View source for 10 49

<!--                       WARNING! WARNING! WARNING!
<!-- This page was generated from the splice base [[Rolfsen_Splice_Base]]. Please do not edit!
<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].)
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Rolfsen_Splice_Base]]. -->
<!--  -->
<!--  -->
{{Rolfsen Knot Page|
n = 10 |
k = 49 |
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: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:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart3.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]]</td></tr>
</table> |
braid_crossings = 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%>-10</td    ><td width=6.66667%>-9</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=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>-7</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>1</td><td>-1</td></tr>
<tr align=center><td>-9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>&nbsp;</td><td>&nbsp;</td><td>3</td></tr>
<tr align=center><td>-11</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>3</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr>
<tr align=center><td>-13</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>-15</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr>
<tr align=center><td>-17</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>6</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>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>4</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>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</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>&nbsp;</td><td>-3</td></tr>
<tr align=center><td>-23</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>-25</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>-27</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^{-6} -2 q^{-7} + q^{-8} +7 q^{-9} -10 q^{-10} -3 q^{-11} +24 q^{-12} -19 q^{-13} -18 q^{-14} +46 q^{-15} -20 q^{-16} -41 q^{-17} +65 q^{-18} -14 q^{-19} -62 q^{-20} +72 q^{-21} -3 q^{-22} -69 q^{-23} +63 q^{-24} +6 q^{-25} -56 q^{-26} +41 q^{-27} +7 q^{-28} -32 q^{-29} +20 q^{-30} +4 q^{-31} -13 q^{-32} +7 q^{-33} + q^{-34} -3 q^{-35} + q^{-36} </math> |
coloured_jones_3 = <math> q^{-9} -2 q^{-10} + q^{-11} +3 q^{-12} +2 q^{-13} -10 q^{-14} -3 q^{-15} +17 q^{-16} +16 q^{-17} -30 q^{-18} -28 q^{-19} +29 q^{-20} +62 q^{-21} -35 q^{-22} -83 q^{-23} +11 q^{-24} +121 q^{-25} +6 q^{-26} -133 q^{-27} -55 q^{-28} +158 q^{-29} +83 q^{-30} -146 q^{-31} -138 q^{-32} +150 q^{-33} +165 q^{-34} -125 q^{-35} -209 q^{-36} +111 q^{-37} +232 q^{-38} -85 q^{-39} -250 q^{-40} +57 q^{-41} +259 q^{-42} -33 q^{-43} -246 q^{-44} +3 q^{-45} +228 q^{-46} +10 q^{-47} -183 q^{-48} -30 q^{-49} +150 q^{-50} +23 q^{-51} -100 q^{-52} -25 q^{-53} +72 q^{-54} +11 q^{-55} -43 q^{-56} -7 q^{-57} +30 q^{-58} - q^{-59} -18 q^{-60} + q^{-61} +13 q^{-62} -2 q^{-63} -8 q^{-64} +2 q^{-65} +3 q^{-66} + q^{-67} -3 q^{-68} + q^{-69} </math> |
coloured_jones_4 = <math> q^{-12} -2 q^{-13} + q^{-14} +3 q^{-15} -2 q^{-16} +2 q^{-17} -11 q^{-18} +3 q^{-19} +19 q^{-20} +6 q^{-22} -50 q^{-23} -15 q^{-24} +55 q^{-25} +36 q^{-26} +52 q^{-27} -121 q^{-28} -100 q^{-29} +50 q^{-30} +92 q^{-31} +212 q^{-32} -137 q^{-33} -229 q^{-34} -75 q^{-35} +50 q^{-36} +439 q^{-37} -3 q^{-38} -246 q^{-39} -266 q^{-40} -195 q^{-41} +558 q^{-42} +219 q^{-43} -41 q^{-44} -346 q^{-45} -565 q^{-46} +449 q^{-47} +352 q^{-48} +322 q^{-49} -215 q^{-50} -892 q^{-51} +178 q^{-52} +312 q^{-53} +683 q^{-54} +57 q^{-55} -1086 q^{-56} -123 q^{-57} +165 q^{-58} +957 q^{-59} +347 q^{-60} -1163 q^{-61} -385 q^{-62} -12 q^{-63} +1125 q^{-64} +604 q^{-65} -1120 q^{-66} -589 q^{-67} -216 q^{-68} +1146 q^{-69} +802 q^{-70} -909 q^{-71} -658 q^{-72} -437 q^{-73} +937 q^{-74} +864 q^{-75} -548 q^{-76} -516 q^{-77} -569 q^{-78} +553 q^{-79} +707 q^{-80} -210 q^{-81} -223 q^{-82} -503 q^{-83} +195 q^{-84} +407 q^{-85} -44 q^{-86} +22 q^{-87} -304 q^{-88} +20 q^{-89} +151 q^{-90} -27 q^{-91} +105 q^{-92} -125 q^{-93} -8 q^{-94} +31 q^{-95} -42 q^{-96} +76 q^{-97} -35 q^{-98} +5 q^{-99} +3 q^{-100} -34 q^{-101} +31 q^{-102} -8 q^{-103} +7 q^{-104} +2 q^{-105} -14 q^{-106} +7 q^{-107} -2 q^{-108} +3 q^{-109} + q^{-110} -3 q^{-111} + q^{-112} </math> |
