TorDiv - A Maple Package

on Toric Varieties and Geometric Invariant Theory

Current version: 1.4 (February 23, 2010), Copyright  2010, F. Berchtold, J. Hausen, S. Keicher, R. Vollmert, M. Widmann


TorDiv is a Maple Package, distributed under the GNU General Public License. It comprises functions on toric varieties and, as this is a strongly related subject, geometric invariant theory of linear torus actions. The aim is to provide an easy-to-use working environment for study and discussion of (advanced) examples.

Toric varieties are entered in terms of their defining fan in the lattice of one parameter subgroups, or, equivalently, by their defining bunch of cones in the divisor class group. Torus actions are entered as lists of weight vectors. TorDiv then offers among others the following functions:

Software Requirements

The TorDiv package requires Maple, Version 8 or higher, and the Maple package convex by Matthias Franz.


For a quick installation of TorDiv, download by clicking the files TorDiv14.ind and TorDiv14.lib, and put them into your personal Maple library directory. Then, similar to any other Maple package, TorDiv is activated via the Maple command "with(TorDiv14);". For more information, see README.

Beta version

TorDiv 1.5: download by clicking the files TorDiv15.ind and TorDiv15.lib.


There is a detailed documentation on the TorDiv 1.4 package: manual.pdf. It contains some mathematical background, descriptions of all functions of the TorDiv package, and an example for each function.
Mathematisches Institut, Universität Tübingen,   updated: March 2012