|Title||Gröbner Bases: A Characterization by Syzygy Completeness and an Implementation|
|Author(s)|| Wolfgang Windsteiger|
|Abstract||Gröbner bases are well-known in polynomial ideal theory. Many problems for ideals can easily be solved after computing a Gröbner basis for the ideal. In this paper we treat a characterization of Gröbner bases by a certain completeness property of the syzygies of the leading monomials of the polynomials in the ideal. We particularly emphasize the one-to-one correspondence between this characterization of Gröbner bases and the traditional characterization by reducibility of polynomials in the ideal.|
Furthermore, we report on an implementation of some variants of the Buchberger algorithm for computing Gröbner bases of polynomials over various coefficients domains with respect to several different orderings of monomials.
Johannes Kepler University Linz|
RISC (Research Institute for Symbolic Computation)|