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{{Rolfsen Knot Page Header|n=10|k=35|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-3,1,-5,10,-2,3,-4,2,-6,9,-7,8,-10,5,-8,7,-9,6/goTop.html}}

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{{:{{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: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]]</td></tr>
<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr>
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.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>

[[Invariants from Braid Theory|Length]] is 11, width is 6.

[[Invariants from Braid Theory|Braid index]] is 6.
</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_22]], ...}

{{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>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>&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>&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>&nbsp;</td><td bgcolor=yellow>3</td><td bgcolor=yellow>1</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>&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>&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>3</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>&nbsp;</td><td>-1</td></tr>
<tr align=center><td>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>4</td><td bgcolor=yellow>4</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>&nbsp;</td><td bgcolor=yellow>3</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>2</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>-5</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>-7</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>-9</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^{18}-2 q^{17}+6 q^{15}-8 q^{14}-4 q^{13}+19 q^{12}-13 q^{11}-16 q^{10}+34 q^9-11 q^8-32 q^7+44 q^6-4 q^5-45 q^4+46 q^3+3 q^2-47 q+39+7 q^{-1} -36 q^{-2} +24 q^{-3} +5 q^{-4} -19 q^{-5} +12 q^{-6} + q^{-7} -7 q^{-8} +5 q^{-9} -2 q^{-11} + q^{-12} </math>|J3=<math>q^{36}-2 q^{35}+2 q^{33}+3 q^{32}-7 q^{31}-5 q^{30}+10 q^{29}+14 q^{28}-16 q^{27}-23 q^{26}+13 q^{25}+42 q^{24}-11 q^{23}-54 q^{22}-4 q^{21}+67 q^{20}+23 q^{19}-73 q^{18}-45 q^{17}+70 q^{16}+68 q^{15}-61 q^{14}-88 q^{13}+46 q^{12}+107 q^{11}-31 q^{10}-118 q^9+12 q^8+127 q^7+4 q^6-130 q^5-19 q^4+126 q^3+33 q^2-117 q-38+96 q^{-1} +45 q^{-2} -77 q^{-3} -39 q^{-4} +52 q^{-5} +31 q^{-6} -33 q^{-7} -17 q^{-8} +16 q^{-9} +9 q^{-10} -12 q^{-11} +3 q^{-12} +5 q^{-13} -4 q^{-14} -6 q^{-15} +7 q^{-16} +3 q^{-17} -3 q^{-18} -5 q^{-19} +4 q^{-20} + q^{-21} -2 