Rational curves over generalized complex numbers

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dc.citation.firstpage56en_US
dc.citation.journalTitleJournal of Symbolic Computationen_US
dc.citation.lastpage84en_US
dc.citation.volumeNumber93en_US
dc.contributor.authorDu, Juanen_US
dc.contributor.authorGoldman, Ronen_US
dc.contributor.authorWang, Xuhuien_US
dc.date.accessioned2019-08-12T17:16:51Zen_US
dc.date.available2019-08-12T17:16:51Zen_US
dc.date.issued2019en_US
dc.description.abstractComplex rational curves have been used to represent circular splines as well as many classical curves including epicycloids, cardioids, Joukowski profiles, and the lemniscate of Bernoulli. Complex rational curves are known to have low degree (typically half the degree of the corresponding rational planar curve), circular precision, invariance with respect to Möbius transformations, special implicit forms, an easy detection procedure, and a fast algorithm for computing their μ-bases. But only certain very special rational planar curves are also complex rational curves. To construct a wider collection of curves with similar appealing properties, we generalize complex rational curves to hyperbolic and parabolic rational curves by invoking the hyperbolic and parabolic numbers. We show that the special properties of complex rational curves extend to these hyperbolic and parabolic rational curves. We also provide examples to flesh out the theory.en_US
dc.identifier.citationDu, Juan, Goldman, Ron and Wang, Xuhui. "Rational curves over generalized complex numbers." <i>Journal of Symbolic Computation,</i> 93, (2019) Elsevier: 56-84. https://doi.org/10.1016/j.jsc.2018.04.010.en_US
dc.identifier.doihttps://doi.org/10.1016/j.jsc.2018.04.010en_US
dc.identifier.urihttps://hdl.handle.net/1911/106219en_US
dc.language.isoengen_US
dc.publisherElsevieren_US
dc.rightsThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier.en_US
dc.subject.keywordComplex numbersen_US
dc.subject.keywordHyperbolic numbersen_US
dc.subject.keywordParabolic numbersen_US
dc.subject.keywordDual real numbersen_US
dc.subject.keywordComplex rational curvesen_US
dc.subject.keywordHyperbolic rational curvesen_US
dc.subject.keywordParabolic rational curvesen_US
dc.subject.keywordμ-Basesen_US
dc.titleRational curves over generalized complex numbersen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpost-printen_US
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