10 132: Difference between revisions

Revision as of 15:57, 16 August 2007

braid_table =

khovanov_table =

10 132: Difference between revisions

Revision as of 15:57, 16 August 2007

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WARNING! WARNING!
-<!--                       WARNING! WARNING! WARNING!
 <!-- This page was generated from the splice base [[Rolfsen_Splice_Base]]. Please do not edit!
 <!-- You probably want to edit the template referred to immediately below. (See [[Category:Knot Page Template]].)
@@ Line 23: / Line 23: @@
 <tr align=center>
 <td width=16.6667%><table cellpadding=0 cellspacing=0>
-  <tr><td>\</td><td>&nbsp;</td><td>r</td></tr>
+  <tr><td>\</td><td>
-<tr><td>&nbsp;</td><td>&nbsp;\&nbsp;</td><td>&nbsp;</td></tr>
-<tr><td>j</td><td>&nbsp;</td><td>\</td></tr>
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-coloured_jones_2 = <math>-q+1+2 q^{-1} -3 q^{-2} + q^{-3} +3 q^{-4} -4 q^{-5} +2 q^{-6} +2 q^{-7} -3 q^{-8} +2 q^{-9} + q^{-10} -3 q^{-11} +2 q^{-12} -2 q^{-14} +2 q^{-15} - q^{-16} - q^{-17} +2 q^{-18} - q^{-19} - q^{-20} + q^{-21} </math> |
-coloured_jones_3 = <math>- q^{-1} +2 q^{-3} + q^{-4} -2 q^{-5} - q^{-6} +2 q^{-7} +3 q^{-8} -2 q^{-9} -2 q^{-10} + q^{-11} +3 q^{-12} -2 q^{-13} -3 q^{-14} + q^{-15} +4 q^{-16} - q^{-17} -4 q^{-18} +5 q^{-20} -5 q^{-22} - q^{-23} +5 q^{-24} + q^{-25} -5 q^{-26} - q^{-27} +4 q^{-28} + q^{-29} -3 q^{-30} - q^{-31} +3 q^{-32} -2 q^{-34} +2 q^{-36} -2 q^{-38} + q^{-40} + q^{-41} - q^{-42} </math> |
-coloured_jones_4 = <math>q^5-q^4-q^3-q^2+5- q^{-2} -6 q^{-3} -2 q^{-4} +9 q^{-5} +2 q^{-6} -9 q^{-8} -3 q^{-9} +10 q^{-10} +3 q^{-11} + q^{-12} -10 q^{-13} -3 q^{-14} +11 q^{-15} +3 q^{-16} - q^{-17} -10 q^{-18} -3 q^{-19} +11 q^{-20} +2 q^{-21} -2 q^{-22} -9 q^{-23} -2 q^{-24} +10 q^{-25} +2 q^{-26} -2 q^{-27} -7 q^{-28} -2 q^{-29} +8 q^{-30} +2 q^{-31} -2 q^{-32} -5 q^{-33} - q^{-34} +6 q^{-35} + q^{-36} -3 q^{-37} -3 q^{-38} + q^{-39} +5 q^{-40} -5 q^{-42} -2 q^{-43} +2 q^{-44} +6 q^{-45} -6 q^{-47} -2 q^{-48} + q^{-49} +6 q^{-50} + q^{-51} -4 q^{-52} -2 q^{-53} - q^{-54} +5 q^{-55} -2 q^{-57} - q^{-58} - q^{-59} +4 q^{-60} - q^{-61} - q^{-62} - q^{-63} - q^{-64} +3 q^{-65} - q^{-68} - q^{-69} + q^{-70} </math> |
-coloured_jones_5 =  |
-coloured_jones_6 =  |
-coloured_jones_7 =  |
-computer_talk =
-         <table>
-         <tr valign=top>
-         <td><pre style="color: blue; border: 0px; padding: 0em">In[1]:=&nbsp;&nbsp;&nbsp;&nbsp;</pre></td>
-         <td align=left><pre style="color: red; border: 0px; padding: 0em">&lt;&lt; KnotTheory`</pre></td>
-         </tr>
-         <tr valign=top><td colspan=2><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr>
-         </table>
-         <table><tr align=left>
-<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>PD[Knot[10, 132]]</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>PD[X[4, 2, 5, 1], X[8, 4, 9, 3], X[5, 12, 6, 13], X[15, 18, 16, 19],
-  X[9, 16, 10, 17], X[17, 10, 18, 11], X[13, 20, 14, 1],
-  X[19, 14, 20, 15], X[11, 6, 12, 7], X[2, 8, 3, 7]]</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>GaussCode[Knot[10, 132]]</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>GaussCode[1, -10, 2, -1, -3, 9, 10, -2, -5, 6, -9, 3, -7, 8, -4, 5, -6,
-, -8, 7]</nowiki></code></td></tr>
-</table>
-         <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>DTCode[Knot[10, 132]]</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>DTCode[4, 8, -12, 2, -16, -6, -20, -18, -10, -14]</nowiki></code></td></tr>
-</table>
-         <table><tr align=left>
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[5]:=</code></td>
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>br = BR[Knot[10, 132]]</nowiki></code></td></tr>
-<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[4, {1, 1, 1, -2, -1, -1, -2, -3, 2, -3, -3}]</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>{First[br], Crossings[br]}</nowiki></code></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>{4, 11}</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>BraidIndex[Knot[10, 132]]</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</nowiki></code></td></tr>
-</table>
-         <table><tr align=left>
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[8]:=</code></td>
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Show[DrawMorseLink[Knot[10, 132]]]</nowiki></code></td></tr>
-<tr align=left><td></td><td>[[Image:10_132_ML.gif]]</td></tr><tr align=left>
-<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>-Graphics-</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> (#[Knot[10, 132]]&) /@ {
-                    SymmetryType, UnknottingNumber, ThreeGenus,
-                    BridgeIndex, SuperBridgeIndex, NakanishiIndex
-                   }</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>{Reversible, 1, 2, 3, NotAvailable, 1}</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>alex = Alexander[Knot[10, 132]][t]</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>     -2   1        2
