Re: Steps towards writing a computer algebra system

From: Richard Fateman (fateman_at_cs.berkeley.edu)
Date: 01/19/05 

Date: Wed, 19 Jan 2005 04:53:16 GMT

Jesse Nochella wrote:
>
> You can find out why some implementation works better than another one.
> You can't do a more thurough analysis than what you can do in
> Mathematica.
Algorithms written in Mathematica are unfortunately likely
to exhibit strange behavior because of bizarre foundational
data structures and storage policies.

A recent posting on the mathematica newsgroup by Maxim Rytin shows

Module[{f, L},
    L = f[];
     Do[L = f[L, i], {i, 10^4}]
  ] // Timing

takes 0.015 seconds, but if you change the name "f" to
the name "weirdness" the program takes about 200 times longer.
Times should not depend so dramatically
  on the name of a variable.

My guess is that building a CAS means, to the original poster,
writing a read-eval-print loop where read = parse infix algebra,
eval = simplify, do some commands like differentiate, and
print = write out the answer.

Eviscerating Mathematica and re-implementing (say) differentiation
as rules would be easy; the original poster would have to say
if this would satisfy his craving.
RJF

> I've seen people embark on big projects like this and spend so much
> time on unimportant details that they ditch the whole thing before
> learning what they wanted to learn. I think the key to really pulling
> stuff like this off for fun is in using a system like Mathematica.
>

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