Involutive bases algorithm incorporating F5 criterion
| Autor: | Benyamin M.-Alizadeh, Amir Hashemi, Vladimir P. Gerdt |
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| Rok vydání: | 2013 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Symbolic Computation Algebra and Number Theory Mathematics - Rings and Algebras Symbolic Computation (cs.SC) Commutative Algebra (math.AC) Mathematics - Commutative Algebra I.1.2 Computational Mathematics Rings and Algebras (math.RA) FOS: Mathematics Computer Science::Symbolic Computation 13P10 Algorithm Mathematics |
| Zdroj: | Journal of Symbolic Computation. 59:1-20 |
| ISSN: | 0747-7171 |
| DOI: | 10.1016/j.jsc.2013.08.002 |
| Popis: | Faugere's F5 algorithm is the fastest known algorithm to compute Groebner bases. It has a signature-based and an incremental structure that allow to apply the F5 criterion for deletion of unnecessary reductions. In this paper, we present an involutive completion algorithm which outputs a minimal involutive basis. Our completion algorithm has a nonincremental structure and in addition to the involutive form of Buchberger's criteria it applies the F5 criterion whenever this criterion is applicable in the course of completion to involution. In doing so, we use the G2V form of the F5 criterion developed by Gao, Guan and Volny IV. To compare the proposed algorithm, via a set of benchmarks, with the Gerdt-Blinkov involutive algorithm (which does not apply the F5 criterion) we use implementations of both algorithms done on the same platform in Maple. 24 pages, 2 figures |
| Databáze: | OpenAIRE |
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