K11a282: Difference between revisions
No edit summary |
DrorsRobot (talk | contribs) No edit summary |
||
Line 1: | Line 1: | ||
<!-- WARNING! WARNING! WARNING! |
<!-- WARNING! WARNING! WARNING! |
||
<!-- This page was generated from the splice |
<!-- This page was generated from the splice template [[Hoste-Thistlethwaite_Splice_Base]]. Please do not edit! |
||
<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].) |
<!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].) |
||
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Hoste-Thistlethwaite_Splice_Base]]. --> |
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Hoste-Thistlethwaite_Splice_Base]]. --> |
||
<!-- --> |
<!-- <math>\text{Null}</math> --> |
||
<!-- --> |
<!-- <math>\text{Null}</math> --> |
||
<!-- WARNING! WARNING! WARNING! |
<!-- WARNING! WARNING! WARNING! |
||
<!-- This page was generated from the splice template [[Hoste-Thistlethwaite Splice Template]]. Please do not edit! |
<!-- This page was generated from the splice template [[Hoste-Thistlethwaite Splice Template]]. Please do not edit! |
||
Line 10: | Line 10: | ||
<!-- The text below simply calls [[Template:Hoste-Thistlethwaite Knot Page]] setting the values of all the parameters appropriately. |
<!-- The text below simply calls [[Template:Hoste-Thistlethwaite Knot Page]] setting the values of all the parameters appropriately. |
||
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Hoste-Thistlethwaite Splice Template]]. --> |
<!-- This page itself was created by running [[Media:KnotPageSpliceRobot.nb]] on [[Hoste-Thistlethwaite Splice Template]]. --> |
||
<!-- --> |
<!-- <math>\text{Null}</math> --> |
||
{{Hoste-Thistlethwaite Knot Page| |
{{Hoste-Thistlethwaite Knot Page| |
||
n = 11 | |
n = 11 | |
||
t = |
t = a | |
||
k = 282 | |
k = 282 | |
||
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-9,2,-5,3,-1,4,-11,5,-2,6,-10,7,-4,8,-3,9,-6,10,-7,11,-8/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-9,2,-5,3,-1,4,-11,5,-2,6,-10,7,-4,8,-3,9,-6,10,-7,11,-8/goTop.html | |
||
braid_table = <table cellspacing=0 cellpadding=0 border=0> |
|||
<tr><td>[[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart1.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart0.gif]]</td></tr> |
|||
<tr><td>[[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart2.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]][[Image:BraidPart3.gif]][[Image:BraidPart0.gif]]</td></tr> |
|||
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart0.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]][[Image:BraidPart4.gif]][[Image:BraidPart1.gif]]</td></tr> |
|||
<tr><td>[[Image:BraidPart0.gif]][[Image:BraidPart0.gif]][[Image:BraidPart2.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> | |
|||
same_alexander = [[K11a81]], | |
same_alexander = [[K11a81]], | |
||
same_jones = [[K11a81]], | |
same_jones = [[K11a81]], | |
||
Line 40: | Line 46: | ||
<tr align=center><td>-15</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> |
<tr align=center><td>-15</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> | |
</table> | |
||
coloured_jones_2 = | |
coloured_jones_2 = <math>\textrm{NotAvailable}(q)</math> | |
||
coloured_jones_3 = | |
coloured_jones_3 = <math>\textrm{NotAvailable}(q)</math> | |
||
coloured_jones_4 = | |
coloured_jones_4 = <math>\textrm{NotAvailable}(q)</math> | |
||
coloured_jones_5 = | |
coloured_jones_5 = <math>\textrm{NotAvailable}(q)</math> | |
||
coloured_jones_6 = | |
coloured_jones_6 = <math>\textrm{NotAvailable}(q)</math> | |
||
coloured_jones_7 = | |
coloured_jones_7 = <math>\textrm{NotAvailable}(q)</math> | |
||
computer_talk = |
computer_talk = |
||
<table> |
<table> |
||
Line 52: | Line 58: | ||
<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 |
<tr valign=top><td colspan=2>Loading KnotTheory` (version of September 2, 2005, 15:8:39)...</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[Knot[11, Alternating, 282]]</nowiki></pre></td></tr> |
