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5 2: Difference between revisions

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-  <tr><td>\</td><td>&nbsp;</td><td>r</td></tr>
+  <tr><td>\</td><td>
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-coloured_jones_2 = <math> q^{-2} - q^{-3} +3 q^{-5} -2 q^{-6} - q^{-7} +4 q^{-8} -3 q^{-9} - q^{-10} +3 q^{-11} -2 q^{-12} - q^{-13} +2 q^{-14} - q^{-15} - q^{-16} + q^{-17} </math> |
-coloured_jones_3 = <math> q^{-3} - q^{-4} + q^{-6} +2 q^{-7} -2 q^{-8} -2 q^{-9} +2 q^{-10} +4 q^{-11} -3 q^{-12} -3 q^{-13} +2 q^{-14} +5 q^{-15} -4 q^{-16} -4 q^{-17} +2 q^{-18} +4 q^{-19} -3 q^{-20} -3 q^{-21} +2 q^{-22} +3 q^{-23} - q^{-24} -3 q^{-25} + q^{-26} +2 q^{-27} -2 q^{-29} + q^{-31} + q^{-32} - q^{-33} </math> |
-coloured_jones_4 = <math> q^{-4} - q^{-5} + q^{-7} +2 q^{-9} -3 q^{-10} - q^{-11} +2 q^{-12} + q^{-13} +5 q^{-14} -6 q^{-15} -3 q^{-16} +2 q^{-17} +2 q^{-18} +7 q^{-19} -8 q^{-20} -4 q^{-21} +2 q^{-22} +2 q^{-23} +9 q^{-24} -9 q^{-25} -5 q^{-26} +2 q^{-27} +2 q^{-28} +8 q^{-29} -8 q^{-30} -4 q^{-31} +2 q^{-32} +2 q^{-33} +7 q^{-34} -6 q^{-35} -3 q^{-36} + q^{-37} + q^{-38} +6 q^{-39} -4 q^{-40} -2 q^{-41} - q^{-42} +5 q^{-44} -2 q^{-45} - q^{-46} - q^{-47} - q^{-48} +3 q^{-49} - q^{-52} - q^{-53} + q^{-54} </math> |
-coloured_jones_5 = <math> q^{-5} - q^{-6} + q^{-8} + q^{-11} -2 q^{-12} - q^{-13} +2 q^{-14} +2 q^{-15} + q^{-16} + q^{-17} -5 q^{-18} -3 q^{-19} + q^{-20} +5 q^{-21} +4 q^{-22} + q^{-23} -7 q^{-24} -6 q^{-25} + q^{-26} +6 q^{-27} +6 q^{-28} +2 q^{-29} -9 q^{-30} -8 q^{-31} + q^{-32} +6 q^{-33} +7 q^{-34} +3 q^{-35} -9 q^{-36} -9 q^{-37} + q^{-38} +6 q^{-39} +8 q^{-40} +2 q^{-41} -8 q^{-42} -8 q^{-43} + q^{-44} +6 q^{-45} +7 q^{-46} + q^{-47} -6 q^{-48} -7 q^{-49} +5 q^{-51} +6 q^{-52} + q^{-53} -4 q^{-54} -5 q^{-55} -2 q^{-56} +3 q^{-57} +5 q^{-58} + q^{-59} - q^{-60} -4 q^{-61} -3 q^{-62} + q^{-63} +3 q^{-64} +2 q^{-65} + q^{-66} -2 q^{-67} -3 q^{-68} + q^{-70} + q^{-71} +2 q^{-72} -2 q^{-74} - q^{-75} + q^{-78} + q^{-79} - q^{-80} </math> |
-coloured_jones_6 = <math> q^{-6} - q^{-7} + q^{-9} - q^{-12} +2 q^{-13} -2 q^{-14} - q^{-15} +3 q^{-16} + q^{-17} + q^{-18} -2 q^{-19} +2 q^{-20} -6 q^{-21} -3 q^{-22} +5 q^{-23} +4 q^{-24} +4 q^{-25} -2 q^{-26} +3 q^{-27} -12 q^{-28} -7 q^{-29} +6 q^{-30} +6 q^{-31} +8 q^{-32} - q^{-33} +4 q^{-34} -17 q^{-35} -10 q^{-36} +6 q^{-37} +8 q^{-38} +10 q^{-39} +6 q^{-41} -20 q^{-42} -12 q^{-43} +6 q^{-44} +8 q^{-45} +11 q^{-46} +8 q^{-48} -21 q^{-49} -13 q^{-50} +6 q^{-51} +8 q^{-52} +12 q^{-53} +8 q^{-55} -20 q^{-56} -12 q^{-57} +6 q^{-58} +8 q^{-59} +11 q^{-60} +6 q^{-62} -18 q^{-63} -11 q^{-64} +5 q^{-65} +7 q^{-66} +9 q^{-67} +6 q^{-69} -15 q^{-70} -9 q^{-71} +3 q^{-72} +5 q^{-73} +7 q^{-74} + q^{-75} +7 q^{-76} -12 q^{-77} -7 q^{-78} + q^{-79} +2 q^{-80} +4 q^{-81} +2 q^{-82} +8 q^{-83} -8 q^{-84} -5 q^{-85} - q^{-86} + q^{-88} +2 q^{-89} +8 q^{-90} -4 q^{-91} -2 q^{-92} -2 q^{-93} - q^{-94} - q^{-95} +6 q^{-97} - q^{-98} - q^{-100} - q^{-101} -2 q^{-102} - q^{-103} +3 q^{-104} + q^{-106} - q^{-109} - q^{-110} + q^{-111} </math> |
-coloured_jones_7 = <math> q^{-7} - q^{-8} + q^{-10} - q^{-13} +2 q^{-15} -2 q^{-16} +2 q^{-18} + q^{-19} + q^{-20} -2 q^{-21} -2 q^{-22} +2 q^{-23} -5 q^{-24} +4 q^{-26} +4 q^{-27} +5 q^{-28} -2 q^{-29} -4 q^{-30} -2 q^{-31} -10 q^{-32} -2 q^{-33} +6 q^{-34} +6 q^{-35} +12 q^{-36} +2 q^{-37} -6 q^{-38} -5 q^{-39} -17 q^{-40} -5 q^{-41} +6 q^{-42} +9 q^{-43} +18 q^{-44} +5 q^{-45} -6 q^{-46} -7 q^{-47} -22 q^{-48} -9 q^{-49} +7 q^{-50} +10 q^{-51} +21 q^{-52} +7 q^{-53} -5 q^{-54} -6 q^{-55} -25 q^{-56} -11 q^{-57} +7 q^{-58} +10 q^{-59} +23 q^{-60} +7 q^{-61} -4 q^{-62} -5 q^{-63} -26 q^{-64} -12 q^{-65} +7 q^{-66} +9 q^{-67} +24 q^{-68} +7 q^{-69} -3 q^{-70} -6 q^{-71} -25 q^{-72} -11 q^{-73} +7 q^{-74} +9 q^{-75} +23 q^{-76} +7 q^{-77} -4 q^{-78} -7 q^{-79} -23 q^{-80} -10 q^{-81} +6 q^{-82} +8 q^{-83} +21 q^{-84} +7 q^{-85} -5 q^{-86} -6 q^{-87} -20 q^{-88} -8 q^{-89} +4 