diff(Matrix,Matrix) -- differentiate a matrix by a matrix

diff(Matrix,Matrix) -- differentiate a matrix by a matrix

Synopsis:

Usage: h = diff(m,n)

Function: diff -- differentiate

Input:

m, an instance of class Matrix: a map m : F <--- P between free modules of ranks f and p.

n, an instance of class Matrix: a map n : G <--- Q between free modules of ranks g and q.

Output:

h, an instance of class Matrix: a matrix with the shape h : dual F ** G <--- dual P ** Q, whose entry in the slot h_g*i+j,q*k+l is the result of differentiating n_j,l by the differential operator corresponding to m_i,k.

If m or n is a ring element, then it is interpreted as a one-by-one matrix. If m is a vector, it is interpreted as a matrix with one column, and if n is a vector, it is interpreted as a matrix with one row. If both m and n are ring elements, then the result will be a ring element rather than a one-by-one matrix. If m is a vector and n is a ring element, then the result will be a vector rather than a matrix with one column.

The most common usage is when m has one column and n has one row. In this case the result h is a matrix whose (i,j)-th entry is the result of differentiating n_j by the differential operator corresponding to m_i.

See also:

diff and contract

Code:

     -- ../../../Macaulay2/m2/matrix.m2:446
     diff(Matrix, Matrix) := Matrix => (m,n) -> (BinaryMatrixOperation ggdiff)(m,n)