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Symbolic integration using homotopy methods

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  • Deconinck, Bernard
  • Nivala, Michael

Abstract

The homotopy algorithm is a powerful method for indefinite integration of total derivatives. By combining these ideas with straightforward Gaussian elimination, we construct an algorithm for the optimal symbolic integration that contain terms that are not total derivatives. The optimization consists of minimizing the number of terms that remain unintegrated. Further, the algorithm imposes an ordering of terms so that the differential order of these remaining terms is minimal. A different method for the summation of difference expressions is presented in .

Suggested Citation

  • Deconinck, Bernard & Nivala, Michael, 2009. "Symbolic integration using homotopy methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(4), pages 825-836.
    • Handle: RePEc:eee:matcom:v:80:y:2009:i:4:p:825-836
    DOI: 10.1016/j.matcom.2009.08.032
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    References listed on IDEAS

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    1. Hereman, W. & Deconinck, B. & Poole, L.D., 2007. "Continuous and discrete homotopy operators: A theoretical approach made concrete," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(4), pages 352-360.
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