DrorsRobot at 07:44, 3 September 2005

2005-09-03T07:44:55Z

← Older revision		Revision as of 03:44, 3 September 2005
Line 16:		Line 16:
	k = 491 \|		k = 491 \|
	KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:5,-4,6,-7:10,-1,4,-5,11,-2,3,-9,8,-6,7,-3,9,-8/goTop.html \|		KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:5,-4,6,-7:10,-1,4,-5,11,-2,3,-9,8,-6,7,-3,9,-8/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:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>		<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr>
	<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]]</td></tr>		<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]]</td></tr>
Line 52:		Line 52:
	<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, 491]]</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, 491]]</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 23:13, 2 September 2005

2005-09-02T23:13:48Z

Show changes

ScottTestRobot at 23:07, 1 September 2005

2005-09-01T23:07:16Z

Show changes

DrorsRobot at 17:10, 31 August 2005

2005-08-31T17:10:50Z

Show changes

ScottKnotPageRobot at 17:34, 30 August 2005

2005-08-30T17:34:41Z

New page

{{Link Page|
n = 11 |
t = a |
k = 491 |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-10,2,-11:5,-4,6,-7:10,-1,4,-5,11,-2,3,-9,8,-6,7,-3,9,-8/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%>-9</td ><td width=6.25%>-8</td ><td width=6.25%>-7</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=12.5%>χ</td></tr>
<tr align=center><td>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 bgcolor=yellow>1</td><td>1</td></tr>
<tr align=center><td>-1</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> </td><td>-1</td></tr>
<tr align=center><td>-3</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>-5</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>7</td><td bgcolor=yellow>3</td><td> </td><td> </td><td>-4</td></tr>
<tr align=center><td>-7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>9</td><td bgcolor=yellow>3</td><td> </td><td> </td><td> </td><td>6</td></tr>
<tr align=center><td>-9</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>8</td><td bgcolor=yellow>7</td><td> </td><td> </td><td> </td><td> </td><td>-1</td></tr>
<tr align=center><td>-11</td><td> </td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>11</td><td bgcolor=yellow>9</td><td> </td><td> </td><td> </td><td> </td><td> </td><td>2</td></tr>
<tr align=center><td>-13</td><td> </td><td> </td><td> </td><td> </td><td bgcolor=yellow>7</td><td bgcolor=yellow>10</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>3</td></tr>
<tr align=center><td>-15</td><td> </td><td> </td><td> </td><td bgcolor=yellow>6</td><td bgcolor=yellow>9</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-3</td></tr>
<tr align=center><td>-17</td><td> </td><td> </td><td bgcolor=yellow>2</td><td bgcolor=yellow>7</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>5</td></tr>
<tr align=center><td>-19</td><td> </td><td bgcolor=yellow>1</td><td bgcolor=yellow>6</td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td> </td><td>-5</td></tr>
<tr align=center><td>-21</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>-23</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, 491]]</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, 491]]]</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>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>PD[Link[11, Alternating, 491]]</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[6, 1, 7, 2], X[10, 3, 11, 4], X[16, 11, 17, 12], X[20, 8, 21, 7],

X[8, 20, 9, 19], X[14, 21, 15, 22], X[22, 15, 19, 16],

X[18, 13, 5, 14], X[12, 17, 13, 18], X[2, 5, 3, 6], X[4, 9, 1, 10]]</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, 491]]</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, -10, 2, -11}, {5, -4, 6, -7},

{10, -1, 4, -5, 11, -2, 3, -9, 8, -6, 7, -3, 9, -8}]</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, 491]]</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, 491]]</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, 491]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L11a491_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, 491]][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, 491]][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, 491]], KnotSignature[Link[11, Alternating, 491]]}</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, -4}</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, 491]][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> -11 3 8 13 16 19 17 16 10 6 2
1 - q + --- - -- + -- - -- + -- - -- + -- - -- + -- - -
10 9 8 7 6 5 4 3 2 q
q q 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[13]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>A2Invariant[Link[11, Alternating, 491]][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> -34 -32 5 8 3 9 4 2 5 2 3
1 - q - q - --- + --- + --- + --- + --- + --- + --- - -- + -- +
28 20 18 16 14 12 10 8 6
q q q q q q q q q

-4
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, 491]][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> 4 6 8 10
2 4 6 8 10 2 a 5 a 4 a a
2 a + 2 a - 10 a + 8 a - 2 a + ---- - ---- + ---- - --- +
2 2 2 2
z z z z

2 2 6 2 8 2 10 2 2 4 4 4 6 4
3 a z - 10 a z + 8 a z - a z + a z - 2 a z - 7 a z +

8 4 4 6 6 6
3 a z - a z - 2 a z</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, 491]][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> 4 6 8 10
2 4 6 8 10 2 a 5 a 4 a a
-2 a + 6 a + 22 a + 21 a + 6 a - ---- - ---- - ---- - --- +
2 2 2 2
z z z z

5 7 9 11
5 a 9 a 5 a a 3 5 7 9
---- + ---- + ---- + --- + a z - 15 a z - 35 a z - 25 a z -
z z z z

11 13 2 2 4 2 6 2 8 2
5 a z + a z + 5 a z - 6 a z - 44 a z - 45 a z -

10 2 12 2 3 3 5 3 7 3 9 3
11 a z + a z + 2 a z + 14 a z + 43 a z + 41 a z +

11 3 13 3 2 4 4 4 6 4 8 4
8 a z - 2 a z - 4 a z + 4 a z + 49 a z + 55 a z +

10 4 12 4 3 5 5 5 7 5 9 5
10 a z - 4 a z - 5 a z - 5 a z - 18 a z - 29 a z -

11 5 13 5 2 6 4 6 6 6 8 6
10 a z + a z + a z - 6 a z - 32 a z - 39 a z -

10 6 12 6 3 7 5 7 7 7 9 7
11 a z + 3 a z + 2 a z - 3 a z - 6 a z + 5 a z +

11 7 4 8 6 8 8 8 10 8 5 9
6 a z + 3 a z + 9 a z + 13 a z + 7 a z + 3 a z +

7 9 9 9 6 10 8 10
7 a z + 4 a z + a z + 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, 491]], Vassiliev[3][Link[11, Alternating, 491]]}</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> 19
{0, -(--)}
3</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, 491]][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>3 5 1 2 1 6 2 7
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ +
5 3 23 9 21 8 19 8 19 7 17 7 17 6
q q q t q t q t q t q t q t

6 9 7 10 11 9 8 7
------ + ------ + ------ + ------ + ------ + ------ + ----- + ----- +
15 6 15 5 13 5 13 4 11 4 11 3 9 3 9 2
q t q t q t q t q t q t q t q t

9 3 7 t t 2
----- + ---- + ---- + -- + - + q t
7 2 7 5 3 q
q t q t q t q</nowiki></pre></td></tr>
</table> }}

L11a491 - Revision history

DrorsRobot at 07:44, 3 September 2005

DrorsRobot at 23:13, 2 September 2005

ScottTestRobot at 23:07, 1 September 2005

DrorsRobot at 17:10, 31 August 2005

ScottKnotPageRobot at 17:34, 30 August 2005