> > > > Thanks Robert, yes, I suspected the numerical integration > prematurely. A plot clearly shows that the culprit are the > real parts of the hyperbolic functions. > > plot([tanh(exp(i*t)).real(), > (exp(exp(i*t))/cosh(exp(i*t))-1).real()],t,0,2*pi) > The two functions are identical, the plot shows different functions. > > > For realpart(tanh(exp(%i*t))/exp(%i*t*v)) I get: > > [...] > > Are you getting something different for that? > > I get for (tanh(exp(i*t))/exp(i*t*v)).real() > > -e^(imag_part(v)*real_part(t) + imag_part(t)*real_part(v))* > sin(imag_part(t)*imag_part(v) - real_part(t)*real_part(v))* > tan(e^(-imag_part(t))*sin(real_part(t)))/(tan(e^(-imag_part(t))* > sin(real_part(t)))^2*tanh(cos(real_part(t))*e^(-imag_part(t)))^2+1)+ > cos(imag_part(t)*imag_part(v) - real_part(t)*real_part(v))* > e^(imag_part(v)*real_part(t) + imag_part(t)*real_part(v))* > tanh(cos(real_part(t))*e^(-imag_part(t)))/(tan(e^(-imag_part(t))* > sin(real_part(t)))^2*tanh(cos(real_part(t))*e^(-imag_part(t)))^2 + 1) > > This might be Pynac-related. Numerical integration with that command might be GSL, not Maxima (you may want to try the .nintegrate() method for Maxima).
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