Re: [Axiom-developer] Is anybody actually doing mathematics with Axiom?

[Martin Rubey]

"Alasdair McAndrew" <address@hidden> writes:

> but does anybody actually use Axiom for mathematics: teaching, research, or
> even fun?  

I am.  For example, I wrote a tiny script to spit out all set partitions in
(Coxeter-) Type B and D and counted the first few terms, then entered them into
Sloane's database, to find the reference Ruedi Suter.

I also used Axiom to check a conjecture on Jeu de Taquin.  To this end I
implemented growth diagrams by Fomin, but I am unable to pursue this project on
my own.

Last year I used the (in my opinion) formidable graphics to show students how a
saddle point and a tangential plane looks like.  Gorgeous!

> Is anybody out there adding further mathematical functionality to Axiom -
> numerical routines, difference equation solvers, discrete mathematics etc
> etc?

I added the guessing package (currently state of the art), and together with
Ralf a project to deal with combinatorial species.

Concerning difference equations, you might know that my favorite would-be
project is a hierarchy covering 

  functions satisfying algebraic diffential equations,
  holonomic functions,
  algebraic functions,
  rational functions
  polynomials

on one hand and 

  "admissible" recurrence relations
  D-finite recurrence relations
  recurrence relations with constant coefficients

on the other hand.  But I could not find a collaborator so far --
unfortunately, Antoine Hersen gave up.  (One needs to know a bit about
Ore-algebras, AKA skew-polynomial rings.)

> FWIW, as Martin well knows, I've been banging my head over pattern matching
> and z-transforms lately. I have a file which works to about 75%; the last
> bit, which involves partial fractions, is still giving me gyp.

Try to formulate a question, then I can try to answer it.

> And on the meta-mathematical side, has anybody got an emacs mode to work
> with *.input files?

Francois Maltey sent me some files, but I am unable to incorporate them into my
emacs mode (which I use myself meanwhile), for lack of time.

Martin