View source for 10 158

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{{Rolfsen Knot Page|
n = 10 |
k = 158 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,5,-2,8,-7,-1,3,-4,-5,2,-6,10,4,-3,9,7,-8,6,-10,-9/goTop.html |
braid_table     = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.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:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.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:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]]</td></tr>
</table> |
braid_crossings = 11 |
braid_width     = 4 |
braid_index     = 4 |
same_alexander  =  |
same_jones      =  |
khovanov_table  = <table border=1>
<tr align=center>
<td width=15.3846%><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=7.69231%>-4</td    ><td width=7.69231%>-3</td    ><td width=7.69231%>-2</td    ><td width=7.69231%>-1</td    ><td width=7.69231%>0</td    ><td width=7.69231%>1</td    ><td width=7.69231%>2</td    ><td width=7.69231%>3</td    ><td width=7.69231%>4</td    ><td width=15.3846%>&chi;</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>2</td><td>2</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>2</td><td bgcolor=yellow>&nbsp;</td><td>-2</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>4</td><td bgcolor=yellow>2</td><td>&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 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 bgcolor=yellow>4</td><td bgcolor=yellow>4</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>4</td><td bgcolor=yellow>5</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 bgcolor=yellow>2</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr>
<tr align=center><td>-5</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>4</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>-7</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>-2</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>1</td></tr>
</table> |
coloured_jones_2 = <math>q^{13}+2 q^{12}-8 q^{11}+2 q^{10}+17 q^9-23 q^8-7 q^7+44 q^6-33 q^5-26 q^4+67 q^3-33 q^2-42 q+73-24 q^{-1} -46 q^{-2} +58 q^{-3} -9 q^{-4} -36 q^{-5} +31 q^{-6} +2 q^{-7} -17 q^{-8} +8 q^{-9} +2 q^{-10} -3 q^{-11} + q^{-12} </math> |
coloured_jones_3 = <math>2 q^{26}-2 q^{24}-12 q^{23}+8 q^{22}+22 q^{21}+4 q^{20}-48 q^{19}-22 q^{18}+69 q^{17}+61 q^{16}-85 q^{15}-110 q^{14}+84 q^{13}+170 q^{12}-71 q^{11}-226 q^{10}+44 q^9+271 q^8-4 q^7-312 q^6-29 q^5+331 q^4+67 q^3-341 q^2-98 q+334+125 q^{-1} -309 q^{-2} -149 q^{-3} +274 q^{-4} +158 q^{-5} -216 q^{-6} -164 q^{-7} +159 q^{-8} +148 q^{-9} -95 q^{-10} -128 q^{-11} +52 q^{-12} +88 q^{-13} -14 q^{-14} -58 q^{-15} +31 q^{-17} +3 q^{-18} -13 q^{-19} -2 q^{-20} +4 q^{-21} +2 q^{-22} -3 q^{-23} + q^{-24} </math> |
