Suppose I have a discrete group G<SL2(C),
and it is finitely generated by some known generators.
That is, G=⟨g1,…,gn⟩.
The Frobenius norm of a matrix m=(abcd)
The set of elements in G
having the same Frobenius norm is a discrete subset of a compact set,
and therefore is finite.
I'm interested in algorithms for enumerating elements of G
by their Frobenius norm.
That is, find all elements of smallest (nontrivial) Frobenius norm,
then find all elements of next smallest Frobenius norm,
I have different techniques for different cases using other properties of the groups, but what is an efficient algorithm to do this generally, knowing only that we are given the generators?