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2024-03-26 08:55:01

This https://arxiv.org/abs/2301.05483 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Factorization of polynomials over the symmetrized tropical semiring and Descartes' rule of sign over ordered valued fields
The symmetrized tropical semiring is an extension of the tropical semifield, initially introduced to solve tropical linear systems using Cramer's rule. It is equivalent to the real tropical hyperfield, which has been used in the study of tropicalizations of semialgebraic sets. Polynomials over the symmetrized tropical semiring, and their factorizations, were considered by Quadrat. Recently, Baker and Lorscheid introduced a notion of multiplicity for the roots of univariate polynomials over hype…