Computing in the jacobian of a plane algebraic curve

Extended abstract
  • Emil J. Volcheck
Conference paper

DOI: 10.1007/3-540-58691-1_60

Part of the Lecture Notes in Computer Science book series (LNCS, volume 877)
Cite this paper as:
Volcheck E.J. (1994) Computing in the jacobian of a plane algebraic curve. In: Adleman L.M., Huang MD. (eds) Algorithmic Number Theory. ANTS 1994. Lecture Notes in Computer Science, vol 877. Springer, Berlin, Heidelberg

Abstract

We describe an algorithm which extends the classical method of adjoints due to Brill and Noether for carrying out the addition operation in the Jacobian variety (represented as the divisor class group) of a plane algebraic curve defined over an algebraic number field K with arbitrary singularities. By working with conjugate sets of Puiseux expansions, we prove this method is rational in the sense that the answers it produces are defined over K. Given a curve with only ordinary multiple points and allowing precomputation of singular places, the running time of addition using this algorithm is dominated by M7 coefficient operations in a field extension of bounded degree, where M is the larger of the degree and the genus of the curve.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Emil J. Volcheck
    • 1
  1. 1.UCLA Dept. of Mathematics and Center for Science and ArtUSA

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