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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 Monomial basis ： ウィキペディア英語版 Monomial basis In mathematics the monomial basis of a polynomial ring is its basis (as vector space or free module over the field or ring of coefficients) that consists in the set of all monomials. The monomials form a basis because every polynomial may be uniquely written as a finite linear combination of monomials (this is an immediate consequence of the definition of a polynomial). ==One indeterminate== The polynomial ring of the univariate polynomial over a field is a -vector space, which has :$1,x,x^2,x^3,\; \backslash ldots$ as an (infinite) basis. More generally, if is a ring, is a free module, which has the same basis. The polynomials of degree at most form also a vector space (or a free module in the case of a ring of coefficients), which has :$1,x,x^2,\backslash ldots$ as a basis The canonical form of a polynomial is its expression on this basis: :$a\_0\; +\; a\_1\; x\; +\; a\_2\; x^2\; +\; \backslash ldots\; +\; a\_d\; x^d,$ or, using the shorter sigma notation: :$\backslash sum\_^d\; a\_ix^i.$ The monomial basis in naturally totally ordered, either by increasing degrees : or by decreasing degrees :$1>x>x^2>\backslash cdots.$ 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「Monomial basis」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.