9 34
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![]() (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 9 34's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
| Planar diagram presentation | X6271 X16,8,17,7 X8394 X2,15,3,16 X14,9,15,10 X10,6,11,5 X4,14,5,13 X18,11,1,12 X12,17,13,18 |
| Gauss code | 1, -4, 3, -7, 6, -1, 2, -3, 5, -6, 8, -9, 7, -5, 4, -2, 9, -8 |
| Dowker-Thistlethwaite code | 6 8 10 16 14 18 4 2 12 |
| Conway Notation | [8*20] |
| Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | ||||
Length is 9, width is 4, Braid index is 4 |
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![]() [{7, 11}, {10, 2}, {11, 4}, {3, 9}, {5, 10}, {4, 8}, {9, 6}, {1, 5}, {2, 7}, {6, 1}, {8, 3}] |
[edit Notes on presentations of 9 34]
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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
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K = Knot["9 34"];
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In[4]:=
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PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
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X6271 X16,8,17,7 X8394 X2,15,3,16 X14,9,15,10 X10,6,11,5 X4,14,5,13 X18,11,1,12 X12,17,13,18 |
In[5]:=
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GaussCode[K]
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Out[5]=
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1, -4, 3, -7, 6, -1, 2, -3, 5, -6, 8, -9, 7, -5, 4, -2, 9, -8 |
In[6]:=
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DTCode[K]
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Out[6]=
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6 8 10 16 14 18 4 2 12 |
(The path below may be different on your system)
In[7]:=
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AppendTo[$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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[8*20] |
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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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 \textrm{BR}(4,\{-1,2,-1,2,-3,2,-1,2,-3\})} |
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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{ 4, 9, 4 } |
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[{7, 11}, {10, 2}, {11, 4}, {3, 9}, {5, 10}, {4, 8}, {9, 6}, {1, 5}, {2, 7}, {6, 1}, {8, 3}] |
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 -t^3+6 t^2-16 t+23-16 t^{-1} +6 t^{-2} - t^{-3} } |
| 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 -z^6-z^2+1} |
| 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 | { 69, 0 } |
| 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^4-4 q^3+8 q^2-10 q+12-12 q^{-1} +10 q^{-2} -7 q^{-3} +4 q^{-4} - q^{-5} } |
| HOMFLY-PT polynomial (db, data sources) | |
| Kauffman polynomial (db, data sources) | |
| The A2 invariant | |
| The G2 invariant |
A1 Invariants.
| Weight | Invariant |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 | |
| 1,1 | |
| 2,0 |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | |
| 1,0,0 |
A4 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0,0 | |
| 1,0,0,0 |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | |
| 1,0 |
D4 Invariants.
| Weight | Invariant |
|---|---|
| 1,0,0,0 |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 1,0 |
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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]:=
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AppendTo[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of August 31, 2006, 11:25:27.5625.
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In[3]:=
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K = Knot["9 34"];
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In[4]:=
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Alexander[K][t]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
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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 -t^3+6 t^2-16 t+23-16 t^{-1} +6 t^{-2} - t^{-3} } |
In[5]:=
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Conway[K][z]
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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 -z^6-z^2+1} |
In[6]:=
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Alexander[K, 2][t]
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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.
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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]:=
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{KnotDet[K], KnotSignature[K]}
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Out[7]=
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{ 69, 0 } |
In[8]:=
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Jones[K][q]
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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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^4-4 q^3+8 q^2-10 q+12-12 q^{-1} +10 q^{-2} -7 q^{-3} +4 q^{-4} - q^{-5} } |
In[9]:=
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HOMFLYPT[K][a, z]
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KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
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Out[9]=
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In[10]:=
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Kauffman[K][a, z]
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KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
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Out[10]=
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"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {K11n32, K11n119,}
Same Jones Polynomial (up to mirroring, ): {}
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 34"];
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In[4]:=
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{A = Alexander[K][t], J = Jones[K][q]}
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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KnotTheory::loading: Loading precomputed data in Jones4Knots`.
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Out[4]=
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{ , } |
In[5]:=
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DeleteCases[Select[AllKnots[], (A === Alexander[#][t]) &], K]
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KnotTheory::loading: Loading precomputed data in DTCode4KnotsTo11`.
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KnotTheory::credits: The GaussCode to PD conversion was written by Siddarth Sankaran at the University of Toronto in the summer of 2005.
