BernsteinSato : Table of Contents

• BernsteinSato -- algorithms for b-functions, local cohomology, and intersection cohomology
• Alg
• AnnFs -- differential annihilator of a polynomial in a Weyl algebra
• AnnIFs(Ideal,RingElement) -- the annihilating ideal of f^s for an arbitrary D-module
• BFunction -- a key in the hashtable created by Drestriction/Dintegration
• bFunction -- b-function
• bFunction(...,Strategy=>...) -- specify strategy for computing b-function
• bFunction(Ideal,List) -- b-function of an ideal
• bFunction(Module,List,List) -- b-function of a holonomic D-module
• bFunctionRoots(RingElement) -- get roots of a b-function
• Boperator -- a key attached by globalB and Dlocalize
• Boundaries -- a key in the hashtable created by Drestriction/Dintegration
• Bpolynomial -- a key attached by globalB
• CohomologyGroups -- a key in the hashtable created by deRham
• Cycles -- a key in the hashtable created by Drestriction/Dintegration
• Ddual -- holonomic dual of a D-module
• deRham -- deRham cohomology groups for the complement of a hypersurface
• deRham(...,Strategy=>...)
• deRhamAll(...,Strategy=>...)
• deRhamAll(RingElement) -- deRham complex for the complement of a hypersurface
• DExt -- Ext groups between holonomic modules
• DExt(...,Info=>...)
• DExt(...,Output=>...)
• DExt(...,Special=>...)
• DExt(...,Strategy=>...)
• DHom -- D-homomorphisms between holonomic D-modules
• DHom(...,Strategy=>...)
• diffRatFun -- derivative of a rational function in a Weyl algebra
• Dintegration -- integration modules of a D-module
• Dintegration(...,Strategy=>...)
• DintegrationAll -- integration modules of a D-module (extended version)
• DintegrationClasses -- integration classes of a D-module
• DintegrationComplex -- derived integration complex of a D-module
• DintegrationIdeal -- integration ideal of a D-module
• DintegrationIdeal(...,Strategy=>...)
• Dlocalize -- localization of a D-module
• Dlocalize(...,Strategy=>...) -- strategy for computing a localization of a D-module
• DlocalizeAll -- localization of a D-module (extended version)
• DlocalizeMap -- localization map from a D-module to its localization
• Dresolution -- resolution of a D-module
• Dresolution(...,LengthLimit=>...) -- the limit for the length of a resolution of a D-module
• Dresolution(...,Strategy=>...) -- strategy for computing a resolution of a D-module
• Drestriction -- restriction modules of a D-module
• DrestrictionAll -- restriction modules of a D-module (extended version)
• DrestrictionClasses -- restriction classes of a D-module
• DrestrictionComplex -- derived restriction complex of a D-module
• DrestrictionIdeal -- restriction ideal of a D-module
• Duality -- an option for polynomialSolutions=>Alg
• Explicit -- a key in the hashtable created by Drestriction/Dintegration
• Exponents -- a key in the hashtable created by Drestriction/Dintegration
• ExternalProduct -- external product of modules or complexes
• ExternalProduct(...,TwistMap=>...) -- indicates whether TwistMap should be computed
• factorBFunction(RingElement) -- factorization of a b-function
• GD -- an option for polynomialSolutions=>Alg
• GenCycles -- a key in the hashtable created by Drestriction/Dintegration
• generalB(...,Exponent=>...) -- specify exponent m for m-generalized Bernstein-Sato polynomial
• generalB(...,Strategy=>...) -- specify strategy for computing generalized Bernstein-Sato polynomial
• generalB(List,RingElement) -- global generalized Bernstein-Sato polynomial
• GeneralBernsteinSato -- a strategy option for lct, globalBFunction
• getIntRoots(RingElement) -- get integer roots of a b-function
• globalB(Ideal,RingElement) -- compute global b-function and b-operator for a D-module and a polynomial
• globalBFunction(...,Strategy=>...) -- specify strategy for computing global b-function
• globalBFunction(RingElement) -- global b-function (else known as the Bernstein-Sato polynomial)
• globalBoperator(RingElement) -- compute a b-operator of a polynomial
