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	<id>https://katlas.org/index.php?action=history&amp;feed=atom&amp;title=Data%3A8_3%2FA-polynomial</id>
	<title>Data:8 3/A-polynomial - Revision history</title>
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	<updated>2026-06-05T19:28:44Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://katlas.org/index.php?title=Data:8_3/A-polynomial&amp;diff=1713534&amp;oldid=prev</id>
		<title>ScottDataRobot at 02:28, 20 February 2013</title>
		<link rel="alternate" type="text/html" href="https://katlas.org/index.php?title=Data:8_3/A-polynomial&amp;diff=1713534&amp;oldid=prev"/>
		<updated>2013-02-20T02:28:53Z</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 22:28, 19 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;L^8 &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;M^{16}+&lt;/del&gt;M^{16}+L^7 \left(-2 M^{24}+3 M^{22}-2 M^{20}+M^{18}+8 M^{16}+M^{14}-2 M^{12}+3 M^{10}-2 M^8\right)+L \left(-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/del&gt; M^{&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;24&lt;/del&gt;}+3 M^{&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;22&lt;/del&gt;}-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/del&gt; M^{20}+M^{18}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+8&lt;/del&gt; M^{16}+M^{14}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-2&lt;/del&gt; M^{12}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+3&lt;/del&gt; M^{10}-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/del&gt; M^8\right)+L^5 \left(-4 M^{32}+16 M^{30}-14 M^{28}-21 M^{26}+24 M^{24}+16 M^{22}-56 M^{20}+17 M^{18}+100 M^{16}+17 M^{14}-56 M^{12}+16 M^{10}+24 M^8-21 M^6-14 M^4+16 M^2-4\right)+L^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/del&gt; \left(&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-4&lt;/del&gt; M^{32}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+16&lt;/del&gt; M^{30}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-14&lt;/del&gt; M^{28}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-21&lt;/del&gt; M^{26}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+24&lt;/del&gt; M^{24}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+16&lt;/del&gt; M^{22}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-56&lt;/del&gt; M^{20}+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;17&lt;/del&gt; M^{18}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+100&lt;/del&gt; M^{16}+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;17&lt;/del&gt; M^{14}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-56&lt;/del&gt; M^{12}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+16&lt;/del&gt; M^{10}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+24&lt;/del&gt; M^8&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-21&lt;/del&gt; M^6&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-14&lt;/del&gt; M^4&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+16&lt;/del&gt; M^2&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-4&lt;/del&gt;\right)+L^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6&lt;/del&gt; \left(M^{32}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-3&lt;/del&gt; M^{30}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+3&lt;/del&gt; M^{28}-M^{26}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-4&lt;/del&gt; M^{24}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-9&lt;/del&gt; M^{22}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+15&lt;/del&gt; M^{20}+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;13&lt;/del&gt; M^{18}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-2&lt;/del&gt; M^{16}+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;13&lt;/del&gt; M^{14}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+15&lt;/del&gt; M^{12}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-9&lt;/del&gt; M^{10}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-4&lt;/del&gt; M^8-M^6&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+3&lt;/del&gt; M^4&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-3&lt;/del&gt; M^2&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+1&lt;/del&gt;\right)+L^2 \left(M^{32}-3 M^{30}+3 M^{28}-M^{26}-4 M^{24}-9 M^{22}+15 M^{20}+13 M^{18}-2 M^{16}+13 M^{14}+15 M^{12}-9 M^{10}-4 M^8-M^6+3 M^4-3 M^2+1\right)+L&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^4&lt;/del&gt; \left(&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6 M^{32}&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;26&lt;/del&gt; M^{&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;30&lt;/del&gt;}+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;22&lt;/del&gt; M^{&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;28}+40 M^{26&lt;/del&gt;}-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;59 M^{24}-64 M^{22}+82&lt;/del&gt; M^{20}+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;50 &lt;/del&gt;M^{18}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-32&lt;/del&gt; M^{16}+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;50 &lt;/del&gt;M^{14}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+82&lt;/del&gt; M^{12}&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-64&lt;/del&gt; M^{10}-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;59&lt;/del&gt; M^8+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;40 &lt;/del&gt;M^&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6+22 M^4-26 M^2+6\right)&lt;/del&gt;&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;L^8 M^{16}+L^7 \left(-2 M^{24}+3 M^{22}-2 M^{20}+M^{18}+8 M^{16}+M^{14}-2 M^{12}+3 M^{10}-2 M^8\right)+L&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;^6&lt;/ins&gt; \left(&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;M^{32}&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt; M^{&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;30&lt;/ins&gt;}+3 M^{&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;28&lt;/ins&gt;}-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;M^{26}-4 