×

Normaliz 2013–2016. (English) Zbl 1400.52012

Böckle, Gebhard (ed.) et al., Algorithmic and experimental methods in algebra, geometry, and number theory. Cham: Springer (ISBN 978-3-319-70565-1/hbk; 978-3-319-70566-8/ebook). 123-146 (2017).
Summary: In this article we describe mathematically relevant extensions to Normaliz that were added to it during the support by the DFG SPP “Algorithmische und Experimentelle Methoden in Algebra, Geometrie und Zahlentheorie”: nonpointed cones, rational polyhedra, homogeneous systems of parameters, bottom decomposition, class groups and systems of module generators of integral closures.
For the entire collection see [Zbl 1394.14002].

MSC:

52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry)
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
91B12 Voting theory
52-03 History of convex and discrete geometry
01A61 History of mathematics in the 21st century
52-04 Software, source code, etc. for problems pertaining to convex and discrete geometry
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] J. Abbott, A.M. Bigatti, C. Söger, Integration of libnormaliz in CoCoALib and CoCoA 5, in \(Mathematical Software - ICMS 2014. 4th International Congress, Seoul, August 5-9, 2014. Proceedings\) (Springer, Berlin, 2014), pp. 647-653 · Zbl 1434.68698
[2] J. Abbott, A.M. Bigatti, G. Lagorio, CoCoA-5: a system for doing Computations in Commutative Algebra. Available at http://cocoa.dima.unige.it
[3] T. Achterberg, SCIP: solving constraint integer programs. Math. Program. Comput. 1, 1-41 (2009). Available from http://mpc.zib.de/index.php/MPC/article/view/4 · Zbl 1171.90476 · doi:10.1007/s12532-008-0001-1
[4] B. Assarf et al., Computing convex hulls and counting integer points with polymake. Preprint (2015). arXiv:1408.4653 · Zbl 1370.90009
[5] A. Bächle, L. Margolis, HeLP - a GAP-package for torsion units in integral group rings. Preprint (2016). arXiv:1507.08174.
[6] S. Borowka et al., SecDec - a program to evaluate dimensionally regulated parameter integrals numerically. Available from https://secdec.hepforge.org/
[7] W. Bruns, J. Gubeladze, \(Polytopes, Rings and K-theory\) (Springer, Berlin, 2009)
[8] W. Bruns, J. Herzog, \(Cohen-Macaulay Rings\) (Cambridge University Press, Cambridge, 1998) · doi:10.1017/CBO9780511608681
[9] W. Bruns, B. Ichim, Normaliz: algorithms for affine monoids and rational cones. J. Algebra 324, 1098-1113 (2010) · Zbl 1203.13033 · doi:10.1016/j.jalgebra.2010.01.031
[10] W. Bruns, R. Koch, Computing the integral closure of an affine semigroup. Univ. Iagel. Acta Math. 39, 59-70 (2001) · Zbl 1006.20045
[11] W. Bruns, C. Söger, Generalized Ehrhart series and integration in Normaliz. J. Symb. Comput. 68, 75-86 (2015) · Zbl 1320.52018 · doi:10.1016/j.jsc.2014.09.004
[12] W. Bruns, R. Hemmecke, B. Ichim, M. Köppe, C. Söger. Challenging computations of Hilbert bases of cones associated with algebraic statistics. Exp. Math. 20, 25-33 (2011) · Zbl 1273.13052 · doi:10.1080/10586458.2011.544574
[13] W. Bruns, B. Ichim, T. Römer, R. Sieg, C. Söger, Normaliz. Algorithms for rational cones and affine monoids. Available at http://normaliz.uos.de
[14] W. Bruns, B. Ichim, C. Söger, The power of pyramid decomposition in Normaliz. J. Symb. Comput. 74, 513-536 (2016) · Zbl 1332.68298 · doi:10.1016/j.jsc.2015.09.003
[15] W. Bruns, R. Sieg, C. Söger, The subdivision of large simplicial cones in Normaliz, in \(MathematicalSoftware - ICMS 2016. 5th International Conference Berlin, July 11-14, 2016. Proceedings\) (Springer, Berlin, 2016), p. 1026 · Zbl 1434.52001
[16] B.A. Burton, Regina: software for 3-manifold theory and normal surfaces. Available from http://regina.sourceforge.net/
[17] W. Decker, G.-M. Greuel, G. Pfister, H. Schönemann, Singular 4-0-2 — a computer algebra system for polynomial computations. Available at http://www.singular.uni-kl.de
[18] D.R. Grayson, M.E. Stillman, Macaulay2, a software system for research in algebraic geometry. Available at http://www.math.uiuc.edu/Macaulay2/
[19] S. Gutsche, M. Horn, C. Söger, NormalizInterface for GAP. Available at https://github.com/gap-packages/NormalizInterface
[20] M. Joswig, B. Müller, A. Paffenholz, Polymake and lattice polytopes, in \(DMTCS proc. AK\), ed. by C. Krattenthaler et al., Proceedings of FPSAC 2009, pp. 491-502 · Zbl 1391.52019
[21] M. Köppe, Y. Zhou, New computer-based search strategies for extreme functions of the Gomory-Johnson infinite group problem. Preprint (2016). arXiv:1506.00017v3
[22] F. Kohl, Y. Li, J. Rauh, R. Yoshida, Semigroups - a computational approach. Preprint (2017). arXiv:1608.03297
[23] A. Schürmann, Exploiting polyhedral symmetries in social choice. Soc. Choice Welf. 40, 1097-1110 (2013) · Zbl 1288.91076 · doi:10.1007/s00355-012-0667-1
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.