdeal,Strategy=>...)
- `dual(MonomialIdeal,RingElement,Strategy=>...)` -- see dual(MonomialIdeal,Strategy=>...)
- dual(MonomialIdeal,Strategy=>...)
- `End(...,Strategy=>...)` -- see End -- module of endomorphisms
- exteriorPower(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
- `gb(...,Strategy=>...)` -- see gb -- compute a Gröbner basis
- `GF(...,Strategy=>...)` -- see GF -- make a finite field
- `groebnerBasis(...,Strategy=>...)` -- see groebnerBasis -- Gröbner basis, as a matrix
- `Hom(...,Strategy=>...)` -- see Hom -- module of homomorphisms
- `homomorphism'(...,Strategy=>...)` -- see homomorphism' -- get the element of Hom from a homomorphism
- `hooks(...,Strategy=>...)` -- see hooks -- list hooks attached to a key
- `intersect(Ideal,Ideal,Strategy=>...)` -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
- `intersect(Module,Module,Strategy=>...)` -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
- `intersectInP(...,Strategy=>...)` -- see intersectInP(...,BasisElementLimit=>...) -- Option for intersectInP
- isPrime(Ideal,Strategy=>...)
- `match(...,Strategy=>...)` -- see match -- regular expression matching
- minors(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
- `parallelApply(...,Strategy=>...)` -- see parallelApply -- apply a function to each element in parallel
- `pushForward(...,Strategy=>...)` -- see pushForward(RingMap,Module) -- compute the pushforward of a module along a ring map
- quotient'(...,Strategy=>...) (missing documentation)
- quotient(...,Strategy=>...)
- `analyticSpread(...,Strategy=>...)`
- `associatedGradedRing(...,Strategy=>...)`
- `distinguished(...,Strategy=>...)`
- `isLinearType(...,Strategy=>...)`
- `isReduction(...,Strategy=>...)`
- `minimalReduction(...,Strategy=>...)`
- `multiplicity(...,Strategy=>...)`
- `normalCone(Ideal,RingElement,Strategy=>...)`
- `normalCone(Ideal,Strategy=>...)`
- `reesAlgebra(...,Strategy=>...)`
- reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
- `specialFiber(...,Strategy=>...)`
- `specialFiberIdeal(...,Strategy=>...)`
- saturate(...,Strategy=>...)
- `syz(...,Strategy=>...)` -- see syz(Matrix) -- compute the syzygy matrix

## Further information

- Default value: null
- Function: reesIdeal -- Compute the defining ideal of the Rees Algebra
- Option key: Strategy -- an optional argument

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/ReesAlgebra.m2:2023:0.