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TitleGröbner Bases and Systems Theory
Author(s) Bruno Buchberger
TypeArticle in Journal
AbstractWe present the basic concepts and results of Gröbner bases theory for readers working or interested in systems theory. The concepts and methods of Gröbner bases theory are presented by examples. No prerequisites, except some notions of elementary mathematics, are necessary for reading this paper. The two main properties of Gröbner bases, the elimination property and the linear independence property, are explained. Most of the many applications of Gröbner bases theory, in particular applications in systems theory, hinge on these two properties. Also, an algorithm based on Gröbner bases for computing complete systems of solutions ('syzygies') for linear diophantine equations with multivariate polynomial coefficients is described. Many fundamental problems of systems theory can be reduced to the problem of syzygies computation.
KeywordsGröbner bases, algorithmic systems theory, computer algebra, algebraic algorithms, polynomial ideals, elimination, residue class rings, syzygies, polynomial diophantine equations
Length29
ISSN0923-6082
File
URL dx.doi.org/10.1023/A:1011949421611
LanguageEnglish
JournalMultidimensional Systems and Signal Processing
Volume12
Number3-4
Pages223-251
PublisherSpringer Science Business Media B.V.
Year2001
MonthJuly
Edition0
Translation No
Refereed No
Organization Johannes Kepler University Linz
Institution RISC (Research Institute for Symbolic Computation)
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