Related papers: Decomposing tropical rational functions
Already for bivariate tropical polynomials, factorization is an NP-Complete problem. In this paper, we give an efficient algorithm for factorization and rational factorization of a rich class of tropical polynomials in $n$ variables.…
In this paper, we survey and study definitions and properties of tropical polynomials, tropical rational functions and in general, tropical meromorphic functions, emphasizing practical techniques that can really carry out computations. For…
In this paper we present algorithmic considerations and theoretical results about the relation between the orders of certain groups associated to the components of a polynomial and the order of the group that corresponds to the polynomial,…
Tropical Newton-Puiseux polynomials defined as piece-wise linear functions with rational coefficients at the variables, play a role of tropical algebraic functions. We provide explicit formulas for tropical Newton-Puiseux polynomials being…
A tropical polynomial in nr variables divided into blocks of r variables each, is r-symmetric, if it is invariant under the action of Sn that permutes the blocks. For r=1 we call these tropical polynomials symmetric. We can define…
In this paper we give an elementary proof of the Fundamental Theorem of Algebra for polynomials over the rational tropical semi-ring. We prove that, tropically, the rational numbers are algebraically closed. We provide a simple algorithm…
We consider optimization problems that are formulated and solved in the framework of tropical mathematics. The problems consist in minimizing or maximizing functionals defined on vectors of finite-dimensional semimodules over idempotent…
Tropical differential equations are introduced and an algorithm is designed which tests solvability of a system of tropical linear differential equations within the complexity polynomial in the size of the system and in its coefficients.…
We introduce tropical Newton-Puiseux polynomials admitting rational exponents. A resolution of a tropical hypersurface is defined by means of a tropical Newton-Puiseux polynomial. A polynomial complexity algorithm for resolubility of a…
A polynomial complexity algorithm is designed which tests whether a point belongs to a given tropical linear variety.
We consider discrete best approximation problems in the setting of tropical algebra, which is concerned with the theory and application of algebraic systems with idempotent operations. Given a set of input--output pairs of an unknown…
A very brief introduction to tropical and idempotent mathematics is presented. Tropical mathematics can be treated as a result of a dequantization of the traditional mathematics as the Planck constant tends to zero taking imaginary values.…
Tropical geometry has recently found several applications in the analysis of neural networks with piecewise linear activation functions. This paper presents a new look at the problem of tropical polynomial division and its application to…
An algorithm to give an explicit description of all the solutions to any tropical linear system $A\odot x=B\odot x$ is presented. The given system is converted into a finite (rather small) number $p$ of pairs $(S,T)$ of classical linear…
The tropical semiring is an algebraic system with addition ``$\max$'' and multiplication ``$+$''. As well as in conventional algebra, linear programming in the tropical semiring has been developed. In this study, we introduce a new type of…
Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials build…
For a tropical univariate polynomial $f$ we define its tropical Hilbert function as the dimension of a tropical linear prevariety of solutions of the tropical Macauley matrix of the polynomial up to a (growing) degree. We show that the…
We give algorithms to compute decompositions of a given polynomial, or more generally mixed tensor, as sum of rank one tensors, and to establish whether such a decomposition is unique. In particular, we present methods to compute the…
Tropical polyhedra have been recently used to represent disjunctive invariants in static analysis. To handle larger instances, tropical analogues of classical linear programming results need to be developed. This motivation leads us to…
In this paper decomposition of periodic orbits in bifurcation diagrams are derived in unidimensional dynamics system $x_{n+1}=f(x_{n};r)$, being $f$ an unimodal function. We proof a theorem which states the necessary and sufficient…