Diamond tradeoff: Difference between revisions

Cmloegcmluin (talk | contribs)
ArrowHead294 (talk | contribs)
m Writing \frac without brackets in LaTeX is bad practice.
Line 219: Line 219:
(MU)^{-1} \\
(MU)^{-1} \\
\left[ \begin{array} {rrr}
\left[ \begin{array} {rrr}
1 & \frac12 \\
1 & \frac{1}{2} \\
0 & \frac14 \\
0 & \frac{1}{4} \\
\end{array} \right]
\end{array} \right]
\end{array}
\end{array}
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(MU)^{-1} \\
(MU)^{-1} \\
\left[ \begin{array} {rrr}
\left[ \begin{array} {rrr}
1 & \frac12 \\
1 & \frac{1}{2} \\
0 & \frac14 \\
0 & \frac{1}{4} \\
\end{array} \right]  
\end{array} \right]  
\end{array}
\end{array}
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1 & 0 \\
1 & 0 \\
0 & 0 \\
0 & 0 \\
0 & \frac14 \\
0 & \frac{1}{4} \\
\end{array} \right]
\end{array} \right]
\end{array}
\end{array}
Line 263: Line 263:




This tells us our generator is {{vector|0 0 <math>\frac14</math>}}, or 5^(1/4). In cents, that's {{nowrap|1200 &times; log<sub>2</sub>(5<sup>{{frac|1|4}}</sup>) &#8776; 696.578{{c}}}}.  
This tells us our generator is <math>\monzo{0 & 0 & \frac{1}{4}}</math>, or 5<sup>{{frac|1|4}}</sup>. In cents, that's {{nowrap|1200 &times; log<sub>2</sub>(5<sup>{{frac|1|4}}</sup>) &#8776; 696.578{{c}}}}.  


==== Third diamond extrema ====
==== Third diamond extrema ====
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(MU)^{-1} \\
(MU)^{-1} \\
\left[ \begin{array} {rrr}
\left[ \begin{array} {rrr}
1 & \frac23 \\
1 & \frac{2}{3} \\
0 & -\frac13 \\
0 & -\frac{1}{3} \\
\end{array} \right]
\end{array} \right]
\end{array}
\end{array}
Line 358: Line 358:
(MU)^{-1} \\
(MU)^{-1} \\
\left[ \begin{array} {rrr}
\left[ \begin{array} {rrr}
1 & \frac23 \\
1 & \frac{2}{3} \\
0 & -\frac13 \\
0 & -\frac{1}{3} \\
\end{array} \right]  
\end{array} \right]  
\end{array}
\end{array}
Line 368: Line 368:
G \\
G \\
\left[ \begin{array} {rrr}
\left[ \begin{array} {rrr}
1 & \frac13 \\
1 & \frac{1}{3} \\
0 & -\frac13 \\
0 & -\frac{1}{3} \\
0 & \frac13 \\
0 & \frac{1}{3} \\
\end{array} \right]
\end{array} \right]
\end{array}
\end{array}