View source for 10 127

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{{Rolfsen Knot Page|
n = 10 |
k = 127 |
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:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.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:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]]</td></tr>
</table> |
braid_crossings = 10 |
braid_width     = 3 |
braid_index     = 3 |
same_alexander  = [[10_150]], [[K11n51]],  |
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%>-8</td    ><td width=7.69231%>-7</td    ><td width=7.69231%>-6</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=15.3846%>&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 bgcolor=yellow>2</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>1</td><td bgcolor=yellow>1</td><td>0</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 bgcolor=yellow>3</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>2</td></tr>
<tr align=center><td>-9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>1</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>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>-13</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>-15</td><td>&nbsp;</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>-2</td></tr>
<tr align=center><td>-17</td><td>&nbsp;</td><td bgcolor=yellow>1</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>1</td></tr>
<tr align=center><td>-19</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>-1</td></tr>
<tr align=center><td>-21</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^{-3} +2 q^{-4} -4 q^{-5} + q^{-6} +8 q^{-7} -9 q^{-8} -4 q^{-9} +17 q^{-10} -12 q^{-11} -11 q^{-12} +25 q^{-13} -12 q^{-14} -17 q^{-15} +28 q^{-16} -9 q^{-17} -17 q^{-18} +22 q^{-19} -4 q^{-20} -12 q^{-21} +11 q^{-22} -6 q^{-24} +4 q^{-25} -2 q^{-27} + q^{-28} </math> |
coloured_jones_3 = <math>2 q^{-4} -6 q^{-7} +4 q^{-8} +7 q^{-9} +3 q^{-10} -16 q^{-11} -4 q^{-12} +14 q^{-13} +19 q^{-14} -22 q^{-15} -23 q^{-16} +12 q^{-17} +40 q^{-18} -12 q^{-19} -45 q^{-20} +56 q^{-22} +6 q^{-23} -61 q^{-24} -14 q^{-25} +65 q^{-26} +22 q^{-27} -68 q^{-28} -26 q^{-29} +65 q^{-30} +32 q^{-31} -62 q^{-32} -31 q^{-33} +49 q^{-34} +36 q^{-35} -42 q^{-36} -29 q^{-37} +25 q^{-38} +27 q^{-39} -16 q^{-40} -19 q^{-41} +7 q^{-42} +13 q^{-43} -3 q^{-44} -8 q^{-45} +2 q^{-46} +4 q^{-47} - q^{-48} -3 q^{-49} +2 q^{-50} + q^{-51} -2 q^{-53} + q^{-54} </math> |
coloured_jones_4 = <math> q^{-4} +2 q^{-5} -4 q^{-7} -2 q^{-8} -3 q^{-9} +9 q^{-10} +12 q^{-11} -5 q^{-12} -8 q^{-13} -25 q^{-14} +6 q^{-15} +33 q^{-16} +11 q^{-17} +8 q^{-18} -57 q^{-19} -27 q^{-20} +32 q^{-21} +34 q^{-22} +63 q^{-23} -62 q^{-24} -69 q^{-25} -13 q^{-26} +26 q^{-27} +138 q^{-28} -24 q^{-29} -85 q^{-30} -80 q^{-31} -24 q^{-32} +196 q^{-33} +35 q^{-34} -68 q^{-35} -136 q^{-36} -89 q^{-37} +229 q^{-38} +84 q^{-39} -41 q^{-40} -170 q^{-41} -140 q^{-42} +242 q^{-43} +115 q^{-44} -15 q^{-45} -187 q^{-46} -172 q^{-47} +234 q^{-48} +131 q^{-49} +13 q^{-50} -176 q^{-51} -189 q^{-52} +187 q^{-53} +125 q^{-54} +51 q^{-55} -128 q^{-56} -181 q^{-57} +109 q^{-58} +85 q^{-59} +75 q^{-60} -54 q^{-61} -133 q^{-62} +38 q^{-63} +25 q^{-64} +64 q^{-65} + q^{-66} -68 q^{-67} +11 q^{-68} -14 q^{-69} +31 q^{-70} +14 q^{-71} -24 q^{-72} +11 q^{-73} -17 q^{-74} +8 q^{-75} +6 q^{-76} -9 q^{-77} +11 q^{-78} -7 q^{-79} + q^{-80} + q^{-81} -5 q^{-82} +5 q^{-83} - q^{-84} + q^{-85} -2 q^{-87} + q^{-88} </math> |
