Computing the Jacobian of a hyperelliptic curve. (English) Zbl 0613.14022

Cantor, David G.

Math. Comput. 48, 95-101 (1987).

In this paper we present algorithms, suitable for computer use, for computation in the Jacobian of a hyperelliptic curve. We present a reduction algorithm which is asymptotically faster than that of Gauss when the genus \(g\) is very large.

MSC:

14H40	Jacobians, Prym varieties
14-04	Software, source code, etc. for problems pertaining to algebraic geometry
12-04	Software, source code, etc. for problems pertaining to field theory
14H05	Algebraic functions and function fields in algebraic geometry
11R58	Arithmetic theory of algebraic function fields
14H45	Special algebraic curves and curves of low genus

Keywords:

algorithms; computation in the Jacobian of a hyperelliptic curve