An Involutive GVW Algorithm and the Computation of Pommaret Bases

被引：0
作者：
Amir Hashemi
Thomas Izgin
Daniel Robertz
Werner M. Seiler
机构：
[1] Isfahan University of Technology,Department of Mathematical Sciences
[2] Universität Kassel,Institut für Mathematik
[3] University of Plymouth,School of Engineering, Computing and Mathematics
来源：
Mathematics in Computer Science | 2021年 / 15卷
关键词：
Gröbner bases; Module of syzygies; Signature-based algorithms; The GVW algorithm; Involutive bases; Quasi-stable position; Linear coordinate transformations; Pommaret bases; 13P10; 68W30;
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摘要：
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.
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页码：419 / 452
页数：33
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