#15348: "R.<a> =" syntactic sugar incorrect for EquationOrder
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       Reporter:  emassop            |        Owner:
           Type:  defect             |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-7.0
      Component:  number fields      |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Jeroen Demeyer     |    Reviewers:
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  u/jdemeyer/ticket/15348            |  64618f5c8b5ac24ccc688ac718ee2b43e42d0328
   Dependencies:                     |     Stopgaps:
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Comment (by emassop):

 Some comments on the docstring of `_defining_names`:

 * There is a test for orders, which have this method overridden, so I
 think it would be better to move this test.
 * I'm not sure about the example "For vector spaces and free modules, we
 get a basis", given that submodules normalize the basis they are given as
 input, so that `_defining_names` does not necessarily return the basis
 that the submodule was defined with. For instance
   {{{
 V = ZZ^3
 vectors = [(0,1,0), (1,3/2,0)]
 M = V.span(vectors)
 print M.basis()
   }}}
   prints
   {{{
 [
 (1, 1/2, 0),
 (0, 1, 0)
 ]
   }}}
   Could you mention something like this as a caveat for this method? Or
 perhaps get rid of this example, given that this method really only is
 interesting for things defined by some explicitly named elements?
 * Please get rid of "generator" and perhaps mention the `names` argument
 used by `R.<...> =`


 Otherwise, this all looks good to me.

--
Ticket URL: <http://trac.sagemath.org/ticket/15348#comment:42>
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