On Gröbner Basis Detection for Zero-dimensional Ideals

Details On Gröbner Basis Detection for Zero-dimensional Ideals On Gröbner Basis Detection for Zero-dimensional Ideals

2011-05-02

arxiv.org/abs/1105.0433v1

Computer Science

Computational Complexity

6 pages

Scientific paper

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.

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