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Normaliz

swMATH ID: 630
Software Authors: Winfried Bruns, Bogdan Ichim, Tim Römer, Christof Söger
Description: 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.
Homepage: https://www.normaliz.uni-osnabrueck.de/
Programming Languages: C,C++
Dependencies: Note that it may be necessary to re-compile Normaliz on your system. Normaliz is compatible with the GNU C++ compiler (source included in the main package) and Microsoft Visual Studio configured for the Intel� C++ compiler.
Keywords: Convex hull; affine monoid; Hilbert basis; normalization; Ehrhart series; lattice points; rational polytope
Related Software: Macaulay2; 4ti2; polymake; SINGULAR; SageMath; GAP; CoCoA; LattE; cdd; GitHub; numericalsgps; nauty; Maple; Mathematica; Gfan; Help; SCIP; lrs; NormalizInterface; Convex
Cited in: 210 Documents
This software is also referenced in ORMS.
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Cited by 289 Authors

24 Bruns, Winfried
20 Villarreal, Rafael Heraclio
9 Söger, Christof
8 Ichim, Bogdan
8 Paffenholz, Andreas
7 García Sánchez, Pedro A.
5 Gitler, Isidoro
5 Michałek, Mateusz
5 Nill, Benjamin
5 Sturmfels, Bernd
4 Bächle, Andreas
4 Diss, Mostapha
4 García García, Juan Ignacio
4 Joswig, Michael
4 Marin-Aragon, Daniel
4 Moyouwou, Issofa
4 Olive, Marc
4 O’Neill, Christopher
4 Schürmann, Achill
4 Simis, Aron
4 Thomas, Rekha R.
4 Valencia, Carlos E.
4 Yoshida, Ruriko
3 Abbott, John A.
3 Bigatti, Anna Maria
3 Conca, Aldo
3 Gubeladze, Joseph
3 Haase, Christian Alexander
3 Hemmecke, Raymond
3 Herr, Katrin
3 Hibi, Takayuki
3 Köppe, Matthias
3 Lorenz, Benjamin
3 Margolis, Leo
3 Martínez-Bernal, José
3 Montaño, Jonathan
3 Moyano Fernández, Julio José
3 Ohsugi, Hidefumi
3 Rehn, Thomas
3 Schepers, Jan
3 Schlenk, Johannes
3 Smaoui, Hatem
3 Sullivant, Seth
3 Vigneron-Tenorio, Alberto
3 Yotsutani, Naoto
2 Al-Ayyoub, Ibrahim
2 Assi, Abdallah
2 Beck, Matthias
2 Boffi, Giandomenico
2 Bogart, Tristram
2 Borowka, Sophia
2 Brandt, Felix
2 Braun, Benjamin
2 Castillo, Federico
2 Dupont, Luis A.
2 El Ouafdi, Abdelhalim
2 Escobar, Cesar A.
2 Heinrich, Gudrun
2 Kamwa, Eric
2 Kappl, Rolf
2 Katthän, Lukas
2 Keicher, Simon
2 Kerner, Martin
2 Kimmerle, Wolfgang
2 Koch, Robert
2 Kohl, Florian
2 Kolev, Boris
2 Konovalov, Olexandr
2 Kubjas, Kaie
2 Logar, Alessandro
2 Moreno Maza, Marc
2 Nitta, Yasufumi
2 Olsen, McCabe
2 Peyton Jones, Simon L.
2 Prendergast-Smith, Artie
2 Rauh, Johannes
2 Ren, Yue
2 Rossmann, Tobias
2 Saito, Shunsuke
2 Santos, Francisco
2 Seceleanu, Alexandra
2 Sieg, Richard
2 Strobel, Martin
2 Swanson, Irena
2 Takemura, Akimichi
2 Thiel, Marko
2 Van Langenhoven, Leen
2 Vasconcelos, Wolmer V.
2 Zhou, Bin
2 Zirke, T.
1 Al-Zoubi, Khaldoun
1 Andjiga, Nicolas Gabriel
1 Arkani-Hamed, Nima
1 Assarf, Benjamin
1 Auffray, Nicolas
1 Avis, David M.
1 Binh, Hong Ngoc
1 Bivià-Ausina, Carles
1 Böhm, Janko
1 Bonanzinga, Vittoria
...and 189 more Authors
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Cited in 88 Serials

