Title  Gröbner Bases: A Characterization by Syzygy Completeness and an Implementation 
Author(s)  Wolfgang Windsteiger 
Type  Master's Theses 
Abstract  Gröbner bases are wellknown 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 onetoone 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. 
Length  152 
File 

Language  English 
Year  1991 
Translation 
No 
Refereed 
No 
Organization 
Johannes Kepler University Linz 
Institution 
RISC (Research Institute for Symbolic Computation) 