Conference Proceedings

Grobner bases and behaviors over finite rings

Margreta Kuijper, Kristina Schindelar

PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009) | IEEE | Published : 2009

Abstract

For several decades Gröbner bases have proved useful tools for different areas in system theory, particularly multidimensional system theory. These areas range from controller design to minimal realizations of linear systems over fields. In this paper we focus on the univariate case and identify the so-called "predictable leading monomial property" as a property of a minimal Gröbner basis that is crucial in many of these areas. The property is stronger than "row reducedness". We revisit the recently developed theory of [17] in which row reducedness is extended to polynomial matrices over the finite ring Zpr (with p a prime integer and r a positive integer), which find applications in error c..

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Grants

Funding Acknowledgements

This research is partially supported by the Australian Research Council (ARC) and the Deutscher Akademischer Austausch Dienst (DAAD) and co-financed by the Deutsche Forschungsgemeinschaft (DFG)