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.

Further information

Default value: null
Function: resolution -- projective resolution
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
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
canonicalBundle(...,Strategy=>...) (missing documentation)
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
cotangentSheaf(...,Strategy=>...) (missing documentation)
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=>...)
dual(SheafMap,Strategy=>...) (missing documentation)
End(...,Strategy=>...) -- see End -- module of endomorphisms
exteriorPower(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic 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)
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
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, Cofactor and Dynamic algorithms
primaryComponent(...,Strategy=>...) -- see primaryComponent -- find a primary component corresponding to an associated prime
pushForward(...,Strategy=>...) (missing documentation)
quotient(...,Strategy=>...)
radical(...,Strategy=>...) -- see radical -- the radical of an ideal
radicalContainment(...,Strategy=>...) -- see radicalContainment -- whether an element is contained in the radical of an ideal
analyticSpread(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
distinguished(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
isLinearType(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
isReduction(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
minimalReduction(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
multiplicity(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
normalCone(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
reesAlgebra(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
specialFiber(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
specialFiberIdeal(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
regSeqInIdeal(...,Strategy=>...) -- see regSeqInIdeal -- a regular sequence contained in an ideal
resolution(...,Strategy=>...)
saturate(...,Strategy=>...)
sheafHom(...,Strategy=>...) (missing documentation)
primaryDecomposition(...,Strategy=>...) -- see strategies for computing primary decomposition
syz(...,Strategy=>...) -- see syz(Matrix) -- compute the syzygy matrix
tangentCone(...,Strategy=>...) -- see tangentCone(Ideal)
tangentSheaf(...,Strategy=>...) (missing documentation)