coloured_jones_4 = <math>q^{44}+2 q^{43}-8 q^{41}-6 q^{40}-6 q^{39}+23 q^{38}+39 q^{37}-11 q^{36}-41 q^{35}-97 q^{34}+13 q^{33}+156 q^{32}+105 q^{31}+2 q^{30}-315 q^{29}-201 q^{28}+199 q^{27}+369 q^{26}+337 q^{25}-455 q^{24}-626 q^{23}-75 q^{22}+542 q^{21}+948 q^{20}-274 q^{19}-995 q^{18}-635 q^{17}+406 q^{16}+1549 q^{15}+177 q^{14}-1101 q^{13}-1211 q^{12}+39 q^{11}+1927 q^{10}+652 q^9-993 q^8-1608 q^7-352 q^6+2060 q^5+1007 q^4-781 q^3-1803 q^2-679 q+1980+1232 q^{-1} -482 q^{-2} -1785 q^{-3} -951 q^{-4} +1639 q^{-5} +1300 q^{-6} -65 q^{-7} -1485 q^{-8} -1121 q^{-9} +1039 q^{-10} +1112 q^{-11} +341 q^{-12} -911 q^{-13} -1030 q^{-14} +389 q^{-15} +666 q^{-16} +491 q^{-17} -318 q^{-18} -658 q^{-19} +10 q^{-20} +211 q^{-21} +338 q^{-22} - q^{-23} -263 q^{-24} -53 q^{-25} -2 q^{-26} +127 q^{-27} +41 q^{-28} -64 q^{-29} -11 q^{-30} -23 q^{-31} +26 q^{-32} +14 q^{-33} -12 q^{-34} +2 q^{-35} -6 q^{-36} +4 q^{-37} +2 q^{-38} -3 q^{-39} + q^{-40} </math> |
coloured_jones_5 = <math>2 q^{66}+2 q^{64}-4 q^{63}-12 q^{62}-12 q^{61}+10 q^{60}+18 q^{59}+46 q^{58}+40 q^{57}-44 q^{56}-112 q^{55}-110 q^{54}-32 q^{53}+157 q^{52}+327 q^{51}+199 q^{50}-151 q^{49}-495 q^{48}-580 q^{47}-124 q^{46}+663 q^{45}+1082 q^{44}+644 q^{43}-502 q^{42}-1585 q^{41}-1535 q^{40}-20 q^{39}+1879 q^{38}+2563 q^{37}+1060 q^{36}-1760 q^{35}-3571 q^{34}-2475 q^{33}+1081 q^{32}+4293 q^{31}+4125 q^{30}+114 q^{29}-4574 q^{28}-5714 q^{27}-1729 q^{26}+4346 q^{25}+7080 q^{24}+3532 q^{23}-3682 q^{22}-8103 q^{21}-5279 q^{20}+2711 q^{19}+8717 q^{18}+6878 q^{17}-1604 q^{16}-9057 q^{15}-8176 q^{14}+547 q^{13}+9079 q^{12}+9223 q^{11}+468 q^{10}-9020 q^9-9999 q^8-1322 q^7+8795 q^6+10574 q^5+2135 q^4-8488 q^3-10991 q^2-2896 q+8024+11225 q^{-1} +3678 q^{-2} -7312 q^{-3} -11259 q^{-4} -4511 q^{-5} +6352 q^{-6} +10977 q^{-7} +5295 q^{-8} -5021 q^{-9} -10328 q^{-10} -5983 q^{-11} +3490 q^{-12} +9194 q^{-13} +6359 q^{-14} -1780 q^{-15} -7664 q^{-16} -6351 q^{-17} +259 q^{-18} +5791 q^{-19} +5805 q^{-20} +1034 q^{-21} -3918 q^{-22} -4867 q^{-23} -1719 q^{-24} +2186 q^{-25} +3616 q^{-26} +1971 q^{-27} -890 q^{-28} -2419 q^{-29} -1710 q^{-30} +80 q^{-31} +1350 q^{-32} +1281 q^{-33} +290 q^{-34} -636 q^{-35} -805 q^{-36} -337 q^{-37} +213 q^{-38} +429 q^{-39} +252 q^{-40} -25 q^{-41} -189 q^{-42} -159 q^{-43} -18 q^{-44} +75 q^{-45} +68 q^{-46} +18 q^{-47} -10 q^{-48} -36 q^{-49} -17 q^{-50} +14 q^{-51} +9 q^{-52} - q^{-53} +3 q^{-54} -2 q^{-55} -6 q^{-56} +4 q^{-57} +2 q^{-58} -3 q^{-59} + q^{-60} </math> |
