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arXiv · 1607.02135

Finding binomials in polynomial ideals

Anders Jensen·Thomas Kahle·Lukas Katthän
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Abstract

We describe an algorithm which finds binomials in a given ideal $I\subset\mathbb{Q}[x_1,\dots,x_n]$ and in particular decides whether binomials exist in $I$ at all. Binomials in polynomial ideals can be well hidden. For example, the lowest degree of a binomial cannot be bounded as a function of the number of indeterminates, the degree of the generators, or the Castelnuovo--Mumford regularity. We approach the detection problem by reduction to the Artinian case using tropical geometry. The Artinian case is solved with algorithms from computational number theory.

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Anders Jensen, Thomas Kahle, Lukas Katthän. 2016-07-07. Finding binomials in polynomial ideals. https://arxiv.org/abs/1607.02135

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