9 25: Difference between revisions
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{{Rolfsen Knot Page| |
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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 29, 2005, 15: |
<tr valign=top><td colspan=2>Loading KnotTheory` (version of August 29, 2005, 15:27:48)...</td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[Knot[9, 25]]</nowiki></pre></td></tr> |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[2]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>PD[Knot[9, 25]]</nowiki></pre></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>PD[X[1, 4, 2, 5], X[3, 8, 4, 9], X[5, 12, 6, 13], X[9, 17, 10, 16], |
<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>PD[X[1, 4, 2, 5], X[3, 8, 4, 9], X[5, 12, 6, 13], X[9, 17, 10, 16], |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>5</nowiki></pre></td></tr> |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[7]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>5</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[DrawMorseLink[Knot[9, 25]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:9_25_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> |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[8]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>Show[DrawMorseLink[Knot[9, 25]]]</nowiki></pre></td></tr><tr><td></td><td align=left>[[Image:9_25_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> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>(#[Knot[9, 25]]&) /@ { |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[9]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki> (#[Knot[9, 25]]&) /@ { |
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SymmetryType, UnknottingNumber, ThreeGenus, |
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BridgeIndex, SuperBridgeIndex, NakanishiIndex |
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}</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Reversible, 2, 2, 3, {4, 7}, 1}</nowiki></pre></td></tr> |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>Out[9]= </nowiki></pre></td><td><pre style="color: black; border: 0px; padding: 0em"><nowiki>{Reversible, 2, 2, 3, {4, 7}, 1}</nowiki></pre></td></tr> |
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<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[Knot[9, 25]][t]</nowiki></pre></td></tr> |
<tr valign=top><td><pre style="color: blue; border: 0px; padding: 0em"><nowiki>In[10]:=</nowiki></pre></td><td><pre style="color: red; border: 0px; padding: 0em"><nowiki>alex = Alexander[Knot[9, 25]][t]</nowiki></pre></td></tr> |
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Revision as of 18:42, 31 August 2005
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 (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 9 25's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
| Planar diagram presentation | X1425 X3849 X5,12,6,13 X9,17,10,16 X13,18,14,1 X17,14,18,15 X15,11,16,10 X11,6,12,7 X7283 |
| Gauss code | -1, 9, -2, 1, -3, 8, -9, 2, -4, 7, -8, 3, -5, 6, -7, 4, -6, 5 |
| Dowker-Thistlethwaite code | 4 8 12 2 16 6 18 10 14 |
| Conway Notation | [22,21,2] |
| Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | |||||
Length is 10, width is 5, Braid index is 5 |
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 [{12, 4}, {3, 10}, {8, 11}, {10, 12}, {9, 5}, {4, 8}, {5, 2}, {1, 3}, {6, 9}, {2, 7}, {11, 6}, {7, 1}] |
[edit Notes on presentations of 9 25]
Computer Talk
The above data is available with the Mathematica package
KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
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AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
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K = Knot["9 25"];
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In[4]:=
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PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
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X1425 X3849 X5,12,6,13 X9,17,10,16 X13,18,14,1 X17,14,18,15 X15,11,16,10 X11,6,12,7 X7283 |
In[5]:=
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GaussCode[K]
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Out[5]=
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-1, 9, -2, 1, -3, 8, -9, 2, -4, 7, -8, 3, -5, 6, -7, 4, -6, 5 |
In[6]:=
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DTCode[K]
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Out[6]=
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4 8 12 2 16 6 18 10 14 |
(The path below may be different on your system)
In[7]:=
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AppendTo[$Path, "C:/bin/LinKnot/"];
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In[8]:=
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ConwayNotation[K]
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Out[8]=
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[22,21,2] |
In[9]:=
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br = BR[K]
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KnotTheory::credits: The minimum braids representing the knots with up to 10 crossings were provided by Thomas Gittings. See arXiv:math.GT/0401051.
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Out[9]=
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In[10]:=
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{First[br], Crossings[br], BraidIndex[K]}
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KnotTheory::credits: The braid index data known to KnotTheory` is taken from Charles Livingston's http://www.indiana.edu/~knotinfo/.
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KnotTheory::loading: Loading precomputed data in IndianaData`.
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Out[10]=
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{ 5, 10, 5 } |
In[11]:=
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Show[BraidPlot[br]]
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Out[11]=
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-Graphics- |
In[12]:=
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Show[DrawMorseLink[K]]
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KnotTheory::credits: "MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005."
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KnotTheory::credits: "DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005."
