Groebner basis
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on Amazon.Dr. Bruno Buchberger accepted the invitation on 14 July 2008 (self-imposed deadline: 14 December 2008).
Groebner bases are certain sets of multivariate nonlinear polynomials for which many fundamental problems can be solved by algorithms. Their importance stems from the fact that, in addition, given any set of multivariate nonlinear polynomials, a corresponding Groebner basis can be found by an algorithm. Thus, many fundamental problems on sets of multivariate non-linear polynomials (and, thereby, many fundamental problems in science and engineering that can be reduced to problems on nonlinear polynomials) can be solved algorithmically.
The theory of Groebner bases and their algorithmic construction was introduced by Bruno Buchberger in his PhD thesis in 1965 and, in the meantime, has been expanded significantly by numerous researchers worldwide with applications in such diverse areas as cryptography, automated theorem proving, automated programming, discrete optimization, systems theory etc.
