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Zapiski Nauchnykh Seminarov POMI, 1999, Volume 258, Pages 185–207
(Mi znsl1038)
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This article is cited in 14 scientific papers (total in 14 papers)
Involutive division technique: some generalizations and optimizations
V. P. Gerdt Joint Institute for Nuclear Research
Abstract:
In this paper, in addition to the earlier introduced involutive divisions, we consider a new class of divisions induced by admissible monomial orderings. We prove that these divisions are noetherian and constructive. Thereby each of them allows one to compute an involutive Gröbner basis of a polynomial ideal by sequentially examining multiplicative reductions of nonmultiplicative prolongations. We study dependence of involutive algorithms on the completion ordering. Based on properties of particular involutive divisions two computational
optimizations are suggested. One of them consists in a special choice of the completion ordering. Another optimization is related to recomputing multiplicative and nonmultiplicative variables in the course of the algorithm.
Received: 15.05.1999
Citation:
V. P. Gerdt, “Involutive division technique: some generalizations and optimizations”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IV, Zap. Nauchn. Sem. POMI, 258, POMI, St. Petersburg, 1999, 185–207; J. Math. Sci. (New York), 108:6 (2002), 1034–1051
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https://www.mathnet.ru/eng/znsl1038 https://www.mathnet.ru/eng/znsl/v258/p185
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Abstract page: | 141 | Full-text PDF : | 88 |
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