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

 Replying to [comment:51 SimonKing]:
 > First of all, Homsets ''are'' cached. But using unique representation,
 it is less easy to break the cache.

 I am glad that UniqueRepresentation works well :-)

 > And I think that we should use any opportunity to reduce the number of
 violations of the unique parent assumption. After all, it is a matter of
 efficiency.

 Agreed, the more unique parents, the better. But you don't have to fix
 all of Sage misfeatures in just this patch :-)

 Besides, I am still not yet sure that we want to strictly enforce 100%
 unique parents. There might be occasional exceptions -- I don't know,
 things like temporarily created parents or what not -- where we might
 want to not have uniqueness.

 > Actually it was. The problem was that (for the sake of explicit
 > documentation) some tests create a polynomial ring directly, not
 > using the `PolynomialRing` constructor. My solution: I introduced a
 > parent method for rings, that removes the ring from the homset
 > cache, and use it after any test that creates a non-unique
 > parent. Of course, it is for internal use only.

 Ok. I could see other use cases. Should this be a method of
 UniqueRepresentation -- of course still for internal use ?

 Cheers,
                    Nicolas

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10667#comment:52>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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