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for Sublinear Time Maximum Inner Product Search (MIPS)
for Sublinear Time Maximum Inner Product Search (MIPS)

Solution
Solution

... In the following, use either a direct proof (by giving values for c and n0 in the definition of big-Oh notation) or cite one of the rules given in the book or in the lecture slides. (a) Show that if f(n) is O(g(n)) and d(n) is O(h(n)), then f(n)+d(n) is O(g(n)+ h(n)). Solution Recall the de_nition o ...
algebra ii final exam review
algebra ii final exam review

Session 4 slides
Session 4 slides

Generalised Integer Programming Based on Logically Defined
Generalised Integer Programming Based on Logically Defined

PDF
PDF

... hypothesis-testing questions [14], [16], [17]. Furthermore, the Rényi entropy and the Rényi entropy rate have revealed several operational characterizations in the problem of fixed-length source coding [7], [6], variable-length source coding [4], [5], [13], [19], error exponent calculations [8], and ...
Keyword Programming in Java
Keyword Programming in Java

Report
Report

Lesson 3
Lesson 3

... When a cubic is divided by a linear expression, the quotient is a quadratic and the remainder, if any, is a constant. Let the quotient by ax² + bx + c Let the remainder be d. 2x³ + 3x² - x + 1 = (x + 2)(ax² + bx + c) + d ...
ML-82 Mini Lecture 12.1 Exponential Functions Learning Objectives
ML-82 Mini Lecture 12.1 Exponential Functions Learning Objectives

slides (PowerPoint)
slides (PowerPoint)

... The two specific forms for the zeta function (infinite series and Euler product) are intrinsically incomplete due to the fact that they are only defined for s > 1. In fact, both the series and product blow up for s  1 . This is a problem, because a central property of the zeta function is its set o ...
Title BP operations and homological properties of
Title BP operations and homological properties of

2.1. Functions on affine varieties. After having defined affine
2.1. Functions on affine varieties. After having defined affine

(pdf)
(pdf)

Notes 1
Notes 1

A Compact Representation for Modular Semilattices and its
A Compact Representation for Modular Semilattices and its

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19 Feb 2010

Chapter 1 Graphs and polynomials
Chapter 1 Graphs and polynomials

Name: Math 2412 Activity 3(Due by Apr. 4) Graph the following
Name: Math 2412 Activity 3(Due by Apr. 4) Graph the following

SOME DISCRETE EXTREME PROBLEMS
SOME DISCRETE EXTREME PROBLEMS

Properties of Logarithms
Properties of Logarithms

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Chapter 4

Lesson 21 - Purdue Math
Lesson 21 - Purdue Math

Solutions
Solutions

The Open World of Super-Recursive Algorithms and
The Open World of Super-Recursive Algorithms and

< 1 ... 18 19 20 21 22 23 24 25 26 ... 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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