coloured_jones_5 = <math>2 q^{-4} +2 q^{-6} -2 q^{-7} -6 q^{-8} -6 q^{-9} +6 q^{-10} +4 q^{-11} +15 q^{-12} +12 q^{-13} -14 q^{-14} -28 q^{-15} -15 q^{-16} -8 q^{-17} +30 q^{-18} +56 q^{-19} +23 q^{-20} -34 q^{-21} -52 q^{-22} -70 q^{-23} -11 q^{-24} +79 q^{-25} +97 q^{-26} +45 q^{-27} -26 q^{-28} -125 q^{-29} -125 q^{-30} -5 q^{-31} +102 q^{-32} +158 q^{-33} +124 q^{-34} -64 q^{-35} -206 q^{-36} -183 q^{-37} -43 q^{-38} +178 q^{-39} +304 q^{-40} +146 q^{-41} -152 q^{-42} -335 q^{-43} -284 q^{-44} +51 q^{-45} +400 q^{-46} +399 q^{-47} +31 q^{-48} -389 q^{-49} -509 q^{-50} -149 q^{-51} +393 q^{-52} +594 q^{-53} +237 q^{-54} -365 q^{-55} -660 q^{-56} -321 q^{-57} +344 q^{-58} +707 q^{-59} +388 q^{-60} -326 q^{-61} -741 q^{-62} -433 q^{-63} +301 q^{-64} +767 q^{-65} +478 q^{-66} -289 q^{-67} -775 q^{-68} -511 q^{-69} +251 q^{-70} +779 q^{-71} +549 q^{-72} -217 q^{-73} -750 q^{-74} -570 q^{-75} +131 q^{-76} +709 q^{-77} +598 q^{-78} -70 q^{-79} -611 q^{-80} -579 q^{-81} -47 q^{-82} +502 q^{-83} +557 q^{-84} +107 q^{-85} -353 q^{-86} -469 q^{-87} -188 q^{-88} +218 q^{-89} +377 q^{-90} +201 q^{-91} -93 q^{-92} -258 q^{-93} -195 q^{-94} +6 q^{-95} +157 q^{-96} +152 q^{-97} +42 q^{-98} -73 q^{-99} -105 q^{-100} -54 q^{-101} +19 q^{-102} +59 q^{-103} +47 q^{-104} +8 q^{-105} -25 q^{-106} -33 q^{-107} -16 q^{-108} +9 q^{-109} +13 q^{-110} +14 q^{-111} +7 q^{-112} -9 q^{-113} -10 q^{-114} - q^{-115} -3 q^{-116} +2 q^{-117} +9 q^{-118} + q^{-119} -4 q^{-120} + q^{-121} -3 q^{-122} -3 q^{-123} +3 q^{-124} +2 q^{-125} - q^{-126} + q^{-127} -2 q^{-129} + q^{-130} </math> |
coloured_jones_6 = <math> q^{-3} +2 q^{-4} -2 q^{-7} -4 q^{-8} -8 q^{-9} -3 q^{-10} +9 q^{-11} +16 q^{-12} +13 q^{-13} +8 q^{-14} - q^{-15} -37 q^{-16} -41 q^{-17} -22 q^{-18} +21 q^{-19} +44 q^{-20} +62 q^{-21} +73 q^{-22} -19 q^{-23} -83 q^{-24} -122 q^{-25} -66 q^{-26} -20 q^{-27} +79 q^{-28} +207 q^{-29} +133 q^{-30} +30 q^{-31} -140 q^{-32} -168 q^{-33} -237 q^{-34} -128 q^{-35} +165 q^{-36} +258 q^{-37} +298 q^{-38} +117 q^{-39} +14 q^{-40} -348 q^{-41} -470 q^{-42} -225 q^{-43} +16 q^{-44} +368 q^{-45} +475 q^{-46} +590 q^{-47} -9 q^{-48} -527 q^{-49} -691 q^{-50} -629 q^{-51} -86 q^{-52} +489 q^{-53} +1213 q^{-54} +738 q^{-55} -28 q^{-56} -788 q^{-57} -1288 q^{-58} -950 q^{-59} -38 q^{-60} +1470 q^{-61} +1492 q^{-62} +844 q^{-63} -395 q^{-64} -1602 q^{-65} -1819 q^{-66} -878 q^{-67} +1303 q^{-68} +1954 q^{-69} +1696 q^{-70} +234 q^{-71} -1564 q^{-72} -2423 q^{-73} -1661 q^{-74} +952 q^{-75} +2121 q^{-76} +2292 q^{-77} +783 q^{-78} -1381 q^{-79} -2751 q^{-80} -2189 q^{-81} +659 q^{-82} +2147 q^{-83} +2629 q^{-84} +1119 q^{-85} -1231 q^{-86} -2915 q^{-87} -2479 q^{-88} +484 q^{-89} +2145 q^{-90} +2817 q^{-91} +1314 q^{-92} -1121 q^{-93} -3001 q^{-94} -2667 q^{-95} +308 q^{-96} +2095 q^{-97} +2937 q^{-98} +1528 q^{-99} -905 q^{-100} -2958 q^{-101} -2827 q^{-102} -46 q^{-103} +1822 q^{-104} +2907 q^{-105} +1814 q^{-106} -411 q^{-107} -2582 q^{-108} -2826 q^{-109} -580 q^{-110} +1161 q^{-111} +2490 q^{-112} +1970 q^{-113} +297 q^{-114} -1740 q^{-115} -2399 q^{-116} -1001 q^{-117} +269 q^{-118} +1601 q^{-119} +1699 q^{-120} +834 q^{-121} -702 q^{-122} -1524 q^{-123} -971 q^{-124} -381 q^{-125} +604 q^{-126} +1022 q^{-127} +867 q^{-128} +9 q^{-129} -620 q^{-130} -544 q^{-131} -504 q^{-132} -11 q^{-133} +358 q^{-134} +529 q^{-135} +196 q^{-136} -107 q^{-137} -125 q^{-138} -298 q^{-139} -157 q^{-140} +22 q^{-141} +204 q^{-142} +110 q^{-143} +26 q^{-144} +53 q^{-145} -104 q^{-146} -95 q^{-147} -48 q^{-148} +55 q^{-149} +23 q^{-150} +12 q^{-151} +67 q^{-152} -21 q^{-153} -32 q^{-154} -33 q^{-155} +14 q^{-156} -5 q^{-157} -7 q^{-158} +39 q^{-159} -4 q^{-161} -15 q^{-162} +5 q^{-163} -7 q^{-164} -11 q^{-165} +17 q^{-166} +2 q^{-167} +3 q^{-168} -5 q^{-169} +3 q^{-170} -3 q^{-171} -7 q^{-172} +5 q^{-173} +2 q^{-175} - q^{-176} + q^{-177} -2 q^{-179} + q^{-180} </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>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</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, 127]]</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, 8, 4, 9], X[14, 6, 15, 5], X[15, 20, 16, 1], 
 
