>
> Sorry, I don't know an easy way. I've always just defined them by hand 
>> whenever needed. 
>> However, I agree with you that a better way is needed. 
>>
>
> I would love for there to be some standard way to define a group action on 
> a set - preferably maintaining other algebraic properties of the set, such 
> as addition!  But I don't know if there is even close to a standard way to 
> do this either. 
>

- There is a standard way to do this, but not a generic method/class for it 
IIRC. You can do this by implementing an _act_on_() method on a wrapper 
class. Yet, this requires some manual input.
- For cyclic actions, there is the DiscreteDynamicalSystem class introduced 
in https://trac.sagemath.org/ticket/24128.
- There is also the Representation class in 
modules/with_basis/representation.py if you want to want to extend the 
action on the set to the module with a basis given by that set.

Likely we will want to implement a class SetWithAction that automates a 
collects the orbit_decomposition functions and similar together as methods 
as a single global entry point.

Best,
Travis


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