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Lecture 7 - Ohio University
Lecture 7 - Ohio University

Polynomials
Polynomials

(x) = -2 x 2 +
(x) = -2 x 2 +

... 46. Estimation Estimate the value of P(x) = -2.03x 3 + πx 2 - x + 5.8 for P(-2.78). Tell whether each statement is sometimes, always, or never true. If it is sometimes true, give examples to support your answer. 47. A quadratic polynomial is a trinomial. 48. The degree of a polynomial in standard fo ...
Final Exam conceptual review
Final Exam conceptual review

Numbers and Polynomials (Handout January 20, 2012)
Numbers and Polynomials (Handout January 20, 2012)

6.3 Dividing Polynomials
6.3 Dividing Polynomials

Section 10
Section 10

Dixon`s Factorization method
Dixon`s Factorization method

Chapter 5.2
Chapter 5.2

Multiplying Polynomials
Multiplying Polynomials

Section 2.4 - Shelton State
Section 2.4 - Shelton State

... Dividing Polynomials; The Factor and Remainder Theorems ...
PDF
PDF

Algorithms and Data Structures 1. Give an algorithm to find the
Algorithms and Data Structures 1. Give an algorithm to find the

... 1. Give an algorithm to find the minimum and maximum of a sequence of n numbers using at most d3n/2e − 2 comparisons. 2. Give an algorithm to find the second largest element in a sequence of n numbers using n + o(n) comparisons in the worst case. (Hint: 1. Start with finding the maximum element. 2. ...
Pre-Calculus Honors - Unit 2 Polynomial Functions
Pre-Calculus Honors - Unit 2 Polynomial Functions

Chapter 2 Introduction to Finite Field
Chapter 2 Introduction to Finite Field

... that every polynomial can be written as a polynomial multiple of g plus a residue polynomial of degree less than r. The field Zp [x]/hgi, which is just the residue class polynomial ring Zp [x] (mod g), establishes the existence of a field with exactly pr elements, corresponding to the p possible cho ...
Precal
Precal

Putnam Training Exercise Polynomials (Answers) 1. Find a
Putnam Training Exercise Polynomials (Answers) 1. Find a

chapter1
chapter1

Partial fraction decomposition algorithm
Partial fraction decomposition algorithm

Chapter 5 Review
Chapter 5 Review

ANALYSIS OF ALGORITHMS
ANALYSIS OF ALGORITHMS

Adding and Subtracting Polynomials
Adding and Subtracting Polynomials

Section 5.5
Section 5.5

Fast Fourier Transforms
Fast Fourier Transforms

< 1 ... 219 220 221 222 223 224 225 226 227 ... 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.
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