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...

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

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...

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...

linear algebra, the minimal polynomial μA of an n × n {\displaystyle n\times n} matrix A over a field F is the monic polynomial P over F of least degree...

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...

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

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

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 number theory, the real parts of the roots of unity are related to one-another by means of the minimal polynomial of 2 cos ⁡ ( 2 π / n ) . {\displaystyle...

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...

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

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

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...

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...

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 −...

the p-adic numbers Q p {\displaystyle \mathbb {Q} _{p}} . Minimal polynomial (field theory) Integral closure – gives a technique for computing integral...

automata? Determine whether the length of the minimal uncompletable word of M {\displaystyle M} is polynomial in l ( M ) {\displaystyle l(M)} , or even in...

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...

In mathematics, the Conway polynomial Cp,n for the finite field Fpn is a particular irreducible polynomial of degree n over Fp that can be used to define...

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

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...

mathematics, a field F is algebraically closed if every non-constant polynomial with coefficients in F has a root in F. In other words, a field is algebraically...

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...

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

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

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

polynomials over a field the polynomial GCD may be computed, like for the integer GCD, by the Euclidean algorithm using long division. The polynomial...

, 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...