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{{Rolfsen Knot Page Header|n=10|k=47|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,10,-2,1,-4,5,-10,2,-3,8,-6,9,-7,4,-5,3,-8,6,-9,7/goTop.html}}

<br style="clear:both" />

{{:{{PAGENAME}} Further Notes and Views}}

{{Knot Presentations}}

<center><table border=1 cellpadding=10><tr align=center valign=top>
<td>
[[Braid Representatives|Minimum Braid Representative]]:
<table cellspacing=0 cellpadding=0 border=0>
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]]</td></tr>
</table>

[[Invariants from Braid Theory|Length]] is 10, width is 3.

[[Invariants from Braid Theory|Braid index]] is 3.
</td>
<td>
[[Lightly Documented Features|A Morse Link Presentation]]:

[[Image:{{PAGENAME}}_ML.gif]]
</td>
</tr></table></center>

{{3D Invariants}}
{{4D Invariants}}
{{Polynomial Invariants}}

=== "Similar" Knots (within the Atlas) ===

Same [[The Alexander-Conway Polynomial|Alexander/Conway Polynomial]]:
{...}

Same [[The Jones Polynomial|Jones Polynomial]] (up to mirroring, <math>q\leftrightarrow q^{-1}</math>): 
{...}

{{Vassiliev Invariants}}

{{Khovanov Homology|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>19</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>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 bgcolor=yellow>1</td><td bgcolor=yellow>&nbsp;</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 bgcolor=yellow>3</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>-2</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 bgcolor=yellow>2</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</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 bgcolor=yellow>4</td><td bgcolor=yellow>3</td><td>&nbsp;</td><td>&nbsp;</td><td>&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 bgcolor=yellow>3</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</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 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>2</td></tr>
<tr align=center><td>5</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>&nbsp;</td><td>0</td></tr>
<tr align=center><td>3</td><td>&nbsp;</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>2</td></tr>
<tr align=center><td>1</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>&nbsp;</td><td>-1</td></tr>
<tr align=center><td>-1</td><td bgcolor=yellow>&nbsp;</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>
<tr align=center><td>-3</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>}}

