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Algorithms for the integration of algebraic functions

  • 10. Integration
  • Conference paper
  • First Online:
Symbolic and Algebraic Computation (EUROSAM 1979)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 72))

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Abstract

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.

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Authors and Affiliations

  1. Computer Laboratory, University of Cambridge, Corn Exchange Street, CB2 3QG, Cambridge

    J. H. Davenport

Authors
  1. J. H. Davenport
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Edward W. Ng

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© 1979 Springer-Verlag Berlin Heidelberg

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Davenport, J.H. (1979). Algorithms for the integration of algebraic functions. In: Ng, E.W. (eds) Symbolic and Algebraic Computation. EUROSAM 1979. Lecture Notes in Computer Science, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09519-5_92

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  • DOI: https://doi.org/10.1007/3-540-09519-5_92

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09519-4

  • Online ISBN: 978-3-540-35128-3

  • eBook Packages: Springer Book Archive

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