OldPolyhedra

Macaulay2 package OldPolyhedra -- for computations with convex polyhedra, cones, and fans. 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. Polyhedra 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. 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.