{{Display Coloured Jones|J2=<math>q^{25}-2 q^{24}+q^{23}+4 q^{22}-7 q^{21}+2 q^{20}+7 q^{19}-13 q^{18}+7 q^{17}+8 q^{16}-20 q^{15}+12 q^{14}+11 q^{13}-25 q^{12}+11 q^{11}+17 q^{10}-26 q^9+7 q^8+20 q^7-22 q^6+q^5+19 q^4-15 q^3-4 q^2+14 q-6-5 q^{-1} +6 q^{-2} - q^{-3} -2 q^{-4} + q^{-5} </math>|J3=<math>-q^{48}+2 q^{47}-q^{46}-q^{45}-2 q^{44}+6 q^{43}+q^{42}-6 q^{41}-6 q^{40}+10 q^{39}+8 q^{38}-6 q^{37}-16 q^{36}+7 q^{35}+15 q^{34}+5 q^{33}-21 q^{32}-11 q^{31}+16 q^{30}+20 q^{29}-11 q^{28}-27 q^{27}+7 q^{26}+24 q^{25}+2 q^{24}-25 q^{23}+11 q^{21}+9 q^{20}-11 q^{19}-8 q^{17}+9 q^{16}+8 q^{15}+q^{14}-24 q^{13}+6 q^{12}+24 q^{11}+5 q^{10}-34 q^9-6 q^8+32 q^7+17 q^6-33 q^5-20 q^4+24 q^3+26 q^2-16 q-26+8 q^{-1} +21 q^{-2} -16 q^{-4} -3 q^{-5} +9 q^{-6} +4 q^{-7} -5 q^{-8} -2 q^{-9} + q^{-10} +2 q^{-11} - q^{-12} </math>|J4=<math>q^{78}-2 q^{77}+q^{76}+q^{75}-q^{74}+3 q^{73}-9 q^{72}+4 q^{71}+6 q^{70}+6 q^{68}-29 q^{67}+6 q^{66}+18 q^{65}+13 q^{64}+15 q^{63}-68 q^{62}-6 q^{61}+32 q^{60}+52 q^{59}+42 q^{58}-127 q^{57}-50 q^{56}+37 q^{55}+121 q^{54}+105 q^{53}-184 q^{52}-133 q^{51}+5 q^{50}+195 q^{49}+204 q^{48}-201 q^{47}-216 q^{46}-65 q^{45}+220 q^{44}+294 q^{43}-168 q^{42}-243 q^{41}-130 q^{40}+190 q^{39}+327 q^{38}-130 q^{37}-211 q^{36}-147 q^{35}+138 q^{34}+307 q^{33}-108 q^{32}-161 q^{31}-132 q^{30}+89 q^{29}+268 q^{28}-90 q^{27}-108 q^{26}-110 q^{25}+37 q^{24}+216 q^{23}-65 q^{22}-47 q^{21}-79 q^{20}-13 q^{19}+147 q^{18}-56 q^{17}+12 q^{16}-28 q^{15}-35 q^{14}+78 q^{13}-75 q^{12}+34 q^{11}+23 q^{10}-12 q^9+45 q^8-102 q^7+8 q^6+38 q^5+25 q^4+56 q^3-93 q^2-29 q+8+31 q^{-1} +73 q^{-2} -47 q^{-3} -33 q^{-4} -22 q^{-5} +6 q^{-6} +57 q^{-7} -7 q^{-8} -11 q^{-9} -21 q^{-10} -11 q^{-11} +25 q^{-12} +3 q^{-13} +2 q^{-14} -7 q^{-15} -8 q^{-16} +6 q^{-17} + q^{-18} +2 q^{-19} - q^{-20} -2 q^{-21} + q^{-22} </math>|J5=<math>-q^{115}+2 q^{114}-q^{113}-q^{112}+q^{111}+4 q^{108}-4 q^{107}-6 q^{106}+3 q^{105}+4 q^{104}+5 q^{103}+10 q^{102}-15 q^{101}-21 q^{100}-2 q^{99}+18 q^{98}+28 q^{97}+23 q^{96}-29 q^{95}-64 q^{94}-25 q^{93}+40 q^{92}+87 q^{91}+58 q^{90}-58 q^{89}-145 q^{88}-79 q^{87}+83 q^{86}+203 q^{85}+135 q^{84}-123 q^{83}-308 q^{82}-178 q^{81}+156 q^{80}+423 q^{79}+287 q^{78}-205 q^{77}-582 q^{76}-394 q^{75}+221 q^{74}+725 q^{73}+569 q^{72}-206 q^{71}-877 q^{70}-735 q^{69}+144 q^{68}+974 q^{67}+903 q^{66}-44 q^{65}-1011 q^{64}-1047 q^{63}-69 q^{62}+1008 q^{61}+1116 q^{60}+176 q^{59}-934 q^{58}-1163 q^{57}-256 q^{56}+875 q^{55}+1123 q^{54}+315 q^{53}-779 q^{52}-1106 q^{51}-334 q^{50}+718 q^{49}+1029 q^{48}+368 q^{47}-630 q^{46}-1013 q^{45}-377 q^{44}+572 q^{43}+930 q^{42}+428 q^{41}-463 q^{40}-919 q^{39}-452 q^{38}+383 q^{37}+812 q^{36}+508 q^{35}-242 q^{34}-761 q^{33}-524 q^{32}+143 q^{31}+615 q^{30}+534 q^{29}-q^{28}-511 q^{27}-496 q^{26}-76 q^{25}+343 q^{24}+434 q^{23}+158 q^{22}-227 q^{21}-332 q^{20}-162 q^{19}+90 q^{18}+230 q^{17}+153 q^{16}-35 q^{15}-123 q^{14}-85 q^{13}-5 q^{12}+47 q^{11}+37 q^{10}-23 q^9-19 q^8+32 q^7+53 q^6+20 q^5-44 q^4-91 q^3-61 q^2+39 q+107+91 