[with patch; positive review] stupid bug in RDF

[was]

This is sad:

sage: RDF(-1).nth_root(2)

Look at the dumb code in real_double.pyx:

    def nth_root(self, int n):
        """
        Returns the $n^{th}$ root of self.
        EXAMPLES:
            sage: r = RDF(-125.0); r.nth_root(3)
            -5.0
            sage: r.nth_root(5)
            -2.6265278044
        """
        if n == 0:
            return RealDoubleElement(float('nan'))
        if self._value < 0 and GSL_IS_EVEN(n):
            pass #return self._complex_double_().pow(1.0/n)
        else:
            return RealDoubleElement(self.__nth_root(n))

Amazingly this was introduced in the very first patch by Tom Boothby in 2006 and nobody ever noticed!!

[was]

This is also bad, bad, bad:

sage: RDF(-1).nth_root(5)^(5)
-1.35861063971

[mhansen]

The code is definitely much better style and correctness-wise after the patch.

+1

[mabshoff]

Merged in Sage 3.0.4.alpha2

[boothby]

wow I'm dumb!