View source for 10 8

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{{Rolfsen Knot Page|
n = 10 |
k = 8 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,6,-4,5,-3,1,-2,9,-7,10,-8,3,-5,4,-6,2,-9,7,-10,8/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]][[Image:BraidPart0.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:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.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:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.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> |
braid_crossings = 11 |
braid_width     = 4 |
braid_index     = 4 |
same_alexander  =  |
same_jones      =  |
khovanov_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%>-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=6.66667%>3</td    ><td width=6.66667%>4</td    ><td width=13.3333%>&chi;</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>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td>1</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 bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>&nbsp;</td><td>0</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>2</td><td bgcolor=yellow>1</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>&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>-3</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>2</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>&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>-7</td><td>&nbsp;</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>&nbsp;</td><td>0</td></tr>
<tr align=center><td>-9</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>&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>&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>2</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>-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>&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>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
</table> |
coloured_jones_2 = <math>q^8-q^7-q^6+3 q^5-q^4-4 q^3+5 q^2+q-7+6 q^{-1} +3 q^{-2} -10 q^{-3} +6 q^{-4} +5 q^{-5} -11 q^{-6} +5 q^{-7} +7 q^{-8} -10 q^{-9} +3 q^{-10} +6 q^{-11} -8 q^{-12} +2 q^{-13} +5 q^{-14} -7 q^{-15} +2 q^{-16} +4 q^{-17} -5 q^{-18} +2 q^{-19} + q^{-20} -2 q^{-21} + q^{-22} </math> |
coloured_jones_3 = <math>q^{18}-q^{17}-q^{16}+3 q^{14}-3 q^{12}-3 q^{11}+5 q^{10}+3 q^9-2 q^8-7 q^7+3 q^6+6 q^5+q^4-8 q^3-q^2+5 q+4-6 q^{-1} -2 q^{-2} +3 q^{-3} +4 q^{-4} -4 q^{-5} - q^{-6} +2 q^{-7} +3 q^{-8} -3 q^{-9} - q^{-10} +2 q^{-11} + q^{-12} -3 q^{-13} + q^{-14} +2 q^{-15} -3 q^{-16} -3 q^{-17} +5 q^{-18} +4 q^{-19} -7 q^{-20} -4 q^{-21} +6 q^{-22} +6 q^{-23} -6 q^{-24} -5 q^{-25} +3 q^{-26} +5 q^{-27} - q^{-28} -3 q^{-29} - q^{-30} +3 q^{-31} + q^{-32} -2 q^{-33} - q^{-34} + q^{-35} + q^{-36} -2 q^{-37} + q^{-38} + q^{-40} -2 q^{-41} + q^{-42} </math> |
