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{{Rolfsen Knot Page|
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n = 10 |
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k = 23 |
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-4,6,-5,7,-8,9,-10,2,-3,4,-6,5,-9,8,-7,3/goTop.html |
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braid_table = <table cellspacing=0 cellpadding=0 border=0>
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<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]]</td></tr>
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<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]]</td></tr>
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braid_crossings = 11 |
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braid_width = 4 |
braid_index = 4 |
same_alexander = [[10_52]], |
same_jones = |
khovanov_table = <table border=1>
<tr align=center>
<td width=13.3333%><table cellpadding=0 cellspacing=0>
<tr><td>\</td><td>&nbsp;</td><td>r</td></tr>
<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr>
<tr><td>j</td><td>&nbsp;</td><td>\</td></tr>
</table></td>
<td width=6.66667%>-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=6.66667%>7</td ><td width=13.3333%>&chi;</td></tr>
<tr align=center><td>17</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td>-1</td></tr>
<tr align=center><td>15</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>&nbsp;</td><td>1</td></tr>
<tr align=center><td>13</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>11</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr>
<tr align=center><td>9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
<tr align=center><td>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
<tr align=center><td>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr>
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>3</td></tr>
<tr align=center><td>-1</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>-3</td><td bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr>
<tr align=center><td>-5</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>-1</td></tr>
</table> |
coloured_jones_2 = <math>q^{23}-2 q^{22}+5 q^{20}-8 q^{19}+17 q^{17}-22 q^{16}-3 q^{15}+41 q^{14}-42 q^{13}-14 q^{12}+70 q^{11}-54 q^{10}-29 q^9+87 q^8-51 q^7-38 q^6+81 q^5-35 q^4-38 q^3+57 q^2-14 q-28+28 q^{-1} - q^{-2} -14 q^{-3} +8 q^{-4} + q^{-5} -3 q^{-6} + q^{-7} </math> |
coloured_jones_3 = <math>-q^{45}+2 q^{44}-q^{42}-3 q^{41}+5 q^{40}+q^{39}-5 q^{38}-5 q^{37}+14 q^{36}+3 q^{35}-22 q^{34}-9 q^{33}+42 q^{32}+15 q^{31}-64 q^{30}-33 q^{29}+93 q^{28}+64 q^{27}-126 q^{26}-100 q^{25}+146 q^{24}+152 q^{23}-165 q^{22}-202 q^{21}+169 q^{20}+252 q^{19}-167 q^{18}-286 q^{17}+148 q^{16}+316 q^{15}-131 q^{14}-322 q^{13}+97 q^{12}+323 q^{11}-70 q^{10}-297 q^9+26 q^8+274 q^7+2 q^6-224 q^5-40 q^4+185 q^3+52 q^2-127 q-67+88 q^{-1} +60 q^{-2} -49 q^{-3} -50 q^{-4} +24 q^{-5} +35 q^{-6} -9 q^{-7} -22 q^{-8} +3 q^{-9} +11 q^{-10} - q^{-11} -4 q^{-12} - q^{-13} +3 q^{-14} - q^{-15} </math> |
