Thank you for your answers. I guess I will stick to an explicitly defined 
action then. Not sure if I am the right person to do a clean up. But I 
guess I can document some functions.

On Saturday, November 25, 2017 at 11:22:50 PM UTC+1, Travis Scrimshaw wrote:
>
> You do have some flexibility on how you want to implement actions. Some of 
> this might be more complicated due to the classes you are inheriting from, 
> including some older code. The easier (but can be more cumbersome and 
> restrictive) way is to implement either _rmul_ / _lmul_ or _acted_upon_ 
> (recommended). However, I do not know if that takes precedence over an 
> explicitly defined action.
>
> There's a few examples of implementations of actions scattered around Sage 
> (such as in matrix/action.pyx) if that can help providing what you need 
> too. As you may have surmised, there is some old code floating around that 
> could use some cleanup and documentation.
>
> On Saturday, November 25, 2017 at 3:42:03 AM UTC-6, Simon Brandhorst wrote:
>>
>> Dear sagers,
>>
>> I am implementing a matrix group action on a submodule of ZZ^n.
>> element*matrix does work but the result lies in the ambient space and 
>> instead I want the
>> elements parent to be the invariant subspace we started with. 
>>
>> This can be done with sage.categories.action.Action
>>
>> However, that file was created in 2007, and it is almost not documented 
>> at all.
>> Is it the way to go anyways?
>>
>> Best
>> Simon
>>
>  

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