ChainComplexExtras : Index
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appendZeroMap -- append a zero map to chain complex
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appendZeroMap(ChainComplex) -- append a zero map to chain complex
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cartanEilenbergResolution -- Computes free resolution of a ChainComplex
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cartanEilenbergResolution(...,LengthLimit=>...) -- How many steps to compute
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cartanEilenbergResolution(ChainComplex) -- Computes free resolution of a ChainComplex
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ChainComplexExtras -- More ChainComplex Functionality.
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chainComplexMap -- Defines a ChainComplexMap via a list of matrices.
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chainComplexMap(...,InitialDegree=>...) -- Specify initial degree.
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chainComplexMap(ChainComplex,ChainComplex,List) -- Defines a ChainComplexMap via a list of matrices.
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extendFromMiddle -- extends a map between ChainComplexes
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extendFromMiddle(ChainComplex,ChainComplex,Matrix,ZZ) -- extends a map between ChainComplexes
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Hom(ChainComplex,ChainComplex) -- Create the homomorphism complex of a pair of chain complexes.
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InitialDegree -- Used to specify an initial degree for chainComplexMap.
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isChainComplex -- tests whether the differentials compose to zero
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isChainComplex(ChainComplex) -- tests whether the differentials compose to zero
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isChainComplexMap -- Test to see if the ChainComplexMap commutes with the differentials.
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isChainComplexMap(ChainComplexMap) -- Test to see if the ChainComplexMap commutes with the differentials.
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isExact -- Test to see if the ChainComplex is exact.
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isExact(...,LengthLimit=>...) -- Option to check exactness only up to a particular homological degree
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isExact(ChainComplex) -- Test to see if the ChainComplex is exact.
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isMinimalChainComplex -- tests for minimality
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isQuasiIsomorphism -- Test to see if the ChainComplexMap is a quasi-isomorphism.
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isQuasiIsomorphism(...,LengthLimit=>...) -- Option to check quasi-isomorphism only up to a certain point
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isQuasiIsomorphism(ChainComplexMap) -- Test to see if the ChainComplexMap is a quasi-isomorphism.
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koszulComplex -- Gives the Koszul complex on the generators of I.
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koszulComplex(...,LengthLimit=>...) -- How many steps to compute
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koszulComplex(Ideal) -- Gives the Koszul complex on the generators of I.
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minimize -- minimal quotient complex of a free ChainComplex
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minimize(ChainComplex) -- minimal quotient complex of a free ChainComplex
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nonzeroMax -- computes the homological position of the last non-zero module in a ChainComplex
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nonzeroMax(ChainComplex) -- computes the homological position of the last non-zero module in a ChainComplex
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nonzeroMin -- computes the homological position of the first non-zero module in a ChainComplex
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nonzeroMin(ChainComplex) -- computes the homological position of the first non-zero module in a ChainComplex
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prependZeroMap -- prepend a zero map to chain complex
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prependZeroMap(ChainComplex) -- prepend a zero map to chain complex
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removeZeroTrailingTerms -- remove trailing zero terms of a chain complex
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removeZeroTrailingTerms(ChainComplex) -- remove trailing zero terms of a chain complex
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resolution(ChainComplex) -- Resolves a ChainComplex.
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resolutionOfChainComplex -- free resolution of a chain complex
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resolutionOfChainComplex(...,LengthLimit=>...) -- How many steps to compute
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resolutionOfChainComplex(ChainComplex) -- free resolution of a chain complex
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scarfComplex -- constructs the algebraic Scarf complex of a monomial ideal
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scarfComplex(MonomialIdeal) -- constructs the algebraic Scarf complex of a monomial ideal
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substitute(ChainComplex,Ring) -- Change the ring over which the ChainComplex is defined.
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taylor -- Gives the nth differential in the Taylor resolution of a monomial ideal I.
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taylor(ZZ,MonomialIdeal) -- Gives the nth differential in the Taylor resolution of a monomial ideal I.
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taylorResolution -- Gives the Taylor resolution of a monomial ideal I.
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taylorResolution(...,LengthLimit=>...) -- How many steps to compute
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taylorResolution(MonomialIdeal) -- Gives the Taylor resolution of a monomial ideal I.
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trivialHomologicalTruncation -- return the trivial truncation of a chain complex
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trivialHomologicalTruncation(ChainComplex,ZZ,ZZ) -- return the trivial truncation of a chain complex