[Axiom-math] Re: [Axiom-developer] APL, J, and Axiom documentation

[root]

>Another thing that comes across fairly clearly in the talk is that Sun
>is planning to use Fortress as a way to create a large scientific
>computing community just like Java was used to create a large "web
>commerce" community.  The marketing person in me can't help but think
>that Axiom's algorithms would be very useful for helping to achieve
>this goal.

<rant>

Oh, please, not ANOTHER attempt. I made myself rather unpopular at the
CalculusFormalLibre conference over this point. A meeting was held to
decide whether there should be an effort to create a new computer
algebra system.

I pointed out that Axiom had been around for about 22 years.
In that time it had a large number of contributors, roughly
300 man-years of research, and about 42 million dollars invested.
It was one of the four large commercial systems along with Maple,
Matlab, and Mathematica. (Axiom was not yet free at the
time but I had been in private discussion with NAG about it).

I did not believe (and still do not) that any new effort will get
that level of sustained funding over so many years. It makes more
sense to start from a prepared base. There are a large number of
not-very-interesting technical issues that need to be re-solved
if you start from scratch. It would be much more productive to
spend any additional resource starting from a prepared base. Then
researchers can add new algorithms and work on the mathematics
rather than the language/porting/graphics/library/interpreter
and all the other uninteresting-but-needed details.

I'm watching Sage struggle over what is essentially a solved problem
in Axiom, that is, how to handle coercion and still be efficient.
That would be fine if it was a research attempt to define a theory
detailing the full lattice of coercions based on category theory.
That would be a lasting contribution to the field of computational
mathematics and would create a much stronger foundation for everyone.

Instead I'm watching what appears to be an ad-hoc war over dynamic
lookup vs performance. Axiom achieves both, getting the dynamic
lookup from the interpreter and performance from the compiler.
Unfortunately Sage is python-based and does not have a compiler.
So this is turning into a python vs cython debate which has NO
long term benefits for the field.

There are many, many more of these debates ahead (eg. noncommutative
issues, OpenMath-like communication issues, non-pythonic type
hierarchies, variable scoping rules, invalid object constructions
(e.g. matrix of streams), simplification, etc.). None of the Sage
discussions of ad-hoc solutions are likely to be of any real
research interest or achieve long term advancement of the field.

Work is being done to rewrite things like symbolic integration
in python when Axiom contains correct, fast, and efficient code
written by the people who invented the theory (Davenport, Trager,
Bronstein, etc.). The Axiom code is well tested and sound. A python
rewrite does not represent an advance.

I do hope that Sage is successful, in whatever sense that might be
taken, since it might expand the number of people who get interested
in the computational mathematics field. But I have to say that I
believe the effort would be much better spent concentrated on a
major code base such as Axiom or Maxima.

Clearly I have an interest in Axiom being chosen so my voice is
highly biased and, therefore, quite suspect and worth ignoring.
Despite that, I do believe I raise a valid point.

Watching SUN pour 42 million dollars into climbing the same mountain
that others have already climbed would be heartbreaking.

</rant>

Tim