Limits of quotients of bivariate real analytic functions

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2013-03

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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
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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C. Cadavid, S. Molina, J.D. Vélez, Limits of quotients of bivariate real analytic functions, Journal of Symbolic Computation, Volume 50, March 2013, Pages 197-207, ISSN 0747-7171, http://dx.doi.org/10.1016/j.jsc.2012.07.004. (http://www.sciencedirect.com/science/article/pii/S0747717112001204) Keywords: Limits; Real analytic functions; Puiseux series; Henselʼs Lemma