  X[9, 16, 10, 17], X[11, 18, 12, 19], X[17, 10, 18, 11], 
 
  X[19, 12, 20, 13], X[6, 14, 7, 13], X[7, 2, 8, 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, 127]]</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, 3, -9, -10, 2, -5, 7, -6, 8, 9, -3, -4, 5, -7, 
 
  6, -8, 4]</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, 127]]</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, 8, -14, 2, 16, 18, -6, 20, 10, 12]</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, 127]]</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, -1, -1, -2, 1, 1, -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>{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>{3, 10}</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, 127]]</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>3</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, 127]]]</nowiki></pre></td></tr><tr><td></td><td  align=left>[[Image:10_127_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, 127]]&) /@ {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, 3, 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, 127]][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>     -3   4    6            2    3
7 - t   + -- - - - 6 t + 4 t  - 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, 127]][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 + z  - 2 z  - 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, 127], Knot[10, 150], Knot[11, NonAlternating, 51]}</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, 127]], KnotSignature[Knot[10, 127]]}</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>{29, -4}</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, 127]][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> -10   2    3    5    5    5    4    2    2
q    - -- + -- - -- + -- - -- + -- - -- + --
        9    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, 127]}</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, 127]][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> -30    -26    2     -20    3     -12    3     -8   2
q    + q    - --- - q    - --- + q    + --- + q   + --
               22           18           10          6
              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, 127]][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>   4      6      8      4  2      6  2      8  2      4  4      6  4
5 a  - 6 a  + 2 a  + 7 a  z  - 9 a  z  + 3 a  z  + 2 a  z  - 5 a  z  + 
 
   8  4    6  6
  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, 127]][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>   4      6      8      5        7        9      11        4  2
5 a  + 6 a  + 2 a  - 5 a  z - 8 a  z - 2 a  z + a   z - 9 a  z  - 
 
      6  2      8  2    10  2      12  2      5  3       7  3
  14 a  z  - 2 a  z  + a   z  - 2 a   z  + 5 a  z  + 16 a  z  + 
 
     9  3      11  3      4  4       6  4      8  4      10  4
  7 a  z  - 4 a   z  + 3 a  z  + 11 a  z  + 4 a  z  - 3 a   z  + 
 
   12  4      5  5       7  5      9  5      11  5      6  6
  a   z  - 3 a  z  - 10 a  z  - 5 a  z  + 2 a   z  - 4 a  z  - 
 
     8  6      10  6    5  7      7  7      9  7    6  8    8  8
  2 a  z  + 2 a   z  + a  z  + 3 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, 127]], Vassiliev[3][Knot[10, 127]]}</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>{1, 1}</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, 127]][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> -5   2      1        1        1        2        1        3
q   + -- + ------ + ------ + ------ + ------ + ------ + ------ + 
       3    21  8    19  7    17  7    17  6    15  6    15  5
      q    q   t    q   t    q   t    q   t    q   t    q   t
 
    2        2        3        3        2       1       3      1
  ------ + ------ + ------ + ------ + ----- + ----- + ----- + ---- + 
   13  5    13  4    11  4    11  3    9  3    9  2    7  2    7
  q   t    q   t    q   t    q   t    q  t    q  t    q  t    q  t
 
   1
  ----
   5
  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, 127], 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> -28    2     4     6    11    12     4    22    17     9    28
q    - --- + --- - --- + --- - --- - --- + --- - --- - --- + --- - 
        27    25    24    22    21    20    19    18    17    16
       q     q     q     q     q     q     q     q     q     q
 
  17    12    25    11    12    17    4    9    8     -6   4    2     -3
  --- - --- + --- - --- - --- + --- - -- - -- + -- + q   - -- + -- + q
   15    14    13    12    11    10    9    8    7          5    4
  q     q     q     q     q     q     q    q    q          q    q</nowiki></pre></td></tr>
         </table>  }}