[GAP Forum] Multivariate Laurent-Polynomials

[Alexander Hulpke]

Dear Forum, Dear Johannes Hahn,

> I'm currently working on some stuff with Hecke-algebras and as there is
> still no CHEVIE for GAP4, I implemented the features I need myself. It
> works fine (more or less) for the equal-parameter case. It would work
> equally fine for the multiparameter-case (almost) without changes if
> there was a good way to deal with multivariate Laurent polynomials.

GAP currently does not have a special representation for multivariate Laurent polynomials, but as it allows for multivariate rational functions, you could add the functionality you desire with moderate work:

In rational function representation, the denominator is simply the lowest exponent occurring, exponents in the numerator then just have to be considered as shifted. 
> 
> So what do want to do? I want to specify a monomial ordering (i.e. a
> total ordering of Z^r which is invariant under addition) and be able to
> do these three elementary things:
> - extract to lowest exponent (w.r.t. the chosen ordering) and its
> coefficient
> - split a Laurent polynomial into the part consisting of all terms with
> positive exponent, the part with negative exponents and the coefficient
> for the exponent zero.

In rational function representation, the denominator is simply the lowest exponent occurring, exponents in the numerator then just have to be considered as shifted. This lets you easily build these two functions.
> 
> - apply the bar-automorphism, i.e. I want to be able to flip all signs
> in the exponents.

If vars is your list of variables, then

invvars:=List(vars,x->1/x);
Value(ratfun,vars,invvars);

will do so.

Best wishes,

   Alexander Hulpke




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