Dear GAP-forum,
In his message of 24th of August, Allan Adler writes:

GAP has attractive features that lend itself to such computations,
namely the facility for working with groups, character tables,
representations, etc. But it is weak in more traditional computer
algebra such as polynomial manipulation.

Invariant computations (which were the initiator for this thread) surely
will need polynomial arithmetic in several variables, which is - at the
moment - not very feasible in GAP, as Joachim Neub"user already pointed
out.
However, if you need polynomial factorisations (over Q or an algebraic extension
Q(alpha)) and basic polynomial routines like resultant etc.; there will
be routines in a future version, that provide these functions. (They are
basically finished and just have to be incorporated.)
Probably this is of some use.

Alexander Hulpke