ScottTestRobot at 22:00, 1 September 2005

2005-09-01T22:00:19Z

DrorsRobot at 22:45, 31 August 2005

2005-08-31T22:45:01Z

← Older revision		Revision as of 18:45, 31 August 2005
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	coloured_jones_5 = <math>-q^{11}+2 q^9+2 q^8-q^6-6 q^5-5 q^4+3 q^3+8 q^2+8 q+4-7 q^{-1} -17 q^{-2} -11 q^{-3} +3 q^{-4} +16 q^{-5} +22 q^{-6} +11 q^{-7} -12 q^{-8} -29 q^{-9} -27 q^{-10} - q^{-11} +27 q^{-12} +44 q^{-13} +26 q^{-14} -20 q^{-15} -56 q^{-16} -47 q^{-17} -2 q^{-18} +60 q^{-19} +77 q^{-20} +20 q^{-21} -59 q^{-22} -89 q^{-23} -50 q^{-24} +53 q^{-25} +111 q^{-26} +60 q^{-27} -45 q^{-28} -107 q^{-29} -84 q^{-30} +37 q^{-31} +123 q^{-32} +79 q^{-33} -34 q^{-34} -107 q^{-35} -97 q^{-36} +28 q^{-37} +123 q^{-38} +84 q^{-39} -30 q^{-40} -108 q^{-41} -94 q^{-42} +24 q^{-43} +118 q^{-44} +86 q^{-45} -25 q^{-46} -103 q^{-47} -92 q^{-48} +14 q^{-49} +104 q^{-50} +86 q^{-51} -5 q^{-52} -85 q^{-53} -88 q^{-54} -10 q^{-55} +71 q^{-56} +79 q^{-57} +25 q^{-58} -45 q^{-59} -71 q^{-60} -37 q^{-61} +22 q^{-62} +53 q^{-63} +43 q^{-64} + q^{-65} -32 q^{-66} -42 q^{-67} -17 q^{-68} +13 q^{-69} +30 q^{-70} +23 q^{-71} +8 q^{-72} -17 q^{-73} -24 q^{-74} -13 q^{-75} +2 q^{-76} +12 q^{-77} +20 q^{-78} +6 q^{-79} -7 q^{-80} -10 q^{-81} -9 q^{-82} -4 q^{-83} +8 q^{-84} +7 q^{-85} +3 q^{-86} + q^{-87} -4 q^{-88} -6 q^{-89} + q^{-91} +4 q^{-93} + q^{-94} -3 q^{-95} -3 q^{-98} +2 q^{-99} +2 q^{-100} - q^{-101} + q^{-103} -2 q^{-104} + q^{-106} + q^{-109} - q^{-110} </math> \|		coloured_jones_5 = <math>-q^{11}+2 q^9+2 q^8-q^6-6 q^5-5 q^4+3 q^3+8 q^2+8 q+4-7 q^{-1} -17 q^{-2} -11 q^{-3} +3 q^{-4} +16 q^{-5} +22 q^{-6} +11 q^{-7} -12 q^{-8} -29 q^{-9} -27 q^{-10} - q^{-11} +27 q^{-12} +44 q^{-13} +26 q^{-14} -20 q^{-15} -56 q^{-16} -47 q^{-17} -2 q^{-18} +60 q^{-19} +77 q^{-20} +20 q^{-21} -59 q^{-22} -89 q^{-23} -50 q^{-24} +53 q^{-25} +111 q^{-26} +60 q^{-27} -45 q^{-28} -107 q^{-29} -84 q^{-30} +37 q^{-31} +123 q^{-32} +79 q^{-33} -34 q^{-34} -107 q^{-35} -97 q^{-36} +28 q^{-37} +123 q^{-38} +84 q^{-39} -30 q^{-40} -108 q^{-41} -94 q^{-42} +24 q^{-43} +118 q^{-44} +86 q^{-45} -25 q^{-46} -103 q^{-47} -92 q^{-48} +14 q^{-49} +104 q^{-50} +86 q^{-51} -5 q^{-52} -85 q^{-53} -88 q^{-54} -10 q^{-55} +71 q^{-56} +79 q^{-57} +25 q^{-58} -45 q^{-59} -71 q^{-60} -37 q^{-61} +22 q^{-62} +53 q^{-63} +43 q^{-64} + q^{-65} -32 q^{-66} -42 q^{-67} -17 q^{-68} +13 q^{-69} +30 q^{-70} +23 q^{-71} +8 q^{-72} -17 q^{-73} -24 q^{-74} -13 q^{-75} +2 q^{-76} +12 q^{-77} +20 q^{-78} +6 q^{-79} -7 q^{-80} -10 q^{-81} -9 q^{-82} -4 q^{-83} +8 q^{-84} +7 q^{-85} +3 q^{-86} + q^{-87} -4 q^{-88} -6 q^{-89} + q^{-91} +4 q^{-93} + q^{-94} -3 q^{-95} -3 q^{-98} +2 q^{-99} +2 q^{-100} - q^{-101} + q^{-103} -2 q^{-104} + q^{-106} + q^{-109} - q^{-110} </math> \|
	coloured_jones_6 = <math>q^{20}-q^{19}-q^{18}-q^{14}+5 q^{13}+q^{12}-2 q^9-6 q^8-10 q^7+4 q^6+4 q^5+9 q^4+12 q^3+10 q^2-5 q-25-14 q^{-1} -14 q^{-2} -3 q^{-3} +18 q^{-4} +40 q^{-5} +33 q^{-6} -5 q^{-7} -15 q^{-8} -41 q^{-9} -57 q^{-10} -32 q^{-11} +30 q^{-12} +73 q^{-13} +60 q^{-14} +55 q^{-15} -6 q^{-16} -97 q^{-17} -125 q^{-18} -65 q^{-19} +35 q^{-20} +95 q^{-21} +165 q^{-22} +117 q^{-23} -51 q^{-24} -179 q^{-25} -194 q^{-26} -84 q^{-27} +47 q^{-28} +234 q^{-29} +259 q^{-30} +59 q^{-31} -160 q^{-32} -278 q^{-33} -203 q^{-34} -46 q^{-35} +241 q^{-36} +349 q^{-37} +154 q^{-38} -113 q^{-39} -303 q^{-40} -263 q^{-41} -117 q^{-42} +223 q^{-43} +380 q^{-44} +195 q^{-45} -84 q^{-46} -300 q^{-47} -273 q^{-48} -148 q^{-49} +210 q^{-50} +384 q^{-51} +202 q^{-52} -76 q^{-53} -295 q^{-54} -270 q^{-55} -152 q^{-56} +205 q^{-57} +380 q^{-58} +203 q^{-59} -72 q^{-60} -289 q^{-61} -267 q^{-62} -157 q^{-63} +191 q^{-64} +366 q^{-65} +213 q^{-66} -49 q^{-67} -263 q^{-68} -258 q^{-69} -180 q^{-70} +142 q^{-71} +322 q^{-72} +226 q^{-73} +11 q^{-74} -191 q^{-75} -225 q^{-76} -216 q^{-77} +47 q^{-78} +228 q^{-79} +216 q^{-80} +88 q^{-81} -73 q^{-82} -142 q^{-83} -222 