  The problem of the determination of the Hilbert-space metric which renders a
given Hamiltonian $H$ self-adjoint is addressed from the point of view of
applicability of computer-assisted algebraic manipulations. An exactly solvable
example of the so called Gegenbauerian quantum-lattice oscillator is recalled
for the purpose. Both the construction of suitable metric (basically, the
solution of the Dieudonne's operator equation) and the determination of its
domain of positivity are shown facilitated by the symbolic algebraic
manipulations and by MAPLE-supported numerics and graphics.
