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109_lecture4_fall05
109_lecture4_fall05

Document
Document

... 2.2.4 Operation in Zn The three binary operations that we discussed for the set Z can also be defined for the set Zn. The result may need to be mapped to Zn using the mod operator. Figure 2.13 Binary operations in Zn ...
Algebra 2 - CP Algebra 2 Overview
Algebra 2 - CP Algebra 2 Overview

Inference of a Phylogenetic Tree: Hierarchical Clustering
Inference of a Phylogenetic Tree: Hierarchical Clustering

... Glenn Blanchette, Richard O’Keefe, and Lubica Benuskova ...
College algebra
College algebra

Polynomial Maps of Modules
Polynomial Maps of Modules

Coins with arbitrary weights, J. Algorithms 25
Coins with arbitrary weights, J. Algorithms 25

1 Exponents - Faculty Directory | Berkeley-Haas
1 Exponents - Faculty Directory | Berkeley-Haas

Primality - Factorization
Primality - Factorization

6_M2306_Hist_chapter6 - Nipissing University Word
6_M2306_Hist_chapter6 - Nipissing University Word

... except for Fibonacci result (1225): roots of x3+2x2+10x=20 are not any of Euclid’s irrationals • Fibonacci did not prove that these roots are not constructible with ruler and compass (i.e. that it is not possible to obtain roots as expressions built from rational numbers and square roots) • Using fi ...
Iterative Solution of Linear Systems
Iterative Solution of Linear Systems

... (plus some dot products, etc.) • If matrix is nn and has m nonzero entries, each iteration is O(max(m,n)) • Conjugate gradients may need n iterations for ...
Waldspurger formula over function fields
Waldspurger formula over function fields

... where for each i, Ri is the left order of Ii . Hence X is a finite disjoint union of genus 0 curves, and the components correspond canonically to left ideal classes of R. Therefore we may identify Pic(X ) with the free abelian group generated by the double cosets in b n+ ,n− . D × \DA∞,× /R ...
test solutions 2
test solutions 2

Section X.55. Cyclotomic Extensions
Section X.55. Cyclotomic Extensions

Predictive Job Scheduling in a Connection Limited System using
Predictive Job Scheduling in a Connection Limited System using

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A Bus Transfer Optimization Model Based on Genetic Algorithm t

Predictive Job Scheduling in a Connection Limited System using
Predictive Job Scheduling in a Connection Limited System using

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Lecture on Polynomial Functions

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Computing the Greatest Common Divisor

Analysis of the impact of parameters values on the Genetic
Analysis of the impact of parameters values on the Genetic

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Section 6.5 Rings and Fields

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Algebraic Structures

1019_Test 3_nov26_solutions
1019_Test 3_nov26_solutions

... Basis Step: n=1. L.H.S=1 = 1. R.H.S. = ∗ 1 ∗ 4 ∗ 1 − 1 = 1. L.H.S.=R.H.S. The ...
Primal Scream - University of Oklahoma
Primal Scream - University of Oklahoma

... Proposition 1. The good numbers are 11, 17, 23, 27, 29, 35, 37, 41, 47, and 53. For the proof, we need to know the even primal numbers of weight less than 54. Lemma 2. An even primal number of weight less than 54 is either a product of two primes, or is one of 2 · 2 · 2, 2 · 11 · 11, 2 · 13 · 13, or ...
Recent Advances on Determining the Number of Real
Recent Advances on Determining the Number of Real

< 1 ... 110 111 112 113 114 115 116 117 118 ... 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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