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Título: On the square-freeness of the offset equation to a rational planar curve
Fecha de publicación: 4-abr-2018
Editorial: World Scientific
Cita bibliográfica: International Journal of Algebra and ComputationVol. 28, No. 03, pp. 395-409 (2018)
ISSN: 1793-6500
0218-1967
Palabras clave: Offset curves
Planar rational curves
Squarefree factorization
Implicit equations
Resumen: It is well known that an implicit equation of the offset to a rational planar curve can be computed by removing the extraneous components of the resultant of two certain polynomials computed from the parametrization of the curve. Furthermore, it is also well known that the implicit equation provided by the non-extraneous component of this resultant has at most two irreducible factors. In this paper, we complete the algebraic description of this resultant by showing that the multiplicity of the factors corresponding to the offset can be com- puted in advance. In particular, when the parametrization is proper, i.e. when the curve is just traced once by the parametrization, we prove that any factor corresponding to a simple component of the off- set has multiplicity 1, while the factor corresponding to the special component, if any, has multiplicity 2. Hence, if the parametrization is proper and there is no special component, the non-extraneous part of the resultant is square-free. In fact, this condition is proven to be also sufficient. Therefore, this result provides a simple test to check whether or not the offset of a given rational curve has a special component, and in turn, whether a given rational curve is the offset of another curve.
Autor/es principal/es: Díaz Toca, Gema M.
Alcázar, Juan Gerardo
Caravantes, Jorge
Facultad/Departamentos/Servicios: Facultades, Departamentos, Servicios y Escuelas::Departamentos de la UMU::Ingeniería y Tecnología de Computadores
URI: http://hdl.handle.net/10201/138177
DOI: https://doi.org/10.1142/S0218196718500194
Tipo de documento: info:eu-repo/semantics/article
Número páginas / Extensión: 18
Derechos: info:eu-repo/semantics/openAccess
Atribución 4.0 Internacional
Descripción: ©2018. This manuscript version is made available under the CC-BY 4.0 license http://creativecommons.org/licenses/by/4.0/ This document is the Accepted, version of a Published Work that appeared in final form in International Journal of Algebra and Computation (iJAC). To access the final edited and published work see https://doi.org/10.1142/S0218196718500194
Aparece en las colecciones:Artículos: Ingeniería y Tecnología de Computadores

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