q^{-1} + q^{-2} -93 q^{-3} -111 q^{-4} -43 q^{-5} +58 q^{-6} +105 q^{-7} +70 q^{-8} -14 q^{-9} -81 q^{-10} -74 q^{-11} -18 q^{-12} +43 q^{-13} +63 q^{-14} +36 q^{-15} -18 q^{-16} -42 q^{-17} -29 q^{-18} -5 q^{-19} +20 q^{-20} +27 q^{-21} +8 q^{-22} -11 q^{-23} -11 q^{-24} -7 q^{-25} -2 q^{-26} +9 q^{-27} +6 q^{-28} -2 q^{-29} -2 q^{-30} - q^{-31} -2 q^{-32} + q^{-33} +2 q^{-34} - q^{-35} </math>|J6=<math>q^{159}-2 q^{158}+q^{157}+q^{156}-q^{155}-3 q^{153}+5 q^{152}-4 q^{151}+4 q^{150}+3 q^{149}-7 q^{148}+q^{147}-10 q^{146}+11 q^{145}-4 q^{144}+16 q^{143}+10 q^{142}-22 q^{141}-4 q^{140}-31 q^{139}+15 q^{138}+54 q^{136}+35 q^{135}-39 q^{134}-19 q^{133}-86 q^{132}-3 q^{131}-3 q^{130}+126 q^{129}+90 q^{128}-44 q^{127}-31 q^{126}-160 q^{125}-32 q^{124}-16 q^{123}+199 q^{122}+116 q^{121}-85 q^{120}-43 q^{119}-178 q^{118}+44 q^{117}+61 q^{116}+271 q^{115}-18 q^{114}-354 q^{113}-200 q^{112}-128 q^{111}+410 q^{110}+487 q^{109}+525 q^{108}-308 q^{107}-1048 q^{106}-802 q^{105}-261 q^{104}+983 q^{103}+1426 q^{102}+1288 q^{101}-387 q^{100}-1945 q^{99}-1935 q^{98}-944 q^{97}+1251 q^{96}+2488 q^{95}+2539 q^{94}+153 q^{93}-2397 q^{92}-3056 q^{91}-2068 q^{90}+825 q^{89}+2965 q^{88}+3630 q^{87}+1098 q^{86}-2099 q^{85}-3489 q^{84}-2940 q^{83}+44 q^{82}+2690 q^{81}+3980 q^{80}+1770 q^{79}-1479 q^{78}-3229 q^{77}-3149 q^{76}-483 q^{75}+2146 q^{74}+3745 q^{73}+1939 q^{72}-1029 q^{71}-2778 q^{70}-2982 q^{69}-691 q^{68}+1706 q^{67}+3410 q^{66}+1961 q^{65}-700 q^{64}-2406 q^{63}-2861 q^{62}-925 q^{61}+1268 q^{60}+3142 q^{59}+2146 q^{58}-211 q^{57}-1981 q^{56}-2841 q^{55}-1369 q^{54}+623 q^{53}+2772 q^{52}+2429 q^{51}+520 q^{50}-1314 q^{49}-2696 q^{48}-1891 q^{47}-259 q^{46}+2112 q^{45}+2531 q^{44}+1305 q^{43}-379 q^{42}-2191 q^{41}-2170 q^{40}-1182 q^{39}+1115 q^{38}+2179 q^{37}+1794 q^{36}+616 q^{35}-1262 q^{34}-1904 q^{33}-1762 q^{32}+22 q^{31}+1316 q^{30}+1658 q^{29}+1241 q^{28}-204 q^{27}-1074 q^{26}-1663 q^{25}-672 q^{24}+318 q^{23}+936 q^{22}+1160 q^{21}+429 q^{20}-149 q^{19}-995 q^{18}-654 q^{17}-223 q^{16}+181 q^{15}+574 q^{14}+378 q^{13}+274 q^{12}-369 q^{11}-218 q^{10}-142 q^9-63 q^8+123 q^7+34 q^6+151 q^5-231 q^4+15 q^3+93 q^2+99 q+117-44 q^{-1} -7 q^{-2} -348 q^{-3} -103 q^{-4} +43 q^{-5} +166 q^{-6} +226 q^{-7} +126 q^{-8} +96 q^{-9} -289 q^{-10} -201 q^{-11} -137 q^{-12} +8 q^{-13} +134 q^{-14} +180 q^{-15} +220 q^{-16} -77 q^{-17} -99 q^{-18} -150 q^{-19} -99 q^{-20} -28 q^{-21} +69 q^{-22} +171 q^{-23} +30 q^{-24} +18 q^{-25} -51 q^{-26} -62 q^{-27} -67 q^{-28} -16 q^{-29} +66 q^{-30} +19 q^{-31} +33 q^{-32} +4 q^{-33} -9 q^{-34} -33 q^{-35} -21 q^{-36} +15 q^{-37} +12 q^{-39} +6 q^{-40} +5 q^{-41} -9 q^{-42} -8 q^{-43} +4 q^{-44} -2 q^{-45} +2 q^{-46} + q^{-47} +2 q^{-48} - q^{-49} -2 q^{-50} + q^{-51} </math>|J7=<math>-q^{210}+2 q^{209}-q^{208}-q^{207}+q^{206}+3 q^{204}-2 q^{203}-5 q^{202}+4 q^{201}-q^{200}+q^{199}+2 q^{198}-2 q^{197}+8 q^{196}-3 q^{195}-15 q^{194}+3 q^{193}-5 q^{192}+9 q^{191}+14 q^{190}-q^{189}+19 q^{188}-8 q^{187}-32 q^{186}-21 q^{185}-31 q^{184}+15 q^{183}+53 