#16617: simple echelon matrix iterator
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   Reporter:  vdelecroix      |            Owner:
       Type:  enhancement     |           Status:  new
   Priority:  major           |        Milestone:  sage-6.3
  Component:  linear algebra  |         Keywords:  matrix
  Merged in:                  |          Authors:  Vincent Delecroix
  Reviewers:                  |  Report Upstream:  N/A
Work issues:                  |           Branch:
     Commit:                  |     Dependencies:
   Stopgaps:                  |
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 The iteration over subspaces over a given vector space takes infinite time
 (mainly because of complicated constructor in classes). We create an
 external "echelon_matrix_iterator" to be used for faster iteration...

 More than incredible:
 {{{
 sage: from sage.matrix.echelon_matrix import echelon_matrix_iterator
 sage: timeit("for m in echelon_matrix_iterator(GF(3),5,3): pass")
 125 loops, best of 3: 1.49 ms per loop
 sage: timeit("for _ in VectorSpace(GF(3),5).subspaces(3): pass")
 5 loops, best of 3: 346 ms per loop
 }}}

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Ticket URL: <http://trac.sagemath.org/ticket/16617>
Sage <http://www.sagemath.org>
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