roots() method of polynomials over QQ misses roots in p-adic extension fields

[pjbruin]

In SageMath 9.3.beta3:

sage: R.<x> = QQ[]
sage: K.<a> = Qq(3).extension(x^2 + 1)
sage: (x^2 + 1).base_extend(K).roots()
[(a + O(3^20), 1),
 (2*a + 2*a*3 + 2*a*3^2 + 2*a*3^3 + 2*a*3^4 + 2*a*3^5 + 2*a*3^6 + 2*a*3^7 + 2*a*3^8 + 2*a*3^9 + 2*a*3^10 + 2*a*3^11 + 2*a*3^12 + 2*a*3^13 + 2*a*3^14 + 2*a*3^15 + 2*a*3^16 + 2*a*3^17 + 2*a*3^18 + 2*a*3^19 + O(3^20),
  1)]
sage: (x^2 + 1).roots(K)  # should return the same as above
[]

This can be fixed by only using the factor_padic() method when we are looking for roots in Z_p or Q_p.

Component: algebra

Author: Peter Bruin

Branch/Commit: 3dfbe69

Reviewer: Marc Mezzarobba

Issue created by migration from https://trac.sagemath.org/ticket/31040

[pjbruin]

Branch: u/pbruin/31040-roots_padic_extension_fields

[pjbruin]

Author: Peter Bruin

[pjbruin]

Commit: 3dfbe69

[mezzarobba]

Reviewer: Marc Mezzarobba

[mezzarobba]

comment:2

lgtm!

[vbraun]

Changed branch from u/pbruin/31040-roots_padic_extension_fields to 3dfbe69