A bivariate preprocessing paradigm for the Buchberger-Möller algorithm (Q989141)

The authors apply a preprocessing paradigm for the Buchberger--Möller algorithm. They give first a simple maximal cartesian subset construction algorithm, which computes a maximal cartesian subset \(\Xi'\) containing the original finite affine set of points \(\Xi\). Later they compute certain lower set with respect to \(\Xi'\) and a Gröbner éscalier and a degree reducing interpolation Newton Gröbner basis for the Lagrange interpolation problem on \(\Xi\). They apply the original Buchberger--Möller algorithm after the preprocessing. They implement their results in \texttt{Maple 12} and demonstrate the timings for the computation on sets of distinct random points with respect to the term order \(\prec_{lex}\) or \(\prec_{tdivlex}\).