View source for 10 88

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{{Rolfsen Knot Page|
n = 10 |
k = 88 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,3,-1,7,-10,5,-3,4,-8,9,-7,2,-5,6,-9,8,-6,10,-2/goTop.html |
braid_table     = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]]</td></tr>
</table> |
braid_crossings = 10 |
braid_width     = 5 |
braid_index     = 5 |
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%>-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=6.66667%>5</td    ><td width=13.3333%>&chi;</td></tr>
<tr align=center><td>11</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>9</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>3</td><td bgcolor=yellow>&nbsp;</td><td>3</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 bgcolor=yellow>5</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>-4</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 bgcolor=yellow>8</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>5</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 bgcolor=yellow>8</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-3</td></tr>
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>9</td><td bgcolor=yellow>8</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
<tr align=center><td>-1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>8</td><td bgcolor=yellow>9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
<tr align=center><td>-3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>8</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>-5</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>8</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>5</td></tr>
<tr align=center><td>-7</td><td>&nbsp;</td><td bgcolor=yellow>1</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>&nbsp;</td><td>-4</td></tr>
<tr align=center><td>-9</td><td bgcolor=yellow>&nbsp;</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>&nbsp;</td><td>3</td></tr>
<tr align=center><td>-11</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^{15}-4 q^{14}+3 q^{13}+12 q^{12}-29 q^{11}+7 q^{10}+59 q^9-84 q^8-12 q^7+150 q^6-138 q^5-65 q^4+239 q^3-153 q^2-123 q+275-123 q^{-1} -153 q^{-2} +239 q^{-3} -65 q^{-4} -138 q^{-5} +150 q^{-6} -12 q^{-7} -84 q^{-8} +59 q^{-9} +7 q^{-10} -29 q^{-11} +12 q^{-12} +3 q^{-13} -4 q^{-14} + q^{-15} </math> |
coloured_jones_3 = <math>-q^{30}+4 q^{29}-3 q^{28}-7 q^{27}+4 q^{26}+24 q^{25}-8 q^{24}-64 q^{23}+12 q^{22}+130 q^{21}+15 q^{20}-245 q^{19}-84 q^{18}+391 q^{17}+229 q^{16}-551 q^{15}-453 q^{14}+674 q^{13}+771 q^{12}-760 q^{11}-1111 q^{10}+745 q^9+1471 q^8-664 q^7-1781 q^6+513 q^5+2025 q^4-325 q^3-2172 q^2+110 q+2223+110 q^{-1} -2172 q^{-2} -325 q^{-3} +2025 q^{-4} +513 q^{-5} -1781 q^{-6} -664 q^{-7} +1471 q^{-8} +745 q^{-9} -1111 q^{-10} -760 q^{-11} +771 q^{-12} +674 q^{-13} -453 q^{-14} -551 q^{-15} +229 q^{-16} +391 q^{-17} -84 q^{-18} -245 q^{-19} +15 q^{-20} +130 q^{-21} +12 q^{-22} -64 q^{-23} -8 q^{-24} +24 q^{-25} +4 q^{-26} -7 q^{-27} -3 q^{-28} +4 q^{-29} - q^{-30} </math> |
