  We perform detailed computations of Lie algebras of infinitesimal
CR-automorphisms associated to three specific model real analytic CR-generic
submanifolds in C^9 by employing differential algebra computer tools -- mostly
within the Maple package DifferentialAlgebra -- in order to automate the
handling of the arising highly complex linear systems of pde's. Before treating
these new examples which prolong previous works of Beloshapka, of Shananina and
of Mamai, we provide general formulas for the explicitation of the concerned
pde systems that are valid in arbitrary codimension k >= 1 and in any CR
dimension n >= 1. Also, we show how Ritt's reduction algorithm can be adapted
to the case under interest, where the concerned pde systems admit so-called
complex conjugations.
