Height: Difference between revisions
Wikispaces>guest **Imported revision 362733876 - Original comment: ** |
Wikispaces>guest **Imported revision 362749812 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:guest|guest]] and made on <tt>2012-09-07 | : This revision was by author [[User:guest|guest]] and made on <tt>2012-09-07 03:49:45 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>362749812</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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=Examples:= | =Examples:= | ||
|| Name: || H(n/d) || H(q) || H(q) simplified by equivalence relation || | || Name: || H(n/d) || H(q) || H(q) simplified by equivalence relation || Abstract || | ||
|| [[Benedetti Height|Benedetti height]] | || [[Benedetti Height|Benedetti height]] | ||
(or [[Tenney Height]]) || [[math]] | (or [[Tenney Height]]) || [[math]] | ||
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[[math]] || [[math]] | [[math]] || [[math]] | ||
T1(q) | T1(q) | ||
[[math]] || | [[math]] || Complexity || | ||
|| Weil Height || [[math]] | || Weil Height || [[math]] | ||
max(n,d) | max(n,d) | ||
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[[math]] || [[math]] | [[math]] || [[math]] | ||
T1(q)+|log_2(q)| | T1(q)+|log_2(q)| | ||
[[math]] || | [[math]] || Complexity+|Span| || | ||
|| Arithmetic Height || [[math]] | || Arithmetic Height || [[math]] | ||
n+d | n+d | ||
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[[math]] || [[math]] | [[math]] || [[math]] | ||
T1(q)+2log_2(q+1)-log_2(q) | T1(q)+2log_2(q+1)-log_2(q) | ||
[[math]] || | [[math]] || Complexity+2(Tartini Tone Span)-Span || | ||
|| [[Kees Height]] || [[math]] | || [[Kees Height]] || [[math]] | ||
max(2^{-v_2(n)}n, | max(2^{-v_2(n)}n, | ||
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[[math]] || [[math]] | [[math]] || [[math]] | ||
T1(2^{-v_2(q)}q)+|log_2(q)-v_2(q)| | T1(2^{-v_2(q)}q)+|log_2(q)-v_2(q)| | ||
[[math]] || | [[math]] || No-2's-Complexity+|No-2's-Span| || | ||
|| || || || || | || || || || || || | ||
Where T1(q) is the [[xenharmonic/Generalized Tenney Norms and Tp Interval Space#The%20Tenney%20Norm%20(T1%20norm)|tenney norm]] of q in monzo form, and vp(x) is the [[http://en.wikipedia.org/wiki/P-adic_order|p-adic valuation]] of x. | Where T1(q) is the [[xenharmonic/Generalized Tenney Norms and Tp Interval Space#The%20Tenney%20Norm%20(T1%20norm)|tenney norm]] of q in monzo form, and vp(x) is the [[http://en.wikipedia.org/wiki/P-adic_order|p-adic valuation]] of x. | ||
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</td> | </td> | ||
<td>H(q) simplified by equivalence relation<br /> | <td>H(q) simplified by equivalence relation<br /> | ||
</td> | |||
<td>Abstract<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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T1(q)&lt;br/&gt;[[math]] | T1(q)&lt;br/&gt;[[math]] | ||
--><script type="math/tex">T1(q)</script><!-- ws:end:WikiTextMathRule:3 --><br /> | --><script type="math/tex">T1(q)</script><!-- ws:end:WikiTextMathRule:3 --><br /> | ||
</td> | |||
<td>Complexity<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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T1(q)+|log_2(q)|&lt;br/&gt;[[math]] | T1(q)+|log_2(q)|&lt;br/&gt;[[math]] | ||
--><script type="math/tex">T1(q)+|log_2(q)|</script><!-- ws:end:WikiTextMathRule:6 --><br /> | --><script type="math/tex">T1(q)+|log_2(q)|</script><!-- ws:end:WikiTextMathRule:6 --><br /> | ||
</td> | |||
<td>Complexity+|Span|<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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T1(q)+2log_2(q+1)-log_2(q)&lt;br/&gt;[[math]] | T1(q)+2log_2(q+1)-log_2(q)&lt;br/&gt;[[math]] | ||
--><script type="math/tex">T1(q)+2log_2(q+1)-log_2(q)</script><!-- ws:end:WikiTextMathRule:9 --><br /> | --><script type="math/tex">T1(q)+2log_2(q+1)-log_2(q)</script><!-- ws:end:WikiTextMathRule:9 --><br /> | ||
</td> | |||
<td>Complexity+2(Tartini Tone Span)-Span<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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T1(2^{-v_2(q)}q)+|log_2(q)-v_2(q)|&lt;br/&gt;[[math]] | T1(2^{-v_2(q)}q)+|log_2(q)-v_2(q)|&lt;br/&gt;[[math]] | ||
--><script type="math/tex">T1(2^{-v_2(q)}q)+|log_2(q)-v_2(q)|</script><!-- ws:end:WikiTextMathRule:12 --><br /> | --><script type="math/tex">T1(2^{-v_2(q)}q)+|log_2(q)-v_2(q)|</script><!-- ws:end:WikiTextMathRule:12 --><br /> | ||
</td> | |||
<td>No-2's-Complexity+|No-2's-Span|<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | |||
</td> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||