Publication at Faculty of Mathematics and Physics |
2015
Abstract
In this paper we apply the rational Puiseux series to study the local properties of algebraic curves at their singular points. In particular we exploit the existence of a bijection between the curve real branches and set of rational Puiseux series at a given point of the curve.
We determine the quadrant which contains any curve half-branch and find the mutual position of all the branches. All this information is extracted from a certain tree representation without the necessity of computing the Puiseux series explicitly.
This study is meant as an element for our new method for a topologically accurate approximation of algebraic curves.