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 76 articles , 1 standard article )

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  1. Assarf, Benjamin; Gawrilow, Ewgenij; Herr, Katrin; Joswig, Michael; Lorenz, Benjamin; Paffenholz, Andreas; Rehn, Thomas: Computing convex hulls and counting integer points with polymake (2017)
  2. Bächle, Andreas; Caicedo, Mauricio: On the prime graph question for almost simple groups with an alternating socle (2017)
  3. Boffi, Giandomenico; Logar, Alessandro: Border bases for lattice ideals (2017)
  4. Breuer, Felix; Zafeirakopoulos, Zafeirakis: Polyhedral omega: a new algorithm for solving linear Diophantine systems (2017)
  5. Bruns, Winfried; Conca, Aldo: Linear resolutions of powers and products (2017)
  6. Bruns, Winfried; Conca, Aldo: Products of Borel fixed ideals of maximal minors (2017)
  7. David Kahle, Christopher O’Neill, Jeff Sommars: A computer algebra system for R: Macaulay2 and the m2r package (2017) arXiv
  8. Donten-Bury, Maria; Keicher, Simon: Computing resolutions of quotient singularities (2017)
  9. Flores-Méndez, A.; Gitler, I.; Reyes, E.: Implosive graphs: square-free monomials on symbolic Rees algebras (2017)
  10. Ichim, Bogdan; Katthän, Lukas; Moyano-Fernández, Julio José: How to compute the Stanley depth of a module (2017)
  11. Ichim, Bogdan; Moyano-Fernández, Julio José: On the score sheets of a round-robin football tournament (2017)
  12. Lercier, Reynald; Olive, Marc: Covariant algebra of the binary nonic and the binary decimic (2017)
  13. Michałek, Mateusz: Finite phylogenetic complexity of $\mathbbZ_p$ and invariants for $\mathbbZ_3$ (2017)
  14. Assi, Abdallah; García-Sánchez, Pedro A.: Numerical semigroups and applications (2016)
  15. Böhm, Janko; Decker, Wolfram; Keicher, Simon; Ren, Yue: Current challenges in developing open source computer algebra systems (2016)
  16. Bruns, Winfried; Gubeladze, Joseph; Michałek, Mateusz: Quantum jumps of normal polytopes (2016)
  17. Bruns, Winfried; Ichim, Bogdan; Söger, Christof: The power of pyramid decomposition in Normaliz (2016)
  18. Bruns, Winfried; Sieg, Richard; Söger, Christof: The subdivision of large simplicial cones in normaliz (2016)
  19. García-Sánchez, P.A.: An overview of the computational aspects of nonunique factorization invariants (2016)
  20. Goddyn, Luis; Huynh, Tony; Deshpande, Tanmay: On Hilbert bases of cuts (2016)

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