coloured_jones_4 = <math>q^{32}-q^{31}-q^{30}+4 q^{27}-q^{26}-2 q^{25}-2 q^{24}-4 q^{23}+8 q^{22}+2 q^{21}-2 q^{19}-11 q^{18}+7 q^{17}+2 q^{16}+5 q^{15}+4 q^{14}-15 q^{13}+4 q^{12}-4 q^{11}+5 q^{10}+11 q^9-12 q^8+7 q^7-11 q^6-q^5+13 q^4-10 q^3+16 q^2-12 q-7+10 q^{-1} -14 q^{-2} +24 q^{-3} -8 q^{-4} -8 q^{-5} +9 q^{-6} -22 q^{-7} +25 q^{-8} -5 q^{-9} -5 q^{-10} +14 q^{-11} -27 q^{-12} +20 q^{-13} -7 q^{-14} -2 q^{-15} +21 q^{-16} -29 q^{-17} +15 q^{-18} -9 q^{-19} +26 q^{-21} -30 q^{-22} +9 q^{-23} -9 q^{-24} +6 q^{-25} +32 q^{-26} -34 q^{-27} - q^{-28} -11 q^{-29} +13 q^{-30} +40 q^{-31} -32 q^{-32} -10 q^{-33} -18 q^{-34} +13 q^{-35} +46 q^{-36} -23 q^{-37} -12 q^{-38} -22 q^{-39} +6 q^{-40} +41 q^{-41} -14 q^{-42} -5 q^{-43} -20 q^{-44} - q^{-45} +29 q^{-46} -9 q^{-47} +3 q^{-48} -13 q^{-49} -4 q^{-50} +16 q^{-51} -8 q^{-52} +7 q^{-53} -6 q^{-54} -3 q^{-55} +8 q^{-56} -8 q^{-57} +7 q^{-58} -2 q^{-59} -2 q^{-60} +3 q^{-61} -5 q^{-62} +4 q^{-63} - q^{-64} + q^{-66} -2 q^{-67} + q^{-68} </math> |
coloured_jones_5 = <math>q^{50}-q^{49}-q^{48}+q^{45}+3 q^{44}-3 q^{42}-2 q^{41}-2 q^{40}-q^{39}+6 q^{38}+5 q^{37}-3 q^{35}-5 q^{34}-7 q^{33}+2 q^{32}+7 q^{31}+5 q^{30}+4 q^{29}-2 q^{28}-9 q^{27}-5 q^{26}-q^{25}+2 q^{24}+8 q^{23}+7 q^{22}-2 q^{21}-2 q^{20}-6 q^{19}-9 q^{18}+7 q^{16}+6 q^{15}+8 q^{14}+2 q^{13}-11 q^{12}-11 q^{11}-3 q^{10}+2 q^9+13 q^8+11 q^7-q^6-10 q^5-11 q^4-6 q^3+8 q^2+11 q+4- q^{-1} -6 q^{-2} -8 q^{-3} +3 q^{-4} +4 q^{-5} -3 q^{-6} + q^{-7} +4 q^{-8} + q^{-9} +7 q^{-10} -3 q^{-11} -17 q^{-12} -9 q^{-13} +7 q^{-14} +18 q^{-15} +20 q^{-16} -2 q^{-17} -30 q^{-18} -27 q^{-19} + q^{-20} +29 q^{-21} +39 q^{-22} +8 q^{-23} -35 q^{-24} -45 q^{-25} -12 q^{-26} +32 q^{-27} +52 q^{-28} +18 q^{-29} -34 q^{-30} -55 q^{-31} -20 q^{-32} +34 q^{-33} +57 q^{-34} +21 q^{-35} -36 q^{-36} -63 q^{-37} -21 q^{-38} +42 q^{-39} +67 q^{-40} +25 q^{-41} -45 q^{-42} -79 q^{-43} -30 q^{-44} +51 q^{-45} +86 q^{-46} +37 q^{-47} -48 q^{-48} -92 q^{-49} -49 q^{-50} +47 q^{-51} +94 q^{-52} +51 q^{-53} -38 q^{-54} -89 q^{-55} -55 q^{-56} +31 q^{-57} +82 q^{-58} +53 q^{-59} -25 q^{-60} -71 q^{-61} -48 q^{-62} +20 q^{-63} +59 q^{-64} +41 q^{-65} -13 q^{-66} -51 q^{-67} -35 q^{-68} +13 q^{-69} +40 q^{-70} +26 q^{-71} -8 q^{-72} -31 q^{-73} -21 q^{-74} +7 q^{-75} +23 q^{-76} +14 q^{-77} -7 q^{-78} -13 q^{-79} -8 q^{-80} + q^{-81} +10 q^{-82} +6 q^{-83} -4 q^{-84} -3 q^{-85} -2 q^{-86} -2 q^{-87} +3 q^{-88} +4 q^{-89} -2 q^{-90} -3 q^{-93} + q^{-94} +2 q^{-95} - q^{-96} + q^{-98} -2 q^{-99} + q^{-100} </math> |
