#19473: FiniteDimensionalAlgebra.is_unitary is not sufficient
-------------------------------------+-------------------------------------
       Reporter:  darij              |        Owner:
           Type:  defect             |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.10
      Component:  algebra            |   Resolution:
       Keywords:  finite-            |    Merged in:
  dimensional algebra, linear        |    Reviewers:
  algebra                            |  Work issues:  check that it works
        Authors:  Darij Grinberg     |  (my sage is still compiling); test
Report Upstream:  N/A                |  for speed regressions
         Branch:                     |       Commit:
  public/algebra/finite_dim_algebra_fixes-19473|  
6fa53aad0a3faf6304a8dea0f5cc92f7009f41f7
   Dependencies:                     |     Stopgaps:
-------------------------------------+-------------------------------------
Changes (by tscrim):

 * commit:  376152ea6bd6616b9b47b184b5e4c508c4850f86 =>
     6fa53aad0a3faf6304a8dea0f5cc92f7009f41f7
 * branch:  public/ticket/19473 =>
     public/algebra/finite_dim_algebra_fixes-19473


Comment:

 Some things with `UniqueRepresentation` are annoying, but overall that
 isn't so big here IMO. Here's my proposal with `UniqueRepresentation` and
 also changing the default category to be `MagmaticAlgebras`. I would like
 to check during construction if the algebra is
 associative/unital/commutative but this is too expensive. Also refining
 the category after the fact can lead to subtle bugs, mainly the elements
 don't know the could have more methods from the refined category. So I'm
 leaving it to the user to pass the correct category (but I left the
 `assume_associative`).
 ----
 New commits:
 
||[http://git.sagemath.org/sage.git/commit/?id=6fa53aad0a3faf6304a8dea0f5cc92f7009f41f7
 6fa53aa]||{{{Adding UniqueRepresentation behavior.}}}||

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Ticket URL: <http://trac.sagemath.org/ticket/19473#comment:7>
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