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undergraduate thesis
Faktorizacija u Z [x]
2019. urn:nbn:hr:126:129523
Repić, Mirna
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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Repić, M. (2019). Faktorizacija u Z [x] (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:129523

Repić, Mirna. "Faktorizacija u Z [x]." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:129523

Repić, Mirna. "Faktorizacija u Z [x]." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:129523

Repić, M. (2019). 'Faktorizacija u Z [x]', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 14 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:129523

Repić M. Faktorizacija u Z [x] [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2025 January 14] Available at: https://urn.nsk.hr/urn:nbn:hr:126:129523

M. Repić, "Faktorizacija u Z [x]", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:129523

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Metadata
TitleFaktorizacija u Z [x]
Title (english)Factorisation in Z [x]
AuthorMirna Repić
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 country2019-09-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
Tema ovog rada je faktorizacija polinoma u Z[x]. Polinomi su matematički izrazi koji sadrže varijable i konstante povezane računskim operacijama zbrajanja, oduzimanja i množenja, te nenegativnih cijelobrojnih potencija. Pokazat ćemo da postupak faktorizacije u Q[x] polinoma iz Z[x] završava u konačno mnogo koraka, kao i dokaz da je polinom ireducibilan u Q[x]. Iznijet ćemo dvije ideje koje će nam pomoći učiniti postupak faktorizacije polinoma izvedivijim. Najprije ćemo uvesti pojam granične vrijednosti za koeficijente koji su djelitelji danog polinoma kojeg želimo faktorizirati. U postupcima traženja graničnih vrijednosti za korijene i koeficijente koristit ćemo metodu bisekcije i Newtonovu metodu. Potom ćemo naći učinkoviti način faktorizacije polinoma modulo M, gdje je M dovoljno velik modul. Pri tom ćemo koristiti Berlekampov algoritam faktorizacije i Henselovu metodu faktorizacije.
Abstract (english)
The theme of this paper is the factorization of polynomials in Z[x]. In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. We will show that finding a factorization in Q[x] of a monic polynomial of degree n in Z[x], or showing that polynomial is irreducible in Q[x], takes finitely many steps. We will present two ideas that will make factoring process more feasible. Foremost, we will introduce the concept of bound for the coefficients of polynomials of a given polynomial. Thereat we will use the method of bisection and Newton’s method. Thus, we will find an efficient way to factor a polynomial modulo M for M a suitably large modulus. For that process we will use Berlekamp’s Factoring Algorithm and the Hensel Factorization Method.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:129523
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
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Created on2019-10-21 07:56:50