10 119 - Revision history

Drorbn: Reverted edits by RicerCdomv (Talk); changed back to last version by Drorbn

2009-05-27T21:23:30Z

Reverted edits by RicerCdomv (Talk); changed back to last version by Drorbn

← Older revision		Revision as of 17:23, 27 May 2009
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	http://www.textmonracboc.com
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RicerCdomv at 09:51, 22 May 2009

2009-05-22T09:51:31Z

← Older revision		Revision as of 05:51, 22 May 2009
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			http://www.textmonracboc.com
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Drorbn: Reverted edits by TroclItroc (Talk); changed back to last version by ScottTestRobot

2008-12-17T11:51:28Z

Reverted edits by TroclItroc (Talk); changed back to last version by ScottTestRobot

← Older revision		Revision as of 07:51, 17 December 2008
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	roldronr
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TroclItroc: acdarcna

2008-12-17T01:10:00Z

acdarcna

← Older revision		Revision as of 21:10, 16 December 2008
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			roldronr
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ScottTestRobot at 22:04, 1 September 2005

2005-09-01T22:04:53Z

Show changes

DrorsRobot at 22:53, 31 August 2005

2005-08-31T22:53:15Z

← Older revision		Revision as of 18:53, 31 August 2005
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	coloured_jones_5 = <math>q^{90}-4 q^{89}+2 q^{88}+9 q^{87}-5 q^{86}-8 q^{85}-8 q^{84}-11 q^{83}+20 q^{82}+71 q^{81}+29 q^{80}-74 q^{79}-149 q^{78}-157 q^{77}+43 q^{76}+386 q^{75}+535 q^{74}+142 q^{73}-629 q^{72}-1233 q^{71}-964 q^{70}+508 q^{69}+2323 q^{68}+2741 q^{67}+615 q^{66}-3068 q^{65}-5523 q^{64}-3818 q^{63}+2301 q^{62}+8706 q^{61}+9376 q^{60}+1607 q^{59}-10271 q^{58}-16735 q^{57}-10010 q^{56}+7863 q^{55}+23717 q^{54}+22560 q^{53}+908 q^{52}-26863 q^{51}-37290 q^{50}-16878 q^{49}+22875 q^{48}+50391 q^{47}+38553 q^{46}-9576 q^{45}-57548 q^{44}-62501 q^{43}-12860 q^{42}+55504 q^{41}+84185 q^{40}+41841 q^{39}-43024 q^{38}-99477 q^{37}-73282 q^{36}+21200 q^{35}+105906 q^{34}+103113 q^{33}+6837 q^{32}-103332 q^{31}-127723 q^{30}-37512 q^{29}+92962 q^{28}+146068 q^{27}+67383 q^{26}-77858 q^{25}-157705 q^{24}-94208 q^{23}+60130 q^{22}+164281 q^{21}+117290 q^{20}-42344 q^{19}-166996 q^{18}-136672 q^{17}+24919 q^{16}+167338 q^{15}+153331 q^{14}-8048 q^{13}-165525 q^{12}-167906 q^{11}-9396 q^{10}+161160 q^9+180507 q^8+28179 q^7-152563 q^6-190371 q^5-48880 q^4+138440 q^3+195494 q^2+70496 q-117398-193539 q^{-1} -91167 q^{-2} +90096 q^{-3} +182525 q^{-4} +107326 q^{-5} -58453 q^{-6} -161747 q^{-7} -115969 q^{-8} +26501 q^{-9} +132782 q^{-10} +114703 q^{-11} +1431 q^{-12} -99257 q^{-13} -103670 q^{-14} -21353 q^{-15} +65902 q^{-16} +85046 q^{-17} +31853 q^{-18} -37406 q^{-19} -63145 q^{-20} -33162 q^{-21} +16513 q^{-22} +41826 q^{-23} +28465 q^{-24} -3794 q^{-25} -24745 q^{-26} -20758 q^{-27} -2018 q^{-28} +12681 q^{-29} +13217 q^{-30} +3546 q^{-31} -5625 q^{-32} -7396 q^{-33} -2904 q^{-34} +2103 q^{-35} +3599 q^{-36} +1790 q^{-37} -611 q^{-38} -1566 q^{-39} -928 q^{-40} +176 q^{-41} +615 q^{-42} +361 q^{-43} -45 q^{-44} -198 q^{-45} -133 q^{-46} - q^{-47} +96 q^{-48} +34 q^{-49} -33 q^{-50} -9 q^{-51} +2 q^{-52} -9 