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GROUP ACTIONS 1. Introduction The symmetric groups S , alternating groups A
GROUP ACTIONS 1. Introduction The symmetric groups S , alternating groups A

1. Group actions and other topics in group theory
1. Group actions and other topics in group theory

An algorithm for computing the Seifert matrix of a link from a braid
An algorithm for computing the Seifert matrix of a link from a braid

Finite Fields
Finite Fields

Properties of Laws and Logarithms
Properties of Laws and Logarithms

Sample pages 2 PDF
Sample pages 2 PDF

CHAP02 Linear Congruences
CHAP02 Linear Congruences

File
File

Parallel implementation of the Sieve of Eratosthenes
Parallel implementation of the Sieve of Eratosthenes

Can there be efficient and natural FHE schemes?
Can there be efficient and natural FHE schemes?

... this kind of scheme is impossible for some of the structures we study. In this part of the work we do not assume a public encryption key, only that the adversary can perform evaluation of ciphertexts. Furthermore, we extend the characterisation of Armknecht et al. [4] to handle all public key FHE sc ...
Find the inverse of the function f(x)=3x-5.
Find the inverse of the function f(x)=3x-5.

Symbolic Analysis of Large Analog Integrated Circuits
Symbolic Analysis of Large Analog Integrated Circuits

An iterative solution to coupled quaternion matrix equations - PMF-a
An iterative solution to coupled quaternion matrix equations - PMF-a

pdf
pdf

Slides Week 5 Modular Arithmetic
Slides Week 5 Modular Arithmetic

... that the numbers you are working with will be kept relatively small. At each stage of an algorithm, the mod function should be applied. Thus to multiply 39 * 15 mod 11 we first take mods to get 39 mod 11 = 6 and 15 mod 11= 4 The multiplication required is now 6*4 mod 11 = 24 mod 11 = 2 ...
A non-archimedean Ax-Lindemann theorem - IMJ-PRG
A non-archimedean Ax-Lindemann theorem - IMJ-PRG

Basic Concepts of Discrete Probability
Basic Concepts of Discrete Probability

Factors and Products
Factors and Products

IMAGE_EUV_&_RPI_Derived_Distributions_of_Plasmaspheric
IMAGE_EUV_&_RPI_Derived_Distributions_of_Plasmaspheric

... • 300 solutions (density at 18 grid locations along x-axis) were randomly generated. • The solutions were transferred and compared to the LOS integration. • The top 50 solutions were used as “parents” to generate a new set of 300 solutions. The parents for each solution were randomly chosen with “be ...
Dynamics of non-archimedean Polish groups - Mathematics
Dynamics of non-archimedean Polish groups - Mathematics

... (ii) Even if M (G) is not trivial, when can one explicitly determine M (G) and show that it is metrizable? These problems have been extensively studied in the last thirty years or so. Let us first give the following definition. Definition 4.2. A topological group G is called extremely amenable if it ...
Math 373-578 Exam 3 - WVU Math Department
Math 373-578 Exam 3 - WVU Math Department

If bases are not equal, then
If bases are not equal, then

... Since all one – to – one functions have inverse functions, the exponential function, f ( x)  a x , a > 0, a ≠ 1, has an inverse. The inverse of the exponential function is called the logarithmic function. The logarithmic function, y  log a x , is read “y is the logarithm of x to the base of a”, a ...
17 Greatest Common Factors and Least Com
17 Greatest Common Factors and Least Com

Automatic Structures: Richness and Limitations
Automatic Structures: Richness and Limitations

topological invariants of knots and links
topological invariants of knots and links

< 1 ... 19 20 21 22 23 24 25 26 27 ... 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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