splitting_field should call the base ring's _splitting_field_univariate_polynomial

[saraedum]

Currently, a polynomial's splitting_field() is only implemented for finite fields and number fields. This can not be easily extended by user provided constructions such as Henselizations, https://github.com/MCLF/henselization.

I'll also fix a bunch of documentation errors while I am at it…

Component: padics

Keywords: padicIMA

Author: Julian Rüth

Branch/Commit: u/saraedum/25938 @ f01d916

Reviewer: David Roe

Issue created by migration from https://trac.sagemath.org/ticket/25938

[saraedum]

Branch: u/saraedum/25938

[saraedum]

New commits:

f01d916

splitting_field() calls _splitting_field_univariate_polynomial()

[saraedum]

Commit: f01d916

[saraedum]

Work Issues: is the patchbot happy?

[saraedum]

comment:4

I only ran rudimentary doctests.

[saraedum]

Changed keywords from none to padicIMA

[roed314]

Reviewer: David Roe

[roed314]

Changed work issues from is the patchbot happy? to none

[roed314]

comment:6

Looks good!

[vbraun]

comment:7

sage -t --long src/sage/rings/number_field/number_field_base.pyx
**********************************************************************
File "src/sage/rings/number_field/number_field_base.pyx", line 423, in sage.rings.number_field.number_field_base.NumberField._splitting_field_univariate_polynomial
Failed example:
    L
Expected:
    Number Field in b with defining polynomial t^2 - 4*t + 6
Got:
    Number Field in b with defining polynomial t^2 + 2
**********************************************************************
1 item had failures:
   1 of   6 in sage.rings.number_field.number_field_base.NumberField._splitting_field_univariate_polynomial
    [79 tests, 1 failure, 1.55 s]
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sage -t --long src/sage/rings/number_field/number_field_base.pyx  # 1 doctest failed
----------------------------------------------------------------------