10 119

2009-05-22T09:51:31Z

RicerCdomv:

http://www.textmonracboc.com



{{Rolfsen Knot Page|
n = 10 |
k = 119 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,8,-5,1,-2,3,-6,7,-8,10,-9,5,-7,6,-4,2,-10,9/goTop.html |
braid_table = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.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:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart2.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]]</td></tr>
</table> |
braid_crossings = 11 |
braid_width = 4 |
braid_index = 4 |
same_alexander = [[K11a84]], |
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%>-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=6.66667%>5</td ><td width=6.66667%>6</td ><td width=13.3333%>χ</td></tr>
<tr align=center><td>13</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>11</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow> </td><td>-3</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>5</td><td bgcolor=yellow>1</td><td> </td><td>4</td></tr>
<tr align=center><td>7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>7</td><td bgcolor=yellow>3</td><td> </td><td> </td><td>-4</td></tr>
<tr align=center><td>5</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>9</td><td bgcolor=yellow>5</td><td> </td><td> </td><td> </td><td>4</td></tr>
<tr align=center><td>3</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>8</td><td bgcolor=yellow>7</td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr>
<tr align=center><td>1</td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>8</td><td bgcolor=yellow>9</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr>
<tr align=center><td>-1</td><td> </td><td> </td><td> </td><td bgcolor=yellow>6</td><td bgcolor=yellow>9</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>3</td></tr>
<tr align=center><td>-3</td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-4</td></tr>
<tr align=center><td>-5</td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow>6</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>5</td></tr>
<tr align=center><td>-7</td><td bgcolor=yellow> </td><td bgcolor=yellow>3</td><td> </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>-9</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^{18}-4 q^{17}+2 q^{16}+15 q^{15}-26 q^{14}-9 q^{13}+67 q^{12}-54 q^{11}-61 q^{10}+146 q^9-54 q^8-144 q^7+206 q^6-21 q^5-214 q^4+216 q^3+26 q^2-232 q+173+59 q^{-1} -185 q^{-2} +97 q^{-3} +56 q^{-4} -99 q^{-5} +34 q^{-6} +27 q^{-7} -30 q^{-8} +7 q^{-9} +5 q^{-10} -4 q^{-11} + q^{-12} </math> |
coloured_jones_3 = <math>q^{36}-4 q^{35}+2 q^{34}+9 q^{33}+q^{32}-29 q^{31}-15 q^{30}+67 q^{29}+55 q^{28}-105 q^{27}-152 q^{26}+128 q^{25}+304 q^{24}-95 q^{23}-495 q^{22}-27 q^{21}+690 q^{20}+243 q^{19}-843 q^{18}-534 q^{17}+920 q^{16}+861 q^{15}-901 q^{14}-1196 q^{13}+816 q^{12}+1476 q^{11}-648 q^{10}-1721 q^9+458 q^8+1881 q^7-232 q^6-1971 q^5+5 q^4+1962 q^3+229 q^2-1864 q-427+1654 q^{-1} +584 q^{-2} -1370 q^{-3} -653 q^{-4} +1028 q^{-5} +645 q^{-6} -701 q^{-7} -547 q^{-8} +417 q^{-9} +414 q^{-10} -227 q^{-11} -261 q^{-12} +100 q^{-13} +151 q^{-14} -45 q^{-15} -74 q^{-16} +23 q^{-17} +28 q^{-18} -9 q^{-19} -10 q^{-20} +3 q^{-21} +5 q^{-22} -4 q^{-23} + q^{-24} </math> |
