Dimension-Dependent Upper Bounds for Gröbner Bases
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Co-author(s): Amir Hashemi |
Reference: Proc. International Symposium on Symbolic and Algebraic
Computation - ISSAC 2017, M. Burr (ed.), ACM, New York 2017, pp. 189--196 |
Description: We improve certain degree bounds for Gröbner 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 Gröbner basis (w.r.t. the degree reverse
lexicographical ordering) of a homogeneous ideal in these positions. |
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