Explicit constructions in splitting fields of polynomials
Received: 15 March 2004 Revised: 4 August 2004
Mathematics Subject Classification (2000): 12E30 - 12F10 - 11Y40
Abstract: We construct a Gröbner Basis of the relation ideal of a polynomial and give an interpolation formula for the basis elements which is sufficiently explicit to be used in practical computations. We prove a constructive version of a theorem of Galois, concerning the solvability of rational polynomials of prime degree. For a number of example polynomials, the computations are carried out.