(* ReadMe File Vertex Enumeration Package for Convex Polytopes and Arrangements Version 0.41 Beta (Nevember 14, 1992) by Komei Fukuda and Ichiro Mizukoshi This package contains Mathematica implementations of Avis-Fukuda algorithms for enumerating all vertices of a convex polyhedron given by a system of linear inequalities, and all vertices (points) of an arrangement given similarly. The package consists of the following six files VE041.ReadMe (This file itself) VertexEnum.m (Mathematica package) VertexEnum-notebook.ma (Mathematica Notebook) Power.m (Supplementary program for VertexEnum.m) FaceLattice.m (Supplementary package to compute the face lattice of a convex polytope) FaceLatice-notebook.ma (Mathematica Notebook) For distribution, the last five files are merged (by shar) and compressed as "VE041.Z". The size of VE041.Z is about 109 Kbytes. In order to unpack the file "VE041.Z", you just have to execute the following: % uncompress VE041.Z % /bin/sh VE041 The notebooks explain how to use these packages through examples. If your environment does not allow you to use notebooks, we suggest you to get it printed before using the package. For the moment, the notebook environment is supported by the Macintosh, NeXT, and Windows versions of Mathematica. This beta release is designed to run under Version 1.2/2.0/2.1 of Mathematica. Few bugs of Version 0.3 have been fixed, including its mishandling of the case when the polyhedron is empty. Also, the notebook for Version 0.3 has been slightly revised. Please send your comments, bug reports etc. to: Komei Fukuda or Ichiro Mizukoshi Graduate School of Systems Management University of Tsukuba, Tokyo 3-29-1 Otsuka, Bunkyo-ku Tokyo 112, Japan +81-3-3942-6876 fukuda@gssm.otsuka.tsukuba.ac.jp or mizukosi@gssm.otsuka.tsukuba.ac.jp *)