x in IntegralDomains() should refine category

[saraedum]

Currently, IntegerModRing refines its category if asked for membership in Fields():

sage: M = IntegerModRing(3)
sage: M.category()
Join of Category of commutative rings ...
sage: M in Fields()
True
sage: M.category()
Join of Category of fields ...

The same does not happen for IntegralDomains():

sage: M = IntegerModRing(5)
sage: M.category()
Join of Category of commutative rings ...
sage: M in IntegralDomains()
False
sage: M.category()
Join of Category of commutative rings ...

The changes on this ticket copy the logic from fields over to integral domains.

Depends on #14482

CC: @simon-king-jena @nthiery

Component: categories

Author: Julian Rueth

Branch/Commit: u/saraedum/ticket/15183 @ 2282a39

Issue created by migration from https://trac.sagemath.org/ticket/15183

[saraedum]

Branch: u/saraedum/ticket/15183

[saraedum]

Dependencies: #14482

[saraedum]

Author: Julian Rueth

[saraedum]

comment:5

Simon, I believe I mostly adapted your code from Fields. Do mind having a look at this?

[sagetrac-git]

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

[changeset:2554616]	Added classes for discrete valuations
[changeset:5af8f0a]	Merge branch 'u/saraedum/ticket/15171' of http://trac.sagemath.org/sage into ticket/15183
[changeset:2907216]	Fixed a missing assignment in DiscreteValueGroup.
[changeset:2249b00]	Added DiscreteValueGroup
[changeset:23db51b]	Merge branch 'u/roed/ticket/14482' of ssh://trac.sagemath.org:2222/sage into ticket/15171

[sagetrac-git]

Commit: 2554616

[saraedum]

Changed dependencies from #14482 to #14482, #15171

[saraedum]

Changed dependencies from #14482, #15171 to #14482