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Out[5]=
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{K11n32, K11n119,} |
In[6]:=
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DeleteCases[
Select[
AllKnots[],
(J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) &
],
K
]
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KnotTheory::loading: Loading precomputed data in Jones4Knots11`.
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Out[6]=
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{} |
Vassiliev invariants
| V2 and V3: | (-1, 0) |
| V2,1 through V6,9: |
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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 are shown, along with their alternating sums (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 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 r} ). 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=} 0 is the signature of 9 34. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. |
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| Integral Khovanov Homology
(db, data source) |
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The Coloured Jones Polynomials
| 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^{12}-4 q^{11}+4 q^{10}+10 q^9-29 q^8+12 q^7+47 q^6-74 q^5+6 q^4+101 q^3-109 q^2-17 q+140-112 q^{-1} -41 q^{-2} +143 q^{-3} -83 q^{-4} -54 q^{-5} +109 q^{-6} -39 q^{-7} -48 q^{-8} +55 q^{-9} -6 q^{-10} -24 q^{-11} +14 q^{-12} +2 q^{-13} -4 q^{-14} + q^{-15} } |
| 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^{24}-4 q^{23}+4 q^{22}+6 q^{21}-9 q^{20}-19 q^{19}+20 q^{18}+56 q^{17}-42 q^{16}-116 q^{15}+49 q^{14}+214 q^{13}-26 q^{12}-350 q^{11}-25 q^{10}+482 q^9+132 q^8-611 q^7-258 q^6+693 q^5+410 q^4-747 q^3-536 q^2+741 q+652-707 q^{-1} -728 q^{-2} +632 q^{-3} +778 q^{-4} -532 q^{-5} -793 q^{-6} +410 q^{-7} +771 q^{-8} -269 q^{-9} -714 q^{-10} +126 q^{-11} +623 q^{-12} -7 q^{-13} -492 q^{-14} -87 q^{-15} +354 q^{-16} +129 q^{-17} -218 q^{-18} -130 q^{-19} +113 q^{-20} +97 q^{-21} -40 q^{-22} -63 q^{-23} +12 q^{-24} +27 q^{-25} -9 q^{-27} -2 q^{-28} +4 q^{-29} - q^{-30} } |
| 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^{40}-4 q^{39}+4 q^{38}+6 q^{37}-13 q^{36}+q^{35}-11 q^{34}+39 q^{33}+37 q^{32}-90 q^{31}-49 q^{30}-48 q^{29}+221 q^{28}+257 q^{27}-272 q^{26}-385 q^{25}-384 q^{24}+633 q^{23}+1098 q^{22}-183 q^{21}-1115 q^{20}-1643 q^{19}+743 q^{18}+2693 q^{17}+949 q^{16}-1582 q^{15}-3886 q^{14}-277 q^{13}+4168 q^{12}+3112 q^{11}-926 q^{10}-6066 q^9-2301 q^8+4550 q^7+5225 q^6+689 q^5-7160 q^4-4285 q^3+3852 q^2+6391 q+2405-7085 q^{-1} -5517 q^{-2} +2637 q^{-3} +6547 q^{-4} +3731 q^{-5} -6164 q^{-6} -5993 q^{-7} +1158 q^{-8} +5920 q^{-9} +4680 q^{-10} -4533 q^{-11} -5807 q^{-12} -524 q^{-13} +4516 q^{-14} +5119 q^{-15} -2308 q^{-16} -4761 q^{-17} -2001 q^{-18} +2412 q^{-19} +4597 q^{-20} -136 q^{-21} -2852 q^{-22} -2485 q^{-23} +330 q^{-24} +3002 q^{-25} +993 q^{-26} -861 q^{-27} -1744 q^{-28} -721 q^{-29} +1195 q^{-30} +844 q^{-31} +189 q^{-32} -641 q^{-33} -622 q^{-34} +191 q^{-35} +277 q^{-36} +256 q^{-37} -76 q^{-38} -211 q^{-39} -15 q^{-40} +17 q^{-41} +74 q^{-42} +12 q^{-43} -33 q^{-44} -3 q^{-45} -5 q^{-46} +9 q^{-47} +2 q^{-48} -4 q^{-49} + q^{-50} } |
