https://katlas.org/index.php?action=history&feed=atom&title=Data%3AL11a511%2FKauffman_Polynomial 2026-06-04T23:46:36Z Revision history for this page on the wiki MediaWiki 1.39.6 https://katlas.org/index.php?title=Data:L11a511/Kauffman_Polynomial&diff=1715326&oldid=prev 2013-02-20T20:38:03Z

<p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:38, 20 February 2013</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="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;"><div>&lt;math&gt;z^<del style="font-weight: bold; text-decoration: none;">{10}</del> a^{-<del style="font-weight: bold; text-decoration: none;">2</del>} <del style="font-weight: bold; text-decoration: none;">+</del>z^<del style="font-weight: bold; text-decoration: none;">{10}</del> a^{-<del style="font-weight: bold; text-decoration: none;">4</del>} +3 z^<del style="font-weight: bold; text-decoration: none;">9</del> a^{-<del style="font-weight: bold; text-decoration: none;">1</del>} <del style="font-weight: bold; text-decoration: none;">+7</del> z^<del style="font-weight: bold; text-decoration: none;">9</del> a^{-<del style="font-weight: bold; text-decoration: none;">3</del>} +<del style="font-weight: bold; text-decoration: none;">4</del> z^<del style="font-weight: bold; text-decoration: none;">9</del> a^{-<del style="font-weight: bold; text-decoration: none;">5</del>} +<del style="font-weight: bold; text-decoration: none;">8</del> z^<del style="font-weight: bold; text-decoration: none;">8</del> a^{-<del style="font-weight: bold; text-decoration: none;">2</del>} <del style="font-weight: bold; text-decoration: none;">+</del>10 z^<del style="font-weight: bold; text-decoration: none;">8</del> a^{-<del style="font-weight: bold; text-decoration: none;">4</del>} +6 z^<del style="font-weight: bold; text-decoration: none;">8</del> a^{-<del style="font-weight: bold; text-decoration: none;">6</del>} <del style="font-weight: bold; text-decoration: none;">+4 </del>z<del style="font-weight: bold; text-decoration: none;">^8+3</del> a<del style="font-weight: bold; text-decoration: none;"> z</del>^<del style="font-weight: bold; text-decoration: none;">7</del>-z^<del style="font-weight: bold; text-decoration: none;">7</del> a^{-<del style="font-weight: bold; text-decoration: none;">1</del>} -<del style="font-weight: bold; text-decoration: none;">13</del> z^<del style="font-weight: bold; text-decoration: none;">7</del> a^{-<del style="font-weight: bold; text-decoration: none;">3</del>} <del style="font-weight: bold; text-decoration: none;">-4</del> z^<del style="font-weight: bold; text-decoration: none;">7</del> a^{-<del style="font-weight: bold; text-decoration: none;">5</del>} <del style="font-weight: bold; text-decoration: none;">+5</del> z^<del style="font-weight: bold; text-decoration: none;">7</del> a^{-<del style="font-weight: bold; text-decoration: none;">7</del>} +<del style="font-weight: bold; text-decoration: none;">a^</del>2 <del style="font-weight: bold; text-decoration: none;">z</del>^<del style="font-weight: bold; text-decoration: none;">6</del>-<del style="font-weight: bold; text-decoration: none;">27</del> z^<del style="font-weight: bold; text-decoration: none;">6</del> a^{-<del style="font-weight: bold; text-decoration: none;">2</del>} -<del style="font-weight: bold; text-decoration: none;">35</del> z^<del style="font-weight: bold; text-decoration: none;">6</del> a^{-<del style="font-weight: bold; text-decoration: none;">4</del>} -<del style="font-weight: bold; text-decoration: none;">14</del> z^<del style="font-weight: bold; text-decoration: none;">6</del> a^{-<del style="font-weight: bold; text-decoration: none;">6</del>} +<del style="font-weight: bold; text-decoration: none;">3</del> z^<del style="font-weight: bold; text-decoration: none;">6</del> a^{-<del style="font-weight: bold; text-decoration: none;">8</del>} -<del style="font-weight: bold; text-decoration: none;">8</del> z<del