View source for 10 78

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{{Rolfsen Knot Page|
n = 10 |
k = 78 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-3,9,-10,2,-7,8,-4,5,-9,3,-5,4,-6,7,-8,6/goTop.html |
braid_table     = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image: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:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.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:BraidPart3.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:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]]</td></tr>
</table> |
braid_crossings = 12 |
braid_width     = 5 |
braid_index     = 5 |
same_alexander  = [[K11n98]], [[K11n105]],  |
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%>-8</td    ><td width=6.66667%>-7</td    ><td width=6.66667%>-6</td    ><td width=6.66667%>-5</td    ><td width=6.66667%>-4</td    ><td width=6.66667%>-3</td    ><td width=6.66667%>-2</td    ><td width=6.66667%>-1</td    ><td width=6.66667%>0</td    ><td width=6.66667%>1</td    ><td width=6.66667%>2</td    ><td width=13.3333%>&chi;</td></tr>
<tr align=center><td>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 bgcolor=yellow>1</td><td>1</td></tr>
<tr align=center><td>-1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>&nbsp;</td><td>-2</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>4</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>3</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>5</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>-7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>3</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>5</td><td bgcolor=yellow>5</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>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</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>3</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr>
<tr align=center><td>-15</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>6</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-4</td></tr>
<tr align=center><td>-17</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr>
<tr align=center><td>-19</td><td bgcolor=yellow>&nbsp;</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>&nbsp;</td><td>-2</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>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
</table> |
coloured_jones_2 = <math>q^2-3 q+11 q^{-1} -13 q^{-2} -10 q^{-3} +37 q^{-4} -21 q^{-5} -37 q^{-6} +69 q^{-7} -16 q^{-8} -73 q^{-9} +91 q^{-10} - q^{-11} -100 q^{-12} +93 q^{-13} +16 q^{-14} -104 q^{-15} +75 q^{-16} +24 q^{-17} -79 q^{-18} +45 q^{-19} +18 q^{-20} -41 q^{-21} +20 q^{-22} +7 q^{-23} -14 q^{-24} +7 q^{-25} + q^{-26} -3 q^{-27} + q^{-28} </math> |
coloured_jones_3 = <math>q^6-3 q^5+5 q^3+6 q^2-13 q-17+20 q^{-1} +39 q^{-2} -21 q^{-3} -71 q^{-4} +6 q^{-5} +115 q^{-6} +21 q^{-7} -149 q^{-8} -75 q^{-9} +182 q^{-10} +139 q^{-11} -190 q^{-12} -221 q^{-13} +191 q^{-14} +288 q^{-15} -153 q^{-16} -371 q^{-17} +126 q^{-18} +416 q^{-19} -62 q^{-20} -474 q^{-21} +19 q^{-22} +486 q^{-23} +50 q^{-24} -504 q^{-25} -92 q^{-26} +478 q^{-27} +141 q^{-28} -441 q^{-29} -166 q^{-30} +378 q^{-31} +174 q^{-32} -299 q^{-33} -170 q^{-34} +232 q^{-35} +131 q^{-36} -150 q^{-37} -107 q^{-38} +105 q^{-39} +64 q^{-40} -60 q^{-41} -40 q^{-42} +40 q^{-43} +15 q^{-44} -21 q^{-45} -7 q^{-46} +14 q^{-47} + q^{-48} -9 q^{-49} +2 q^{-50} +3 q^{-51} + q^{-52} -3 q^{-53} + q^{-54} </math> |
