View source for 10 40

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{{Rolfsen Knot Page|
n = 10 |
k = 40 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-4,8,-5,9,-10,2,-3,4,-8,7,-6,5,-9,6,-7,3/goTop.html |
braid_table     = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.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:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.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:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]]</td></tr>
</table> |
braid_crossings = 11 |
braid_width     = 4 |
braid_index     = 4 |
same_alexander  = [[10_103]],  |
same_jones      = [[10_103]],  |
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%>-3</td    ><td width=6.66667%>-2</td    ><td width=6.66667%>-1</td    ><td width=6.66667%>0</td    ><td width=6.66667%>1</td    ><td width=6.66667%>2</td    ><td width=6.66667%>3</td    ><td width=6.66667%>4</td    ><td width=6.66667%>5</td    ><td width=6.66667%>6</td    ><td width=6.66667%>7</td    ><td width=13.3333%>&chi;</td></tr>
<tr align=center><td>17</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>15</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>&nbsp;</td><td>2</td></tr>
<tr align=center><td>13</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>-3</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 bgcolor=yellow>5</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>3</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 bgcolor=yellow>7</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-3</td></tr>
<tr align=center><td>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</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>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>7</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>5</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>-1</td></tr>
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</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>4</td></tr>
<tr align=center><td>-1</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>&nbsp;</td><td>&nbsp;</td><td>-3</td></tr>
<tr align=center><td>-3</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>-5</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^{23}-3 q^{22}+q^{21}+9 q^{20}-16 q^{19}+35 q^{17}-43 q^{16}-12 q^{15}+82 q^{14}-71 q^{13}-38 q^{12}+130 q^{11}-83 q^{10}-67 q^9+150 q^8-71 q^7-79 q^6+132 q^5-42 q^4-70 q^3+86 q^2-14 q-44+37 q^{-1} -17 q^{-3} +9 q^{-4} + q^{-5} -3 q^{-6} + q^{-7} </math> |
coloured_jones_3 = <math>-q^{45}+3 q^{44}-q^{43}-4 q^{42}-2 q^{41}+13 q^{40}+3 q^{39}-26 q^{38}-10 q^{37}+50 q^{36}+25 q^{35}-83 q^{34}-59 q^{33}+129 q^{32}+111 q^{31}-173 q^{30}-194 q^{29}+216 q^{28}+296 q^{27}-240 q^{26}-417 q^{25}+247 q^{24}+536 q^{23}-225 q^{22}-653 q^{21}+191 q^{20}+741 q^{19}-138 q^{18}-796 q^{17}+69 q^{16}+828 q^{15}-14 q^{14}-803 q^{13}-66 q^{12}+768 q^{11}+110 q^{10}-669 q^9-177 q^8+580 q^7+195 q^6-445 q^5-218 q^4+336 q^3+196 q^2-216 q-173+132 q^{-1} +131 q^{-2} -70 q^{-3} -88 q^{-4} +30 q^{-5} +54 q^{-6} -11 q^{-7} -29 q^{-8} +3 q^{-9} +14 q^{-10} -2 q^{-11} -4 q^{-12} - q^{-13} +3 q^{-14} - q^{-15} </math> |
coloured_jones_4 = <math>q^{74}-3 q^{73}+q^{72}+4 q^{71}-3 q^{70}+5 q^{69}-16 q^{68}+5 q^{67}+22 q^{66}-12 q^{65}+14 q^{64}-66 q^{63}+11 q^{62}+93 q^{61}-4 q^{60}+24 q^{59}-230 q^{58}-24 q^{57}+268 q^{56}+125 q^{55}+105 q^{54}-616 q^{53}-271 q^{52}+498 q^{51}+534 q^{50}+486 q^{49}-1190 q^{48}-945 q^{47}+510 q^{46}+1203 q^{45}+1425 q^{44}-1648 q^{43}-2023 q^{42}+q^{41}+1818 q^{40}+2866 q^{39}-1646 q^{38}-3136 q^{37}-1014 q^{36}+2039 q^{35}+4381 q^{34}-1153 q^{33}-3872 q^{32}-2167 q^{31}+1794 q^{30}+5480 q^{29}-399 q^{28}-4043 q^{27}-3094 q^{26}+1222 q^{25}+5924 q^{24}+385 q^{23}-3674 q^{22}-3610 q^{21}+459 q^{20}+5652 q^{19}+1077 q^{18}-2814 q^{17}-3639 q^{16}-395 q^{15}+4702 q^{14}+1538 q^{13}-1621 q^{12}-3121 q^{11}-1107 q^{10}+3258 q^9+1578 q^8-456 q^7-2156 q^6-1372 q^5+1758 q^4+1165 q^3+264 q^2-1103 q-1120+675 q^{-1} +583 q^{-2} +423 q^{-3} -371 q^{-4} -634 q^{-5} +171 q^{-6} +167 q^{-7} +268 q^{-8} -58 q^{-9} -252 q^{-10} +32 q^{-11} +9 q^{-12} +103 q^{-13} +7 q^{-14} -74 q^{-15} +12 q^{-16} -10 q^{-17} +25 q^{-18} +5 q^{-19} -17 q^{-20} +5 q^{-21} -3 q^{-22} +4 q^{-23} + q^{-24} -3 q^{-25} + q^{-26} </math> |
coloured_jones_5 = <math>\textrm{NotAvailable}(q)</math> |
coloured_jones_6 = <math>\textrm{NotAvailable}(q)</math> |
coloured_jones_7 = <math>\textrm{NotAvailable}(q)</math> |
computer_talk = 
         <table>
         <tr valign=top>
         <td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td>
         <td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td>
         </tr>
         <tr valign=top><td colspan=2>Loading KnotTheory` (version of August 29, 2005, 15:27:48)...</td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[Knot[10, 40]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[1, 4, 2, 5], X[3, 10, 4, 11], X[11, 1, 12, 20], X[5, 13, 6, 12], 
 
