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master's thesis
Gröbnerove baze
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:118171
Tepeš, Tatjana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Tepeš, T. (2016). Gröbnerove baze (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:118171

Tepeš, Tatjana. "Gröbnerove baze." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:118171

Tepeš, Tatjana. "Gröbnerove baze." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:118171

Tepeš, T. (2016). 'Gröbnerove baze', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:118171

Tepeš T. Gröbnerove baze [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 November 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:118171

T. Tepeš, "Gröbnerove baze", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:118171

Metadata
TitleGröbnerove baze
AuthorTatjana Tepeš
MentorOzren Perše (mentor)
Committee memberOzren Perše (predsjednik povjerenstva)
Committee memberDražen Adamović (član povjerenstva)
Committee memberMirko Primc (član povjerenstva)
Committee memberIlja Gogić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2016-11-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu, glavni cilj nam je proučiti pojam Gröbnerove baze. Rad se sastoji od dva poglavlja. U prvom poglavlju upoznajemo osnovne algebarske strukture koje su nam bile potrebne u daljnjim razmatranjima. Upoznajemo grupe, prstene i ideale, te nešto više pažnje posvećujemo polinomima, koji su bitni u radu. Također definiramo Noetherin prsten, te jedno poglavlje posvećujemo monomima, monomijalnim uređajima, te leksikografskom uređaju. U drugom poglavlju smo konačno mogli definirati Gröbnerovu bazu, te navesti neka njena svojstva. Vrlo važan nam je bio Buchbergerov teorem, koji daje kriterij za određivanje je li neka baza Gröbnerova, te istoimeni algoritam za izračunavanje Gröbnerove baze.
Abstract (english)
In this diploma thesis the main goal is to study the concept of Gröbner basis. The thesis consists of two chapters. In the first chapter we introduce the basic algebraic structures which were important in further considerations. We get to know groups, rings and ideals, and more attention was devoted to polynomials which are very important in our work. We also define Noetherian ring, and one chapter is devoted to monomials, monomial order and lexicographic order. In the second chapter we define the determine Gröbner basis, and prove some of its properties. Buchberger’s theorem was very important to us because it gives us criterion for determining whether the basis is Gröbner, and Buchberger’s algorithm gives us the Gröbner basis.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:118171
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-03-29 12:21:34