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Fast reduction of the Risch differential equation

  • Manuel Bronstein
Differential Algebra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 358)

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References

  1. Bronstein, M. (1987), “Integration of Elementary Functions,” Ph.D. thesis, Dpt. of Mathematics, Univ. of California, Berkeley.Google Scholar
  2. Bronstein, M. (1988), The Transcendental Risch Differential Equation, Journal of Symbolic Computation (to appear). Also IBM Research Report RC 13460.Google Scholar
  3. Char, B. W., Geddes, K.O., Gonnet, G. O., Watt, S. M. (1985), “Maple Users's Guide,” WATCOM Publ. Ltd., Waterloo, Ontario.Google Scholar
  4. Davenport, J. H. (1984), Intégration algorithmique des fonctions élémentairement transcendantes sur une courbe algébrique, Annales de l'Institut Fourier 34 fasc.2, 271–276.Google Scholar
  5. Davenport, J. H. (1986), The Risch Differential Equation Problem, SIAM Journal on Computing 15, No.4, 903–918. Also Technical Report 83-4, Dpt. of Computer and Information Sciences, Univ. of Delaware.Google Scholar
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  7. Risch, R. (1968), On the Integration of Elementary Functions which are built up using Algebraic Operations, Report SP-2801/002/00. System Development Corp., Santa Monica, CA.Google Scholar
  8. Risch, R. (1969), The Problem of Integration In Finite Terms, Trans. Amer. Math. Soc. 139, 167–189.Google Scholar
  9. Rothstein, M. (1976), “Aspects of Symbolic Integration and Simplification of Exponential and Primitive Functions,” Ph.D. thesis, Univ. of Wisconsin, Madison.Google Scholar
  10. Trager, B. M. (1984), “Integration of Algebraic Functions,” Ph.D. thesis, Dpt. of EECS, Mass. Inst. of Tech..Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Manuel Bronstein
    • 1
  1. 1.T.J.Watson Research CenterIBM Research DivisionYorktown Heights

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