Fraction field of Ore polynomial ring

[caruso]

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.

[caruso]

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

[git]

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

​a74ddac

reduced trace and reduced norm

[git]

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

​7cf9e02	doctest in ore_function_field.py
​f50aca6	more doctests

[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

[git]

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

​15edb98

fix pickling

[caruso]

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]

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.)

[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

[caruso]

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]

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.

[git]

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

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

[caruso]

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.

[git]

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

​44c9913

typos

[tscrim]

Replying to caruso:

Replying to tscrim:

One other thing: the extend_to_fraction_field needs doctests.

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

Wrong method: RingDerivationWithoutTwist.extend_to_fraction_field. Sorry, I didn't realize there was more than one.

[tscrim]

Sorry, two places: RingDerivationWithTwist_generic.extend_to_fraction_field as well.

[git]

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

​e1fc660

more doctests

[caruso]

Fixed.

Also, I tried to reorganize a bit the documentation and separate commutative polynomials from noncommutative polynomials. I created a new file doc/en/reference/noncommutative_polynomial_rings/index.rst but I probably did something wrong because this file is not found when building the documentation. Do you know what's going on, here?

[tscrim]

I think you also need the conf.py file.

[git]

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

​1cc0ed8	Merge branch 'develop' into t/29629/ore_polynomials_rebased
​59d3ed2	Merge branch 't/29629/ore_polynomials_rebased' into t/29678/ore_functions
​200d7bd	update doctests
​f6ea4fd	Merge branch 't/29629/ore_polynomials_rebased' into t/29678/ore_functions

[git]

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

​548a1dc

add conf.py

[caruso]

Replying to tscrim:

I think you also need the conf.py file.

Oh, I see. Thanks.

[tscrim]

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?

[caruso]

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

[git]

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

​d3c744e

accept more errors in trying to inverse the twisting morphism

[git]

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

​7e3abda

typos in doctests

[tscrim]

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

However, no bare excepts.

[caruso]

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]

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.

[caruso]

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]

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]

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

[caruso]

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]

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

[caruso]

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]

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.

[git]

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

​c40eebe

:module: -> :mod:

[tscrim]

Thank you. LGTM.