• 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
Slides
Slides

... there  a  cycle  of  cost  ≤  k  that  visits   each  vertex  at  least  once?   •  Hamiltonian  cycle:  Give  graph  G,   is  there  a  cycle  that  visits  each   vertex  exactly  once?   •  Knapsack:  Given  a  set  of  items   ...
Multiplying Polynomials
Multiplying Polynomials

20. Cyclotomic III - Math-UMN
20. Cyclotomic III - Math-UMN

Section 4.3 - math-clix
Section 4.3 - math-clix

Better polynomials for GNFS - Mathematical Sciences Institute, ANU
Better polynomials for GNFS - Mathematical Sciences Institute, ANU

An answer to your question
An answer to your question

PDF
PDF

Problem Set 7
Problem Set 7

... Problem 2: For G = SO(3), identify a maximal torus T , the space G/T , and the Weyl group W . Give an explicit construction of the irreducible representations of G, compute their characters, and use the Weyl integration formula to show that they are orthonormal. Problem 3: For G = SU (3), explicitly ...
rec07
rec07

Math/Stat 2300 Smoothing (4.3): Low
Math/Stat 2300 Smoothing (4.3): Low

Prime Factoriazation
Prime Factoriazation

2.2_1330
2.2_1330

PED-HSM11A2TR-08-1103-005
PED-HSM11A2TR-08-1103-005

PPT
PPT

UNIT-I - WordPress.com
UNIT-I - WordPress.com

PDF
PDF

Lecture
Lecture

Practice
Practice

Here
Here

Pseudocode Structure Diagrams
Pseudocode Structure Diagrams

Mathematics
Mathematics

Fibonacci Numbers and Chebyshev Polynomials Takahiro Yamamoto December 2, 2015
Fibonacci Numbers and Chebyshev Polynomials Takahiro Yamamoto December 2, 2015

... This rather bizarre relation has an elegant proof led by combinatorial models[3]. In the combinatorial model, the Fibonacci number fn+1 counts the ways to fill a 1 × n stripe using 1 × 1 square and 1 × 2 dominos. As it turns out, Chebyshev polynomials counts the same objects as the Fibonacci numbers ...
Lecture Notes 13
Lecture Notes 13

5.4 Quotient Fields
5.4 Quotient Fields

Note Template - Garnet Valley School
Note Template - Garnet Valley School

... End Behavior - _______________________________________________________________ ...
< 1 ... 187 188 189 190 191 192 193 194 195 ... 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