q^{182}+37 q^{181}+66 q^{180}+6 q^{179}-71 q^{178}-89 q^{177}-135 q^{176}-40 q^{175}+86 q^{174}+146 q^{173}+230 q^{172}+119 q^{171}-60 q^{170}-188 q^{169}-357 q^{168}-283 q^{167}-30 q^{166}+211 q^{165}+508 q^{164}+475 q^{163}+220 q^{162}-100 q^{161}-591 q^{160}-772 q^{159}-587 q^{158}-157 q^{157}+593 q^{156}+1056 q^{155}+1088 q^{154}+701 q^{153}-306 q^{152}-1280 q^{151}-1793 q^{150}-1609 q^{149}-311 q^{148}+1301 q^{147}+2559 q^{146}+2856 q^{145}+1469 q^{144}-891 q^{143}-3267 q^{142}-4448 q^{141}-3197 q^{140}-52 q^{139}+3662 q^{138}+6125 q^{137}+5417 q^{136}+1698 q^{135}-3481 q^{134}-7620 q^{133}-7923 q^{132}-3991 q^{131}+2586 q^{130}+8606 q^{129}+10320 q^{128}+6658 q^{127}-948 q^{126}-8760 q^{125}-12246 q^{124}-9364 q^{123}-1238 q^{122}+8123 q^{121}+13363 q^{120}+11646 q^{119}+3569 q^{118}-6799 q^{117}-13573 q^{116}-13188 q^{115}-5656 q^{114}+5121 q^{113}+13031 q^{112}+13915 q^{111}+7159 q^{110}-3550 q^{109}-12035 q^{108}-13816 q^{107}-7966 q^{106}+2275 q^{105}+10885 q^{104}+13307 q^{103}+8176 q^{102}-1520 q^{101}-9915 q^{100}-12538 q^{99}-7948 q^{98}+1120 q^{97}+9126 q^{96}+11823 q^{95}+7644 q^{94}-934 q^{93}-8592 q^{92}-11254 q^{91}-7346 q^{90}+785 q^{89}+8057 q^{88}+10769 q^{87}+7264 q^{86}-414 q^{85}-7490 q^{84}-10389 q^{83}-7325 q^{82}-126 q^{81}+6693 q^{80}+9890 q^{79}+7526 q^{78}+981 q^{77}-5652 q^{76}-9303 q^{75}-7761 q^{74}-1991 q^{73}+4345 q^{72}+8450 q^{71}+7932 q^{70}+3154 q^{69}-2757 q^{68}-7359 q^{67}-7956 q^{66}-4327 q^{65}+988 q^{64}+5945 q^{63}+7688 q^{62}+5399 q^{61}+916 q^{60}-4224 q^{59}-7051 q^{58}-6213 q^{57}-2797 q^{56}+2231 q^{55}+5993 q^{54}+6576 q^{53}+4464 q^{52}-95 q^{51}-4431 q^{50}-6395 q^{49}-5746 q^{48}-1991 q^{47}+2555 q^{46}+5563 q^{45}+6365 q^{44}+3782 q^{43}-453 q^{42}-4147 q^{41}-6276 q^{40}-5025 q^{39}-1507 q^{38}+2319 q^{37}+5428 q^{36}+5507 q^{35}+3083 q^{34}-387 q^{33}-3983 q^{32}-5198 q^{31}-3992 q^{30}-1325 q^{29}+2263 q^{28}+4221 q^{27}+4115 q^{26}+2470 q^{25}-609 q^{24}-2800 q^{23}-3547 q^{22}-2961 q^{21}-637 q^{20}+1401 q^{19}+2546 q^{18}+2717 q^{17}+1264 q^{16}-247 q^{15}-1393 q^{14}-2101 q^{13}-1340 q^{12}-353 q^{11}+527 q^{10}+1295 q^9+948 q^8+502 q^7+q^6-677 q^5-509 q^4-290 q^3-78 q^2+361 q+150+3 q^{-1} -52 q^{-2} -348 q^{-3} -49 q^{-4} +156 q^{-5} +225 q^{-6} +477 q^{-7} +173 q^{-8} -114 q^{-9} -291 q^{-10} -596 q^{-11} -350 q^{-12} -47 q^{-13} +160 q^{-14} +559 q^{-15} +480 q^{-16} +275 q^{-17} +40 q^{-18} -420 q^{-19} -465 q^{-20} -371 q^{-21} -228 q^{-22} +172 q^{-23} +325 q^{-24} +375 q^{-25} +348 q^{-26} +11 q^{-27} -167 q^{-28} -264 q^{-29} -321 q^{-30} -119 q^{-31} -3 q^{-32} +127 q^{-33} +257 q^{-34} +155 q^{-35} +64 q^{-36} -35 q^{-37} -146 q^{-38} -102 q^{-39} -88 q^{-40} -44 q^{-41} +70 q^{-42} +73 q^{-43} +73 q^{-44} +38 q^{-45} -28 q^{-46} -19 q^{-47} -35 q^{-48} -45 q^{-49} -4 q^{-50} +10 q^{-51} +26 q^{-52} +24 q^{-53} -5 q^{-54} +3 q^{-55} -2 q^{-56} -14 q^{-57} -6 q^{-58} -4 q^{-59} +6 q^{-60} +8 q^{-61} -2 q^{-62} +2 q^{-64} -2 q^{-65} - q^{-66} -2 q^{-67} + q^{-68} +2 q^{-69} - q^{-70} </math>}}

