Monzos and interval space: Difference between revisions
Wikispaces>guest **Imported revision 362413524 - Original comment: ** |
Wikispaces>guest **Imported revision 362415124 - 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>2012-09-05 22: | : This revision was by author [[User:guest|guest]] and made on <tt>2012-09-05 22:54:43 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>362415124</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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Given a rational number q, we can rewrite it in monzo form by the following definition: | Given a rational number q, we can rewrite it in monzo form by the following definition: | ||
[[math]] | [[math]] | ||
q = |v_2 q \,v_3 q \, v_5 q \dotso v_p q\rangle | q = |v_2 (q) \,v_3 (q) \, v_5 (q) \dotso v_p (q)\rangle | ||
[[math]] | [[math]] | ||
The [[Tenney Height|Tenney height]] of this monzo is given by | The [[Tenney Height|Tenney height]] of this monzo is given by | ||
[[math]] | [[math]] | ||
\| |v_2 q \, v_3 q \dotso v_p q \rangle \| = |v_2 q| + |v_3 q| \log_2 3 + \dotsb + |v_p q| \log_2 p | \| |v_2 (q) \, v_3 (q) \dotso v_p (q) \rangle \| = |v_2 (q)| + |v_3 (q)| \log_2 3 + \dotsb + |v_p (q)| \log_2 p | ||
[[math]] | [[math]] | ||
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<!-- ws:start:WikiTextMathRule:4: | <!-- ws:start:WikiTextMathRule:4: | ||
[[math]]&lt;br/&gt; | [[math]]&lt;br/&gt; | ||
q = |v_2 q \,v_3 q \, v_5 q \dotso v_p q\rangle&lt;br/&gt;[[math]] | q = |v_2 (q) \,v_3 (q) \, v_5 (q) \dotso v_p (q)\rangle&lt;br/&gt;[[math]] | ||
--><script type="math/tex">q = |v_2 q \,v_3 q \, v_5 q \dotso v_p q\rangle</script><!-- ws:end:WikiTextMathRule:4 --><br /> | --><script type="math/tex">q = |v_2 (q) \,v_3 (q) \, v_5 (q) \dotso v_p (q)\rangle</script><!-- ws:end:WikiTextMathRule:4 --><br /> | ||
<br /> | <br /> | ||
The <a class="wiki_link" href="/Tenney%20Height">Tenney height</a> of this monzo is given by<br /> | The <a class="wiki_link" href="/Tenney%20Height">Tenney height</a> of this monzo is given by<br /> | ||
<!-- ws:start:WikiTextMathRule:5: | <!-- ws:start:WikiTextMathRule:5: | ||
[[math]]&lt;br/&gt; | [[math]]&lt;br/&gt; | ||
\| |v_2 q \, v_3 q \dotso v_p q \rangle \| = |v_2 q| + |v_3 q| \log_2 3 + \dotsb + |v_p q| \log_2 p&lt;br/&gt;[[math]] | \| |v_2 (q) \, v_3 (q) \dotso v_p (q) \rangle \| = |v_2 (q)| + |v_3 (q)| \log_2 3 + \dotsb + |v_p (q)| \log_2 p&lt;br/&gt;[[math]] | ||
--><script type="math/tex">\| |v_2 q \, v_3 q \dotso v_p q \rangle \| = |v_2 q| + |v_3 q| \log_2 3 + \dotsb + |v_p q| \log_2 p</script><!-- ws:end:WikiTextMathRule:5 --><br /> | --><script type="math/tex">\| |v_2 (q) \, v_3 (q) \dotso v_p (q) \rangle \| = |v_2 (q)| + |v_3 (q)| \log_2 3 + \dotsb + |v_p (q)| \log_2 p</script><!-- ws:end:WikiTextMathRule:5 --><br /> | ||
<br /> | <br /> | ||
Where vp(q) is the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/P-adic_order" rel="nofollow">p-adic valuation</a> of q.<br /> | Where vp(q) is the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/P-adic_order" rel="nofollow">p-adic valuation</a> of q.<br /> | ||