bFunction(...,Strategy=>...) -- specify strategy for computing b-function
Description
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IntRing -- the simplest algorithm available. The idea is to compute in(-w,w)(I) intersect it with k[t1,...,tn](ti = xiDi)Call the ideal obtained J. Finally J + (t1 + ... + tn- s) \cap k[s] is generated by the b-function that we are looking for.
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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
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NonGeneric -- uses 5.1.6 in Saito-Sturmfels-Takayama (1999)
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Default:IntRing
Functions with optional argument named Strategy :
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addHook(...,Strategy=>...) -- see addHook -- add a hook function to an object for later processing
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adjoint(...,Strategy=>...) (missing documentation)
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annihilator(...,Strategy=>...) -- see annihilator -- the annihilator ideal
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associatedPrimes(...,Strategy=>...) -- see associatedPrimes -- find associated primes
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basis(...,Strategy=>...) -- see basis -- basis or generating set of all or part of a ring, ideal or module
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bFunction(...,Strategy=>...) -- specify strategy for computing b-function
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canonicalBundle(...,Strategy=>...) (missing documentation)
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mingens(...,Strategy=>...) -- see Complement -- a Strategy option value
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trim(...,Strategy=>...) -- see Complement -- a Strategy option value
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compose(Module,Module,Module,Strategy=>...) -- see compose -- composition as a pairing on Hom-modules
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cotangentSheaf(...,Strategy=>...) (missing documentation)
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deRham(...,Strategy=>...)
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deRhamAll(...,Strategy=>...)
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determinant(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
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DExt(...,Strategy=>...)
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DHom(...,Strategy=>...)
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Dintegration(...,Strategy=>...)
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DintegrationAll(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
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DintegrationClasses(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
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DintegrationComplex(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
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DintegrationIdeal(...,Strategy=>...)
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Drestriction(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
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DrestrictionAll(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
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DrestrictionClasses(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
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DrestrictionComplex(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
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DrestrictionIdeal(...,Strategy=>...) -- see DintegrationIdeal(...,Strategy=>...)
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Dlocalize(...,Strategy=>...) -- strategy for computing a localization of a D-module
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DlocalizeAll(...,Strategy=>...) -- see Dlocalize(...,Strategy=>...) -- strategy for computing a localization of a D-module
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DlocalizeMap(...,Strategy=>...) -- see Dlocalize(...,Strategy=>...) -- strategy for computing a localization of a D-module
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Dresolution(...,Strategy=>...) -- strategy for computing a resolution of a D-module
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dual(ChainComplex,Strategy=>...) (missing documentation)
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dual(Matrix,Strategy=>...) (missing documentation)
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dual(MonomialIdeal,List,Strategy=>...) -- see dual(MonomialIdeal,Strategy=>...)
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dual(MonomialIdeal,RingElement,Strategy=>...) -- see dual(MonomialIdeal,Strategy=>...)
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dual(MonomialIdeal,Strategy=>...)
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dual(SheafMap,Strategy=>...) (missing documentation)
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End(...,Strategy=>...) -- see End -- module of endomorphisms
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exteriorPower(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
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gb(...,Strategy=>...) -- see gb -- compute a Gröbner basis
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gbw(...,Strategy=>...) -- see gbw -- compute a Gröbner basis with respect to a weight vector
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gcdLLL(...,Strategy=>...) (missing documentation)
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generalB(...,Strategy=>...) -- specify strategy for computing generalized Bernstein-Sato polynomial
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GF(...,Strategy=>...) -- see GF -- make a finite field
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globalBFunction(...,Strategy=>...) -- specify strategy for computing global b-function
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groebnerBasis(...,Strategy=>...) -- see groebnerBasis -- Gröbner basis, as a matrix
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hermite(...,Strategy=>...) (missing documentation)
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Hom(...,Strategy=>...) -- see Hom -- module of homomorphisms
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homomorphism'(...,Strategy=>...) -- see homomorphism' -- get the element of Hom from a homomorphism
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hooks(...,Strategy=>...) -- see hooks -- list hooks attached to a key
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idealizer(...,Strategy=>...) -- see idealizer -- compute Hom(I,I) as a quotient ring
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integralClosure(...,Strategy=>...) -- control the algorithm used
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intersect(Ideal,Ideal,Strategy=>...) -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
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intersect(Module,Module,Strategy=>...) -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
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intersectInP(...,Strategy=>...) -- see intersectInP(...,BasisElementLimit=>...) -- Option for intersectInP
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intersectionCohomology(...,Strategy=>...) -- see intersectionCohomology -- intersection cohomology of an irreducible affine variety
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isInMultiplierIdeal(...,Strategy=>...) -- see isInMultiplierIdeal(RingElement,Ideal,QQ) -- multiplier ideal membership test
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isPrimary(...,Strategy=>...) -- see isPrimary -- determine whether a submodule is primary
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isPrime(Ideal,Strategy=>...) -- see isPrime(Ideal) -- whether an ideal is prime
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lct(...,Strategy=>...) -- specify strategy for computing lct
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LLL(...,Strategy=>...) -- choose among different algorithms
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localCohom(...,Strategy=>...) -- specify strategy for local cohomology
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localize(...,Strategy=>...) -- see localize -- localize an ideal at a prime ideal
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match(...,Strategy=>...) -- see match -- regular expression matching
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decompose(Ideal,Strategy=>...) -- see minimalPrimes -- minimal primes of an ideal
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minimalPrimes(...,Strategy=>...) -- see minimalPrimes -- minimal primes of an ideal
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minors(...,Strategy=>...) -- choose between Bareiss, Cofactor and Dynamic algorithms
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jumpingCoefficients(...,Strategy=>...) -- see multiplierIdeal(Ideal,QQ) -- multiplier ideal
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multiplierIdeal(...,Strategy=>...) -- see multiplierIdeal(Ideal,QQ) -- multiplier ideal
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parallelApply(...,Strategy=>...) -- see parallelApply -- apply a function to each element in parallel
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polynomialExt(...,Strategy=>...)
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primaryComponent(...,Strategy=>...) -- see primaryComponent -- find a primary component corresponding to an associated prime
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pushForward(...,Strategy=>...) (missing documentation)
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quotient(...,Strategy=>...)
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radical(...,Strategy=>...) -- see radical -- the radical of an ideal
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radicalContainment(...,Strategy=>...) -- see radicalContainment -- whether an element is contained in the radical of an ideal
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rationalFunctionExt(...,Strategy=>...)
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analyticSpread(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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distinguished(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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isLinearType(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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isReduction(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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minimalReduction(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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multiplicity(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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normalCone(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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reesAlgebra(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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specialFiber(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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specialFiberIdeal(...,Strategy=>...) -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
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regSeqInIdeal(...,Strategy=>...) -- see regSeqInIdeal -- a regular sequence contained in an ideal
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resolution(...,Strategy=>...)
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saturate(...,Strategy=>...)
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sheafHom(...,Strategy=>...) (missing documentation)
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primaryDecomposition(...,Strategy=>...) -- see strategies for computing primary decomposition
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syz(...,Strategy=>...) -- see syz(Matrix) -- compute the syzygy matrix
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tangentCone(...,Strategy=>...) -- see tangentCone(Ideal)
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tangentSheaf(...,Strategy=>...) (missing documentation)