10 91: Difference between revisions
No edit summary |
No edit summary |
||
(4 intermediate revisions by 2 users not shown) | |||
Line 1: | Line 1: | ||
<!-- 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 | |
|||
<!-- provide an anchor so we can return to the top of the page --> |
|||
k = 91 | |
|||
<span id="top"></span> |
|||
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-5,4,-10,2,-1,6,-7,3,-4,9,-8,10,-6,7,-3,5,-9,8,-2/goTop.html | |
|||
<!-- --> |
|||
braid_table = <table cellspacing=0 cellpadding=0 border=0> |
|||
<!-- this relies on transclusion for next and previous links --> |
|||
<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
|||
{{Knot Navigation Links|ext=gif}} |
|||
<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]]</td></tr> |
|||
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]]</td></tr> |
|||
{{Rolfsen Knot Page Header|n=10|k=91|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-5,4,-10,2,-1,6,-7,3,-4,9,-8,10,-6,7,-3,5,-9,8,-2/goTop.html}} |
|||
</table> | |
|||
braid_crossings = 10 | |
|||
<br style="clear:both" /> |
|||
braid_width = 3 | |
|||
braid_index = 3 | |
|||
{{:{{PAGENAME}} Further Notes and Views}} |
|||
same_alexander = | |
|||
same_jones = [[10_43]], | |
|||
{{Knot Presentations}} |
|||
khovanov_table = <table border=1> |
|||
{{3D Invariants}} |
|||
{{4D Invariants}} |
|||
{{Polynomial Invariants}} |
|||
{{Vassiliev Invariants}} |
|||
{{Khovanov Homology|table=<table border=1> |
|||
<tr align=center> |
<tr align=center> |
||
<td width=13.3333%><table cellpadding=0 cellspacing=0> |
<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> </td><td> \ </td><td> </td></tr> |
||
<tr><td>j</td><td> </td><td>\</td></tr> |
<tr><td>j</td><td> </td><td>\</td></tr> |
||
</table></td> |
</table></td> |
||
<td width=6.66667%>-5</td ><td width=6.66667%>-4</td ><td width=6.66667%>-3</td ><td width=6.66667%>-2</td ><td width=6.66667%>-1</td ><td width=6.66667%>0</td ><td width=6.66667%>1</td ><td width=6.66667%>2</td ><td width=6.66667%>3</td ><td width=6.66667%>4</td ><td width=6.66667%>5</td ><td width=13.3333%>χ</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> </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> </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> </td><td bgcolor=yellow>2</td><td bgcolor=yellow> </td><td>2</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> </td><td bgcolor=yellow>2</td><td bgcolor=yellow> </td><td>2</td></tr> |
||
Line 41: | Line 39: | ||
<tr align=center><td>-9</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>-9</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>-11</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> |
<tr align=center><td>-11</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> |
</table> | |
||
coloured_jones_2 = <math>q^{15}-3 q^{14}+2 q^{13}+7 q^{12}-17 q^{11}+5 q^{10}+30 q^9-43 q^8-5 q^7+72 q^6-66 q^5-31 q^4+114 q^3-73 q^2-58 q+132-60 q^{-1} -71 q^{-2} +113 q^{-3} -32 q^{-4} -64 q^{-5} +71 q^{-6} -7 q^{-7} -40 q^{-8} +30 q^{-9} +2 q^{-10} -15 q^{-11} +8 q^{-12} + q^{-13} -3 q^{-14} + q^{-15} </math> | |
|||
{{Computer Talk Header}} |
|||
