Interesting Comment re Mathematica vs Everybody Else

> I have not played with Maple or MuPAD for five years or so, and so
> cannot really compare them now.  Five years ago Mathematica seemed to
> handle more of the problems that I threw at it, and that was before I
> knew anyone from Wolfram.  Every few months I look at Axiom, Maxima,
> sympy etc..., but frankly they are not close to being in the same
> league, and seem to be losing ground over time 
I don't know much about Mathematica, but some of my coleagues use Maple once 
in a while, and i agree with you about the fact that, often, the same problem 
requires more work from the user to be solved in maxima than in maple. 
Anyways, it is not a question of capability (at the end, both are 
Turing-complete), but of usability. Anyways, all general purpose CAS that i 
have seen make some mistakes in specific cases, which forced the user to 
think twice befure using them for serious stuff beyond education.

> (I would have expected 
> computer algebra to be a place where open source would shine, but
> alas, it seems not.)  The Sage project seems to have promise, but
> right now it looks like a bunch of distinct tools and a lot of duct
> tape.
> The more specialized tools like MacCaulay, CoCoA, Gap, Pari/GP, 4ti2,
> etc. are amazing in their niches, but have no pretenses to being
> widely applicable.
>
That is exactly the point: math researchers usually don't want to use a 
general purpose tool, but the killer-app in their specific field. It makes 
little sense to calculate groebner basis, or character tables with 
Mathematica, Maple or Maxima. Hence, the same researchers that use these 
specialized tools, help improving them (after all, they are the ones that do 
research in those very specific algorithms). And thats how specifc open 
source CAS keep improving, but general purpose ones stay in a second level.
One exception would be Axiom, that, besides a general purpose CAS, can handle 
nested definitions of algebraic structures (i don't know any other CAS that 
can do this), which can be usefull for some specific lines of research.

Besides that, i consider that the main target for general purpose CAS'es is 
actually education, and in that niche efficiency of algorithms is secondary 
to pedagogical questions (such as easyness of learning). Considering that, i 
think that differences in that aspect between Mathematica, Maple, and Maxima 
(depending on the GUI) are no big enough to say that Maxima plays in another 
league.

Best:


Miguel Marco Buzunariz
Departamento de Matematicas
Universidad de Zaragoza.