An Involutive GVW Algorithm and the Computation of Pommaret Bases
The GVW algorithm computes simultaneously Gröbner 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 a...
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| Veröffentlicht in: | Mathematics in computer science 2021-09, Vol.15 (3), p.419-452 |
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| creator | Hashemi, Amir Izgin, Thomas Robertz, Daniel Seiler, Werner M. |
| description | The GVW algorithm computes simultaneously Gröbner 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 Gröbner basis. A prototype implementation of the developed algorithms in
Maple
is described. |
| doi_str_mv | 10.1007/s11786-021-00512-5 |
| format | Article |
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Maple
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| title | An Involutive GVW Algorithm and the Computation of Pommaret Bases |
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