Computing the topology of a planar or space hyperelliptic curve
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 t...
| Authors: | ; ; ; |
|---|---|
| Format: | Article |
| Publication date: | 2020 |
| Country: | España |
| Institution: | Universidad de Alcalá (UAH) |
| Repository: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Language: | English |
| OAI Identifier: | oai:ebuah.uah.es:10017/58588 |
| Online Access: | http://hdl.handle.net/10017/58588 https://dx.doi.org/10.1016/j.cagd.2020.101830 |
| Access Level: | Open access |
| Keyword: | Hyperelliptic curves Topology Birational mappings Complexity Algebraic curves Matemáticas Mathematics |
| Summary: | 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 Mapleimplementation of these algorithms, and present several examples. Complexity and certification issues are also discussed. |
|---|