View source for 8 2

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{{Rolfsen Knot Page|
n = 8 |
k = 2 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-2,7,-5,8,-6,3,-4,2,-7,5,-8,6/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:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.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:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]]</td></tr>
</table> |
braid_crossings = 8 |
braid_width     = 3 |
braid_index     = 3 |
same_alexander  = [[K11n6]],  |
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%>-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=7.69231%>1</td    ><td width=7.69231%>2</td    ><td width=15.3846%>&chi;</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>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 bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>&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>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>1</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>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>-7</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>&nbsp;</td><td>1</td></tr>
<tr align=center><td>-9</td><td>&nbsp;</td><td>&nbsp;</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>0</td></tr>
<tr align=center><td>-11</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>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr>
<tr align=center><td>-13</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>-15</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>-17</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^2-q-1+3 q^{-1} - q^{-2} -3 q^{-3} +5 q^{-4} -5 q^{-6} +5 q^{-7} + q^{-8} -7 q^{-9} +5 q^{-10} +2 q^{-11} -7 q^{-12} +4 q^{-13} +3 q^{-14} -6 q^{-15} +3 q^{-16} +2 q^{-17} -4 q^{-18} +3 q^{-19} -2 q^{-21} + q^{-22} </math> |
coloured_jones_3 = <math>q^6-q^5-q^4+3 q^2-3-2 q^{-1} +5 q^{-2} +2 q^{-3} -3 q^{-4} -5 q^{-5} +5 q^{-6} +4 q^{-7} -2 q^{-8} -6 q^{-9} +3 q^{-10} +4 q^{-11} -6 q^{-13} +2 q^{-14} +3 q^{-15} -4 q^{-17} + q^{-18} + q^{-19} + q^{-20} - q^{-21} - q^{-22} + q^{-24} +2 q^{-25} -2 q^{-26} - q^{-27} +2 q^{-29} - q^{-30} + q^{-31} -2 q^{-32} + q^{-34} +2 q^{-35} -2 q^{-36} -2 q^{-37} +2 q^{-38} + q^{-39} -2 q^{-41} + q^{-42} </math> |
coloured_jones_4 = <math>q^{12}-q^{11}-q^{10}+4 q^7-q^6-2 q^5-2 q^4-3 q^3+8 q^2+q-1-3 q^{-1} -8 q^{-2} +9 q^{-3} +2 q^{-4} +2 q^{-5} - q^{-6} -12 q^{-7} +9 q^{-8} +3 q^{-10} +2 q^{-11} -12 q^{-12} +10 q^{-13} -3 q^{-14} + q^{-15} +3 q^{-16} -12 q^{-17} +14 q^{-18} -4 q^{-19} -3 q^{-20} + q^{-21} -11 q^{-22} +20 q^{-23} -3 q^{-24} -7 q^{-25} -2 q^{-26} -11 q^{-27} +25 q^{-28} -2 q^{-29} -11 q^{-30} -4 q^{-31} -10 q^{-32} +29 q^{-33} - q^{-34} -15 q^{-35} -6 q^{-36} -8 q^{-37} +32 q^{-38} + q^{-39} -18 q^{-40} -9 q^{-41} -7 q^{-42} +31 q^{-43} +3 q^{-44} -14 q^{-45} -10 q^{-46} -10 q^{-47} +25 q^{-48} +5 q^{-49} -8 q^{-50} -7 q^{-51} -11 q^{-52} +17 q^{-53} +3 q^{-54} -3 q^{-55} -2 q^{-56} -10 q^{-57} +10 q^{-58} + q^{-59} -6 q^{-62} +4 q^{-63} + q^{-65} -2 q^{-67} + q^{-68} </math> |
coloured_jones_5 = <math>q^{20}-q^{19}-q^{18}+q^{15}+3 q^{14}-3 q^{12}-2 q^{11}-2 q^{10}+6 q^8+4 q^7-q^6-4 q^5-5 q^4-4 q^3+5 q^2+7 q+3- q^{-1} -6 q^{-2} -7 q^{-3} +2 q^{-4} +5 q^{-5} +4 q^{-6} +2 q^{-7} -3 q^{-8} -7 q^{-9} +3 q^{-10} +3 q^{-11} + q^{-12} -3 q^{-14} -5 q^{-15} +6 q^{-16} +7 q^{-17} -5 q^{-19} -8 q^{-20} -8 q^{-21} +11 q^{-22} +14 q^{-23} +5 q^{-24} -7 q^{-25} -18 q^{-26} -14 q^{-27} +12 q^{-28} +22 q^{-29} +12 q^{-30} -6 q^{-31} -25 q^{-32} -22 q^{-33} +9 q^{-34} +29 q^{-35} +20 q^{-36} -3 q^{-37} -29 q^{-38} -29 q^{-39} +4 q^{-40} +33 q^{-41} +27 q^{-42} -32 q^{-44} -33 q^{-45} +35 q^{-47} +34 q^{-48} + q^{-49} -36 q^{-50} -37 q^{-51} -2 q^{-52} +39 q^{-53} +41 q^{-54} + q^{-55} -40 q^{-56} -42 q^{-57} -4 q^{-58} +39 q^{-59} +46 q^{-60} +5 q^{-61} -39 q^{-62} -43 q^{-63} -10 q^{-64} +33 q^{-65} +45 q^{-66} +9 q^{-67} -29 q^{-68} -36 q^{-69} -13 q^{-70} +23 q^{-71} +36 q^{-72} +7 q^{-73} -19 q^{-74} -24 q^{-75} -9 q^{-76} +14 q^{-77} +22 q^{-78} +5 q^{-79} -13 q^{-80} -14 q^{-81} -3 q^{-82} +8 q^{-83} +10 q^{-84} +3 q^{-85} -6 q^{-86} -8 q^{-87} - q^{-88} +5 q^{-89} +2 q^{-90} +3 q^{-91} -2 q^{-92} -4 q^{-93} +2 q^{-95} + q^{-97} -2 q^{-99} + q^{-100} </math> |
