Content deleted Content added
|
|
|
:<math>\begin{align}
&\begin{pmatrix}S(x)\Gamma(x)\\ x^6\end{pmatrix} &\\ [6pt]
={} &\begin{pmatrix}\alpha^{-7} +\alpha^{4}x+ \alpha^{-1}x^2+ \alpha^{6}x^3+ \alpha^{-1}x^4+ \alpha^{5}x^5 +\alpha^{7}x^6+ \alpha^{-3}x^7 \\ x^6\end{pmatrix} \\ [6pt]
&={} &\begin{pmatrix}\alpha^{7}+ \alpha^{-3}x & 1\\ 1 & 0\end{pmatrix}
\begin{pmatrix}x^6\\ \alpha^{-7} +\alpha^{4}x +\alpha^{-1}x^2 +\alpha^{6}x^3 +\alpha^{-1}x^4 +\alpha^{5}x^5 +2\alpha^{7}x^6 +2\alpha^{-3}x^7\end{pmatrix} \\ [6pt]
&={} &\begin{pmatrix}\alpha^{7}+ \alpha^{-3}x & 1\\ 1 & 0\end{pmatrix}
\begin{pmatrix}\alpha^4 + \alpha^{-5}x & 1\\ 1 & 0\end{pmatrix} \times \\
&\qquad \times \begin{pmatrix} \alpha^{-7}+ \alpha^{4}x+ \alpha^{-1}x^2+ \alpha^{6}x^3+ \alpha^{-1}x^4+ \alpha^{5}x^5\\ \alpha^{-3} +(\alpha^{-7}+\alpha^{3})x+ (\alpha^{3}+ \alpha^{-1})x^2+ (\alpha^{-5}+ \alpha^{-6})x^3+ (\alpha^3+ \alpha^{1})x^4+ 2\alpha^{-6}x^5+ 2x^6\end{pmatrix} \\ [6pt]
&={} &\begin{pmatrix}(1+ \alpha^{-4})+ (\alpha^{1}+ \alpha^{2})x+ \alpha^{7}x^2 & \alpha^{7}+ \alpha^{-3}x \\ \alpha^4+ \alpha^{-5}x & 1\end{pmatrix}
\begin{pmatrix} \alpha^{-7} + \alpha^{4}x + \alpha^{-1}x^2+ \alpha^{6}x^3+ \alpha^{-1}x^4+ \alpha^{5}x^5\\ \alpha^{-3}+ \alpha^{-2}x+ \alpha^{0}x^2+ \alpha^{-2}x^3+ \alpha^{-6}x^4\end{pmatrix} \\ [6pt]
&={} &\begin{pmatrix}\alpha^{-3}+ \alpha^{5}x+ \alpha^{7}x^2 & \alpha^{7}+ \alpha^{-3}x \\ \alpha^4+ \alpha^{-5}x & 1\end{pmatrix}
\begin{pmatrix}\alpha^{-5}+ \alpha^{-4}x & 1\\ 1 & 0 \end{pmatrix} \times \\
&\qquad \times \begin{pmatrix} \alpha^{-3}+ \alpha^{-2}x+ \alpha^{0}x^2+ \alpha^{-2}x^3+ \alpha^{-6}x^4\\ (\alpha^{7}+ \alpha^{-7})+ (2\alpha^{-7}+ \alpha^{4})x+ (\alpha^{-5}+ \alpha^{-6}+ \alpha^{-1})x^2+ (\alpha^{-7}+ \alpha^{-4}+ \alpha^{6})x^3+ (\alpha^{4}+ \alpha^{-6}+ \alpha^{-1})x^4+ 2\alpha^{5}x^5\end{pmatrix} \\ [6pt]
={} &= \begin{pmatrix} \alpha^{7}x+ \alpha^{5}x^2+ \alpha^{3}x^3 & \alpha^{-3}+ \alpha^{5}x+ \alpha^{7}x^2\\ \alpha^{3}+ \alpha^{-5}x+ \alpha^{6}x^2 & \alpha^4+ \alpha^{-5}x\end{pmatrix}
\begin{pmatrix} \alpha^{-3}+ \alpha^{-2}x+ \alpha^{0}x^2+ \alpha^{-2}x^3+ \alpha^{-6}x^4\\ \alpha^{-4}+ \alpha^{4}x+ \alpha^{2}x^2+ \alpha^{-5}x^3\end{pmatrix}.
\end{align}</math>
|
