Limits of quotients of bivariate real analytic functions
Fecha
2013-03-01
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ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
Resumen
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.
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Hensel's Lemma, Limits, Puiseux series, Real analytic functions