View source for 10 86

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{{Rolfsen Knot Page|
n = 10 |
k = 86 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,3,-6,5,-1,2,-3,6,-8,9,-10,7,-5,4,-2,10,-9,8,-7/goTop.html |
braid_table     = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[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:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.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:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]]</td></tr>
</table> |
braid_crossings = 11 |
braid_width     = 4 |
braid_index     = 4 |
same_alexander  = [[K11a190]],  |
same_jones      = [[10_60]],  |
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%>-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=6.66667%>6</td    ><td width=13.3333%>&chi;</td></tr>
<tr align=center><td>13</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>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 bgcolor=yellow>2</td><td bgcolor=yellow>&nbsp;</td><td>-2</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 bgcolor=yellow>4</td><td bgcolor=yellow>1</td><td>&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 bgcolor=yellow>6</td><td bgcolor=yellow>2</td><td>&nbsp;</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 bgcolor=yellow>7</td><td bgcolor=yellow>4</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>7</td><td bgcolor=yellow>6</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>7</td><td bgcolor=yellow>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>-1</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>-3</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>6</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>-5</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>-7</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>-9</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^{18}-3 q^{17}+q^{16}+10 q^{15}-17 q^{14}-5 q^{13}+43 q^{12}-37 q^{11}-36 q^{10}+97 q^9-45 q^8-90 q^7+146 q^6-30 q^5-140 q^4+163 q^3-2 q^2-159 q+140+22 q^{-1} -133 q^{-2} +88 q^{-3} +28 q^{-4} -77 q^{-5} +37 q^{-6} +16 q^{-7} -27 q^{-8} +9 q^{-9} +4 q^{-10} -4 q^{-11} + q^{-12} </math> |
coloured_jones_3 = <math>q^{36}-3 q^{35}+q^{34}+5 q^{33}+2 q^{32}-17 q^{31}-7 q^{30}+35 q^{29}+28 q^{28}-60 q^{27}-72 q^{26}+78 q^{25}+150 q^{24}-78 q^{23}-252 q^{22}+37 q^{21}+367 q^{20}+53 q^{19}-479 q^{18}-179 q^{17}+556 q^{16}+345 q^{15}-602 q^{14}-520 q^{13}+605 q^{12}+689 q^{11}-567 q^{10}-845 q^9+504 q^8+966 q^7-411 q^6-1056 q^5+312 q^4+1084 q^3-183 q^2-1078 q+76+990 q^{-1} +43 q^{-2} -872 q^{-3} -113 q^{-4} +696 q^{-5} +167 q^{-6} -525 q^{-7} -167 q^{-8} +355 q^{-9} +147 q^{-10} -226 q^{-11} -104 q^{-12} +128 q^{-13} +67 q^{-14} -68 q^{-15} -40 q^{-16} +38 q^{-17} +16 q^{-18} -15 q^{-19} -7 q^{-20} +5 q^{-21} +4 q^{-22} -4 q^{-23} + q^{-24} </math> |
