#18384: random_matrix with algorithm "subspaces" doesn't choose the rank 
correctly
------------------------------+--------------------------------------
   Reporter:  ddrake          |            Owner:
       Type:  defect          |           Status:  new
   Priority:  major           |        Milestone:  sage-6.7
  Component:  linear algebra  |         Keywords:  matrix random rank
  Merged in:                  |          Authors:
  Reviewers:                  |  Report Upstream:  N/A
Work issues:                  |           Branch:
     Commit:                  |     Dependencies:
   Stopgaps:                  |
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 Using Sage 6.5, when I do
 {{{
 random_matrix(QQ, 7,4, algorithm='subspaces')
 }}}
 almost always it says
 {{{
 Error in lines 1-1
 Traceback (most recent call last):
 File "/projects/e51fbbc4-453b-
 4f00a470028a1136adeb/.sagemathcloud/sage_server.py", line 879, in execute
 exec compile(block+'\n', '', 'single') in namespace, locals
 File "", line 1, in <module>
 File "/usr/local/sage/sage-6.5/local/lib/python2.7/site-
 packages/sage/matrix/constructor.py", line 1364, in random_matrix
 return random_subspaces_matrix(parent, *args, **kwds)
 File "/usr/local/sage/sage-6.5/local/lib/python2.7/site-
 packages/sage/matrix/constructor.py", line 3583, in
 random_subspaces_matrix
 raise ValueError("rank cannot exceed the number of rows or columns.")
 ValueError: rank cannot exceed the number of rows or columns.
 }}}
 If I run that many times, it does produce a matrix -- perhaps 5-10% of the
 time.

 The documentation says it randomly generates the rank, but it does not
 seem smart enough to generate a rank that is possible for the given
 dimensions.

--
Ticket URL: <http://trac.sagemath.org/ticket/18384>
Sage <http://www.sagemath.org>
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