Skip to content

Combinatorial and Discrete Geometry

Version 10.8 Reference Manual

Home - Combinatorial and Discrete Geometry

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

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
Formal modules generated by 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.
Generating Function of Polyhedron’s Integral Points

Combinatorial polyhedron
Combinatorial face of a polyhedron
PolyhedronFaceLattice
Face iterator for polyhedra
List of faces
Conversions

Finite polyhedral complexes

Toric lattices
Convex rational polyhedral cones
Catalog of common polyhedral convex cones
Find maximal angles between polyhedral convex cones
Rational polyhedral fans
Morphisms between toric lattices compatible with fans
Point collections
Toric plotter
Groebner Fans

Base class for polyhedra: Initialization and access to Vrepresentation and Hrepresentation
Base class for polyhedra: Implementation of the ConvexSet_base API
Base class for polyhedra: Methods related to lattice points
Base class for polyhedra: Methods regarding the combinatorics of a polyhedron
Base class for polyhedra: Graph-theoretic methods
Base class for polyhedra: Methods for constructing new polyhedra
Base class for polyhedra: Methods for plotting and affine hull projection
Base class for polyhedra: Methods for triangulation and volume computation
Base class for polyhedra: Miscellaneous methods
Base class for polyhedra over \(\QQ\)
Base class for polyhedra over \(\ZZ\)
Base class for polyhedra over RDF

The cdd backend for polyhedral computations
The cdd backend for polyhedral computations, floating point version
The Python backend
The Python backend, using number fields internally
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 of a point configuration
Base classes for triangulations
A triangulation

Abstract base classes for classes in geometry
Convex Sets
Linear Expressions
Newton Polygons
Relative Interiors of Polyhedra and Cones
Ribbon Graphs
Pseudolines
Voronoi diagram

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

Index – Q

quotient() (sage.geometry.toric_lattice.ToricLattice_generic method)

Copyright © 2005--2025, The Sage Development Team

Made with Sphinx and @pradyunsg's Furo