Tenney norm: Difference between revisions

@@ Line 7: / Line 7: @@
 <math>\log_2 (nd)</math>
-The Tenney height of a [[monzo]] b = {{monzo| ''b''<sub>π (2)</sub> ''b''<sub>π (3)</sub> … ''b''<sub>π (''p'')</sub> }} is given by
+The Tenney height of a [[Harmonic limit|''p''-limit]] [[monzo]] b = {{monzo| ''b''<sub>1</sub> ''b''<sub>2</sub> … ''b''<sub>π (''p'')</sub> }} is given by
-<math>\lVert W^{-1}b \rVert_1 \\
+<math>\lVert W^{-1} \vec b \rVert_1 \\
-= \vert b_{\pi (2)} \vert + \log_2 (3) \vert b_{\pi (3)} \vert + \ldots + \log_2 (p) \vert b_{\pi (p)} \vert \\
+= \vert b_1 \vert + \log_2 (3) \vert b_2 \vert + \ldots + \log_2 (p) \vert b_{\pi (p)} \vert \\
-= \log_2 (2^{|b_{\pi (2)}|} \cdot 3^{|b_{\pi (2)}|} \cdot \ldots \cdot p^{|b_{\pi (p)}|})</math>
+= \log_2 (2^{|b_1|} \cdot 3^{|b_2|} \cdot \ldots \cdot p^{|b_{\pi (p)}|})</math>
 where W is the Tenney weighter such that, for the prime basis Q = {{val| 2 3 5 … ''p'' }},