I would like to thank Todd Coffey for excellent programming assistance with the following program.
To run the program yourself you need the following files:
The Mathematica code for the program : save this file as "Inhomo",
Mathematica commands to construct the equations : save this file as "Full",
The trivial variables: save this file as "varDeg6",
The Maple program used for the conversion: save this file as "specific.txt",
The Maple code for step 2 : save this file as "specific_correlate.ms",
The Maple code for computing the intial data : save this file as "specific_initial_6.ms",
Adding the conjugate relationship for the real variable : save this file as "fixNewL6.ms",
Maple code for step 5 : save this file as "current6.ms",
Maple code for step 6 : save this file as "finish.ms",
Maple code to run steps 5 and 6 in the background : save this file as "do6.txt".