| 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^{60}-4 q^{59}+4 q^{58}+6 q^{57}-13 q^{56}-3 q^{55}+9 q^{54}+8 q^{53}+20 q^{52}-q^{51}-74 q^{50}-72 q^{49}+59 q^{48}+181 q^{47}+190 q^{46}-60 q^{45}-449 q^{44}-571 q^{43}-30 q^{42}+957 q^{41}+1364 q^{40}+462 q^{39}-1505 q^{38}-2883 q^{37}-1772 q^{36}+1892 q^{35}+5191 q^{34}+4347 q^{33}-1364 q^{32}-7900 q^{31}-8689 q^{30}-897 q^{29}+10381 q^{28}+14640 q^{27}+5444 q^{26}-11494 q^{25}-21368 q^{24}-12686 q^{23}+10324 q^{22}+27973 q^{21}+21796 q^{20}-6404 q^{19}-32886 q^{18}-31910 q^{17}-198 q^{16}+35624 q^{15}+41435 q^{14}+8486 q^{13}-35518 q^{12}-49461 q^{11}-17413 q^{10}+33241 q^9+55091 q^8+25783 q^7-29202 q^6-58452 q^5-32910 q^4+24528 q^3+59579 q^2+38437 q-19500-59226 q^{-1} -42519 q^{-2} +14722 q^{-3} +57635 q^{-4} +45366 q^{-5} -9932 q^{-6} -55165 q^{-7} -47442 q^{-8} +5096 q^{-9} +51828 q^{-10} +48808 q^{-11} +119 q^{-12} -47403 q^{-13} -49515 q^{-14} -5832 q^{-15} +41709 q^{-16} +49272 q^{-17} +11825 q^{-18} -34528 q^{-19} -47595 q^{-20} -17694 q^{-21} +25954 q^{-22} +44084 q^{-23} +22696 q^{-24} -16564 q^{-25} -38434 q^{-26} -25897 q^{-27} +7098 q^{-28} +30858 q^{-29} +26727 q^{-30} +1204 q^{-31} -22142 q^{-32} -24730 q^{-33} -7381 q^{-34} +13309 q^{-35} +20490 q^{-36} +10678 q^{-37} -5684 q^{-38} -14834 q^{-39} -11161 q^{-40} +191 q^{-41} +9102 q^{-42} +9415 q^{-43} +2841 q^{-44} -4309 q^{-45} -6681 q^{-46} -3662 q^{-47} +1183 q^{-48} +3834 q^{-49} +3097 q^{-50} +451 q^{-51} -1768 q^{-52} -2043 q^{-53} -810 q^{-54} +531 q^{-55} +1028 q^{-56} +678 q^{-57} -7 q^{-58} -438 q^{-59} -373 q^{-60} -86 q^{-61} +126 q^{-62} +147 q^{-63} +79 q^{-64} -22 q^{-65} -67 q^{-66} -23 q^{-67} +9 q^{-68} +9 q^{-69} +8 q^{-70} +5 q^{-71} -9 q^{-72} -2 q^{-73} +4 q^{-74} - q^{-75} } |
| 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^{84}-4 q^{83}+4 q^{82}+6 q^{81}-13 q^{80}-3 q^{79}+5 q^{78}+28 q^{77}-11 q^{76}-18 q^{75}+15 q^{74}-87 q^{73}-16 q^{72}+93 q^{71}+214 q^{70}+60 q^{69}-172 q^{68}-226 q^{67}-596 q^{66}-201 q^{65}+616 q^{64}+1477 q^{63}+1095 q^{62}-260 q^{61}-1676 q^{60}-3767 q^{59}-2705 q^{58}+1083 q^{57}+6329 q^{56}+7879 q^{55}+4218 q^{54}-3277 q^{53}-14376 q^{52}-16750 q^{51}-7389 q^{50}+12518 q^{49}+28184 q^{48}+29057 q^{47}+10529 q^{46}-27268 q^{45}-53389 q^{44}-48973 q^{43}-4566 q^{42}+51710 q^{41}+87565 q^{40}+72590 q^{39}-6610 q^{38}-94578 q^{37}-136646 q^{36}-85215 q^{35}+30912 q^{34}+151409 q^{33}+191466 q^{32}+92051 q^{31}-82084 q^{30}-229420 