On a tropical dual Nullstellensatz
Dima Grigoriev
TL;DR
This paper investigates a conjecture related to a tropical dual Nullstellensatz, proving it for univariate cases, and explores the solvability of associated tropical linear systems using Cayley matrices.
Contribution
It introduces and proves a tropical effective dual Nullstellensatz for univariate tropical polynomial systems, extending understanding of tropical algebraic geometry.
Findings
Proves the conjecture for univariate tropical polynomials
Establishes a link between tropical Nullstellensatz and tropical linear systems
Uses Cayley matrices to analyze tropical polynomial solvability
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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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems