We describe a new method to determine the minimality and identifiability of a
Waring decomposition A of a specific form (symmetric tensor) T in three
variables. Our method, which is based on the Hilbert function of A, can
distinguish between forms in the span of the Veronese image of A, which in
general contains both identifiable and not identifiable points, depending on
the choice of coefficients in the decomposition. This makes our method
applicable for all values of the length r of the decomposition, from 2 up
to the generic rank, a range which was not achievable before. Though the method
in principle can handle all cases of specific ternary forms, we introduce and
describe it in details for forms of degree 8
