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Dimension-Dependent Upper Bounds for Grobner Bases

2017/05/08 by Hashemi, Amir, Seiler, Werner M.
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.1705.02776

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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