coloured_jones_4 = <math>q^{74}-2 q^{73}+q^{71}-q^{70}+6 q^{69}-7 q^{68}+q^{67}+2 q^{66}-9 q^{65}+18 q^{64}-15 q^{63}+8 q^{62}+10 q^{61}-31 q^{60}+26 q^{59}-38 q^{58}+35 q^{57}+52 q^{56}-59 q^{55}+10 q^{54}-122 q^{53}+71 q^{52}+173 q^{51}-33 q^{50}-16 q^{49}-338 q^{48}+32 q^{47}+366 q^{46}+140 q^{45}+55 q^{44}-687 q^{43}-196 q^{42}+514 q^{41}+462 q^{40}+335 q^{39}-1028 q^{38}-600 q^{37}+480 q^{36}+797 q^{35}+793 q^{34}-1213 q^{33}-1024 q^{32}+275 q^{31}+999 q^{30}+1249 q^{29}-1207 q^{28}-1303 q^{27}+5 q^{26}+1024 q^{25}+1562 q^{24}-1055 q^{23}-1387 q^{22}-248 q^{21}+893 q^{20}+1683 q^{19}-785 q^{18}-1276 q^{17}-468 q^{16}+617 q^{15}+1612 q^{14}-425 q^{13}-980 q^{12}-612 q^{11}+238 q^{10}+1335 q^9-67 q^8-553 q^7-605 q^6-116 q^5+899 q^4+139 q^3-145 q^2-425 q-291+451 q^{-1} +145 q^{-2} +87 q^{-3} -192 q^{-4} -259 q^{-5} +157 q^{-6} +55 q^{-7} +118 q^{-8} -41 q^{-9} -139 q^{-10} +39 q^{-11} -3 q^{-12} +63 q^{-13} +4 q^{-14} -51 q^{-15} +12 q^{-16} -10 q^{-17} +19 q^{-18} +5 q^{-19} -14 q^{-20} +4 q^{-21} -3 q^{-22} +4 q^{-23} + q^{-24} -3 q^{-25} + q^{-26} </math> |
coloured_jones_5 = <math>-q^{110}+2 q^{109}-q^{107}+q^{106}-2 q^{105}-4 q^{104}+5 q^{103}+3 q^{102}-2 q^{101}+6 q^{100}-3 q^{99}-16 q^{98}+2 q^{97}+7 q^{96}+2 q^{95}+22 q^{94}+7 q^{93}-31 q^{92}-24 q^{91}-12 q^{90}+3 q^{89}+62 q^{88}+62 q^{87}-12 q^{86}-78 q^{85}-113 q^{84}-66 q^{83}+108 q^{82}+225 q^{81}+152 q^{80}-73 q^{79}-341 q^{78}-373 q^{77}-13 q^{76}+470 q^{75}+645 q^{74}+264 q^{73}-518 q^{72}-1043 q^{71}-677 q^{70}+447 q^{69}+1435 q^{68}+1296 q^{67}-135 q^{66}-1779 q^{65}-2102 q^{64}-438 q^{63}+1989 q^{62}+2960 q^{61}+1289 q^{60}-1912 q^{59}-3843 q^{58}-2381 q^{57}+1622 q^{56}+4573 q^{55}+3543 q^{54}-997 q^{53}-5126 q^{52}-4747 q^{51}+248 q^{50}+5422 q^{49}+5807 q^{48}+633 q^{47}-5505 q^{46}-6700 q^{45}-1477 q^{44}+5383 q^{43}+7358 q^{42}+2295 q^{41}-5167 q^{40}-7803 q^{39}-2949 q^{38}+4802 q^{37}+8036 q^{36}+3566 q^{35}-4415 q^{34}-8118 q^{33}-3992 q^{32}+3882 q^{31}+7988 q^{30}+4446 q^{29}-3318 q^{28}-7724 q^{27}-4713 q^{26}+2576 q^{25}+7218 q^{24}+4999 q^{23}-1794 q^{22}-6551 q^{21}-5039 q^{20}+876 q^{19}+5623 q^{18}+5033 q^{17}-44 q^{16}-4570 q^{15}-4668 q^{14}-795 q^{13}+3370 q^{12}+4225 q^{11}+1345 q^{10}-2226 q^9-3433 q^8-1729 q^7+1136 q^6+2674 q^5+1758 q^4-336 q^3-1767 q^2-1601 q-248+1052 q^{-1} +1256 q^{-2} +501 q^{-3} -440 q^{-4} -874 q^{-5} -563 q^{-6} +80 q^{-7} +502 q^{-8} +477 q^{-9} +118 q^{-10} -242 q^{-11} -335 q^{-12} -162 q^{-13} +70 q^{-14} +194 q^{-15} +152 q^{-16} +5 q^{-17} -103 q^{-18} -102 q^{-19} -19 q^{-20} +35 q^{-21} +56 q^{-22} +32 q^{-23} -18 q^{-24} -35 q^{-25} -9 q^{-26} +8 q^{-27} +5 q^{-28} +12 q^{-29} +2 q^{-30} -14 q^{-31} - q^{-32} +6 q^{-33} - q^{-34} +3 q^{-36} -4 q^{-37} - q^{-38} +3 q^{-39} - q^{-40} </math> |
coloured_jones_6 = <math>q^{153}-2 q^{152}+q^{150}-q^{149}+2 q^{148}+6 q^{146}-9 q^{145}-3 q^{144}+4 q^{143}-7 q^{142}+5 q^{141}+4 q^{140}+26 q^{139}-21 q^{138}-14 q^{137}+7 q^{136}-27 q^{135}+14 q^{133}+80 q^{132}-26 q^{131}-30 q^{130}+6 q^{129}-81 q^{128}-42 q^{127}+18 q^{126}+201 q^{125}+17 q^{124}-17 q^{123}+9 q^{122}-224 q^{121}-208 q^{120}-55 q^{119}+409 q^{118}+220 q^{117}+184 q^{116}+134 q^{115}-498 q^{114}-715 q^{113}-507 q^{112}+527 q^{111}+653 q^{110}+952 q^{109}+899 q^{108}-586 q^{107}-1684 q^{106}-1970 q^{105}-260 q^{104}+775 q^{103}+2458 q^{102}+3250 q^{101}+771 q^{100}-2277 q^{99}-4655 q^{98}-3262 q^{97}-1227 q^{96}+3484 q^{95}+7381 q^{94}+5300 q^{93}-102 q^{92}-6893 q^{91}-8586 q^{90}-7429 q^{89}+1084 q^{88}+11113 q^{87}+12954 q^{86}+7100 q^{85}-5282 q^{84}-13580 q^{83}-17441 q^{82}-6965 q^{81}+10716 q^{80}+20597 q^{79}+18465 q^{78}+2210 q^{77}-14418 q^{76}-27630 q^{75}-19214 q^{74}+4499 q^{73}+24329 q^{72}+29944 