coloured_jones_4 = <math>q^{12}-3 q^{11}+5 q^9+6 q^7-20 q^6-10 q^5+20 q^4+15 q^3+48 q^2-63 q-73+5 q^{-1} +42 q^{-2} +207 q^{-3} -55 q^{-4} -186 q^{-5} -151 q^{-6} -56 q^{-7} +484 q^{-8} +152 q^{-9} -167 q^{-10} -426 q^{-11} -467 q^{-12} +642 q^{-13} +527 q^{-14} +215 q^{-15} -559 q^{-16} -1150 q^{-17} +425 q^{-18} +786 q^{-19} +925 q^{-20} -296 q^{-21} -1796 q^{-22} -157 q^{-23} +679 q^{-24} +1685 q^{-25} +337 q^{-26} -2147 q^{-27} -862 q^{-28} +227 q^{-29} +2250 q^{-30} +1114 q^{-31} -2165 q^{-32} -1487 q^{-33} -384 q^{-34} +2556 q^{-35} +1832 q^{-36} -1935 q^{-37} -1935 q^{-38} -1003 q^{-39} +2574 q^{-40} +2368 q^{-41} -1481 q^{-42} -2109 q^{-43} -1539 q^{-44} +2234 q^{-45} +2579 q^{-46} -846 q^{-47} -1871 q^{-48} -1828 q^{-49} +1542 q^{-50} +2311 q^{-51} -225 q^{-52} -1249 q^{-53} -1692 q^{-54} +768 q^{-55} +1619 q^{-56} +114 q^{-57} -543 q^{-58} -1186 q^{-59} +237 q^{-60} +855 q^{-61} +137 q^{-62} -88 q^{-63} -622 q^{-64} +34 q^{-65} +335 q^{-66} +33 q^{-67} +68 q^{-68} -243 q^{-69} +3 q^{-70} +98 q^{-71} -30 q^{-72} +65 q^{-73} -71 q^{-74} +9 q^{-75} +23 q^{-76} -33 q^{-77} +29 q^{-78} -15 q^{-79} +8 q^{-80} +5 q^{-81} -15 q^{-82} +7 q^{-83} -2 q^{-84} +3 q^{-85} + q^{-86} -3 q^{-87} + q^{-88} </math> |
coloured_jones_5 = <math>q^{20}-3 q^{19}+5 q^{17}-q^{14}-13 q^{13}-10 q^{12}+20 q^{11}+24 q^{10}+15 q^9-3 q^8-56 q^7-73 q^6-6 q^5+95 q^4+136 q^3+88 q^2-84 q-266-247 q^{-1} +10 q^{-2} +354 q^{-3} +498 q^{-4} +234 q^{-5} -339 q^{-6} -792 q^{-7} -670 q^{-8} +96 q^{-9} +1021 q^{-10} +1246 q^{-11} +453 q^{-12} -947 q^{-13} -1890 q^{-14} -1363 q^{-15} +526 q^{-16} +2330 q^{-17} +2460 q^{-18} +481 q^{-19} -2372 q^{-20} -3676 q^{-21} -1889 q^{-22} +1841 q^{-23} +4588 q^{-24} +3713 q^{-25} -654 q^{-26} -5126 q^{-27} -5569 q^{-28} -1114 q^{-29} +4963 q^{-30} +7379 q^{-31} +3298 q^{-32} -4271 q^{-33} -8692 q^{-34} -5714 q^{-35} +2866 q^{-36} +9720 q^{-37} +8094 q^{-38} -1232 q^{-39} -10049 q^{-40} -10306 q^{-41} -869 q^{-42} +10197 q^{-43} +12248 q^{-44} +2792 q^{-45} -9783 q^{-46} -13878 q^{-47} -4919 q^{-48} +9370 q^{-49} +15252 q^{-50} +6696 q^{-51} -8586 q^{-52} -16326 q^{-53} -8590 q^{-54} +7858 q^{-55} +17149 q^{-56} +10152 q^{-57} -6755 q^{-58} -17634 q^{-59} -11764 q^{-60} +5584 q^{-61} +17702 q^{-62} +13016 q^{-63} -4006 q^{-64} -17210 q^{-65} -14083 q^{-66} +2285 q^{-67} +16123 q^{-68} +14575 q^{-69} -404 q^{-70} -14357 q^{-71} -14485 q^{-72} -1426 q^{-73} +12114 q^{-74} +13721 q^{-75} +2846 q^{-76} -9509 q^{-77} -12209 q^{-78} -3915 q^{-79} +6902 q^{-80} +10360 q^{-81} +4233 q^{-82} -4577 q^{-83} -8067 q^{-84} -4187 q^{-85} +2674 q^{-86} +6027 q^{-87} +3574 q^{-88} -1346 q^{-89} -4079 q^{-90} -2876 q^{-91} +489 q^{-92} +2662 q^{-93} +2044 q^{-94} -46 q^{-95} -1543 q^{-96} -1416 q^{-97} -129 q^{-98} +879 q^{-99} +848 q^{-100} +166 q^{-101} -413 q^{-102} -513 q^{-103} -150 q^{-104} +210 q^{-105} +260 q^{-106} +97 q^{-107} -72 q^{-108} -122 q^{-109} -70 q^{-110} +15 q^{-111} +64 q^{-112} +34 q^{-113} -8 q^{-114} -7 q^{-115} -17 q^{-116} -19 q^{-117} +11 q^{-118} +12 q^{-119} -5 q^{-120} +10 q^{-121} - q^{-122} -11 q^{-123} + q^{-124} +3 q^{-125} -2 q^{-126} +3 q^{-127} + q^{-128} -3 q^{-129} + q^{-130} </math> |
