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{{Khovanov Homology|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>4</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>-3</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>5</td><td bgcolor=yellow>4</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>6</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>4</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>-1</td></tr>
<tr align=center><td>-5</td><td>&nbsp;</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>3</td></tr>
<tr align=center><td>-7</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>-9</td><td bgcolor=yellow>&nbsp;</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>1</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>}}
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<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><pre style="border: 0px; padding: 0em">Loading KnotTheory` (version of August 17, 2005, 14:44:34)...</pre></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>Crossings[Knot[10, 79]]</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>10</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>PD[Knot[10, 79]]</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>PD[X[6, 2, 7, 1], X[8, 4, 9, 3], X[12, 6, 13, 5], X[18, 13, 19, 14], 
 
  X[16, 9, 17, 10], X[10, 17, 11, 18], X[20, 15, 1, 16], 
 
  X[14, 19, 15, 20], X[2, 8, 3, 7], X[4, 12, 5, 11]]</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>GaussCode[Knot[10, 79]]</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>GaussCode[1, -9, 2, -10, 3, -1, 9, -2, 5, -6, 10, -3, 4, -8, 7, -5, 6, 
 
  -4, 8, -7]</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[Knot[10, 79]]</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[3, {-1, -1, -1, 2, 2, -1, -1, 2, 2, 2}]</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>alex = Alexander[Knot[10, 79]][t]</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   3    7    12             2      3    4
15 + t   - -- + -- - -- - 12 t + 7 t  - 3 t  + t
            3    2   t
           t    t</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>Conway[Knot[10, 79]][z]</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>       2      4      6    8
1 + 5 z  + 9 z  + 5 z  + z</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>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[8]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 79]}</nowiki></pre></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>{KnotDet[Knot[10, 79]], KnotSignature[Knot[10, 79]]}</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>{61, 0}</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>J=Jones[Knot[10, 79]][q]</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>      -5   2    5    8    9            2      3      4    5
11 - q   + -- - -- + -- - - - 9 q + 8 q  - 5 q  + 2 q  - q
            4    3    2   q
           q    q    q</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>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[11]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 79]}</nowiki></pre></td></tr>
<math>\textrm{Include}(\textrm{ColouredJonesM.mhtml})</math>
<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>A2Invariant[Knot[10, 79]][q]</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>     -14    3    5       2      10    14
1 - q    - --- + -- + 5 q  - 3 q   - q
            10    2
           q     q</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>Kauffman[Knot[10, 79]][a, z]</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>     5       2   2 z   2 z   11 z               3        5         2
11 + -- + 5 a  + --- - --- - ---- - 11 a z - 2 a  z + 2 a  z - 28 z  + 
      2           5     3     a
     a           a     a
 
   2       2                         3      3       3
  z    13 z        2  2    4  2   3 z    4 z    22 z          3
  -- - ----- - 13 a  z  + a  z  - ---- + ---- + ----- + 22 a z  + 
   4     2                          5      3      a
  a     a                          a      a
 
                                 4       4                         5
     3  3      5  3       4   4 z    12 z        2  4      4  4   z
  4 a  z  - 3 a  z  + 32 z  - ---- + ----- + 12 a  z  - 4 a  z  + -- - 
                                4      2                           5
                               a      a                           a
 
     5       5                                          6      6
  6 z    15 z          5      3  5    5  5       6   2 z    7 z
  ---- - ----- - 15 a z  - 6 a  z  + a  z  - 18 z  + ---- - ---- - 
    3      a                                           4      2
   a                                                  a      a
 
                         7      7                                8
     2  6      4  6   3 z    4 z         7      3  7      8   3 z
  7 a  z  + 2 a  z  + ---- + ---- + 4 a z  + 3 a  z  + 6 z  + ---- + 
                        3     a                                 2
                       a                                       a
 
             9
     2  8   z       9
  3 a  z  + -- + a z
            a</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>{Vassiliev[2][Knot[10, 79]], Vassiliev[3][Knot[10, 79]]}</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>{0, 0}</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>Kh[Knot[10, 79]][q, t]</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>6           1        1       1       4       1       4       4
- + 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 + 5 q  t + 4 q  t  + 4 q  t  + q  t  + 4 q  t  + 
   3     q t
  q  t
 
   7  4    9  4    11  5
  q  t  + q  t  + q   t</nowiki></pre></td></tr>
</table>

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