q^{71}+13646 q^{70}-9826 q^{69}-34056 q^{68}-31338 q^{67}-5273 q^{66}+23073 q^{65}+37723 q^{64}+24760 q^{63}-2185 q^{62}-35722 q^{61}-39791 q^{60}-14694 q^{59}+18893 q^{58}+40962 q^{57}+32583 q^{56}+5219 q^{55}-34283 q^{54}-43984 q^{53}-21536 q^{52}+14213 q^{51}+41035 q^{50}+36931 q^{49}+10954 q^{48}-31401 q^{47}-45125 q^{46}-26050 q^{45}+9668 q^{44}+39080 q^{43}+38960 q^{42}+15662 q^{41}-27138 q^{40}-43968 q^{39}-29319 q^{38}+4319 q^{37}+34768 q^{36}+39083 q^{35}+20320 q^{34}-20434 q^{33}-39874 q^{32}-31363 q^{31}-2562 q^{30}+27008 q^{29}+36274 q^{28}+24452 q^{27}-10960 q^{26}-31701 q^{25}-30622 q^{24}-9790 q^{23}+15895 q^{22}+29167 q^{21}+25815 q^{20}-711 q^{19}-19866 q^{18}-25357 q^{17}-14301 q^{16}+4128 q^{15}+18301 q^{14}+22281 q^{13}+6499 q^{12}-7574 q^{11}-16143 q^{10}-13598 q^9-4053 q^8+7118 q^7+14566 q^6+8058 q^5+824 q^4-6573 q^3-8568 q^2-6308 q-208+6421 q^{-1} +5171 q^{-2} +3461 q^{-3} -523 q^{-4} -2972 q^{-5} -4304 q^{-6} -2388 q^{-7} +1378 q^{-8} +1551 q^{-9} +2352 q^{-10} +1220 q^{-11} +157 q^{-12} -1614 q^{-13} -1599 q^{-14} -176 q^{-15} -284 q^{-16} +703 q^{-17} +761 q^{-18} +781 q^{-19} -247 q^{-20} -509 q^{-21} -118 q^{-22} -487 q^{-23} -18 q^{-24} +153 q^{-25} +457 q^{-26} +23 q^{-27} -71 q^{-28} +73 q^{-29} -224 q^{-30} -87 q^{-31} -38 q^{-32} +170 q^{-33} - q^{-34} -15 q^{-35} +77 q^{-36} -59 q^{-37} -31 q^{-38} -32 q^{-39} +58 q^{-40} -12 q^{-41} -15 q^{-42} +31 q^{-43} -13 q^{-44} -5 q^{-45} -12 q^{-46} +21 q^{-47} -4 q^{-48} -10 q^{-49} +9 q^{-50} -3 q^{-51} -3 q^{-53} +4 q^{-54} + q^{-55} -3 q^{-56} + q^{-57} </math> |
coloured_jones_7 = |
computer_talk =
<table>
<tr valign=top>
<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td>
<td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td>
</tr>
<tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr>
</table>
<table><tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[2]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[Knot[10, 23]]</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, 12, 4, 13], X[13, 1, 14, 20], X[5, 15, 6, 14],
X[7, 17, 8, 16], X[15, 7, 16, 6], X[19, 9, 20, 8], X[9, 19, 10, 18],
X[17, 11, 18, 10], X[11, 2, 12, 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, 23]]</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, -4, 6, -5, 7, -8, 9, -10, 2, -3, 4, -6, 5, -9,
8, -7, 3]</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, 23]]</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, 12, 14, 16, 18, 2, 20, 6, 10, 8]</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, 23]]</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, 2, 2, 2, 2, 3, -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, 23]]</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, 23]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:10_23_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, 23]]&) /@ {
SymmetryType, UnknottingNumber, ThreeGenus,
BridgeIndex, SuperBridgeIndex, NakanishiIndex
}</nowiki></code></td></tr>
<tr align=left>
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Reversible, 1, 3, 2, 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, 23]][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 7 13 2 3
-15 + -- - -- + -- + 13 t - 7 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, 23]][z]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 4 6
