Re: Symbolic Math as Computer Science

Rouben Rostamian wrote: 
In article <o9OdnWTfnrYsqQzenZ2dnUVZ_v-dnZ2d@xxxxxxxxxxxxx>,
Hatto von Aquitanien  <abbot@xxxxxxxxxxxxxx> wrote:

Is there much in the way of academic computer scientific literature on the
mechanisms underlying symbolic computing?  I don't (believe I) mean _Modern
Computer Algebra_ by von zur Gathen and Gerhard.  I'm really thinking in
terms of implementation along the lines of compiler theory, and formal
language theory.

My limited experience with such systems is pretty much exclusively with
Mathematica.  Does anybody happen to know of literature that reveals how
Mathematica works at the fundamental level?



You will find the following useful:

   Peter Norvig: Paradigms of AI Programming.

You might also find Abelson/Sussman: Structure and INterpretation of
Computer Programs, esp. the section on data abstraction and polynomials
to relate "computer science" data strutures to symbolic math.

There is also Knuth's Art of Computer Programming, volume 2.

You will find lots of details in the book
Algorithms for Computer Algebra by K. O. Geddes et al.

I think you may also find some stuff of interest to you in the literature
on the Axiom system, or Maxima. (which has an extensible parser for
the compiler buffs).

But mostly compiler theory and formal language theory have to do with only
about 5% of the symbolic math system-building task. ..How to build a
parser or maybe even a 2-d handwriting recognizer front end that
can handle some subset of "math". I assume you are also interested
in data structures and representation  and maybe things like
object-oriented programming etc  by way of "academic CS".

Maybe you could clarify your question?

If you want to see how to program Mathematica, you can look at an
open-source version of a mockup of it, the front end parser,
simplification, display, a few commands (e.g. D[], Integrate[]) in
MockMMA.
  If you want to know some of the "secrets" inside Mathematica,
see my review of it in J. Symbolic Computation (version is also online).
RJF

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