View source for 10 125

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{{Rolfsen Knot Page|
n = 10 |
k = 125 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-3,9,-10,2,5,-7,6,-8,-9,3,4,-5,7,-6,8,-4/goTop.html |
braid_table     = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]]</td></tr>
</table> |
braid_crossings = 10 |
braid_width     = 3 |
braid_index     = 3 |
same_alexander  =  |
same_jones      =  |
khovanov_table  = <table border=1>
<tr align=center>
<td width=15.3846%><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=7.69231%>-5</td    ><td width=7.69231%>-4</td    ><td width=7.69231%>-3</td    ><td width=7.69231%>-2</td    ><td width=7.69231%>-1</td    ><td width=7.69231%>0</td    ><td width=7.69231%>1</td    ><td width=7.69231%>2</td    ><td width=7.69231%>3</td    ><td width=15.3846%>&chi;</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 bgcolor=yellow>1</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 bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>&nbsp;</td><td>0</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>1</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>3</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>&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 bgcolor=yellow>1</td><td bgcolor=yellow>2</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 bgcolor=yellow>1</td><td bgcolor=yellow>&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 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>1</td></tr>
<tr align=center><td>-5</td><td>&nbsp;</td><td bgcolor=yellow>1</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>0</td></tr>
<tr align=center><td>-7</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>-9</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>-1</td></tr>
</table> |
coloured_jones_2 = <math>q^{11}-q^{10}-q^9+q^8-q^6+q^4-q^3+q^2+2 q^{-1} - q^{-2} +2 q^{-4} -2 q^{-5} +2 q^{-7} -2 q^{-8} - q^{-9} +2 q^{-10} - q^{-11} - q^{-12} + q^{-13} </math> |
coloured_jones_3 = <math>-q^{21}+2 q^{20}-q^{18}-2 q^{17}+3 q^{16}+2 q^{15}-4 q^{14}-3 q^{13}+4 q^{12}+5 q^{11}-5 q^{10}-5 q^9+3 q^8+6 q^7-4 q^6-4 q^5+2 q^4+6 q^3-4 q^2-3 q+2+5 q^{-1} -3 q^{-2} -2 q^{-3} + q^{-4} +4 q^{-5} - q^{-6} -2 q^{-7} +2 q^{-9} - q^{-10} - q^{-11} + q^{-13} - q^{-14} - q^{-15} + q^{-16} + q^{-17} - q^{-18} -2 q^{-19} + q^{-20} +2 q^{-21} -2 q^{-23} + q^{-25} + q^{-26} - q^{-27} </math> |
coloured_jones_4 = <math>-q^{33}+q^{32}+q^{31}-q^{29}-2 q^{28}+3 q^{27}+q^{26}-q^{25}-4 q^{24}-q^{23}+7 q^{22}+2 q^{21}-3 q^{20}-8 q^{19}-q^{18}+10 q^{17}+4 q^{16}-2 q^{15}-11 q^{14}-3 q^{13}+11 q^{12}+4 q^{11}-q^{10}-10 q^9-3 q^8+9 q^7+3 q^6-8 q^4-3 q^3+8 q^2+3 q+1-7 q^{-1} -4 q^{-2} +6 q^{-3} +4 q^{-4} +2 q^{-5} -5 q^{-6} -5 q^{-7} +4 q^{-8} +3 q^{-9} +3 q^{-10} -2 q^{-11} -5 q^{-12} + q^{-13} + q^{-14} +3 q^{-15} + q^{-16} -4 q^{-17} - q^{-18} - q^{-19} + q^{-20} +3 q^{-21} -2 q^{-22} - q^{-24} - q^{-25} +3 q^{-26} -2 q^{-27} + q^{-28} - q^{-30} +3 q^{-31} -3 q^{-32} +4 q^{-36} -2 q^{-37} - q^{-38} - q^{-39} - q^{-40} +3 q^{-41} - q^{-44} - q^{-45} + q^{-46} </math> |
