View source for 10 115

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{{Rolfsen Knot Page|
n = 10 |
k = 115 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,7,-8,2,-1,4,-5,8,-7,6,-9,10,-2,3,-4,9,-6,5,-3/goTop.html |
braid_table     = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]]</td></tr>
</table> |
braid_crossings = 12 |
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>6</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>-5</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>9</td><td bgcolor=yellow>6</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>10</td><td bgcolor=yellow>8</td><td>&nbsp;</td><td>&nbsp;</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>8</td><td bgcolor=yellow>10</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr>
<tr align=center><td>-3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>9</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>6</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>-5</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}+4 q^{13}+11 q^{12}-33 q^{11}+13 q^{10}+64 q^9-101 q^8-6 q^7+172 q^6-166 q^5-70 q^4+278 q^3-181 q^2-142 q+321-142 q^{-1} -181 q^{-2} +278 q^{-3} -70 q^{-4} -166 q^{-5} +172 q^{-6} -6 q^{-7} -101 q^{-8} +64 q^{-9} +13 q^{-10} -33 q^{-11} +11 q^{-12} +4 q^{-13} -4 q^{-14} + q^{-15} </math> |
coloured_jones_3 = <math>-q^{30}+4 q^{29}-4 q^{28}-6 q^{27}+8 q^{26}+23 q^{25}-21 q^{24}-68 q^{23}+41 q^{22}+156 q^{21}-36 q^{20}-312 q^{19}-34 q^{18}+538 q^{17}+197 q^{16}-774 q^{15}-501 q^{14}+978 q^{13}+926 q^{12}-1100 q^{11}-1406 q^{10}+1085 q^9+1901 q^8-962 q^7-2322 q^6+733 q^5+2658 q^4-470 q^3-2840 q^2+148 q+2923+148 q^{-1} -2840 q^{-2} -470 q^{-3} +2658 q^{-4} +733 q^{-5} -2322 q^{-6} -962 q^{-7} +1901 q^{-8} +1085 q^{-9} -1406 q^{-10} -1100 q^{-11} +926 q^{-12} +978 q^{-13} -501 q^{-14} -774 q^{-15} +197 q^{-16} +538 q^{-17} -34 q^{-18} -312 q^{-19} -36 q^{-20} +156 q^{-21} +41 q^{-22} -68 q^{-23} -21 q^{-24} +23 q^{-25} +8 q^{-26} -6 q^{-27} -4 q^{-28} +4 q^{-29} - q^{-30} </math> |
coloured_jones_4 = <math>q^{50}-4 q^{49}+4 q^{48}+6 q^{47}-13 q^{46}+2 q^{45}-15 q^{44}+40 q^{43}+49 q^{42}-94 q^{41}-61 q^{40}-89 q^{39}+246 q^{38}+385 q^{37}-253 q^{36}-518 q^{35}-744 q^{34}+642 q^{33}+1807 q^{32}+368 q^{31}-1400 q^{30}-3385 q^{29}-217 q^{28}+4490 q^{27}+3818 q^{26}-590 q^{25}-8228 q^{24}-5045 q^{23}+5642 q^{22}+10246 q^{21}+5143 q^{20}-11875 q^{19}-13751 q^{18}+1667 q^{17}+15820 q^{16}+15318 q^{15}-10566 q^{14}-22033 q^{13}-6857 q^{12}+16840 q^{11}+25391 q^{10}-4814 q^9-26115 q^8-15813 q^7+13604 q^6+31686 q^5+2140 q^4-25795 q^3-22277 q^2+8365 q+33665+8365 q^{-1} -22277 q^{-2} -25795 q^{-3} +2140 q^{-4} +31686 q^{-5} +13604 q^{-6} -15813 q^{-7} -26115 q^{-8} -4814 q^{-9} +25391 q^{-10} +16840 q^{-11} -6857 q^{-12} -22033 q^{-13} -10566 q^{-14} +15318 q^{-15} +15820 q^{-16} +1667 q^{-17} -13751 q^{-18} -11875 q^{-19} +5143 q^{-20} +10246 q^{-21} +5642 q^{-22} -5045 q^{-23} -8228 q^{-24} -590 q^{-25} +3818 q^{-26} +4490 q^{-27} -217 q^{-28} -3385 q^{-29} -1400 q^{-30} +368 q^{-31} +1807 q^{-32} +642 q^{-33} -744 q^{-34} -518 q^{-35} -253 q^{-36} +385 q^{-37} +246 q^{-38} -89 q^{-39} -61 q^{-40} -94 q^{-41} +49 q^{-42} +40 q^{-43} -15 q^{-44} +2 q^{-45} -13 q^{-46} +6 q^{-47} +4 q^{-48} -4 q^{-49} + q^{-50} </math> |
coloured_jones_5 =  |
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, 115]]</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, 6, 15, 5], X[20, 15, 1, 16], X[16, 7, 17, 8], 
 
