polymake and Lattice Polytopes

Michael Joswig; Benjamin Müller; Andreas Paffenholz

doi:10.46298/dmtcs.2690

Michael Joswig ; Benjamin Müller ; Andreas Paffenholz - polymake and Lattice Polytopes

dmtcs:2690 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2690

polymake and Lattice PolytopesConference paper

Authors: Michael Joswig ¹; Benjamin Müller ²; Andreas Paffenholz ²

1 Institut für Mathematik [Berlin]
2 Institut für Mathematik

The $\mathtt{polymake}$ software system deals with convex polytopes and related objects from geometric combinatorics. This note reports on a new implementation of a subclass for lattice polytopes. The features displayed are enabled by recent changes to the $\mathtt{polymake}$ core, which will be discussed briefly.

https://doi.org/10.46298/dmtcs.2690

Source: HAL:hal-01185382v1

Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)

Section: Proceedings

Published on: January 1, 2009

Imported on: January 31, 2017

Keywords: polymake system,lattice polytope,Hilbert basis,toric geometry,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

Bibliographic References

11 Documents citing this article

Yuji Sano, 2021, A polar dual to the momentum of toric Fano manifolds, Complex Manifolds, 8, 1, pp. 230-246, 10.1515/coma-2020-0116, https://doi.org/10.1515/coma-2020-0116.

Bernard Mourrain;Simon Telen;Marc Van Barel, 2019, Truncated normal forms for solving polynomial systems: Generalized and efficient algorithms, Journal of Symbolic Computation, 102, pp. 63-85, 10.1016/j.jsc.2019.10.009, https://doi.org/10.1016/j.jsc.2019.10.009.

Andreas Paffenholz, Springer eBooks, polyDB: A Database for Polytopes and Related Objects, pp. 533-547, 2017, 10.1007/978-3-319-70566-8_23.

Winfried Bruns;Richard Sieg;Christof Söger, Springer eBooks, Normaliz 2013–2016, pp. 123-146, 2017, 10.1007/978-3-319-70566-8_5.

Gennadiy Averkov;Barbara Langfeld, 2016, Homometry and Direct-Sum Decompositions of Lattice-Convex Sets, arXiv (Cornell University), 56, 1, pp. 216-249, 10.1007/s00454-016-9786-2, https://arxiv.org/abs/1412.7676.

Winfried Bruns;Bogdan Ichim;Christof Söger, 2015, The power of pyramid decomposition in Normaliz, Journal of Symbolic Computation, 74, pp. 513-536, 10.1016/j.jsc.2015.09.003, https://doi.org/10.1016/j.jsc.2015.09.003.

Benjamin Nill;Andreas Paffenholz, 2011, Examples of Kähler–Einstein toric Fano manifolds associated to non-symmetric reflexive polytopes, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 52, 2, pp. 297-304, 10.1007/s13366-011-0041-y.

Benjamin Nill;Günter M. Ziegler, 2011, Projecting Lattice Polytopes Without Interior Lattice Points, arXiv (Cornell University), 36, 3, pp. 462-467, 10.1287/moor.1110.0503, http://arxiv.org/abs/1101.4292.

Christian Haase;Benjamin Lorenz;Andreas Paffenholz, Lecture notes in computer science, Generating Smooth Lattice Polytopes, pp. 315-328, 2010, 10.1007/978-3-642-15582-6_51.

Winfried Bruns;Bogdan Ichim, 2010, Normaliz: Algorithms for affine monoids and rational cones, Journal of Algebra, 324, 5, pp. 1098-1113, 10.1016/j.jalgebra.2010.01.031, https://doi.org/10.1016/j.jalgebra.2010.01.031.

Winfried Bruns;Bogdan Ichim;Christof Söger, Lecture notes in computer science, Introduction to Normaliz 2.5, pp. 209-212, 2010, 10.1007/978-3-642-15582-6_36.

Sources : OpenCitations, OpenAlex & Crossref

Share and export

Consultation statistics

This page has been seen 360 times.

This article's PDF has been downloaded 921 times.