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master's thesis
Algoritmi na polinomima
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:915128
Zlodi, Ivana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Zlodi, I. (2014). Algoritmi na polinomima (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:915128

Zlodi, Ivana. "Algoritmi na polinomima." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:915128

Zlodi, Ivana. "Algoritmi na polinomima." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:915128

Zlodi, I. (2014). 'Algoritmi na polinomima', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:915128

Zlodi I. Algoritmi na polinomima [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2024 November 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:915128

I. Zlodi, "Algoritmi na polinomima", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:915128

Metadata
TitleAlgoritmi na polinomima
AuthorIvana Zlodi
MentorGoran Muić (mentor)
Committee memberGoran Muić (predsjednik povjerenstva)
Committee memberRobert Manger (član povjerenstva)
Committee memberNela Bosner (član povjerenstva)
Committee memberVjekoslav Kovač (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-07-11, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu dokazali smo algoritam za dijeljenje polinoma u više varijabli s obzirom na fiksni monomijalni uređaj. Algoritam smo dobili proširenjem algoritma dijeljenja polinoma u jednoj varijabli. Vidjeli smo da ostatak nije jedinstveno okarakteriziran kao u slučaju jedne varijable. Uvođenjem Groebnerovih baza pokazali smo da algoritam postiže puni potencijal kada je u paru s Groebnerovim bazama. Zatim, smo vidjeli da svaki nenul ideal u prstenu polinoma ima Groebnerovu bazu, te smo naučili kako provjeriti je li dana baza Groebnerova. Pokazali smo kako pomoću algoritma dijeljenja i Groebnerovih baza provjeriti pripadnost polinoma idealu. Na kraju, pokazali smo kako Buchbergerovim algoritmom konstruirati Greobnerovu bazu.
Abstract (english)
In this thesis, we have proved the division algorithm for polynomials in several variables with respect to a fixed monomial order. We have got this algorithm by extending the division algorithm for polynomials in one variable. It was shown that the remainder is not uniquely characterized as in the case of one variable. By introduction Groebner basis we have shown that the algorithm achieves full potential when it is paired with Groebner basis. Also, every nonzero ideal in a polynomial ring has Groebner base, and we learned how to check whether the base is Groebner. We showed by using a division algorithm and Groebner basis how to check if polynomial lies in the ideal. Finally, we showed how to construct Groebner base with Buchberger’s algorithm.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:915128
Study programmeTitle: Finance and Business 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 on2019-02-20 12:41:41