Normaliz

Normaliz is a tool for computations in affine monoids, vector configurations, lattice polytopes, and rational cones. Its input data can be specified in terms of a system of generators or vertices or a system of linear homogeneous Diophantine equations, inequalities and congruences or a binomial ideal. Normaliz computes the dual cone of a rational cone (in other words, given generators, Normaliz computes the defining hyperplanes, and vice versa), convex hulls, a triangulation of a vector, the Hilbert basis of a (not necessarily pointed) rational cone, the lattice points of a rational polytope or unbounded polyhedron, the integer hull, the normalization of an affine monoid, the Hilbert (or Ehrhart) series and the Hilbert (or Ehrhart) (quasi) polynomial under a Z-grading (for example, for rational polytopes), generalized (or weighted) Ehrhart series and Lebesgue integrals of polynomials over rational polytopes via NmzIntegrate, a description of the cone and lattice under consideration by a system of inequalities, equations and congruences.

This software is also referenced in ORMS.


References in zbMATH (referenced in 67 articles , 1 standard article )

Showing results 1 to 20 of 67.
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  1. Boffi, Giandomenico; Logar, Alessandro: Border bases for lattice ideals (2017)
  2. Donten-Bury, Maria; Keicher, Simon: Computing resolutions of quotient singularities (2017)
  3. Ichim, Bogdan; Katthän, Lukas; Moyano-Fernández, Julio José: How to compute the Stanley depth of a module (2017)
  4. Lercier, Reynald; Olive, Marc: Covariant algebra of the binary nonic and the binary decimic (2017)
  5. Michałek, Mateusz: Finite phylogenetic complexity of $\mathbbZ_p$ and invariants for $\mathbbZ_3$ (2017)
  6. Böhm, Janko; Decker, Wolfram; Keicher, Simon; Ren, Yue: Current challenges in developing open source computer algebra systems (2016)
  7. Bruns, Winfried; Gubeladze, Joseph; Michałek, Mateusz: Quantum jumps of normal polytopes (2016)
  8. Bruns, Winfried; Ichim, Bogdan; Söger, Christof: The power of pyramid decomposition in Normaliz (2016)
  9. Bruns, Winfried; Sieg, Richard; Söger, Christof: The subdivision of large simplicial cones in normaliz (2016)
  10. García-Sánchez, P.A.: An overview of the computational aspects of nonunique factorization invariants (2016)
  11. Goddyn, Luis; Huynh, Tony; Deshpande, Tanmay: On Hilbert bases of cuts (2016)
  12. Gräbe, Hans-Gert: Semantic-aware fingerprints of symbolic research data (2016)
  13. Rauh, Johannes; Sullivant, Seth: Lifting Markov bases and higher codimension toric fiber products (2016)
  14. Andreas Baechle, Leo Margolis: HeLP -- A GAP-package for torsion units in integral group rings (2015) arXiv
  15. Bogart, Tristram; Haase, Christian; Hering, Milena; Lorenz, Benjamin; Nill, Benjamin; Paffenholz, Andreas; Rote, Günter; Santos, Francisco; Schenck, Hal: Finitely many smooth $d$-polytopes with $n$ lattice points (2015)
  16. Bruns, Winfried: Binomial regular sequences and free sums (2015)
  17. Bruns, Winfried; Söger, Christof: The computation of generalized Ehrhart series in normaliz (2015)
  18. Kappl, Rolf; Nilles, Hans Peter; Schmitz, Matthias: $R$ symmetries and a heterotic MSSM (2015)
  19. Kubjas, Kaie: Low degree minimal generators of phylogenetic semigroups (2015)
  20. Lorenz, Benjamin; Nill, Benjamin: On smooth Gorenstein polytopes (2015)

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