The power of pyramid decomposition in Normaliz

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 Norm...

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Bibliographic Details
Published in:Journal of symbolic computation 2016-05, Vol.74, p.513-536
Main Authors: Bruns, Winfried, Ichim, Bogdan, Söger, Christof
Format: Article
Language:English
Subjects:
Ehrhart series
Hilbert basis
Hilbert series
Pyramid decomposition
Rational polytope
Triangulation
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Summary: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 ≈5⋅1011 that arise in the computation of Ehrhart series related to the theory of social choice.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2015.09.003