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{{Rolfsen Knot Page|
n = 10 |
k = 82 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,6,-5,1,-2,3,-6,9,-7,10,-8,5,-4,2,-9,7,-10,8/goTop.html |
braid_table     = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]]</td></tr>
</table> |
braid_crossings = 10 |
braid_width     = 3 |
braid_index     = 3 |
same_alexander  =  |
same_jones      =  |
khovanov_table  = <table border=1>
<tr align=center>
<td width=13.3333%><table cellpadding=0 cellspacing=0>
  <tr><td>\</td><td>&nbsp;</td><td>r</td></tr>
<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr>
<tr><td>j</td><td>&nbsp;</td><td>\</td></tr>
</table></td>
  <td width=6.66667%>-6</td    ><td width=6.66667%>-5</td    ><td width=6.66667%>-4</td    ><td width=6.66667%>-3</td    ><td width=6.66667%>-2</td    ><td width=6.66667%>-1</td    ><td width=6.66667%>0</td    ><td width=6.66667%>1</td    ><td width=6.66667%>2</td    ><td width=6.66667%>3</td    ><td width=6.66667%>4</td    ><td width=13.3333%>&chi;</td></tr>
<tr align=center><td>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td>1</td></tr>
<tr align=center><td>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>2</td></tr>
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>-1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr>
<tr align=center><td>-3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>-5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>-7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr>
<tr align=center><td>-9</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-3</td></tr>
<tr align=center><td>-11</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr>
<tr align=center><td>-13</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>-15</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
</table> |
coloured_jones_2 = <math>q^{10}-3 q^9+q^8+9 q^7-14 q^6-4 q^5+30 q^4-23 q^3-23 q^2+54 q-20-49 q^{-1} +71 q^{-2} -9 q^{-3} -70 q^{-4} +74 q^{-5} +5 q^{-6} -75 q^{-7} +60 q^{-8} +13 q^{-9} -58 q^{-10} +36 q^{-11} +11 q^{-12} -31 q^{-13} +17 q^{-14} +4 q^{-15} -12 q^{-16} +7 q^{-17} + q^{-18} -3 q^{-19} + q^{-20} </math> |
coloured_jones_3 = <math>q^{21}-3 q^{20}+q^{19}+5 q^{18}+q^{17}-14 q^{16}-6 q^{15}+28 q^{14}+19 q^{13}-41 q^{12}-44 q^{11}+46 q^{10}+81 q^9-39 q^8-119 q^7+13 q^6+149 q^5+30 q^4-165 q^3-83 q^2+166 q+130-140 q^{-1} -183 q^{-2} +119 q^{-3} +211 q^{-4} -72 q^{-5} -250 q^{-6} +45 q^{-7} +259 q^{-8} +2 q^{-9} -276 q^{-10} -31 q^{-11} +263 q^{-12} +71 q^{-13} -247 q^{-14} -90 q^{-15} +203 q^{-16} +105 q^{-17} -153 q^{-18} -103 q^{-19} +103 q^{-20} +80 q^{-21} -54 q^{-22} -56 q^{-23} +28 q^{-24} +25 q^{-25} -11 q^{-26} -7 q^{-27} +10 q^{-28} -6 q^{-29} -8 q^{-30} +6 q^{-31} +10 q^{-32} -5 q^{-33} -8 q^{-34} +3 q^{-35} +3 q^{-36} + q^{-37} -3 q^{-38} + q^{-39} </math> |