coloured_jones_3 = <math>-q^{30}+3 q^{29}-2 q^{28}-3 q^{27}+2 q^{26}+10 q^{25}-7 q^{24}-22 q^{23}+12 q^{22}+47 q^{21}-14 q^{20}-83 q^{19}-5 q^{18}+136 q^{17}+44 q^{16}-187 q^{15}-115 q^{14}+225 q^{13}+215 q^{12}-244 q^{11}-323 q^{10}+229 q^9+438 q^8-200 q^7-527 q^6+142 q^5+607 q^4-92 q^3-639 q^2+16 q+668+33 q^{-1} -635 q^{-2} -109 q^{-3} +597 q^{-4} +158 q^{-5} -512 q^{-6} -210 q^{-7} +417 q^{-8} +231 q^{-9} -302 q^{-10} -233 q^{-11} +197 q^{-12} +204 q^{-13} -107 q^{-14} -159 q^{-15} +46 q^{-16} +109 q^{-17} -15 q^{-18} -63 q^{-19} + q^{-20} +34 q^{-21} -17 q^{-23} + q^{-24} +9 q^{-25} -2 q^{-26} -3 q^{-27} - q^{-28} +3 q^{-29} - q^{-30} </math> | |
|||
coloured_jones_4 = <math>q^{50}-3 q^{49}+2 q^{48}+3 q^{47}-6 q^{46}+5 q^{45}-9 q^{44}+13 q^{43}+12 q^{42}-36 q^{41}+7 q^{40}-22 q^{39}+63 q^{38}+69 q^{37}-111 q^{36}-55 q^{35}-116 q^{34}+174 q^{33}+302 q^{32}-104 q^{31}-187 q^{30}-509 q^{29}+114 q^{28}+721 q^{27}+300 q^{26}-47 q^{25}-1200 q^{24}-519 q^{23}+866 q^{22}+1083 q^{21}+838 q^{20}-1649 q^{19}-1666 q^{18}+236 q^{17}+1671 q^{16}+2323 q^{15}-1370 q^{14}-2687 q^{13}-988 q^{12}+1617 q^{11}+3716 q^{10}-552 q^9-3121 q^8-2165 q^7+1083 q^6+4534 q^5+313 q^4-3026 q^3-2936 q^2+416 q+4757+1021 q^{-1} -2574 q^{-2} -3304 q^{-3} -310 q^{-4} +4422 q^{-5} +1622 q^{-6} -1731 q^{-7} -3262 q^{-8} -1130 q^{-9} +3469 q^{-10} +1985 q^{-11} -544 q^{-12} -2629 q^{-13} -1770 q^{-14} +2001 q^{-15} +1777 q^{-16} +538 q^{-17} -1466 q^{-18} -1770 q^{-19} +607 q^{-20} +994 q^{-21} +923 q^{-22} -356 q^{-23} -1122 q^{-24} -84 q^{-25} +204 q^{-26} +621 q^{-27} +139 q^{-28} -418 q^{-29} -114 q^{-30} -114 q^{-31} +210 q^{-32} +129 q^{-33} -90 q^{-34} +4 q^{-35} -85 q^{-36} +36 q^{-37} +31 q^{-38} -25 q^{-39} +27 q^{-40} -21 q^{-41} +7 q^{-42} +3 q^{-43} -12 q^{-44} +8 q^{-45} -3 q^{-46} +3 q^{-47} + q^{-48} -3 q^{-49} + q^{-50} </math> | |
|||
<table> |
|||
coloured_jones_5 = <math>-q^{75}+3 q^{74}-2 q^{73}-3 q^{72}+6 q^{71}-q^{70}-6 q^{69}+3 q^{68}-2 q^{67}-2 q^{66}+22 q^{65}+10 q^{64}-35 q^{63}-35 q^{62}-14 q^{61}+34 q^{60}+107 q^{59}+88 q^{58}-72 q^{57}-228 q^{56}-209 q^{55}+14 q^{54}+372 q^{53}+514 q^{52}+182 q^{51}-468 q^{50}-938 q^{49}-678 q^{48}+328 q^{47}+1371 q^{46}+1509 q^{45}+325 q^{44}-1548 q^{43}-2596 q^{42}-1597 q^{41}+1056 q^{40}+3515 q^{39}+3554 q^{38}+459 q^{37}-3840 q^{36}-5798 q^{35}-3089 q^{34}+2962 q^{33}+7757 q^{32}+6696 q^{31}-607 q^{30}-8849 q^{29}-10669 q^{28}-3151 q^{27}+8499 q^{26}+14342 q^{25}+7991 q^{24}-6670 q^{23}-17145 q^{22}-13088 q^{21}+3492 q^{20}+18635 q^{19}+17969 q^{18}+426 q^{17}-18898 q^{16}-21909 q^{15}-4603 q^{14}+18078 q^{13}+24907 q^{12}+8390 q^{11}-16658 q^{10}-26697 q^9-11701 q^8+14891 q^7+27835 q^6+14198 q^5-13147 q^4-28094 q^3-16309 q^2+11273 q+28211+17899 q^{-1} -9449 q^{-2} -27598 q^{-3} -19461 q^{-4} +7162 q^{-5} +26783 q^{-6} +20773 q^{-7} -4555 q^{-8} -25029 q^{-9} -21909 q^{-10} +1273 q^{-11} +22542 q^{-12} +22476 q^{-13} +2280 q^{-14} -18873 q^{-15} -22211 q^{-16} -5907 q^{-17} +14372 q^{-18} +20710 q^{-19} +8955 q^{-20} -9222 q^{-21} -17972 q^{-22} -10953 q^{-23} +4216 q^{-24} +14111 q^{-25} +11461 q^{-26} +107 q^{-27} -9724 q^{-28} -10525 q^{-29} -3075 q^{-30} +5492 q^{-31} +8413 q^{-32} +4509 q^{-33} -2015 q^{-34} -5802 q^{-35} -4576 q^{-36} -259 q^{-37} +3308 q^{-38} +3688 q^{-39} +1360 q^{-40} -1367 q^{-41} -2477 q^{-42} -1556 q^{-43} +220 q^{-44} +1341 q^{-45} +1226 q^{-46} +304 q^{-47} -549 q^{-48} -768 q^{-49} -396 q^{-50} +123 q^{-51} +386 q^{-52} +290 q^{-53} +38 q^{-54} -129 q^{-55} -167 q^{-56} -81 q^{-57} +39 q^{-58} +71 q^{-59} +37 q^{-60} +15 q^{-61} -13 q^{-62} -35 q^{-63} -8 q^{-64} +10 q^{-65} -3 q^{-66} +7 q^{-67} +8 q^{-68} -5 q^{-69} -3 q^{-70} +3 q^{-71} -3 q^{-72} - q^{-73} +3 q^{-74} - q^{-75} </math> | |
