  We construct a Gr\"obner Basis of the relation ideal of a polynomial, give an
interpolation formula for the basis elements and explain the connection of the
interpolation formula to the Buchberger--M\"oller algorithm. We present a
situation in which the usage of the Buchberger--M\"oller algorithm is obsolete
since one can compute its result directly. We prove a constructive version of a
theorem of Galois, concerning the solvability of rational polynomials of prime
degree. Computations are carried out for a number of example polynomials.
