Construction of linear systems on hyperelliptic curves (Q1267069)

The author gives an algorithm for finding a basis of the Riemann-Roch space \(L(D)\) for a divisor on a hyperelliptic curve. The algorithm uses the convergence of a continued fraction expansion of the Laurent expansion at a point at infinity of a function on the curve associated to the divisor. The author has previously studied continued fraction expansions in hyperelliptic function fields [\textit{T. G. Berry}, Arch. Math. 55, No. 3, 259-266 (1990; Zbl 0728.14027)]. It is shown that this algorithm specializes to give a Jacobian reduction algorithm due to \textit{D. G. Cantor} [Math. Comput. 48, 95-101 (1987; Zbl 0613.14022)], and that it is related to ideas of Chebychev. While the author expects that this algorithm is more efficient than the Brill-Noether algorithm (using adjoint curves) in the hyperelliptic case, no direct comparisons are made.