coloured_jones_4 = <math>q^{36}-3 q^{35}+q^{34}+5 q^{33}-3 q^{32}+q^{31}-17 q^{30}+6 q^{29}+31 q^{28}+2 q^{26}-80 q^{25}-20 q^{24}+92 q^{23}+63 q^{22}+70 q^{21}-192 q^{20}-160 q^{19}+76 q^{18}+156 q^{17}+317 q^{16}-183 q^{15}-346 q^{14}-142 q^{13}+54 q^{12}+610 q^{11}+75 q^{10}-282 q^9-387 q^8-362 q^7+613 q^6+361 q^5+142 q^4-315 q^3-838 q^2+230 q+347+671 q^{-1} +132 q^{-2} -1066 q^{-3} -287 q^{-4} +8 q^{-5} +1021 q^{-6} +702 q^{-7} -1021 q^{-8} -699 q^{-9} -426 q^{-10} +1169 q^{-11} +1170 q^{-12} -859 q^{-13} -969 q^{-14} -796 q^{-15} +1194 q^{-16} +1505 q^{-17} -624 q^{-18} -1125 q^{-19} -1119 q^{-20} +1053 q^{-21} +1697 q^{-22} -245 q^{-23} -1049 q^{-24} -1369 q^{-25} +629 q^{-26} +1593 q^{-27} +218 q^{-28} -631 q^{-29} -1346 q^{-30} +61 q^{-31} +1095 q^{-32} +466 q^{-33} -62 q^{-34} -942 q^{-35} -289 q^{-36} +457 q^{-37} +353 q^{-38} +270 q^{-39} -420 q^{-40} -273 q^{-41} +58 q^{-42} +102 q^{-43} +265 q^{-44} -99 q^{-45} -113 q^{-46} -41 q^{-47} -33 q^{-48} +132 q^{-49} -3 q^{-50} -13 q^{-51} -21 q^{-52} -44 q^{-53} +40 q^{-54} +3 q^{-55} +8 q^{-56} - q^{-57} -17 q^{-58} +7 q^{-59} - q^{-60} +3 q^{-61} + q^{-62} -3 q^{-63} + q^{-64} </math> |
coloured_jones_5 = <math>q^{55}-3 q^{54}+q^{53}+5 q^{52}-3 q^{51}-3 q^{50}-2 q^{49}-5 q^{48}+8 q^{47}+26 q^{46}+4 q^{45}-31 q^{44}-41 q^{43}-32 q^{42}+31 q^{41}+108 q^{40}+106 q^{39}-27 q^{38}-179 q^{37}-220 q^{36}-83 q^{35}+215 q^{34}+417 q^{33}+287 q^{32}-154 q^{31}-571 q^{30}-595 q^{29}-108 q^{28}+598 q^{27}+929 q^{26}+536 q^{25}-383 q^{24}-1102 q^{23}-1021 q^{22}-135 q^{21}+962 q^{20}+1393 q^{19}+795 q^{18}-423 q^{17}-1376 q^{16}-1401 q^{15}-459 q^{14}+859 q^{13}+1665 q^{12}+1436 q^{11}+186 q^{10}-1382 q^9-2220 q^8-1566 q^7+444 q^6+2563 q^5+3042 q^4+999 q^3-2321 q^2-4246 q-2819+1451 q^{-1} +5150 q^{-2} +4654 q^{-3} -199 q^{-4} -5449 q^{-5} -6364 q^{-6} -1414 q^{-7} +5459 q^{-8} +7770 q^{-9} +2920 q^{-10} -5011 q^{-11} -8830 q^{-12} -4455 q^{-13} +4544 q^{-14} +9608 q^{-15} +5625 q^{-16} -3920 q^{-17} -10143 q^{-18} -6722 q^{-19} +3459 q^{-20} +10556 q^{-21} +7526 q^{-22} -2918 q^{-23} -10877 q^{-24} -8367 q^{-25} +2456 q^{-26} +11079 q^{-27} +9088 q^{-28} -1726 q^{-29} -11082 q^{-30} -9890 q^{-31} +827 q^{-32} +10747 q^{-33} +10478 q^{-34} +438 q^{-35} -9888 q^{-36} -10864 q^{-37} -1855 q^{-38} +8497 q^{-39} +10718 q^{-40} +3252 q^{-41} -6585 q^{-42} -9951 q^{-43} -4402 q^{-44} +4437 q^{-45} +8603 q^{-46} +4982 