[Axiom-developer] Poster at Mathinfo 06

[Martin Rubey]

Dear all,

I am quite happy to announce that I will have a poster at Mathinfo 06,

"Fourth Colloquium on Mathematics and Computer Science,
Algorithms, Trees, Combinatorics and Probabilities"

http://mathinfo06.iecn.u-nancy.fr/

where I will present my axiom package for guessing formulas. *

Thus, I slightly disagree with the following:

> And on the mathematics front I seems we aren't doing much better.  In spite
> of a lot of apparent interest, we still have not collected nor have there
> been initiated more than just a few (two or three) projects involving Axiom.

It is probably true that we have only two or three projects involving Axiom,
but at least Combinat by Ralf et al. and the implementation of GFUN by Antoine
are very promising, if they happen. (and I sure hope they will!)

I think it is not sooo important to have many projects. I'd rather have one or
two "killer applications".

If I'm very lucky, I'll by able to convince Neil Sloane to replace his bunch of
programs by mine :-)

> Is there nothing we can do to improve this situation?

No, there is a lot we can do. From *my* perspective, the following are the
"most important tasks":

* free Aldor and/or start writing an Aldor interpreter or maybe modify the
  current spad interpreter to understand Aldor. The main features missing are:
  dependent types and extend, maybe generators.

* free the Algebra and SumIt sources. 

* write a replacement for HyperDoc and MathAction that uses AllProse. Note that
  AllProse is able to produce html, mathml etc., whatever you want. The main
  feature missing is the "HyperDoc browse" facility. Step zero: make AllProse
  use axiom, then in a first step, one could transform the existing pamphlet
  files into AllProse. If one restricts oneself to the few commands understood
  by HyperDoc between \begin{+++} and \end{+++}, this won't break HyperDoc.

* implement the summation algorithms from RISC, i.e., sigma.

* implement a nice domain for differentially algebraic power series in
  cooperation with Antoine.

Finally:

> I have a project to document the integration routines in axiom. I have
> several sources of text (Trager's thesis, Bronstein's thesis, etc) as
> well as 4800 integrals that came from the Maple test suite (reported
> on elsewhere in this mailing list). I've modified axiom to tell me
> where each integral resolves and am classifying the various integrals
> into sets of examples. That way each of the 40ish 'integrate' routines
> will have example input associated with it.


> I have a project to add the numeric libraries back into Axiom.  Axiom
> is now a member of the Numerical Mathematics Consortium.  As a side
> effect, I'm rewriting the routines into literate form, finding
> research papers explaining the theory, such as convergence and
> sensitivity, and adding that to the documentation. I'm currently
> making the BLAS library literate.

 
> I have a research effort to rewrite the algebra using provisos.
> This uses the idea of generalized intervals to contain conditional
> statements that constrain the validity of computations.

seem very sensible to me too. Although I'm a bit doubtful with respect to the
last item. I think, it is a quite complicated thing and one should note that
axiom rather takes a different approach to these things: an integer in Axiom
really is an integer. A polynomial really is a polynomial. So, what is the
domain of "generic" integers, "generic" polynomials? I don't think that there
will be an easy answer to this.

Martin

PS: I will certainly promote Axiom there a little. :-)