Trac #22142: Inconsistent handling of exact function arguments

At the moment we have
{{{
sage: polylog(QQbar(sqrt(2)),3)
polylog(1.414213562373095?, 3)
}}}
and
{{{
sage: log(QQbar(sqrt(2)))
0.346573590279973
sage: type(_)
<type 'sage.rings.real_mpfr.RealNumber'>
}}}
So the logarithm of an exact value loses the exactness.

I would expect a symbolic expression
{{{
sage: log(QQbar(sqrt(2)))
log(1.414213562373095?)
}}}
where the argument is the symbolic encapsulation of `QQbar(sqrt(2))`
(for the same reason why the logarithm of the integer 2 becomes the
symbolic `log(2)`.

This is fixed for all `GinacFunctions` in Pynac git master. The ticket
should doctest them in the resp. files under `sage/functions`.

URL: https://trac.sagemath.org/22142
Reported by: dkrenn
Ticket author(s): Daniel Krenn
Reviewer(s): Ralf Stephan

src/sage/functions/log.py

@@ -219,6 +219,15 @@ def __init__(self):
             3.141592653589793j
             sage: log(x).subs(x=float(-1))
             3.141592653589793j
+
+        :trac:`22142`::
+
+            sage: log(QQbar(sqrt(2)))
+            log(1.414213562373095?)
+            sage: log(QQbar(sqrt(2))*1.)
+            0.346573590279973
+            sage: polylog(QQbar(sqrt(2)),3)
+            polylog(1.414213562373095?, 3)
         """
         GinacFunction.__init__(self, 'log', latex_name=r'\log',
                                conversions=dict(maxima='log', fricas='log'))