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Journal Articles Computer Aided Geometric Design Year : 2020

Computing the topology of a plane or space hyperelliptic curve

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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Dates and versions

hal-01968776 , version 1 (03-01-2019)
hal-01968776 , version 2 (27-02-2020)

Identifiers

Cite

Juan Gerardo Alcázar, Jorge Caravantes, Gema M Diaz-Toca, Elias Tsigaridas. Computing the topology of a plane or space hyperelliptic curve. Computer Aided Geometric Design, 2020, ⟨10.1016/j.cagd.2020.101830⟩. ⟨hal-01968776v2⟩
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