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n = 5 | |
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n = 5 | |
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k = 1 | |
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k = 1 | |
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KnotilusURL = <nowiki>http://srankin.math.uwo.ca/cgi-bin/retrieve.cgi/-1,4,-2,5,-3,1,-4,2,-5,3/goTop.html</nowiki> | |
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braid_table = <nowiki><table cellspacing=0 cellpadding=0 border=0> |
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<tr><td>[[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]][[Image:BraidPart3.gif]]</td></tr> |
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<tr><td>[[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]][[Image:BraidPart4.gif]]</td></tr> |
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</table></nowiki> | |
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braid_crossings = 5 | |
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braid_width = 2 | |
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braid_index = 2 | |
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same_alexander = <nowiki>[[10_132]], </nowiki> | |
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same_alexander = <nowiki>[[10_132]], </nowiki> | |
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same_jones = <nowiki>[[10_132]], </nowiki> | |
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same_jones = <nowiki>[[10_132]], </nowiki> | |
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coloured_jones_2 = <math> q^{-19} - q^{-18} + q^{-16} -2 q^{-15} + q^{-13} - q^{-12} + q^{-10} - q^{-9} + q^{-7} + q^{-4} </math> | |
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khovanov_table = <math>\textrm{WikiForm}(\textrm{<table border=1>$\backslash $n<tr align=center>$\backslash $n<td width=20.$\%$><table cellpadding=0 cellspacing=0>$\backslash $n <tr><td>$\backslash \backslash $</td><td>$\&$nbsp;</td><td>r</td></tr>$\backslash $n<tr><td>$\&$nbsp;</td><td>$\&$nbsp;$\backslash \backslash \&$nbsp;</td><td>$\&$nbsp;</td></tr>$\backslash $n<tr><td>j</td><td>$\&$nbsp;</td><td>$\backslash \backslash $</td></tr>$\backslash $n</table></td>$\backslash $n <td width=10.$\%$>-5</td ><td width=10.$\%$>-4</td ><td width=10.$\%$>-3</td ><td width=10.$\%$>-2</td ><td width=10.$\%$>-1</td ><td width=10.$\%$>0</td ><td width=20.$\%$>$\&$chi;</td></tr>$\backslash $n<tr align=center><td>-3</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td bgcolor=yellow>1</td><td>1</td></tr>$\backslash $n<tr align=center><td>-5</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td bgcolor=yellow>$\&$nbsp;</td><td bgcolor=yellow>1</td><td>1</td></tr>$\backslash $n<tr align=center><td>-7</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>$\&$nbsp;</td><td>$\&$nbsp;</td><td>1</td></tr>$\backslash $n<tr align=center><td>-9</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td bgcolor=yellow>$\&$nbsp;</td><td bgcolor=yellow>$\&$nbsp;</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>0</td></tr>$\backslash $n<tr align=center><td>-11</td><td>$\&$nbsp;</td><td bgcolor=yellow>1</td><td bgcolor=yellow>1</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>0</td></tr>$\backslash $n<tr align=center><td>-13</td><td bgcolor=yellow>$\&$nbsp;</td><td bgcolor=yellow>$\&$nbsp;</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>0</td></tr>$\backslash $n<tr align=center><td>-15</td><td bgcolor=yellow>1</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>$\&$nbsp;</td><td>-1</td></tr>$\backslash $n</table>})</math> | |
