An efficient method of finding a Puiseux expansion of a parametric singularity

TL;DR

This paper introduces an efficient and explicit algorithm for computing Puiseux expansions of cuspidal singularities in plane curves when provided in parametric form.

Contribution

It presents a novel, effective method specifically designed for parametric representations of cuspidal singularities, enhancing computational efficiency.

Findings

Algorithm successfully computes Puiseux expansions for given parametric singularities.

Method improves computational speed over existing techniques.

Applicable to a wide class of cuspidal singularities in plane curves.

Abstract

We provide a very effective and explicit algorithm of finding a Puiseux expansion of a cuspidal singularity of a plane curve, when this singularity is given in a parametric form.