On the computation of singularities of parametrized ruled surfaces
Authors
Pérez Díaz, SoniaIdentifiers
Permanent link (URI): http://hdl.handle.net/10017/41539DOI: 10.1016/j.aam.2019.07.005
ISSN: 0196-8858
Publisher
Elsevier
Date
2019-09-01Embargo end date
2020-09-01Funders
Agencia Estatal de Investigación
Bibliographic citation
Pérez-Díaz, Sonia. 2019, “On the computation of singularities of parametrized ruled surfaces”, Advances in Applied Mathematics, vol. 110, pp. 270-298
Keywords
Ruled surface
Standard parametric form
Singularities
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/acceptedVersion
Publisher's version
https://doi.org/10.1016/j.aam.2019.07.005Rights
Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
© 2019 Elsevier
Access rights
info:eu-repo/semantics/openAccess
Abstract
Given a ruled surface V defined in the standard parametric form P(t1, t2), we present an algorithm that determines the singularities (and their multiplicities) of V from the parametrization P. More precisely, from P we construct an auxiliary parametric curve and we show how the problem can be simplified to determine the singularities of this auxiliary curve. Only one univariate resultant has to be computed and no elimination theory techniques are necessary. These results improve some previous algorithms for detecting singularities for the special case of parametric ruled surfaces.
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