#13263: matrix() for elements in quotients of polynomial ring broken over 
inexact
rings
-----------------------------------+----------------------------------------
   Reporter:  saraedum             |             Owner:  malb                   
           
       Type:  defect               |            Status:  new                    
           
   Priority:  minor                |         Milestone:  sage-5.3               
           
  Component:  commutative algebra  |          Keywords:  padic, quotient ring, 
inexact ring
Work issues:                       |   Report Upstream:  N/A                    
           
  Reviewers:                       |           Authors:                         
           
  Merged in:                       |      Dependencies:                         
           
   Stopgaps:                       |  
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 The following code fails:

 {{{
 sage: R.<T>=Qp(3,prec=2)[]
 sage: S.<Tbar>=R.quo(T^2+1)
 sage: S(T^2).matrix()
 TypeError: cannot construct an element of Full MatrixSpace of 2 by 2 dense
 matrices over 3-adic Field with capped relative precision 2 from [2 + 2*3
 + O(3^2), 0, O(3^2), 0, 2 + 2*3 + O(3^2), 0, O(3^2)]!
 sage: S(T^2)
 (O(3^2))*Tbar^2 + (2 + 2*3 + O(3^2))
 }}}

 The term {{{(O(3^2))*Tbar^2}}} should not be present since we modded out
 by {{{T^2+1}}}.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13263>
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