q^{-23} + q^{-24} </math>|J4=<math>q^{60}-2 q^{59}+2 q^{57}-q^{56}+4 q^{55}-9 q^{54}-q^{53}+10 q^{52}+14 q^{50}-30 q^{49}-15 q^{48}+23 q^{47}+12 q^{46}+52 q^{45}-57 q^{44}-56 q^{43}+9 q^{42}+15 q^{41}+137 q^{40}-47 q^{39}-91 q^{38}-47 q^{37}-48 q^{36}+217 q^{35}+16 q^{34}-46 q^{33}-87 q^{32}-189 q^{31}+209 q^{30}+66 q^{29}+89 q^{28}-27 q^{27}-330 q^{26}+94 q^{25}+25 q^{24}+247 q^{23}+133 q^{22}-398 q^{21}-57 q^{20}-103 q^{19}+357 q^{18}+325 q^{17}-385 q^{16}-186 q^{15}-259 q^{14}+412 q^{13}+490 q^{12}-333 q^{11}-276 q^{10}-392 q^9+417 q^8+604 q^7-251 q^6-320 q^5-491 q^4+359 q^3+646 q^2-128 q-283-537 q^{-1} +220 q^{-2} +577 q^{-3} +7 q^{-4} -155 q^{-5} -484 q^{-6} +53 q^{-7} +393 q^{-8} +76 q^{-9} +5 q^{-10} -331 q^{-11} -54 q^{-12} +185 q^{-13} +58 q^{-14} +94 q^{-15} -162 q^{-16} -64 q^{-17} +51 q^{-18} +6 q^{-19} +94 q^{-20} -53 q^{-21} -33 q^{-22} +2 q^{-23} -20 q^{-24} +56 q^{-25} -11 q^{-26} -8 q^{-27} -4 q^{-28} -19 q^{-29} +23 q^{-30} - q^{-31} + q^{-32} - q^{-33} -9 q^{-34} +6 q^{-35} + q^{-37} -2 q^{-39} + q^{-40} </math>|J5=<math>q^{90}-2 q^{89}+2 q^{87}-q^{86}+2 q^{84}-5 q^{83}-2 q^{82}+9 q^{81}+3 q^{80}-3 q^{79}-2 q^{78}-16 q^{77}-9 q^{76}+20 q^{75}+30 q^{74}+11 q^{73}-13 q^{72}-49 q^{71}-52 q^{70}+14 q^{69}+73 q^{68}+83 q^{67}+27 q^{66}-79 q^{65}-140 q^{64}-75 q^{63}+54 q^{62}+160 q^{61}+163 q^{60}+5 q^{59}-166 q^{58}-199 q^{57}-104 q^{56}+82 q^{55}+227 q^{54}+198 q^{53}+22 q^{52}-142 q^{51}-237 q^{50}-199 q^{49}-10 q^{48}+208 q^{47}+327 q^{46}+246 q^{45}-44 q^{44}-408 q^{43}-531 q^{42}-213 q^{41}+384 q^{40}+791 q^{39}+569 q^{38}-237 q^{37}-1005 q^{36}-976 q^{35}-4 q^{34}+1129 q^{33}+1376 q^{32}+340 q^{31}-1166 q^{30}-1751 q^{29}-708 q^{28}+1124 q^{27}+2062 q^{26}+1094 q^{25}-1034 q^{24}-2322 q^{23}-1437 q^{22}+902 q^{21}+2518 q^{20}+1763 q^{19}-774 q^{18}-2679 q^{17}-2026 q^{16}+642 q^{15}+2783 q^{14}+2269 q^{13}-501 q^{12}-2866 q^{11}-2471 q^{10}+356 q^9+2881 q^8+2637 q^7-156 q^6-2829 q^5-2786 q^4-57 q^3+2684 q^2+2832 q+339-2418 q^{-1} -2830 q^{-2} -597 q^{-3} +2062 q^{-4} +2667 q^{-5} +843 q^{-6} -1607 q^{-7} -2417 q^{-8} -997 q^{-9} +1135 q^{-10} +2040 q^{-11} +1068 q^{-12} -701 q^{-13} -1613 q^{-14} -1013 q^{-15} +334 q^{-16} +1172 q^{-17} +904 q^{-18} -87 q^{-19} -808 q^{-20} -699 q^{-21} -68 q^{-22} +484 q^{-23} +537 q^{-24} +131 q^{-25} -288 q^{-26} -356 q^{-27} -136 q^{-28} +129 q^{-29} +244 q^{-30} +119 q^{-31} -63 q^{-32} -138 q^{-33} -96 q^{-34} +10 q^{-35} +93 q^{-36} +66 q^{-37} -4 q^{-38} -36 q^{-39} -48 q^{-40} -20 q^{-41} +34 q^{-42} +28 q^{-43} +3 q^{-44} -2 q^{-45} -16 q^{-46} -17 q^{-47} +9 q^{-48} +10 