coloured_jones_4 = <math>q^{50}-4 q^{49}+3 q^{48}+7 q^{47}-9 q^{46}+q^{45}-23 q^{44}+28 q^{43}+57 q^{42}-50 q^{41}-41 q^{40}-138 q^{39}+126 q^{38}+337 q^{37}-50 q^{36}-251 q^{35}-716 q^{34}+162 q^{33}+1214 q^{32}+557 q^{31}-431 q^{30}-2424 q^{29}-760 q^{28}+2541 q^{27}+2732 q^{26}+658 q^{25}-5136 q^{24}-3919 q^{23}+2771 q^{22}+6350 q^{21}+4546 q^{20}-7050 q^{19}-9106 q^{18}+165 q^{17}+9436 q^{16}+10854 q^{15}-6275 q^{14}-14088 q^{13}-4965 q^{12}+10078 q^{11}+17176 q^{10}-2981 q^9-16783 q^8-10469 q^7+8268 q^6+21342 q^5+1199 q^4-16789 q^3-14594 q^2+5083 q+22721+5083 q^{-1} -14594 q^{-2} -16789 q^{-3} +1199 q^{-4} +21342 q^{-5} +8268 q^{-6} -10469 q^{-7} -16783 q^{-8} -2981 q^{-9} +17176 q^{-10} +10078 q^{-11} -4965 q^{-12} -14088 q^{-13} -6275 q^{-14} +10854 q^{-15} +9436 q^{-16} +165 q^{-17} -9106 q^{-18} -7050 q^{-19} +4546 q^{-20} +6350 q^{-21} +2771 q^{-22} -3919 q^{-23} -5136 q^{-24} +658 q^{-25} +2732 q^{-26} +2541 q^{-27} -760 q^{-28} -2424 q^{-29} -431 q^{-30} +557 q^{-31} +1214 q^{-32} +162 q^{-33} -716 q^{-34} -251 q^{-35} -50 q^{-36} +337 q^{-37} +126 q^{-38} -138 q^{-39} -41 q^{-40} -50 q^{-41} +57 q^{-42} +28 q^{-43} -23 q^{-44} + q^{-45} -9 q^{-46} +7 q^{-47} +3 q^{-48} -4 q^{-49} + q^{-50} </math> |
coloured_jones_5 = <math>-q^{75}+4 q^{74}-3 q^{73}-7 q^{72}+9 q^{71}+4 q^{70}-2 q^{69}+3 q^{68}-21 q^{67}-34 q^{66}+40 q^{65}+84 q^{64}+33 q^{63}-59 q^{62}-199 q^{61}-197 q^{60}+113 q^{59}+531 q^{58}+543 q^{57}-109 q^{56}-1040 q^{55}-1392 q^{54}-320 q^{53}+1822 q^{52}+3134 q^{51}+1551 q^{50}-2527 q^{49}-5861 q^{48}-4569 q^{47}+2283 q^{46}+9758 q^{45}+10091 q^{44}+71 q^{43}-13769 q^{42}-18660 q^{41}-6376 q^{40}+16455 q^{39}+29950 q^{38}+17815 q^{37}-15371 q^{36}-42477 q^{35}-34960 q^{34}+8400 q^{33}+53555 q^{32}+56888 q^{31}+6187 q^{30}-60539 q^{29}-81348 q^{28}-27953 q^{27}+60590 q^{26}+105028 q^{25}+55924 q^{24}-52997 q^{23}-125046 q^{22}-86597 q^{21}+37910 q^{20}+138741 q^{19}+117296 q^{18}-17294 q^{17}-145636 q^{16}-144641 q^{15}-6338 q^{14}+145775 q^{13}+167068 q^{12}+30435 q^{11}-140607 q^{10}-183710 q^9-53108 q^8+131586 q^7+194854 q^6+73319 q^5-119974 q^4-201061 q^3-91032 q^2+106443 q+203085+106443 q^{-1} -91032 q^{-2} -201061 q^{-3} -119974 q^{-4} +73319 q^{-5} +194854 q^{-6} +131586 q^{-7} -53108 q^{-8} -183710 q^{-9} -140607 q^{-10} +30435 q^{-11} +167068 q^{-12} +145775 q^{-13} -6338 q^{-14} -144641 q^{-15} -145636 q^{-16} -17294 q^{-17} +117296 q^{-18} +138741 