Dear Nicolas,

> As I said last message I'm looking for a mean of computing the orbit of a
> multivariate polynomial.
Multivariate polynomials in GAP3 are not very efficient (they are formed by
iterated indeterminates. Having a group acting on them would become horribly
slow.). If the polynomials have special form you can
sometimes reduce the group action to acting on lists or on lists of lists.

GAP4 contains true multivariate polynomials and there will be functions that
permit the calculation of group orbits.

If you need further hints how to proceed, I would need to know a little bit
more. For example what types your polynomials are, how long do you suspect
the orbits to be, and whether you need to calculate orbits just a few times
by hand or inside an algorithm.

> Is this forum the good place for this question ?
Yes (as long as the question if of potential interest to other people on the
list. For problems with installation &c. there is the address 'gap-trouble'.)

I'm really interested by connecting Axiom (or Aldor) with Gap, so I'm looking
for technical informations about GAP's core.

We are planning to add an OpenMath interface to GAP that would permit
connecting Axiom with GAP. Steve Linton, who knows more about this but
is away at the moment, will answer this part in the new year.

Best regards,

Alexander