10 26
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![]() (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 26's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
Knot presentations
Planar diagram presentation | X6271 X16,8,17,7 X12,3,13,4 X2,15,3,16 X14,5,15,6 X4,13,5,14 X20,12,1,11 X8,20,9,19 X18,10,19,9 X10,18,11,17 |
Gauss code | 1, -4, 3, -6, 5, -1, 2, -8, 9, -10, 7, -3, 6, -5, 4, -2, 10, -9, 8, -7 |
Dowker-Thistlethwaite code | 6 12 14 16 18 20 4 2 10 8 |
Conway Notation | [32113] |
Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | ||||
Length is 11, width is 4, Braid index is 4 |
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![]() [{2, 13}, {1, 7}, {12, 4}, {13, 9}, {8, 10}, {9, 11}, {10, 12}, {5, 3}, {4, 6}, {7, 5}, {6, 2}, {3, 8}, {11, 1}] |
[edit Notes on presentations of 10 26]
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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
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K = Knot["10 26"];
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In[4]:=
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PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
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X6271 X16,8,17,7 X12,3,13,4 X2,15,3,16 X14,5,15,6 X4,13,5,14 X20,12,1,11 X8,20,9,19 X18,10,19,9 X10,18,11,17 |
In[5]:=
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GaussCode[K]
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Out[5]=
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1, -4, 3, -6, 5, -1, 2, -8, 9, -10, 7, -3, 6, -5, 4, -2, 10, -9, 8, -7 |
In[6]:=
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DTCode[K]
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Out[6]=
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6 12 14 16 18 20 4 2 10 8 |
(The path below may be different on your system)
In[7]:=
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AppendTo[$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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[32113] |
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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,-1,-1,2,-1,2,2,2,3,-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, 11, 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[{2, 13}, {1, 7}, {12, 4}, {13, 9}, {8, 10}, {9, 11}, {10, 12}, {5, 3}, {4, 6}, {7, 5}, {6, 2}, {3, 8}, {11, 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 -2 t^3+7 t^2-13 t+17-13 t^{-1} +7 t^{-2} -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 -2 z^6-5 z^4-3 z^2+1} |
2nd Alexander ideal (db, data sources) | |
Determinant and Signature | { 61, 0 } |
Jones polynomial | |
HOMFLY-PT polynomial (db, data sources) | |
Kauffman polynomial (db, data sources) | |
The A2 invariant | |
The G2 invariant |
A1 Invariants.
Weight | Invariant |
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1 | |
2 | |
3 | |
4 | |
5 |
A2 Invariants.
Weight | Invariant |
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1,0 | |
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^{36}-4 q^{34}+10 q^{32}-20 q^{30}+38 q^{28}-64 q^{26}+100 q^{24}-144 q^{22}+197 q^{20}-246 q^{18}+290 q^{16}-322 q^{14}+326 q^{12}-292 q^{10}+226 q^8-124 q^6-12 q^4+172 q^2-332+474 q^{-2} -590 q^{-4} +656 q^{-6} -672 q^{-8} +630 q^{-10} -537 q^{-12} +410 q^{-14} -250 q^{-16} +98 q^{-18} +56 q^{-20} -180 q^{-22} +272 q^{-24} -322 q^{-26} +329 q^{-28} -318 q^{-30} +274 q^{-32} -220 q^{-34} +166 q^{-36} -118 q^{-38} +78 q^{-40} -46 q^{-42} +27 q^{-44} -14 q^{-46} +6 q^{-48} -2 q^{-50} + q^{-52} } |
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^{32}-q^{30}-q^{28}+3 q^{26}+q^{24}-3 q^{22}+6 q^{18}-8 q^{14}+3 q^{12}+8 q^{10}-5 q^8-7 q^6+6 q^4+2 q^2-6- q^{-2} +5 q^{-4} -3 q^{-6} -4 q^{-8} +7 q^{-10} +2 q^{-12} -5 q^{-14} +5 q^{-16} +9 q^{-18} -3 q^{-20} -4 q^{-22} +4 q^{-24} +3 q^{-26} -7 q^{-28} -5 q^{-30} +3 q^{-32} + q^{-34} -3 q^{-36} - q^{-38} +2 q^{-40} + q^{-42} + q^{-48} } |
A3 Invariants.
