Let me mention that this question of powering is intimately related to
the question whether the powering operator should be part of the
coercion model. This has been done by Jeroen Demeyer years ago in 2017
(see https://github.com/sagemath/sage/issues/24247). Unless we revert
this, the parent of a**b should only depend on parent(a) and parent(b)
(whatever values have a and b).

To my mind, if there is a coercion between parents f : A -> B (such as
ZZ -> QQ or QQ -> AA or AA -> QQbar), it should be the case that f(a1)
** f(a2) is identical (ie value and parent) to f(a1 ** a2) whenever a1
and a2 have parents A.

On Fri, 30 Aug 2024 at 10:17, Kwankyu Lee <ekwan...@gmail.com> wrote:
>
> I agree that there should be an internal nth root method,
>
>
> There is. It is x.nth_root(n).
>
>
> Now the PR https://github.com/sagemath/sage/pull/38362 adding deprecation 
> warnings to the use of AA(x)^(1/n) to get the real root is ready.
>
> After one year deprecation period, the PR 
> https://github.com/sagemath/sage/pull/38564 will change the behavior of 
> AA(x)^(1/n) as promised.
>
> Please look around both PRs. If there is no objection for #38362, I will set 
> it to positive review soon.
>
> If anyone has objections, please state them in #38362.
>
>
>
>
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