Meta-ticket: add integral curves over finite fields

[kwankyu]

We add integral curves over finite fields, tightly coupled with global function field machinery of Sage. The curves are space curves, including plane curves, in projective or affine spaces.

The main new functionalities are

• finding all closed points (for each degree) of a curve,

• finding all singular closed points of a curve.

Along the way, some old code in curves section of Sage is cleaned.

---

This ticket is now a meta-ticket to merge the code in multi steps:

step	ticket	comments
1	#27953	Add integral curves attached with function fields
2	#27954	Add closed points

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The author was supported by NRF of Korea 2018, 2019, 2020

Component: algebraic geometry

Reviewer: Kwankyu Lee, Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/27873

[kwankyu]

Branch: u/klee/27873

[kwankyu]

Author: Kwankyu Lee

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

3c2286b	fix
d51b9a6	fix
0724b5c	fix
1547849	fix
a79c2ca	fix
56c3aff	fix
1adabe3	Merge branch 'develop' into curves
9c999b0	fix
5063823	fix
4360779	fix

[sagetrac-git]

Commit: 4360779

[sagetrac-git]

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

218d2f1

Add integral curves over finite fields

[sagetrac-git]

Changed commit from 4360779 to 218d2f1

[sagetrac-git]

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

265cacd

pyflakes fixes

[sagetrac-git]

Changed commit from 218d2f1 to 265cacd

[kwankyu]

Dependencies: #27850

[sagetrac-git]

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

5448b0f

Another pyflakes fix

[sagetrac-git]

Changed commit from 265cacd to 5448b0f

[sagetrac-git]

Changed commit from 5448b0f to a488c75

[sagetrac-git]

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

a488c75

Some cures for slow doctests

[sagetrac-git]

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

13e1371

Add integral curves over finite fields

[sagetrac-git]

Changed commit from a488c75 to 13e1371

[sagetrac-git]

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

e746df9

Improve doctest coverage

[sagetrac-git]

Changed commit from 13e1371 to e746df9

[embray]

comment:30

Ticket retargeted after milestone closed

[mkoeppe]

comment:31

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.

[nbruin]

comment:33

Nitpick about terminology: the set of closed points of a curve over a finite field is infinite. The closed points of degree bounded by N form finite sets, for each N.
(ah, OK. the relevant code knows this. It's just the ticket description that's not reflecting it)

[kwankyu]

comment:35

Replying to @nbruin:

Nitpick about terminology: the set of closed points of a curve over a finite field is infinite. The closed points of degree bounded by N form finite sets, for each N.
(ah, OK. the relevant code knows this. It's just the ticket description that's not reflecting it)

Right. Thanks for attention. I welcome more nitpicks.

[mkoeppe]

comment:37

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

[kwankyu]

comment:38

The mission is complete.

[tscrim]

Reviewer: Travis Scrimshaw

[slel]

Changed author from Kwankyu Lee to none

[slel]

Changed reviewer from Travis Scrimshaw to Kwankyu Lee, Travis Scrimshaw