On a tropical dual Nullstellensatz

2011/08/02 by Dima Grigoriev, Grigoriev, Dima
Mathematics · #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.CO

paper · pdf · doi:10.48550/arxiv.1108.0519

arxiv created 2011/08/02 · arxiv updated 2011/08/03

Abstract

Since a tropical Nullstellensatz fails even for tropical univariate polynomials we study a conjecture on a tropical \it dual Nullstellensatz for tropical polynomial systems in terms of solvability of a tropical linear system with the Cayley matrix associated to the tropical polynomial system. The conjecture on a tropical effective dual Nullstellensatz is proved for tropical univariate polynomials.

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