On W-characteristic sets of lexicographic Gröbner bases

Abstract

The structures of lexicographic (LEX) Gröbner bases were studied first by Lazard [4] for bivariate ideals and then extended to general zero-dimensional multivariate (radical) ideals [3, 6, 2]. Based on the structures of LEX Gröbner bases, algorithms have been proposed to compute triangular decompositions out of LEX Gröbner bases for zero-dimensional ideals [5, 2]. The relationships between LEX Gröbner bases and Ritt characteristic sets were explored in [1] and then made clearer in [8] with the concept of W-characteristic sets.