  We give an explicit procedure which computes for degree $d \leq 3$ the
correlation functions of topological sigma model (A-model) on a projective Fano
hypersurface $X$ as homogeneous polynomials of degree $d$ in the correlation
functions of degree 1 (number of lines). We extend this formalism to the case
of Calabi-Yau hypersurfaces and explain how the polynomial property is
preserved. Our key tool is the construction of universal recursive formulas
which express the structural constants of the quantum cohomology ring of $X$ as
weighted homogeneous polynomial functions in the constants of the Fano
hypersurface with the same degree and dimension one more. We propose some
conjectures about the existence and the form of the recursive formulas for the
structural constants of rational curves of arbitrary degree. Our recursive
formulas should yield the coefficients of the hypergeometric series used in the
mirror calculation. Assuming the validity of the conjectures we find the
recursive laws for rational curves of degree 4 and 5.
