Full description
Gfan is a software package for computing Gröbner fans and tropical
varieties. These are polyhedral fans associated to polynomial
ideals. The maximal cones of a Gröbner fan are in bijection with the
marked reduced Gröbner bases of its defining ideal. The software
computes all marked reduced Gröbner bases of an ideal. Their union
is a universal Gröbner basis. The tropical variety of a polynomial
ideal is a certain subcomplex of the Gröbner fan. Gfan contains
algorithms for computing this complex for general ideals and
specialized algorithms for tropical curves, tropical hypersurfaces
and tropical varieties of prime ideals. In addition to the above
core functions the package contains many tools which are useful in
the study of Gröbner bases, initial ideals and tropical
geometry. The full list of commands can be found in Appendix B of
the manual. For ordinary Gröbner basis computations Gfan is not
competitive in speed compared to programs such as CoCoA, Singular
and Macaulay2.
Packages