Fraction field of Ore polynomial ring

[xcaruso]

We implement the fraction field of Ore polynomial rings.

The elements of the fraction field are represented by fractions of the form denom^(-1) * num.

Depends on #29629

Component: algebra

Author: Xavier Caruso

Branch/Commit: c40eebe

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/29678

[xcaruso]

Branch: u/caruso/ore_functions

[xcaruso]

Last 10 new commits:

52932e0	fix typos
31a3c07	add documentation
0a232cd	LaTeX representation of derivations
d456551	implement Hilbert shift
f225cbc	fix pyflakes
9067b73	Ore functions (first draft)
d0a9712	Hilbert shift
650079d	polish implementation
f6835a3	implement extend_to_fraction_field for derivations
2e9458b	register coercion from a Ore ring to its fraction field

[xcaruso]

Author: Xavier Caruso

[xcaruso]

Commit: 2e9458b

[xcaruso]

Changed dependencies from #29269 to #29629

[sagetrac-git]

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

a74ddac

reduced trace and reduced norm

[sagetrac-git]

Changed commit from 2e9458b to a74ddac

[sagetrac-git]

Changed commit from a74ddac to f50aca6

[sagetrac-git]

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

7cf9e02	doctest in ore_function_field.py
f50aca6	more doctests

[sagetrac-git]

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

0c8f04d	Merge branch 'develop' into t/29678/ore_functions
b35e1d0	fix one doctest
131d78e	Merge branch 'develop' into t/29629/ore_polynomials_rebased
4f273e8	Merge branch 't/29629/ore_polynomials_rebased' into t/29678/ore_functions
648cf6d	remove trailing spaces

[sagetrac-git]

Changed commit from f50aca6 to 648cf6d

[sagetrac-git]

Changed commit from 648cf6d to 15edb98

[sagetrac-git]

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

15edb98

fix pickling

[xcaruso]

comment:8

There is still a small issue with category (elements are not instances of parent.category().element_class) but I don't know how I should fix it. Any ideas?

[tscrim]

comment:9

Typically that means you are returning elements that are not instances of ParentObject.element_class. If this is for a morphism parent, you can simply silence that warning. (This is a common practice as there can be many morphism types, but we don't (yet) have a good framework for these things. I have seen a workaround for this that just dynamically creates the new element class, but I forget where in the Sage code this is done.)

[sagetrac-git]

Changed commit from 15edb98 to 070792b

[sagetrac-git]

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

445913a	abstract method degree raises NotImplementedError
fdbded7	add full-stop after math formulas
c778356	remove import sage
bf17a36	Merge branch 'develop' of https://github.com/sagemath/sage into t/29629/ore_polynomials_rebased
f7b0edd	Merge branch 't/29629/ore_polynomials_rebased' into t/29678/ore_functions
94a1a5c	lazy import
15f6dfa	fix indentation
a9bae69	update documentation
3cf021a	Merge branch 't/29629/ore_polynomials_rebased' into t/29678/ore_functions
070792b	let extend_to_fraction_field be more tolerant

[xcaruso]

comment:11

Here is my issue:

sage: k.<a> = GF(5^3)
sage: Frob = k.frobenius_endomorphism()
sage: S.<x> = k['x', Frob]
sage: K = S.fraction_field()
sage: K(x)._test_category()
Traceback (most recent call last):
...
AssertionError: False is not true

K.category().element_class is sage.categories.algebras.Algebras.element_class but K(x) is an instance is an instance of sage.rings.polynomial.ore_function_element.OreFunction_with_large_center which, apparently, does not define from the former (although OreFunction_with_large_center derives from AlgebraElement).

[tscrim]

comment:12

This should be your problem: In OreFunctionField._element_constructor_, you need to change

-self.Element(self, *args, **kwds)
+self.element_class(self, *args, **kwds)

This also needs to be changed for OrePolynomialRing._element_constructor_:

-C = self.Element
+C = self.element_class

One other thing: the extend_to_fraction_field needs doctests.

[sagetrac-git]

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

c7d0acd	reorganize documentation
ec0e24b	Element -> element_class
8c0efe7	add a doctest

[sagetrac-git]

Changed commit from 070792b to 8c0efe7

[xcaruso]

comment:14

Replying to @tscrim:

This should be your problem: In OreFunctionField._element_constructor_, you need to change

-self.Element(self, *args, **kwds)
+self.element_class(self, *args, **kwds)

This also needs to be changed for OrePolynomialRing._element_constructor_:

-C = self.Element
+C = self.element_class

Thanks, It indeed fixes the problem!

