Trac #12807: Taking the real part of a sum of exponentials with imagi…

…nary exponents gives wrong result

In sage 4.8 the following computation gives 1/2, while the right result
is -3/2:
{{{
sage: a = exp(i*2*pi/3)
sage: b = exp(i*pi/3)
sage: c = 2*a-b
sage: c.real()
1/2
}}}

Doing the computation numerically gives the right result:
{{{
sage: N(c).real()
-1.50000000000000
}}}
and asking maxima directly also works:
{{{
sage: (c.maxima_methods().rectform()).real()
-3/2
}}}

This is sage 4.8 running on Fedora 16, linux 3.1.0-7.fc16.x86_64 SMP.

URL: http://trac.sagemath.org/12807
Reported by: inaki
Ticket author(s): Ralf Stephan
Reviewer(s): Travis Scrimshaw

src/sage/symbolic/expression.pyx

@@ -6407,6 +6407,13 @@ cdef class Expression(CommutativeRingElement):
 
             sage: a = SR(2).real_part(hold=True); a.simplify()
             2
+
+        TESTS:
+
+        Check that :trac:`12807` is fixed::
+
+            sage: (6*exp(i*pi/3)-6*exp(i*2*pi/3)).real_part()
+            6
         """
         return new_Expression_from_GEx(self._parent,
                 g_hold_wrapper(g_real_part, self._gobj, hold))