View source for 9 14

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{{Rolfsen Knot Page|
n = 9 |
k = 14 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-2,9,-7,8,-6,3,-4,2,-5,6,-8,7,-9,5/goTop.html |
braid_table     = <table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]]</td></tr>
<tr><td>[[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>
</table> |
braid_crossings = 10 |
braid_width     = 5 |
braid_index     = 5 |
same_alexander  =  |
same_jones      = [[K11n53]],  |
khovanov_table  = <table border=1>
<tr align=center>
<td width=14.2857%><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=7.14286%>-3</td    ><td width=7.14286%>-2</td    ><td width=7.14286%>-1</td    ><td width=7.14286%>0</td    ><td width=7.14286%>1</td    ><td width=7.14286%>2</td    ><td width=7.14286%>3</td    ><td width=7.14286%>4</td    ><td width=7.14286%>5</td    ><td width=7.14286%>6</td    ><td width=14.2857%>&chi;</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>&nbsp;</td><td bgcolor=yellow>1</td><td>1</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>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>&nbsp;</td><td>-1</td></tr>
<tr align=center><td>9</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>1</td></tr>
<tr align=center><td>7</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>5</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>1</td></tr>
<tr align=center><td>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>-1</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>4</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>2</td></tr>
<tr align=center><td>-3</td><td>&nbsp;</td><td bgcolor=yellow>1</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>-1</td></tr>
<tr align=center><td>-5</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>2</td></tr>
<tr align=center><td>-7</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>-1</td></tr>
</table> |
coloured_jones_2 = <math>q^{18}-2 q^{17}-q^{16}+6 q^{15}-5 q^{14}-6 q^{13}+15 q^{12}-5 q^{11}-16 q^{10}+23 q^9-2 q^8-27 q^7+28 q^6+4 q^5-34 q^4+27 q^3+9 q^2-33 q+21+9 q^{-1} -23 q^{-2} +13 q^{-3} +5 q^{-4} -11 q^{-5} +6 q^{-6} + q^{-7} -3 q^{-8} + q^{-9} </math> |
coloured_jones_3 = <math>q^{36}-2 q^{35}-q^{34}+2 q^{33}+5 q^{32}-4 q^{31}-9 q^{30}+3 q^{29}+17 q^{28}-q^{27}-23 q^{26}-7 q^{25}+30 q^{24}+16 q^{23}-34 q^{22}-27 q^{21}+32 q^{20}+41 q^{19}-30 q^{18}-49 q^{17}+21 q^{16}+60 q^{15}-14 q^{14}-65 q^{13}+3 q^{12}+70 q^{11}+8 q^{10}-73 q^9-18 q^8+72 q^7+29 q^6-71 q^5-33 q^4+61 q^3+41 q^2-58 q-34+42 q^{-1} +34 q^{-2} -37 q^{-3} -20 q^{-4} +23 q^{-5} +17 q^{-6} -21 q^{-7} -5 q^{-8} +12 q^{-9} +4 q^{-10} -11 q^{-11} + q^{-12} +6 q^{-13} - q^{-14} -3 q^{-15} - q^{-16} +3 q^{-17} - q^{-18} </math> |
