On Gröbner Basis Detection for Zero-dimensional Ideals

Prabhanjan Ananth; Ambedkar Dukkipati

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arXiv · 1105.0433

On Gröbner Basis Detection for Zero-dimensional Ideals

Prabhanjan Ananth·Ambedkar Dukkipati

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Abstract

The Gröbner 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 Gröbner 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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Prabhanjan Ananth, Ambedkar Dukkipati. 2011-05-02. On Gröbner Basis Detection for Zero-dimensional Ideals. https://arxiv.org/abs/1105.0433

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