• 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
PDF
PDF

UNDECIDABILITY OF LINEAR INEQUALITIES IN GRAPH
UNDECIDABILITY OF LINEAR INEQUALITIES IN GRAPH

topological invariants of knots and links
topological invariants of knots and links

Splittings of Bicommutative Hopf algebras - Mathematics
Splittings of Bicommutative Hopf algebras - Mathematics

NOTES ON IDEALS 1. Introduction Let R be a commutative ring. An
NOTES ON IDEALS 1. Introduction Let R be a commutative ring. An

ON THE ERROR TERM OF THE LOGARITHM OF THE LCM OF A
ON THE ERROR TERM OF THE LOGARITHM OF THE LCM OF A

LEC01 - aiub study guide
LEC01 - aiub study guide

Rings with no Maximal Ideals
Rings with no Maximal Ideals

A refinement of the Artin conductor and the base change conductor
A refinement of the Artin conductor and the base change conductor

... then de Shalit’s recipe [CY01, A1.9] shows that c(T ) = cGal (T̂ ), where c(T ) is the classical base change conductor of T , which is defined in terms of algebraic Néron models, and where cGal (T̂ ) is the base change conductor of T̂ , defined Galois-theoretically. It is easily seen that ˆ· induce ...
Belief Propagation in Monoidal Categories
Belief Propagation in Monoidal Categories

Let m be a positive integer. Show that a mod m = b mod m if a ≡ b
Let m be a positive integer. Show that a mod m = b mod m if a ≡ b

SQUare FOrm Factorization - American Mathematical Society
SQUare FOrm Factorization - American Mathematical Society

logarithm - Bansal Classes
logarithm - Bansal Classes

VARIATIONS ON THE BAER–SUZUKI THEOREM 1. Introduction
VARIATIONS ON THE BAER–SUZUKI THEOREM 1. Introduction

Logarithms Tutorial for Chemistry Students 1
Logarithms Tutorial for Chemistry Students 1

... Caution! The most common errors come from students mistakenly using two completely fictitious rules (there are no rules that even resemble these): loga (u + v) 6= loga u + loga v (logarithm of a sum) and logb (u − v) 6= logb u − logb v (logarithm of a difference). The practical implication of these ...
MS133 - Mathematical, Computing, & Information Sciences
MS133 - Mathematical, Computing, & Information Sciences

Isograph: Neighbourhood Graph Construction Based On Geodesic Distance For Semi-Supervised Learning
Isograph: Neighbourhood Graph Construction Based On Geodesic Distance For Semi-Supervised Learning

Precalculus: A Prelude to Calculus 1st Edition Paper
Precalculus: A Prelude to Calculus 1st Edition Paper

41(3)
41(3)

Serial Categories and an Infinite Pure Semisimplicity Conjecture
Serial Categories and an Infinite Pure Semisimplicity Conjecture

6.1. Elliptic Curve Cryptography
6.1. Elliptic Curve Cryptography

14 Primitive roots mod p and Indices
14 Primitive roots mod p and Indices

The class number one problem for
The class number one problem for

Preprint - U.I.U.C. Math
Preprint - U.I.U.C. Math

Chapter 6, Ideals and quotient rings Ideals. Finally we are ready to
Chapter 6, Ideals and quotient rings Ideals. Finally we are ready to

< 1 ... 20 21 22 23 24 25 26 27 28 ... 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