Geodesic
On modular computation of Gröbner bases with integer coefficients
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Tome 421 (2014), pp. 133-137 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {S. Yu. Orevkov},
     title = {On modular computation of {Gr\"obner} bases with integer coefficients},
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     year = {2014},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_421_a10/}
}
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S. Yu. Orevkov. On modular computation of Gröbner bases with integer coefficients. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Tome 421 (2014), pp. 133-137. http://geodesic.mathdoc.fr/item/ZNSL_2014_421_a10/

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