Multi-variate Polynomials and Newton-Puiseux Expansions

Abstract

The classical Newton polygon method for the local resolution of algebraic equations in one variable can be extended to the case of multi-variate equations of the type f(y) = 0, f ∈ ℂ [x 1,..., x N ][y]. For this purpose we will use a generalization of the Newton polygon - the Newton polyhedron - and a generalization of Puiseux series for several variables.KeywordsSeries SolutionNewton AlgorithmNewton PolygonNewton PolyhedronEdge PathThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.