q^{-90} +6 q^{-91} +18 q^{-92} +7 q^{-93} -3 q^{-94} -4 q^{-95} -16 q^{-96} -7 q^{-97} +2 q^{-98} +2 q^{-99} +14 q^{-100} +8 q^{-101} - q^{-102} - q^{-103} -12 q^{-104} -6 q^{-105} - q^{-106} -2 q^{-107} +10 q^{-108} +7 q^{-109} + q^{-110} +2 q^{-111} -6 q^{-112} -5 q^{-113} -3 q^{-114} -5 q^{-115} +6 q^{-116} +5 q^{-117} + q^{-118} +5 q^{-119} -2 q^{-120} -2 q^{-121} -3 q^{-122} -6 q^{-123} +2 q^{-124} +2 q^{-125} +4 q^{-127} + q^{-128} + q^{-129} - q^{-130} -5 q^{-131} - q^{-134} +2 q^{-135} + q^{-136} +2 q^{-137} + q^{-138} -2 q^{-139} - q^{-140} - q^{-142} + q^{-145} + q^{-146} - q^{-147} </math> |
-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[5, 2]]</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[1, 4, 2, 5], X[3, 8, 4, 9], X[5, 10, 6, 1], X[9, 6, 10, 7],
-  X[7, 2, 8, 3]]</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[5, 2]]</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, 5, -2, 1, -3, 4, -5, 2, -4, 3]</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[5, 2]]</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, 10, 2, 6]</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[5, 2]]</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[3, {-1, -1, -1, -2, 1, -2}]</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>{3, 6}</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[5, 2]]</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</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[5, 2]]]</nowiki></code></td></tr>
-<tr align=left><td></td><td>[[Image:5_2_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[5, 2]]&) /@ {
-                 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, 1, 2, {3, 4}, 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[5, 2]][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
--3 + - + 2 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[5, 2]][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
-+ 2 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, 2]}</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[5, 2]], KnotSignature[Knot[5, 2]]}</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>{7, -2}</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[5, 2]][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>  -6    -5    -4   2     -2   1
--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[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, 2], Knot[11, NonAlternating, 57]}</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[5, 2]][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>  -20    -18    -12    -10    -8    -6    -2
--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[5, 2]][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> 2    4    6    2  2    4  2
-a  + a  - a  + 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[5, 2]][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>  2    4    6      5        7      2  2    4  2      6  2    3  3
--a  + a  + a  - 2 a  z - 2 a  z + a  z  - a  z  - 2 a  z  + a  z  +
-3    7  3    4  4    6  4
-a  z  + 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[5, 2]], Vassiliev[3][Knot[5, 2]]}</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>{2, -3}</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[5, 2]][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
-q   + - + ------ + ----- + ----- + ----- + ----- + ----
-      q    13  5    9  4    9  3    7  2    5  2    3
-          q   t    q  t    q  t    q  t    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[5, 2], 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> -17    -16    -15    2     -13    2     3     -10   3    4     -7
-q    - q    - q    + --- - q    - --- + --- - q    - -- + -- - q   -
-12    11           9    8
-                     q            q     q            q    q
-3     -3    -2
-  -- + -- - q   + q
-5
-  q    q</nowiki></code></td></tr>
-</table>  }}

5 2: Difference between revisions

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