The power of pyramid decomposition in Normaliz

Abstract

We describe the use of pyramid decomposition in Normaliz, a software tool for the computation of Hilbert bases and enumerative data of rational cones and affine monoids. Pyramid decomposition in connection with efficient parallelization and streamlined evaluation of simplicial cones has enabled Normaliz to process triangulations of size $\approx 5\cdot 10^{11}$ that arise in the computation of Hilbert series related to combinatorial voting theory.

Updated to the current implementation

References in corpus (3)

• Exploiting Polyhedral Symmetries in Social Choice
• The Hilbert basis method for D-flat directions and the superpotential
• Software for Exact Integration of Polynomials over Polyhedra

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• An Invitation to Ehrhart Theory: Polyhedral Geometry and its Applications in Enumerative Combinatorics