|||
<tr valign=top> |
|||
coloured_jones_6 = <math>q^{105}-3 q^{104}+2 q^{103}+3 q^{102}-6 q^{101}+q^{100}+2 q^{99}+12 q^{98}-14 q^{97}-8 q^{96}+15 q^{95}-25 q^{94}+7 q^{93}+27 q^{92}+58 q^{91}-36 q^{90}-77 q^{89}-11 q^{88}-97 q^{87}+34 q^{86}+169 q^{85}+302 q^{84}+16 q^{83}-276 q^{82}-284 q^{81}-559 q^{80}-147 q^{79}+484 q^{78}+1234 q^{77}+849 q^{76}-80 q^{75}-793 q^{74}-2194 q^{73}-1887 q^{72}-313 q^{71}+2537 q^{70}+3551 q^{69}+2869 q^{68}+1050 q^{67}-3700 q^{66}-6342 q^{65}-5967 q^{64}-478 q^{63}+4858 q^{62}+9191 q^{61}+10410 q^{60}+2728 q^{59}-7034 q^{58}-15523 q^{57}-14134 q^{56}-6802 q^{55}+7861 q^{54}+23234 q^{53}+23849 q^{52}+11495 q^{51}-12269 q^{50}-29867 q^{49}-37265 q^{48}-19839 q^{47}+16729 q^{46}+45406 q^{45}+52441 q^{44}+24454 q^{43}-19536 q^{42}-65917 q^{41}-72831 q^{40}-29596 q^{39}+35411 q^{38}+89040 q^{37}+88092 q^{36}+34718 q^{35}-59002 q^{34}-119154 q^{33}-102892 q^{32}-19619 q^{31}+87988 q^{30}+143067 q^{29}+113841 q^{28}-8420 q^{27}-127717 q^{26}-165565 q^{25}-95838 q^{24}+46498 q^{23}+161601 q^{22}+180174 q^{21}+59278 q^{20}-99921 q^{19}-193612 q^{18}-157902 q^{17}-8568 q^{16}+147835 q^{15}+213957 q^{14}+113025 q^{13}-60656 q^{12}-192734 q^{11}-191017 q^{10}-51704 q^9+123426 q^8+222040 q^7+143230 q^6-29311 q^5-181179 q^4-203498 q^3-78262 q^2+102264 q+219914+159665 q^{-1} -6143 q^{-2} -168365 q^{-3} -209024 q^{-4} -99321 q^{-5} +81117 q^{-6} +213551 q^{-7} +174522 q^{-8} +21046 q^{-9} -148142 q^{-10} -210655 q^{-11} -125587 q^{-12} +46924 q^{-13} +194108 q^{-14} +187585 q^{-15} +61072 q^{-16} -106664 q^{-17} -196275 q^{-18} -152758 q^{-19} -6737 q^{-20} +146927 q^{-21} +182468 q^{-22} +104375 q^{-23} -40544 q^{-24} -149852 q^{-25} -159220 q^{-26} -64249 q^{-27} +72105 q^{-28} +141464 q^{-29} +123658 q^{-30} +28175 q^{-31} -74816 q^{-32} -125975 q^{-33} -93435 q^{-34} -2444 q^{-35} +71507 q^{-36} +99955 q^{-37} +64147 q^{-38} -3491 q^{-39} -64028 q^{-40} -77508 q^{-41} -40748 q^{-42} +7897 q^{-43} +48882 q^{-44} +54839 q^{-45} +30361 q^{-46} -10217 q^{-47} -36791 q^{-48} -36070 q^{-49} -19814 q^{-50} +7008 q^{-51} +24391 q^{-52} +26333 q^{-53} +11319 q^{-54} -5617 q^{-55} -14610 q^{-56} -16581 q^{-57} -7703 q^{-58} +2995 q^{-59} +10522 q^{-60} +9183 q^{-61} +4074 q^{-62} -1070 q^{-63} -5984 q^{-64} -5680 q^{-65} -2630 q^{-66} +1543 q^{-67} +2850 q^{-68} +2744 q^{-69} +1756 q^{-70} -741 q^{-71} -1724 q^{-72} -1606 q^{-73} -351 q^{-74} +186 q^{-75} +668 q^{-76} +952 q^{-77} +214 q^{-78} -212 q^{-79} -446 q^{-80} -185 q^{-81} -167 q^{-82} +8 q^{-83} +274 q^{-84} +117 q^{-85} +29 q^{-86} -75 q^{-87} -13 q^{-88} -72 q^{-89} -49 q^{-90} +53 q^{-91} +22 q^{-92} +18 q^{-93} -12 q^{-94} +14 q^{-95} -11 q^{-96} -18 q^{-97} +9 q^{-98} +3 q^{-100} -3 q^{-101} +3 q^{-102} + q^{-103} -3 q^{-104} + q^{-105} </math> | |
|||
<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:= </pre></td> |
|||
