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)

is ‖.

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,

etc.

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?

**Answer**

**Attribution***Source : Link , Question Author : j0equ1nn , Answer Author : Community*