#9138: Categories for polynomial rings
--------------------------+-------------------------------------------------
   Reporter:  jbandlow    |       Owner:  nthiery                  
       Type:  defect      |      Status:  needs_review             
   Priority:  major       |   Milestone:  sage-4.7                 
  Component:  categories  |    Keywords:  introspection, categories
     Author:  Simon King  |    Upstream:  N/A                      
   Reviewer:              |      Merged:                           
Work_issues:              |  
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Changes (by newvalueoldvalue):

  * status:  new => needs_review
  * author:  => Simon King


Comment:

 Since #9944 almost has a positive review but does not entirely fix the bug
 reported here, I'm posting my patch here, building on top of that.

 Examples:

 With the patches from #9944:
 {{{
 sage: QQ['x'].category()        # why not additionally an algebra?
 Category of euclidean domains
 sage: QQ['x','y'].category()    # why not an algebra?
 Category of commutative rings
 sage: SteenrodAlgebra(2)['x'].category()  # this is wrong
 Category of commutative rings
 sage: QQ['x','y'].sum([1,1])
 Traceback (most recent call last):
 ...
 AttributeError:
 
'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular'
 object has no attribute 'sum'
 }}}

 Adding my (not yet submitted) patch, I get:
 {{{
 sage: QQ['x'].category()
 Join of Category of euclidean domains and Category of commutative algebras
 over Rational Field
 sage: QQ['x','y'].category()
 Category of commutative algebras over Rational Field
 sage: SteenrodAlgebra(2)['x'].category()
 Category of algebras over mod 2 Steenrod algebra
 sage: QQ['x','y'].sum([1,1])
 2
 }}}

 So, I think the bug reported here is fixed. For me, all doctests pass.

 Depends on #9944

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9138#comment:8>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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