Newton-Puiseux algorithm and triple points for planes curves

2022/04/12 by Stefano Canino, Canino, Stefano, Alessandro Gimigliano +3
Computer Science · Engineering · #14H20 #14H50 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2204.05691

openalex publication_date 2022/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper is an introduction to the use of the classical Newton-Puiseux procedure, oriented to an algorithmic description of it. This procedure enables to get polynomial approximations for parameterizations of branches of an algebraic plane curve at a singular point. We look for an approach that can be easily grasped and almost self contained. We illustrate the use of the algorithm, first in a completely worked out example of a curve with a point of multiplicity 6, and secondly in the study of triple points on reduced plane curves.

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