View source for 10 94

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{{Knot Navigation Links|ext=gif}}

{{Rolfsen Knot Page Header|n=10|k=94|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,7,-9,4,-1,2,-6,8,-7,3,-10,5,-4,6,-8,9,-3,10,-5/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:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.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>): 
{[[10_41]], ...}

{{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%>-4</td  ><td width=6.66667%>-3</td  ><td width=6.66667%>-2</td  ><td width=6.66667%>-1</td  ><td width=6.66667%>0</td  ><td width=6.66667%>1</td  ><td width=6.66667%>2</td  ><td width=6.66667%>3</td  ><td width=6.66667%>4</td  ><td width=6.66667%>5</td  ><td width=6.66667%>6</td  ><td width=13.3333%>&chi;</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>&nbsp;</td><td bgcolor=yellow>1</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>&nbsp;</td><td bgcolor=yellow>2</td><td bgcolor=yellow>&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>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>1</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>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>2</td><td>&nbsp;</td><td>&nbsp;</td><td>-3</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>6</td><td bgcolor=yellow>4</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>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>6</td><td bgcolor=yellow>5</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>&nbsp;</td><td bgcolor=yellow>5</td><td bgcolor=yellow>6</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>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>7</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>&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>&nbsp;</td><td>-2</td></tr>
<tr align=center><td>-3</td><td>&nbsp;</td><td bgcolor=yellow>1</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>&nbsp;</td><td>&nbsp;</td><td>3</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>&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>&nbsp;</td><td>1</td></tr>
</table>}}