Weight | Invariant |
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0,1,0 | |
1,0,0 |
A4 Invariants.
Weight | Invariant |
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0,1,0,0 | |
1,0,0,0 |
B2 Invariants.
Weight | Invariant |
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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^{28}-2 q^{26}+4 q^{24}-7 q^{22}+10 q^{20}-13 q^{18}+16 q^{16}-16 q^{14}+16 q^{12}-12 q^{10}+8 q^8-6 q^4+16 q^2-23+28 q^{-2} -31 q^{-4} +30 q^{-6} -29 q^{-8} +22 q^{-10} -16 q^{-12} +7 q^{-14} -7 q^{-18} +12 q^{-20} -14 q^{-22} +16 q^{-24} -14 q^{-26} +13 q^{-28} -10 q^{-30} +7 q^{-32} -5 q^{-34} +3 q^{-36} - q^{-38} + q^{-40} } |
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^{46}-2 q^{42}-2 q^{40}+2 q^{38}+6 q^{36}+q^{34}-8 q^{32}-7 q^{30}+6 q^{28}+14 q^{26}+q^{24}-15 q^{22}-10 q^{20}+11 q^{18}+16 q^{16}-2 q^{14}-16 q^{12}-4 q^{10}+13 q^8+10 q^6-9 q^4-10 q^2+6+11 q^{-2} -2 q^{-4} -11 q^{-6} - q^{-8} +9 q^{-10} +2 q^{-12} -11 q^{-14} -5 q^{-16} +10 q^{-18} +8 q^{-20} -10 q^{-22} -14 q^{-24} +5 q^{-26} +18 q^{-28} +4 q^{-30} -15 q^{-32} -11 q^{-34} +10 q^{-36} +16 q^{-38} -12 q^{-42} -6 q^{-44} +7 q^{-46} +7 q^{-48} -2 q^{-50} -6 q^{-52} -2 q^{-54} +3 q^{-56} +2 q^{-58} - q^{-60} - q^{-62} + q^{-66} } |
D4 Invariants.
Weight | Invariant |
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1,0,0,0 | 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^{38}-2 q^{36}+2 q^{34}-3 q^{32}+6 q^{30}-8 q^{28}+8 q^{26}-9 q^{24}+14 q^{22}-13 q^{20}+11 q^{18}-11 q^{16}+13 q^{14}-6 q^{12}+3 q^{10}-q^8-q^6+12 q^4-12 q^2+17-20 q^{-2} +24 q^{-4} -23 q^{-6} +21 q^{-8} -27 q^{-10} +18 q^{-12} -19 q^{-14} +11 q^{-16} -13 q^{-18} +3 q^{-20} + q^{-22} -2 q^{-24} +8 q^{-26} -7 q^{-28} +15 q^{-30} -9 q^{-32} +13 q^{-34} -11 q^{-36} +11 q^{-38} -9 q^{-40} +6 q^{-42} -7 q^{-44} +4 q^{-46} -3 q^{-48} +2 q^{-50} - q^{-52} + q^{-54} } |
G2 Invariants.
