Computing the topology of a real algebraic plane curve whose defining equations are available only “by values”

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URI: http://hdl.handle.net/10902/5251
ISSN: 0167-8396
ISSN: 1879-2332
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Autoría
Corless, Robert M.; Díaz Toca, Gema MaríaAutoridad Unican; Fioravanti Villanueva, Mario Alfredo; González Vega, LaureanoAutoridad Unican; Fernández Rua, Ignacio; Shakoori, Azar
Fecha
2013-10
Derechos
© 2013 Elsevier B.V. This is the author’s version of a work that was accepted for publication in Computer Aided Geometric Design. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Aided Geometric Design, Vol. 30, Iss. 7, Pag. 675–706, (2013), DOI:10.1016/j.cagd.2013.04.003
Publicado en
Computer Aided Geometric Design, Vol. 30, Iss. 7, Pag. 675–706, (2013)
Editorial
Elsevier
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Palabras clave
Computations in the Lagrange Basis
Algebraic curve topology
Parametric curve topology
Generalized eigenvalues
Resumen/Abstract
This paper is devoted to introducing a new approach for computing the topology of a real algebraic plane curve presented either parametrically or defined by its implicit equation when the corresponding polynomials which describe the curve are known only “by values”. This approach is based on the replacement of the usual algebraic manipulation of the polynomials (and their roots) appearing in the topology determination of the given curve with the computation of numerical matrices (and their eigenvalues). Such numerical matrices arise from a typical construction in Elimination Theory known as the Bézout matrix which in our case is specified by the values of the defining polynomial equations on several sample points.
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