{{Display Coloured Jones|J2=<math>q^{20}-3 q^{19}+2 q^{18}+6 q^{17}-15 q^{16}+9 q^{15}+19 q^{14}-43 q^{13}+20 q^{12}+46 q^{11}-81 q^{10}+23 q^9+79 q^8-104 q^7+11 q^6+98 q^5-97 q^4-9 q^3+94 q^2-67 q-24+70 q^{-1} -31 q^{-2} -27 q^{-3} +36 q^{-4} -6 q^{-5} -15 q^{-6} +10 q^{-7} + q^{-8} -3 q^{-9} + q^{-10} </math>|J3=<math>q^{39}-3 q^{38}+2 q^{37}+2 q^{36}-7 q^{34}+3 q^{33}+10 q^{32}-8 q^{31}-14 q^{30}+21 q^{29}+21 q^{28}-44 q^{27}-43 q^{26}+83 q^{25}+81 q^{24}-124 q^{23}-146 q^{22}+161 q^{21}+231 q^{20}-182 q^{19}-321 q^{18}+176 q^{17}+406 q^{16}-148 q^{15}-469 q^{14}+102 q^{13}+504 q^{12}-46 q^{11}-509 q^{10}-18 q^9+492 q^8+81 q^7-456 q^6-137 q^5+395 q^4+197 q^3-332 q^2-229 q+241+259 q^{-1} -161 q^{-2} -245 q^{-3} +71 q^{-4} +219 q^{-5} -9 q^{-6} -164 q^{-7} -37 q^{-8} +112 q^{-9} +46 q^{-10} -58 q^{-11} -44 q^{-12} +26 q^{-13} +29 q^{-14} -8 q^{-15} -15 q^{-16} +2 q^{-17} +5 q^{-18} + q^{-19} -3 q^{-20} + q^{-21} </math>|J4=<math>q^{64}-3 q^{63}+2 q^{62}+2 q^{61}-4 q^{60}+8 q^{59}-13 q^{58}+5 q^{57}+5 q^{56}-13 q^{55}+39 q^{54}-34 q^{53}-11 q^{51}-49 q^{50}+128 q^{49}-7 q^{48}+20 q^{47}-112 q^{46}-240 q^{45}+235 q^{44}+187 q^{43}+271 q^{42}-231 q^{41}-786 q^{40}+58 q^{39}+473 q^{38}+1020 q^{37}+5 q^{36}-1566 q^{35}-698 q^{34}+403 q^{33}+2063 q^{32}+874 q^{31}-2018 q^{30}-1745 q^{29}-294 q^{28}+2750 q^{27}+2000 q^{26}-1809 q^{25}-2418 q^{24}-1261 q^{23}+2752 q^{22}+2758 q^{21}-1206 q^{20}-2456 q^{19}-1987 q^{18}+2280 q^{17}+2954 q^{16}-546 q^{15}-2063 q^{14}-2381 q^{13}+1582 q^{12}+2781 q^{11}+122 q^{10}-1436 q^9-2550 q^8+703 q^7+2313 q^6+793 q^5-568 q^4-2417 q^3-259 q^2+1471 q+1195+412 q^{-1} -1778 q^{-2} -906 q^{-3} +396 q^{-4} +996 q^{-5} +1052 q^{-6} -782 q^{-7} -871 q^{-8} -383 q^{-9} +348 q^{-10} +990 q^{-11} -5 q^{-12} -361 q^{-13} -501 q^{-14} -152 q^{-15} +492 q^{-16} +194 q^{-17} +34 q^{-18} -228 q^{-19} -214 q^{-20} +113 q^{-21} +80 q^{-22} +93 q^{-23} -34 q^{-24} -88 q^{-25} +9 q^{-26} +2 q^{-27} +32 q^{-28} +4 q^{-29} -18 q^{-30} +2 q^{-31} -3 q^{-32} +5 q^{-33} + q^{-34} -3 q^{-35} + q^{-36} </math>|J5=<math>q^{95}-3 q^{94}+2 q^{93}+2 q^{92}-4 q^{91}+4 q^{90}+2 q^{89}-11 q^{88}+11 q^{86}+12 q^{84}+4 q^{83}-44 q^{82}-32 q^{81}+22 q^{80}+61 q^{79}+81 q^{78}+20 q^{77}-136 q^{76}-211 q^{75}-76 q^{74}+201 q^{73}+416 q^{72}+296 q^{71}-218 q^{70}-761 q^{69}-753 q^{68}+68 q^{67}+1191 q^{66}+1559 q^{65}+467 q^{64}-1545 q^{63}-2787 q^{62}-1659 q^{61}+1585 q^{60}+4340 q^{59}+3639 q^{58}-885 q^{57}-5879 q^{56}-6507 q^{55}-867 q^{54}+7029 q^{53}+9896 q^{52}+3793 q^{51}-7210 q^{50}-13343 q^{49}-7751 q^{48}+6177 q^{47}+16249 q^{46}+12173 q^{45}-3926 q^{44}-18039 q^{43}-16463 