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Gap Inequalities for the Max-Cut Problem: a
Gap Inequalities for the Max-Cut Problem: a

Cryptography and Number Theory
Cryptography and Number Theory

NSE CHARACTERIZATION OF THE SIMPLE GROUP L2(3n) Hosein
NSE CHARACTERIZATION OF THE SIMPLE GROUP L2(3n) Hosein

P - CSUN.edu
P - CSUN.edu

On the Equivalence of Certain Consequences of the Proper Forcing
On the Equivalence of Certain Consequences of the Proper Forcing

... We will denote by TOP(col) a statement of TOP, with the additional assumption that A = B = co,; that is, the following axiom: 2.4. TOP(col). Suppose (T, : a C co,) is such that T, C a for all a. Suppose also that for any uncountable X C co, there exists P3< col, such that {X} U {T, : a > fl} has the ...
Advanced NUMBERTHEORY
Advanced NUMBERTHEORY

... The present text constitutes slightly more than enough for a secondsemester course, carrying the student on to the twentieth Century by motivating some heroic nineteenth-Century developments in algebra and analysis. The relation of this textbook to the great treatises Will necessarily be like that o ...
Math 301, Linear Congruences Linear
Math 301, Linear Congruences Linear

Essential dimension and algebraic stacks
Essential dimension and algebraic stacks

A Bousfield-Kan algorithm for computing homotopy
A Bousfield-Kan algorithm for computing homotopy

Ordered and Unordered Factorizations of Integers
Ordered and Unordered Factorizations of Integers

On the existence of equiangular tight frames
On the existence of equiangular tight frames

... There are two families of ETFs that arise for every dimension d and one family in dimension one with arbitrary number of vectors. (1) (Orthonormal Bases). When N = d, the sole examples of ETFs are unitary (and orthogonal) matrices. Evidently, the absolute inner product α between distinct vectors is ...
section 3.3
section 3.3

The Knot Quandle
The Knot Quandle

MathTools v2.4.3
MathTools v2.4.3

higher algebra
higher algebra

Higher regulators and values of L
Higher regulators and values of L

... 1.6. ~ -Cohomologies of Algebraic Manifolds. We denote by H c H the complete subcategory consisting of those pairs (V, V) for which ~ is a (smooth) projective algebraic variety. Let ~ R or simply ~7~be the category of smooth quasiprojective schemes over R. According to GAGA, we have the functor g:~- ...
7-6 Properties of Logarithms
7-6 Properties of Logarithms

Elliptic Curves - Department of Mathematics
Elliptic Curves - Department of Mathematics

... that the discrete logarithm problem in E1 (Fq ) is equivalent to the discrete logarithm problem in E2 (Fq ). In other words, the discrete logarithm problem on Fq -isomorphic curves has exactly the same security. To reduce storage in some applications it might be desirable to choose a model for ellip ...
Notes for Number Theory
Notes for Number Theory

Coping with friction for non-penetrating rigid body simulation
Coping with friction for non-penetrating rigid body simulation

Chapter 4 The Group Zoo
Chapter 4 The Group Zoo

Smooth numbers: computational number theory and beyond
Smooth numbers: computational number theory and beyond

L. ALAOGLU AND P. ERDŐS Reprinted from the Vol. 56, No. 3, pp
L. ALAOGLU AND P. ERDŐS Reprinted from the Vol. 56, No. 3, pp

Class Field Theory
Class Field Theory

Publikationen - Mathematisches Institut
Publikationen - Mathematisches Institut

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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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