From the 1 of 10 linked papers with an AI index.
10 papers
On the Number of Real Zeros of Random Sparse Polynomial Systems
Alperen A. Ergür, Máté L. Telek, Josué Tonelli-Cueto
The paper derives an upper bound on the expected number of positive real solutions of a random sparse polynomial system, showing it depends only on the number of terms per polynomi…
Copositivity, discriminants and nonseparable signed supports
Elisenda Feliu, Joan Ferrer, Máté L. Telek
We establish a connection between discriminants and copositivity of sparse Laurent polynomials. More generally, we consider signomials, which are defined on the positive orthant by…
A note on o-minimal tropicalizations
Lorenzo Baldi, Máté L. Telek
In this note, we provide several equivalent descriptions of the tropicalization of definable sets in a polynomially bounded o-minimal expansion of a real closed field. We show that…
Root bounds of vertical systems using tropical geometry
Elisenda Feliu, Paul Alexander Helminck, Oskar Henriksson +3
Sparse polynomial systems with vertical coefficient dependencies arise naturally when describing the critical points of optimization problems and, when augmented with linear forms,…
Toric extensions of Pólya's theorem
Lorenzo Baldi, Rainer Sinn, Máté L. Telek +1
The classical version of Pólya's theorem provides a simple method for certifying that a homogeneous polynomial of degree d is strictly copositive, that is, it takes only positive…
Computing positive tropical varieties and lower bounds on the number of positive roots
Kemal Rose, Máté L. Telek
We present two effective tools for computing the positive tropicalization of algebraic varieties. First, we outline conditions under which the initial ideal can be used to compute…