q^{42}+767 q^{41}+18567 q^{40}+20004 q^{39}+2694 q^{38}-17892 q^{37}-22400 q^{36}-5971 q^{35}+16382 q^{34}+23618 q^{33}+8658 q^{32}-14466 q^{31}-23833 q^{30}-10608 q^{29}+12469 q^{28}+23334 q^{27}+11921 q^{26}-10514 q^{25}-22459 q^{24}-12816 q^{23}+8650 q^{22}+21309 q^{21}+13516 q^{20}-6687 q^{19}-19936 q^{18}-14173 q^{17}+4472 q^{16}+18273 q^{15}+14765 q^{14}-1980 q^{13}-16079 q^{12}-15114 q^{11}-886 q^{10}+13335 q^9+15054 q^8+3680 q^7-9920 q^6-14137 q^5-6338 q^4+6090 q^3+12432 q^2+8112 q-2169-9668 q^{-1} -8940 q^{-2} -1349 q^{-3} +6417 q^{-4} +8388 q^{-5} +3926 q^{-6} -2899 q^{-7} -6808 q^{-8} -5237 q^{-9} -84 q^{-10} +4425 q^{-11} +5228 q^{-12} +2223 q^{-13} -2006 q^{-14} -4181 q^{-15} -3107 q^{-16} -73 q^{-17} +2604 q^{-18} +3054 q^{-19} +1266 q^{-20} -1079 q^{-21} -2232 q^{-22} -1680 q^{-23} -65 q^{-24} +1298 q^{-25} +1450 q^{-26} +592 q^{-27} -467 q^{-28} -957 q^{-29} -678 q^{-30} -13 q^{-31} +478 q^{-32} +511 q^{-33} +186 q^{-34} -169 q^{-35} -277 q^{-36} -174 q^{-37} +130 q^{-39} +113 q^{-40} +19 q^{-41} -41 q^{-42} -39 q^{-43} -29 q^{-44} +6 q^{-45} +27 q^{-46} +6 q^{-47} -6 q^{-48} - q^{-49} -3 q^{-50} -3 q^{-51} +5 q^{-52} + q^{-53} -3 q^{-54} + q^{-55} </math>|J6=<math>q^{132}-3 q^{131}+2 q^{130}+2 q^{129}-4 q^{128}+4 q^{127}-2 q^{126}+4 q^{125}-16 q^{124}+6 q^{123}+24 q^{122}-16 q^{121}+10 q^{120}-12 q^{119}-7 q^{118}-58 q^{117}+23 q^{116}+114 q^{115}+24 q^{113}-67 q^{112}-106 q^{111}-230 q^{110}+49 q^{109}+398 q^{108}+213 q^{107}+191 q^{106}-186 q^{105}-535 q^{104}-929 q^{103}-187 q^{102}+1025 q^{101}+1192 q^{100}+1275 q^{99}+89 q^{98}-1663 q^{97}-3400 q^{96}-2206 q^{95}+1253 q^{94}+3791 q^{93}+5717 q^{92}+3575 q^{91}-2211 q^{90}-9329 q^{89}-10398 q^{88}-3749 q^{87}+5863 q^{86}+16309 q^{85}+17335 q^{84}+5570 q^{83}-15195 q^{82}-28684 q^{81}-24253 q^{80}-4001 q^{79}+27437 q^{78}+45846 q^{77}+35069 q^{76}-5452 q^{75}-48249 q^{74}-64110 q^{73}-41443 q^{72}+19312 q^{71}+75854 q^{70}+87674 q^{69}+36364 q^{68}-45260 q^{67}-104637 q^{66}-103483 q^{65}-23708 q^{64}+80141 q^{63}+138724 q^{62}+101857 q^{61}-6168 q^{60}-116553 q^{59}-160243 q^{58}-87818 q^{57}+48286 q^{56}+158531 q^{55}+158071 q^{54}+50968 q^{53}-93242 q^{52}-183941 q^{51}-139743 q^{50}+1003 q^{49}+144507 q^{48}+181507 q^{47}+95214 q^{46}-56446 q^{45}-176214 q^{44}-161683 q^{43}-34928 q^{42}+117935 q^{41}+177797 q^{40}+114897 q^{39}-27884 q^{38}-157073 q^{37}-162353 q^{36}-53444 q^{35}+95387 q^{34}+165160 q^{33}+120705 q^{32}-9091 q^{31}-138620 q^{30}-157689 q^{29}-66087 q^{28}+75147 q^{27}+151950 q^{26}+125991 q^{25}+11328 q^{24}-116998 q^{23}-152588 q^{22}-83371 q^{21}+46553 q^{20}+132448 q^{19}+132174 