The subdivision of large simplicial cones in normaliz
Autor(en): | Bruns, W. Sieg, R. Söger, C. |
Herausgeber: | Greuel, G.-M. Sommese, A. Koch, T. Paule, P. |
Stichwörter: | Generating functions; Geometry; Hilbert basis; Hilbert series; Integer programming; Lattice points; Open systems; Polyhedron; Rational cone; Simplicial cones, Open source software; Software engineering, Diophantine system | Erscheinungsdatum: | 2016 | Herausgeber: | Springer Verlag | Journal: | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Volumen: | 9725 | Startseite: | 102 | Seitenende: | 109 | Zusammenfassung: | Normaliz is an open-source software for the computation of lattice points in rational polyhedra, or, in a different language, the solutions of linear diophantine systems. The two main computational goals are (i) finding a system of generators of the set of lattice points and (ii) counting elements degree-wise in a generating function, the Hilbert Series. In the homogeneous case, in which the polyhedron is a cone, the set of generators is the Hilbert basis of the intersection of the cone and the lattice, an affine monoid. We will present some improvements to the Normaliz algorithm by subdividing simplicial cones with huge volumes. In the first approach the subdivision points are found by integer programming techniques. For this purpose we interface to the integer programming solver SCIP to our software. In the second approach we try to find good subdivision points in an approximating overcone that is faster to compute. © Springer International Publishing Switzerland 2016. |
Beschreibung: | Conference of 5th International Conference on Mathematical Software, ICMS 2016 ; Conference Date: 11 July 2016 Through 14 July 2016; Conference Code:178349 |
ISBN: | 9783319424316 | ISSN: | 03029743 | DOI: | 10.1007/978-3-319-42432-3_13 | Externe URL: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-84978807298&doi=10.1007%2f978-3-319-42432-3_13&partnerID=40&md5=75c5e847ec9ea8446040e3b14615e56c |
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geprüft am 02.05.2024