Design and implementation of symbolic algorithms for the computation of generalized asymptotes
Authors
Fernandez de Sevilla Vellon, Maria de los Angeles; Magdalena Benedicto, Rafael; Pérez Díaz, SoniaIdentifiers
Permanent link (URI): http://hdl.handle.net/10017/57923DOI: 10.1007/s10472-023-09856-z
ISSN: 1012-2443
Publisher
Springer
Date
2023-07-03Affiliation
Universidad de Alcalá. Departamento de Ciencias de la Computación; Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente MatemáticasFunders
Agencia Estatal de Investigación
Bibliographic citation
Fernández de Sevilla, M., Magdalena Benedicto, R. & Pérez Díaz, S. 2023, "Design and implementation of symbolic algorithms for the computation of generalized asymptotes", Annals of Mathematics and Artificial Intelligence, vol. 91, pp. 537-561.
Keywords
Algebraic curves
Infinity branches
Convergent branches
Approaching curves
Generalized asymptotes
Algorithm performance
Hardware usage
Project
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113192GB-I00/ES/VISUALIZACION MATEMATICA: FUNDAMENTOS, ALGORITMOS Y APLICACIONES/
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica, Técnica y de Innovación 2021-2023/PID2021-127946OB-100
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Publisher's version
https://doi.org/10.1007/s10472-023-09856-zRights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Access rights
info:eu-repo/semantics/openAccess
Abstract
In this paper we present two algorithms for computing the g-asymptotes or generalized
asymptotes, of a plane algebraic curve, C , implicitly or parametrically defined. The asymptotes of a curve C reflect the status of C at points with sufficiently large coordinates. It
is well known that an asymptote of a curve C is a line such that the distance between C
and the line approaches zero as they tend to infinity. However, a curve C may have more
general curves than lines describing the status of C at infinity. These curves are known as
g-asymptotes or generalized asymptotes. The pseudocodes of these algorithms are presented,
as well as the corresponding implementations. For this purpose, we use the algebra software
Maple. A comparative analysis of the algorithms is carried out, based on some properties of
the input curves and their results to analyze the efficiency of the algorithms and to establish
comparative criteria. The results presented in this paper are a starting point to generalize
this study to surfaces or to curves defined by a non-rational parametrization, as well as to
improve the efficiency of the algorithms. Additionally, the methods developed can provide
a new and different approach in prediction (regression) or classification algorithms in the
machine learning field.
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