From prime numbers to irreducible multivariate polynomials
From prime numbers to irreducible multivariate polynomials

Ring class groups and ring class fields
Ring class groups and ring class fields

- Triumph Learning
- Triumph Learning

Ring Theory (Math 113), Summer 2014 - Math Berkeley
Ring Theory (Math 113), Summer 2014 - Math Berkeley

Write Numbers Using Prime Factorization
Write Numbers Using Prime Factorization

MATH 3110 Section 4.2
MATH 3110 Section 4.2

An Algorithm For Finding the Optimal Embedding of
An Algorithm For Finding the Optimal Embedding of

2.5 Fundemental Theorem of Algebra and Polynomial Roots
2.5 Fundemental Theorem of Algebra and Polynomial Roots

3-1, 3-2, 3-3, 3-4. 3-1. 1. Let c = ∑ i ai, then ∀n > 0, p(n)
3-1, 3-2, 3-3, 3-4. 3-1. 1. Let c = ∑ i ai, then ∀n > 0, p(n)

The Quadratic Sieve Factoring Algorithm
The Quadratic Sieve Factoring Algorithm

Chapter 4 Number Theory
Chapter 4 Number Theory

Programming and Problem Solving with C++, 2/e
Programming and Problem Solving with C++, 2/e

Robust Ray Intersection with Interval Arithmetic
Robust Ray Intersection with Interval Arithmetic

2.3.3
2.3.3

Unit 11: Factoring
Unit 11: Factoring

Efficient Diffie-Hellman Two Party Key Agreement
Efficient Diffie-Hellman Two Party Key Agreement

Review of Numbers
Review of Numbers

... form. It is easier to work with small numbers rather than large numbers. ...
Kolmogoroff algorithms are stronger than turing machines
Kolmogoroff algorithms are stronger than turing machines

... one edge entering each vertex. We will also assume that each edge of a binary tree is labeled by 0 or 1 (we will call this a labeling of the edges) ...
LINES OF BEST FIT and LINEAR REGRESSION and
LINES OF BEST FIT and LINEAR REGRESSION and

Module 5 - pgcc.edu
Module 5 - pgcc.edu

Lecture 6
Lecture 6

math.uni-bielefeld.de
math.uni-bielefeld.de

Count Bounded Slices
Count Bounded Slices

Quick Review Sheet Math 1314 Symmetry Transformations
Quick Review Sheet Math 1314 Symmetry Transformations

Section 11.6
Section 11.6

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.