ScottTestRobot at 22:03, 1 September 2005

2005-09-01T22:03:19Z

DrorsRobot at 22:50, 31 August 2005

2005-08-31T22:50:16Z

← Older revision		Revision as of 18:50, 31 August 2005
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	coloured_jones_5 = <math>2 q^{66}+2 q^{64}-4 q^{63}-12 q^{62}-12 q^{61}+10 q^{60}+18 q^{59}+46 q^{58}+40 q^{57}-44 q^{56}-112 q^{55}-110 q^{54}-32 q^{53}+157 q^{52}+327 q^{51}+199 q^{50}-151 q^{49}-495 q^{48}-580 q^{47}-124 q^{46}+663 q^{45}+1082 q^{44}+644 q^{43}-502 q^{42}-1585 q^{41}-1535 q^{40}-20 q^{39}+1879 q^{38}+2563 q^{37}+1060 q^{36}-1760 q^{35}-3571 q^{34}-2475 q^{33}+1081 q^{32}+4293 q^{31}+4125 q^{30}+114 q^{29}-4574 q^{28}-5714 q^{27}-1729 q^{26}+4346 q^{25}+7080 q^{24}+3532 q^{23}-3682 q^{22}-8103 q^{21}-5279 q^{20}+2711 q^{19}+8717 q^{18}+6878 q^{17}-1604 q^{16}-9057 q^{15}-8176 q^{14}+547 q^{13}+9079 q^{12}+9223 q^{11}+468 q^{10}-9020 q^9-9999 q^8-1322 q^7+8795 q^6+10574 q^5+2135 q^4-8488 q^3-10991 q^2-2896 q+8024+11225 q^{-1} +3678 q^{-2} -7312 q^{-3} -11259 q^{-4} -4511 q^{-5} +6352 q^{-6} +10977 q^{-7} +5295 q^{-8} -5021 q^{-9} -10328 q^{-10} -5983 q^{-11} +3490 q^{-12} +9194 q^{-13} +6359 q^{-14} -1780 q^{-15} -7664 q^{-16} -6351 q^{-17} +259 q^{-18} +5791 q^{-19} +5805 q^{-20} +1034 q^{-21} -3918 q^{-22} -4867 q^{-23} -1719 q^{-24} +2186 q^{-25} +3616 q^{-26} +1971 q^{-27} -890 q^{-28} -2419 q^{-29} -1710 q^{-30} +80 q^{-31} +1350 q^{-32} +1281 q^{-33} +290 q^{-34} -636 q^{-35} -805 q^{-36} -337 q^{-37} +213 q^{-38} +429 q^{-39} +252 q^{-40} -25 q^{-41} -189 q^{-42} -159 q^{-43} -18 q^{-44} +75 q^{-45} +68 q^{-46} +18 q^{-47} -10 q^{-48} -36 q^{-49} -17 q^{-50} +14 q^{-51} +9 q^{-52} - q^{-53} +3 q^{-54} -2 q^{-55} -6 q^{-56} +4 q^{-57} +2 q^{-58} -3 q^{-59} + q^{-60} </math> \|		coloured_jones_5 = <math>2 q^{66}+2 q^{64}-4 q^{63}-12 q^{62}-12 q^{61}+10 q^{60}+18 q^{59}+46 q^{58}+40 q^{57}-44 q^{56}-112 q^{55}-110 q^{54}-32 q^{53}+157 q^{52}+327 q^{51}+199 q^{50}-151 q^{49}-495 q^{48}-580 q^{47}-124 q^{46}+663 q^{45}+1082 q^{44}+644 q^{43}-502 q^{42}-1585 q^{41}-1535 q^{40}-20 q^{39}+1879 q^{38}+2563 q^{37}+1060 q^{36}-1760 q^{35}-3571 q^{34}-2475 q^{33}+1081 q^{32}+4293 q^{31}+4125 q^{30}+114 q^{29}-4574 q^{28}-5714 q^{27}-1729 q^{26}+4346 q^{25}+7080 q^{24}+3532 q^{23}-3682 q^{22}-8103 q^{21}-5279 q^{20}+2711 q^{19}+8717 q^{18}+6878 q^{17}-1604 q^{16}-9057 q^{15}-8176 q^{14}+547 q^{13}+9079 q^{12}+9223 q^{11}+468 q^{10}-9020 q^9-9999 q^8-1322 q^7+8795 q^6+10574 q^5+2135 q^4-8488 q^3-10991 q^2-2896 q+8024+11225 q^{-1} +3678 q^{-2} -7312 q^{-3} -11259 q^{-4} -4511 q^{-5} +6352 q^{-6} +10977 q^{-7} +5295 q^{-8} -5021 q^{-9} -10328 q^{-10} -5983 q^{-11} +3490 q^{-12} +9194 q^{-13} +6359 q^{-14} -1780 q^{-15} -7664 q^{-16} -6351 q^{-17} +259 q^{-18} +5791 q^{-19} +5805 q^{-20} +1034 q^{-21} -3918 q^{-22} -4867 q^{-23} -1719 q^{-24} +2186 q^{-25} +3616 q^{-26} +1971 q^{-27} -890 q^{-28} -2419 q^{-29} -1710 q^{-30} +80 q^{-31} +1350 q^{-32} +1281 q^{-33} +290 q^{-34} -636 q^{-35} -805 q^{-36} -337 q^{-37} +213 q^{-38} +429 q^{-39} +252 q^{-40} -25 q^{-41} -189 q^{-42} -159 q^{-43} -18 q^{-44} +75 q^{-45} +68 q^{-46} +18 q^{-47} -10 q^{-48} -36 q^{-49} -17 q^{-50} +14 q^{-51} +9 q^{-52} - q^{-53} +3 q^{-54} -2 q^{-55} -6 q^{-56} +4 q^{-57} +2 q^{-58} -3 q^{-59} + q^{-60} </math> \|
