#13018: Positive definite check for exact matrices
----------------------------------+-----------------------------------------
       Reporter:  rbeezer         |         Owner:  jason, was  
           Type:  enhancement     |        Status:  needs_review
       Priority:  minor           |     Milestone:  sage-5.1    
      Component:  linear algebra  |    Resolution:              
       Keywords:  sd40.5          |   Work issues:              
Report Upstream:  N/A             |     Reviewers:  Dan Drake   
        Authors:  Rob Beezer      |     Merged in:              
   Dependencies:  #12966          |      Stopgaps:              
----------------------------------+-----------------------------------------

Old description:

> Implements an "is_positive_definite()" method for matrices over exact
> rings.
>
> '''Depends:'''
>   1. #12966
>
> '''Apply:'''
>   1. [attachment: trac_13018-is-positive-definite-v1.patch]

New description:

 Implements an "is_positive_definite()" method for matrices over exact
 rings.

 '''Depends:'''
   1. #12966

 '''Apply:'''
   1. [attachment: trac_13018-is-positive-definite-v2.patch]

--

Comment (by rbeezer):

 Thanks, Dan.  Standalone "v2" patch fixes the grammar.  For matrices that
 are positive definite the doctest now includes the (positive) determinants
 of the leading principal submatrices.  For those that are not positive
 definite there is an example vector violating the defining condition
 (which was a '''great''' suggestion).

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13018#comment:4>
Sage <http://www.sagemath.org>
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