The following functions return non-trivial structural properties of invariant rings.

HilbertSeries(R) : RngInvar -> FldFunUElt

The Hilbert series of the invariant ring R=K[V]^G, returned as an element of the rational function field Z(t). The Molien series of G will be used if possible; otherwise (the modular matrix group case) secondary invariants for R will be constructed to determine the result.

Given the invariant ring R=K[V]^G of the group G over the field K, return true iff R is Cohen-Macaulay. This is always true in the non-modular case. Otherwise, secondary invariants for R will be constructed to determine the result.