Faktorizace polynomů nad konečnými tělesy

Abstract

Nazcv prace: Faktorizace polynoinu nad konccnynii telesy Autor: Milan Straka Katcdra (ustav): Katcdra algebry Vedouci bakalarske prace: Mgr. Jan Zcmlicka, Ph.D. E-mail vedouciho: Jan.Zemlicka((hnff. cuni.cz Abstrakt: Cilem prace je prozkoumat problem rozkladu polynomn nad konecnym telc- scm na soucin ircducibilnich polynoinu. PopHanim nekolika algoritmu hledaji- cich tento rozklad se ukaze, ze tento problem je vzdy fcsitclny v polynornialnim case vzhleclem kc stupni polynomu a poctu prvku konecneho telcsa. U jeduoho z algoritnm je po])sana implenientace s vclnii clobrou asymptotic- kou casovou slozito.sti O(nLylD log c/}, kdc i\. jc stupen rozkladaneho polynuinn nad telesem « q prvky. Program pouzivajiei jcdnodnssi, ale prakticky rychlcjsi variantu tohoto algoritnm jc soucasti ])racc. Klicova slova: faktorizace, kouecna telesa, polynoniy, algoritmns Title: Factoring polynomials over finite fields Author: Milan Straka Department: Department of Algebra Supervisor: Mgr. Jan Zemlicka, Ph.D. Supervisor's e-mail address: Jan. Zcirilicka@mJJ.cum.cz Abstract: The goal of this work is to present the problem of the decomposition of a polyno- mial over a finite field into a product of irreducible polynomials. By describing algorithms solving this problem, we show that the decomposition can always be found in...

Nazcv prace: Faktorizace polynoinu nad konccnynii telesy Autor: Milan Straka Katcdra (ustav): Katcdra algebry Vedouci bakalarske prace: Mgr. Jan Zcmlicka, Ph.D. E-mail vedouciho: Jan.Zemlicka((hnff. cuni.cz Abstrakt: Cilem prace je prozkoumat problem rozkladu polynomn nad konecnym telc- scm na soucin ircducibilnich polynoinu. PopHanim nekolika algoritmu hledaji- cich tento rozklad se ukaze, ze tento problem je vzdy fcsitclny v polynornialnim case vzhleclem kc stupni polynomu a poctu prvku konecneho telcsa. U jeduoho z algoritnm je po])sana implenientace s vclnii clobrou asymptotic- kou casovou slozito.sti O(nLylD log c/}, kdc i\. jc stupen rozkladaneho polynuinn nad telesem « q prvky. Program pouzivajiei jcdnodnssi, ale prakticky rychlcjsi variantu tohoto algoritnm jc soucasti ])racc. Klicova slova: faktorizace, kouecna telesa, polynoniy, algoritmns Title: Factoring polynomials over finite fields Author: Milan Straka Department: Department of Algebra Supervisor: Mgr. Jan Zemlicka, Ph.D. Supervisor's e-mail address: Jan. Zcirilicka@mJJ.cum.cz Abstract: The goal of this work is to present the problem of the decomposition of a polyno- mial over a finite field into a product of irreducible polynomials. By describing algorithms solving this problem, we show that the decomposition can always be found in...