An algorithm for determining the radii of convergence of algebraic power series

TL;DR

This paper presents a geometric-based algorithm to accurately determine the radii of convergence for algebraic power series, overcoming limitations of traditional iterative methods.

Contribution

It introduces a novel algorithm leveraging geometric properties of algebraic functions to compute convergence radii precisely.

Findings

Algorithm successfully computes radii of convergence.

Testing confirms accuracy and efficiency.

Method overcomes limitations of iterative approaches.

Abstract

This paper describes an algorithm for determining radii of convergence of power expansions for algebraic functions and the testing done to check it. Since the current methods for computing these series are iterative, standard methods for computing radii of convergence cannot in general, be used. However, relying on geometric properties of algebraic functions, convergence radii of these series can be determined precisely.