#11900: Serious regression caused by #9138
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   Reporter:  SimonKing                                         |          
Owner:  tbd                  
       Type:  defect                                            |         
Status:  needs_work           
   Priority:  critical                                          |      
Milestone:  sage-4.8             
  Component:  performance                                       |       
Keywords:  categories regression
Work_issues:  Laurent series rings are fields. CFF is a field.  |       
Upstream:  N/A                  
   Reviewer:  Jeroen Demeyer, Nicolas M. ThiƩry                 |         
Author:  Simon King           
     Merged:                                                    |   
Dependencies:  #9138 #11911         
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Comment(by SimonKing):

 Replying to [comment:148 nthiery]:
 > Indeed; sorry, I should have posted the patch here since we did not get
 to work with the Sage-Combinat queue. Please merge it in your patch as you
 feel appropriate.

 Meanwhile I wonder whether that change shouldn't better be put on a
 different ticket. Namely, using the meet instead of the current algorithm
 (recall: The algorithm used in _category_for_hom was used before, I merely
 factored it out) actually would change things.

 Namely, the meet may return a join category. But the current algorithm for
 determining the category for a homset will not return a join category,
 unless the categories of both parents coincide.

 Example:
 {{{
 sage: Algebras(QQ)._meet_(Category.join([Fields(), ModulesWithBasis(QQ)]))
 Join of Category of rings and Category of vector spaces over Rational
 Field
 sage: PA = Parent(category=Algebras(QQ))
 sage: PJ = Parent(category=Category.join([Fields(),
 ModulesWithBasis(QQ)]))
 sage: H = Hom(PA,PJ); H
 Set of Homomorphisms from <type 'sage.structure.parent.Parent'> to <type
 'sage.structure.parent.Parent'>
 sage: H.category()
 Category of hom sets in Category of rings
 sage: H.category().base_category
 Category of rings
 }}}

 Using the meet would be a non-trivial change that probably has little to
 do with a speedup. So, better move it to another ticket, isn't it?

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11900#comment:149>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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