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Out[12]=
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-Graphics- |
In[13]:=
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ap = ArcPresentation[K]
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Out[13]=
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ArcPresentation[{12, 4}, {3, 10}, {8, 11}, {10, 12}, {9, 5}, {4, 8}, {5, 2}, {1, 3}, {6, 9}, {2, 7}, {11, 6}, {7, 1}] |
In[14]:=
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Draw[ap]
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Out[14]=
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-Graphics- |
Three dimensional invariants
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Four dimensional invariants
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Polynomial invariants
| Alexander polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -3 t^2+12 t-17+12 t^{-1} -3 t^{-2} } |
| Conway polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1-3 z^4} |
| 2nd Alexander ideal (db, data sources) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \{1\}} |
| Determinant and Signature | { 47, -2 } |
| Jones polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q-2+5 q^{-1} -7 q^{-2} +8 q^{-3} -8 q^{-4} +7 q^{-5} -5 q^{-6} +3 q^{-7} - q^{-8} } |
| HOMFLY-PT polynomial (db, data sources) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -a^8+3 z^2 a^6+3 a^6-2 z^4 a^4-4 z^2 a^4-3 a^4-z^4 a^2+a^2+z^2+1} |
| Kauffman polynomial (db, data sources) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^5 a^9-2 z^3 a^9+z a^9+3 z^6 a^8-7 z^4 a^8+4 z^2 a^8-a^8+3 z^7 a^7-4 z^5 a^7-2 z^3 a^7+z a^7+z^8 a^6+6 z^6 a^6-18 z^4 a^6+13 z^2 a^6-3 a^6+6 z^7 a^5-10 z^5 a^5+5 z^3 a^5-z a^5+z^8 a^4+6 z^6 a^4-15 z^4 a^4+13 z^2 a^4-3 a^4+3 z^7 a^3-3 z^5 a^3+3 z^3 a^3-z a^3+3 z^6 a^2-3 z^4 a^2+2 z^2 a^2-a^2+2 z^5 a-2 z^3 a+z^4-2 z^2+1} |
| The A2 invariant | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{26}-q^{24}+2 q^{22}+q^{18}+2 q^{16}-2 q^{14}-2 q^{10}+q^6-q^4+3 q^2+ q^{-4} } |
| The G2 invariant | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{128}-2 q^{126}+5 q^{124}-8 q^{122}+7 q^{120}-4 q^{118}-6 q^{116}+19 q^{114}-29 q^{112}+34 q^{110}-28 q^{108}+4 q^{106}+23 q^{104}-50 q^{102}+63 q^{100}-55 q^{98}+26 q^{96}+12 q^{94}-46 q^{92}+60 q^{90}-48 q^{88}+22 q^{86}+15 q^{84}-38 q^{82}+41 q^{80}-18 q^{78}-14 q^{76}+48 q^{74}-60 q^{72}+50 q^{70}-13 q^{68}-30 q^{66}+68 q^{64}-87 q^{62}+79 q^{60}-45 q^{58}-6 q^{56}+48 q^{54}-78 q^{52}+76 q^{50}-50 q^{48}+8 q^{46}+26 q^{44}-46 q^{42}+38 q^{40}-14 q^{38}-20 q^{36}+43 q^{34}-43 q^{32}+21 q^{30}+13 q^{28}-44 q^{26}+63 q^{24}-54 q^{22}+31 q^{20}-q^{18}-27 q^{16}+43 q^{14}-43 q^{12}+34 q^{10}-14 q^8+11 q^4-16 q^2+15-11 q^{-2} +8 q^{-4} -2 q^{-6} - q^{-8} +3 q^{-10} -3 q^{-12} +3 q^{-14} - q^{-16} + q^{-18} } |
Further Quantum Invariants
Further quantum knot invariants for 9_25.
A1 Invariants.
| Weight | Invariant |
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| 1 | |
| 2 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{48}-2 q^{46}-2 q^{44}+7 q^{42}-2 q^{40}-9 q^{38}+11 q^{36}+3 q^{34}-15 q^{32}+7 q^{30}+8 q^{28}-12 q^{26}+q^{24}+8 q^{22}-3 q^{20}-6 q^{18}+3 q^{16}+9 q^{14}-10 q^{12}-3 q^{10}+16 q^8-8 q^6-8 q^4+12 q^2-2-5 q^{-2} +4 q^{-4} - q^{-8} + q^{-10} } |
