Köppe, Matthias A primal Barvinok algorithm based on irrational decompositions. (English) Zbl 1135.05003 SIAM J. Discrete Math. 21, No. 1, 220-236 (2007). Summary: We introduce variants of A.I. Barvinok’s algorithm [Math. Oper. Res. 19, No. 4, 769–779 (1994; Zbl 0821.90085)] for counting lattice points in polyhedra. The new algorithms are based on irrational signed decomposition in the primal space and the construction of rational generating functions for cones with low index. We give computational results that show that the new algorithms are faster than the existing algorithms by a large factor. Cited in 16 Documents MSC: 05A15 Exact enumeration problems, generating functions 52B12 Special polytopes (linear programming, centrally symmetric, etc.) 52C07 Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry) 68W30 Symbolic computation and algebraic computation Keywords:rational generating functions; irrational decompositions Citations:Zbl 0821.90085 Software:LattE; NTL PDFBibTeX XMLCite \textit{M. Köppe}, SIAM J. Discrete Math. 21, No. 1, 220--236 (2007; Zbl 1135.05003) Full Text: DOI arXiv