ScottTestRobot at 22:04, 1 September 2005

2005-09-01T22:04:46Z

DrorsRobot at 22:53, 31 August 2005

2005-08-31T22:53:06Z

← Older revision		Revision as of 18:53, 31 August 2005
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	coloured_jones_3 = <math>q^6-2 q^5+2 q^3+4 q^2-8 q-6+11 q^{-1} +20 q^{-2} -21 q^{-3} -34 q^{-4} +18 q^{-5} +71 q^{-6} -20 q^{-7} -101 q^{-8} -7 q^{-9} +153 q^{-10} +33 q^{-11} -186 q^{-12} -92 q^{-13} +230 q^{-14} +144 q^{-15} -243 q^{-16} -223 q^{-17} +261 q^{-18} +281 q^{-19} -246 q^{-20} -351 q^{-21} +232 q^{-22} +402 q^{-23} -203 q^{-24} -438 q^{-25} +165 q^{-26} +459 q^{-27} -128 q^{-28} -449 q^{-29} +79 q^{-30} +429 q^{-31} -48 q^{-32} -372 q^{-33} +8 q^{-34} +314 q^{-35} +9 q^{-36} -239 q^{-37} -25 q^{-38} +174 q^{-39} +27 q^{-40} -117 q^{-41} -21 q^{-42} +70 q^{-43} +17 q^{-44} -41 q^{-45} -10 q^{-46} +22 q^{-47} +5 q^{-48} -11 q^{-49} - q^{-50} +3 q^{-51} +2 q^{-52} -3 q^{-53} + q^{-54} </math> \|		coloured_jones_3 = <math>q^6-2 q^5+2 q^3+4 q^2-8 q-6+11 q^{-1} +20 q^{-2} -21 q^{-3} -34 q^{-4} +18 q^{-5} +71 q^{-6} -20 q^{-7} -101 q^{-8} -7 q^{-9} +153 q^{-10} +33 q^{-11} -186 q^{-12} -92 q^{-13} +230 q^{-14} +144 q^{-15} -243 q^{-16} -223 q^{-17} +261 q^{-18} +281 q^{-19} -246 q^{-20} -351 q^{-21} +232 q^{-22} +402 q^{-23} -203 q^{-24} -438 q^{-25} +165 q^{-26} +459 q^{-27} -128 q^{-28} -449 q^{-29} +79 q^{-30} +429 q^{-31} -48 q^{-32} -372 q^{-33} +8 q^{-34} +314 q^{-35} +9 q^{-36} -239 q^{-37} -25 q^{-38} +174 q^{-39} +27 q^{-40} -117 q^{-41} -21 q^{-42} +70 q^{-43} +17 q^{-44} -41 q^{-45} -10 q^{-46} +22 q^{-47} +5 q^{-48} -11 q^{-49} - q^{-50} +3 q^{-51} +2 q^{-52} -3 q^{-53} + q^{-54} </math> \|
	coloured_jones_4 = <math>q^{12}-2 q^{11}+2 q^9-q^8+5 q^7-10 q^6-2 q^5+11 q^4+20 q^2-37 q-23+27 q^{-1} +20 q^{-2} +83 q^{-3} -83 q^{-4} -102 q^{-5} -3 q^{-6} +49 q^{-7} +272 q^{-8} -73 q^{-9} -237 q^{-10} -178 q^{-11} -26 q^{-12} +591 q^{-13} +123 q^{-14} -284 q^{-15} -505 q^{-16} -369 q^{-17} +877 q^{-18} +515 q^{-19} -57 q^{-20} -811 q^{-21} -986 q^{-22} +919 q^{-23} +929 q^{-24} +473 q^{-25} -898 q^{-26} -1697 q^{-27} +668 q^{-28} +1180 q^{-29} +1145 q^{-30} -727 q^{-31} -2296 q^{-32} +233 q^{-33} +1225 q^{-34} +1775 q^{-35} -402 q^{-36} -2677 q^{-37} -245 q^{-38} +1105 q^{-39} +2234 q^{-40} -16 q^{-41} -2775 q^{-42} -676 q^{-43} +831 q^{-44} +2427 q^{-45} +374 q^{-46} -2532 q^{-47} -948 q^{-48} +421 q^{-49} +2241 q^{-50} +677 q^{-51} -1951 q^{-52} -950 q^{-53} -9 q^{-54} +1697 q^{-55} +758 q^{-56} -1221 q^{-57} -682 q^{-58} -268 q^{-59} +1015 q^{-60} +593 q^{-61} -613 q^{-62} -331 q^{-63} -286 q^{-64} +476 q^{-65} +329 q^{-66} -262 q^{-67} -88 q^{-68} -178 q^{-69} +180 q^{-70} +134 q^{-71} -106 q^{-72} + q^{-73} -77 q^{-74} +60 q^{-75} +42 q^{-76} -42 q^{-77} +12 q^{-78} -24 q^{-79} +16 q^{-80} +11 q^{-81} -13 q^{-82} +5 q^{-83} -5 q^{-84} +3 q^{-85} +2 q^{-86} -3 q^{-87} + q^{-88} </math> \|		coloured_jones_4 = <math>q^{12}-2 q^{11}+2 q^9-q^8+5 q^7-10 q^6-2 q^5+11 q^4+20 q^2-37 q-23+27 q^{-1} +20 q^{-2} +83 q^{-3} -83 q^{-4} -102 q^{-5} -3 q^{-6} +49 q^{-7} +272 q^{-8} -73 q^{-9} -237 q^{-10} -178 q^{-11} -26 q^{-12} +591 q^{-13} +123 q^{-14} -284 q^{-15} -505 q^{-16} -369 q^{-17} +877 q^{-18} +515 q^{-19} -57 q^{-20} -811 q^{-21} -986 q^{-22} +919 q^{-23} +929 q^{-24} +473 q^{-25} -898 q^{-26} -1697 q^{-27} +668 q^{-28} +1180 q^{-29} +1145 q^{-30} -727 q^{-31} -2296 q^{-32} +233 q^{-33} +1225 q^{-34} +1775 q^{-35} -402 q^{-36} -2677 q^{-37} -245 q^{-38} +1105 q^{-39} +2234 q^{-40} -16 q^{-41} -2775 q^{-42} -676 q^{-43} +831 q^{-44} +2427 q^{-45} +374 q^{-46} -2532 q^{-47} -948 q^{-48} +421 q^{-49} +2241 q^{-50} +677 q^{-51} -1951 q^{-52} -950 q^{-53} -9 q^{-54} +1697 q^{-55} +758 q^{-56} -1221 q^{-57} -682 q^{-58} -268 q^{-59} +1015 q^{-60} +593 q^{-61} -613 q^{-62} -331 q^{-63} -286 q^{-64} +476 q^{-65} +329 q^{-66} -262 q^{-67} -88 q^{-68} -178 q^{-69} +180 q^{-70} +134 q^{-71} -106 q^{-72} + q^{-73} -77 q^{-74} +60 q^{-75} +42 q^{-76} -42 q^{-77} +12 q^{-78} -24 q^{-79} +16 q^{-80} +11 q^{-81} -13 q^{-82} +5 q^{-83} -5 q^{-84} +3 q^{-85} +2 q^{-86} -3 q^{-87} + q^{-88} </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, 25]]</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, 25]]</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[5, 14, 6, 15], X[3, 13, 4, 12], X[13, 3, 14, 2],		<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[5, 14, 6, 15], X[3, 13, 4, 12], X[13, 3, 14, 2],
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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, 25]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_25_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, 25]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_25_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, 25]]&) /@ {~~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, 25]]&) /@ {
			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, 25]][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, 25]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:40, 30 August 2005

