An Involutive GVW Algorithm and the Computation of Pommaret Bases

• DOI: 10.1007/s11786-021-00512-5
• Publication Date: 2021-06-07T05:02:37Z
• Authors: Amir Hashemi; Thomas Izgin; Daniel Robertz; Werner M. Seiler
• Keywords: 0102 computer and information sciences; 01 natural sciences

The GVW algorithm computes simultaneously Grobner bases of a given ideal and of the syzygy module of the given generating set. In this work, we discuss an extension of it to involutive bases. Pommaret bases play here a special role in several respects. We distinguish between a fully involutive GVW algorithm which determines involutive bases for both the given ideal and the syzygy module and a semi-involutive version which computes for the syzygy module only an ordinary Grobner basis. A prototype implementation of the developed algorithms in Maple is described.