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Construction of Janet Bases II. Polynomial Bases

In: Computer Algebra in Scientific Computing CASC 2001

Author

Listed:
  • Vladimir P. Gerdt

    (Joint Institute for Nuclear Research, Laboratory of Information Technologies)

  • Yuri A. Blinkov

    (Saratov University, Department of Mathematics and Mechanics)

  • Denis A. Yanovich

    (Joint Institute for Nuclear Research, Laboratory of Information Technologies)

Abstract

In this paper we give a detailed description of an algorithm for computation of polynomial Janet bases and present its implementation in C, C++ and Reduce. This algorithm extends to polynomial ideals the algorithm for computation of monomial Janet bases presented in the first part of our paper and improves the specialization to Janet division of the general algorithm for computation of involutive polynomial bases. The computational efficiency of our codes is compared with that of computer algebra system Singular which provides one of the best implementations of the Buchberger algorithm for computation of Gröbner bases.

Suggested Citation

  • Vladimir P. Gerdt & Yuri A. Blinkov & Denis A. Yanovich, 2001. "Construction of Janet Bases II. Polynomial Bases," Springer Books, in: Victor G. Ganzha & Ernst W. Mayr & Evgenii V. Vorozhtsov (ed.), Computer Algebra in Scientific Computing CASC 2001, pages 249-263, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56666-0_19
    DOI: 10.1007/978-3-642-56666-0_19
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