#18942: Weird bug in roots of a polynomial in relative number field extension
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       Reporter:  robharron                     |        Owner:
           Type:  defect                        |       Status:  new
       Priority:  major                         |    Milestone:  sage-6.8
      Component:  number fields                 |   Resolution:
       Keywords:  Relative number field, roots  |    Merged in:
        Authors:                                |    Reviewers:
Report Upstream:  N/A                           |  Work issues:
         Branch:                                |       Commit:
   Dependencies:                                |     Stopgaps:
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Comment (by pbruin):

 In fact, in the above example we have
 {{{
 sage: K == L
 True
 }}}
 which causes a cache lookup in `PolynomialRing` to return `K['x']` when
 given `L` as input.

 We should probably make number fields satisfy `K == L` if and only if `K
 is L`, i.e. make them inherit from `WithEqualityById`.  Doing this in the
 most naive way unfortunately leads to a number of doctest failures.

--
Ticket URL: <http://trac.sagemath.org/ticket/18942#comment:2>
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