5 papers
On the Solution Sets of the Cone-Volume Map
Tom Baumbach, Zhang Chen, Martin Henk
For a fixed set of outer unit normals, we consider the cone-volume map which associates to a vector of support numbers the cone-volume…
The Moment Method for Computing Real Points of Sparse Polynomial Systems
Tom Baumbach, Matías Bender
One of the most important problems in computational algebra is the computation of real solutions of a polynomial system. Lasserre, Laurent, and Rostalski introduced a numerical met…
On the discrete logarithmic Minkowski problem in the plane
Tom Baumbach
The paper characterizes the convex hull of the closure of the cone-volume set $C_\cv(U)$, consisting of all cone-volume vectors of polygons with outer unit normals vectors containe…
The canonical form, scissors congruence and adjoint degrees of polytopes
Tom Baumbach, Ansgar Freyer, Julian Weigert +1
We study the canonical form as a valuation in the context of scissors congruence for polytopes. We identify the degree of its numerator - the adjoint polynomial $\operatorname{…
On polynomial inequalities for cone-volumes of polytopes
Tom Baumbach, Martin Henk
Motivated by the discrete logarithmic Minkowski problem we study for a given matrix its cone-volume set consisting of all the cone-volu…