View source for 10 164

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{{Rolfsen Knot Page|
n = 10 |
k = 164 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,3,-6,7,-4,-1,2,8,-5,6,-9,4,10,-2,-3,9,-7,5,-8,-10/goTop.html |
braid_table     = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]]</td></tr>
</table> |
braid_crossings = 11 |
braid_width     = 4 |
braid_index     = 4 |
same_alexander  = [[10_10]],  |
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%>-5</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=15.3846%>&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 bgcolor=yellow>2</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>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>&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>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>2</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>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>3</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>-3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>4</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>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr>
<tr align=center><td>-7</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>-2</td></tr>
<tr align=center><td>-9</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>-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>-1</td></tr>
</table> |
coloured_jones_2 = <math>q^{10}-8 q^8+8 q^7+12 q^6-29 q^5+11 q^4+35 q^3-50 q^2+4 q+56-57 q^{-1} -7 q^{-2} +62 q^{-3} -46 q^{-4} -17 q^{-5} +52 q^{-6} -24 q^{-7} -21 q^{-8} +30 q^{-9} -5 q^{-10} -14 q^{-11} +9 q^{-12} + q^{-13} -3 q^{-14} + q^{-15} </math> |
coloured_jones_3 = <math>-2 q^{20}+4 q^{19}+3 q^{18}+q^{17}-21 q^{16}-5 q^{15}+36 q^{14}+28 q^{13}-51 q^{12}-72 q^{11}+65 q^{10}+121 q^9-53 q^8-184 q^7+36 q^6+229 q^5+7 q^4-276 q^3-38 q^2+290 q+82-301 q^{-1} -109 q^{-2} +286 q^{-3} +140 q^{-4} -265 q^{-5} -160 q^{-6} +229 q^{-7} +177 q^{-8} -182 q^{-9} -184 q^{-10} +124 q^{-11} +184 q^{-12} -70 q^{-13} -163 q^{-14} +16 q^{-15} +132 q^{-16} +21 q^{-17} -92 q^{-18} -38 q^{-19} +52 q^{-20} +38 q^{-21} -22 q^{-22} -28 q^{-23} +7 q^{-24} +14 q^{-25} - q^{-26} -5 q^{-27} - q^{-28} +3 q^{-29} - q^{-30} </math> |
coloured_jones_4 = <math>q^{34}-6 q^{32}-5 q^{31}+12 q^{30}+18 q^{29}+16 q^{28}-31 q^{27}-80 q^{26}-6 q^{25}+77 q^{24}+168 q^{23}+26 q^{22}-268 q^{21}-221 q^{20}+4 q^{19}+480 q^{18}+404 q^{17}-333 q^{16}-643 q^{15}-456 q^{14}+664 q^{13}+1046 q^{12}-17 q^{11}-939 q^{10}-1180 q^9+485 q^8+1568 q^7+529 q^6-896 q^5-1771 q^4+98 q^3+1746 q^2+972 q-635-2039 q^{-1} -246 q^{-2} +1657 q^{-3} +1193 q^{-4} -327 q^{-5} -2034 q^{-6} -505 q^{-7} +1389 q^{-8} +1269 q^{-9} +26 q^{-10} -1820 q^{-11} -744 q^{-12} +939 q^{-13} +1218 q^{-14} +442 q^{-15} -1358 q^{-16} -898 q^{-17} +323 q^{-18} +932 q^{-19} +775 q^{-20} -682 q^{-21} -780 q^{-22} -219 q^{-23} +413 q^{-24} +765 q^{-25} -76 q^{-26} -378 q^{-27} -381 q^{-28} -46 q^{-29} +424 q^{-30} +149 q^{-31} -11 q^{-32} -204 q^{-33} -170 q^{-34} +105 q^{-35} +78 q^{-36} +80 q^{-37} -33 q^{-38} -81 q^{-39} +5 q^{-40} +3 q^{-41} +31 q^{-42} +5 q^{-43} -17 q^{-44} + q^{-45} -3 q^{-46} +5 q^{-47} + q^{-48} -3 q^{-49} + q^{-50} </math> |
coloured_jones_5 = <math>-2 q^{51}+4 q^{50}+2 q^{49}+3 q^{48}-q^{47}-23 q^{46}-30 q^{45}+12 q^{44}+56 q^{43}+79 q^{42}+69 q^{41}-96 q^{40}-248 q^{39}-212 q^{38}+41 q^{37}+404 q^{36}+604 q^{35}+252 q^{34}-553 q^{33}-1136 q^{32}-874 q^{31}+354 q^{30}+1728 q^{29}+1932 q^{28}+325 q^{27}-2134 q^{26}-3245 q^{25}-1583 q^{24}+1988 q^{23}+4596 q^{22}+3434 q^{21}-1263 q^{20}-5652 q^{19}-5470 q^{18}-186 q^{17}+6145 q^{16}+7564 q^{15}+1987 q^{14}-6043 q^{13}-9195 q^{12}-4024 q^{11}+5405 q^{10}+10402 q^9+5826 q^8-4454 q^7-10965 q^6-7379 q^5+3386 q^4+11191 q^3+8414 q^2-2384 q-10991-9169 q^{-1} +1495 q^{-2} +10715 q^{-3} +9557 q^{-4} -747 q^{-5} -10229 q^{-6} -9816 q^{-7} +10 q^{-8} +9698 q^{-9} +9940 q^{-10} +737 q^{-11} -8957 q^{-12} -9989 q^{-13} -1618 q^{-14} +8002 q^{-15} +9897 q^{-16} +2623 q^{-17} -6731 q^{-18} -9584 q^{-19} -3692 q^{-20} +5146 q^{-21} +8900 q^{-22} +4681 q^{-23} -3267 q^{-24} -7815 q^{-25} -5366 q^{-26} +1318 q^{-27} +6246 q^{-28} +5563 q^{-29} +507 q^{-30} -4376 q^{-31} -5178 q^{-32} -1847 q^{-33} +2408 q^{-34} +4209 q^{-35} +2578 q^{-36} -691 q^{-37} -2898 q^{-38} -2612 q^{-39} -517 q^{-40} +1544 q^{-41} +2104 q^{-42} +1098 q^{-43} -434 q^{-44} -1349 q^{-45} -1144 q^{-46} -218 q^{-47} +622 q^{-48} +842 q^{-49} +460 q^{-50} -114 q^{-51} -474 q^{-52} -419 q^{-53} -105 q^{-54} +183 q^{-55} +250 q^{-56} +149 q^{-57} -17 q^{-58} -127 q^{-59} -102 q^{-60} -17 q^{-61} +39 q^{-62} +42 q^{-63} +28 q^{-64} -7 q^{-65} -26 q^{-66} -7 q^{-67} +5 q^{-68} +2 q^{-69} +3 q^{-70} +3 q^{-71} -5 q^{-72} - q^{-73} +3 q^{-74} - q^{-75} </math> |
coloured_jones_6 =  |
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, 164]]</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[14, 7, 15, 8], X[15, 2, 16, 3], X[5, 12, 6, 13], 
 
