#10667: Morphisms and Objects of Categories
--------------------------------------------------+-------------------------
   Reporter:  SimonKing                           |          Owner:  nthiery    
                  
       Type:  enhancement                         |         Status:  needs_work 
                  
   Priority:  major                               |      Milestone:  sage-5.0   
                  
  Component:  categories                          |       Keywords:  objects 
morphisms containment
Work_issues:  Cope with non-unique number fields  |       Upstream:  N/A        
                  
   Reviewer:                                      |         Author:  Simon King 
                  
     Merged:                                      |   Dependencies:  #9138, 
#11115, #11780        
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Changes (by SimonKing):

  * work_issues:  Cartesian products => Cope with non-unique number fields


Comment:

 I think I found a valid work-around: Sometimes, a number field is created
 with passing the option `cache=False` to the number field constructor. If
 that option is used, I suggest to call the new
 `_remove_from_homset_cache`. It seems to work!

 With that change (not yet posted), we have
 {{{
 sage: E = EllipticCurve('389a'); P = E.heegner_point(-7, 5); P
 Heegner point of discriminant -7 and conductor 5 on elliptic curve of
 conductor 389
 sage:  z = P.point_exact(100, optimize=True)
 }}}
 With the old patch, one would have the following error:
 {{{
 AssertionError: BUG in coercion model
     Apparently there are two versions of
         Number Field in a with defining polynomial x^12 + 4*x^11 + 56*x^10
 + 170*x^9 + 1130*x^8 + 2564*x^7 + 10791*x^6 + 18054*x^5 + 51340*x^4 +
 57530*x^3 + 102986*x^2 + 53724*x + 35001
     in the cache.
 }}}

 Running doctests, and then I hope the most serious problems have finally
 disappeared...

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10667#comment:56>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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