coloured_jones_7 = <math>-q^{140}+3 q^{139}-2 q^{138}-3 q^{137}+6 q^{136}-q^{135}-2 q^{134}-8 q^{133}-q^{132}+24 q^{131}-5 q^{130}-12 q^{129}+9 q^{128}-13 q^{127}-10 q^{126}-28 q^{125}+107 q^{123}+46 q^{122}-22 q^{121}-43 q^{120}-146 q^{119}-98 q^{118}-102 q^{117}+34 q^{116}+439 q^{115}+423 q^{114}+214 q^{113}-160 q^{112}-761 q^{111}-853 q^{110}-796 q^{109}-210 q^{108}+1276 q^{107}+2062 q^{106}+2114 q^{105}+966 q^{104}-1551 q^{103}-3331 q^{102}-4503 q^{101}-3647 q^{100}+359 q^{99}+4648 q^{98}+8226 q^{97}+8480 q^{96}+3476 q^{95}-3482 q^{94}-11393 q^{93}-15909 q^{92}-12223 q^{91}-2920 q^{90}+11191 q^{89}+23390 q^{88}+25430 q^{87}+17552 q^{86}-1768 q^{85}-24994 q^{84}-39645 q^{83}-41137 q^{82}-22049 q^{81}+12339 q^{80}+45867 q^{79}+67945 q^{78}+61275 q^{77}+23695 q^{76}-30157 q^{75}-85168 q^{74}-109777 q^{73}-86340 q^{72}-20184 q^{71}+73631 q^{70}+149589 q^{69}+167802 q^{68}+112693 q^{67}-13360 q^{66}-156006 q^{65}-248112 q^{64}-240273 q^{63}-106294 q^{62}+102642 q^{61}+295626 q^{60}+380223 q^{59}+282191 q^{58}+28014 q^{57}-278825 q^{56}-498532 q^{55}-491176 q^{54}-234937 q^{53}+174113 q^{52}+557006 q^{51}+697131 q^{50}+498890 q^{49}+23069 q^{48}-528379 q^{47}-859848 q^{46}-783000 q^{45}-295636 q^{44}+401905 q^{43}+946025 q^{42}+1045961 q^{41}+611059 q^{40}-189095 q^{39}-940980 q^{38}-1251817 q^{37}-927406 q^{36}-81393 q^{35}+847907 q^{34}+1379085 q^{33}+1208434 q^{32}+372926 q^{31}-688799 q^{30}-1424863 q^{29}-1428063 q^{28}-649734 q^{27}+493157 q^{26}+1401264 q^{25}+1577280 q^{24}+885628 q^{23}-292144 q^{22}-1329981 q^{21}-1660056 q^{20}-1067682 q^{19}+109185 q^{18}+1235684 q^{17}+1691414 q^{16}+1194554 q^{15}+40634 q^{14}-1138216 q^{13}-1688281 q^{12}-1275815 q^{11}-155218 q^{10}+1052033 q^9+1670034 q^8+1324510 q^7+237205 q^6-982038 q^5-1647416 q^4-1356453 q^3-300176 q^2+926937 q+1631196+1384848 q^{-1} +354411 q^{-2} -878768 q^{-3} -1619062 q^{-4} -1419481 q^{-5} -417387 q^{-6} +825039 q^{-7} +1609342 q^{-8} +1464942 q^{-9} +497790 q^{-10} -751578 q^{-11} -1587939 q^{-12} -1517934 q^{-13} -605726 q^{-14} +643232 q^{-15} +1541628 q^{-16} +1569085 q^{-17} +738971 q^{-18} -490362 q^{-19} -1451106 q^{-20} -1600154 q^{-21} -889095 q^{-22} +289369 q^{-23} +1302550 q^{-24} +1589981 q^{-25} +1035402 q^{-26} -49707 q^{-27} -1088279 q^{-28} -1516805 q^{-29} -1151186 q^{-30} -207003 q^{-31} +814744 q^{-32} +1366862 q^{-33} +1206888 q^{-34} +448642 q^{-35} -502674 q^{-36} -1140697 q^{-37} -1180870 q^{-38} -638782 q^{-39} +187587 q^{-40} +855626 q^{-41} +1064750 q^{-42} +747466 q^{-43} +90940 q^{-44} -545478 q^{-45} -871645 q^{-46} -759540 q^{-47} -295978 q^{-48} +252223 q^{-49} +630712 q^{-50} +680531 q^{-51} +407382 q^{-52} -14127 q^{-53} -382931 q^{-54} -536608 q^{-55} -424989 q^{-56} -143221 q^{-57} +167515 q^{-58} +364088 q^{-59} +368655 q^{-60} +215994 q^{-61} -10817 q^{-62} -201155 q^{-63} -271514 q^{-64} -217968 q^{-65} -77732 q^{-66} +74444 q^{-67} +166205 q^{-68} +175493 q^{-69} +107793 q^{-70} +5076 q^{-71} -78580 q^{-72} -116915 q^{-73} -98125 q^{-74} -40710 q^{-75} +19953 q^{-76} +62796 q^{-77} +70393 q^{-78} +46335 q^{-79} +10071 q^{-80} -24744 q^{-81} -41254 q^{-82} -36242 q^{-83} -19084 q^{-84} +3547 q^{-85} +19079 q^{-86} +22466 q^{-87} +17185 q^{-88} +4852 q^{-89} -6219 q^{-90} -11397 q^{-91} -11531 q^{-92} -5868 q^{-93} +431 q^{-94} +4384 q^{-95} +6340 q^{-96} +4485 q^{-97} +1356 