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arXiv · 1705.02776

Dimension-Dependent Upper Bounds for Grobner Bases

Amir Hashemi·Werner M. Seiler
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Abstract

We improve certain degree bounds for Grobner bases of polynomial ideals in generic position. We work exclusively in deterministically verifiable and achievable generic positions of a combinatorial nature, namely either strongly stable position or quasi stable position. Furthermore, we exhibit new dimension- (and depth-)dependent upper bounds for the Castelnuovo-Mumford regularity and the degrees of the elements of the reduced Grobner basis (w.r.t. the degree reverse lexicographical ordering) of a homogeneous ideal in these positions.

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Amir Hashemi, Werner M. Seiler. 2017-05-08. Dimension-Dependent Upper Bounds for Grobner Bases. https://arxiv.org/abs/1705.02776

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