Limits of quotients of polynomial functions in three variables

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dc.citation.journalTitleACM Communications in Computer Algebra
dc.contributor.authorVelez, Juan D.
dc.contributor.authorHernandez, Juan P.
dc.contributor.authorCadavid, Carlos A.
dc.contributor.departmentUniversidad EAFIT. Departamento de Cienciasspa
dc.contributor.researchgroupMatemáticas y Aplicacionesspa
dc.creatorVelez, Juan D.
dc.creatorHernandez, Juan P.
dc.creatorCadavid, Carlos A.
dc.date.accessioned2021-04-12T14:04:21Z
dc.date.available2021-04-12T14:04:21Z
dc.date.issued2017-06-01
dc.description.abstractA method for computing limits of quotients of real analytic functions in two variables was developed in [4]. In this article we generalize the results obtained in that paper to the case of quotients q = f(x, y, z)/g(x, y, z) of polynomial functions in three variables with rational coefficients. The main idea consists in examining the behavior of the function q along certain real variety X(q) (the discriminant variety associated to q). The original problem is then solved by reducing to the case of functions of two variables. The inductive step is provided by the key fact that any algebraic curve is birationally equivalent to a plane curve. Our main result is summarized in Theorem 2. In Section 4 we describe an effective method for computing such limits. We provide a high level description of an algorithm that generalizes the one developed in [4], now available in Maple as the limit/multi command.eng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=7594
dc.identifier.doi10.1145/3151131.3151132
dc.identifier.issn19322232
dc.identifier.issn19322240
dc.identifier.otherWOS;000412828200002
dc.identifier.otherSCOPUS;2-s2.0-85032878328
dc.identifier.urihttp://hdl.handle.net/10784/27708
dc.language.isoengeng
dc.publisherASSOC COMPUTING MACHINERY
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85032878328&doi=10.1145%2f3151131.3151132&partnerID=40&md5=426a974ec7d3b564e9685c249685b447
dc.rightshttps://v2.sherpa.ac.uk/id/publication/issn/1932-2232
dc.sourceACM Communications in Computer Algebra
dc.subjectComputation theoryeng
dc.subjectFunctionseng
dc.subjectA-planeeng
dc.subjectAlgebraic curveseng
dc.subjectAnalytic functionseng
dc.subjectDiscriminant varietieseng
dc.subjectHigh level descriptioneng
dc.subjectPolynomial functionseng
dc.subjectRational coefficientseng
dc.subjectRational functionseng
dc.titleLimits of quotients of polynomial functions in three variableseng
dc.typearticleeng
dc.typeinfo:eu-repo/semantics/articleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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