coloured_jones_6 = <math>q^{30}-3 q^{29}+5 q^{27}-7 q^{24}+6 q^{23}-13 q^{22}-10 q^{21}+29 q^{20}+15 q^{19}+15 q^{18}-27 q^{17}+4 q^{16}-67 q^{15}-73 q^{14}+59 q^{13}+86 q^{12}+135 q^{11}+15 q^{10}+72 q^9-230 q^8-365 q^7-121 q^6+67 q^5+422 q^4+376 q^3+666 q^2-130 q-844-955 q^{-1} -799 q^{-2} +100 q^{-3} +744 q^{-4} +2323 q^{-5} +1444 q^{-6} -63 q^{-7} -1674 q^{-8} -2939 q^{-9} -2571 q^{-10} -1234 q^{-11} +3406 q^{-12} +4632 q^{-13} +4209 q^{-14} +1127 q^{-15} -3451 q^{-16} -7082 q^{-17} -8074 q^{-18} -771 q^{-19} +5024 q^{-20} +10428 q^{-21} +9987 q^{-22} +3545 q^{-23} -7307 q^{-24} -16786 q^{-25} -12513 q^{-26} -4203 q^{-27} +10689 q^{-28} +20320 q^{-29} +19700 q^{-30} +4209 q^{-31} -17836 q^{-32} -25635 q^{-33} -23755 q^{-34} -2739 q^{-35} +21464 q^{-36} +37278 q^{-37} +27093 q^{-38} -3643 q^{-39} -28813 q^{-40} -44708 q^{-41} -28428 q^{-42} +6501 q^{-43} +44747 q^{-44} +51694 q^{-45} +23351 q^{-46} -16022 q^{-47} -55896 q^{-48} -56423 q^{-49} -21155 q^{-50} +37030 q^{-51} +67591 q^{-52} +53235 q^{-53} +8682 q^{-54} -53313 q^{-55} -77196 q^{-56} -51845 q^{-57} +18441 q^{-58} +71658 q^{-59} +77422 q^{-60} +36285 q^{-61} -41293 q^{-62} -88186 q^{-63} -77893 q^{-64} -3050 q^{-65} +67801 q^{-66} +93735 q^{-67} +60290 q^{-68} -26534 q^{-69} -92520 q^{-70} -97465 q^{-71} -22458 q^{-72} +61055 q^{-73} +104478 q^{-74} +79605 q^{-75} -12244 q^{-76} -93390 q^{-77} -112292 q^{-78} -39902 q^{-79} +52519 q^{-80} +111176 q^{-81} +95965 q^{-82} +3219 q^{-83} -89748 q^{-84} -122656 q^{-85} -57530 q^{-86} +38902 q^{-87} +110931 q^{-88} +108825 q^{-89} +22424 q^{-90} -76852 q^{-91} -124197 q^{-92} -73977 q^{-93} +17489 q^{-94} +98016 q^{-95} +112533 q^{-96} +42840 q^{-97} -52366 q^{-98} -110636 q^{-99} -82112 q^{-100} -7603 q^{-101} +71011 q^{-102} +100433 q^{-103} +55677 q^{-104} -22378 q^{-105} -81793 q^{-106} -74838 q^{-107} -25953 q^{-108} +38032 q^{-109} +73539 q^{-110} +53566 q^{-111} +1206 q^{-112} -47522 q^{-113} -53940 q^{-114} -30082 q^{-115} +11806 q^{-116} +42539 q^{-117} +38927 q^{-118} +11098 q^{-119} -20559 q^{-120} -29958 q^{-121} -22676 q^{-122} -1132 q^{-123} +19006 q^{-124} +21589 q^{-125} +10109 q^{-126} -6202 q^{-127} -12561 q^{-128} -12368 q^{-129} -3839 q^{-130} +6575 q^{-131} +9300 q^{-132} +5608 q^{-133} -1184 q^{-134} -3864 q^{-135} -5131 q^{-136} -2622 q^{-137} +1863 q^{-138} +3229 q^{-139} +2249 q^{-140} -160 q^{-141} -773 q^{-142} -1700 q^{-143} -1236 q^{-144} +513 q^{-145} +947 q^{-146} +724 q^{-147} -75 q^{-148} -10 q^{-149} -466 q^{-150} -507 q^{-151} +164 q^{-152} +240 q^{-153} +206 q^{-154} -56 q^{-155} +86 q^{-156} -105 q^{-157} -192 q^{-158} +53 q^{-159} +45 q^{-160} +57 q^{-161} -31 q^{-162} +56 q^{-163} -16 q^{-164} -64 q^{-165} +16 q^{-166} +16 q^{-168} -12 q^{-169} +20 q^{-170} + q^{-171} -17 q^{-172} +5 q^{-173} -3 q^{-174} +3 q^{-175} -2 q^{-176} +3 q^{-177} + q^{-178} -3 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><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, 78]]</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[11, 17, 12, 16], 
 
