On Gr\"obner Basis Detection for Zero-dimensional Ideals
Computational Complexity
2011-05-04 v1
Abstract
The Gr\"obner basis detection (GBD) is defined as follows: Given a set of polynomials, decide whether there exists -and if "yes" find- a term order such that the set of polynomials is a Gr\"obner basis. This problem was shown to be NP-hard by Sturmfels and Wiegelmann. We show that GBD when studied in the context of zero dimensional ideals is also NP-hard. An algorithm to solve GBD for zero dimensional ideals is also proposed which runs in polynomial time if the number of indeterminates is a constant.
Keywords
Cite
@article{arxiv.1105.0433,
title = {On Gr\"obner Basis Detection for Zero-dimensional Ideals},
author = {Prabhanjan Ananth and Ambedkar Dukkipati},
journal= {arXiv preprint arXiv:1105.0433},
year = {2011}
}
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6 pages