Consider the following classic problem in combinatorics: how many neckleces with $n$ black/white beds are there up to rotations? You can formulate the question in the language of group theory: acting with $\mathbb{Z}/n\mathbb{Z}$ on $\{0,1\}^n$ by circular shift, how many orbits are there?
I'm looking for an algorithm that lists representatives for the orbits. In particular I'd like to have the source code of a working, self-contained implementation of it (or a precise link to the relevant code in some big package as GAP).
This question looks similar in nature, but the particular problem it's different and I don't see a natural way to adapt the answer given there.