Hi,

> Oh, that's terrible, why would a program need its own programming
> language?

Well, why not, think of all kinds of DSPs?

I don't think there was any language suitable to express these
very abstract algebraic structures we need for CA. And in some
way, I doubt that there is such a language today, except, maybe,
Haskell. (All the OO things like C++ or Python can be used to
write algebraic code of course, but it will always be less
concise.) But this is my personal conclusion.

The SPAD language is indeed hard to learn but the ideas are very
elegant and perfectly useful for its purpose. Actually, writing
code in it is very difficult also because of the SPAD compiler
which is not helpful at all in finding programming errors.

> http://www.euclideanspace.com/maths/standards/program/spad/syntax/index.htm

Oh, forget about that. The much better source for information
about SPAD is the "Aldor User Guide". Aldor is the SPAD successor
and became free software in the last year.
It is more clean and well defined but still similar enough
in concept and structure.

Anyway, I'd be surprised if there are more than 50 or 100
people worldwide being able to read and program in Aldor.
(And I'd count myself as 0.5 at most.)

> I think that having its own language, SPAD, is a big hindrance
> to its development today.

Maybe a bit, but I'm not too sure about that. Maxima is written
in Lisp and the development there is extremely slow.

> In any case I suggest to find someone who is practical with Axiom's
> SPAD in order to see if parts of it can be copied into SymPy.

Personally, I'd say that this is a waste of time. Reading the
Axiom source may help to gain even better understanding of the
math, but it would be much easier to just write the code anew.

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