coloured_jones_5 = <math>q^{51}-q^{50}-q^{48}-q^{47}+q^{46}+2 q^{45}+q^{44}-q^{43}-q^{42}-2 q^{41}+q^{40}+q^{39}+q^{38}+q^{37}+q^{36}-q^{35}-2 q^{34}-5 q^{33}-q^{32}+3 q^{31}+8 q^{30}+5 q^{29}-4 q^{28}-10 q^{27}-7 q^{26}+q^{25}+10 q^{24}+11 q^{23}-10 q^{21}-10 q^{20}-2 q^{19}+8 q^{18}+11 q^{17}+2 q^{16}-8 q^{15}-9 q^{14}-q^{13}+6 q^{12}+9 q^{11}-7 q^9-7 q^8+5 q^6+8 q^5-4 q^3-6 q^2-2 q+2+7 q^{-1} +3 q^{-2} - q^{-3} -5 q^{-4} -4 q^{-5} -2 q^{-6} +6 q^{-7} +5 q^{-8} +3 q^{-9} -3 q^{-10} -6 q^{-11} -5 q^{-12} +3 q^{-13} +6 q^{-14} +6 q^{-15} -6 q^{-17} -7 q^{-18} - q^{-19} +4 q^{-20} +6 q^{-21} +4 q^{-22} -3 q^{-23} -6 q^{-24} -3 q^{-25} - q^{-26} +3 q^{-27} +5 q^{-28} - q^{-30} -2 q^{-31} -3 q^{-32} - q^{-33} +2 q^{-34} + q^{-35} +2 q^{-36} + q^{-37} - q^{-38} - q^{-39} - q^{-40} - q^{-41} + q^{-42} + q^{-43} + q^{-44} - q^{-47} - q^{-51} + q^{-53} + q^{-54} + q^{-55} -2 q^{-57} -2 q^{-58} + q^{-60} + q^{-61} +2 q^{-62} -2 q^{-64} - q^{-65} + q^{-68} + q^{-69} - q^{-70} </math> |
coloured_jones_6 = <math>-q^{71}+2 q^{69}+q^{68}-q^{66}-q^{65}-3 q^{64}-2 q^{63}+4 q^{62}+4 q^{61}+q^{60}-q^{59}-2 q^{58}-6 q^{57}-5 q^{56}+5 q^{55}+9 q^{54}+5 q^{53}+2 q^{52}-4 q^{51}-12 q^{50}-14 q^{49}+2 q^{48}+17 q^{47}+14 q^{46}+11 q^{45}-4 q^{44}-20 q^{43}-29 q^{42}-7 q^{41}+20 q^{40}+24 q^{39}+24 q^{38}+3 q^{37}-19 q^{36}-40 q^{35}-18 q^{34}+13 q^{33}+23 q^{32}+31 q^{31}+11 q^{30}-12 q^{29}-39 q^{28}-20 q^{27}+8 q^{26}+18 q^{25}+28 q^{24}+12 q^{23}-11 q^{22}-36 q^{21}-16 q^{20}+10 q^{19}+18 q^{18}+24 q^{17}+10 q^{16}-13 q^{15}-35 q^{14}-14 q^{13}+11 q^{12}+19 q^{11}+21 q^{10}+9 q^9-12 q^8-32 q^7-12 q^6+8 q^5+16 q^4+18 q^3+10 q^2-9 q-26-10 q^{-1} +5 q^{-2} +11 q^{-3} +13 q^{-4} +11 q^{-5} -5 q^{-6} -19 q^{-7} -7 q^{-8} +5 q^{-10} +7 q^{-11} +12 q^{-12} -11 q^{-14} -2 q^{-15} -4 q^{-16} - q^{-17} +9 q^{-19} +3 q^{-20} -3 q^{-21} +5 q^{-22} -3 q^{-23} -4 q^{-24} -8 q^{-25} +3 q^{-26} + q^{-28} +11 q^{-29} +2 q^{-30} - q^{-31} -10 q^{-32} -3 q^{-33} -7 q^{-34} - q^{-35} +12 q^{-36} +6 q^{-37} +5 q^{-38} -4 q^{-39} -3 q^{-40} -11 q^{-41} -6 q^{-42} +6 q^{-43} +3 q^{-44} +7 q^{-45} +3 q^{-46} +3 q^{-47} -7 q^{-48} -6 q^{-49} + q^{-50} -3 q^{-51} +2 q^{-52} +3 q^{-53} +5 q^{-54} - q^{-55} - q^{-56} +2 q^{-57} -4 q^{-58} - q^{-59} - q^{-60} + q^{-61} - q^{-62} +5 q^{-64} -2 q^{-65} + q^{-66} - q^{-68} -2 q^{-69} -2 q^{-70} +4 q^{-71} -3 q^{-72} + q^{-73} + q^{-74} + q^{-75} - q^{-77} +4 q^{-78} -4 q^{-79} - q^{-80} - q^{-81} +5 q^{-85} - q^{-86} - q^{-88} - q^{-89} -2 q^{-90} - q^{-91} +3 q^{-92} + q^{-94} - q^{-97} - q^{-98} + q^{-99} </math> |
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, 125]]</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, 8, 4, 9], X[5, 14, 6, 15], X[20, 16, 1, 15], 
 
