Derivations for inseparable function fields

[saraedum]

This ticket implements derivations for inseparable extensions of function fields.

[git]

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

​4ac15f9	Merge branch 'ticket/16561' into ticket/16564
​5c3e74b	Merge branch 'develop' into ticket/16523
​a54e0dd	Merge branch 'ticket/16523' into ticket/16563
​d7d61e6	Merge branch 'ticket/16563' into ticket/16562
​0f3870b	Merge branch 'ticket/16563' into ticket/16575
​8a61285	Merge branch 'ticket/16575' into ticket/16576
​517e8b3	Merge branch 'ticket/16576' into ticket/16562
​0a63b2e	minor docstring fix
​ff61625	Merge branch 'ticket/16563' into ticket/16562
​1e32dae	Merge branch 'ticket/16562' into ticket/16564

[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
​8406f2e	Merge branch 'u/saraedum/ticket/16561' of git://trac.sagemath.org/sage into t/16564/ticket/16564
​716ec10	Merge branch 'develop' into t/16562/ticket/16562
​a2ab48b	Fixed docstring syntax error
​cb3a16b	Merge branch 'u/saraedum/ticket/16562' of git://trac.sagemath.org/sage into t/16564/ticket/16564

[git]

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

​256f7cf

Fixed doctests which failed due to changed printing of function fields and their morphisms

[git]

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

​9137595	Fix minor issues in function field docstrings
​a6852c5	cleanup code and docstrings
​bd18422	Merge branch 'develop' into t/16576/ticket/16576
​5daae9a	fix typos
​aa5b887	Merge branch 'u/saraedum/ticket/16563' in 8.0.b8
​eebe2c8	Merge branch 'develop' into t/16563/public/16563
​9aca052	Merge branch 't/16563/public/16563' into t/16575/ticket/16575
​4cce86f	Merge branch 't/16575/ticket/16575' into t/16576/ticket/16576
​4460407	Merge branch 't/16576/ticket/16576' into t/16562/ticket/16562
​6ccffea	Merge branch 't/16562/ticket/16562' into t/16564/ticket/16564

[git]

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

​303e2c6

removed merge artifacts

[git]

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

​4bba9ae	is_separable method added to function field class
​444fb59	INPUT and OUTPUT blocks added to documentation.
​3cbf43f	Fix docbuilding errors
​05d66cd	Merge remote-tracking branch 'trac/u/saraedum/add__is_separable__to_function_field_class' into t/16564/ticket/16564

[git]

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

​6ee8eee

fix relative imports

[saraedum]

Last 10 new commits:

​cb3a16b	Merge branch 'u/saraedum/ticket/16562' of git://trac.sagemath.org/sage into t/16564/ticket/16564
​256f7cf	Fixed doctests which failed due to changed printing of function fields and their morphisms
​f594422	Merge branch 't/16576/ticket/16576' into t/16562/ticket/16562
​9645e83	Added forgotten . before constructor.
​4460407	Merge branch 't/16576/ticket/16576' into t/16562/ticket/16562
​6ccffea	Merge branch 't/16562/ticket/16562' into t/16564/ticket/16564
​303e2c6	removed merge artifacts
​05d66cd	Merge remote-tracking branch 'trac/u/saraedum/add__is_separable__to_function_field_class' into t/16564/ticket/16564
​6ee8eee	fix relative imports
​beed937	Merge remote-tracking branch 'trac/u/saraedum/ticket/16564' into 16564

[git]

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

​3816bd9

Merge remote-tracking branch 'trac/develop' into 16564

[saraedum]

New commits:

​3816bd9

Merge remote-tracking branch 'trac/develop' into 16564

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New commits:

​3816bd9

Merge remote-tracking branch 'trac/develop' into 16564

[git]

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

​1f3aebe

Change is_separable() to be recursive

[git]

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

[sijsling]

Changing FunctionFieldIsomorphism to FunctionFieldVectorSpaceIsomorphism in line 424 of function_field/maps.py yields a working version. All that remains are some small failures in doctests, which I have attached.

[git]

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

​682fb80

Merge remote-tracking branch 'trac/develop' into 16564

[saraedum]

Thanks, that renaming was not intentional. The printing of morphisms has changed, so these errors are expected.

[git]

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

​268984f	Fix incorrect merge in 3816bd9c2790857e8f06a1b9c7b27da05c315bf3
​6ea2e69	Adapt doctest output to changed printing

[sijsling]

This builds for me along with its documentation, and looks pretty great. Here are some remarks.

(1) In the method _test_derivation you may also want to test that d(f) is zero, or more precisely that if we calculate d(f) term by term we also get 0. Or yet differently, the lift to a derivation in both x and y should send f to zero.

(2) Similarly, you may want to check that the deriviation is non-trivial.

(3) In the docstring, it seems better to use k for the field of constants instead of K, simply for consistency, and leave K to be the function field in question. You may also want to point out that you do not assume K to be the function field of an absolutely irreducible curve. (This is why you need k to be perfect.)

In the first part of the description of the algorithm, you may want to write "a rational function field F over k" instead of "another function field F", and in the complementary case you can mention that this is where you use the hypothesis on k being perfect.

Points (1) and (2) are not very important; indeed, I performed done thousands of ad hoc tests of them without a single error, and the algorithms are mathematically correct as far as I can judge. Only the points in (3) apply. They are very small and apart from them this addition seems completely neat.

[sijsling]

Sorry, I messed up this fancy terminology: where I wrote "absolutely irreducible" I should have written "geometrically reduced", or perhaps "geometrically integral".

[saraedum]

sijsling thanks for the review. If you want to make these changes yourself, please feel free to make them and I'll review. Otherwise, I'll hopfefully get around to make the necessary changes myself soon.

[git]

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

​6ccffea	Merge branch 't/16562/ticket/16562' into t/16564/ticket/16564
​303e2c6	removed merge artifacts
​05d66cd	Merge remote-tracking branch 'trac/u/saraedum/add__is_separable__to_function_field_class' into t/16564/ticket/16564
​6ee8eee	fix relative imports
​beed937	Merge remote-tracking branch 'trac/u/saraedum/ticket/16564' into 16564
​3816bd9	Merge remote-tracking branch 'trac/develop' into 16564
​682fb80	Merge remote-tracking branch 'trac/develop' into 16564
​268984f	Fix incorrect merge in 3816bd9c2790857e8f06a1b9c7b27da05c315bf3
​6ea2e69	Adapt doctest output to changed printing
​3a07e34	Improve documentation and tests

[saraedum]

Thanks, I made a minimal change to the unit test code. If your happy with this and doctests pass, then we can set this to positive review :)

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New commits:

​f63c4ff

Do not assert in tests

[sijsling]

I am of course fine with that! Rebuilt just to be sure and of course everything still worked. So now it is up to the bot to see if there are other issues.

[saraedum]

The pyflakes complaints are not bugs and are fine anyway with Python 3 as list comprehensions do not leak variables anymore.

The failing doctest in sage.databases.sql_db.SQLDatabase.__init__ can't really be caused by the changes here.

[swewers]

As other have said before: the change are all fine, and it would be very nice to have them available soon. The problems with the patchbot seem to be unrelated to this ticket.