Hi,
Let f be the following function:
f(t, z0, z1) = (z0z1 - 1)(z0 - z1)/((tz0 - 1)(tz1 - 1)(t - z0)(t - z1)z0)
f is a nice holomorphic function and I would like to compute the contour integral
\int_{|z1|=1} \int_{|z0|=1} f(t, z0, z1) dz0/z0 dz1/z1
Assuming 0 < t < 1, the result should be -4 pi^2/(t^2-1).
In Sage:
var("z0, z1, theta0, theta1")
assume(0 < t < 1)
f = (z0z1 - 1)(z0 - z1)/((tz0 - 1)(tz1 - 1)(t - z0)(t - z1)z0)
g = f.subs({z0: exp(Itheta0), z1: exp(Itheta1)})
Now if I integrate with respect to theta0 first: g.integrate(theta0, 0, 2pi) Sage answers that the integral is zero. If I integrate with respect to theta1 first: factor(g.integrate(theta1, 0, 2pi).integrate(theta0, 0, 2pi)) Sage answers that the integral is -4pi^2/t^2 which is also clearly wrong...
Maple finds the right answer.
What can I do to make Sage compute it right? (This is a test I need to compute much more complicated integrals after this so I have to make sure Sage gives me the right answer).
