Relation ideals and the Buchberger--Möller algorithm

Details Relation ideals and the Buchberger--Möller algorithm Relation ideals and the Buchberger--Möller algorithm

2004-11-11

arxiv.org/abs/math/0411261v1

Mathematics

Number Theory

33 pages

Scientific paper

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 We present a situation in which the usage of the Buchberger--M\"oller algorithm is obsolete since one can compute its result directly.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.

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