Geometry

Combinatorial Geometry

Sage includes classes for convex rational polyhedral cones and fans, Groebner fans, lattice and reflexive polytopes (with integral coordinates), and generic polytopes and polyhedra (with rational or numerical coordinates).

• Toric lattices
• Convex rational polyhedral cones
• Rational polyhedral fans
• Morphisms between toric lattices compatible with fans
• Point collections
• Toric plotter
• Groebner Fans
• Lattice and reflexive polytopes
• Polyhedra
• Parents for Polyhedra
• H(yperplane) and V(ertex) representation objects for polyhedra
• Library of commonly used, famous, or interesting polytopes
• Functions for plotting polyhedra
• A class to keep information about faces of a polyhedron
• Generate cdd .ext / .ine file format
• Lattice Euclidean Group Elements
• Access the PALP database(s) of reflexive lattice polytopes
• Fast Lattice Polygons using PPL.
• Fast Lattice Polytopes using PPL.
• Polytopes
• Pseudolines
• Triangulations of a point configuration
• Base classes for triangulations
• A triangulation
• Hyperplane Arrangements
• Library of Hyperplane Arrangements
• Hyperplanes
• Affine Subspaces of a Vector Space
• Plotting of Hyperplane Arrangements
• Linear Expressions
• Newton Polygons

Hyperbolic Geometry

• Hyperbolic Points
• Hyperbolic Isometries
• Hyperbolic Geodesics
• Hyperbolic Models
• Interface to Hyperbolic Models

Backends for Polyhedral Computations

• The cdd backend for polyhedral computations
• The PPL (Parma Polyhedra Library) backend for polyhedral computations
• The Python backend
• Double Description Algorithm for Cones
• Double Description for Arbitrary Polyhedra
• Base class for polyhedra
• Base class for polyhedra over \(\QQ\)
• Base class for polyhedra over \(\ZZ\)
• Base class for polyhedra over RDF.

Internals

• Find isomorphisms between fans.
• Hasse diagrams of finite atomic and coatomic lattices.
• Cython helper methods to compute integral points in polyhedra.

Indices and Tables

• Index
• Module Index
• Search Page