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On an Algorithmic Optimization in Computation of Involutive Bases

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Abstract

An optimization of a general algorithm for computation of the minimal involutive basis is suggested. It can be applied for an arbitrary constructive involutive division. The optimization suggested minimizes the number of redistributions between elements of an intermediate basis required in the process of computations

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REFERENCES

  1. Gerdt, V.P. and Blinkov, Yu.A., Minimal Involutive Bases, Math. Comput. Simulation, 1998, vol. 45, pp. 543–560.

    Google Scholar 

  2. Gerdt, V.P., Involutive Division Technique: Some Generalizations and Optimizations, Zap. nauchn. seminarov SPOMI (St. Petersburg), 1999, vol. 258, pp. 185–206.

    Google Scholar 

  3. Gerdt, V.P. and Blinkov, Yu.A., Involutive Bases of Polynomial Ideals, Math. Comput. Simulation, 1998, vol. 45, pp. 519–542.

    Google Scholar 

  4. Gerdt, V.P., Completion of Linear Differential Systems to Involution, Computer Algebra in Scientific Computing CASC'99, Ganzha, V.G., Mayr, E.W., and Vorozhtsov, E.V., Eds., Berlin: Springer, 1999, pp. 115–137.

    Google Scholar 

  5. Gerdt, V.P., Blinkov, Yu.A., and Yanovich, D.A., Construction of Janet Bases I. Monomial Bases, Computer Algebra in Scientific Computing, CASC'01, Ganzha, V.G., Mayr, E.W., and Vorozhtsov, E.V., Eds., Berlin: Springer, 2001, pp. 233–247.

    Google Scholar 

  6. Gerdt, V.P., Blinkov, Yu.A., and Yanovich, D.A., Construction of Janet Bases II. Polynomial Bases, Computer Algebra in Scientific Computing, CASC'01, Ganzha, V.G., Mayr, E.W., and Vorozhtsov, E.V., Eds., Berlin: Springer, 2001, pp. 249–263.

    Google Scholar 

  7. Gerdt, V.P., Blinkov, Yu.A., and Yanovich, D.A., Fast Search for the Janet Divisor, Programmirovanie, 2001, no. 1, pp. 22–24.

  8. Gerdt, V.P. and Blinkov, Yu.A., Involutive Division of Monomials, Programmirovanie, 1998, no. 6, pp. 22–24.

  9. Chen, Yu-Fu and Gao, X.-S., Vector Representation of Involutive Divisions, Mathematics-Mechanization Research Preprints, Beijing, 1999, no. 18, pp. 9–22.

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Gerdt, V.P. On an Algorithmic Optimization in Computation of Involutive Bases. Programming and Computer Software 28, 62–65 (2002). https://doi.org/10.1023/A:1014816631983

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