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coloured_jones_2 = <math> q^{-4} + q^{-7} - q^{-9} + q^{-10} - q^{-12} + q^{-13} -2 q^{-15} + q^{-16} - q^{-18} + q^{-19} </math> |
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coloured_jones_3 = <math>- q^{-36} + q^{-35} + q^{-31} - q^{-29} + q^{-27} - q^{-25} - q^{-21} + q^{-18} - q^{-17} + q^{-14} - q^{-13} + q^{-10} + q^{-6} </math> | |
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coloured_jones_3 = <math> q^{-6} + q^{-10} - q^{-13} + q^{-14} - q^{-17} + q^{-18} - q^{-21} - q^{-25} + q^{-27} - q^{-29} + q^{-31} + q^{-35} - q^{-36} </math> |
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coloured_jones_4 = <math> q^{-58} - q^{-57} - q^{-54} + q^{-53} - q^{-52} + q^{-51} - q^{-49} + q^{-48} - q^{-47} + q^{-46} + q^{-45} - q^{-44} + q^{-43} - q^{-42} + q^{-41} - q^{-39} + q^{-38} - q^{-37} + q^{-36} - q^{-34} + q^{-33} - q^{-32} - q^{-29} + q^{-28} - q^{-27} + q^{-23} - q^{-22} + q^{-18} - q^{-17} + q^{-13} + q^{-8} </math> | |
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coloured_jones_4 = <math> q^{-8} + q^{-13} - q^{-17} + q^{-18} - q^{-22} + q^{-23} - q^{-27} + q^{-28} - q^{-29} - q^{-32} + q^{-33} - q^{-34} + q^{-36} - q^{-37} + q^{-38} - q^{-39} + q^{-41} - q^{-42} + q^{-43} - q^{-44} + q^{-45} + q^{-46} - q^{-47} + q^{-48} - q^{-49} + q^{-51} - q^{-52} + q^{-53} - q^{-54} - q^{-57} + q^{-58} </math> |
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coloured_jones_5 = <math>- q^{-85} + q^{-84} + q^{-81} - q^{-79} + q^{-75} - q^{-73} - q^{-72} + q^{-69} - q^{-66} + q^{-63} - q^{-60} + q^{-58} + q^{-57} - q^{-54} + q^{-52} - q^{-48} + q^{-46} - q^{-42} + q^{-40} - q^{-39} - q^{-36} + q^{-34} - q^{-33} + q^{-28} - q^{-27} + q^{-22} - q^{-21} + q^{-16} + q^{-10} </math> | |
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coloured_jones_5 = <math> q^{-10} + q^{-16} - q^{-21} + q^{-22} - q^{-27} + q^{-28} - q^{-33} + q^{-34} - q^{-36} - q^{-39} + q^{-40} - q^{-42} + q^{-46} - q^{-48} + q^{-52} - q^{-54} + q^{-57} + q^{-58} - q^{-60} + q^{-63} - q^{-66} + q^{-69} - q^{-72} - q^{-73} + q^{-75} - q^{-79} + q^{-81} + q^{-84} - q^{-85} </math> |
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coloured_jones_6 = <math> q^{-117} - q^{-116} - q^{-113} +2 q^{-110} - q^{-109} - q^{-106} + q^{-104} +2 q^{-103} - q^{-102} -2 q^{-99} + q^{-97} +2 q^{-96} - q^{-95} -2 q^{-92} +2 q^{-89} - q^{-88} -2 q^{-85} + q^{-83} +2 q^{-82} - q^{-81} -2 q^{-78} + q^{-76} +2 q^{-75} - q^{-74} - q^{-71} + q^{-69} +2 q^{-68} - q^{-67} - q^{-64} +2 q^{-61} - q^{-60} - q^{-57} +2 q^{-54} - q^{-53} - q^{-50} + q^{-47} - q^{-46} - q^{-43} + q^{-40} - q^{-39} + q^{-33} - q^{-32} + q^{-26} - q^{-25} + q^{-19} + q^{-12} </math> | |
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coloured_jones_6 = <math> q^{-12} + q^{-19} - q^{-25} + q^{-26} - q^{-32} + q^{-33} - q^{-39} + q^{-40} - q^{-43} - q^{-46} + q^{-47} - q^{-50} - q^{-53} +2 q^{-54} - q^{-57} - q^{-60} +2 q^{-61} - q^{-64} - q^{-67} +2 q^{-68} + q^{-69} - q^{-71} - q^{-74} +2 q^{-75} + q^{-76} -2 q^{-78} - q^{-81} +2 q^{-82} + q^{-83} -2 q^{-85} - q^{-88} +2 q^{-89} -2 q^{-92} - q^{-95} +2 q^{-96} + q^{-97} -2 q^{-99} - q^{-102} +2 q^{-103} + q^{-104} - q^{-106} - q^{-109} +2 q^{-110} - q^{-113} - q^{-116} + q^{-117} </math> |
