Finding binomials in polynomial ideals

Anders Nedergaard Jensen, Thomas Kahle, Lukas Katthän

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Abstract

We describe an algorithm which finds binomials in a given ideal I⊂ Q[x 1, ⋯ , 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.

Original languageEnglish
Article number16
JournalResearch In the Mathematical Sciences
Volume4
Issue16
ISSN2197-9847
DOIs
Publication statusPublished - 2017

Keywords

  • Algorithm
  • Binomial detection
  • Binomial ideal
  • Tropical geometry

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