Better interface to Galois groups

[roed314]

You currently have to decide explicitly whether you want a fully functional Galois group (type=None) or a fast Galois group (type="pari"). We should instead create an object that lazily computes any relevant attributes so that we can have a unified interface.

Depends on #28781
Depends on #26817

Component: number fields

Author: David Roe

Branch/Commit: 1a4b1eb

Reviewer: Travis Scrimshaw, Xavier Caruso

Issue created by migration from https://trac.sagemath.org/ticket/28782

[roed314]

Dependencies: #28781, #26817

[roed314]

Branch: u/roed/gal_revision

[embray]

comment:3

Ticket retargeted after milestone closed

[mkoeppe]

comment:4

Batch modifying tickets that will likely not be ready for 9.1, based on a review of the ticket title, branch/review status, and last modification date.

[mkoeppe]

comment:6

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[sagetrac-git]

Commit: 8453ffb

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

[sagetrac-git]

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

3efc05e	Working on galois group revisions
5de987b	Working on changing Galois groups so that they can be implemented for things other than number fields
43c23a9	Changing inheritance for GaloisGroups
9d1a658	Merge branch 't/28782/gal_revision' of /home/roed/sage9 into t/28782/galois_update

[sagetrac-git]

Changed commit from 8453ffb to 9d1a658

[sagetrac-git]

Changed commit from 9d1a658 to 14c1448

[sagetrac-git]

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

14c1448

Working on Galois groups of number fields

[sagetrac-git]

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

d5b9025

Fixing some documentation, moving code up to sage.groups.galois_group

[sagetrac-git]

Changed commit from 14c1448 to d5b9025

[sagetrac-git]

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

7e435cb

Add some docstrings

[sagetrac-git]

Changed commit from d5b9025 to 7e435cb

[sagetrac-git]

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

1ac12b4

Fixing doctests elsewhere in Sage

[sagetrac-git]

Changed commit from 7e435cb to 1ac12b4

[sagetrac-git]

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

6ce601e

Fix more doctests

[sagetrac-git]

Changed commit from 1ac12b4 to 6ce601e

[sagetrac-git]

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

52dc1e7	Fix pyflakes
4480e4a	Fix blocks plugin report
94687b1	Fix doctest (embeddings)

[sagetrac-git]

Changed commit from 6ce601e to 94687b1

[tscrim]

comment:16

I think you can replace

-@cached_method(key=lambda self, algorithm: self._get_algorithm(algorithm))
+@cached_method(key=GaloisGroup._get_algorithm)

but I haven't tested it yet. Otherwise I would be okay setting this to a positive review (although I am not someone who uses this code).

[sagetrac-git]

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

82ff4d3

Fix relative fields, implement Travis' suggestion on key for _pol_galgp

[sagetrac-git]

Changed commit from 94687b1 to 82ff4d3

[roed314]

comment:18

Thanks Travis. I also fixed a couple issues Xavier Caruso pointed out. I'm happy with the current state of this ticket (and am also planning on working on followups soon).

---

New commits:

82ff4d3

Fix relative fields, implement Travis' suggestion on key for _pol_galgp

[tscrim]

comment:19

One trivially failing test:

        Check that it works for relative number fields.  This behavior will change in the future::

            sage: K.<a> = NumberField(x^3 - 2)
            sage: L.<b> = NumberField(x^2 - x + 17*a)
            sage: G = L.galois_group()
            ...DeprecationWarning: Use .absolute_field().galois_group() if you want the Galois group of the absolute field
            See https://trac.sagemath.org/28782 for details.
            sage: G                   <----------------------------------
            sage: M, emb = G._gcdata

I think you meant to remove this line. Once this is fixed, you can set a positive review.

[tscrim]

Reviewer: Travis Scrimshaw, Xavier Caruso

[sagetrac-git]

Changed commit from 82ff4d3 to bdc5d06

[sagetrac-git]

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

bdc5d06

Fix doctest

[roed314]

comment:21

Fixed. Thanks, both of you!

[vbraun]

comment:22

PDF docs fail to build

[sagetrac-git]

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

1a4b1eb

Fix doc build

[sagetrac-git]

Changed commit from bdc5d06 to 1a4b1eb

[roed314]

comment:24

Sorry about that. I fixed the error and tested the docbuild for both html and pdf.

[vbraun]

Changed branch from u/roed/gal_revision to 1a4b1eb