IOSR Journal of Computer Engineering (IOSR-JCE)
IOSR Journal of Computer Engineering (IOSR-JCE)

EE CS ASP: A SEJITS Implementation for Python
EE CS ASP: A SEJITS Implementation for Python

Integers, Prime Factorization, and More on Primes
Integers, Prime Factorization, and More on Primes

... Proof. (1) By the Euclidean algorithm, there exist integers m, n such that ma + nb = 1. Multiplying c to both sides we have mac + nbc = c. Since a | bc, i.e., bc = qa for some integer q, then c = mac + nqa = (mc + nq)a, which means that a is a divisor of c. (2) If p - a, then gcd(p, a) = 1. Thus by ...
The Multiple Knapsack Problem Approached by a Binary Differential
The Multiple Knapsack Problem Approached by a Binary Differential

FOURTH PROBLEM SHEET FOR ALGEBRAIC NUMBER THEORY
FOURTH PROBLEM SHEET FOR ALGEBRAIC NUMBER THEORY

Paper Title (use style: paper title)
Paper Title (use style: paper title)

Paper Title (use style: paper title)
Paper Title (use style: paper title)

Lecture 3. Order of Operations1 Some arithmetic expressions
Lecture 3. Order of Operations1 Some arithmetic expressions

Algebra Quals Fall 2012 1. This is an immediate consequence of the
Algebra Quals Fall 2012 1. This is an immediate consequence of the

prime factor
prime factor



, ,n N X N X
, ,n N X N X

TCSS 343: Large Integer Multiplication Suppose we want to multiply
TCSS 343: Large Integer Multiplication Suppose we want to multiply

LATTICES WITH SYMMETRY 1. Introduction Let G be a finite
LATTICES WITH SYMMETRY 1. Introduction Let G be a finite

Henry Cohn`s home page
Henry Cohn`s home page

MATH 254A: RINGS OF INTEGERS AND DEDEKIND DOMAINS 1
MATH 254A: RINGS OF INTEGERS AND DEDEKIND DOMAINS 1

Binomial coefficients and p-adic limits
Binomial coefficients and p-adic limits

Finite fields Michel Waldschmidt Contents
Finite fields Michel Waldschmidt Contents

The Kazhdan-Lusztig polynomial of a matroid
The Kazhdan-Lusztig polynomial of a matroid

Recall: Even and Odd Functions and Symmetry
Recall: Even and Odd Functions and Symmetry

Math 345 Sp 07 Day 8 1. Definition of unit: In ring R, an element a is
Math 345 Sp 07 Day 8 1. Definition of unit: In ring R, an element a is

Name: Math 2412 Activity 2(Due by Feb. 28) Find the quadratic
Name: Math 2412 Activity 2(Due by Feb. 28) Find the quadratic

... values, then what can you conclude about p  x  and q  x  ? Consider the previous problem. ...
2. Permutation groups Throughout this section, assume that G is a
2. Permutation groups Throughout this section, assume that G is a

Lesson 6-2
Lesson 6-2

Complex Polynomial Identities
Complex Polynomial Identities

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.