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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 Universal quadratic form ： ウィキペディア英語版 Universal quadratic form In mathematics, a universal quadratic form is a quadratic form over a ring that represents every element of the ring.〔Lam (2005) p.10〕 A non-singular form over a field which represents zero non-trivially is universal.〔Rajwade (1993) p.146〕 ==Examples== * Over the real numbers, the form ''x''2 in one variable is not universal, as it cannot represent negative numbers: the two-variable form over R is universal. * Lagrange's four-square theorem states that every positive integer is the sum of four squares. Hence the form over Z is universal. * Over a finite field, any non-singular quadratic form of dimension 2 or more is universal.〔Lam (2005) p.36〕 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「Universal quadratic form」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.