  X[7, 17, 8, 16], X[15, 19, 16, 18], X[19, 15, 20, 14], 
 
  X[13, 7, 14, 6], X[17, 9, 18, 8], X[9, 2, 10, 3]]</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[3]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>GaussCode[Knot[10, 40]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[-1, 10, -2, 1, -4, 8, -5, 9, -10, 2, -3, 4, -8, 7, -6, 5, -9, 
 
  6, -7, 3]</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[4]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>DTCode[Knot[10, 40]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>DTCode[4, 10, 12, 16, 2, 20, 6, 18, 8, 14]</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[5]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>br = BR[Knot[10, 40]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[4, {1, 1, 1, 2, -1, 2, 2, -3, 2, -3, -3}]</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[6]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{First[br], Crossings[br]}</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{4, 11}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>BraidIndex[Knot[10, 40]]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>4</nowiki></pre></td></tr>
         <tr  valign=top><td><pre style="color: blue; border: 0px; padding:  0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red;  border: 0px; padding:  0em"><nowiki>Show[DrawMorseLink[Knot[10, 40]]]</nowiki></pre></td></tr><tr><td></td><td  align=left>[[Image:10_40_ML.gif]]</td></tr><tr valign=top><td><tt><font  color=blue>Out[8]=</font></tt><td><tt><font  color=black>-Graphics-</font></tt></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki> (#[Knot[10, 40]]&) /@ {
                   SymmetryType, UnknottingNumber, ThreeGenus,
                   BridgeIndex, SuperBridgeIndex, NakanishiIndex
                  }</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Reversible, 2, 3, 2, NotAvailable, 1}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[Knot[10, 40]][t]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>      2    8    17             2      3
-21 + -- - -- + -- + 17 t - 8 t  + 2 t
       3    2   t
      t    t</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[11]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[Knot[10, 40]][z]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>       2      4      6
1 + 3 z  + 4 z  + 2 z</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[12]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 40], Knot[10, 103]}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{KnotDet[Knot[10, 40]], KnotSignature[Knot[10, 40]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{75, 2}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[14]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Jones[Knot[10, 40]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>      -2   3              2       3       4      5      6      7    8
-6 - q   + - + 10 q - 11 q  + 13 q  - 12 q  + 9 q  - 6 q  + 3 q  - q
           q</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[15]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 40], Knot[10, 103]}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[16]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>A2Invariant[Knot[10, 40]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[16]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>      -6    -4    -2      2    4      6    8    12      14      16
-1 - q   + q   - q   + 3 q  - q  + 4 q  + q  + q   - 3 q   + 2 q   - 
 