  X[15, 13, 16, 12], X[17, 20, 18, 1], X[9, 18, 10, 19], 
 
  X[19, 10, 20, 11], 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, 78]]</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, -7, 8, -4, 5, -9, 3, -5, 4, -6, 
 
  7, -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[10, 78]]</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, 18, 16, 6, 12, 20, 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, 78]]</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[5, {-1, -1, -2, 1, -2, -1, 3, -2, -4, 3, -4, -4}]</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>{5, 12}</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, 78]]</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>5</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, 78]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:10_78_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, 78]]&) /@ {
                   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, 78]][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   7    16             2    3
21 - t   + -- - -- - 16 t + 7 t  - t
            2   t
           t</nowiki></code></td></tr>
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<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, 78]][z]</nowiki></code></td></tr>
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<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  + z  - z</nowiki></code></td></tr>
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<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>
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<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, 78], Knot[11, NonAlternating, 98], 
 
  Knot[11, NonAlternating, 105]}</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, 78]], KnotSignature[Knot[10, 78]]}</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>{69, -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, 78]][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>     -10   3    5    9    11   11   11   8    6    3
1 + q    - -- + -- - -- + -- - -- + -- - -- + -- - -
            9    8    7    6    5    4    3    2   q
           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[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, 78]}</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, 78]][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>     -32    -30    2     -26    -24    3     2     2     2     -12
1 + q    + q    - --- - q    - q    - --- + --- + --- + --- - q    + 
                   28                  22    20    16    14
                  q                   q     q     q     q
 
   3    2     -6    -4    -2
  --- - -- + q   + q   - q
   10    8
  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, 78]][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      8    10      2  2      4  2      6  2      8  2
a  - a  + 4 a  - 4 a  + a   + 2 a  z  - 3 a  z  + 7 a  z  - 3 a  z  + 
 
   2  4      4  4      6  4    4  6
  a  z  - 3 a  z  + 3 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, 78]][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      8    10    3        5        7        9
-a  - a  - 4 a  - 4 a  - a   - a  z - 3 a  z + 2 a  z + 6 a  z + 
 
     11        2  2      4  2       6  2       8  2    10  2    12  2
  2 a   z + 3 a  z  + 6 a  z  + 11 a  z  + 10 a  z  + a   z  - a   z  + 
 
     3  3       5  3      7  3      9  3      11  3      2  4
  7 a  z  + 15 a  z  + 5 a  z  - 7 a  z  - 4 a   z  - 3 a  z  - 
 
     4  4      6  4       8  4      10  4    12  4      3  5
  4 a  z  - 7 a  z  - 10 a  z  - 3 a   z  + a   z  - 9 a  z  - 
 
      5  5       7  5      11  5    2  6      4  6      6  6
  21 a  z  - 15 a  z  + 3 a   z  + a  z  - 5 a  z  - 8 a  z  + 
 
     8  6      10  6      3  7      5  7      7  7      9  7
  2 a  z  + 4 a   z  + 3 a  z  + 6 a  z  + 7 a  z  + 4 a  z  + 
 
     4  8      6  8      8  8    5  9    7  9
  3 a  z  + 6 a  z  + 3 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, 78]], Vassiliev[3][Knot[10, 78]]}</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, -5}</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, 78]][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    4      1        2        1        3        2        6
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + 
 5    3    21  8    19  7    17  7    17  6    15  6    15  5
q    q    q   t    q   t    q   t    q   t    q   t    q   t
 
    3        5        6        6        5       5       6      3
  ------ + ------ + ------ + ------ + ----- + ----- + ----- + ---- + 
   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
 
   5     t    2 t      2
  ---- + -- + --- + q t
   5      3    q
  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, 78], 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> -28    3     -26    7    14     7    20    41    18    45    79
q    - --- + q    + --- - --- + --- + --- - --- + --- + --- - --- + 
        27           25    24    23    22    21    20    19    18
       q            q     q     q     q     q     q     q     q
 
  24    75    104   16    93    100    -11   91    73   16   69   37
  --- + --- - --- + --- + --- - --- - q    + --- - -- - -- + -- - -- - 
   17    16    15    14    13    12           10    9    8    7    6
  q     q     q     q     q     q            q     q    q    q    q
 
  21   37   10   13   11          2
  -- + -- - -- - -- + -- - 3 q + q
   5    4    3    2   q
  q    q    q    q</nowiki></code></td></tr>
</table>  }}