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On an installation of Buchberger’s algorithm. (English) Zbl 0675.13013
The authors describe a new version of the Buchberger algorithm for calculating Gröbner bases of polynomial ideals [B. Buchberger, Multidimensional Systems Theory, Progress, directions and open problems, Math. Appl., D. Reidel Publ. Co. 16, 184-232 (1985; Zbl 0587.13009)]. It has the advantage that superfluous reductions of so-called S-polynomials are detected more easily thus speeding up the computations. The authors have implemented their version into the computer algebra systems Scratchpad II and Reduce 3.3. Several examples demonstrate that not only the running time is diminished but that the resulting Gröbner bases also have fewer elements.
Reviewer: Michael Pohst

13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
68W30 Symbolic computation and algebraic computation
Full Text: DOI
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