Computing Groebner Fans of Toric Ideals
Birkett Huber and Rekha Thomas
Experimental Mathematics 9 (2000) 321-331.
The monomial initial ideals of a graded polynomial ideal are in
bijection with the vertices of a convex polytope known as the state
polytope of the ideal. The Groebner fan of the ideal is the normal
fan of its state polytope. In this paper we present a software
system called TiGERS for computing
the Groebner fan of a toric ideal by enumerating the edge graph
of its state polytope. The key contributions are an inexpensive
algorithm for local
change of Groebner bases in toric ideals and the
identification of a reverse search tree on the vertices
of the state polytope. Using these ideas we
obtain a combinatorial Groebner walk procedure for toric ideals.
TiGERS has been used to compute state polytopes
with over 200,000 vertices.
postscript file of the paper
Software: TiGERS (written by Birkett Huber)
The distribution is contained in a file named TiGERS_0.9.uu.
To unpack it use the commands:
tar -xvf TiGERS_0.9.tar
You now have a directory named TiGERS_0.9
The README file now contains further information.