{{Computer Talk Header}}

<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><pre style="border: 0px; padding: 0em">Loading KnotTheory` (version of August 29, 2005, 15:27:48)...</pre></td></tr>

<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>PD[Knot[10, 47]]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[1, 4, 2, 5], X[3, 8, 4, 9], X[9, 17, 10, 16], X[5, 15, 6, 14], 
 
  X[15, 7, 16, 6], X[11, 19, 12, 18], X[13, 1, 14, 20], 
 
  X[17, 11, 18, 10], X[19, 13, 20, 12], X[7, 2, 8, 3]]</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[3]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>GaussCode[Knot[10, 47]]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[-1, 10, -2, 1, -4, 5, -10, 2, -3, 8, -6, 9, -7, 4, -5, 3, -8, 
 
  6, -9, 7]</nowiki></pre></td></tr>

<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>DTCode[Knot[10, 47]]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>DTCode[4, 8, 14, 2, 16, 18, 20, 6, 10, 12]</nowiki></pre></td></tr>

<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 = BR[Knot[10, 47]]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[3, {1, 1, 1, 1, 1, -2, 1, 1, -2, -2}]</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[6]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{First[br], Crossings[br]}</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{3, 10}</nowiki></pre></td></tr>

<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>BraidIndex[Knot[10, 47]]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>3</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[DrawMorseLink[Knot[10, 47]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_47_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[8]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>(#[Knot[10, 47]]&) /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Reversible, {2, 3}, 4, 3, NotAvailable, 1}</nowiki></pre></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>alex = Alexander[Knot[10, 47]][t]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>     -4   3    6    7            2      3    4
7 + t   - -- + -- - - - 7 t + 6 t  - 3 t  + t
           3    2   t
          t    t</nowiki></pre></td></tr>

<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>Conway[Knot[10, 47]][z]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[11]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>       2      4      6    8
1 + 6 z  + 8 z  + 5 z  + z</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[12]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 47]}</nowiki></pre></td></tr>

<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>{KnotDet[Knot[10, 47]], KnotSignature[Knot[10, 47]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{41, 4}</nowiki></pre></td></tr>