q^{-19} +37910 q^{-20} -86597 q^{-21} -125046 q^{-22} -52997 q^{-23} +55924 q^{-24} +105028 q^{-25} +60590 q^{-26} -27953 q^{-27} -81348 q^{-28} -60539 q^{-29} +6187 q^{-30} +56888 q^{-31} +53555 q^{-32} +8400 q^{-33} -34960 q^{-34} -42477 q^{-35} -15371 q^{-36} +17815 q^{-37} +29950 q^{-38} +16455 q^{-39} -6376 q^{-40} -18660 q^{-41} -13769 q^{-42} +71 q^{-43} +10091 q^{-44} +9758 q^{-45} +2283 q^{-46} -4569 q^{-47} -5861 q^{-48} -2527 q^{-49} +1551 q^{-50} +3134 q^{-51} +1822 q^{-52} -320 q^{-53} -1392 q^{-54} -1040 q^{-55} -109 q^{-56} +543 q^{-57} +531 q^{-58} +113 q^{-59} -197 q^{-60} -199 q^{-61} -59 q^{-62} +33 q^{-63} +84 q^{-64} +40 q^{-65} -34 q^{-66} -21 q^{-67} +3 q^{-68} -2 q^{-69} +4 q^{-70} +9 q^{-71} -7 q^{-72} -3 q^{-73} +4 q^{-74} - q^{-75} </math> |
coloured_jones_6 = <math>q^{105}-4 q^{104}+3 q^{103}+7 q^{102}-9 q^{101}-4 q^{100}-3 q^{99}+22 q^{98}-10 q^{97}-2 q^{96}+44 q^{95}-68 q^{94}-58 q^{93}-20 q^{92}+145 q^{91}+95 q^{90}+46 q^{89}+125 q^{88}-408 q^{87}-531 q^{86}-317 q^{85}+615 q^{84}+967 q^{83}+1024 q^{82}+876 q^{81}-1619 q^{80}-3217 q^{79}-3248 q^{78}+420 q^{77}+4033 q^{76}+6961 q^{75}+7385 q^{74}-1329 q^{73}-11203 q^{72}-17531 q^{71}-10354 q^{70}+4368 q^{69}+23577 q^{68}+35863 q^{67}+19355 q^{66}-14959 q^{65}-52800 q^{64}-59173 q^{63}-30996 q^{62}+33402 q^{61}+99926 q^{60}+104116 q^{59}+38455 q^{58}-79161 q^{57}-162940 q^{56}-165555 q^{55}-42543 q^{54}+151254 q^{53}+271312 q^{52}+233769 q^{51}+13377 q^{50}-249520 q^{49}-414572 q^{48}-308643 q^{47}+46760 q^{46}+420480 q^{45}+576578 q^{44}+343984 q^{43}-145228 q^{42}-645910 q^{41}-753595 q^{40}-338824 q^{39}+352823 q^{38}+902403 q^{37}+878082 q^{36}+270412 q^{35}-643372 q^{34}-1182741 q^{33}-942447 q^{32}-39231 q^{31}+986653 q^{30}+1396470 q^{29}+904710 q^{28}-317470 q^{27}-1371425 q^{26}-1527787 q^{25}-639520 q^{24}+759338 q^{23}+1682298 q^{22}+1515191 q^{21}+201994 q^{20}-1266624 q^{19}-1892397 q^{18}-1214631 q^{17}+352347 q^{16}+1696603 q^{15}+1921584 q^{14}+704085 q^{13}-991256 q^{12}-2009256 q^{11}-1615471 q^{10}-55878 q^9+1547088 q^8+2110070 q^7+1076094 q^6-686020 q^5-1969547 q^4-1844533 q^3-390299 q^2+1337527 q+2158285+1337527 q^{-1} -390299 q^{-2} -1844533 q^{-3} -1969547 q^{-4} -686020 q^{-5} +1076094 q^{-6} +2110070 q^{-7} +1547088 q^{-8} -55878 q^{-9} -1615471 q^{-10} -2009256 q^{-11} -991256 q^{-12} +704085 q^{-13} +1921584 q^{-14} +1696603 q^{-15} +352347 q^{-16} -1214631 q^{-17} -1892397 q^{-18} -1266624 q^{-19} +201994 q^{-20} +1515191 q^{-21} +1682298 q^{-22} +759338 q^{-23} -639520 q^{-24} -1527787 q^{-25} -1371425 q^{-26} -317470 q^{-27} +904710 q^{-28} +1396470 q^{-29} +986653 q^{-30} -39231 q^{-31} -942447 q^{-32} -1182741 q^{-33} -643372 q^{-34} +270412 q^{-35} +878082 q^{-36} +902403 