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TitleOn the complexity of the F5 Gröbner basis algorithm
Author(s) Magali Bardet, Jean-Charles Faugère, Bruno Salvy
TypeArticle in Journal
AbstractWe study the complexity of Gröbner bases computation, in particular in the generic situation where the variables are in simultaneous Noether position with respect to the system.
We give a bound on the number of polynomials of degree d in a Gröbner basis computed by Faugère's F5 algorithm (2002) in this generic case for the grevlex ordering (which is also a bound on the number of polynomials for a reduced Gröbner basis, independently of the algorithm used). Next, we analyse more precisely the structure of the polynomials in the Gröbner bases with signatures that F5 computes and use it to bound the complexity of the algorithm.

Our estimates show that the version of F5F5 we analyse, which uses only standard Gaussian elimination techniques, outperforms row reduction of the Macaulay matrix with the best known algorithms for moderate degrees, and even for degrees up to the thousands if Strassen's multiplication is used. The degree being fixed, the factor of improvement grows exponentially with the number of variables.
KeywordsF5 algorithm, Complexity, Regular sequences, Noether position
Length22
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717114000935
LanguageEnglish
JournalJournal of Symbolic Computation
Volume70
Number0
Pages49--70
Year2015
MonthSeptember
Translation No
Refereed No
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