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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 rational function ： ウィキペディア英語版 rational function In mathematics, a rational function is any function which can be defined by a rational fraction, ''i.e.'' an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers, they may be taken in any field ''K''. In this case, one speaks of a rational function and a rational fraction ''over K''. The values of the variables may be taken in any field ''L'' containing ''K''. Then the domain of the function is the set of the values of the variables for which the denominator is not zero and the codomain is ''L''. By modifying the definition to use equivalence classes the set of rational functions becomes a field. ==Definitions== A function $f(x)$ is called a rational function if and only if it can be written in the form :$f(x)\; =\; \backslash frac$ where $P\backslash ,$ and $Q\backslash ,$ are polynomials in $x\backslash ,$ and $Q\backslash ,$ is not the zero polynomial. The domain of $f\backslash ,$ is the set of all points $x\backslash ,$ for which the denominator $Q(x)\backslash ,$ is not zero. However, if $\backslash textstyle\; P$ and $\backslash textstyle\; Q$ have a non constant polynomial greatest common divisor $\backslash textstyle\; R$, then setting $\backslash textstyle\; P=P\_1R$ and $\backslash textstyle\; Q=Q\_1R$ produces a rational function :$f\_1(x)\; =\; \backslash frac,$ which may have a larger domain than $f(x)$, and is equal to $f(x)$ on the domain of $f(x).$ It is a common usage to identify $f(x)$ and $f\_1(x)$, that is to extend "by continuity" the domain of $f(x)$ to that of $f\_1(x).$ Indeed, one can define a rational fraction as an equivalence class of fractions of polynomials, where two fractions ''A''(''x'')/''B''(''x'') and ''C''(''x'')/''D''(''x'') are considered equivalent if ''A''(''x'')''D''(''x'')=''B''(''x'')''C''(''x''). In this case $\backslash frac$ is equivalent to $\backslash frac$. 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「rational function」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.