ChainComplexExtras : Table of Contents

• ChainComplexExtras -- some additional ChainComplex Functions
• 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
• cartanEilenbergResolution(...,LengthLimit=>...) -- How many steps to compute
• chainComplexMap -- Defines a ChainComplexMap via a list of matrices.
• chainComplexMap(...,InitialDegree=>...) -- Specify initial degree.
• Concentration (missing documentation)
• 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
• 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.
• isElement -- test whether a ring element lies in a monomial ideal
• isExact(ChainComplex) -- Test to see if the ChainComplex is exact.
• isExact(ChainComplex,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(...,Concentration=>...) -- Option to check quasi-isomorphism only up to a certain homological degree
• 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
• koszulComplex -- Gives the Koszul complex on the generators of I.
• minimize(ChainComplex) -- 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