  Starting from our previous papers [AGMO] and [ABC], we prove the existence of
a non-empty Euclidean open subset whose elements are polynomial vectors with 4
components, in 3 variables, degrees, respectively, 2,3,3,3 and rank 6, which
are not identifiable over $ \mathbb{C} $ but are identifiable over $ \mathbb{R}
$. This result has been obtained via computer-aided procedures suitably adapted
to investigate the number of Waring decompositions for general polynomial
vectors over the fields of complex and real numbers. Furthermore, by means of
the Hessian criterion ([COV]), we prove identifiability over $ \mathbb{C} $ for
polynomial vectors in many cases of sub-generic rank.
