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(..., Vars => ...)
- AppellF1(List) -- 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
- 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
- Cycles -- a key in the hashtable created by Drestriction/Dintegration
- 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 => ...)
- 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 matrix over a Weyl algebra
- Dprune(..., optGB => ...) -- indicates whether Grobner basis should be computed
- Drank -- an old name of holonomicRank
- 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
- 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
- Fourier -- Fourier transform for Weyl algebra
- FourierInverse -- Inverse Fourier map (D-modules)
- gbw -- Groebner basis 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
- getDtrace -- (internal) -- get the INFOLEVEL switch
- getHomSwitch -- (internal) -- get the HOMOGENIZATION switch
- getIntRoots(RingElement) -- get integer roots of a b-function
- gkz -- GKZ A-hypergeometric ideal
- gkz(..., Vars => ...)
- 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
- 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
- jumpingCoefficients(Ideal) -- jumping coefficients and corresponding multiplier ideals
- 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
- LocMap -- a key created by Dlocalize
- LocModule -- a key created by Dlocalize
- LocStrategy
- logCohomology(RingElement) -- logarithmic cohomology groups in two variables
- makeCyclic(Matrix) -- finds a cyclic generator of a D-module
- makeWeylAlgebra(PolynomialRing) -- 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
- Oaku -- an option for Dlocalize=>Strategy
- OaTa -- an option for localCohom=>Strategy
- OaTaWa -- an option for localCohom => LocStrategy
- OmegaRes -- a key in the hashtable created by deRham
- optGB -- indicates whether Grobner basis should be computed
- OTW -- an option for Dlocalize=>Strategy
- 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(RingElement) -- annihilator of a polynomial in 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 sigular locus)
- RatExt(..., Strategy => ...)
- RatSols -- rational solutions of a holonomic system
- ReducedB -- a strategy option for global b-functions
- 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
- Special
- stafford(Ideal) -- computes 2 generators for a given ideal in the Weyl algebra
- 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