Tropical Combinatorial Nullstellensatz and Sparse Polynomials

Abstract

Tropical algebra emerges in many fields of mathematics such as algebraic geometry, mathematical physics and combinatorial optimization. In part, its importance is related to the fact that it makes various parameters of mathematical objects computationally accessible. Tropical polynomials play a fundamental role in this, especially for the case of algebraic geometry. On the other hand, many algebraic questions behind tropical polynomials remain open. In this paper we address four basic questions on tropical polynomials closely related to their computational properties: * An extended abstract of a preliminary version [17] appeared in the proceedings of the 21st International Symposium on Fundamentals of Computation Theory (FCT 2017).