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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 Budan's theorem ： ウィキペディア英語版 Budan's theorem In mathematics, Budan's theorem, named for François Budan de Boislaurent, is an early theorem for computing an upper bound on the number of real roots a polynomial has inside an open interval by counting the number of sign variations or sign changes in the sequences of coefficients. Since 1836, the statement of Budan's theorem has been replaced in the literature by the statement of an equivalent theorem by Joseph Fourier, and the latter has been referred to under various names, including Budan's. Budan's original theorem forms the basis of the fastest known method for the isolation of the real roots of polynomials. ==Sign variation== :Let $c\_0,\; c\_1,\; c\_2,\; \backslash ldots$ be a finite or infinite sequence of real numbers. Suppose and the following conditions hold: # If $r\; =\; l\; +\; 1$ the numbers $c\_l$ and $c\_r$ have opposite signs. # If $r\; \backslash ge\; l\; +\; 2$ the numbers $c\_,\; \backslash ldots,\; c\_$ are all zero and the numbers $c\_l$ and $c\_r$ have opposite signs. : This is called a ''sign variation'' or ''sign change'' between the numbers $c\_l$ and $c\_r$. : For a univariate polynomial $p(x)$, the number of sign variations of $p(x)$ is defined as the number of sign variations in the sequence of its coefficients. 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「Budan's 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.