Non-commutative element multiplication in matrix operations (was Lexicographic ordering)

On Tue, Dec 16, 2008 at 11:09 AM, Askunky <askunky at yahoo.fr> wrote:

>  Hi, thanks for your answer.
> This *is not* the right answer... it matches the right answer when + and *
> are both commutative. If A,B,C,D are blocks of the initial matrix, then the
> computation should give
> matrix([A^2+B*C,A*B+B*D],[C*A+ D*C,C*B+D^2])
>

It would have helped us give you a useful reply if you had been clear that
A,B,C,D in your original question referred to objects with non-commutative
multiplication (in your case, blocks).  I don't understand what this has to
do with your subject line "Lexicographic ordering".

Anyway, you can select the multiplication used by matrix multiplication
using matrix_element_mult:

     `matrix_element_mult' is the operation invoked in place of
     multiplication in a matrix multiplication.  `matrix_element_mult'
     can be assigned any binary operator.  The assigned value may be
     the name of an operator enclosed in quote marks, the name of a
     function, or a lambda expression.

So set this parameter:

     matrix_element_mult: "."$

and

     matrix([a,b],[c,d])^^2 =>
         matrix([b . c+a^^2,b . d+a . b],[d . c+c . a,d^^2+c . b])

If some variables are scalars (with commutative multiplication) and others
not, you may want to look at declare(...,scalar) and declare(...,nonscalar).

              -s