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4.2 Factors and Prime Factorization
4.2 Factors and Prime Factorization

Math 20 Module 4 Review - Westwind Alternate School
Math 20 Module 4 Review - Westwind Alternate School

... y=(x-1)( x2 +x-6) y=(x-1)(x+3)(x-2) Review the remainder theorem This leads us to the Remainder Theorem which states: If a polynomial f(x) is divided by (x − r) and a remainder R is obtained, then f(r) = R. 12) When P(x) = x3 - 3x2 + kx + 2 is divided by x - 2 the remainder is 4. a. Determine the va ...
Algorithms
Algorithms

Carryless Arithmetic Mod 10
Carryless Arithmetic Mod 10

... divisors and least common multiples, and so on. Some seem exotic, while other familiar sequences simply become periodic. For example, the analog of the Fibonacci numbers coincides with the sequence of Fibonacci numbers read mod 10, A003893, which becomes periodic with period 60 (the periodicity of t ...
2. EUCLIDEAN RINGS
2. EUCLIDEAN RINGS

COUNTING PERRON NUMBERS BY ABSOLUTE VALUE 1
COUNTING PERRON NUMBERS BY ABSOLUTE VALUE 1

Here
Here

MULTIPLY POLYNOMIALS
MULTIPLY POLYNOMIALS

A Critical Review of the Notion of the Algorithm in Computer Science
A Critical Review of the Notion of the Algorithm in Computer Science

Lecture 3 — October 16th 3.1 K-means
Lecture 3 — October 16th 3.1 K-means

... 1. Compute the probability of Z given X : pθt (z|x) (Corresponding to qt+1 = arg maxq L(q, θt )) 2. Write the complete likelihood lc = log(pθt (x, z)). 3. E-Step : calculate the expected value of the complete log likelihood function, with respect to the conditional distribution of Z given X under th ...
DO NOW
DO NOW

Notes
Notes

... residual with extra precision. What do we do if we have a factorization with a not-tiny backward error? After checking the residual to see that the error is unacceptably large, we might want a way of fixing the problem. One method for doing this is iterative refinement, which relies on the idea that ...
A Noncommutatlve Marclnkiewlcz Theorem
A Noncommutatlve Marclnkiewlcz Theorem

Math 342 Homework Due Tuesday, April 6 1. Let B be the basis of R
Math 342 Homework Due Tuesday, April 6 1. Let B be the basis of R

Foundations of Cryptography, 23rd of September 2016
Foundations of Cryptography, 23rd of September 2016

Euclid`s Algorithm - faculty.cs.tamu.edu
Euclid`s Algorithm - faculty.cs.tamu.edu

Section 5.2 – Counting Factors, Greatest Common Factor, Least
Section 5.2 – Counting Factors, Greatest Common Factor, Least

slides - CS.Duke
slides - CS.Duke

Document
Document

1 First Theme: Sums of Squares
1 First Theme: Sums of Squares

Solving Sparse Linear Equations Over Finite Fields
Solving Sparse Linear Equations Over Finite Fields

MJ2A - Ch 4.3 Prime Factorization
MJ2A - Ch 4.3 Prime Factorization

do not write on this sheet
do not write on this sheet

Zero Product Principle
Zero Product Principle

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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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