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... Up to now, most of what we have only solved were equations with a degree of 1. 2x + 8 = 4x +6 -2x + 8 = 6 -2x = -2 x=1 ...
x - El Camino College
x - El Camino College

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CSCI 120 Introduction to Computation History of computing (draft)

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Group 1 - Sara, Heather, and Bill Week 11 – Day 1 Title: Prime

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The Fundamental Theorem of Algebra - A History.

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Prune-and-Search

... Since at least half of xi,i+1’s are smaller or greater (depending on xm < x* or x* < xm) than x*, at least one quarter of the points can be removed. 6. Repeat 1 ~ 5 until the number of the remaining points is small enough. 7. Solve the reduced problem directly. ...
Group 1 - Sara, Heather, and Bill Week 11 – Day 1 Title: Prime
Group 1 - Sara, Heather, and Bill Week 11 – Day 1 Title: Prime

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CSCI6268L10

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INTERPOLATING BASIS IN THE SPACE C∞[−1, 1]d 1. Introduction

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Random number theory - Dartmouth Math Home

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How to find zeros of f(x) when it`s in expanded form and factoring

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FACTORING WITH CONTINUED FRACTIONS, THE PELL

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Algorithms Lecture 1 Name:_________________

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... The Euclidean algorithm determines the greatest common divisor of two integers very efficiently. It is based on the following theorem. Theorem 1.8.1 (|a|  |b|) 1. If b = 0, then gcd(a, b) = |a|. 2. If b  0, then gcd(a, b) = gcd(|b|, a mod |b|). Proof. The first assertion is obviously correct. We p ...
Factoring…Taking Polynomials apart
Factoring…Taking Polynomials apart

this PDF file - Illinois Mathematics Teacher
this PDF file - Illinois Mathematics Teacher

< 1 ... 119 120 121 122 123 124 125 126 127 ... 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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