Fix conversion from AA to RealField()

[sagetrac-tmonteil]

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.

CC: @videlec

Component: numerical

Keywords: mpfr, RIF

Issue created by migration from https://trac.sagemath.org/ticket/16163

[videlec]

comment:5

Why should it be accurate? The documentation of the method real_number is

Given a ``RealField``, compute a good approximation to self in
that field. The approximation will be off by at most two
ulp's, except for numbers which are very close to 0, which
will have an absolute error at most
``2**(-(field.prec()-1))``. Also, the rounding mode of the
field is respected.