English

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.

Keywords

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

R2 v1 2026-06-22T19:39:58.868Z