Limits of quotients of bivariate real analytic functions

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 Hense...

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Autores:
Molina, Sergio
Cadavid Moreno, Carlos Alberto
Vélez Caicedo, Juan Diego
Tipo de recurso:
Fecha de publicación:
2013
Institución:
Universidad EAFIT
Repositorio:
Repositorio EAFIT
Idioma:
spa
OAI Identifier:
oai:repository.eafit.edu.co:10784/5066
Acceso en línea:
http://hdl.handle.net/10784/5066
Palabra clave:
FUNCIONES ANALÍTICAS
CÁLCULO
ANÁLISIS VECTORIAL
CÁLCULO INTEGRAL
DERIVADAS (MATEMÁTICAS)
SUCESIONES (MATEMÁTICAS)
SERIES (MATEMÁTICAS)
Calculus
Analytic functions
Vector analysis
Calculus, integral
Sequences (mathematics)
Series
Límites
Rights
License
Copyright © 2015 Elsevier B.V
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network_acronym_str REPOEAFIT2
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repository_id_str
spelling 2015-03-06T19:20:03Z2013-032015-03-06T19:20:03ZC. Cadavid, S. Molina, J.D. Vélez, Limits of quotients of bivariate real analytic functions, Journal of Symbolic Computation, Volume 50, March 2013, Pages 197-207, ISSN 0747-7171, http://dx.doi.org/10.1016/j.jsc.2012.07.004. (http://www.sciencedirect.com/science/article/pii/S0747717112001204) Keywords: Limits; Real analytic functions; Puiseux series; Henselʼs Lemma0747-7171http://hdl.handle.net/10784/506610.1016/j.jsc.2012.07.004Necessary 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 providedNecessary 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 providedspaELSEVIERJournal of Symbolic Computation. Volume 50, March 2013, Pages 197–207http://dx.doi.org/10.1016/j.jsc.2012.07.004Copyright © 2015 Elsevier B.VAcceso restringidohttp://purl.org/coar/access_right/c_16ecLimits of quotients of bivariate real analytic functionsarticleinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionpublishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1FUNCIONES ANALÍTICASCÁLCULOANÁLISIS VECTORIALCÁLCULO INTEGRALDERIVADAS (MATEMÁTICAS)SUCESIONES (MATEMÁTICAS)SERIES (MATEMÁTICAS)CalculusAnalytic functionsVector analysisCalculus, integralSequences (mathematics)SeriesLímitesUniversidad EAFIT. Escuela de Ciencias y Humanidades. Grupo de Investigación Análisis Funcional y AplicacionesCarlos Cadavid M.(ccadavid@eafit.edu.co)Molina, Sergio95ccca28-8267-464a-90dc-7475a9f90b52-1Cadavid Moreno, Carlos Alberto764e393f-833e-4a28-a155-25a4799a8098-1Vélez Caicedo, Juan Diego84f3b6cb-3d98-4f68-a998-de4025bfc80b-1Análisis Funcional y AplicacionesJournal of Symbolic Computation50207197ORIGINALtexto_completo.pdftexto_completo.pdfapplication/pdf231193https://repository.eafit.edu.co/bitstreams/244d53eb-003a-4914-9a57-b2e30e83dddc/downloaddcd2690f3fbca18baf77fac633bc5893MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-82556https://repository.eafit.edu.co/bitstreams/e9290ce1-23ad-4b6f-abd5-71f4f1ddfdb3/download76025f86b095439b7ac65b367055d40cMD5310784/5066oai:repository.eafit.edu.co:10784/50662024-12-04 11:49:46.728restrictedhttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co
dc.title.eng.fl_str_mv Limits of quotients of bivariate real analytic functions
title Limits of quotients of bivariate real analytic functions
spellingShingle Limits of quotients of bivariate real analytic functions
FUNCIONES ANALÍTICAS
CÁLCULO
ANÁLISIS VECTORIAL
CÁLCULO INTEGRAL
DERIVADAS (MATEMÁTICAS)
SUCESIONES (MATEMÁTICAS)
SERIES (MATEMÁTICAS)
Calculus
Analytic functions
Vector analysis
Calculus, integral
Sequences (mathematics)
Series
