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
- appendZeroMap -- append a zero map to chain complex
- cartanEilenbergResolution -- Computes free resolution of a ChainComplex
- chainComplexMap -- Defines a ChainComplexMap via a list of matrices.
- 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.
- isExact -- Test to see if the ChainComplex is exact.
- isMinimalChainComplex -- tests for minimality
- isQuasiIsomorphism -- Test to see if the ChainComplexMap is a quasi-isomorphism.
- koszulComplex -- Gives the Koszul complex on the generators of I.
- minimize -- 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
- 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
Symbols
- InitialDegree -- Used to specify an initial degree for chainComplexMap.