Re: [Axiom-developer] Comparison of CAS's?

[Martin Rubey]

Gabriel Dos Reis <address@hidden> writes:

> "Alasdair McAndrew" <address@hidden> writes:
> 
> | As far as I know, nobody has tried to compare CAS's since Michael Wester's
> | attempts in the 1990's. 
> 
> Not that I know of.  I believe Wester's work date back from late
> 1990s.  Everywhere else in computer science, that would be an
> eternity, but not in compuer algebra it seems...
> 
> I believe many of his issues with Axioms are still unresolved.

Yes. By comparison, the MuPAD team runs the test suite with every new release
and is now doing really well.

> You need to know all systems you compare in depth enough to make a fair
> comparision.  Furthermore, CASes are to solve problems.  So you have to come
> up with realistic problems to solve and express the solutions in "native
> styles" for each of them.

Well, this is one approach.  However, I think that this setting is not as
realistic as it may seem.  Many researchers I know indeed use one tool for
this, another one for that, and they avoid general purpose CAS altogether.
(Others don't, of course.  I'd say it's a small majority that uses mainly
general purpose CAS.)

Even though Mathematica does better than Axiom on Wester's suite, I prefer
Axiom, because it provides more possibilities, and after a while, I find it
easier to use.  A good example is the demonstration of Cayley's theorem on the
characteristic polynomial, as pointed out by Francois Maltey recently.

>From a user's perspective, I believe that MuPAD is currently the best CAS
around.  However, it's programming language has some severe limitations, which
Aldor does not have.

On the other hand, Axiom is free, and MuPAD is not, not even gratis anymore.

Apart from all that, if our goal was to make Axiom pass more tests of Wester's
suite, we need Gruntz algorithm for limits and an implementation of Zeilberger
for summation, as far as I recall.  However, I think that this is not quite the
right way to go about it.



Martin