Universal Journal of Computational Mathematics(CEASE PUBLICATION) Vol. 1(1), pp. 5 - 14
DOI: 10.13189/ujcmj.2013.010102
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On Groebner Bases and Their Use in Solving Some Practical Problems

Matej Mencinger^1,2,*
1 University of Maribor, Faculty of Civil Engineering, Smetanova 17, 2000, Maribor, Slovenia
² Institute of Mathematics, Physics and Mechanics, Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

ABSTRACT

Groebner basis are an important theoretical building block of modern (polynomial) ring theory. The origin of Groebner basis theory goes back to solving some theoretical problems concerning the ideals in polynomial rings, as well as solving polynomial systems of equations. In this article four practical applications of Groebner basis theory are considered; we use Groebner basis to solve the systems of nonlinear polynomial equations, to solve an integer programming problem, to solve the problem of chromatic number of a graph, and finally we consider an original example from the theory of systems of ordinary (polynomial) differential equations. For practical computations we use systems »MATHEMATICA« and »SINGULAR«.

KEYWORDS
Polynomial system of (differential) equations, integer linear programming, chromatic number of a graph, polynomial rings, Groebner basis, CAS systems

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Matej Mencinger , "On Groebner Bases and Their Use in Solving Some Practical Problems," Universal Journal of Computational Mathematics(CEASE PUBLICATION), Vol. 1, No. 1, pp. 5 - 14, 2013. DOI: 10.13189/ujcmj.2013.010102.

(b). APA Format:
Matej Mencinger (2013). On Groebner Bases and Their Use in Solving Some Practical Problems. Universal Journal of Computational Mathematics(CEASE PUBLICATION), 1(1), 5 - 14. DOI: 10.13189/ujcmj.2013.010102.