style="font-weight: bold; text-decoration: none;">^6-8</del> a<del style="font-weight: bold; text-decoration: none;"> z</del>^<del style="font-weight: bold; text-decoration: none;">5</del>-<del style="font-weight: bold; text-decoration: none;">10</del> z^<del style="font-weight: bold; text-decoration: none;">5</del> a^{-<del style="font-weight: bold; text-decoration: none;">1</del>} +<del style="font-weight: bold; text-decoration: none;">7</del> z^<del style="font-weight: bold; text-decoration: none;">5</del> a^{-<del style="font-weight: bold; text-decoration: none;">3</del>} -<del style="font-weight: bold; text-decoration: none;">2</del> z^<del style="font-weight: bold; text-decoration: none;">5</del> a^{-<del style="font-weight: bold; text-decoration: none;">5</del>} <del style="font-weight: bold; text-decoration: none;">-10</del> z^<del style="font-weight: bold; text-decoration: none;">5</del> a^{-<del style="font-weight: bold; text-decoration: none;">7</del>} <del style="font-weight: bold; text-decoration: none;">+</del>z^<del style="font-weight: bold; text-decoration: none;">5</del> a^{-<del style="font-weight: bold; text-decoration: none;">9</del>} -<del style="font-weight: bold; text-decoration: none;">3</del> a^<del style="font-weight: bold; text-decoration: none;">2 z^</del>4<del style="font-weight: bold; text-decoration: none;">+35</del> z<del style="font-weight: bold; text-decoration: none;">^4 a</del>^{-2} +<del style="font-weight: bold; text-decoration: none;">53 z^4</del> a^{-4} +<del style="font-weight: bold; text-decoration: none;">17</del> z^<del style="font-weight: bold; text-decoration: none;">4</del> a^{-<del style="font-weight: bold; text-decoration: none;">6</del>} -<del style="font-weight: bold; text-decoration: none;">6</del> z^<del style="font-weight: bold; text-decoration: none;">4</del> a^{-<del style="font-weight: bold; text-decoration: none;">8</del>} +<del style="font-weight: bold; text-decoration: none;">2</del> z^<del style="font-weight: bold; text-decoration: none;">4+</del>5 a<del style="font-weight: bold; text-decoration: none;"> z</del>^3+<del style="font-weight: bold; text-decoration: none;">9</del> z^3 a^{-<del style="font-weight: bold; text-decoration: none;">1</del>} <del style="font-weight: bold; text-decoration: none;">+5</del> z<del style="font-weight: bold; text-decoration: none;">^3</del> a^{-3} +<del style="font-weight: bold; text-decoration: none;">9</del> <del style="font-weight: bold; text-decoration: none;">z</del>^3 <del style="font-weight: bold; text-decoration: none;">a</del>^{-<del style="font-weight: bold; text-decoration: none;">5</del>} +<del style="font-weight: bold; text-decoration: none;">6 </del>z^<del style="font-weight: bold; text-decoration: none;">3</del> a^{-<del style="font-weight: bold; text-decoration: none;">7</del>} <del style="font-weight: bold; text-decoration: none;">-2</del> z^<del style="font-weight: bold; text-decoration: none;">3</del> a^{-<del style="font-weight: bold; text-decoration: none;">9</del>} +<del style="font-weight: bold; text-decoration: none;">3 </del>a^2 z^<del style="font-weight: bold; text-decoration: none;">2</del>-<del style="font-weight: bold; text-decoration: none;">29</del> z^<del style="font-weight: bold; text-decoration: none;">2</del> a^{-2} -<del style="font-weight: bold; text-decoration: none;">35</del> <del style="font-weight: bold; text-decoration: none;">z</del>^2 <del style="font-weight: bold; text-decoration: none;">a</del>^<del style="font-weight: bold; text-decoration: none;">{-</del>4<del style="font-weight: bold; text-decoration: none;">} -9</del> z^<del style="font-weight: bold; text-decoration: none;">2</del> a^{-<del style="font-weight: bold; text-decoration: none;">6</del>} +2 z^2 a^{-<del style="font-weight: bold; text-decoration: none;">8</del>} -2 <del style="font-weight: bold; text-decoration: none;">z</del>^2<del style="font-weight: