Limits of quotients of real analytic functions in two variables
Algebraic Geometry
2010-11-09 v1
Abstract
Necessary and sufficient conditions for the existence of limits of the form {equation*} \lim_{(x,y)\rightarrow (a,b)}\frac{f(x,y)}{g(x,y)} {equation*} are given, under the hipothesis that and are real analytic functions near the point , and has an isolated zero at . An algorithm (implemented in MAPLE 12) is also provided. This algorithm determines the existence of the limit, and computes it in case it exists. It is shown to be more powerful than the one found in the latest versions of MAPLE. The main tools used throughout are Hensel's Lemma and the theory of Puiseux series.
Keywords
Cite
@article{arxiv.1011.1591,
title = {Limits of quotients of real analytic functions in two variables},
author = {Carlos A. Cadavid and Juan D. Velez and Sergio Molina},
journal= {arXiv preprint arXiv:1011.1591},
year = {2010}
}