Normal forms: Difference between revisions
Wikispaces>clumma **Imported revision 287870160 - Original comment: ** |
Wikispaces>clumma **Imported revision 287870288 - 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:clumma|clumma]] and made on <tt>2011-12-21 05: | : This revision was by author [[User:clumma|clumma]] and made on <tt>2011-12-21 05:53:16 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>287870288</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">[[toc | <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">[[toc]] | ||
An integral matrix is a matrix whose entries are all integers. An important normalized form for integral matricies is [[http://en.wikipedia.org/wiki/Hermite_normal_form|Hermite normal form]], and by using Hermite normal form we may define normalized forms of lists of [[Harmonic Limit|p-limit]] musical intervals (or [[Monzos and Interval Space|monzos]]) or lists of [[Vals and Tuning Space|vals]], the normal interval (or monzo) list and the normal val list. | An integral matrix is a matrix whose entries are all integers. An important normalized form for integral matricies is [[http://en.wikipedia.org/wiki/Hermite_normal_form|Hermite normal form]], and by using Hermite normal form we may define normalized forms of lists of [[Harmonic Limit|p-limit]] musical intervals (or [[Monzos and Interval Space|monzos]]) or lists of [[Vals and Tuning Space|vals]], the normal interval (or monzo) list and the normal val list. | ||
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[u] end:</pre></div> | [u] end:</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>Normal lists</title></head><body><!-- ws:start:WikiTextTocRule:6:&lt;img id=&quot;wikitext@@toc@@ | <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>Normal lists</title></head><body><!-- ws:start:WikiTextTocRule:6:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --><div style="margin-left: 2em;"><a href="#x-Normal interval lists">Normal interval lists</a></div> | ||
<!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --><div style="margin-left: 2em;"><a href="#x-Normal val lists">Normal val lists</a></div> | |||
<!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --><div style="margin-left: 2em;"><a href="#x-Maple code">Maple code</a></div> | |||
<!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --></div> | |||
<!-- ws:end:WikiTextTocRule:10 --><br /> | <!-- ws:end:WikiTextTocRule:10 --><br /> | ||
An integral matrix is a matrix whose entries are all integers. An important normalized form for integral matricies is <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Hermite_normal_form" rel="nofollow">Hermite normal form</a>, and by using Hermite normal form we may define normalized forms of lists of <a class="wiki_link" href="/Harmonic%20Limit">p-limit</a> musical intervals (or <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">monzos</a>) or lists of <a class="wiki_link" href="/Vals%20and%20Tuning%20Space">vals</a>, the normal interval (or monzo) list and the normal val list.<br /> | An integral matrix is a matrix whose entries are all integers. An important normalized form for integral matricies is <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Hermite_normal_form" rel="nofollow">Hermite normal form</a>, and by using Hermite normal form we may define normalized forms of lists of <a class="wiki_link" href="/Harmonic%20Limit">p-limit</a> musical intervals (or <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">monzos</a>) or lists of <a class="wiki_link" href="/Vals%20and%20Tuning%20Space">vals</a>, the normal interval (or monzo) list and the normal val list.<br /> | ||