coloured_jones_6 = <math>q^{93}+2 q^{92}-6 q^{89}-8 q^{88}-16 q^{87}-6 q^{86}+23 q^{85}+49 q^{84}+53 q^{83}+27 q^{82}-13 q^{81}-149 q^{80}-201 q^{79}-151 q^{78}+72 q^{77}+294 q^{76}+462 q^{75}+520 q^{74}-12 q^{73}-624 q^{72}-1148 q^{71}-961 q^{70}-286 q^{69}+958 q^{68}+2323 q^{67}+2127 q^{66}+724 q^{65}-1827 q^{64}-3549 q^{63}-4097 q^{62}-1793 q^{61}+2869 q^{60}+6130 q^{59}+6668 q^{58}+2524 q^{57}-3377 q^{56}-9745 q^{55}-10545 q^{54}-3860 q^{53}+5739 q^{52}+14062 q^{51}+14064 q^{50}+6345 q^{49}-9153 q^{48}-20164 q^{47}-18853 q^{46}-5949 q^{45}+13461 q^{44}+25817 q^{43}+24981 q^{42}+4011 q^{41}-20582 q^{40}-33606 q^{39}-26563 q^{38}-281 q^{37}+27898 q^{36}+42963 q^{35}+25729 q^{34}-8209 q^{33}-38908 q^{32}-46125 q^{31}-21794 q^{30}+18315 q^{29}+52054 q^{28}+46125 q^{27}+10739 q^{26}-33987 q^{25}-57558 q^{24}-41701 q^{23}+3463 q^{22}+52198 q^{21}+59237 q^{20}+27904 q^{19}-24708 q^{18}-61232 q^{17}-55134 q^{16}-9724 q^{15}+48293 q^{14}+65607 q^{13}+39708 q^{12}-16293 q^{11}-61087 q^{10}-62882 q^9-19072 q^8+43936 q^7+68412 q^6+47482 q^5-9520 q^4-59520 q^3-67754 q^2-26585 q+38770+69206 q^{-1} +53985 q^{-2} -1702 q^{-3} -55314 q^{-4} -70716 q^{-5} -35066 q^{-6} +29559 q^{-7} +66002 q^{-8} +59592 q^{-9} +9892 q^{-10} -44730 q^{-11} -68900 q^{-12} -44099 q^{-13} +13888 q^{-14} +54540 q^{-15} +60275 q^{-16} +23623 q^{-17} -25874 q^{-18} -57448 q^{-19} -48179 q^{-20} -4933 q^{-21} +33670 q^{-22} +50518 q^{-23} +32154 q^{-24} -3966 q^{-25} -36090 q^{-26} -41141 q^{-27} -17708 q^{-28} +10460 q^{-29} +31009 q^{-30} +28894 q^{-31} +10489 q^{-32} -13435 q^{-33} -24716 q^{-34} -18027 q^{-35} -4160 q^{-36} +11338 q^{-37} +16738 q^{-38} +12231 q^{-39} +65 q^{-40} -8917 q^{-41} -10062 q^{-42} -6722 q^{-43} +603 q^{-44} +5509 q^{-45} +6757 q^{-46} +2925 q^{-47} -1027 q^{-48} -2934 q^{-49} -3501 q^{-50} -1529 q^{-51} +529 q^{-52} +2083 q^{-53} +1423 q^{-54} +510 q^{-55} -182 q^{-56} -934 q^{-57} -729 q^{-58} -283 q^{-59} +371 q^{-60} +290 q^{-61} +217 q^{-62} +155 q^{-63} -124 q^{-64} -165 q^{-65} -125 q^{-66} +59 q^{-67} +14 q^{-68} +28 q^{-69} +59 q^{-70} -8 q^{-71} -23 q^{-72} -31 q^{-73} +20 q^{-74} -3 q^{-75} -6 q^{-76} +14 q^{-77} - q^{-78} -2 q^{-79} -6 q^{-80} +4 q^{-81} +2 q^{-82} -3 q^{-83} + q^{-84} </math> |
coloured_jones_7 =  |
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, 158]]</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[6, 2, 7, 1], X[3, 10, 4, 11], X[14, 8, 15, 7], X[8, 14, 9, 13], 
 
