(a) If [e.sup.g/h] is an exponential factor for the polynomial differential system (1) and h is not a constant polynomial
, then h = 0 is an invariant algebraic surface.
Arguably our nicest result is Theorem 4.6, expressing t(P, x) associated to a graded Eulerian poset [??] by defining two linear operators C, D : Q[x] [right arrow] Q[x] that need to be substituted into the reverse of the cd-index and applied to the constant polynomial
b) The principal ideal I is generated by a constant polynomial
or a polynomial of the kind
In the case where the number of constant polynomials
are more than one, the inequality (7) is not valid in general case.