#16163: Fix converion from AA to RealField()
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   Reporter:  tmonteil   |            Owner:  tmonteil
       Type:  defect     |           Status:  new
   Priority:  major      |        Milestone:  sage-6.2
  Component:  numerical  |         Keywords:  mpfr, RIF
  Merged in:             |          Authors:
  Reviewers:             |  Report Upstream:  N/A
Work issues:             |           Branch:
     Commit:             |     Dependencies:
   Stopgaps:             |
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 As discussed in #16120, the conversion from `AA` to `RR` is not accurate:

 {{{
 sage: UCF.<E> = UniversalCyclotomicField()
 sage: e = AA(3/2*E(7) + E(7)^3 + E(7)^4 + 3/2*E(7)^6)
 sage: RR(e).exact_rational() - e
 1.328?e-17
 sage: RR(e).nextbelow().exact_rational() - e
 -6.0?e-19
 }}}

 The aim of this ticket is to fix this.

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Ticket URL: <http://trac.sagemath.org/ticket/16163>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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