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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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https://hal.inria.fr/hal-01968776
Contributor : Elias Tsigaridas <>
Submitted on : Thursday, February 27, 2020 - 9:23:42 PM
Last modification on : Friday, March 6, 2020 - 12:04:39 PM

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

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