( cross-posted in Mathematics SE )
>
http://math.stackexchange.com/questions/1088447/how-to-implement-a-group-action-in-sage-for-educational-purposes
> implement a group action in Sage ( for educational purposes )?
>
> Let S= {"A","B","C","D"} and S4= SymmetricGroup(4). I want to create a
> table of the action S4 x S -> S which standardly permutes the letters in
> the set. The table should look like:
>
>
Even more useful - perhaps as something to add to the documentation - would
be a nice example of making a *class* out of this so that one could
actually (right-or-left-)multiply things user-created by elements of S4 in
a correct manner. In this case maybe we actually have this built in for
permutations of sets?
> Permutation. A. B. C. D
> () A. B. C. D
> (1 2 ) B. A. C. D.
> etc.
>
> How can this be done with Sage? ( The Set and Group in the question are
> just examples, I want to be able to create a table for any action.| i
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