gfanTropicalBasis -- tropical basis of an ideal

Synopsis

Usage:

gfanTropicalBasis(I)
Inputs:
- I, an ideal,
Optional inputs:
- h
Outputs:
- L, a list, of polynomials that give a tropical basis of I

Description

This method produces a tropical basis of a given homogeneous ideal. If the ideal is not homogeneous, it must be homogenized using the h option.

i1 : QQ[x,y];

i2 : gfanTropicalBasis ideal {x^2+y^2, x^2-x*y}

       2    2   2
o2 = {x  + y , x  - x*y, 1}

o2 : List

gfan Documentation

This program computes a tropical basis for an ideal defining a tropical curve. Defining a tropical curve means that the Krull dimension of R/I is at most 1 + the dimension of the homogeneity space of I where R is the polynomial ring. The input is a generating set for the ideal. If the input is not homogeneous option -h must be used.
Options:
-h:
 Homogenise the input before computing a tropical basis and dehomogenise the output. This is needed if the input generators are not already homogeneous.

Ways to use gfanTropicalBasis :

gfanTropicalBasis(Ideal)

For the programmer

The object gfanTropicalBasis is a method function with options.