q^{-47} -2356 q^{-48} -6754 q^{-49} -4992 q^{-50} +622 q^{-51} +4837 q^{-52} +4407 q^{-53} +532 q^{-54} -3037 q^{-55} -3508 q^{-56} -1115 q^{-57} +1653 q^{-58} +2498 q^{-59} +1232 q^{-60} -696 q^{-61} -1640 q^{-62} -1061 q^{-63} +178 q^{-64} +944 q^{-65} +802 q^{-66} +90 q^{-67} -520 q^{-68} -546 q^{-69} -145 q^{-70} +237 q^{-71} +332 q^{-72} +155 q^{-73} -88 q^{-74} -198 q^{-75} -120 q^{-76} +30 q^{-77} +93 q^{-78} +73 q^{-79} +16 q^{-80} -43 q^{-81} -53 q^{-82} -6 q^{-83} +17 q^{-84} +12 q^{-85} +16 q^{-86} -3 q^{-87} -13 q^{-88} -2 q^{-89} +3 q^{-90} - q^{-91} +3 q^{-92} + q^{-93} -3 q^{-94} + q^{-95} </math> |
coloured_jones_6 = <math>q^{78}-3 q^{77}+q^{76}+5 q^{75}-3 q^{74}-3 q^{73}-6 q^{72}+10 q^{71}-3 q^{70}+3 q^{69}+29 q^{68}-15 q^{67}-31 q^{66}-50 q^{65}+16 q^{64}+18 q^{63}+57 q^{62}+149 q^{61}+13 q^{60}-108 q^{59}-269 q^{58}-138 q^{57}-83 q^{56}+165 q^{55}+588 q^{54}+435 q^{53}+110 q^{52}-592 q^{51}-726 q^{50}-907 q^{49}-356 q^{48}+952 q^{47}+1486 q^{46}+1487 q^{45}+150 q^{44}-801 q^{43}-2351 q^{42}-2430 q^{41}-528 q^{40}+1390 q^{39}+3160 q^{38}+2606 q^{37}+1802 q^{36}-1595 q^{35}-3927 q^{34}-3673 q^{33}-2004 q^{32}+1294 q^{31}+3033 q^{30}+5316 q^{29}+2875 q^{28}-323 q^{27}-2954 q^{26}-4788 q^{25}-4200 q^{24}-3084 q^{23}+2559 q^{22}+4694 q^{21}+6288 q^{20}+5394 q^{19}+1266 q^{18}-4553 q^{17}-10970 q^{16}-8683 q^{15}-4599 q^{14}+5123 q^{13}+13899 q^{12}+16169 q^{11}+8088 q^{10}-8616 q^9-18535 q^8-22543 q^7-10353 q^6+10285 q^5+28258 q^4+28942 q^3+8648 q^2-15292 q-36555-33436 q^{-1} -8032 q^{-2} +27043 q^{-3} +45373 q^{-4} +32754 q^{-5} +1665 q^{-6} -37824 q^{-7} -52042 q^{-8} -32205 q^{-9} +13503 q^{-10} +50279 q^{-11} +52582 q^{-12} +23344 q^{-13} -28472 q^{-14} -60533 q^{-15} -52249 q^{-16} -3779 q^{-17} +46271 q^{-18} +63647 q^{-19} +41071 q^{-20} -16261 q^{-21} -61493 q^{-22} -64549 q^{-23} -17582 q^{-24} +39891 q^{-25} +68311 q^{-26} +52193 q^{-27} -6878 q^{-28} -60252 q^{-29} -71364 q^{-30} -26411 q^{-31} +35246 q^{-32} +70996 q^{-33} +59376 q^{-34} -459 q^{-35} -59542 q^{-36} -76726 q^{-37} -33819 q^{-38} +31002 q^{-39} +73370 q^{-40} +66752 q^{-41} +7641 q^{-42} -56589 q^{-43} -81421 q^{-44} -44089 q^{-45} +21451 q^{-46} +71209 q^{-47} +74062 q^{-48} +21515 q^{-49} -44801 q^{-50} -79670 q^{-51} -55378 q^{-52} +3232 q^{-53} +57328 q^{-54} +73753 q^{-55} +37124 q^{-56} -22204 q^{-57} -64074 q^{-58} -58169 q^{-59} -16982 q^{-60} +31733 q^{-61} +58619 q^{-62} +43188 q^{-63} +1708 q^{-64} -37044 q^{-65} -45851 q^{-66} -26624 q^{-67} +6394 q^{-68} +33388 q^{-69} +34266 q^{-70} +13927 q^{-71} -12191 q^{-72} -25040 q^{-73} -21824 q^{-74} -6427 q^{-75} +11918 