489
回編集
差分
編集の要約なし
+\sin x &=& +\sin_zx &=& -\sin_{z^{-1}}x &=& \exp_4^{(3)}x-\exp_4^{(1)}x &\leftarrow[~~0~,+1,~~0~,-1]\\
\end{array}
$$z=\mathrm{P}^{\frac15}=e^{\frac{2\pi}5i}$$ の場合（$$\phi'=\phi-1=\frac{\sqrt5-1}2$$）
\begin{array}{c}
+\cos_zx && &=& +\exp_5^{(0)}x-\exp_4^{(3)}x-\phi'\exp_4^{(2)}x+\phi'\exp_4^{(1)}x &\leftarrow[+1~,~~0~~,-1~,-\phi',+\phi']\\
-\sin_zx &=& +\sin_{z^{-1}}x &=& +\exp_5^{(1)}x-\exp_4^{(4)}x-\phi'\exp_4^{(3)}x+\phi'\exp_4^{(2)}x &\leftarrow[~~0~~,-1~,-\phi',+\phi',+1~]\\
&& -\cos_{z^{-1}}x &=& +\exp_5^{(2)}x-\exp_4^{(5)}x-\phi'\exp_4^{(4)}x+\phi'\exp_4^{(3)}x &\leftarrow[-1~,-\phi',+\phi',+1~,~~0~~]\\
&=& (+\sin_{z^{-1}}x)'' &=& +\exp_5^{(3)}x-\exp_4^{(0)}x-\phi'\exp_4^{(5)}x+\phi'\exp_4^{(4)}x &\leftarrow[-\phi',+\phi',+1~,~~0~~,-1~]\\
&=& (-\cos_{z^{-1}}x)'' &=& +\exp_5^{(4)}x-\exp_4^{(1)}x-\phi'\exp_4^{(0)}x+\phi'\exp_4^{(5)}x &\leftarrow[+\phi',+1~,~~0~~,-1~,-\phi']\\
\\
-\cos_zx && &=& -\exp_5^{(0)}x+\exp_4^{(3)}x+\phi'\exp_4^{(2)}x-\phi'\exp_4^{(1)}x &\leftarrow[-1~,~~0~~,+1~,+\phi',-\phi']\\
+\sin_zx &=& -\sin_{z^{-1}}x &=& -\exp_5^{(1)}x+\exp_4^{(4)}x+\phi'\exp_4^{(3)}x-\phi'\exp_4^{(2)}x &\leftarrow[~~0~~,+1~,+\phi',-\phi',-1~]\\
&& +\cos_{z^{-1}}x &=& -\exp_5^{(2)}x+\exp_4^{(0)}x+\phi'\exp_4^{(4)}x-\phi'\exp_4^{(3)}x &\leftarrow[+1~,+\phi',-\phi',-1~,~~0~~]\\
&& (-\sin_{z^{-1}}x)'' &=& -\exp_5^{(3)}x+\exp_4^{(1)}x+\phi'\exp_4^{(0)}x-\phi'\exp_4^{(4)}x &\leftarrow[+\phi',-\phi',-1~,~~0~~,+1~]\\
&& (+\cos_{z^{-1}}x)'' &=& -\exp_5^{(4)}x+\exp_4^{(2)}x+\phi'\exp_4^{(1)}x-\phi'\exp_4^{(0)}x &\leftarrow[-\phi',-1~,~~0~~,+1~,+\phi']\\
\end{array}
$$z=\mathrm{P}^{\frac16}=e^{\frac{2\pi}6i}=e^{\frac{\pi}3i}$$ の場合