coloured_jones_4 = <math>q^{60}-4 q^{59}+2 q^{58}+9 q^{57}-5 q^{56}-2 q^{55}-35 q^{54}+9 q^{53}+78 q^{52}+24 q^{51}-2 q^{50}-234 q^{49}-123 q^{48}+256 q^{47}+344 q^{46}+343 q^{45}-653 q^{44}-912 q^{43}-60 q^{42}+923 q^{41}+1908 q^{40}-284 q^{39}-2244 q^{38}-2063 q^{37}+229 q^{36}+4410 q^{35}+2383 q^{34}-2044 q^{33}-5254 q^{32}-3503 q^{31}+5323 q^{30}+6610 q^{29}+1610 q^{28}-6835 q^{27}-9280 q^{26}+2669 q^{25}+9461 q^{24}+7637 q^{23}-4976 q^{22}-14134 q^{21}-2500 q^{20}+9273 q^{19}+13279 q^{18}-726 q^{17}-16431 q^{16}-7818 q^{15}+6885 q^{14}+17045 q^{13}+3954 q^{12}-16512 q^{11}-12057 q^{10}+3581 q^9+18858 q^8+8212 q^7-14791 q^6-14952 q^5-359 q^4+18417 q^3+11734 q^2-10923 q-15659-4667 q^{-1} +14854 q^{-2} +13309 q^{-3} -5243 q^{-4} -12982 q^{-5} -7653 q^{-6} +8713 q^{-7} +11442 q^{-8} -153 q^{-9} -7596 q^{-10} -7376 q^{-11} +2925 q^{-12} +6895 q^{-13} +1895 q^{-14} -2602 q^{-15} -4508 q^{-16} +81 q^{-17} +2698 q^{-18} +1345 q^{-19} -242 q^{-20} -1752 q^{-21} -309 q^{-22} +666 q^{-23} +403 q^{-24} +151 q^{-25} -454 q^{-26} -84 q^{-27} +124 q^{-28} +38 q^{-29} +63 q^{-30} -91 q^{-31} -2 q^{-32} +27 q^{-33} -8 q^{-34} +11 q^{-35} -14 q^{-36} +3 q^{-37} +5 q^{-38} -4 q^{-39} + q^{-40} </math> |
coloured_jones_5 = <math>q^{90}-4 q^{89}+2 q^{88}+9 q^{87}-5 q^{86}-8 q^{85}-8 q^{84}-11 q^{83}+20 q^{82}+71 q^{81}+29 q^{80}-74 q^{79}-149 q^{78}-157 q^{77}+43 q^{76}+386 q^{75}+535 q^{74}+142 q^{73}-629 q^{72}-1233 q^{71}-964 q^{70}+508 q^{69}+2323 q^{68}+2741 q^{67}+615 q^{66}-3068 q^{65}-5523 q^{64}-3818 q^{63}+2301 q^{62}+8706 q^{61}+9376 q^{60}+1607 q^{59}-10271 q^{58}-16735 q^{57}-10010 q^{56}+7863 q^{55}+23717 q^{54}+22560 q^{53}+908 q^{52}-26863 q^{51}-37290 q^{50}-16878 q^{49}+22875 q^{48}+50391 q^{47}+38553 q^{46}-9576 q^{45}-57548 q^{44}-62501 q^{43}-12860 q^{42}+55504 q^{41}+84185 q^{40}+41841 q^{39}-43024 q^{38}-99477 q^{37}-73282 q^{36}+21200 q^{35}+105906 q^{34}+103113 q^{33}+6837 q^{32}-103332 q^{31}-127723 q^{30}-37512 q^{29}+92962 q^{28}+146068 q^{27}+67383 q^{26}-77858 q^{25}-157705 q^{24}-94208 q^{23}+60130 q^{22}+164281 q^{21}+117290 q^{20}-42344 q^{19}-166996 q^{18}-136672 q^{17}+24919 q^{16}+167338 q^{15}+153331 q^{14}-8048 q^{13}-165525 q^{12}-167906 q^{11}-9396 q^{10}+161160 q^9+180507 q^8+28179 q^7-152563 q^6-190371 q^5-48880 q^4+138440 q^3+195494 q^2+70496 q-117398-193539 q^{-1} -91167 q^{-2} +90096 q^{-3} +182525 q^{-4} +107326 q^{-5} -58453 q^{-6} -161747 q^{-7} -115969 q^{-8} +26501 q^{-9} +132782 q^{-10} +114703 q^{-11} +1431 q^{-12} -99257 q^{-13} -103670 q^{-14} -21353 q^{-15} +65902 q^{-16} +85046 q^{-17} +31853 q^{-18} -37406 q^{-19} -63145 q^{-20} -33162 q^{-21} +16513 q^{-22} +41826 q^{-23} +28465 q^{-24} -3794 q^{-25} -24745 q^{-26} -20758 q^{-27} -2018 q^{-28} +12681 q^{-29} +13217 q^{-30} +3546 q^{-31} -5625 q^{-32} -7396 q^{-33} -2904 q^{-34} +2103 q^{-35} +3599 q^{-36} +1790 q^{-37} -611 q^{-38} -1566 q^{-39} -928 q^{-40} +176 q^{-41} +615 q^{-42} +361 q^{-43} -45 q^{-44} -198 q^{-45} -133 q^{-46} - q^{-47} +96 q^{-48} +34 q^{-49} -33 q^{-50} -9 q^{-51} +2 q^{-52} -9 q^{-53} +12 q^{-54} +7 q^{-55} -14 q^{-56} +3 q^{-57} +5 q^{-58} -4 q^{-59} + q^{-60} </math> |