q^{-37} +352823 q^{-38} -338824 q^{-39} -753595 q^{-40} -645910 q^{-41} -145228 q^{-42} +343984 q^{-43} +576578 q^{-44} +420480 q^{-45} +46760 q^{-46} -308643 q^{-47} -414572 q^{-48} -249520 q^{-49} +13377 q^{-50} +233769 q^{-51} +271312 q^{-52} +151254 q^{-53} -42543 q^{-54} -165555 q^{-55} -162940 q^{-56} -79161 q^{-57} +38455 q^{-58} +104116 q^{-59} +99926 q^{-60} +33402 q^{-61} -30996 q^{-62} -59173 q^{-63} -52800 q^{-64} -14959 q^{-65} +19355 q^{-66} +35863 q^{-67} +23577 q^{-68} +4368 q^{-69} -10354 q^{-70} -17531 q^{-71} -11203 q^{-72} -1329 q^{-73} +7385 q^{-74} +6961 q^{-75} +4033 q^{-76} +420 q^{-77} -3248 q^{-78} -3217 q^{-79} -1619 q^{-80} +876 q^{-81} +1024 q^{-82} +967 q^{-83} +615 q^{-84} -317 q^{-85} -531 q^{-86} -408 q^{-87} +125 q^{-88} +46 q^{-89} +95 q^{-90} +145 q^{-91} -20 q^{-92} -58 q^{-93} -68 q^{-94} +44 q^{-95} -2 q^{-96} -10 q^{-97} +22 q^{-98} -3 q^{-99} -4 q^{-100} -9 q^{-101} +7 q^{-102} +3 q^{-103} -4 q^{-104} + q^{-105} </math> |
coloured_jones_7 = <math>-q^{140}+4 q^{139}-3 q^{138}-7 q^{137}+9 q^{136}+4 q^{135}+3 q^{134}-17 q^{133}-15 q^{132}+33 q^{131}-8 q^{130}-16 q^{129}+42 q^{128}+30 q^{127}+13 q^{126}-121 q^{125}-168 q^{124}+67 q^{123}+72 q^{122}+153 q^{121}+345 q^{120}+206 q^{119}+28 q^{118}-744 q^{117}-1273 q^{116}-608 q^{115}+135 q^{114}+1493 q^{113}+2823 q^{112}+2540 q^{111}+1128 q^{110}-2911 q^{109}-7248 q^{108}-7552 q^{107}-4466 q^{106}+3929 q^{105}+14027 q^{104}+18818 q^{103}+16073 q^{102}-110 q^{101}-24199 q^{100}-41450 q^{99}-42981 q^{98}-16792 q^{97}+30828 q^{96}+75952 q^{95}+97722 q^{94}+66617 q^{93}-17353 q^{92}-118190 q^{91}-190921 q^{90}-173528 q^{89}-48185 q^{88}+141342 q^{87}+318844 q^{86}+366831 q^{85}+218101 q^{84}-93530 q^{83}-454180 q^{82}-657775 q^{81}-546567 q^{80}-108698 q^{79}+519225 q^{78}+1018197 q^{77}+1077733 q^{76}+567378 q^{75}-394097 q^{74}-1360104 q^{73}-1798579 q^{72}-1366682 q^{71}-78293 q^{70}+1520419 q^{69}+2618368 q^{68}+2535184 q^{67}+1042851 q^{66}-1289355 q^{65}-3349882 q^{64}-3995819 q^{63}-2580161 q^{62}+454017 q^{61}+3732829 q^{60}+5554146 q^{59}+4652596 q^{58}+1132131 q^{57}-3491647 q^{56}-6921359 q^{55}-7080887 q^{54}-3483098 q^{53}+2414596 q^{52}+7768501 q^{51}+9563059 q^{50}+6458604 q^{49}-417981 q^{48}-7822357 q^{47}-11746214 q^{46}-9770005 q^{45}-2404931 q^{44}+6931124 q^{43}+13296490 q^{42}+13053332 q^{41}+5814614 q^{40}-5113233 q^{39}-14002256 q^{38}-15949372 q^{37}-9459051 q^{36}+2549624 q^{35}+13795700 q^{34}+18181824 q^{33}+12981758 q^{32}+470475 q^{31}-12777028 q^{30}-19616672 q^{29}-16076808 q^{28}-3614657 q^{27}+11154661 q^{26}+20259777 q^{25}+18557545 q^{24}+6592876 q^{23}-9195152 q^{22}-20238112 q^{21}-20364308 q^{20}-9198979 q^{19}+7151404 q^{18}+19740523 q^{17}+21549728 