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Method of Separative Monomials for Involutive Divisions

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Abstract

A method of separative monomials is presented for constructing a partition of a set of monomials associated with a certain involutive division. Given a particular set, the method is capable of constructing a search tree of an involutive divisor with various balancing criteria.

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REFERENCES

  1. Gerdt, V.P. and Blinkov, Yu.A.,Involutive Bases of Polynomial Ideals, Math. Comp. Simul., 1998, vol. 45, pp. 519–542.

    Google Scholar 

  2. Gerdt, V.P. and Blinkov, Yu.A., Minimal Involutive Bases, Math. Comp. Simul., 1998, vol. 45, pp.543–560.

    Google Scholar 

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

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

  5. Buchberger, B., Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory, Symbolic and Algebraic Computations, Buchberger, B., Collins, G., and Loos, R., Eds., Wien: Springer, 1982. Translated under the title Komp'yuternaya algebra. Simvol'nye i algebraicheskie vychisleniya, Moscow: Mir, 1986.

    Google Scholar 

  6. Apel, J., Theory of Involutive Divisions and an Application to Hilbert Function, J. Symol. Comp., 1998, vol. 25, pp. 683–704.

    Google Scholar 

  7. 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 

  8. Gerdt, V.P., Involutive Division Technique: Some Generalizations and Optimizations, Notes of SPOMI, St. Petersburg, 1999, vol. 258, pp. 115–137.

    Google Scholar 

  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. Gerdt, V.P., Yanovich, D., and Blinkov, Yu.A., Fast Search of the Janet Divisor, Programmirovanie, 2000.

  11. Thomas, J., Differential Systems, New York: AMS, 1937.

    Google Scholar 

  12. Janet, M., Leçons sur les Systèmes d'Equations aux Dérivées Partielles, Cahiers Scientifiques, IV, Paris: Gauthier-Villars, 1929.

    Google Scholar 

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Blinkov, Y.A. Method of Separative Monomials for Involutive Divisions. Programming and Computer Software 27, 139–141 (2001). https://doi.org/10.1023/A:1010986332560

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