#7852: solve_left for RDF matrices is WRONG
------------------------------+---------------------------------------------
   Reporter:  was             |          Owner:  was            
       Type:  defect          |         Status:  positive_review
   Priority:  blocker         |      Milestone:  sage-4.7.2     
  Component:  linear algebra  |       Keywords:                 
Work_issues:                  |       Upstream:  N/A            
   Reviewer:  Martin Raum     |         Author:  Rob Beezer     
     Merged:                  |   Dependencies:                 
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Changes (by leif):

  * priority:  major => blocker


Old description:

> Observe the docstring for solve_left for an RDF matrix:
> {{{
> sage: A = random_matrix(RDF,3)
> sage: A.solve_left?
> Solve the equation A*x = b, where
>
>         EXAMPLES:
>             sage: A = matrix(RDF, 3,3, [1,2,5,7.6,2.3,1,1,2,-1]); A
>             [ 1.0  2.0  5.0]
>             [ 7.6  2.3  1.0]
>             [ 1.0  2.0 -1.0]
>             sage: b = vector(RDF,[1,2,3])
>             sage: x = A.solve_left(b); x
>             (-0.113695090439, 1.39018087855, -0.333333333333)
>             sage: A*x
>             (1.0, 2.0, 3.0)
> }}}
>
> But that is solve_right.
>
> This was evidently introduced by maybe Grout's "Switch the RDF and CDF
> matrices to a numpy 1.2 backend; factor out common functionality to
> matrix_double_dense.pyx.".
>
> Reported by Stephanie Dietzel

New description:

 Observe the docstring for solve_left for an RDF matrix:
 {{{
 sage: A = random_matrix(RDF,3)
 sage: A.solve_left?
 Solve the equation A*x = b, where

         EXAMPLES:
             sage: A = matrix(RDF, 3,3, [1,2,5,7.6,2.3,1,1,2,-1]); A
             [ 1.0  2.0  5.0]
             [ 7.6  2.3  1.0]
             [ 1.0  2.0 -1.0]
             sage: b = vector(RDF,[1,2,3])
             sage: x = A.solve_left(b); x
             (-0.113695090439, 1.39018087855, -0.333333333333)
             sage: A*x
             (1.0, 2.0, 3.0)
 }}}

 But that is solve_right.

 This was evidently introduced by maybe Grout's "Switch the RDF and CDF
 matrices to a numpy 1.2 backend; factor out common functionality to
 matrix_double_dense.pyx.".

 Reported by Stephanie Dietzel

 ----

 Apply [attachment:trac_7852-solve-linear-systems-CDF.patch] to the Sage
 library.

--

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7852#comment:12>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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