Computing Gröbner fans
This paper presents algorithms for computing the Gröbner fan of an arbitrary polynomial ideal. The computation involves enumeration of all reduced Gröbner bases of the ideal. Our algorithms are based on a uniform definition of the Gröbner fan that applies to both homogeneous and non-homogeneous ideals and a proof that this object is a polyhedral complex. We show that the cells of a Gröbner fan can easily be oriented acyclically and with a unique sink, allowing their enumeration by the memory-less reverse search procedure. The significance of this follows from the fact that Gröbner fans are not always normal fans of polyhedra, in which case reverse search applies automatically. Computational results using our implementation of these algorithms in the software package Gfan are included.
PRO 060522.pdf
openaccess
305.07 KB
Adobe PDF
5ab6143306bb30c77f763d9e473fc1ac