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L8n8 - Revision history
2026-05-05T02:36:21Z
Revision history for this page on the wiki
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DrorsRobot at 07:57, 3 September 2005
2005-09-03T07:57:41Z
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<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 03:57, 3 September 2005</td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>k = 8 |</div></td>
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<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>braid_table = <table cellspacing=0 cellpadding=0 border=0<ins style="font-weight: bold; text-decoration: none;"> style="white-space: pre"</ins>></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]]</td></tr></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </tr></div></td>
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<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> <tr valign=top><td colspan=2>Loading KnotTheory` (version of September <del style="font-weight: bold; text-decoration: none;">2</del>, 2005, <del style="font-weight: bold; text-decoration: none;">15</del>:<del style="font-weight: bold; text-decoration: none;">8</del>:<del style="font-weight: bold; text-decoration: none;">39</del>)...</td></tr></div></td>
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<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> <tr valign=top><td colspan=2>Loading KnotTheory` (version of September <ins style="font-weight: bold; text-decoration: none;">3</ins>, 2005, <ins style="font-weight: bold; text-decoration: none;">2</ins>:<ins style="font-weight: bold; text-decoration: none;">11</ins>:<ins style="font-weight: bold; text-decoration: none;">43</ins>)...</td></tr></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Crossings[Link[8, NonAlternating, 8]]</nowiki></pre></td></tr></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> <tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Crossings[Link[8, NonAlternating, 8]]</nowiki></pre></td></tr></div></td>
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DrorsRobot
https://katlas.org/index.php?title=L8n8&diff=47990&oldid=prev
DrorsRobot at 23:27, 2 September 2005
2005-09-02T23:27:07Z
<p></p>
<a href="https://katlas.org/index.php?title=L8n8&diff=47990&oldid=45995">Show changes</a>
DrorsRobot
https://katlas.org/index.php?title=L8n8&diff=45995&oldid=prev
DrorsRobot at 17:21, 31 August 2005
2005-08-31T17:21:03Z
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<a href="https://katlas.org/index.php?title=L8n8&diff=45995&oldid=41658">Show changes</a>
DrorsRobot
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ScottKnotPageRobot at 15:57, 30 August 2005
2005-08-30T15:57:55Z
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<a href="https://katlas.org/index.php?title=L8n8&diff=41658&oldid=37018">Show changes</a>
ScottKnotPageRobot
https://katlas.org/index.php?title=L8n8&diff=37018&oldid=prev
ScottTestRobot at 01:14, 29 August 2005
2005-08-29T01:14:40Z
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<p><b>New page</b></p><div><!-- --><br />
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{{Knot Navigation Links|ext=gif}}<br />
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{{Link Page Header|n=8|t=n|k=8|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,-4,5:2,-1,-6,7:-5,4,3,-8:-7,6,8,-3/goTop.html}}<br />
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{{:{{PAGENAME}} Further Notes and Views}}<br />
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{{Link Presentations}}<br />
{{Link Polynomial Invariants}}<br />
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{{Khovanov Homology|table=<table border=1><br />
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<tr><td>\</td><td>&nbsp;</td><td>r</td></tr><br />
<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr><br />
<tr><td>j</td><td>&nbsp;</td><td>\</td></tr><br />
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<td width=7.69231%>-4</td ><td width=7.69231%>-3</td ><td width=7.69231%>-2</td ><td width=7.69231%>-1</td ><td width=7.69231%>0</td ><td width=7.69231%>1</td ><td width=7.69231%>2</td ><td width=7.69231%>3</td ><td width=7.69231%>4</td ><td width=15.3846%>&chi;</td></tr><br />
<tr align=center><td>8</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=red>1</td><td>1</td></tr><br />
<tr align=center><td>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=red>1</td><td>1</td></tr><br />
<tr align=center><td>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=red>1</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=red>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr><br />
