K11n58: Difference between revisions
No edit summary |
No edit summary |
||
Line 1: | Line 1: | ||
<!-- 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 base [[Hoste-Thistlethwaite_Splice_Base]]. Please do not edit! |
|||
<!-- --> <!-- |
|||
<!-- 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]]. --> |
|||
<!-- --> |
|||
<!-- --> |
|||
<!-- WARNING! WARNING! WARNING! |
|||
<!-- This page was generated from the splice template [[Hoste-Thistlethwaite Splice Template]]. Please do not edit! |
|||
<!-- Almost certainly, you want to edit [[Template:Hoste-Thistlethwaite Knot Page]], which actually produces this page. |
|||
<!-- 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]]. --> |
|||
<!-- --> |
|||
{{Hoste-Thistlethwaite Knot Page| |
{{Hoste-Thistlethwaite Knot Page| |
||
n = 11 | |
n = 11 | |
||
t = n | |
t = <nowiki>n</nowiki> | |
||
k = 58 | |
k = 58 | |
||
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,2,-1,3,-8,4,-2,-5,11,-6,10,-7,-3,8,5,-9,6,-10,7,-11,9/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-4,2,-1,3,-8,4,-2,-5,11,-6,10,-7,-3,8,5,-9,6,-10,7,-11,9/goTop.html | |
||
Line 41: | Line 50: | ||
<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 August 29, 2005, 15:33:11)...</td></tr> |
<tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr> |
||
</table> |
|||
<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, NonAlternating, 58]]</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<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> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[2]:=</code></td> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Crossings[Knot[11, NonAlternating, 58]]</nowiki></code></td></tr> |
|||
<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, NonAlternating, 58]]</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[4, 2, 5, 1], X[8, 4, 9, 3], X[14, 5, 15, 6], X[2, 8, 3, 7], |
|||
X[9, 17, 10, 16], X[11, 18, 12, 19], X[13, 20, 14, 21], |
X[9, 17, 10, 16], X[11, 18, 12, 19], X[13, 20, 14, 21], |
||
Line 51: | Line 70: | ||
X[6, 15, 7, 16], X[17, 1, 18, 22], X[19, 12, 20, 13], |
X[6, 15, 7, 16], X[17, 1, 18, 22], X[19, 12, 20, 13], |
||
X[21, 10, 22, 11]]</nowiki></ |
X[21, 10, 22, 11]]</nowiki></code></td></tr> |
||
</table> |
|||
<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, NonAlternating, 58]]</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<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, -4, 2, -1, 3, -8, 4, -2, -5, 11, -6, 10, -7, -3, 8, 5, -9, |
|||
<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, NonAlternating, 58]]</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, -4, 2, -1, 3, -8, 4, -2, -5, 11, -6, 10, -7, -3, 8, 5, -9, |
|||
6, -10, 7, -11, 9]</nowiki></ |
6, -10, 7, -11, 9]</nowiki></code></td></tr> |
||
</table> |
|||
<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, NonAlternating, 58]]</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<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[Knot[11, NonAlternating, 58]]</nowiki></pre></td></tr> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td> |
|||
<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, NonAlternating, 58]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:K11n58_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><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>BR[Knot[11, NonAlternating, 58]]</nowiki></code></td></tr> |
|||
<tr align=left> |
|||
<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> -3 4 8 2 3 |
|||
<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, NonAlternating, 58]]</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, NonAlternating, 58]]]</nowiki></code></td></tr> |
|||
<tr align=left><td></td><td>[[Image:K11n58_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, NonAlternating, 58]][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> -3 4 8 2 3 |
|||
-9 + t - -- + - + 8 t - 4 t + t |
-9 + t - -- + - + 8 t - 4 t + t |
||
2 t |
2 t |
||
t</nowiki></ |
t</nowiki></code></td></tr> |
||
</table> |
|||
<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, NonAlternating, 58]][z]</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<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> 2 4 6 |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td> |
|||
1 + z + 2 z + z</nowiki></pre></td></tr> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Conway[Knot[11, NonAlternating, 58]][z]</nowiki></code></td></tr> |
|||
<tr align=left> |
|||
<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[8, 16], Knot[10, 156], Knot[11, NonAlternating, 15], |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td> |
|||
<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> 2 4 6 |
|||
1 + z + 2 z + z</nowiki></code></td></tr> |
|||
</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[8, 16], Knot[10, 156], Knot[11, NonAlternating, 15], |
|||
Knot[11, NonAlternating, 56], Knot[11, NonAlternating, 58]}</nowiki></ |
Knot[11, NonAlternating, 56], Knot[11, NonAlternating, 58]}</nowiki></code></td></tr> |
||
</table> |
|||
<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, NonAlternating, 58]], KnotSignature[Knot[11, NonAlternating, 58]]}</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<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>{35, -2}</nowiki></pre></td></tr> |