coloured_jones_6 = <math>q^{126}-4 q^{125}+2 q^{124}+9 q^{123}-5 q^{122}-8 q^{121}-14 q^{120}+16 q^{119}+13 q^{117}+76 q^{116}-19 q^{115}-87 q^{114}-173 q^{113}-37 q^{112}+32 q^{111}+212 q^{110}+597 q^{109}+324 q^{108}-193 q^{107}-1077 q^{106}-1170 q^{105}-1074 q^{104}+156 q^{103}+2687 q^{102}+3644 q^{101}+2879 q^{100}-1066 q^{99}-4766 q^{98}-8642 q^{97}-7628 q^{96}+740 q^{95}+10641 q^{94}+18227 q^{93}+14755 q^{92}+3147 q^{91}-19152 q^{90}-35574 q^{89}-31743 q^{88}-7345 q^{87}+31458 q^{86}+59060 q^{85}+63137 q^{84}+18940 q^{83}-48250 q^{82}-100827 q^{81}-104108 q^{80}-39317 q^{79}+63176 q^{78}+162419 q^{77}+167622 q^{76}+70659 q^{75}-92693 q^{74}-232947 q^{73}-253500 q^{72}-121546 q^{71}+132952 q^{70}+331550 q^{69}+362644 q^{68}+165312 q^{67}-169952 q^{66}-455762 q^{65}-502014 q^{64}-207811 q^{63}+237928 q^{62}+607679 q^{61}+632205 q^{60}+258986 q^{59}-338753 q^{58}-797916 q^{57}-763179 q^{56}-261150 q^{55}+483253 q^{54}+980938 q^{53}+900348 q^{52}+205544 q^{51}-692790 q^{50}-1177502 q^{49}-962377 q^{48}-71166 q^{47}+920165 q^{46}+1389200 q^{45}+936713 q^{44}-174355 q^{43}-1196663 q^{42}-1510284 q^{41}-793359 q^{40}+480296 q^{39}+1513405 q^{38}+1523101 q^{37}+489665 q^{36}-882073 q^{35}-1734843 q^{34}-1385111 q^{33}-80578 q^{32}+1351700 q^{31}+1832666 q^{30}+1041271 q^{29}-468324 q^{28}-1721154 q^{27}-1748009 q^{26}-549293 q^{25}+1105672 q^{24}+1949534 q^{23}+1414470 q^{22}-119797 q^{21}-1634951 q^{20}-1964344 q^{19}-894103 q^{18}+889871 q^{17}+2005998 q^{16}+1695002 q^{15}+170021 q^{14}-1543644 q^{13}-2140097 q^{12}-1212056 q^{11}+657080 q^{10}+2026626 q^9+1970649 q^8+515939 q^7-1359164 q^6-2260711 q^5-1577469 q^4+273280 q^3+1883026 q^2+2187926 q+976970-931323 q^{-1} -2157307 q^{-2} -1893519 q^{-3} -296676 q^{-4} +1414673 q^{-5} +2136498 q^{-6} +1404434 q^{-7} -260131 q^{-8} -1666401 q^{-9} -1908538 q^{-10} -843657 q^{-11} +667373 q^{-12} +1658528 q^{-13} +1507905 q^{-14} +382318 q^{-15} -886523 q^{-16} -1479924 q^{-17} -1046864 q^{-18} -30361 q^{-19} +905971 q^{-20} +1169119 q^{-21} +662338 q^{-22} -186409 q^{-23} -807055 q^{-24} -821489 q^{-25} -355208 q^{-26} +263383 q^{-27} +622264 q^{-28} +537974 q^{-29} +145088 q^{-30} -263289 q^{-31} -421230 q^{-32} -312460 q^{-33} -34549 q^{-34} +205459 q^{-35} +267735 q^{-36} +157234 q^{-37} -20098 q^{-38} -133588 q^{-39} -149712 q^{-40} -70701 q^{-41} +29488 q^{-42} +83394 q^{-43} +72557 q^{-44} +22346 q^{-45} -21110 q^{-46} -43985 q^{-47} -32343 q^{-48} -4874 q^{-49} +15681 q^{-50} +19492 q^{-51} +10333 q^{-52} +734 q^{-53} -8165 q^{-54} -8255 q^{-55} -2932 q^{-56} +1772 q^{-57} +3263 q^{-58} +2009 q^{-59} +1067 q^{-60} -1037 q^{-61} -1411 q^{-62} -502 q^{-63} +221 q^{-64} +369 q^{-65} +109 q^{-66} +266 q^{-67} -120 q^{-68} -199 q^{-69} -16 q^{-70} +55 q^{-71} +42 q^{-72} -52 q^{-73} +49 q^{-74} -5 q^{-75} -34 q^{-76} +11 q^{-77} +8 q^{-78} +7 q^{-79} -14 q^{-80} +3 q^{-81} +5 q^{-82} -4 q^{-83} + q^{-84} </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, 119]]</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, 18, 8, 19], X[3, 9, 4, 8], X[17, 3, 18, 2],