coloured_jones_4 = <math>q^{60}-3 q^{59}+q^{58}+5 q^{57}-3 q^{56}+2 q^{55}-20 q^{54}+5 q^{53}+38 q^{52}+3 q^{51}+5 q^{50}-110 q^{49}-40 q^{48}+133 q^{47}+120 q^{46}+127 q^{45}-330 q^{44}-344 q^{43}+103 q^{42}+406 q^{41}+734 q^{40}-377 q^{39}-994 q^{38}-559 q^{37}+391 q^{36}+1931 q^{35}+411 q^{34}-1352 q^{33}-1951 q^{32}-740 q^{31}+2943 q^{30}+2111 q^{29}-497 q^{28}-3202 q^{27}-3026 q^{26}+2778 q^{25}+3815 q^{24}+1615 q^{23}-3375 q^{22}-5530 q^{21}+1377 q^{20}+4651 q^{19}+4120 q^{18}-2450 q^{17}-7379 q^{16}-560 q^{15}+4560 q^{14}+6254 q^{13}-1004 q^{12}-8355 q^{11}-2442 q^{10}+3861 q^9+7718 q^8+594 q^7-8432 q^6-4039 q^5+2628 q^4+8275 q^3+2218 q^2-7385 q-5009+862 q^{-1} +7494 q^{-2} +3471 q^{-3} -5169 q^{-4} -4799 q^{-5} -904 q^{-6} +5353 q^{-7} +3656 q^{-8} -2575 q^{-9} -3333 q^{-10} -1752 q^{-11} +2785 q^{-12} +2650 q^{-13} -776 q^{-14} -1528 q^{-15} -1449 q^{-16} +1003 q^{-17} +1299 q^{-18} -127 q^{-19} -394 q^{-20} -724 q^{-21} +274 q^{-22} +441 q^{-23} -48 q^{-24} -33 q^{-25} -247 q^{-26} +83 q^{-27} +117 q^{-28} -39 q^{-29} +12 q^{-30} -64 q^{-31} +24 q^{-32} +27 q^{-33} -15 q^{-34} +5 q^{-35} -11 q^{-36} +5 q^{-37} +4 q^{-38} -4 q^{-39} + q^{-40} </math> |
coloured_jones_5 = <math>q^{90}-3 q^{89}+q^{88}+5 q^{87}-3 q^{86}-3 q^{85}-q^{84}-8 q^{83}+7 q^{82}+33 q^{81}+7 q^{80}-34 q^{79}-49 q^{78}-55 q^{77}+24 q^{76}+158 q^{75}+172 q^{74}-7 q^{73}-257 q^{72}-412 q^{71}-230 q^{70}+340 q^{69}+840 q^{68}+731 q^{67}-156 q^{66}-1300 q^{65}-1684 q^{64}-581 q^{63}+1523 q^{62}+2982 q^{61}+2159 q^{60}-1004 q^{59}-4260 q^{58}-4597 q^{57}-826 q^{56}+4805 q^{55}+7614 q^{54}+4225 q^{53}-3834 q^{52}-10322 q^{51}-9027 q^{50}+617 q^{49}+11705 q^{48}+14535 q^{47}+4929 q^{46}-10781 q^{45}-19505 q^{44}-12334 q^{43}+6863 q^{42}+22812 q^{41}+20666 q^{40}-229 q^{39}-23484 q^{38}-28502 q^{37}-8628 q^{36}+21169 q^{35}+34956 q^{34}+18484 q^{33}-16239 q^{32}-39168 q^{31}-28268 q^{30}+9307 q^{29}+41107 q^{28}+37174 q^{27}-1435 q^{26}-41061 q^{25}-44630 q^{24}-6620 q^{23}+39533 q^{22}+50662 q^{21}+14294 q^{20}-37217 q^{19}-55325 q^{18}-21333 q^{17}+34336 q^{16}+59023 q^{15}+27774 q^{14}-31154 q^{13}-61711 q^{12}-33812 q^{11}+27296 q^{10}+63595 q^9+39487 q^8-22719 q^7-63913 q^6-44837 q^5+16788 q^4+62654 q^3+49337 q^2-9890 q-58758-52380 q^{-1} +1869 q^{-2} +52532 q^{-3} +53204 q^{-4} +5914 q^{-5} -43679 q^{-6} -51174 q^{-7} -12926 q^{-8} +33457 q^{-9} +46221 q^{-10} +17683 q^{-11} -22717 q^{-12} -38834 q^{-13} -19890 q^{-14} +13155 q^{-15} +30052 q^{-16} +19223 q^{-17} -5516 q^{-18} -21252 q^{-19} -16558 q^{-20} +642 q^{-21} +13546 q^{-22} +12625 q^{-23} +1908 q^{-24} -7661 q^{-25} -8702 q^{-26} -2561 q^{-27} +3823 q^{-28} +5310 q^{-29} +2194 q^{-30} -1604 q^{-31} -2895 q^{-32} -1527 q^{-33} +584 q^{-34} +1453 q^{-35} +818 q^{-36} -184 q^{-37} -618 q^{-38} -403 q^{-39} +46 q^{-40} +289 q^{-41} +158 q^{-42} -52 q^{-43} -110 q^{-44} -43 q^{-45} +26 q^{-46} +36 q^{-47} +32 q^{-48} -22 q^{-49} -35 q^{-50} +10 q^{-51} +13 q^{-52} -4 q^{-53} +5 q^{-54} + q^{-55} -11 q^{-56} +5 q^{-57} +4 q^{-58} -4 q^{-59} + q^{-60} </math> |
