On the construction of staggered linear bases

Masoumeh Javanbakhat, Masoumeh Javanbakhat, Amir Hashemi

Abstract: A staggered linear basis is a specific basis for a polynomial ideal generating the ideal as a linear vector space. There are some algorithms in the literature to compute these bases and we show that they do not work properly. In this paper, due to the strong connection between Gröbner bases and staggered linear bases and by applying a signature-based structure, we present a new and correct algorithm to compute staggered linear bases. Since the output of this algorithm also remains a Gröbner basis for its input ideal, we conclude the paper by discussing the performance of this algorithm compared with the newest signature-based algorithm to compute Gröbner bases.