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Tropical Effective Primary and Dual Nullstellens\"atze
Tropical algebra is an emerging field with a number of applications in
various areas of mathematics. In many of these applications appeal to tropical
polynomials allows to study properties of mathematical objects such as
algebraic varieties and algebraic curves from the computational point of view.
This makes it important to study both mathematical and computational aspects of
tropical polynomials.
In this paper we prove a tropical Nullstellensatz and moreover we show an
effective formulation of this theorem. Nullstellensatz is a natural step in
building algebraic theory of tropical polynomials and its effective version is
relevant for computational aspects of this field.
On our way we establish a simple formulation of min-plus and tropical linear
dualities. We also observe a close connection between tropical and min-plus
polynomial systems