Solutions - Math Berkeley
Solutions - Math Berkeley

Chapter 1 Numerical Algorithms and Roundoff Errors
Chapter 1 Numerical Algorithms and Roundoff Errors

On the Classification and Algorithmic Analysis of Carmichael Numbers
On the Classification and Algorithmic Analysis of Carmichael Numbers

STRONGLY ZERO-PRODUCT PRESERVING MAPS ON
STRONGLY ZERO-PRODUCT PRESERVING MAPS ON

There are 526915620 nonisomorphic one-factorizations of K12
There are 526915620 nonisomorphic one-factorizations of K12

Document
Document

STRONGLY ZERO-PRODUCT PRESERVING MAPS ON NORMED
STRONGLY ZERO-PRODUCT PRESERVING MAPS ON NORMED

Derived splinters in positive characteristic
Derived splinters in positive characteristic

maximal subspaces of zeros of quadratic forms over finite fields
maximal subspaces of zeros of quadratic forms over finite fields

A polynomial time algorithm for Rayleigh ratio on
A polynomial time algorithm for Rayleigh ratio on

Is na Prime Number? - CSE-IITK
Is na Prime Number? - CSE-IITK

1 (mod n)
1 (mod n)

... Euclidean algorithm(a,b) (for great common divisor) input： a  b  0 output：d  gcd( a, b) (1) Set r0=a and r1=b (2) Determine the first n  0 so that rn+1=0, where ri+1=ri-1 mod ri ...
High Dimensional Similarity Joins: Algorithms and Performance
High Dimensional Similarity Joins: Algorithms and Performance

The Correlation of PLATO® Curricula to Common Core by HS
The Correlation of PLATO® Curricula to Common Core by HS

Solve Simple Linear Equation using Evolutionary Algorithm
Solve Simple Linear Equation using Evolutionary Algorithm

definability of linear equation systems over
definability of linear equation systems over

chapter 2 - Mr.F Teach
chapter 2 - Mr.F Teach

CS 573 Algorithms ¬ Sariel Har-Peled October 16, 2014
CS 573 Algorithms ¬ Sariel Har-Peled October 16, 2014

Guess Paper – 2012 Class – X Subject – Mathematics REAL
Guess Paper – 2012 Class – X Subject – Mathematics REAL

Technology Exercises Critical Thinking Exercises
Technology Exercises Critical Thinking Exercises

Model Theory of Valued fields
Model Theory of Valued fields

... 1 6∈ ML ∩ RK ⊃ MK ). It follows that if UK , UL denote the groups of units of RK , RL respectively then UL ∩ K = UK . Hence we have a canonical embedding K ∗ /UK → L∗ /UL . This gives a valuation on L – the value group is just L∗ /UL . Definition 1.2.2 (i) A valued field (K, v, Γ) is henselian if th ...
, Elementary Number Theory
, Elementary Number Theory

A measure of the local connectivity between graph vertices
A measure of the local connectivity between graph vertices

Contents 1. Recollections 1 2. Integers 1 3. Modular Arithmetic 3 4
Contents 1. Recollections 1 2. Integers 1 3. Modular Arithmetic 3 4

4 Number Theory 1 4.1 Divisors
4 Number Theory 1 4.1 Divisors

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.