L10n25: Difference between revisions
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KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-9,2,-10:9,-1,-4,5,10,-2,-3,8,-7,4,-5,3,-6,7,-8,6/goTop.html | |
KnotilusURL = http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/1,-9,2,-10:9,-1,-4,5,10,-2,-3,8,-7,4,-5,3,-6,7,-8,6/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 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, 25]]</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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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[3]:=</code></td> |
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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>2</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[4]:=</code></td> |
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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[10, 3, 11, 4], X[11, 17, 12, 16], X[7, 15, 8, 14], |
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X[15, 9, 16, 8], X[17, 5, 18, 20], X[13, 18, 14, 19], |
X[15, 9, 16, 8], X[17, 5, 18, 20], X[13, 18, 14, 19], |
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X[19, 12, 20, 13], X[2, 5, 3, 6], X[4, 9, 1, 10]]</nowiki></ |
X[19, 12, 20, 13], X[2, 5, 3, 6], X[4, 9, 1, 10]]</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[5]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[5]:=</code></td> |
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-6, 7, -8, 6}]</nowiki></ |
-6, 7, -8, 6}]</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, 25]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:L10n25_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, 25]]]</nowiki></code></td></tr> |
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<tr align=left><td></td><td>[[Image:L10n25_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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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[7]:=</code></td> |
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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>1</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td> |
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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 - ---- + q - q + q - q |
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7/2 |
7/2 |
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q</nowiki></ |
q</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[9]:=</code></td> |
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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 + q - q - q + q + q |
q + --- + --- + --- + q + q - q - q + q + q |
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16 14 12 |
16 14 12 |
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q q q</nowiki></ |
q q q</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>Out[10]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki> 3 5 |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[10]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[10]:=</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> 3 5 |
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1 3 a 4 a 2 a z z 3 5 3 |
1 3 a 4 a 2 a z z 3 5 3 |
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-(---) + --- - ---- + ---- - -- - - + 6 a z - 7 a z + a z + 5 a z - |
-(---) + --- - ---- + ---- - -- - - + 6 a z - 7 a z + a z + 5 a z - |
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3 3 5 |
3 3 5 |
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2 a z + a z</nowiki></ |
2 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, 25]][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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-2 2 4 1 3 a 4 a 2 a 2 z z |
-2 2 4 1 3 a 4 a 2 a 2 z z |
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3 + a + 3 a + 2 a - --- - --- - ---- - ---- - --- + - + 13 a z + |
3 + a + 3 a + 2 a - --- - --- - ---- - ---- - --- + - + 13 a z + |
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7 3 7 5 7 2 8 4 8 |
7 3 7 5 7 2 8 4 8 |
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2 a z - 3 a z - a z - a z - a z</nowiki></ |
2 a z - 3 a z - a z - a z - a z</nowiki></code></td></tr> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[12]:=</code></td> |
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<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[12]:=</code></td> |
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2 + -- + q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + |
2 + -- + q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + |
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2 12 6 8 5 8 4 6 4 6 3 4 3 6 2 |
2 12 6 8 5 8 4 6 4 6 3 4 3 6 2 |
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----- + ----- + - + ---- + t + q t + q t + q t + q t + q t |
----- + ----- + - + ---- + t + q t + q t + q t + q t + q t |
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4 2 2 2 t 2 |
4 2 2 2 t 2 |
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q t q t q t</nowiki></ |
q t q t q t</nowiki></code></td></tr> |
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</table> }} |
Revision as of 17:30, 1 September 2005
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(Knotscape image) |
See the full Thistlethwaite Link Table (up to 11 crossings). |
Link Presentations
[edit Notes on L10n25's Link Presentations]
Planar diagram presentation | X6172 X10,3,11,4 X11,17,12,16 X7,15,8,14 X15,9,16,8 X17,5,18,20 X13,18,14,19 X19,12,20,13 X2536 X4,9,1,10 |
Gauss code | {1, -9, 2, -10}, {9, -1, -4, 5, 10, -2, -3, 8, -7, 4, -5, 3, -6, 7, -8, 6} |
A Braid Representative | {{{braid_table}}} |
A Morse Link Presentation |
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...) | (db) |
Jones polynomial | (db) |
Signature | 1 (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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