coloured_jones_6 = <math>q^{72}-q^{71}-q^{70}+q^{67}+4 q^{65}-q^{64}-3 q^{63}-2 q^{62}-2 q^{61}-2 q^{59}+10 q^{58}+3 q^{57}-2 q^{55}-5 q^{54}-4 q^{53}-12 q^{52}+10 q^{51}+5 q^{50}+6 q^{49}+5 q^{48}+2 q^{47}-q^{46}-21 q^{45}+3 q^{44}-5 q^{43}+2 q^{42}+4 q^{41}+12 q^{40}+14 q^{39}-15 q^{38}+8 q^{37}-12 q^{36}-9 q^{35}-13 q^{34}+4 q^{33}+18 q^{32}-6 q^{31}+26 q^{30}+q^{29}-2 q^{28}-25 q^{27}-12 q^{26}+2 q^{25}-18 q^{24}+31 q^{23}+14 q^{22}+20 q^{21}-14 q^{20}-9 q^{19}-6 q^{18}-39 q^{17}+16 q^{16}+6 q^{15}+26 q^{14}-3 q^{13}+8 q^{12}+9 q^{11}-38 q^{10}+10 q^9-10 q^8+12 q^7-17 q^6+7 q^5+24 q^4-21 q^3+30 q^2-3 q+7-42 q^{-1} -21 q^{-2} +13 q^{-3} -18 q^{-4} +54 q^{-5} +27 q^{-6} +33 q^{-7} -47 q^{-8} -51 q^{-9} -19 q^{-10} -43 q^{-11} +57 q^{-12} +54 q^{-13} +77 q^{-14} -24 q^{-15} -60 q^{-16} -48 q^{-17} -82 q^{-18} +34 q^{-19} +60 q^{-20} +116 q^{-21} +15 q^{-22} -47 q^{-23} -61 q^{-24} -117 q^{-25} -2 q^{-26} +44 q^{-27} +140 q^{-28} +54 q^{-29} -20 q^{-30} -56 q^{-31} -137 q^{-32} -38 q^{-33} +13 q^{-34} +142 q^{-35} +80 q^{-36} +11 q^{-37} -34 q^{-38} -135 q^{-39} -63 q^{-40} -21 q^{-41} +128 q^{-42} +84 q^{-43} +31 q^{-44} -9 q^{-45} -122 q^{-46} -70 q^{-47} -42 q^{-48} +118 q^{-49} +84 q^{-50} +38 q^{-51} - q^{-52} -123 q^{-53} -82 q^{-54} -52 q^{-55} +125 q^{-56} +105 q^{-57} +59 q^{-58} +2 q^{-59} -141 q^{-60} -118 q^{-61} -79 q^{-62} +126 q^{-63} +137 q^{-64} +100 q^{-65} +26 q^{-66} -141 q^{-67} -151 q^{-68} -120 q^{-69} +97 q^{-70} +139 q^{-71} +126 q^{-72} +59 q^{-73} -108 q^{-74} -143 q^{-75} -134 q^{-76} +60 q^{-77} +104 q^{-78} +108 q^{-79} +67 q^{-80} -68 q^{-81} -103 q^{-82} -107 q^{-83} +43 q^{-84} +66 q^{-85} +67 q^{-86} +45 q^{-87} -49 q^{-88} -65 q^{-89} -65 q^{-90} +47 q^{-91} +44 q^{-92} +34 q^{-93} +17 q^{-94} -47 q^{-95} -40 q^{-96} -33 q^{-97} +53 q^{-98} +32 q^{-99} +14 q^{-100} -44 q^{-102} -22 q^{-103} -13 q^{-104} +46 q^{-105} +19 q^{-106} + q^{-107} -4 q^{-108} -32 q^{-109} -6 q^{-110} -2 q^{-111} +29 q^{-112} +5 q^{-113} -4 q^{-114} - q^{-115} -19 q^{-116} +3 q^{-117} +15 q^{-119} -2 q^{-120} -3 q^{-121} +2 q^{-122} -11 q^{-123} +5 q^{-124} - q^{-125} +6 q^{-126} -2 q^{-127} +2 q^{-129} -6 q^{-130} +3 q^{-131} - q^{-132} +2 q^{-133} - q^{-134} + q^{-136} -2 q^{-137} + q^{-138} </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, 8]]</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, 6, 2, 7], X[7, 16, 8, 17], X[5, 13, 6, 12], X[3, 15, 4, 14], 
 
