Solving invariance equations involving homogeneous means with the help of computer

Our aim is to solve the invariance equation when each of the means M,N,K is either a Gini or a Stolarsky mean with possibly different parameters. This implies that we have to consider six different invariance equations. With the help of the computer algebra system Maple V Release 9, which enables us to perform the tedious computations, we completely describe the general solutions of these six equations.