#9138: Categories for all rings
---------------------------------+------------------------------------------
   Reporter:  jbandlow           |          Owner:  nthiery                     
                  
       Type:  defect             |         Status:  needs_work                  
                  
   Priority:  major              |      Milestone:  sage-4.7.1                  
                  
  Component:  categories         |       Keywords:  introspection, categories 
for rings           
Work_issues:  Steenrod algebras  |       Upstream:  N/A                         
                  
   Reviewer:                     |         Author:  Simon King                  
                  
     Merged:                     |   Dependencies:  sage-4.7, #11268, #11139, 
#9976, #9944, #11269
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Comment(by SimonKing):

 Replying to [comment:71 SimonKing]:
 > Perhaps a "register_coercion" during initialisation could help.

 Actually, that registration should take place in the `__init_extra__`
 method that is defined in `sage.categories.algebras`. Without my patch,
 the rather generic coercion from the base ring is registered no matter
 what, which means that it could result in a very slow coerce map from the
 base ring.

 Therefore, my patch modifies `__init_extra__` so that the generic coercion
 is only registered if no "better" coercion has been registered before. It
 could be that that is a problem for Steenrod algebras.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9138#comment:72>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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