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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 arithmetic ： ウィキペディア英語版 Polynomial arithmetic Polynomial arithmetic is a branch of algebra dealing with some properties of polynomials which share strong analogies with properties of number theory relative to integers. It includes basic mathematical operations such as addition, subtraction, and multiplication, as well as more elaborate operations like Euclidean division, and properties related to roots of polynomials. The latter are essentially connected to the fact that the set ''K''() of univariate polynomials with coefficients in a field ''K'' is a commutative ring, such as the ring of integers $\backslash mathbb$. ==Elementary operations on polynomials== Addition and subtraction of two polynomials are performed by adding or subtracting corresponding coefficients. If : $f(x)\; =\; \backslash sum\_^n\; a\_ix^i;\; g(x)\; =\; \backslash sum\_^m\; b\_ix^i$ then addition is defined as : $f(x)+g(x)=\; \backslash sum\_^m\; (a\_i+b\_i)x^i$ where m > n Multiplication is performed much the same way as addition and subtraction, but instead by multiplying the corresponding coefficients. If $f(x)\; =\; \backslash sum\_^n\; a\_ix^i;\; g(x)\; =\; \backslash sum\_^m\; b\_ix^i$ then multiplication is defined as $f(x)\backslash times\; g(x)=\backslash sum\_^\; c\_ix^i$ where $c\_k=a\_0b\_k+a\_1b\_+\backslash cdots+a\_b\_1+a\_kb\_0$. Note that we treat $a\_i$ as zero for $i>n$ and that the degree of the product is equal to the sum of the degrees of the two polynomials. 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 arithmetic」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.