T(6,5) - Revision history

ScottKnotPageRobot at 15:37, 31 August 2005

2005-08-31T15:37:59Z

@@ Line 1: / Line 1: @@
-<!-- This page was  generated from the splice template "Torus_Knot_Splice_Template". Please do not edit! -->
+<!-- This page was generated from the splice template [[Torus_Knot_Splice_Base]]. Please do not edit!
 {{Torus Knot Page|
 m = 6 |

ScottKnotPageRobot at 16:15, 30 August 2005

2005-08-30T16:15:46Z

Show changes

ScottTestRobot at 00:45, 29 August 2005

2005-08-29T00:45:39Z

← Older revision		Revision as of 20:45, 28 August 2005
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	<!-- -->		<!-- -->
			<!-- This knot page was produced from [[Torus Knots Splice Template]] -->

	<!-- -->		<!-- -->
			<!-- -->

	<span id="top"></span>		<span id="top"></span>
			<!-- -->

	{{Knot Navigation Links\|ext=jpg}}		{{Knot Navigation Links\|ext=jpg}}

		⚫	{{Torus Knot Page Header\|m=6\|n=5\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-3,-6,-9,13,14,15,16,-20,-23,-2,-5,9,10,11,12,-16,-19,-22,-1,5,6,7,8,-12,-15,-18,-21,1,2,3,4,-8,-11,-14,-17,21,22,23,24,-4,-7,-10,-13,17,18,19,20,-24/goTop.html}}
	{\| align=left
	\|- valign=top
	\|[[Image:{{PAGENAME}}.jpg]]
⚫	\|{{Torus Knot ~~Site~~ ~~Links~~\|m=6\|n=5\|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-3,-6,-9,13,14,15,16,-20,-23,-2,-5,9,10,11,12,-16,-19,-22,-1,5,6,7,8,-12,-15,-18,-21,1,2,3,4,-8,-11,-14,-17,21,22,23,24,-4,-7,-10,-13,17,18,19,20,-24/goTop.html}}

	{{:{{PAGENAME}} Quick Notes}}
	\|}

	<br style="clear:both" />		<br style="clear:both" />
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	{{Vassiliev Invariants}}		{{Vassiliev Invariants}}

	~~===[[~~Khovanov Homology~~]]=~~==		{{Khovanov Homology\|table=<table border=1>

	The coefficients of the monomials <math>t^rq^j</math> are shown, along with their alternating sums <math>\chi</math> (fixed <math>j</math>, alternation over <math>r</math>). The squares with <font class=HLYellow>yellow</font> highlighting are those on the "critical diagonals", where <math>j-2r=s+1</math> or <math>j-2r=s+1</math>, where <math>s=</math>{{Data:{{PAGENAME}}/Signature}} is the signature of {{PAGENAME}}. Nonzero entries off the critical diagonals (if any exist) are highlighted in <font class=HLRed>red</font>.

	<center><table border=1>
	<tr align=center>		<tr align=center>
	<td width=11.1111%><table cellpadding=0 cellspacing=0>		<td width=11.1111%><table cellpadding=0 cellspacing=0>
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	<tr align=center><td>21</td><td bgcolor=red>1</td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>		<tr align=center><td>21</td><td bgcolor=red>1</td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
	<tr align=center><td>19</td><td bgcolor=red>1</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>		<tr align=center><td>19</td><td bgcolor=red>1</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
	</table>~~</center>~~		</table>}}

	{{Computer Talk Header}}		{{Computer Talk Header}}
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	2, 3, 4}]</nowiki></pre></td></tr>		2, 3, 4}]</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>alex = Alexander[TorusKnot[6, 5]][t]</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>alex = Alexander[TorusKnot[6, 5]][t]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -10 -9 -5 -3 3 5 9 10		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -10 -9 -5 -3
	1 + t - t + t - t - ~~t + t - t + t</nowiki></pre></td></tr>~~		1 + Alternating - Alternating + Alternating - Alternating -

