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makeHomotopiesOnHomology -- Homology of a complex as exterior module

Usage:

(H,h) = makeHomotopiesOnHomology(ff, C)
Inputs:
- ff, a matrix, matrix of elements homotopic to 0 on C
- C, a complex,
Outputs:
- H, a hash table, Homology of C, indexed by places in the C
- h, a hash table, homotopies for elements of f on the homology of C

Description

The script calls makeHomotopies1 to produce homotopies for the ff_i on C, and then computes their action on the Homology of C.

See also

exteriorTorModule -- Tor as a module over an exterior algebra or bigraded algebra
exteriorExtModule -- Ext(M,k) or Ext(M,N) as a module over an exterior algebra

Ways to use makeHomotopiesOnHomology:

makeHomotopiesOnHomology(Matrix,Complex)

For the programmer

The object makeHomotopiesOnHomology is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CompleteIntersectionResolutions.m2:2694:0.