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Multiplying Polynomials Using Algebra Tiles
Multiplying Polynomials Using Algebra Tiles

Concrete Algebra - the School of Mathematics, Applied Mathematics
Concrete Algebra - the School of Mathematics, Applied Mathematics

EXAMPLES OF REFINABLE COMPONENTWISE POLYNOMIALS
EXAMPLES OF REFINABLE COMPONENTWISE POLYNOMIALS

Factorization of multivariate polynomials
Factorization of multivariate polynomials

... scope of this thesis, we restrict ourselves to some very basic definitions and facts that are used throughout this text. A short summary of concepts of univariate polynomial rings and finite fields can be found in [Lee09]. For an extensive introduction, we refer the reader to [Bos06] or any other in ...
MA2215: Fields, rings, and modules
MA2215: Fields, rings, and modules

6.6 The Fundamental Theorem of Algebra
6.6 The Fundamental Theorem of Algebra

Math 601 Solutions to Homework 3
Math 601 Solutions to Homework 3

Factoring Polynomials Completely
Factoring Polynomials Completely

Algorithm for computing μ-bases of univariate polynomials
Algorithm for computing μ-bases of univariate polynomials

3-Calabi-Yau Algebras from Steiner Systems
3-Calabi-Yau Algebras from Steiner Systems

... arises naturally in the geometry of Calabi-Yau manifolds and it appears when one tries to do noncommutative geometry. As shown by Ginzburg [Gin06], numerous concrete examples of Calabi-Yau algebras are found “in nature”, and in most cases they arise as a certain quotient of the free associative alge ...
Shiftless Decomposition and Polynomial
Shiftless Decomposition and Polynomial

Hypergeometric Solutions of Linear Recurrences with Polynomial
Hypergeometric Solutions of Linear Recurrences with Polynomial

Factors of disconnected graphs and polynomials with nonnegative
Factors of disconnected graphs and polynomials with nonnegative

Notes in ring theory - University of Leeds
Notes in ring theory - University of Leeds

Abel–Ruffini theorem
Abel–Ruffini theorem

A Pari/GP Tutorial
A Pari/GP Tutorial

From prime numbers to irreducible multivariate polynomials
From prime numbers to irreducible multivariate polynomials

Document
Document

... Henc, Dividend= (divisor)(quotient)+ remainder. The polynomials P(x) and D(x) are called the dividend and divisor, respectively. Q(x) is the quotient and R(x) is the remainder. ...
COMPUTING MINIMAL POLYNOMIALS OF MATRICES
COMPUTING MINIMAL POLYNOMIALS OF MATRICES

Combinatorial Nullstellensatz
Combinatorial Nullstellensatz

Separation of Multilinear Circuit and Formula Size
Separation of Multilinear Circuit and Formula Size

EIGENVALUES OF PARTIALLY PRESCRIBED
EIGENVALUES OF PARTIALLY PRESCRIBED

Subfield-Compatible Polynomials over Finite Fields - Rose
Subfield-Compatible Polynomials over Finite Fields - Rose

Algebraic Geometry
Algebraic Geometry

Chapter 7
Chapter 7

< 1 2 3 4 5 6 7 8 9 10 ... 28 >

Resultant

In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients, which is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (over their field of coefficients). In some older texts, the resultant is also called eliminant.The resultant is widely used in number theory, either directly or through the discriminant, which is essentially the resultant of a polynomial and its derivative. The resultant of two polynomials with rational or polynomial coefficients may be computed efficiently on a computer. It is a basic tool of computer algebra, and is a built-in function of most computer algebra systems. It is used, among others, for cylindrical algebraic decomposition, integration of rational functions and drawing of curves defined by a bivariate polynomial equation.The resultant of n homogeneous polynomials in n variables or multivariate resultant, sometimes called Macaulay's resultant, is a generalization of the usual resultant introduced by Macaulay. It is, with Gröbner bases, one of the main tools of effective elimination theory (elimination theory on computers).
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