DrorsRobot at 07:16, 3 September 2005

2005-09-03T07:16:35Z

← Older revision		Revision as of 03:16, 3 September 2005
Line 16:		Line 16:
	k = 329 \|		k = 329 \|
	KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,3,-11,4,-10,5,-8:10,-1,2,-3,6,-9,7,-5,8,-6,11,-4,9,-7/goTop.html \|		KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,3,-11,4,-10,5,-8:10,-1,2,-3,6,-9,7,-5,8,-6,11,-4,9,-7/goTop.html \|
	braid_table = <table cellspacing=0 cellpadding=0 border=0>		braid_table = <table cellspacing=0 cellpadding=0 border=0 style="white-space: pre">
	<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]]</td></tr>		<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]]</td></tr>
	<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]]</td></tr>		<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]]</td></tr>
Line 49:		Line 49:
	<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td>		<td align=left><pre style="color: red; border: 0px; padding: 0em"><< KnotTheory`</pre></td>
	</tr>		</tr>
	<tr valign=top><td colspan=2>Loading KnotTheory` (version of September 2, 2005, 15:8:39)...</td></tr>		<tr valign=top><td colspan=2>Loading KnotTheory` (version of September 3, 2005, 2:11:43)...</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[Link[11, Alternating, 329]]</nowiki></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[Link[11, Alternating, 329]]</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>11</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>11</nowiki></pre></td></tr>

DrorsRobot at 22:45, 2 September 2005

2005-09-02T22:45:11Z

Show changes

ScottTestRobot at 22:37, 1 September 2005

2005-09-01T22:37:35Z

Show changes

DrorsRobot at 16:49, 31 August 2005

2005-08-31T16:49:25Z

Show changes

ScottKnotPageRobot at 17:17, 30 August 2005

2005-08-30T17:17:12Z

New page

{{Link Page|
n = 11 |
t = a |
k = 329 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-2,3,-11,4,-10,5,-8:10,-1,2,-3,6,-9,7,-5,8,-6,11,-4,9,-7/goTop.html |
khovanov_table = <table border=1>
<tr align=center>
<td width=12.5%><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=6.25%>-6</td ><td width=6.25%>-5</td ><td width=6.25%>-4</td ><td width=6.25%>-3</td ><td width=6.25%>-2</td ><td width=6.25%>-1</td ><td width=6.25%>0</td ><td width=6.25%>1</td ><td width=6.25%>2</td ><td width=6.25%>3</td ><td width=6.25%>4</td ><td width=6.25%>5</td ><td width=12.5%>χ</td></tr>
<tr align=center><td>10</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>-1</td></tr>
<tr align=center><td>8</td><td> </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>2</td></tr>
<tr align=center><td>6</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>5</td><td bgcolor=yellow>1</td><td> </td><td>-4</td></tr>
<tr align=center><td>4</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>6</td><td bgcolor=yellow>2</td><td> </td><td> </td><td>4</td></tr>
<tr align=center><td>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>8</td><td bgcolor=yellow>5</td><td> </td><td> </td><td> </td><td>-3</td></tr>
<tr align=center><td>0</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>10</td><td bgcolor=yellow>6</td><td> </td><td> </td><td> </td><td> </td><td>4</td></tr>
<tr align=center><td>-2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>8</td><td bgcolor=yellow>9</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>1</td></tr>
<tr align=center><td>-4</td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>7</td><td bgcolor=yellow>9</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-2</td></tr>
<tr align=center><td>-6</td><td> </td><td> </td><td> </td><td bgcolor=yellow>4</td><td bgcolor=yellow>8</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>4</td></tr>
<tr align=center><td>-8</td><td> </td><td> </td><td bgcolor=yellow>3</td><td bgcolor=yellow>7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-4</td></tr>
<tr align=center><td>-10</td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow>5</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>4</td></tr>
<tr align=center><td>-12</td><td bgcolor=yellow> </td><td bgcolor=yellow>2</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-2</td></tr>
<tr align=center><td>-14</td><td bgcolor=yellow>1</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> |
computer_talk =
<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>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</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[Link[11, Alternating, 329]]</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>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>Length[Skeleton[Link[11, Alternating, 329]]]</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>2</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>PD[Link[11, Alternating, 329]]</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>PD[X[10, 1, 11, 2], X[2, 11, 3, 12], X[12, 3, 13, 4], X[20, 5, 21, 6],

