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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 421, Pages 133–137
(Mi znsl5755)
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This article is cited in 1 scientific paper (total in 1 paper)
On modular computation of Gröbner bases with integer coefficients
S. Yu. Orevkovab a Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia
b Université Paul Sabatier, Toulouse, France
Abstract:
Let $I_1\subset I_2\subset\dots$ be an increasing sequence of ideals of the ring $\mathbb Z[X]$, $X=(x_1,\dots,x_n)$ and let $I$ be their union. We propose an algorithm to compute the Gröbner base of $I$ under the assumption that the Gröbner bases of the ideal $\mathbb QI$ of the ring $\mathbb Q[X]$ and the the ideals $I\otimes(\mathbb Z/m\mathbb Z)$ of the rings $(\mathbb Z/m\mathbb Z)[X]$ are known.
Such an algorithmic problem arises, for example, in the construction of Markov and semi-Markov traces on cubic Hecke algebras.
Key words and phrases:
Gröbner base, modular computation.
Received: 18.11.2013
Citation:
S. Yu. Orevkov, “On modular computation of Gröbner bases with integer coefficients”, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Zap. Nauchn. Sem. POMI, 421, POMI, St. Petersburg, 2014, 133–137; J. Math. Sci. (N. Y.), 200:6 (2014), 722–724
Linking options:
https://www.mathnet.ru/eng/znsl5755 https://www.mathnet.ru/eng/znsl/v421/p133
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Abstract page: | 242 | Full-text PDF : | 59 | References: | 40 |
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