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coloured_jones_7 = <math>- q^{-154} + q^{-153} + q^{-150} - q^{-147} - q^{-146} + q^{-145} + q^{-142} - q^{-141} - q^{-139} - q^{-138} + q^{-137} + q^{-136} + q^{-134} - q^{-133} - q^{-131} - q^{-130} + q^{-129} + q^{-128} + q^{-127} + q^{-126} - q^{-125} - q^{-123} - q^{-122} + q^{-121} + q^{-119} + q^{-118} - q^{-117} - q^{-115} - q^{-114} + q^{-113} + q^{-111} + q^{-110} - q^{-109} - q^{-108} - q^{-107} - q^{-106} + q^{-105} + q^{-103} + q^{-102} - q^{-101} - q^{-100} - q^{-98} + q^{-97} + q^{-95} + q^{-94} - q^{-93} - q^{-92} - q^{-90} + q^{-89} + q^{-87} + q^{-86} - q^{-85} - q^{-82} + q^{-81} + q^{-79} + q^{-78} - q^{-77} - q^{-74} + q^{-71} + q^{-70} - q^{-69} - q^{-66} + q^{-63} + q^{-62} - q^{-61} - q^{-58} + q^{-54} - q^{-53} - q^{-50} + q^{-46} - q^{-45} + q^{-38} - q^{-37} + q^{-30} - q^{-29} + q^{-22} + q^{-14} </math> |
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}} |
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coloured_jones_7 = <math> q^{-14} + q^{-22} - q^{-29} + q^{-30} - q^{-37} + q^{-38} - q^{-45} + q^{-46} - q^{-50} - q^{-53} + q^{-54} - q^{-58} - q^{-61} + q^{-62} + q^{-63} - q^{-66} - q^{-69} + q^{-70} + q^{-71} - q^{-74} - q^{-77} + q^{-78} + q^{-79} + q^{-81} - q^{-82} - q^{-85} + q^{-86} + q^{-87} + q^{-89} - q^{-90} - q^{-92} - q^{-93} + q^{-94} + q^{-95} + q^{-97} - q^{-98} - q^{-100} - q^{-101} + q^{-102} + q^{-103} + q^{-105} - q^{-106} - q^{-107} - q^{-108} - q^{-109} + q^{-110} + q^{-111} + q^{-113} - q^{-114} - q^{-115} - q^{-117} + q^{-118} + q^{-119} + q^{-121} - q^{-122} - q^{-123} - q^{-125} + q^{-126} + q^{-127} + q^{-128} + q^{-129} - q^{-130} - q^{-131} - q^{-133} + q^{-134} + q^{-136} + q^{-137} - q^{-138} - q^{-139} - q^{-141} + q^{-142} + q^{-145} - q^{-146} - q^{-147} + q^{-150} + q^{-153} - q^{-154} </math> | |
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computer_talk = |
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<table> |
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<tr valign=top> |
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<td><pre style="color: blue; border: 0px; padding: 0em">In[1]:= </pre></td> |
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<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><nowiki>Loading KnotTheory` (version of August 29, 2005, 15:33:11)...</nowiki></td></tr> |
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</table> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 2 |$\backslash $nin = <nowiki>PD[Knot[5, 1]]</nowiki> |$\backslash $nout = <nowiki>PD[X[1, 6, 2, 7], X[3, 8, 4, 9], X[5, 10, 6, 1], X[7, 2, 8, 3], $\backslash $n $\backslash $n X[9, 4, 10, 5]]</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 3 |$\backslash $nin = <nowiki>GaussCode[Knot[5, 1]]</nowiki> |$\backslash $nout = <nowiki>GaussCode[-1, 4, -2, 5, -3, 1, -4, 2, -5, 3]</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 4 |$\backslash $nin = <nowiki>DTCode[Knot[5, 1]]</nowiki> |$\backslash $nout = <nowiki>DTCode[6, 8, 10, 2, 4]</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 5 |$\backslash $nin = <nowiki>br = BR[Knot[5, 1]]</nowiki> |$\backslash $nout = <nowiki>BR[2, $\{$-1, -1, -1, -1, -1$\}$]</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 6 |$\backslash $nin = <nowiki>$\{$First[br], Crossings[br]$\}$</nowiki> |$\backslash $nout = <nowiki>$\{$2, 5$\}$</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 7 |$\backslash $nin = <nowiki>BraidIndex[Knot[5, 1]]</nowiki> |$\backslash $nout = <nowiki>2</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{<tr valign=top><td><pre style=$\texttt{"}$color: blue; border: 0px; padding: 0em$\texttt{"}$><nowiki>In[8]:=</nowiki></pre></td><td><pre