10 80

2008-12-19T20:19:11Z

DarorAcele: cnaeld

domc4tvi



{{Rolfsen Knot Page|
n = 10 |
k = 80 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-3,9,-10,2,-5,6,-9,3,-4,8,-7,5,-6,4,-8,7/goTop.html |
braid_table = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.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:BraidPart1.gif]][[Image:BraidPart4.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:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.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:BraidPart4.gif]][[Image:BraidPart0.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> </td><td>r</td></tr>
<tr><td> </td><td> \ </td><td> </td></tr>
<tr><td>j</td><td> </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%>χ</td></tr>
<tr align=center><td>-5</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>1</td><td>1</td></tr>
<tr align=center><td>-7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>2</td><td bgcolor=yellow>1</td><td>-1</td></tr>
<tr align=center><td>-9</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>4</td><td bgcolor=yellow> </td><td> </td><td>4</td></tr>
<tr align=center><td>-11</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>4</td><td bgcolor=yellow>2</td><td> </td><td> </td><td>-2</td></tr>
<tr align=center><td>-13</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>7</td><td bgcolor=yellow>4</td><td> </td><td> </td><td> </td><td>3</td></tr>
<tr align=center><td>-15</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>5</td><td bgcolor=yellow>4</td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr>
<tr align=center><td>-17</td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>6</td><td bgcolor=yellow>7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr>
<tr align=center><td>-19</td><td> </td><td> </td><td> </td><td bgcolor=yellow>4</td><td bgcolor=yellow>5</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>-21</td><td> </td><td> </td><td bgcolor=yellow>2</td><td bgcolor=yellow>6</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-4</td></tr>
<tr align=center><td>-23</td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow>4</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>3</td></tr>
<tr align=center><td>-25</td><td bgcolor=yellow> </td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-2</td></tr>
<tr align=center><td>-27</td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
</table> |
coloured_jones_2 = <math> q^{-6} -2 q^{-7} + q^{-8} +8 q^{-9} -12 q^{-10} -4 q^{-11} +33 q^{-12} -27 q^{-13} -28 q^{-14} +71 q^{-15} -30 q^{-16} -68 q^{-17} +103 q^{-18} -17 q^{-19} -103 q^{-20} +112 q^{-21} +4 q^{-22} -114 q^{-23} +95 q^{-24} +20 q^{-25} -93 q^{-26} +58 q^{-27} +21 q^{-28} -51 q^{-29} +23 q^{-30} +11 q^{-31} -17 q^{-32} +6 q^{-33} +2 q^{-34} -3 q^{-35} + q^{-36} </math> |
coloured_jones_3 = <math> q^{-9} -2 q^{-10} + q^{-11} +3 q^{-12} +3 q^{-13} -12 q^{-14} -4 q^{-15} +21 q^{-16} +23 q^{-17} -40 q^{-18} -46 q^{-19} +41 q^{-20} +106 q^{-21} -48 q^{-22} -154 q^{-23} +235 q^{-25} +47 q^{-26} -278 q^{-27} -149 q^{-28} +327 q^{-29} +237 q^{-30} -322 q^{-31} -361 q^{-32} +320 q^{-33} +449 q^{-34} -272 q^{-35} -543 q^{-36} +224 q^{-37} +608 q^{-38} -160 q^{-39} -649 q^{-40} +89 q^{-41} +666 q^{-42} -25 q^{-43} -635 q^{-44} -51 q^{-45} +589 q^{-46} +94 q^{-47} -490 q^{-48} -140 q^{-49} +395 q^{-50} +137 q^{-51} -272 q^{-52} -135 q^{-53} +183 