bold; text-decoration: none;">-6</del> z<del style="font-weight: bold; text-decoration: none;"> a</del>^{-<del style="font-weight: bold; text-decoration: none;">1</del>} -<del style="font-weight: bold; text-decoration: none;">8 z</del> a^{-<del style="font-weight: bold; text-decoration: none;">3</del>} <del style="font-weight: bold; text-decoration: none;">-</del>3 z a^{-<del style="font-weight: bold; text-decoration: none;">5</del>} -z a^{-<del style="font-weight: bold; text-decoration: none;">7</del>} -<del style="font-weight: bold; text-decoration: none;">a^2+12</del> a^<del style="font-weight: bold; text-decoration: none;">{</del>-<del style="font-weight: bold; text-decoration: none;">2} +</del>10 a^{-<del style="font-weight: bold; text-decoration: none;">4</del>} +<del style="font-weight: bold; text-decoration: none;">2</del> a^<del style="font-weight: bold; text-decoration: none;">{-6} </del>+<del style="font-weight: bold; text-decoration: none;">4+2</del> a^{-1} z^{-1} +2 a^{-<del style="font-weight: bold; text-decoration: none;">3</del>} z^{-1} <del style="font-weight: bold; text-decoration: none;">-2</del> <del style="font-weight: bold; text-decoration: none;">a</del>^<del style="font-weight: bold; text-decoration: none;">{</del>-<del style="font-weight: bold; text-decoration: none;">2}</del> z^<del style="font-weight: bold; text-decoration: none;">{-</del>2<del style="font-weight: bold; text-decoration: none;">}</del> <del style="font-weight: bold; text-decoration: none;">- a</del>^<del style="font-weight: bold; text-decoration: none;">{</del>-<del style="font-weight: bold; text-decoration: none;">4}</del> z^<del style="font-weight: bold; text-decoration: none;">{-</del>2<del style="font-weight: bold; text-decoration: none;">} </del>- z^{-2} &lt;/math&gt;</div></td> <td class="diff-marker" data-marker="+"></td> <td style="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;"><div>&lt;math&gt;z^<ins style="font-weight: bold; text-decoration: none;">5</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">9</ins>} <ins style="font-weight: bold; text-decoration: none;">-2 </ins>z^<ins style="font-weight: bold; text-decoration: none;">3</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">9</ins>} +3 z^<ins style="font-weight: bold; text-decoration: none;">6</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">8</ins>} <ins style="font-weight: bold; text-decoration: none;">-6</ins> z^<ins style="font-weight: bold; text-decoration: none;">4</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">8</ins>} +<ins style="font-weight: bold; text-decoration: none;">2</ins> z^<ins style="font-weight: bold; text-decoration: none;">2</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">8</ins>} +<ins style="font-weight: bold; text-decoration: none;">5</ins> z^<ins style="font-weight: bold; text-decoration: none;">7</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">7</ins>} <ins style="font-weight: bold; text-decoration: none;">-</ins>10 z^<ins style="font-weight: bold; text-decoration: none;">5</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">7</ins>} +6 z^<ins style="font-weight: bold; text-decoration: none;">3</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">7</ins>} <ins style="font-weight: bold; text-decoration: none;">-</ins>z a^<ins style="font-weight: bold; text-decoration: none;">{</ins>-<ins style="font-weight: bold; text-decoration: none;">7} +6 </ins>z^<ins style="font-weight: bold; text-decoration: none;">8</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">6</ins>} -<ins style="font-weight: bold; text-decoration: none;">14</ins> z^<ins style="font-weight: bold; text-decoration: none;">6</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">6</ins>} <ins style="font-weight: bold; text-decoration: none;">+17</ins> z^<ins style="font-weight: bold; text-decoration: none;">4</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">6</ins>} <ins