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ChainComplexExtras -- More ChainComplex Functionality.

Description

This package provides more functionality for working with ChainComplex objects.

Authors

Version

This documentation describes version 1.1 of ChainComplexExtras.

Citation

If you have used this package in your research, please cite it as follows:

@misc{ChainComplexExtrasSource,
  title = {{ChainComplexExtras: some additional ChainComplex Functions. Version~1.1}},
  author = {David Eisenbud and Frank Moore and Frank-Olaf Schreyer and Gregory G. Smith and Lily Silverstein},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

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) -- 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) -- 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, defined in ChainComplexExtras.m2.

The source of this document is in ChainComplexExtras.m2:769:0.