field theory, a branch of mathematics, the minimal polynomial of an element α of an extension field of a field is, roughly speaking, the polynomial of...

Minimal polynomial can mean: Minimal polynomial (field theory) Minimal polynomial (linear algebra) This disambiguation page lists mathematics articles...

In finite field theory, a branch of mathematics, a primitive polynomial is the minimal polynomial of a primitive element of the finite field GF(pm). This...

Minimum polynomial can refer to: Minimal polynomial (field theory) Minimal polynomial (linear algebra) This disambiguation page lists articles associated...

particular field theory, the conjugate elements or algebraic conjugates of an algebraic element α, over a field extension L/K, are the roots of the minimal polynomial...

minimal polynomial μA of an n × n matrix A over a field F is the monic polynomial P over F of least degree such that P(A) = 0. Any other polynomial Q...

complex numbers. Field extensions are fundamental in algebraic number theory, and in the study of polynomial roots through Galois theory, and are widely...

mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates...

deterministic polynomial-time algorithm exists belong to the complexity class P, which is central in the field of computational complexity theory. Cobham's...

characteristic polynomial to zero. In spectral graph theory, the characteristic polynomial of a graph is the characteristic polynomial of its adjacency...

be convenient for Galois theory, is no longer in use. Separable polynomials are used to define separable extensions: A field extension K ⊂ L is a separable...

derivative of polynomials forms a differential field. These fields are central to differential Galois theory, a variant of Galois theory dealing with linear...

place of polynomials.) In the case of RCF, the definable sets are the semialgebraic sets. Thus the study of o-minimal structures and theories generalises...

the minimal polynomial of every element of E over F is a separable polynomial, that is, has distinct roots. Galois extension A normal, separable field extension...

In mathematics, a field F is algebraically closed if every non-constant polynomial in F[x] (the univariate polynomial ring with coefficients in F) has...

In mathematics, exponential polynomials are functions on fields, rings, or abelian groups that take the form of polynomials in a variable and an exponential...

any intermediate field between L {\displaystyle L} and K {\displaystyle K} , and let g {\displaystyle g} be the minimal polynomial of α {\displaystyle...

polynomial may refer to: Primitive polynomial (field theory), a minimal polynomial of an extension of finite fields Primitive polynomial (ring theory)...

of GF(7). The minimal polynomial of a primitive element is a primitive polynomial. The number of primitive elements in a finite field GF(q) is φ(q −...

integers Zp are the ring of integers of the p-adic numbers Qp . Minimal polynomial (field theory) Integral closure – gives a technique for computing integral...

F} by adjoining a single element whose minimal polynomial is separable. To use a piece of jargon, finite fields are perfect. A more general algebraic structure...

Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation with...

indeterminates, the generic polynomial of degree two in x is a x 2 + b x + c . {\displaystyle ax^{2}+bx+c.} However in Galois theory, a branch of algebra, and...

generating set of an ideal in a polynomial ring K [ x 1 , … , x n ] {\displaystyle K[x_{1},\ldots ,x_{n}]} over a field K {\displaystyle K} . A Gröbner...

In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the...

, the minimal polynomial of α {\displaystyle \alpha } over F is a separable polynomial (i.e., its formal derivative is not the zero polynomial, or equivalently...

may also be defined as the monic polynomial with integer coefficients that is the minimal polynomial over the field of the rational numbers of any primitive...

"extremal" polynomials for many other properties. In 1952, Cornelius Lanczos showed that the Chebyshev polynomials are important in approximation theory for...

ordered field such that, in this ordering, the intermediate value theorem holds for all polynomials over F with degree ≥ 0. F is a weakly o-minimal ordered...

extensions and their relationship to the polynomials that give rise to them via Galois groups is called Galois theory, so named in honor of Évariste Galois...