M^{24}-9 M^{22}+15&lt;/ins&gt; M^{20}+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;13 &lt;/ins&gt;M^{18}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-2&lt;/ins&gt; M^{16}+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;13 &lt;/ins&gt;M^{14}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+15&lt;/ins&gt; M^{12}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-9&lt;/ins&gt; M^{10}-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/ins&gt; M^8&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-M^6+3 M^4-3 M^2+1&lt;/ins&gt;\right)+L^5 \left(-4 M^{32}+16 M^{30}-14 M^{28}-21 M^{26}+24 M^{24}+16 M^{22}-56 M^{20}+17 M^{18}+100 M^{16}+17 M^{14}-56 M^{12}+16 M^{10}+24 M^8-21 M^6-14 M^4+16 M^2-4\right)+L^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;4&lt;/ins&gt; \left(&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;6&lt;/ins&gt; M^{32}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-26&lt;/ins&gt; M^{30}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+22&lt;/ins&gt; M^{28}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+40&lt;/ins&gt; M^{26}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-59&lt;/ins&gt; M^{24}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-64&lt;/ins&gt; M^{22}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+82&lt;/ins&gt; M^{20}+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;50&lt;/ins&gt; M^{18}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-32&lt;/ins&gt; M^{16}+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;50&lt;/ins&gt; M^{14}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+82&lt;/ins&gt; M^{12}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-64&lt;/ins&gt; M^{10}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-59&lt;/ins&gt; M^8&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+40&lt;/ins&gt; M^6&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+22&lt;/ins&gt; M^4&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-26&lt;/ins&gt; M^2&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+6&lt;/ins&gt;\right)+L^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt; \left(&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-4 &lt;/ins&gt;M^{32}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+16&lt;/ins&gt; M^{30}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-14&lt;/ins&gt; M^{28}-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;21 &lt;/ins&gt;M^{26}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+24&lt;/ins&gt; M^{24}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+16&lt;/ins&gt; M^{22}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-56&lt;/ins&gt; M^{20}+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;17&lt;/ins&gt; M^{18}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+100&lt;/ins&gt; M^{16}+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;17&lt;/ins&gt; M^{14}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-56&lt;/ins&gt; M^{12}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+16&lt;/ins&gt; M^{10}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+24&lt;/ins&gt; M^8-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;21 &lt;/ins&gt;M^6&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-14&lt;/ins&gt; M^4&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+16&lt;/ins&gt; M^2&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-4&lt;/ins&gt;\right)+L^2 \left(M^{32}-3 M^{30}+3 M^{28}-M^{26}-4 M^{24}-9 M^{22}+15 M^{20}+13 M^{18}-2 M^{16}+13 M^{14}+15 M^{12}-9 M^{10}-4 M^8-M^6+3 M^4-3 M^2+1\right)+L \left(-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt; M^{&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;24&lt;/ins&gt;}+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3&lt;/ins&gt; M^{&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;22&lt;/ins&gt;}-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt; M^{20}+M^{18}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+8&lt;/ins&gt; M^{16}+M^{14}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-2&lt;/ins&gt; M^{12}&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+3&lt;/ins&gt; M^{10}-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2&lt;/ins&gt; M^8&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\right)&lt;/ins&gt;+M^&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{16}&lt;/ins&gt;&amp;lt;/math&amp;gt;&lt;/div&gt;&lt;/td&gt;
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		<author><name>ScottDataRobot</name></author>
	</entry>
	<entry>
		<id>https://katlas.org/index.php?title=Data:8_3/A-polynomial&amp;diff=146884&amp;oldid=prev</id>
		<title>ScottDataRobot at 23:31, 25 May 2006</title>
		<link rel="alternate" type="text/html" href="https://katlas.org/index.php?title=Data:8_3/A-polynomial&amp;diff=146884&amp;oldid=prev"/>
		<updated>2006-05-25T23:31:08Z</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;L^8 M^{16}+M^{16}+L^7 \left(-2 M^{24}+3 M^{22}-2 M^{20}+M^{18}+8 M^{16}+M^{14}-2 M^{12}+3 M^{10}-2 M^8\right)+L \left(-2 M^{24}+3 M^{22}-2 M^{20}+M^{18}+8 M^{16}+M^{14}-2 M^{12}+3 M^{10}-2 M^8\right)+L^5 \left(-4 M^{32}+16 M^{30}-14 M^{28}-21 M^{26}+24 M^{24}+16 M^{22}-56 M^{20}+17 M^{18}+100 M^{16}+17 M^{14}-56 M^{12}+16 M^{10}+24 M^8-21 M^6-14 M^4+16 M^2-4\right)+L^3 \left(-4 M^{32}+16 M^{30}-14 M^{28}-21 M^{26}+24 M^{24}+16 M^{22}-56 M^{20}+17 M^{18}+100 M^{16}+17 M^{14}-56 M^{12}+16 M^{10}+24 M^8-21 M^6-14 M^4+16 M^2-4\right)+L^6 \left(M^{32}-3 M^{30}+3 M^{28}-M^{26}-4 M^{24}-9 M^{22}+15 M^{20}+13 M^{18}-2 M^{16}+13 M^{14}+15 M^{12}-9 M^{10}-4 M^8-M^6+3 M^4-3 M^2+1\right)+L^2 \left(M^{32}-3 M^{30}+3 M^{28}-M^{26}-4 M^{24}-9 M^{22}+15 M^{20}+13 M^{18}-2 M^{16}+13 M^{14}+15 M^{12}-9 M^{10}-4 M^8-M^6+3 M^4-3 M^2+1\right)+L^4 \left(6 M^{32}-26 M^{30}+22 M^{28}+40 M^{26}-59 M^{24}-64 M^{22}+82 M^{20}+50 M^{18}-32 M^{16}+50 M^{14}+82 M^{12}-64 M^{10}-59 M^8+40 M^6+22 M^4-26 M^2+6\right)&amp;lt;/math&amp;gt;&lt;/div&gt;</summary>
		<author><name>ScottDataRobot</name></author>
	</entry>
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