Would it be better to hold a vote to decide on the ways to deal with this 
issue, rather than on this particular PR?
Namely, the alternatives are

1) do nothing
2) bring AA in line with Python
3) bring RR in line with AA

Arguments against 2) are that it's mathematically weird, and that other 
projects such as numpy
are happy with their number types not blindly mimicking the choice made by 
Python.

My vote is for 3), as 1) leaves the inconsistency between AA and RR 
unresolved.

Dima





On Tuesday, September 3, 2024 at 3:19:16 AM UTC+1 Kwankyu Lee wrote:

> The PR https://github.com/sagemath/sage/pull/38362 is for adding 
> deprecation warning to the use of AA(x)^(1/n) to get the real root.
> The PR https://github.com/sagemath/sage/pull/38564 will change the 
> behavior of AA(x)^(1/n) after one year deprecation period.
> Adding P(x).pow(m/n) = AA(x).nth_root(n)**m will be provided for 
> fractional power computation in the parent P (including AA).
>
> Voting for this change is going on 
> https://github.com/sagemath/sage/pull/38362.
>

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