Dimension-Dependent Upper Bounds for Grobner Bases
Symbolic Computation
2017-05-09 v1 Commutative Algebra
Algebraic Geometry
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.
Cite
@article{arxiv.1705.02776,
title = {Dimension-Dependent Upper Bounds for Grobner Bases},
author = {Amir Hashemi and Werner M. Seiler},
journal= {arXiv preprint arXiv:1705.02776},
year = {2017}
}
Comments
8 pages, to be published in the proceedings of ISSAC'17