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master's thesis
Polinomi u Z[x] i Q[x]
2018. urn:nbn:hr:126:514084
Bolješić, Luka
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Algebra, Analysis and Number Theory Research Group

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Bolješić, L. (2018). Polinomi u Z[x] i Q[x] (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:514084

Bolješić, Luka. "Polinomi u Z[x] i Q[x]." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:514084

Bolješić, Luka. "Polinomi u Z[x] i Q[x]." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:514084

Bolješić, L. (2018). 'Polinomi u Z[x] i Q[x]', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 11 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:514084

Bolješić L. Polinomi u Z[x] i Q[x] [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2018 [cited 2024 November 11] Available at: https://urn.nsk.hr/urn:nbn:hr:126:514084

L. Bolješić, "Polinomi u Z[x] i Q[x]", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:126:514084

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Metadata
TitlePolinomi u Z[x] i Q[x]
AuthorLuka Bolješić
MentorIvan Matić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Algebra, Analysis and Number Theory Research Group)
Osijek
Defense date and country2018-10, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
Na početku ovog rada stavljen je naglasak na polinome s racionalnim koeficijentima te na provjeravanje njihove ireducibilnosti. Objašnjeno je zašto polinomi s racionalnim koeficijentima imaju jednaku faktorizaciju kao polinomi s cjelobrojnim koeficijentima, te je iskazana je i dokazana Gaussova lema za polinome s cjelobrojnim koeficijentima. Navedeni su brojni primjeri u kojima se provjerava ireducibilnost polinoma s cjelobrojnim koeficijentima na različite načine. U drugom dijelu iskazan je i dokazan Kineski teorem o ostatcima za polinome te su navedene neke bitne posljedice tog teorema. Na kraju je opisana metoda od tri koraka koja se koristi za brzo množenje polinoma.
Abstract (english)
In this master’s thesis, the initial focus was on polynomials with rational coefficients and determining their ireducibility. The conclusion has been reached as to why polynomials with rational coefficients possess the same factorization as polynomials with integer coefficients. The proof for Gauss lemma for polynomials with integer coefficients has also been presented. Numerous examples that explore the ireducibility of polynomials with integer coefficients have been presented in various ways. Within the second part of this master’s thesis, the Chinese polynomial remainder theorem has been presented as well as its proof and some important ramifications of this theorem were discussed. Ultimately, a three-step method used for fast polynomial multiplication was described
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:514084
Study programmeTitle: Mathematics and Computer Science
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2018-10-17 09:43:06