2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165989In this paper, an explanation of the Newton-Peiseux algorithm is given. This explanation is supplemented with well-worked and explained examples of how to use the algorithm to find fractional power series expansions for all branches of a polynomial at the origin.Algebraic Geometry14Bxx, 14B05, 14Hxx, 14H20, 32Sxx, 58Kxxtext