View source for 7 3

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{{Knot Navigation Links|ext=gif}}

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

[[Invariants from Braid Theory|Length]] is 8, 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=16.6667%><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=8.33333%>0</td  ><td width=8.33333%>1</td  ><td width=8.33333%>2</td  ><td width=8.33333%>3</td  ><td width=8.33333%>4</td  ><td width=8.33333%>5</td  ><td width=8.33333%>6</td  ><td width=8.33333%>7</td  ><td width=16.6667%>&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 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 bgcolor=yellow>&nbsp;</td><td bgcolor=yellow>&nbsp;</td><td>0</td></tr>
<tr align=center><td>15</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>13</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>&nbsp;</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 bgcolor=yellow>1</td><td bgcolor=yellow>2</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 bgcolor=yellow>1</td><td bgcolor=yellow>1</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>&nbsp;</td><td>0</td></tr>
<tr align=center><td>7</td><td>&nbsp;</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>1</td></tr>
<tr align=center><td>5</td><td bgcolor=yellow>1</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>0</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>1</td></tr>
</table>}}

{{Display Coloured Jones|J2=<math>q^{25}-q^{24}+2 q^{22}-3 q^{21}-q^{20}+5 q^{19}-5 q^{18}-2 q^{17}+8 q^{16}-6 q^{15}-2 q^{14}+7 q^{13}-4 q^{12}-2 q^{11}+5 q^{10}-2 q^9-2 q^8+3 q^7-q^5+q^4</math>|J3=<math>-q^{48}+q^{47}-q^{44}+2 q^{43}-q^{41}-2 q^{40}+4 q^{39}+2 q^{38}-4 q^{37}-5 q^{36}+6 q^{35}+6 q^{34}-7 q^{33}-7 q^{32}+6 q^{31}+10 q^{30}-9 q^{29}-8 q^{28}+6 q^{27}+9 q^{26}-7 q^{25}-7 q^{24}+4 q^{23}+8 q^{22}-4 q^{21}-6 q^{20}+q^{19}+7 q^{18}-q^{17}-4 q^{16}-2 q^{15}+5 q^{14}+q^{13}-2 q^{12}-2 q^{11}+2 q^{10}+q^9-q^7+q^6</math>|J4=<math>q^{78}-q^{77}-q^{74}+2 q^{73}-2 q^{72}+q^{71}+q^{70}-3 q^{69}+3 q^{68}-4 q^{67}+2 q^{66}+4 q^{65}-3 q^{64}+4 q^{63}-10 q^{62}+q^{61}+7 q^{60}+q^{59}+8 q^{58}-18 q^{57}-3 q^{56}+10 q^{55}+4 q^{54}+14 q^{53}-24 q^{52}-6 q^{51}+10 q^{50}+5 q^{49}+19 q^{48}-27 q^{47}-8 q^{46}+10 q^{45}+5 q^{44}+18 q^{43}-25 q^{42}-7 q^{41}+8 q^{40}+4 q^{39}+17 q^{38}-20 q^{37}-6 q^{36}+4 q^{35}+2 q^{34}+16 q^{33}-13 q^{32}-5 q^{31}-q^{30}-q^{29}+15 q^{28}-6 q^{27}-2 q^{26}-4 q^{25}-4 q^{24}+11 q^{23}-q^{22}+q^{21}-4 q^{20}-5 q^{19}+6 q^{18}+2 q^{16}-q^{15}-3 q^{14}+2 q^{13}+q^{11}-q^9+q^8</math>|J5=<math>-q^{115}+q^{114}+q^{111}-2 q^{109}+q^{108}-q^{106}+2 q^{105}+2 q^{104}-3 q^{103}-q^{101}-3 q^{100}+3 q^{99}+4 q^{98}+q^{96}-3 q^{95}-8 q^{94}+4 q^{92}+7 q^{91}+7 q^{90}-q^{89}-14 q^{88}-10 q^{87}-q^{86}+12 q^{85}+18 q^{84}+6 q^{83}-17 q^{82}-21 q^{81}-9 q^{80}+16 q^{79}+25 q^{78}+13 q^{77}-14 q^{76}-29 q^{75}-15 q^{74}+17 q^{73}+27 q^{72}+15 q^{71}-9 q^{70}-33 q^{69}-18 q^{68}+17 q^{67}+27 q^{66}+16 q^{65}-10 q^{64}-31 q^{63}-17 q^{62}+15 q^{61}+26 q^{60}+14 q^{59}-8 q^{58}-27 q^{57}-16 q^{56}+11 q^{55}+21 q^{54}+13 q^{53}-3 q^{52}-21 q^{51}-14 q^{50}+4 q^{49}+13 q^{48}+12 q^{47}+4 q^{46}-12 q^{45}-12 q^{44}-2 q^{43}+3 q^{42}+8 q^{41}+10 q^{40}-3 q^{39}-7 q^{38}-5 q^{37}-4 q^{36}+q^{35}+10 q^{34}+3 q^{33}-3 q^{31}-7 q^{30}-3 q^{29}+5 q^{28}+3 q^{27}+4 q^{26}-4 q^{24}-4 q^{23}+2 q^{22}+2 q^{20}+2 q^{19}-q^{18}-2 