I've been assigned to write a computer program which then calculates the Laurent series of a function. Of course I'm familiar with the concept, but I've always calculated the Laurent series in an ad hoc way using Taylor series, never used an algorithmic method. I'd be grateful if someone helps me in finding an algorithm to produce the Laurent series using the inputs mentioned in the question below :-)
Given a fractional function containing polynomials in both numerator
and denominator; find its Laurent series in all convergence domains.
The polynomials are given by its zeros. For example, the function
((z-1)(z+i))/(z^2(z-1)(z+1)) is given in the input as:
+ 1+0i 0-1i
0+0i 0+0i 1+0i -1+0i
The first sign (+ or -) defines the sign of the fraction.
The output of the above example is the Laurent series around z0=0 in two convergence domains: |z|<1 and |z|>1.