X[5, 15, 6, 14], X[9, 17, 10, 16], X[15, 11, 16, 10],

X[11, 5, 12, 4], X[13, 20, 14, 1], X[19, 12, 20, 13]]</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, 119]]</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[-1, 4, -3, 8, -5, 1, -2, 3, -6, 7, -8, 10, -9, 5, -7, 6, -4,

2, -10, 9]</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, 119]]</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, 8, 14, 18, 16, 4, 20, 10, 2, 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, 119]]</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, 2, -1, -3, 2, -1, 2, 3, 3, 2}]</nowiki></code></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{First[br], Crossings[br]}</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[6]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{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, 119]]</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, 119]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:10_119_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, 119]]&) /@ {
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, 1, 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, 119]][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 10 23 2 3
31 - -- + -- - -- - 23 t + 10 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, 119]][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 - z - 2 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, 119], Knot[11, Alternating, 84]}</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, 119]], KnotSignature[Knot[10, 119]]}</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>{101, 0}</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, 119]][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> -4 4 9 13 2 3 4 5 6
16 + q - -- + -- - -- - 17 q + 16 q - 12 q + 8 q - 4 q + q
3 2 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, 119]}</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, 119]][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> -12 2 2 2 3 3 2 4 6 8 10
-3 + q - --- + -- + -- - -- + -- + q + q - q + 4 q - 3 q +
10 8 6 4 2
q q q q q

12 14 16 18
q + q - 2 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, 119]][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> 2 2 4 4
-2 2 2 z z 2 2 4 z 2 z 2 4
-1 + a + a - 2 z + -- - -- + a z - 2 z + -- - ---- + a z -
4 2 4 2
a a a a

6
6 z
z - --
2
a</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, 119]][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> 2 2
-2 2 z 3 z 4 z 2 z z 2 2
-1 - a - a - -- - --- - --- - 2 a z + 6 z + -- + -- + 4 a z +
5 3 a 6 2
a a a a

3 3 3 4 4 4
7 z 19 z 22 z 3 3 3 4 2 z 8 z 13 z
---- + ----- + ----- + 9 a z - a z - 7 z - ---- + ---- + ----- -
5 3 a 6 4 2
a a a a a

5 5 5
2 4 4 4 10 z 26 z 37 z 5 3 5 6
9 a z + a z - ----- - ----- - ----- - 17 a z + 4 a z - 7 z +
5 3 a
a a

6 6 6 7 7 7
z 14 z 31 z 2 6 4 z 5 z 13 z 7 8
-- - ----- - ----- + 9 a z + ---- + ---- + ----- + 12 a z + 9 z +
6 4 2 5 3 a
a a a a a

8 8 9 9
6 z 15 z 3 z 3 z
---- + ----- + ---- + ----
4 2 3 a
a a a</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, 119]], Vassiliev[3][Knot[10, 119]]}</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>{-1, 0}</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, 119]][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>9 1 3 1 6 3 7 6
- + 8 q + ----- + ----- + ----- + ----- + ----- + ---- + --- + 9 q t +
q 9 4 7 3 5 3 5 2 3 2 3 q t
q t q t q t q t q t q t

3 3 2 5 2 5 3 7 3 7 4 9 4
8 q t + 7 q t + 9 q t + 5 q t + 7 q t + 3 q t + 5 q t +

9 5 11 5 13 6
q t + 3 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, 119], 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> -12 4 5 7 30 27 34 99 56 97 185 59
173 + q - --- + --- + -- - -- + -- + -- - -- + -- + -- - --- + -- -
11 10 9 8 7 6 5 4 3 2 q
q q q q q q q q q q

2 3 4 5 6 7 8
232 q + 26 q + 216 q - 214 q - 21 q + 206 q - 144 q - 54 q +

9 10 11 12 13 14 15 16
146 q - 61 q - 54 q + 67 q - 9 q - 26 q + 15 q + 2 q -

17 18
4 q + q</nowiki></code></td></tr>
</table> }}

Knot Atlas - User contributions [en]

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