View source for 10 31

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{{Rolfsen Knot Page|
n = 10 |
k = 31 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-6,7,-8,9,-3,4,-10,2,-4,3,-5,6,-9,8,-7,5/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:BraidPart0.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:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.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:BraidPart0.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 = 12 |
braid_width     = 5 |
braid_index     = 5 |
same_alexander  = [[10_68]],  |
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>1</td><td bgcolor=yellow>&nbsp;</td><td>1</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>3</td><td bgcolor=yellow>1</td><td>&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>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>1</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>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>3</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>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>4</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>4</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
<tr align=center><td>-3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</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>-2</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>&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>&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>&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>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr>
</table> |
coloured_jones_2 = <math>q^{15}-2 q^{14}+5 q^{12}-8 q^{11}+16 q^9-21 q^8-3 q^7+38 q^6-37 q^5-13 q^4+63 q^3-47 q^2-27 q+78-45 q^{-1} -35 q^{-2} +72 q^{-3} -30 q^{-4} -34 q^{-5} +50 q^{-6} -12 q^{-7} -26 q^{-8} +25 q^{-9} - q^{-10} -13 q^{-11} +8 q^{-12} + q^{-13} -3 q^{-14} + q^{-15} </math> |
coloured_jones_3 = <math>-q^{30}+2 q^{29}-q^{27}-3 q^{26}+5 q^{25}+q^{24}-5 q^{23}-4 q^{22}+13 q^{21}+q^{20}-19 q^{19}-6 q^{18}+36 q^{17}+10 q^{16}-55 q^{15}-24 q^{14}+76 q^{13}+52 q^{12}-103 q^{11}-79 q^{10}+113 q^9+128 q^8-132 q^7-160 q^6+124 q^5+208 q^4-129 q^3-227 q^2+105 q+258-97 q^{-1} -256 q^{-2} +67 q^{-3} +256 q^{-4} -42 q^{-5} -238 q^{-6} +12 q^{-7} +212 q^{-8} +16 q^{-9} -177 q^{-10} -39 q^{-11} +138 q^{-12} +53 q^{-13} -98 q^{-14} -59 q^{-15} +64 q^{-16} +53 q^{-17} -36 q^{-18} -42 q^{-19} +17 q^{-20} +30 q^{-21} -7 q^{-22} -19 q^{-23} +3 q^{-24} +10 q^{-25} - q^{-26} -4 q^{-27} - q^{-28} +3 q^{-29} - q^{-30} </math> |
coloured_jones_4 = <math>q^{50}-2 q^{49}+q^{47}-q^{46}+6 q^{45}-7 q^{44}+q^{43}+2 q^{42}-9 q^{41}+17 q^{40}-14 q^{39}+10 q^{38}+9 q^{37}-34 q^{36}+23 q^{35}-30 q^{34}+41 q^{33}+44 q^{32}-70 q^{31}+6 q^{30}-95 q^{29}+84 q^{28}+146 q^{27}-64 q^{26}-21 q^{25}-267 q^{24}+65 q^{23}+301 q^{22}+63 q^{21}+39 q^{20}-536 q^{19}-113 q^{18}+403 q^{17}+306 q^{16}+274 q^{15}-781 q^{14}-427 q^{13}+349 q^{12}+542 q^{11}+640 q^{10}-892 q^9-735 q^8+170 q^7+664 q^6+987 q^5-867 q^4-923 q^3-36 q^2+660 q+1213-751 q^{-1} -969 q^{-2} -215 q^{-3} +552 q^{-4} +1288 q^{-5} -548 q^{-6} -875 q^{-7} -371 q^{-8} +343 q^{-9} +1215 q^{-10} -275 q^{-11} -645 q^{-12} -466 q^{-13} +63 q^{-14} +980 q^{-15} -17 q^{-16} -316 q^{-17} -438 q^{-18} -187 q^{-19} +632 q^{-20} +111 q^{-21} -18 q^{-22} -281 q^{-23} -283 q^{-24} +296 q^{-25} +87 q^{-26} +123 q^{-27} -102 q^{-28} -220 q^{-29} +96 q^{-30} +12 q^{-31} +110 q^{-32} -5 q^{-33} -111 q^{-34} +28 q^{-35} -18 q^{-36} +52 q^{-37} +10 q^{-38} -42 q^{-39} +13 q^{-40} -12 q^{-41} +16 q^{-42} +5 q^{-43} -13 q^{-44} +4 q^{-45} -3 q^{-46} +4 q^{-47} + q^{-48} -3 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, 31]]</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[1, 4, 2, 5], X[3, 12, 4, 13], X[9, 14, 10, 15], X[13, 10, 14, 11], 
 
