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I helped @antonydellavecchia today to figure out how to do this:
julia> G = symmetric_group(10)
Symmetric group of degree 10
julia> m = gset(G, on_sets, [collect(1:3)])
G-set of
symmetric group of degree 10
with seeds [[1, 2, 3]]
julia> I = [3,4,5]; J = [2,7,9];
julia> is_conjugate_with_data(m, I, J)
(true, (1,6,10,5,2,8,3,7)(4,9))The hard part really was to find is_conjugate_with_data, which isn't a great name here. Well, we should keep supporting it as it's been documented for a while now, but I think we can offer a better default name.
One idea would be to use transport or transporter or so.
For reference, in GAP it is called RepresentativeAction, but I don't think this is a great name either (but having representative_action as another alias might help people coming from GAP? Though for those, perhaps we should just have a "map of common GAP commands to their OSCAR counterparts" somewhere?