4 citations · 6 across the 8 of their papers we have counts for
8 papers
Bounds on the infimum of polynomials over a generic semi-algebraic set using asymptotic critical values
Boulos El Hilany, Elias Tsigaridas
We present precise bit and degree estimates for the optimal value of the polynomial optimization problem , where is a semi-al…
The polyhedral type of a polynomial map on the plane
Boulos El Hilany, Kemal Rose
Two continuous maps are said to be topologically equivalent if there exist homeomorphisms satisfying $ψ\circ…
The tropical non-properness set of a polynomial map
Boulos El Hilany
We study some discrete invariants of Newton non-degenerate polynomial maps defined over an algebraically closed field of Puiseux series $\mathbb…
Coupler curves of moving graphs and counting realizations of rigid graphs
Georg Grasegger, Boulos El Hilany, Niels Lubbes
A calligraph is a graph that for almost all edge length assignments moves with one degree of freedom in the plane, if we fix an edge and consider the vertices as revolute joints. T…
The tropical discriminant of a polynomial map on a plane
Boulos El Hilany
The discriminant of a polynomial map is central to problems from affine geometry and singularity theory. Standard methods for characterizing it rely on elimination techniques that…
Computing the non-properness set of real polynomial maps in the plane
Boulos El Hilany, Elias Tsigaridas
We introduce novel mathematical and computational tools to develop a complete algorithm for computing the set of non-properness of polynomials maps in the plane. In particular, thi…
Signed counts of real simple rational functions
Boulos El Hilany, Johannes Rau
We study the problem of counting real simple rational functions with prescribed ramification data (i.e. a particular class of oriented real Hurwitz numbers of genus ). We in…
Counting positive intersection points of a trinomial and a -nomial curves via Groethendieck's dessin d'enfant
Boulos El Hilany
We consider real polynomial systems in two variables where has monomial terms and has monomials terms. We prove that the number of positive isolated s…