## Convex

 swMATH ID: 7770 Software Authors: Matthias Franz Description: Convex - a Maple package for convex geometry. Convex is a Maple package for computations in rational convex geometry. Here ”rational” means that all coordinates must be rational numbers. The package provides functions for ”linear” as well as ”affine” convex geometry. In the affine setting, the basic objects are polyhedra, which are intersections of finitely many (affine) halfspaces. Polyhedra can also be described as the convex hull of finitely many points and rays. A bounded polyhedron is also called a polytope. In the Convex package, polyhedra are represented by the type POLYHEDRON and polytopes by the subtype POLYTOPE. A POLYHEDRON may contain lines and may not be full-dimensional. The most important functions to define a POLYHEDRON are convhull and intersection. The linear setting is based on cones, which are intersections of finitely many linear halfspaces (i.e., whose boundary contains the origin). Cones are generated by finitely many rays. In the Convex package, cones are represented by the type CONE. They may contain lines and may not be full-dimensional. A CONE can be created from either description with the functions poshull and intersection, respectively. The Convex package can deal with polyhedral complexes (simplicial complexes, for example) and fans. See the types PCOMPLEX and FAN. It also provides functions to do calculations in the face lattice of a cone or polyhedron, see the types CFACE and PFACE. The functions traverse and traverse2 are some kind of map for faces: One can apply a given function to all faces of a cone or polyhedron, or to all pairs (f1, f2), where f1 is a facet of f2. See CONE[traverse], CONE[traverse2] and POLYHEDRON[traverse], POLYHEDRON[traverse2]. More generally, these functions can be used with fans and polyhedral complexes. Homepage: https://math.sci.uwo.ca/~mfranz/convex/ Dependencies: Maple Related Software: Maple; Magma; MDSpackage; Gfan; Normaliz; polymake; GAP; toric; ToricVarieties; TorDiv; AMPL; LattE; PolyLib; PPL; CPLEX; cdd; Macaulay2; CaTS; TiGERS; Monoid Cited in: 33 Publications
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### Cited by 52 Authors

 3 Kroupa, Tomáš 3 Roux, Alet 2 Bourqui, David 2 Le Boudec, Pierre 2 Lusares, Gina 2 Rassart, Etienne 2 Studený, Milan 2 Zastawniak, Tomasz 1 Altunbulak, Murat 1 Amaris, Armando J. R. 1 Amaris, Armando Rodado 1 Billey, Sara C. 1 Chirivì, Rocco 1 Choi, Suyoung 1 Christophersen, Jan Arthur 1 Cox, Murray P. 1 D’Andrea, Carlos 1 Diss, Mostapha 1 Dutour-Sikiric, Mathieu 1 El Ouafdi, Abdelhalim 1 Fahrner, Anne 1 Garnier, Arthur 1 Ginnis, Alexandros I. 1 González-Torres, Raúl Ernesto 1 Goodman, Jacob Eli 1 Grabisch, Michel 1 Guillemin, Victor W. 1 Hausen, Jürgen 1 Hemmecke, Raymond 1 Kaklis, Panagiotis D. 1 Karousos, E. I. 1 Keicher, Simon 1 Keller, Wolfgang 1 Klyachko, Alexander Anatol’evich 1 Lepelley, Dominique 1 Loughran, Daniel 1 Mahajne, Muhammad 1 Martinet, Jacques 1 Morrison, Ian 1 O’Rourke, Joseph 1 Park, Hanchul 1 Rodado, Amaris Armando 1 Rossi, Michele 1 Schürmann, Achill 1 Smaoui, Hatem 1 Sombra, Martín 1 Spreafico, Mauro 1 Swinarski, David 1 Terracini, Lea 1 Tóth, Csaba D. 1 Vigeland, Magnus Dehli 1 Vomlel, Jiří
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### Cited in 29 Serials

 2 Discrete Applied Mathematics 2 Journal of Algebra 2 International Journal of Approximate Reasoning 1 Communications in Mathematical Physics 1 Journal of Mathematical Biology 1 Arkiv för Matematik 1 Mathematics of Computation 1 Acta Arithmetica 1 Advances in Mathematics 1 Computing 1 Journal of Combinatorial Theory. Series A 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Annalen 1 Michigan Mathematical Journal 1 Monatshefte für Mathematik 1 Theory and Decision 1 Tôhoku Mathematical Journal. Second Series 1 Mathematical Social Sciences 1 Acta Applicandae Mathematicae 1 Linear Algebra and its Applications 1 Expositiones Mathematicae 1 Applicable Algebra in Engineering, Communication and Computing 1 Experimental Mathematics 1 International Journal of Theoretical and Applied Finance 1 LMS Journal of Computation and Mathematics 1 Cubo 1 Proyecciones 1 Mathematics in Computer Science 1 Discrete Mathematics and its Applications
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### Cited in 23 Fields

 14 Algebraic geometry (14-XX) 7 Convex and discrete geometry (52-XX) 6 Number theory (11-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Combinatorics (05-XX) 3 Commutative algebra (13-XX) 3 Group theory and generalizations (20-XX) 3 Numerical analysis (65-XX) 3 Computer science (68-XX) 2 Manifolds and cell complexes (57-XX) 2 Probability theory and stochastic processes (60-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Quantum theory (81-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)