q^{18}+40951 q^{17}-82204 q^{16}-138997 q^{15}-102946 q^{14}+4767 q^{13}+96351 q^{12}+128048 q^{11}+73582 q^{10}-31451 q^9-105278 q^8-109818 q^7-40252 q^6+42040 q^5+99972 q^4+90405 q^3+21863 q^2-50746 q-88427-66082 q^{-1} -13942 q^{-2} +48522 q^{-3} +74828 q^{-4} +52409 q^{-5} +4740 q^{-6} -41627 q^{-7} -56203 q^{-8} -44217 q^{-9} -2967 q^{-10} +33095 q^{-11} +45216 q^{-12} +32694 q^{-13} +3772 q^{-14} -20968 q^{-15} -36810 q^{-16} -26171 q^{-17} -5167 q^{-18} +15116 q^{-19} +25233 q^{-20} +21136 q^{-21} +8596 q^{-22} -10706 q^{-23} -18002 q^{-24} -16746 q^{-25} -7232 q^{-26} +4280 q^{-27} +12409 q^{-28} +14222 q^{-29} +5761 q^{-30} -1610 q^{-31} -8158 q^{-32} -9283 q^{-33} -6138 q^{-34} +108 q^{-35} +5846 q^{-36} +5829 q^{-37} +4516 q^{-38} +490 q^{-39} -2675 q^{-40} -4416 q^{-41} -3105 q^{-42} -200 q^{-43} +1170 q^{-44} +2474 q^{-45} +1874 q^{-46} +722 q^{-47} -917 q^{-48} -1343 q^{-49} -828 q^{-50} -519 q^{-51} +333 q^{-52} +611 q^{-53} +640 q^{-54} +97 q^{-55} -161 q^{-56} -171 q^{-57} -289 q^{-58} -87 q^{-59} +39 q^{-60} +162 q^{-61} +48 q^{-62} +11 q^{-63} +17 q^{-64} -53 q^{-65} -29 q^{-66} -13 q^{-67} +30 q^{-68} + q^{-69} -4 q^{-70} +11 q^{-71} -6 q^{-72} -3 q^{-73} -3 q^{-74} +5 q^{-75} + q^{-76} -3 q^{-77} + q^{-78} </math>|J7=<math>q^{175}-3 q^{174}+2 q^{173}+2 q^{172}-4 q^{171}+4 q^{170}-2 q^{169}-q^{167}-10 q^{166}+19 q^{165}+8 q^{164}-18 q^{163}+5 q^{162}-15 q^{161}-5 q^{160}+q^{159}-22 q^{158}+81 q^{157}+52 q^{156}-48 q^{155}-36 q^{154}-105 q^{153}-34 q^{152}+17 q^{151}-4 q^{150}+269 q^{149}+221 q^{148}-70 q^{147}-199 q^{146}-470 q^{145}-260 q^{144}+56 q^{143}+235 q^{142}+909 q^{141}+813 q^{140}+45 q^{139}-757 q^{138}-1865 q^{137}-1601 q^{136}-340 q^{135}+1184 q^{134}+3515 q^{133}+3848 q^{132}+1861 q^{131}-1680 q^{130}-6640 q^{129}-8380 q^{128}-5724 q^{127}+802 q^{126}+10672 q^{125}+16707 q^{124}+15085 q^{123}+4513 q^{122}-14385 q^{121}-29965 q^{120}-33273 q^{119}-19039 q^{118}+13087 q^{117}+46263 q^{116}+63451 q^{115}+50372 q^{114}+1733 q^{113}-60331 q^{112}-105985 q^{111}-105078 q^{110}-41237 q^{109}+60425 q^{108}+154271 q^{107}+186189 q^{106}+117900 q^{105}-29815 q^{104}-194866 q^{103}-289047 q^{102}-238228 q^{101}-48084 q^{100}+206381 q^{99}+396985 q^{98}+399254 q^{97}+185801 q^{96}-166238 q^{95}-486164 q^{94}-584376 q^{93}-381608 q^{92}+58293 q^{91}+527985 q^{90}+764882 q^{89}+619520 q^{88}+120754 q^{87}-500862 q^{86}-909006 q^{85}-869481 q^{84}-355415 q^{83}+397541 q^{82}+988808 q^{81}+1095124 q^{80}+617173 q^{79}-227763 q^{78}-991741 q^{77}-1266294 q^{76}-869673 q^{75}+18068 q^{74}+922380 q^{73}+1364500 q^{72}+1080639 q^{71}+199484 q^{70}-800665 