#7728: Make matrix factorizations immutable and cached
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   Reporter:  dagss           |       Owner:  was                 
       Type:  defect          |      Status:  new                 
   Priority:  major           |   Milestone:  sage-4.3.1          
  Component:  linear algebra  |    Keywords:                      
Work_issues:                  |      Author:  Dag Sverre Seljebotn
   Upstream:  N/A             |    Reviewer:                      
     Merged:                  |  
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 The attached patch (based on 4.3.rc0):

  - changes Cholesky (all/most matrices) and SVD, QR and LU factorizations
 (double_dense only) so that the returned resulting matrices are immutable
  - adds caching for Cholesky, SVD and QR
  - adds pickle-able caching for LU (and it is likely there was a a bug
 with pickling/unpickling a matrix with a cached factorization which this
 patch fixes...)
  - improves doctests for SVD and QR (I wanted to more easily check that my
 changes didn't cause regressions...)
  - adds methods {{{zero_at}}} and {{{round}}} to dense double matrices
 (used in said doctests)

 I hope the doctest improvements can be accepted as part of the patch even
 if I didn't bother to split it up.

 Note that when dealing with matrix factorization doctesting, just avoiding
 0 in the input goes very far with creating readable tests.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7728>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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