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undergraduate thesis
Faktorizacija u Z [x]
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. urn:nbn:hr:126:129523
Repić, Mirna
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Algebra and Calculus Research Group

Cite this document

Repić, M. (2019). Faktorizacija u Z [x] (Undergraduate thesis). 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 27 March 2023, 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 2023 March 27] 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)
(Algebra and Calculus 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
Terms of useLicence In copyright icon
RepositoryRepository of Department of Mathematics Osijek
Created on2019-10-21 07:56:50