Element enumeration

Definition part
An element enumeration for $$H$$ is an algorithm that outputs a sequence of elements of $$G$$ such that:


 * Every element in the sequence lies inside $$H$$
 * The sequence contains every element of $$H$$

Note that because of repetitions of elements, the enumeration may itself be much longer and take more time to compute than the size of $$H$$.

Stronger subgroup description rules

 * generating set gives an element enumeration if we consider all the generators, all the products of length two of generators and so on.
 * Membership test uses an element enumeration of the whole group to obtain an element enumeration of the subgroup, by filtering in only those elements which are in the subgroup