RE: [Axiom-developer] SAGE, Axiom, and usage

[Bill Page]

Gaby,

On August 23, 2006 12:13 PM you wrote:
> ...
> Bill Page wrote:
> | 
> | Chudnovsky was not making the distinction between "symbolic
> | computation" and "computer algebra" that Steven Watt is making
> | in the papers that I cited previously. Perhaps Gaby, you were
> | also was using "symbolic" in this more general sense? 
> 
> Yes, and as a matter of fact, I'm deeply sceptical of your
> previous assertion.

Which assertion?

1) That making the distinction drawn by Steven Watt between
   "symbolic computation" and "computer algebra" is important for
   understanding the difference between Axiom and systems like
   Mathematica and Maple.

2) That Axiom is not particularly well suited for teaching introductory
   symbolic computation.

3) That Axiom was not designed primarily to do symbolic computation
   (in the sense defined by Steven Watt) but rather to implement the
   computer algebra in a manner which today we would probably call
   and object-oriented approach.

Or was it something else that I said?

> Furthermore, I'm unconvinced that Axiom will attract people if we
> insist on painting it in a corner.
>

On the contrary, I do not think I am "painting it into a corner".
I agree with Steven Watt (I hope I am not overstating his views.)
that the proper foundation for all mathematical computation is really
the kind of computer algebra implemented by Axiom and Aldor. Pure
symbolic manipulation of expressions is just another domain
(SExpression) in Axiom. The fact that it is not particularly well
developed in Axiom is because the Axiom developers were largely
concerned with other issues. The Expression domain constructor (not
to be confused with SExpression!) in Axiom was an early and still
incomplete attempt to provide Axiom with some of the abilities to
symbolic manipulate symbolic expressions like Maple and Mathematica
while retaining some underlying general algebraic structure. It
seems clear from Steven Watt's paper that this is still "research
in progress".

> [...]
> 
> | I wonder what Dr. Chudnovsky would write today if asked to
> | compare the Axiom open source project to other open source
> | projects and the commercial counterparts?
> 
> you mean after Axiom has been deeply hibernating,

??? Axiom wasn't really "hibernating" until 2001 and it became
open source in 2003.

> and now has great difficulties taking again the leadership of
> principled CAS?

Do you think Axiom ever really had a "leadership" role? Certainly
as a research project at IBM up to about 1992 it was far ahead of
it's time in both mathematics and computer programming language
design. I know that experience with Axiom influenced the designs
of both Maple and MuPad. But I seriously doubt whether it is
possible for the Axiom open source project to regain that status.
Although I must admit the very fact that *you* are interested in
pursuing this work is very encouraging to me. :)

> Unless we have gotten a time-travel machine, I don't believe what
> is happening to Axiom today must be retroactively used to redesign
> its past foundation.
> 

Could you explain what you mean by "retroactively used to redesign
its past foundation"?

Regards,
Bill Page.