  X[15, 1, 16, 20], X[5, 17, 6, 16], X[19, 7, 20, 6], X[7, 19, 8, 18], 
 
  X[17, 9, 18, 8], X[11, 2, 12, 3]]</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, 31]]</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, -2, 1, -6, 7, -8, 9, -3, 4, -10, 2, -4, 3, -5, 6, -9, 
 
  8, -7, 5]</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, 31]]</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[4, 12, 16, 18, 14, 2, 10, 20, 8, 6]</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, 31]]</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, -1, -1, -2, 1, 3, -2, 3, 3, 4, -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, 31]]</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, 31]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:10_31_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, 31]]&) /@ {
                   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, 2, 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, 31]][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>     4    14             2
21 + -- - -- - 14 t + 4 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, 31]][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 + 2 z  + 4 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, 31], Knot[10, 68]}</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, 31]], KnotSignature[Knot[10, 31]]}</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>{57, 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, 31]][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    9            2      3      4    5
10 - q   + -- - -- + -- - - - 8 q + 7 q  - 4 q  + 2 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, 31]}</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, 31]][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    -4   2       2    6      8
-q    + q    + q    - --- + q   - q   - q   + -- + 3 q  + q  + 2 q  - 
                       10                      2
                      q                       q
 
     10    16
  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, 31]][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
     -4    -2    2      2   z    z     4  2      4   z     2  4
2 - a   + a   - a  + 3 z  - -- + -- - a  z  + 2 z  + -- + a  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, 31]][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
     -4    -2    2   2 z   2 z   2 z              3         2   3 z
2 - a   - a   + a  + --- + --- - --- - 4 a z - 2 a  z - 10 z  + ---- - 
                      5     3     a                               4
                     a     a                                     a
 
     2                          3      3      3
  2 z       2  2      4  2   3 z    3 z    6 z          3      3  3
  ---- - 3 a  z  + 2 a  z  - ---- - ---- + ---- + 15 a z  + 7 a  z  - 
    2                          5      3     a
   a                          a      a
 
                       4      4                        5      5
     5  3       4   5 z    3 z       2  4      4  4   z    2 z
  2 a  z  + 20 z  - ---- + ---- + 5 a  z  - 7 a  z  + -- - ---- - 
                      4      2                         5     3
                     a      a                         a     a
 
     5                                           6      6
  4 z          5       3  5    5  5       6   2 z    3 z       2  6
  ---- - 12 a z  - 10 a  z  + a  z  - 14 z  + ---- - ---- - 6 a  z  + 
   a                                            4      2
                                               a      a
 
               7    7                                8              9
     4  6   2 z    z         7      3  7      8   2 z       2  8   z
  3 a  z  + ---- + -- + 3 a z  + 4 a  z  + 5 z  + ---- + 3 a  z  + -- + 
              3    a                                2              a
             a                                     a
 
     9
  a z</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, 31]], Vassiliev[3][Knot[10, 31]]}</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>{2, 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, 31]][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       3       2       4       3
- + 6 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
 
   5      4               3        3  2      5  2    5  3      7  3
  ---- + --- + 4 q t + 4 q  t + 3 q  t  + 4 q  t  + q  t  + 3 q  t  + 
   3     q t
  q  t
 
   7  4    9  4    11  5
  q  t  + 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, 31], 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    8    13     -10   25   26   12   50   34
78 + q    - --- + q    + --- - --- - q    + -- - -- - -- + -- - -- - 
             14           12    11           9    8    7    6    5
            q            q     q            q    q    q    q    q
 
  30   72   35   45              2       3       4       5       6
  -- + -- - -- - -- - 27 q - 47 q  + 63 q  - 13 q  - 37 q  + 38 q  - 
   4    3    2   q
  q    q    q
 
     7       8       9      11      12      14    15
  3 q  - 21 q  + 16 q  - 8 q   + 5 q   - 2 q   + q</nowiki></code></td></tr>
</table>  }}