#17585: Implement coordinate_ring() for free module elements
-------------------------------------+-------------------------------------
       Reporter:  jdemeyer           |        Owner:
           Type:  defect             |       Status:  new
       Priority:  major              |    Milestone:  sage-6.5
      Component:  linear algebra     |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Jeroen Demeyer     |    Reviewers:
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  u/jdemeyer/ticket/17585            |  f7ef4c52a51b5c3da33b795a150476d00cbeb63a
   Dependencies:  #10513, #17578,    |     Stopgaps:
  #17561, #17583, #17584, #17587,    |
  #16399, #17602                     |
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Comment (by nbruin):

 I noticed this in one of the commits:
 {{{#!diff
 - from sage.categories.all import FreeModules
 - category = FreeModules(base_ring.category())
 + from sage.categories.all import Fields, FreeModules, VectorSpaces
 + if base_ring in Fields():
 +    category = VectorSpaces(base_ring)
 + else:
 +    category = FreeModules(base_ring)
 }}}
 It's important for performance and and memory-leaking that categories do
 *not* refer to their base rings. This information is already stored in the
 parent. Thus, the `FreeModules(base_ring.category())` is quite
 intentional. Please keep it in.

 Furthermore, since we were getting "Vectorspaces" before as well, I think
 the category code itself will do the "base_ring in Fields()" check
 already. No need to do it twice.

--
Ticket URL: <http://trac.sagemath.org/ticket/17585#comment:11>
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