Further improvements to splitting_field()

[jdemeyer]

1. Implement an "early abort" option to stop if it's clear that the degree will be huge.
2. Add some more examples (more indirect examples will be added by Implement division_field() for elliptic curves #11905)

Depends on #2217

CC: @JohnCremona @fchapoton

Component: number fields

Author: Jeroen Demeyer

Branch/Commit: u/jdemeyer/ticket/15626 @ 776795d

Reviewer: John Cremona

Issue created by migration from https://trac.sagemath.org/ticket/15626

[jdemeyer]

Branch: u/jdemeyer/ticket/15626

[jdemeyer]

New commits:

8f0baae	Further improvements to splitting_field()
c50eb3e	No need to specify caller_name in verbose()
6df69b6	Add comments, small cosmetic changes
9e2dd44	Make q monic before computing cubic resolvent
9b5558e	Implement splitting fields for number fields

[jdemeyer]

Commit: 8f0baae

[jdemeyer]

Dependencies: #2217

[sagetrac-git]

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

dd4fe5f	Further improvements to splitting_field()
c50eb3e	No need to specify caller_name in verbose()
6df69b6	Add comments, small cosmetic changes
9e2dd44	Make q monic before computing cubic resolvent
9b5558e	Implement splitting fields for number fields

[sagetrac-git]

Changed commit from 8f0baae to dd4fe5f

[jdemeyer]

Changed dependencies from #2217 to none

[jdemeyer]

Dependencies: #2217

[sagetrac-git]

Changed commit from dd4fe5f to df52508

[sagetrac-git]

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

df52508	Further improvements to splitting_field()
c50eb3e	No need to specify caller_name in verbose()
6df69b6	Add comments, small cosmetic changes
9e2dd44	Make q monic before computing cubic resolvent
9b5558e	Implement splitting fields for number fields

[sagetrac-git]

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

776795d

Do polynomial consistency check only for minimal dm

[sagetrac-git]

Changed commit from df52508 to 776795d

[JohnCremona]

comment:10

Note to self as reviewer: commits up to c50eb3e have been merged in #2217, so the ones to review here are: df52508, 776795d.

[JohnCremona]

Reviewer: John Cremona

[JohnCremona]

comment:11

The Abort class is a great idea and very well implemented. It would never have occurred to me to implement the early abort this way, and it has led me to think about other situations where a similar strategy might be useful! The examples are good.

All tests in sage/rings pass. For some reason when I tested the whole of Sage built with this branch I got various doctest errors in sage/crypto but I cannot believe that it has anything to do with these changes, so they are not stopping me giving it a positive review. Now I am looking forward to looking at the elliptic curve division field code!