coloured_jones_6 = <math>q^{126}-3 q^{125}+q^{124}+5 q^{123}-3 q^{122}-3 q^{121}-6 q^{120}+11 q^{119}-6 q^{118}+2 q^{117}+36 q^{116}-12 q^{115}-34 q^{114}-64 q^{113}+15 q^{112}+8 q^{111}+58 q^{110}+212 q^{109}+63 q^{108}-114 q^{107}-386 q^{106}-256 q^{105}-221 q^{104}+153 q^{103}+951 q^{102}+939 q^{101}+458 q^{100}-872 q^{99}-1480 q^{98}-2191 q^{97}-1348 q^{96}+1551 q^{95}+3667 q^{94}+4470 q^{93}+1779 q^{92}-1567 q^{91}-6965 q^{90}-8891 q^{89}-4253 q^{88}+3577 q^{87}+12111 q^{86}+13795 q^{85}+9898 q^{84}-5375 q^{83}-20138 q^{82}-24163 q^{81}-14723 q^{80}+7482 q^{79}+28012 q^{78}+40584 q^{77}+23462 q^{76}-10408 q^{75}-43520 q^{74}-56495 q^{73}-35264 q^{72}+9746 q^{71}+65414 q^{70}+79732 q^{69}+49309 q^{68}-17449 q^{67}-84252 q^{66}-108409 q^{65}-70457 q^{64}+30397 q^{63}+113178 q^{62}+140979 q^{61}+80993 q^{60}-37677 q^{59}-149944 q^{58}-183072 q^{57}-86106 q^{56}+60905 q^{55}+193357 q^{54}+211356 q^{53}+96949 q^{52}-98225 q^{51}-251243 q^{50}-234333 q^{49}-81608 q^{48}+149522 q^{47}+295467 q^{46}+262635 q^{45}+42068 q^{44}-225248 q^{43}-338241 q^{42}-253263 q^{41}+22341 q^{40}+292268 q^{39}+387729 q^{38}+208818 q^{37}-124040 q^{36}-364988 q^{35}-388924 q^{34}-127938 q^{33}+224382 q^{32}+446201 q^{31}+344619 q^{30}-3130 q^{29}-337739 q^{28}-468645 q^{27}-252669 q^{26}+140303 q^{25}+459420 q^{24}+435194 q^{23}+98897 q^{22}-295968 q^{21}-511686 q^{20}-343815 q^{19}+67432 q^{18}+457327 q^{17}+498664 q^{16}+181748 q^{15}-255115 q^{14}-539917 q^{13}-420255 q^{12}-3045 q^{11}+443852 q^{10}+550837 q^9+267014 q^8-196650 q^7-547249 q^6-493228 q^5-96211 q^4+391391 q^3+576548 q^2+361549 q-92712-498207 q^{-1} -538289 q^{-2} -213187 q^{-3} +271456 q^{-4} +533135 q^{-5} +430358 q^{-6} +49581 q^{-7} -365907 q^{-8} -505885 q^{-9} -307088 q^{-10} +102215 q^{-11} +397083 q^{-12} +417423 q^{-13} +170523 q^{-14} -180849 q^{-15} -377194 q^{-16} -316834 q^{-17} -44298 q^{-18} +210691 q^{-19} +309425 q^{-20} +206130 q^{-21} -23860 q^{-22} -204142 q^{-23} -235447 q^{-24} -104588 q^{-25} +58231 q^{-26} +164379 q^{-27} +155999 q^{-28} +47129 q^{-29} -68521 q^{-30} -123296 q^{-31} -85066 q^{-32} -12345 q^{-33} +56286 q^{-34} +79259 q^{-35} +45817 q^{-36} -6054 q^{-37} -43433 q^{-38} -40971 q^{-39} -20795 q^{-40} +8598 q^{-41} +26906 q^{-42} +22179 q^{-43} +6273 q^{-44} -9439 q^{-45} -12023 q^{-46} -10175 q^{-47} -1804 q^{-48} +5938 q^{-49} +6546 q^{-50} +3296 q^{-51} -1155 q^{-52} -1766 q^{-53} -2813 q^{-54} -1297 q^{-55} +923 q^{-56} +1214 q^{-57} +715 q^{-58} -221 q^{-59} +91 q^{-60} -473 q^{-61} -326 q^{-62} +187 q^{-63} +166 q^{-64} +50 q^{-65} -143 q^{-66} +118 q^{-67} -57 q^{-68} -57 q^{-69} +61 q^{-70} +23 q^{-71} -2 q^{-72} -59 q^{-73} +39 q^{-74} - q^{-75} -18 q^{-76} +16 q^{-77} + q^{-78} + q^{-79} -11 q^{-80} +5 q^{-81} +4 q^{-82} -4 q^{-83} + q^{-84} </math> |
coloured_jones_7 = <math>\textrm{NotAvailable}(q)</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, 15:27:48)...</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, 86]]</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[6, 2, 7, 1], X[16, 8, 17, 7], X[8, 3, 9, 4], X[2, 15, 3, 16], 
 