coloured_jones_6 = <math>q^{30}-q^{29}-q^{28}+q^{25}+4 q^{23}-q^{22}-3 q^{21}-2 q^{20}-2 q^{19}-q^{17}+10 q^{16}+2 q^{15}-q^{14}-3 q^{13}-5 q^{12}-4 q^{11}-8 q^{10}+13 q^9+5 q^8+4 q^7+q^6-3 q^5-6 q^4-16 q^3+11 q^2+2 q+6+3 q^{-1} +3 q^{-2} -2 q^{-3} -19 q^{-4} +12 q^{-5} -2 q^{-6} +4 q^{-7} - q^{-8} +3 q^{-9} -19 q^{-11} +18 q^{-12} + q^{-13} +8 q^{-14} -5 q^{-15} -2 q^{-16} -6 q^{-17} -26 q^{-18} +20 q^{-19} +8 q^{-20} +21 q^{-21} -3 q^{-23} -14 q^{-24} -42 q^{-25} +11 q^{-26} +10 q^{-27} +35 q^{-28} +13 q^{-29} +6 q^{-30} -16 q^{-31} -57 q^{-32} -5 q^{-33} +3 q^{-34} +42 q^{-35} +25 q^{-36} +21 q^{-37} -8 q^{-38} -65 q^{-39} -20 q^{-40} -10 q^{-41} +40 q^{-42} +30 q^{-43} +35 q^{-44} +6 q^{-45} -65 q^{-46} -30 q^{-47} -23 q^{-48} +33 q^{-49} +29 q^{-50} +45 q^{-51} +22 q^{-52} -60 q^{-53} -35 q^{-54} -34 q^{-55} +23 q^{-56} +25 q^{-57} +51 q^{-58} +38 q^{-59} -54 q^{-60} -40 q^{-61} -42 q^{-62} +15 q^{-63} +23 q^{-64} +55 q^{-65} +48 q^{-66} -49 q^{-67} -47 q^{-68} -49 q^{-69} +11 q^{-70} +25 q^{-71} +62 q^{-72} +56 q^{-73} -49 q^{-74} -56 q^{-75} -57 q^{-76} +7 q^{-77} +29 q^{-78} +70 q^{-79} +64 q^{-80} -45 q^{-81} -60 q^{-82} -64 q^{-83} - q^{-84} +25 q^{-85} +70 q^{-86} +68 q^{-87} -33 q^{-88} -50 q^{-89} -61 q^{-90} -8 q^{-91} +13 q^{-92} +56 q^{-93} +59 q^{-94} -23 q^{-95} -32 q^{-96} -45 q^{-97} -4 q^{-98} +3 q^{-99} +37 q^{-100} +40 q^{-101} -23 q^{-102} -18 q^{-103} -27 q^{-104} +7 q^{-105} +3 q^{-106} +22 q^{-107} +22 q^{-108} -26 q^{-109} -9 q^{-110} -13 q^{-111} +11 q^{-112} +4 q^{-113} +13 q^{-114} +10 q^{-115} -22 q^{-116} -3 q^{-117} -7 q^{-118} +9 q^{-119} +2 q^{-120} +8 q^{-121} +4 q^{-122} -14 q^{-123} + q^{-124} -4 q^{-125} +5 q^{-126} +4 q^{-128} + q^{-129} -6 q^{-130} +2 q^{-131} -2 q^{-132} +2 q^{-133} + q^{-135} -2 q^{-137} + q^{-138} </math> |
coloured_jones_7 = <math>q^{42}-q^{41}-q^{40}+q^{37}+q^{35}+3 q^{34}-q^{33}-3 q^{32}-2 q^{31}-3 q^{30}+q^{29}+q^{27}+9 q^{26}+3 q^{25}-q^{24}-3 q^{23}-8 q^{22}-3 q^{21}-4 q^{20}-4 q^{19}+11 q^{18}+8 q^{17}+6 q^{16}+5 q^{15}-9 q^{14}-4 q^{13}-8 q^{12}-13 q^{11}+6 q^{10}+5 q^9+8 q^8+13 q^7-4 q^6-4 q^4-16 q^3+4 q^2-2 q+2+14 q^{-1} -5 q^{-2} + q^{-3} - q^{-4} -14 q^{-5} +10 q^{-6} +2 q^{-7} + q^{-8} +16 q^{-9} -9 q^{-10} -6 q^{-11} -8 q^{-12} -23 q^{-13} +12 q^{-14} +8 q^{-15} +12 q^{-16} +30 q^{-17} - q^{-18} -7 q^{-19} -17 q^{-20} -43 q^{-21} -7 q^{-22} +2 q^{-23} +17 q^{-24} +50 q^{-25} +20 q^{-26} +10 q^{-27} -11 q^{-28} -58 q^{-29} -32 q^{-30} -22 q^{-31} +3 q^{-32} +55 q^{-33} +41 q^{-34} +36 q^{-35} +11 q^{-36} -52 q^{-37} -44 q^{-38} -46 q^{-39} -25 q^{-40} +40 q^{-41} +44 q^{-42} +54 q^{-43} +36 q^{-44} -30 q^{-45} -35 q^{-46} -54 q^{-47} -49 q^{-48} +14 q^{-49} +28 q^{-50} +54 q^{-51} +52 q^{-52} -5 q^{-53} -12 q^{-54} -44 q^{-55} -57 q^{-56} -9 q^{-57} + q^{-58} +37 q^{-59} +55 q^{-60} +16 q^{-61} +12 q^{-62} -22 q^{-63} -52 q^{-64} -25 q^{-65} -27 q^{-66} +13 q^{-67} +49 q^{-68} +30 q^{-69} +36 q^{-70} + q^{-71} -42 q^{-72} -36 q^{-73} -49 q^{-74} -11 q^{-75} +38 q^{-76} +41 q^{-77} +57 q^{-78} +21 q^{-79} -33 q^{-80} -43 q^{-81} -67 q^{-82} -31 q^{-83} +30 q^{-84} +50 q^{-85} +73 q^{-86} +33 q^{-87} -28 q^{-88} -52 q^{-89} -80 q^{-90} -40 q^{-91} +30 q^{-92} +62 q^{-93} +85 q^{-94} +38 q^{-95} -32 q^{-96} -68 q^{-97} -90 q^{-98} -41 q^{-99} +36 q^{-100} +76 q^{-101} +97 q^{-102} +45 q^{-103} -37 q^{-104} -84 q^{-105} -103 q^{-106} -49 q^{-107} +33 q^{-108} +84 q^{-109} +108 q^{-110} +59 q^{-111} -25 q^{-112} -80 q^{-113} -109 q^{-114} -66 q^{-115} +13 q^{-116} +67 q^{-117} +103 q^{-118} +70 q^{-119} +2 q^{-120} -50 q^{-121} -92 q^{-122} -70 q^{-123} -12 q^{-124} +35 q^{-125} +73 q^{-126} +59 q^{-127} +17 q^{-128} -14 q^{-129} -54 q^{-130} -49 q^{-131} -16 q^{-132} +4 q^{-133} +36 q^{-134} +30 q^{-135} +12 q^{-136} +6 q^{-137} -19 q^{-138} -16 q^{-139} -7 q^{-140} -11 q^{-141} +9 q^{-142} +6 q^{-143} -2 q^{-144} +11 q^{-145} +5 q^{-147} +4 q^{-148} -15 q^{-149} - q^{-150} -7 q^{-151} -7 q^{-152} +11 q^{-153} +3 q^{-154} +10 q^{-155} +8 q^{-156} -10 q^{-157} -4 q^{-158} -8 q^{-159} -6 q^{-160} +8 q^{-161} +2 q^{-162} +5 q^{-163} +6 q^{-164} -6 q^{-165} - q^{-166} -4 q^{-167} -4 q^{-168} +5 q^{-169} +2 q^{-171} +2 q^{-172} -3 q^{-173} -2 q^{-176} +2 q^{-177} + q^{-179} -2 q^{-181} + q^{-182} </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><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[8, 2]]</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[5, 12, 6, 13], X[3, 11, 4, 10], X[11, 3, 12, 2], 
 
