ScottTestRobot at 22:03, 1 September 2005

2005-09-01T22:03:45Z

DrorsRobot at 22:51, 31 August 2005

2005-08-31T22:51:08Z

← Older revision		Revision as of 18:51, 31 August 2005
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	coloured_jones_5 = <math>-2 q^{11}+4 q^9+5 q^8+q^7-3 q^6-16 q^5-14 q^4+5 q^3+25 q^2+31 q+15-28 q^{-1} -65 q^{-2} -51 q^{-3} +15 q^{-4} +91 q^{-5} +106 q^{-6} +38 q^{-7} -93 q^{-8} -181 q^{-9} -121 q^{-10} +72 q^{-11} +225 q^{-12} +237 q^{-13} +25 q^{-14} -271 q^{-15} -363 q^{-16} -125 q^{-17} +238 q^{-18} +474 q^{-19} +293 q^{-20} -206 q^{-21} -562 q^{-22} -419 q^{-23} +104 q^{-24} +609 q^{-25} +571 q^{-26} -35 q^{-27} -625 q^{-28} -648 q^{-29} -73 q^{-30} +618 q^{-31} +736 q^{-32} +121 q^{-33} -599 q^{-34} -748 q^{-35} -193 q^{-36} +571 q^{-37} +786 q^{-38} +211 q^{-39} -549 q^{-40} -772 q^{-41} -244 q^{-42} +513 q^{-43} +770 q^{-44} +268 q^{-45} -481 q^{-46} -745 q^{-47} -293 q^{-48} +420 q^{-49} +713 q^{-50} +330 q^{-51} -344 q^{-52} -664 q^{-53} -362 q^{-54} +243 q^{-55} +587 q^{-56} +391 q^{-57} -127 q^{-58} -486 q^{-59} -399 q^{-60} +12 q^{-61} +359 q^{-62} +373 q^{-63} +92 q^{-64} -220 q^{-65} -316 q^{-66} -159 q^{-67} +89 q^{-68} +227 q^{-69} +180 q^{-70} +19 q^{-71} -125 q^{-72} -161 q^{-73} -84 q^{-74} +35 q^{-75} +111 q^{-76} +99 q^{-77} +33 q^{-78} -50 q^{-79} -89 q^{-80} -59 q^{-81} +3 q^{-82} +52 q^{-83} +61 q^{-84} +25 q^{-85} -21 q^{-86} -43 q^{-87} -33 q^{-88} - q^{-89} +28 q^{-90} +23 q^{-91} +8 q^{-92} -7 q^{-93} -18 q^{-94} -10 q^{-95} +5 q^{-96} +8 q^{-97} +2 q^{-98} +3 q^{-99} -2 q^{-100} -6 q^{-101} + q^{-102} +3 q^{-103} - q^{-104} + q^{-106} -2 q^{-107} +2 q^{-109} - q^{-110} </math> \|		coloured_jones_5 = <math>-2 q^{11}+4 q^9+5 q^8+q^7-3 q^6-16 q^5-14 q^4+5 q^3+25 q^2+31 q+15-28 q^{-1} -65 q^{-2} -51 q^{-3} +15 q^{-4} +91 q^{-5} +106 q^{-6} +38 q^{-7} -93 q^{-8} -181 q^{-9} -121 q^{-10} +72 q^{-11} +225 q^{-12} +237 q^{-13} +25 q^{-14} -271 q^{-15} -363 q^{-16} -125 q^{-17} +238 q^{-18} +474 q^{-19} +293 q^{-20} -206 q^{-21} -562 q^{-22} -419 q^{-23} +104 q^{-24} +609 q^{-25} +571 q^{-26} -35 q^{-27} -625 q^{-28} -648 q^{-29} -73 q^{-30} +618 q^{-31} +736 q^{-32} +121 q^{-33} -599 q^{-34} -748 q^{-35} -193 q^{-36} +571 q^{-37} +786 q^{-38} +211 q^{-39} -549 q^{-40} -772 q^{-41} -244 q^{-42} +513 q^{-43} +770 q^{-44} +268 q^{-45} -481 q^{-46} -745 q^{-47} -293 q^{-48} +420 q^{-49} +713 q^{-50} +330 q^{-51} -344 q^{-52} -664 q^{-53} -362 q^{-54} +243 q^{-55} +587 q^{-56} +391 q^{-57} -127 q^{-58} -486 q^{-59} -399 q^{-60} +12 q^{-61} +359 q^{-62} +373 q^{-63} +92 q^{-64} -220 q^{-65} -316 q^{-66} -159 q^{-67} +89 q^{-68} +227 q^{-69} +180 q^{-70} +19 q^{-71} -125 q^{-72} -161 q^{-73} -84 q^{-74} +35 q^{-75} +111 q^{-76} +99 q^{-77} +33 q^{-78} -50 q^{-79} -89 q^{-80} -59 q^{-81} +3 q^{-82} +52 q^{-83} +61 q^{-84} +25 q^{-85} -21 q^{-86} -43 q^{-87} -33 q^{-88} - q^{-89} +28 q^{-90} +23 q^{-91} +8 q^{-92} -7 q^{-93} -18 q^{-94} -10 q^{-95} +5 q^{-96} +8 q^{-97} +2 q^{-98} +3 q^{-99} -2 q^{-100} -6 q^{-101} + q^{-102} +3 q^{-103} - q^{-104} + q^{-106} -2 q^{-107} +2 q^{-109} - q^{-110} </math> \|
