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

3 APR - Algorithmes, Programmes et Résolution
LIP6 - Laboratoire d'Informatique de Paris 6
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 $V[X_1,... ,X_k]$.
Keywords :
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-01072255
Contributor : Annick Valibouze <>
Submitted on : Tuesday, October 7, 2014 - 11:03:51 PM
Last modification on : Tuesday, June 23, 2020 - 12:30:04 PM

### Citation

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. ⟨10.1016/j.jalgebra.2014.11.018⟩. ⟨hal-01072255⟩

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