q^{-49} +4 q^{-51} -3 q^{-52} -7 q^{-53} +2 q^{-54} +2 q^{-55} + q^{-57} -2 q^{-59} + q^{-60} </math>|J6=<math>q^{126}-2 q^{125}+2 q^{123}-q^{122}-2 q^{120}+6 q^{119}-6 q^{118}-3 q^{117}+11 q^{116}-q^{115}-2 q^{114}-13 q^{113}+12 q^{112}-14 q^{111}-8 q^{110}+36 q^{109}+14 q^{108}+5 q^{107}-43 q^{106}+7 q^{105}-55 q^{104}-38 q^{103}+80 q^{102}+72 q^{101}+75 q^{100}-55 q^{99}+6 q^{98}-162 q^{97}-170 q^{96}+53 q^{95}+131 q^{94}+235 q^{93}+50 q^{92}+153 q^{91}-233 q^{90}-378 q^{89}-160 q^{88}-6 q^{87}+284 q^{86}+157 q^{85}+522 q^{84}-21 q^{83}-336 q^{82}-310 q^{81}-304 q^{80}-39 q^{79}-181 q^{78}+653 q^{77}+281 q^{76}+174 q^{75}+151 q^{74}-79 q^{73}-315 q^{72}-1049 q^{71}-79 q^{70}-218 q^{69}+454 q^{68}+1126 q^{67}+1289 q^{66}+531 q^{65}-1460 q^{64}-1367 q^{63}-2050 q^{62}-695 q^{61}+1387 q^{60}+3221 q^{59}+2903 q^{58}-157 q^{57}-1803 q^{56}-4397 q^{55}-3511 q^{54}-267 q^{53}+4179 q^{52}+5792 q^{51}+2917 q^{50}-285 q^{49}-5705 q^{48}-6862 q^{47}-3692 q^{46}+3198 q^{45}+7698 q^{44}+6564 q^{43}+2897 q^{42}-5203 q^{41}-9364 q^{40}-7647 q^{39}+696 q^{38}+8017 q^{37}+9509 q^{36}+6528 q^{35}-3394 q^{34}-10533 q^{33}-10960 q^{32}-2188 q^{31}+7252 q^{30}+11336 q^{29}+9566 q^{28}-1301 q^{27}-10792 q^{26}-13248 q^{25}-4584 q^{24}+6227 q^{23}+12356 q^{22}+11709 q^{21}+433 q^{20}-10720 q^{19}-14752 q^{18}-6362 q^{17}+5315 q^{16}+12954 q^{15}+13222 q^{14}+1892 q^{13}-10414 q^{12}-15733 q^{11}-7912 q^{10}+4177 q^9+13030 q^8+14349 q^7+3582 q^6-9333 q^5-15934 q^4-9452 q^3+2209 q^2+11893 q+14709+5625 q^{-1} -6869 q^{-2} -14545 q^{-3} -10393 q^{-4} -540 q^{-5} +8990 q^{-6} +13375 q^{-7} +7173 q^{-8} -3324 q^{-9} -11136 q^{-10} -9671 q^{-11} -2930 q^{-12} +4926 q^{-13} +10062 q^{-14} +7055 q^{-15} -147 q^{-16} -6647 q^{-17} -7105 q^{-18} -3691 q^{-19} +1384 q^{-20} +5925 q^{-21} +5217 q^{-22} +1360 q^{-23} -2894 q^{-24} -3925 q^{-25} -2838 q^{-26} -416 q^{-27} +2671 q^{-28} +2875 q^{-29} +1304 q^{-30} -883 q^{-31} -1584 q^{-32} -1495 q^{-33} -728 q^{-34} +984 q^{-35} +1215 q^{-36} +704 q^{-37} -223 q^{-38} -474 q^{-39} -579 q^{-40} -484 q^{-41} +375 q^{-42} +442 q^{-43} +284 q^{-44} -94 q^{-45} -117 q^{-46} -197 q^{-47} -262 q^{-48} +181 q^{-49} +163 q^{-50} +121 q^{-51} -53 q^{-52} -24 q^{-53} -73 q^{-54} -147 q^{-55} +87 q^{-56} +59 q^{-57} +62 q^{-58} -20 q^{-59} +5 q^{-60} -27 q^{-61} -76 q^{-62} +33 q^{-63} +13 q^{-64} +29 q^{-65} -6 q^{-66} +11 q^{-67} -6 q^{-68} -31 q^{-69} +11 q^{-70} -2 q^{-71} +10 q^{-72} -2 q^{-73} +5 q^{-74} -9 q^{-76} +4 q^{-77} -2 q^{-78} +2 q^{-79} + q^{-81} -2 q^{-83} + q^{-84} </math>|J7=Not Available}}