q^{69}-1389807 q^{68}-1230508 q^{67}-393982 q^{66}+655093 q^{65}+1356333 q^{64}+1314536 q^{63}+545256 q^{62}-512090 q^{61}-1286708 q^{60}-1342653 q^{59}-647125 q^{58}+390980 q^{57}+1204370 q^{56}+1332481 q^{55}+705063 q^{54}-299606 q^{53}-1126300 q^{52}-1303303 q^{51}-732784 q^{50}+234885 q^{49}+1061215 q^{48}+1271349 q^{47}+746410 q^{46}-187597 q^{45}-1009452 q^{44}-1245203 q^{43}-759780 q^{42}+144221 q^{41}+964206 q^{40}+1227969 q^{39}+783101 q^{38}-92845 q^{37}-916086 q^{36}-1215920 q^{35}-820069 q^{34}+23538 q^{33}+853711 q^{32}+1201354 q^{31}+869761 q^{30}+69530 q^{29}-767224 q^{28}-1174366 q^{27}-925729 q^{26}-186111 q^{25}+649301 q^{24}+1122377 q^{23}+976647 q^{22}+321900 q^{21}-496172 q^{20}-1035467 q^{19}-1008835 q^{18}-464207 q^{17}+311737 q^{16}+904681 q^{15}+1005049 q^{14}+596843 q^{13}-105025 q^{12}-729095 q^{11}-952809 q^{10}-698377 q^9-103849 q^8+515423 q^7+842248 q^6+748498 q^5+292499 q^4-280904 q^3-677366 q^2-732689 q-433424+51925 q^{-1} +471075 q^{-2} +646911 q^{-3} +507064 q^{-4} +142400 q^{-5} -250530 q^{-6} -502497 q^{-7} -503040 q^{-8} -275515 q^{-9} +47079 q^{-10} +323627 q^{-11} +428409 q^{-12} +332780 q^{-13} +108730 q^{-14} -143171 q^{-15} -304628 q^{-16} -315951 q^{-17} -198092 q^{-18} -6279 q^{-19} +163929 q^{-20} +242973 q^{-21} +217545 q^{-22} +102698 q^{-23} -38052 q^{-24} -143161 q^{-25} -181886 q^{-26} -139635 q^{-27} -48441 q^{-28} +47088 q^{-29} +115234 q^{-30} +126652 q^{-31} +88156 q^{-32} +23020 q^{-33} -45828 q^{-34} -85074 q^{-35} -86621 q^{-36} -57023 q^{-37} -6993 q^{-38} +36694 q^{-39} +60738 q^{-40} +60134 q^{-41} +34151 q^{-42} +509 q^{-43} -28341 q^{-44} -43758 q^{-45} -38176 q^{-46} -20332 q^{-47} +2480 q^{-48} +22238 q^{-49} +28615 q^{-50} +24031 q^{-51} +11049 q^{-52} -5012 q^{-53} -14943 q^{-54} -18150 q^{-55} -14068 q^{-56} -4414 q^{-57} +4131 q^{-58} +9997 q^{-59} +10928 q^{-60} +6630 q^{-61} +1590 q^{-62} -3321 q^{-63} -6056 q^{-64} -5363 q^{-65} -3300 q^{-66} -76 q^{-67} +2515 q^{-68} +2964 q^{-69} +2534 q^{-70} +1160 q^{-71} -408 q^{-72} -1139 q^{-73} -1558 q^{-74} -1057 q^{-75} -148 q^{-76} +288 q^{-77} +613 q^{-78} +543 q^{-79} +272 q^{-80} +100 q^{-81} -217 q^{-82} -303 q^{-83} -136 q^{-84} -58 q^{-85} +53 q^{-86} +66 q^{-87} +42 q^{-88} +79 q^{-89} +2 q^{-90} -44 q^{-91} -24 q^{-92} -14 q^{-93} +11 q^{-94} +4 q^{-95} -9 q^{-96} +13 q^{-97} +6 q^{-98} -6 q^{-99} -3 q^{-100} -3 q^{-101} +5 q^{-102} + q^{-103} -3 q^{-104} + q^{-105} </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, 94]]</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[6, 2, 7, 1], X[2, 8, 3, 7], X[18, 12, 19, 11], X[14, 5, 15, 6], 
 
