10 12 - Revision history

ScottTestRobot at 21:59, 1 September 2005

2005-09-01T21:59:24Z

DrorsRobot at 22:43, 31 August 2005

2005-08-31T22:43:42Z

← Older revision		Revision as of 18:43, 31 August 2005
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	coloured_jones_3 = <math>-q^{45}+2 q^{44}-q^{42}-3 q^{41}+4 q^{40}+2 q^{39}-4 q^{38}-5 q^{37}+10 q^{36}+5 q^{35}-13 q^{34}-14 q^{33}+24 q^{32}+21 q^{31}-28 q^{30}-38 q^{29}+32 q^{28}+58 q^{27}-31 q^{26}-79 q^{25}+23 q^{24}+101 q^{23}-14 q^{22}-116 q^{21}-3 q^{20}+133 q^{19}+11 q^{18}-135 q^{17}-28 q^{16}+141 q^{15}+31 q^{14}-128 q^{13}-46 q^{12}+122 q^{11}+47 q^{10}-98 q^9-57 q^8+82 q^7+52 q^6-50 q^5-57 q^4+37 q^3+42 q^2-13 q-37+7 q^{-1} +24 q^{-2} -16 q^{-4} - q^{-5} +10 q^{-6} - q^{-7} -5 q^{-8} +4 q^{-10} -2 q^{-11} - q^{-12} +2 q^{-14} - q^{-15} </math> \|		coloured_jones_3 = <math>-q^{45}+2 q^{44}-q^{42}-3 q^{41}+4 q^{40}+2 q^{39}-4 q^{38}-5 q^{37}+10 q^{36}+5 q^{35}-13 q^{34}-14 q^{33}+24 q^{32}+21 q^{31}-28 q^{30}-38 q^{29}+32 q^{28}+58 q^{27}-31 q^{26}-79 q^{25}+23 q^{24}+101 q^{23}-14 q^{22}-116 q^{21}-3 q^{20}+133 q^{19}+11 q^{18}-135 q^{17}-28 q^{16}+141 q^{15}+31 q^{14}-128 q^{13}-46 q^{12}+122 q^{11}+47 q^{10}-98 q^9-57 q^8+82 q^7+52 q^6-50 q^5-57 q^4+37 q^3+42 q^2-13 q-37+7 q^{-1} +24 q^{-2} -16 q^{-4} - q^{-5} +10 q^{-6} - q^{-7} -5 q^{-8} +4 q^{-10} -2 q^{-11} - q^{-12} +2 q^{-14} - q^{-15} </math> \|
	coloured_jones_4 = <math>q^{74}-2 q^{73}+q^{71}-q^{70}+6 q^{69}-6 q^{68}+q^{66}-8 q^{65}+16 q^{64}-11 q^{63}+6 q^{62}+7 q^{61}-24 q^{60}+22 q^{59}-29 q^{58}+18 q^{57}+34 q^{56}-30 q^{55}+29 q^{54}-84 q^{53}+7 q^{52}+74 q^{51}+q^{50}+80 q^{49}-159 q^{48}-61 q^{47}+68 q^{46}+51 q^{45}+214 q^{44}-191 q^{43}-165 q^{42}-21 q^{41}+61 q^{40}+394 q^{39}-142 q^{38}-237 q^{37}-163 q^{36}+5 q^{35}+549 q^{34}-48 q^{33}-253 q^{32}-286 q^{31}-78 q^{30}+633 q^{29}+35 q^{28}-226 q^{27}-354 q^{26}-151 q^{25}+645 q^{24}+91 q^{23}-173 q^{22}-368 q^{21}-210 q^{20}+581 q^{19}+131 q^{18}-84 q^{17}-330 q^{16}-263 q^{15}+439 q^{14}+142 q^{13}+33 q^{12}-227 q^{11}-284 q^{10}+244 q^9+102 q^8+125 q^7-90 q^6-238 q^5+82 q^4+22 q^3+135 q^2+15 q-141+9 q^{-1} -39 q^{-2} +86 q^{-3} +44 q^{-4} -60 q^{-5} +6 q^{-6} -47 q^{-7} +34 q^{-8} +27 q^{-9} -22 q^{-10} +14 q^{-11} -26 q^{-12} +9 q^{-13} +9 q^{-14} -11 q^{-15} +12 q^{-16} -8 q^{-17} +2 q^{-18} +2 q^{-19} -6 q^{-20} +5 q^{-21} - q^{-22} + q^{-23} -2 q^{-25} + q^{-26} </math> \|		coloured_jones_4 = <math>q^{74}-2 q^{73}+q^{71}-q^{70}+6 q^{69}-6 q^{68}+q^{66}-8 q^{65}+16 q^{64}-11 q^{63}+6 q^{62}+7 q^{61}-24 q^{60}+22 q^{59}-29 q^{58}+18 q^{57}+34 q^{56}-30 q^{55}+29 q^{54}-84 q^{53}+7 q^{52}+74 q^{51}+q^{50}+80 q^{49}-159 q^{48}-61 q^{47}+68 q^{46}+51 q^{45}+214 q^{44}-191 q^{43}-165 q^{42}-21 q^{41}+61 q^{40}+394 q^{39}-142 q^{38}-237 q^{37}-163 q^{36}+5 q^{35}+549 q^{34}-48 q^{33}-253 q^{32}-286 q^{31}-78 q^{30}+633 q^{29}+35 q^{28}-226 q^{27}-354 q^{26}-151 q^{25}+645 q^{24}+91 q^{23}-173 q^{22}-368 q^{21}-210 q^{20}+581 q^{19}+131 q^{18}-84 q^{17}-330 q^{16}-263 q^{15}+439 q^{14}+142 q^{13}+33 q^{12}-227 q^{11}-284 q^{10}+244 q^9+102 q^8+125 q^7-90 q^6-238 q^5+82 q^4+22 q^3+135 q^2+15 q-141+9 q^{-1} -39 q^{-2} +86 q^{-3} +44 q^{-4} -60 q^{-5} +6 q^{-6} -47 q^{-7} +34 q^{-8} +27 q^{-9} -22 q^{-10} +14 q^{-11} -26 q^{-12} +9 q^{-13} +9 q^{-14} -11 q^{-15} +12 q^{-16} -8 q^{-17} +2 q^{-18} +2 q^{-19} -6 q^{-20} +5 q^{-21} - q^{-22} + q^{-23} -2 q^{-25} + q^{-26} </math> \|
