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Fast reduction of the Risch differential equation

  • Differential Algebra
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 358))

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References

  • Bronstein, M. (1987), “Integration of Elementary Functions,” Ph.D. thesis, Dpt. of Mathematics, Univ. of California, Berkeley.

    Google Scholar 

  • Bronstein, M. (1988), The Transcendental Risch Differential Equation, Journal of Symbolic Computation (to appear). Also IBM Research Report RC 13460.

    Google Scholar 

  • Char, B. W., Geddes, K.O., Gonnet, G. O., Watt, S. M. (1985), “Maple Users's Guide,” WATCOM Publ. Ltd., Waterloo, Ontario.

    Google Scholar 

  • 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 

  • 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 

  • Jenks, R. D., Sutor, R. S., Watt, S. M., Scratchpad II: An Abstract Datatype System for Mathematical Computation, in “Scientific Software,” IMA Volumes in Mathematics and Its Applications, Volume 4, Springer-Verlag, New York (to appear).

    Google Scholar 

  • 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 

  • Risch, R. (1969), The Problem of Integration In Finite Terms, Trans. Amer. Math. Soc. 139, 167–189.

    Google Scholar 

  • Rothstein, M. (1976), “Aspects of Symbolic Integration and Simplification of Exponential and Primitive Functions,” Ph.D. thesis, Univ. of Wisconsin, Madison.

    Google Scholar 

  • Trager, B. M. (1984), “Integration of Algebraic Functions,” Ph.D. thesis, Dpt. of EECS, Mass. Inst. of Tech..

    Google Scholar 

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P. Gianni

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© 1989 Springer-Verlag Berlin Heidelberg

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Bronstein, M. (1989). Fast reduction of the Risch differential equation. In: Gianni, P. (eds) Symbolic and Algebraic Computation. ISSAC 1988. Lecture Notes in Computer Science, vol 358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51084-2_6

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  • DOI: https://doi.org/10.1007/3-540-51084-2_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51084-0

  • Online ISBN: 978-3-540-46153-1

  • eBook Packages: Springer Book Archive

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