Generating contours of integration: An application of PROLOG in symbolic computing

  • Gábor Belovári
  • J. A. Campbell
Tuesday Morning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 87)


One standard technique of evaluation of real definite integrals is transformation to a complex variable, and integration over a closed contour in the complex plane by means of Cauchy's Theorem. Textbook presentation of the technique tends to rely on examples, and to state no general principles governing generation of appropriate contours or applicability of the technique. This note states some general principles and a computation strategy, and outlines their implementation in a PROLOG program for automatic deduction of appropriate contours. The program complements the functions of existing systems of symbolic computing programs for integration and for manipulations in complex analysis.


Real Axis Distinguished Point Logic Programming Closed Contour Automatic Deduction 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    For a general survey of properties and applications of MACSYMA, see Proc.1977 MACSYMA Users' Conf., NASA publication CP-2012, NASA, Washington, D.C.(1977)Google Scholar
  2. 2.
    J.A. Campbell, J.G. Kent and R.J. Moore, B.I.T. 16, 241 (1976).Google Scholar
  3. 3.
    L.V. Ahlfors, "Complex Analysis", McGraw-Hill, N.Y.(1966)Google Scholar
  4. 4.
    J.H. Curtiss, "Introduction to Functions of a Complex Variable" M. Dekker Inc., N.Y. (1978)Google Scholar
  5. 5.
    P. Roussel, "PROLOG: Manuel de reference et d'utilisation", internal report, Groupe d'Intelligence Artificielle, Université d'Aix-Marseille (1975); L.M. Pereira, F.C.N. Pereira and D.H.D. Warren, User's Guide to DECsystem-10 PROLOG", Department of Artificial Intelligence, University of Edinburgh (1978.)Google Scholar
  6. 6.
    L.P. Hughston and R.S. Ward (eds.), "Advances in Twistor Theory". Pitman, London (1979)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • Gábor Belovári
    • 1
  • J. A. Campbell
    • 2
  1. 1.Alkotás u. 25.II.VII.53BudapestHungary
  2. 2.Department of Computer ScienceUniversity of ExeterExeterEngland

Personalised recommendations