Programming and Computer Software

, Volume 39, Issue 2, pp 61–66 | Cite as

Indefinite integration as term rewriting: Integrals containing tangent

  • J. Hu
  • Y. Hou
  • A. D. Rich
  • D. J. Jeffrey


We describe the development of a term-rewriting system for indefinite integration; it is also called a rule-based evaluation system. The development is separated into modules, and we describe the module for a wide class of integrands containing the tangent function.


Recurrence Relation Computer Algebra System Mathematical Beauty Algebraic Simplification Term Rewrite 
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.


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  1. 1.
    Buchberger, B., Mathematica as a Rewrite Language, Ida, T., Ohori, A., and Takeichi, M., eds., Functional and Logic Programming (Proceedings of the 2nd Fuji International Workshop on Functional and Logic Programming, November 1–4, 1996, Shonan Village Center), pp. 1–13, Copyright: World Scientific, Singapore—New Jersey—London—Hong Kong, 1996.Google Scholar
  2. 2.
    Richard J. Fateman, A Review of Mathematica, J. Symb. Computation, 1992, vol. 13, no. 5, pp. 545–579.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Hardy, G.H., A Mathematician’s Apology, Canto, Cambridge University Press, 2012.zbMATHGoogle Scholar
  4. 4.
    Jeffrey, D.J., Integration to Obtain Expressions Valid on Domains of Maximum Extent, Manuel Bronstein, Ed., ISSAC’93: Proceedings of the 1993 International Symposium on Symbolic and Algebraic Computation, ACM Press, 1993, pp. 34–41.CrossRefGoogle Scholar
  5. 5.
    Daniel Lazard and Renaud Rioboo, Integration of Rational Functions: Rational Computation of the Logarithmic Part, J. Symb. Computation, 1990, vol. 9, pp. 113–115.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Rich, A.D., Rule Based Mathematics. Website:
  7. 7.
    Rich, A.D. and Jeffrey, D.J., A Knowledge Repository for Indefinite Integration Based on Transformation Rules, Intelligent Computer Mathematics, vol. 5625 of LNCS, Springer, 2009, pp. 480–485.CrossRefGoogle Scholar
  8. 8.
    Robert H. Risch, The Problem of Integration in Finite Terms, Trans. Amer. Math. Soc., 1969, vol. 139, pp. 167–189.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Michael Rothstein, A New Algorithm for the Integration of Exponential and Logarithmic Functions, Proceedings of the 1977 MACSYMA Users Conference, 1977, pp. 263–274.Google Scholar
  10. 10.
    Barry M. Trager, Algebraic Factoring and Rational Function Integration, Jenks, R.D., Ed., Proceedings of the 1976 ACM Symposium on Symbolic and Algebraic Computation SYMSAC’76, ACM Press, 1976, pp. 219–226.CrossRefGoogle Scholar
  11. 11.
    Detmar Martin Welz, Recurrence Relations for Integrals Containing Tangent, Personal Communication, 2011.Google Scholar

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© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Department of Applied MathematicsThe University of Western OntarioLondonCanada

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