Publication: Computing the topology of a planar or space hyperelliptic curve
Authors
Alcázar, Juan Gerardo ; Caravantes, Jorge ; Díaz Toca, Gema M. ; Tsigaridas, Elias
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Publisher
Elsevier
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DOI
https://doi.org/10.1016/j.cagd.2020.101830
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info:eu-repo/semantics/article
Description
©2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
This document is the Accepted version of a Published Work that appeared in final form inComputer Aided Geometric Design. To access the final edited and published work see https://doi.org/10.1016/j.cagd.2020.101830
Abstract
We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image of a planar curve (the Weierstrass form of the curve), whose topology is easy to compute, under a birational mapping of the plane or the space. We report on a Maple implementation of these algorithms, and present several examples. Complexity and certification issues are also discussed.
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Citation
Computer Aided Geometric Design
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