• 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 →
 
Sign in Sign up
Upload
Computability of Heyting algebras and Distributive Lattices
Computability of Heyting algebras and Distributive Lattices

Commutative Algebra I
Commutative Algebra I

Number Theory - FIU Faculty Websites
Number Theory - FIU Faculty Websites

Representations of GL_2(A_Q^\infty)
Representations of GL_2(A_Q^\infty)

ON THE DISTRIBUTION OF EXTREME VALUES
ON THE DISTRIBUTION OF EXTREME VALUES

Solutions to Assignment 7 22.3 Let S be the set of all infinite
Solutions to Assignment 7 22.3 Let S be the set of all infinite

Not Always Buried Deep
Not Always Buried Deep

F H preliminaries insert
F H preliminaries insert

... structure, Fibonacci heaps (abbreviated F-heaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. F-heaps support arbitrary deletion from an n-item heap in qlogn) amortized time and all other standard heap operations in o( 1) amortized time. Using F-heaps we are able ...
Chapter 5 Resource Masters
Chapter 5 Resource Masters

A Common Recursion For Laplacians of Matroids and Shifted
A Common Recursion For Laplacians of Matroids and Shifted

... shifted simplicial pair (Theorem 5.7). This naturally generalizes a formula for a single shifted complex [16]; the graph case goes back to Merris [29]. Similarly, we generalize a related conjectured inequality on the Laplacian spectrum of an arbitrary simplicial complex [16] to an arbitrary simplici ...
Elementary Number Theory - science.uu.nl project csg
Elementary Number Theory - science.uu.nl project csg

Running Time of Euclidean Algorithm
Running Time of Euclidean Algorithm

Elementary Number Theory
Elementary Number Theory

Leonard Eugene Dickson and his work in the
Leonard Eugene Dickson and his work in the

Elementary Number Theory
Elementary Number Theory

Fun with Fields by William Andrew Johnson A dissertation submitted
Fun with Fields by William Andrew Johnson A dissertation submitted

Student_Solution_Chap_02
Student_Solution_Chap_02

NORMALITY OF NUMBERS GENERATED BY THE VALUES OF
NORMALITY OF NUMBERS GENERATED BY THE VALUES OF

... is normal in base 10. These examples correspond to the choice f (x) = x in (1.1). Davenport and Erdös [5] considered the case where f (x) is a polynomial whose values at x = 1, 2, . . . are always integers and showed that in this case the numbers θq (f ) and τq (f ) are normal. For f (x) a polynomi ...
0 pts - OpenStudy
0 pts - OpenStudy

Modules and Vector Spaces
Modules and Vector Spaces

Étale Cohomology
Étale Cohomology

160-Lab06BKG - Western Oregon University
160-Lab06BKG - Western Oregon University

Enforcement in Abstract Argumentation via Boolean Optimization
Enforcement in Abstract Argumentation via Boolean Optimization

... are used as practical NP-oracles by calling them several times, refining the solution each time [32, 33, 56]. The computational problems where we perform acceptance queries on a given AF are in this work regarded as static, or non-dynamic, since we assume that the AF does not change in time. However ...
Document
Document

SCENERY RECONSTRUCTION: AN OVERVIEW 1
SCENERY RECONSTRUCTION: AN OVERVIEW 1

... be wrong by Ornstein, who presented an example of a transformation which is K but not Bernoulli. Evidently his transformation was constructed for the particular purpose to resolve Kolmogorov’s conjecture. In 1971, Ornstein, Adler, and Weiss came up with a very natural example which is K but appeared ...
< 1 2 3 4 5 6 ... 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 © 2023
  • DMCA
  • Privacy
  • Terms
  • Report