  X[20, 14, 1, 13], X[8, 15, 9, 16], X[10, 4, 11, 3], X[16, 9, 17, 10], 
 
  X[4, 17, 5, 18], X[12, 20, 13, 19]]</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, 94]]</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, -2, 7, -9, 4, -1, 2, -6, 8, -7, 3, -10, 5, -4, 6, -8, 9, 
 
  -3, 10, -5]</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, 94]]</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[6, 10, 14, 2, 16, 18, 20, 8, 4, 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, 94]]</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, -2, 1, 1, -2, -2, 1, -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, 94]]</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, 94]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_94_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, 94]]&) /@ {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>{Chiral, 2, 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, 94]][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   4    9    14             2      3    4
-15 - t   + -- - -- + -- + 14 t - 9 t  + 4 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, 94]][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 - 2 z  - 5 z  - 4 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, 94]}</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, 94]], KnotSignature[Knot[10, 94]]}</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>{71, 2}</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, 94]][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>      -3   3    6              2       3      4      5      6    7
-8 + q   - -- + - + 11 q - 12 q  + 11 q  - 9 q  + 6 q  - 3 q  + q
            2   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, 41], Knot[10, 94]}</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, 94]][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>     -8    -6   2       2      4      6      8    10    14      16
1 + q   - q   + -- + 2 q  - 3 q  + 2 q  - 3 q  + q   - q   + 2 q   - 
                 4
                q
 
   18    20
  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, 94]][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             4       4         6
    2    4       2   5 z    12 z       4   4 z    13 z     6   z
3 + -- - -- + 5 z  + ---- - ----- + 4 z  + ---- - ----- + z  + -- - 
     4    2            4      2              4      2           4
    a    a            a      a              a      a           a
 
     6    8
  6 z    z
  ---- - --
    2     2
   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, 94]][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       2
    2    4    3 z   5 z   3 z            2   z    2 z    6 z    18 z
3 + -- + -- - --- - --- - --- - a z - 7 z  - -- + ---- - ---- - ----- + 
     4    2    5     3     a                  8     6      4      2
    a    a    a     a                        a     a      a      a
 
               3      3       3       3                     4      4
     2  2   3 z    9 z    16 z    10 z         3       4   z    6 z
  2 a  z  - ---- + ---- + ----- + ----- + 6 a z  + 11 z  + -- - ---- + 
              7      5      3       a                       8     6
             a      a      a                               a     a
 
      4       4                5       5       5       5
  10 z    31 z       2  4   3 z    10 z    15 z    11 z         5
  ----- + ----- - 3 a  z  + ---- - ----- - ----- - ----- - 9 a z  - 
    4       2                 7      5       3       a
   a       a                 a      a       a
 
             6      6       6              7      7
      6   5 z    9 z    27 z     2  6   6 z    3 z         7      8
  12 z  + ---- - ---- - ----- + a  z  + ---- + ---- + 3 a z  + 4 z  + 
            6      4      2               5      3
           a      a      a               a      a
 
     8      8      9      9
  5 z    9 z    2 z    2 z
  ---- + ---- + ---- + ----
    4      2      3     a
   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, 94]], Vassiliev[3][Knot[10, 94]]}</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>{-2, -2}</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, 94]][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     1       2       1       4      2      4    4 q
7 q + 5 q  + ----- + ----- + ----- + ----- + ---- + --- + --- + 
              7  4    5  3    3  3    3  2      2   q t    t
             q  t    q  t    q  t    q  t    q t
 
     3        5        5  2      7  2      7  3      9  3      9  4
  6 q  t + 6 q  t + 5 q  t  + 6 q  t  + 4 q  t  + 5 q  t  + 2 q  t  + 
 
     11  4    11  5      13  5    15  6
  4 q   t  + q   t  + 2 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, 94], 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>       -10   3     -8   10   15   6    36   27   31   70
-24 + q    - -- + q   + -- - -- - -- + -- - -- - -- + -- - 67 q + 
              9          7    6    5    4    3    2   q
             q          q    q    q    q    q    q
 
      2      3       4       5       6        7       8       9
  94 q  - 9 q  - 97 q  + 98 q  + 11 q  - 104 q  + 79 q  + 23 q  - 
 
      10       11       12       13       14      15       16      17
  81 q   + 46 q   + 20 q   - 43 q   + 19 q   + 9 q   - 15 q   + 6 q   + 
 
     18      19    20
  2 q   - 3 q   + q</nowiki></pre></td></tr>

</table>

See/edit the [[Rolfsen_Splice_Template]].

 [[Category:Knot Page]]