Finding binomials in polynomial ideals

  title={Finding binomials in polynomial ideals},
  author={Anders Jensen and Thomas Kahle and Lukas Katth{\"a}n},
  journal={Research in the Mathematical Sciences},
  • Anders Jensen, Thomas Kahle, Lukas Katthän
  • Published 2016
  • Mathematics, Computer Science
  • Research in the Mathematical Sciences
  • We describe an algorithm which finds binomials in a given ideal $$I\subset \mathbb {Q}[x_1,\dots ,x_n]$$I⊂Q[x1,⋯,xn] 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… CONTINUE READING

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