gfanTropicalBruteForce -- computes the tropical variety of an ideal

Synopsis

Usage:

gfanTropicalBruteForce(L)
Inputs:
- L, a marked polynomial list, a marked reduced Groebner basis for a homogeneous ideal
Outputs:
- F, an instance of the type Fan, describing the tropical variety of the ideal of L

Description

This method computes the tropical variety of a marked reduced Groebner basis (given in the form of a marked polynomial list).

The following example is taken from the gfan documentation (v0.4 p.20).

i1 : QQ[a,b,c,d,e,f,g,h,i,j]

o1 = QQ[a..j]

o1 : PolynomialRing

i2 : gfanTropicalBruteForce gfanBuchberger ideal "bf-ah-ce, bg-ai-de, cg-aj-df, ci-bj-dh, fi-ej-gh"

o2 = Fan{...1...}

o2 : Fan

gfan Documentation This program takes a marked reduced Groebner basis for a homogeneous ideal and computes the tropical variety of the ideal as a subfan of the Groebner fan. The program is slow but works for any homogeneous ideal. If you know that your ideal is prime over the complex numbers or you simply know that its tropical variety is pure and connected in codimension one then use gfan_tropicalstartingcone and gfan_tropicaltraverse instead.Options:

Ways to use gfanTropicalBruteForce :

"gfanTropicalBruteForce(List)"

For the programmer

The object gfanTropicalBruteForce is a method function with options.