Symmetries and similarities of planar algebraic curves using harmonic polynomials
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/58574DOI: 10.1016/j.cam.2019.02.036
ISSN: 0377-0427
Publisher
Elsevier
Date
2019-09Funders
Agencia Estatal de Investigación
Bibliographic citation
Alcázar Arribas, J.G., Lávička, M. & Vršek, J. 2019, “Symmetries and similarities of planar algebraic curves using harmonic polynomials”, Journal of Computational and Applied Mathematics, vol. 357, pp. 302-318.
Keywords
Planar algebraic curves
Symmetry detection
Similarity
Harmonic polynomials
Dihedral groups
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.cam.2019.02.036Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2019 Elsevier
Access rights
info:eu-repo/semantics/openAccess
Abstract
We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not two given implicit planar algebraic curves are similar, i.e. equal up to a similarity transformation. Both algorithms are based on the fact, well-known in Harmonic Analysis, that the Laplacian commutes with orthogonal transformations, and on efficient algorithms to find the symmetries / similarities of a harmonic algebraic curve / two given harmonic algebraic curves. In fact, we show that, except for some special cases, the problem can be reduced to the harmonic case.
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