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Math 249B. Unirationality 1. Introduction This handout aims to prove
Math 249B. Unirationality 1. Introduction This handout aims to prove

Euclid`s Number-Theoretical Work
Euclid`s Number-Theoretical Work

(ID ÈÈ^i+i)f(c)viVi.
(ID ÈÈ^i+i)f(c)viVi.

A Tropical Analog of Descartes` Rule of Signs
A Tropical Analog of Descartes` Rule of Signs

12 Prime ideals
12 Prime ideals

On a limit involving the product of prime numbers 1 Introduction
On a limit involving the product of prime numbers 1 Introduction

the prime number theorem for rankin-selberg l
the prime number theorem for rankin-selberg l

... if π is not equivalent to π 0 . In fact, when π and π 0 are not twisted equivalent, i.e., when π 6 ∼ = π 0 ⊗αit for any t ∈ R, where α(g) = | det(g)|, (2.1) was proved in [15]. In the remaining case when m = m 0 and π ∼ = π 0 ⊗ αiτ0 for some non-zero τ0 ∈ R, (2.1) was established in [16]. It is a fa ...
The Euclidean Algorithm and Its Consequences
The Euclidean Algorithm and Its Consequences

Wave front Method Based Path Planning Algorithm
Wave front Method Based Path Planning Algorithm

cs.bham.ac.uk - Semantic Scholar
cs.bham.ac.uk - Semantic Scholar

x - Cinvestav
x - Cinvestav

... Extended Euclidean Algorithm A constructive version of THM2 which gives s and t will give explicit inverses. This is what the extended Euclidean algorithm does. The extended Euclidean algorithm works the same as the regular Euclidean algorithm except that we keep track of more details –namely the q ...
Exponents, Radicals, and Polynomials
Exponents, Radicals, and Polynomials

Inversion of Extremely Ill-Conditioned Matrices in Floating-Point
Inversion of Extremely Ill-Conditioned Matrices in Floating-Point

Aalborg Universitet Trigonometric quasi-greedy bases for Lp(T;w) Nielsen, Morten
Aalborg Universitet Trigonometric quasi-greedy bases for Lp(T;w) Nielsen, Morten

... enk (t) 1/p w(t) enk (t) k∈N and w(t)1/p k∈N form a bi-orthogonal Schauder basis system in Lp (T) whenever w ∈ Ap (T). 3. Trigonometric quasi-greedy bases for Lp (T; w) Proposition 2.3 tells us that T is a Schauder basis for Lp (T; w) if and only if w ∈ Ap (T). In this section we prove the main resu ...
Open Source Data Mining: Workshop Report
Open Source Data Mining: Workshop Report

Full text
Full text

5-7 Roots and Zeros 12-4
5-7 Roots and Zeros 12-4

Chapter 7
Chapter 7

Complexity of Checking Identities in Monoids of Partial
Complexity of Checking Identities in Monoids of Partial

[hal-00137158, v1] Well known theorems on triangular systems and
[hal-00137158, v1] Well known theorems on triangular systems and

Document
Document

Optimal Penney Ante Strategy via Correlation Polynomial Identities
Optimal Penney Ante Strategy via Correlation Polynomial Identities

Berlekamp, E.R.; (1966)Negacyclic codes for the Lee Metric."
Berlekamp, E.R.; (1966)Negacyclic codes for the Lee Metric."

Document
Document

... the language L is in the class RP . We define ZPP = RP ∩ coRP . Another, maybe more intuitive, way to define randomized classes is to consider randomized Turing machines. A randomized TM is essentially a nondeterministic TM; we define a probability measure on the set of possible computation paths su ...
Rank conjecture revisited
Rank conjecture revisited

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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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