Conclusion
The paper proposes a declarative description of the Buchberger algorithm. This is an executable specification and it may serve as a source for the construction and justification of a whole family of various sequential and parallel implementations of the algorithm. We consider one of such parallel implementations in the algebraic programming environment APS.
Experiments with the program have been conducted using a simulation model. The operation of four processors was simulated. The results of the first experiments showed that with sufficiently large examples the program achieves efficiency of the order of 0.8(acceleration by a factor of 3.2). A broader experimental study requires a more powerful simulation system and access to multiprocessor systems.
New experiments are being designed using larger models and local networks. The entire “hidden” part of the Buchberger algorithm, i.e., the functions reduce, Spl, and all that is necessary for their efficient implementation in an algebraic programming system, has been developed by the author's student V. A. Volkov using vector-monomial representation of polynomials. This is the subject of a separate publication.
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Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 52–62, March–April, 1995.
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Letichevskii, A.A. Paralielization of the Buchberger algorithm. Cybern Syst Anal 31, 199–206 (1995). https://doi.org/10.1007/BF02366919
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DOI: https://doi.org/10.1007/BF02366919