Finding binomials in polynomial ideals
2017; Springer Nature; Volume: 4; Issue: 1 Linguagem: Inglês
10.1186/s40687-017-0106-0
ISSN2522-0144
AutoresAnders Jensen, Thomas Kahle, Lukas Katthän,
Tópico(s)Algebraic Geometry and Number Theory
ResumoWe 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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