doc
doc

Pre-Calculus II
Pre-Calculus II

Outline Fast Multipole Methods CMSC 858M/AMSC 698R Lecture(s) 3(4)
Outline Fast Multipole Methods CMSC 858M/AMSC 698R Lecture(s) 3(4)

... For |y-x*|< r*, the sum of the series is a continuous and infinitely differentiable function of y. ...
Worksheet - West High School
Worksheet - West High School

1 A little probability of error goes a long way
1 A little probability of error goes a long way

MATH 1200 Section B — Prof. Madras Problem for Tutorial and
MATH 1200 Section B — Prof. Madras Problem for Tutorial and

PPT
PPT

MatlabTutorial
MatlabTutorial

1 Introduction
1 Introduction

Galois Field in Cryptography
Galois Field in Cryptography

Section 2.5 The Fundamental Theorem of Algebra Important
Section 2.5 The Fundamental Theorem of Algebra Important

Shiftless Decomposition and Polynomial
Shiftless Decomposition and Polynomial

Fast, Parallel Algorithm for Multiplying Polynomials with Integer
Fast, Parallel Algorithm for Multiplying Polynomials with Integer

Factors oF aLgebraic eXpressions
Factors oF aLgebraic eXpressions

8-2 Adding, Subtracting, and Multiplying Polynomials
8-2 Adding, Subtracting, and Multiplying Polynomials

Unit Overview - The K-12 Curriculum Project
Unit Overview - The K-12 Curriculum Project

296.1 theoretical computer science introduction
296.1 theoretical computer science introduction

Seed and Sieve of Odd Composite Numbers with
Seed and Sieve of Odd Composite Numbers with

Introduction to the course - go here for Roundcubemail
Introduction to the course - go here for Roundcubemail

solving polynomial equations by radicals31
solving polynomial equations by radicals31

Finite Fields
Finite Fields

Polynomial
Polynomial

Notes on Multiplying Polynomials (1)
Notes on Multiplying Polynomials (1)

H2
H2

Assignment 2, 12 Oct 2015, due 20 Oct 2015
Assignment 2, 12 Oct 2015, due 20 Oct 2015

... 1. Let L = (R, F, C) be a finite first-order relational language with F = C = ∅ and let M = (S, ι) be a finite L-structure. Show that there is an L-sentence φM whose models are precisely the L-structures isomorphic to M. 2. (a) Let L = {0, +, ×} where + and × are binary function symbols and 0 is a c ...

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.