Computing syzygies over V[X_1,…,X_k], V a valuation domain

Abstract : We give an algorithm for computing the $V$-saturation of any finitely generated submodule of $V[X_1,... ,X_k]^m (k \in N, m \in N^*)$, where $V$ is a valuation domain. Our algorithm is based on a notion of "echelon form" which ensures its correctness. The proposed algorithm terminates when two (Hilbert) series on the quotient field and the residue field of $V$ coincide. As application, our algorithm computes syzygies over $V[X_1,... ,X_k]$.
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Article dans une revue
Journal of Algebra, Elsevier, 2015, Computational Section, 425, pp.133-145. 〈http://www.sciencedirect.com/science/article/pii/S0021869314006759〉. 〈10.1016/j.jalgebra.2014.11.018〉
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https://hal.archives-ouvertes.fr/hal-01072255
Contributeur : Annick Valibouze <>
Soumis le : mardi 7 octobre 2014 - 23:03:51
Dernière modification le : jeudi 21 mars 2019 - 14:23:26

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Lionel Ducos, Annick Valibouze, Ihsen Yengui. Computing syzygies over V[X_1,…,X_k], V a valuation domain. Journal of Algebra, Elsevier, 2015, Computational Section, 425, pp.133-145. 〈http://www.sciencedirect.com/science/article/pii/S0021869314006759〉. 〈10.1016/j.jalgebra.2014.11.018〉. 〈hal-01072255〉

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