coloured_jones_5 = <math> q^{-15} -2 q^{-16} + q^{-17} +3 q^{-18} -2 q^{-19} -2 q^{-20} + q^{-21} -5 q^{-22} +4 q^{-23} +16 q^{-24} +3 q^{-25} -16 q^{-26} -15 q^{-27} -26 q^{-28} +9 q^{-29} +59 q^{-30} +60 q^{-31} -9 q^{-32} -75 q^{-33} -128 q^{-34} -62 q^{-35} +111 q^{-36} +220 q^{-37} +154 q^{-38} -51 q^{-39} -318 q^{-40} -338 q^{-41} -45 q^{-42} +336 q^{-43} +505 q^{-44} +313 q^{-45} -272 q^{-46} -682 q^{-47} -541 q^{-48} +13 q^{-49} +648 q^{-50} +884 q^{-51} +332 q^{-52} -515 q^{-53} -962 q^{-54} -759 q^{-55} +44 q^{-56} +967 q^{-57} +1110 q^{-58} +444 q^{-59} -541 q^{-60} -1290 q^{-61} -1129 q^{-62} +5 q^{-63} +1184 q^{-64} +1603 q^{-65} +881 q^{-66} -792 q^{-67} -2058 q^{-68} -1669 q^{-69} +111 q^{-70} +2105 q^{-71} +2624 q^{-72} +735 q^{-73} -2083 q^{-74} -3268 q^{-75} -1679 q^{-76} +1673 q^{-77} +3936 q^{-78} +2621 q^{-79} -1305 q^{-80} -4281 q^{-81} -3476 q^{-82} +726 q^{-83} +4614 q^{-84} +4245 q^{-85} -263 q^{-86} -4766 q^{-87} -4888 q^{-88} -246 q^{-89} +4898 q^{-90} +5453 q^{-91} +696 q^{-92} -4953 q^{-93} -5942 q^{-94} -1145 q^{-95} +4912 q^{-96} +6344 q^{-97} +1666 q^{-98} -4761 q^{-99} -6647 q^{-100} -2184 q^{-101} +4356 q^{-102} +6783 q^{-103} +2788 q^{-104} -3794 q^{-105} -6656 q^{-106} -3288 q^{-107} +2924 q^{-108} +6252 q^{-109} +3736 q^{-110} -2038 q^{-111} -5513 q^{-112} -3845 q^{-113} +993 q^{-114} +4554 q^{-115} +3790 q^{-116} -202 q^{-117} -3461 q^{-118} -3336 q^{-119} -493 q^{-120} +2381 q^{-121} +2807 q^{-122} +813 q^{-123} -1446 q^{-124} -2102 q^{-125} -967 q^{-126} +736 q^{-127} +1485 q^{-128} +874 q^{-129} -256 q^{-130} -919 q^{-131} -739 q^{-132} -3 q^{-133} +535 q^{-134} +512 q^{-135} +127 q^{-136} -245 q^{-137} -353 q^{-138} -151 q^{-139} +105 q^{-140} +196 q^{-141} +124 q^{-142} -12 q^{-143} -100 q^{-144} -95 q^{-145} -17 q^{-146} +51 q^{-147} +50 q^{-148} +18 q^{-149} -6 q^{-150} -30 q^{-151} -24 q^{-152} +9 q^{-153} +13 q^{-154} +2 q^{-155} +9 q^{-156} -4 q^{-157} -10 q^{-158} + q^{-159} +3 q^{-160} -2 q^{-161} +3 q^{-162} + q^{-163} -3 q^{-164} + q^{-165} </math> |
coloured_jones_6 = <math> q^{-18} -2 q^{-19} + q^{-20} +3 q^{-21} -2 q^{-22} -2 q^{-23} -3 q^{-24} +7 q^{-25} -4 q^{-26} + q^{-27} +18 q^{-28} -6 q^{-29} -14 q^{-30} -26 q^{-31} +11 q^{-32} -3 q^{-33} +16 q^{-34} +80 q^{-35} +18 q^{-36} -35 q^{-37} -124 q^{-38} -53 q^{-39} -70 q^{-40} +31 q^{-41} +273 q^{-42} +215 q^{-43} +92 q^{-44} -255 q^{-45} -282 q^{-46} -451 q^{-47} -242 q^{-48} +426 q^{-49} +679 q^{-50} +722 q^{-51} +56 q^{-52} -289 q^{-53} -1139 q^{-54} -1213 q^{-55} -192 q^{-56} +726 q^{-57} +1596 q^{-58} +1172 q^{-59} +883 q^{-60} -1033 q^{-61} -2196 q^{-62} -1764 q^{-63} -709 q^{-64} +1146 q^{-65} +1823 q^{-66} +2971 q^{-67} +931 q^{-68} -1169 q^{-69} -2337 q^{-70} -2724 q^{-71} -1479 q^{-72} -319 q^{-73} +3247 q^{-74} +3080 q^{-75} +2287 q^{-76} +569 q^{-77} -1923 q^{-78} -3765 q^{-79} -5031 q^{-80} -741 q^{-81} +1534 q^{-82} +4841 q^{-83} +6038 q^{-84} +3853 q^{-85} -1567 q^{-86} -8292 q^{-87} -7378 q^{-88} -5412 q^{-89} +2308 q^{-90} +9640 q^{-91} +12321 q^{-92} +6273 q^{-93} -6117 q^{-94} -12041 q^{-95} -14969 q^{-96} -5916 q^{-97} +7818 q^{-98} +18862 q^{-99} +16640 q^{-100} +1555 q^{-101} -11654 q^{-102} -22733 q^{-103} -16559 q^{-104} +992 q^{-105} +20875 q^{-106} +25452 q^{-107} +11417 q^{-108} -6958 q^{-109} -26535 q^{-110} -25864 q^{-111} -7635 q^{-112} +19197 q^{-113} +30886 q^{-114} +20112 q^{-115} -894 q^{-116} -27214 q^{-117} -32251 q^{-118} -15125 q^{-119} +16299 q^{-120} +33658 q^{-121} +26376 q^{-122} +4206 q^{-123} -26760 q^{-124} -36359 q^{-125} -20636 q^{-126} +13767 q^{-127} +35282 q^{-128} +30977 q^{-129} +8172 q^{-130} -26057 q^{-131} -39398 q^{-132} -25252 q^{-133} +10985 q^{-134} +35995 q^{-135} +35014 q^{-136} +12603 q^{-137} -23783 q^{-138} -41087 q^{-139} -30043 q^{-140} +5916 q^{-141} +33877 q^{-142} +37709 q^{-143} +18451 q^{-144} -17672 q^{-145} -38986 q^{-146} -33663 q^{-147} -1981 q^{-148} +26646 q^{-149} +36104 q^{-150} +23614 q^{-151} -7840 q^{-152} -30942 q^{-153} -32690 q^{-154} -9664 q^{-155} +15236 q^{-156} +28304 q^{-157} +24224 q^{-158} +1736 q^{-159} -18758 q^{-160} -25605 q^{-161} -12863 q^{-162} +4383 q^{-163} +16862 q^{-164} +19110 q^{-165} +6667 q^{-166} -7621 q^{-167} -15495 q^{-168} -10696 q^{-169} -1703 q^{-170} +6957 q^{-171} +11498 q^{-172} +6459 q^{-173} -1231 q^{-174} -7100 q^{-175} -6233 q^{-176} -2976 q^{-177} +1467 q^{-178} +5371 q^{-179} +4009 q^{-180} +812 q^{-181} -2451 q^{-182} -2655 q^{-183} -2075 q^{-184} -390 q^{-185} +2030 q^{-186} +1869 q^{-187} +854 q^{-188} -626 q^{-189} -813 q^{-190} -1033 q^{-191} -604 q^{-192} +648 q^{-193} +695 q^{-194} +490 q^{-195} -95 q^{-196} -125 q^{-197} -408 q^{-198} -396 q^{-199} +171 q^{-200} +195 q^{-201} +211 q^{-202} +6 q^{-203} +49 q^{-204} -122 q^{-205} -184 q^{-206} +37 q^{-207} +30 q^{-208} +68 q^{-209} +2 q^{-210} +48 q^{-211} -24 q^{-212} -62 q^{-213} +10 q^{-214} -3 q^{-215} +17 q^{-216} -5 q^{-217} +19 q^{-218} -2 q^{-219} -16 q^{-220} +5 q^{-221} -3 q^{-222} +3 q^{-223} -2 q^{-224} +3 q^{-225} + q^{-226} -3 q^{-227} + q^{-228} </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, 49]]</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[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[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, 49]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[-1, 10, -2, 1, -3, 9, -10, 2, -5, 7, -6, 8, -9, 3, -4, 5, -7, 
 
