A note on dynamic gröbner bases computation

Abstract

For most applications of Gröbner bases, one needs only a nice Gröbner basis of a given ideal and does not need to specify the monomial ordering. From a nice basis, we mean a basis with small size. For this purpose, Gritzmann and Sturmfels [14] introduced the method of dynamic Gröbner bases computation and also a variant of Buchberger’s algorithm to compute a nice Gröbner basis. Caboara and Perry [6] improved this approach by reducing the size and number of intermediate linear programs. In this paper, we improve the latter approach by proposing an algorithm to compute nicer Gröbner bases. The proposed algorithm has been implemented in Sage and its efficiency is discussed via a set of benchmark polynomials.