Macaulay2 » Documentation
Packages » Saturation :: saturate(...,Strategy=>...)

Description

Iterate

saturate(I,J,Strategy => Iterate) -- indicates that successive ideal or module quotients should be used.

This value is the default.

Linear

saturate(I,J,Strategy => Linear)Strategy => Linear -- indicates that the reverse lex order should be used to compute the saturation.

This presumes that J is a single, linear polynomial, and that I is homogeneous.

Bayer

saturate(I,f,Strategy => Bayer) -- indicates that the method of Bayer's thesis should be used.

The method is to compute (I:f) for I and f homogeneous, add a new variable z, compute a Gröbner basis of (I,f-z) in reverse lex order, divide by z, and finally replace z by f.

Eliminate

saturate(I,f,Strategy => Eliminate) -- indicates that the saturation (I:f) should be computed by eliminating fz from (I,f*z-1), where z is a new variable.

Further information

• Default value: null
• Function: saturate -- saturation of ideal or submodule
• Option key: Strategy -- an optional argument

Functions with optional argument named Strategy :

• addHook(...,Strategy=>...) -- see addHook -- add a hook function to an object for later processing
• adjoint(...,Strategy=>...) (missing documentation)
• 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
• determinant(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
• dual(ChainComplex,Strategy=>...) (missing documentation)
• dual(Matrix,Strategy=>...) (missing documentation)
• 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
• match(...,Strategy=>...) -- see match -- regular expression matching
• minors(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
• pushForward(...,Strategy=>...) (missing documentation)
• quotient(...,Strategy=>...)
• resolution(...,Strategy=>...)
• saturate(...,Strategy=>...)
• syz(...,Strategy=>...) -- see syz(Matrix) -- compute the syzygy matrix