ScottTestRobot at 22:04, 1 September 2005

2005-09-01T22:04:25Z

DrorsRobot at 22:52, 31 August 2005

2005-08-31T22:52:27Z

← Older revision		Revision as of 18:52, 31 August 2005
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	coloured_jones_5 = <math>-q^{70}+q^{69}+q^{68}-q^{65}-2 q^{64}+2 q^{62}+q^{61}+q^{60}-q^{59}-q^{58}-q^{57}+q^{55}+q^{54}-3 q^{53}-q^{52}+2 q^{51}+2 q^{50}+4 q^{49}+2 q^{48}-5 q^{47}-7 q^{46}-3 q^{45}+5 q^{43}+8 q^{42}+4 q^{41}-q^{40}-4 q^{39}-5 q^{38}-6 q^{37}-3 q^{36}+4 q^{34}+11 q^{33}+11 q^{32}+6 q^{31}-8 q^{30}-19 q^{29}-20 q^{28}-6 q^{27}+13 q^{26}+31 q^{25}+26 q^{24}+2 q^{23}-23 q^{22}-41 q^{21}-29 q^{20}+5 q^{19}+37 q^{18}+49 q^{17}+25 q^{16}-20 q^{15}-55 q^{14}-53 q^{13}-14 q^{12}+49 q^{11}+74 q^{10}+40 q^9-23 q^8-80 q^7-75 q^6+4 q^5+83 q^4+87 q^3+22 q^2-72 q-108-33 q^{-1} +73 q^{-2} +106 q^{-3} +47 q^{-4} -66 q^{-5} -117 q^{-6} -46 q^{-7} +68 q^{-8} +111 q^{-9} +51 q^{-10} -65 q^{-11} -118 q^{-12} -47 q^{-13} +68 q^{-14} +112 q^{-15} +50 q^{-16} -65 q^{-17} -118 q^{-18} -48 q^{-19} +67 q^{-20} +113 q^{-21} +52 q^{-22} -59 q^{-23} -114 q^{-24} -60 q^{-25} +48 q^{-26} +106 q^{-27} +70 q^{-28} -25 q^{-29} -92 q^{-30} -79 q^{-31} -5 q^{-32} +67 q^{-33} +78 q^{-34} +33 q^{-35} -32 q^{-36} -65 q^{-37} -49 q^{-38} -4 q^{-39} +39 q^{-40} +48 q^{-41} +29 q^{-42} -8 q^{-43} -33 q^{-44} -32 q^{-45} -16 q^{-46} +10 q^{-47} +25 q^{-48} +21 q^{-49} +6 q^{-50} -5 q^{-51} -17 q^{-52} -13 q^{-53} - q^{-54} +2 q^{-55} +7 q^{-56} +8 q^{-57} +2 q^{-58} -2 q^{-59} - q^{-60} -4 q^{-61} -4 q^{-62} + q^{-64} +2 q^{-65} +2 q^{-66} +2 q^{-67} - q^{-68} -2 q^{-69} - q^{-70} + q^{-73} + q^{-74} - q^{-75} </math> \|		coloured_jones_5 = <math>-q^{70}+q^{69}+q^{68}-q^{65}-2 q^{64}+2 q^{62}+q^{61}+q^{60}-q^{59}-q^{58}-q^{57}+q^{55}+q^{54}-3 q^{53}-q^{52}+2 q^{51}+2 q^{50}+4 q^{49}+2 q^{48}-5 q^{47}-7 q^{46}-3 q^{45}+5 q^{43}+8 q^{42}+4 q^{41}-q^{40}-4 q^{39}-5 q^{38}-6 q^{37}-3 q^{36}+4 q^{34}+11 q^{33}+11 q^{32}+6 q^{31}-8 q^{30}-19 q^{29}-20 q^{28}-6 q^{27}+13 q^{26}+31 q^{25}+26 q^{24}+2 q^{23}-23 q^{22}-41 q^{21}-29 q^{20}+5 q^{19}+37 q^{18}+49 q^{17}+25 q^{16}-20 q^{15}-55 q^{14}-53 q^{13}-14 q^{12}+49 q^{11}+74 q^{10}+40 q^9-23 q^8-80 q^7-75 q^6+4 q^5+83 q^4+87 q^3+22 q^2-72 q-108-33 q^{-1} +73 q^{-2} +106 q^{-3} +47 q^{-4} -66 q^{-5} -117 q^{-6} -46 q^{-7} +68 q^{-8} +111 q^{-9} +51 q^{-10} -65 q^{-11} -118 q^{-12} -47 q^{-13} +68 q^{-14} +112 q^{-15} +50 q^{-16} -65 q^{-17} -118 q^{-18} -48 q^{-19} +67 q^{-20} +113 q^{-21} +52 q^{-22} -59 q^{-23} -114 q^{-24} -60 q^{-25} +48 q^{-26} +106 q^{-27} +70 q^{-28} -25 q^{-29} -92 q^{-30} -79 q^{-31} -5 q^{-32} +67 q^{-33} +78 q^{-34} +33 q^{-35} -32 q^{-36} -65 q^{-37} -49 q^{-38} -4 q^{-39} +39 q^{-40} +48 q^{-41} +29 q^{-42} -8 q^{-43} -33 q^{-44} -32 q^{-45} -16 q^{-46} +10 q^{-47} +25 q^{-48} +21 q^{-49} +6 q^{-50} -5 q^{-51} -17 q^{-52} -13 q^{-53} - q^{-54} +2 q^{-55} +7 q^{-56} +8 q^{-57} +2 q^{-58} -2 q^{-59} - q^{-60} -4 q^{-61} -4 q^{-62} + q^{-64} +2 q^{-65} +2 q^{-66} +2 q^{-67} - q^{-68} -2 q^{-69} - q^{-70} + q^{-73} + q^{-74} - q^{-75} </math> \|
