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ChainComplexExtras :: ChainComplexExtras

ChainComplexExtras -- More ChainComplex Functionality.

Authors

Version

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.

Exports

  • 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.