q^{16}+11338004 q^{15}-5213041 q^{14}-18966439 q^{13}-22240226 q^{12}-13018279 q^{11}+3484032 q^{10}+18080389 q^9+22588382 q^8+14321596 q^7-1979218 q^6-17180052 q^5-22733021 q^4-15371342 q^3+639284 q^2+16291800 q+22770653+16291800 q^{-1} +639284 q^{-2} -15371342 q^{-3} -22733021 q^{-4} -17180052 q^{-5} -1979218 q^{-6} +14321596 q^{-7} +22588382 q^{-8} +18080389 q^{-9} +3484032 q^{-10} -13018279 q^{-11} -22240226 q^{-12} -18966439 q^{-13} -5213041 q^{-14} +11338004 q^{-15} +21549728 q^{-16} +19740523 q^{-17} +7151404 q^{-18} -9198979 q^{-19} -20364308 q^{-20} -20238112 q^{-21} -9195152 q^{-22} +6592876 q^{-23} +18557545 q^{-24} +20259777 q^{-25} +11154661 q^{-26} -3614657 q^{-27} -16076808 q^{-28} -19616672 q^{-29} -12777028 q^{-30} +470475 q^{-31} +12981758 q^{-32} +18181824 q^{-33} +13795700 q^{-34} +2549624 q^{-35} -9459051 q^{-36} -15949372 q^{-37} -14002256 q^{-38} -5113233 q^{-39} +5814614 q^{-40} +13053332 q^{-41} +13296490 q^{-42} +6931124 q^{-43} -2404931 q^{-44} -9770005 q^{-45} -11746214 q^{-46} -7822357 q^{-47} -417981 q^{-48} +6458604 q^{-49} +9563059 q^{-50} +7768501 q^{-51} +2414596 q^{-52} -3483098 q^{-53} -7080887 q^{-54} -6921359 q^{-55} -3491647 q^{-56} +1132131 q^{-57} +4652596 q^{-58} +5554146 q^{-59} +3732829 q^{-60} +454017 q^{-61} -2580161 q^{-62} -3995819 q^{-63} -3349882 q^{-64} -1289355 q^{-65} +1042851 q^{-66} +2535184 q^{-67} +2618368 q^{-68} +1520419 q^{-69} -78293 q^{-70} -1366682 q^{-71} -1798579 q^{-72} -1360104 q^{-73} -394097 q^{-74} +567378 q^{-75} +1077733 q^{-76} +1018197 q^{-77} +519225 q^{-78} -108698 q^{-79} -546567 q^{-80} -657775 q^{-81} -454180 q^{-82} -93530 q^{-83} +218101 q^{-84} +366831 q^{-85} +318844 q^{-86} +141342 q^{-87} -48185 q^{-88} -173528 q^{-89} -190921 q^{-90} -118190 q^{-91} -17353 q^{-92} +66617 q^{-93} +97722 q^{-94} +75952 q^{-95} +30828 q^{-96} -16792 q^{-97} -42981 q^{-98} -41450 q^{-99} -24199 q^{-100} -110 q^{-101} +16073 q^{-102} +18818 q^{-103} +14027 q^{-104} +3929 q^{-105} -4466 q^{-106} -7552 q^{-107} -7248 q^{-108} -2911 q^{-109} +1128 q^{-110} +2540 q^{-111} +2823 q^{-112} +1493 q^{-113} +135 q^{-114} -608 q^{-115} -1273 q^{-116} -744 q^{-117} +28 q^{-118} +206 q^{-119} +345 q^{-120} +153 q^{-121} +72 q^{-122} +67 q^{-123} -168 q^{-124} -121 q^{-125} +13 q^{-126} +30 q^{-127} +42 q^{-128} -16 q^{-129} -8 q^{-130} +33 q^{-131} -15 q^{-132} -17 q^{-133} +3 q^{-134} +4 q^{-135} +9 q^{-136} -7 q^{-137} -3 q^{-138} +4 q^{-139} - q^{-140} </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>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</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, 88]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[4, 2, 5, 1], X[20, 14, 1, 13], X[8, 3, 9, 4], X[2, 9, 3, 10], 
 