| 3 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{93}+2 q^{91}+2 q^{89}-3 q^{87}-7 q^{85}+2 q^{83}+16 q^{81}+q^{79}-23 q^{77}-12 q^{75}+29 q^{73}+29 q^{71}-29 q^{69}-46 q^{67}+19 q^{65}+59 q^{63}-2 q^{61}-68 q^{59}-15 q^{57}+66 q^{55}+30 q^{53}-55 q^{51}-40 q^{49}+44 q^{47}+44 q^{45}-29 q^{43}-44 q^{41}+11 q^{39}+40 q^{37}+7 q^{35}-36 q^{33}-28 q^{31}+29 q^{29}+46 q^{27}-17 q^{25}-61 q^{23}+3 q^{21}+70 q^{19}+14 q^{17}-69 q^{15}-25 q^{13}+55 q^{11}+36 q^9-39 q^7-35 q^5+24 q^3+27 q-8 q^{-1} -18 q^{-3} +3 q^{-5} +9 q^{-7} - q^{-9} -4 q^{-11} + q^{-13} + q^{-15} - q^{-19} + q^{-21} } |
| 4 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{152}-2 q^{150}-2 q^{148}+3 q^{146}+3 q^{144}+7 q^{142}-9 q^{140}-16 q^{138}-q^{136}+11 q^{134}+41 q^{132}-q^{130}-47 q^{128}-44 q^{126}-10 q^{124}+101 q^{122}+72 q^{120}-33 q^{118}-123 q^{116}-129 q^{114}+98 q^{112}+190 q^{110}+105 q^{108}-121 q^{106}-295 q^{104}-53 q^{102}+211 q^{100}+299 q^{98}+33 q^{96}-349 q^{94}-252 q^{92}+79 q^{90}+374 q^{88}+218 q^{86}-243 q^{84}-338 q^{82}-85 q^{80}+301 q^{78}+291 q^{76}-93 q^{74}-289 q^{72}-165 q^{70}+170 q^{68}+258 q^{66}+32 q^{64}-191 q^{62}-191 q^{60}+36 q^{58}+196 q^{56}+152 q^{54}-78 q^{52}-215 q^{50}-129 q^{48}+113 q^{46}+288 q^{44}+76 q^{42}-208 q^{40}-305 q^{38}-32 q^{36}+357 q^{34}+254 q^{32}-95 q^{30}-388 q^{28}-210 q^{26}+269 q^{24}+329 q^{22}+82 q^{20}-286 q^{18}-287 q^{16}+78 q^{14}+232 q^{12}+171 q^{10}-100 q^8-202 q^6-36 q^4+74 q^2+119+7 q^{-2} -73 q^{-4} -33 q^{-6} -2 q^{-8} +40 q^{-10} +13 q^{-12} -14 q^{-14} -4 q^{-16} -7 q^{-18} +7 q^{-20} +2 q^{-22} -3 q^{-24} +2 q^{-26} -2 q^{-28} + q^{-30} - q^{-34} + q^{-36} } |
| 5 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{225}+2 q^{223}+2 q^{221}-3 q^{219}-3 q^{217}-3 q^{215}+9 q^{211}+16 q^{209}+q^{207}-20 q^{205}-29 q^{203}-19 q^{201}+19 q^{199}+61 q^{197}+65 q^{195}-8 q^{193}-97 q^{191}-128 q^{189}-59 q^{187}+101 q^{185}+232 q^{183}+192 q^{181}-50 q^{179}-314 q^{177}-380 q^{175}-132 q^{173}+317 q^{171}+608 q^{169}+433 q^{167}-179 q^{165}-764 q^{163}-819 q^{161}-168 q^{159}+769 q^{157}+1205 q^{155}+673 q^{153}-549 q^{151}-1463 q^{149}-1236 q^{147}+92 q^{145}+1502 q^{143}+1753 q^{141}+499 q^{139}-1299 q^{137}-2079 q^{135}-1103 q^{133}+880 q^{131}+2172 q^{129}+1600 q^{127}-375 q^{125}-2039 q^{123}-1894 q^{121}-105 q^{119}+1723 q^{117}+1983 q^{115}+488 q^{113}-1347 q^{111}-1887 q^{109}-723 q^{107}+973 q^{105}+1668 q^{103}+846 q^{101}-645 q^{99}-1424 q^{97}-882 q^{95}+374 q^{93}+1185 q^{91}+903 q^{89}-124 q^{87}-979 q^{85}-964 q^{83}-132 q^{81}+798 q^{79}+1067 q^{77}+447 q^{75}-597 q^{73}-1215 q^{71}-837 q^{69}+336 q^{67}+1349 q^{65}+1278 q^{63}+33 q^{61}-1400 q^{59}-1722 q^{57}-511 q^{55}+1301 q^{53}+2085 q^{51}+1038 q^{49}-1011 q^{47}-2255 q^{45}-1542 q^{43}+537 q^{41}+2191 q^{39}+1913 q^{37}-10 q^{35}-1840 q^{33}-2044 q^{31}-521 q^{29}+1324 q^{27}+1924 q^{25}+878 q^{23}-749 q^{21}-1559 q^{19}-1024 q^{17}+235 q^{15}+1098 q^{13}+964 q^{11}+102 q^9-649 q^7-735 q^5-264 q^3+292 q+489 q^{-1} +271 q^{-3} -86 q^{-5} -266 q^{-7} -199 q^{-9} -12 q^{-11} +122 q^{-13} +116 q^{-15} +34 q^{-17} -43 q^{-19} -59 q^{-21} -23 q^{-23} +13 q^{-25} +20 q^{-27} +12 q^{-29} +3 q^{-31} -10 q^{-33} -6 q^{-35} +3 q^{-37} +3 q^{-43} - q^{-45} -2 q^{-47} + q^{-49} - q^{-53} + q^{-55} } |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{26}-q^{24}+2 q^{22}+q^{18}+2 q^{16}-2 q^{14}-2 q^{10}+q^6-q^4+3 q^2+ q^{-4} } |
