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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 Primitive element (finite field) ： ウィキペディア英語版 Primitive element (finite field) In field theory, a primitive element of a finite field ''GF''(''q'') is a generator of the multiplicative group of the field. In other words, $\backslash alpha\; \backslash in\; \backslash mathrm(q)$ is called a primitive element if it is a primitive (''q''-1) root of unity in ''GF''(''q''); this means that all the non-zero elements of $\backslash mathrm(q)$ can be written as $\backslash alpha^i$ for some (positive) integer $i$. For example, 2 is a primitive element of the field ''GF''(''3'') and ''GF''(''5''), but not of ''GF''(''7'') since it generates the cyclic subgroup of order 3 ; however, 3 is a primitive element of ''GF''(''7''). The minimal polynomial of a primitive element is a primitive polynomial. ==Properties== 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「Primitive element (finite field)」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.