	coloured_jones_5 = \|		coloured_jones_5 = <math>\textrm{NotAvailable}(q)</math> \|
	coloured_jones_6 = \|		coloured_jones_6 = <math>\textrm{NotAvailable}(q)</math> \|
	coloured_jones_7 = \|		coloured_jones_7 = <math>\textrm{NotAvailable}(q)</math> \|
	computer_talk =		computer_talk =
	<table>		<table>
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	<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td>		<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td>
	</tr>		</tr>
	<tr valign=top><td colspan=2>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</td></tr>		<tr valign=top><td colspan=2>Loading KnotTheory` (version of August 29, 2005, 15:27:48)...</td></tr>
	<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>PD[Knot[10, 12]]</nowiki></pre></td></tr>		<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>PD[Knot[10, 12]]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[1, 4, 2, 5], X[3, 10, 4, 11], X[13, 19, 14, 18], X[5, 15, 6, 14],		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[1, 4, 2, 5], X[3, 10, 4, 11], X[13, 19, 14, 18], X[5, 15, 6, 14],
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	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>4</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>4</nowiki></pre></td></tr>
	<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>Show[DrawMorseLink[Knot[10, 12]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_12_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[8]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr>		<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>Show[DrawMorseLink[Knot[10, 12]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_12_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[8]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr>
	<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>(#[Knot[10, 12]]&) /@ {~~SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}</nowiki></pre></td></tr>~~		<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> (#[Knot[10, 12]]&) /@ {
			SymmetryType, UnknottingNumber, ThreeGenus,
			BridgeIndex, SuperBridgeIndex, NakanishiIndex
			}</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Reversible, 2, 3, 2, NotAvailable, 1}</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Reversible, 2, 3, 2, NotAvailable, 1}</nowiki></pre></td></tr>
	<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>alex = Alexander[Knot[10, 12]][t]</nowiki></pre></td></tr>		<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>alex = Alexander[Knot[10, 12]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:35, 30 August 2005

