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

## Synopsis

• 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.

## Further information

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

## Functions with optional argument named Strategy :

• "annihilator(...,Strategy=>...)" -- see annihilator -- the annihilator ideal
• "associatedPrimes(...,Strategy=>...)" -- see associatedPrimes -- find associated primes
• "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
• determinant(...,Strategy=>...) -- choose between Bareiss and Cofactor algorithms
• "dual(MonomialIdeal,List,Strategy=>...)" -- see dual(MonomialIdeal,Strategy=>...)
• "dual(MonomialIdeal,RingElement,Strategy=>...)" -- see dual(MonomialIdeal,Strategy=>...)
• dual(MonomialIdeal,Strategy=>...)
• exteriorPower(...,Strategy=>...) -- choose between Bareiss and Cofactor algorithms
• "gb(...,Strategy=>...)" -- see gb -- compute a Gröbner basis
• gcdLLL(...,Strategy=>...) (missing documentation)
• "GF(...,Strategy=>...)" -- see GF -- make a finite field
• "groebnerBasis(...,Strategy=>...)" -- see groebnerBasis -- Gröbner basis, as a matrix
• hermite(...,Strategy=>...) (missing documentation)
• "hooks(...,Strategy=>...)" -- see hooks -- list hooks attached to a key
• "idealizer(...,Strategy=>...)" -- see idealizer -- compute Hom(I,I) as a quotient ring
• integralClosure(...,Strategy=>...) -- control the algorithm used
• "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
• "isPrimary(...,Strategy=>...)" -- see isPrimary -- determine whether a submodule is primary
• "isPrime(Ideal,Strategy=>...)" -- see isPrime(Ideal) -- whether an ideal is prime
• LLL(...,Strategy=>...) -- choose among different algorithms
• "localize(...,Strategy=>...)" -- see localize -- localize an ideal at a prime ideal
• "match(...,Strategy=>...)" -- see match -- regular expression matching
• "decompose(Ideal,Strategy=>...)" -- see minimalPrimes -- minimal primes of an ideal
• "minimalPrimes(...,Strategy=>...)" -- see minimalPrimes -- minimal primes of an ideal
• minors(...,Strategy=>...) -- choose between Bareiss and Cofactor algorithms
• "primaryComponent(...,Strategy=>...)" -- see primaryComponent -- find a primary component corresponding to an associated prime
• pushForward(...,Strategy=>...) (missing documentation)
• quotient(...,Strategy=>...)
• "radicalContainment(...,Strategy=>...)" -- see radicalContainment -- whether an element is contained in the radical of an ideal
• "distinguished(...,Strategy=>...)"
• "isLinearType(...,Strategy=>...)"
• "isReduction(...,Strategy=>...)"
• "minimalReduction(...,Strategy=>...)"
• "multiplicity(...,Strategy=>...)"
• "normalCone(...,Strategy=>...)"
• "reesAlgebra(...,Strategy=>...)"
• reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "specialFiber(...,Strategy=>...)"
• "specialFiberIdeal(...,Strategy=>...)"
• "regSeqInIdeal(...,Strategy=>...)" -- see regSeqInIdeal -- a regular sequence contained in an ideal
• resolution(...,Strategy=>...)
• saturate(...,Strategy=>...)
• "primaryDecomposition(...,Strategy=>...)" -- see strategies for computing primary decomposition
• "syz(...,Strategy=>...)" -- see syz(Matrix) -- compute the syzygy matrix
• "tangentCone(...,Strategy=>...)" -- see tangentCone(Ideal)