  X[9, 2, 10, 3], X[11, 18, 12, 19], X[5, 17, 6, 16], X[17, 5, 18, 4], 
 
  X[20, 16, 1, 15], 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, 158]]</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, 5, -2, 8, -7, -1, 3, -4, -5, 2, -6, 10, 4, -3, 9, 7, -8, 
 
  6, -10, -9]</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, 158]]</nowiki></code></td></tr>
<tr align=left>
<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, -10, -16, 14, -2, -18, 8, 20, -4, -12]</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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, 158]]</nowiki></code></td></tr>
<tr align=left>
<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[4, {-1, -1, -1, -2, 1, 1, 3, 2, -1, 2, 3}]</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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>
<tr align=left>
<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>{4, 11}</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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, 158]]</nowiki></code></td></tr>
<tr align=left>
<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>4</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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, 158]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:10_158_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>
</table>
         <table><tr align=left>
<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, 158]]&) /@ {
                    SymmetryType, UnknottingNumber, ThreeGenus,
                    BridgeIndex, SuperBridgeIndex, NakanishiIndex
                   }</nowiki></code></td></tr>
<tr align=left>
<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>{Reversible, 2, 3, 3, NotAvailable, 1}</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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, 158]][t]</nowiki></code></td></tr>
<tr align=left>
<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>      -3   4    10             2    3
15 - t   + -- - -- - 10 t + 4 t  - t
            2   t
           t</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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, 158]][z]</nowiki></code></td></tr>
<tr align=left>
<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>       2      4    6
1 - 3 z  - 2 z  - z</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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>
<tr align=left>
<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, 158]}</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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, 158]], KnotSignature[Knot[10, 158]]}</nowiki></code></td></tr>
<tr align=left>
<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>{45, 0}</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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, 158]][q]</nowiki></code></td></tr>
<tr align=left>
<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>     -4   3    6    7            2      3      4
8 + q   - -- + -- - - - 8 q + 6 q  - 4 q  + 2 q
           3    2   q
          q    q</nowiki></code></td></tr>
</table>
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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, 158]}</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, 158]][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>      -12    -10   2     -6    -4   2     2      4    6    8    10
-2 + q    - q    + -- + q   - q   + -- + q  - 2 q  - q  + q  - q   + 
                    8                2
                   q                q
 
     12    14
  2 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, 158]][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                     4
      -4      2      2   z       2  2      4   z     2  4    6
-2 + a   + 2 a  - 6 z  + -- + 2 a  z  - 4 z  + -- + a  z  - z
                          2                     2
                         a                     a</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, 158]][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      2
      -4      2   2 z   z            2   5 z    2 z       2  2
-2 + a   - 2 a  + --- + - - a z + 9 z  - ---- - ---- + 5 a  z  - 
                   3    a                  4      2
                  a                       a      a
 
             3      3                                 4    4
   4  2   4 z    2 z         3      3  3       4   3 z    z
  a  z  - ---- + ---- + 3 a z  - 3 a  z  - 13 z  + ---- - -- - 
            3     a                                  4     2
           a                                        a     a
 
                     5      5                              6
     2  4    4  4   z    7 z         5      3  5      6   z
  8 a  z  + a  z  + -- - ---- - 5 a z  + 3 a  z  + 6 z  + -- + 
                     3    a                                2
                    a                                     a
 
             7      7                  8
     2  6   z    5 z         7    8   z
  5 a  z  + -- + ---- + 4 a z  + z  + --
             3    a                    2
            a                         a</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, 158]], Vassiliev[3][Knot[10, 158]]}</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>{-3, -1}</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, 158]][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           1       2       1       4       2      3      4
- + 4 q + ----- + ----- + ----- + ----- + ----- + ---- + --- + 4 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      9  4
  4 q  t + 2 q  t  + 4 q  t  + 2 q  t  + 2 q  t  + 2 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, 158], 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>      -12    3     2    8    17   2    31   36   9    58   46   24
73 + 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       9
  42 q - 33 q  + 67 q  - 26 q  - 33 q  + 44 q  - 7 q  - 23 q  + 17 q  + 
 
     10      11      12    13
  2 q   - 8 q   + 2 q   + q</nowiki></code></td></tr>
</table>  }}