Examinando por Autor "Velez, J. D."

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    Limits of quotients of bivariate real analytic functions
    (ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 2013-03-01) Cadavid, C.; Molina, S.; Velez, J. D.; Cadavid, C.; Molina, S.; Velez, J. D.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
    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. © 2012 Elsevier B.V.