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Practice A
Practice A

Hovhannes Khudaverdian's notes
Hovhannes Khudaverdian's notes

... of arithmetical operations ”+”, ”-”, ”×”, ”:” and n-th roots. But what about a given polynomial equation of the order n ≥ 5 Abel Theorem states that roots of the equation x5 + ax4 + bx3 + cx2 + dx + e = 0 cannot be expressed via coefficients a, b, c, d, e, if we use only radicals and arithmetic oper ...
Computational Classification of Numbers and
Computational Classification of Numbers and

Chapter4
Chapter4

... • The Euclidian algorithm is an efficient method for computing the greatest common divisor of two integers. It is based on the idea that gcd(a,b) is equal to gcd(a,c) when a > b and c is the remainder when a is divided by b. Example: Find gcd(91, 287): ...
9 Radical extensions
9 Radical extensions

45 b a b a b a 2 = b a 2b a = 2 2 b c = b corb c = = b a
45 b a b a b a 2 = b a 2b a = 2 2 b c = b corb c = = b a

Multiple-precision zero-finding methods and the complexity of
Multiple-precision zero-finding methods and the complexity of

Kernel Estimation and Model Combination in A Bandit Problem with
Kernel Estimation and Model Combination in A Bandit Problem with

Partial Sums of Powers of Prime Factors
Partial Sums of Powers of Prime Factors

New Generic Hybrids Based Upon Genetic Algorithms Michael Affenzeller
New Generic Hybrids Based Upon Genetic Algorithms Michael Affenzeller

On the Lower Central Series of PI-Algebras
On the Lower Central Series of PI-Algebras

An Elementary Proof of the Prime Number Theorem
An Elementary Proof of the Prime Number Theorem

part 2.2 - UCL Computer Science
part 2.2 - UCL Computer Science

Notes - CMU (ECE)
Notes - CMU (ECE)

Matching in Graphs - Temple University
Matching in Graphs - Temple University

... time. It was developed and published by Harold Kuhn in 1955, who gave the name "Hungarian method" because the algorithm was largely based on the earlier works of two Hungarian mathematicians: Dénes Kőnig and Jenő Egerváry. James Munkres reviewed the algorithm in 1957 and observed that it is (strong ...
decision analysis - CIS @ Temple University
decision analysis - CIS @ Temple University

Matching in Graphs - CIS @ Temple University
Matching in Graphs - CIS @ Temple University

decision analysis - Temple University
decision analysis - Temple University

On the proportion of numbers coprime to a given integer
On the proportion of numbers coprime to a given integer

Data-Oblivious Data Structures
Data-Oblivious Data Structures

... (branching-sensitive) static information flow control [14, 13]. For example, we may specify that (i) a register is tagged as secret when its value is read from a secret memory location or is updated based on another secret register; (ii) a register does not become public again until it is directly o ...
Section 6.4
Section 6.4

Key to Homework 1 August 26, 2005 Math 521 Direction: This
Key to Homework 1 August 26, 2005 Math 521 Direction: This

CHAPTER 3: Cyclic Codes
CHAPTER 3: Cyclic Codes

... IV054 Hamming codes as cyclic codes Definition (Again!) Let r be a positive integer and let H be an r * (2r -1) matrix whose columns are distinct non-zero vectors of V(r,2). Then the code having H as its parity-check matrix is called binary Hamming code denoted by Ham (r,2). It can be shown that: T ...
Efficient and Secure Function Evaluation
Efficient and Secure Function Evaluation

THE INTEGERS
THE INTEGERS

< 1 ... 56 57 58 59 60 61 62 63 64 ... 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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