			3 5 9 10
			Alternating + Alternating - Alternating + Alternating</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>Conway[TorusKnot[6, 5]][z]</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>Conway[TorusKnot[6, 5]][z]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6 8 10 12		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6 8 10 12
Line 111:		Line 104:
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 175}</nowiki></pre></td></tr>		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 175}</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>Kh[TorusKnot[6, 5]][q, t]</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>Kh[TorusKnot[6, 5]][q, t]</nowiki></pre></td></tr>
	<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 19 21 23 2 27 3 25 4 27 4 29 5 31 5		<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 19 21 2 23 4 25 3 27
	q + q + q ~~t +~~ q t + q ~~t +~~ q t + q ~~t +~~ q t +		q + q + Alternating q + Alternating q + Alternating q +

			4 27 6 27 5 29
			Alternating q + Alternating q + Alternating q +

			6 29 8 29 5 31
			Alternating q + Alternating q + Alternating q +

			7 31 8 31 7 33
			Alternating q + 2 Alternating q + Alternating q +

	27 6 29 6 31 7 33 7 29 8 31 8 33 9		9 33 10 33 9 35
	q ~~t +~~ q t + q ~~t +~~ q ~~t + q t~~ + 2 q ~~t +~~ q t +		Alternating q + Alternating q + 2 Alternating q +

	35 9 33 10 37 11 35 12 37 12 41 12		12 35 11 37 12 37
	2 q ~~t +~~ q t + 2 q ~~t +~~ q t + q ~~t +~~ q t +		Alternating q + 2 Alternating q + Alternating q +

	39 13 41 13		13 39 12 41 13 41
	q t + q t</nowiki></pre></td></tr>		Alternating q + Alternating q + Alternating q</nowiki></pre></td></tr>
	</table>		</table>

	{{Category:Knot Page}}		[[Category:Knot Page]]

ScottTestRobot at 23:43, 28 August 2005

2005-08-28T23:43:06Z

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-<!-- Script generated - do not edit! -->
+<!--  -->
 <!--  -->
@@ Line 10: / Line 10: @@
 |- valign=top
 |[[Image:{{PAGENAME}}.jpg]]
-|Visit [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-3,-6,-9,13,14,15,16,-20,-23,-2,-5,9,10,11,12,-16,-19,-22,-1,5,6,7,8,-12,-15,-18,-21,1,2,3,4,-8,-11,-14,-17,21,22,23,24,-4,-7,-10,-13,17,18,19,20,-24/goTop.html {{PAGENAME}}'s page] at [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/html/start.html Knotilus]!
+|{{Torus Knot Site Links|m=6|n=5|KnotilusURL=http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-3,-6,-9,13,14,15,16,-20,-23,-2,-5,9,10,11,12,-16,-19,-22,-1,5,6,7,8,-12,-15,-18,-21,1,2,3,4,-8,-11,-14,-17,21,22,23,24,-4,-7,-10,-13,17,18,19,20,-24/goTop.html}}
 {{:{{PAGENAME}} Quick Notes}}
@@ Line 22: / Line 20: @@
 {{Knot Presentations}}
 {{Polynomial Invariants}}
 {{Vassiliev Invariants}}
@@ Line 139: / Line 123: @@
   q   t   + q   t</nowiki></pre></td></tr>
 </table>

ScottTestRobot at 01:24, 28 August 2005

2005-08-28T01:24:57Z

Show changes

DrorsRobot at 02:46, 27 August 2005

2005-08-27T02:46:39Z

Show changes

DrorsRobot at 02:19, 27 August 2005

2005-08-27T02:19:14Z

New page

{{Knot Navigation Links|prev=T(23,2).jpg|next=T(25,2).jpg}}

Visit [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-3,-6,-9,13,14,15,16,-20,-23,-2,-5,9,10,11,12,-16,-19,-22,-1,5,6,7,8,-12,-15,-18,-21,1,2,3,4,-8,-11,-14,-17,21,22,23,24,-4,-7,-10,-13,17,18,19,20,-24/goTop.html T(6,5)'s page] at [http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/html/start.html Knotilus]!

