Affine equivalences, isometries and symmetries of ruled rational surfaces
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/58570DOI: 10.1016/j.cam.2019.07.004
ISSN: 0377-0427
Publisher
Elsevier
Date
2020-01-15Funders
Ministerio de Economía y Competitividad
Bibliographic citation
Alcázar Arribas, J.G. & Quintero, E. 2020, “Affine equivalences, isometries and symmetries of ruled rational surfaces”, Journal of Computational and Applied Mathematics, vol. 364, art. no. 112339, pp. 1-14.
Keywords
Affine equivalences
Symmetries
Ruled surfaces
Algorithms
Algebraic surfaces
Project
info:eu-repo/grantAgreement/MINECO//MTM2014-54141-P/ES/CONSTRUCCIONES ALGEBRO-GEOMETRICAS: FUNDAMENTOS, ALGORITMOS Y APLICACIONES/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1016/j.cam.2019.07.004Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2019 Elsevier
Access rights
info:eu-repo/semantics/openAccess
Abstract
An algorithmic method is presented for computing all the affine equivalences between two rational ruled surfaces defined by rational parametrizations. The algorithm works directly in parametric rational form, i.e. without computing or making use of the implicit equation of the surface. The method translates the problem into parameter space, and relies on polynomial system solving. Geometrically, the problem is related to finding the projective equivalences between two projective curves (corresponding to the directions of the rulings of the surfaces). This problem was recently addressed in a paper by Hauer and Jüttler, and we exploit the ideas by these authors in the algorithm presented in this paper. The general idea for affine equivalences is adapted to computing the isometries between two rational ruled surfaces, and the symmetries of a given rational ruled surface. The efficiency of the method is shown through several examples.
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