ScottTestRobot at 22:02, 1 September 2005

2005-09-01T22:02:16Z

DrorsRobot at 22:48, 31 August 2005

2005-08-31T22:48:00Z

← Older revision		Revision as of 18:48, 31 August 2005
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	coloured_jones_5 = <math>-3 q^{11}+8 q^9+9 q^8+q^7-8 q^6-41 q^5-38 q^4+16 q^3+86 q^2+120 q+52-124 q^{-1} -295 q^{-2} -238 q^{-3} +95 q^{-4} +512 q^{-5} +581 q^{-6} +138 q^{-7} -657 q^{-8} -1148 q^{-9} -624 q^{-10} +681 q^{-11} +1694 q^{-12} +1430 q^{-13} -313 q^{-14} -2264 q^{-15} -2453 q^{-16} -304 q^{-17} +2500 q^{-18} +3528 q^{-19} +1345 q^{-20} -2518 q^{-21} -4499 q^{-22} -2455 q^{-23} +2129 q^{-24} +5219 q^{-25} +3640 q^{-26} -1581 q^{-27} -5639 q^{-28} -4590 q^{-29} +837 q^{-30} +5778 q^{-31} +5383 q^{-32} -197 q^{-33} -5683 q^{-34} -5842 q^{-35} -445 q^{-36} +5457 q^{-37} +6153 q^{-38} +908 q^{-39} -5161 q^{-40} -6232 q^{-41} -1325 q^{-42} +4800 q^{-43} +6246 q^{-44} +1674 q^{-45} -4403 q^{-46} -6154 q^{-47} -2023 q^{-48} +3900 q^{-49} +5990 q^{-50} +2420 q^{-51} -3288 q^{-52} -5736 q^{-53} -2818 q^{-54} +2517 q^{-55} +5318 q^{-56} +3223 q^{-57} -1607 q^{-58} -4729 q^{-59} -3509 q^{-60} +619 q^{-61} +3895 q^{-62} +3622 q^{-63} +343 q^{-64} -2885 q^{-65} -3436 q^{-66} -1159 q^{-67} +1779 q^{-68} +2958 q^{-69} +1675 q^{-70} -730 q^{-71} -2221 q^{-72} -1830 q^{-73} -128 q^{-74} +1400 q^{-75} +1642 q^{-76} +638 q^{-77} -632 q^{-78} -1201 q^{-79} -829 q^{-80} +67 q^{-81} +722 q^{-82} +726 q^{-83} +227 q^{-84} -300 q^{-85} -488 q^{-86} -311 q^{-87} +38 q^{-88} +264 q^{-89} +244 q^{-90} +62 q^{-91} -92 q^{-92} -137 q^{-93} -87 q^{-94} +16 q^{-95} +68 q^{-96} +50 q^{-97} +5 q^{-98} -15 q^{-99} -24 q^{-100} -17 q^{-101} +9 q^{-102} +11 q^{-103} +2 q^{-104} -5 q^{-107} +3 q^{-109} - q^{-110} </math> \|		coloured_jones_5 = <math>-3 q^{11}+8 q^9+9 q^8+q^7-8 q^6-41 q^5-38 q^4+16 q^3+86 q^2+120 q+52-124 q^{-1} -295 q^{-2} -238 q^{-3} +95 q^{-4} +512 q^{-5} +581 q^{-6} +138 q^{-7} -657 q^{-8} -1148 q^{-9} -624 q^{-10} +681 q^{-11} +1694 q^{-12} +1430 q^{-13} -313 q^{-14} -2264 q^{-15} -2453 q^{-16} -304 q^{-17} +2500 q^{-18} +3528 q^{-19} +1345 q^{-20} -2518 q^{-21} -4499 q^{-22} -2455 q^{-23} +2129 q^{-24} +5219 q^{-25} +3640 q^{-26} -1581 q^{-27} -5639 q^{-28} -4590 q^{-29} +837 q^{-30} +5778 q^{-31} +5383 q^{-32} -197 q^{-33} -5683 q^{-34} -5842 q^{-35} -445 q^{-36} +5457 q^{-37} +6153 q^{-38} +908 q^{-39} -5161 q^{-40} -6232 q^{-41} -1325 q^{-42} +4800 q^{-43} +6246 q^{-44} +1674 q^{-45} -4403 q^{-46} -6154 q^{-47} -2023 q^{-48} +3900 q^{-49} +5990 q^{-50} +2420 q^{-51} -3288 q^{-52} -5736 q^{-53} -2818 