If yes, you should use a proper computer algebra system (Mathematica, Maple, Maxima, yacas, ...). Despite all the love for Perl, using a tool better suited for the job will save you lots of time and trouble.
Perhaps you are right. With all the difficulty I had coming up with a compelling example for discussion, that's probably a symptom of me trying to shove a square peg in a round hole. Yes, symbolic calculations would simplify most of what I'm doing, so maybe I should indeed use a full math language--I can always glue in a bit of Perl if absolutely necessary. Thank you.