The Newton-Puiseux algorithm and effective algebraic series
Combinatorics
2025-09-18 v5 Commutative Algebra
Abstract
We explain how to encode an algebraic series by finite data and how to do effective arithmetic on the level of these encodings. The reasoning is based on the Newton-Puiseux algorithm and an effective equality test for algebraic series. Furthermore, we discuss how to derive information about the support of an algebraic series. Based thereon, we show how to identify the polynomial and rational solutions of a polynomial equation.
Cite
@article{arxiv.2209.00875,
title = {The Newton-Puiseux algorithm and effective algebraic series},
author = {Manfred Buchacher},
journal= {arXiv preprint arXiv:2209.00875},
year = {2025}
}
Comments
14 pages, comes with a Mathematica implementation of the Newton-Puiseux algorithm and a Mathematica notebook