{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:42:23Z","timestamp":1760233343934,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,26]],"date-time":"2022-12-26T00:00:00Z","timestamp":1672012800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades\u2014Agencia Estatal de Investigaci\u00f3n","award":["PID2020-113192GB-I00","PID2021-127946OB-I00"],"award-info":[{"award-number":["PID2020-113192GB-I00","PID2021-127946OB-I00"]}]},{"name":"State Plan for Scientific and Technical Research and Innovation of the Spanish MCI","award":["PID2020-113192GB-I00","PID2021-127946OB-I00"],"award-info":[{"award-number":["PID2020-113192GB-I00","PID2021-127946OB-I00"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We present symbolic algorithms for computing the g-asymptotes, or generalized asymptotes, of a plane algebraic curve, C, implicitly or parametrically defined. The g-asymptotes generalize the classical concept of asymptotes of a plane algebraic curve. Both notions have been previously studied for analyzing the geometry and topology of a curve at infinity points, as well as to detect the symmetries that can occur in coordinates far from the origin. Thus, based on this research, and in order to solve practical problems in the fields of science and engineering, we present the pseudocodes and implementations of algorithms based on the Puiseux series expansion to construct the g-asymptotes of a plane algebraic curve, implicitly or parametrically defined. Additionally, we propose some new symbolic methods and their corresponding implementations which improve the efficiency of the preceding. These new methods are based on the computation of limits and derivatives; they show higher computational performance, demanding fewer hardware resources and system requirements, as well as reducing computer overload. Finally, as a novelty in this research area, a comparative analysis for all the algorithms is carried out, considering the properties of the input curves and their outcomes, to analyze their efficiency and to establish comparative criteria between them.<\/jats:p>","DOI":"10.3390\/sym15010069","type":"journal-article","created":{"date-parts":[[2022,12,27]],"date-time":"2022-12-27T07:30:06Z","timestamp":1672126206000},"page":"69","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Some New Symbolic Algorithms for the Computation of Generalized Asymptotes"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1799-7313","authenticated-orcid":false,"given":"Elena","family":"Campo-Montalvo","sequence":"first","affiliation":[{"name":"Department of Computer Engineering, University of Alcal\u00e1, 28871 Alcal\u00e1 de Henares, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0630-1141","authenticated-orcid":false,"given":"Mari\u00e1n","family":"Fern\u00e1ndez de Sevilla","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Alcal\u00e1, 28871 Alcal\u00e1 de Henares, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3752-8231","authenticated-orcid":false,"given":"J. Rafael","family":"Magdalena Benedicto","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, University of Valencia, 46010 Val\u00e8ncia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0174-5325","authenticated-orcid":false,"given":"Sonia","family":"P\u00e9rez-D\u00edaz","sequence":"additional","affiliation":[{"name":"Department of Physics and Mathematics, University of Alcal\u00e1, 28871 Alcal\u00e1 de Henares, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,26]]},"reference":[{"key":"ref_1","unstructured":"Maxwell, E. (1962). An Analytical Calculus, Cambridge University Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1016\/j.jalgebra.2007.03.030","article-title":"Computing the asymptotes for a real plane algebraic curve","volume":"316","author":"Zeng","year":"2007","journal-title":"J. Algebra"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bajaj, C.L. (1994). 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