localCohom(...,Strategy=>...) -- specify strategy for local cohomology

Description

This option together with LocStrategy determines a strategy for localCohom(...Ideal...) and localCohom(...Ideal, Module...).

• Walther -- the algorithm of U. Walther that uses Cech complex.
• LocStrategy => null -- used only for localCohom(...Ideal...), localizations are done by straitforward computation of annihilators and b-polynomials as described in [1].
• LocStrategy => OaTaWa -- localizations are done following Oaku-Takayama-Walther method.
• LocStrategy => Oaku -- localizations are done following Oaku's algorithm.
• OaTa -- restriction algorithm is used, which is due to T. Oaku and N. Takayama [2]

For detailed description of the algorithms see

• [1]U. Walther, Algorithmic computation of local cohomology modules and the local cohomological dimension of algebraic varieties (JPAA (139), 1999.)
• [2]Oaku, TakayamaAlgorithms for D-modules...

Further information

• Default value: Walther
• Function: localCohom -- local cohomology
• Option key: Strategy -- an optional argument

Functions with optional argument named Strategy :

• "addHook(...,Strategy=>...)" -- see addHook -- add a hook function to an object for later processing
• "annihilator(...,Strategy=>...)" -- see annihilator -- the annihilator ideal
• "associatedPrimes(...,Strategy=>...)" -- see associatedPrimes -- find associated primes
• "basis(...,Strategy=>...)" -- see basis -- basis or generating set of all or part of a ring, ideal or module
• bFunction(...,Strategy=>...) -- specify strategy for computing b-function
• "mingens(...,Strategy=>...)" -- see Complement -- a Strategy option value
• "trim(...,Strategy=>...)" -- see Complement -- a Strategy option value
• deRham(...,Strategy=>...)
• deRhamAll(...,Strategy=>...)
• determinant(...,Strategy=>...) -- choose between Bareiss and Cofactor algorithms
• DExt(...,Strategy=>...)
• DHom(...,Strategy=>...)
• DintegrateAll(...,Strategy=>...) (missing documentation)
• DintegrateClasses(...,Strategy=>...) (missing documentation)
• DintegrateComplex(...,Strategy=>...) (missing documentation)
• DintegrateIdeal(...,Strategy=>...) (missing documentation)
• Dintegration(...,Strategy=>...)
• "Dintegrate(...,Strategy=>...)" -- see DintegrationIdeal(...,Strategy=>...)
• "DintegrationAll(...,Strategy=>...)" -- see DintegrationIdeal(...,Strategy=>...)
• "DintegrationClasses(...,Strategy=>...)" -- see DintegrationIdeal(...,Strategy=>...)
• "DintegrationComplex(...,Strategy=>...)" -- see DintegrationIdeal(...,Strategy=>...)
• DintegrationIdeal(...,Strategy=>...)
• "Drestrict(...,Strategy=>...)" -- see DintegrationIdeal(...,Strategy=>...)
• "Drestriction(...,Strategy=>...)" -- see DintegrationIdeal(...,Strategy=>...)
• "DrestrictionAll(...,Strategy=>...)" -- see DintegrationIdeal(...,Strategy=>...)
• "DrestrictionClasses(...,Strategy=>...)" -- see DintegrationIdeal(...,Strategy=>...)
• "DrestrictionComplex(...,Strategy=>...)" -- see DintegrationIdeal(...,Strategy=>...)
• "DrestrictionIdeal(...,Strategy=>...)" -- see DintegrationIdeal(...,Strategy=>...)
• DlocalizationAll(...,Strategy=>...) (missing documentation)
• DlocalizationMap(...,Strategy=>...) (missing documentation)
• "Dlocalization(...,Strategy=>...)" -- see Dlocalize(...,Strategy=>...) -- strategy for computing a localization of a D-module
• Dlocalize(...,Strategy=>...) -- strategy for computing a localization of a D-module
• "DlocalizeAll(...,Strategy=>...)" -- see Dlocalize(...,Strategy=>...) -- strategy for computing a localization of a D-module
• "DlocalizeMap(...,Strategy=>...)" -- see Dlocalize(...,Strategy=>...) -- strategy for computing a localization of a D-module
• Dres(...,Strategy=>...) -- strategy for computing a resolution of a D-module
• "Dresolution(...,Strategy=>...)" -- see Dres(...,Strategy=>...) -- strategy for computing a resolution of a D-module
• DrestrictAll(...,Strategy=>...) (missing documentation)
• DrestrictClasses(...,Strategy=>...) (missing documentation)
• DrestrictComplex(...,Strategy=>...) (missing documentation)
• DrestrictIdeal(...,Strategy=>...) (missing documentation)
