Sparse FGLM using the block Wiedemann algorithm

Abstract

Overview. Computing the Gröbner basis of an ideal with respect to a term ordering is an essential step in solving systems of polynomials; in what follows, we restrict our attention to systems with finitely many solutions. Certain term orderings, such as the degree reverse lexicographical ordering (degrevlex), make the computation of the Gröbner basis faster, while other orderings, such as the lexicographical ordering (lex), make it easier to find the coordinates of the solutions. Thus, one typically first computes a Gröbner basis for the degrevlex ordering, and then converts it to either a lex Gröbner basis or a related representation, such as Rouillier's Rational Univariate Representation [8].