Combinatorial and Discrete Geometry

Sage includes classes for hyperplane arrangements, polyhedra, toric varieties (including polyhedral cones and fans), triangulations and some other helper classes and functions.

Hyperplane arrangements

• Hyperplane Arrangements
• Library of Hyperplane Arrangements
• Hyperplanes
• Affine Subspaces of a Vector Space
• Plotting of Hyperplane Arrangements

Polyhedral computations

Polyhedra

• Library of commonly used, famous, or interesting polytopes
• Polyhedra
• Parents for Polyhedra
• H(yperplane) and V(ertex) representation objects for polyhedra
• Functions for plotting polyhedra
• A class to keep information about faces of a polyhedron
• Generate cdd .ext / .ine file format

Lattice polyhedra

• Lattice and reflexive polytopes
• Lattice Euclidean Group Elements
• Access the PALP database(s) of reflexive lattice polytopes
• Fast Lattice Polygons using PPL.
• Fast Lattice Polytopes using PPL.

Toric geometry

• Toric lattices
• Convex rational polyhedral cones
• Rational polyhedral fans
• Morphisms between toric lattices compatible with fans
• Point collections
• Toric plotter
• Groebner Fans

Base classes for polyhedra

• Base class for polyhedra
• Base class for polyhedra over \(\QQ\)
• Base class for polyhedra over \(\ZZ\)
• Base class for polyhedra over RDF.

Backends for Polyhedra

• The cdd backend for polyhedral computations
• The Python backend
• The Normaliz backend for polyhedral computations
• The polymake backend for polyhedral computations
• The PPL (Parma Polyhedra Library) backend for polyhedral computations
• Double Description Algorithm for Cones
• Double Description for Arbitrary Polyhedra

Triangulations

• Triangulations of a point configuration
• Base classes for triangulations
• A triangulation

Miscellaneous

• Linear Expressions
• Newton Polygons
• Ribbon Graphs
• Pseudolines
• Voronoi diagram

Helper functions

• Find isomorphisms between fans.
• Construction of finite atomic and coatomic lattices from incidences.
• Cython helper methods to compute integral points in polyhedra.
• Helper Functions For Freeness Of Hyperplane Arrangements

Indices and Tables

• Index
• Module Index
• Search Page