It is not perhaps easier, but an alternative way that I have used to 
calculate orbit decompsitions it to use 

from sage.groups.perm_gps.partn_ref.refinement_graphs import get_orbits

This works just by casting your group action as a subset of the permutation 
group action on the set. To define the action I (quite slowly) just acted 
via the group and found the corresponding index of the transformed element, 
so I agree a better way would be useful. 

On Thursday, April 28, 2022 at 2:09:03 PM UTC+1 axio...@yahoo.de wrote:

> I am very frequently using the function
>
> Signature:      orbit_decomposition(L, cyc_act) -> 'list[list]'
> Docstring:     
>    Return the orbit decomposition of "L" by the action of "cyc_act".
>
>    INPUT:
>
>    * "L" -- list
>    * "cyc_act" -- bijective function from "L" to "L"
>
>    OUTPUT:
>
>    * a list of lists, the orbits under the cyc_act acting on "L"
>
> which I have to import using
>
> from sage.combinat.cyclic_sieving_phenomenon import orbit_decomposition
>
> I am guessing that this function might be useful for other people, and 
> will probably be reimplemented over and over again (it is not hard to do 
> that, of course).
>
> My question is: wouldn't it make sense to make it available in an easier 
> way?  if so, how?
>
> Martin
>
>

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