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ON THE TATE AND MUMFORD-TATE CONJECTURES IN
ON THE TATE AND MUMFORD-TATE CONJECTURES IN

Intro Abstract Algebra
Intro Abstract Algebra



Intro Abstract Algebra
Intro Abstract Algebra

Computational Aspects of Pseudospectra in Hydrodynamic Stability
Computational Aspects of Pseudospectra in Hydrodynamic Stability

Connections between relation algebras and cylindric algebras
Connections between relation algebras and cylindric algebras

FACTORING IN QUADRATIC FIELDS 1. Introduction √
FACTORING IN QUADRATIC FIELDS 1. Introduction √

Research Article Classification of Textual E-Mail Spam
Research Article Classification of Textual E-Mail Spam

Full text
Full text

... Taking logarithms in the last inequality above we get ...
Algebra Qual Solutions September 12, 2009 UCLA ALGEBRA QUALIFYING EXAM Solutions
Algebra Qual Solutions September 12, 2009 UCLA ALGEBRA QUALIFYING EXAM Solutions

Lecture notes up to 08 Mar 2017
Lecture notes up to 08 Mar 2017

log √x
log √x

Sum of Cubes
Sum of Cubes

Slides of the talk
Slides of the talk

Report - angelika
Report - angelika

Universal unramified cohomology of cubic fourfolds containing a plane
Universal unramified cohomology of cubic fourfolds containing a plane

Rainbow Arithmetic Progressions in Finite Abelian Groups.
Rainbow Arithmetic Progressions in Finite Abelian Groups.

(pdf)
(pdf)

Every set has its divisor
Every set has its divisor

On intersecting a set of parallel line segments with a convex polygon
On intersecting a set of parallel line segments with a convex polygon

Title: Asymptotic distribution of integers with certain prime
Title: Asymptotic distribution of integers with certain prime

Activity 2 Further Exploration of Exponential Functions
Activity 2 Further Exploration of Exponential Functions

3 Congruence arithmetic
3 Congruence arithmetic

Additive decompositions of sets with restricted prime factors
Additive decompositions of sets with restricted prime factors

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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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