q^{29}-229647 q^{28}-78266 q^{27}+154170 q^{26}+312752 q^{25}+257079 q^{24}+23502 q^{23}-255646 q^{22}-371665 q^{21}-251033 q^{20}+63988 q^{19}+363413 q^{18}+413536 q^{17}+186123 q^{16}-191750 q^{15}-441171 q^{14}-408894 q^{13}-75882 q^{12}+328123 q^{11}+497760 q^{10}+330085 q^9-83203 q^8-430541 q^7-498059 q^6-197997 q^5+250860 q^4+508808 q^3+414062 q^2+14014 q-380135-523707 q^{-1} -273997 q^{-2} +175604 q^{-3} +482484 q^{-4} +448797 q^{-5} +83170 q^{-6} -323134 q^{-7} -517342 q^{-8} -318813 q^{-9} +109774 q^{-10} +442844 q^{-11} +462028 q^{-12} +141818 q^{-13} -259898 q^{-14} -495577 q^{-15} -356319 q^{-16} +34442 q^{-17} +384479 q^{-18} +463670 q^{-19} +209578 q^{-20} -170599 q^{-21} -447370 q^{-22} -389077 q^{-23} -65372 q^{-24} +286036 q^{-25} +435588 q^{-26} +280278 q^{-27} -44606 q^{-28} -348258 q^{-29} -389585 q^{-30} -173593 q^{-31} +140530 q^{-32} +348024 q^{-33} +315023 q^{-34} +92020 q^{-35} -193995 q^{-36} -321541 q^{-37} -239573 q^{-38} -16250 q^{-39} +199049 q^{-40} +271427 q^{-41} +178557 q^{-42} -29574 q^{-43} -186479 q^{-44} -217687 q^{-45} -115811 q^{-46} +42172 q^{-47} +156660 q^{-48} +170542 q^{-49} +71966 q^{-50} -45861 q^{-51} -123612 q^{-52} -118831 q^{-53} -48992 q^{-54} +38852 q^{-55} +94087 q^{-56} +80016 q^{-57} +30049 q^{-58} -29789 q^{-59} -61282 q^{-60} -55241 q^{-61} -18946 q^{-62} +22114 q^{-63} +38216 q^{-64} +33982 q^{-65} +11198 q^{-66} -11458 q^{-67} -24328 q^{-68} -20110 q^{-69} -5535 q^{-70} +5890 q^{-71} +13020 q^{-72} +10756 q^{-73} +4175 q^{-74} -3742 q^{-75} -6640 q^{-76} -4888 q^{-77} -2203 q^{-78} +1492 q^{-79} +2913 q^{-80} +2695 q^{-81} +623 q^{-82} -680 q^{-83} -1006 q^{-84} -1063 q^{-85} -320 q^{-86} +212 q^{-87} +552 q^{-88} +242 q^{-89} +59 q^{-90} -27 q^{-91} -163 q^{-92} -92 q^{-93} -26 q^{-94} +72 q^{-95} +16 q^{-96} +2 q^{-97} +15 q^{-98} -14 q^{-99} -8 q^{-100} -5 q^{-101} +9 q^{-102} +2 q^{-103} -4 q^{-104} + q^{-105} } |
| 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^{112}-4 q^{111}+4 q^{110}+6 q^{109}-13 q^{108}-3 q^{107}+5 q^{106}+24 q^{105}+9 q^{104}-49 q^{103}-2 q^{102}+2 q^{101}-31 q^{100}+28 q^{99}+75 q^{98}+158 q^{97}+48 q^{96}-291 q^{95}-318 q^{94}-260 q^{93}-66 q^{92}+534 q^{91}+917 q^{90}+1208 q^{89}+482 q^{88}-1471 q^{87}-2844 q^{86}-3329 q^{85}-1711 q^{84}+2371 q^{83}+6470 q^{82}+9138 q^{81}+6836 q^{80}-2254 q^{79}-13194 q^{78}-21631 q^{77}-19779 q^{76}-3481 q^{75}+20489 q^{74}+43605 q^{73}+49176 q^{72}+25233 q^{71}-21814 q^{70}-75414 q^{69}-103193 q^{68}-77368 q^{67}+217 q^{66}+106234 q^{65}+185323 q^{64}+179387 q^{63}+71464 q^{62}-113375 q^{61}-286642 q^{60}-341928 q^{59}-223202 q^{58}+56051 q^{57}+375169 q^{56}+559280 q^{55}+480840 q^{54}+112560 q^{53}-400811 q^{52}-797484 q^{51}-843686 q^{50}-430400 q^{49}+298839 q^{48}+993820 q^{47}+1278907 q^{46}+910274 q^{45}-15765 q^{44}-1073367 q^{43}-1718343 q^{42}-1520174 q^{41}-470669 