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Smoothness of Schubert varieties via patterns in root subsystems
Smoothness of Schubert varieties via patterns in root subsystems

Dedekind Domains
Dedekind Domains

ON THE ERROR TERM OF THE LOGARITHM OF THE LCM OF A
ON THE ERROR TERM OF THE LOGARITHM OF THE LCM OF A

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Chapter 4 Practice

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Lecture 5 Message Authentication and Hash Functions

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Information Protection Based on Extraction of Square Roots of

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TRILINEAR FORMS AND TRIPLE PRODUCT EPSILON FACTORS 1

On the number of prime factors of a finite arithmetical progression
On the number of prime factors of a finite arithmetical progression

A Concentration Inequalities B Benchmark C
A Concentration Inequalities B Benchmark C

Triangularizability of Polynomially Compact Operators
Triangularizability of Polynomially Compact Operators

Sharp estimation of the almost-sure Lyapunov exponent for the
Sharp estimation of the almost-sure Lyapunov exponent for the

Availability-aware Mapping of Service Function Chains
Availability-aware Mapping of Service Function Chains

... Ksγi dγi . The primary VNFs of the request are mapped to the sites along the selected path while balancing load across all these sites, subject to the delay, site capacity, link capacity and function constraints. Note that without the function constraint, our algorithm can still work. Backup mapping ...
The Chinese Remainder Theorem
The Chinese Remainder Theorem

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Basic Number Theory

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Math 676. Some basics concerning absolute values A remarkable

Explicit estimates for the distribution of numbers free of large prime
Explicit estimates for the distribution of numbers free of large prime

Here - Math-Boise State
Here - Math-Boise State

... that any nonempty set of whole numbers has a minimal element. Theorem (division algorithm): For any integer a and positive integer b, there are unique integers q and r such that a = bq + r and 0 ≤ r < b. Definition: For a given integer a and positive integer b, we define a div b as q and a mod b as ...
On integers n for which X n – 1 has divisors of every degree
On integers n for which X n – 1 has divisors of every degree

... a given squarefull part. For example, 4 is the only starter for 4. Similarly, there are only three starters for 49: 294 = 2 · 3 · 72 , 1470 = 2 · 3 · 5 · 72 , and 735 = 3 · 5 · 72 . For other squarefull numbers, examining the corresponding set of starters becomes much more complicated. For example, ...
VISIBLE EVIDENCE FOR THE BIRCH AND SWINNERTON
VISIBLE EVIDENCE FOR THE BIRCH AND SWINNERTON

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INTEGRAL DOMAINS OF FINITE t-CHARACTER Introduction An

Likelihood inference for generalized Pareto distribution
Likelihood inference for generalized Pareto distribution

and two-dimensional arrays
and two-dimensional arrays

... from an Input File • The reading of a series of values from a file into an array can be represented by a simple DOWHILE loop • In the pseudocode algorithm illustrated on page 92 of the textbook, values are read from an input file and assigned to the elements of an array, starting with the first elem ...
The Summation Package Sigma: Underlying Principles - RISC-Linz
The Summation Package Sigma: Underlying Principles - RISC-Linz

... is also a solution of this combined recurrence. The fact that both sides of the equation (3) agree with the first 10 initial values finally shows the correctness of (3). However, at that time we were not able to find the explicit evaluations (1) and (2). This has been changed partially in [Sch00], w ...
booklet of abstracts - DU Department of Computer Science Home
booklet of abstracts - DU Department of Computer Science Home

... Starting with Euler, the existence of sets of mutually orthogonal latin squares has been a fascinating study with connections to algebra, finite geometry, combinatorial designs, number theory, and applications in communications, statistical design, networking, coding theory, and computation. Still t ...
on the structure and ideal theory of complete local rings
on the structure and ideal theory of complete local rings

< 1 ... 12 13 14 15 16 17 18 19 20 ... 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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