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# gfanTropicalLinearSpace -- equations of a tropical linear space from Plücker coordinates

## Synopsis

• Usage:
(L, S) = gfanTropicalLinearSpace(P,N,D)
• Inputs:
• P, a list, of Plücker coordinates
• N, an integer, ambient dimension
• D, an integer, subspace dimension
• Optional inputs:
• d
• n
• trees
• Outputs:
• L, a list, polynomials defining the linear space
• S, , a string describing which variable corresponds to which minor

## Description

This method takes Plücker coordinates for a linear subspace and computes the polynomials which define the corresponding tropical linear space. The output is a pair which contains both the defining polynomials and a string which describes which coordinate corresponds to which minor.

 i1 : (L, S) = gfanTropicalLinearSpace({1,2,3}, 3, 1); i2 : L 998 997 999 997 999 998 o2 = {t x0 + t x1, t x0 + t x2, t x1 + t x2} o2 : List i3 : S o3 = 0,1,0,=1 1,0,0,=2 0,0,1,=0 1,0,0,=2 0,0,1,=0 0,1,0,=1

gfan Documentation This program generates tropical equations for a tropical linear space in the Speyer sense given the tropical Pluecker coordinates as input.Options:-d value: Specify d.-n value: Specify n.--trees: list the boundary trees (assumes d=3)

## Ways to use gfanTropicalLinearSpace :

• "gfanTropicalLinearSpace(List,ZZ,ZZ)"

## For the programmer

The object gfanTropicalLinearSpace is .