q^{-53} +12 q^{-54} +7 q^{-55} -14 q^{-56} +3 q^{-57} +5 q^{-58} -4 q^{-59} + q^{-60} </math> \|		coloured_jones_5 = <math>q^{90}-4 q^{89}+2 q^{88}+9 q^{87}-5 q^{86}-8 q^{85}-8 q^{84}-11 q^{83}+20 q^{82}+71 q^{81}+29 q^{80}-74 q^{79}-149 q^{78}-157 q^{77}+43 q^{76}+386 q^{75}+535 q^{74}+142 q^{73}-629 q^{72}-1233 q^{71}-964 q^{70}+508 q^{69}+2323 q^{68}+2741 q^{67}+615 q^{66}-3068 q^{65}-5523 q^{64}-3818 q^{63}+2301 q^{62}+8706 q^{61}+9376 q^{60}+1607 q^{59}-10271 q^{58}-16735 q^{57}-10010 q^{56}+7863 q^{55}+23717 q^{54}+22560 q^{53}+908 q^{52}-26863 q^{51}-37290 q^{50}-16878 q^{49}+22875 q^{48}+50391 q^{47}+38553 q^{46}-9576 q^{45}-57548 q^{44}-62501 q^{43}-12860 q^{42}+55504 q^{41}+84185 q^{40}+41841 q^{39}-43024 q^{38}-99477 q^{37}-73282 q^{36}+21200 q^{35}+105906 q^{34}+103113 q^{33}+6837 q^{32}-103332 q^{31}-127723 q^{30}-37512 q^{29}+92962 q^{28}+146068 q^{27}+67383 q^{26}-77858 q^{25}-157705 q^{24}-94208 q^{23}+60130 q^{22}+164281 q^{21}+117290 q^{20}-42344 q^{19}-166996 q^{18}-136672 q^{17}+24919 q^{16}+167338 q^{15}+153331 q^{14}-8048 q^{13}-165525 q^{12}-167906 q^{11}-9396 q^{10}+161160 q^9+180507 q^8+28179 q^7-152563 q^6-190371 q^5-48880 q^4+138440 q^3+195494 q^2+70496 q-117398-193539 q^{-1} -91167 q^{-2} +90096 q^{-3} +182525 q^{-4} +107326 q^{-5} -58453 q^{-6} -161747 q^{-7} -115969 q^{-8} +26501 q^{-9} +132782 q^{-10} +114703 q^{-11} +1431 q^{-12} -99257 q^{-13} -103670 q^{-14} -21353 q^{-15} +65902 q^{-16} +85046 q^{-17} +31853 q^{-18} -37406 q^{-19} -63145 q^{-20} -33162 q^{-21} +16513 q^{-22} +41826 q^{-23} +28465 q^{-24} -3794 q^{-25} -24745 q^{-26} -20758 q^{-27} -2018 q^{-28} +12681 q^{-29} +13217 q^{-30} +3546 q^{-31} -5625 q^{-32} -7396 q^{-33} -2904 q^{-34} +2103 q^{-35} +3599 q^{-36} +1790 q^{-37} -611 q^{-38} -1566 q^{-39} -928 q^{-40} +176 q^{-41} +615 q^{-42} +361 q^{-43} -45 q^{-44} -198 q^{-45} -133 q^{-46} - q^{-47} +96 q^{-48} +34 q^{-49} -33 q^{-50} -9 q^{-51} +2 q^{-52} -9 q^{-53} +12 q^{-54} +7 q^{-55} -14 q^{-56} +3 q^{-57} +5 q^{-58} -4 q^{-59} + q^{-60} </math> \|
	coloured_jones_6 = <math>q^{126}-4 q^{125}+2 q^{124}+9 q^{123}-5 q^{122}-8 q^{121}-14 q^{120}+16 q^{119}+13 q^{117}+76 q^{116}-19 q^{115}-87 q^{114}-173 q^{113}-37 q^{112}+32 q^{111}+212 q^{110}+597 q^{109}+324 q^{108}-193 q^{107}-1077 q^{106}-1170 q^{105}-1074 q^{104}+156 q^{103}+2687 q^{102}+3644 q^{101}+2879 q^{100}-1066 q^{99}-4766 q^{98}-8642 q^{97}-7628 q^{96}+740 q^{95}+10641 q^{94}+18227 q^{93}+14755 q^{92}+3147 q^{91}-19152 q^{90}-35574 q^{89}-31743 q^{88}-7345 q^{87}+31458 q^{86}+59060 q^{85}+63137 q^{84}+18940 q^{83}-48250 q^{82}-100827 q^{81}-104108 q^{80}-39317 q^{79}+63176 q^{78}+162419 q^{77}+167622 q^{76}+70659 q^{75}-92693 q^{74}-232947 q^{73}-253500 q^{72}-121546 q^{71}+132952 q^{70}+331550 q^{69}+362644 q^{68}+165312 q^{67}-169952 q^{66}-455762 q^{65}-502014 q^{64}-207811 q^{63}+237928 q^{62}+607679 q^{61}+632205 q^{60}+258986 q^{59}-338753 q^{58}-797916 q^{57}-763179 q^{56}-261150 q^{55}+483253 q^{54}+980938 q^{53}+900348 q^{52}+205544 q^{51}-692790 q^{50}-1177502 q^{49}-962377 q^{48}-71166 q^{47}+920165 q^{46}+1389200 q^{45}+936713 q^{44}-174355 q^{43}-1196663 q^{42}-1510284 q^{41}-793359 q^{40}+480296 q^{39}+1513405 q^{38}+1523101 q^{37}+489665 q^{36}-882073 q^{35}-1734843 q^{34}-1385111 q^{33}-80578 q^{32}+1351700 q^{31}+1832666 q^{30}+1041271 q^{29}-468324 