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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 1.2 of ChainComplexExtras, released May 20, 2026.

Citation

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

@misc{ChainComplexExtrasSource,
  title = {{ChainComplexExtras: some additional ChainComplex Functions. Version~1.2}},
  author = {David Eisenbud and Frank Moore and Frank-Olaf Schreyer and Gregory G. Smith and Lily Silverstein and Eduardo Saenz De Cabezon Irigaray and Oscar Fernandez-Ramos and Christof Soeger},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages}}
}

Exports

  • Functions and commands
    • AHH -- n-th map in the Aramova-Herzog-Hibi resolution
    • AHHResolution -- Aramova-Herzog-Hibi minimal free resolution of a squarefree-stable ideal
    • appendZeroMap -- append a zero map to chain complex
    • cartanEilenbergResolution -- Computes free resolution of a ChainComplex
    • chainComplexMap -- Defines a ChainComplexMap via a list of matrices.
    • EK -- n-th map in the Eliahou-Kervaire resolution
    • EKResolution -- Eliahou-Kervaire minimal free resolution of a stable monomial ideal
    • extendFromMiddle -- extends a map between ChainComplexes
    • isChainComplex -- tests whether the differentials compose to zero
    • isChainComplexMap -- Test to see if the ChainComplexMap commutes with the differentials.
    • isElement -- test whether a ring element lies in a monomial ideal
    • isMinimalChainComplex -- tests for minimality
    • isResolution -- test whether a chain complex resolves the quotient by a monomial ideal
    • isSQStable -- test whether a squarefree monomial ideal is squarefree stable
    • isStable -- test whether a monomial ideal is stable
    • 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
    • resolutionOfChainComplex -- free resolution of a chain complex
    • scarfComplex -- constructs the algebraic Scarf complex of a monomial ideal
    • taylor -- Gives the nth differential in the Taylor resolution of a monomial ideal I.
    • taylorResolution -- Gives the Taylor resolution of a monomial ideal I.
    • trivialHomologicalTruncation -- return the trivial truncation of a chain complex
  • Methods
    • AHH(ZZ,MonomialIdeal) -- see AHH -- n-th map in the Aramova-Herzog-Hibi resolution
    • AHHResolution(MonomialIdeal) -- see AHHResolution -- Aramova-Herzog-Hibi minimal free resolution of a squarefree-stable ideal
    • 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.
    • EK(ZZ,MonomialIdeal) -- see EK -- n-th map in the Eliahou-Kervaire resolution
    • EKResolution(MonomialIdeal) -- see EKResolution -- Eliahou-Kervaire minimal free resolution of a stable monomial ideal
    • 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.
    • isElement(RingElement,MonomialIdeal) -- see isElement -- test whether a ring element lies in a monomial ideal
    • isExact(ChainComplex) -- Test to see if the ChainComplex is exact.
    • isResolution(ChainComplex,MonomialIdeal) -- see isResolution -- test whether a chain complex resolves the quotient by a monomial ideal
    • isSQStable(MonomialIdeal) -- see isSQStable -- test whether a squarefree monomial ideal is squarefree stable
    • isStable(MonomialIdeal) -- see isStable -- test whether a monomial ideal is stable
    • 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
    • Concentration (missing documentation)
    • 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.m2:1053:0.