ScottTestRobot at 22:00, 1 September 2005

2005-09-01T22:00:37Z

DrorsRobot at 22:45, 31 August 2005

2005-08-31T22:45:25Z

← Older revision		Revision as of 18:45, 31 August 2005
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	coloured_jones_5 = <math>2 q^{-4} +2 q^{-6} -2 q^{-7} -6 q^{-8} -6 q^{-9} +6 q^{-10} +4 q^{-11} +15 q^{-12} +12 q^{-13} -14 q^{-14} -28 q^{-15} -15 q^{-16} -8 q^{-17} +30 q^{-18} +56 q^{-19} +23 q^{-20} -34 q^{-21} -52 q^{-22} -70 q^{-23} -11 q^{-24} +79 q^{-25} +97 q^{-26} +45 q^{-27} -26 q^{-28} -125 q^{-29} -125 q^{-30} -5 q^{-31} +102 q^{-32} +158 q^{-33} +124 q^{-34} -64 q^{-35} -206 q^{-36} -183 q^{-37} -43 q^{-38} +178 q^{-39} +304 q^{-40} +146 q^{-41} -152 q^{-42} -335 q^{-43} -284 q^{-44} +51 q^{-45} +400 q^{-46} +399 q^{-47} +31 q^{-48} -389 q^{-49} -509 q^{-50} -149 q^{-51} +393 q^{-52} +594 q^{-53} +237 q^{-54} -365 q^{-55} -660 q^{-56} -321 q^{-57} +344 q^{-58} +707 q^{-59} +388 q^{-60} -326 q^{-61} -741 q^{-62} -433 q^{-63} +301 q^{-64} +767 q^{-65} +478 q^{-66} -289 q^{-67} -775 q^{-68} -511 q^{-69} +251 q^{-70} +779 q^{-71} +549 q^{-72} -217 q^{-73} -750 q^{-74} -570 q^{-75} +131 q^{-76} +709 q^{-77} +598 q^{-78} -70 q^{-79} -611 q^{-80} -579 q^{-81} -47 q^{-82} +502 q^{-83} +557 q^{-84} +107 q^{-85} -353 q^{-86} -469 q^{-87} -188 q^{-88} +218 q^{-89} +377 q^{-90} +201 q^{-91} -93 q^{-92} -258 q^{-93} -195 q^{-94} +6 q^{-95} +157 q^{-96} +152 q^{-97} +42 q^{-98} -73 q^{-99} -105 q^{-100} -54 q^{-101} +19 q^{-102} +59 q^{-103} +47 q^{-104} +8 q^{-105} -25 q^{-106} -33 q^{-107} -16 q^{-108} +9 q^{-109} +13 q^{-110} +14 q^{-111} +7 q^{-112} -9 q^{-113} -10 q^{-114} - q^{-115} -3 q^{-116} +2 q^{-117} +9 q^{-118} + q^{-119} -4 q^{-120} + q^{-121} -3 q^{-122} -3 q^{-123} +3 q^{-124} +2 q^{-125} - q^{-126} + q^{-127} -2 q^{-129} + q^{-130} </math> \|		coloured_jones_5 = <math>2 q^{-4} +2 q^{-6} -2 q^{-7} -6 q^{-8} -6 q^{-9} +6 q^{-10} +4 q^{-11} +15 q^{-12} +12 q^{-13} -14 q^{-14} -28 q^{-15} -15 q^{-16} -8 q^{-17} +30 q^{-18} +56 q^{-19} +23 q^{-20} -34 q^{-21} -52 q^{-22} -70 q^{-23} -11 q^{-24} +79 q^{-25} +97 q^{-26} +45 q^{-27} -26 q^{-28} -125 q^{-29} -125 q^{-30} -5 q^{-31} +102 q^{-32} +158 q^{-33} +124 q^{-34} -64 q^{-35} -206 q^{-36} -183 q^{-37} -43 q^{-38} +178 q^{-39} +304 q^{-40} +146 q^{-41} -152 q^{-42} -335 q^{-43} -284 q^{-44} +51 q^{-45} +400 q^{-46} +399 q^{-47} +31 q^{-48} -389 q^{-49} -509 q^{-50} -149 q^{-51} +393 q^{-52} +594 q^{-53} +237 q^{-54} -365 q^{-55} -660 q^{-56} -321 q^{-57} +344 q^{-58} +707 q^{-59} +388 q^{-60} -326 q^{-61} -741 q^{-62} -433 q^{-63} +301 q^{-64} +767 q^{-65} +478 q^{-66} -289 q^{-67} -775 q^{-68} -511 q^{-69} +251 q^{-70} +779 q^{-71} +549 q^{-72} -217 q^{-73} -750 q^{-74} -570 q^{-75} +131 q^{-76} +709 q^{-77} +598 q^{-78} -70 q^{-79} -611 q^{-80} -579 q^{-81} -47 q^{-82} +502 q^{-83} +557 q^{-84} +107 q^{-85} -353 q^{-86} -469 q^{-87} -188 q^{-88} +218 q^{-89} +377 q^{-90} +201 q^{-91} -93 q^{-92} -258 q^{-93} -195 q^{-94} +6 q^{-95} +157 q^{-96} +152 q^{-97} +42 q^{-98} -73 q^{-99} -105 q^{-100} -54 q^{-101} +19 q^{-102} +59 q^{-103} +47 q^{-104} +8 q^{-105} -25 q^{-106} -33 q^{-107} -16 q^{-108} +9 q^{-109} +13 q^{-110} +14 q^{-111} +7 q^{-112} -9 q^{-113} -10 q^{-114} - q^{-115} -3 q^{-116} +2 q^{-117} +9 q^{-118} + q^{-119} -4 q^{-120} + q^{-121} -3 q^{-122} -3 q^{-123} +3 q^{-124} +2 q^{-125} - q^{-126} + q^{-127} -2 q^{-129} + q^{-130} </math> \|
