  The position-momentum uncertainty-like inequality based on moments of
arbitrary order for d-dimensional quantum systems, which is a generalization of
the celebrated Heisenberg formulation of the uncertainty principle, is improved
here by use of the Renyi-entropy-based uncertainty relation. The accuracy of
the resulting lower bound is physico-computationally analyzed for the two main
prototypes in d-dimensional physics: the hydrogenic and oscillator-like
systems.