q^{17}+q^{16}+q^{13}-q^{11}+q^{10}</math>|J6=<math>q^{159}-q^{158}-q^{155}+3 q^{152}-2 q^{151}+q^{149}-2 q^{148}-q^{147}-q^{146}+6 q^{145}-2 q^{144}+3 q^{142}-4 q^{141}-4 q^{140}-3 q^{139}+9 q^{138}-2 q^{137}+2 q^{136}+8 q^{135}-4 q^{134}-9 q^{133}-10 q^{132}+8 q^{131}-4 q^{130}+7 q^{129}+20 q^{128}+2 q^{127}-10 q^{126}-20 q^{125}-q^{124}-18 q^{123}+9 q^{122}+36 q^{121}+18 q^{120}-28 q^{118}-13 q^{117}-42 q^{116}+q^{115}+49 q^{114}+37 q^{113}+16 q^{112}-29 q^{111}-20 q^{110}-65 q^{109}-11 q^{108}+56 q^{107}+50 q^{106}+28 q^{105}-26 q^{104}-18 q^{103}-80 q^{102}-18 q^{101}+57 q^{100}+54 q^{99}+33 q^{98}-25 q^{97}-13 q^{96}-86 q^{95}-22 q^{94}+57 q^{93}+54 q^{92}+35 q^{91}-25 q^{90}-13 q^{89}-84 q^{88}-21 q^{87}+55 q^{86}+53 q^{85}+33 q^{84}-23 q^{83}-13 q^{82}-79 q^{81}-20 q^{80}+48 q^{79}+49 q^{78}+30 q^{77}-18 q^{76}-8 q^{75}-70 q^{74}-20 q^{73}+35 q^{72}+40 q^{71}+27 q^{70}-9 q^{69}+2 q^{68}-58 q^{67}-21 q^{66}+18 q^{65}+26 q^{64}+21 q^{63}+q^{62}+15 q^{61}-41 q^{60}-19 q^{59}+2 q^{58}+11 q^{57}+10 q^{56}+6 q^{55}+25 q^{54}-23 q^{53}-10 q^{52}-6 q^{51}-q^{50}-3 q^{49}+2 q^{48}+25 q^{47}-8 q^{46}+q^{45}-3 q^{44}-4 q^{43}-11 q^{42}-5 q^{41}+16 q^{40}-2 q^{39}+7 q^{38}+2 q^{37}+q^{36}-10 q^{35}-8 q^{34}+7 q^{33}-3 q^{32}+5 q^{31}+3 q^{30}+4 q^{29}-4 q^{28}-5 q^{27}+3 q^{26}-3 q^{25}+q^{24}+q^{23}+3 q^{22}-q^{21}-2 q^{20}+2 q^{19}-q^{18}+q^{15}-q^{13}+q^{12}</math>|J7=<math>-q^{210}+q^{209}+q^{206}-q^{203}-2 q^{202}+2 q^{201}-q^{199}+2 q^{198}+q^{196}-q^{195}-5 q^{194}+3 q^{193}+q^{192}-2 q^{191}+3 q^{190}+4 q^{188}-2 q^{187}-9 q^{186}+3 q^{185}+q^{184}-2 q^{183}+5 q^{182}+q^{181}+9 q^{180}-q^{179}-13 q^{178}-q^{177}-6 q^{176}-6 q^{175}+8 q^{174}+6 q^{173}+19 q^{172}+9 q^{171}-11 q^{170}-5 q^{169}-22 q^{168}-23 q^{167}+q^{166}+5 q^{165}+35 q^{164}+34 q^{163}+8 q^{162}+3 q^{161}-36 q^{160}-53 q^{159}-27 q^{158}-12 q^{157}+43 q^{156}+66 q^{155}+40 q^{154}+32 q^{153}-38 q^{152}-82 q^{151}-63 q^{150}-46 q^{149}+39 q^{148}+88 q^{147}+74 q^{146}+65 q^{145}-30 q^{144}-96 q^{143}-88 q^{142}-79 q^{141}+25 q^{140}+101 q^{139}+93 q^{138}+88 q^{137}-22 q^{136}-98 q^{135}-95 q^{134}-98 q^{133}+14 q^{132}+104 q^{131}+100 q^{130}+97 q^{129}-19 q^{128}-97 q^{127}-92 q^{126}-106 q^{125}+9 q^{124}+104 q^{123}+100 q^{122}+100 q^{121}-19 q^{120}-95 q^{119}-93 q^{118}-104 q^{117}+10 q^{116}+102 q^{115}+99 q^{114}+98 q^{113}-17 q^{112}-95 q^{111}-91 q^{110}-99 q^{109}+8 q^{108}+96 q^{107}+94 q^{106}+95 q^{105}-13 q^{104}-88 q^{103}-83 q^{102}-93 q^{101}+2 q^{100}+82 q^{99}+83 q^{98}+88 q^{97}-2 q^{96}-69 q^{95}-69 q^{94}-87 q^{93}-11 q^{92}+60 q^{91}+63 q^{90}+79 q^{89}+14 q^{88}-41 q^{87}-46 q^{86}-78 q^{85}-25 q^{84}+30 q^{83}+37 q^{82}+64 q^{81}+26 q^{80}-12 q^{79}-16 q^{78}-58 q^{77}-34 q^{76}+4 q^{75}+8 q^{74}+41 q^{73}+25 q^{72}+7 q^{71}+12 q^{70}-31 q^{69}-26 q^{68}-8 q^{67}-13 q^{66}+14 q^{65}+12 q^{64}+8 q^{63}+24 q^{62}-7 q^{61}-8 q^{60}-q^{59}-18 q^{58}-3 q^{57}-4 q^{56}-2 q^{55}+18 q^{54}+q^{53}+5 q^{52}+11 q^{51}-8 q^{50}-6 q^{49}-8 q^{48}-10 q^{47}+7 q^{46}-3 q^{45}+5 q^{44}+13 q^{43}+q^{42}+q^{41}-5 q^{40}-8 q^{39}+2 q^{38}-5 q^{37}-q^{36}+6 q^{35}+3 q^{34}+3 q^{33}-q^{32}-4 q^{31}+3 q^{30}-3 q^{29}-2 q^{28}+q^{27}+q^{26}+2 q^{25}-2 q^{23}+2 q^{22}-q^{20}+q^{17}-q^{15}+q^{14}</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[7, 3]]</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[10, 4, 11, 3], X[14, 8, 1, 7], X[8, 14, 9, 13], 
 