	coloured_jones_6 = <math>q^{93}+2 q^{92}-6 q^{89}-8 q^{88}-16 q^{87}-6 q^{86}+23 q^{85}+49 q^{84}+53 q^{83}+27 q^{82}-13 q^{81}-149 q^{80}-201 q^{79}-151 q^{78}+72 q^{77}+294 q^{76}+462 q^{75}+520 q^{74}-12 q^{73}-624 q^{72}-1148 q^{71}-961 q^{70}-286 q^{69}+958 q^{68}+2323 q^{67}+2127 q^{66}+724 q^{65}-1827 q^{64}-3549 q^{63}-4097 q^{62}-1793 q^{61}+2869 q^{60}+6130 q^{59}+6668 q^{58}+2524 q^{57}-3377 q^{56}-9745 q^{55}-10545 q^{54}-3860 q^{53}+5739 q^{52}+14062 q^{51}+14064 q^{50}+6345 q^{49}-9153 q^{48}-20164 q^{47}-18853 q^{46}-5949 q^{45}+13461 q^{44}+25817 q^{43}+24981 q^{42}+4011 q^{41}-20582 q^{40}-33606 q^{39}-26563 q^{38}-281 q^{37}+27898 q^{36}+42963 q^{35}+25729 q^{34}-8209 q^{33}-38908 q^{32}-46125 q^{31}-21794 q^{30}+18315 q^{29}+52054 q^{28}+46125 q^{27}+10739 q^{26}-33987 q^{25}-57558 q^{24}-41701 q^{23}+3463 q^{22}+52198 q^{21}+59237 q^{20}+27904 q^{19}-24708 q^{18}-61232 q^{17}-55134 q^{16}-9724 q^{15}+48293 q^{14}+65607 q^{13}+39708 q^{12}-16293 q^{11}-61087 q^{10}-62882 q^9-19072 q^8+43936 q^7+68412 q^6+47482 q^5-9520 q^4-59520 q^3-67754 q^2-26585 q+38770+69206 q^{-1} +53985 q^{-2} -1702 q^{-3} -55314 q^{-4} -70716 q^{-5} -35066 q^{-6} +29559 q^{-7} +66002 q^{-8} +59592 q^{-9} +9892 q^{-10} -44730 q^{-11} -68900 q^{-12} -44099 q^{-13} +13888 q^{-14} +54540 q^{-15} +60275 q^{-16} +23623 q^{-17} -25874 q^{-18} -57448 q^{-19} -48179 q^{-20} -4933 q^{-21} +33670 q^{-22} +50518 q^{-23} +32154 q^{-24} -3966 q^{-25} -36090 q^{-26} -41141 q^{-27} -17708 q^{-28} +10460 q^{-29} +31009 q^{-30} +28894 q^{-31} +10489 q^{-32} -13435 q^{-33} -24716 q^{-34} -18027 q^{-35} -4160 q^{-36} +11338 q^{-37} +16738 q^{-38} +12231 q^{-39} +65 q^{-40} -8917 q^{-41} -10062 q^{-42} -6722 q^{-43} +603 q^{-44} +5509 q^{-45} +6757 q^{-46} +2925 q^{-47} -1027 q^{-48} -2934 q^{-49} -3501 q^{-50} -1529 q^{-51} +529 q^{-52} +2083 q^{-53} +1423 q^{-54} +510 q^{-55} -182 q^{-56} -934 q^{-57} -729 q^{-58} -283 q^{-59} +371 q^{-60} +290 q^{-61} +217 q^{-62} +155 q^{-63} -124 q^{-64} -165 q^{-65} -125 q^{-66} +59 q^{-67} +14 q^{-68} +28 q^{-69} +59 q^{-70} -8 q^{-71} -23 q^{-72} -31 q^{-73} +20 q^{-74} -3 q^{-75} -6 q^{-76} +14 q^{-77} - q^{-78} -2 q^{-79} -6 q^{-80} +4 q^{-81} +2 q^{-82} -3 q^{-83} + q^{-84} </math> \|		coloured_jones_6 = <math>q^{93}+2 q^{92}-6 q^{89}-8 q^{88}-16 q^{87}-6 q^{86}+23 q^{85}+49 q^{84}+53 q^{83}+27 q^{82}-13 q^{81}-149 q^{80}-201 q^{79}-151 q^{78}+72 q^{77}+294 q^{76}+462 q^{75}+520 q^{74}-12 q^{73}-624 q^{72}-1148 q^{71}-961 q^{70}-286 q^{69}+958 q^{68}+2323 q^{67}+2127 q^{66}+724 