article

On an installation of Buchberger's algorithm

Authors:

Rüdiger Gebauer,

H. Michael MöllerAuthors Info & Claims

Journal of Symbolic Computation, Volume 6, Issue 2-3

Pages 275 - 286

https://doi.org/10.1016/S0747-7171(88)80048-8

Published: 01 December 1988 Publication History

Abstract

Buchberger's algorithm calculates Groebner bases of polynomial ideals. Its efficiency dependsstrongly on practical criteria for detecting superfluous reductions. Buchberger recommends two criteria. The more important one is interpreted in this paper as a criterion for detecting redundant elements in a basis of a module of syzygies. We present a method for obtaining a reduced, nearly minimal basis of that module. The simple procedure for detecting (redundant syzygies and) superfluous reductions is incorporated now in our installation of Buchberger's algorithm in SCRATCHPAD II and REDUCE 3.3. The paper concludes with statistics stressing the good computational properties of these installations.

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Cited By

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Mora T(2023)Further perspectives on eliminationApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-023-00618-234:5(745-749)Online publication date: 20-Jul-2023
https://dl.acm.org/doi/10.1007/s00200-023-00618-2
Seed TCoppins CKing AEvans N(2023)Polynomial Analysis of Modular ArithmeticStatic Analysis10.1007/978-3-031-44245-2_22(508-539)Online publication date: 22-Oct-2023
https://dl.acm.org/doi/10.1007/978-3-031-44245-2_22
Hashemi ALichtblau D(2023)On the Complexity of Linear Algebra Operations over Algebraic Extension FieldsComputer Algebra in Scientific Computing10.1007/978-3-031-41724-5_8(141-161)Online publication date: 28-Aug-2023
https://dl.acm.org/doi/10.1007/978-3-031-41724-5_8
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Index Terms

On an installation of Buchberger's algorithm
1. Theory of computation
  1. Computational complexity and cryptography
    1. Problems, reductions and completeness
  2. Models of computation
    1. Computability

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Published In

cover image Journal of Symbolic Computation

Journal of Symbolic Computation Volume 6, Issue 2-3

Oct./Dec. 1988

247 pages

ISSN:0747-7171

Editor:
Bruno Buchberger

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Academic Press, Inc.

United States

Publication History

Published: 01 December 1988

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Mora T(2023)Further perspectives on eliminationApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-023-00618-234:5(745-749)Online publication date: 20-Jul-2023
https://dl.acm.org/doi/10.1007/s00200-023-00618-2
Seed TCoppins CKing AEvans N(2023)Polynomial Analysis of Modular ArithmeticStatic Analysis10.1007/978-3-031-44245-2_22(508-539)Online publication date: 22-Oct-2023
https://dl.acm.org/doi/10.1007/978-3-031-44245-2_22
Hashemi ALichtblau D(2023)On the Complexity of Linear Algebra Operations over Algebraic Extension FieldsComputer Algebra in Scientific Computing10.1007/978-3-031-41724-5_8(141-161)Online publication date: 28-Aug-2023
https://dl.acm.org/doi/10.1007/978-3-031-41724-5_8
Ceria MMora F(2022)De Nugis Groebnerialium 6: Rump, Ufnarovski, ZachariasApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-022-00583-233:6(725-749)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1007/s00200-022-00583-2
Malbos PRen IChyzak FLabahn G(2021)Completion in Operads via Essential SyzygiesProceedings of the 2021 International Symposium on Symbolic and Algebraic Computation10.1145/3452143.3465552(305-312)Online publication date: 18-Jul-2021
https://dl.acm.org/doi/10.1145/3452143.3465552
Berthomieu JEder CSafey El Din MChyzak FLabahn G(2021)msolveProceedings of the 2021 International Symposium on Symbolic and Algebraic Computation10.1145/3452143.3465545(51-58)Online publication date: 18-Jul-2021
https://dl.acm.org/doi/10.1145/3452143.3465545
Peifer DStillman MHalpern-Leistner DDaumé HSingh A(2020)Learning selection strategies in Buchberger's algorithmProceedings of the 37th International Conference on Machine Learning10.5555/3524938.3525640(7575-7585)Online publication date: 13-Jul-2020
https://dl.acm.org/doi/10.5555/3524938.3525640
Perry J(2020)A dynamic F4 algorithm to compute Gröbner basesApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-020-00450-y31:5-6(411-434)Online publication date: 1-Nov-2020
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Langeloh G(2020)A comparison of unrestricted dynamic Gröbner Basis algorithmsApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-020-00449-531:5-6(389-409)Online publication date: 1-Nov-2020
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Ceria MMora T(2020)Toward involutive bases over effective ringsApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-020-00448-631:5-6(359-387)Online publication date: 1-Nov-2020
https://dl.acm.org/doi/10.1007/s00200-020-00448-6
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Applying IsRewritten criterion on Buchberger algorithm

On the use of Buchberger criteria in G2V algorithm for calculating Gröbner bases

Exploring the Dynamic Buchberger Algorithm

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