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

Further information

Default value: IntRing
Function: bFunction -- b-function
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
"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
bFunction(...,Strategy=>...) -- specify strategy for computing b-function
"mingens(...,Strategy=>...)" -- see Complement -- a Strategy option value
"trim(...,Strategy=>...)" -- see Complement -- a Strategy option value
deRham(...,Strategy=>...)
deRhamAll(...,Strategy=>...)
determinant(...,Strategy=>...) -- choose between Bareiss and Cofactor algorithms
DExt(...,Strategy=>...)
DHom(...,Strategy=>...)
DintegrateAll(...,Strategy=>...) (missing documentation)
DintegrateClasses(...,Strategy=>...) (missing documentation)
DintegrateComplex(...,Strategy=>...) (missing documentation)
DintegrateIdeal(...,Strategy=>...) (missing documentation)
Dintegration(...,Strategy=>...)
"Dintegrate(...,Strategy=>...)" -- see DintegrationIdeal(...,Strategy=>...)
"DintegrationAll(...,Strategy=>...)" -- see DintegrationIdeal(...,Strategy=>...)
"DintegrationClasses(...,Strategy=>...)" -- see DintegrationIdeal(...,Strategy=>...)
"DintegrationComplex(...,Strategy=>...)" -- see DintegrationIdeal(...,Strategy=>...)
DintegrationIdeal(...,Strategy=>...)
"Drestrict(...,Strategy=>...)" -- see 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=>...)
DlocalizationAll(...,Strategy=>...) (missing documentation)
DlocalizationMap(...,Strategy=>...) (missing documentation)
"Dlocalization(...,Strategy=>...)" -- see Dlocalize(...,Strategy=>...) -- strategy for computing a localization of a D-module
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
Dres(...,Strategy=>...) -- strategy for computing a resolution of a D-module
"Dresolution(...,Strategy=>...)" -- see Dres(...,Strategy=>...) -- strategy for computing a resolution of a D-module
DrestrictAll(...,Strategy=>...) (missing documentation)
DrestrictClasses(...,Strategy=>...) (missing documentation)
DrestrictComplex(...,Strategy=>...) (missing documentation)
DrestrictIdeal(...,Strategy=>...) (missing documentation)
"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)
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
hermite(...,Strategy=>...) (missing documentation)
"hooks(...,Strategy=>...)" -- see hooks -- list hooks attached to a key
ICcohom(...,Strategy=>...) (missing documentation)
"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
"isInMultiplierIdeal(...,Strategy=>...)" -- see isInMultiplierIdeal(RingElement,Ideal,QQ) -- multiplier ideal membership test
"isPrimary(...,Strategy=>...)" -- see isPrimary -- determine whether a submodule is primary
"isPrime(Ideal,Strategy=>...)" -- see isPrime(Ideal) -- whether an ideal is prime
lct(...,Strategy=>...) -- specify strategy for computing lct
LLL(...,Strategy=>...) -- choose among different algorithms
localCohom(...,Strategy=>...) -- specify strategy for local cohomology
"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
"jumpingCoefficients(...,Strategy=>...)" -- see multiplierIdeal(Ideal,QQ) -- multiplier ideal
"multiplierIdeal(...,Strategy=>...)" -- see multiplierIdeal(Ideal,QQ) -- multiplier ideal
PolyExt(...,Strategy=>...)
"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
RatExt(...,Strategy=>...)
"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=>...)
"primaryDecomposition(...,Strategy=>...)" -- see strategies for computing primary decomposition
"syz(...,Strategy=>...)" -- see syz(Matrix) -- compute the syzygy matrix
"tangentCone(...,Strategy=>...)" -- see tangentCone(Ideal)

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

Description

Further information

Functions with optional argument named Strategy :

Functions with optional argument named `Strategy` :