q^{65}-1827 q^{64}-3549 q^{63}-4097 q^{62}-1793 q^{61}+2869 q^{60}+6130 q^{59}+6668 q^{58}+2524 q^{57}-3377 q^{56}-9745 q^{55}-10545 q^{54}-3860 q^{53}+5739 q^{52}+14062 q^{51}+14064 q^{50}+6345 q^{49}-9153 q^{48}-20164 q^{47}-18853 q^{46}-5949 q^{45}+13461 q^{44}+25817 q^{43}+24981 q^{42}+4011 q^{41}-20582 q^{40}-33606 q^{39}-26563 q^{38}-281 q^{37}+27898 q^{36}+42963 q^{35}+25729 q^{34}-8209 q^{33}-38908 q^{32}-46125 q^{31}-21794 q^{30}+18315 q^{29}+52054 q^{28}+46125 q^{27}+10739 q^{26}-33987 q^{25}-57558 q^{24}-41701 q^{23}+3463 q^{22}+52198 q^{21}+59237 q^{20}+27904 q^{19}-24708 q^{18}-61232 q^{17}-55134 q^{16}-9724 q^{15}+48293 q^{14}+65607 q^{13}+39708 q^{12}-16293 q^{11}-61087 q^{10}-62882 q^9-19072 q^8+43936 q^7+68412 q^6+47482 q^5-9520 q^4-59520 q^3-67754 q^2-26585 q+38770+69206 q^{-1} +53985 q^{-2} -1702 q^{-3} -55314 q^{-4} -70716 q^{-5} -35066 q^{-6} +29559 q^{-7} +66002 q^{-8} +59592 q^{-9} +9892 q^{-10} -44730 q^{-11} -68900 q^{-12} -44099 q^{-13} +13888 q^{-14} +54540 q^{-15} +60275 q^{-16} +23623 q^{-17} -25874 q^{-18} -57448 q^{-19} -48179 q^{-20} -4933 q^{-21} +33670 q^{-22} +50518 q^{-23} +32154 q^{-24} -3966 q^{-25} -36090 q^{-26} -41141 q^{-27} -17708 q^{-28} +10460 q^{-29} +31009 q^{-30} +28894 q^{-31} +10489 q^{-32} -13435 q^{-33} -24716 q^{-34} -18027 q^{-35} -4160 q^{-36} +11338 q^{-37} +16738 q^{-38} +12231 q^{-39} +65 q^{-40} -8917 q^{-41} -10062 q^{-42} -6722 q^{-43} +603 q^{-44} +5509 q^{-45} +6757 q^{-46} +2925 q^{-47} -1027 q^{-48} -2934 q^{-49} -3501 q^{-50} -1529 q^{-51} +529 q^{-52} +2083 q^{-53} +1423 q^{-54} +510 q^{-55} -182 q^{-56} -934 q^{-57} -729 q^{-58} -283 q^{-59} +371 q^{-60} +290 q^{-61} +217 q^{-62} +155 q^{-63} -124 q^{-64} -165 q^{-65} -125 q^{-66} +59 q^{-67} +14 q^{-68} +28 q^{-69} +59 q^{-70} -8 q^{-71} -23 q^{-72} -31 q^{-73} +20 q^{-74} -3 q^{-75} -6 q^{-76} +14 q^{-77} - q^{-78} -2 q^{-79} -6 q^{-80} +4 q^{-81} +2 q^{-82} -3 q^{-83} + q^{-84} </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, 158]]</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, 158]]</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[6, 2, 7, 1], X[3, 10, 4, 11], X[14, 8, 15, 7], X[8, 14, 9, 13],		<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[6, 2, 7, 1], X[3, 10, 4, 11], X[14, 8, 15, 7], X[8, 14, 9, 13],
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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, 158]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_158_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, 158]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_158_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, 158]]&) /@ {~~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, 158]]&) /@ {
			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, 158]][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, 158]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:39, 30 August 2005

