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We take the functional theoretic algebra ''C''() of curves. For each loop ''γ'' at 1, and each positive integer ''n'', we define a curve called ''n''-curve. The ''n''-curves are interesting in two ways. #Their f-products, sums and differences give rise to many beautiful curves. #Using the ''n''-curves, we can define a transformation of curves, called ''n''-curving. == Multiplicative inverse of a curve == A curve ''γ'' in the functional theoretic algebra ''C''(), is invertible, i.e. : exists if : If , where , then : The set ''G'' of invertible curves is a non-commutative group under multiplication. Also the set ''H'' of loops at 1 is an Abelian subgroup of ''G.'' If , then the mapping is an inner automorphism of the group ''G.'' We use these concepts to define ''n''-curves and ''n''-curving. 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「N-curve」の詳細全文を読む スポンサード リンク
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