Dmodules : Table of Contents

• Dmodules -- algorithms for D-modules
• Alg
• AnnFs -- the annihilating ideal of f^s
• annFS -- a key created by Dlocalize
• AnnFs(List) -- the annihilating ideal of f_1^{s_1}...f_r^{s_r}
• AnnFs(RingElement) -- the annihilating ideal of f^s
• AnnG -- a key created by makeCyclic
• AnnIFs(Ideal,RingElement) -- the annihilating ideal of f^s for an arbitrary D-module
• AppellF1 -- Appell F1 system of PDE's
• BasisElts -- a key of the hashtable generated by diffOps
• BFunction -- a key in the hashtable created by Drestriction/Dintegration
• Bfunction -- a key created by Dlocalize
• 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
• BMM -- the characteristic cycle of the localized $D$-module
• Boperator -- a key attached by globalB and Dlocalize
• Boundaries -- a key in the hashtable created by Drestriction/Dintegration
• Bpolynomial -- a key attached by globalB
• Canonical Series Tutorial -- Computing series solutions to regular holonomic systems
• charIdeal -- characteristic ideal of a D-module
• CohomologyGroups -- a key in the hashtable created by deRham
• createDpairs(PolynomialRing) -- pairs up the variables in Weyl algebra
• cssExpts -- the exponents of the canonical series solutions of I in the direction of a weight vector
• cssExptsMult -- the exponents (and multiplicities) of the canonical series solutions of I in the direction of a weight vector
• Cycles -- a key in the hashtable created by Drestriction/Dintegration
• D-modules tutorial -- Algebraic computations for linear differential equations
• Ddim -- dimension of a D-module
• 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=>...)
• diffOps -- differential operators of up to the given order for a quotient polynomial ring
• Dintegrate -- Dintegrate* is an (OBSOLETE) abbreviation for Dintegration*
• 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=>...)
• distraction -- the image in the thetaRing of a torus-fixed ideal in a Weyl algebra
• Dlocalization -- Dlocalization* is an OBSOLETE name for Dlocalize*
• 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
• dpairInds -- a key attached by createDpairs
• dpairVars -- a key attached by createDpairs
• Dprune -- prunes a D-module
• Dprune(...,optGB=>...) -- indicates whether a Grobner basis should be computed
• Dres -- abbreviation for Dresolution
• Dres(...,LengthLimit=>...) -- the limit for the length of a resolution of a D-module
• Dres(...,Strategy=>...) -- strategy for computing a resolution of a D-module
• Dresolution -- resolution of a D-module
• Drestrict -- an (OBSOLETE) abbreviation for Drestriction
• 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
• Dtrace(ZZ) -- set the depth of comments made by D-module routines
• Dtransposition -- standard transposition for Weyl algebra
• Duality -- an option for PolySols=>Alg
• eulerOperators (missing documentation)
• 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
• extractDiffsAlgebra -- underlying polynomial ring in the differentials of a Weyl algebra
• extractVarsAlgebra -- underlying polynomial ring in the ordinary variables of a Weyl algebra
• factorBFunction(RingElement) -- factorization of a b-function
• Fourier -- Fourier transform for Weyl algebra
• FourierInverse -- Inverse Fourier map (D-modules)
• gbw -- Groebner bases w.r.t. a weight
• GD -- an option for PolySols=>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
• Generator -- a key created by makeCyclic
• GeneratorPower -- a key created by Dlocalize
• genToDistractionGens -- the image in the thetaRing of a torus-fixed element in a Weyl algebra
• getDtrace -- (internal) -- get the INFOLEVEL switch
• getHomSwitch -- (internal) -- get the HOMOGENIZATION switch
• getIntRoots(RingElement) -- get integer roots of a b-function
• gkz -- The A-hypergeometric systems of Gelfand, Kapranov and Zelevinsky (GKZ)
• 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
• GroundField
• hasRationalSing(List) -- check if a complete intersection has at most rational singularities
• holonomicRank -- rank of a D-module
• HomologyModules -- a key in a hashtable; an option of DExt
• ICcohom (missing documentation)
• ICmodule (missing documentation)
• indicialIdeal -- the image in the thetaRing of an indicial ideal in a Weyl algebra
• Info
• IntegrateBfunction -- a key created by Dlocalize
• IntegrateComplex -- a key in the hashtable created by Dintegration
• IntRing -- a strategy option for b-functions
• inw -- initial form/ideal w.r.t. a weight
• isHolonomic -- determines whether a D-module (or ideal in Weyl algebra) is holonomic
• isInMultiplierIdeal(RingElement,Ideal,QQ) -- multiplier ideal membership test
• isTorusFixed -- checks if an ideal in a Weyl algebra is torus-fixed
• 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
• LocalizeMap -- a key in the hashtable created by deRham
• LocCohomStrategy (missing documentation)
• LocMap -- a key created by Dlocalize
• LocModule -- a key created by Dlocalize
• LocStrategy
• logCohomology(RingElement) -- logarithmic cohomology groups in two variables
• makeCyclic -- finds a cyclic generator of a D-module
• makeWeylAlgebra -- Weyl algebra corresponding to a polynomial ring
• multiplierIdeal(Ideal,QQ) -- multiplier ideal
• None -- an option for DExt=>Special
• NonGeneric -- a strategy option for b-functions
• OaTa -- an option for localCohom=>Strategy
• OaTaWa -- an option for localCohom => LocStrategy
• OmegaRes -- a key in the hashtable created by deRham
• Output
• paramBpoly(...,GroundField=>...) -- characteristic for modular computation
• paramBpoly(RingElement,String) -- compute the list of all possible Bernstein-Sato polynomials for a polynomial with parametric coefficients
• pInfo -- prints tracing info
• PolyAnn -- annihilator of a polynomial in the Weyl algebra
• PolyExt -- Ext groups between a holonomic module and a polynomial ring
• PolyExt(...,Strategy=>...)
• PolyGens -- a key of the hashtable generated by diffOps
• PolySols -- polynomial solutions of a holonomic system
• PolySols(...,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
• putWeylAlgebra(HashTable) -- transforms output of diffOps into elements of Weyl algebra
• RatAnn -- annihilator of a rational function in Weyl algebra
• RatExt -- Ext(holonomic D-module, polynomial ring localized at the singular locus)
• RatExt(...,Strategy=>...)
• RatSols -- rational solutions of a holonomic system
• ReducedB -- a strategy option for global b-functions
• reiffen -- Reiffen's curve
• Schreyer -- strategy for computing a resolution of a D-module
• setHomSwitch(Boolean) -- toggles the use of homogeneous Weyl algebra
• SetVariables -- name for an optional argument
• singLocus -- singular locus of a D-module
• solveFrobeniusIdeal -- solving Frobenius ideals
• Special
• stafford -- computes 2 generators for a given ideal in the Weyl algebra
• toricIdealPartials (missing documentation)
• TransferCycles -- a key in the hashtable created by deRham
• TryGeneric -- a strategy option for b-functions
• twistInvMap -- a key attached by ExternalProduct
• TwistMap -- indicates whether TwistMap should be computed
• twistMap -- a key attached by ExternalProduct
• Vars
• Vhomogenize -- strategy for computing a resolution of a D-module
• ViaAnnFs -- a strategy option for global b-functions
• 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