# makeHomotopies1 -- returns a system of first homotopies

## Synopsis

• Usage:
H = makeHomotopies1(f,F,d)
• Inputs:
• f, , 1xn matrix of elements of S
• F, , admitting homotopies for the entries of f
• d, an integer, how far back to compute the homotopies (defaults to length of F)
• Outputs:
• H, , 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