Add tests in the category of euclidean domains

[saraedum]

Currently, there are no generic tests in the category of euclidean domain which test the correctness of the quotient with remainder.

Depends on #14482
Depends on #15192

Component: categories

Keywords: sd59

Author: Julian Rueth

Branch/Commit: 6261466

Reviewer: Peter Bruin, Travis Scrimshaw, Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/15191

[saraedum]

Branch: u/saraedum/ticket/15191

[saraedum]

Dependencies: #14482, #15192

[saraedum]

Author: Julian Rueth

[sagetrac-git]

Commit: 654b8a8

[sagetrac-git]

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

[changeset:654b8a8]

Implement a non-trivial some_elements() for polynomial rings

[pjbruin]

Changed branch from u/saraedum/ticket/15191 to u/pbruin/15191-EuclideanDomains_tests

[pjbruin]

comment:7

resolved merge conflicts

[pjbruin]

Changed commit from 654b8a8 to 9c44bec

[pjbruin]

Work Issues: fix doctest failures

[pjbruin]

comment:8

After resolving the conflicts there are various doctest failures:

sage -t --long src/sage/rings/padics/padic_base_leaves.py  # 3 doctests failed
sage -t --long src/sage/rings/polynomial/polynomial_ring.py  # 1 doctest failed
sage -t --long src/doc/en/thematic_tutorials/coercion_and_categories.rst  # 3 doctests failed
sage -t --long src/doc/en/thematic_tutorials/tutorial-objects-and-classes.rst  # 2 doctests failed

Some of these are due to the testsuite running euclidean_degree() on random elements; these may be zero, which causes

NotImplementedError: euclidean degree not defined for the zero element

[saraedum]

Changed keywords from none to sd59

[saraedum]

Changed branch from u/pbruin/15191-EuclideanDomains_tests to u/saraedum/ticket/15191

[sagetrac-git]

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

f60c865

Fixed documentation doctests

[tscrim]

Changed commit from f60c865 to ce64f71

[tscrim]

Changed work issues from fix doctest failures to none

[saraedum]

comment:14

Like many inexact rings, the p-adics have zerodivisors. Not in theory of course, but in practice (i.e. the p-adics are an integral domain but typically implemented with finite precision which leads to zero-divisors). That's why I put the continue there if a or a*b are zero. I had put a remark in the commit message but not in the code (which was probably not very smart).

The check you put there is valid for exact rings however. As you say it should probably not be in the category of euclidean domains. Would you mind moving this to a different ticket?

[sagetrac-git]

Changed commit from ce64f71 to 75fa2db

[sagetrac-git]

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

75fa2db

Made a note about zero divisors.

[tscrim]

comment:16

Okay, I'v reverted the change and created #16596 for the zero divisors tests (I'll post a branch there shortly).

[sagetrac-git]

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

dfb049e	Merge branch 'public/ticket/euclidean_domains_tests-15191' of ssh://trac.sagemath.org:22/sage into 15191
7f30ddc	trac #15191 change bad syntax of 2 input blocks

[sagetrac-git]

Changed commit from 75fa2db to 7f30ddc

[sagetrac-git]

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

248dfbc

Some more review tweaks and fixes.

[sagetrac-git]

Changed commit from 7f30ddc to 248dfbc

[sagetrac-git]

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

6261466

Stupid typo...

[sagetrac-git]

Changed commit from 248dfbc to 6261466

[saraedum]

comment:21

Thanks for your review patches. What is the status of this ticket now? Do you want a review of your latest changes?

[tscrim]

comment:22

Yes please (and Frédéric's too). If you're happy with the changes, then I believe it's a positive review. (Also I'd appreciate a review of #16596 too.)

[tscrim]

Changed reviewer from Peter Bruin, Travis Scrimshaw to Peter Bruin, Travis Scrimshaw, Frédéric Chapoton

[vbraun]

Changed branch from public/ticket/euclidean_domains_tests-15191 to 6261466