| 1,1 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{68}-4 q^{66}+12 q^{64}-28 q^{62}+52 q^{60}-86 q^{58}+130 q^{56}-176 q^{54}+212 q^{52}-234 q^{50}+232 q^{48}-194 q^{46}+126 q^{44}-30 q^{42}-80 q^{40}+196 q^{38}-303 q^{36}+380 q^{34}-432 q^{32}+438 q^{30}-410 q^{28}+342 q^{26}-244 q^{24}+138 q^{22}-19 q^{20}-76 q^{18}+154 q^{16}-198 q^{14}+214 q^{12}-206 q^{10}+174 q^8-142 q^6+107 q^4-74 q^2+50-30 q^{-2} +21 q^{-4} -10 q^{-6} +6 q^{-8} -2 q^{-10} + q^{-12} } |
| 2,0 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{66}+q^{64}-q^{62}-4 q^{60}-2 q^{58}+4 q^{56}+2 q^{54}-3 q^{52}+8 q^{48}+5 q^{46}-8 q^{44}-5 q^{42}+4 q^{40}-q^{38}-8 q^{36}-3 q^{34}+6 q^{32}+q^{30}-q^{28}+4 q^{26}+q^{24}-2 q^{22}+5 q^{20}+4 q^{18}-7 q^{16}-2 q^{14}+7 q^{12}+q^{10}-9 q^8-2 q^6+9 q^4-5+ q^{-2} +4 q^{-4} + q^{-6} - q^{-8} + q^{-12} } |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{54}-2 q^{52}+q^{50}+3 q^{48}-7 q^{46}+3 q^{44}+4 q^{42}-11 q^{40}+6 q^{38}+7 q^{36}-10 q^{34}+4 q^{32}+7 q^{30}-5 q^{28}-q^{26}+3 q^{24}+2 q^{22}-4 q^{20}-4 q^{18}+8 q^{16}-5 q^{14}-8 q^{12}+12 q^{10}-3 q^8-7 q^6+10 q^4-3+4 q^{-2} + q^{-4} - q^{-6} + q^{-8} } |
| 1,0,0 |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^{54}+2 q^{52}-5 q^{50}+7 q^{48}-9 q^{46}+11 q^{44}-12 q^{42}+11 q^{40}-8 q^{38}+5 q^{36}+2 q^{34}-6 q^{32}+13 q^{30}-17 q^{28}+21 q^{26}-23 q^{24}+20 q^{22}-18 q^{20}+12 q^{18}-8 q^{16}+q^{14}+4 q^{12}-8 q^{10}+11 q^8-11 q^6+12 q^4-8 q^2+7-4 q^{-2} +3 q^{-4} - q^{-6} + q^{-8} } |
| 1,0 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{88}-2 q^{84}-2 q^{82}+3 q^{80}+5 q^{78}-2 q^{76}-8 q^{74}-3 q^{72}+9 q^{70}+8 q^{68}-7 q^{66}-12 q^{64}+q^{62}+13 q^{60}+6 q^{58}-10 q^{56}-8 q^{54}+5 q^{52}+9 q^{50}-2 q^{48}-8 q^{46}+8 q^{42}+2 q^{40}-8 q^{38}-3 q^{36}+7 q^{34}+6 q^{32}-6 q^{30}-8 q^{28}+4 q^{26}+10 q^{24}-2 q^{22}-12 q^{20}-3 q^{18}+11 q^{16}+8 q^{14}-7 q^{12}-11 q^{10}+q^8+11 q^6+4 q^4-4 q^2-5+ q^{-2} +4 q^{-4} +2 q^{-6} - q^{-8} - q^{-10} + q^{-14} } |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{128}-2 q^{126}+5 q^{124}-8 q^{122}+7 q^{120}-4 q^{118}-6 q^{116}+19 q^{114}-29 q^{112}+34 q^{110}-28 q^{108}+4 q^{106}+23 q^{104}-50 q^{102}+63 q^{100}-55 q^{98}+26 q^{96}+12 q^{94}-46 q^{92}+60 q^{90}-48 q^{88}+22 q^{86}+15 q^{84}-38 q^{82}+41 q^{80}-18 q^{78}-14 q^{76}+48 q^{74}-60 q^{72}+50 q^{70}-13 q^{68}-30 q^{66}+68 q^{64}-87 q^{62}+79 q^{60}-45 q^{58}-6 q^{56}+48 q^{54}-78 q^{52}+76 q^{50}-50 q^{48}+8 q^{46}+26 q^{44}-46 q^{42}+38 q^{40}-14 q^{38}-20 q^{36}+43 q^{34}-43 q^{32}+21 q^{30}+13 q^{28}-44 q^{26}+63 q^{24}-54 q^{22}+31 q^{20}-q^{18}-27 q^{16}+43 q^{14}-43 q^{12}+34 q^{10}-14 q^8+11 q^4-16 q^2+15-11 q^{-2} +8 q^{-4} -2 q^{-6} - q^{-8} +3 q^{-10} -3 q^{-12} +3 q^{-14} - q^{-16} + q^{-18} } |
.
