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 61 articles , 1 standard article )

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  1. Ichim, Bogdan; Katthän, Lukas; Moyano-Fernández, Julio José: How to compute the Stanley depth of a module (2017)
  2. Böhm, Janko; Decker, Wolfram; Keicher, Simon; Ren, Yue: Current challenges in developing open source computer algebra systems (2016)
  3. Bruns, Winfried; Gubeladze, Joseph; Michałek, Mateusz: Quantum jumps of normal polytopes (2016)
  4. Bruns, Winfried; Ichim, Bogdan; Söger, Christof: The power of pyramid decomposition in Normaliz (2016)
  5. Bruns, Winfried; Sieg, Richard; Söger, Christof: The subdivision of large simplicial cones in normaliz (2016)
  6. Goddyn, Luis; Huynh, Tony; Deshpande, Tanmay: On Hilbert bases of cuts (2016)
  7. Gräbe, Hans-Gert: Semantic-aware fingerprints of symbolic research data (2016)
  8. Rauh, Johannes; Sullivant, Seth: Lifting Markov bases and higher codimension toric fiber products (2016)
  9. 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)
  10. Bruns, Winfried: Binomial regular sequences and free sums (2015)
  11. Bruns, Winfried; Söger, Christof: The computation of generalized Ehrhart series in normaliz (2015)
  12. Kappl, Rolf; Nilles, Hans Peter; Schmitz, Matthias: $R$ symmetries and a heterotic MSSM (2015)
  13. Kubjas, Kaie: Low degree minimal generators of phylogenetic semigroups (2015)
  14. Lorenz, Benjamin; Nill, Benjamin: On smooth Gorenstein polytopes (2015)
  15. Rossmann, Tobias: Computing topological zeta functions of groups, algebras, and modules. II. (2015)
  16. Teitler, Zach: Software for multiplier ideals (2015)
  17. Van Langenhoven, Leen; Veys, Willem: Semigroup and Poincaré series for a finite set of divisorial valuations (2015)
  18. Abbott, John; Bigatti, Anna Maria: What is new in CoCoA? (2014)
  19. Abbott, John; Bigatti, Anna Maria; Söger, Christof: Integration of libnormaliz in CoCoALib and CoCoA 5 (2014)
  20. Haws, David; del Campo, Abraham Martín; Takemura, Akimichi; Yoshida, Ruriko: Markov degree of the three-state toric homogeneous Markov chain model (2014)

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