  6, -8, 4]</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[Knot[10, 49]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>DTCode[4, 8, 14, 2, 16, 18, 6, 20, 10, 12]</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>br = BR[Knot[10, 49]]</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, 2, -1, -3, -2, -2, -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, 49]]</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, 49]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:10_49_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, 49]]&) /@ {
                   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, 3, 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, 49]][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    8    12             2      3
-13 + -- - -- + -- + 12 t - 8 t  + 3 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, 49]][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 + 7 z  + 10 z  + 3 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, 49]}</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[13]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{KnotDet[Knot[10, 49]], KnotSignature[Knot[10, 49]]}</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[13]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{59, -6}</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[14]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Jones[Knot[10, 49]][q]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[14]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -13    3     5     8    9    10   9    6    5    2     -3
q    - --- + --- - --- + -- - -- + -- - -- + -- - -- + q
        12    11    10    9    8    7    6    5    4
       q     q     q     q    q    q    q    q    q</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[15]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[15]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[10, 49]}</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[16]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>A2Invariant[Knot[10, 49]][q]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[16]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -40    -38    -36    3     2     -28    2     3     3     2     2
q    + q    - q    - --- - --- - q    - --- + --- + --- + --- + --- - 
                      32    30           26    24    20    18    14
                     q     q            q     q     q     q     q
 