Visit [http://www.math.toronto.edu/~drorbn/KAtlas/TorusKnots/6.5.html T(6,5)'s page] at the original [http://www.math.toronto.edu/~drorbn/KAtlas/index.html Knot Atlas]!

===Knot presentations===

{|
|'''[[Planar Diagrams|Planar diagram presentation]]'''
|style="padding-left: 1em;" | X19,29,20,28 X10,30,11,29 X1,31,2,30 X40,32,41,31 X11,21,12,20 X2,22,3,21 X41,23,42,22 X32,24,33,23 X3,13,4,12 X42,14,43,13 X33,15,34,14 X24,16,25,15 X43,5,44,4 X34,6,35,5 X25,7,26,6 X16,8,17,7 X35,45,36,44 X26,46,27,45 X17,47,18,46 X8,48,9,47 X27,37,28,36 X18,38,19,37 X9,39,10,38 X48,40,1,39
|-
|'''[[Gauss Codes|Gauss code]]'''
|style="padding-left: 1em;" | {-3, -6, -9, 13, 14, 15, 16, -20, -23, -2, -5, 9, 10, 11, 12, -16, -19, -22, -1, 5, 6, 7, 8, -12, -15, -18, -21, 1, 2, 3, 4, -8, -11, -14, -17, 21, 22, 23, 24, -4, -7, -10, -13, 17, 18, 19, 20, -24}
|-
|'''[[DT (Dowker-Thistlethwaite) Codes|Dowker-Thistlethwaite code]]'''
|style="padding-left: 1em;" | 30 12 -34 -16 38 20 -42 -24 46 28 -2 -32 6 36 -10 -40 14 44 -18 -48 22 4 -26 -8
|}

===Polynomial invariants===

{{Polynomial Invariants|name=T(6,5)}}

===[[Finite Type (Vassiliev) Invariants|Vassiliev invariants]]===
{| style="margin-left: 1em;"
|-
|'''V2 and V3'''
|style="padding-left: 1em;" | {0, 175})
|}

[[Khovanov Homology]]. The coefficients of the monomials <math>t^rq^j</math> are shown, along with their alternating sums <math>\chi</math> (fixed <math>j</math>, alternation over <math>r</math>). The squares with yellow highlighting are those on the "critical diagonals", where <math>j-2r=s+1</math> or <math>j-2r=s+1</math>, where <math>s=</math>16 is the signature of T(6,5). Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

<center><table border=1>
<tr align=center>
<td width=11.1111%><table cellpadding=0 cellspacing=0>
<tr><td>\</td><td> </td><td>r</td></tr>
<tr><td> </td><td> \ </td><td> </td></tr>
<tr><td>j</td><td> </td><td>\</td></tr>
</table></td>
<td width=5.55556%>0</td ><td width=5.55556%>1</td ><td width=5.55556%>2</td ><td width=5.55556%>3</td ><td width=5.55556%>4</td ><td width=5.55556%>5</td ><td width=5.55556%>6</td ><td width=5.55556%>7</td ><td width=5.55556%>8</td ><td width=5.55556%>9</td ><td width=5.55556%>10</td ><td width=5.55556%>11</td ><td width=5.55556%>12</td ><td width=5.55556%>13</td ><td width=11.1111%>χ</td></tr>
<tr align=center><td>41</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow>1</td><td>0</td></tr>
<tr align=center><td>39</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td bgcolor=red>1</td><td>-1</td></tr>
<tr align=center><td>37</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow>2</td><td bgcolor=red>1</td><td> </td><td>-1</td></tr>
<tr align=center><td>35</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>2</td><td bgcolor=yellow> </td><td> </td><td bgcolor=red>1</td><td> </td><td>-1</td></tr>
<tr align=center><td>33</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>1</td><td bgcolor=yellow> </td><td bgcolor=yellow>1</td><td bgcolor=red>1</td><td> </td><td> </td><td> </td><td>-1</td></tr>
<tr align=center><td>31</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>1</td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>0</td></tr>
<tr align=center><td>29</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=red>1</td><td bgcolor=yellow>1</td><td bgcolor=yellow> </td><td bgcolor=red>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>27</td><td> </td><td> </td><td> </td><td bgcolor=red>1</td><td bgcolor=red>1</td><td bgcolor=yellow> </td><td bgcolor=yellow>1</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>25</td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>23</td><td> </td><td> </td><td bgcolor=red>1</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>21</td><td bgcolor=red>1</td><td> </td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>19</td><td bgcolor=red>1</td><td bgcolor=yellow> </td><td bgcolor=yellow> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
</table></center>

