On modular computation of Groebner bases with integer coefficients
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2013
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929611922735104 |
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| author | Orevkov, S. Yu. |
| author_facet | Orevkov, S. Yu. |
| contents | Let $I_1\subset I_2\subset\dots$ be an increasing sequence of ideals of the ring $\Bbb Z[X]$, $X=(x_1,\dots,x_n)$ 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 $\Bbb Q I$ of the ring $\Bbb Q[X]$ and the the ideals $I\otimes(\Bbb Z/m\Bbb Z)$ of the rings $(\Bbb Z/m\Bbb Z)[X]$ are known.
Such an algorithmic problem arises, for example, in the construction of Markov and semi-Markov traces on cubic Hecke algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1312_6331 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | On modular computation of Groebner bases with integer coefficients Orevkov, S. Yu. Commutative Algebra Symbolic Computation 13P10 Let $I_1\subset I_2\subset\dots$ be an increasing sequence of ideals of the ring $\Bbb Z[X]$, $X=(x_1,\dots,x_n)$ 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 $\Bbb Q I$ of the ring $\Bbb Q[X]$ and the the ideals $I\otimes(\Bbb Z/m\Bbb Z)$ of the rings $(\Bbb Z/m\Bbb Z)[X]$ are known. Such an algorithmic problem arises, for example, in the construction of Markov and semi-Markov traces on cubic Hecke algebras. |
| title | On modular computation of Groebner bases with integer coefficients |
| topic | Commutative Algebra Symbolic Computation 13P10 |
| url | https://arxiv.org/abs/1312.6331 |