#13539: Add inverse_of_unit() for padics
---------------------------+------------------------------------------------
   Reporter:  saraedum     |             Owner:  roed        
       Type:  enhancement  |            Status:  new         
   Priority:  minor        |         Milestone:  sage-5.4    
  Component:  padics       |          Keywords:              
Work issues:               |   Report Upstream:  N/A         
  Reviewers:               |           Authors:  Julian Rueth
  Merged in:               |      Dependencies:              
   Stopgaps:               |  
---------------------------+------------------------------------------------
 Currently, the padics lack an {{{inverse_of_unit()}}} method:
 {{{
 sage: (-1).inverse_of_unit()
 -1
 sage: ZpCA(3)(-1).inverse_of_unit()
 AttributeError
 }}}

 The drawback with simply using {{{~}}} is that it puts the result in the
 fraction field and it can be annoying to always convert it back to the
 original ring when implementing general algorithms for all padics rings
 and fields:

 {{{
 sage: t = ZpCA(3,2)(-1)
 sage: t
 sage: t.parent()
 sage: ~t
 sage: (~t).parent()
 }}}

 The attached patch implements a method {{{inverse_of_unit()}}} and fixes a
 conversion error that came up when testing it.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13539>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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