Relation ideals and the Buchberger--Möller algorithm

Abstract

We 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 We present a situation in which the usage of the Buchberger--Möller algorithm is obsolete since one can compute its result directly.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 pages