#14982: When a parent is equipped with an embedding, consider coercions that 
don't
go through the embedding
-------------------------------------+-------------------------------------
       Reporter:  mmezzarobba        |        Owner:
           Type:  defect             |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.4
      Component:  coercion           |   Resolution:
       Keywords:  embedding          |    Merged in:
        Authors:  Marc Mezzarobba,   |    Reviewers:
  Vincent Delecroix                  |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  d99564520a5fd599c0fea62b86d0bdbfbd35c1a4
  u/mmezzarobba/14982-coerce_embeddings|     Stopgaps:
   Dependencies:                     |
-------------------------------------+-------------------------------------

Comment (by vdelecroix):

 Salut Marc,

 I am quite confused by the following
 {{{
 sage: K = QuadraticField(2)
 sage: RR.coerce_map_from(K)
 Composite map:
   From: Number Field in a with defining polynomial x^2 - 2
   To:   Real Field with 53 bits of precision
   Defn:   Generic morphism:
           From: Number Field in a with defining polynomial x^2 - 2
           To:   Real Lazy Field
           Defn: a -> 1.414213562373095?
         then
           Conversion via _mpfr_ method map:
           From: Real Lazy Field
           To:   Real Field with 53 bits of precision
 }}}
 But elements of `K` do implement directly an `_mpfr_` method
 {{{
 sage: K.an_element()._mpfr_
 <built-in method _mpfr_ of
 
sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic
 object at 0x7f3e3d94ff68>
 }}}
 So why the discovery does not choose this direct conversion map instead of
 going through the real lazy field? (note: this method `_mpfr_` is
 completely broken, but it does not change anything to the story)

 Vincent

--
Ticket URL: <http://trac.sagemath.org/ticket/14982#comment:60>
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