On Sunday, October 23, 2016 at 11:33:21 PM UTC-7, Ralf Stephan wrote:
>
>
> Since you say pow is special we can fix this for the special case
> exponent in QQbar. Useful? 
>

Pow is not *that* special. Sage does have the notion of "actions" in the 
coercion framework. The map discovery framework is probably a little less 
extensive in those cases because there is no "common parent" that can be 
discovered, but you can define new actions, and I would assume they can be 
partial (raise an exception if values don't meet expectations). It sounds 
like real fields could have a partial right action from positive reals on 
them, via power notation.

It seems that actions presently are mainly used for scalar multiplication 
operations presently. However, `_get_action_` does seem to accept a "^" 
argument as well, so it would seem that action discovery could work.

I think people haven't bothered with "^" too much because in most cases 
you'd just accept integer actions and that's it. However, there are other 
scenarios where "^" is useful. For instance (as pointed out here), positive 
real exponents. (right) group actions on rings is another one.

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