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Relation ideals and the Buchberger--Möller algorithm

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 We present a situation in which the usage of the Buchberger--Möller algorithm is obsolete since one can compute its result directly.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

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Mathias Lederer. 2004-11-11. Relation ideals and the Buchberger--Möller algorithm. https://arxiv.org/abs/math/0411261

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