Finding binomials in polynomial ideals

TY - JOUR

T1 - Finding binomials in polynomial ideals

AU - Jensen, Anders Nedergaard

AU - Kahle, Thomas

AU - Katthän, Lukas

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

KW - Algorithm

KW - Binomial detection

KW - Binomial ideal

KW - Tropical geometry

UR - http://www.scopus.com/inward/record.url?scp=85050373482&partnerID=8YFLogxK

U2 - 10.1186/s40687-017-0106-0

DO - 10.1186/s40687-017-0106-0

M3 - Journal article

SN - 2197-9847

VL - 4

JO - Research In the Mathematical Sciences

JF - Research In the Mathematical Sciences

IS - 16

M1 - 16

ER -