Computer Talk
The above data is available with the Mathematica package
KnotTheory`, as shown in the (simulated) Mathematica session below. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting. This Mathematica session is also available (albeit only for the knot 5_2) as the notebook PolynomialInvariantsSession.nb.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
|
AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
|
In[3]:=
|
K = Knot["9 25"];
|
In[4]:=
|
Alexander[K][t]
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
Out[4]=
|
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -3 t^2+12 t-17+12 t^{-1} -3 t^{-2} } |
In[5]:=
|
Conway[K][z]
|
Out[5]=
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Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1-3 z^4} |
In[6]:=
|
Alexander[K, 2][t]
|
KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.
|
Out[6]=
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Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \{1\}} |
In[7]:=
|
{KnotDet[K], KnotSignature[K]}
|
Out[7]=
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{ 47, -2 } |
In[8]:=
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Jones[K][q]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[8]=
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Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q-2+5 q^{-1} -7 q^{-2} +8 q^{-3} -8 q^{-4} +7 q^{-5} -5 q^{-6} +3 q^{-7} - q^{-8} } |
In[9]:=
|
HOMFLYPT[K][a, z]
|
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
|
Out[9]=
|
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -a^8+3 z^2 a^6+3 a^6-2 z^4 a^4-4 z^2 a^4-3 a^4-z^4 a^2+a^2+z^2+1} |
In[10]:=
|
Kauffman[K][a, z]
|
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
|
Out[10]=
|
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^5 a^9-2 z^3 a^9+z a^9+3 z^6 a^8-7 z^4 a^8+4 z^2 a^8-a^8+3 z^7 a^7-4 z^5 a^7-2 z^3 a^7+z a^7+z^8 a^6+6 z^6 a^6-18 z^4 a^6+13 z^2 a^6-3 a^6+6 z^7 a^5-10 z^5 a^5+5 z^3 a^5-z a^5+z^8 a^4+6 z^6 a^4-15 z^4 a^4+13 z^2 a^4-3 a^4+3 z^7 a^3-3 z^5 a^3+3 z^3 a^3-z a^3+3 z^6 a^2-3 z^4 a^2+2 z^2 a^2-a^2+2 z^5 a-2 z^3 a+z^4-2 z^2+1} |
"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {K11n134,}
Same Jones Polynomial (up to mirroring, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q\leftrightarrow q^{-1}} ): {K11n25,}
Computer Talk
The above data is available with the Mathematica package
KnotTheory`. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting.
(The path below may be different on your system, and possibly also the KnotTheory` date)
In[1]:=
|
AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
|
Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
|
In[3]:=
|
K = Knot["9 25"];
|
In[4]:=
|
{A = Alexander[K][t], J = Jones[K][q]}
|
KnotTheory::loading: Loading precomputed data in PD4Knots`.
|
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
|
Out[4]=
|
{ Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -3 t^2+12 t-17+12 t^{-1} -3 t^{-2} } , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q-2+5 q^{-1} -7 q^{-2} +8 q^{-3} -8 q^{-4} +7 q^{-5} -5 q^{-6} +3 q^{-7} - q^{-8} } } |
In[5]:=
|
DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]
|
KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.
|
KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.
|
Out[5]=
|
{K11n134,} |
In[6]:=
|
DeleteCases[
Select[
AllKnots[],
(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) &
],
K
]
|
KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
|
Out[6]=
|
{K11n25,} |
Vassiliev invariants
| V2 and V3: | (0, -1) |
| V2,1 through V6,9: |
|
V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.
Khovanov Homology
