Factoring matrix expressions, even trivial ones?

For your trivial case, you could always do something like this:

/* Returns a list [ const, m/const ], where const is the GCD of the
vector/matrix entries. */
matrix_constant(m) :=
  block([const, flat, inflag:true],
   if mapatom(m)
     then [1,m]
   elseif member(op(m),["[",op(matrix())])
     then
       (flat: if op(m)="[" then m else apply('append,args(m)),
        const: xreduce('gcd,flat,1),
        [const, m/const] )
   else [1,m])$

This gets its basic behavior from GCD, so there may be some surprising
cases:

    matrix_constant([a/3,a/2]) => [a/6,[2,3]]
    matrix_constant([a,a/x]) => [a/x,[x,1]]

You can define your own variant of GCD if necessary.

         -s



On Fri, May 3, 2013 at 9:30 AM, Henry Baker <hbaker1 at pipeline.com> wrote:

> Is there any way for Maxima to factor 'a' back out of a*M, as below?
>
> Maxima 5.28.0-2 http://maxima.sourceforge.net
> using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
> Distributed under the GNU Public License. See the file COPYING.
> Dedicated to the memory of William Schelter.
> The function bug_report() provides bug reporting information.
> (%i1) M:transpose([x,y]);
>                                      [ x ]
> (%o1)                                [   ]
>                                      [ y ]
> (%i2) a*M;
>                                     [ a x ]
> (%o2)                               [     ]
>                                     [ a y ]
> (%i3) %,factor;
>                                     [ a x ]
> (%o3)                               [     ]
>                                     [ a y ]
> (%i4) ????
>
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