Direct symbolic transformation from 3D cartesian into hyperboloidal coordinates

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URI: http://hdl.handle.net/10902/5254
ISSN: 0096-3003
ISSN: 1873-5649
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Autoría
Diaz Toca, Gema María
Fecha
2014-02
Derechos
© 2013 Elsevier Inc. All rights reserved. This is the author’s version of a work that was accepted for publication in Applied Mathematics and Computation. 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 Applied Mathematics and Computation, Vol. 228, Pp. 349–365, DOI:10.1016/j.amc.2013.11.099
Publicado en
Applied Mathematics and Computation, Vol. 228, Pp. 349–365, (2014
Editorial
Elsevier
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Palabras clave
Coordinate transformations
3D cartesian and hyperboloidal coordinates
Symbolic computation
Resumen/Abstract
A direct transformation from cartesian coordinates into hyperboloidal coordinates (considered for biaxial hyperboloids) is presented in this paper. The transformation problem is reduced to the problem of finding the smallest positive root of a fourth degree polynomial. The analysis of the polynomial’s roots is performed by an algebraically complete stratification, based on symbolic techniques (mainly Sturm–Habicht sequences and its properties related to real root counting), of a planar region situated in the positive quadrant. Two approaches for computing the polynomial’s roots are presented, one based on the Merriman method and the other one obtained using the Computer Algebra System Maple. Our approach improves the solution presented in Feltens (2011) [1], being reduced to a few evaluations of symbolic expressions.
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