| The coefficients of the monomials Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^rq^j} are shown, along with their alternating sums Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \chi} (fixed Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j} , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j-2r=s+1} or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle j-2r=s-1} , where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle s=} -2 is the signature of 9 25. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
|
| Integral Khovanov Homology
(db, data source) |
|
The Coloured Jones Polynomials
The Coloured Jones Polynomials (in the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n+1}
-dimensional representation of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle sl(2)}
)
| Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle J_n} |
| 2 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^4-2 q^3+q^2+5 q-11+4 q^{-1} +19 q^{-2} -31 q^{-3} +4 q^{-4} +43 q^{-5} -50 q^{-6} -3 q^{-7} +62 q^{-8} -56 q^{-9} -12 q^{-10} +65 q^{-11} -45 q^{-12} -19 q^{-13} +52 q^{-14} -25 q^{-15} -20 q^{-16} +30 q^{-17} -7 q^{-18} -12 q^{-19} +10 q^{-20} -3 q^{-22} + q^{-23} } |
| 3 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^9-2 q^8+q^7+q^6+q^5-7 q^4+4 q^3+11 q^2-5 q-28+14 q^{-1} +46 q^{-2} -8 q^{-3} -87 q^{-4} +10 q^{-5} +121 q^{-6} +11 q^{-7} -167 q^{-8} -34 q^{-9} +204 q^{-10} +67 q^{-11} -234 q^{-12} -98 q^{-13} +248 q^{-14} +130 q^{-15} -251 q^{-16} -155 q^{-17} +240 q^{-18} +173 q^{-19} -218 q^{-20} -184 q^{-21} +185 q^{-22} +188 q^{-23} -145 q^{-24} -184 q^{-25} +101 q^{-26} +173 q^{-27} -60 q^{-28} -148 q^{-29} +20 q^{-30} +120 q^{-31} +6 q^{-32} -87 q^{-33} -20 q^{-34} +55 q^{-35} +23 q^{-36} -29 q^{-37} -20 q^{-38} +14 q^{-39} +12 q^{-40} -5 q^{-41} -5 q^{-42} +3 q^{-44} - q^{-45} } |
| 4 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{16}-2 q^{15}+q^{14}+q^{13}-3 q^{12}+5 q^{11}-7 q^{10}+6 q^9+6 q^8-17 q^7+8 q^6-17 q^5+33 q^4+33 q^3-59 q^2-23 q-57+113 q^{-1} +145 q^{-2} -104 q^{-3} -133 q^{-4} -223 q^{-5} +215 q^{-6} +416 q^{-7} -43 q^{-8} -287 q^{-9} -588 q^{-10} +216 q^{-11} +784 q^{-12} +204 q^{-13} -347 q^{-14} -1067 q^{-15} +38 q^{-16} +1077 q^{-17} +553 q^{-18} -244 q^{-19} -1456 q^{-20} -235 q^{-21} +1174 q^{-22} +837 q^{-23} -32 q^{-24} -1631 q^{-25} -477 q^{-26} +1088 q^{-27} +974 q^{-28} +198 q^{-29} -1587 q^{-30} -637 q^{-31} +861 q^{-32} +974 q^{-33} +421 q^{-34} -1361 q^{-35} -725 q^{-36} +526 q^{-37} +850 q^{-38} +617 q^{-39} -977 q^{-40} -715 q^{-41} +140 q^{-42} +597 q^{-43} +712 q^{-44} -516 q^{-45} -559 q^{-46} -155 q^{-47} +266 q^{-48} +615 q^{-49} -134 q^{-50} -293 q^{-51} -243 q^{-52} +2 q^{-53} +373 q^{-54} +40 q^{-55} -67 q^{-56} -158 q^{-57} -90 q^{-58} +146 q^{-59} +46 q^{-60} +23 q^{-61} -53 q^{-62} -61 q^{-63} +35 q^{-64} +12 q^{-65} +20 q^{-66} -7 q^{-67} -19 q^{-68} +5 q^{-69} +5 q^{-71} -3 q^{-73} + q^{-74} } |
| 5 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{25}-2 q^{24}+q^{23}+q^{22}-3 q^{21}+q^{20}+5 q^{19}-5 q^{18}+q^{17}+4 q^{16}-12 q^{15}-3 q^{14}+18 q^{13}+4 q^{12}+9 q^{11}-3 q^{10}-48 q^9-39 q^8+34 q^7+81 q^6+91 q^5+3 q^4-182 q^3-226 q^2-33 q+261+448 q^{-1} +221 q^{-2} -379 q^{-3} -782 q^{-4} -504 q^{-5} +347 q^{-6} +1199 q^{-7} +1083 q^{-8} -245 q^{-9} -1645 q^{-10} -1763 q^{-11} -188 q^{-12} +2009 q^{-13} +2710 q^{-14} +801 q^{-15} -2245 q^{-16} -3608 q^{-17} -1711 q^{-18} +2213 q^{-19} +4540 q^{-20} +2724 q^{-21} -1967 q^{-22} -5262 q^{-23} -3790 q^{-24} +1500 q^{-25} +5784 q^{-26} +4773 q^{-27} -920 q^{-28} -6046 q^{-29} -5602 q^{-30} +289 q^{-31} +6106 q^{-32} +6206 q^{-33} +325 q^{-34} -5975 q^{-35} -6615 