Will Free Axiom change our world? (was ...Re: [Maxima] Case sensitivity,)

Some time ago...
>>>--- Martin RUBEY <rubey@labri.fr> wrote:
>>>
>>>>Axiom is on the way to become THE powerful free CAS, 
...
Someone else wrote...

>>>...
>>>I agree it looks powerful, but aside from the whole proof based
>>>approach they seem to want to take, are they really that much more
>>>capable than us?  
>>
>>I think yes, but I don't know. I think Richard would know. It might
>>depend on what you want to do.
> 
> 
> Hmm.  Well, competition is good.
>  
> 
>>>Also, there's no code publicly available yet, as far as I know.
>>
>>They take a very profound approach (document before release), but
>>there is  a 'private' archive where you can get the code from. Ask
> Tim 

Yes, Tim Daly or other Axiom experts should comment, but my view is that
Axiom was a noble attempt to be far more principled and less ad-hoc
than Macsyma or other systems.  As such it could provide cleaner
and more efficient foundations for building computer algebra programs.
In practice it was not more efficient, and it became necessary to
allow ad-hoc constructions nevertheless.  If you want to write
programs that manipulate polynomials over non-commutative rings, Axiom
helps. Or Clifford Algebras.  But when Axiom introduces a domain
"integration result"  then writing programs to manipulate them
is not so neat.  So part of the reason Axiom didn't wipe out the
competition is that math is messy.

    There were also problems in getting the front-end to be nice for
  persons without a graduate algebra education. And writing additional
programs is hard unless you have a similar degree. If you are a
physicist with an applied math problem, you might have difficulties
writing a program.

    And the advanced algorithms for commonly programmed tasks
(like Risch integration) were not necessarily better than those
in Maple or Mathematica or Macsyma.

    The poor marketing by NAG, perhaps caused in part by IBM
was another problem, but this should not be an issue if Axiom
is free.

I think it will be good to have Axiom available, and from
an academic point of view it would be nicer to build some
things on it. If they make the user-interface, plotting, etc
available (stuff that may not be so close to the foundation),
it might be good, too. From a practical point of view, I don't expect
that Maxima would find much in the way of advanced algorithms
that should be imported from Axiom, or done by calls to Axiom.

RJF