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The Rational Zero Test The ultimate objective for this section of the
The Rational Zero Test The ultimate objective for this section of the

Gröbner Bases of Bihomogeneous Ideals Generated - PolSys
Gröbner Bases of Bihomogeneous Ideals Generated - PolSys

POLYNOMIALS IN ASYMPTOTICALLY FREE RANDOM MATRICES
POLYNOMIALS IN ASYMPTOTICALLY FREE RANDOM MATRICES

The ring of evenly weighted points on the projective line
The ring of evenly weighted points on the projective line

Efficient Identity Testing and Polynomial Factorization over Non
Efficient Identity Testing and Polynomial Factorization over Non

... Arvind et al. observed that given a monomial m and a homogeneous non-commutative circuit C, one can compute the formal left and right derivatives of C with respect to m efficiently [AJR15]. We need this result too in our algorithm. To sketch the algorithm, consider an easy case when the given polyno ...
Division rings and their theory of equations.
Division rings and their theory of equations.

CHAP10 Solubility By Radicals
CHAP10 Solubility By Radicals

Solution
Solution

Factorization in Integral Domains II
Factorization in Integral Domains II

Euler and the Fundamental Theorem of Algebra
Euler and the Fundamental Theorem of Algebra

Factoring in Skew-Polynomial Rings over Finite Fields
Factoring in Skew-Polynomial Rings over Finite Fields

KNOT SIGNATURE FUNCTIONS ARE INDEPENDENT 1
KNOT SIGNATURE FUNCTIONS ARE INDEPENDENT 1

roots of unity - Stanford University
roots of unity - Stanford University

Algebra IIA Unit III: Polynomial Functions Lesson 1
Algebra IIA Unit III: Polynomial Functions Lesson 1

Document
Document

4.6: The Fundamental Theorem of Algebra
4.6: The Fundamental Theorem of Algebra

MATH 480
MATH 480

The Power of Depth 2 Circuits over Algebras
The Power of Depth 2 Circuits over Algebras

On the complexity of integer matrix multiplication
On the complexity of integer matrix multiplication

Document
Document

Polynomials
Polynomials

Constructibility of Regular n-Gons
Constructibility of Regular n-Gons

... We now know that a is constructible if and only if there is a tower of fields Q ⊂ K1 ⊂ K2 ⊂ · · · ⊂ Km such that a ∈ Km and the degree of each field extension is 2. Let us formally define degree and relate the degree of the field extension to the nth roots of unity and the polynomial equation xn = 1 ...
Slides (Lecture 5 and 6)
Slides (Lecture 5 and 6)

04 commutative rings I
04 commutative rings I

... Let X be the set of polynomials expressible in the form H − S · M for some polynomial S. Let R = H − Q · M be an element of X of minimal degree. Claim that deg R < deg M . If not, let a be the highest-degree coefficient of R, let b be the highest-degree coefficient of M , and define G = (ab−1 ) · xd ...
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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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