q^{-98} -1230 q^{-99} -3135 q^{-100} -2534 q^{-101} -1169 q^{-102} -75 q^{-103} +1210 q^{-104} +1319 q^{-105} +912 q^{-106} +321 q^{-107} -593 q^{-108} -618 q^{-109} -388 q^{-110} -264 q^{-111} +134 q^{-112} +228 q^{-113} +277 q^{-114} +241 q^{-115} -99 q^{-116} -138 q^{-117} -84 q^{-118} -96 q^{-119} +5 q^{-121} +52 q^{-122} +97 q^{-123} -7 q^{-124} -24 q^{-125} -12 q^{-126} -22 q^{-127} +2 q^{-128} -12 q^{-129} +22 q^{-131} + q^{-132} -4 q^{-133} -3 q^{-135} +3 q^{-136} -3 q^{-137} - q^{-138} +3 q^{-139} - q^{-140} </math> | |
|||
<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td> |
|||
computer_talk = |
|||
</tr> |
|||
<table> |
|||
<tr valign=top><td colspan=2><pre style="border: 0px; padding: 0em">Loading KnotTheory` (version of August 17, 2005, 14:44:34)...</pre></td></tr> |
|||
<tr valign=top> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Crossings[Knot[10, 91]]</nowiki></pre></td></tr> |
|||
<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><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[6, 2, 7, 1], X[20, 6, 1, 5], X[16, 9, 17, 10], X[10, 3, 11, 4], |
|||
<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, 91]]</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[6, 2, 7, 1], X[20, 6, 1, 5], X[16, 9, 17, 10], X[10, 3, 11, 4], |
|||
X[2, 18, 3, 17], X[14, 7, 15, 8], X[8, 15, 9, 16], X[12, 20, 13, 19], |
X[2, 18, 3, 17], X[14, 7, 15, 8], X[8, 15, 9, 16], X[12, 20, 13, 19], |
||
X[18, 12, 19, 11], X[4, 13, 5, 14]]</nowiki></ |
X[18, 12, 19, 11], X[4, 13, 5, 14]]</nowiki></code></td></tr> |
||
</table> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[4]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>GaussCode[Knot[10, 91]]</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[1, -5, 4, -10, 2, -1, 6, -7, 3, -4, 9, -8, 10, -6, 7, -3, 5, |
|||
<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, 91]]</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, -5, 4, -10, 2, -1, 6, -7, 3, -4, 9, -8, 10, -6, 7, -3, 5, |
|||
-9, 8, -2]</nowiki></ |
-9, 8, -2]</nowiki></code></td></tr> |
||
</table> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[5]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>BR[Knot[10, 91]]</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[3, {-1, -1, -1, 2, -1, 2, 2, -1, 2, 2}]</nowiki></pre></td></tr> |
|||
< |
<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, 91]]</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, 10, 20, 14, 16, 18, 4, 8, 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, 91]]</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[3, {-1, -1, -1, 2, -1, 2, 2, -1, 2, 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>{3, 10}</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, 91]]</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>3</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, 91]]]</nowiki></code></td></tr> |
|||
<tr align=left><td></td><td>[[Image:10_91_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, 91]]&) /@ { |
|||
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, 4, 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, 91]][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> -4 4 9 14 2 3 4 |
|||
17 + t - -- + -- - -- - 14 t + 9 t - 4 t + t |
