ScottTestRobot at 21:59, 1 September 2005

2005-09-01T21:59:09Z

DrorsRobot at 22:43, 31 August 2005

2005-08-31T22:43:23Z

← Older revision		Revision as of 18:43, 31 August 2005
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	coloured_jones_5 = <math>-q^{110}+2 q^{109}-2 q^{107}+q^{106}-2 q^{104}+5 q^{103}+q^{102}-9 q^{101}-q^{100}+5 q^{99}+2 q^{98}+14 q^{97}+2 q^{96}-27 q^{95}-23 q^{94}+5 q^{93}+28 q^{92}+53 q^{91}+24 q^{90}-61 q^{89}-95 q^{88}-51 q^{87}+50 q^{86}+161 q^{85}+138 q^{84}-42 q^{83}-216 q^{82}-245 q^{81}-59 q^{80}+264 q^{79}+409 q^{78}+187 q^{77}-232 q^{76}-552 q^{75}-440 q^{74}+127 q^{73}+692 q^{72}+708 q^{71}+97 q^{70}-726 q^{69}-1031 q^{68}-429 q^{67}+682 q^{66}+1319 q^{65}+830 q^{64}-506 q^{63}-1548 q^{62}-1283 q^{61}+231 q^{60}+1708 q^{59}+1724 q^{58}+100 q^{57}-1758 q^{56}-2131 q^{55}-487 q^{54}+1770 q^{53}+2467 q^{52}+842 q^{51}-1687 q^{50}-2749 q^{49}-1195 q^{48}+1621 q^{47}+2940 q^{46}+1468 q^{45}-1463 q^{44}-3105 q^{43}-1742 q^{42}+1382 q^{41}+3158 q^{40}+1917 q^{39}-1164 q^{38}-3198 q^{37}-2131 q^{36}+1045 q^{35}+3114 q^{34}+2212 q^{33}-739 q^{32}-2992 q^{31}-2341 q^{30}+532 q^{29}+2730 q^{28}+2318 q^{27}-177 q^{26}-2405 q^{25}-2288 q^{24}-77 q^{23}+1974 q^{22}+2098 q^{21}+378 q^{20}-1517 q^{19}-1865 q^{18}-539 q^{17}+1038 q^{16}+1521 q^{15}+659 q^{14}-626 q^{13}-1169 q^{12}-641 q^{11}+294 q^{10}+803 q^9+568 q^8-69 q^7-507 q^6-437 q^5-45 q^4+276 q^3+293 q^2+94 q-127-184 q^{-1} -81 q^{-2} +49 q^{-3} +95 q^{-4} +53 q^{-5} -7 q^{-6} -44 q^{-7} -37 q^{-8} +2 q^{-9} +23 q^{-10} +12 q^{-11} -2 q^{-12} - q^{-13} -10 q^{-14} -4 q^{-15} +11 q^{-16} + q^{-17} -5 q^{-18} + q^{-19} -3 q^{-21} +4 q^{-22} + q^{-23} -3 q^{-24} + q^{-25} </math> \|		coloured_jones_5 = <math>-q^{110}+2 q^{109}-2 q^{107}+q^{106}-2 q^{104}+5 q^{103}+q^{102}-9 q^{101}-q^{100}+5 q^{99}+2 q^{98}+14 q^{97}+2 q^{96}-27 q^{95}-23 q^{94}+5 q^{93}+28 q^{92}+53 q^{91}+24 q^{90}-61 q^{89}-95 q^{88}-51 q^{87}+50 q^{86}+161 q^{85}+138 q^{84}-42 q^{83}-216 q^{82}-245 q^{81}-59 q^{80}+264 q^{79}+409 q^{78}+187 q^{77}-232 q^{76}-552 q^{75}-440 q^{74}+127 q^{73}+692 q^{72}+708 q^{71}+97 q^{70}-726 q^{69}-1031 q^{68}-429 q^{67}+682 q^{66}+1319 q^{65}+830 q^{64}-506 q^{63}-1548 q^{62}-1283 q^{61}+231 q^{60}+1708 q^{59}+1724 q^{58}+100 q^{57}-1758 q^{56}-2131 q^{55}-487 q^{54}+1770 q^{53}+2467 q^{52}+842 q^{51}-1687 q^{50}-2749 q^{49}-1195 q^{48}+1621 q^{47}+2940 q^{46}+1468 q^{45}-1463 q^{44}-3105 q^{43}-1742 q^{42}+1382 q^{41}+3158 q^{40}+1917 q^{39}-1164 q^{38}-3198 q^{37}-2131 q^{36}+1045 q^{35}+3114 q^{34}+2212 q^{33}-739 q^{32}-2992 q^{31}-2341 q^{30}+532 q^{29}+2730 q^{28}+2318 q^{27}-177 q^{26}-2405 q^{25}-2288 q^{24}-77 q^{23}+1974 q^{22}+2098 q^{21}+378 q^{20}-1517 q^{19}-1865 q^{18}-539 q^{17}+1038 q^{16}+1521 q^{15}+659 q^{14}-626 q^{13}-1169 q^{12}-641 q^{11}+294 q^{10}+803 q^9+568 q^8-69 q^7-507 q^6-437 q^5-45 q^4+276 q^3+293 q^2+94 q-127-184 q^{-1} -81 q^{-2} +49 q^{-3} +95 q^{-4} +53 q^{-5} -7 q^{-6} -44 q^{-7} -37 q^{-8} +2 q^{-9} +23 q^{-10} +12 q^{-11} -2 q^{-12} - q^{-13} -10 q^{-14} -4 q^{-15} +11 q^{-16} + q^{-17} -5 q^{-18} + q^{-19} -3 q^{-21} +4 q^{-22} + q^{-23} -3 q^{-24} + q^{-25} </math> \|