q^{-76} +18345 q^{-77} +12565 q^{-78} +130 q^{-79} -8631 q^{-80} -11256 q^{-81} -7032 q^{-82} +1861 q^{-83} +6599 q^{-84} +6378 q^{-85} +2139 q^{-86} -1540 q^{-87} -3953 q^{-88} -3710 q^{-89} -260 q^{-90} +1755 q^{-91} +2312 q^{-92} +1069 q^{-93} +20 q^{-94} -1161 q^{-95} -1533 q^{-96} -185 q^{-97} +463 q^{-98} +820 q^{-99} +386 q^{-100} +163 q^{-101} -364 q^{-102} -661 q^{-103} -98 q^{-104} +96 q^{-105} +311 q^{-106} +156 q^{-107} +153 q^{-108} -84 q^{-109} -261 q^{-110} -60 q^{-111} -24 q^{-112} +87 q^{-113} +43 q^{-114} +87 q^{-115} +2 q^{-116} -72 q^{-117} -15 q^{-118} -23 q^{-119} +16 q^{-120} +25 q^{-122} +5 q^{-123} -15 q^{-124} +2 q^{-125} -6 q^{-126} +3 q^{-127} - q^{-128} +3 q^{-129} + q^{-130} -3 q^{-131} + q^{-132} </math> |
coloured_jones_7 = <math>q^{105}-3 q^{104}+q^{103}+5 q^{102}-3 q^{101}-3 q^{100}-6 q^{99}+6 q^{98}+12 q^{97}-8 q^{96}+6 q^{95}+10 q^{94}-16 q^{93}-26 q^{92}-41 q^{91}+6 q^{90}+76 q^{89}+46 q^{88}+67 q^{87}+39 q^{86}-79 q^{85}-150 q^{84}-274 q^{83}-157 q^{82}+146 q^{81}+311 q^{80}+515 q^{79}+476 q^{78}+82 q^{77}-345 q^{76}-1034 q^{75}-1244 q^{74}-641 q^{73}+155 q^{72}+1419 q^{71}+2168 q^{70}+1927 q^{69}+1023 q^{68}-1195 q^{67}-3255 q^{66}-3837 q^{65}-3138 q^{64}-240 q^{63}+3190 q^{62}+5443 q^{61}+6370 q^{60}+3622 q^{59}-1238 q^{58}-5822 q^{57}-9224 q^{56}-7979 q^{55}-3200 q^{54}+2987 q^{53}+9746 q^{52}+11975 q^{51}+9178 q^{50}+2980 q^{49}-6316 q^{48}-12313 q^{47}-13642 q^{46}-10644 q^{45}-1690 q^{44}+6900 q^{43}+13181 q^{42}+15963 q^{41}+11257 q^{40}+4073 q^{39}-4503 q^{38}-13756 q^{37}-17258 q^{36}-17364 q^{35}-11832 q^{34}+905 q^{33}+13252 q^{32}+25589 q^{31}+31084 q^{30}+22737 q^{29}+5227 q^{28}-21326 q^{27}-45132 q^{26}-51161 q^{25}-37738 q^{24}-1252 q^{23}+44366 q^{22}+74957 q^{21}+78577 q^{20}+42293 q^{19}-22043 q^{18}-83392 q^{17}-117236 q^{16}-96077 q^{15}-23117 q^{14}+68266 q^{13}+141795 q^{12}+152136 q^{11}+86431 q^{10}-26730 q^9-143331 q^8-198453 q^7-157725 q^6-37398 q^5+117268 q^4+224549 q^3+225545 q^2+116048 q-65594-225596 q^{-1} -279447 q^{-2} -197716 q^{-3} -4731 q^{-4} +200891 q^{-5} +312574 q^{-6} +273053 q^{-7} +84760 q^{-8} -155868 q^{-9} -323974 q^{-10} -334103 q^{-11} -164262 q^{-12} +97583 q^{-13} +315163 q^{-14} +377966 q^{-15} +236813 q^{-16} -34453 q^{-17} -292507 q^{-18} -404840 q^{-19} -296738 q^{-20} -26454 q^{-21} +261167 q^{-22} +417350 q^{-23} +343536 q^{-24} +80554 q^{-25} -228062 q^{-26} -419971 q^{-27} -377010 q^{-28} -124735 q^{-29} +196753 q^{-30} +416587 q^{-31} +400284 q^{-32} +158918 q^{-33} -170943 q^{-34} -411425 q^{-35} -415711 q^{-36} -183943 q^{-37} +151132 q^{-38} +407191 q^{-39} +427414 