categories for polynomial rings

[robertwb]

Currently, they're always just commutative rings.

Apply:

1. attachment: 9944-poly-cat.patch
2. attachment: trac-9944-poly_cat_doctests.patch
3. attachment: trac-9944-poly-cat-review.patch
4. attachment: trac-9944-polynomial_speedup.patch
5. attachment: trac9944_abvar_endomorphism.patch
6. attachment: trac9944_faster_and_cleaner_coercion.2.patch
7. attachment: trac9944_addendum.patch

Note

The same result can be obtained with the original patches:

1. attachment: 9944-poly-cat.patch
2. attachment: trac-9944-poly_cat_doctests.patch
3. attachment: trac-9944-poly-cat-review.patch
4. attachment: trac9944_polynomial_speedup.patch (Note the name difference to 4. above)
5. attachment: trac9944_abvar_endomorphism.patch
6. attachment: trac9944_faster_and_cleaner_coercion.patch (Note the name difference to 6. above)
7. attachment: trac9944_addendum.patch

Depends on #11139

CC: @sagetrac-sage-combinat

Component: categories

Author: Robert Bradshaw, Simon King

Reviewer: Nicolas M. Thiéry, Mike Hansen, Martin Raum

Merged: sage-4.7.1.alpha2

Issue created by migration from https://trac.sagemath.org/ticket/9944

[robertwb]

comment:1

Attachment: 9944-poly-cat.patch.gz

[nthiery]

comment:2

Hi Robert!

I have been through the patch, and it sounds good! I won't have the time to actually test it before some time, so please anyone beat me to it!

Just one micro question: does PolynomialRing actually check that the ring is commutative?

Cheers

[mwhansen]

Author: Robert Bradshaw

[mwhansen]

Reviewer: Nicolas M. Thiéry, Mike Hansen

[mwhansen]

comment:3

Attachment: trac_9944.patch.gz

I went ahead and moved the functionality to it's own category since we want the mathematical information at the category level.  Could someone look over these changes?

[robertwb]

comment:4

The first patch only concerned univarite polynomial rings, the logic is not all correct for multivariate polynomial rings (though on an orthogonal note, that could use some fixing up as well). It seems odd to have a category of univariate polynomial rings over a fixed basering, which is why I put the logic into the concrete object. I suppose the category should a be declared as a graded R-algebra as well (do we have join categories yet?).

I don't know if PolynomialRing asserts its basering is commutative, but IIRC it's been assumed for a long time.

[robertwb]

comment:5

Apply only 9944-poly-cat.patch

[robertwb]

Attachment: 9944-poly-cat-doctests.patch.gz

[robertwb]

comment:6

Apply 9944-poly-cat.patch and 9944-poly-cat-doctests.patch .