• "dual(MonomialIdeal,List,Strategy=>...)" -- see dual(MonomialIdeal,Strategy=>...)
• "dual(MonomialIdeal,RingElement,Strategy=>...)" -- see dual(MonomialIdeal,Strategy=>...)
• dual(MonomialIdeal,Strategy=>...)
• exteriorPower(...,Strategy=>...) -- choose between Bareiss and Cofactor algorithms
• "gb(...,Strategy=>...)" -- see gb -- compute a Gröbner basis
• gcdLLL(...,Strategy=>...) (missing documentation)
• generalB(...,Strategy=>...) -- specify strategy for computing generalized Bernstein-Sato polynomial
• "GF(...,Strategy=>...)" -- see GF -- make a finite field
• globalBFunction(...,Strategy=>...) -- specify strategy for computing global b-function
• "groebnerBasis(...,Strategy=>...)" -- see groebnerBasis -- Gröbner basis, as a matrix
• hermite(...,Strategy=>...) (missing documentation)
• "hooks(...,Strategy=>...)" -- see hooks -- list hooks attached to a key
• ICcohom(...,Strategy=>...) (missing documentation)
• "idealizer(...,Strategy=>...)" -- see idealizer -- compute Hom(I,I) as a quotient ring
• integralClosure(...,Strategy=>...) -- control the algorithm used
• "intersect(Ideal,Ideal,Strategy=>...)" -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
• "intersect(Module,Module,Strategy=>...)" -- see intersect(Ideal,Ideal) -- compute an intersection of a sequence of ideals or modules
• "intersectInP(...,Strategy=>...)" -- see intersectInP(...,BasisElementLimit=>...) -- Option for intersectInP
• "isInMultiplierIdeal(...,Strategy=>...)" -- see isInMultiplierIdeal(RingElement,Ideal,QQ) -- multiplier ideal membership test
• "isPrimary(...,Strategy=>...)" -- see isPrimary -- determine whether a submodule is primary
• "isPrime(Ideal,Strategy=>...)" -- see isPrime(Ideal) -- whether an ideal is prime
• lct(...,Strategy=>...) -- specify strategy for computing lct
• LLL(...,Strategy=>...) -- choose among different algorithms
• localCohom(...,Strategy=>...) -- specify strategy for local cohomology
• "localize(...,Strategy=>...)" -- see localize -- localize an ideal at a prime ideal
• "match(...,Strategy=>...)" -- see match -- regular expression matching
• "decompose(Ideal,Strategy=>...)" -- see minimalPrimes -- minimal primes of an ideal
• "minimalPrimes(...,Strategy=>...)" -- see minimalPrimes -- minimal primes of an ideal
• minors(...,Strategy=>...) -- choose between Bareiss and Cofactor algorithms
• "jumpingCoefficients(...,Strategy=>...)" -- see multiplierIdeal(Ideal,QQ) -- multiplier ideal
• "multiplierIdeal(...,Strategy=>...)" -- see multiplierIdeal(Ideal,QQ) -- multiplier ideal
• PolyExt(...,Strategy=>...)
• "primaryComponent(...,Strategy=>...)" -- see primaryComponent -- find a primary component corresponding to an associated prime
• pushForward(...,Strategy=>...) (missing documentation)
• quotient(...,Strategy=>...)
• "radical(...,Strategy=>...)" -- see radical -- the radical of an ideal
• "radicalContainment(...,Strategy=>...)" -- see radicalContainment -- whether an element is contained in the radical of an ideal
• RatExt(...,Strategy=>...)
• "analyticSpread(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "distinguished(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "isLinearType(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "isReduction(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "minimalReduction(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "multiplicity(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "normalCone(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "reesAlgebra(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "specialFiber(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "specialFiberIdeal(...,Strategy=>...)" -- see reesIdeal(...,Strategy=>...) -- Choose a strategy for the saturation step
• "regSeqInIdeal(...,Strategy=>...)" -- see regSeqInIdeal -- a regular sequence contained in an ideal
• resolution(...,Strategy=>...)
• saturate(...,Strategy=>...)
• "primaryDecomposition(...,Strategy=>...)" -- see strategies for computing primary decomposition
• "syz(...,Strategy=>...)" -- see syz(Matrix) -- compute the syzygy matrix
• "tangentCone(...,Strategy=>...)" -- see tangentCone(Ideal)