View source for 10 24

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{{Rolfsen Knot Page Header|n=10|k=24|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-5,7,-8,9,-6,10,-2,3,-4,2,-10,5,-9,8,-7,6/goTop.html}}

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{{:{{PAGENAME}} Further Notes and Views}}

{{Knot Presentations}}

<center><table border=1 cellpadding=10><tr align=center valign=top>
<td>
[[Braid Representatives|Minimum Braid Representative]]:
<table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[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]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.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:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.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: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>

[[Invariants from Braid Theory|Length]] is 12, width is 5.

[[Invariants from Braid Theory|Braid index]] is 5.
</td>
<td>
[[Lightly Documented Features|A Morse Link Presentation]]:

[[Image:{{PAGENAME}}_ML.gif]]
</td>
</tr></table></center>

{{3D Invariants}}
{{4D Invariants}}
{{Polynomial Invariants}}

=== "Similar" Knots (within the Atlas) ===

Same [[The Alexander-Conway Polynomial|Alexander/Conway Polynomial]]:
{[[10_18]], ...}

Same [[The Jones Polynomial|Jones Polynomial]] (up to mirroring, <math>q\leftrightarrow q^{-1}</math>): 
{...}

{{Vassiliev Invariants}}

{{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%>-8</td  ><td width=6.66667%>-7</td  ><td width=6.66667%>-6</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=13.3333%>&chi;</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>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</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>&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>-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 bgcolor=yellow>4</td><td bgcolor=yellow>1</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>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>2</td><td>&nbsp;</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 bgcolor=yellow>5</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</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>4</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>-9</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>-11</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>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
<tr align=center><td>-13</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>-15</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>-17</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>-19</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>}}

{{Display Coloured Jones|J2=<math>q^4-2 q^3+q^2+5 q-10+4 q^{-1} +16 q^{-2} -29 q^{-3} +9 q^{-4} +36 q^{-5} -53 q^{-6} +9 q^{-7} +56 q^{-8} -67 q^{-9} +3 q^{-10} +65 q^{-11} -61 q^{-12} -7 q^{-13} +60 q^{-14} -42 q^{-15} -15 q^{-16} +43 q^{-17} -20 q^{-18} -14 q^{-19} +21 q^{-20} -5 q^{-21} -8 q^{-22} +6 q^{-23} -2 q^{-25} + q^{-26} </math>|J3=<math>q^9-2 q^8+q^7+q^6+2 q^5-7 q^4+2 q^3+8 q^2-19+9 q^{-1} +25 q^{-2} -8 q^{-3} -52 q^{-4} +26 q^{-5} +70 q^{-6} -27 q^{-7} -112 q^{-8} +39 q^{-9} +147 q^{-10} -34 q^{-11} -194 q^{-12} +33 q^{-13} +224 q^{-14} -13 q^{-15} -254 q^{-16} -3 q^{-17} +263 q^{-18} +28 q^{-19} -262 q^{-20} -52 q^{-21} +250 q^{-22} +72 q^{-23} -221 q^{-24} -99 q^{-25} +196 q^{-26} +109 q^{-27} -154 q^{-28} -124 q^{-29} +119 q^{-30} +120 q^{-31} -75 q^{-32} -116 q^{-33} +44 q^{-34} +96 q^{-35} -15 q^{-36} -73 q^{-37} -5 q^{-38} +52 q^{-39} +11 q^{-40} -28 q^{-41} -15 q^{-42} +16 q^{-43} +9 q^{-44} -5 q^{-45} -7 q^{-46} +3 q^{-47} +2 q^{-48} -2 q^{-50} + q^{-51} </math>|J4=<math>q^{16}-2 q^{15}+q^{14}+q^{13}-2 q^{12}+5 q^{11}-9 q^{10}+4 q^9+6 q^8-9 q^7+15 q^6-24 q^5+13 q^4+16 q^3-32 q^2+30 q-43+46 q^{-1} +37 q^{-2} -95 q^{-3} +27 q^{-4} -68 q^{-5} +146 q^{-6} +106 q^{-7} -222 q^{-8} -54 q^{-9} -127 q^{-10} +346 q^{-11} +286 q^{-12} -371 q^{-13} -249 q^{-14} -295 q^{-15} +589 q^{-16} +602 q^{-17} -435 q^{-18} -493 q^{-19} -586 q^{-20} +741 q^{-21} +942 q^{-22} -352 q^{-23} -633 q^{-24} -898 q^{-25} +718 q^{-26} +1151 q^{-27} -176 q^{-28} -604 q^{-29} -1102 q^{-30} +562 q^{-31} +1165 q^{-32} +12 q^{-33} -444 q^{-34} -1165 q^{-35} +339 q^{-36} +1028 q^{-37} +183 q^{-38} -214 q^{-39} -1112 q^{-40} +85 q^{-41} +786 q^{-42} +323 q^{-43} +49 q^{-44} -952 q^{-45} -154 q^{-46} +475 q^{-47} +373 q^{-48} +282 q^{-49} -673 q^{-50} -290 q^{-51} +151 q^{-52} +289 q^{-53} +398 q^{-54} -343 q^{-55} -264 q^{-56} -70 q^{-57} +118 q^{-58} +342 q^{-59} -89 q^{-60} -127 q^{-61} -125 q^{-62} -19 q^{-63} +190 q^{-64} +11 q^{-65} -12 q^{-66} -71 q^{-67} -53 q^{-68} +66 q^{-69} +11 q^{-70} +20 q^{-71} -18 q^{-72} -29 q^{-73} +16 q^{-74} - q^{-75} +10 q^{-76} - q^{-77} -9 q^{-78} +4 q^{-79} - q^{-80} +2 q^{-81} -2 q^{-83} + q^{-84} </math>|J5=Not Available|J6=Not Available|J7=Not Available}}