11 Journal of Symbolic Computation
9 Journal of Algebra
7 International Journal of Algebra and Computation
6 Journal of Pure and Applied Algebra
6 Discrete & Computational Geometry
5 Journal of High Energy Physics
4 Discrete Mathematics
4 European Journal of Combinatorics
4 Mathematical Programming Computation
3 Beiträge zur Algebra und Geometrie
3 Advances in Mathematics
3 Proceedings of the American Mathematical Society
3 Results in Mathematics
3 Tôhoku Mathematical Journal. Second Series
3 Advances in Applied Mathematics
3 Journal of Algebraic Combinatorics
3 The Electronic Journal of Combinatorics
3 Annals of Combinatorics
3 ACM Communications in Computer Algebra
3 The Journal of Software for Algebra and Geometry
2 Computer Physics Communications
2 Discrete Applied Mathematics
2 Mathematics of Computation
2 Annals of the Institute of Statistical Mathematics
2 Collectanea Mathematica
2 Kodai Mathematical Journal
2 Nagoya Mathematical Journal
2 Theory and Decision
2 Mathematical Social Sciences
2 Experimental Mathematics
2 Revista Matemática Complutense
2 Journal of Algebra and its Applications
2 Research in the Mathematical Sciences
2 European Journal of Mathematics
2 RSME Springer Series
1 Archive for Rational Mechanics and Analysis
1 International Journal of Engineering Science
1 Indian Journal of Pure & Applied Mathematics
1 Israel Journal of Mathematics
1 Nuclear Physics. B
1 Rocky Mountain Journal of Mathematics
1 Acta Mathematica Vietnamica
1 Archiv der Mathematik
1 Automatica
1 Illinois Journal of Mathematics
1 Inventiones Mathematicae
1 Journal of Combinatorial Theory. Series A
1 Mathematische Annalen
1 Memoirs of the American Mathematical Society
1 Michigan Mathematical Journal
1 Proceedings of the London Mathematical Society. Third Series
1 Quaestiones Mathematicae
1 Ricerche di Matematica
1 Semigroup Forum
1 Theoretical Computer Science
1 Transactions of the American Mathematical Society
1 Operations Research Letters
1 Social Choice and Welfare
1 Graphs and Combinatorics
1 SIAM Journal on Discrete Mathematics
1 SIAM Journal on Matrix Analysis and Applications
1 Annals of Operations Research
1 Linear Algebra and its Applications
1 Mathematical Programming. Series A. Series B
1 Journal of Algebraic Geometry
1 Combinatorics, Probability and Computing
1 Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
1 Analele Științifice ale Universității “Ovidius” Constanța. Seria: Matematică
1 Séminaire Lotharingien de Combinatoire
1 The Ramanujan Journal
1 Taiwanese Journal of Mathematics
1 Journal of Combinatorial Optimization
1 Journal of Integer Sequences
1 Annales Henri Poincaré
1 Advances in Geometry
1 Foundations of Computational Mathematics
1 Mediterranean Journal of Mathematics
1 Discrete Optimization
1 London Mathematical Society Lecture Note Series
1 Journal of Mathematics and Music
1 Optimization Letters
1 Algebra & Number Theory
1 São Paulo Journal of Mathematical Sciences
1 Annales de l’Institut Henri Poincaré D. Combinatorics, Physics and their Interactions
1 SIAM Journal on Applied Algebra and Geometry
1 Springer Monographs in Mathematics
1 Discrete Mathematics and its Applications
1 Combinatorial Theory

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