An Involutive GVW Algorithm and the Computation of Pommaret Bases

被引：0
作者：
Hashemi, Amir [1 ]
Izgin, Thomas [2 ]
Robertz, Daniel [3 ]
Seiler, Werner M. [2 ]
机构：
[1] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran
[2] Univ Kassel, Inst Math, Heinrich Plett Str 40, D-34132 Kassel, Germany
[3] Univ Plymouth, Sch Engn Comp & Math, 2-5 Kirkby Pl, Plymouth PL4 8AA, Devon, England
来源：
MATHEMATICS IN COMPUTER SCIENCE | 2021年 / 15卷 / 03期
关键词：
Grobner bases; Module of syzygies; Signature-based algorithms; The GVW algorithm; Involutive bases; Quasi-stable position; Linear coordinate transformations; Pommaret bases;
D O I：
10.1007/s11786-021-00512-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：419 / 452
页数：34
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