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Fast Search for the Janet Divisor

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Abstract

An algorithm for fast search for the involutive monomial Janet divisor is suggested. Such search is an important part of the construction of monomial and polynomial Janet bases. For a data structure for a finite set of monomials, the binary tree is taken, which reflects properties of the Janet division.

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REFERENCES

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  5. Zharkov, A.Yu. and Blinkov, Yu.A., Involutive Systems of Algebraic Equations, Programmirovanie, 1994, no. 1, pp. 53-56.

  6. Zharkov, A.Yu. and Blinkov, Yu.A., Involutive Approach to Investigating Polynomial Systems, Math. Comput. Simulation, 1996, vol. 42, pp. 323-332.

    Google Scholar 

  7. Gerdt, V.P., Kornyak, V.V., Berth, M., and Czichowsky, G., Construction of Involutive Monomial Sets for Different Involutive Divisions, Computer Algebra in Scientific Computing, Ganzha, V.G., Mayr, E.W., and Vorozhtsov, E.V., Eds., Berlin: Springer, 1999, pp.147-157.

    Google Scholar 

  8. Gerdt, V.P. and Blinkov, Yu.A., Involutive Divisions 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.

  10. Janet, M., Leçons sur les Systèmes d'Equations aux Dérivées Partielles, Paris: Cahiers Sci., 1929.

    Google Scholar 

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Authors and Affiliations

  1. Laboratory of Computing Engineering and Automation, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia

    V. P. Gerdt & D. A. Yanovich

  2. Department of Mechanics and Mathematics, Saratov State University, Saratov, 410071, Russia

    Yu. A. Blinkov

Authors
  1. V. P. Gerdt
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  2. D. A. Yanovich
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  3. Yu. A. Blinkov
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Gerdt, V.P., Yanovich, D.A. & Blinkov, Y.A. Fast Search for the Janet Divisor. Programming and Computer Software 27, 22–24 (2001). https://doi.org/10.1023/A:1007130618376

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