On Groebner bases and their use in solving some practical problems

Povzetek

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 .

Ključne besede

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

Podatki

Jezik:	Angleški jezik
Leto izida:	2013
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UM FGPA - Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo
UDK:	517.1
COBISS:	17085206
ISSN:	Y507-4134
Št. ogledov:	917
Št. prenosov:	64
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Neznan jezik
URN:	URN:SI:UM:
Vrsta dela (COBISS):	Delo ni kategorizirano
Strani:	str. 5-14
Letnik:	ǂVol. ǂ1
Zvezek:	ǂno. ǂ1
Čas izdaje:	June 2013
Ključne besede (UDK):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;analysis;matematična analiza;
DOI:	10.13189/ujcmj.2013.010102
ID:	1439631