A nonhomogeneous orbit closure of a diagonal subgroup
A nonhomogeneous orbit closure of a diagonal subgroup

Section 6 – 3: Combining Like Terms in Polynomials
Section 6 – 3: Combining Like Terms in Polynomials

CENTRAL SEQUENCE ALGEBRAS OF VON NEUMANN
CENTRAL SEQUENCE ALGEBRAS OF VON NEUMANN

Chapter 3_3 Properties of Logarithms _Blitzer
Chapter 3_3 Properties of Logarithms _Blitzer

... reduce arithmetic computations. • Multiplication and division are reduced to simple addition and subtraction. • Exponentiation and root operations are reduced to more simple exponent multiplication or division. • Changing the base of numbers is simplified. • Scientific and graphing calculators provi ...
EXAMPLE SHEET 1 1. If k is a commutative ring, prove that b k
EXAMPLE SHEET 1 1. If k is a commutative ring, prove that b k

GEOMETRY HW 8 1 Compute the cohomology with Z and Z 2
GEOMETRY HW 8 1 Compute the cohomology with Z and Z 2

NUMBER THEORY
NUMBER THEORY

Theorem 1. Every subset of a countable set is countable.
Theorem 1. Every subset of a countable set is countable.

HIGHER EULER CHARACTERISTICS - UMD MATH
HIGHER EULER CHARACTERISTICS - UMD MATH

On finite primary rings and their groups of units
On finite primary rings and their groups of units

DUBLIN CITY UNIVERSITY
DUBLIN CITY UNIVERSITY

Document
Document

Light leaves and Lusztig`s conjecture 1 Introduction
Light leaves and Lusztig`s conjecture 1 Introduction

Finitely generated groups with automatic presentations
Finitely generated groups with automatic presentations

Introduction to Mathematics
Introduction to Mathematics

... Secondly, although the problem made perfect sense on an unpainted chessboard, its solution made use of the usual coloring of the chessboard into black and white squares. This coloring can be thought of as an additional structure imposed on the problem. With this structure in place, we have an easy s ...
Elementary Number Theory
Elementary Number Theory

Basics of associative algebras
Basics of associative algebras

Understanding Cryptography
Understanding Cryptography

NOETHERIANITY OF THE SPACE OF IRREDUCIBLE
NOETHERIANITY OF THE SPACE OF IRREDUCIBLE

Analysis of Algorithms
Analysis of Algorithms

Divisors of terms of recurrence sequences
Divisors of terms of recurrence sequences

LCNT
LCNT

... measure in Lecture 1; the classification of local fields in Lecture 2; Artin Reciprocity and the Existence Theorem from class field theory in Lecture 5; basic facts about algebraic geometry in Lectures 6 and 7; properties of `-adic cohomology in Lecture 8, which is inessential for the rest of the le ...
arXiv:math/0602485v1 [math.NT] 22 Feb 2006
arXiv:math/0602485v1 [math.NT] 22 Feb 2006

1 Vector Spaces
1 Vector Spaces

Practice Midterm Solutions
Practice Midterm Solutions

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.