翻訳と辞書 Words near each other ・ Algebraic ・ Algebraic & Geometric Topology ・ Algebraic analysis ・ Algebraic character ・ Algebraic closure ・ Algebraic cobordism ・ Algebraic code-excited linear prediction ・ Algebraic combinatorics ・ Algebraic connectivity ・ Algebraic curve ・ Algebraic cycle ・ Algebraic data type ・ Algebraic definition ・ Algebraic differential equation ・ Algebraic differential geometry ・ Algebraic element ・ Algebraic enumeration ・ Algebraic equation ・ Algebraic Eraser ・ Algebraic expression ・ Algebraic extension ・ Algebraic formula for the variance ・ Algebraic fraction ・ Algebraic function ・ Algebraic function field ・ Algebraic geometry ・ Algebraic Geometry (book) ・ Algebraic geometry and analytic geometry ・ Algebraic geometry of projective spaces ・ Algebraic graph theory Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Algebraic element ： ウィキペディア英語版 Algebraic element In mathematics, if ''L'' is a field extension of ''K'', then an element ''a'' of ''L'' is called an algebraic element over ''K'', or just algebraic over ''K'', if there exists some non-zero polynomial ''g''(''x'') with coefficients in ''K'' such that ''g''(''a'')=0. Elements of ''L'' which are not algebraic over ''K'' are called transcendental over ''K''. These notions generalize the algebraic numbers and the transcendental numbers (where the field extension is C/Q, C being the field of complex numbers and Q being the field of rational numbers). == Examples == * The square root of 2 is algebraic over Q, since it is the root of the polynomial ''g''(''x'') = ''x''2 - 2 whose coefficients are rational. * Pi is transcendental over Q but algebraic over the field of real numbers R: it is the root of ''g''(''x'') = ''x'' - π, whose coefficients (1 and -π) are both real, but not of any polynomial with only rational coefficients. (The definition of the term transcendental number uses C/Q, not C/R.) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Algebraic element」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.