Algoritmi za faktorizaciju polinoma

Abstract

Diplomski rad podijeljen je na četiri poglavlja. Prvo poglavlje čine osnovni teoremi i svojstva polinoma koja se koriste u radu. U preostala tri poglavlja su opisana tri osnovna algoritma za faktorizaciju polinoma: Kroneckerov algoritam, Berlekampov algoritam i LLL- algoritam. Svako poglavlje, koje opisuje jedan algoritam, podijeljeno je na tri dijela. Prvi dio se sastoji od teorema koji su nam potrebni za razumijevanje algoritma. U drugom dijelu, algoritam je raspisan po koracima, dok je u trećem dijelu komentirana složenost algoritma.This master’s thesis consists of four chapters, first of which contains theorems and properties of polynomials being used in it. Remaining three chapters focus on three main algorithms for factorization of polynomials: algorithm of Kronecker, algorithm of Berklamp, and, ultimately, the LLL- algorithm. Every chapter takes one of the mentioned algorithms and breaks it down in three parts. First part introduces all theorems needed for proper understanding of the algorithm itself, while the second part describes the algorithm in question going through it step by step. Finally, third part of every chapter comments on the complexity of the given algorithm