L10n108: Difference between revisions
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,4,-3,-10:-9,2,-7,6:-2,-1,5,3,-8,9:-4,-5,10,8,-6,7/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,4,-3,-10:-9,2,-7,6:-2,-1,5,3,-8,9:-4,-5,10,8,-6,7/goTop.html | |
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<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> |
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</tr> |
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<tr valign=top><td colspan=2>Loading KnotTheory` (version of August |
<tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr> |
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<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>10</nowiki></pre></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[2]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Crossings[Link[10, NonAlternating, 108]]</nowiki></code></td></tr> |
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< |
<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[2]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>10</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[3]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>4</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[4]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>PD[X[6, 1, 7, 2], X[5, 12, 6, 13], X[3, 8, 4, 9], X[15, 2, 16, 3], |
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X[16, 7, 17, 8], X[19, 11, 20, 14], X[13, 15, 14, 20], |
X[16, 7, 17, 8], X[19, 11, 20, 14], X[13, 15, 14, 20], |
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X[9, 18, 10, 19], X[11, 10, 12, 5], X[4, 17, 1, 18]]</nowiki></ |
X[9, 18, 10, 19], X[11, 10, 12, 5], X[4, 17, 1, 18]]</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td> |
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{-4, -5, 10, 8, -6, 7}]</nowiki></ |
{-4, -5, 10, 8, -6, 7}]</nowiki></code></td></tr> |
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</table> |
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<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[Link[10, NonAlternating, 108]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L10n108_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> |
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< |
<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[6]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Show[DrawMorseLink[Link[10, NonAlternating, 108]]]</nowiki></code></td></tr> |
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<tr align=left><td></td><td>[[Image:L10n108_ML.gif]]</td></tr><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[6]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>-Graphics-</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[7]:=</code></td> |
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<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>-5</nowiki></code></td></tr> |
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</table> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[8]:=</code></td> |
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-q + q - ----- + q - ---- + q - ---- + |
-q + q - ----- + q - ---- + q - ---- + |
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13/2 9/2 5/2 |
13/2 9/2 5/2 |
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-(3/2) 1 |
-(3/2) 1 |
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q - ------- |
q - ------- |
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Sqrt[q]</nowiki></ |
Sqrt[q]</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[9]:=</code></td> |
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q + --- + --- + --- + --- + --- + --- + --- + --- + --- + -- + -- + |
q + --- + --- + --- + --- + --- + --- + --- + --- + --- + -- + -- + |
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26 24 22 20 18 16 14 12 10 8 6 |
26 24 22 20 18 16 14 12 10 8 6 |
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-4 -2 |
-4 -2 |
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q + q</nowiki></ |
q + q</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</code></td> |
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a 3 a 3 a a 4 a 9 a 6 a a 3 5 |
a 3 a 3 a a 4 a 9 a 6 a a 3 5 |
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-(--) + ---- - ---- + -- - ---- + ---- - ---- + -- - 7 a z + 13 a z - |
-(--) + ---- - ---- + -- - ---- + ---- - ---- + -- - 7 a z + 13 a z - |
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7 5 5 7 |
7 5 5 7 |
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a z + a z</nowiki></ |
a z + a z</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[11]:=</code></td> |
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<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Link[10, NonAlternating, 108]][a, z]</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[11]:=</code></td> |
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4 6 8 a 3 a 3 a a 3 a 6 a 3 a |
4 6 8 a 3 a 3 a a 3 a 6 a 3 a |
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10 a + 19 a + 10 a + -- + ---- + ---- + -- - ---- - ---- - ---- - |
10 a + 19 a + 10 a + -- + ---- + ---- + -- - ---- - ---- - ---- - |
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7 7 4 8 6 8 |
7 7 4 8 6 8 |
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3 a z - a z - a z</nowiki></ |
3 a z - a z - a z</nowiki></code></td></tr> |
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</table> |
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<table><tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td> |
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<tr align=left> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td> |
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-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + |
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + |
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6 4 18 6 16 6 14 6 16 5 14 4 12 4 |
6 4 18 6 16 6 14 6 16 5 14 4 12 4 |
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-- + t |
-- + t |
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4 |
4 |
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q</nowiki></ |
q</nowiki></code></td></tr> |
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</table> }} |
Revision as of 18:48, 1 September 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L10n108's Link Presentations]
Planar diagram presentation | X6172 X5,12,6,13 X3849 X15,2,16,3 X16,7,17,8 X19,11,20,14 X13,15,14,20 X9,18,10,19 X11,10,12,5 X4,17,1,18 |
Gauss code | {1, 4, -3, -10}, {-9, 2, -7, 6}, {-2, -1, 5, 3, -8, 9}, {-4, -5, 10, 8, -6, 7} |
A Braid Representative | {{{braid_table}}} |
A Morse Link Presentation |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (db) |
Signature | -5 (db) |
HOMFLY-PT polynomial | (db) |
Kauffman polynomial | (db) |
Khovanov Homology
The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). |
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Integral Khovanov Homology
(db, data source) |
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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 Link Page master template (intermediate). See/edit the Link_Splice_Base (expert). Back to the top. |
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