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Hello!

I am wondering how to solve the following problem efficiently.

I have a Permuation Group $G$ acting on $A = {1,\ldots,n}$ and I wish to compute the orbits of $G$ but not the ones of $G$ acting on $A$ but rather for $G$ acting on some $S \subseteq A \times A$ in the natural way. That is if $g \in G$ and $x = {a,b} \in S$ then $x^g = {a^g,b^g} \in S$

Other software for permuation groups (magma, gap) allows to do this by specifing an additional option "on sets/on tuples" to compute the specifed orbits.

I am wondering how could I do the same in sage, given a permuation group $G$ and an $S$ as described above.

Thanks!