<tr align=center><td>0</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=red>1</td><td bgcolor=red>6</td><td bgcolor=red>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>4</td></tr><br />
<tr align=center><td>-2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=red>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr><br />
<tr align=center><td>-4</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=red>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>-6</td><td bgcolor=red>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
<tr align=center><td>-8</td><td bgcolor=red>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr><br />
</table>}}<br />
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<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td><br />
<td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td><br />
</tr><br />
<tr valign=top><td colspan=2><pre style="border: 0px; padding: 0em">Loading KnotTheory` (version of August 17, 2005, 14:44:34)...</pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Crossings[Link[8, NonAlternating, 8]]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>8</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[3]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[Link[8, NonAlternating, 8]]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[6, 1, 7, 2], X[2, 5, 3, 6], X[16, 11, 13, 12], X[3, 11, 4, 10], <br />
<br />
X[9, 1, 10, 4], X[7, 15, 8, 14], X[13, 5, 14, 8], X[12, 15, 9, 16]]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[4]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>GaussCode[Link[8, NonAlternating, 8]]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[{1, -2, -4, 5}, {2, -1, -6, 7}, {-5, 4, 3, -8}, <br />
<br />
{-7, 6, 8, -3}]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[5]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>BR[Link[8, NonAlternating, 8]]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[Link[8, NonAlternating, 8]]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[6]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[Link[8, NonAlternating, 8]][t]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>Indeterminate</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[Link[8, NonAlternating, 8]][z]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>Indeterminate</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[8]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{}</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{KnotDet[Link[8, NonAlternating, 8]], KnotSignature[Link[8, NonAlternating, 8]]}</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Indeterminate, 0}</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>J=Jones[Link[8, NonAlternating, 8]][q]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -(7/2) -(3/2) 2 3/2 7/2<br />
-q - q - ------- - 2 Sqrt[q] - q - q<br />
Sqrt[q]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[11]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{}</nowiki></pre></td></tr><br />
<math>\textrm{Include}(\textrm{ColouredJonesM.mhtml})</math><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[12]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>A2Invariant[Link[8, NonAlternating, 8]][q]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -12 2 4 6 9 12 2 4 6 8<br />
13 + q + --- + -- + -- + -- + -- + 12 q + 9 q + 6 q + 4 q + <br />
10 8 6 4 2<br />
q q q q q<br />
<br />
10 12<br />
2 q + q</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Link[8, NonAlternating, 8]][a, z]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 3 2<br />
8 2 1 3 3 a a 6 3 3 a 4<br />
-15 - -- - 8 a - ----- - ---- - --- - -- + -- + ----- + ---- + ---- + <br />
2 3 3 3 3 3 2 2 2 2 3<br />
a a z a z z z z a z z a z<br />
<br />
3 2<br />
9 9 a 4 a 6 z 14 z 3 2 6 z<br />
--- + --- + ---- - --- - ---- - 14 a z - 6 a z + 12 z + ---- + <br />
a z z z 3 a 2<br />
a a<br />
<br />
3 3 4 5<br />
2 2 5 z 7 z 3 3 3 4 z 2 4 z<br />
6 a z + ---- + ---- + 7 a z + 5 a z - 2 z - -- - a z - -- - <br />
3 a 2 3<br />
a a a<br />
<br />
5<br />
z 5 3 5<br />
-- - a z - a z<br />
a</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[14]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{Vassiliev[2][Link[8, NonAlternating, 8]], Vassiliev[3][Link[8, NonAlternating, 8]]}</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 0}</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[15]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[Link[8, NonAlternating, 8]][q, t]</nowiki></pre></td></tr><br />
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 3 2 1 1 1 1 4 2 6 4 8 4<br />
6 + -- + 3 q + ----- + ----- + ----- + - + t + q t + q t + q t<br />
2 8 4 6 4 4 2 t<br />
q q t q t q t</nowiki></pre></td></tr><br />
</table><br />
<br />
[[Category:Knot Page]]</div>
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