The power of pyramid decomposition in Normaliz. (May 2016)

• Record Type: Journal Article
• Authors: Bruns, Winfried; Ichim, Bogdan; Söger, Christof
• Is Part Of: Journal of symbolic computation. Volume 74(2016)
• Page Start: 513
• Page End: 536
• Publication Date: 2016-05
• Subjects: 52B20 -- 13F20 -- 14M25 -- 91B12; Hilbert basis -- Ehrhart series -- Hilbert series -- Rational polytope -- Volume -- Triangulation -- Pyramid decomposition; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.09.003
• Languages: English
• ISSNs: 0747-7171

Abstract

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 ≈ 5 ⋅ 10 11 that arise in the computation of Ehrhart series related to the theory of social choice.