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Gröbner bases: A short introduction for systems theorists. (English) Zbl 1023.68882

Moreno-Díaz, Roberto (ed.) et al., Computer aided systems theory - EUROCAST 2001. A selection of papers from the 8th international workshop, Las Palmas de Gran Canaria, Spain, February 19-23, 2001. Revised papers. Berlin: Springer. Lect. Notes Comput. Sci. 2178, 1-19 (2001).
Summary: In this paper, we give a brief overview on Gröbner bases theory, addressed to novices without prior knowledge in the field. After explaining the general strategy for solving problems via the Gröbner approach, we develop the concept of Gröbner bases by studying uniquenss of polynomial division (“reduction”). For explicitly constructing Gröbner bases, the crucial notion of S-polynomials is introduced, leading to the complete algorithmic solution of the construction problem. The algorithm is applied to examples from polynomial equation solving and algebraic relations. After a short discussion of complexity issues, we conclude the paper with some historical remarks and references.
For the entire collection see [Zbl 0977.00038].

MSC:

68W30 Symbolic computation and algebraic computation

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