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ChainComplexExtras : Table of Contents
ChainComplexExtras
-- More ChainComplex Functionality.
appendZeroMap
-- append a zero map to chain complex
cartanEilenbergResolution
-- Computes free resolution of a ChainComplex
cartanEilenbergResolution(...,LengthLimit=>...)
-- How many steps to compute
chainComplexMap
-- Defines a ChainComplexMap via a list of matrices.
chainComplexMap(...,InitialDegree=>...)
-- Specify initial degree.
extendFromMiddle
-- 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
isChainComplexMap
-- 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
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
koszulComplex
-- Gives the Koszul complex on the generators of I.
koszulComplex(...,LengthLimit=>...)
-- How many steps to compute
minimize
-- minimal quotient complex of a free ChainComplex
nonzeroMax
-- 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
prependZeroMap
-- prepend a zero map to chain complex
removeZeroTrailingTerms
-- 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
scarfComplex
-- 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.
taylorResolution
-- Gives the Taylor resolution of a monomial ideal I.
taylorResolution(...,LengthLimit=>...)
-- How many steps to compute
trivialHomologicalTruncation
-- return the trivial truncation of a chain complex