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The structure of the F5 algorithm to compute Gr\"obner bases makes it very efficient.
On some formulæ in elimination
F. S. Macaulay · 1902
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Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal
Buchberger, B · 1965
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Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
Buchberger, B · 1970
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A criterion for detecting unnecessary reductions in the construction of Gröbner bases
Buchberger, B · 1979
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Gröbner bases, Gaussian elimination and resolution of systems of algebraic equations
Daniel Lazard · 1983
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On an installation of Buchberger’s algorithm
Gebauer, R. and Möller, H. M · 1988
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Gröbner bases computation using syzygies
Möller, H.M., Traverso, C., and Mora, T · 1992
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Gröbner Bases
Becker, T., Weispfenning, V., and Kredel, H · 1993
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The Magma algebra system. I. The user language
Bosma, W., Cannon, J., and Playoust, C · 1997
Cited alongside, same era.
A new efficient algorithm for computing Gröbner bases (F4)
Faugère, J.-C · 1999
Cited alongside, same era.
A new efficient algorithm for computing Gröbner bases without reduction to zero F5
Faugère, J.-C · 2002
Cited alongside, same era.
Applications des bases de Gröbner à la cryptographie
Gwénolé Ars · 2005
Cited alongside, same era.
Cryptochallenge 11 is broken or an efficient attack of the C* cryptosystem
Jean-Charles Faugère · 2005
Cited alongside, same era.
Computing in Algebraic Geometry - A Quick Start in Singular
Decker, W. and Lossen, C · 2006
Cited alongside, same era.
On the criteria of the F5 Algorithm
Eder, C · 2008
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On efficient computation of Grobner bases
Gash, J. M · 2008
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PolyBoRi: A framework for Gröbner basis computations with Boolean polynomials
Brickenstein, M. and Dreyer, A · 2009
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Slimgb: Gröbner bases with slim polynomials
Michael Brickenstein · 2010
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Singular 3-1-1 — A computer algebra system for polynomial computations
Decker, W., Greuel, G.-M., Pfister, G., and Schönemann, H · 2010
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F5C: A Variant of Faugère’s F5 Algorithm with reduced Gröbner bases
Eder, C. and Perry, J · 2010
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A Singular
Greuel, G.-M. and Pfister, G · 2007
Cited alongside, same era.
Faugère’s F5 Algorithm revisited
Stegers, T · 2007
Cited alongside, same era.
Asympotic expansion of the degree of regularity for semi-regular systems of equations
Magali Bardet, Jean-Charles Faugère, and Bruno Salvy
Cited in the paper.
MXL3: An efficient algorithm for computing Gröbner bases of zero-dimensional ideals
Mohamed Saied Emam Mohamed, Daniel Cabarcas, Jintai Ding, Johannes Buchmann, and Stanislav Bulygin · 2010
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