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	<id>https://katlas.org/index.php?action=history&amp;feed=atom&amp;title=Data%3AL9a31%2FKauffman_Polynomial</id>
	<title>Data:L9a31/Kauffman Polynomial - Revision history</title>
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	<updated>2026-05-13T14:34:01Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://katlas.org/index.php?title=Data:L9a31/Kauffman_Polynomial&amp;diff=1717536&amp;oldid=prev</id>
		<title>ScottDataRobot at 21:24, 20 February 2013</title>
		<link rel="alternate" type="text/html" href="https://katlas.org/index.php?title=Data:L9a31/Kauffman_Polynomial&amp;diff=1717536&amp;oldid=prev"/>
		<updated>2013-02-20T21:24:47Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 17:24, 20 February 2013&lt;/td&gt;
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  &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;
  &lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;
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  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-2 &lt;/del&gt;a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;8&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;8-5&lt;/del&gt; a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;9&lt;/del&gt; a&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; z&lt;/del&gt;^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7-4&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7 a^{-1} -&lt;/del&gt;5 a^4 z^6-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/del&gt; a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6-3 z^6&lt;/del&gt; a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{-2} -2&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3 &lt;/del&gt;a^5&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; z^5+8&lt;/del&gt; a^3 z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5+20&lt;/del&gt; a z^5+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;8 &lt;/del&gt;z^5 a^{-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1&lt;/del&gt;} &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-z^5&lt;/del&gt; a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{-&lt;/del&gt;3&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;}&lt;/del&gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-a&lt;/del&gt;^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4+7&lt;/del&gt; a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/del&gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;z^&lt;/del&gt;4&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+12&lt;/del&gt; a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/del&gt; z&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^4&lt;/del&gt;+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6 &lt;/del&gt;z&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^4&lt;/del&gt; a^{-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/del&gt;} +&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;10&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/del&gt;+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/del&gt; a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3-&lt;/del&gt;8 a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/del&gt; z^3&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-18 a&lt;/del&gt; z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3-5 z^3&lt;/del&gt; a^{-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1&lt;/del&gt;} &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/del&gt;2 z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3 a^{&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3} +a^&lt;/del&gt;6 z^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2-&lt;/del&gt;4 a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/del&gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;z^2-&lt;/del&gt;10 a^2 z^2&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/del&gt;2 z^2 a^{-2} -&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7&lt;/del&gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;z&lt;/del&gt;^2&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+4 a^3 z&lt;/del&gt;+9 a z+4 z a^{-1} -z a^{-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/del&gt;} +a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/del&gt;+3 a^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2+3&lt;/del&gt;-a&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^3&lt;/del&gt; z^{-1} &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/del&gt;3 a z^{-1} &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/del&gt;2 a^{-1} z^{-1} &amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;
  &lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;
  &lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;math&amp;gt;a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a^6&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2+3&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3+&lt;/ins&gt;5 a^4 z^6-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4+4&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt;-a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4+&lt;/ins&gt;5 a^3 z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;7-8&lt;/ins&gt; a&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^3&lt;/ins&gt; z^5+z^5 a^{-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt;} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+8&lt;/ins&gt; a^3 &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;z&lt;/ins&gt;^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3-2&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{-3}&lt;/ins&gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-&lt;/ins&gt;4 a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt; z+z a^{-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt;} +&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a^3&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{-1} &lt;/ins&gt;+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt; z^8&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+4&lt;/ins&gt; a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt; z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6+&lt;/ins&gt;3 z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6&lt;/ins&gt; a^{-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt;} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-12 a^&lt;/ins&gt;2 z^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/ins&gt;-6 z^4 a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{-2}&lt;/ins&gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/ins&gt;10 a^2 z^2&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/ins&gt;2 z^2 a^{-2} -&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a&lt;/ins&gt;^2+9 a z&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^7&lt;/ins&gt;+4 z&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^7&lt;/ins&gt; a^{-1} -&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;20 a &lt;/ins&gt;z&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^5-8 z^5&lt;/ins&gt; a^{-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1&lt;/ins&gt;} +&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;18 &lt;/ins&gt;a&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; z&lt;/ins&gt;^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt;+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5 z^&lt;/ins&gt;3 a^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1} -9 &lt;/ins&gt;a z&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-4 z a&lt;/ins&gt;^{-1} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/ins&gt;3 a z^{-1} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/ins&gt;2 a^{-1} z^{-1} &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+2 z^8+2 z^6-10 z^4+7 z^2-3&lt;/ins&gt;&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>ScottDataRobot</name></author>
	</entry>
	<entry>
		<id>https://katlas.org/index.php?title=Data:L9a31/Kauffman_Polynomial&amp;diff=70087&amp;oldid=prev</id>
		<title>ScottDataRobot at 09:20, 26 August 2005</title>
		<link rel="alternate" type="text/html" href="https://katlas.org/index.php?title=Data:L9a31/Kauffman_Polynomial&amp;diff=70087&amp;oldid=prev"/>
		<updated>2005-08-26T09:20:02Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&amp;lt;math&amp;gt;-2 a^2 z^8-2 z^8-5 a^3 z^7-9 a z^7-4 z^7 a^{-1} -5 a^4 z^6-4 a^2 z^6-3 z^6 a^{-2} -2 z^6-3 a^5 z^5+8 a^3 z^5+20 a z^5+8 z^5 a^{-1} -z^5 a^{-3} -a^6 z^4+7 a^4 z^4+12 a^2 z^4+6 z^4 a^{-2} +10 z^4+3 a^5 z^3-8 a^3 z^3-18 a z^3-5 z^3 a^{-1} +2 z^3 a^{-3} +a^6 z^2-4 a^4 z^2-10 a^2 z^2-2 z^2 a^{-2} -7 z^2+4 a^3 z+9 a z+4 z a^{-1} -z a^{-3} +a^4+3 a^2+3-a^3 z^{-1} -3 a z^{-1} -2 a^{-1} z^{-1} &amp;lt;/math&amp;gt;&lt;/div&gt;</summary>
		<author><name>ScottDataRobot</name></author>
	</entry>
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