{{Computer Talk Header}}

<table>
<tr valign=top>
<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=    </pre></td>
<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td>
</tr>
<tr valign=top><td colspan=2><pre style="border: 0px; padding: 0em">Loading KnotTheory` (version of August 19, 2005, 13:11:25)...</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>Crossings[TorusKnot[6, 5]]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[2]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>24</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>PD[TorusKnot[6, 5]]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[3]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>PD[X[19, 29, 20, 28], X[10, 30, 11, 29], X[1, 31, 2, 30],

X[40, 32, 41, 31], X[11, 21, 12, 20], X[2, 22, 3, 21],

X[41, 23, 42, 22], X[32, 24, 33, 23], X[3, 13, 4, 12],

X[42, 14, 43, 13], X[33, 15, 34, 14], X[24, 16, 25, 15],

X[43, 5, 44, 4], X[34, 6, 35, 5], X[25, 7, 26, 6], X[16, 8, 17, 7],

X[35, 45, 36, 44], X[26, 46, 27, 45], X[17, 47, 18, 46],

X[8, 48, 9, 47], X[27, 37, 28, 36], X[18, 38, 19, 37],

X[9, 39, 10, 38], X[48, 40, 1, 39]]</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>GaussCode[TorusKnot[6, 5]]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[4]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>GaussCode[-3, -6, -9, 13, 14, 15, 16, -20, -23, -2, -5, 9, 10, 11, 12,

-16, -19, -22, -1, 5, 6, 7, 8, -12, -15, -18, -21, 1, 2, 3, 4, -8,

-11, -14, -17, 21, 22, 23, 24, -4, -7, -10, -13, 17, 18, 19, 20, -24]</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[TorusKnot[6, 5]]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[5]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>BR[5, {1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1,

2, 3, 4}]</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>alex = Alexander[TorusKnot[6, 5]][t]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[6]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> -10 -9 -5 -3 3 5 9 10
1 + t - t + t - t - t + t - t + t</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>Conway[TorusKnot[6, 5]][z]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 2 4 6 8 10 12
1 + 35 z + 329 z + 1288 z + 2518 z + 2718 z + 1729 z +

14 16 18 20
665 z + 152 z + 19 z + z</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>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[8]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{}</nowiki></pre></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>{KnotDet[TorusKnot[6, 5]], KnotSignature[TorusKnot[6, 5]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{5, 16}</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>J=Jones[TorusKnot[6, 5]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[10]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 10 12 14 17 19
q + q + q - q - q</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>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[11]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{}</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>A2Invariant[TorusKnot[6, 5]][q]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[12]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>NotAvailable</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>Kauffman[TorusKnot[6, 5]][a, z]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[13]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>NotAvailable</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>{Vassiliev[2][TorusKnot[6, 5]], Vassiliev[3][TorusKnot[6, 5]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[14]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{0, 175}</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>Kh[TorusKnot[6, 5]][q, t]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[15]=   </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 19 21 23 2 27 3 25 4 27 4 29 5 31 5
q + q + q t + q t + q t + q t + q t + q t +

27 6 29 6 31 7 33 7 29 8 31 8 33 9
q t + q t + q t + q t + q t + 2 q t + q t +

35 9 33 10 37 11 35 12 37 12 41 12
2 q t + q t + 2 q t + q t + q t + q t +

39 13 41 13
q t + q t</nowiki></pre></td></tr>
</table>