• 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
Full text
Full text

... while determining the units of the quadratic field extension Q( \/5) of the rational field Q. Using an appropriate norm on Q(\/E)9 we also find all solutions to the Diophantine equation x2 - 5y2 = ±4 and solve a certain binomial coefficient equation. Except for the definitions of basic algebraic str ...
1.2 Prime Factorization
1.2 Prime Factorization

Probabilistic Skyline Operator over sliding Windows
Probabilistic Skyline Operator over sliding Windows

... SSKY Techniques presented in Section IV to continuously compute q-skyline (i.e., skyline with the probability not less than a given q) against a sliding window. Naïve approach on basic problem is about 20 times slower than SSKY, so it’s been ruled out ...
The space complexity of approximating the frequency moments Noga Alon Yossi Matias
The space complexity of approximating the frequency moments Noga Alon Yossi Matias

Pre-Algebra Lecture 2. Factors
Pre-Algebra Lecture 2. Factors

Constructible, open, and closed sets
Constructible, open, and closed sets

First-order characterization of function field
First-order characterization of function field

GS-2012 - TIFR GS Admissions
GS-2012 - TIFR GS Admissions

1 Divide and Conquer with Reduce
1 Divide and Conquer with Reduce

GCDs and Relatively Prime Numbers
GCDs and Relatively Prime Numbers

Two new direct linear solvers in the QR family
Two new direct linear solvers in the QR family

Cyclic Groups
Cyclic Groups

A Risk Minimization Framework for Information Retrieval
A Risk Minimization Framework for Information Retrieval

T(n)
T(n)

Chapter 2, Section 2.4
Chapter 2, Section 2.4

Prime Factorization
Prime Factorization

Some Cardinality Questions
Some Cardinality Questions

THE INTEGERS 1. Divisibility and Factorization Without discussing
THE INTEGERS 1. Divisibility and Factorization Without discussing

Dr. Ahmed Hessein Kamel - Abstract
Dr. Ahmed Hessein Kamel - Abstract

Algebra Notes
Algebra Notes

SOME MAXIMAL FUNCTION FIELDS AND ADDITIVE
SOME MAXIMAL FUNCTION FIELDS AND ADDITIVE

... Aut(H/F ) explicitly. Moreover in Theorem 3.17 we give a condition for maximal function fields F of the form (1.1) to be the same (see also Corollary 3.18). This paper is closely connected with [A-G] and [G-K-M] (see Remarks 3.3 and 3.19). The emphases here is on obtaining explicit equations for max ...
Karp Algorithm
Karp Algorithm

Performance analysis and optimization of parallel Best
Performance analysis and optimization of parallel Best

prime factorization - Jefferson School District
prime factorization - Jefferson School District

Irrational Zeros Rational Zero Theorem Synthetic & Long Division
Irrational Zeros Rational Zero Theorem Synthetic & Long Division

... You are often asked to find all the zeros (roots or x-intercepts) of polynomials. To do this in the most efficient way, use the rational zero test.  First, there are some general concepts.  When you FOIL a pair of quadratic binomials with leading coefficients of ...
< 1 ... 108 109 110 111 112 113 114 115 116 ... 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