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Challenging Computations of Hilbert Bases of Cones Associated with Algebraic Statistics Winfried Brunsa; Raymond Hemmeckeb; Bogdan Ichimc; Matthias Köpped; Christof Sögera a Universität Osnabrück, FB Mathematik/Informatik, Osnabrück, Germany b Zentrum Mathematik, M9, Technische Universität München, Garching, Germany c Institute of Mathematics, Bucharest,… (More)
Article history: Received 27 January 2014 Accepted 26 August 2015 Available online 16 September 2015 MSC: 52B20 13F20 14M25 91B12
Acknowledgements First of all I would like to thank my advisor Winfried Bruns for his inspiring guidance and support. Our discussions have been very helpful, and I am always enjoying to work with him. I also wish to thank all my colleagues at the Institute for Mathematics. They are providing a very pleasant working atmosphere. Many thanks also to Merle for… (More)
Article history: Received 15 October 2013 Accepted 29 March 2014 Available online 19 September 2014 MSC: 52B20 13F20 14M25 91B12
The software Normaliz implements algorithms for rational cones and affine monoids. In this note we present recent developments. They include the support for (unbounded) polyhedra and semi-open cones. Furthermore, we report on improved algorithms and parallelization, which allow us to compute significantly larger examples.
In this paper we introduce the version 2.5 of Normaliz , a program for the computation of Hilbert bases of rational cones and the normalizations of affine monoids. It may also be used for solving dio-phantine linear systems of inequalities, equations and congruences. We present some of the new features of the program, as well as some recent achievements.