Derivations for separable function fields

[saraedum]

This ticket implements derivations for extensions of function fields.

Depends on #16518

Component: commutative algebra

Keywords: sd59

Author: Julian Rüth, Kwankyu Lee

Branch/Commit: da7cb4d

Reviewer: Vincent Delecroix, Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/16561

[saraedum]

Branch: u/saraedum/ticket/16561

[saraedum]

Commit: 4441e47

[saraedum]

New commits:

dc81be8	Derivations for rational function fields
547f8da	is_perfect() for fields
be532e5	Added copyright header to finite_field_base.pyx
4441e47	Added derivation for non-rational function fields

[sagetrac-git]

Changed commit from 4441e47 to da3faa0

[sagetrac-git]

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

da3faa0

Added derivations for non-rational separable function fields

[sagetrac-git]

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

fa528e8

Merge branch 'develop' into ticket/16561

[sagetrac-git]

Changed commit from da3faa0 to fa528e8

[mezzarobba]

Work Issues: BuildFailed

[sagetrac-git]

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

724b02c	Merge branch 'develop' into t/16561/ticket/16561
ac8427a	Fixed format errors in docstrings

[sagetrac-git]

Changed commit from fa528e8 to ac8427a

[videlec]

comment:10

Hello Julian,

It seems that the only derivation you are testing is y^2 - x. I have nothing against the square root but it would be cool to have a bit more diversity in the doctests. And it would be cool to have somewhere non trivial examples of

sage: d(p+q) == d(p) + d(q)
True
sage: d(p*q) == d(p)*q + p*d(q)
True

In the ALGORITHM block, I would rather use formula instead of algorithm. And you mentioned the non-separable case that this ticket is not about.

Beyond documentation, everything looks good to me.

Vincent

[videlec]

Changed work issues from BuildFailed to none

[videlec]

Reviewer: Vinent Delecroix

[saraedum]

Changed reviewer from Vinent Delecroix to Vincent Delecroix

[saraedum]

comment:12

Thanks for the comments. I will try to make some changes.

[sagetrac-git]

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

f967e4f	test Leibniz's law for function field derivations
d11261c	TestSuite for inseparable and non-perfect base function fields
06770a3	Fixed wording of function field derivation docstring

[kwankyu]

comment:30

Replying to @saraedum:

My experience with this has been that there is virtually no movement in function fields in Sage. So, I'd like to point people to places where they can help if they'd like.

Ok. I agree that function fields part of Sage needs much attention. I had been forced to move to Magma because of this at some point and was surprised when I returned to Sage to find that there was not much changed in that situation :-(

[kwankyu]

comment:31

Hi Julian,

I am interested in pushing this ticket. If you do not have a plan to work on this, then I could work. Would this be ok with you?

[saraedum]

comment:32

Yes, hooray! Please go ahead. Let me know if you need any help :)

[kwankyu]

Changed branch from u/saraedum/ticket/16561 to u/klee/16561

[kwankyu]

New commits:

fcc68c1	Merge sage 7.6
4bb538e	Improve docstrings

[kwankyu]

Changed commit from 7d8f22a to 4bb538e

[sagetrac-git]

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

2847da0

Trim code and docstrings

[sagetrac-git]

Changed commit from 4bb538e to 2847da0

[sagetrac-git]

Changed commit from 2847da0 to 939fda6

[sagetrac-git]

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

939fda6

Refine docstrings

[tscrim]

comment:37

IMO, a better idiom for the _test_derivative is instead of catching the NotImplementedError and returning as normal would be to let it raise the error and instead explicit skip the test:

TestSuite(X).run(skip='_test_derivative')

[sagetrac-git]

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

1a0414c	Merge branch 'develop'
da7cb4d	Improve _test_derivative test

[sagetrac-git]

Changed commit from 939fda6 to da7cb4d

[tscrim]

comment:39

I think this is good to go, so I'm setting it to a positive review. If there are any objections, feel free to set it back.

[tscrim]

Changed reviewer from Vincent Delecroix to Vincent Delecroix, Travis Scrimshaw

[tscrim]

Changed author from Julian Rüth to Julian Rüth, Kwankyu Lee

[kwankyu]

comment:40

I have no objection :-) Thank you!

[vbraun]

Changed branch from u/klee/16561 to da7cb4d