Coset enumeration

Definition part
A coset enumeration of $$H$$ in $$G$$ is essentially a description of the action of $$G$$ on the coset space $$X = G/H$$. It provides the following data:


 * A set $$X$$ encoded as strings, with a membership test for $$X$$
 * An algorithm that takes as input $$g \in G$$ and $$x \in X$$ (in terms of their encodings) and outputs $$g.x$$
 * A distinguished element in $$X$$ for which we are told that the isotropy is exactly $$H$$

Stronger description rules

 * Coset representative function

Weaker description rules

 * Coset-separating function
 * Membership test