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 155 articles , 2 standard articles )

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  1. Arkani-Hamed, Nima; Lam, Thomas; Spradlin, Marcus: Non-perturbative geometries for planar (\mathcalN= 4) SYM amplitudes (2021)
  2. Borzì, Alessio; D’Alì, Alessio: Graded algebras with cyclotomic Hilbert series (2021)
  3. Bruns, Winfried; García-Sánchez, Pedro A.; Moci, Luca: The monoid of monotone functions on a poset and quasi-arithmetic multiplicities for uniform matroids (2021)
  4. Higashitani, Akihiro; Nakajima, Yusuke: Generalized (F)-signatures of Hibi rings (2021)
  5. Krone, Robert; Kubjas, Kaie: Uniqueness of nonnegative matrix factorizations by rigidity theory (2021)
  6. Vodička, Martin: Normality of the Kimura 3-parameter model (2021)
  7. Assi, Abdallah; D’Anna, Marco; García-Sánchez, Pedro A.: Numerical semigroups and applications (2020)
  8. Braun, Benjamin; Davis, Brian: Antichain simplices (2020)
  9. Bruns, Winfried; García-Sánchez, Pedro; O’Neill, Christopher; Wilburne, Dane: Wilf’s conjecture in fixed multiplicity (2020)
  10. Colmenarejo, Laura; Galuppi, Francesco; Michałek, Mateusz: Toric geometry of path signature varieties (2020)
  11. Diss, Mostapha; Mahajne, Muhammad: Social acceptability of Condorcet committees (2020)
  12. El Ouafdi, Abdelhalim; Lepelley, Dominique; Smaoui, Hatem: Probabilities of electoral outcomes: from three-candidate to four-candidate elections (2020)
  13. Imbesi, Maurizio; La Barbiera, Monica: Integral closure of bipartite graph ideals (2020)
  14. Kohl, Florian; Olsen, McCabe; Sanyal, Raman: Unconditional reflexive polytopes (2020)
  15. Al-Ayyoub, Ibrahim; Jaradat, Imad; Al-Zoubi, Khaldoun: On the normality of a class of monomial ideals via the Newton polyhedron (2019)
  16. Al-Ayyoub, Ibrahim; Nasernejad, Mehrdad; Roberts, Leslie G.: Normality of cover ideals of graphs and normality under some operations (2019)
  17. Binh, Hông Ngoc: An effective characterization of complete monomial ideals in two variables (2019)
  18. Bruns, Winfried; Ichim, Bogdan; Söger, Christof: Computations of volumes and Ehrhart series in four candidates elections (2019)
  19. Burr, Michael A.; Lipman, Drew J.: Quadratic-monomial generated domains from mixed signed, directed graphs (2019)
  20. Dao, Hailong; Montaño, Jonathan: Length of local cohomology of powers of ideals (2019)

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