Monzos and interval space: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 141256641 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 141259095 - 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:genewardsmith|genewardsmith]] and made on <tt>2010-05-11 18: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-11 18:36:20 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>141259095</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">A [[Harmonic Limit|p-limit]] rational number q can by definition be factored into primes of size less than or equal to p, giving q = 2^e2 3^e3 ... p^ep, where the exponents are integers (positive, negative, or zero.) This is often written in [[http://mathworld.wolfram.com/Bra.html|bra vector]] notation as <e2 e3 ... ep|, in which case it is called a **monzo**, whee the name refers to the enthusiastic advocacy of [[Joe Monzo]] .</pre></div> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">A [[Harmonic Limit|p-limit]] rational number q can by definition be factored into primes of size less than or equal to p, giving q = 2^e2 3^e3 ... p^ep, where the exponents are integers (positive, negative, or zero.) This is often written in [[http://mathworld.wolfram.com/Bra.html|bra vector]] notation as <e2 e3 ... ep|, in which case it is called a **monzo**, whee the name refers to the enthusiastic advocacy of [[Joe Monzo]]. | ||
The [[Tenney Height|Tenney height]] of this monzo is given by | |||
|| <e2 e3 ... ep| || = |e2| + log2(3)|e3| + ... + log2(p) |ep| | |||
which is a [[http://en.wikipedia.org/wiki/Normed_vector_space|vector space norm]]. The monzos with this norm now define a [[http://en.wikipedia.org/wiki/Lattice_%28group%29|lattice]], which is a discrete subgroup spanning a finite dimensional real normed vector space.</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Monzos and Interval Space</title></head><body>A <a class="wiki_link" href="/Harmonic%20Limit">p-limit</a> rational number q can by definition be factored into primes of size less than or equal to p, giving q = 2^e2 3^e3 ... p^ep, where the exponents are integers (positive, negative, or zero.) This is often written in <a class="wiki_link_ext" href="http://mathworld.wolfram.com/Bra.html" rel="nofollow">bra vector</a> notation as &lt;e2 e3 ... ep|, in which case it is called a <strong>monzo</strong>, whee the name refers to the enthusiastic advocacy of <a class="wiki_link" href="/Joe%20Monzo">Joe Monzo</a> .</body></html></pre></div> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Monzos and Interval Space</title></head><body>A <a class="wiki_link" href="/Harmonic%20Limit">p-limit</a> rational number q can by definition be factored into primes of size less than or equal to p, giving q = 2^e2 3^e3 ... p^ep, where the exponents are integers (positive, negative, or zero.) This is often written in <a class="wiki_link_ext" href="http://mathworld.wolfram.com/Bra.html" rel="nofollow">bra vector</a> notation as &lt;e2 e3 ... ep|, in which case it is called a <strong>monzo</strong>, whee the name refers to the enthusiastic advocacy of <a class="wiki_link" href="/Joe%20Monzo">Joe Monzo</a>.<br /> | ||
<br /> | |||
The <a class="wiki_link" href="/Tenney%20Height">Tenney height</a> of this monzo is given by<br /> | |||
<br /> | |||
|| &lt;e2 e3 ... ep| || = |e2| + log2(3)|e3| + ... + log2(p) |ep|<br /> | |||
<br /> | |||
which is a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Normed_vector_space" rel="nofollow">vector space norm</a>. The monzos with this norm now define a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lattice_%28group%29" rel="nofollow">lattice</a>, which is a discrete subgroup spanning a finite dimensional real normed vector space.</body></html></pre></div> | |||
Revision as of 18:36, 11 May 2010
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2010-05-11 18:36:20 UTC.
- The original revision id was 141259095.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
A [[Harmonic Limit|p-limit]] rational number q can by definition be factored into primes of size less than or equal to p, giving q = 2^e2 3^e3 ... p^ep, where the exponents are integers (positive, negative, or zero.) This is often written in [[http://mathworld.wolfram.com/Bra.html|bra vector]] notation as <e2 e3 ... ep|, in which case it is called a **monzo**, whee the name refers to the enthusiastic advocacy of [[Joe Monzo]]. The [[Tenney Height|Tenney height]] of this monzo is given by || <e2 e3 ... ep| || = |e2| + log2(3)|e3| + ... + log2(p) |ep| which is a [[http://en.wikipedia.org/wiki/Normed_vector_space|vector space norm]]. The monzos with this norm now define a [[http://en.wikipedia.org/wiki/Lattice_%28group%29|lattice]], which is a discrete subgroup spanning a finite dimensional real normed vector space.
Original HTML content:
<html><head><title>Monzos and Interval Space</title></head><body>A <a class="wiki_link" href="/Harmonic%20Limit">p-limit</a> rational number q can by definition be factored into primes of size less than or equal to p, giving q = 2^e2 3^e3 ... p^ep, where the exponents are integers (positive, negative, or zero.) This is often written in <a class="wiki_link_ext" href="http://mathworld.wolfram.com/Bra.html" rel="nofollow">bra vector</a> notation as <e2 e3 ... ep|, in which case it is called a <strong>monzo</strong>, whee the name refers to the enthusiastic advocacy of <a class="wiki_link" href="/Joe%20Monzo">Joe Monzo</a>.<br /> <br /> The <a class="wiki_link" href="/Tenney%20Height">Tenney height</a> of this monzo is given by<br /> <br /> || <e2 e3 ... ep| || = |e2| + log2(3)|e3| + ... + log2(p) |ep|<br /> <br /> which is a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Normed_vector_space" rel="nofollow">vector space norm</a>. The monzos with this norm now define a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lattice_%28group%29" rel="nofollow">lattice</a>, which is a discrete subgroup spanning a finite dimensional real normed vector space.</body></html>