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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 Grace–Walsh–Szegő theorem ： ウィキペディア英語版 Grace–Walsh–Szegő theorem In mathematics, the Grace–Walsh–Szegő coincidence theorem〔"A converse to the Grace–Walsh–Szegő theorem", ''Mathematical Proceedings of the Cambridge Philosophical Society'', August 2009, 147(02):447–453. DOI:10.1017/S0305004109002424〕〔J. H. Grace, "The zeros of a polynomial", ''Proceedings of the Cambridge Philosophical Society'' 11 (1902), 352–357.〕 is a result named after John Hilton Grace, Joseph L. Walsh, Gábor Szegő. == Statement == Suppose ''ƒ''(''z''1, ..., ''z''''n'') is a polynomial with complex coefficients, and that it is * symmetric, i.e. invariant under permutations of the variables, and * multi-affine, i.e. affine in each variable separately. Let ''A'' be a circular region in the complex plane. If either ''A'' is convex or the degree of ''ƒ'' is ''n'', then for any $\backslash zeta\_1,\backslash ldots,\backslash zeta\_n\backslash in\; A$ there exists $\backslash zeta\backslash in\; A$ such that : $f(\backslash zeta\_1,\backslash ldots,\backslash zeta\_n)\; =\; f(\backslash zeta,\backslash ldots,\backslash zeta).\; \backslash ,$ 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「Grace–Walsh–Szegő 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.