#18258: Fix coercion for matrix groups / matrix spaces
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   Reporter:  vdelecroix      |            Owner:
       Type:  enhancement     |           Status:  new
   Priority:  major           |        Milestone:  sage-6.7
  Component:  linear algebra  |         Keywords:
  Merged in:                  |          Authors:
  Reviewers:                  |  Report Upstream:  N/A
Work issues:                  |           Branch:
     Commit:                  |     Dependencies:  #18231
   Stopgaps:                  |
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 Add several fix to matrix groups and matrix spaces:
  - matrix space should not override the `__call__` of `Parent`
  - matrix groups should by default define a coercion embedding to the
 associated matrix space
  - use the method `_matrix_` to define a default conversion to matrix
 spaces

 It would solve the two following issues
 {{{
 sage: G = SL(3,QQ)
 sage: M = MatrixSpace(QQ,3)
 sage: G.one() == M.identity_matrix()  # pb 1
 False
 sage: G.one() + M.identity_matrix()   # pb 2
 ... BOOM ...
 }}}

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Ticket URL: <http://trac.sagemath.org/ticket/18258>
Sage <http://www.sagemath.org>
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