  X[7, 14, 8, 15], X[9, 16, 10, 1], X[13, 6, 14, 7], X[15, 8, 16, 9]]</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[8, 2]]</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, 4, -3, 1, -2, 7, -5, 8, -6, 3, -4, 2, -7, 5, -8, 6]</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[8, 2]]</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, 10, 12, 14, 16, 2, 6, 8]</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[8, 2]]</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, 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, 8}</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[8, 2]]</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[8, 2]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:8_2_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[8, 2]]&) /@ {
                 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, 2, {4, 5}, 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[8, 2]][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   3    3            2    3
3 - t   + -- - - - 3 t + 3 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[8, 2]][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>       4    6
1 - 3 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[8, 2], Knot[11, NonAlternating, 6]}</nowiki></code></td></tr>
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<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[8, 2]], KnotSignature[Knot[8, 2]]}</nowiki></code></td></tr>
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<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>{17, -4}</nowiki></code></td></tr>
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<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[8, 2]][q]</nowiki></code></td></tr>
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<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>     -8   2    2    3    3    2    2    1
1 + q   - -- + -- - -- + -- - -- + -- - -
           7    6    5    4    3    2   q
          q    q    q    q    q    q</nowiki></code></td></tr>
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<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>
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<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[8, 2]}</nowiki></code></td></tr>
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<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[8, 2]][q]</nowiki></code></td></tr>
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<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>     -24    -18    -16    -12    -10    -6    -4    -2
1 + q    - q    - q    - q    + q    + q   + q   + q</nowiki></code></td></tr>
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<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[8, 2]][a, z]</nowiki></code></td></tr>
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<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    6      2  2      4  2      6  2    2  4      4  4
3 a  - 3 a  + a  + 4 a  z  - 7 a  z  + 3 a  z  + a  z  - 5 a  z  + 
 
