Re: [Axiom-math] Simplification rules

[Martin Rubey]

Bertfried Fauser <address@hidden> writes:

> Dear Martin,
> 
> I am _very_ interested in any combinatorics code already implemented in
> AXIOM, where could I get it?

You can have a look at http://wiki.axiom-developer.org/SandBoxCombinat


(The innovative bit of code is that the final line of code

TreeClass: CombinatorialClassCategory 
  == UnionClass(Atom, CrossClass(TreeClass, TreeClass)) add;

actually creates the DOMAIN TreeClass. Recursively!

Note that we were - for a start - only interested in implementing
species. Thus: no symmetric functions there.

> Regarding Lascoux, you think of implementing Lambda-ring issues in a CAS?  I
> tried this but failed (due to my own inability).

Well, I know very little about Lascoux, but it seems that he has some good
ideas about using the computer efficiently. I just want to learn about
symmetric functions, and somehow I like his approach using "alphabets" (i.e.,
lambda rings). But again, I don't know enough yet.

> However, I think I have _new_ mathenatical results which will allow hopefully
> faster computations also. This could go directly into a Combinat pacpage.

Great!

> I am not sure if you know, but there will be a (in the beginning small,
> but now already big) conference on symmetric functions (math, not CAS) at
> the MPI MIS in Leipzig, see www.mis.mpg.de/conferences, if you are
> interested I would be lad to see you there.

I didn't know, but anyway, I cannot come. In September my older daughter starts
with school and I guess she'll need me a bit and I'm on at least one Conference
already...

> For the moment being, I will try to fix my maple code and then start to
> transfere it into AXIOM routines. Perhaps bundeling this into a
> category/domain can be done later. However, it would be good to have the same
> data structures as in Combinat, I'll look that up.

I'm not quite sure what sort of datastructures you have in mind
here. Datastructures for what?