style="font-weight: bold; text-decoration: none;">-9</ins> z^<ins style="font-weight: bold; text-decoration: none;">2</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">6</ins>} +2 <ins style="font-weight: bold; text-decoration: none;">a</ins>^<ins style="font-weight: bold; text-decoration: none;">{</ins>-<ins style="font-weight: bold; text-decoration: none;">6} +4</ins> z^<ins style="font-weight: bold; text-decoration: none;">9</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">5</ins>} -<ins style="font-weight: bold; text-decoration: none;">4</ins> z^<ins style="font-weight: bold; text-decoration: none;">7</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">5</ins>} -<ins style="font-weight: bold; text-decoration: none;">2</ins> z^<ins style="font-weight: bold; text-decoration: none;">5</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">5</ins>} +<ins style="font-weight: bold; text-decoration: none;">9</ins> z^<ins style="font-weight: bold; text-decoration: none;">3</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">5</ins>} -<ins style="font-weight: bold; text-decoration: none;">3</ins> z a^<ins style="font-weight: bold; text-decoration: none;">{</ins>-<ins style="font-weight: bold; text-decoration: none;">5}</ins> <ins style="font-weight: bold; text-decoration: none;">+</ins>z^<ins style="font-weight: bold; text-decoration: none;">{10}</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">4</ins>} +<ins style="font-weight: bold; text-decoration: none;">10</ins> z^<ins style="font-weight: bold; text-decoration: none;">8</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">4</ins>} -<ins style="font-weight: bold; text-decoration: none;">35</ins> z^<ins style="font-weight: bold; text-decoration: none;">6</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">4</ins>} <ins style="font-weight: bold; text-decoration: none;">+53</ins> z^<ins style="font-weight: bold; text-decoration: none;">4</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">4</ins>} <ins style="font-weight: bold; text-decoration: none;">-35 </ins>z^<ins style="font-weight: bold; text-decoration: none;">2</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">4</ins>} - a^<ins style="font-weight: bold; text-decoration: none;">{-</ins>4<ins style="font-weight: bold; text-decoration: none;">}</ins> z^{-2} +<ins style="font-weight: bold; text-decoration: none;">10</ins> a^{-4} +<ins style="font-weight: bold; text-decoration: none;">7</ins> z^<ins style="font-weight: bold; text-decoration: none;">9</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">3</ins>} -<ins style="font-weight: bold; text-decoration: none;">13</ins> z^<ins style="font-weight: bold; text-decoration: none;">7</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">3</ins>} +<ins style="font-weight: bold; text-decoration: none;">7</ins> z^5 a^<ins style="font-weight: bold; text-decoration: none;">{-</ins>3<ins style="font-weight: bold; text-decoration: none;">} </ins>+<ins style="font-weight: bold; text-decoration: none;">5</ins> z^3 a^{-<ins style="font-weight: bold; text-decoration: none;">3</ins>} <ins style="font-weight: bold; text-decoration: none;">-8</ins> z a^{-3} +<ins style="font-weight: bold; text-decoration: none;">2</ins> <ins style="font-weight: bold; text-decoration: none;">a</ins>^<ins style="font-weight: bold; text-decoration: none;">{-</ins>3<ins style="font-weight: bold; text-decoration: none;">}</ins> <ins style="font-weight: bold; text-decoration: none;">z</ins>^{-<ins style="font-weight: bold; text-decoration: none;">1</ins>} +z^<ins style="font-weight: bold; text-decoration: none;">{10}</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">2</ins>} <ins style="font-weight: bold; text-decoration: none;">+8</ins> z^<ins style="font-weight: bold; text-decoration: none;">8</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">2</ins>} +a^2 