Computing the Ehrhart polynomial of a convex lattice polytope

The nth Birkhoff polytope is the set of all doubly stochastic n n matrices, that is, those matrices with nonnegative real coefficients in which every row and column sums to one. A wide open problem concerns the volumes of these polytopes, which have ...

Let V be a real vector space of dimension n and let $M\subset V$ be a lattice. Let $P\subset V$ be an n-dimensional polytope with vertices in M, and let $\phi :V\to \mathbb{C}$ be a homogeneous polynomial function of degree d. For $q\in {\mathbb{Z}}_{>0}$ and any face F of P, let $D_{\phi ,F}(q)$ be the sum of ...$$${}_{}\mathbb{}$${}_{}$${}_{}$

Polynomial ranges are commonly used for numerically solving polynomial systems with interval Newton solvers. Often ranges are computed using the convex hull property of the tensorial Bernstein basis, which is exponential size in the number n of ...