q^{-40} +202430 q^{-41} -137432 q^{-42} -405703 q^{-43} -438133 q^{-44} -218015 q^{-45} +127069 q^{-46} +407318 q^{-47} +451159 q^{-48} +234645 q^{-49} -116843 q^{-50} -410023 q^{-51} -467104 q^{-52} -256389 q^{-53} +101019 q^{-54} +410025 q^{-55} +485514 q^{-56} +285538 q^{-57} -75241 q^{-58} -401454 q^{-59} -501391 q^{-60} -321524 q^{-61} +35128 q^{-62} +377573 q^{-63} +508816 q^{-64} +360309 q^{-65} +18722 q^{-66} -333930 q^{-67} -499139 q^{-68} -393445 q^{-69} -82426 q^{-70} +268990 q^{-71} +466223 q^{-72} +411992 q^{-73} +146770 q^{-74} -187803 q^{-75} -407913 q^{-76} -407073 q^{-77} -200167 q^{-78} +99580 q^{-79} +327782 q^{-80} +375102 q^{-81} +232986 q^{-82} -17228 q^{-83} -236211 q^{-84} -318697 q^{-85} -238645 q^{-86} -47240 q^{-87} +145329 q^{-88} +246292 q^{-89} +218615 q^{-90} +86908 q^{-91} -68242 q^{-92} -170403 q^{-93} -179246 q^{-94} -100329 q^{-95} +12623 q^{-96} +102195 q^{-97} +131276 q^{-98} +92925 q^{-99} +19427 q^{-100} -49942 q^{-101} -84989 q^{-102} -73050 q^{-103} -31339 q^{-104} +16175 q^{-105} +47526 q^{-106} +49468 q^{-107} +29851 q^{-108} +1405 q^{-109} -21905 q^{-110} -28819 q^{-111} -22099 q^{-112} -7330 q^{-113} +7487 q^{-114} +13906 q^{-115} +13180 q^{-116} +7051 q^{-117} -883 q^{-118} -5172 q^{-119} -6478 q^{-120} -4481 q^{-121} -748 q^{-122} +1140 q^{-123} +2197 q^{-124} +1916 q^{-125} +595 q^{-126} +229 q^{-127} -347 q^{-128} -433 q^{-129} +110 q^{-130} -192 q^{-131} -185 q^{-132} -307 q^{-133} -579 q^{-134} -9 q^{-135} +196 q^{-136} +329 q^{-137} +583 q^{-138} +249 q^{-139} +70 q^{-140} -204 q^{-141} -551 q^{-142} -273 q^{-143} -96 q^{-144} +53 q^{-145} +286 q^{-146} +186 q^{-147} +184 q^{-148} +57 q^{-149} -182 q^{-150} -131 q^{-151} -99 q^{-152} -51 q^{-153} +58 q^{-154} +39 q^{-155} +71 q^{-156} +60 q^{-157} -33 q^{-158} -18 q^{-159} -29 q^{-160} -24 q^{-161} +10 q^{-162} - q^{-163} +13 q^{-164} +14 q^{-165} -7 q^{-166} -2 q^{-168} -6 q^{-169} +3 q^{-170} - q^{-171} +3 q^{-172} + q^{-173} -3 q^{-174} + q^{-175} </math> |
computer_talk = 
         <table>
         <tr valign=top>
         <td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td>
         <td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td>
         </tr>
         <tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr>
         </table>
         <table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[2]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[Knot[10, 82]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[2]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[X[1, 6, 2, 7], X[7, 16, 8, 17], X[3, 9, 4, 8], X[15, 3, 16, 2], 
 
