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ChainComplexExtras -- More ChainComplex Functionality.


This package provides more functionality for working with ChainComplex objects.



This documentation describes version 1.1 of ChainComplexExtras.

Source code

The source code from which this documentation is derived is in the file ChainComplexExtras.m2.


  • Functions and commands
  • Methods
    • appendZeroMap(ChainComplex) -- see appendZeroMap -- append a zero map to chain complex
    • cartanEilenbergResolution(ChainComplex) -- see cartanEilenbergResolution -- Computes free resolution of a ChainComplex
    • chainComplexMap(ChainComplex,ChainComplex,List) -- see chainComplexMap -- Defines a ChainComplexMap via a list of matrices.
    • extendFromMiddle(ChainComplex,ChainComplex,Matrix,ZZ) -- see extendFromMiddle -- extends a map between ChainComplexes
    • Hom(ChainComplex,ChainComplex) -- Create the homomorphism complex of a pair of chain complexes.
    • isChainComplex(ChainComplex) -- see isChainComplex -- tests whether the differentials compose to zero
    • isChainComplexMap(ChainComplexMap) -- see isChainComplexMap -- Test to see if the ChainComplexMap commutes with the differentials.
    • isExact(ChainComplex) -- see isExact -- Test to see if the ChainComplex is exact.
    • isQuasiIsomorphism(ChainComplexMap) -- see isQuasiIsomorphism -- Test to see if the ChainComplexMap is a quasi-isomorphism.
    • koszulComplex(Ideal) -- see koszulComplex -- Gives the Koszul complex on the generators of I.
    • minimize(ChainComplex) -- see minimize -- minimal quotient complex of a free ChainComplex
    • nonzeroMax(ChainComplex) -- see nonzeroMax -- computes the homological position of the last non-zero module in a ChainComplex
    • nonzeroMin(ChainComplex) -- see nonzeroMin -- computes the homological position of the first non-zero module in a ChainComplex
    • prependZeroMap(ChainComplex) -- see prependZeroMap -- prepend a zero map to chain complex
    • removeZeroTrailingTerms(ChainComplex) -- see removeZeroTrailingTerms -- remove trailing zero terms of a chain complex
    • resolution(ChainComplex) -- Resolves a ChainComplex.
    • resolutionOfChainComplex(ChainComplex) -- see resolutionOfChainComplex -- free resolution of a chain complex
    • scarfComplex(MonomialIdeal) -- see scarfComplex -- constructs the algebraic Scarf complex of a monomial ideal
    • substitute(ChainComplex,Ring) -- Change the ring over which the ChainComplex is defined.
    • taylor(ZZ,MonomialIdeal) -- see taylor -- Gives the nth differential in the Taylor resolution of a monomial ideal I.
    • taylorResolution(MonomialIdeal) -- see taylorResolution -- Gives the Taylor resolution of a monomial ideal I.
    • trivialHomologicalTruncation(ChainComplex,ZZ,ZZ) -- see trivialHomologicalTruncation -- return the trivial truncation of a chain complex
  • Symbols
    • InitialDegree -- Used to specify an initial degree for chainComplexMap.

For the programmer

The object ChainComplexExtras is a package.