  X[8, 19, 9, 20], X[18, 11, 19, 12], X[10, 4, 11, 3], X[4, 10, 5, 9], 
 
  X[12, 17, 13, 18], X[2, 14, 3, 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, 115]]</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, -10, 7, -8, 2, -1, 4, -5, 8, -7, 6, -9, 10, -2, 3, -4, 9, 
 
  -6, 5, -3]</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, 115]]</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, 14, 16, 4, 18, 2, 20, 12, 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, 115]]</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[5, {1, -2, 1, 3, 2, 2, -4, -3, 2, -3, -3, -4}]</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>{5, 12}</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, 115]]</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>5</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, 115]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:10_115_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, 115]]&) /@ {
                    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>{NegativeAmphicheiral, 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, 115]][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   9    26             2    3
37 - t   + -- - -- - 26 t + 9 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, 115]][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 + z  + 3 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, 115]}</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, 115]], KnotSignature[Knot[10, 115]]}</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>{109, 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, 115]][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   4    9    14   17              2      3      4    5
19 - q   + -- - -- + -- - -- - 17 q + 14 q  - 9 q  + 4 q  - 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, 115]}</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, 115]][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    2     4    2     -6   2    5       2      4    6
-1 - q    + q    + --- - --- + -- - q   - -- + -- + 5 q  - 2 q  - q  + 
                    12    10    8          4    2
                   q     q     q          q    q
 
     8      10      12    14    16
  2 q  - 4 q   + 2 q   + 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, 115]][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                           4
     -2    2    2   z    z     2  2    4  2    4   2 z       2  4    6
3 - a   - a  + z  - -- + -- + a  z  - a  z  - z  + ---- + 2 a  z  - z
                     4    2                          2
                    a    a                          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, 115]][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   2 z   5 z              3        2   2 z    z     2  2
3 + a   + a  - --- - --- - 5 a z - 2 a  z - 6 z  + ---- - -- - a  z  + 
                3     a                              4     2
               a                                    a     a
 
             3      3       3
     4  2   z    8 z    22 z          3      3  3    5  3       4
  2 a  z  - -- + ---- + ----- + 22 a z  + 8 a  z  - a  z  + 12 z  - 
             5     3      a
            a     a
 
     4    4                      5       5       5
  5 z    z     2  4      4  4   z    13 z    34 z          5
  ---- + -- + a  z  - 5 a  z  + -- - ----- - ----- - 34 a z  - 
    4     2                      5     3       a
   a     a                      a     a
 
                                6      6                          7
      3  5    5  5       6   4 z    9 z       2  6      4  6   8 z
  13 a  z  + a  z  - 26 z  + ---- - ---- - 9 a  z  + 4 a  z  + ---- + 
                               4      2                          3
                              a      a                          a
 
      7                                  8                9
  13 z          7      3  7       8   8 z       2  8   3 z         9
  ----- + 13 a z  + 8 a  z  + 16 z  + ---- + 8 a  z  + ---- + 3 a z
    a                                   2               a
                                       a</nowiki></code></td></tr>
</table>
         <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, 115]], Vassiliev[3][Knot[10, 115]]}</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>
</table>
         <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, 115]][q, t]</nowiki></code></td></tr>
<tr align=left>
<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>10            1        3       1       6       3       8       6
-- + 10 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
 
   9      8               3        3  2      5  2      5  3      7  3
  ---- + --- + 8 q t + 9 q  t + 6 q  t  + 8 q  t  + 3 q  t  + 6 q  t  + 
   3     q t
  q  t
 
   7  4      9  4    11  5
  q  t  + 3 q  t  + q   t</nowiki></code></td></tr>
</table>
         <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, 115], 2][q]</nowiki></code></td></tr>
<tr align=left>
<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    4     4    11    33    13    64   101   6    172   166
321 + q    - --- + --- + --- - --- + --- + -- - --- - -- + --- - --- - 
              14    13    12    11    10    9    8     7    6     5
             q     q     q     q     q     q    q     q    q     q
 
  70   278   181   142                2        3       4        5
  -- + --- - --- - --- - 142 q - 181 q  + 278 q  - 70 q  - 166 q  + 
   4    3     2     q
  q    q     q
 
       6      7        8       9       10       11       12      13
  172 q  - 6 q  - 101 q  + 64 q  + 13 q   - 33 q   + 11 q   + 4 q   - 
 
     14    15
  4 q   + q</nowiki></code></td></tr>
</table>  }}