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 142 articles , 2 standard articles )

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  1. Braun, Benjamin; Davis, Brian: Antichain simplices (2020)
  2. El Ouafdi, Abdelhalim; Lepelley, Dominique; Smaoui, Hatem: Probabilities of electoral outcomes: from three-candidate to four-candidate elections (2020)
  3. Al-Ayyoub, Ibrahim; Jaradat, Imad; Al-Zoubi, Khaldoun: On the normality of a class of monomial ideals via the Newton polyhedron (2019)
  4. Al-Ayyoub, Ibrahim; Nasernejad, Mehrdad; Roberts, Leslie G.: Normality of cover ideals of graphs and normality under some operations (2019)
  5. Binh, Hông Ngoc: An effective characterization of complete monomial ideals in two variables (2019)
  6. Bruns, Winfried; Ichim, Bogdan; Söger, Christof: Computations of volumes and Ehrhart series in four candidates elections (2019)
  7. Burr, Michael A.; Lipman, Drew J.: Quadratic-monomial generated domains from mixed signed, directed graphs (2019)
  8. Dao, Hailong; Montaño, Jonathan: Length of local cohomology of powers of ideals (2019)
  9. García-García, J. I.; Marín-Aragón, D.; Moreno-Frías, M. A.: On divisor-closed submonoids and minimal distances in finitely generated monoids (2019)
  10. García-García, J. I.; Marín-Aragón, D.; Vigneron-Tenorio, A.: A characterization of some families of Cohen-Macaulay, Gorenstein and/or Buchsbaum rings (2019)
  11. García-Sánchez, Pedro A.; O’Neill, Christopher; Webb, Gautam: The computation of factorization invariants for affine semigroups (2019)
  12. Hibi, Takayuki; Tsuchiya, Akiyoshi: The depth of a reflexive polytope (2019)
  13. Kim, Donggyun; Kim, Sangjib; Park, Euisung: On the structures of hive algebras and tensor product algebras for general linear groups of low rank (2019)
  14. Michałek, Mateusz; Ventura, Emanuele: Phylogenetic complexity of the Kimura 3-parameter model (2019)
  15. Yotsutani, Naoto; Zhou, Bin: Relative algebro-geometric stabilities of toric manifolds (2019)
  16. Avis, David; Jordan, Charles: \textttmplrs: a scalable parallel vertex/facet enumeration code (2018)
  17. Bächle, Andreas; Herman, Allen; Konovalov, Alexander; Margolis, Leo; Singh, Gurmail: The status of the Zassenhaus conjecture for small groups (2018)
  18. Castillo, Federico; Liu, Fu; Nill, Benjamin; Paffenholz, Andreas: Smooth polytopes with negative Ehrhart coefficients (2018)
  19. García-García, J. I.; Marín-Aragón, D.; Vigneron-Tenorio, A.: An extension of Wilf’s conjecture to affine semigroups (2018)
  20. Gimenez, Philippe; Martínez-Bernal, José; Simis, Aron; Villarreal, Rafael H.; Vivares, Carlos E.: Symbolic powers of monomial ideals and Cohen-Macaulay vertex-weighted digraphs (2018)

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