2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73196We construct a Gröbner 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--Möller algorithm. We present a situation in which the usage of the Buchberger--Möller algorithm is obsolete since one can compute its result directly.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.33 pagesNumber TheoryCommutative Algebra12F10; 13P10text