Algorithms for the integration of algebraic functions

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


The problem of finding elementary integrals of algebraic functions has long been recognised as difficult, and has sometimes been thought insoluble. Risch [18] stated a theorem characterising the integrands with elementary integrals, and we can use the language of algebraic geometry and the techniques of [2] to yield an algorithm that will always produce the integral if it exists. We explain the difficulty in the way of extending this algorithm, and outline some ways of solving it. Using work of Manin [9, 10] we are able to solve the problem in all cases where the algebraic expressions depend on a parameter as well as on the variable of integration.


Elliptic Curf Abelian Variety Algebraic Curve Algebraic Curf Finite Order 
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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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