#19333: RIF roots are sometimes too precise
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   Reporter:  jdemeyer          |            Owner:
       Type:  defect            |           Status:  new
   Priority:  major             |        Milestone:  sage-6.9
  Component:  basic arithmetic  |         Keywords:
  Merged in:                    |          Authors:  Jeroen Demeyer
  Reviewers:                    |  Report Upstream:  N/A
Work issues:                    |           Branch:
     Commit:                    |     Dependencies:
   Stopgaps:                    |
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 The root finder in `RIF` sometimes returns roots which have too much
 precision:
 {{{
 sage: R.<x> = QQ[]
 sage: parent((x-1).roots(RIF)[0][0])
 Real Interval Field with 106 bits of precision
 }}}
 The answer should have 53 bits of precision.

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Ticket URL: <http://trac.sagemath.org/ticket/19333>
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