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Section 2.5 Zeros of Polynomial Functions
Section 2.5 Zeros of Polynomial Functions

PDF
PDF

Typed - CEMC
Typed - CEMC

Lecture 3.4
Lecture 3.4

12. Polynomials over UFDs
12. Polynomials over UFDs

A fast algorithm for approximate polynomial gcd based on structured
A fast algorithm for approximate polynomial gcd based on structured

Hilbert`s Nullstellensatz and the Beginning of Algebraic Geometry
Hilbert`s Nullstellensatz and the Beginning of Algebraic Geometry

... n = 1 is easy, because for single variable polynomial rings k[X], one can divide one polynoinial f by another polynomial 9 of degree deg 9 = d and get a remainder T such that either T = 0 or deg T < d. The proof given in (ii) of example 2.3 above to show that all ideals in Z are principal (singly ge ...
Lecture Thursday
Lecture Thursday

Universal Identities I
Universal Identities I

... for indeterminates A, B, C, A0 , B 0 , and C 0 and f, g, and h in Z[A, B, C, A0 , B 0 , C 0 ]. Notice (2.1) implies a similar formula for sums of three squares in any commutative ring by specializing the 6 indeterminates to any 6 elements of any commutative ring. So (2.1) implies that sums of three ...
20. Cyclotomic III - Math-UMN
20. Cyclotomic III - Math-UMN

Section X.56. Insolvability of the Quintic
Section X.56. Insolvability of the Quintic

Chapter 1 PLANE CURVES
Chapter 1 PLANE CURVES

Rings of constants of the form k[f]
Rings of constants of the form k[f]

ON THE EXPECTED NUMBER OF ZEROS OF A RANDOM
ON THE EXPECTED NUMBER OF ZEROS OF A RANDOM

Institutionen för matematik, KTH.
Institutionen för matematik, KTH.

Applications of Logic to Field Theory
Applications of Logic to Field Theory

... algebraically closed fields of characteristic zero and cardinality κ are isomorphic. Similarly, for each prime p, ACF ∪ {ψp } is uncountably categorical. Thus, for example, C is the unique (up to isomorphism) algebraically closed field of characteristic zero having cardinality 2ℵ0 . To see that ACF ...
Inversion Modulo Zero-dimensional Regular Chains
Inversion Modulo Zero-dimensional Regular Chains

... invertible, and if so, compute its inverse. We are also interested the generalization to matrices over RT : given a (d × d) matrix A ∈ Md (RT ), decide whether it is invertible, and if so, compute its inverse. We simply call this the problem of invertibility test / inversion in RT (or in Md (RT )). ...
math 1314 noes 3.3 and 3.4
math 1314 noes 3.3 and 3.4

The Wavelet Transform
The Wavelet Transform

On derivatives of polynomials over finite fields through integration
On derivatives of polynomials over finite fields through integration

Nemo/Hecke: Computer Algebra and Number
Nemo/Hecke: Computer Algebra and Number

William Stallings, Cryptography and Network Security 3/e
William Stallings, Cryptography and Network Security 3/e

Multilinear spectral theory
Multilinear spectral theory

Algebra Expressions and Real Numbers
Algebra Expressions and Real Numbers

... 3) Use a graphing utility to find the first real zero of the function. Confirm using synthetic division. 4) Find all remaining zeros of the function. ...
Algebra Workshop 1: Simple manipulation of expressions
Algebra Workshop 1: Simple manipulation of expressions

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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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