One other thing: the extend_to_fraction_field needs doctests.

There were already doctests. But I've added one more.

[sagetrac-git]

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

44c9913

typos

[xcaruso]

comment:23

Replying to @tscrim:

I think you also need the conf.py file.

Oh, I see. Thanks.

[tscrim]

comment:24

Rather than be a direct file that refers back to conf_sub.py, the other folders are symlinks. Could you do the same thing here?

[xcaruso]

comment:25

My conf.py is a symlink, isn't it?

[sagetrac-git]

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

d3c744e

accept more errors in trying to inverse the twisting morphism

[sagetrac-git]

Changed commit from 548a1dc to d3c744e

[sagetrac-git]

Changed commit from d3c744e to 7e3abda

[sagetrac-git]

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

7e3abda

typos in doctests

[tscrim]

comment:28

Ah, I see. Git is just handling it in a strange way. Sorry for the noise.

However, no bare excepts.

[xcaruso]

comment:29

Btw, I saw that there are pyflakes warnings in conf.py due to the imports (on two consecutive lines):

from sage.docs.conf import release, exclude_patterns
from sage.docs.conf import *

Shouldn't we remove the second import?

[tscrim]

comment:30

I wouldn't touch the conf.py files here. That should be a separate ticket as that is outside of the scope and could have larger impact to Sage's doc.

[xcaruso]

comment:31

Replying to @tscrim:

I wouldn't touch the conf.py files here. That should be a separate ticket as that is outside of the scope and could have larger impact to Sage's doc.

Yes, I agree.

[tscrim]

comment:32

The only thing missing from me giving this a positive review is taking care of the bare except: (this can catch keyboard interrupts I've been told, so it is essentially prohibited to have in Sage code).

[tscrim]

Changed commit from 7e3abda to 1c7a67c

[tscrim]

comment:33

Here is a version with my docbuild fixes from #29629.

---

New commits:

f111d30	Merge branch 'u/caruso/ore_polynomials_rebased' of git://trac.sagemath.org/sage into u/caruso/ore_polynomials_rebased
5d822f3	Fixing the doc and != for polynomial injection maps.
1c7a67c	Merge branch 'u/tscrim/ore_polynomials-29629' of git://trac.sagemath.org/sage into u/caruso/ore_polynomials-29629

[tscrim]

Changed branch from u/caruso/ore_functions to u/tscrim/ore_functions-29678

[xcaruso]

Changed branch from u/tscrim/ore_functions-29678 to u/caruso/ore_functions-29678

[xcaruso]

Changed commit from 1c7a67c to b327f51

[xcaruso]

comment:35

OK, I've added an explicit list of exceptions.

I also rebased the commit on my branch because I thought you have forgotten to include the core of this ticket in your merge :-). I hope everything is now merged correctly.

---

Last 10 new commits:

8c0efe7	add a doctest
44c9913	typos
e1fc660	more doctests
59d3ed2	Merge branch 't/29629/ore_polynomials_rebased' into t/29678/ore_functions
f6ea4fd	Merge branch 't/29629/ore_polynomials_rebased' into t/29678/ore_functions
548a1dc	add conf.py
d3c744e	accept more errors in trying to inverse the twisting morphism
7e3abda	typos in doctests
055bdeb	Merge branch 't/29629/ore_polynomials_rebased' into t/29678/ore_functions
b327f51	add list of exceptions

[tscrim]

comment:36

Whoops, bad copy-paste of the branch name. ^^;; If the patchbot comes back green, then positive review. Thank you.

[xcaruso]

comment:37

The patchbots reported a bunch of errors in the documentation (some files are not found). However, I'm not sure that they are related to this ticket. Do you know what's happening here?

[tscrim]

comment:38

In ore_polynomial_ring.py:

-:module:`sage.rings.polynomial.ore_function_field`
+:mod:`sage.rings.polynomial.ore_function_field`

That is at least the current docbuild failure.

[sagetrac-git]

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

c40eebe

:module: -> :mod:

[sagetrac-git]

Changed commit from b327f51 to c40eebe

[tscrim]

comment:40

Thank you. LGTM.

[tscrim]

Reviewer: Travis Scrimshaw

[vbraun]

Changed branch from u/caruso/ore_functions-29678 to c40eebe