Translate 
Abstract
In this work, we explore the relation between the tropicalization of a real semi-algebraic set S={f1<0,…,fk<0} defined in the positive orthant and the combinatorial properties of the defining polynomials f1,…,fk. We describe a cone that depends only on the face structure of the Newton polytopes of f1,…,fk and the signs attained by these polynomials. This cone provides an inner approximation of the real tropicalization, and it coincides with the real tropicalization if S={f<0} and the polynomial f has generic coefficients. Furthermore, we show that for a maximally sparse polynomial f the real tropicalization of S={f<0} is determined by the outer normal cones of the Newton polytope of f and the signs of its coefficients. Our arguments are valid also for signomials, that is, polynomials with real exponents defined in the positive orthant.
Highlights
Real algebraic varieties, or more generally, semi-algebraic sets, play a central role in applications, e.g. in chemical reaction network theory [7] or in robotics [29]
One of the roots of tropical geometry goes back to 1971 when Bergman [3] studied the logarithmic limit of an algebraic variety V in the complex torus (C∗)n
This seems to be a quite restrictive assumption, but it is automatically satisfied for polynomials whose set of exponent vectors equals the set of vertices of the Newton polytope
Summary
More generally, semi-algebraic sets, play a central role in applications, e.g. in chemical reaction network theory [7] or in robotics [29]. As a consequence of this, we show that if S is defined by one polynomial f , i.e. S = f −1(R
Sign-in/Register to view highlights & summary 
Published Version
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
