bFunction(...,Strategy=>...) -- specify strategy for computing b-function

Description

IntRing -- the simplest algorithm available. The idea is to compute in_(-w,w)(I) intersect it with k[t₁,...,t_n](t_i = x_iD_i)Call the ideal obtained J. Finally J + (t₁ + ... + t_n- s) \cap k[s] is generated by the b-function that we are looking for.
TryGeneric -- checks whether the ideal is generic and if that is the case uses Alg.5.1.5 in Saito-Sturmfels-Takayama (1999) otherwise is equivalent to NonGeneric
NonGeneric -- uses 5.1.6 in Saito-Sturmfels-Takayama (1999)
Default:IntRing

Functions with optional argument named Strategy:

addHook(...,Strategy=>...) -- see addHook -- add a hook function to an object for later processing
annihilator(...,Strategy=>...) (missing documentation)
basis(...,Strategy=>...) -- see basis -- basis or generating set of all or part of a ring, ideal or module
bFunction(...,Strategy=>...) -- specify strategy for computing b-function
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=>...) (missing documentation)
deRham(...,Strategy=>...)
deRhamAll(...,Strategy=>...)
determinant(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
DExt(...,Strategy=>...)
DHom(...,Strategy=>...)
Dintegration(...,Strategy=>...)
DintegrationAll(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
DintegrationClasses(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
DintegrationComplex(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
DintegrationIdeal(...,Strategy=>...)
Drestriction(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
DrestrictionAll(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
DrestrictionClasses(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
DrestrictionComplex(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
DrestrictionIdeal(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
Dlocalize(...,Strategy=>...) -- strategy for computing a localization of a D-module
DlocalizeAll(...,Strategy=>...) -- see Dlocalize(...,Strategy=>...) -- strategy for computing a localization of a D-module
DlocalizeMap(...,Strategy=>...) -- see Dlocalize(...,Strategy=>...) -- strategy for computing a localization of a D-module
Dresolution(...,Strategy=>...) -- strategy for computing a resolution of a D-module
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
gbw(...,Strategy=>...) -- see gbw -- compute a Gröbner basis with respect to a weight vector
generalB(...,Strategy=>...) -- specify strategy for computing generalized Bernstein-Sato polynomial
GF(...,Strategy=>...) -- see GF -- make a finite field
globalBFunction(...,Strategy=>...) -- specify strategy for computing global b-function
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
intersectionCohomology(...,Strategy=>...) -- see intersectionCohomology -- intersection cohomology of an irreducible affine variety
isInMultiplierIdeal(...,Strategy=>...) -- see isInMultiplierIdeal(RingElement,Ideal,QQ) -- multiplier ideal membership test
isPrime(Ideal,Strategy=>...) (missing documentation)
lct(...,Strategy=>...) -- specify strategy for computing lct
localCohom(...,Strategy=>...) -- specify strategy for local cohomology
match(...,Strategy=>...) -- see match -- regular expression matching
minors(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
jumpingCoefficients(...,Strategy=>...) -- see multiplierIdeal(Ideal,QQ) -- multiplier ideal
multiplierIdeal(...,Strategy=>...) -- see multiplierIdeal(Ideal,QQ) -- multiplier ideal
normalCone(Ideal,RingElement,Strategy=>...) (missing documentation)
normalCone(Ideal,Strategy=>...) (missing documentation)
parallelApply(...,Strategy=>...) -- see parallelApply -- apply a function to each element in parallel
polynomialExt(...,Strategy=>...)
pushForward(...,Strategy=>...) -- see pushForward(RingMap,Module) -- compute the pushforward of a module along a ring map
quotient'(...,Strategy=>...) (missing documentation)
quotient(...,Strategy=>...) (missing documentation)
rationalFunctionExt(...,Strategy=>...)
resolution(...,Strategy=>...)
saturate(...,Strategy=>...) (missing documentation)
syz(...,Strategy=>...) -- see syz(Matrix) -- compute the syzygy matrix

Further information

Default value: IntRing
Function: bFunction -- b-function
Option key: Strategy -- an optional argument

The source of this document is in BernsteinSato/DOC/bFunctions.m2:41:0.