q^{28}-1721154 q^{27}-1748009 q^{26}-549293 q^{25}+1105672 q^{24}+1949534 q^{23}+1414470 q^{22}-119797 q^{21}-1634951 q^{20}-1964344 q^{19}-894103 q^{18}+889871 q^{17}+2005998 q^{16}+1695002 q^{15}+170021 q^{14}-1543644 q^{13}-2140097 q^{12}-1212056 q^{11}+657080 q^{10}+2026626 q^9+1970649 q^8+515939 q^7-1359164 q^6-2260711 q^5-1577469 q^4+273280 q^3+1883026 q^2+2187926 q+976970-931323 q^{-1} -2157307 q^{-2} -1893519 q^{-3} -296676 q^{-4} +1414673 q^{-5} +2136498 q^{-6} +1404434 q^{-7} -260131 q^{-8} -1666401 q^{-9} -1908538 q^{-10} -843657 q^{-11} +667373 q^{-12} +1658528 q^{-13} +1507905 q^{-14} +382318 q^{-15} -886523 q^{-16} -1479924 q^{-17} -1046864 q^{-18} -30361 q^{-19} +905971 q^{-20} +1169119 q^{-21} +662338 q^{-22} -186409 q^{-23} -807055 q^{-24} -821489 q^{-25} -355208 q^{-26} +263383 q^{-27} +622264 q^{-28} +537974 q^{-29} +145088 q^{-30} -263289 q^{-31} -421230 q^{-32} -312460 q^{-33} -34549 q^{-34} +205459 q^{-35} +267735 q^{-36} +157234 q^{-37} -20098 q^{-38} -133588 q^{-39} -149712 q^{-40} -70701 q^{-41} +29488 q^{-42} +83394 q^{-43} +72557 q^{-44} +22346 q^{-45} -21110 q^{-46} -43985 q^{-47} -32343 q^{-48} -4874 q^{-49} +15681 q^{-50} +19492 q^{-51} +10333 q^{-52} +734 q^{-53} -8165 q^{-54} -8255 q^{-55} -2932 q^{-56} +1772 q^{-57} +3263 q^{-58} +2009 q^{-59} +1067 q^{-60} -1037 q^{-61} -1411 q^{-62} -502 q^{-63} +221 q^{-64} +369 q^{-65} +109 q^{-66} +266 q^{-67} -120 q^{-68} -199 q^{-69} -16 q^{-70} +55 q^{-71} +42 q^{-72} -52 q^{-73} +49 q^{-74} -5 q^{-75} -34 q^{-76} +11 q^{-77} +8 q^{-78} +7 q^{-79} -14 q^{-80} +3 q^{-81} +5 q^{-82} -4 q^{-83} + q^{-84} </math> \|		coloured_jones_6 = <math>q^{126}-4 q^{125}+2 q^{124}+9 q^{123}-5 q^{122}-8 q^{121}-14 q^{120}+16 q^{119}+13 q^{117}+76 q^{116}-19 q^{115}-87 q^{114}-173 q^{113}-37 q^{112}+32 q^{111}+212 q^{110}+597 q^{109}+324 q^{108}-193 q^{107}-1077 q^{106}-1170 q^{105}-1074 q^{104}+156 q^{103}+2687 q^{102}+3644 q^{101}+2879 q^{100}-1066 q^{99}-4766 q^{98}-8642 q^{97}-7628 q^{96}+740 q^{95}+10641 q^{94}+18227 q^{93}+14755 q^{92}+3147 q^{91}-19152 q^{90}-35574 q^{89}-31743 q^{88}-7345 q^{87}+31458 q^{86}+59060 q^{85}+63137 q^{84}+18940 q^{83}-48250 q^{82}-100827 q^{81}-104108 q^{80}-39317 q^{79}+63176 q^{78}+162419 q^{77}+167622 q^{76}+70659 q^{75}-92693 q^{74}-232947 q^{73}-253500 q^{72}-121546 q^{71}+132952 q^{70}+331550 q^{69}+362644 q^{68}+165312 q^{67}-169952 q^{66}-455762 q^{65}-502014 q^{64}-207811 q^{63}+237928 q^{62}+607679 q^{61}+632205 q^{60}+258986 q^{59}-338753 q^{58}-797916 q^{57}-763179 q^{56}-261150 q^{55}+483253 q^{54}+980938 q^{53}+900348 q^{52}+205544 q^{51}-692790 q^{50}-1177502 q^{49}-962377 q^{48}-71166 q^{47}+920165 q^{46}+1389200 q^{45}+936713 q^{44}-174355 q^{43}-1196663 q^{42}-1510284 q^{41}-793359 q^{40}+480296 q^{39}+1513405 q^{38}+1523101 q^{37}+489665 q^{36}-882073 q^{35}-1734843 q^{34}-1385111 q^{33}-80578 q^{32}+1351700 q^{31}+1832666 q^{30}+1041271 q^{29}-468324 q^{28}-1721154 q^{27}-1748009 q^{26}-549293 q^{25}+1105672 q^{24}+1949534 q^{23}+1414470 q^{22}-119797 q^{21}-1634951 q^{20}-1964344 q^{19}-894103 q^{18}+889871 q^{17}+2005998 q^{16}+1695002 q^{15}+170021 q^{14}-1543644 q^{13}-2140097 q^{12}-1212056 q^{11}+657080 q^{10}+2026626 q^9+1970649 q^8+515939 q^7-1359164 q^6-2260711 q^5-1577469 q^4+273280 q^3+1883026 q^2+2187926 q+976970-931323 q^{-1} -2157307 q^{-2} -1893519 q^{-3} -296676 