An involutive GVW algorithm and the computation of Pommaret bases
Several algorithms computing Gröbner bases have been introduced after Buchberger's algorithm in 1965. Among them, \textit{S. Gao} et al. proposed an algorithm [Math. Comput. 85, No. 297, 449--465 (2016; Zbl 1331.13018)] that computes simultaneously Gröbner bases of a given ideal and of the syzygy module of the given generating set. This algorithm is often referred to as GVW algorithm. In this paper, the authors present two variants of GVW algorithm that compute involutive bases. The first one is a fully involutive GVW algorithm because it determines an involutive basis both for the given ideal and its syzygy module. The second one is a semi-involutive one, in the sense that it computes an involutive basis for the given ideal and a Gröbner basis for the syzygy module. The authors highlight benefits and issues of both variants. A prototype implementation in Maple 2019 is available, and the authors describe it in the paper giving some benchmark computations.
scientific article; zbMATH DE number 7433042
scientific article