(at least) the sources of GAP4 contain functions calculating Molien
Series. It would be very helpful for me if somebody could point me to
background material (theoretical or algorithmical) of the
Theoretical background can be found in books that deal
with polynomial invariants of finite groups.
title="Algorithms in Invariant Theory",
series = "Texts and Monographs in Symbolic Computation",
Another point is that knowing the character (and the conjugacy
classes) suffices. This seems to be a folklore result, at least
I don't know any appropriate reference.
Once this is realized, actual implementation of the
computation is straighforward, assuming
that one has a tool to manipulate rational functions of one variable.