GroupAction is the class of all group actions on polynomial rings for the purpose of computing invariants. This is not typically used directly, delegating creation to the various constructor functions for different kinds of group actions:
Each class implements different algorithms to compute invariants. Although mathematically speaking all the above group actions are linearly reductive (at least in the non modular case), the class LinearlyReductiveAction should be used only when none of the other classes apply because it has fewer and possibly less efficient methods.
The class GroupAction is implemented as a HashTable. When created it stores information such as the action (in a format dependent upon the group) and the polynomial ring being acted upon.
The object GroupAction is a type, with ancestor classes HashTable < Thing.