2005-08-30T14:39:18Z

Show changes

DrorsRobot at 01:06, 30 August 2005

2005-08-30T01:06:51Z

← Older revision		Revision as of 21:06, 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

2005-08-29T22:27:10Z

Show changes

ScottTestRobot at 00:12, 29 August 2005

2005-08-29T00:12:55Z

← Older revision		Revision as of 20:12, 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=158\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,5,-2,8,-7,-1,3,-4,-5,2,-6,10,4,-3,9,7,-8,6,-10,-9/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.gif]]
⚫	\|{{Rolfsen Knot ~~Site~~ ~~Links~~\|n=10\|k=158\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,5,-2,8,-7,-1,3,-4,-5,2,-6,10,4,-3,9,7,-8,6,-10,-9/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>-7</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>-7</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>-9</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>-9</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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	4 q t + 2 q t + 4 q t + 2 q t + 2 q t + 2 q t</nowiki></pre></td></tr>		4 q t + 2 q t + 4 q t + 2 q t + 2 q t + 2 q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]

ScottTestRobot at 01:49, 28 August 2005

2005-08-28T01:49:30Z

Show changes

ScottKnotPageRobot: Resetting knot page to basic template.

2005-08-23T22:51:44Z

Resetting knot page to basic template.

New page

10 158 - Revision history

ScottTestRobot at 22:03, 1 September 2005

DrorsRobot at 22:50, 31 August 2005

ScottKnotPageRobot at 14:39, 30 August 2005

DrorsRobot at 01:06, 30 August 2005

DrorsRobot at 22:27, 29 August 2005

ScottTestRobot at 00:12, 29 August 2005

ScottTestRobot at 01:49, 28 August 2005

ScottKnotPageRobot: Resetting knot page to basic template.