Benedetti height: Difference between revisions
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=== Vector form === | === Vector form === | ||
The Benedetti height of a [[Harmonic limit|''p''-limit]] [[monzo]] m = {{monzo| ''m''<sub>1</sub> ''m''<sub>2</sub> … ''m''<sub>π (''p'')</sub> }} (π being the [[Wikipedia: prime-counting function|prime-counting function]]) is given by | The Benedetti height of a [[Harmonic limit|''p''-limit]] [[monzo]] '''m''' = {{monzo| ''m''<sub>1</sub> ''m''<sub>2</sub> … ''m''<sub>π (''p'')</sub> }} (π being the [[Wikipedia: prime-counting function|prime-counting function]]) is given by | ||
<math>2^{\lVert H \vec m \rVert_1} \\ | <math>2^{\lVert H \vec m \rVert_1} \\ | ||
= 2^{|m_1|} \cdot 3^{|m_2|} \cdot \ldots \cdot p^{|m_{\pi (p)}|}</math> | = 2^{|m_1|} \cdot 3^{|m_2|} \cdot \ldots \cdot p^{|m_{\pi (p)}|}</math> | ||
where H is the transformation matrix such that, for the prime basis Q = {{val| 2 3 5 … ''p'' }}, | where ''H'' is the transformation matrix such that, for the prime basis ''Q'' = {{val| 2 3 5 … ''p'' }}, | ||
<math>H = \operatorname {diag} (\log_2 (Q))</math> | <math>H = \operatorname {diag} (\log_2 (Q))</math> | ||
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[[Category:Interval complexity measures]] | [[Category:Interval complexity measures]] | ||
[[Category:Tenney-weighted measures]] | |||
[[Category:Tenney]] | |||