{{Computer Talk Header}}

<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 29, 2005, 15:27:48)...</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>PD[Knot[10, 24]]</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[11, 14, 12, 15], X[3, 13, 4, 12], X[13, 3, 14, 2], 
 
  X[5, 16, 6, 17], X[9, 20, 10, 1], X[19, 6, 20, 7], X[7, 18, 8, 19], 
 
  X[17, 8, 18, 9], X[15, 10, 16, 11]]</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, 24]]</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, 4, -3, 1, -5, 7, -8, 9, -6, 10, -2, 3, -4, 2, -10, 5, -9, 
 
  8, -7, 6]</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, 24]]</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, 12, 16, 18, 20, 14, 2, 10, 8, 6]</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, 24]]</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[5, {-1, -1, -2, 1, -2, -2, -2, -3, 2, 4, -3, 4}]</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>{5, 12}</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, 24]]</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>5</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, 24]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_24_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, 24]]&) /@ {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, 2, 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, 24]][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>      4    14             2
-19 - -- + -- + 14 t - 4 t
       2   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, 24]][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
1 - 2 z  - 4 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, 18], Knot[10, 24]}</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, 24]], KnotSignature[Knot[10, 24]]}</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>{55, -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, 24]][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>      -9   2    4    7    8    9    9    7    5
-2 + q   - -- + -- - -- + -- - -- + -- - -- + - + q
            8    7    6    5    4    3    2   q
           q    q    q    q    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, 24]}</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, 24]][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> -28    2     2     -18    2     -12    -10    -8    -6    -4   3     4
q    + --- - --- - q    - --- + q    - q    + q   + q   - q   + -- + q
        22    20           14                                    2
       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, 24]][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    4    6    8    2      4  2    6  2    8  2    2  4
1 + a  - a  - a  + a  + z  - 3 a  z  - a  z  + a  z  - a  z  - 
 
     4  4    6  4
  2 a  z  - a  z</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, 24]][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    4    6    8      3        5        9        2      2  2
1 - a  - a  + a  + a  + 2 a  z + 4 a  z - 2 a  z - 2 z  + 2 a  z  + 
 
     4  2      6  2      8  2      10  2        3      5  3      7  3
  5 a  z  - 5 a  z  - 2 a  z  + 4 a   z  - 2 a z  - 7 a  z  - 2 a  z  + 
 
     9  3    4      2  4      4  4      6  4      8  4      10  4
  7 a  z  + z  - 3 a  z  - 5 a  z  + 6 a  z  + 3 a  z  - 4 a   z  + 
 
       5      3  5    5  5      7  5      9  5      2  6    4  6
  2 a z  - 2 a  z  + a  z  - 2 a  z  - 7 a  z  + 3 a  z  + a  z  - 
 
     6  6      8  6    10  6      3  7    5  7      9  7      4  8
  8 a  z  - 5 a  z  + a   z  + 3 a  z  + a  z  + 2 a  z  + 2 a  z  + 
 
     6  8      8  8    5  9    7  9
  4 a  z  + 2 a  z  + a  z  + a  z</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, 24]], Vassiliev[3][Knot[10, 24]]}</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>{-2, 5}</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, 24]][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>2    4     1        1        1        3        1        4        3
-- + - + ------ + ------ + ------ + ------ + ------ + ------ + ------ + 
 3   q    19  8    17  7    15  7    15  6    13  6    13  5    11  5
q        q   t    q   t    q   t    q   t    q   t    q   t    q   t
 
    4        4       5       4       4       5      3      4     t
  ------ + ----- + ----- + ----- + ----- + ----- + ---- + ---- + - + 
   11  4    9  4    9  3    7  3    7  2    5  2    5      3     q
  q   t    q  t    q  t    q  t    q  t    q  t    q  t   q  t
 
         3  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, 24], 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>       -26    2     6     8     5    21    14    20    43    15
-10 + q    - --- + --- - --- - --- + --- - --- - --- + --- - --- - 
              25    23    22    21    20    19    18    17    16
             q     q     q     q     q     q     q     q     q
 
  42    60     7    61    65     3    67   56   9    53   36   9
  --- + --- - --- - --- + --- + --- - -- + -- + -- - -- + -- + -- - 
   15    14    13    12    11    10    9    8    7    6    5    4
  q     q     q     q     q     q     q    q    q    q    q    q
 
  29   16   4          2      3    4
  -- + -- + - + 5 q + q  - 2 q  + q
   3    2   q
  q    q</nowiki></pre></td></tr>

</table>

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