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*7. Polynomials
*7. Polynomials

POLYNOMIAL RINGS AND UNIQUE FACTORIZATION DOMAINS 1
POLYNOMIAL RINGS AND UNIQUE FACTORIZATION DOMAINS 1

On the Relation between Polynomial Identity Testing and Finding
On the Relation between Polynomial Identity Testing and Finding

... whose indices belong to I. A polynomial f , depending on X, is said to be decomposable if it can be written as f (X) = g(XS ) · h(X[n]\S ) for some ∅ ( S ( [n]. The indecomposable factors of a polynomial f (X) are polynomials f1 (XI1 ), . . . , fk (XIk ) such that the Ij -s are disjoint sets of indi ...
VECTOR SPACES OF LINEARIZATIONS FOR MATRIX
VECTOR SPACES OF LINEARIZATIONS FOR MATRIX

SOME TOPICS IN ALGEBRAIC EQUATIONS Institute of Numerical
SOME TOPICS IN ALGEBRAIC EQUATIONS Institute of Numerical

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Polynomial Factoring Algorithms and their Computational Complexity

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Preliminary version

Lesson 11: The Special Role of Zero in Factoring
Lesson 11: The Special Role of Zero in Factoring

... This lesson focuses on the first part of standard A-APR.B.3, identifying zeros of polynomials presented in factored form. Although the terms root and zero are interchangeable, for consistency only the term zero is used throughout this lesson and in later lessons. The second part of the standard, usi ...
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Determining the Number of Polynomial Integrals

A LOWER BOUND FOR AVERAGE VALUES OF DYNAMICAL
A LOWER BOUND FOR AVERAGE VALUES OF DYNAMICAL

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Precalculus PreAP/D Rev 2017 2.5: Rational Zero Test “I WILL

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Extension of the semidefinite characterization of sum of squares

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Full text

EFFECTIVE RESULTS FOR DISCRIMINANT EQUATIONS OVER
EFFECTIVE RESULTS FOR DISCRIMINANT EQUATIONS OVER

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polynomials - MK Home Tuition

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MATHEMATICS - ALGEBRA GRADES 9

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contributions to the theory of finite fields

Intersection Theory course notes
Intersection Theory course notes

... definition one can consider a generic polynomial xk − t, which has k distinct roots for all t 6= 0. We will now prove the Fundamental Theorem of Algebra in the following form. Theorem 2.1 Any complex polynomial f of degree n has exactly n complex roots counted with multiplicities. Note that this the ...
Aurifeuillian factorizations - American Mathematical Society
Aurifeuillian factorizations - American Mathematical Society

File - North Meck Math III
File - North Meck Math III

lect 15, Factoring - People @ EECS at UC Berkeley
lect 15, Factoring - People @ EECS at UC Berkeley

Section 3-2 Finding Rational Zeros of Polynomials
Section 3-2 Finding Rational Zeros of Polynomials

Lecture 28: Eigenvalues - Harvard Mathematics Department
Lecture 28: Eigenvalues - Harvard Mathematics Department

Invariant Theory of Finite Groups
Invariant Theory of Finite Groups

x - HCC Learning Web
x - HCC Learning Web

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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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