X[16, 8, 17, 7], X[18, 14, 19, 13], X[22, 16, 9, 15],

X[8, 18, 1, 17], X[14, 22, 15, 21], X[6, 9, 7, 10], X[4, 19, 5, 20]]</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>GaussCode[Link[11, Alternating, 329]]</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>GaussCode[{1, -2, 3, -11, 4, -10, 5, -8},

{10, -1, 2, -3, 6, -9, 7, -5, 8, -6, 11, -4, 9, -7}]</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>BR[Link[11, Alternating, 329]]</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>BR[Link[11, Alternating, 329]]</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>Show[DrawMorseLink[Link[11, Alternating, 329]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11a329_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[7]=</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[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[Link[11, Alternating, 329]][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>ComplexInfinity</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>Conway[Link[11, Alternating, 329]][z]</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>ComplexInfinity</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>Select[AllKnots[], (alex === Alexander[#][t])&]</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>{}</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>{KnotDet[Link[11, Alternating, 329]], KnotSignature[Link[11, Alternating, 329]]}</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>{Infinity, -1}</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>J=Jones[Link[11, Alternating, 329]][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> -(13/2) 3 7 11 15 17 18
-q + ----- - ---- + ---- - ---- + ---- - ------- + 14 Sqrt[q] -
11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q

3/2 5/2 7/2 9/2
11 q + 7 q - 3 q + q</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>A2Invariant[Link[11, Alternating, 329]][q]</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> -18 -16 3 -12 2 2 2 5 2 4 6
5 + q - q + --- - q + --- + -- - -- + -- - -- - q + q -
14 10 8 6 4 2
q q q q q q

8 10 12
3 q + q - q</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>HOMFLYPT[Link[11, Alternating, 329]][a, z]</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> 3 3
1 3 a 2 a 7 z 3 9 z 3 3 3
--- - --- + ---- + --- - 16 a z + 7 a z + ---- - 25 a z + 9 a z +
a z z z a a

5 7
5 z 5 3 5 z 7 3 7 9
---- - 19 a z + 5 a z + -- - 7 a z + a z - a z
a a</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>Kauffman[Link[11, Alternating, 329]][a, z]</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> 3
-2 2 1 3 a 2 a 8 z 3 5
-3 - a - 3 a + --- + --- + ---- - --- - 17 a z - 6 a z + 2 a z -
a z z z a

2 2 3
7 2 2 z 7 z 2 2 4 2 6 2 4 z
a z + 18 z - ---- + ---- + 14 a z + 4 a z - a z - ---- +
4 2 3
a a a

3 4
18 z 3 3 3 5 3 7 3 4 3 z
----- + 34 a z + 7 a z - 3 a z + 2 a z - 29 z + ---- -
a 4
a

4 5 5
12 z 2 4 4 4 6 4 8 z 18 z 5
----- - 28 a z - 9 a z + 5 a z + ---- - ----- - 45 a z -
2 3 a
a a

6 6
3 5 5 5 7 5 6 z 14 z 2 6
10 a z + 8 a z - a z + 20 z - -- + ----- + 19 a z +
4 2
a a

7 7
4 6 6 6 3 z 14 z 7 3 7 5 7
11 a z - 3 a z - ---- + ----- + 31 a z + 9 a z - 5 a z -
3 a
a

8 9
8 5 z 2 8 4 8 5 z 9 3 9 10
3 z - ---- - 4 a z - 6 a z - ---- - 10 a z - 5 a z - 2 z -
2 a
a

2 10
2 a z</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>{Vassiliev[2][Link[11, Alternating, 329]], Vassiliev[3][Link[11, Alternating, 329]]}</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[16]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 101
{0, -(---)}
24</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>Kh[Link[11, Alternating, 329]][q, t]</nowiki></pre></td></tr>
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[17]=  </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 9 1 2 1 5 3 7 4
10 + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- +
2 14 6 12 5 10 5 10 4 8 4 8 3 6 3
q q t q t q t q t q t q t q t

8 7 9 8 2 2 2 4 2
----- + ----- + ---- + ---- + 6 t + 8 q t + 5 q t + 6 q t +
6 2 4 2 4 2
q t q t q t q t

4 3 6 3 6 4 8 4 10 5
2 q t + 5 q t + q t + 2 q t + q t</nowiki></pre></td></tr>
</table> }}

L11a329 - Revision history

DrorsRobot at 07:16, 3 September 2005

DrorsRobot at 22:45, 2 September 2005

ScottTestRobot at 22:37, 1 September 2005

DrorsRobot at 16:49, 31 August 2005

ScottKnotPageRobot at 17:17, 30 August 2005