A survey on recent advances and future challenges in the computation of asymptotes

Authors
Pérez Díaz, SoniaUniversity of Alcalá Author; Blasco Lorenzo, ÁngelUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/42182
ISSN: 0161-1712
Date
2019
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas
Funders
Agencia Estatal de Investigación
Bibliographic citation
International Journal of Mathematics and Mathematical Sciences, 2019
Keywords
Implicit algebraic plane curve
Parametric plane curve
Infinity branches
Asymptotes
Perfect curves
Approaching curves
Project
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-88796-P/ES/COMPUTACION SIMBOLICA: NUEVOS RETOS EN ALGEBRA Y GEOMETRIA Y SUS APLICACIONES/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Rights
https://www.hindawi.com/journals/apm/guidelines/
Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
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info:eu-repo/semantics/openAccess
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Abstract
In this paper, we summarize two algorithms for computing all the generalizedasymptotes of a plane algebraic curve implicitly or parametrically de-fined. The approach is based on the notion of perfect curve introducedfrom the concepts and results presented in [Blasco and Pérez-Díaz(2014)],[Blasco and Pérez-Díazz(2014-b)] and [Blasco and Pérez-Díaz(2015)]. From these results, we derive a new method that allow to easily compute horizontal and vertical asymptotes.
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