-+ t   - - - t + t
-          t</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>Conway[Knot[10, 132]][z]</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>       2    4
-+ 3 z  + z</nowiki></code></td></tr>
-</table>
-         <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[], (alex === Alexander[#][t])&]</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[5, 1], Knot[10, 132]}</nowiki></code></td></tr>
-</table>
-         <table><tr align=left>
-<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>{KnotDet[Knot[10, 132]], KnotSignature[Knot[10, 132]]}</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>{5, 0}</nowiki></code></td></tr>
-</table>
-         <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>Jones[Knot[10, 132]][q]</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>  -7    -6    -5    -4    -2
--q   + q   - q   + q   + q</nowiki></code></td></tr>
-</table>
-         <table><tr align=left>
-<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>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[15]:=</code></td>
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Knot[5, 1], Knot[10, 132]}</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>A2Invariant[Knot[10, 132]][q]</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>  -22    -20    -18    -14    -12    2     -8    -6
--q    - q    - q    + q    + q    + --- + q   + q
-                                    q</nowiki></code></td></tr>
-</table>
-         <table><tr align=left>
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[17]:=</code></td>
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>HOMFLYPT[Knot[10, 132]][a, z]</nowiki></code></td></tr>
-<tr align=left>
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[17]:=</code></td>
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>   4      6      4  2    6  2    4  4
-a  - 2 a  + 4 a  z  - a  z  + a  z</nowiki></code></td></tr>
-</table>
-         <table><tr align=left>
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[18]:=</code></td>
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kauffman[Knot[10, 132]][a, z]</nowiki></code></td></tr>
-<tr align=left>
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[18]:=</code></td>
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>   4      6            3        5        7      2  2      4  2
-a  + 2 a  - a z - 4 a  z - 8 a  z - 5 a  z - a  z  - 7 a  z  -
-2      3  3       5  3       7  3       4  4       6  4
-a  z  + 9 a  z  + 19 a  z  + 10 a  z  + 10 a  z  + 10 a  z  -
-5       5  5      7  5      4  6      6  6    3  7      5  7
-a  z  - 12 a  z  - 6 a  z  - 6 a  z  - 6 a  z  + a  z  + 2 a  z  +
-7    4  8    6  8
-  a  z  + a  z  + a  z</nowiki></code></td></tr>
-</table>
-         <table><tr align=left>
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[19]:=</code></td>
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{Vassiliev[2][Knot[10, 132]], Vassiliev[3][Knot[10, 132]]}</nowiki></code></td></tr>
-<tr align=left>
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[19]:=</code></td>
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>{3, -5}</nowiki></code></td></tr>
-</table>
-         <table><tr align=left>
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[20]:=</code></td>
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>Kh[Knot[10, 132]][q, t]</nowiki></code></td></tr>
-<tr align=left>
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[20]:=</code></td>
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki> -3   1     1        1        1        1       1       1       1
-q   + - + ------ + ------ + ------ + ----- + ----- + ----- + ----- +
-      q    15  7    11  6    11  5    9  4    7  4    9  3    5  3
-          q   t    q   t    q   t    q  t    q  t    q  t    q  t
-1
-  ----- + ---
-2   q t
-  q  t</nowiki></code></td></tr>
-</table>
-         <table><tr align=left>
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">In[21]:=</code></td>
-<td><code style="white-space: pre; color: red; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>ColouredJones[Knot[10, 132], 2][q]</nowiki></code></td></tr>
-<tr align=left>
-<td width=70px><code style="color: blue; border: 0px; padding: 0em">Out[21]:=</code></td>
-<td><code style="white-space: pre; color: black; border: 0px; padding: 0em; background-color: rgb(255,255,255);"><nowiki>     -21    -20    -19    2     -17    -16    2     2     2     3
-+ q    - q    - q    + --- - q    - q    + --- - --- + --- - --- +
-15    14    12    11
-                         q                   q     q     q     q
-   -10   2    3    2    2    4    3     -3   3    2
-  q    + -- - -- + -- + -- - -- + -- + q   - -- + - - q
-8    7    6    5    4          2   q
-         q    q    q    q    q    q          q</nowiki></code></td></tr>
-</table>  }}

10 132: Difference between revisions

Revision as of 15:57, 16 August 2007

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