q^{-84} -56 q^{-85} +91 q^{-86} +149 q^{-87} +120 q^{-88} +39 q^{-89} -21 q^{-90} -156 q^{-91} -95 q^{-92} -25 q^{-93} +42 q^{-94} +70 q^{-95} +72 q^{-96} +67 q^{-97} -52 q^{-98} -47 q^{-99} -52 q^{-100} -28 q^{-101} -9 q^{-102} +28 q^{-103} +67 q^{-104} +5 q^{-105} +14 q^{-106} -13 q^{-107} -22 q^{-108} -36 q^{-109} -14 q^{-110} +24 q^{-111} - q^{-112} +23 q^{-113} +12 q^{-114} +7 q^{-115} -17 q^{-116} -14 q^{-117} +4 q^{-118} -15 q^{-119} +5 q^{-120} +6 q^{-121} +13 q^{-122} -3 q^{-123} -3 q^{-124} +7 q^{-125} -11 q^{-126} -3 q^{-127} -2 q^{-128} +7 q^{-129} - q^{-130} - q^{-131} +8 q^{-132} -4 q^{-133} -2 q^{-134} -3 q^{-135} +3 q^{-136} - q^{-137} -2 q^{-138} +6 q^{-139} - q^{-140} - q^{-141} -2 q^{-142} + q^{-143} -2 q^{-145} +3 q^{-146} - q^{-149} - q^{-152} + q^{-153} </math> \|		coloured_jones_6 = <math>q^{20}-q^{19}-q^{18}-q^{14}+5 q^{13}+q^{12}-2 q^9-6 q^8-10 q^7+4 q^6+4 q^5+9 q^4+12 q^3+10 q^2-5 q-25-14 q^{-1} -14 q^{-2} -3 q^{-3} +18 q^{-4} +40 q^{-5} +33 q^{-6} -5 q^{-7} -15 q^{-8} -41 q^{-9} -57 q^{-10} -32 q^{-11} +30 q^{-12} +73 q^{-13} +60 q^{-14} +55 q^{-15} -6 q^{-16} -97 q^{-17} -125 q^{-18} -65 q^{-19} +35 q^{-20} +95 q^{-21} +165 q^{-22} +117 q^{-23} -51 q^{-24} -179 q^{-25} -194 q^{-26} -84 q^{-27} +47 q^{-28} +234 q^{-29} +259 q^{-30} +59 q^{-31} -160 q^{-32} -278 q^{-33} -203 q^{-34} -46 q^{-35} +241 q^{-36} +349 q^{-37} +154 q^{-38} -113 q^{-39} -303 q^{-40} -263 q^{-41} -117 q^{-42} +223 q^{-43} +380 q^{-44} +195 q^{-45} -84 q^{-46} -300 q^{-47} -273 q^{-48} -148 q^{-49} +210 q^{-50} +384 q^{-51} +202 q^{-52} -76 q^{-53} -295 q^{-54} -270 q^{-55} -152 q^{-56} +205 q^{-57} +380 q^{-58} +203 q^{-59} -72 q^{-60} -289 q^{-61} -267 q^{-62} -157 q^{-63} +191 q^{-64} +366 q^{-65} +213 q^{-66} -49 q^{-67} -263 q^{-68} -258 q^{-69} -180 q^{-70} +142 q^{-71} +322 q^{-72} +226 q^{-73} +11 q^{-74} -191 q^{-75} -225 q^{-76} -216 q^{-77} +47 q^{-78} +228 q^{-79} +216 q^{-80} +88 q^{-81} -73 q^{-82} -142 q^{-83} -222 q^{-84} -56 q^{-85} +91 q^{-86} +149 q^{-87} +120 q^{-88} +39 q^{-89} -21 q^{-90} -156 q^{-91} -95 q^{-92} -25 q^{-93} +42 q^{-94} +70 q^{-95} +72 q^{-96} +67 q^{-97} -52 q^{-98} -47 q^{-99} -52 q^{-100} -28 q^{-101} -9 q^{-102} +28 q^{-103} +67 q^{-104} +5 q^{-105} +14 q^{-106} -13 q^{-107} -22 q^{-108} -36 q^{-109} -14 q^{-110} +24 q^{-111} - q^{-112} +23 q^{-113} +12 q^{-114} +7 q^{-115} -17 q^{-116} -14 q^{-117} +4 q^{-118} -15 q^{-119} +5 q^{-120} +6 q^{-121} +13 q^{-122} -3 q^{-123} -3 q^{-124} +7 q^{-125} -11 q^{-126} -3 q^{-127} -2 q^{-128} +7 q^{-129} - q^{-130} - q^{-131} +8 q^{-132} -4 q^{-133} -2 q^{-134} -3 q^{-135} +3 q^{-136} - q^{-137} -2 q^{-138} +6 q^{-139} - q^{-140} - q^{-141} -2 q^{-142} + q^{-143} -2 q^{-145} +3 q^{-146} - q^{-149} - q^{-152} + q^{-153} </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, 126]]</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, 126]]</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[4, 2, 5, 1], X[8, 4, 9, 3], X[5, 14, 6, 15], X[15, 20, 16, 1],		<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[4, 2, 5, 1], X[8, 4, 9, 3], X[5, 14, 6, 15], X[15, 20, 16, 1],
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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>3</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>3</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, 126]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_126_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, 126]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_126_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, 126]]&) /@ {~~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, 126]]&) /@ {
			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, 3, 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, 3, 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, 126]][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, 126]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:36, 30 August 2005

