#17741: Polynomial __div__ override redundant with coercion.
-------------------------+-------------------------------------------------
       Reporter:         |        Owner:
  robertwb               |       Status:  needs_work
           Type:         |    Milestone:  sage-6.9
  enhancement            |   Resolution:
       Priority:  major  |    Merged in:
      Component:         |    Reviewers:
  coercion               |  Work issues:
       Keywords:         |       Commit:
        Authors:         |  f5a59a3400508531d6d19803dc277c01e896f8d8
  Robert Bradshaw        |     Stopgaps:
Report Upstream:  N/A    |
         Branch:         |
  public/17741           |
   Dependencies:         |
  #17740                 |
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Changes (by vdelecroix):

 * status:  needs_review => needs_work


Comment:

 I still get the error as in [comment:8]. Though the following works well
 {{{
 sage: (x+5) / R.base_ring()(2)
 8*x + 10
 }}}
 and one can check
 {{{
 sage: cm = get_coercion_model()
 sage: R.<x> = Integers(15)[]
 sage: a = cm.get_action(R, R.base_ring(), operator.div)
 sage: a(x+5,2)
 8*x + 10
 }}}

 The problem is when we divide by an integer
 {{{
 sage: cm.get_action(R, ZZ, operator.div)
 <NOTHING>
 }}}
 The above fails because the following does
 {{{
 sage: cm = get_coercion_model()
 sage: R.<x> = Integers(15)[]
 sage: right_mul = cm.get_action(R, ZZ, operator.mul)
 sage: action = ~right_mul
 Traceback (most recent call last):
 ...
 CoercionException: x (=Ring of integers modulo 15) is not in Category of
 integral domains
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/17741#comment:10>
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