A rational convex Polyhedron
is the intersection of finitely many affine half-spaces over QQ
or equivalently, the convex hull of a finite set of vertices and rays. A rational convex polyhedral Cone
is the intersection of finitely many linear half-spaces over QQ
or equivalently, the positive hull of a finite set of rays. A Fan
is a finite collection of cones such that for each cone all its faces are in the fan and for two cones in the fan the intersection is a face of each.
uses the FourierMotzkin
package by Gregory G. Smith
. Each polyhedron or cone is saved in both descriptions and a fan is saved as the list of its generating cones.
Here are some examples illustrating the main uses of this package.
For an introduction to polyhedra and cones, we recommend Gunter M. Ziegler's Lectures on Polytopes
, Graduate Texts in Mathematics 152, Springer-Verlag, New York, 1995.
The author would like to thank Nathan Ilten
for contributing several functions to the package.