2010-10-14 06:01, Oscar Gerardo Lazo Arjona skrev:
I've been trying to solve this integral:
sage: numerical_integral(sqrt(sec(x)-1),pi/2,pi)
(nan, nan)
But that failed also... So I tried with mathematica:
numerical integration should be fairly easy to extend to complex
numbers. Am I missing something?
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)
... giving the same result as Mathematica (although numerically).
It seems to me that the integration is performed by gsl, and the gsl
integration routine seems only to take real-valued functions as
arguments, but I have not looked at this previously, so I may be missing
something as well.
Regards
Johan
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