  X[12, 6, 13, 5], X[2, 10, 3, 9], X[4, 12, 5, 11]]</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[7, 3]]</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, -6, 2, -7, 5, -1, 3, -4, 6, -2, 7, -5, 4, -3]</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[7, 3]]</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, 12, 14, 2, 4, 8]</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[7, 3]]</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, 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, 8}</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[7, 3]]</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[7, 3]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:7_3_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[7, 3]]&) /@ {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, {3, 4}, 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[7, 3]][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    3            2
3 + -- - - - 3 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[7, 3]][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 + 5 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[7, 3]}</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[7, 3]], KnotSignature[Knot[7, 3]]}</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>{13, 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[7, 3]][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> 2    3      4      5      6      7    8    9
q  - q  + 2 q  - 2 q  + 3 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[7, 3]}</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[7, 3]][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> 6    10    14      16    18    20    22    24    26    28
q  + q   + q   + 2 q   + q   + q   - q   - q   - 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[7, 3]][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
-2   2     -4   z    3 z    3 z    z    z
-- + -- + a   - -- + ---- + ---- + -- + --
 8    6          8     6      4     6    4
a    a          a     a      a     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[7, 3]][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    3     3
-2   2     -4   2 z   z    3 z   z     6 z    4 z    3 z    z     z
-- - -- + a   - --- + -- + --- - --- + ---- + ---- - ---- + --- - -- - 
 8    6          11    9    7     10     8      6      4     11    9
a    a          a     a    a     a      a      a      a     a     a
 
     3      3    4       4      4    4    5      5    5    6    6
  4 z    2 z    z     3 z    3 z    z    z    2 z    z    z    z
  ---- - ---- + --- - ---- - ---- + -- + -- + ---- + -- + -- + --
    7      5     10     8      6     4    9     7     5    8    6
   a      a     a      a      a     a    a     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[7, 3]], Vassiliev[3][Knot[7, 3]]}</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>{5, 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[7, 3]][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    5    5      7  2    9  2    9  3    11  3      11  4    13  4
q  + q  + q  t + q  t  + q  t  + q  t  + q   t  + 2 q   t  + q   t  + 
 
     15  5    15  6    19  7
  2 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[7, 3], 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> 4    5      7      8      9      10      11      12      13      14
q  - q  + 3 q  - 2 q  - 2 q  + 5 q   - 2 q   - 4 q   + 7 q   - 2 q   - 
 
     15      16      17      18      19    20      21      22    24
  6 q   + 8 q   - 2 q   - 5 q   + 5 q   - q   - 3 q   + 2 q   - q   + 
 
   25
  q</nowiki></pre></td></tr>

</table>

See/edit the [[Rolfsen_Splice_Template]].

 [[Category:Knot Page]]