Finding binomials in polynomial ideals

2016/07/07 by Jensen, Anders, Kahle, Thomas, Katthän, Lukas · 3 citations
#11R04 #11Y16 #11Y40 #13P05 #13P99 #14T05 #68W30 (Secondary) #68W99 (Primary) #Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.1607.02135

Abstract

We describe an algorithm which finds binomials in a given ideal I⊂ℚ[x₁,…,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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Related

• Computing the Binomial Part of a Polynomial Ideal
• Binomial Ideals
• Binomial edge ideals of crown graphs
• Regularity and depth of binomial ideals arising from combinatorics
• The Castelnuovo-Mumford regularity of binomial edge ideals