|||
<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, NonAlternating, 58]], KnotSignature[Knot[11, NonAlternating, 58]]}</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>{35, -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, NonAlternating, 58]][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> -5 3 4 5 6 2 3 4 |
|||
-5 + q - -- + -- - -- + - + 5 q - 3 q + 2 q - q |
-5 + q - -- + -- - -- + - + 5 q - 3 q + 2 q - q |
||
4 3 2 q |
4 3 2 q |
||
q q q</nowiki></ |
q q q</nowiki></code></td></tr> |
||
</table> |
|||
<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 align=left> |
|||
<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, NonAlternating, 56], Knot[11, NonAlternating, 58]}</nowiki></pre></td></tr> |
|||
<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, NonAlternating, 56], Knot[11, NonAlternating, 58]}</nowiki></code></td></tr> |
|||
</table> |
|||
<table><tr align=left> |
|||
<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, NonAlternating, 58]][q]</nowiki></pre></td></tr> |
|||
< |
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[13]:=</code></td> |
||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>A2Invariant[Knot[11, NonAlternating, 58]][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> -16 -12 2 -2 2 4 8 12 |
|||
3 + q - q - -- + q + q + 2 q - q - q |
3 + q - q - -- + q + q + 2 q - q - q |
||
8 |
8 |
||
q</nowiki></ |
q</nowiki></code></td></tr> |
||
</table> |
|||
<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, NonAlternating, 58]][a, z]</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<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 |
|||
<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, NonAlternating, 58]][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 |
|||
2 2 4 2 z 4 z 3 5 2 8 z |
2 2 4 2 z 4 z 3 5 2 8 z |
||
6 + -- + 4 a + a - --- - --- - 4 a z - 3 a z - a z - 17 z - ---- - |
6 + -- + 4 a + a - --- - --- - 4 a z - 3 a z - a z - 17 z - ---- - |
||
Line 114: | Line 189: | ||
2 8 z 9 |
2 8 z 9 |
||
2 a z + -- + a z |
2 a z + -- + a z |
||
a</nowiki></ |
a</nowiki></code></td></tr> |
||
</table> |
|||
<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, NonAlternating, 58]], Vassiliev[3][Knot[11, NonAlternating, 58]]}</nowiki></pre></td></tr> |
|||
<table><tr align=left> |
|||
<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>{1, 1}</nowiki></pre></td></tr> |
|||
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[15]:=</code></td> |
|||
<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Vassiliev[2][Knot[11, NonAlternating, 58]], Vassiliev[3][Knot[11, NonAlternating, 58]]}</nowiki></code></td></tr> |
|||
<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>{1, 1}</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, NonAlternating, 58]][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>3 4 1 2 1 2 2 3 2 3 t |
|||
-- + - + ------ + ----- + ----- + ----- + ----- + ---- + ---- + --- + |
-- + - + ------ + ----- + ----- + ----- + ----- + ---- + ---- + --- + |
||
3 q 11 4 9 3 7 3 7 2 5 2 5 3 q |
3 q 11 4 9 3 7 3 7 2 5 2 5 3 q |
||
Line 124: | Line 209: | ||
2 3 2 3 3 5 3 5 4 7 4 9 5 |
2 3 2 3 3 5 3 5 4 7 4 9 5 |
||
2 q t + 2 q t + 3 q t + q t + 2 q t + q t + q t + q t</nowiki></ |
2 q t + 2 q t + 3 q t + q t + 2 q t + q t + q t + q t</nowiki></code></td></tr> |
||
</table> }} |
Revision as of 17:26, 1 September 2005
|
|
(Knotscape image) |
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots. |
Knot presentations
Planar diagram presentation | X4251 X8493 X14,5,15,6 X2837 X9,17,10,16 X11,18,12,19 X13,20,14,21 X6,15,7,16 X17,1,18,22 X19,12,20,13 X21,10,22,11 |
Gauss code | 1, -4, 2, -1, 3, -8, 4, -2, -5, 11, -6, 10, -7, -3, 8, 5, -9, 6, -10, 7, -11, 9 |
Dowker-Thistlethwaite code | 4 8 14 2 -16 -18 -20 6 -22 -12 -10 |
A Braid Representative | {{{braid_table}}} |
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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
|
In[3]:=
|
K = Knot["K11n58"];
|
In[4]:=
|
Alexander[K][t]
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
Out[4]=
|
In[5]:=
|
Conway[K][z]
|
Out[5]=
|
In[6]:=
|
Alexander[K, 2][t]
|
KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.
|
Out[6]=
|
In[7]:=
|
{KnotDet[K], KnotSignature[K]}
|
Out[7]=
|
{ 35, -2 } |
In[8]:=
|
Jones[K][q]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
|
Out[8]=
|
In[9]:=
|
HOMFLYPT[K][a, z]
|
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
|
Out[9]=
|
In[10]:=
|
Kauffman[K][a, z]
|
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
|
Out[10]=
|
"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {8_16, 10_156, K11n15, K11n56,}
Same Jones Polynomial (up to mirroring, ): {K11n56,}
KnotTheory`
. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
|
AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
|
In[3]:=
|
K = Knot["K11n58"];
|
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]=
|
{8_16, 10_156, K11n15, K11n56,} |
In[6]:=
|
DeleteCases[
Select[
AllKnots[],
(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) &
],
K
]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
|
Out[6]=
|
{K11n56,} |
Vassiliev invariants
V2 and V3: | (1, 1) |
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 K11n58. 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. |
|