Miles Reid's notes
Miles Reid's notes

Homework assignment 9 Section 6.2 pp. 189 Exercise 5. Let
Homework assignment 9 Section 6.2 pp. 189 Exercise 5. Let

Unit Overview - Orange Public Schools
Unit Overview - Orange Public Schools

pdf-file - Institut for Matematiske Fag
pdf-file - Institut for Matematiske Fag

Math 850 Algebra - San Francisco State University
Math 850 Algebra - San Francisco State University

Curriculum Map: Algebra 1 - Merrillville Community School
Curriculum Map: Algebra 1 - Merrillville Community School

Factoring via Strong Lattice Reduction Algorithms 1 Introduction
Factoring via Strong Lattice Reduction Algorithms 1 Introduction

On Optimal Solution of the General Two Jugs Problem
On Optimal Solution of the General Two Jugs Problem

Integer Factoring
Integer Factoring

x - HCC Learning Web
x - HCC Learning Web

THE GEOMETRY OF THE ADELES Contents 1. Introduction 1 2
THE GEOMETRY OF THE ADELES Contents 1. Introduction 1 2

The Euclidean Algorithm and Diophantine Equations
The Euclidean Algorithm and Diophantine Equations

... Divide b into a and let r1 be the remainder. Divide r1 into b and let r2 be the remainder. Divide r2 into r1 and let r3 be the remainder. Continue to divide the remainder into the divisor until you get a remainder of zero. gcd(a, b)  the last nonzero remainder. ...
Document
Document

Parametric Integer Programming in Fixed Dimension
Parametric Integer Programming in Fixed Dimension

WORKING WITH INTEGERS: 1. Adding Rules: Positive + Positive
WORKING WITH INTEGERS: 1. Adding Rules: Positive + Positive

Different terms
Different terms

Ring Theory
Ring Theory

Least Common Multiple
Least Common Multiple

CHAPTER 7 ELEMENTARY FUNCTIONS I
CHAPTER 7 ELEMENTARY FUNCTIONS I

OSTROWSKI`S THEOREM FOR F(T) On Q, Ostrowski`s theorem
OSTROWSKI`S THEOREM FOR F(T) On Q, Ostrowski`s theorem

OSTROWSKI’S THEOREM FOR F (T )
OSTROWSKI’S THEOREM FOR F (T )

Thomas L. Magnanti and Georgia Perakis
Thomas L. Magnanti and Georgia Perakis

Deterministic factorization of sums and differences of powers
Deterministic factorization of sums and differences of powers

Prime Numbers
Prime Numbers

quantifier elimination for Presburger arithmetic
quantifier elimination for Presburger arithmetic

Factorization of polynomials over finite fields

In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them.The case of the factorization of univariate polynomials over a finite field, which is the subject of this article, is especially important, because all the algorithms (including the case of multivariate polynomials over the rational numbers), which are sufficiently efficient to be implemented, reduce the problem to this case (see Polynomial factorization). It is also interesting for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory.As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article.