  X[16, 10, 17, 9], X[18, 12, 19, 11], X[10, 18, 11, 17], 
 
  X[12, 20, 13, 19], X[13, 6, 14, 7], X[7, 2, 8, 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, 125]]</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, -3, 9, -10, 2, 5, -7, 6, -8, -9, 3, 4, -5, 7, 
 
  -6, 8, -4]</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, 125]]</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, 8, 14, 2, -16, -18, 6, -20, -10, -12]</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, 125]]</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[3, {1, 1, 1, 1, 1, -2, -1, -1, -1, -2}]</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>{3, 10}</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, 125]]</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>3</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, 125]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:10_125_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, 125]]&) /@ {
                    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, 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, 125]][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   2    2            2    3
-1 + t   - -- + - + 2 t - 2 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, 125]][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 + 3 z  + 4 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, 125]}</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, 125]], KnotSignature[Knot[10, 125]]}</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>{11, 2}</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, 125]][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>      -4    -3    -2   2          2    3    4
-1 - q   + q   - q   + - + 2 q - 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, 125]}</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, 125]][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>     -12    -10    -8    -4   2       2    4    8    10    12
3 - q    - q    - q   + q   + -- + 2 q  + q  - q  - q   - q
                               2
                              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, 125]][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                     4
    3       2       2   4 z       2  2      4   z     2  4    6
7 - -- - 3 a  + 11 z  - ---- - 4 a  z  + 6 z  - -- - a  z  + z
     2                    2                      2
    a                    a                      a</nowiki></code></td></tr>
</table>
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<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, 125]][a, z]</nowiki></code></td></tr>
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<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
    3       2   z    z    6 z              3         2   z    6 z
7 + -- + 3 a  + -- - -- - --- - 8 a z - 4 a  z - 15 z  + -- - ---- - 
     2           5    3    a                              4     2
    a           a    a                                   a     a
 
             3      3                                   4
     2  2   z    8 z          3       3  3       4   2 z        2  4
  8 a  z  + -- + ---- + 17 a z  + 10 a  z  + 13 z  + ---- + 11 a  z  - 
             3    a                                    2
            a                                         a
 
     5                                         7
  5 z          5      3  5      6      2  6   z         7    3  7
  ---- - 11 a z  - 6 a  z  - 6 z  - 6 a  z  + -- + 2 a z  + a  z  + 
   a                                          a
 
   8    2  8
  z  + 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, 125]], Vassiliev[3][Knot[10, 125]]}</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>{3, 0}</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, 125]][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>       3     1       1       1       1      1     q    5      5  2
2 q + q  + ----- + ----- + ----- + ----- + ---- + - + q  t + q  t  + 
            9  5    5  4    5  3    3  2      2   t
           q  t    q  t    q  t    q  t    q t
 
   9  3
  q  t</nowiki></code></td></tr>
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<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, 125], 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> -13    -12    -11    2     -9   2    2    2    2     -2   2    2
q    - q    - q    + --- - q   - -- + -- - -- + -- - q   + - + q  - 
                      10          8    7    5    4         q
                     q           q    q    q    q
 
   3    4    6    8    9    10    11
  q  + q  - q  + q  - q  - q   + q</nowiki></code></td></tr>
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