Fix ComplexNumber.__pow__ to allow float^complex

[Karl-Dieter Crisman]

In sage.rings.complex_number.ComplexNumber.__pow__??

def __pow__(self, right, modulus):

    try:
        return (self.log()*right).exp()
    except TypeError:
        pass

makes it so that

float(5)^(0.5+14.1347251*i)

doesn't work.

This means plotting even mpmath.li for complex values with a lambda function won't work nicely.

[Samuel Lelièvre]

Please @kcrisman can you provide the plotting example you had in mind?

Please @tmonteil can you test on 32-bit?

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New commits:

​f86837f

11323: Fix complex number power so float^complex works

[Karl-Dieter Crisman]

Please @kcrisman can you provide the plotting example you had in mind?

From a decade ago?

I am not sure. I think I had attempted something like this directly, rather than parametrically.

import mpmath
parametric_plot((lambda t: mpmath.ei(log(20)*(0.5+i*RR(t))).real, lambda t: mpmath.ei(log(20)*(0.5+i*RR(t))).imag), (0,14.1), rgbcolor=hue(0.7), plot_points=300) + point((mpmath.ei(log(20)*(0.5+i*14.1)).real, mpmath.ei(log(20)*(0.5+i*14.1)).imag), color='red',size=20)

where I used that on this domain the log integral is the exp integral of the log and somehow that avoided the problem.

But I can't remember what exactly I tried that failed, because presumably I discarded it. Sorry!

[Matthias Köppe]

Moving to 9.4, as 9.3 has been released.

[Trevor Karn]

Should line 1695 isinstance(right, (int, long, Integer)) be changed to isinstance(right, (int, Integer)), for python 3, or should it be left as is for backwards compatibility?

[Travis Scrimshaw]

It's not hurting anything by being there, so I would say leave it since it is not related to this ticket. It might also matter for 16-bit machines since this is Cython code (I'm not 100% sure of this however).

LGTM.

[Samuel Lelièvre]

Thanks!