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makeHomotopies1 -- returns a system of first homotopies

Usage:

H = makeHomotopies1(f,F,d)
Inputs:
- f, a matrix, 1xn matrix of elements of S
- F, a complex, admitting homotopies for the entries of f
- d, an integer, how far back to compute the homotopies (defaults to length of F)
Outputs:
- H, a hash table, gives the homotopy from F_i corresponding to f_j as the value $H#\{j,i\}$

Description

Same as makeHomotopies, but only computes the ordinary homotopies, not the higher ones. Used in exteriorTorModule

See also

makeHomotopies -- returns a system of higher homotopies
exteriorTorModule -- Tor as a module over an exterior algebra or bigraded algebra

Ways to use makeHomotopies1:

makeHomotopies1(Matrix,Complex)
makeHomotopies1(Matrix,Complex,ZZ)

For the programmer

The object makeHomotopies1 is a method function.

The source of this document is in CompleteIntersectionResolutions.m2:3801:0.