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arXiv · 2304.00303

An algorithm for computing syzygies on $V[X]$ when $V$ is a valuation domain

Henri Lombardi·Claude Quitté·Ihsen Yengui
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Abstract

We give an algorithm for computing the V-saturation of any finitely-generated submodule of a power of V[X], where V is a valuation domain. Our algorithm is based on a notion of "echelon form" which ensures its correctness. This allows us to compute a finite system of generators for the syzygy module of any finitely generated submodule of a power of V[X].

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Henri Lombardi, Claude Quitté, Ihsen Yengui. 2023-04-01. An algorithm for computing syzygies on $V[X]$ when $V$ is a valuation domain. https://doi.org/10.1080/00927872.2013.794360

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