- field polynomial
- мат. характеристический многочлен
Большой англо-русский и русско-английский словарь. 2001.
field polynomial
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Polynomial arithmetic — includes basic mathematical operations such as addition, subtraction, and multiplication. These operations are defined naturally as if the variable x was an element of S. Division is defined similarly, but requires that S be a field. Examples of… … 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
Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it … Wikipedia
Field extension — In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties. For… … Wikipedia
Polynomial — In mathematics, a polynomial (from Greek poly, many and medieval Latin binomium, binomial [1] [2] [3], the word has been introduced, in Latin, by Franciscus Vieta[4]) is an expression of finite length constructed from variables (also known as… … Wikipedia
Polynomial factorization — In mathematics and computer algebra, polynomial factorization typically refers to factoring a polynomial into irreducible polynomials over a given field. Formulation of the questionOther factorizations, such as square free factorization exist,… … Wikipedia
Field of definition — In mathematics, the field of definition of an algebraic variety V is essentially the smallest field to which the coefficients of the polynomials defining V can belong. Given polynomials, with coefficients in a field K , it may not be obvious… … Wikipedia
Polynomial matrix — Not to be confused with matrix polynomial. A polynomial matrix or sometimes matrix polynomial is a matrix whose elements are univariate or multivariate polynomials. A λ matrix is a matrix whose elements are polynomials in λ. A univariate… … Wikipedia
Polynomial code — In coding theory, a polynomial code is a type of linear code whose set of valid code words consists of those polynomials (usually of some fixed length) that are divisible by a given fixed polynomial (of shorter length, called the generator… … Wikipedia
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 expression — In mathematics, and in particular in the field of algebra, a polynomial expression in one or more given entities E 1, E 2, ..., is any meaningful expression constructed from copies of those entities together with (usually numeric) constants,… … Wikipedia
