is an open source tool for computations in affine monoids, vector configurations, lattice polytopes, and rational cones. Normaliz also computes algebraic polyhedra, i.e., polyhedra defined over real algebraic extensions of Q.
- automorphism groups of polyhedra and monoids
- convex hulls and dual cones
- conversion from generators to constraints and vice versa
- projections of cones and polyhedra
- triangulations, disjoint decompositions and Stanley decompositions
- Hilbert basis of rational, not necessarily pointed cones
- normalization of affine monoids
- lattice points of rational polytopes and (unbounded) polyhedra
- Euclidean and lattice normalized volumes of polytopes
- Hilbert (or Ehrhart) series and (quasi) polynomials under Z-gradings (for example, for rational polytopes)
- generalized (or weighted) Ehrhart series and Lebesgue integrals of polynomials over rational polytopes
Normaliz offers the API libnormaliz that allows the user to access the Normaliz computations from any C++ program.
Online exploration of Normaliz: https://mybinder.org/v2/gh/Normaliz/NormalizJupyter/master
The Normaliz project was partially supported by the DFG SPP 1489 “Algorithmische und experimentelle Methoden in Algebra, Geometrie und Zahlentheorie”.