q^{40}+964613 q^{39}+2073346 q^{38}+2192067 q^{37}+1139954 q^{36}-633602 q^{35}-2263880 q^{34}-2829249 q^{33}-1922465 q^{32}+89307 q^{31}+2235800 q^{30}+3341119 q^{29}+2725638 q^{28}+609765 q^{27}-1986923 q^{26}-3661296 q^{25}-3449927 q^{24}-1377286 q^{23}+1555703 q^{22}+3768099 q^{21}+4023424 q^{20}+2119469 q^{19}-1015128 q^{18}-3681754 q^{17}-4408420 q^{16}-2762212 q^{15}+444233 q^{14}+3454987 q^{13}+4609291 q^{12}+3261430 q^{11}+87493 q^{10}-3149968 q^9-4658362 q^8-3610169 q^7-537899 q^6+2826220 q^5+4604709 q^4+3825894 q^3+890834 q^2-2522244 q-4494135-3945409 q^{-1} -1157376 q^{-2} +2257688 q^{-3} +4364984 q^{-4} +4006145 q^{-5} +1360966 q^{-6} -2029292 q^{-7} -4235883 q^{-8} -4042274 q^{-9} -1535296 q^{-10} +1820136 q^{-11} +4112104 q^{-12} +4076227 q^{-13} +1709872 q^{-14} -1604177 q^{-15} -3981713 q^{-16} -4116003 q^{-17} -1909743 q^{-18} +1351280 q^{-19} +3823412 q^{-20} +4156866 q^{-21} +2147420 q^{-22} -1036621 q^{-23} -3607912 q^{-24} -4177817 q^{-25} -2420560 q^{-26} +641548 q^{-27} +3304202 q^{-28} +4148097 q^{-29} +2710187 q^{-30} -164342 q^{-31} -2887912 q^{-32} -4027779 q^{-33} -2978499 q^{-34} -377124 q^{-35} +2346613 q^{-36} +3778094 q^{-37} +3175544 q^{-38} +942327 q^{-39} -1691930 q^{-40} -3373205 q^{-41} -3244729 q^{-42} -1469069 q^{-43} +962632 q^{-44} +2808633 q^{-45} +3139347 q^{-46} +1886766 q^{-47} -224497 q^{-48} -2115194 q^{-49} -2838187 q^{-50} -2127516 q^{-51} -438709 q^{-52} +1355500 q^{-53} +2354958 q^{-54} +2150543 q^{-55} +946552 q^{-56} -617661 q^{-57} -1746377 q^{-58} -1954553 q^{-59} -1238823 q^{-60} -6866 q^{-61} +1097392 q^{-62} +1583164 q^{-63} +1299853 q^{-64} +447271 q^{-65} -504567 q^{-66} -1116612 q^{-67} -1160225 q^{-68} -672613 q^{-69} +46196 q^{-70} +648950 q^{-71} +889664 q^{-72} +700205 q^{-73} +237065 q^{-74} -260227 q^{-75} -574945 q^{-76} -587886 q^{-77} -349646 q^{-78} -1773 q^{-79} +292569 q^{-80} +407982 q^{-81} +333928 q^{-82} +133949 q^{-83} -89221 q^{-84} -229710 q^{-85} -249493 q^{-86} -162516 q^{-87} -23369 q^{-88} +93644 q^{-89} +149147 q^{-90} +132781 q^{-91} +63605 q^{-92} -14057 q^{-93} -69180 q^{-94} -83861 q^{-95} -59274 q^{-96} -18707 q^{-97} +19848 q^{-98} +41277 q^{-99} +39464 q^{-100} +23395 q^{-101} +1684 q^{-102} -15056 q^{-103} -19946 q^{-104} -16215 q^{-105} -7040 q^{-106} +2517 q^{-107} +7576 q^{-108} +8655 q^{-109} +5620 q^{-110} +985 q^{-111} -1979 q^{-112} -3381 q^{-113} -2854 q^{-114} -1311 q^{-115} -33 q^{-116} +1072 q^{-117} +1289 q^{-118} +675 q^{-119} +178 q^{-120} -253 q^{-121} -344 q^{-122} -232 q^{-123} -197 q^{-124} +20 q^{-125} +141 q^{-126} +92 q^{-127} +39 q^{-128} -24 q^{-129} -21 q^{-130} +5 q^{-131} -26 q^{-132} -10 q^{-133} +14 q^{-134} +8 q^{-135} +5 q^{-136} -9 q^{-137} -2 q^{-138} +4 q^{-139} - q^{-140} } |
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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