科研之友
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摘要
Necessary and sufficient conditions for the existence of limits of the form lim((x, y)-%26gt;(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%26apos;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.
- 出版日期2013-3