  X[13, 5, 14, 4], X[15, 3, 16, 2], X[9, 18, 10, 19], X[11, 20, 12, 1], 
 
  X[17, 8, 18, 9], X[19, 10, 20, 11]]</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, 8]]</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, 6, -4, 5, -3, 1, -2, 9, -7, 10, -8, 3, -5, 4, -6, 2, -9, 
 
  7, -10, 8]</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, 8]]</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[6, 14, 12, 16, 18, 20, 4, 2, 8, 10]</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, 8]]</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[4, {-1, -1, -1, -1, -1, 2, -1, 2, 3, -2, 3}]</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>{4, 11}</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, 8]]</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>4</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, 8]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:10_8_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, 8]]&) /@ {
                  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, 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, 8]][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>    2    5    5            2      3
5 - -- + -- - - - 5 t + 5 t  - 2 t
     3    2   t
    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, 8]][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  - 7 z  - 2 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, 8]}</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[10, 8]], KnotSignature[Knot[10, 8]]}</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>{29, -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[10, 8]][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    3    4    4    4    4    3        2
2 + q   - -- + -- - -- + -- - -- + -- - - - q + 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[10, 8]}</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[10, 8]][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    -14    -12    -8    -6    2    4    6
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[10, 8]][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    6      2      2  2      4  2      6  2    4      2  4
3 - 3 a  + a  + 4 z  - 7 a  z  - 3 a  z  + 3 a  z  + z  - 5 a  z  - 
 
     4  4    6  4    2  6    4  6
  4 a  z  + 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[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, 8]][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    6    3      5        7         2       2  2      4  2
3 + 3 a  - a  - a  z + a  z + 2 a  z - 13 z  - 18 a  z  + 3 a  z  + 
 
     6  2      8  2    10  2        3      3  3      5  3      7  3
  5 a  z  - 2 a  z  + a   z  - 6 a z  + 5 a  z  + 2 a  z  - 7 a  z  + 
 
     9  3       4       2  4    4  4       6  4      8  4         5
  2 a  z  + 16 z  + 30 a  z  + a  z  - 10 a  z  + 3 a  z  + 11 a z  - 
 
   3  5      5  5      7  5      6       2  6      4  6      6  6
  a  z  - 8 a  z  + 4 a  z  - 7 z  - 17 a  z  - 6 a  z  + 4 a  z  - 
 
       7      3  7      5  7    8      2  8      4  8      9    3  9
  6 a z  - 3 a  z  + 3 a  z  + 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[10, 8]], Vassiliev[3][Knot[10, 8]]}</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, 4}</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, 8]][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>2    3      1        1        1        2        1        2        2
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ----- + 
 5    3    17  6    15  5    13  5    13  4    11  4    11  3    9  3
q    q    q   t    q   t    q   t    q   t    q   t    q   t    q  t
 
    2       2      2      2     2 t   t        2      3    5  4
  ----- + ----- + ---- + ---- + --- + - + 2 q t  + q t  + q  t
   9  2    7  2    7      5      3    q
  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[10, 8], 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     -20    2     5     4     2     7     5     2
-7 + q    - --- + q    + --- - --- + --- + --- - --- + --- + --- - 
             21           19    18    17    16    15    14    13
            q            q     q     q     q     q     q     q
 
   8     6     3    10   7    5    11   5    6    10   3    6
  --- + --- + --- - -- + -- + -- - -- + -- + -- - -- + -- + - + q + 
   12    11    10    9    8    7    6    5    4    3    2   q
  q     q     q     q    q    q    q    q    q    q    q
 
     2      3    4      5    6    7    8
  5 q  - 4 q  - q  + 3 q  - q  - q  + q</nowiki></code></td></tr>
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