q^{-54} +2517 q^{-55} +5318 q^{-56} +3223 q^{-57} -1607 q^{-58} -4729 q^{-59} -3509 q^{-60} +619 q^{-61} +3895 q^{-62} +3622 q^{-63} +343 q^{-64} -2885 q^{-65} -3436 q^{-66} -1159 q^{-67} +1779 q^{-68} +2958 q^{-69} +1675 q^{-70} -730 q^{-71} -2221 q^{-72} -1830 q^{-73} -128 q^{-74} +1400 q^{-75} +1642 q^{-76} +638 q^{-77} -632 q^{-78} -1201 q^{-79} -829 q^{-80} +67 q^{-81} +722 q^{-82} +726 q^{-83} +227 q^{-84} -300 q^{-85} -488 q^{-86} -311 q^{-87} +38 q^{-88} +264 q^{-89} +244 q^{-90} +62 q^{-91} -92 q^{-92} -137 q^{-93} -87 q^{-94} +16 q^{-95} +68 q^{-96} +50 q^{-97} +5 q^{-98} -15 q^{-99} -24 q^{-100} -17 q^{-101} +9 q^{-102} +11 q^{-103} +2 q^{-104} -5 q^{-107} +3 q^{-109} - q^{-110} </math> \|
	coloured_jones_6 = <math>q^{20}-q^{19}-q^{18}-4 q^{15}-6 q^{14}+12 q^{13}+18 q^{12}+17 q^{11}+12 q^{10}-15 q^9-73 q^8-119 q^7-58 q^6+82 q^5+209 q^4+324 q^3+253 q^2-134 q-630-856 q^{-1} -523 q^{-2} +198 q^{-3} +1300 q^{-4} +1951 q^{-5} +1294 q^{-6} -609 q^{-7} -2681 q^{-8} -3456 q^{-9} -2456 q^{-10} +1087 q^{-11} +4970 q^{-12} +6313 q^{-13} +3413 q^{-14} -2521 q^{-15} -7902 q^{-16} -9913 q^{-17} -4600 q^{-18} +5066 q^{-19} +13055 q^{-20} +13151 q^{-21} +4322 q^{-22} -8584 q^{-23} -18998 q^{-24} -16515 q^{-25} -2300 q^{-26} +15477 q^{-27} +24091 q^{-28} +17301 q^{-29} -1647 q^{-30} -23264 q^{-31} -28939 q^{-32} -15195 q^{-33} +10547 q^{-34} +29799 q^{-35} +29961 q^{-36} +9877 q^{-37} -20547 q^{-38} -35841 q^{-39} -26993 q^{-40} +1815 q^{-41} +28935 q^{-42} +37062 q^{-43} +19851 q^{-44} -14457 q^{-45} -36622 q^{-46} -33554 q^{-47} -5576 q^{-48} +24928 q^{-49} +38699 q^{-50} +25382 q^{-51} -9057 q^{-52} -34412 q^{-53} -35586 q^{-54} -9898 q^{-55} +20901 q^{-56} +37694 q^{-57} +27646 q^{-58} -5207 q^{-59} -31543 q^{-60} -35634 q^{-61} -12640 q^{-62} +17120 q^{-63} +35796 q^{-64} +28945 q^{-65} -1280 q^{-66} -27854 q^{-67} -35025 q^{-68} -15869 q^{-69} +11907 q^{-70} +32552 q^{-71} +30215 q^{-72} +4490 q^{-73} -21635 q^{-74} -32940 q^{-75} -20007 q^{-76} +3792 q^{-77} +26096 q^{-78} +30067 q^{-79} +11841 q^{-80} -11680 q^{-81} -27089 q^{-82} -22755 q^{-83} -6197 q^{-84} +15291 q^{-85} +25517 q^{-86} +17400 q^{-87} +248 q^{-88} -16295 q^{-89} -20316 q^{-90} -13648 q^{-91} +2574 q^{-92} +15408 q^{-93} +16740 q^{-94} +8868 q^{-95} -3732 q^{-96} -11789 q^{-97} -13892 q^{-98} -6123 q^{-99} +3758 q^{-100} +9611 q^{-101} +9724 q^{-102} +4246 q^{-103} -2066 q^{-104} -7726 q^{-105} -6979 q^{-106} -2972 q^{-107} +1709 q^{-108} +4799 q^{-109} +4796 q^{-110} +2753 q^{-111} -1394 q^{-112} -3073 q^{-113} -3146 q^{-114} -1634 q^{-115} +344 q^{-116} +1802 