157 Coprime factorisation algorithm

and

G(s)={{M(s)}\over{N(s)}}={{\tilde{M}(1/(1+s))}\over{\tilde{N}(1/(1+s))}}={{P(s% )}\over{Q(s)}}.

We have shown that ${\bf C}(x)$ is the field generated by ${\cal S}$ .

Algorithm

1) Write $G$ as a quotient of polynomials with no common zeros.

2) Introduce $\lambda$ and clear the denominators.

3) Apply the Euclidean algorithm for polynomials.

4) Convert back to the original variables.