  X[5, 15, 6, 14], X[9, 5, 10, 4], X[11, 18, 12, 19], X[13, 20, 14, 1], 
 
  X[17, 10, 18, 11], X[19, 12, 20, 13]]</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[Knot[10, 82]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[-1, 4, -3, 6, -5, 1, -2, 3, -6, 9, -7, 10, -8, 5, -4, 2, -9, 
 
  7, -10, 8]</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[Knot[10, 82]]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[6, 8, 14, 16, 4, 18, 20, 2, 10, 12]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>br = BR[Knot[10, 82]]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BR[3, {-1, -1, -1, -1, 2, -1, 2, -1, 2, 2}]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{First[br], Crossings[br]}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[6]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{3, 10}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BraidIndex[Knot[10, 82]]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[7]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>3</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Show[DrawMorseLink[Knot[10, 82]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:10_82_ML.gif]]</td></tr><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>-Graphics-</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> (#[Knot[10, 82]]&) /@ {
                   SymmetryType, UnknottingNumber, ThreeGenus,
                   BridgeIndex, SuperBridgeIndex, NakanishiIndex
                  }</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Chiral, 1, 4, 3, NotAvailable, 1}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>alex = Alexander[Knot[10, 82]][t]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>       -4   4    8    12             2      3    4
-13 - t   + -- - -- + -- + 12 t - 8 t  + 4 t  - t
             3    2   t
            t    t</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Conway[Knot[10, 82]][z]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>       4      6    8
1 - 4 z  - 4 z  - z</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[10, 82]}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[13]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{KnotDet[Knot[10, 82]], KnotSignature[Knot[10, 82]]}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[13]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{63, -2}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[14]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Jones[Knot[10, 82]][q]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[14]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>      -7   3    5    8    10   10   10            2    3
-7 + q   - -- + -- - -- + -- - -- + -- + 5 q - 3 q  + q
            6    5    4    3    2   q
           q    q    q    q    q</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[15]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[15]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[10, 82]}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[16]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>A2Invariant[Knot[10, 82]][q]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[16]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -20    -18    -16    2     -12    -10    -8   4     -4   2     2
q    - q    + q    - --- - q    + q    - q   + -- - q   + -- - q  + 
                      14                        6          2
                     q                         q          q
 
   4    6    8
  q  - q  + q</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[17]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>HOMFLYPT[Knot[10, 82]][a, z]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[17]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>       2      2  2      4  2      4       2  4      4  4    6
1 + 4 z  - 8 a  z  + 4 a  z  + 4 z  - 12 a  z  + 4 a  z  + z  - 
 
     2  6    4  6    2  8
  6 a  z  + a  z  - a  z</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[18]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Knot[10, 82]][a, z]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[18]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>                                        2
    z              5      7        2   z        2  2      4  2
1 - - - 2 a z + 2 a  z + a  z - 6 z  + -- - 13 a  z  - 5 a  z  - 
    a                                   2
                                       a
 
             3                                                      4
   8  2   7 z          3      3  3      5  3      7  3       4   3 z
  a  z  + ---- + 10 a z  + 5 a  z  - 2 a  z  - 4 a  z  + 14 z  - ---- + 
           a                                                       2
                                                                  a
 
                                              5
      2  4       4  4      6  4    8  4   10 z         5      3  5
  32 a  z  + 10 a  z  - 4 a  z  + a  z  - ----- - 8 a z  - 4 a  z  - 
                                            a
 
                               6
     5  5      7  5       6   z        2  6      4  6      6  6
  3 a  z  + 3 a  z  - 14 z  + -- - 27 a  z  - 8 a  z  + 4 a  z  + 
                               2
                              a
 
     7
  3 z         7    3  7      5  7      8      2  8      4  8        9
  ---- - 2 a z  - a  z  + 4 a  z  + 4 z  + 8 a  z  + 4 a  z  + 2 a z  + 
   a
 
     3  9
  2 a  z</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[19]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Vassiliev[2][Knot[10, 82]], Vassiliev[3][Knot[10, 82]]}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[19]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{0, 0}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[20]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kh[Knot[10, 82]][q, t]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[20]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>5    6     1        2        1        3        2       5       3
-- + - + ------ + ------ + ------ + ------ + ----- + ----- + ----- + 
 3   q    15  6    13  5    11  5    11  4    9  4    9  3    7  3
q        q   t    q   t    q   t    q   t    q  t    q  t    q  t
 
    5       5      5      5     3 t                2      3  2
  ----- + ----- + ---- + ---- + --- + 4 q t + 2 q t  + 3 q  t  + 
   7  2    5  2    5      3      q
  q  t    q  t    q  t   q  t
 
   3  3      5  3    7  4
  q  t  + 2 q  t  + q  t</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[21]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>ColouredJones[Knot[10, 82], 2][q]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[21]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>       -20    3     -18    7    12     4    17    31    11    36
-20 + q    - --- + q    + --- - --- + --- + --- - --- + --- + --- - 
              19           17    16    15    14    13    12    11
             q            q     q     q     q     q     q     q
 
  58    13   60   75   5    74   70   9    71   49              2
  --- + -- + -- - -- + -- + -- - -- - -- + -- - -- + 54 q - 23 q  - 
   10    9    8    7    6    5    4    3    2   q
  q     q    q    q    q    q    q    q    q
 
      3       4      5       6      7    8      9    10
  23 q  + 30 q  - 4 q  - 14 q  + 9 q  + q  - 3 q  + q</nowiki></code></td></tr>
</table>  }}