How to compute the unique geodesic between 2 points A and B in the orthant space F_{\omega}:

1. In the software Maple, load the following packages and the macro GTP.m in the preamble:

with(LinearAlgebra);
with(simplex); 
with(combinat);
read "filepath\GTP.m";

2. Define the orthant space F_{\omega} with a list of its maximal dimensional cones in \omega. For example: 

F:=[{1,2},{2,3},{3,4},{4,1}];

3. Introduce the coordinates of A and B in the ambient space. For example:

A:=[2,3,0,0];
B:=[0,0,1,6];

4. The command

Geo(A,B,F);

gives the nodes along the unique geodesic path between A and B:

[[2, 3, 0, 0], [1, 0, 0, 0], [0, 0, 0, 3], [0, 0, 1, 6]].