   18    20    22    24
  q   - q   + q   - q</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[17]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>HOMFLYPT[Knot[10, 40]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[17]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>                          2      2      2         4      4      4
      -6   3       2   2 z    3 z    4 z     4   z    3 z    3 z
-1 - a   + -- - 2 z  - ---- + ---- + ---- - z  - -- + ---- + ---- + 
            2            6      4      2          6     4      2
           a            a      a      a          a     a      a
 
   6    6
  z    z
  -- + --
   4    2
  a    a</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[18]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Knot[10, 40]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[18]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>                                                 2    2    2      2
      -6   3    z    2 z   2 z            2   3 z    z    z    7 z
-1 + a   - -- + -- + --- + --- + a z + 4 z  + ---- + -- + -- + ---- - 
            2    9    3     a                   8     6    4     2
           a    a    a                         a     a    a     a
 
     3      3      3      3    3                      4      4      4
  2 z    2 z    6 z    3 z    z         3      4   6 z    5 z    2 z
  ---- + ---- + ---- + ---- - -- - 2 a z  - 6 z  - ---- - ---- - ---- - 
    9      7      5      3    a                      8      6      4
   a      a      a      a                           a      a      a
 
     4    5      5       5       5      5                    6      6
  9 z    z    6 z    13 z    12 z    5 z       5      6   3 z    5 z
  ---- + -- - ---- - ----- - ----- - ---- + a z  + 3 z  + ---- - ---- + 
    2     9     7      5       3      a                     8      4
   a     a     a      a       a                            a      a
 
   6      7      7      7      7      8      8      8    9    9
  z    4 z    7 z    7 z    4 z    3 z    6 z    3 z    z    z
  -- + ---- + ---- + ---- + ---- + ---- + ---- + ---- + -- + --
   2     7      5      3     a       6      4      2     5    3
  a     a      a      a             a      a      a     a    a</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[19]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{Vassiliev[2][Knot[10, 40]], Vassiliev[3][Knot[10, 40]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[19]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{3, 4}</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[20]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[Knot[10, 40]][q, t]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[20]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>         3     1       2      1      4    2 q      3        5
6 q + 5 q  + ----- + ----- + ---- + --- + --- + 6 q  t + 5 q  t + 
              5  3    3  2      2   q t    t
             q  t    q  t    q t
 
     5  2      7  2      7  3      9  3      9  4      11  4
  7 q  t  + 6 q  t  + 5 q  t  + 7 q  t  + 4 q  t  + 5 q   t  + 
 
     11  5      13  5    13  6      15  6    17  7
  2 q   t  + 4 q   t  + q   t  + 2 q   t  + q   t</nowiki></pre></td></tr>
         <tr valign=top><td><pre style="color:    blue; border: 0px; padding: 0em"><nowiki>In[21]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>ColouredJones[Knot[10, 40], 2][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre   style="color: blue; border: 0px; padding: 0em"><nowiki>Out[21]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>       -7   3     -5   9    17   37              2       3       4
-44 + q   - -- + q   + -- - -- + -- - 14 q + 86 q  - 70 q  - 42 q  + 
             6          4    3   q
            q          q    q
 
       5       6       7        8       9       10        11       12
  132 q  - 79 q  - 71 q  + 150 q  - 67 q  - 83 q   + 130 q   - 38 q   - 
 
      13       14       15       16       17       19      20    21
  71 q   + 82 q   - 12 q   - 43 q   + 35 q   - 16 q   + 9 q   + q   - 
 
     22    23
  3 q   + q</nowiki></pre></td></tr>
         </table>  }}