• hasRationalSing(List) -- check if a complete intersection has at most rational singularities
• HomologyModules -- a key in a hashtable; an option of DExt
• IHmodule -- intersection (co)homology module of an irreducible closed subvariety
• Info
• IntegrateComplex -- a key in the hashtable created by Dintegration
• intersectionCohomology -- intersection cohomology of an irreducible affine variety
• isInMultiplierIdeal(RingElement,Ideal,QQ) -- multiplier ideal membership test
• jumpingCoefficients(Ideal) -- jumping coefficients and corresponding multiplier ideals
• kappaAnnF1PlanarCurve -- D-annihilator of 1/f for a planar curve
• kOrderAnnFa -- k-th order D-annihilator of a power of a polynomial
• lct(...,Strategy=>...) -- specify strategy for computing lct
• lct(Ideal) -- compute the log canonical threshold for an ideal
• localBFunction(RingElement,Ideal) -- local b-function (a.k.a. the local Bernstein-Sato polynomial)
• localCohom -- local cohomology
• localCohom(...,LocStrategy=>...) -- specify localization strategy for local cohomology
• localCohom(...,Strategy=>...) -- specify strategy for local cohomology
• localCohom(Ideal) -- local cohomology of a polynomial ring
• localCohom(Ideal,Module) -- local cohomology of a D-module
• localCohom(List,Ideal) -- local cohomology of a polynomial ring
• localCohom(List,Ideal,Module) -- local cohomology of a D-module
• localCohom(ZZ,Ideal) -- local cohomology of a polynomial ring
• localCohom(ZZ,Ideal,Module) -- local cohomology of a D-module
• localizeCharacteristicCycle -- the characteristic cycle of the localized $D$-module
• LocalizeMap -- a key in the hashtable created by deRham
• LocStrategy
• logCohomology(RingElement) -- logarithmic cohomology groups in two variables
• multiplierIdeal(Ideal,QQ) -- multiplier ideal
• None -- an option for DExt=>Special
• OaTa -- an option for localCohom=>Strategy
• OaTaWa -- an option for localCohom => LocStrategy
• OmegaRes -- a key in the hashtable created by deRham
• Output
• paramBpoly(RingElement,File) -- compute the list of all possible Bernstein-Sato polynomials for a polynomial with parametric coefficients
• polynomialAnnihilator -- annihilator of a polynomial in the Weyl algebra
• polynomialExt -- Ext groups between a holonomic module and a polynomial ring
• polynomialExt(...,Strategy=>...)
• polynomialSolutions -- polynomial solutions of a holonomic system
• polynomialSolutions(...,Alg=>...) -- algorithm for finding polynomial solutions
• populateCechComplexCC(Ideal,List) -- Cech complex skeleton for the computation of the characteristic cycles of local cohomology modules
• PreCycles -- a key in the hashtable created by deRham
• projMap1 -- a key attached by ExternalProduct
• projMap2 -- a key attached by ExternalProduct
• pruneCechComplexCC(MutableHashTable) -- reduction of the Cech complex that produces characteristic cycles of local cohomology modules
• pruneLocalCohom(HashTable) -- prunes local cohomology modules
• rationalFunctionAnnihilator -- annihilator of a rational function in Weyl algebra
• rationalFunctionExt -- Ext(holonomic D-module, polynomial ring localized at the singular locus)
• rationalFunctionExt(...,Strategy=>...)
• rationalFunctionSolutions -- rational solutions of a holonomic system
• reiffen -- Reiffen's curve
• Schreyer -- strategy for computing a resolution of a D-module
• Special
• TransferCycles -- a key in the hashtable created by deRham
• twistInvMap -- a key attached by ExternalProduct
• TwistMap -- indicates whether TwistMap should be computed
• twistMap -- a key attached by ExternalProduct
• Vhomogenize -- strategy for computing a resolution of a D-module
• ViaBFunction -- a strategy option for lct
• ViaColonIdeal (missing documentation)
• ViaElimination (missing documentation)
• ViaLinearAlgebra -- an option for generalB=>Strategy
• VResolution -- a key in the hashtable created by Drestriction/Dintegration
• Walther -- an option for localCohom=>Strategy
• WeylClosure -- Weyl closure of an ideal