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#
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/.inefile format - Formal modules generated by polyhedra
Lattice polyhedra#
Combinatorial Polyhedra#
Polyhedral complexes#
Toric geometry#
Base classes for polyhedra#
- Base class for polyhedra: Initialization and access to Vrepresentation and Hrepresentation
- Base class for polyhedra: Implementation of the
ConvexSet_baseAPI - 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
Backends for Polyhedra#
- 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