	coloured_jones_6 = <math> q^{-3} +2 q^{-4} -2 q^{-7} -4 q^{-8} -8 q^{-9} -3 q^{-10} +9 q^{-11} +16 q^{-12} +13 q^{-13} +8 q^{-14} - q^{-15} -37 q^{-16} -41 q^{-17} -22 q^{-18} +21 q^{-19} +44 q^{-20} +62 q^{-21} +73 q^{-22} -19 q^{-23} -83 q^{-24} -122 q^{-25} -66 q^{-26} -20 q^{-27} +79 q^{-28} +207 q^{-29} +133 q^{-30} +30 q^{-31} -140 q^{-32} -168 q^{-33} -237 q^{-34} -128 q^{-35} +165 q^{-36} +258 q^{-37} +298 q^{-38} +117 q^{-39} +14 q^{-40} -348 q^{-41} -470 q^{-42} -225 q^{-43} +16 q^{-44} +368 q^{-45} +475 q^{-46} +590 q^{-47} -9 q^{-48} -527 q^{-49} -691 q^{-50} -629 q^{-51} -86 q^{-52} +489 q^{-53} +1213 q^{-54} +738 q^{-55} -28 q^{-56} -788 q^{-57} -1288 q^{-58} -950 q^{-59} -38 q^{-60} +1470 q^{-61} +1492 q^{-62} +844 q^{-63} -395 q^{-64} -1602 q^{-65} -1819 q^{-66} -878 q^{-67} +1303 q^{-68} +1954 q^{-69} +1696 q^{-70} +234 q^{-71} -1564 q^{-72} -2423 q^{-73} -1661 q^{-74} +952 q^{-75} +2121 q^{-76} +2292 q^{-77} +783 q^{-78} -1381 q^{-79} -2751 q^{-80} -2189 q^{-81} +659 q^{-82} +2147 q^{-83} +2629 q^{-84} +1119 q^{-85} -1231 q^{-86} -2915 q^{-87} -2479 q^{-88} +484 q^{-89} +2145 q^{-90} +2817 q^{-91} +1314 q^{-92} -1121 q^{-93} -3001 q^{-94} -2667 q^{-95} +308 q^{-96} +2095 q^{-97} +2937 q^{-98} +1528 q^{-99} -905 q^{-100} -2958 q^{-101} -2827 q^{-102} -46 q^{-103} +1822 q^{-104} +2907 q^{-105} +1814 q^{-106} -411 q^{-107} -2582 q^{-108} -2826 q^{-109} -580 q^{-110} +1161 q^{-111} +2490 q^{-112} +1970 q^{-113} +297 q^{-114} -1740 q^{-115} -2399 q^{-116} -1001 q^{-117} +269 q^{-118} +1601 q^{-119} +1699 q^{-120} +834 q^{-121} -702 q^{-122} -1524 q^{-123} -971 q^{-124} -381 q^{-125} +604 q^{-126} +1022 q^{-127} +867 q^{-128} +9 q^{-129} -620 q^{-130} -544 q^{-131} -504 q^{-132} -11 q^{-133} +358 q^{-134} +529 q^{-135} +196 q^{-136} -107 q^{-137} -125 q^{-138} -298 q^{-139} -157 q^{-140} +22 q^{-141} +204 q^{-142} +110 q^{-143} +26 q^{-144} +53 q^{-145} -104 q^{-146} -95 q^{-147} -48 q^{-148} +55 q^{-149} +23 q^{-150} +12 q^{-151} +67 q^{-152} -21 q^{-153} -32 q^{-154} -33 q^{-155} +14 q^{-156} -5 q^{-157} -7 q^{-158} +39 q^{-159} -4 q^{-161} -15 q^{-162} +5 q^{-163} -7 q^{-164} -11 q^{-165} +17 q^{-166} +2 q^{-167} +3 q^{-168} -5 q^{-169} +3 q^{-170} -3 q^{-171} -7 q^{-172} +5 q^{-173} +2 q^{-175} - q^{-176} + q^{-177} -2 q^{-179} + q^{-180} </math> \|		coloured_jones_6 = <math> q^{-3} +2 q^{-4} -2 q^{-7} -4 q^{-8} -8 q^{-9} -3 q^{-10} +9 q^{-11} +16 q^{-12} +13 q^{-13} +8 q^{-14} - q^{-15} -37 q^{-16} -41 q^{-17} -22 q^{-18} +21 q^{-19} +44 q^{-20} +62 q^{-21} +73 q^{-22} -19 q^{-23} -83 q^{-24} -122 q^{-25} -66 q^{-26} -20 q^{-27} +79 q^{-28} +207 q^{-29} +133 q^{-30} +30 q^{-31} -140 q^{-32} -168 q^{-33} -237 q^{-34} -128 q^{-35} +165 q^{-36} +258 q^{-37} +298 q^{-38} +117 q^{-39} +14 q^{-40} -348 q^{-41} -470 q^{-42} -225 q^{-43} +16 q^{-44} +368 q^{-45} +475 q^{-46} +590 q^{-47} -9 q^{-48} -527 q^{-49} -691 q^{-50} -629 q^{-51} -86 q^{-52} +489 q^{-53} +1213 q^{-54} +738 q^{-55} -28 q^{-56} -788 q^{-57} -1288 q^{-58} -950 q^{-59} -38 q^{-60} +1470 q^{-61} +1492 q^{-62} +844 q^{-63} -395 q^{-64} -1602 q^{-65} -1819 q^{-66} -878 q^{-67} +1303 q^{-68} +1954 q^{-69} +1696 q^{-70} +234 q^{-71} -1564 q^{-72} -2423 q^{-73} -1661 q^{-74} +952 q^{-75} +2121 q^{-76} +2292 q^{-77} +783 