Georgia Institute of Technology College of Sciences

Deciding if a polynomial ideal contains monomials is a problem which can be solved by standard Gr\"obner basis techniques. Deciding if a polynomial ideal contains binomials is more complicated. We show how the general case can be reduced to the case of a zero-dimensional ideals using projections and stable intersections in tropical geometry. In the case of rational coefficients the zero-dimensional problem can then be solved with Ge's algorithm relying on the LLL lattice basis reduction algorithm. In case binomials exists, one will be computed.This is joint work with Thomas Kahle and Lukas Katthän.