Minimal solutions of the rational interpolation problem

Abstract: We explore connections between the approach of solving the rational interpolation problem via resolutions of ideals and syzygies with the standard method provided by the Extended Euclidean Algorithm. As a consequence, we obtain explicit descriptions for solutions of "minimal" degrees in terms of the degrees of elements appearing in the EEA. This allows us to describe the minimal degree in a $\mu$-basis of a polynomial planar parametrization in terms of a "critical" degree arising in the EEA.