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