17 + t - -- + -- - -- - 14 t + 9 t - 4 t + t |
||
3 2 t |
3 2 t |
||
t t</nowiki></ |
t t</nowiki></code></td></tr> |
||
</table> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[7]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Conway[Knot[10, 91]][z]</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6 8 |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td> |
|||
1 + 2 z + 5 z + 4 z + z</nowiki></pre></td></tr> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Conway[Knot[10, 91]][z]</nowiki></code></td></tr> |
|||
<tr align=left> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[8]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 91]}</nowiki></pre></td></tr> |
|||
< |
<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 8 |
|||
1 + 2 z + 5 z + 4 z + z</nowiki></code></td></tr> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>J=Jones[Knot[10, 91]][q]</nowiki></pre></td></tr> |
|||
</table> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -5 3 6 9 11 2 3 4 5 |
|||
<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, 91]}</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, 91]], KnotSignature[Knot[10, 91]]}</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>{73, 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, 91]][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> -5 3 6 9 11 2 3 4 5 |
|||
13 - q + -- - -- + -- - -- - 11 q + 9 q - 6 q + 3 q - q |
13 - q + -- - -- + -- - -- - 11 q + 9 q - 6 q + 3 q - q |
||
4 3 2 q |
4 3 2 q |
||
q q q</nowiki></ |
q q q</nowiki></code></td></tr> |
||
</table> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[11]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 43], Knot[10, 91]}</nowiki></pre></td></tr> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[15]:=</code></td> |
|||
<math>\textrm{Include}(\textrm{ColouredJonesM.mhtml})</math> |
|||
<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> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -14 -12 2 -8 -4 4 2 4 8 10 |
|||
<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, 43], Knot[10, 91]}</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, 91]][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> -14 -12 2 -8 -4 4 2 4 8 10 |
|||
-1 - q + q - --- + q - q + -- + 4 q - q + q - 2 q + |
-1 - q + q - --- + q - q + -- + 4 q - q + q - 2 q + |
||
10 2 |
10 2 |
||
Line 91: | Line 179: | ||
12 14 |
12 14 |
||
q - q</nowiki></ |
q - q</nowiki></code></td></tr> |
||
</table> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Knot[10, 91]][a, z]</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 2 |
|||
<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, 91]][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 4 |
|||
2 2 2 5 z 2 2 4 4 z 2 4 |
|||
5 - -- - 2 a + 12 z - ---- - 5 a z + 13 z - ---- - 4 a z + |
|||
2 2 2 |
|||
a a a |
|||
6 |
|||
6 z 2 6 8 |
|||
6 z - -- - a 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, 91]][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 3 z 6 z 5 2 z 9 z |
2 2 3 z 6 z 5 2 z 9 z |
||
5 + -- + 2 a - --- - --- - 4 a z + a z - 19 z + -- - ---- - |
5 + -- + 2 a - --- - --- - 4 a z + a z - 19 z + -- - ---- - |
||
Line 121: | Line 231: | ||
---- + a z + 4 a z + 9 z + ---- + 4 a z + ---- + 2 a z |
