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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 Reciprocal polynomial ： ウィキペディア英語版 Reciprocal polynomial In algebra, the reciprocal polynomial of a polynomial of degree with coefficients from an arbitrary field, such as :$p(x)\; =\; a\_0\; +\; a\_1x\; +\; a\_2x^2\; +\; \backslash cdots\; +\; a\_nx^n,\; \backslash ,\backslash !$ is the polynomial : $p^$ *(x) = a_n + a_x + \cdots + a_0x^n = x^n p(x^). Essentially, the coefficients are written in reverse order. They arise naturally in linear algebra as the characteristic polynomial of the inverse of a matrix. In the special case that the polynomial has complex coefficients, that is, :$p(z)\; =\; a\_0\; +\; a\_1z\; +\; a\_2z^2\; +\; \backslash cdots\; +\; a\_nz^n,\; \backslash ,\backslash !$ the conjugate reciprocal polynomial, given by, :$p^(z)\; =\; \backslash overline\; +\; \backslash overlinez^n\; =\; z^n\backslash overline)\},$ where $\backslash overline$ denotes the complex conjugate of $a\_i\; \backslash ,\backslash !$, is also called the reciprocal polynomial when no confusion can arise. A polynomial is called self-reciprocal if . The coefficients of a self-reciprocal polynomial satisfy , and in this case is also called a palindromic polynomial. In the conjugate reciprocal case, the coefficients must be real to satisfy the condition. == Properties == Reciprocal polynomials have several connections with their original polynomials, including: # is a root of polynomial if and only if is a root of . # If then is irreducible if and only if is irreducible. # is primitive if and only if is primitive.〔 Other properties of reciprocal polynomials may be obtained, for instance: * If a polynomial is self-reciprocal and irreducible then it must have even degree.〔 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「Reciprocal 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.