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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 Polynomial decomposition ： ウィキペディア英語版 Polynomial decomposition In mathematics, a polynomial decomposition expresses a polynomial ''f'' as the functional composition $g\; \backslash circ\; h$ of polynomials ''g'' and ''h'', where ''g'' and ''h'' have degree greater than 1.〔Composition of polynomials may also be thought of as substitution of one polynomial as the value of the variable of another.〕 Algorithms are known for decomposing polynomials in polynomial time. Polynomials which are decomposable in this way are composite polynomials; those which are not are prime or indecomposable polynomials〔J.F. Ritt, "Prime and Composite Polynomials", ''Transactions of the American Mathematical Society'' 23:1:51-66 (January, 1922) 〕 (not to be confused with irreducible polynomials, which cannot be factored into products of polynomials). ==Examples== In the simplest case, one of the polynomials is a monomial. For example, :$f\; =\; x^6\; -\; 3\; x^3\; +\; 1$ decomposes into :$g\; =\; x^2\; -\; 3\; x\; +\; 1$ and $h\; =\; x^3$ since :$f(x)\; =\; (g\; \backslash circ\; h)(x)\; =\; g(h(x))\; =\; g(x^3)\; =\; (x^3)^2\; -\; 3\; (x^3)\; +\; 1.$ Less trivially, : $$ \begin & x^6-6 x^5+21 x^4-44 x^3+68 x^2-64 x+41 \\ = {} & (x^3+9 x^2+32 x+41) \circ (x^2-2 x). \end{align} 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「Polynomial decomposition」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.