   -12    -10
  q    + q</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[17]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>HOMFLYPT[Knot[10, 49]][a, z]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[17]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 6      8      10      12      6  2       8  2       10  2    12  2
a  + 5 a  - 7 a   + 2 a   + 4 a  z  + 12 a  z  - 10 a   z  + a   z  + 
 
     6  4      8  4      10  4    6  6      8  6
  4 a  z  + 9 a  z  - 3 a   z  + a  z  + 2 a  z</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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, 49]][a, z]</nowiki></code></td></tr>
<tr align=left>
<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>  6      8      10      12      9         11      15        6  2
-a  + 5 a  + 7 a   + 2 a   - 9 a  z - 10 a   z + a   z + 4 a  z  - 
 
      8  2       10  2      12  2    16  2      7  3       9  3
  13 a  z  - 20 a   z  - 2 a   z  - a   z  + 3 a  z  + 22 a  z  + 
 
      11  3    13  3      15  3      6  4       8  4       10  4
  24 a   z  + a   z  - 4 a   z  - 4 a  z  + 15 a  z  + 26 a   z  + 
 
     12  4      14  4    16  4      7  5       9  5       11  5
  2 a   z  - 4 a   z  + a   z  - 6 a  z  - 18 a  z  - 19 a   z  - 
 
     13  5      15  5    6  6       8  6       10  6      12  6
  4 a   z  + 3 a   z  + a  z  - 11 a  z  - 19 a   z  - 3 a   z  + 
 
     14  6      7  7      9  7      11  7      13  7      8  8
  4 a   z  + 2 a  z  + 3 a  z  + 5 a   z  + 4 a   z  + 3 a  z  + 
 
     10  8      12  8    9  9    11  9
  6 a   z  + 3 a   z  + a  z  + a   z</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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, 49]], Vassiliev[3][Knot[10, 49]]}</nowiki></code></td></tr>
<tr align=left>
<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>{7, -16}</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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, 49]][q, t]</nowiki></code></td></tr>
<tr align=left>
<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> -7    -5      1        2        1        3        2        5
q   + q   + ------- + ------ + ------ + ------ + ------ + ------ + 
             27  10    25  9    23  9    23  8    21  8    21  7
            q   t     q   t    q   t    q   t    q   t    q   t
 
    3        4        5        6        4        3        6
  ------ + ------ + ------ + ------ + ------ + ------ + ------ + 
   19  7    19  6    17  6    17  5    15  5    15  4    13  4
  q   t    q   t    q   t    q   t    q   t    q   t    q   t
 
    3        3        2        3      2
  ------ + ------ + ------ + ----- + ----
   13  3    11  3    11  2    9  2    7
  q   t    q   t    q   t    q  t    q  t</nowiki></code></td></tr>
</table>
         <table><tr align=left>
<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, 49], 2][q]</nowiki></code></td></tr>
<tr align=left>
<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> -36    3     -34    7    13     4    20    32     7    41    56
q    - --- + q    + --- - --- + --- + --- - --- + --- + --- - --- + 
        35           33    32    31    30    29    28    27    26
       q            q     q     q     q     q     q     q     q
 
   6    63    69     3    72    62    14    65    41    20    46
  --- + --- - --- - --- + --- - --- - --- + --- - --- - --- + --- - 
   25    24    23    22    21    20    19    18    17    16    15
  q     q     q     q     q     q     q     q     q     q     q
 
  18    19    24     3    10    7     -8   2     -6
  --- - --- + --- - --- - --- + -- + q   - -- + q
   14    13    12    11    10    9          7
  q     q     q     q     q     q          q</nowiki></code></td></tr>
</table>  }}