An Involutive GVW Algorithm and the Computation of Pommaret Bases

Amir Hashemi; Thomas Izgin; Daniel Robertz; Werner M. Seiler

doi:10.1007/s11786-021-00512-5

An Involutive GVW Algorithm and the Computation of Pommaret Bases

Amir Hashemi, Thomas Izgin^*, Daniel Robertz, Werner M. Seiler

^*Corresponding author for this work

School of Engineering, Computing and Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	419-452
Number of pages	34
Journal	Mathematics in Computer Science
Volume	15
Issue number	3
DOIs	https://doi.org/10.1007/s11786-021-00512-5
Publication status	Published - Sept 2021

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

Keywords

Gröbner bases
Involutive bases
Linear coordinate transformations
Module of syzygies
Pommaret bases
Quasi-stable position
Signature-based algorithms
The GVW algorithm

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10.1007/s11786-021-00512-5

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title = "An Involutive GVW Algorithm and the Computation of Pommaret Bases",

abstract = "The GVW algorithm computes simultaneously Gr{\"o}bner 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 Gr{\"o}bner basis. A prototype implementation of the developed algorithms in Maple is described.",

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doi = "10.1007/s11786-021-00512-5",

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T1 - An Involutive GVW Algorithm and the Computation of Pommaret Bases

AU - Hashemi, Amir

AU - Izgin, Thomas

AU - Robertz, Daniel

AU - Seiler, Werner M.

PY - 2021/9

Y1 - 2021/9

N2 - 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.

AB - 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.

KW - Gröbner bases

KW - Involutive bases

KW - Linear coordinate transformations

KW - Module of syzygies

KW - Pommaret bases

KW - Quasi-stable position

KW - Signature-based algorithms

KW - The GVW algorithm

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DO - 10.1007/s11786-021-00512-5

M3 - Article

AN - SCOPUS:85107552206

SN - 1661-8270

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SP - 419

EP - 452

JO - Mathematics in Computer Science

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ER -

An Involutive GVW Algorithm and the Computation of Pommaret Bases

Abstract

ASJC Scopus subject areas

Keywords

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