6 citations · 10 across the 5 of their papers we have counts for
6 papers
On the frontiers of polynomial computations in tropical geometry
Thorsten Theobald
We study some basic algorithmic problems concerning the intersection of tropical hypersurfaces in general dimension: deciding whether this intersection is nonempty, whether it is a…
Radii minimal projections of polytopes and constrained optimization of symmetric polynomials
Rene Brandenberg, Thorsten Theobald
We provide a characterization of the radii minimal projections of polytopes onto -dimensional subspaces in Euclidean space $\E^n$. Applied on simplices this characterization all…
First steps in tropical geometry
Jürgen Richter-Gebert, Bernd Sturmfels, Thorsten Theobald
Tropical algebraic geometry is the geometry of the tropical semiring . Its objects are polyhedral cell complexes which behave like complex algebraic varieties.…
Algebraic methods for computing smallest enclosing and circumscribing cylinders of simplices
R. Brandenberg, T. Theobald
We provide an algebraic framework to compute smallest enclosing and smallest circumscribing cylinders of simplices in Euclidean space $\E^n$. Explicitly, the computation of a small…
Common transversals and tangents to two lines and two quadrics in P^3
Gábor Megyesi, Frank Sottile, Thorsten Theobald
We solve the following geometric problem, which arises in several three-dimensional applications in computational geometry: For which arrangements of two lines and two spheres in R…
Lines Tangent to 2n-2 spheres in R^n
Frank Sottile, Thorsten Theobald
We show that there are 3 \cdot 2^(n-1) complex common tangent lines to 2n-2 general spheres in R^n and that there is a choice of spheres with all common tangents real.