z^<ins style="font-weight: bold; text-decoration: none;">6</ins>-<ins style="font-weight: bold; text-decoration: none;">27</ins> z^<ins style="font-weight: bold; text-decoration: none;">6</ins> a^{-2} -<ins style="font-weight: bold; text-decoration: none;">3</ins> <ins style="font-weight: bold; text-decoration: none;">a</ins>^2 <ins style="font-weight: bold; text-decoration: none;">z</ins>^4<ins style="font-weight: bold; text-decoration: none;">+35</ins> z^<ins style="font-weight: bold; text-decoration: none;">4</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">2</ins>} +<ins style="font-weight: bold; text-decoration: none;">3 a^</ins>2<ins style="font-weight: bold; text-decoration: none;"> z^2-29</ins> z^2 a^{-<ins style="font-weight: bold; text-decoration: none;">2</ins>} -2 <ins style="font-weight: bold; text-decoration: none;">a</ins>^<ins style="font-weight: bold; text-decoration: none;">{-</ins>2<ins style="font-weight: bold; text-decoration: none;">}</ins> z^{-<ins style="font-weight: bold; text-decoration: none;">2</ins>} -<ins style="font-weight: bold; text-decoration: none;">a^2+12</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">2</ins>} <ins style="font-weight: bold; text-decoration: none;">+</ins>3 z<ins style="font-weight: bold; text-decoration: none;">^9</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">1</ins>} <ins style="font-weight: bold; text-decoration: none;">+3 a z^7</ins>-z<ins style="font-weight: bold; text-decoration: none;">^7</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">1</ins>} -<ins style="font-weight: bold; text-decoration: none;">8</ins> a<ins style="font-weight: bold; text-decoration: none;"> z</ins>^<ins style="font-weight: bold; text-decoration: none;">5</ins>-10<ins style="font-weight: bold; text-decoration: none;"> z^5</ins> a^{-<ins style="font-weight: bold; text-decoration: none;">1</ins>} +<ins style="font-weight: bold; text-decoration: none;">5</ins> a<ins style="font-weight: bold; text-decoration: none;"> z</ins>^<ins style="font-weight: bold; text-decoration: none;">3</ins>+<ins style="font-weight: bold; text-decoration: none;">9 z^3</ins> a^{-1}<ins style="font-weight: bold; text-decoration: none;"> -6</ins> z<ins style="font-weight: bold; text-decoration: none;"> a</ins>^{-1} +2 a^{-<ins style="font-weight: bold; text-decoration: none;">1</ins>} z^{-1} <ins style="font-weight: bold; text-decoration: none;">+4</ins> <ins style="font-weight: bold; text-decoration: none;">z</ins>^<ins style="font-weight: bold; text-decoration: none;">8</ins>-<ins style="font-weight: bold; text-decoration: none;">8</ins> z^<ins style="font-weight: bold; text-decoration: none;">6+</ins>2 <ins style="font-weight: bold; text-decoration: none;">z</ins>^<ins style="font-weight: bold; text-decoration: none;">4</ins>-<ins style="font-weight: bold; text-decoration: none;">2</ins> z^2- z^{-2} <ins style="font-weight: bold; text-decoration: none;">+4</ins>&lt;/math&gt;</div></td> </tr> </table>

ScottDataRobot https://katlas.org/index.php?title=Data:L11a511/Kauffman_Polynomial&diff=81043&oldid=prev 2005-08-26T19:06:41Z

<p></p> <p><b>New page</b></p><div>&lt;math&gt;z^{10} a^{-2} +z^{10} a^{-4} +3 z^9 a^{-1} +7 z^9 a^{-3} +4 z^9 a^{-5} +8 z^8 a^{-2} +10 z^8 a^{-4} +6 z^8 a^{-6} +4 z^8+3 a z^7-z^7 a^{-1} -13 z^7 a^{-3} -4 z^7 a^{-5} +5 z^7 a^{-7} +a^2 z^6-27 z^6 a^{-2} -35 z^6 a^{-4} -14 z^6 a^{-6} +3 z^6 a^{-8} -8 z^6-8 a z^5-10 z^5 a^{-1} +7 z^5 a^{-3} -2 z^5 a^{-5} -10 z^5 a^{-7} +z^5 a^{-9} -3 a^2 z^4+35 z^4 a^{-2} +53 z^4 a^{-4} +17 z^4 a^{-6} -6 z^4 a^{-8} +2 z^4+5 a z^3+9 z^3 a^{-1} +5 z^3 a^{-3} +9 z^3 a^{-5} +6 z^3 a^{-7} -2 z^3 a^{-9} +3 a^2 z^2-29 z^2 a^{-2} -35 z^2 a^{-4} -9 z^2 a^{-6} +2 z^2 a^{-8} -2 z^2-6 z a^{-1} -8 z a^{-3} -3 z a^{-5} -z a^{-7} -a^2+12 a^{-2} +10 a^{-4} +2 a^{-6} +4+2 a^{-1} z^{-1} +2 a^{-3} z^{-1} -2 a^{-2} z^{-2} - a^{-4} z^{-2} - z^{-2} &lt;/math&gt;</div>

ScottDataRobot