Sparse FGLM using the block Wiedemann algorithm

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].