Difference between revisions of "Questions"
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(Created page with "==On $(A_2,A_7)$== ===sol 1=== $$ \begin{bmatrix} z_0^{(1)} & z_0^{(2)} \\ z_1^{(1)} & z_1^{(2)} \\ z_2^{(1)} & z_2^{(2)} \\ z_3^{(1)} & z_3^{(2)} \\ z_4^{(1)} & z_4^{(2)...") |
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| Line 24: | Line 24: | ||
\end{bmatrix} | \end{bmatrix} | ||
$$ | $$ | ||
| + | Here $2.24698\cdots$ is a solution of $x^3-2 x^2-x+1=0$. | ||
| + | |||
===sol 2=== | ===sol 2=== | ||
| Line 49: | Line 51: | ||
\end{bmatrix} | \end{bmatrix} | ||
$$ | $$ | ||
| + | where $1.61803\cdots$ is the Golden ratio. | ||
Revision as of 04:58, 28 September 2013
On $(A_2,A_7)$
sol 1
$$ \begin{bmatrix}
z_0^{(1)} & z_0^{(2)} \\
z_1^{(1)} & z_1^{(2)} \\
z_2^{(1)} & z_2^{(2)} \\
z_3^{(1)} & z_3^{(2)} \\
z_4^{(1)} & z_4^{(2)} \\
z_5^{(1)} & z_5^{(2)} \\
z_6^{(1)} & z_6^{(2)} \\
z_7^{(1)} & z_7^{(2)}
\end{bmatrix} = \begin{bmatrix}
1. & 1. \\ 2.24698 & 2.24698 \\ 2.80194 & 2.80194 \\ 2.24698 & 2.24698 \\ 1. & 1. \\ 0 & 0 \\ 0 & 0 \\ 1. & 1.
\end{bmatrix} $$ Here $2.24698\cdots$ is a solution of $x^3-2 x^2-x+1=0$.
sol 2
$$ \begin{bmatrix}
z_0^{(1)} & z_0^{(2)} \\
z_1^{(1)} & z_1^{(2)} \\
z_2^{(1)} & z_2^{(2)} \\
z_3^{(1)} & z_3^{(2)} \\
z_4^{(1)} & z_4^{(2)} \\
z_5^{(1)} & z_5^{(2)} \\
z_6^{(1)} & z_6^{(2)} \\
z_7^{(1)} & z_7^{(2)}
\end{bmatrix} = \begin{bmatrix}
1. & 1. \\ 1.61803 & 1.61803 \\ 1. & 1. \\ 0 & 0 \\ 0 & 0 \\ 1. & 1. \\ 1.61803 & 1.61803 \\ 1. & 1.
\end{bmatrix} $$ where $1.61803\cdots$ is the Golden ratio.