2005-08-30T14:36:13Z

Show changes

DrorsRobot at 01:03, 30 August 2005

2005-08-30T01:03:27Z

← Older revision		Revision as of 21:03, 29 August 2005
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			{\| 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 22:24, 29 August 2005

2005-08-29T22:24:07Z

Show changes

ScottTestRobot at 00:09, 29 August 2005

2005-08-29T00:09:15Z

← Older revision		Revision as of 20:09, 28 August 2005
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			<!-- -->
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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=126\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,-3,9,10,-2,-5,7,-6,8,-9,3,-4,5,-7,6,-8,4/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=126\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,-3,9,10,-2,-5,7,-6,8,-9,3,-4,5,-7,6,-8,4/goTop.html}}
	\|{{:{{PAGENAME}} Quick Notes}}
	\|}

	<br style="clear:both" />		<br style="clear:both" />
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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>
	<tr align=center>		<tr align=center>
	<td width=15.3846%><table cellpadding=0 cellspacing=0>		<td width=15.3846%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>-15</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>		<tr align=center><td>-15</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>
	<tr align=center><td>-17</td><td bgcolor=yellow>1</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>-17</td><td bgcolor=yellow>1</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 t q t</nowiki></pre></td></tr>		q t q t q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:46, 28 August 2005

2005-08-28T01:46:40Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:11Z

Resetting knot page to basic template.

New page

10 126 - Revision history

ScottTestRobot at 22:00, 1 September 2005

DrorsRobot at 22:45, 31 August 2005

ScottKnotPageRobot at 14:36, 30 August 2005

DrorsRobot at 01:03, 30 August 2005

DrorsRobot at 22:24, 29 August 2005

ScottTestRobot at 00:09, 29 August 2005

ScottTestRobot at 01:46, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.