q^{-54} +101 q^{-55} -107 q^{-56} -68 q^{-57} +57 q^{-58} +40 q^{-59} -29 q^{-60} -20 q^{-61} +15 q^{-62} +8 q^{-63} -8 q^{-64} - q^{-65} +2 q^{-66} +2 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} +3 q^{-17} -13 q^{-18} +2 q^{-19} +23 q^{-20} +2 q^{-21} +10 q^{-22} -66 q^{-23} -29 q^{-24} +71 q^{-25} +65 q^{-26} +95 q^{-27} -178 q^{-28} -198 q^{-29} +30 q^{-30} +186 q^{-31} +446 q^{-32} -162 q^{-33} -501 q^{-34} -346 q^{-35} +72 q^{-36} +1042 q^{-37} +306 q^{-38} -547 q^{-39} -1014 q^{-40} -663 q^{-41} +1409 q^{-42} +1157 q^{-43} +96 q^{-44} -1454 q^{-45} -1910 q^{-46} +1079 q^{-47} +1853 q^{-48} +1329 q^{-49} -1243 q^{-50} -3118 q^{-51} +145 q^{-52} +2001 q^{-53} +2639 q^{-54} -487 q^{-55} -3885 q^{-56} -967 q^{-57} +1680 q^{-58} +3659 q^{-59} +445 q^{-60} -4181 q^{-61} -1953 q^{-62} +1124 q^{-63} +4274 q^{-64} +1340 q^{-65} -4028 q^{-66} -2697 q^{-67} +388 q^{-68} +4375 q^{-69} +2115 q^{-70} -3331 q^{-71} -3008 q^{-72} -492 q^{-73} +3752 q^{-74} +2547 q^{-75} -2118 q^{-76} -2635 q^{-77} -1209 q^{-78} +2480 q^{-79} +2321 q^{-80} -852 q^{-81} -1654 q^{-82} -1345 q^{-83} +1130 q^{-84} +1516 q^{-85} -101 q^{-86} -645 q^{-87} -925 q^{-88} +309 q^{-89} +674 q^{-90} +64 q^{-91} -93 q^{-92} -416 q^{-93} +42 q^{-94} +203 q^{-95} +12 q^{-96} +40 q^{-97} -130 q^{-98} +8 q^{-99} +46 q^{-100} -18 q^{-101} +28 q^{-102} -30 q^{-103} +5 q^{-104} +10 q^{-105} -11 q^{-106} +8 q^{-107} -5 q^{-108} +2 q^{-109} +2 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} +2 q^{-21} -7 q^{-22} +3 q^{-23} +20 q^{-24} +5 q^{-25} -17 q^{-26} -17 q^{-27} -39 q^{-28} + q^{-29} +79 q^{-30} +94 q^{-31} +9 q^{-32} -92 q^{-33} -214 q^{-34} -153 q^{-35} +126 q^{-36} +381 q^{-37} +376 q^{-38} +48 q^{-39} -545 q^{-40} -823 q^{-41} -395 q^{-42} +508 q^{-43} +1274 q^{-44} +1214 q^{-45} -131 q^{-46} -1702 q^{-47} -2145 q^{-48} -896 q^{-49} +1524 q^{-50} +3359 q^{-51} +2484 q^{-52} -766 q^{-53} -3951 q^{-54} -4525 q^{-55} -1224 q^{-56} +4003 q^{-57} +6550 q^{-58} +3830 q^{-59} -2604 q^{-60} -7995 q^{-61} -7264 q^{-62} +170 q^{-63} +8421 q^{-64} +10422 q^{-65} +3609 q^{-66} -7489 q^{-67} -13298 q^{-68} -7784 q^{-69} +5219 q^{-70} +14955 q^{-71} +12355 q^{-72} -1888 q^{-73} -15744 q^{-74} -16305 q^{-75} -2091 q^{-76} +15203 q^{-77} +19868 q^{-78} +6267 q^{-79} -14086 q^{-80} -22458 q^{-81} -10256 q^{-82} +12272 q^{-83} +24470 q^{-84} +13933 q^{-85} -10390 q^{-86} -25821 q^{-87} -17131 q^{-88} +8352 q^{-89} +26751 q^{-90} +19975 q^{-91} -6296 q^{-92} -27310 q^{-93} -22483 q^{-94} +4155 q^{-95} +27344 q^{-96} +24699 q^{-97} -1680 q^{-98} -26836 q^{-99} -26529 q^{-100} -1020 q^{-101} +25343 q^{-102} +27760 q^{-103} +4154 q^{-104} -22979 q^{-105} -28067 q^{-106} -7181 q^{-107} +19354 q^{-108} +27214 q^{-109} +10069 q^{-110} -15129 q^{-111} -24980 q^{-112} -11960 q^{-113} +10274 q^{-114} +21512 q^{-115} +12956 q^{-116} -5870 q^{-117} -17207 q^{-118} -12414 q^{-119} +2016 q^{-120} +12596 q^{-121} +10972 q^{-122} +539 q^{-123} -8363 q^{-124} -8673 q^{-125} -1959 q^{-126} +4889 q^{-127} +6265 q^{-128} +2323 q^{-129} -2445 q^{-130} -4066 q^{-131} -2062 q^{-132} +981 q^{-133} +2362 q^{-134} +1508 q^{-135} -229 q^{-136} -1223 q^{-137} -966 q^{-138} -51 q^{-139} +571 q^{-140} +529 q^{-141} +106 q^{-142} -230 q^{-143} -250 q^{-144} -94 q^{-145} +79 q^{-146} +124 q^{-147} +42 q^{-148} -34 q^{-149} -29 q^{-150} -23 q^{-151} -8 q^{-152} +28 q^{-153} +10 q^{-154} -14 