Relation ideals and the Buchberger--M\"oller algorithm
Number Theory
2007-05-23 v1 Commutative Algebra
Abstract
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 We present a situation in which the usage of the Buchberger--M\"oller algorithm is obsolete since one can compute its result directly.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.
Cite
@article{arxiv.math/0411261,
title = {Relation ideals and the Buchberger--M\"oller algorithm},
author = {Mathias Lederer},
journal= {arXiv preprint arXiv:math/0411261},
year = {2007}
}
Comments
33 pages