Weight | Invariant |
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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^{66}-2 q^{64}+4 q^{62}-6 q^{60}+5 q^{58}-3 q^{56}-2 q^{54}+12 q^{52}-20 q^{50}+28 q^{48}-29 q^{46}+17 q^{44}+q^{42}-27 q^{40}+53 q^{38}-65 q^{36}+62 q^{34}-39 q^{32}+43 q^{28}-73 q^{26}+85 q^{24}-66 q^{22}+28 q^{20}+16 q^{18}-49 q^{16}+60 q^{14}-40 q^{12}+4 q^{10}+37 q^8-57 q^6+47 q^4-6 q^2-47+94 q^{-2} -108 q^{-4} +83 q^{-6} -27 q^{-8} -44 q^{-10} +103 q^{-12} -130 q^{-14} +114 q^{-16} -64 q^{-18} -4 q^{-20} +59 q^{-22} -92 q^{-24} +83 q^{-26} -49 q^{-28} - q^{-30} +38 q^{-32} -57 q^{-34} +41 q^{-36} - q^{-38} -41 q^{-40} +69 q^{-42} -70 q^{-44} +38 q^{-46} +11 q^{-48} -57 q^{-50} +88 q^{-52} -83 q^{-54} +59 q^{-56} -14 q^{-58} -29 q^{-60} +57 q^{-62} -62 q^{-64} +51 q^{-66} -27 q^{-68} +2 q^{-70} +16 q^{-72} -24 q^{-74} +24 q^{-76} -17 q^{-78} +9 q^{-80} - q^{-82} -4 q^{-84} +4 q^{-86} -5 q^{-88} +3 q^{-90} - q^{-92} + q^{-94} } |
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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["10 26"];
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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 -2 t^3+7 t^2-13 t+17-13 t^{-1} +7 t^{-2} -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 -2 z^6-5 z^4-3 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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In[7]:=
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{KnotDet[K], KnotSignature[K]}
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Out[7]=
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{ 61, 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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Out[8]=
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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: {}
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}} ): {}
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["10 26"];
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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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{ 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 -2 t^3+7 t^2-13 t+17-13 t^{-1} +7 t^{-2} -2 t^{-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^6-2 q^5+4 q^4-7 q^3+9 q^2-10 q+10-8 q^{-1} +6 q^{-2} -3 q^{-3} + q^{-4} } } |
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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{} |
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: | (-3, -2) |
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 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 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 10 26. 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^{18}-2 q^{17}+6 q^{15}-8 q^{14}-4 q^{13}+21 q^{12}-17 q^{11}-18 q^{10}+47 q^9-23 q^8-42 q^7+73 q^6-19 q^5-67 q^4+85 q^3-8 q^2-78 q+78+2 q^{-1} -67 q^{-2} +53 q^{-3} +7 q^{-4} -41 q^{-5} +25 q^{-6} +6 q^{-7} -16 q^{-8} +7 q^{-9} +2 q^{-10} -3 q^{-11} + q^{-12} } |
