Residue at Simple Pole

Problem

If z0 is a simple pole of F(z) = P(z) / Q(z), the residue there is P(z0) / Q'(z0).

Given polynomial coefficient lists for P and Q and the real pole z0 (with Q(z0) = 0 and Q'(z0) != 0), return the residue.

Hint

At a simple pole the residue is the limit of (z - z0) * F(z).

case 1

in: [[1],[-1,0,1],1]

expected: 0.5

case 2

in: [[0,1],[-1,0,1],-1]

expected: 0.5

case 3

in: [[2],[-2,1],2]

expected: 2

case 4

in: [[1,1],[-4,0,1],2]

expected: 0.75

Starter codePython

def residue_simple_pole(p_coeffs, q_coeffs, z0):
    # Your code here
    pass

4 test cases · run your code against them in the editor