  Near full-null degenerate singular points of analytic vector fields,
asymptotic behaviors of orbits are not given by eigenvectors but totally
decided by nonlinearities. Especially, in the case of high full-null
degeneracy, i.e., the lowest degree of nonlinearities is high, such a singular
point may have irregular exceptional directions and the blow-up technique can
be hardly applied, which leaves a problem how to determine numbers of orbits
and (elliptic, hyperbolic and parabolic) tangential sectors in this case. In
this paper we work on this problem. Using Newton polygons to decompose
nonlinearities into principal parts and remainder parts, we convert the problem
to the numbers of nonzero real roots of edge-polynomials of principal parts.
Computing Newton polygons for multiplication and differentiation of analytic
functions and giving Newton polygons for addition, which was not found in
literatures, we determine semi-definiteness of the Lie-bracket of principal
parts and therefore obtain criteria for those numbers.
