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Morphisms of Algebraic Stacks
Morphisms of Algebraic Stacks

The sums of the reciprocals of Fibonacci polynomials and Lucas
The sums of the reciprocals of Fibonacci polynomials and Lucas

Congruence graphs and newforms
Congruence graphs and newforms

COMMUTATIVE ALGEBRA Contents Introduction 5
COMMUTATIVE ALGEBRA Contents Introduction 5

COMMUTATIVE ALGEBRA Contents Introduction 5 0.1. What is
COMMUTATIVE ALGEBRA Contents Introduction 5 0.1. What is

Algebra - University at Albany
Algebra - University at Albany

Congruences
Congruences

THE DISTRIBUTION OF PRIME NUMBERS Andrew Granville and K
THE DISTRIBUTION OF PRIME NUMBERS Andrew Granville and K

Constraint Satisfaction Complexity and Logic Phokion G. Kolaitis
Constraint Satisfaction Complexity and Logic Phokion G. Kolaitis

Integers Modulo m
Integers Modulo m

Limitations
Limitations

M-100 7-1A GCF Factor Lec
M-100 7-1A GCF Factor Lec

universidad complutense de madrid - E
universidad complutense de madrid - E

Number Theory & RSA
Number Theory & RSA

Greatest Common Factor (GCF)
Greatest Common Factor (GCF)

Section2.2notes
Section2.2notes

Algebra II Module 1: Teacher Materials
Algebra II Module 1: Teacher Materials

solutions to the first homework
solutions to the first homework

Parallelogram polyominoes, the sandpile model on Km,n, and a q,t
Parallelogram polyominoes, the sandpile model on Km,n, and a q,t

Here - People
Here - People

Problem Set 1 Solutions
Problem Set 1 Solutions

Notes
Notes

Nearly Prime Subsemigroups of βN
Nearly Prime Subsemigroups of βN

Linear Algebra
Linear Algebra

on highly composite and similar numbers
on highly composite and similar numbers

1 2 3 4 5 ... 231 >

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.
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