A Market-Based Study of Optimal ATM`S Deployment Strategy
A Market-Based Study of Optimal ATM`S Deployment Strategy

... The problem of ATM deployment is seen to be NP-complete problem (it is analogous to the file server placement problem) [3]. In order to solve this problem, three algorithms are designed and compared namely; Heuristic Approach using Convolution (HAC) [4], Rank Based Genetic Algorithm using Convolutio ...
Elements of Coding Theory
Elements of Coding Theory

... of the matrix H. But by the construction of H, this is impossible. Assume wt(y) = 1 ⇒ some row hi has all zeros. Again, impossible by construction. Thus wt(y) is at least 3 and we are done. • From the properties of the matrix used above, we see that we may generalize the H matrix for codes of block ...
LINEAR DEPENDENCE OF POWERS OF LINEAR FORMS Andrzej
LINEAR DEPENDENCE OF POWERS OF LINEAR FORMS Andrzej

THEOREM 1.1. Let G be a finite sovable group. Let two subgroups U
THEOREM 1.1. Let G be a finite sovable group. Let two subgroups U

Combinatorial Enumeration of Partitions of a Convex Polygon
Combinatorial Enumeration of Partitions of a Convex Polygon

§ 4-2 Prime and Composite Numbers
§ 4-2 Prime and Composite Numbers

Chapter 1 Introduction to prime number theory
Chapter 1 Introduction to prime number theory

Lecture notes on Witt vectors
Lecture notes on Witt vectors

An Improved BKW Algorithm for LWE with Applications to
An Improved BKW Algorithm for LWE with Applications to

Eigenvectors and Eigenvalues
Eigenvectors and Eigenvalues

MATHEMATICAL REMINISCENCES: HOW TO KEEP THE POT BOILING
MATHEMATICAL REMINISCENCES: HOW TO KEEP THE POT BOILING

... Schneider proved that as a vector space over rationals dim(Va ∩Vb ) ≤ 2 (rediscovery by S. Lang and myself independently of each other). Using this it was possible to deduce as a corollary ([4]) the following. Let t be any fixed transcendental number. Consider the number f (N ) of algebraic numbers ...
Prime Numbers in Quadratic Fields
Prime Numbers in Quadratic Fields

A79 INTEGERS 13 (2013) - RIMS, Kyoto University
A79 INTEGERS 13 (2013) - RIMS, Kyoto University

Galois Theory and elementary mathematics II.
Galois Theory and elementary mathematics II.

Unit E “Exponential and Logarithmic Functions”
Unit E “Exponential and Logarithmic Functions”

... 54. Nancy wants to invest $4000 in saving certificates that bear an interest rate of 9.75% per year, compounded semiannually. How long a period of time should she choose in order to save a minimum of $5000? ...
Isotriviality and the Space of Morphisms on Projective Varieties
Isotriviality and the Space of Morphisms on Projective Varieties

Licensed to: iChapters User
Licensed to: iChapters User

Chapter 4.7 & 4.8 - Help-A-Bull
Chapter 4.7 & 4.8 - Help-A-Bull

Let T be a locally finite rooted tree and G < Iso(T) be a
Let T be a locally finite rooted tree and G < Iso(T) be a

Finite flat group schemes course
Finite flat group schemes course

Solutions - Math Berkeley
Solutions - Math Berkeley

HYPERELLIPTIC JACOBIANS AND SIMPLE GROUPS U3 1
HYPERELLIPTIC JACOBIANS AND SIMPLE GROUPS U3 1

COMPETITION CELL
COMPETITION CELL

Ideals
Ideals

solution guide - Harvard Math Department
solution guide - Harvard Math Department

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.