q^{-36} -884 q^{-37} +5728 q^{-38} +6824 q^{-39} +1369 q^{-40} -5355 q^{-41} -6884 q^{-42} -1814 q^{-43} +4896 q^{-44} +6809 q^{-45} +2224 q^{-46} -4328 q^{-47} -6602 q^{-48} -2625 q^{-49} +3640 q^{-50} +6267 q^{-51} +3003 q^{-52} -2837 q^{-53} -5780 q^{-54} -3320 q^{-55} +1944 q^{-56} +5103 q^{-57} +3543 q^{-58} -1002 q^{-59} -4285 q^{-60} -3580 q^{-61} +116 q^{-62} +3314 q^{-63} +3398 q^{-64} +662 q^{-65} -2310 q^{-66} -3008 q^{-67} -1176 q^{-68} +1331 q^{-69} +2422 q^{-70} +1442 q^{-71} -512 q^{-72} -1754 q^{-73} -1427 q^{-74} -79 q^{-75} +1094 q^{-76} +1215 q^{-77} +402 q^{-78} -532 q^{-79} -895 q^{-80} -515 q^{-81} +157 q^{-82} +564 q^{-83} +457 q^{-84} +53 q^{-85} -283 q^{-86} -340 q^{-87} -134 q^{-88} +115 q^{-89} +209 q^{-90} +119 q^{-91} -19 q^{-92} -98 q^{-93} -94 q^{-94} -16 q^{-95} +49 q^{-96} +50 q^{-97} +12 q^{-98} -9 q^{-99} -21 q^{-100} -20 q^{-101} +7 q^{-102} +12 q^{-103} +2 q^{-104} -5 q^{-107} +3 q^{-109} - q^{-110} } |
| 6 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{36}-2 q^{35}+q^{34}+q^{33}-3 q^{32}+q^{31}+q^{30}+7 q^{29}-10 q^{28}-q^{27}+9 q^{26}-13 q^{25}+q^{24}+9 q^{23}+28 q^{22}-24 q^{21}-19 q^{20}+13 q^{19}-46 q^{18}-4 q^{17}+51 q^{16}+119 q^{15}-15 q^{14}-69 q^{13}-52 q^{12}-220 q^{11}-82 q^{10}+166 q^9+468 q^8+248 q^7-36 q^6-281 q^5-904 q^4-671 q^3+129 q^2+1296 q+1406+843 q^{-1} -286 q^{-2} -2463 q^{-3} -2814 q^{-4} -1280 q^{-5} +2022 q^{-6} +3948 q^{-7} +4080 q^{-8} +1692 q^{-9} -3997 q^{-10} -7111 q^{-11} -6048 q^{-12} +341 q^{-13} +6591 q^{-14} +10268 q^{-15} +7942 q^{-16} -2671 q^{-17} -11812 q^{-18} -14534 q^{-19} -6166 q^{-20} +6068 q^{-21} +17110 q^{-22} +18345 q^{-23} +3858 q^{-24} -13313 q^{-25} -23788 q^{-26} -16818 q^{-27} +302 q^{-28} +20740 q^{-29} +29289 q^{-30} +14325 q^{-31} -9763 q^{-32} -29726 q^{-33} -27651 q^{-34} -8996 q^{-35} +19526 q^{-36} +36660 q^{-37} +24647 q^{-38} -2982 q^{-39} -30850 q^{-40} -34893 q^{-41} -17980 q^{-42} +15180 q^{-43} +39209 q^{-44} +31596 q^{-45} +3769 q^{-46} -28659 q^{-47} -37739 q^{-48} -24145 q^{-49} +10297 q^{-50} +38309 q^{-51} +34815 q^{-52} +8783 q^{-53} -25138 q^{-54} -37536 q^{-55} -27577 q^{-56} +5901 q^{-57} +35503 q^{-58} +35603 q^{-59} +12527 q^{-60} -20802 q^{-61} -35488 q^{-62} -29521 q^{-63} +1281 q^{-64} +30969 q^{-65} +34848 q^{-66} +16129 q^{-67} -14860 q^{-68} -31473 q^{-69} -30505 q^{-70} -4448 q^{-71} +23891 q^{-72} +32060 q^{-73} +19627 q^{-74} -6779 q^{-75} -24549 q^{-76} -29514 q^{-77} -10684 q^{-78} +14058 q^{-79} +25993 q^{-80} +21279 q^{-81} +2141 q^{-82} -14620 q^{-83} -24835 q^{-84} -14902 q^{-85} +3352 q^{-86} +16539 q^{-87} +18845 q^{-88} +8669 q^{-89} -3934 q^{-90} -16341 q^{-91} -14471 q^{-92} -4504 q^{-93} +6245 q^{-94} +12251 q^{-95} +10001 q^{-96} +3585 q^{-97} -6897 q^{-98} -9567 q^{-99} -6822 q^{-100} -880 q^{-101} +4656 q^{-102} +6712 q^{-103} +5644 q^{-104} -498 q^{-105} -3620 q^{-106} -4667 q^{-107} -2986 q^{-108} -165 q^{-109} +2389 q^{-110} +3804 q^{-111} +1480 q^{-112} -58 q^{-113} -1619 q^{-114} -1905 q^{-115} -1366 q^{-116} -17 q^{-117} +1418 q^{-118} +950 q^{-119} +732 q^{-120} -54 q^{-121} -510 q^{-122} -820 q^{-123} -452 q^{-124} +252 q^{-125} +207 q^{-126} +391 q^{-127} +194 q^{-128} +39 q^{-129} -248 q^{-130} -225 q^{-131} +3 q^{-132} -31 q^{-133} +92 q^{-134} +80 q^{-135} +76 q^{-136} -45 q^{-137} -57 q^{-138} - q^{-139} -29 q^{-140} +9 q^{-141} +12 q^{-142} +29 q^{-143} -7 q^{-144} -12 q^{-145} +5 q^{-146} -7 q^{-147} +5 q^{-150} -3 q^{-152} + q^{-153} } |