2005-08-30T14:35:17Z

Show changes

DrorsRobot at 01:02, 30 August 2005

2005-08-30T01:02:28Z

← Older revision		Revision as of 21:02, 29 August 2005
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	</table>		</table>

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	See/edit the [[Rolfsen_Splice_Template]].		\|align=left\|See/edit the [[Rolfsen_Splice_Template]].

			Back to the [[#top\|top]].
			\|align=right\|{{Knot Navigation Links\|ext=gif}}
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	[[Category:Knot Page]]		[[Category:Knot Page]]

DrorsRobot at 22:14, 29 August 2005

2005-08-29T22:14:13Z

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ScottTestRobot at 00:08, 29 August 2005

2005-08-29T00:08:06Z

← Older revision		Revision as of 20:08, 28 August 2005
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		⚫	{{Rolfsen Knot Page Header\|n=10\|k=12\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-4,6,-5,7,-10,2,-8,9,-3,4,-6,5,-7,3,-9,8/goTop.html}}
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	{{Vassiliev Invariants}}		{{Vassiliev Invariants}}

	~~===[[~~Khovanov Homology~~]]=~~==		{{Khovanov Homology\|table=<table border=1>

	The coefficients of the monomials <math>t^rq^j</math> are shown, along with their alternating sums <math>\chi</math> (fixed <math>j</math>, alternation over <math>r</math>). The squares with <font class=HLYellow>yellow</font> highlighting are those on the "critical diagonals", where <math>j-2r=s+1</math> or <math>j-2r=s+1</math>, where <math>s=</math>{{Data:{{PAGENAME}}/Signature}} is the signature of {{PAGENAME}}. Nonzero entries off the critical diagonals (if any exist) are highlighted in <font class=HLRed>red</font>.

	<center><table border=1>
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	<tr align=center><td>-3</td><td bgcolor=yellow> </td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>		<tr align=center><td>-3</td><td bgcolor=yellow> </td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
	<tr align=center><td>-5</td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr>		<tr align=center><td>-5</td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr>
	</table>~~</center>~~		</table>}}

	{{Computer Talk Header}}		{{Computer Talk Header}}

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	3 q t + q t + q t + q t</nowiki></pre></td></tr>		3 q t + q t + q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

Scott at 23:45, 28 August 2005

2005-08-28T23:45:19Z

← Older revision		Revision as of 19:45, 28 August 2005
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	{\| align=left		{\| align=left
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	\|[[Image:{{PAGENAME}}.gif]]		\|[[Image:{{PAGENAME}}.gif]]
	\|{{Rolfsen Knot Site Links\|n=10\|k=12\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-4,6,-5,7,-10,2,-8,9,-3,4,-6,5,-7,3,-9,8/goTop.html}}		\|{{Rolfsen Knot Site Links\|n=10\|k=12\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-4,6,-5,7,-10,2,-8,9,-3,4,-6,5,-7,3,-9,8/goTop.html}}
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	\|{{:{{PAGENAME}} Quick Notes}}		\|{{:{{PAGENAME}} Quick Notes}}
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Scott at 23:44, 28 August 2005

2005-08-28T23:44:54Z

← Older revision		Revision as of 19:44, 28 August 2005
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	{\| align=left		{\| align=left
	\|- valign=top		\|- valign=top rowspan=2
	\|[[Image:{{PAGENAME}}.gif]]		\|[[Image:{{PAGENAME}}.gif]]
	\|{{Rolfsen Knot Site Links\|n=10\|k=12\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-4,6,-5,7,-10,2,-8,9,-3,4,-6,5,-7,3,-9,8/goTop.html}}		\|{{Rolfsen Knot Site Links\|n=10\|k=12\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-4,6,-5,7,-10,2,-8,9,-3,4,-6,5,-7,3,-9,8/goTop.html}}
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Scott at 23:44, 28 August 2005

2005-08-28T23:44:29Z

← Older revision		Revision as of 19:44, 28 August 2005
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	\|[[Image:{{PAGENAME}}.gif]]		\|[[Image:{{PAGENAME}}.gif]]
	\|{{Rolfsen Knot Site Links\|n=10\|k=12\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-4,6,-5,7,-10,2,-8,9,-3,4,-6,5,-7,3,-9,8/goTop.html}}		\|{{Rolfsen Knot Site Links\|n=10\|k=12\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-4,6,-5,7,-10,2,-8,9,-3,4,-6,5,-7,3,-9,8/goTop.html}}
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	\|{{:{{PAGENAME}} Quick Notes}}		\|{{:{{PAGENAME}} Quick Notes}}
	\|}		\|}

ScottTestRobot at 01:46, 28 August 2005

2005-08-28T01:46:01Z

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