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^{36}-2 q^{35}+2 q^{33}+3 q^{32}-7 q^{31}-4 q^{30}+9 q^{29}+14 q^{28}-18 q^{27}-24 q^{26}+19 q^{25}+49 q^{24}-22 q^{23}-76 q^{22}+11 q^{21}+113 q^{20}+9 q^{19}-150 q^{18}-39 q^{17}+180 q^{16}+85 q^{15}-207 q^{14}-133 q^{13}+219 q^{12}+187 q^{11}-224 q^{10}-237 q^9+214 q^8+284 q^7-199 q^6-318 q^5+178 q^4+335 q^3-144 q^2-343 q+117+322 q^{-1} -77 q^{-2} -295 q^{-3} +51 q^{-4} +244 q^{-5} -19 q^{-6} -197 q^{-7} +5 q^{-8} +141 q^{-9} +9 q^{-10} -100 q^{-11} -8 q^{-12} +60 q^{-13} +11 q^{-14} -37 q^{-15} -7 q^{-16} +20 q^{-17} +4 q^{-18} -10 q^{-19} - q^{-20} +3 q^{-21} +2 q^{-22} -3 q^{-23} + q^{-24} } |
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^{60}-2 q^{59}+2 q^{57}-q^{56}+4 q^{55}-9 q^{54}+10 q^{52}-3 q^{51}+14 q^{50}-30 q^{49}-11 q^{48}+28 q^{47}+8 q^{46}+51 q^{45}-74 q^{44}-62 q^{43}+29 q^{42}+41 q^{41}+173 q^{40}-103 q^{39}-175 q^{38}-65 q^{37}+37 q^{36}+417 q^{35}-18 q^{34}-273 q^{33}-296 q^{32}-135 q^{31}+695 q^{30}+231 q^{29}-206 q^{28}-564 q^{27}-530 q^{26}+834 q^{25}+552 q^{24}+95 q^{23}-714 q^{22}-1046 q^{21}+758 q^{20}+801 q^{19}+541 q^{18}-689 q^{17}-1526 q^{16}+520 q^{15}+920 q^{14}+1002 q^{13}-543 q^{12}-1877 q^{11}+220 q^{10}+921 q^9+1372 q^8-328 q^7-2038 q^6-84 q^5+798 q^4+1577 q^3-66 q^2-1949 q-330+537 q^{-1} +1532 q^{-2} +196 q^{-3} -1579 q^{-4} -436 q^{-5} +198 q^{-6} +1220 q^{-7} +351 q^{-8} -1042 q^{-9} -353 q^{-10} -68 q^{-11} +764 q^{-12} +334 q^{-13} -551 q^{-14} -172 q^{-15} -159 q^{-16} +373 q^{-17} +207 q^{-18} -246 q^{-19} -32 q^{-20} -122 q^{-21} +147 q^{-22} +93 q^{-23} -101 q^{-24} +14 q^{-25} -61 q^{-26} +51 q^{-27} +33 q^{-28} -39 q^{-29} +14 q^{-30} -22 q^{-31} +14 q^{-32} +10 q^{-33} -12 q^{-34} +5 q^{-35} -5 q^{-36} +3 q^{-37} +2 q^{-38} -3 q^{-39} + q^{-40} } |
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^{90}-2 q^{89}+2 q^{87}-q^{86}+2 q^{84}-5 q^{83}-q^{82}+9 q^{81}+q^{80}-6 q^{79}-13 q^{77}-5 q^{76}+26 q^{75}+22 q^{74}-3 q^{73}-18 q^{72}-51 q^{71}-39 q^{70}+45 q^{69}+93 q^{68}+73 q^{67}-7 q^{66}-147 q^{65}-191 q^{64}-38 q^{63}+181 q^{62}+314 q^{61}+213 q^{60}-163 q^{59}-502 q^{58}-437 q^{57}+25 q^{56}+606 q^{55}+806 q^{54}+272 q^{53}-652 q^{52}-1158 q^{51}-739 q^{50}+452 q^{49}+1490 q^{48}+1360 q^{47}-45 q^{46}-1643 q^{45}-2015 q^{44}-631 q^{43}+1527 q^{42}+2634 q^{41}+1511 q^{40}-1137 q^{39}-3071 q^{38}-2462 q^{37}+417 q^{36}+3257 q^{35}+3447 q^{34}+496 q^{33}-3180 q^{32}-4281 q^{31}-1568 q^{30}+2828 q^{29}+4993 q^{28}+2659 q^{27}-2307 q^{26}-5484 q^{25}-3739 q^{24}+1671 q^{23}+5837 q^{22}+4696 q^{21}-974 q^{20}-6040 q^{19}-5572 q^{18}+287 q^{17}+6150 q^{16}+6316 q^{15}+387 q^{14}-6152 q^{13}-6949 q^{12}-1057 q^{11}+6039 q^{10}+7485 q^9+1702 q^8-5807 q^7-7803 q^6-2376 q^5+5351 q^4+7995 q^3+3001 q^2-4759 q-7836-3559 q^{-1} +3883 q^{-2} +7477 q^{-3} +3966 q^{-4} -2970 q^{-5} -6708 q^{-6} -4157 q^{-7} +1925 q^{-8} +5771 q^{-9} +4070 q^{-10} -1029 q^{-11} -4588 q^{-12} -3727 q^{-13} +244 q^{-14} +3452 q^{-15} +3154 q^{-16} +231 q^{-17} -2326 q^{-18} -2484 q^{-19} -525 q^{-20} +1489 q^{-21} +1786 q^{-22} +540 q^{-23} -806 q^{-24} -1179 q^{-25} -500 q^{-26} +427 q^{-27} +716 q^{-28} +336 q^{-29} -175 q^{-30} -393 q^{-31} -222 q^{-32} +72 q^{-33} +206 q^{-34} +117 q^{-35} -27 q^{-36} -100 q^{-37} -60 q^{-38} +20 q^{-39} +41 q^{-40} +26 q^{-41} - q^{-42} -29 q^{-43} -16 q^{-44} +15 q^{-45} +10 q^{-46} -4 q^{-47} +8 q^{-48} -8 q^{-49} -11 q^{-50} +10 q^{-51} +4 q^{-52} -6 q^{-53} +3 q^{-54} + q^{-55} -5 q^{-56} +3 q^{-57} +2 q^{-58} -3 q^{-59} + q^{-60} } |
