Advertisement

The parallel Risch algorithm (I)

  • James H. Davenport
4. Algorithms II
Part of the Lecture Notes in Computer Science book series (LNCS, volume 144)

Keywords

Partial Fraction Rational Part Algebraic Closure Differential Algebra Differential Field 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

5. References

  1. Caviness & Rothstein,1975.
    Caviness, B.F. & Rothstein, M., A Liouville Theorem on Integration in Finite Terms for Line Integrals. Comm. Algebra 3(1975) pp. 781–795.Google Scholar
  2. Davenport & Trager,1982.
    Davenport,J.H. & Trager,B.M., On the Parallel Risch Algorithm (II). To appear.Google Scholar
  3. ffitch,1981.
    ffitch,J.P., User-based Integration Software. Proc. SYMSAC 81, pp. 245–248Google Scholar
  4. Kaplansky,1957.
    Kaplansky, I., An Introduction to Differential Algebra. Publications de l'Institut de Mathėmatique de l'Universitė de Nancago V, Hermann, Paris, 1957 (2nd. ed. 1976).Google Scholar
  5. Kolchin,1973.
    Kolchin, E.R., Differential Algebra and Algebraic Groups. Academic Press, London, 1973.Google Scholar
  6. Moses,1967.
    Moses,J., Symbolic Integration. Ph.D. Thesis & Project MAC TR-47, M.I.T., 1967.Google Scholar
  7. Moses,1976.
    Moses,J., An Introduction to the Risch Integration Algorithm. Proc. ACM Annual Conference 1976, pp. 425–428.Google Scholar
  8. Norman & Davenport,1979.
    Norman,A.C. & Davenport,J.H., Symbolic Integration — the Dust Settles? Proc. EUROSAM 79 pp. 398–407. Zbl. 399.68056.Google Scholar
  9. Norman & Moore,1977.
    Norman,A.C. & Moore,P.M.A., Implementing the New Risch Integration Algorithm. Proc. 4th. Int. Colloquium on Advanced Computing Methods in Theoretical Physics, Marseilles, 1977.Google Scholar
  10. Risch,1969.
    Risch, R.H., The Problem of Integration in Finite Terms. Trans. A.M.S. 139(1969) pp. 167–189. MR 38(1969) #5759.Google Scholar
  11. Risch,1970.
    Risch,1970 Risch, R.H., The Solution of the Problem of Integration in Finite Terms. Bulletin AMS 76(1970) pp. 605–608. MR 42(1971) #4530.Google Scholar
  12. Risch,1979.
    Risch,1979 Risch, R.H., Algebraic Properties of the Elementary Functions of Analysis. Amer. J. Math. 101(1979) pp. 743–759. MR 81b: 12029.Google Scholar
  13. Rosenlicht,1976.
    Rosenlicht,1976 Rosenlicht, M., On Liouville's Theory of Elementary Functions. Pacific J. Math 65(1976), pp. 485–492.Google Scholar
  14. Yun,1977.
    Yun,1977 Yun, D.Y.Y., Fast Algorithm for Rational Function Integration. IBM Research Report RC 6563 (6 Jan. 1977). Proc. IFIP 77 (ed. B. Gilchrist), North-Holland, Amsterdam-New York-Oxford, 1977, pp. 493–498.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • James H. Davenport
    • 1
  1. 1.Emmanuel CollegeCambridgeEngland

Personalised recommendations