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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 Hermite constant ： ウィキペディア英語版 Hermite constant In mathematics, the Hermite constant, named after Charles Hermite, determines how short an element of a lattice in Euclidean space can be. The constant $\backslash gamma\_n$ for integers ''n'' > 0 is defined as follows. For a lattice ''L'' in Euclidean space R''n'' unit covolume, i.e. vol(R''n''/''L'') = 1, let λ1(''L'') denote the least length of a nonzero element of ''L''. Then $\backslash sqrt$ is the maximum of λ1(''L'') over all such lattices ''L''. The square root in the definition of the Hermite constant is a matter of historical convention. With the definition as stated, it turns out that the Hermite constant grows linearly in ''n''. Alternatively, the Hermite constant $\backslash gamma\_n$ can be defined as the square of the maximal systole of a flat ''n''-dimensional torus of unit volume. ==Example== The Hermite constant is known in dimensions 1–8 and 24. For ''n'' = 2, one has $\backslash gamma\_2\; =\; \backslash tfrac\{\backslash sqrt\{3\}\}$. This value is attained by the hexagonal lattice of the Eisenstein integers.〔Cassels (1971) 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「Hermite constant」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.