The computerisation of algebraic geometry

  • J. H. Davenport
4. Algebraic Fields
Part of the Lecture Notes in Computer Science book series (LNCS, volume 72)


This paper is concerned with the problems of performing computer algebra when the variables involved are related by some algebraic dependencies. It is shown that heuristic or ad hoc treatment of such cases leads rapidly to problems, and the proper mathematical foundations for the treatment of algebraic functions are presented. The formalism leads directly to the requirement for algorithms to find the genus of an algebraic curve, and to discover what function, if any, is associated with a given divisor. These algorithms and the relevant computational techniques are briefly described. In a concluding section the areas where these techniques are required in an integration scheme for algebraic functions are explained.


Algebraic Geometry Local Parameter Algebraic Curve Algebraic Curf Algebraic Expression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • J. H. Davenport
    • 1
  1. 1.Computer LaboratoryUniversity of CambridgeCambridge

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