Computing the topology of a plane or space hyperelliptic curve

被引：2

作者：

Gerardo Alcazar, Juan ^{[1
]}

Caravantes, Jorge ^{[1
]}

Diaz-Toca, Gema M. ^{[2
]}

Tsigaridas, Elias ^{[3
,4
,5
]}

机构：

[1] Univ Alcala, Dept Fis & Matemat, E-28871 Madrid, Spain

[2] Univ Murcia, Dept Ingn & Tecnol Comp, E-30100 Murcia, Spain

[3] Sorbonne Univ, Inria Paris, Paris, France

[4] Sorbonne Univ, Inst Math Jussieu Paris Rive Gauche, Paris, France

[5] Paris Univ, Paris, France

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 2020年 / 78卷 / 78期

关键词：

Hyperelliptic curves; Topology; Birational mappings; Complexity; Algebraic curves; OFFSETS; APPROXIMATION;

D O I：

10.1016/j.cagd.2020.101830

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

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. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：19

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