Limits of quotients of bivariate real analytic functions

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Date
2013-03Author
Molina, Sergio
Cadavid Moreno, Carlos Alberto
Vélez Caicedo, Juan Diego
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Abstract
Necessary and sufficient conditions for the existence of limits of the form lim(x,y)→(a,b) f (x, y)/g(x, y) are given, under the hypothesis that f and g are real analytic functions near the point (a, b), and g has an isolated zero at (a, b) -- The given criterion uses a constructive version of Hensel’s Lemma which could be implemented in a computer algebra system in the case where f and g are polynomials with rational coefficients, or more generally, with coefficients in a real finite extension of the rationals -- A high level
description of an algorithm for determining the existence of the limit as well as its computation is provided
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