q^{-155} +5 q^{-156} -9 q^{-158} +5 q^{-159} +4 q^{-160} -5 q^{-161} +2 q^{-162} +2 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} +8 q^{-25} -6 q^{-26} +22 q^{-28} -4 q^{-29} -15 q^{-30} -33 q^{-31} +12 q^{-32} -10 q^{-33} +11 q^{-34} +107 q^{-35} +46 q^{-36} -27 q^{-37} -166 q^{-38} -94 q^{-39} -145 q^{-40} -15 q^{-41} +382 q^{-42} +418 q^{-43} +291 q^{-44} -275 q^{-45} -464 q^{-46} -945 q^{-47} -777 q^{-48} +387 q^{-49} +1277 q^{-50} +1853 q^{-51} +970 q^{-52} +41 q^{-53} -2344 q^{-54} -3576 q^{-55} -2259 q^{-56} +354 q^{-57} +3854 q^{-58} +5097 q^{-59} +5151 q^{-60} -221 q^{-61} -6123 q^{-62} -8961 q^{-63} -7421 q^{-64} -401 q^{-65} +7345 q^{-66} +15251 q^{-67} +11758 q^{-68} +1384 q^{-69} -11545 q^{-70} -20292 q^{-71} -17888 q^{-72} -5285 q^{-73} +17736 q^{-74} +28626 q^{-75} +25578 q^{-76} +5859 q^{-77} -20827 q^{-78} -39416 q^{-79} -37853 q^{-80} -5435 q^{-81} +28402 q^{-82} +52431 q^{-83} +45719 q^{-84} +9834 q^{-85} -39229 q^{-86} -71461 q^{-87} -53396 q^{-88} -7204 q^{-89} +53714 q^{-90} +85123 q^{-91} +66914 q^{-92} -907 q^{-93} -77001 q^{-94} -100285 q^{-95} -69625 q^{-96} +15833 q^{-97} +95843 q^{-98} +122768 q^{-99} +63685 q^{-100} -44277 q^{-101} -119857 q^{-102} -130841 q^{-103} -46846 q^{-104} +71245 q^{-105} +153696 q^{-106} +127270 q^{-107} +10843 q^{-108} -108362 q^{-109} -170090 q^{-110} -108664 q^{-111} +27591 q^{-112} +157840 q^{-113} +172030 q^{-114} +65196 q^{-115} -81111 q^{-116} -186771 q^{-117} -154700 q^{-118} -15210 q^{-119} +148440 q^{-120} +198150 q^{-121} +107147 q^{-122} -53884 q^{-123} -191824 q^{-124} -186057 q^{-125} -49336 q^{-126} +136763 q^{-127} +214526 q^{-128} +139486 q^{-129} -30031 q^{-130} -192429 q^{-131} -210457 q^{-132} -80100 q^{-133} +121623 q^{-134} +224952 q^{-135} +169705 q^{-136} -1170 q^{-137} -183335 q^{-138} -228998 q^{-139} -115272 q^{-140} +91816 q^{-141} +220603 q^{-142} +196390 q^{-143} +40424 q^{-144} -151162 q^{-145} -229384 q^{-146} -150503 q^{-147} +40685 q^{-148} +186513 q^{-149} +203544 q^{-150} +86451 q^{-151} -91437 q^{-152} -195465 q^{-153} -165771 q^{-154} -18423 q^{-155} +121201 q^{-156} +174229 q^{-157} +112632 q^{-158} -22997 q^{-159} -129229 q^{-160} -143829 q^{-161} -57173 q^{-162} +48484 q^{-163} +113847 q^{-164} +101941 q^{-165} +23230 q^{-166} -58221 q^{-167} -93143 q^{-168} -59535 q^{-169} -266 q^{-170} +51631 q^{-171} +65110 q^{-172} +33763 q^{-173} -11911 q^{-174} -42600 q^{-175} -37820 q^{-176} -15340 q^{-177} +12999 q^{-178} +28872 q^{-179} +22358 q^{-180} +4240 q^{-181} -12619 q^{-182} -15584 q^{-183} -11188 q^{-184} -586 q^{-185} +8545 q^{-186} +9270 q^{-187} +4402 q^{-188} -1926 q^{-189} -3949 q^{-190} -4536 q^{-191} -1945 q^{-192} +1578 q^{-193} +2573 q^{-194} +1748 q^{-195} +20 q^{-196} -412 q^{-197} -1203 q^{-198} -890 q^{-199} +183 q^{-200} +505 q^{-201} +419 q^{-202} +26 q^{-203} +111 q^{-204} -220 q^{-205} -270 q^{-206} +34 q^{-207} +85 q^{-208} +71 q^{-209} -31 q^{-210} +71 q^{-211} -30 q^{-212} -71 q^{-213} +18 q^{-214} +14 q^{-215} +15 q^{-216} -22 q^{-217} +21 q^{-218} -19 q^{-220} +7 q^{-221} + q^{-222} +4 q^{-223} -5 q^{-224} +2 q^{-225} +2 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]:=    </pre></td>
<td align=left><pre style="color: red; border: 0px; padding: 0em"><< 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, 80]]</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, 12, 6, 13], X[13, 18, 14, 19],

