On Tuesday, March 26, 2013 7:01:40 AM UTC+1, tom d wrote:

> Specify the action!  [...] The 'usual' actions then become special 
> predefined objects, like the special graphs, maybe summoned up 
> automatically using the permutation/whatever's __call__ function if it's an 
> idiomatic action like \sigma(3).


The group action framework is just the implementation, you still haven't 
answered the question that this thread was about: Should permutation 
actions on nested containers automatically discover one possible action or 
not. As you said, in the group action framework you can implement either 
possibility. You can also implement either if you don't use it. 

In any case, http://trac.sagemath.org/14291 is about hooking up GAP and not 
creating a framework for group actions. So in the interest of a finite 
amout of work per ticket, we should probably fall back to only allow 
explicitly specified group actions (OnPoints/OnTuples etc) there. Once your 
group action framework is in place it'll be easy enough to hook that up 
into the orbit method as well.

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