Geodesic
Proof of the Faug\`ere Criterion for the F5 Algorithm
Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 502-510.

Voir la notice de l'article provenant de la source Math-Net.Ru

he validity of the Faugère criterion for the F5 algorithm is established.
Keywords: F5 algorithm, Faugère criterion, Gröbner basis, polynomial ideal, head term. 
@article{MZM_2010_88_4_a1,
     author = {O. N. German},
     title = {Proof of the {Faug\`ere} {Criterion} for the {F5} {Algorithm}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {502--510},
     publisher = {mathdoc},
     volume = {88},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a1/}
}
TY  - JOUR
AU  - O. N. German
TI  - Proof of the Faug\`ere Criterion for the F5 Algorithm
JO  - Matematičeskie zametki
PY  - 2010
SP  - 502
EP  - 510
VL  - 88
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a1/
LA  - ru
ID  - MZM_2010_88_4_a1
ER  - 
%0 Journal Article
%A O. N. German
%T Proof of the Faug\`ere Criterion for the F5 Algorithm
%J Matematičeskie zametki
%D 2010
%P 502-510
%V 88
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a1/
%G ru
%F MZM_2010_88_4_a1
O. N. German. Proof of the Faug\`ere Criterion for the F5 Algorithm. Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 502-510. http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a1/

[1] J.-Ch. Faugère, “A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)”, Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2002, 75–83 | MR | Zbl

[2] J.-Ch. Faugère, Calcul efficace des bases de Gröbner et applications, Habilitation à diriger des recherches, Université Paris VI, 2007

[3] T. Stegers, Faugère's F5 algorithm revisited, Thesis for the degree of Diplom-Mathematiker, Technische Universität Darmstadt, 2005 http://wwwcsif.cs.ucdavis.edu/s̃tegers/

[4] J. M. Gash, On efficient computation of Gröbner bases, PhD Thesis, Indiana University, Bloomington, 2008

[5] C. Eder, On the criteria of the F5 algorithm, arXiv: math.AC/0804.2033

[6] C. Eder, J. Perry, F5C: a variant of Faugère's F5 algorithm with reduced Gröbner bases, arXiv: math.AC/0906.2967

[7] A. I. Zobnin, “Obobschenie algoritma F5 vychisleniya bazisa Grebnera polinomialnykh idealov”, Programmirovanie, 36:2 (2010), 75–82