contract'(Matrix,Matrix) -- contract a matrix by a matrix, the dual notion

Synopsis

Function: contract'
Usage:

h = contract'(m,n)
Inputs:
- m, a matrix, a map m : F <--- P between free modules of ranks f and p.
- n, a matrix, a map n : G <--- Q between free modules of ranks g and q.
Outputs:
- h, a matrix, a matrix with the shape h : F ** dual G <--- P ** dual Q, whose entry in the slot h_g*i+j,q*k+l is the result of contracting m_i,k, by n_j,l.

This function is identical to diff'(Matrix,Matrix), except that the multiplication by integers that occurs during differentiation is omitted.