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