#19939: Fixes and improvements to EuclideanRings.ParentMethods._test_quo_rem and
quo_rem for fields
-------------------------------------+-------------------------------------
       Reporter:  nthiery            |        Owner:
           Type:  defect             |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-7.1
      Component:  categories         |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Nicolas M. Thiéry  |    Reviewers:  Samuel Lelièvre
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  
u/nthiery/fix_euclideanrings_parentmethods__test_quo_rem_to_use__not_r_is_zero____rather_than__r__0_|
  6e8e4c0ff892df6a6f963513c9e8e3dd2be75b66
   Dependencies:  #19937             |     Stopgaps:
-------------------------------------+-------------------------------------
Changes (by nthiery):

 * reviewer:  Jeroen Demeyer, Samuel Lelièvre => Samuel Lelièvre


Old description:



New description:

 This ticket:

 - Fixes `EuclideanRings.ParentMethods._test_quo_rem` to use an `not
   is_zero` instead of `!=0`. This is more consistent and does not
   require coercion.

 - Improves `EuclideanRings.ParentMethods._test_quo_rem` to check that
   the results are in the same parent

 - Fixes `quo_rem` for fields to return the zero of the field instead of 0

 - Makes the two implementations `FieldElement.quo_rem` and
   `Fields.ElementMethods.quo_rem` consistent and reference each other.

--

Comment:

 New commits:
 
||[http://git.sagemath.org/sage.git/commit/?id=8a3978cb86984ef3e329a90251f62699be17778e
 8a3978c]||{{{19939: Improved EuclideanRings.ParentMethods._test_quo_rem to
 check the parents of the return values of quo_rem}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=4a9c931379ad9d0b04b03361a86d46306946194a
 4a9c931]||{{{19939: fix doctests of Fields.ElementMethods.quo_rem to
 actually exercise its code}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=6e8e4c0ff892df6a6f963513c9e8e3dd2be75b66
 6e8e4c0]||{{{19939: fix the two duplicated implementations of quo_rem for
 Fields to be consistent and refer to each other}}}||

--
Ticket URL: <http://trac.sagemath.org/ticket/19939#comment:14>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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