| 7 | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q^{49}-2 q^{48}+q^{47}+q^{46}-3 q^{45}+q^{44}+q^{43}+3 q^{42}+2 q^{41}-12 q^{40}+4 q^{39}+8 q^{38}-9 q^{37}+2 q^{36}+2 q^{35}+15 q^{34}+8 q^{33}-47 q^{32}-4 q^{31}+20 q^{30}-8 q^{29}+23 q^{28}+17 q^{27}+58 q^{26}+23 q^{25}-143 q^{24}-96 q^{23}-36 q^{22}-9 q^{21}+152 q^{20}+191 q^{19}+277 q^{18}+144 q^{17}-377 q^{16}-540 q^{15}-567 q^{14}-327 q^{13}+414 q^{12}+954 q^{11}+1430 q^{10}+1109 q^9-402 q^8-1739 q^7-2768 q^6-2573 q^5-380 q^4+2316 q^3+5012 q^2+5548 q+2388-2370 q^{-1} -7721 q^{-2} -10214 q^{-3} -6877 q^{-4} +623 q^{-5} +10484 q^{-6} +16861 q^{-7} +14375 q^{-8} +4244 q^{-9} -11540 q^{-10} -24697 q^{-11} -25884 q^{-12} -13868 q^{-13} +9592 q^{-14} +32412 q^{-15} +40381 q^{-16} +28983 q^{-17} -1848 q^{-18} -37526 q^{-19} -57242 q^{-20} -49960 q^{-21} -12323 q^{-22} +38102 q^{-23} +73166 q^{-24} +74995 q^{-25} +34149 q^{-26} -31469 q^{-27} -86279 q^{-28} -102321 q^{-29} -61840 q^{-30} +17521 q^{-31} +93437 q^{-32} +128109 q^{-33} +93677 q^{-34} +3851 q^{-35} -93581 q^{-36} -150173 q^{-37} -126202 q^{-38} -30131 q^{-39} +86429 q^{-40} +165930 q^{-41} +156317 q^{-42} +58993 q^{-43} -73228 q^{-44} -174769 q^{-45} -181702 q^{-46} -87249 q^{-47} +56185 q^{-48} +176989 q^{-49} +200831 q^{-50} +112483 q^{-51} -37527 q^{-52} -173938 q^{-53} -213557 q^{-54} -133252 q^{-55} +19431 q^{-56} +167410 q^{-57} +220610 q^{-58} +149010 q^{-59} -3390 q^{-60} -159021 q^{-61} -223169 q^{-62} -160099 q^{-63} -10179 q^{-64} +150009 q^{-65} +222740 q^{-66} +167515 q^{-67} +21258 q^{-68} -141101 q^{-69} -220251 q^{-70} -172291 q^{-71} -30665 q^{-72} +132140 q^{-73} +216507 q^{-74} +175603 q^{-75} +39315 q^{-76} -122795 q^{-77} -211642 q^{-78} -178042 q^{-79} -48156 q^{-80} +112108 q^{-81} +205276 q^{-82} +180019 q^{-83} +58062 q^{-84} -99274 q^{-85} -196848 q^{-86} -181260 q^{-87} -69252 q^{-88} +83491 q^{-89} +185321 q^{-90} +181081 q^{-91} +81626 q^{-92} -64344 q^{-93} -169860 q^{-94} -178470 q^{-95} -94293 q^{-96} +42096 q^{-97} +149911 q^{-98} +172010 q^{-99} +105726 q^{-100} -17597 q^{-101} -125246 q^{-102} -160638 q^{-103} -114329 q^{-104} -7281 q^{-105} +96865 q^{-106} +143639 q^{-107} +117833 q^{-108} +30299 q^{-109} -66111 q^{-110} -121194 q^{-111} -115123 q^{-112} -49018 q^{-113} +35809 q^{-114} +94658 q^{-115} +105401 q^{-116} +61050 q^{-117} -8534 q^{-118} -66080 q^{-119} -89559 q^{-120} -65447 q^{-121} -12985 q^{-122} +38731 q^{-123} +69413 q^{-124} +62059 q^{-125} +26964 q^{-126} -15169 q^{-127} -47756 q^{-128} -52635 q^{-129} -33026 q^{-130} -2300 q^{-131} +27660 q^{-132} +39557 q^{-133} +32200 q^{-134} +12759 q^{-135} -11470 q^{-136} -25676 q^{-137} -26572 q^{-138} -16839 q^{-139} +373 q^{-140} +13644 q^{-141} +18824 q^{-142} +16002 q^{-143} +5406 q^{-144} -4743 q^{-145} -11038 q^{-146} -12491 q^{-147} -7209 q^{-148} -564 q^{-149} +5046 q^{-150} +8191 q^{-151} +6327 q^{-152} +2770 q^{-153} -1113 q^{-154} -4371 q^{-155} -4446 q^{-156} -3090 q^{-157} -820 q^{-158} +1866 q^{-159} +2551 q^{-160} +2323 q^{-161} +1311 q^{-162} -374 q^{-163} -1079 q^{-164} -1465 q^{-165} -1226 q^{-166} -177 q^{-167} +368 q^{-168} +717 q^{-169} +757 q^{-170} +279 q^{-171} +71 q^{-172} -258 q^{-173} -484 q^{-174} -237 q^{-175} -99 q^{-176} +92 q^{-177} +198 q^{-178} +94 q^{-179} +115 q^{-180} +37 q^{-181} -100 q^{-182} -75 q^{-183} -62 q^{-184} -4 q^{-185} +42 q^{-186} -3 q^{-187} +29 q^{-188} +29 q^{-189} -9 q^{-190} -12 q^{-191} -20 q^{-192} -2 q^{-193} +12 q^{-194} -5 q^{-195} +7 q^{-197} -5 q^{-200} +3 q^{-202} - q^{-203} } |
Computer Talk
Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session, or any of the Computer Talk sections above.
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Rolfsen Knot Page master template (intermediate). See/edit the Rolfsen_Splice_Base (expert). Back to the top. |
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