FINITE SIMPLICIAL MULTICOMPLEXES
FINITE SIMPLICIAL MULTICOMPLEXES

Integral domains in which nonzero locally principal ideals are
Integral domains in which nonzero locally principal ideals are

2. Groups I - Math User Home Pages
2. Groups I - Math User Home Pages

A FIRST COURSE IN NUMBER THEORY Contents 1. Introduction 2
A FIRST COURSE IN NUMBER THEORY Contents 1. Introduction 2

Arithmetic and music in twelve easy steps
Arithmetic and music in twelve easy steps

The path to recent progress on small gaps between primes
The path to recent progress on small gaps between primes

4. Morphisms
4. Morphisms

DISTORTION MAPS FOR GENUS TWO CURVES 1. Introduction Let
DISTORTION MAPS FOR GENUS TWO CURVES 1. Introduction Let

THE ARITHMETIC LARGE SIEVE WITH AN APPLICATION TO THE
THE ARITHMETIC LARGE SIEVE WITH AN APPLICATION TO THE

paper
paper

Notes - Math Berkeley
Notes - Math Berkeley

Grade 7/8 Math Circles Continued Fractions A Fraction of
Grade 7/8 Math Circles Continued Fractions A Fraction of

Generalization at Higher Types
Generalization at Higher Types

New conjectures in number theory
New conjectures in number theory

The Essential Dimension of Finite Group Schemes Corso di Laurea Magistrale in Matematica
The Essential Dimension of Finite Group Schemes Corso di Laurea Magistrale in Matematica

PDF
PDF

On the Asymptotic Behaviour of General Partition Functions
On the Asymptotic Behaviour of General Partition Functions

How to lie without being (easily) convicted and the lengths of proofs
How to lie without being (easily) convicted and the lengths of proofs

Meshing for Numerical Approach
Meshing for Numerical Approach

12-5A Perfect Cubes and Cube Roots
12-5A Perfect Cubes and Cube Roots

Principles of Public Key Cryptography Applications of
Principles of Public Key Cryptography Applications of

Optimality of Walrand-Varaiya Type Policies and Markov Sources
Optimality of Walrand-Varaiya Type Policies and Markov Sources

... While block coding achieves the minimum possible rate at a given distortion level, it relies on encoding blocks of data (X0 , . . . , XT −1 ), which may not be practical as the encoder has to wait until it has all T source symbols before it can encode and transmit the data. By using zero-delay sourc ...
Algebra II Module 1: Polynomial, Rational, and Radical
Algebra II Module 1: Polynomial, Rational, and Radical

On different notions of tameness in arithmetic geometry
On different notions of tameness in arithmetic geometry

2.1 Pairwise Alignment
2.1 Pairwise Alignment

...  Finding informative elements in protein and DNA sequences. Many of these research problems aim at learning about functionality or the structure of protein without performing any experiments and actually without having to physically construct the protein itself. The basic idea is that similar seque ...

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.