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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Transcendental number theory ： ウィキペディア英語版 Transcendental number theory Transcendental number theory is a branch of number theory that investigates transcendental numbers, in both qualitative and quantitative ways. ==Transcendence== (詳細はfundamental theorem of algebra tells us that if we have a non-zero polynomial with integer coefficients then that polynomial will have a root in the complex numbers. That is, for any polynomial ''P'' with integer coefficients there will be a complex number α such that ''P''(α) = 0. Transcendence theory is concerned with the converse question, given a complex number α, is there a polynomial ''P'' with integer coefficients such that ''P''(α) = 0? If no such polynomial exists then the number is called transcendental. More generally the theory deals with algebraic independence of numbers. A set of numbers is called algebraically independent over a field ''k'' if there is no non-zero polynomial ''P'' in ''n'' variables with coefficients in ''k'' such that ''P''(α1,α2,…,α''n'') = 0. So working out if a given number is transcendental is really a special case of algebraic independence where our set consists of just one number. A related but broader notion than "algebraic" is whether there is a closed-form expression for a number, including exponentials and logarithms as well as algebraic operations. There are various definitions of "closed-form", and questions about closed-form can often be reduced to questions about transcendence. 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「Transcendental number theory」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.