On Oct 14, 4:54 am, Johan Grönqvist <johan.gronqv...@gmail.com> wrote:
> A workaround seems to be to integrate the real and imaginary parts
> separately:
>
> sage: numerical_integral(real(sqrt(sec(x)-1)),pi/2, pi)
> (1.9175999157365625e-16, 5.0010185963949996e-17)
> sage: numerical_integral(imag(sqrt(sec(x)-1)),pi/2, pi)
> (3.1415926269162875, 2.3498999460392589e-06)

I think it would be enough to add an option to numerical_integral on
the likes of:

sage: numerical_integral(sqrt(sec(x)-1),pi/2, pi,complex=True)

so that it would do the following internally:

rea=numerical_integral(rea(sqrt(sec(x)-1)),pi/2, pi)
ima=numerical_integral(imag(sqrt(sec(x)-1)),pi/2, pi)

return ( rea[0]+I*ima[0], rea[1], ima[1])

what do you think? I could do this myself very easily if we agree that
this is a good idea.

Oscar

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