20.500.12556/DKUM-50457 On Groebner bases and their use in solving some practical problems 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 . polynomial system of (differential) equations integer linear programming chromatic number of a graph polynomial rings Groebner basis CAS systems true false false Angleški jezik Neznan jezik Delo ni kategorizirano 2015-07-10 12:40:10 2015-07-10 12:40:10 2022-05-29 03:07:03 2021-05-09 03:29:09 2013 0 0 str. 5-14 no. 1 Vol. 1 June 2013 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.1 17085206 URN:SI:UM:DK:IBYNFQVE http://www.hrpub.org/download/201306/ujcmj.2013.010102.pdf 1 https://dk.um.si/Dokument.php?lang=slv&id=75016 Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo 0 0 0