#11356: Companion matrix constructor
------------------------------+---------------------------------------------
   Reporter:  rbeezer         |          Owner:  jason, was    
       Type:  enhancement     |         Status:  needs_work    
   Priority:  minor           |      Milestone:  sage-4.7.1    
  Component:  linear algebra  |       Keywords:  beginner, sd31
Work_issues:                  |       Upstream:  N/A           
   Reviewer:                  |         Author:  Rob Beezer    
     Merged:                  |   Dependencies:                
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Old description:

> This will be used to construct the output of an upcoming rational
> canonical form.
>
> '''Apply:'''
>
>   1. [attachment:trac_11356-companion-matrix-v3.patch]

New description:

 This will be used to construct the output of an upcoming rational
 canonical form.

 '''Apply:'''

   1. [attachment:trac_11356-companion-matrix-v4.patch]

--

Comment(by rbeezer):

 Replying to [comment:13 ddrake]:

 Thanks, Dan.

 Seems like an input list of {{{[1]}}} should be a monic polynomial that
 creates an empty matrix.  Code does that before latest patch and a test of
 this has been added in the v4 patch.

 So I made an input empty list fail in the v4 patch and added a test.  In
 this case, {{{n = -1}}}, so various existing array references will fail,
 thus requiring its own error message.  I tried to build an "empty
 polynomial" from an empty list, but just got the zero polynomial.  So I
 think an empty list is the only danger, thus the error message reads this
 way.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11356#comment:14>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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