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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 Length of a polynomial ： ウィキペディア英語版 Height of a polynomial In mathematics, the height and length of a polynomial ''P'' with complex coefficients are measures of its "size". For a polynomial ''P'' of degree ''n'' given by :$P\; =\; a\_0\; +\; a\_1\; x\; +\; a\_2\; x^2\; +\; \backslash cdots\; +\; a\_n\; x^n\; ,$ the height ''H''(''P'') is defined to be the maximum of the magnitudes of its coefficients: :$H(P)\; =\; \backslash underset\; \backslash ,|a\_i|\; \backslash ,$ and the length ''L''(''P'') is similarly defined as the sum of the magnitudes of the coefficients: :$L(P)\; =\; \backslash sum\_^n\; |a\_i|.\backslash ,$ The Mahler measure ''M''(''P'') of ''P'' is also a measure of the size of ''P''. The three functions ''H''(''P''), ''L''(''P'') and ''M''(''P'') are related by the inequalities :$\backslash binom^\; H(P)\; \backslash le\; M(P)\; \backslash le\; H(P)\; \backslash sqrt\; ;$ :$L(p)\; \backslash le\; 2^n\; M(p)\; \backslash le\; 2^n\; L(p)\; ;$ :$H(p)\; \backslash le\; L(p)\; \backslash le\; n\; H(p)$ where $\backslash scriptstyle\; \backslash binom$ is the binomial coefficient. ==References== * * * 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「Height of a polynomial」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.