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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 Gauss–Lucas theorem ： ウィキペディア英語版 Gauss–Lucas theorem In complex analysis, a branch of mathematics, the Gauss–Lucas theorem gives a geometrical relation between the roots of a polynomial ''P'' and the roots of its derivative ''P'''. The set of roots of a real or complex polynomial is a set of points in the complex plane. The theorem states that the roots of ''P''' all lie within the convex hull of the roots of ''P'', that is the smallest convex polygon containing the roots of ''P''. When ''P'' has a single root then this convex hull is a single point and when the roots lie on a line then the convex hull is a segment of this line. The Gauss–Lucas theorem, named after Carl Friedrich Gauss and Félix Lucas is similar in spirit to Rolle's theorem. ==Formal statement== If ''P'' is a (nonconstant) polynomial with complex coefficients, all zeros of ''P''' belong to the convex hull of the set of zeros of ''P''.〔Marden (1966), Theorem (6,1).〕 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「Gauss–Lucas theorem」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.