	coloured_jones_6 = <math>q^{99}-q^{98}-q^{97}+q^{94}+3 q^{92}-q^{91}-2 q^{90}-q^{89}-q^{88}+4 q^{85}-q^{84}-2 q^{80}+q^{79}+4 q^{78}-4 q^{77}-2 q^{76}-2 q^{75}-3 q^{73}+6 q^{72}+9 q^{71}+q^{70}-q^{69}-2 q^{68}-5 q^{67}-13 q^{66}+3 q^{64}+3 q^{63}+4 q^{62}+10 q^{61}+8 q^{60}-5 q^{59}-3 q^{57}-11 q^{56}-16 q^{55}-6 q^{54}+3 q^{53}+5 q^{52}+17 q^{51}+28 q^{50}+16 q^{49}-5 q^{48}-20 q^{47}-25 q^{46}-38 q^{45}-24 q^{44}+16 q^{43}+33 q^{42}+46 q^{41}+36 q^{40}+30 q^{39}-28 q^{38}-59 q^{37}-54 q^{36}-50 q^{35}-8 q^{34}+32 q^{33}+99 q^{32}+69 q^{31}+44 q^{30}-8 q^{29}-84 q^{28}-117 q^{27}-106 q^{26}+8 q^{25}+56 q^{24}+146 q^{23}+147 q^{22}+61 q^{21}-73 q^{20}-184 q^{19}-159 q^{18}-119 q^{17}+72 q^{16}+200 q^{15}+236 q^{14}+110 q^{13}-85 q^{12}-214 q^{11}-287 q^{10}-100 q^9+110 q^8+293 q^7+262 q^6+75 q^5-165 q^4-352 q^3-225 q^2-q+276+325 q^{-1} +175 q^{-2} -116 q^{-3} -361 q^{-4} -273 q^{-5} -54 q^{-6} +258 q^{-7} +341 q^{-8} +208 q^{-9} -102 q^{-10} -362 q^{-11} -281 q^{-12} -65 q^{-13} +255 q^{-14} +343 q^{-15} +213 q^{-16} -101 q^{-17} -363 q^{-18} -282 q^{-19} -65 q^{-20} +255 q^{-21} +343 q^{-22} +213 q^{-23} -102 q^{-24} -359 q^{-25} -285 q^{-26} -70 q^{-27} +250 q^{-28} +346 q^{-29} +226 q^{-30} -93 q^{-31} -343 q^{-32} -298 q^{-33} -106 q^{-34} +208 q^{-35} +337 q^{-36} +270 q^{-37} -19 q^{-38} -269 q^{-39} -305 q^{-40} -194 q^{-41} +69 q^{-42} +253 q^{-43} +300 q^{-44} +121 q^{-45} -82 q^{-46} -215 q^{-47} -241 q^{-48} -116 q^{-49} +55 q^{-50} +195 q^{-51} +173 q^{-52} +109 q^{-53} -15 q^{-54} -123 q^{-55} -155 q^{-56} -97 q^{-57} - q^{-58} +51 q^{-59} +109 q^{-60} +92 q^{-61} +39 q^{-62} -32 q^{-63} -54 q^{-64} -64 q^{-65} -58 q^{-66} -4 q^{-67} +28 q^{-68} +47 q^{-69} +33 q^{-70} +30 q^{-71} - q^{-72} -27 q^{-73} -28 q^{-74} -22 q^{-75} -8 q^{-76} +18 q^{-78} +16 q^{-79} +10 q^{-80} +3 q^{-81} -2 q^{-82} -7 q^{-83} -8 q^{-84} -5 q^{-85} -2 q^{-86} + q^{-87} +2 q^{-88} +4 q^{-89} +3 q^{-90} +3 q^{-91} - q^{-92} - q^{-93} -2 q^{-94} -2 q^{-95} -2 q^{-96} +3 q^{-98} + q^{-100} - q^{-103} - q^{-104} + q^{-105} </math> \|		coloured_jones_6 = <math>q^{99}-q^{98}-q^{97}+q^{94}+3 q^{92}-q^{91}-2 q^{90}-q^{89}-q^{88}+4 q^{85}-q^{84}-2 q^{80}+q^{79}+4 q^{78}-4 q^{77}-2 q^{76}-2 q^{75}-3 q^{73}+6 q^{72}+9 q^{71}+q^{70}-q^{69}-2 q^{68}-5 q^{67}-13 q^{66}+3 q^{64}+3 q^{63}+4 q^{62}+10 q^{61}+8 q^{60}-5 q^{59}-3 q^{57}-11 q^{56}-16 q^{55}-6 q^{54}+3 q^{53}+5 q^{52}+17 q^{51}+28 q^{50}+16 q^{49}-5 q^{48}-20 q^{47}-25 q^{46}-38 q^{45}-24 q^{44}+16 q^{43}+33 q^{42}+46 q^{41}+36 q^{40}+30 q^{39}-28 q^{38}-59 q^{37}-54 q^{36}-50 q^{35}-8 q^{34}+32 q^{33}+99 q^{32}+69 q^{31}+44 q^{30}-8 q^{29}-84 q^{28}-117 q^{27}-106 q^{26}+8 q^{25}+56 q^{24}+146 q^{23}+147 q^{22}+61 q^{21}-73 q^{20}-184 q^{19}-159 q^{18}-119 q^{17}+72 q^{16}+200 q^{15}+236 q^{14}+110 q^{13}-85 q^{12}-214 q^{11}-287 q^{10}-100 q^9+110 q^8+293 q^7+262 q^6+75 q^5-165 q^4-352 q^3-225 q^2-q+276+325 q^{-1} +175 q^{-2} -116 q^{-3} -361 q^{-4} -273 q^{-5} -54 q^{-6} +258 q^{-7} +341 q^{-8} +208 q^{-9} -102 q^{-10} -362 q^{-11} -281 q^{-12} -65 q^{-13} +255 q^{-14} +343 q^{-15} +213 q^{-16} -101 q^{-17} -363 q^{-18} -282 q^{-19} -65 q^{-20} +255 q^{-21} +343 q^{-22} +213 q^{-23} -102 q^{-24} -359 q^{-25} -285 q^{-26} -70 q^{-27} +250 q^{-28} +346 q^{-29} +226 q^{-30} -93 q^{-31} -343 q^{-32} -298 q^{-33} -106 q^{-34} +208 q^{-35} +337 q^{-36} +270 q^{-37} -19 q^{-38} -269 q^{-39} -305 q^{-40} -194 q^{-41} +69 q^{-42} +253 q^{-43} +300 q^{-44} +121 