  X[14, 7, 15, 8], X[18, 15, 19, 16], X[12, 6, 13, 5], 
 
  X[10, 18, 11, 17], X[16, 12, 17, 11], X[6, 19, 7, 20]]</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[3]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>GaussCode[Knot[10, 88]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[1, -4, 3, -1, 7, -10, 5, -3, 4, -8, 9, -7, 2, -5, 6, -9, 8, 
 
  -6, 10, -2]</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[4]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>DTCode[Knot[10, 88]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>DTCode[4, 8, 12, 14, 2, 16, 20, 18, 10, 6]</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[5]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>br = BR[Knot[10, 88]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[5, {-1, 2, -1, -3, 2, -3, 2, 4, -3, 4}]</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[6]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{First[br], Crossings[br]}</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{5, 10}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>BraidIndex[Knot[10, 88]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=&nbsp;&nbsp;</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[10, 88]]]</nowiki></pre></td></tr><tr><td></td><td  align=left>[[Image:10_88_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, 88]]&) /@ {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]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{NegativeAmphicheiral, 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, 88]][t]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>      -3   8    24             2    3
35 - t   + -- - -- - 24 t + 8 t  - t
            2   t
           t</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[11]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[Knot[10, 88]][z]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>     2      4    6
1 - z  + 2 z  - z</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[12]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 88]}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{KnotDet[Knot[10, 88]], KnotSignature[Knot[10, 88]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{101, 0}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[14]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Jones[Knot[10, 88]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>      -5   4    8    13   16              2      3      4    5
17 - q   + -- - -- + -- - -- - 16 q + 13 q  - 8 q  + 4 q  - q
            4    3    2   q
           q    q    q</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[15]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 88]}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[16]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>A2Invariant[Knot[10, 88]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[16]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>      -16    -14    2     3    3    2    3       2      4      8
-3 - q    + q    + --- - --- + -- - -- + -- + 3 q  - 2 q  + 3 q  - 
                    12    10    8    4    2
                   q     q     q    q    q
 
     10      12    14    16
  3 q   + 2 q   + q   - q</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[17]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>HOMFLYPT[Knot[10, 88]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[17]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>                        2      2                               4
      -2    2      2   z    2 z       2  2    4  2      4   2 z
-1 + a   + a  - 3 z  - -- + ---- + 2 a  z  - a  z  - 2 z  + ---- + 
                        4     2                               2
                       a     a                               a
 
     2  4    6
  2 a  z  - z</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[18]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Knot[10, 88]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[18]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>                                                    2      2
      -2    2   z    4 z            3        2   3 z    7 z
-1 - a   - a  - -- - --- - 4 a z - a  z + 8 z  + ---- + ---- + 
                 3    a                            4      2
                a                                 a      a
 
                       3      3       3
     2  2      4  2   z    6 z    19 z          3      3  3    5  3
  7 a  z  + 3 a  z  - -- + ---- + ----- + 19 a z  + 6 a  z  - a  z  - 
                       5     3      a
                      a     a
 
            4       4                         5       5       5
     4   6 z    10 z        2  4      4  4   z    11 z    32 z
  8 z  - ---- - ----- - 10 a  z  - 6 a  z  + -- - ----- - ----- - 
           4      2                           5     3       a
          a      a                           a     a
 
                                          6      6
        5       3  5    5  5       6   4 z    2 z       2  6
  32 a z  - 11 a  z  + a  z  - 12 z  + ---- - ---- - 2 a  z  + 
                                         4      2
                                        a      a
 
               7       7                                  8
     4  6   7 z    14 z          7      3  7       8   6 z       2  8
  4 a  z  + ---- + ----- + 14 a z  + 7 a  z  + 12 z  + ---- + 6 a  z  + 
              3      a                                   2
             a                                          a
 
     9
  2 z         9
  ---- + 2 a z
   a</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[19]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{Vassiliev[2][Knot[10, 88]], Vassiliev[3][Knot[10, 88]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[19]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{-1, 0}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[20]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[Knot[10, 88]][q, t]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[20]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>9           1        3       1       5       3       8       5
- + 9 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + 
q          11  5    9  4    7  4    7  3    5  3    5  2    3  2
          q   t    q  t    q  t    q  t    q  t    q  t    q  t
 
   8      8               3        3  2      5  2      5  3      7  3
  ---- + --- + 8 q t + 8 q  t + 5 q  t  + 8 q  t  + 3 q  t  + 5 q  t  + 
   3     q t
  q  t
 
   7  4      9  4    11  5
  q  t  + 3 q  t  + q   t</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[21]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>ColouredJones[Knot[10, 88], 2][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[21]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>       -15    4     3    12    29     7    59   84   12   150   138
275 + q    - --- + --- + --- - --- + --- + -- - -- - -- + --- - --- - 
              14    13    12    11    10    9    8    7    6     5
             q     q     q     q     q     q    q    q    q     q
 
  65   239   153   123                2        3       4        5
  -- + --- - --- - --- - 123 q - 153 q  + 239 q  - 65 q  - 138 q  + 
   4    3     2     q
  q    q     q
 
       6       7       8       9      10       11       12      13
  150 q  - 12 q  - 84 q  + 59 q  + 7 q   - 29 q   + 12 q   + 3 q   - 
 
     14    15
  4 q   + q</nowiki></pre></td></tr>
         </table>  }}