|||
</table> |
|||
<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> |
|||
<table><tr align=left> |
|||
< |
<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[Knot[11, Alternating, 282]]</nowiki></pre></td></tr> |
||
<td>< |
<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[6, 2, 7, 1], X[10, 4, 11, 3], X[16, 5, 17, 6], X[14, 8, 15, 7], |
||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[2]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>11</nowiki></code></td></tr> |
|||
</table> |
|||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[Knot[11, Alternating, 282]]</nowiki></code></td></tr> |
|||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[X[6, 2, 7, 1], X[10, 4, 11, 3], X[16, 5, 17, 6], X[14, 8, 15, 7], |
|||
X[4, 10, 5, 9], X[18, 11, 19, 12], X[20, 13, 21, 14], |
X[4, 10, 5, 9], X[18, 11, 19, 12], X[20, 13, 21, 14], |
||
X[22, 16, 1, 15], X[2, 17, 3, 18], X[12, 19, 13, 20], X[8, 21, 9, 22]]</nowiki></ |
X[22, 16, 1, 15], X[2, 17, 3, 18], X[12, 19, 13, 20], X[8, 21, 9, 22]]</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[Knot[11, Alternating, 282]]</nowiki></pre></td></tr> |
|||
</table> |
|||
<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[1, -9, 2, -5, 3, -1, 4, -11, 5, -2, 6, -10, 7, -4, 8, -3, 9, |
|||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[Knot[11, Alternating, 282]]</nowiki></code></td></tr> |
|||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>GaussCode[1, -9, 2, -5, 3, -1, 4, -11, 5, -2, 6, -10, 7, -4, 8, -3, 9, |
|||
-6, 10, -7, 11, -8]</nowiki></ |
-6, 10, -7, 11, -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[Knot[11, Alternating, 282]]</nowiki></pre></td></tr> |
|||
</table> |
|||
<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[4, {1, -2, 3, -2, 1, -2, -2, -2, 3, -2, 3}]</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<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>Show[DrawMorseLink[Knot[11, Alternating, 282]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:K11a282_ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[6]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td> |
|||
<td>< |
<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>alex = Alexander[Knot[11, Alternating, 282]][t]</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> -4 6 16 26 2 3 4 |
|||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BR[Knot[11, Alternating, 282]]</nowiki></code></td></tr> |
|||
</table> |
|||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Show[DrawMorseLink[Knot[11, Alternating, 282]]]</nowiki></code></td></tr> |
|||
<tr align=left><td></td><td>[[Image:K11a282_ML.gif]]</td></tr><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[6]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>-Graphics-</nowiki></code></td></tr> |
|||
</table> |
|||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>alex = Alexander[Knot[11, Alternating, 282]][t]</nowiki></code></td></tr> |
|||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[7]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -4 6 16 26 2 3 4 |
|||
-29 - t + -- - -- + -- + 26 t - 16 t + 6 t - t |
-29 - t + -- - -- + -- + 26 t - 16 t + 6 t - t |
||
3 2 t |
3 2 t |
||
t t</nowiki></ |
t t</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>Conway[Knot[11, Alternating, 282]][z]</nowiki></pre></td></tr> |
|||
</table> |
|||
<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> 6 8 |
|||
<table><tr align=left> |
|||
1 - 2 z - z</nowiki></pre></td></tr> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td> |
|||
<td>< |
<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>Select[AllKnots[], (alex === Alexander[#][t])&]</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>{Knot[11, Alternating, 81], Knot[11, Alternating, 282]}</nowiki></pre></td></tr> |
|||
<tr align=left> |
|||
< |
<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>{KnotDet[Knot[11, Alternating, 282]], KnotSignature[Knot[11, Alternating, 282]]}</nowiki></pre></td></tr> |