2005-08-30T14:40:50Z

Show changes

DrorsRobot at 01:08, 30 August 2005

2005-08-30T01:08:39Z

← Older revision		Revision as of 21:08, 29 August 2005
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	</table>		</table>

			{\| width=100%
	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}}
			\|}

	[[Category:Knot Page]]		[[Category:Knot Page]]

DrorsRobot at 22:15, 29 August 2005

2005-08-29T22:15:15Z

Show changes

ScottTestRobot at 00:14, 29 August 2005

2005-08-29T00:14:57Z

← Older revision		Revision as of 20:14, 28 August 2005
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	<span id="top"></span>		<span id="top"></span>
			<!-- -->

	<!-- this relies on transclusion for next and previous links -->		<!-- this relies on transclusion for next and previous links -->
	{{Knot Navigation Links\|ext=gif}}		{{Knot Navigation Links\|ext=gif}}

		⚫	{{Rolfsen Knot Page Header\|n=10\|k=25\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-2,6,-8,9,-7,10,-5,3,-4,2,-10,8,-9,7,-6,5/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=25\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-2,6,-8,9,-7,10,-5,3,-4,2,-10,8,-9,7,-6,5/goTop.html}}
	\|{{:{{PAGENAME}} Quick Notes}}
	\|}

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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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	<td width=13.3333%><table cellpadding=0 cellspacing=0>		<td width=13.3333%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>-19</td><td bgcolor=yellow> </td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-2</td></tr>		<tr align=center><td>-19</td><td bgcolor=yellow> </td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-2</td></tr>
	<tr align=center><td>-21</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>-21</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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	q t q</nowiki></pre></td></tr>		q t q</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:51, 28 August 2005

2005-08-28T01:51:22Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:49:40Z

Resetting knot page to basic template.

New page

10 25 - Revision history

ScottTestRobot at 22:04, 1 September 2005

DrorsRobot at 22:53, 31 August 2005

ScottKnotPageRobot at 14:40, 30 August 2005

DrorsRobot at 01:08, 30 August 2005

DrorsRobot at 22:15, 29 August 2005

ScottTestRobot at 00:14, 29 August 2005

ScottTestRobot at 01:51, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.