How to Compute a Puiseux Expansion

TL;DR

This paper explains the Newton-Peiseux algorithm for computing fractional power series expansions of polynomial branches at the origin, providing detailed examples to clarify the method.

Contribution

It offers a clear, detailed explanation of the Newton-Peiseux algorithm along with illustrative examples, enhancing understanding of fractional power series expansions.

Findings

Algorithm effectively computes Puiseux expansions for polynomial branches.

Examples demonstrate practical application of the method.

Clarifies steps involved in the Newton-Peiseux process.

Abstract

In this paper, an explanation of the Newton-Peiseux algorithm is given. This explanation is supplemented with well-worked and explained examples of how to use the algorithm to find fractional power series expansions for all branches of a polynomial at the origin.