polynomial basis
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Polynomial basis — In mathematics, the polynomial basis is a basis for finite extensions of finite fields.Let α ∈ GF( p m ) be the root of a primitive polynomial of degree m over GF( p ). The polynomial basis of GF( p m ) is then:{ 0, 1, alpha, ldots, alpha^{m… … Wikipedia
Polynomial interpolation — In the mathematical subfield of numerical analysis, polynomial interpolation is the interpolation of a given data set by a polynomial. In other words, given some data points (such as obtained by sampling), the aim is to find a polynomial which… … Wikipedia
Polynomial ring — In mathematics, especially in the field of abstract algebra, a polynomial ring is a ring formed from the set of polynomials in one or more variables with coefficients in another ring. Polynomial rings have influenced much of mathematics, from the … Wikipedia
Polynomial long division — In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division. It can be done easily by hand,… … Wikipedia
polynomial — /pol euh noh mee euhl/, adj. 1. consisting of or characterized by two or more names or terms. n. 2. Algebra. a. (in one variable) an expression consisting of the sum of two or more terms each of which is the product of a constant and a variable… … Universalium
Basis function — In mathematics, particularly numerical analysis, a basis function is an element of the basis for a function space. The term is a degeneration of the term basis vector for a more general vector space; that is, each function in the function space… … Wikipedia
Polynomial — In der Mathematik ist ein Polynom (von griech. πολύ / polý und lat. nomen = „mehrnamig“) eine Summe von Vielfachen von Potenzen mit natürlichzahligen Exponenten einer Variablen, die in den meisten Fällen mit x bezeichnet wird. In der elementaren… … Deutsch Wikipedia
Canonical basis — In mathematics, the notion of canonical basis refers to a basis of an algebraic structure which is canonical in a sense that depends on the precise context:* In a coordinate space, and more generally in a free module, it refers to the standard… … Wikipedia
Primitive polynomial — In field theory, a branch of mathematics, a primitive polynomial is the minimal polynomial of a primitive element of the finite extension field GF( p m ). In other words, a polynomial F(X) with coefficients in GF( p ) = Z/ p Z is a primitive… … Wikipedia
Normal basis — In mathematics, a normal basis in field theory is a special kind of basis for Galois extensions of finite degree, characterised as forming a single orbit for the Galois group. The normal basis theorem states that any finite Galois extension of… … Wikipedia
Dual basis in a field extension — In mathematics, the linear algebra concept of dual basis can be applied in the context of a finite extension L/K, by using the field trace. This requires the property that the field trace TrL/K provides a non degenerate quadratic form over K.… … Wikipedia
