**MATHIAS LEDERER**
*Explicit constructions in splitting fields of polynomials
*

Mathematics Subject Classification (2000):

**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.

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