	coloured_jones_6 = <math>q^{153}-2 q^{152}+2 q^{150}-q^{149}-2 q^{147}+6 q^{146}-6 q^{145}-2 q^{144}+11 q^{143}-3 q^{142}-4 q^{141}-13 q^{140}+15 q^{139}-12 q^{138}-2 q^{137}+40 q^{136}+5 q^{135}-13 q^{134}-55 q^{133}+11 q^{132}-40 q^{131}+123 q^{129}+70 q^{128}+10 q^{127}-140 q^{126}-54 q^{125}-175 q^{124}-67 q^{123}+257 q^{122}+283 q^{121}+212 q^{120}-147 q^{119}-148 q^{118}-548 q^{117}-432 q^{116}+213 q^{115}+571 q^{114}+754 q^{113}+268 q^{112}+108 q^{111}-1003 q^{110}-1279 q^{109}-499 q^{108}+387 q^{107}+1340 q^{106}+1291 q^{105}+1343 q^{104}-779 q^{103}-2139 q^{102}-2047 q^{101}-1012 q^{100}+990 q^{99}+2286 q^{98}+3647 q^{97}+947 q^{96}-1858 q^{95}-3616 q^{94}-3609 q^{93}-1140 q^{92}+2000 q^{91}+6025 q^{90}+4038 q^{89}+347 q^{88}-3910 q^{87}-6293 q^{86}-4749 q^{85}-209 q^{84}+7174 q^{83}+7295 q^{82}+4009 q^{81}-2419 q^{80}-7843 q^{79}-8568 q^{78}-3712 q^{77}+6702 q^{76}+9565 q^{75}+7832 q^{74}+172 q^{73}-7986 q^{72}-11495 q^{71}-7246 q^{70}+5260 q^{69}+10601 q^{68}+10808 q^{67}+2762 q^{66}-7292 q^{65}-13269 q^{64}-9958 q^{63}+3692 q^{62}+10823 q^{61}+12730 q^{60}+4755 q^{59}-6367 q^{58}-14165 q^{57}-11759 q^{56}+2300 q^{55}+10589 q^{54}+13842 q^{53}+6259 q^{52}-5291 q^{51}-14366 q^{50}-12922 q^{49}+804 q^{48}+9790 q^{47}+14251 q^{46}+7601 q^{45}-3686 q^{44}-13634 q^{43}-13488 q^{42}-1121 q^{41}+7974 q^{40}+13616 q^{39}+8730 q^{38}-1279 q^{37}-11490 q^{36}-13007 q^{35}-3237 q^{34}+4967 q^{33}+11417 q^{32}+9006 q^{31}+1493 q^{30}-7898 q^{29}-10923 q^{28}-4636 q^{27}+1467 q^{26}+7737 q^{25}+7748 q^{24}+3485 q^{23}-3817 q^{22}-7419 q^{21}-4482 q^{20}-1153 q^{19}+3722 q^{18}+5140 q^{17}+3793 q^{16}-754 q^{15}-3722 q^{14}-2957 q^{13}-2008 q^{12}+860 q^{11}+2376 q^{10}+2690 q^9+525 q^8-1187 q^7-1203 q^6-1489 q^5-297 q^4+600 q^3+1306 q^2+522 q-136-164 q^{-1} -670 q^{-2} -356 q^{-3} -44 q^{-4} +448 q^{-5} +191 q^{-6} +44 q^{-7} +128 q^{-8} -191 q^{-9} -149 q^{-10} -105 q^{-11} +126 q^{-12} +19 q^{-13} +3 q^{-14} +97 q^{-15} -35 q^{-16} -35 q^{-17} -46 q^{-18} +42 q^{-19} -11 q^{-20} -13 q^{-21} +34 q^{-22} -7 q^{-23} -4 q^{-24} -14 q^{-25} +18 q^{-26} -4 q^{-27} -9 q^{-28} +9 q^{-29} -3 q^{-30} -3 q^{-32} +4 q^{-33} + q^{-34} -3 q^{-35} + q^{-36} </math> \|		coloured_jones_6 = <math>q^{153}-2 q^{152}+2 q^{150}-q^{149}-2 q^{147}+6 q^{146}-6 q^{145}-2 q^{144}+11 q^{143}-3 q^{142}-4 q^{141}-13 q^{140}+15 q^{139}-12 q^{138}-2 q^{137}+40 q^{136}+5 q^{135}-13 q^{134}-55 q^{133}+11 q^{132}-40 q^{131}+123 q^{129}+70 q^{128}+10 q^{127}-140 q^{126}-54 q^{125}-175 q^{124}-67 q^{123}+257 q^{122}+283 q^{121}+212 q^{120}-147 q^{119}-148 q^{118}-548 q^{117}-432 q^{116}+213 q^{115}+571 q^{114}+754 q^{113}+268 q^{112}+108 q^{111}-1003 q^{110}-1279 