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^{126}-2 q^{125}+2 q^{123}-q^{122}-2 q^{120}+6 q^{119}-6 q^{118}-2 q^{117}+11 q^{116}-3 q^{115}-4 q^{114}-14 q^{113}+17 q^{112}-11 q^{111}-5 q^{110}+39 q^{109}+5 q^{108}-10 q^{107}-56 q^{106}+19 q^{105}-38 q^{104}-19 q^{103}+111 q^{102}+74 q^{101}+32 q^{100}-125 q^{99}-21 q^{98}-180 q^{97}-146 q^{96}+182 q^{95}+276 q^{94}+297 q^{93}-40 q^{92}+8 q^{91}-535 q^{90}-663 q^{89}-105 q^{88}+400 q^{87}+886 q^{86}+617 q^{85}+707 q^{84}-701 q^{83}-1620 q^{82}-1354 q^{81}-445 q^{80}+1073 q^{79}+1762 q^{78}+2839 q^{77}+603 q^{76}-1846 q^{75}-3253 q^{74}-3091 q^{73}-875 q^{72}+1671 q^{71}+5699 q^{70}+4221 q^{69}+819 q^{68}-3447 q^{67}-6282 q^{66}-5716 q^{65}-2183 q^{64}+6247 q^{63}+8317 q^{62}+6902 q^{61}+849 q^{60}-6364 q^{59}-11004 q^{58}-9989 q^{57}+1541 q^{56}+8808 q^{55}+13402 q^{54}+9446 q^{53}-478 q^{52}-12397 q^{51}-18276 q^{50}-7858 q^{49}+3090 q^{48}+15938 q^{47}+18619 q^{46}+10345 q^{45}-7659 q^{44}-22779 q^{43}-18115 q^{42}-7413 q^{41}+12715 q^{40}+24440 q^{39}+22182 q^{38}+1482 q^{37}-22100 q^{36}-25658 q^{35}-18883 q^{34}+5635 q^{33}+25911 q^{32}+31729 q^{31}+11443 q^{30}-18097 q^{29}-29698 q^{28}-28415 q^{27}-2122 q^{26}+24733 q^{25}+38251 q^{24}+19818 q^{23}-13356 q^{22}-31571 q^{21}-35451 q^{20}-8775 q^{19}+22785 q^{18}+42667 q^{17}+26403 q^{16}-8864 q^{15}-32380 q^{14}-40746 q^{13}-14621 q^{12}+20206 q^{11}+45409 q^{10}+32020 q^9-3705 q^8-31467 q^7-44351 q^6-20643 q^5+15511 q^4+45193 q^3+36470 q^2+3228 q-26904-44552 q^{-1} -26330 q^{-2} +7636 q^{-3} +39858 q^{-4} +37603 q^{-5} +10926 q^{-6} -17871 q^{-7} -39064 q^{-8} -28980 q^{-9} -1762 q^{-10} +29034 q^{-11} +32992 q^{-12} +16016 q^{-13} -6794 q^{-14} -27995 q^{-15} -25997 q^{-16} -8665 q^{-17} +16005 q^{-18} +23124 q^{-19} +15693 q^{-20} +1745 q^{-21} -15209 q^{-22} -18130 q^{-23} -10219 q^{-24} +5736 q^{-25} +12094 q^{-26} +10841 q^{-27} +4982 q^{-28} -5564 q^{-29} -9403 q^{-30} -7460 q^{-31} +724 q^{-32} +4225 q^{-33} +5165 q^{-34} +4105 q^{-35} -931 q^{-36} -3431 q^{-37} -3749 q^{-38} -347 q^{-39} +669 q^{-40} +1516 q^{-41} +2098 q^{-42} +232 q^{-43} -809 q^{-44} -1349 q^{-45} -61 q^{-46} -183 q^{-47} +130 q^{-48} +762 q^{-49} +175 q^{-50} -108 q^{-51} -391 q^{-52} +160 q^{-53} -152 q^{-54} -117 q^{-55} +237 q^{-56} +35 q^{-57} -15 q^{-58} -126 q^{-59} +138 q^{-60} -48 q^{-61} -77 q^{-62} +79 q^{-63} +2 q^{-64} -9 q^{-65} -53 q^{-66} +64 q^{-67} -11 q^{-68} -30 q^{-69} +28 q^{-70} - q^{-71} - q^{-72} -22 q^{-73} +21 q^{-74} -12 q^{-76} +9 q^{-77} - q^{-78} + q^{-79} -5 q^{-80} +3 q^{-81} +2 q^{-82} -3 q^{-83} + q^{-84} } |
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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