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]].