Interesting Comment re Mathematica vs Everybody Else

 

> -----Original Message-----
> From: maxima-bounces at math.utexas.edu 
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Miguel Marco
>
<snip>

I tend to disagree about most (not all) mathematicians.
They don't want to use a killer-app in their specific field.
They want to write a journal paper about an algorithm, and in
order to do so they pick a subset of the problems space
that is so restricted as to be uninteresting to anyone else.
Rarely do such programs ever make it into a general CAS
because they don't work better on usual problems, or solve
problems of such remote interest that no programmer cares
to spend time to include them in the general stream of commands.

Thus such theoretical 'advances' are ignored because they deserve
to be ignored.

Unfortunately, nested definitions of algebraic structures, as
possible in Axiom, does not make for a selling point for most
people; in fact it seems to get in the way. 

I agree that the most prevalent application for CAS seems to be
in education.  This changes the financial incentives for
building advanced math into a commercial CAS, and tends to
convert open-source CAS work into graphical user interface
research (not that GUI stuff is trivial, just that it tends to trivialize
the math as "a back end to the GUI" which could, for example,
give wrong answers or be very slow, and the GUI programmer
might not care or even know...)
RJF


> >
> 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.
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