q^{109}-499 q^{108}+387 q^{107}+1340 q^{106}+1291 q^{105}+1343 q^{104}-779 q^{103}-2139 q^{102}-2047 q^{101}-1012 q^{100}+990 q^{99}+2286 q^{98}+3647 q^{97}+947 q^{96}-1858 q^{95}-3616 q^{94}-3609 q^{93}-1140 q^{92}+2000 q^{91}+6025 q^{90}+4038 q^{89}+347 q^{88}-3910 q^{87}-6293 q^{86}-4749 q^{85}-209 q^{84}+7174 q^{83}+7295 q^{82}+4009 q^{81}-2419 q^{80}-7843 q^{79}-8568 q^{78}-3712 q^{77}+6702 q^{76}+9565 q^{75}+7832 q^{74}+172 q^{73}-7986 q^{72}-11495 q^{71}-7246 q^{70}+5260 q^{69}+10601 q^{68}+10808 q^{67}+2762 q^{66}-7292 q^{65}-13269 q^{64}-9958 q^{63}+3692 q^{62}+10823 q^{61}+12730 q^{60}+4755 q^{59}-6367 q^{58}-14165 q^{57}-11759 q^{56}+2300 q^{55}+10589 q^{54}+13842 q^{53}+6259 q^{52}-5291 q^{51}-14366 q^{50}-12922 q^{49}+804 q^{48}+9790 q^{47}+14251 q^{46}+7601 q^{45}-3686 q^{44}-13634 q^{43}-13488 q^{42}-1121 q^{41}+7974 q^{40}+13616 q^{39}+8730 q^{38}-1279 q^{37}-11490 q^{36}-13007 q^{35}-3237 q^{34}+4967 q^{33}+11417 q^{32}+9006 q^{31}+1493 q^{30}-7898 q^{29}-10923 q^{28}-4636 q^{27}+1467 q^{26}+7737 q^{25}+7748 q^{24}+3485 q^{23}-3817 q^{22}-7419 q^{21}-4482 q^{20}-1153 q^{19}+3722 q^{18}+5140 q^{17}+3793 q^{16}-754 q^{15}-3722 q^{14}-2957 q^{13}-2008 q^{12}+860 q^{11}+2376 q^{10}+2690 q^9+525 q^8-1187 q^7-1203 q^6-1489 q^5-297 q^4+600 q^3+1306 q^2+522 q-136-164 q^{-1} -670 q^{-2} -356 q^{-3} -44 q^{-4} +448 q^{-5} +191 q^{-6} +44 q^{-7} +128 q^{-8} -191 q^{-9} -149 q^{-10} -105 q^{-11} +126 q^{-12} +19 q^{-13} +3 q^{-14} +97 q^{-15} -35 q^{-16} -35 q^{-17} -46 q^{-18} +42 q^{-19} -11 q^{-20} -13 q^{-21} +34 q^{-22} -7 q^{-23} -4 q^{-24} -14 q^{-25} +18 q^{-26} -4 q^{-27} -9 q^{-28} +9 q^{-29} -3 q^{-30} -3 q^{-32} +4 q^{-33} + q^{-34} -3 q^{-35} + q^{-36} </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[9, 21]]</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[9, 21]]</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[9, 12, 10, 13], X[3, 11, 4, 10], X[11, 3, 12, 2],		<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[9, 12, 10, 13], X[3, 11, 4, 10], X[11, 3, 12, 2],
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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>5</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>5</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[9, 21]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:9_21_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[9, 21]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:9_21_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[9, 21]]&) /@ {~~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[9, 21]]&) /@ {
			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, 2, 2, {4, 7}, 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, 2, 2, {4, 7}, 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[9, 21]][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[9, 21]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:35, 30 August 2005

