Convex

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.


References in zbMATH (referenced in 20 articles )

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  1. Roux, Alet; Zastawniak, Tomasz: American and Bermudan options in currency markets with proportional transaction costs (2016)
  2. Studený, Milan; Kroupa, Tomáš: Core-based criterion for extreme supermodular functions (2016)
  3. Amaris, Armando J.R.; Cox, Murray P.: A flexible theoretical representation for the temporal dynamics of structured populations as paths on polytope complexes (2015)
  4. Hausen, Jürgen; Keicher, Simon: A software package for Mori dream spaces (2015)
  5. Roux, Alet; Zastawniak, Tomasz: Linear vector optimization and European option pricing under proportional transaction costs (2015)
  6. Bourqui, David: Some examples of curves countings on surfaces (2013)
  7. Bourqui, David: Moduli spaces of curves and Cox rings (2012)
  8. Le Boudec, Pierre: Manin’s conjecture for a quartic del Pezzo surface with $\Bbb A_3$ singularity and four lines (2012)
  9. Le Boudec, Pierre: Manin’s conjecture for two quartic del Pezzo surfaces with $3\boldA_1$ and $\boldA_1 + \boldA_2$ singularity types (2012)
  10. Loughran, Daniel: Manin’s conjecture for a singular quartic del Pezzo surface (2012)
  11. Christophersen, Jan Arthur: Deformations of equivelar Stanley-Reisner abelian surfaces (2011)
  12. Morrison, Ian; Swinarski, David: Gröbner techniques for low-degree Hilbert stability (2011)
  13. D’Andrea, Carlos; Sombra, Martín: The Newton polygon of a rational plane curve (2010)
  14. Studený, Milan; Vomlel, Jiří; Hemmecke, Raymond: A geometric view on learning Bayesian network structures (2010)
  15. Vigeland, Magnus Dehli: Smooth tropical surfaces with infinitely many tropical lines (2010)
  16. Ginnis, Alexandros I.; Karousos, E.I.; Kaklis, P.D.: A discrete methodology for controlling the sign of curvature and torsion for NURBS (2009)
  17. Altunbulak, Murat; Klyachko, Alexander: The Pauli principle revisited (2008)
  18. Kroupa, Tomáš: Geometry of possibility measures on finite sets (2008)
  19. Billey, Sara; Guillemin, Victor; Rassart, Etienne: A vector partition function for the multiplicities of $\fraksl_k\Bbb C$ (2004)
  20. Rassart, Etienne: A polynomiality property for Littlewood-Richardson coefficients (2004)