Cortadellas Benítez, TeresaD'Andrea, Carlos, 1973-Montoro López, M. Eulàlia2023-03-082023-03-0820200041-6932https://hdl.handle.net/2445/194832We explore connections between the approach of solving the rational interpolation problem via resolutions of ideals and syzygies, and the standard method provided by the Extended Euclidean Algorithm (EEA). As a consequence, we obtain explicit descriptions for solutions of minimal degrees in terms of the degrees of elements appearing in the EEA. This result allows us to describe the minimal degree in a μ-basis of a polynomial planar parametrization in terms of a critical degree arising in the EEA.17 p.application/pdfengcc-by (c) Cortadellas Benítez, Teresa et al., 2020https://creativecommons.org/licenses/by/4.0/Teoria de l'aproximacióTeoria de nombresHomologiaInterpolació (Matemàtica)Approximation theoryNumber theoryHomologyInterpolationinfo:eu-repo/semantics/article7082852023-03-08info:eu-repo/semantics/openAccess