• 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
File - North Meck Math III
File - North Meck Math III

Section 3.2
Section 3.2

... locating zeros and local extrema. With calculator graphs we can make excellent approximations for both. On a graph, there is no obvious relation between zeros and turning points, but in calculus we learn that every turning point of a polynomial function f occurs at a zero of another polynomial funct ...
Rationality and the Tangent Function
Rationality and the Tangent Function

... numbers more directly to nth roots of unity. The natural approach to Proposition 2 presented here uses basic field theory [A, H] and likely was known to Kronecker and Sylvester, although the author knows no reference. The cosine result, a common exercise in algebra texts, and the sine result were pr ...
It`s Greek to Me - Education World
It`s Greek to Me - Education World

It`s Greek to Me - TI Education
It`s Greek to Me - TI Education

Lecture Notes for Sections R7 (Castillo
Lecture Notes for Sections R7 (Castillo

Exam 1 – 02/29/12 SOLUTIONS
Exam 1 – 02/29/12 SOLUTIONS

Prior Knowledge Sheet to review over long weekend
Prior Knowledge Sheet to review over long weekend

Genetic Algorithms
Genetic Algorithms

Chapter #6
Chapter #6

Analytical Algebra II Course Proficiencies
Analytical Algebra II Course Proficiencies

SODA07 - Microsoft Research
SODA07 - Microsoft Research

ppt
ppt

... Convergence in energy and displacement u : exact displacement solution to a problem that makes the potential energy of the system a minimum corresponding stress  (u)  (u ) and strain Exact strain energy of the body ...
Primality tests and Fermat factorization
Primality tests and Fermat factorization

WPEssink CARV 2013 V4.2
WPEssink CARV 2013 V4.2

Factoring Polynomials Completely
Factoring Polynomials Completely

chebyshev polynomials and markov-bernstein type
chebyshev polynomials and markov-bernstein type

2 Integral Domains and Fields
2 Integral Domains and Fields

Math 581 Problem Set 6 Solutions
Math 581 Problem Set 6 Solutions

The Search for Aurifeuillian-Like Factorizations
The Search for Aurifeuillian-Like Factorizations

Integers and division
Integers and division

... • Approach 1: if any number x < n divides it. If yes it is a composite. If we test all numbers x < n and do not find the proper divisor then n is a prime. • Approach 2: if any prime number x < n divides it. If yes it is a composite. If we test all primes x < n and do not find a proper divisor then n ...
M211 (ITC450 earlier)
M211 (ITC450 earlier)

THE DIFFERENTIAL CLOSURE OF A
THE DIFFERENTIAL CLOSURE OF A

selected solutions to Homework 11
selected solutions to Homework 11

Higher complexity search problems for bounded arithmetic and a
Higher complexity search problems for bounded arithmetic and a

< 1 ... 94 95 96 97 98 99 100 101 102 ... 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