   6  4    4  6
  a  z  - a  z</nowiki></code></td></tr>
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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[8, 2]][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      4    6    3      5      7      9        2  2       4  2
-3 a  - 3 a  - a  + a  z + a  z - a  z - a  z + 7 a  z  + 12 a  z  + 
 
     6  2    8  2    10  2      3  3    5  3      7  3      9  3
  3 a  z  - a  z  + a   z  + 3 a  z  - a  z  - 2 a  z  + 2 a  z  - 
 
     2  4       4  4      6  4      8  4      3  5      5  5
  5 a  z  - 12 a  z  - 5 a  z  + 2 a  z  - 4 a  z  - 2 a  z  + 
 
     7  5    2  6      4  6      6  6    3  7    5  7
  2 a  z  + a  z  + 3 a  z  + 2 a  z  + a  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[8, 2]], Vassiliev[3][Knot[8, 2]]}</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>{0, 1}</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[8, 2]][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> -5   2      1        1        1        1        1        2
q   + -- + ------ + ------ + ------ + ------ + ------ + ------ + 
       3    17  6    15  5    13  5    13  4    11  4    11  3
      q    q   t    q   t    q   t    q   t    q   t    q   t
 
    1       1       2      1      1     t       2
  ----- + ----- + ----- + ---- + ---- + -- + q t
   9  3    9  2    7  2    7      5      3
  q  t    q  t    q  t    q  t   q  t   q</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[8, 2], 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>      -22    2     3     4     2     3     6     3     4     7     2
-1 + q    - --- + --- - --- + --- + --- - --- + --- + --- - --- + --- + 
             21    19    18    17    16    15    14    13    12    11
            q     q     q     q     q     q     q     q     q     q
 
   5    7     -8   5    5    5    3     -2   3        2
  --- - -- + q   + -- - -- + -- - -- - q   + - - q + q
   10    9          7    6    4    3         q
  q     q          q    q    q    q</nowiki></code></td></tr>
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