• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
LECTURE 1 INTRODUCTION Origin of word: Algorithm The word
LECTURE 1 INTRODUCTION Origin of word: Algorithm The word

Algorithms and Data Structures
Algorithms and Data Structures

Polynomial and Synthetic Division 2.3
Polynomial and Synthetic Division 2.3

Math 107A Name: Sec # HW #13 December 8, 2010 Score: 1. (a
Math 107A Name: Sec # HW #13 December 8, 2010 Score: 1. (a

on shank`s algorithm for modular square roots
on shank`s algorithm for modular square roots

Determine the number of odd binomial coefficients in the expansion
Determine the number of odd binomial coefficients in the expansion

18.1 Multiplying Polynomial Expressions by Monomials
18.1 Multiplying Polynomial Expressions by Monomials

SECTION 1-2 Polynomials: Basic Operations
SECTION 1-2 Polynomials: Basic Operations

PPT
PPT

... Simulate the mapping xy00...0  xyf (x)00...0, (i.e., clean up the “garbage”) To do this, use an additional register and: 1. compute xy00...000...0  xyf (x)g(x) (ignoring the 2nd register in this step) 2. compute xyf (x)g(x)  xyf (x)f (x)g(x) (using CN ...
Section 1.6 - watertown.k12.wi.us
Section 1.6 - watertown.k12.wi.us

Deployment of Sensing Devices on Critical Infrastructure
Deployment of Sensing Devices on Critical Infrastructure

... Step 4 Compute the product of all the common prime factors and return it as gcd(m,n) ...
Name:
Name:

... Subtract the following polynomials: 2 x 3  6 x 2  11x  16  x 3  2 x 2  4 x  18 Expand each product and simplify the polynomial: a) 2x  8x  7 ...
6-3 Dividing polynomials
6-3 Dividing polynomials

... write down all the coefficients, and put the zero from x+2 = 0 (x = -2) at the left Bring down the first number (1) Multiply (-2) by (1) and put the answer under the (5) Add 5 + (-2) and put the answer under the line Multiply (-2) by (3) and put the answer under the (6) Add (-6) to the (6) and the p ...
THE FUNDAMENTAL THEOREM OF ALGEBRA VIA PROPER
THE FUNDAMENTAL THEOREM OF ALGEBRA VIA PROPER

Learning Algorithms for Solving MDPs References: Barto, Bradtke
Learning Algorithms for Solving MDPs References: Barto, Bradtke

... 2. Asynchronous stochastic approximation: Only update or “back up” some of the components of at time . Let  be an infinite sequence of times at which state  is updated. Then ...
PPT
PPT

AES S-Boxes in depth
AES S-Boxes in depth

... Note that calculating the product of two polynomials and the multiplicative inverse of a polynomial requires both reducing coeficients modulo p and reducing polynomials modulo m(p). The reduced polynomial can be calculated easily with long division while the best way to compute the multiplicative in ...
x 2 + bx + c
x 2 + bx + c

Project 2
Project 2

A Quick Review of MTH070
A Quick Review of MTH070

... • Complete all possible rational arithmetic. ...
Algebra 2 PreAP/GT
Algebra 2 PreAP/GT

... Using synthetic division, the Remainder Theorem, the Factor Theorem along with the fact that we have one real positive root, let’s try our possible rational roots to see if we can find the positive real root. (Note: there is no guarantee that the positive real root is a rational root) In case you do ...
4.1 Polynomial Functions
4.1 Polynomial Functions

1 Lecture 13 Polynomial ideals
1 Lecture 13 Polynomial ideals

Multiply Polynomials * The Area Model
Multiply Polynomials * The Area Model

2 – a
2 – a

< 1 ... 184 185 186 187 188 189 190 191 192 ... 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.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report