	coloured_jones_6 = <math>q^{20}-q^{19}-q^{18}-q^{15}-3 q^{14}+7 q^{13}+5 q^{12}+4 q^{11}+4 q^{10}-4 q^9-18 q^8-33 q^7-6 q^6+15 q^5+36 q^4+59 q^3+50 q^2-15 q-107-112 q^{-1} -82 q^{-2} -3 q^{-3} +144 q^{-4} +254 q^{-5} +196 q^{-6} -41 q^{-7} -230 q^{-8} -366 q^{-9} -356 q^{-10} -31 q^{-11} +419 q^{-12} +653 q^{-13} +447 q^{-14} +29 q^{-15} -539 q^{-16} -989 q^{-17} -737 q^{-18} +86 q^{-19} +950 q^{-20} +1223 q^{-21} +885 q^{-22} -138 q^{-23} -1415 q^{-24} -1719 q^{-25} -862 q^{-26} +660 q^{-27} +1756 q^{-28} +1972 q^{-29} +820 q^{-30} -1277 q^{-31} -2417 q^{-32} -1957 q^{-33} -92 q^{-34} +1760 q^{-35} +2741 q^{-36} +1817 q^{-37} -762 q^{-38} -2614 q^{-39} -2691 q^{-40} -811 q^{-41} +1440 q^{-42} +3028 q^{-43} +2439 q^{-44} -286 q^{-45} -2512 q^{-46} -2979 q^{-47} -1211 q^{-48} +1127 q^{-49} +3030 q^{-50} +2685 q^{-51} -21 q^{-52} -2365 q^{-53} -3025 q^{-54} -1361 q^{-55} +927 q^{-56} +2952 q^{-57} +2749 q^{-58} +139 q^{-59} -2220 q^{-60} -2991 q^{-61} -1457 q^{-62} +718 q^{-63} +2805 q^{-64} +2765 q^{-65} +380 q^{-66} -1936 q^{-67} -2874 q^{-68} -1619 q^{-69} +323 q^{-70} +2445 q^{-71} +2712 q^{-72} +792 q^{-73} -1347 q^{-74} -2518 q^{-75} -1786 q^{-76} -317 q^{-77} +1729 q^{-78} +2413 q^{-79} +1239 q^{-80} -466 q^{-81} -1774 q^{-82} -1699 q^{-83} -971 q^{-84} +719 q^{-85} +1691 q^{-86} +1368 q^{-87} +374 q^{-88} -741 q^{-89} -1140 q^{-90} -1207 q^{-91} -177 q^{-92} +689 q^{-93} +949 q^{-94} +700 q^{-95} +113 q^{-96} -309 q^{-97} -838 q^{-98} -494 q^{-99} -77 q^{-100} +266 q^{-101} +418 q^{-102} +366 q^{-103} +251 q^{-104} -249 q^{-105} -256 q^{-106} -258 q^{-107} -134 q^{-108} -7 q^{-109} +152 q^{-110} +295 q^{-111} +53 q^{-112} +43 q^{-113} -84 q^{-114} -122 q^{-115} -154 q^{-116} -55 q^{-117} +112 q^{-118} +40 q^{-119} +103 q^{-120} +41 q^{-121} +3 q^{-122} -89 q^{-123} -74 q^{-124} +13 q^{-125} -22 q^{-126} +41 q^{-127} +34 q^{-128} +40 q^{-129} -22 q^{-130} -30 q^{-131} +6 q^{-132} -25 q^{-133} +3 q^{-134} +6 q^{-135} +22 q^{-136} -4 q^{-137} -8 q^{-138} +9 q^{-139} -9 q^{-140} -2 q^{-141} -2 q^{-142} +8 q^{-143} -2 q^{-144} -4 q^{-145} +5 q^{-146} -2 q^{-147} - q^{-149} +2 q^{-150} -2 q^{-152} + q^{-153} </math> \|		coloured_jones_6 = <math>q^{20}-q^{19}-q^{18}-q^{15}-3 q^{14}+7 q^{13}+5 q^{12}+4 q^{11}+4 q^{10}-4 q^9-18 q^8-33 q^7-6 q^6+15 q^5+36 q^4+59 q^3+50 q^2-15 q-107-112 q^{-1} -82 q^{-2} -3 q^{-3} +144 q^{-4} +254 q^{-5} +196 q^{-6} -41 q^{-7} -230 q^{-8} -366 q^{-9} -356 q^{-10} -31 q^{-11} +419 q^{-12} +653 q^{-13} +447 q^{-14} +29 q^{-15} -539 q^{-16} -989 q^{-17} -737 q^{-18} +86 q^{-19} +950 q^{-20} +1223 q^{-21} +885 q^{-22} -138 q^{-23} -1415 q^{-24} -1719 q^{-25} -862 q^{-26} +660 q^{-27} +1756 q^{-28} +1972 q^{-29} +820 q^{-30} -1277 q^{-31} -2417 q^{-32} -1957 q^{-33} -92 q^{-34} +1760 q^{-35} +2741 q^{-36} +1817 q^{-37} -762 q^{-38} -2614 q^{-39} -2691 q^{-40} -811 q^{-41} +1440 q^{-42} +3028 q^{-43} +2439 q^{-44} -286 q^{-45} -2512 q^{-46} -2979 q^{-47} -1211 q^{-48} +1127 q^{-49} +3030 q^{-50} +2685 q^{-51} -21 q^{-52} -2365 q^{-53} -3025 q^{-54} -1361 q^{-55} +927 q^{-56} +2952 q^{-57} +2749 q^{-58} +139 q^{-59} -2220 q^{-60} -2991 q^{-61} -1457 q^{-62} +718 q^{-63} +2805 q^{-64} +2765 q^{-65} +380 q^{-66} -1936 q^{-67} -2874 q^{-68} -1619 q^{-69} +323 q^{-70} +2445 q^{-71} +2712 q^{-72} +792 q^{-73} -1347 q^{-74} -2518 q^{-75} -1786 q^{-76} -317 q^{-77} +1729 q^{-78} +2413 q^{-79} +1239 q^{-80} -466 q^{-81} -1774 q^{-82} -1699 q^{-83} -971 q^{-84} +719 q^{-85} +1691 q^{-86} +1368 q^{-87} +374 q^{-88} -741 q^{-89} -1140 q^{-90} -1207 q^{-91} -177 