2019/01/13 by Dominic C. Milioto, Milioto, Dominic C.
Computer Science · #Algebraic Geometry (math.AG) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1901.03996
openalex publication_date 2019/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper describes an algorithm for determining the branching geometry of algebraic functions. The graphs of these complex-valued functions have a complicated interweaving structure that can be described by analytic branches separated by singular points. Power expansions for the branches in discs centered at a point can be computed using the Newton Polygon method, and expansions around annular regions centered at the origin computed using a version of Laurent's Theorem applied to algebraic functions. However, neither of the methods enable a determination of the region of convergence of the power series. In this paper, a method using analytic continuation is used to determine the domain of analyticity for the branches, and the Root Test used to numerically check the results.