---- + a z + 4 a z + 9 z + ---- + 4 a z + ---- + 2 a z |
||
a 2 a |
a 2 a |
||
a</nowiki></ |
a</nowiki></code></td></tr> |
||
</table> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[14]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{Vassiliev[2][Knot[10, 91]], Vassiliev[3][Knot[10, 91]]}</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 0}</nowiki></pre></td></tr> |
|||
< |
<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, 91]], Vassiliev[3][Knot[10, 91]]}</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>{2, 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, 91]][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 1 2 1 4 2 5 4 |
|||
- + 7 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + |
- + 7 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + |
||
q 11 5 9 4 7 4 7 3 5 3 5 2 3 2 |
q 11 5 9 4 7 4 7 3 5 3 5 2 3 2 |
||
Line 136: | Line 256: | ||
7 4 9 4 11 5 |
7 4 9 4 11 5 |
||
q t + 2 q t + q t</nowiki></ |
q t + 2 q t + q t</nowiki></code></td></tr> |
||
</table> |
</table> |
||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[21]:=</code></td> |
|||
[[Category:Knot Page]] |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>ColouredJones[Knot[10, 91], 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> -15 3 -13 8 15 2 30 40 7 71 64 |
|||
132 + q - --- + q + --- - --- + --- + -- - -- - -- + -- - -- - |
|||
14 12 11 10 9 8 7 6 5 |
|||
q q q q q q q q q |
|||
32 113 71 60 2 3 4 5 6 |
|||
-- + --- - -- - -- - 58 q - 73 q + 114 q - 31 q - 66 q + 72 q - |
|||
4 3 2 q |
|||
q q q |
|||
7 8 9 10 11 12 13 14 15 |
|||
5 q - 43 q + 30 q + 5 q - 17 q + 7 q + 2 q - 3 q + q</nowiki></code></td></tr> |
|||
</table> }} |
Latest revision as of 16:57, 1 September 2005
|
|
(KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 91's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
Planar diagram presentation | X6271 X20,6,1,5 X16,9,17,10 X10,3,11,4 X2,18,3,17 X14,7,15,8 X8,15,9,16 X12,20,13,19 X18,12,19,11 X4,13,5,14 |
Gauss code | 1, -5, 4, -10, 2, -1, 6, -7, 3, -4, 9, -8, 10, -6, 7, -3, 5, -9, 8, -2 |
Dowker-Thistlethwaite code | 6 10 20 14 16 18 4 8 2 12 |
Conway Notation | [.3.2.20] |
Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||
Length is 10, width is 3, Braid index is 3 |
[{3, 6}, {2, 5}, {1, 3}, {7, 14}, {6, 11}, {8, 13}, {9, 7}, {10, 8}, {4, 9}, {5, 10}, {14, 12}, {11, 2}, {13, 4}, {12, 1}] |
[edit Notes on presentations of 10 91]
KnotTheory`
. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
|
AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
|
In[3]:=
|
K = Knot["10 91"];
|
In[4]:=
|
PD[K]
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
Out[4]=
|
X6271 X20,6,1,5 X16,9,17,10 X10,3,11,4 X2,18,3,17 X14,7,15,8 X8,15,9,16 X12,20,13,19 X18,12,19,11 X4,13,5,14 |
In[5]:=
|
GaussCode[K]
|
Out[5]=
|
1, -5, 4, -10, 2, -1, 6, -7, 3, -4, 9, -8, 10, -6, 7, -3, 5, -9, 8, -2 |
In[6]:=
|
DTCode[K]
|
Out[6]=
|
6 10 20 14 16 18 4 8 2 12 |
(The path below may be different on your system)
In[7]:=
|
AppendTo[$Path, "C:/bin/LinKnot/"];
|
In[8]:=
|
ConwayNotation[K]
|
Out[8]=
|
[.3.2.20] |
In[9]:=
|
br = BR[K]
|
KnotTheory::credits: The minimum braids representing the knots with up to 10 crossings were provided by Thomas Gittings. See arXiv:math.GT/0401051.
