PUISEUX POWER SERIES SOLUTIONS FOR SYSTEMS OF EQUATIONS
Fuensanta Aroca, Giovanna Ilardi, Lucía López de Medrano · International Journal of Mathematics · 2010
We give an algorithm to compute term-by-term multivariate Puiseux series expansions of series arising as local parametrizations of zeroes of systems of algebraic equations at singular points. The algorithm is an extension of Newton's method for plane algebraic curves, replacing the Newton polygon by the tropical variety of the ideal generated by the system. As a corollary we deduce a property of tropical varieties of quasi-ordinary singularities.