Re: [Axiom-mail] Matrix algebra

[Martin Rubey]

address@hidden writes:

> For symbolic computation can Axiom recognize that matrix multiplication in
> general does not commute, that is, for square matrices A and B, AB is not (in
> general) equal to BA?

Well, currently, there is no domain specially geared towards symbolic matrix
calculations, however:

* if you know the dimensions (and they are not too big), you do not have a
  problem at all, just use generic matrices

* otherwise, you can use a noncommutative polynomial ring, for example XPOLY:

(1) -> p1:XPOLY INT := x+y

   (1)  x 1 + y 1
                                                    Type: XPolynomial Integer
(2) -> p2:XPOLY INT := x-y

   (2)  x 1 + y(- 1)
                                                    Type: XPolynomial Integer
(3) -> p1*p2

   (3)  x(x 1 + y(- 1)) + y(x 1 + y(- 1))
                                                    Type: XPolynomial Integer
(4) -> p2*p1

   (4)  x(x 1 + y 1) + y(x(- 1) + y(- 1))
                                                    Type: XPolynomial Integer
(5) -> p1*p2-p2*p1

   (5)  x y(- 2) + y x 2
                                                    Type: XPolynomial Integer


* if you need more general expressions in variables, you will probably have to
  build your own domain, unfortunately.

Hope this helps,

Martin