Oberwolfach References on Mathematical Software

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LattE integrale

LattE (Lattice point Enumeration) is a computer software dedicated to the problems of counting lattice points and integrationinside convex polytopes. LattE contains the first ever implementation of Barvinok's algorithm. The latest version, LattE integrale, has the ability to directly compute integrals of polynomial functions over polytopes and in particular to do exact volume computations. Version 1.6 added the capability of computing the highest coefficients of weighted Ehrhart quasipolynomials.

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Normaliz is a tool for computations in affine monoids, vector configurations, lattice polytopes, and rational cones. Its input data can be specified in terms of a system of generators or vertices or a system of linear homogeneous Diophantine equations, inequalities and congruences or a binomial ideal. Normaliz computes the dual cone of a rational cone (in other words, given generators, Normaliz computes the defining hyperplanes, and vice versa), a placing (or lexicographic) triangulation of a vector configuration (resulting in a triangulation of the cone generated by it), the Hilbert basis of a rational cone, the lattice points of a lattice polytope, the normalization of an affine monoid, the Hilbert (or Ehrhart) series and the Hilbert (or Ehrhart) (quasi) polynomial under a Z-grading (for example, for rational polytopes), NEW: generalized (or weighted) Ehrhart series and Lebesgue integrals of polynomials over rational polytopes via NmzIntegrate, a description of the cone and lattice under consideration by a system of inequalities, equations and congruences

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Sums over integral points of a polygon

Maple program for computing the sum of values of a polynomial function over the set of integral points of a polygon and the corresponding weighted Ehrhart quasi-polynomial.

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