# algebraic numbers

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algebraic numbers
numbers used in algebraic equations (Mathematics)

English contemporary dictionary. 2014.

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• Algebraic number — In mathematics, an algebraic number is a complex number that is a root of a non zero polynomial in one variable with rational (or equivalently, integer) coefficients. Complex numbers such as pi that are not algebraic are said to be transcendental …   Wikipedia

• Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …   Wikipedia

• Algebraic closure — In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics.Using Zorn s lemma, it can be shown that every field has an… …   Wikipedia

• algebraic number — Math. 1. a root of an algebraic equation with integral coefficients. 2. root1 (def. 10b). [1930 35] * * *       real number for which there exists a polynomial equation with integer coefficients such that the given real number is a solution.… …   Universalium

• algebraic number theory — noun The subfield of number theory where algebraic numbers are studied using algebra …   Wiktionary

• Algebraic-group factorisation algorithm — Algebraic group factorisation algorithms are algorithms for factoring an integer N by working in an algebraic group defined modulo N whose group structure is the direct sum of the reduced groups obtained by performing the equations defining the… …   Wikipedia

• Algebraic topology — is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism. In many situations this is too much to hope for… …   Wikipedia

• Algebraic statistics — is a fairly recent field of statistics which utilizes the tools of algebraic geometry and commutative algebra in order to study problems related to discrete random variables with finite state spaces. Such problems include parameter estimation,… …   Wikipedia

• Algebraic — Al ge*bra ic, Algebraical Al ge*bra ic*al, a. 1. Of or pertaining to algebra; using algebra; according to the laws of algebra; containing an operation of algebra, or deduced from such operation; as, algebraic characters; algebraical writings;… …   The Collaborative International Dictionary of English

• Algebraic curve — Algebraic Al ge*bra ic, Algebraical Al ge*bra ic*al, a. 1. Of or pertaining to algebra; using algebra; according to the laws of algebra; containing an operation of algebra, or deduced from such operation; as, algebraic characters; algebraical… …   The Collaborative International Dictionary of English