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In mathematics, a norm form is a homogeneous form in ''n'' variables constructed from the field norm of a field extension ''L''/''K'' of degree ''n''.〔.〕 That is, writing ''N'' for the norm mapping to ''K'', and selecting a basis :''e''1, ..., ''e''''n'' for ''L'' as a vector space over ''K'', the form is given by :''N''(''x''1''e''1 + ... + ''x''''n''''e''''n'') in variables :''x''1, ..., ''x''''n''. In number theory norm forms are studied as Diophantine equations, where they generalize, for example, the Pell equation.〔.〕 For this application the field ''K'' is usually the rational number field, the field ''L'' is an algebraic number field, and the basis is taken of some order in the ring of integers ''O''''L'' of ''L''. ==References== 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「Norm form」の詳細全文を読む スポンサード リンク
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