style=$\texttt{"}$color: red; border: 0px; padding: 0em$\texttt{"}$><nowiki>Show[DrawMorseLink[Knot[5, 1]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:5$\_$1$\_$ML.gif]]</td></tr><tr valign=top><td><tt><font color=blue>Out[8]=</font></tt><td><tt><font color=black>-Graphics-</font></tt></td></tr><nowiki>})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 9 |$\backslash $nin = <nowiki> ($\#$[Knot[5, 1]]$\&$) /@ $\{\backslash $n SymmetryType, UnknottingNumber, ThreeGenus,$\backslash $n BridgeIndex, SuperBridgeIndex, NakanishiIndex$\backslash $n $\}$</nowiki> |$\backslash $nout = <nowiki>$\{$Reversible, 2, 2, 2, 3, 1$\}$</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 10 |$\backslash $nin = <nowiki>alex = Alexander[Knot[5, 1]][t]</nowiki> |$\backslash $nout = <nowiki> -2 1 2$\backslash $n1 + t - - - t + t$\backslash $n t</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 11 |$\backslash $nin = <nowiki>Conway[Knot[5, 1]][z]</nowiki> |$\backslash $nout = <nowiki> 2 4$\backslash $n1 + 3 z + z</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 12 |$\backslash $nin = <nowiki>Select[AllKnots[], (alex === Alexander[$\#$][t])$\&$]</nowiki> |$\backslash $nout = <nowiki>$\{$Knot[5, 1], Knot[10, 132]$\}$</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 13 |$\backslash $nin = <nowiki>$\{$KnotDet[Knot[5, 1]], KnotSignature[Knot[5, 1]]$\}$</nowiki> |$\backslash $nout = <nowiki>$\{$5, -4$\}$</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 14 |$\backslash $nin = <nowiki>Jones[Knot[5, 1]][q]</nowiki> |$\backslash $nout = <nowiki> -7 -6 -5 -4 -2$\backslash $n-q + q - q + q + q</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 15 |$\backslash $nin = <nowiki>Select[AllKnots[], (J === Jones[$\#$][q] || (J /. q-> 1/q) === Jones[$\#$][q])$\&$]</nowiki> |$\backslash $nout = <nowiki>$\{$Knot[5, 1], Knot[10, 132]$\}$</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 16 |$\backslash $nin = <nowiki>A2Invariant[Knot[5, 1]][q]</nowiki> |$\backslash $nout = <nowiki> -22 -20 -18 -14 -12 2 -8 -6$\backslash $n-q - q - q + q + q + --- + q + q$\backslash $n 10$\backslash $n q</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 17 |$\backslash $nin = <nowiki>HOMFLYPT[Knot[5, 1]][a, z]</nowiki> |$\backslash $nout = <nowiki> 4 6 4 2 6 2 4 4$\backslash $n3 a - 2 a + 4 a z - a z + a z</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 18 |$\backslash $nin = <nowiki>Kauffman[Knot[5, 1]][a, z]</nowiki> |$\backslash $nout = <nowiki> 4 6 5 7 9 4 2 6 2 8 2$\backslash $n3 a + 2 a - 2 a z - a z + a z - 4 a z - 3 a z + a z + $\backslash $n $\backslash $n 5 3 7 3 4 4 6 4$\backslash $n a z + a z + a z + a z</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 19 |$\backslash $nin = <nowiki>$\{$Vassiliev[2][Knot[5, 1]], Vassiliev[3][Knot[5, 1]]$\}$</nowiki> |$\backslash $nout = <nowiki>$\{$3, -5$\}$</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 20 |$\backslash $nin = <nowiki>Kh[Knot[5, 1]][q, t]</nowiki> |$\backslash $nout = <nowiki> -5 -3 1 1 1 1$\backslash $nq + q + ------ + ------ + ------ + -----$\backslash $n 15 5 11 4 11 3 7 2$\backslash $n q t q t q t q t</nowiki> $\}\}$})</math> |
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<math>\textrm{WikiForm}(\textrm{$\{\{$InOut |$\backslash $nn = 21 |$\backslash $nin = <nowiki>ColouredJones[Knot[5, 1], 2][q]</nowiki> |$\backslash $nout = <nowiki> -19 -18 -16 2 -13 -12 -10 -9 -7 -4$\backslash $nq - q + q - --- + q - q + q - q + q + q$\backslash $n 15$\backslash $n q</nowiki> $\}\}$})</math> }} |
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