4 papers · 1 filter
Osculating Geometry and Higher-Order Distance Loci
Sandra Di Rocco, Kemal Rose, Luca Sodomaco
We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Eucli…
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…
Certifying zeros of polynomial systems using interval arithmetic
Paul Breiding, Kemal Rose, Sascha Timme
We establish interval arithmetic as a practical tool for certification in numerical algebraic geometry. Our software HomotopyContinuation.jl now has a built-in function certify, wh…
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 $Ï\ci…