• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
1 The convolution inverse of an arithmetic function
1 The convolution inverse of an arithmetic function

Powers of Two as Sums of Two Lucas Numbers
Powers of Two as Sums of Two Lucas Numbers

Direct-sum decompositions over one-dimensional Cohen-Macaulay rings
Direct-sum decompositions over one-dimensional Cohen-Macaulay rings

CLASS NOTES ON LINEAR ALGEBRA 1. Matrices Suppose that F is
CLASS NOTES ON LINEAR ALGEBRA 1. Matrices Suppose that F is

Chapter 3 3 Introduction
Chapter 3 3 Introduction

Mixed Tate motives over Z
Mixed Tate motives over Z

... of even Tate twists (since multiple zeta values are real numbers, we need not consider odd Tate twists). In keeping with the usual terminology for multiple zeta values, we refer to the grading on HMT+ as the weight, which is one half the motivic weight. After making some choices, the motivic multipl ...
Algebra I: Section 6. The structure of groups. 6.1 Direct products of
Algebra I: Section 6. The structure of groups. 6.1 Direct products of

Math Fundamentals for Statistics I (Math 52) Unit 4: Multiplication
Math Fundamentals for Statistics I (Math 52) Unit 4: Multiplication

6. Divisors Definition 6.1. We say that a scheme X is regular in
6. Divisors Definition 6.1. We say that a scheme X is regular in

7. Divisors Definition 7.1. We say that a scheme X is regular in
7. Divisors Definition 7.1. We say that a scheme X is regular in

on the structure of algebraic algebras and related rings
on the structure of algebraic algebras and related rings

Chapter 11 Power Point
Chapter 11 Power Point

Introductory Number Theory
Introductory Number Theory

UNSOLVED PROBLEMS SOME UNSOLVED PROBLEMS by In this
UNSOLVED PROBLEMS SOME UNSOLVED PROBLEMS by In this

local version - University of Arizona Math
local version - University of Arizona Math

... choose a decomposition group Dv ⊂ G and we let Iv and F rv be the corresponding inertia group and geometric Frobenius class. We write deg v for the degree of v and qv = q deg v for the cardinality of the residue field at v. For positive integers n we write Fqn for the subfield of F of cardinality q ...
CSCI 2610 - Discrete Mathematics
CSCI 2610 - Discrete Mathematics

Keyword programming in Java
Keyword programming in Java

A syntactic congruence for languages of birooted trees
A syntactic congruence for languages of birooted trees

... Otherwise, the disjoint product is left undefined. We shall write ∃x ∗ y to denote both the existence of such a partial product and its value. It is straightforward to check that the disjoint product is associative in the following sense: the disjoint product x ∗ (y ∗ z) is defined if, and only if, ...
7-1 - Garnet Valley
7-1 - Garnet Valley

Polynomial Bridgeland stability conditions and the large volume limit
Polynomial Bridgeland stability conditions and the large volume limit

MULTIPLICATIVE GROUPS IN Zm 1. Abstract Our goal will be to find
MULTIPLICATIVE GROUPS IN Zm 1. Abstract Our goal will be to find

Basic Maths
Basic Maths

topics in discrete mathematics - HMC Math
topics in discrete mathematics - HMC Math

A Book of Abstract Algebra
A Book of Abstract Algebra

Computer Mathematics using Pascal, 2nd Edition
Computer Mathematics using Pascal, 2nd Edition

< 1 ... 17 18 19 20 21 22 23 24 25 ... 231 >

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.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report