Approximate nth root of polynomial in a number field

[roed314]

One of the dominant steps in creating a general p-adic extension is finding the (approximate) nth root of a polynomial over a number field, given a valuation v. Ie, given a polynomial f(x), an integer n and a precision k, find a polynomial g(x) with v(f(x) - g(x)^n) >= k. There's also a version of this on the approximate side (ie with coefficients in a p-adic field).

Depends on #28466

CC: @saraedum @xcaruso

Component: padics

Keywords: pAdicBordeaux

Issue created by migration from https://trac.sagemath.org/ticket/33370