Computing Limits of Quotients of Multivariate Real Analytic Functions

TL;DR

This paper introduces an algorithm to compute limits of quotients of multivariate real analytic functions, leveraging bounds on the Lojasiewicz exponent, particularly when the denominator's zero is isolated at the limit point.

Contribution

It presents a novel algorithm that computes such limits using Lojasiewicz exponent bounds, addressing cases with isolated zeros in the denominator.

Findings

Algorithm successfully computes limits in specified cases.

Utilizes Lojasiewicz exponent bounds for limit calculation.

Applicable when the denominator has an isolated zero at the limit point.

Abstract

We present an algorithm for computing limits of quotients of real analytic functions. The algorithm is based on computation of a bound on the Lojasiewicz exponent and requires the denominator to have an isolated zero at the limit point.