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Can sage find the poles of a complex function, and the residues at those poles?

Hi all,

I searched the SAGE reference and didn't find the word residue in realtion to functions of a complex variable. The function I'm working with is not the ratio of two polynomials in Z, which can be factored out to find the poles and zeros. It's actually like this:

f(z) = A* sinh(z)/ (B* z^2* sinh(z)+ C* z* cosh(z)-D* sin(z))

got this from laplace transforming a partial differential equation I want to solve. I'm following the technique used in a paper I'm trying to apply to a different geometry/coordinate system, and if I can get the residues at the poles, I can get a series solution to the PDE. However, I can't fill in the omitted steps in the paper due to my never having taken a course in complex variables. Hence my interest in finding the residues at the poles programmatically.

I would greatly appreciate a clue or two. Thank you.