An Involutive GVW Algorithm and the Computation of Pommaret Bases
Co-author(s): Amir Hashemi, Thomas Izgin and Daniel Robertz
Reference: Mathematics in Computer Science, 15 (2021) 419-452
Description: The GVW algorithm computes simultaneously Gröbner bases for a given ideal and its syzygy module. We discuss an extension of this approach to involutive bases, in particular to Pommaret bases. We distinguish between a fully involutive GVW algorithm determining involutive bases of both ideal and syzygy module and a semi-involutive variant computing only an ordinary Gröbner basis for the syzygy module. A prototypical implementation in Maple is described together with some benchmark computations.
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