#8972: Inversion and fraction fields for power series rings
-------------------------+--------------------------------------------------
   Reporter:  SimonKing  |       Owner:  AlexGhitza                       
       Type:  defect     |      Status:  new                              
   Priority:  major      |   Milestone:  sage-4.4.2                       
  Component:  algebra    |    Keywords:  power series ring, fraction field
     Author:             |    Upstream:  N/A                              
   Reviewer:             |      Merged:                                   
Work_issues:             |  
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 This ticket is about at least three bugs related with inversion of
 elements of power series rings.

 Here is the first:
 {{{
 sage: R.<x> = ZZ[[]]
 sage: (1/x).parent()
 Laurent Series Ring in x over Integer Ring
 sage: (x/x).parent()
 Power Series Ring in x over Integer Ring
 }}}
 ''Both'' parents are wrong. Usually, the parent of ``a/b`` is the fraction
 field of the parent of ``a,b``, even if ``a==b``. And neither above parent
 is a field.

 Next bug:
 {{{
 sage: (1/(2*x)).parent()
 ERROR: An unexpected error occurred while tokenizing input
 The following traceback may be corrupted or invalid
 The error message is: ('EOF in multi-line statement', (919, 0))

 ---------------------------------------------------------------------------
 TypeError                                 Traceback (most recent call
 last)
 ... very long traceback
 TypeError: no conversion of this rational to integer
 }}}

 And the third:
 {{{
 sage: F = FractionField(R)
 sage: 1/x in F
 False
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8972>
Sage <http://www.sagemath.org>
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