Dear GAP Forum,

Nicolas Thiery asked about various issues concerned with developing software
for invariant theory in GAP and C++. He asked:

nthiery@icare.mines.edu said:
> - are there any benchmarks for comparing the speed of basic
> manipulations of polynomials between MuPAD and Gap

Not as far as I know. A very, very quick and crude test, suggests that MuPAD
is much faster for polynomials over the integers (or rationals) but that GAP
is much faster for polynomials over small finite fields. I don't use MuPAD at
all regularly though, so I may have been doing something stupid.

- are there functions in gap to compute series expansions of rational
functions ?
- is the Polya enumeration implemented ? (Consider the action of a
permutation group on lists containing elements with given weights,
and compute the generating series of the orbits).

No, neither of these functions is implemented at present, nor ae there data
structures for potentially infinite series expansions (although there are
concepts such as potentially infinite virtual lists, on which they could be
implemented).

Do keep us posted with the progress of your project, if you go ahead, and
please consider the possibility of eventually "publishing" the software as a
GAP share package (see http://www-groups.dcs.st-and.ac.uk/~gap/Info4/share.html
).

Steve Linton

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