  X[9, 19, 10, 18], X[3, 11, 4, 10], X[17, 5, 18, 4], X[19, 9, 20, 8], 
 
  X[11, 16, 12, 17], X[20, 13, 1, 14]]</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, 164]]</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, 3, -6, 7, -4, -1, 2, 8, -5, 6, -9, 4, 10, -2, -3, 9, -7, 
 
  5, -8, -10]</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, 164]]</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, -12, 14, -18, -16, 20, -2, -4, -8]</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, 164]]</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, -2, 1, -2, -2, -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, 164]]</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, 164]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:10_164_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, 164]]&) /@ {
                    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, 1, 2, 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, 164]][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    11             2
17 + -- - -- - 11 t + 3 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, 164]][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
1 + z  + 3 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, 10], Knot[10, 164]}</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, 164]], KnotSignature[Knot[10, 164]]}</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, 164]][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>     -5   3    5    7    8            2      3
8 - q   + -- - -- + -- - - - 6 q + 5 q  - 2 q
           4    3    2   q
          q    q    q</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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>
<tr align=left>
<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, 164]}</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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, 164]][q]</nowiki></code></td></tr>
<tr align=left>
<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>  -16    -14    -12    2     -8    -6   2       2    4    6    8      10
-q    + q    + q    - --- + q   - q   + -- + 3 q  - q  + q  + q  - 2 q
                       10                2
                      q                 q</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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, 164]][a, z]</nowiki></code></td></tr>
<tr align=left>
<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      2   2 z     4  2      4    2  4
3 - a   - a  + 4 z  - ---- - a  z  + 2 z  + a  z
                        2
                       a</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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, 164]][a, z]</nowiki></code></td></tr>
<tr align=left>
<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    2   2 z   5 z              3        2   6 z       4  2
3 + a   + a  - --- - --- - 5 a z - 2 a  z - 9 z  - ---- + 3 a  z  + 
                3     a                              2
               a                                    a
 
     3       3                                           4
  3 z    10 z          3      3  3      5  3      4   4 z       2  4
  ---- + ----- + 16 a z  + 7 a  z  - 2 a  z  + 8 z  + ---- - 3 a  z  - 
    3      a                                            2
   a                                                   a
 
               5                                        6
     4  4   6 z          5       3  5    5  5      6   z     2  6
  7 a  z  - ---- - 17 a z  - 10 a  z  + a  z  - 3 z  + -- - a  z  + 
             a                                          2
                                                       a
 
               7
     4  6   3 z         7      3  7      8      2  8
  3 a  z  + ---- + 7 a z  + 4 a  z  + 2 z  + 2 a  z
             a</nowiki></code></td></tr>
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         <table><tr align=left>
<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, 164]], Vassiliev[3][Knot[10, 164]]}</nowiki></code></td></tr>
<tr align=left>
<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>{1, 0}</nowiki></code></td></tr>
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         <table><tr align=left>
<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, 164]][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>4           1        2       1       3       2       4       3
- + 5 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
 
   4      4               3        3  2      5  2      7  3
  ---- + --- + 3 q t + 3 q  t + 2 q  t  + 3 q  t  + 2 q  t
   3     q t
  q  t</nowiki></code></td></tr>
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         <table><tr align=left>
<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, 164], 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>      -15    3     -13    9    14     5    30   21   24   52   17
56 + q    - --- + q    + --- - --- - --- + -- - -- - -- + -- - -- - 
             14           12    11    10    9    8    7    6    5
            q            q     q     q     q    q    q    q    q
 
  46   62   7    57             2       3       4       5       6
  -- + -- - -- - -- + 4 q - 50 q  + 35 q  + 11 q  - 29 q  + 12 q  + 
   4    3    2   q
  q    q    q
 
     7      8    10
  8 q  - 8 q  + q</nowiki></code></td></tr>
</table>  }}