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Computing a hyperelliptic integral using arithmetic in the Jacobian of the curve

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Abstract

In this paper, we describe an efficient algorithm for computing an elementary antiderivative of an algebraic function defined on a hyperelliptic curve. Our algorithm combines B. M. Trager's integration algorithm and a technique for computing in the Jacobian of a hyperelliptic curve introduced by D. G. Cantor. Our method has been implemented and successfully compared to Trager's general algorithm.

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Authors and Affiliations

  1. Laboratoire d'Arithmétique, Calcul Formel et Optimisation, Université de Limoges, 123 Avenue Albert THOMAS, F-87060, Limoges Cedex

    Laurent Bertrand

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  1. Laurent Bertrand
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Work partially made at Departement Informatik ETH Zurich

Unité de Recherche Associée au CNRS 1586

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Bertrand, L. Computing a hyperelliptic integral using arithmetic in the Jacobian of the curve. AAECC 6, 275–298 (1995). https://doi.org/10.1007/BF01235720

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  • DOI: https://doi.org/10.1007/BF01235720

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