On the puiseux theorem

Abstract

In 1850, Puiseux solved the problem of finding roots of complex polynomials in two variables and proved that the field of these series is algebraically closed. His proof provided an algorithm constructing the roots. In this article, based on the paper “Ha Huy Vui, Nguyen Hong Duc. On the Lojasiewicz exponent near the fibre of polynomial mappings, Ann. Polon. Math. 94 (2008), 43-52”, we give a different algorithm computing Newton - Puiseux roots of a complex polynomial in two variables. This algorithm is more effective in practice.