resolution(...,Strategy=>...)

Description

Strategy => n -- an option for resolution which specifies which algorithm to use. Strategies are specified by number and the algorithms available are

Strategy => 0 -- Compute syzygies on the Gröbner bases of each syzygy module. The algorithm uses important speedups due to R. La Scala. This algorithm appears to be on the average the fastest.
Strategy => 1 -- An older version of algorithm 0, which doesn't allow as much experimentation, but can sometimes be marginally faster.
Strategy => 2 -- Compute syzygies on the minimal generators of each matrix in the resolution. Over quotient rings, it's preferred.
Strategy => 3 -- Same as algorithm 2, but compute those Hilbert functions which allow removal of S-pairs (a la Robbiano, et al.). Sometimes this improvement can be very dramatic.

All algorithms use induced monomial orders (Schreyer orders), since this makes an enormous improvement to the efficiency of the algorithm.

Functions with optional argument named Strategy:

addHook(...,Strategy=>...) -- see addHook -- add a hook function to an object for later processing
annihilator(...,Strategy=>...)
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(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
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=>...)
resolution(...,Strategy=>...)
saturate(...,Strategy=>...)
syz(...,Strategy=>...) -- see syz(Matrix) -- compute the syzygy matrix

Further information

Default value: null
Function: resolution -- projective resolution
Option key: Strategy -- an optional argument

The source of this document is in OldChainComplexes/docs/doc10.m2:145:0.