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 $H#\{j,i\}$