{{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, 35]]</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[7, 10, 8, 11], X[3, 9, 4, 8], X[9, 3, 10, 2], 
 
  X[5, 16, 6, 17], X[11, 1, 12, 20], X[13, 19, 14, 18], 
 
  X[17, 15, 18, 14], X[19, 13, 20, 12], X[15, 6, 16, 7]]</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, 35]]</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, 4, -3, 1, -5, 10, -2, 3, -4, 2, -6, 9, -7, 8, -10, 5, -8, 
 
  7, -9, 6]</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, 35]]</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, 16, 10, 2, 20, 18, 6, 14, 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, 35]]</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[6, {-1, 2, -1, 2, 3, -2, -4, 3, 5, -4, 5}]</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>{6, 11}</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, 35]]</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>6</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, 35]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:10_35_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, 35]]&) /@ {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, 2, 2, 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, 35]][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>     2    12             2
21 + -- - -- - 12 t + 2 t
      2   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, 35]][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
1 - 4 z  + 2 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, 35]}</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, 35]], KnotSignature[Knot[10, 35]]}</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>{49, 0}</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, 35]][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>     -4   2    4    6            2      3      4      5    6
8 + q   - -- + -- - - - 8 q + 7 q  - 6 q  + 4 q  - 2 q  + q
           3    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, 22], Knot[10, 35]}</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, 35]][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> -14    -12    -10    -8   2    2     2    6    8      10    14    16
q    + q    - q    + q   - -- + -- + q  - q  + q  - 2 q   + q   - q   + 
                            4    2
                           q    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, 35]][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                   4
     -6    -4    2    4   2 z       2  2    4   z
1 + a   - a   - a  + a  - ---- - 2 a  z  + z  + --
                            4                    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, 35]][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
     -6    -4    2    4   2 z   z    z          3        2   4 z
1 - a   - a   + a  + a  - --- - -- + - + a z + a  z - 3 z  + ---- + 
                           5     3   a                         6
                          a     a                             a
 
     2      2                          3      3
  3 z    3 z       2  2      4  2   6 z    5 z         3      3  3
  ---- - ---- - 3 a  z  - 2 a  z  + ---- + ---- - 2 a z  - 3 a  z  + 
    4      2                          5      3
   a      a                          a      a
 
            4       4              5      5    5
     4   4 z    10 z     4  4   7 z    6 z    z       3  5      6
  5 z  - ---- + ----- + a  z  - ---- - ---- - -- + 2 a  z  - 3 z  + 
           6      2               5      3    a
          a      a               a      a
 
   6      6       6                7                      8      8
  z    5 z    11 z       2  6   2 z         7      8   2 z    4 z
  -- - ---- - ----- + 2 a  z  + ---- + 2 a z  + 2 z  + ---- + ---- + 
   6     4      2                 5                      4      2
  a     a      a                 a                      a      a
 
   9    9
  z    z
  -- + --
   3   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, 35]], Vassiliev[3][Knot[10, 35]]}</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>{-4, -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, 35]][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>5           1       1       1       3       1      3      3
- + 4 q + ----- + ----- + ----- + ----- + ----- + ---- + --- + 4 q t + 
q          9  4    7  3    5  3    5  2    3  2    3     q t
          q  t    q  t    q  t    q  t    q  t    q  t
 
     3        3  2      5  2      5  3      7  3    7  4      9  4
  4 q  t + 3 q  t  + 4 q  t  + 3 q  t  + 3 q  t  + q  t  + 3 q  t  + 
 
   9  5    11  5    13  6
  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, 35], 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>      -12    2    5    7     -7   12   19   5    24   36   7
39 + q    - --- + -- - -- + q   + -- - -- + -- + -- - -- + - - 47 q + 
             11    9    8          6    5    4    3    2   q
            q     q    q          q    q    q    q    q
 
     2       3       4      5       6       7       8       9
  3 q  + 46 q  - 45 q  - 4 q  + 44 q  - 32 q  - 11 q  + 34 q  - 
 
      10       11       12      13      14      15      17    18
  16 q   - 13 q   + 19 q   - 4 q   - 8 q   + 6 q   - 2 q   + q</nowiki></pre></td></tr>

</table>

See/edit the [[Rolfsen_Splice_Template]].

 [[Category:Knot Page]]