Límites
title_short Limits of quotients of bivariate real analytic functions
title_full Limits of quotients of bivariate real analytic functions
title_fullStr Limits of quotients of bivariate real analytic functions
title_full_unstemmed Limits of quotients of bivariate real analytic functions
title_sort Limits of quotients of bivariate real analytic functions
dc.creator.fl_str_mv Molina, Sergio
Cadavid Moreno, Carlos Alberto
Vélez Caicedo, Juan Diego
dc.contributor.department.none.fl_str_mv Universidad EAFIT. Escuela de Ciencias y Humanidades. Grupo de Investigación Análisis Funcional y Aplicaciones
dc.contributor.eafitauthor.spa.fl_str_mv Carlos Cadavid M.(ccadavid@eafit.edu.co)
dc.contributor.author.none.fl_str_mv Molina, Sergio
Cadavid Moreno, Carlos Alberto
Vélez Caicedo, Juan Diego
dc.contributor.researchgroup.spa.fl_str_mv Análisis Funcional y Aplicaciones
dc.subject.lemb.spa.fl_str_mv FUNCIONES ANALÍTICAS
CÁLCULO
ANÁLISIS VECTORIAL
CÁLCULO INTEGRAL
DERIVADAS (MATEMÁTICAS)
SUCESIONES (MATEMÁTICAS)
SERIES (MATEMÁTICAS)
topic FUNCIONES ANALÍTICAS
CÁLCULO
ANÁLISIS VECTORIAL
CÁLCULO INTEGRAL
DERIVADAS (MATEMÁTICAS)
SUCESIONES (MATEMÁTICAS)
SERIES (MATEMÁTICAS)
Calculus
Analytic functions
Vector analysis
Calculus, integral
Sequences (mathematics)
Series
Límites
dc.subject.keyword.eng.fl_str_mv Calculus
Analytic functions
Vector analysis
Calculus, integral
Sequences (mathematics)
Series
dc.subject.keyword.spa.fl_str_mv Límites
description 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
publishDate 2013
dc.date.issued.none.fl_str_mv 2013-03
dc.date.available.none.fl_str_mv 2015-03-06T19:20:03Z
dc.date.accessioned.none.fl_str_mv 2015-03-06T19:20:03Z
dc.type.eng.fl_str_mv article
info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
publishedVersion
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.local.spa.fl_str_mv Artículo
status_str publishedVersion
dc.identifier.citation.spa.fl_str_mv C. Cadavid, S. Molina, J.D. Vélez, Limits of quotients of bivariate real analytic functions, Journal of Symbolic Computation, Volume 50, March 2013, Pages 197-207, ISSN 0747-7171, http://dx.doi.org/10.1016/j.jsc.2012.07.004. (http://www.sciencedirect.com/science/article/pii/S0747717112001204) Keywords: Limits; Real analytic functions; Puiseux series; Henselʼs Lemma
dc.identifier.issn.spa.fl_str_mv 0747-7171
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10784/5066
dc.identifier.doi.none.fl_str_mv 10.1016/j.jsc.2012.07.004
identifier_str_mv C. Cadavid, S. Molina, J.D. Vélez, Limits of quotients of bivariate real analytic functions, Journal of Symbolic Computation, Volume 50, March 2013, Pages 197-207, ISSN 0747-7171, http://dx.doi.org/10.1016/j.jsc.2012.07.004. (http://www.sciencedirect.com/science/article/pii/S0747717112001204) Keywords: Limits; Real analytic functions; Puiseux series; Henselʼs Lemma
0747-7171
10.1016/j.jsc.2012.07.004
url http://hdl.handle.net/10784/5066
dc.language.iso.eng.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Journal of Symbolic Computation. Volume 50, March 2013, Pages 197–207
dc.relation.uri.none.fl_str_mv http://dx.doi.org/10.1016/j.jsc.2012.07.004
dc.rights.spa.fl_str_mv Copyright © 2015 Elsevier B.V
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_16ec
dc.rights.local.spa.fl_str_mv Acceso restringido
rights_invalid_str_mv Copyright © 2015 Elsevier B.V
Acceso restringido
http://purl.org/coar/access_right/c_16ec
dc.publisher.spa.fl_str_mv ELSEVIER
institution Universidad EAFIT
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