On Monday 12 of July 2010 19:07:32 you wrote:
> -----maxima-bounces at math.utexas.edu wrote: -----
>
> >I checked also that when I write:
> >eq: transpose(A . B . C);
> >I obtain as expected
> > transpose(C) . transpose(B) . transpose(A)
> >
> >Is this possible to do it in back, e.g.:
> >eq1: transpose(C) . transpose(B) . transpose(A)
> >and get: transpose(A . B . C)
>
> Pattern matching is a popular way to do such things. An alternative is to
> substitute a
> function for "."; for example:
>
> (%i1) transpose_p(x) := not mapatom(x) and op(x)=nounify('transpose)$
>
> (%i2) transpose_dot(e) := subst("." = lambda([[s]], if
> every('transpose_p, s) then 'transpose(xreduce(".", reverse(map('first,
> s)))) else funmake(".", s)),e)$
>
> (%i4) transpose_dot(transpose(a) . transpose(b) - %pi);
> (%o4) transpose(b . a)-%pi
[...]
I do not understood how it work but it work. I'm still very beginner in
maxima. I will try it understand in next few days.
> This code doesn't handle expressions such as
>
> (%i10) transpose_dot(a.b . transpose(p) . transpose(q));
> (%o10) a . b . transpose(p) . transpose(q)
I do not know why this not work, but maybe after a few days I will be know.
> Similarly, you can make a substitution on "+" that does transpose(a) +
> transpose(b) --> transpose(a+b).
>
> The built-in simplifications for transpose expressions cannot be turned
> off, so I'd guess that
> the function transpose_dot will not work all that well--whenever an
> expression is (re-)evaluated, whatever
> work transpose_dot did will be reversed.
I understand.
> --Barton
Thank you very much for this example.
I will try to undersatand how it is done.
Zbigniew