article
Limits of quotients of bivariate real analytic functions
Fecha
2013-03-01Registro en:
7477171
WOS;000312574000010
SCOPUS;2-s2.0-84870249582
10.1016/j.jsc.2012.07.004
Autor
Cadavid, C.
Molina, S.
Velez, J. D.
Cadavid, C.
Molina, S.
Velez, J. D.
Institución
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.