q^{-4} +1414673 q^{-5} +2136498 q^{-6} +1404434 q^{-7} -260131 q^{-8} -1666401 q^{-9} -1908538 q^{-10} -843657 q^{-11} +667373 q^{-12} +1658528 q^{-13} +1507905 q^{-14} +382318 q^{-15} -886523 q^{-16} -1479924 q^{-17} -1046864 q^{-18} -30361 q^{-19} +905971 q^{-20} +1169119 q^{-21} +662338 q^{-22} -186409 q^{-23} -807055 q^{-24} -821489 q^{-25} -355208 q^{-26} +263383 q^{-27} +622264 q^{-28} +537974 q^{-29} +145088 q^{-30} -263289 q^{-31} -421230 q^{-32} -312460 q^{-33} -34549 q^{-34} +205459 q^{-35} +267735 q^{-36} +157234 q^{-37} -20098 q^{-38} -133588 q^{-39} -149712 q^{-40} -70701 q^{-41} +29488 q^{-42} +83394 q^{-43} +72557 q^{-44} +22346 q^{-45} -21110 q^{-46} -43985 q^{-47} -32343 q^{-48} -4874 q^{-49} +15681 q^{-50} +19492 q^{-51} +10333 q^{-52} +734 q^{-53} -8165 q^{-54} -8255 q^{-55} -2932 q^{-56} +1772 q^{-57} +3263 q^{-58} +2009 q^{-59} +1067 q^{-60} -1037 q^{-61} -1411 q^{-62} -502 q^{-63} +221 q^{-64} +369 q^{-65} +109 q^{-66} +266 q^{-67} -120 q^{-68} -199 q^{-69} -16 q^{-70} +55 q^{-71} +42 q^{-72} -52 q^{-73} +49 q^{-74} -5 q^{-75} -34 q^{-76} +11 q^{-77} +8 q^{-78} +7 q^{-79} -14 q^{-80} +3 q^{-81} +5 q^{-82} -4 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, 119]]</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, 119]]</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[7, 18, 8, 19], X[3, 9, 4, 8], X[17, 3, 18, 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, 6, 2, 7], X[7, 18, 8, 19], X[3, 9, 4, 8], X[17, 3, 18, 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>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, 119]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_119_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, 119]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_119_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, 119]]&) /@ {~~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, 119]]&) /@ {
			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, 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>{Chiral, 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, 119]][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, 119]][t]</nowiki></pre></td></tr>

ScottKnotPageRobot at 14:40, 30 August 2005

2005-08-30T14:40:56Z

Show changes

DrorsRobot at 01:08, 30 August 2005

2005-08-30T01:08:46Z

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DrorsRobot at 22:23, 29 August 2005

2005-08-29T22:23:40Z

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ScottTestRobot at 00:15, 29 August 2005

2005-08-29T00:15:08Z

← Older revision		Revision as of 20:15, 28 August 2005
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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>-7</td><td bgcolor=yellow> </td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-3</td></tr>		<tr align=center><td>-7</td><td bgcolor=yellow> </td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-3</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> </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> </td><td> </td><td>1</td></tr>
	</table>~~</center>~~		</table>}}

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

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	q t + 3 q t + q t</nowiki></pre></td></tr>		q t + 3 q t + q t</nowiki></pre></td></tr>
	</table>		</table>

			[[Category:Knot Page]]