F. Winkler. Knuth-Bendix Procedure and Buchberger Algorithm - A Synthesis. In Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC'89), pages 5567, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....For this purpose, we need a generic algorithm that decomposes as much as possible the dioeerent phases into independent steps. Hence strategies can be integrated and modied separately at each step of the algorithm. Gr#bner bases computation can be seen as a completion for rewrite systems [Buc87, Win89] modulo some simplications of the polynomials. In this section, we will not assume an associativecommutative (AC) completion procedure as in [Mar93, B#n91, BG94] We consider an algorithm similar to standard completion that does not take into account the properties of the AC operators. In fact, ....

F. Winkler. Knuth-Bendix Procedure and Buchberger Algorithm - A Synthesis. In Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC'89), pages 5567, 1989.

....the quotient is non zero, using the well founded ordering defined on polynomials we have Theorem 4.1 Any finite subset P of a polynomial ring E[x 1 ; x n ] induces a rewriting relation P which is Noetherian. The proof, making strong use of term orderings on polynomials, can be found in [54, 57]. We emphasize here that the reflexive, symmetric and transitive closure of the rewriting relation defined above, and denoted by , is equivalent to the ideal congruence relation, which is a standard relation when considering rings and ideals. We are going to give the definition of congruence in ....

F. Winkler. Knuth Bendix procedure and Buchberger algorithm: a syntesis. In ISAAC-89, 1989. 33

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