Galois groups for finite fields

[roed314]

We should add Galois groups of finite fields, in parallel to the Galois groups of number fields. They will be used in #25902 for algebraic tori.

Depends on #28782
Depends on #23801

CC: @saraedum @xcaruso

Component: finite rings

Author: David Roe

Branch/Commit: f09750d

Reviewer: Xavier Caruso

Issue created by migration from https://trac.sagemath.org/ticket/31469

[roed314]

Branch: u/roed/gf_galois

[roed314]

Last 10 new commits:

82ff4d3	Fix relative fields, implement Travis' suggestion on key for _pol_galgp
bdc5d06	Fix doctest
15a2bf6	Working on Galois groups over finite fields
ea5b428	Working on Galois groups of finite fields
4b67449	Working on Galois groups of finite fields
02e858b	Working on subfields of finite fields
cf896f3	Fix test failure, documentation in algebraic closure
424a96e	Merge branch 'u/roed/subfields' of git://trac.sagemath.org/sage into t/31469/gf_galois
c80ede2	Choose default variable name in subfield, as in subfields
57dc39b	Merge branch 't/23801/subfields' into t/31469/gf_galois

[roed314]

Dependencies: #28782, #23801

[roed314]

Author: David Roe

[roed314]

Commit: 57dc39b

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

7937212

Refactor galois groups for abelian groups

[sagetrac-git]

Changed commit from 57dc39b to 7937212

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

b3fcfc5

Fix pyflakes, coverage

[sagetrac-git]

Changed commit from 7937212 to b3fcfc5

[mkoeppe]

comment:6

Sage development has entered the release candidate phase for 9.3. Setting a new milestone for this ticket based on a cursory review of ticket status, priority, and last modification date.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

1c99275	Merge branch 'develop' into t/31469/gf_galois
24cf4dd	Reviewer suggestions

[sagetrac-git]

Changed commit from b3fcfc5 to 24cf4dd

[xcaruso]

comment:8

OK, perfect. LGTM.

[xcaruso]

Reviewer: Xavier Caruso

[sagetrac-git]

Changed commit from 24cf4dd to f09750d

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

f09750d

Fix a bug with relative number field Galois groups

[roed314]

comment:10

The definition of _field_degree as the relative degree was wrong, since for the moment we're converting Galois groups of relative extensions to the Galois group of the corresponding absolute field (for backward compatibility and because we can't compute Galois groups of relative extensions in general).

[xcaruso]

comment:11

Good point.

[vbraun]

Changed branch from u/roed/gf_galois to f09750d