Normaliz

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 119 articles , 2 standard articles )

Showing results 1 to 20 of 119.
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  1. Avis, David; Jordan, Charles: mplrs: a scalable parallel vertex/facet enumeration code (2018)
  2. Castillo, Federico; Liu, Fu; Nill, Benjamin; Paffenholz, Andreas: Smooth polytopes with negative Ehrhart coefficients (2018)
  3. García-García, J. I.; Marín-Aragón, D.; Vigneron-Tenorio, A.: An extension of Wilf’s conjecture to affine semigroups (2018)
  4. Hamano, Ginji; Hibi, Takayuki; Ohsugi, Hidefumi: Ehrhart series of fractional stable set polytopes of finite graphs (2018)
  5. Hanany, Amihay; Sperling, Marcus: Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional $ \mathcalN=4 $ theories (2018)
  6. Assarf, Benjamin; Gawrilow, Ewgenij; Herr, Katrin; Joswig, Michael; Lorenz, Benjamin; Paffenholz, Andreas; Rehn, Thomas: Computing convex hulls and counting integer points with polymake (2017)
  7. Bächle, Andreas; Caicedo, Mauricio: On the prime graph question for almost simple groups with an alternating socle (2017)
  8. Bächle, Andreas; Kimmerle, Wolfgang; Margolis, Leo: Algorithmic aspects of units in group rings (2017)
  9. Boffi, Giandomenico; Logar, Alessandro: Border bases for lattice ideals (2017)
  10. Breuer, Felix; Zafeirakopoulos, Zafeirakis: Polyhedral omega: a new algorithm for solving linear Diophantine systems (2017)
  11. Bruns, Winfried; Conca, Aldo: Linear resolutions of powers and products (2017)
  12. Bruns, Winfried; Conca, Aldo: Products of Borel fixed ideals of maximal minors (2017)
  13. Bruns, Winfried; Sieg, Richard; Söger, Christof: Normaliz 2013--2016 (2017)
  14. David Kahle, Christopher O’Neill, Jeff Sommars: A computer algebra system for R: Macaulay2 and the m2r package (2017) arXiv
  15. Donten-Bury, Maria; Keicher, Simon: Computing resolutions of quotient singularities (2017)
  16. Fei, Jiarui: Cluster algebras, invariant theory, and Kronecker coefficients I (2017)
  17. Flores-Méndez, A.; Gitler, I.; Reyes, E.: Implosive graphs: square-free monomials on symbolic Rees algebras (2017)
  18. Ichim, Bogdan; Katthän, Lukas; Moyano-Fernández, Julio José: How to compute the Stanley depth of a module (2017)
  19. Ichim, Bogdan; Moyano-Fernández, Julio José: On the score sheets of a round-robin football tournament (2017)
  20. Jing, Rui-Juan; Moreno Maza, Marc: Computing the integer points of a polyhedron, II: complexity estimates (2017)

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