Inclusion of CM-fields and divisibility of relative class numbers
Inclusion of CM-fields and divisibility of relative class numbers

Information Gathering and Reward Exploitation of Subgoals for
Information Gathering and Reward Exploitation of Subgoals for

Section 2.2
Section 2.2

... Definition: The greatest common divisor of two natural numbers a and b , denoted as gcd( a, b) , is the largest natural number that divides a and b with no remainder. Elementary Method for Computing the gcd of Two Numbers Decompose each number into its prime factors. The gcd is obtained by multiplyi ...
The Z-densities of the Fibonacci sequence
The Z-densities of the Fibonacci sequence

pdf file
pdf file

Trigonometric sums
Trigonometric sums

A Simple Linear-Space Data Structure for Constant
A Simple Linear-Space Data Structure for Constant

ON THE LARGEST PRIME FACTOR OF NUMERATORS OF
ON THE LARGEST PRIME FACTOR OF NUMERATORS OF

Sample pages 2 PDF
Sample pages 2 PDF

Non-Negative Matrix Factorization Revisited: Uniqueness and
Non-Negative Matrix Factorization Revisited: Uniqueness and

... algorithm for symmetric NMF is proposed, which is very different from existing ones. It alternates between Procrustes rotation and projection onto the non-negative orthant to find a non-negative matrix close to the span of the dominant subspace. Simulation results show promising performance with res ...
On Gromov`s theory of rigid transformation groups: a dual approach
On Gromov`s theory of rigid transformation groups: a dual approach

Unit 1: Extending the Number System
Unit 1: Extending the Number System

Chapter 1 The Fundamental Theorem of Arithmetic
Chapter 1 The Fundamental Theorem of Arithmetic

File
File

Quadrature Rules With an Even Number of Multiple Nodes and a
Quadrature Rules With an Even Number of Multiple Nodes and a

Explain.
Explain.

Degrees of curves in abelian varieties
Degrees of curves in abelian varieties

Chapter 3: Complex Numbers
Chapter 3: Complex Numbers

"The Sieve Re-Imagined: Integer Factorization Methods"
"The Sieve Re-Imagined: Integer Factorization Methods"

A Totient Function Inequality
A Totient Function Inequality

Author`s Version
Author`s Version

Period of the power generator and small values of the Carmichael
Period of the power generator and small values of the Carmichael

ON THE RELATIVE CLASS NUMBER OF SPECIAL CYCLOTOMIC
ON THE RELATIVE CLASS NUMBER OF SPECIAL CYCLOTOMIC

ON THE RELATIVE CLASS NUMBER OF SPECIAL CYCLOTOMIC
ON THE RELATIVE CLASS NUMBER OF SPECIAL CYCLOTOMIC

THE PUK´ANSZKY INVARIANT FOR MASAS IN
THE PUK´ANSZKY INVARIANT FOR MASAS IN

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.