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ChainComplexExtras : Index
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appendZeroMap
-- append a zero map to chain complex
appendZeroMap(ChainComplex)
-- append a zero map to chain complex
cartanEilenbergResolution
-- Computes free resolution of a ChainComplex
cartanEilenbergResolution(...,LengthLimit=>...)
-- How many steps to compute
cartanEilenbergResolution(ChainComplex)
-- Computes free resolution of a ChainComplex
ChainComplexExtras
-- More ChainComplex Functionality.
chainComplexMap
-- Defines a ChainComplexMap via a list of matrices.
chainComplexMap(...,InitialDegree=>...)
-- Specify initial degree.
chainComplexMap(ChainComplex,ChainComplex,List)
-- Defines a ChainComplexMap via a list of matrices.
extendFromMiddle
-- extends a map between ChainComplexes
extendFromMiddle(ChainComplex,ChainComplex,Matrix,ZZ)
-- extends a map between ChainComplexes
Hom(ChainComplex,ChainComplex)
-- Create the homomorphism complex of a pair of chain complexes.
InitialDegree
-- Used to specify an initial degree for chainComplexMap.
isChainComplex
-- tests whether the differentials compose to zero
isChainComplex(ChainComplex)
-- tests whether the differentials compose to zero
isChainComplexMap
-- Test to see if the ChainComplexMap commutes with the differentials.
isChainComplexMap(ChainComplexMap)
-- Test to see if the ChainComplexMap commutes with the differentials.
isExact
-- Test to see if the ChainComplex is exact.
isExact(...,LengthLimit=>...)
-- Option to check exactness only up to a particular homological degree
isExact(ChainComplex)
-- Test to see if the ChainComplex is exact.
isMinimalChainComplex
-- tests for minimality
isQuasiIsomorphism
-- Test to see if the ChainComplexMap is a quasi-isomorphism.
isQuasiIsomorphism(...,LengthLimit=>...)
-- Option to check quasi-isomorphism only up to a certain point
isQuasiIsomorphism(ChainComplexMap)
-- Test to see if the ChainComplexMap is a quasi-isomorphism.
koszulComplex
-- Gives the Koszul complex on the generators of I.
koszulComplex(...,LengthLimit=>...)
-- How many steps to compute
koszulComplex(Ideal)
-- Gives the Koszul complex on the generators of I.
minimize
-- minimal quotient complex of a free ChainComplex
minimize(ChainComplex)
-- minimal quotient complex of a free ChainComplex
nonzeroMax
-- computes the homological position of the last non-zero module in a ChainComplex
nonzeroMax(ChainComplex)
-- computes the homological position of the last non-zero module in a ChainComplex
nonzeroMin
-- computes the homological position of the first non-zero module in a ChainComplex
nonzeroMin(ChainComplex)
-- computes the homological position of the first non-zero module in a ChainComplex
prependZeroMap
-- prepend a zero map to chain complex
prependZeroMap(ChainComplex)
-- prepend a zero map to chain complex
removeZeroTrailingTerms
-- remove trailing zero terms of a chain complex
removeZeroTrailingTerms(ChainComplex)
-- remove trailing zero terms of a chain complex
resolution(ChainComplex)
-- Resolves a ChainComplex.
resolutionOfChainComplex
-- free resolution of a chain complex
resolutionOfChainComplex(...,LengthLimit=>...)
-- How many steps to compute
resolutionOfChainComplex(ChainComplex)
-- free resolution of a chain complex
scarfComplex
-- constructs the algebraic Scarf complex of a monomial ideal
scarfComplex(MonomialIdeal)
-- constructs the algebraic Scarf complex of a monomial ideal
substitute(ChainComplex,Ring)
-- Change the ring over which the ChainComplex is defined.
taylor
-- Gives the nth differential in the Taylor resolution of a monomial ideal I.
taylor(ZZ,MonomialIdeal)
-- Gives the nth differential in the Taylor resolution of a monomial ideal I.
taylorResolution
-- Gives the Taylor resolution of a monomial ideal I.
taylorResolution(...,LengthLimit=>...)
-- How many steps to compute
taylorResolution(MonomialIdeal)
-- Gives the Taylor resolution of a monomial ideal I.
trivialHomologicalTruncation
-- return the trivial truncation of a chain complex
trivialHomologicalTruncation(ChainComplex,ZZ,ZZ)
-- return the trivial truncation of a chain complex