coloured_jones_4 = <math>q^{60}-2 q^{59}-q^{58}+2 q^{57}+q^{56}+6 q^{55}-8 q^{54}-7 q^{53}+2 q^{52}+3 q^{51}+26 q^{50}-12 q^{49}-23 q^{48}-11 q^{47}-5 q^{46}+63 q^{45}+3 q^{44}-29 q^{43}-38 q^{42}-46 q^{41}+93 q^{40}+35 q^{39}-50 q^{37}-112 q^{36}+86 q^{35}+48 q^{34}+58 q^{33}-18 q^{32}-166 q^{31}+49 q^{30}+14 q^{29}+107 q^{28}+52 q^{27}-177 q^{26}+12 q^{25}-58 q^{24}+124 q^{23}+128 q^{22}-152 q^{21}-8 q^{20}-140 q^{19}+115 q^{18}+193 q^{17}-109 q^{16}-20 q^{15}-215 q^{14}+98 q^{13}+243 q^{12}-59 q^{11}-26 q^{10}-273 q^9+67 q^8+266 q^7-4 q^6-15 q^5-295 q^4+22 q^3+240 q^2+34 q+23-256 q^{-1} -20 q^{-2} +164 q^{-3} +35 q^{-4} +61 q^{-5} -170 q^{-6} -30 q^{-7} +80 q^{-8} +3 q^{-9} +69 q^{-10} -82 q^{-11} -14 q^{-12} +28 q^{-13} -23 q^{-14} +48 q^{-15} -29 q^{-16} +2 q^{-17} +8 q^{-18} -25 q^{-19} +23 q^{-20} -8 q^{-21} +5 q^{-22} +3 q^{-23} -12 q^{-24} +6 q^{-25} -2 q^{-26} +3 q^{-27} + q^{-28} -3 q^{-29} + q^{-30} </math> |
coloured_jones_5 = <math>q^{90}-2 q^{89}-q^{88}+2 q^{87}+q^{86}+2 q^{85}+2 q^{84}-6 q^{83}-9 q^{82}+2 q^{81}+7 q^{80}+11 q^{79}+12 q^{78}-9 q^{77}-29 q^{76}-20 q^{75}+6 q^{74}+33 q^{73}+46 q^{72}+15 q^{71}-46 q^{70}-69 q^{69}-41 q^{68}+30 q^{67}+93 q^{66}+84 q^{65}-4 q^{64}-97 q^{63}-122 q^{62}-49 q^{61}+81 q^{60}+149 q^{59}+99 q^{58}-31 q^{57}-145 q^{56}-150 q^{55}-34 q^{54}+112 q^{53}+169 q^{52}+98 q^{51}-36 q^{50}-152 q^{49}-159 q^{48}-51 q^{47}+101 q^{46}+175 q^{45}+145 q^{44}+6 q^{43}-174 q^{42}-234 q^{41}-108 q^{40}+115 q^{39}+290 q^{38}+248 q^{37}-39 q^{36}-334 q^{35}-360 q^{34}-65 q^{33}+337 q^{32}+481 q^{31}+175 q^{30}-335 q^{29}-575 q^{28}-283 q^{27}+314 q^{26}+661 q^{25}+386 q^{24}-294 q^{23}-738 q^{22}-477 q^{21}+273 q^{20}+802 q^{19}+568 q^{18}-251 q^{17}-869 q^{16}-644 q^{15}+225 q^{14}+906 q^{13}+737 q^{12}-183 q^{11}-951 q^{10}-787 q^9+120 q^8+922 q^7+866 q^6-38 q^5-899 q^4-868 q^3-49 q^2+772 q+880+147 q^{-1} -674 q^{-2} -794 q^{-3} -212 q^{-4} +491 q^{-5} +716 q^{-6} +257 q^{-7} -368 q^{-8} -560 q^{-9} -260 q^{-10} +207 q^{-11} +448 q^{-12} +235 q^{-13} -130 q^{-14} -291 q^{-15} -192 q^{-16} +34 q^{-17} +207 q^{-18} +146 q^{-19} -18 q^{-20} -106 q^{-21} -96 q^{-22} -22 q^{-23} +63 q^{-24} +67 q^{-25} +14 q^{-26} -25 q^{-27} -35 q^{-28} -18 q^{-29} +6 q^{-30} +20 q^{-31} +16 q^{-32} -4 q^{-33} -10 q^{-34} -2 q^{-35} -7 q^{-36} +3 q^{-37} +8 q^{-38} -3 q^{-40} +2 q^{-41} -3 q^{-42} - q^{-43} +3 q^{-44} - q^{-45} </math> |
