The power of pyramid decomposition in Normaliz

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• 作者：Winfried Bruns^a ; ^{wbruns@uos.de" class="auth_mail" title="E-mail the corresponding author} ; Bogdan Ichim^b ; ^{bogdan.ichim@imar.ro" class="auth_mail" title="E-mail the corresponding author} ; Christof Sö ; ger^a ; ^{csoeger@uos.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：52B20 ; 13F20 ; 14M25 ; 91B12
• 刊名：Journal of Symbolic Computation
• 出版年：2016
• 出版时间：May-June 2016
• 年：2016
• 卷：74
• 期：Complete
• 页码：513-536
• 全文大小：596 K

文摘

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$\approx 5\cdot {10}^{11}$ that arise in the computation of Ehrhart series related to the theory of social choice.