X[9, 16, 10, 17], X[17, 10, 18, 11], X[15, 20, 16, 1],

X[19, 14, 20, 15], X[11, 6, 12, 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, 80]]</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, 6, -9, 3, -4, 8, -7, 5, -6,

4, -8, 7]</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, 80]]</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, 12, 2, 16, 6, 18, 20, 10, 14]</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, 80]]</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, 2, -1, -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, 80]]</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, 80]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:10_80_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, 80]]&) /@ {
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>{Chiral, 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, 80]][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 9 15 2 3
-17 + -- - -- + -- + 15 t - 9 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, 80]][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 + 6 z + 9 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, 80]}</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, 80]], KnotSignature[Knot[10, 80]]}</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>{71, -6}</nowiki></code></td></tr>
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<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, 80]][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> -13 3 6 10 11 12 11 8 6 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, 80]}</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, 80]][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 -34 3 2 -28 3 3 -22 3
q + q - q + q - --- - --- - q - --- + --- - q + --- +
32 30 26 24 20
q q q q q

2 3 -12 -10
--- + --- - q + q
18 14
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, 80]][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
2 a + 3 a - 6 a + 2 a + 5 a z + 9 a z - 9 a z + a z +

6 4 8 4 10 4 6 6 8 6
4 a z + 8 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, 80]][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 7 9 11 13
-2 a + 3 a + 6 a + 2 a + a z - 8 a z - 12 a z - 2 a z +

15 6 2 8 2 10 2 12 2 14 2
a z + 5 a z - 7 a z - 13 a z + 2 a z + 2 a z -

16 2 7 3 9 3 11 3 13 3 15 3
a z + 2 a z + 22 a z + 29 a z + 6 a z - 3 a z -

6 4 8 4 10 4 12 4 14 4 16 4
4 a z + 8 a z + 13 a z - 5 a z - 5 a z + a z -

7 5 9 5 11 5 13 5 15 5 6 6
5 a z - 23 a z - 29 a z - 8 a z + 3 a z + a z -

8 6 10 6 12 6 14 6 7 7 9 7
8 a z - 15 a z - a z + 5 a z + 2 a z + 6 a z +

11 7 13 7 8 8 10 8 12 8 9 9 11 9
10 a z + 6 a z + 3 a z + 7 a z + 4 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, 80]], Vassiliev[3][Knot[10, 80]]}</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>{6, -12}</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, 80]][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 4 2 6
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

4 5 6 7 5 4 7
------ + ------ + ------ + ------ + ------ + ------ + ------ +
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

4 4 2 4 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, 80], 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 2 6 17 11 23 51 21 58 93
q - --- + --- + --- - --- + --- + --- - --- + --- + --- - --- +
35 34 33 32 31 30 29 28 27 26
q q q q q q q q q q

20 95 114 4 112 103 17 103 68 30 71
--- + --- - --- + --- + --- - --- - --- + --- - --- - --- + --- -
25 24 23 22 21 20 19 18 17 16 15
q q q q q q q q q q q

28 27 33 4 12 8 -8 2 -6
--- - --- + --- - --- - --- + -- + q - -- + q
14 13 12 11 10 9 7
q q q q q q q</nowiki></code></td></tr>
</table> }}

Knot Atlas - User contributions [en]

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