isTropicalBasis -- checks if a list of polynomials is a tropical basis for the ideal they generate

Synopsis

Usage:

isTropicalBasis(L)

isTropicalBasis(L,Strategy=>S)
Inputs:
- L, a list, of polynomials
Optional inputs:
- Strategy => a string, default value "gfan", Strategy (currently only "gfan")
Outputs:
- F, a Boolean value, whether the list of polynomials is a tropical basis for the ideal it generates

Description

This method checks if the intersection of the tropical hypersurfaces associated to the polynomials in the list equals the tropicalization of the variety corresponding to the ideal they generate.

i1 : QQ[x,y,z]

o1 = QQ[x..z]

o1 : PolynomialRing

i2 : isTropicalBasis({x+y+z,2*x+3*y-z})

o2 = false

i3 : isTropicalBasis(flatten entries gens Grassmannian (1,4,QQ[a..l]))

o3 = true

Ways to use isTropicalBasis :

isTropicalBasis(List)

For the programmer

The object isTropicalBasis is a method function with options.