<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>Jones[Knot[10, 47]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>    1            2      3      4      5      6      7      8    9
2 - - - 3 q + 5 q  - 5 q  + 7 q  - 6 q  + 5 q  - 4 q  + 2 q  - q
    q</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[15]:=</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>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Knot[10, 47]}</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[16]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>A2Invariant[Knot[10, 47]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[16]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>  -2    2    6    8      10    12      14    18    20      22    26
-q   - q  + q  + q  + 4 q   + q   + 3 q   - q   - q   - 2 q   - q</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[17]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>HOMFLYPT[Knot[10, 47]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[17]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>                  2       2      2      4       4      4    6      6
-5   9    3    8 z    21 z    7 z    5 z    18 z    5 z    z    7 z
-- + -- - -- - ---- + ----- - ---- - ---- + ----- - ---- - -- + ---- - 
 6    4    2     6      4       2      6      4       2     6     4
a    a    a     a      a       a      a      a       a     a     a
 
   6    8
  z    z
  -- + --
   2    4
  a    a</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[18]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kauffman[Knot[10, 47]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[18]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>                                                   2     2       2
5    9    3     z    2 z   z    9 z   8 z   3 z   z     z    15 z
-- + -- + -- - --- + --- - -- - --- - --- - --- - --- + -- - ----- - 
 6    4    2    11    9     7    5     3     a     10    8     6
a    a    a    a     a     a    a     a           a     a     a
 
      2      2    3       3      3       3       3      3      4
  26 z    9 z    z     3 z    2 z    19 z    20 z    7 z    2 z
  ----- - ---- + --- - ---- + ---- + ----- + ----- + ---- + ---- - 
    4       2     11     9      7      5       3      a      10
   a       a     a      a      a      a       a             a
 
     4       4       4       4      5      5       5       5      5
  3 z    15 z    35 z    15 z    3 z    5 z    14 z    11 z    5 z
  ---- + ----- + ----- + ----- + ---- - ---- - ----- - ----- - ---- + 
    8      6       4       2       9      7      5       3      a
   a      a       a       a       a      a      a       a
 
     6       6       6       6      7    7    7    7      8      8
  3 z    10 z    23 z    10 z    3 z    z    z    z    3 z    5 z
  ---- - ----- - ----- - ----- + ---- + -- - -- + -- + ---- + ---- + 
    8      6       4       2       7     5    3   a      6      4
   a      a       a       a       a     a    a          a      a
 
     8    9    9
  2 z    z    z
  ---- + -- + --
    2     5    3
   a     a    a</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[19]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>{Vassiliev[2][Knot[10, 47]], Vassiliev[3][Knot[10, 47]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[19]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{6, 11}</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[20]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Kh[Knot[10, 47]][q, t]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[20]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>                                         3
   3      5     1      1     q    2 q   q       5        7
3 q  + 3 q  + ----- + ---- + -- + --- + -- + 3 q  t + 2 q  t + 
               3  3      2    2    t    t
              q  t    q t    t
 
     7  2      9  2      9  3      11  3      11  4      13  4
  4 q  t  + 3 q  t  + 2 q  t  + 4 q   t  + 3 q   t  + 2 q   t  + 
 
   13  5      15  5    15  6    17  6    19  7
  q   t  + 3 q   t  + q   t  + q   t  + q   t</nowiki></pre></td></tr>

<tr valign=top><td><pre style="color:  blue; border: 0px; padding: 0em"><nowiki>In[21]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>ColouredJones[Knot[10, 47], 2][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre  style="color: blue; border: 0px; padding: 0em"><nowiki>Out[21]=&nbsp;&nbsp;</nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>      -5   2     -3   6    5             2       3       4    5
-6 + q   - -- - q   + -- - - + 14 q - 4 q  - 15 q  + 19 q  + q  - 
            4          2   q
           q          q
 
      6       7      8       9       10       11       12       13
  22 q  + 20 q  + 7 q  - 26 q  + 17 q   + 11 q   - 25 q   + 11 q   + 
 
      14       15      16      17       18      19      20      21
  12 q   - 20 q   + 8 q   + 7 q   - 13 q   + 7 q   + 2 q   - 7 q   + 
 
     22    23      24    25
  4 q   + q   - 2 q   + q</nowiki></pre></td></tr>

</table>

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