Details:
Title  Gröbner Bases and Systems Theory  Author(s)  Bruno Buchberger  Type  Article in Journal  Abstract  We 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.
 Keywords  Gröbner bases, algorithmic systems theory, computer algebra, algebraic algorithms, polynomial ideals, elimination, residue class rings, syzygies, polynomial diophantine equations  Length  29  ISSN  09236082 
File 
 URL 
dx.doi.org/10.1023/A:1011949421611 
Language  English  Journal  Multidimensional Systems and Signal Processing  Volume  12  Number  34  Pages  223251  Publisher  Springer Science Business Media B.V.  Year  2001  Month  July  Edition  0  Translation 
No  Refereed 
No  Organization 
Johannes Kepler University Linz  Institution 
RISC (Research Institute for Symbolic Computation) 