q^{-92} +689 q^{-93} +949 q^{-94} +700 q^{-95} +113 q^{-96} -309 q^{-97} -838 q^{-98} -494 q^{-99} -77 q^{-100} +266 q^{-101} +418 q^{-102} +366 q^{-103} +251 q^{-104} -249 q^{-105} -256 q^{-106} -258 q^{-107} -134 q^{-108} -7 q^{-109} +152 q^{-110} +295 q^{-111} +53 q^{-112} +43 q^{-113} -84 q^{-114} -122 q^{-115} -154 q^{-116} -55 q^{-117} +112 q^{-118} +40 q^{-119} +103 q^{-120} +41 q^{-121} +3 q^{-122} -89 q^{-123} -74 q^{-124} +13 q^{-125} -22 q^{-126} +41 q^{-127} +34 q^{-128} +40 q^{-129} -22 q^{-130} -30 q^{-131} +6 q^{-132} -25 q^{-133} +3 q^{-134} +6 q^{-135} +22 q^{-136} -4 q^{-137} -8 q^{-138} +9 q^{-139} -9 q^{-140} -2 q^{-141} -2 q^{-142} +8 q^{-143} -2 q^{-144} -4 q^{-145} +5 q^{-146} -2 q^{-147} - q^{-149} +2 q^{-150} -2 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, 143]]</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, 143]]</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[10, 4, 11, 3], X[5, 14, 6, 15], X[7, 16, 8, 17],		<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[10, 4, 11, 3], X[5, 14, 6, 15], X[7, 16, 8, 17],
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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, 143]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_143_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, 143]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_143_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, 143]]&) /@ {~~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, 143]]&) /@ {
			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, 1, 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, 1, 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, 143]][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, 143]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:39, 30 August 2005

2005-08-30T14:39:44Z

Show changes

DrorsRobot at 01:07, 30 August 2005

2005-08-30T01:07:22Z

← Older revision		Revision as of 21:07, 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 22:25, 29 August 2005

2005-08-29T22:25:33Z

Show changes

ScottTestRobot at 00:13, 29 August 2005

2005-08-29T00:13:32Z

← Older revision		Revision as of 20:13, 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=143\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,-3,5,-4,9,10,-2,-7,8,-9,3,-5,4,-6,7,-8,6/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=143\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,-3,5,-4,9,10,-2,-7,8,-9,3,-5,4,-6,7,-8,6/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>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>		<tr align=center><td>-15</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>-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 q t q t q t</nowiki></pre></td></tr>		q t q t q t q t q t q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:50, 28 August 2005

2005-08-28T01:50:08Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:28Z

Resetting knot page to basic template.

New page

10 143 - Revision history

ScottTestRobot at 22:03, 1 September 2005

DrorsRobot at 22:51, 31 August 2005

ScottKnotPageRobot at 14:39, 30 August 2005

DrorsRobot at 01:07, 30 August 2005

DrorsRobot at 22:25, 29 August 2005

ScottTestRobot at 00:13, 29 August 2005

ScottTestRobot at 01:50, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.