Abstract
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 the 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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