matching or some other thing for sums of exponentials?

On 10/03/2011 09:01 PM, Edwin Woollett wrote:

> Some code from my dirac2.mac code file (Maxima by Example,
> Ch. 13) seems to work here:
>...


I think this is very similar to using multthru, such as:
(%i455) myee: (a*exp(b) + exp(c));

                                    c       b
(%o455)                           %e  + a %e
(%i456) exp(c)*multthru(1/exp(c),myee);
                                   b - c        c
(%o456)                       (a %e      + 1) %e


The issue I have is that there are several locations within this big
ugly expression where this *type* of simplification could occur, but I
want to get maxima to traverse the expression tree and recognize when it
is possible and carry it out.

I thought pattern matching would be the way, but I can't figure out how
to match a sum of two exponentials multiplied by constants in a reliable
way (since it doesn't have a unique match it gives me some kinds of
warnings)

(%i457) matchdeclare([consta],atom,[expa,expb],lambda([x],not(atom(x))
and op(x)="^" and part(x,1)=%e));
(%o457)                              done

(%i458) defrule(sumexp,consta*expa+expb,expb*(consta*(expa/expb)+1));
defmatch: expa consta
         will be matched uniquely since sub-parts would otherwise be
ambigious.


                                             consta expa
(%o458)      sumexp : expb + consta expa -> (----------- + 1) expb
                                                expb

I guess I could use "scanmap" with a function I'd write that checks to
see if the expression is a sum of the right form, and then performs the
simplification.