coloured_jones_6 = <math>q^{126}-2 q^{125}-q^{124}+2 q^{123}+q^{122}+2 q^{121}-2 q^{120}+4 q^{119}-8 q^{118}-9 q^{117}+5 q^{116}+6 q^{115}+12 q^{114}+16 q^{112}-22 q^{111}-35 q^{110}-9 q^{109}+5 q^{108}+36 q^{107}+21 q^{106}+70 q^{105}-21 q^{104}-79 q^{103}-68 q^{102}-48 q^{101}+30 q^{100}+43 q^{99}+193 q^{98}+62 q^{97}-60 q^{96}-133 q^{95}-165 q^{94}-86 q^{93}-49 q^{92}+295 q^{91}+209 q^{90}+108 q^{89}-57 q^{88}-200 q^{87}-245 q^{86}-311 q^{85}+201 q^{84}+214 q^{83}+285 q^{82}+170 q^{81}+27 q^{80}-189 q^{79}-516 q^{78}-37 q^{77}-79 q^{76}+170 q^{75}+243 q^{74}+381 q^{73}+195 q^{72}-341 q^{71}-51 q^{70}-447 q^{69}-301 q^{68}-148 q^{67}+447 q^{66}+615 q^{65}+212 q^{64}+436 q^{63}-453 q^{62}-784 q^{61}-930 q^{60}-15 q^{59}+645 q^{58}+765 q^{57}+1296 q^{56}+92 q^{55}-879 q^{54}-1711 q^{53}-848 q^{52}+151 q^{51}+960 q^{50}+2146 q^{49}+1001 q^{48}-494 q^{47}-2172 q^{46}-1702 q^{45}-668 q^{44}+748 q^{43}+2720 q^{42}+1943 q^{41}+167 q^{40}-2283 q^{39}-2349 q^{38}-1514 q^{37}+326 q^{36}+3007 q^{35}+2713 q^{34}+832 q^{33}-2217 q^{32}-2784 q^{31}-2212 q^{30}-69 q^{29}+3160 q^{28}+3299 q^{27}+1356 q^{26}-2150 q^{25}-3128 q^{24}-2763 q^{23}-352 q^{22}+3297 q^{21}+3795 q^{20}+1786 q^{19}-2085 q^{18}-3443 q^{17}-3262 q^{16}-644 q^{15}+3332 q^{14}+4210 q^{13}+2258 q^{12}-1817 q^{11}-3570 q^{10}-3697 q^9-1116 q^8+3007 q^7+4328 q^6+2736 q^5-1174 q^4-3219 q^3-3810 q^2-1684 q+2192+3857 q^{-1} +2909 q^{-2} -334 q^{-3} -2323 q^{-4} -3321 q^{-5} -1975 q^{-6} +1165 q^{-7} +2814 q^{-8} +2515 q^{-9} +269 q^{-10} -1243 q^{-11} -2327 q^{-12} -1750 q^{-13} +391 q^{-14} +1636 q^{-15} +1707 q^{-16} +415 q^{-17} -438 q^{-18} -1290 q^{-19} -1195 q^{-20} +47 q^{-21} +765 q^{-22} +919 q^{-23} +276 q^{-24} -49 q^{-25} -574 q^{-26} -664 q^{-27} -20 q^{-28} +291 q^{-29} +409 q^{-30} +117 q^{-31} +64 q^{-32} -207 q^{-33} -323 q^{-34} -9 q^{-35} +87 q^{-36} +155 q^{-37} +33 q^{-38} +67 q^{-39} -58 q^{-40} -139 q^{-41} + q^{-42} +14 q^{-43} +50 q^{-44} +2 q^{-45} +41 q^{-46} -11 q^{-47} -49 q^{-48} +4 q^{-49} -3 q^{-50} +14 q^{-51} -5 q^{-52} +17 q^{-53} - q^{-54} -14 q^{-55} +4 q^{-56} -3 q^{-57} +3 q^{-58} -2 q^{-59} +3 q^{-60} + q^{-61} -3 q^{-62} + q^{-63} </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[9, 14]]</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[5, 12, 6, 13], X[3, 11, 4, 10], X[11, 3, 12, 2], 
 
