How to use 4ti2int64.exe in Windows: 1) Type the dimensions of the matrix in the first row of a .txt file 2 4 2) Type the matrix into the .txt file by row 3 2 1 0 0 1 2 3 3) Open a command prompt 4) Change the directory to the folder containing 4ti2 5) Type 4ti2int64.exe (name of computation file) (name of text file) For example, "4ti2.int64.exe markov example.txt" generates the markov basis of the matrix above 6) Rename the output file as a .txt file For example, if the output above is named example.txt.mar, change it to example.mar.txt 7) The output should look like this: 3 4 <-- Dimensions of markov basis matrix 0 1 -2 1 <-- 1 -2 1 0 <-- Elements of markov basis 1 -1 -1 1 <--