q^{-117} +2310 q^{-118} +876 q^{-119} -93 q^{-120} -990 q^{-121} -1126 q^{-122} -794 q^{-123} -39 q^{-124} +677 q^{-125} +499 q^{-126} +424 q^{-127} +43 q^{-128} -185 q^{-129} -363 q^{-130} -227 q^{-131} +50 q^{-132} +44 q^{-133} +140 q^{-134} +88 q^{-135} +46 q^{-136} -66 q^{-137} -63 q^{-138} -4 q^{-139} -23 q^{-140} +15 q^{-141} +15 q^{-142} +26 q^{-143} -9 q^{-144} -11 q^{-145} +5 q^{-146} -7 q^{-147} +5 q^{-150} -3 q^{-152} + q^{-153} </math> \|		coloured_jones_6 = <math>q^{20}-q^{19}-q^{18}-4 q^{15}-6 q^{14}+12 q^{13}+18 q^{12}+17 q^{11}+12 q^{10}-15 q^9-73 q^8-119 q^7-58 q^6+82 q^5+209 q^4+324 q^3+253 q^2-134 q-630-856 q^{-1} -523 q^{-2} +198 q^{-3} +1300 q^{-4} +1951 q^{-5} +1294 q^{-6} -609 q^{-7} -2681 q^{-8} -3456 q^{-9} -2456 q^{-10} +1087 q^{-11} +4970 q^{-12} +6313 q^{-13} +3413 q^{-14} -2521 q^{-15} -7902 q^{-16} -9913 q^{-17} -4600 q^{-18} +5066 q^{-19} +13055 q^{-20} +13151 q^{-21} +4322 q^{-22} -8584 q^{-23} -18998 q^{-24} -16515 q^{-25} -2300 q^{-26} +15477 q^{-27} +24091 q^{-28} +17301 q^{-29} -1647 q^{-30} -23264 q^{-31} -28939 q^{-32} -15195 q^{-33} +10547 q^{-34} +29799 q^{-35} +29961 q^{-36} +9877 q^{-37} -20547 q^{-38} -35841 q^{-39} -26993 q^{-40} +1815 q^{-41} +28935 q^{-42} +37062 q^{-43} +19851 q^{-44} -14457 q^{-45} -36622 q^{-46} -33554 q^{-47} -5576 q^{-48} +24928 q^{-49} +38699 q^{-50} +25382 q^{-51} -9057 q^{-52} -34412 q^{-53} -35586 q^{-54} -9898 q^{-55} +20901 q^{-56} +37694 q^{-57} +27646 q^{-58} -5207 q^{-59} -31543 q^{-60} -35634 q^{-61} -12640 q^{-62} +17120 q^{-63} +35796 q^{-64} +28945 q^{-65} -1280 q^{-66} -27854 q^{-67} -35025 q^{-68} -15869 q^{-69} +11907 q^{-70} +32552 q^{-71} +30215 q^{-72} +4490 q^{-73} -21635 q^{-74} -32940 q^{-75} -20007 q^{-76} +3792 q^{-77} +26096 q^{-78} +30067 q^{-79} +11841 q^{-80} -11680 q^{-81} -27089 q^{-82} -22755 q^{-83} -6197 q^{-84} +15291 q^{-85} +25517 q^{-86} +17400 q^{-87} +248 q^{-88} -16295 q^{-89} -20316 q^{-90} -13648 q^{-91} +2574 q^{-92} +15408 q^{-93} +16740 q^{-94} +8868 q^{-95} -3732 q^{-96} -11789 q^{-97} -13892 q^{-98} -6123 q^{-99} +3758 q^{-100} +9611 q^{-101} +9724 q^{-102} +4246 q^{-103} -2066 q^{-104} -7726 q^{-105} -6979 q^{-106} -2972 q^{-107} +1709 q^{-108} +4799 q^{-109} +4796 q^{-110} +2753 q^{-111} -1394 q^{-112} -3073 q^{-113} -3146 q^{-114} -1634 q^{-115} +344 q^{-116} +1802 q^{-117} +2310 q^{-118} +876 q^{-119} -93 q^{-120} -990 q^{-121} -1126 q^{-122} -794 q^{-123} -39 q^{-124} +677 q^{-125} +499 q^{-126} +424 q^{-127} +43 q^{-128} -185 q^{-129} -363 q^{-130} -227 q^{-131} +50 q^{-132} +44 q^{-133} +140 q^{-134} +88 