Tropical conics for the layman

Abstract

We present a simple and elementary procedure to sketch the tropical conic given by a degree-two homogeneous tropical polynomial. These conics are trees of a very particular kind. Given such a tree, we explain how to compute a defining polynomial. Finally, we characterize those degree-two tropical polynomials which are reducible and factorize them. We show that there exist irreducible degree-two tropical polynomials giving rise to pairs of tropical lines.