Geodesic
Asymmetric approach to computation of Gr\"obner bases
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 3, pp. 73-88.

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A new approach to Buchberger's algorithm based on the use of essential multiplications and nonmultiplicative prolongations instead of traditional $S$-polynomials is described. In the framework of this approach, both Buchberger's algorithm for computing Gröbner bases and Gerdt–Blinkov algorithm for computing involutive bases obtain a unified form of description. The new approach is based on consideration of the process of determining an $S$-polynomial as a process of constructing a nonmultiplicative prolongation of a polynomial and its subsequent reducing with respect to an essential multiplication. An advantage of the method is that some “redundant” $S$-pairs are automatically excluded from consideration. 
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E. V. Pankratiev; A. S. Semenov. Asymmetric approach to computation of Gr\"obner bases. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 3, pp. 73-88. http://geodesic.mathdoc.fr/item/FPM_2006_12_3_a4/

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