  X[13, 18, 14, 1], X[9, 15, 10, 14], X[7, 17, 8, 16], X[15, 9, 16, 8], 
 
  X[17, 7, 18, 6]]</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[9, 14]]</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, 1, -2, 9, -7, 8, -6, 3, -4, 2, -5, 6, -8, 7, -9, 5]</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[9, 14]]</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, 10, 12, 16, 14, 2, 18, 8, 6]</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[9, 14]]</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[5, {1, 1, 2, -1, -3, 2, -3, 4, -3, 4}]</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>{5, 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[9, 14]]</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>5</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[9, 14]]]</nowiki></code></td></tr>
<tr align=left><td></td><td>[[Image:9_14_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[9, 14]]&) /@ {
                  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, 2, 2, {4, 7}, 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[9, 14]][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    9            2
15 + -- - - - 9 t + 2 t
      2   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[9, 14]][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
1 - 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[9, 14]}</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[9, 14]], KnotSignature[Knot[9, 14]]}</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>{37, 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[9, 14]][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>     -3   3    4            2      3      4      5    6
6 - q   + -- - - - 6 q + 6 q  - 5 q  + 3 q  - 2 q  + q
           2   q
          q</nowiki></code></td></tr>
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<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>
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<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[9, 14], Knot[11, NonAlternating, 53]}</nowiki></code></td></tr>
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<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[9, 14]][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>  -10    -8    -6    -4   2     2    4    8      10    12    16    18
-q    + q   + q   - q   + -- + q  + q  + q  - 2 q   - q   - q   + q   + 
                           2
                          q
 
   20
  q</nowiki></code></td></tr>
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<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[9, 14]][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                 4
     -6   2     -2    2   2 z    z     2  2    4   z
1 + a   - -- + a   + z  - ---- + -- - a  z  + z  + --
           4                4     2                 2
          a                a     a                 a</nowiki></code></td></tr>
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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[9, 14]][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
     -6   2     -2   3 z   5 z   2 z   4 z    10 z    8 z       2  2
1 - a   - -- - a   - --- - --- - --- + ---- + ----- + ---- - 2 a  z  + 
           4          5     3     a      6      4       2
          a          a     a            a      a       a
 
     3       3      3                              4      4       4
  9 z    15 z    2 z         3    3  3      4   4 z    9 z    12 z
  ---- + ----- + ---- - 3 a z  + a  z  - 4 z  - ---- - ---- - ----- + 
    5      3      a                               6      4      2
   a      a                                      a      a      a
 
               5       5      5                    6      6      7
     2  4   8 z    16 z    4 z         5      6   z    3 z    2 z
  3 a  z  - ---- - ----- - ---- + 4 a z  + 4 z  + -- + ---- + ---- + 
              5      3      a                      6     2      5
             a      a                             a     a      a
 
     7      7    8    8
  5 z    3 z    z    z
  ---- + ---- + -- + --
    3     a      4    2
   a            a    a</nowiki></code></td></tr>
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<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[9, 14]], Vassiliev[3][Knot[9, 14]]}</nowiki></code></td></tr>
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<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, -2}</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[9, 14]][q, t]</nowiki></code></td></tr>
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<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>4           1       2       1      2      2               3
- + 3 q + ----- + ----- + ----- + ---- + --- + 3 q t + 3 q  t + 
q          7  3    5  2    3  2    3     q t
          q  t    q  t    q  t    q  t
 
     3  2      5  2      5  3      7  3    7  4      9  4    9  5
  3 q  t  + 3 q  t  + 2 q  t  + 3 q  t  + q  t  + 2 q  t  + q  t  + 
 
   11  5    13  6
  q   t  + q   t</nowiki></code></td></tr>
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<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[9, 14], 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>      -9   3     -7   6    11   5    13   23   9             2
21 + q   - -- + q   + -- - -- + -- + -- - -- + - - 33 q + 9 q  + 
            8          6    5    4    3    2   q
           q          q    q    q    q    q
 
      3       4      5       6       7      8       9       10
  27 q  - 34 q  + 4 q  + 28 q  - 27 q  - 2 q  + 23 q  - 16 q   - 
 
     11       12      13      14      15    16      17    18
  5 q   + 15 q   - 6 q   - 5 q   + 6 q   - q   - 2 q   + q</nowiki></code></td></tr>
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