Integration: Solving the Risch differential equation

  • John Abbott
Advanced Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 378)


We describe the first complete implementation of Davenport's algorithm [Davenport86] for the solution of the Risch differential equation. Our code forms part of a new integration package written in REDUCE which operates over algebraic number fields.


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    J H Davenport, “The Parallel Risch Algorithm (I),” Proc. EUROCAM 82, LNCS 144(1982), alsoGoogle Scholar
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    J H Davenport, and B M Trager, “On the Parallel Risch Algorithm (II),” ACM ToMS, 11(4) (Dec 1985).Google Scholar
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    J H Davenport, “The Risch Differential Equation Problem,” SIAM J Comp., 15(4) (Nov 1986).Google Scholar
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    J P Fitch, “User Based Integration Software,” Proc. 1981 ACM SYMSAC(Snowbird), (1981).Google Scholar
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    R H Risch, “The Problem of Integration in Finite Terms,” Trans. AMS, #139 (1969).Google Scholar
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    M Rothstein, and B F Caviness, “A Structure Theorem for Exponential and Primitive Functions,” SIAM J Comp., 8(3) (Aug 1979)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • John Abbott
    • 1
  1. 1.School of Mathematical SciencesUniversity of BathBathEngland

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