  X[14, 5, 15, 6], X[4, 9, 5, 10], X[20, 14, 1, 13], X[10, 20, 11, 19], 
 
  X[18, 12, 19, 11], X[12, 18, 13, 17]]</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, 86]]</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, -6, 5, -1, 2, -3, 6, -8, 9, -10, 7, -5, 4, -2, 10, 
 
  -9, 8, -7]</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, 86]]</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[6, 8, 14, 16, 4, 18, 20, 2, 12, 10]</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, 86]]</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[4, {-1, -1, 2, -1, 2, -1, 2, 2, 3, -2, 3}]</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>{4, 11}</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, 86]]</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>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, 86]]]</nowiki></pre></td></tr><tr><td></td><td  align=left>[[Image:10_86_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, 86]]&) /@ {
                   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>{Chiral, 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, 86]][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>     2    9    19             2      3
25 - -- + -- - -- - 19 t + 9 t  - 2 t
      3    2   t
     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, 86]][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  - 3 z  - 2 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, 86], Knot[11, Alternating, 190]}</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, 86]], KnotSignature[Knot[10, 86]]}</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>{85, 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, 86]][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>      -4   4    8    11              2       3      4      5    6
14 + q   - -- + -- - -- - 14 q + 13 q  - 10 q  + 6 q  - 3 q  + q
            3    2   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, 60], Knot[10, 86]}</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, 86]][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>      -12    2     -8    -6   2    4       2      6      8      10
-1 + q    - --- + q   + q   - -- + -- + 2 q  - 2 q  + 2 q  - 3 q   + 
             10                4    2
            q                 q    q
 
   12    14    16    18
  q   + 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, 86]][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      4                 6
     -4   2    2 z    4 z     2  2      4   z    3 z     2  4    6   z
2 + a   - -- + ---- - ---- + a  z  - 2 z  + -- - ---- + a  z  - z  - --
           2     4      2                    4     2                  2
          a     a      a                    a     a                  a</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, 86]][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
     -4   2    2 z   4 z   3 z          2   2 z    2 z    6 z
2 + a   + -- - --- - --- - --- - a z + z  + ---- - ---- - ---- + 
           2    5     3     a                 6      4      2
          a    a     a                       a      a      a
 
               3       3       3                                4
     2  2   8 z    15 z    13 z         3      3  3      4   3 z
  3 a  z  + ---- + ----- + ----- + 4 a z  - 2 a  z  - 7 z  - ---- + 
              5      3       a                                 6
             a      a                                         a
 
     4       4                        5       5       5
  7 z    13 z       2  4    4  4   9 z    17 z    23 z          5
  ---- + ----- - 9 a  z  + a  z  - ---- - ----- - ----- - 11 a z  + 
    4      2                         5      3       a
   a      a                         a      a
 
                    6       6       6                7      7      7
     3  5      6   z    10 z    21 z       2  6   3 z    3 z    9 z
  4 a  z  - 2 z  + -- - ----- - ----- + 8 a  z  + ---- + ---- + ---- + 
                    6     4       2                 5      3     a
                   a     a       a                 a      a
 
                     8       8      9      9
       7      8   4 z    10 z    2 z    2 z
  9 a z  + 6 z  + ---- + ----- + ---- + ----
                    4      2       3     a
                   a      a       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, 86]], Vassiliev[3][Knot[10, 86]]}</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, -1}</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, 86]][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>8           1       3       1       5       3      6      5
- + 7 q + ----- + ----- + ----- + ----- + ----- + ---- + --- + 7 q t + 
q          9  4    7  3    5  3    5  2    3  2    3     q t
          q  t    q  t    q  t    q  t    q  t    q  t
 
     3        3  2      5  2      5  3      7  3      7  4      9  4
  7 q  t + 6 q  t  + 7 q  t  + 4 q  t  + 6 q  t  + 2 q  t  + 4 q  t  + 
 
   9  5      11  5    13  6
  q  t  + 2 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, 86], 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>       -12    4     4    9    27   16   37   77   28   88   133   22
140 + q    - --- + --- + -- - -- + -- + -- - -- + -- + -- - --- + -- - 
              11    10    9    8    7    6    5    4    3    2    q
             q     q     q    q    q    q    q    q    q    q
 
             2        3        4       5        6       7       8
  159 q - 2 q  + 163 q  - 140 q  - 30 q  + 146 q  - 90 q  - 45 q  + 
 
      9       10       11       12      13       14       15    16
  97 q  - 36 q   - 37 q   + 43 q   - 5 q   - 17 q   + 10 q   + q   - 
 
     17    18
  3 q   + q</nowiki></pre></td></tr>
         </table>  }}