The goal of this book is to explain, at the graduate student level, connections between
tropical geometry and optimization. Building bridges between these two subject areas is …

We prove a fundamental theorem for tropical partial differential equations analogue of the
fundamental theorem of tropical geometry in this context. We extend results from Aroca et al …

Tropical Differential Algebraic Geometry considers difficult or even intractable problems in
Differential Equations and tries to extract information on their solutions from a restricted …

Tropical differential equations are introduced and an algorithm is designed which tests
solvability of a system of tropical linear differential equations within the complexity …

Abstract Tropical Differential Algebraic Geometry considers difficult or even intractable
problems in Differential Equations and tries to extract information on their solutions from a …

Initial forms and a notion of basisfor tropical differential equations Page 1 Pacific Journal of
Mathematics INITIAL FORMS AND A NOTION OF BASIS FOR TROPICAL DIFFERENTIAL …

In this paper, the concept of tropical differential Gröbner basis is introduced, which is a
natural generalization of the tropical Gröbner basis to the recently introduced tropical …

We construct a general framework for tropical differential equations based on idempotent
semirings and an idempotent version of differential algebra. Over a differential ring equipped …

The purpose of this paper is fourfold. The first is to develop the theory of tropical differential
algebraic geometry from scratch; the second is to present the tropical fundamental theorem …

We study the notion of degeneration for affine schemes associated with systems of algebraic
differential equations with coefficients in the fraction field of a multivariate formal power …