q^{-78} -1381 q^{-79} -2751 q^{-80} -2189 q^{-81} +659 q^{-82} +2147 q^{-83} +2629 q^{-84} +1119 q^{-85} -1231 q^{-86} -2915 q^{-87} -2479 q^{-88} +484 q^{-89} +2145 q^{-90} +2817 q^{-91} +1314 q^{-92} -1121 q^{-93} -3001 q^{-94} -2667 q^{-95} +308 q^{-96} +2095 q^{-97} +2937 q^{-98} +1528 q^{-99} -905 q^{-100} -2958 q^{-101} -2827 q^{-102} -46 q^{-103} +1822 q^{-104} +2907 q^{-105} +1814 q^{-106} -411 q^{-107} -2582 q^{-108} -2826 q^{-109} -580 q^{-110} +1161 q^{-111} +2490 q^{-112} +1970 q^{-113} +297 q^{-114} -1740 q^{-115} -2399 q^{-116} -1001 q^{-117} +269 q^{-118} +1601 q^{-119} +1699 q^{-120} +834 q^{-121} -702 q^{-122} -1524 q^{-123} -971 q^{-124} -381 q^{-125} +604 q^{-126} +1022 q^{-127} +867 q^{-128} +9 q^{-129} -620 q^{-130} -544 q^{-131} -504 q^{-132} -11 q^{-133} +358 q^{-134} +529 q^{-135} +196 q^{-136} -107 q^{-137} -125 q^{-138} -298 q^{-139} -157 q^{-140} +22 q^{-141} +204 q^{-142} +110 q^{-143} +26 q^{-144} +53 q^{-145} -104 q^{-146} -95 q^{-147} -48 q^{-148} +55 q^{-149} +23 q^{-150} +12 q^{-151} +67 q^{-152} -21 q^{-153} -32 q^{-154} -33 q^{-155} +14 q^{-156} -5 q^{-157} -7 q^{-158} +39 q^{-159} -4 q^{-161} -15 q^{-162} +5 q^{-163} -7 q^{-164} -11 q^{-165} +17 q^{-166} +2 q^{-167} +3 q^{-168} -5 q^{-169} +3 q^{-170} -3 q^{-171} -7 q^{-172} +5 q^{-173} +2 q^{-175} - q^{-176} + q^{-177} -2 q^{-179} + q^{-180} </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, 127]]</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, 127]]</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, 8, 4, 9], X[14, 6, 15, 5], 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[1, 4, 2, 5], X[3, 8, 4, 9], X[14, 6, 15, 5], 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, 127]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_127_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, 127]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_127_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, 127]]&) /@ {~~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, 127]]&) /@ {
			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, 127]][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, 127]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:36, 30 August 2005

2005-08-30T14:36:30Z

Show changes

DrorsRobot at 01:03, 30 August 2005

2005-08-30T01:03:47Z

← 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

2005-08-29T22:24:13Z

Show changes

ScottTestRobot at 00:09, 29 August 2005

2005-08-29T00:09:40Z

← 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=127\|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=127\|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>-19</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>-1</td></tr>		<tr align=center><td>-19</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>-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>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>1</td></tr>
	</table>~~</center>~~		</table>}}

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

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

			[[Category:Knot Page]]

ScottTestRobot at 01:46, 28 August 2005

2005-08-28T01:46:53Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:12Z

Resetting knot page to basic template.

New page

10 127 - 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.