||
<td>< |
<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>{127, -2}</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>J=Jones[Knot[11, Alternating, 282]][q]</nowiki></pre></td></tr> |
|||
1 - 2 z - z</nowiki></code></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> -7 4 8 13 18 20 20 2 3 4 |
|||
</table> |
|||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (alex === Alexander[#][t])&]</nowiki></code></td></tr> |
|||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[11, Alternating, 81], Knot[11, Alternating, 282]}</nowiki></code></td></tr> |
|||
</table> |
|||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{KnotDet[Knot[11, Alternating, 282]], KnotSignature[Knot[11, Alternating, 282]]}</nowiki></code></td></tr> |
|||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{127, -2}</nowiki></code></td></tr> |
|||
</table> |
|||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>J=Jones[Knot[11, Alternating, 282]][q]</nowiki></code></td></tr> |
|||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -7 4 8 13 18 20 20 2 3 4 |
|||
-17 + q - -- + -- - -- + -- - -- + -- + 13 q - 8 q + 4 q - q |
-17 + q - -- + -- - -- + -- - -- + -- + 13 q - 8 q + 4 q - q |
||
6 5 4 3 2 q |
6 5 4 3 2 q |
||
q q q q q</nowiki></ |
q q q q q</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[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></pre></td></tr> |
|||
</table> |
|||
<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>{Knot[11, Alternating, 81], Knot[11, Alternating, 282]}</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]</nowiki></code></td></tr> |
|||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[11, Alternating, 81], Knot[11, Alternating, 282]}</nowiki></code></td></tr> |
|||
</table> |
|||
<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[Knot[11, Alternating, 282]][q]</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
< |
<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> -20 2 2 2 -12 3 3 5 2 -2 2 |
||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>A2Invariant[Knot[11, Alternating, 282]][q]</nowiki></code></td></tr> |
|||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[13]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -20 2 2 2 -12 3 3 5 2 -2 2 |
|||
1 + q - --- + --- - --- - q + --- - -- + -- - -- + q - 3 q + |
1 + q - --- + --- - --- - q + --- - -- + -- - -- + q - 3 q + |
||
18 16 14 10 8 6 4 |
18 16 14 10 8 6 4 |
||
Line 156: | Line 101: | ||
4 6 8 10 12 |
4 6 8 10 12 |
||
3 q - q + q + q - q</nowiki></ |
3 q - q + 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>Kauffman[Knot[11, Alternating, 282]][a, z]</nowiki></pre></td></tr> |
|||
</table> |
|||
<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> 2 3 3 |
|||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[14]:=</code></td> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Knot[11, Alternating, 282]][a, z]</nowiki></code></td></tr> |
|||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[14]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 3 3 |
|||
2 5 z 2 2 4 2 6 2 2 z 5 z 3 |
2 5 z 2 2 4 2 6 2 2 z 5 z 3 |
||
1 - 14 z - ---- - 12 a z - 2 a z + a z + ---- - ---- - 9 a z + |
1 - 14 z - ---- - 12 a z - 2 a z + a z + ---- - ---- - 9 a z + |
||
Line 196: | Line 136: | ||
4 8 6 z 9 3 9 10 2 10 |
4 8 6 z 9 3 9 10 2 10 |
||
12 a z + ---- + 15 a z + 9 a z + 3 z + 3 a z |
12 a z + ---- + 15 a z + 9 a z + 3 z + 3 a z |
||
a</nowiki></ |
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>{Vassiliev[2][Knot[11, Alternating, 282]], Vassiliev[3][Knot[11, Alternating, 282]]}</nowiki></pre></td></tr> |
|||
</table> |
|||
<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>{0, 0}</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
< |
<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>Kh[Knot[11, Alternating, 282]][q, t]</nowiki></pre></td></tr> |
||
<td>< |
<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>10 11 1 3 1 5 3 8 5 |
