#15183: x in IntegralDomains() should refine category
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       Reporter:  saraedum           |        Owner:
           Type:  enhancement        |       Status:  needs_review
       Priority:  minor              |    Milestone:  sage-6.0
      Component:  categories         |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Julian Rueth       |    Reviewers:
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  u/saraedum/ticket/15183            |  2282a39caa83c83ceef1000eb028014f5556a606
   Dependencies:  #14482             |     Stopgaps:
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Comment (by SimonKing):

 Replying to [comment:13 saraedum]:
 > What does `Fields.__contains__` do? It calls `.is_field()`

 No, it calls `sage.rings.ring._is_Field`, and this is where `.is_field()`
 might be called and the refinement might happen.

 > Integral domains should do the same, call `.is_integral_domain()` which
 is as expensive.
 >
 > > But `IntegralDomains` has no custom implementation of `__contains__`.
 So, could you elaborate a bit more on the reason of your suggestion?
 > I believe that's why the check `IntegerModRing(2) in IntegralDomains()`
 failed, right?

 Do you suggest to introduce a custom `IntegralDomains.__contains__`?

--
Ticket URL: <http://trac.sagemath.org/ticket/15183#comment:15>
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