|
Out[9]=
|
In[10]:=
|
{First[br], Crossings[br], BraidIndex[K]}
|
KnotTheory::credits: The braid index data known to KnotTheory` is taken from Charles Livingston's http://www.indiana.edu/~knotinfo/.
|
KnotTheory::loading: Loading precomputed data in IndianaData`.
|
Out[10]=
|
{ 3, 10, 3 } |
In[11]:=
|
Show[BraidPlot[br]]
|
Out[11]=
|
-Graphics- |
In[12]:=
|
Show[DrawMorseLink[K]]
|
KnotTheory::credits: "MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005."
|
KnotTheory::credits: "DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005."
|
Out[12]=
|
-Graphics- |
In[13]:=
|
ap = ArcPresentation[K]
|
Out[13]=
|
ArcPresentation[{3, 6}, {2, 5}, {1, 3}, {7, 14}, {6, 11}, {8, 13}, {9, 7}, {10, 8}, {4, 9}, {5, 10}, {14, 12}, {11, 2}, {13, 4}, {12, 1}] |
In[14]:=
|
Draw[ap]
|
Out[14]=
|
-Graphics- |
Three dimensional invariants
|
Four dimensional invariants
|
Polynomial invariants
A1 Invariants.
Weight | Invariant |
---|---|
1 | |
2 | |
3 | |
4 | |
5 | |
6 |
A2 Invariants.
Weight | Invariant |
---|---|
1,0 | |
1,1 | |
2,0 |
A3 Invariants.
Weight | Invariant |
---|---|
0,1,0 | |
1,0,0 | |
1,0,1 |
A4 Invariants.
Weight | Invariant |
---|---|
0,1,0,0 | |
1,0,0,0 |
B2 Invariants.
Weight | Invariant |
---|---|
0,1 | |
1,0 |
D4 Invariants.
Weight | Invariant |
---|---|
1,0,0,0 |
G2 Invariants.
Weight | Invariant |
---|---|
1,0 |
.
KnotTheory`
, as shown in the (simulated) Mathematica session below. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting. This Mathematica session is also available (albeit only for the knot 5_2) as the notebook PolynomialInvariantsSession.nb.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
|
AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
|
In[3]:=
|
K = Knot["10 91"];
|
In[4]:=
|
Alexander[K][t]
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
Out[4]=
|
In[5]:=
|
Conway[K][z]
|
Out[5]=
|
In[6]:=
|
Alexander[K, 2][t]
|
KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.
|
Out[6]=
|
In[7]:=
|
{KnotDet[K], KnotSignature[K]}
|
Out[7]=
|
{ 73, 0 } |
In[8]:=
|
Jones[K][q]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
|
Out[8]=
|
In[9]:=
|
HOMFLYPT[K][a, z]
|
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
|
Out[9]=
|
In[10]:=
|
Kauffman[K][a, z]
|
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
|
Out[10]=
|
"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {}
Same Jones Polynomial (up to mirroring, ): {10_43,}
KnotTheory`
. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
|
AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
|
In[3]:=
|
K = Knot["10 91"];
|
In[4]:=
|
{A = Alexander[K][t], J = Jones[K][q]}
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
|
Out[4]=
|
{ , } |
In[5]:=
|
DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]
|
KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.
|
KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.
|
Out[5]=
|
{} |
In[6]:=
|
DeleteCases[
Select[
AllKnots[],
(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) &
],
K
]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
|
Out[6]=
|
{10_43,} |
Vassiliev invariants
V2 and V3: | (2, 0) |
V2,1 through V6,9: |
|
V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.
Khovanov Homology
The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where or , where 0 is the signature of 10 91. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
|
Integral Khovanov Homology
(db, data source) |
|
The Coloured Jones Polynomials
2 | |
3 | |
4 | |
5 | |
6 | |
7 |
Computer Talk
Much of the above data can be recomputed by Mathematica using the package KnotTheory`
. See A Sample KnotTheory` Session, or any of the Computer Talk sections above.
Modifying This Page
Read me first: Modifying Knot Pages
See/edit the Rolfsen Knot Page master template (intermediate). See/edit the Rolfsen_Splice_Base (expert). Back to the top. |
|