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