1 + 3 z + 5 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>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[10, 23], Knot[10, 52]}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[13]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{KnotDet[Knot[10, 23]], KnotSignature[Knot[10, 23]]}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[13]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{59, 2}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[14]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Jones[Knot[10, 23]][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> -2 3 2 3 4 5 6 7 8
-5 - q + - + 8 q - 9 q + 10 q - 9 q + 7 q - 4 q + 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, 23]}</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, 23]][q]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[16]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -6 -4 2 4 6 10 12 14 16 18
-q + q + 2 q - 2 q + 2 q + q + 2 q - q + 2 q - q -
20 24
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, 23]][a, z]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[17]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 2 2 4 4 4 6 6
-2 3 2 3 z 6 z 2 z 4 z 4 z 3 z z z
-- + -- - 2 z - ---- + ---- + ---- - z - -- + ---- + ---- + -- + --
6 4 6 4 2 6 4 2 4 2
a a a a a a a a a a</nowiki></code></td></tr>
</table>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[18]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Knot[10, 23]][a, z]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[18]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 2 2 2
2 3 2 z z 2 z 2 z z 2 3 z 6 z 13 z z
-- + -- + --- + -- - --- - --- - - + 3 z + ---- - ---- - ----- - -- -
6 4 9 7 5 3 a 8 6 4 2
a a a a a a a a a a
3 3 3 3 3 4 4
3 z 2 z 3 z 9 z 5 z 3 4 5 z 5 z
---- - ---- + ---- + ---- + ---- - 2 a z - 7 z - ---- + ---- +
9 7 5 3 a 8 6
a a a a a a
4 4 5 5 5 5 5 6
20 z 3 z z 2 z 2 z 9 z 9 z 5 6 2 z
----- + ---- + -- - ---- - ---- - ---- - ---- + a z + 3 z + ---- -
4 2 9 7 5 3 a 8
a a a a a a a
6 6 6 7 7 7 7 8 8 8
3 z 13 z 5 z 2 z z 3 z 4 z 2 z 5 z 3 z
---- - ----- - ---- + ---- + -- + ---- + ---- + ---- + ---- + ---- +
6 4 2 7 5 3 a 6 4 2
a a a a a a a a a
9 9
z z
-- + --
5 3
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, 23]], Vassiliev[3][Knot[10, 23]]}</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>{3, 5}</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[20]:=</code></td>
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kh[Knot[10, 23]][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> 3 1 2 1 3 2 q 3 5
5 q + 4 q + ----- + ----- + ---- + --- + --- + 5 q t + 4 q t +
5 3 3 2 2 q t t
q t q t q t
5 2 7 2 7 3 9 3 9 4 11 4 11 5
5 q t + 5 q t + 4 q t + 5 q t + 3 q t + 4 q t + q t +
13 5 13 6 15 6 17 7
3 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, 23], 2][q]</nowiki></code></td></tr>
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[21]:=</code></td>
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -7 3 -5 8 14 -2 28 2 3
-28 + q - -- + q + -- - -- - q + -- - 14 q + 57 q - 38 q -
6 4 3 q
q q q
4 5 6 7 8 9 10 11
35 q + 81 q - 38 q - 51 q + 87 q - 29 q - 54 q + 70 q -
12 13 14 15 16 17 19 20
14 q - 42 q + 41 q - 3 q - 22 q + 17 q - 8 q + 5 q -
22 23
2 q + q</nowiki></code></td></tr>
</table> }}

Revision as of 09:49, 9 March 2007

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