2005-08-30T14:35:03Z

Show changes

DrorsRobot at 01:02, 30 August 2005

2005-08-30T01:02:12Z

← Older revision		Revision as of 21:02, 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 22:03, 29 August 2005

2005-08-29T22:03:13Z

Show changes

ScottTestRobot at 00:07, 29 August 2005

2005-08-29T00:07:50Z

← Older revision		Revision as of 20:07, 28 August 2005
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	<!-- 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=9\|k=21\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-6,7,-8,9,-2,3,-4,2,-5,6,-9,8,-7,5/goTop.html}}
	{\| align=left
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	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=9\|k=21\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-6,7,-8,9,-2,3,-4,2,-5,6,-9,8,-7,5/goTop.html}}
	\|{{:{{PAGENAME}} Quick Notes}}
	\|}

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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>
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	<tr align=center><td>-1</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> </td><td>-2</td></tr>		<tr align=center><td>-1</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> </td><td>-2</td></tr>
	<tr align=center><td>-3</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>1</td></tr>		<tr align=center><td>-3</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>1</td></tr>
	</table>~~</center>~~		</table>}}

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

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

			[[Category:Knot Page]]

ScottTestRobot at 01:45, 28 August 2005

2005-08-28T01:45:51Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T21:22:16Z

Resetting knot page to basic template.

New page

9 21 - Revision history

ScottTestRobot at 21:59, 1 September 2005

DrorsRobot at 22:43, 31 August 2005

ScottKnotPageRobot at 14:35, 30 August 2005

DrorsRobot at 01:02, 30 August 2005

DrorsRobot at 22:03, 29 August 2005

ScottTestRobot at 00:07, 29 August 2005

ScottTestRobot at 01:45, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.