q^{-135} +46 q^{-136} -66 q^{-137} -63 q^{-138} -4 q^{-139} -23 q^{-140} +15 q^{-141} +15 q^{-142} +26 q^{-143} -9 q^{-144} -11 q^{-145} +5 q^{-146} -7 q^{-147} +5 q^{-150} -3 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, 159]]</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, 159]]</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, 6, 2, 7], X[3, 9, 4, 8], X[18, 11, 19, 12], X[20, 13, 1, 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, 6, 2, 7], X[3, 9, 4, 8], X[18, 11, 19, 12], X[20, 13, 1, 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>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, 159]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_159_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, 159]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_159_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, 159]]&) /@ {~~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, 159]]&) /@ {
			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, 159]][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, 159]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:38, 30 August 2005

2005-08-30T14:38:14Z

Show changes

DrorsRobot at 01:05, 30 August 2005

2005-08-30T01:05:38Z

← Older revision		Revision as of 21:05, 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 22:27, 29 August 2005

2005-08-29T22:27:17Z

Show changes

ScottTestRobot at 00:11, 29 August 2005

2005-08-29T00:11:38Z

← Older revision		Revision as of 20:11, 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=159\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,5,-2,6,-8,1,-9,2,-10,8,3,-7,4,9,-5,10,-6,-3,7,-4/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=159\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,5,-2,6,-8,1,-9,2,-10,8,3,-7,4,9,-5,10,-6,-3,7,-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>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>2</td></tr>		<tr align=center><td>-15</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>2</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 01:48, 28 August 2005

2005-08-28T01:48:17Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:45Z

Resetting knot page to basic template.

New page

10 159 - Revision history

ScottTestRobot at 22:02, 1 September 2005

DrorsRobot at 22:48, 31 August 2005

ScottKnotPageRobot at 14:38, 30 August 2005

DrorsRobot at 01:05, 30 August 2005

DrorsRobot at 22:27, 29 August 2005

ScottTestRobot at 00:11, 29 August 2005

ScottTestRobot at 01:48, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.