Geodesic
Improved Buchberger's algorithm
Trudy Instituta matematiki, Tome 20 (2012) no. 1, pp. 3-13 
S. V. Agievich. Improved Buchberger's algorithm. Trudy Instituta matematiki, Tome 20 (2012) no. 1, pp. 3-13. http://geodesic.mathdoc.fr/item/TIMB_2012_20_1_a0/
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     title = {Improved {Buchberger's} algorithm},
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     url = {http://geodesic.mathdoc.fr/item/TIMB_2012_20_1_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We propose an improved Buchberger's algorithm that jointly uses known and new criteria of elimination of critical pairs. New criteria are based on construction of a minimal set of generators of the module generated by the critical syzygies.

[1] Koks D., Littl Dzh., O'Shi D., Idealy, mnogoobraziya i algoritmy, Mir, M., 2000

[2] Boulier F., A new criterion to avoid useless critical pairs in Buchberger's algorithm, Technical report LIFL 2001-07, , 2001 http://www.lifl.fr/b̃oulier/PUBLICATIONS/LIFL2001-07.ps.gz

[3] Gebauer R., Möller H. M., “On an Installation of Buchberger's Algorithm”, J. of Symbolic Computation, 1987, no. 6, 257–286

[4] Caboara M., Kreuzer M., Robbiano L., “Efficiently computing minimal sets of critical pairs”, J. of Symbolic Computation, 38:4 (2004), 1169–1190 | DOI | MR

[5] Mora T., Solving Polynomial Equation Systems, v. II, Macaulay's Paradigm and Gröbner Theory, Cambridge University Press, 2005 | MR