||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[15]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{0, 0}</nowiki></code></td></tr> |
|||
</table> |
|||
<table><tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[16]:=</code></td> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kh[Knot[11, Alternating, 282]][q, t]</nowiki></code></td></tr> |
|||
<tr align=left> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[16]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>10 11 1 3 1 5 3 8 5 |
|||
-- + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + |
-- + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + |
||
3 q 15 6 13 5 11 5 11 4 9 4 9 3 7 3 |
3 q 15 6 13 5 11 5 11 4 9 4 9 3 7 3 |
||
Line 221: | Line 151: | ||
3 3 5 3 5 4 7 4 9 5 |
3 3 5 3 5 4 7 4 9 5 |
||
3 q t + 5 q t + q t + 3 q t + q t</nowiki></ |
3 q t + 5 q t + q t + 3 q t + q t</nowiki></pre></td></tr> |
||
</table> }} |
</table> }} |
Revision as of 17:13, 2 September 2005
|
|
(Knotscape image) |
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots. |
Knot presentations
Planar diagram presentation | X6271 X10,4,11,3 X16,5,17,6 X14,8,15,7 X4,10,5,9 X18,11,19,12 X20,13,21,14 X22,16,1,15 X2,17,3,18 X12,19,13,20 X8,21,9,22 |
Gauss code | 1, -9, 2, -5, 3, -1, 4, -11, 5, -2, 6, -10, 7, -4, 8, -3, 9, -6, 10, -7, 11, -8 |
Dowker-Thistlethwaite code | 6 10 16 14 4 18 20 22 2 12 8 |
A Braid Representative | |||||
A Morse Link Presentation |
Three dimensional invariants
|
Four dimensional invariants
|
Polynomial invariants
KnotTheory`
, as shown in the (simulated) Mathematica session below. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting. This Mathematica session is also available (albeit only for the knot 5_2) as the notebook PolynomialInvariantsSession.nb.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
|
AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
|
In[3]:=
|
K = Knot["K11a282"];
|
In[4]:=
|
Alexander[K][t]
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
Out[4]=
|
In[5]:=
|
Conway[K][z]
|
Out[5]=
|
In[6]:=
|
Alexander[K, 2][t]
|
KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.
|
Out[6]=
|
In[7]:=
|
{KnotDet[K], KnotSignature[K]}
|
Out[7]=
|
{ 127, -2 } |
In[8]:=
|
Jones[K][q]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
|
Out[8]=
|
In[9]:=
|
HOMFLYPT[K][a, z]
|
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
|
Out[9]=
|
In[10]:=
|
Kauffman[K][a, z]
|
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
|
Out[10]=
|
"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {K11a81,}
Same Jones Polynomial (up to mirroring, ): {K11a81,}
KnotTheory`
. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
|
AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
|
In[3]:=
|
K = Knot["K11a282"];
|
In[4]:=
|
{A = Alexander[K][t], J = Jones[K][q]}
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
|
Out[4]=
|
{ , } |
In[5]:=
|
DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]
|
KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.
|
KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.
|
Out[5]=
|
{K11a81,} |
In[6]:=
|
DeleteCases[
Select[
AllKnots[],
(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) &
],
K
]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
|
Out[6]=
|
{K11a81,} |
Vassiliev invariants
V2 and V3: | (0, 0) |
V2,1 through V6,9: |
|
V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.
Khovanov Homology
The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where or , where -2 is the signature of K11a282. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
|
Integral Khovanov Homology
(db, data source) |
|
Computer Talk
Much of the above data can be recomputed by Mathematica using the package KnotTheory`
. See A Sample KnotTheory` Session.
Modifying This Page
Read me first: Modifying Knot Pages.
See/edit the Hoste-Thistlethwaite Knot Page master template (intermediate). See/edit the Hoste-Thistlethwaite_Splice_Base (expert). Back to the top. |
|