#12876: Fix element and parent classes of Hom categories to be abstract, and
simplify the Hom logic.
--------------------------------------------------------+-------------------
       Reporter:  nthiery                               |         Owner:  
nthiery                                                       
           Type:  enhancement                           |        Status:  
needs_work                                                    
       Priority:  major                                 |     Milestone:  
sage-5.1                                                      
      Component:  categories                            |    Resolution:        
                                                        
       Keywords:  categories, Hom                       |   Work issues:  Fix 
the review-nt patch, fix doctests in map.pyx and homset.py
Report Upstream:  N/A                                   |     Reviewers:  Simon 
King                                                    
        Authors:  Nicolas M. ThiƩry                     |     Merged in:        
                                                        
   Dependencies:  #715, #11521, #12875, #12877, #12215  |      Stopgaps:        
                                                        
--------------------------------------------------------+-------------------
Changes (by SimonKing):

  * work_issues:  Fix the review-nt patch => Fix the review-nt patch, fix
                  doctests in map.pyx and homset.py


Comment:

 I get four errors with `make ptestlong`:
 {{{
 ----------------------------------------------------------------------

 The following tests failed:

         sage -t  --long -force_lib devel/sage/sage/categories/homset.py #
 2 doctests failed
         sage -t  --long -force_lib devel/sage/sage/categories/map.pyx # 2
 doctests failed
 ----------------------------------------------------------------------
 }}}
 namely
 {{{
 sage -t --long -force_lib "devel/sage/sage/categories/homset.py"
 **********************************************************************
 File
 
"/mnt/local/king/SAGE/stable/sage-5.0.beta13/devel/sage/sage/categories/homset.py",
 line 228:
     sage: Hom(PA,PJ).category()
 Expected:
     Join of Category of hom sets in Category of rings and Category of hom
 sets in Category of modules over Rational Field
 Got:
     Category of hom sets in Category of modules over Rational Field
 **********************************************************************
 File
 
"/mnt/local/king/SAGE/stable/sage-5.0.beta13/devel/sage/sage/categories/homset.py",
 line 337:
     sage: End(QQ).category()
 Expected:
     Category of hom sets in Category of rings
 Got:
     Category of hom sets in Category of sets
 **********************************************************************
 }}}
 and
 {{{
 sage -t --long -force_lib "devel/sage/sage/categories/map.pyx"
 **********************************************************************
 File
 
"/mnt/local/king/SAGE/stable/sage-5.0.beta13/devel/sage/sage/categories/map.pyx",
 line 382:
     sage: phi.category()
 Expected:
     Category of hom sets in Category of rings
 Got:
     Category of hom sets in Category of sets
 **********************************************************************
 File
 
"/mnt/local/king/SAGE/stable/sage-5.0.beta13/devel/sage/sage/categories/map.pyx",
 line 388:
     sage: f.category()
 Expected:
     Join of Category of hom sets in Category of rings and Category of hom
 sets in Category of modules over Rational Field
 Got:
     Category of hom sets in Category of modules over Rational Field
 **********************************************************************
 }}}

 For reference, I have
 {{{
 king@mpc622:/mnt/local/king/SAGE/stable/sage-5.0.beta13/devel/sage$ hg
 qapplied
 trac_12808-classcall_speedup-fh.patch
 trac_12808_nested_class_cython.patch
 trac_12808-classcall_cdef.patch
 trac12215_weak_cached_function.patch
 trac12215_segfault_fixes.patch
 trac_715_combined.patch
 trac_11521_homset_weakcache_combined.patch
 trac_12875-category-fix_abvar_homspace-nt.patch
 trac_12877-category-for_more_rings_and_schemes-nt.patch
 trac_12876_category-fix_abstract_class-nt-rel11521.patch
 trac_12876_category-fix_abstract_class-nt-rel11521-review-nt.patch
 }}}
 How is that different from your setting?

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12876#comment:35>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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