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 129 articles , 2 standard articles )

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  1. Dao, Hailong; Montaño, Jonathan: Length of local cohomology of powers of ideals (2019)
  2. García-García, J. I.; Marín-Aragón, D.; Moreno-Frías, M. A.: On divisor-closed submonoids and minimal distances in finitely generated monoids (2019)
  3. Michałek, Mateusz; Ventura, Emanuele: Phylogenetic complexity of the Kimura 3-parameter model (2019)
  4. Avis, David; Jordan, Charles: \textttmplrs: a scalable parallel vertex/facet enumeration code (2018)
  5. Bächle, Andreas; Herman, Allen; Konovalov, Alexander; Margolis, Leo; Singh, Gurmail: The status of the Zassenhaus conjecture for small groups (2018)
  6. Castillo, Federico; Liu, Fu; Nill, Benjamin; Paffenholz, Andreas: Smooth polytopes with negative Ehrhart coefficients (2018)
  7. García-García, J. I.; Marín-Aragón, D.; Vigneron-Tenorio, A.: An extension of Wilf’s conjecture to affine semigroups (2018)
  8. 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)
  9. Hamano, Ginji; Hibi, Takayuki; Ohsugi, Hidefumi: Ehrhart series of fractional stable set polytopes of finite graphs (2018)
  10. Hanany, Amihay; Sperling, Marcus: Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional ( \mathcalN=4 ) theories (2018)
  11. Kohl, Florian; Li, Yanxi; Rauh, Johannes; Yoshida, Ruriko: Semigroups -- a computational approach (2018)
  12. Olsen, McCabe: Hilbert bases and lecture hall partitions (2018)
  13. Assarf, Benjamin; Gawrilow, Ewgenij; Herr, Katrin; Joswig, Michael; Lorenz, Benjamin; Paffenholz, Andreas; Rehn, Thomas: Computing convex hulls and counting integer points with \textttpolymake (2017)
  14. Bächle, Andreas; Caicedo, Mauricio: On the prime graph question for almost simple groups with an alternating socle (2017)
  15. Bächle, Andreas; Kimmerle, Wolfgang; Margolis, Leo: Algorithmic aspects of units in group rings (2017)
  16. Boffi, Giandomenico; Logar, Alessandro: Border bases for lattice ideals (2017)
  17. Breuer, Felix; Zafeirakopoulos, Zafeirakis: Polyhedral omega: a new algorithm for solving linear Diophantine systems (2017)
  18. Bruns, Winfried; Conca, Aldo: Linear resolutions of powers and products (2017)
  19. Bruns, Winfried; Conca, Aldo: Products of Borel fixed ideals of maximal minors (2017)
  20. Bruns, Winfried; Sieg, Richard; Söger, Christof: Normaliz 2013--2016 (2017)

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