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 168 articles , 2 standard articles )

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  1. Bruns, Winfried: Automorphism groups and normal forms in Normaliz (2022)
  2. Diss, Mostapha; Gori, Michele: Majority properties of positional social preference correspondences (2022)
  3. Dunfield, Nathan M.; Garoufalidis, Stavros; Rubinstein, J. Hyam: Counting essential surfaces in (3)-manifolds (2022)
  4. Grisalde, Gonzalo; Seceleanu, Alexandra; Villarreal, Rafael H.: Rees algebras of filtrations of covering polyhedra and integral closure of powers of monomial ideals (2022)
  5. Koley, Mitra; Römer, Tim: Seminormality, canonical modules, and regularity of cut polytopes (2022)
  6. Köppe, Matthias; Wang, Jiawei: Dual-feasible functions for integer programming and combinatorial optimization: algorithms, characterizations, and approximations (2022)
  7. Ma, Ziyue; He, Zhou; Li, Zhiwu; Giua, Alessandro: Design of supervisors for linear marking specifications in labeled Petri nets (2022)
  8. Nanduri, Ramakrishna: On regularity of symbolic Rees algebras and symbolic powers of vertex cover ideals of graphs (2022)
  9. Arkani-Hamed, Nima; Lam, Thomas; Spradlin, Marcus: Non-perturbative geometries for planar (\mathcalN= 4) SYM amplitudes (2021)
  10. Bächle, Andreas; Margolis, Leo: From examples to methods: Two cases from the study of units in integral group rings (2021)
  11. Borzì, Alessio; D’Alì, Alessio: Graded algebras with cyclotomic Hilbert series (2021)
  12. Bruns, Winfried; García-Sánchez, Pedro A.; Moci, Luca: The monoid of monotone functions on a poset and quasi-arithmetic multiplicities for uniform matroids (2021)
  13. Bruns, Winfried; Ichim, Bogdan: Polytope volume by descent in the face lattice and applications in social choice (2021)
  14. DiPasquale, Michael; Drabkin, Ben: On resurgence via asymptotic resurgence (2021)
  15. Haase, Christian; Paffenholz, Andreas; Piechnik, Lindsey C.; Santos, Francisco: Existence of unimodular triangulations -- positive results (2021)
  16. Higashitani, Akihiro; Nakajima, Yusuke: Generalized (F)-signatures of Hibi rings (2021)
  17. Krone, Robert; Kubjas, Kaie: Uniqueness of nonnegative matrix factorizations by rigidity theory (2021)
  18. Pintye, Norbert; Prendergast-Smith, Artie: Effective cycles on some linear blowups of projective spaces (2021)
  19. Vodička, Martin: Normality of the Kimura 3-parameter model (2021)
  20. Assi, Abdallah; D’Anna, Marco; García-Sánchez, Pedro A.: Numerical semigroups and applications (2020)

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