q^{-45} -82 q^{-46} -215 q^{-47} -241 q^{-48} -116 q^{-49} +55 q^{-50} +195 q^{-51} +173 q^{-52} +109 q^{-53} -15 q^{-54} -123 q^{-55} -155 q^{-56} -97 q^{-57} - q^{-58} +51 q^{-59} +109 q^{-60} +92 q^{-61} +39 q^{-62} -32 q^{-63} -54 q^{-64} -64 q^{-65} -58 q^{-66} -4 q^{-67} +28 q^{-68} +47 q^{-69} +33 q^{-70} +30 q^{-71} - q^{-72} -27 q^{-73} -28 q^{-74} -22 q^{-75} -8 q^{-76} +18 q^{-78} +16 q^{-79} +10 q^{-80} +3 q^{-81} -2 q^{-82} -7 q^{-83} -8 q^{-84} -5 q^{-85} -2 q^{-86} + q^{-87} +2 q^{-88} +4 q^{-89} +3 q^{-90} +3 q^{-91} - q^{-92} - q^{-93} -2 q^{-94} -2 q^{-95} -2 q^{-96} +3 q^{-98} + q^{-100} - q^{-103} - q^{-104} + q^{-105} </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, 153]]</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, 153]]</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[12, 6, 13, 5], X[13, 18, 14, 19],		<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[12, 6, 13, 5], X[13, 18, 14, 19],
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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, 153]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_153_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, 153]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_153_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, 153]]&) /@ {~~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, 153]]&) /@ {
			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>{Chiral, 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>{Chiral, 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, 153]][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, 153]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:40, 30 August 2005

2005-08-30T14:40:29Z

Show changes

DrorsRobot at 01:08, 30 August 2005

2005-08-30T01:08:13Z

← 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 22:26, 29 August 2005

2005-08-29T22:26:41Z

Show changes

ScottTestRobot at 00:14, 29 August 2005

2005-08-29T00:14:30Z

← 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=153\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,3,-9,10,-2,-5,6,9,-3,-4,8,-7,5,-6,4,-8,7/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=153\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-1,3,-9,10,-2,-5,6,9,-3,-4,8,-7,5,-6,4,-8,7/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=13.3333%><table cellpadding=0 cellspacing=0>		<td width=13.3333%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>-9</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>		<tr align=center><td>-9</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>
	<tr align=center><td>-11</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>-11</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 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

2005-08-28T01:50:59Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:39Z

Resetting knot page to basic template.

New page

10 153 - Revision history

ScottTestRobot at 22:04, 1 September 2005

DrorsRobot at 22:52, 31 August 2005

ScottKnotPageRobot at 14:40, 30 August 2005

DrorsRobot at 01:08, 30 August 2005

DrorsRobot at 22:26, 29 August 2005

ScottTestRobot at 00:14, 29 August 2005

ScottTestRobot at 01:50, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.