Advertisement

Derivations of identities by symbolic computation

  • Akira Nakamura
Article
  • 27 Downloads

Abstract

We have made the implementation of symbolic computation programs which can derive identity relations for arbitrarily given mathematical expressions. Simulations of relatively easy several concrete examples have been shown to run within practical speeds.

Key words

identity relation orthogonal polynomial Toda equation 

References

  1. [1]
    M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards Applied Mathematics Series,55, National Bureau of Standards, US Dept. of Commerce, USA, 1964.Google Scholar
  2. [2]
    A. Erdelyi et al., Higher Transcendental Functions Vol. I. Robert E. Krieger Publishing Co., Malabar, Florida, 1953.MATHGoogle Scholar
  3. [3]
    R. Hirota, The Direct Method in Soliton Theory. Cambridge U.P., Cambridge, UK, 2004.MATHGoogle Scholar
  4. [4]
    M.B. Monagan et al., Maple Introductory Programming Guide. Waterloo Maple Inc., Canada, 2005.Google Scholar
  5. [5]
    S. Moriguchi et al., Mathematical Formulas III. Iwanami Shoten, Tokyo, 1960 (in Japanese).Google Scholar
  6. [6]
    A. Nakamura, Toda equation and its solutions in special functions. Journal of the Physical Society of Japan,65 (1996), 1589–1597.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    A. Nakamura, Ladder operator approach of special functions and the N-soliton solutions of the 2 + 1 dimensional finite Toda equation. Journal of the Physical Society of Japan,73 (2004), 838–842.MATHCrossRefGoogle Scholar
  8. [8]
    A. Nakamura, Ladder operator approach of special functions for 1 + 1d discrete systems and theN-soliton solutions of the quotient-difference equation. Journal of the Physical Society of Japan,73 (2004), 2667–2679.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    A. Nakamura, Ladder operation method by dressed special functions and the Gram-type soliton solutions of the 2 + 1 dimensional finite Toda equation. Journal of the Physical Society of Japan,74 (2005), 1963–1972.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Y. Nakamura, Applied Integrable Systems. Shokabo, Tokyo, 2000 (in Japanese).Google Scholar
  11. [11]
    T. Saito, T. Takeshima and T. Hilano, Symbolic Computation Software Born in Japan. SEG Shuppan, Tokyo, 1998 (in Japanese).Google Scholar
  12. [12]
    N. Takayama and M. Noro, Risa/Asir Drill-Mathematical Programming Introduction by using Risa/Asir. Kobe, 2002 (in Japanese).Google Scholar
  13. [13]
    S. Wolfram, Mathematica Book. Wolfram Media, 2003.Google Scholar

Copyright information

© JJIAM Publishing Committee 2006

Authors and Affiliations

  1. 1.Department of Linguistics and Information SciencesOsaka University of Foreign StudiesOsakaJapan

Personalised recommendations