Limits of quotients of bivariate real analytic functions

详细信息    查看全文

• 作者：C. Cadavid^a ; ^{ccadavid@eafit.edu.co} ; S. Molina^b ; ^{sdaladierm@hotmail.com} ; J.D. Vé ; lez^c ; ^{jdvelez14@gmail.com}
• 关键词：Limits ; Real analytic functions ; Puiseux series ; Hensel?s Lemma
• 刊名：Journal of Symbolic Computation
• 出版年：2013
• 出版时间：March, 2013
• 年：2013
• 卷：50
• 期：Complete
• 页码：197-207
• 全文大小：225 K

文摘

Necessary and sufficient conditions for the existence of limits of the form are given, under the hypothesis that f and g are real analytic functions near the point , and g has an isolated zero at . 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.