10 140
From Knot Atlas
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 (KnotPlot image) |
See the full Rolfsen Knot Table. Visit 10 140's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) |
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10_140 is also known as the pretzel knot P(4,3,-3). |
Knot presentations
| Planar diagram presentation | X1425 X3,10,4,11 X11,19,12,18 X14,5,15,6 X6,17,7,18 X16,7,17,8 X8,15,9,16 X13,1,14,20 X19,13,20,12 X9,2,10,3 |
| Gauss code | -1, 10, -2, 1, 4, -5, 6, -7, -10, 2, -3, 9, -8, -4, 7, -6, 5, 3, -9, 8 |
| Dowker-Thistlethwaite code | 4 10 -14 -16 2 18 20 -8 -6 12 |
| Conway Notation | [4,3,21-] |
| Minimum Braid Representative | A Morse Link Presentation | An Arc Presentation | ||||
Length is 11, width is 4, Braid index is 4 |
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 [{9, 2}, {1, 7}, {6, 8}, {7, 9}, {10, 13}, {8, 12}, {13, 11}, {12, 5}, {4, 6}, {5, 3}, {2, 4}, {3, 10}, {11, 1}] |
[edit Notes on presentations of 10 140]
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[$Path, "C:/drorbn/projects/KAtlas/"];
<< KnotTheory`
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Loading KnotTheory` version of May 31, 2006, 14:15:20.091.
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In[3]:=
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K = Knot["10 140"];
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In[4]:=
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PD[K]
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KnotTheory::loading: Loading precomputed data in PD4Knots`.
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Out[4]=
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X1425 X3,10,4,11 X11,19,12,18 X14,5,15,6 X6,17,7,18 X16,7,17,8 X8,15,9,16 X13,1,14,20 X19,13,20,12 X9,2,10,3 |
In[5]:=
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GaussCode[K]
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Out[5]=
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-1, 10, -2, 1, 4, -5, 6, -7, -10, 2, -3, 9, -8, -4, 7, -6, 5, 3, -9, 8 |
In[6]:=
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DTCode[K]
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Out[6]=
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4 10 -14 -16 2 18 20 -8 -6 12 |
(The path below may be different on your system)
In[7]:=
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AppendTo[$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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[4,3,21-] |
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,\{1,1,1,-2,-1,-1,-1,-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[{9, 2}, {1, 7}, {6, 8}, {7, 9}, {10, 13}, {8, 12}, {13, 11}, {12, 5}, {4, 6}, {5, 3}, {2, 4}, {3, 10}, {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 t^2-2 t+3-2 t^{-1} + 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 z^4+2 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 \left\{2,t^2+t+1\right\}} |
| Determinant and Signature | { 9, 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 1- q^{-1} + q^{-2} - q^{-3} +2 q^{-4} - q^{-5} + q^{-6} - q^{-7} } |
| 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 -z^2 a^6-2 a^6+z^4 a^4+4 z^2 a^4+4 a^4-z^2 a^2-2 a^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 a^6 z^8+a^4 z^8+a^7 z^7+2 a^5 z^7+a^3 z^7-6 a^6 z^6-6 a^4 z^6-6 a^7 z^5-11 a^5 z^5-5 a^3 z^5+11 a^6 z^4+12 a^4 z^4+a^2 z^4+10 a^7 z^3+16 a^5 z^3+6 a^3 z^3-8 a^6 z^2-12 a^4 z^2-4 a^2 z^2-4 a^7 z-6 a^5 z-2 a^3 z+2 a^6+4 a^4+2 a^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^{22}-q^{20}-q^{18}+2 q^{14}+2 q^{12}+2 q^{10}-q^6-q^4+1+ q^{-2} } |
| 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^{108}+q^{104}-q^{102}-q^{96}+q^{94}-q^{92}-q^{90}-q^{88}-q^{86}-q^{82}-4 q^{80}-4 q^{70}+q^{68}+3 q^{66}-q^{62}-q^{60}+3 q^{58}+5 q^{56}+2 q^{54}-q^{52}+q^{50}+3 q^{48}+4 q^{46}-2 q^{42}+q^{40}+3 q^{38}+q^{36}-q^{34}-2 q^{30}+q^{28}-3 q^{24}-q^{20}-q^{18}+q^{16}-q^{14}-q^{12}-q^8+q^6+2+ q^{-4} + q^{-6} + q^{-10} } |
Further Quantum Invariants
Further quantum knot invariants for 10_140.
A1 Invariants.
| Weight | Invariant |
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| 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^{15}+q^9+q^7+ q^{-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^{44}-q^{40}-q^{34}-q^{32}+q^{28}+q^{26}+q^{22}-q^{18}-q^{14}-q^{12}+q^{10}+q^8+q^6+q^2+2- q^{-4} } |
| 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^{87}+q^{83}+q^{81}-q^{77}+q^{73}+q^{71}-q^{67}-2 q^{65}-q^{63}+q^{59}-q^{55}+2 q^{51}+2 q^{49}-q^{45}+q^{41}-2 q^{37}-2 q^{35}-q^{29}+q^{25}+q^{23}+q^{17}+q^{15}-q^{11}-q^9+2 q^7+3 q^5-2 q+3 q^{-3} + q^{-5} - q^{-7} - q^{-9} } |
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^{22}-q^{20}-q^{18}+2 q^{14}+2 q^{12}+2 q^{10}-q^6-q^4+1+ q^{-2} } |
| 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^{60}+2 q^{56}-2 q^{54}+2 q^{52}-2 q^{50}-2 q^{46}-4 q^{44}-4 q^{40}+2 q^{38}+q^{36}+4 q^{34}+4 q^{32}+4 q^{30}+q^{28}-2 q^{26}-4 q^{24}-4 q^{22}-4 q^{20}-2 q^{18}+6 q^{14}+2 q^{12}+6 q^{10}+2 q^8+2 q^4-2 q^2+2-2 q^{-2} + q^{-4} } |
| 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^{58}+q^{56}+q^{54}-q^{48}-2 q^{46}-4 q^{44}-4 q^{42}-3 q^{40}+4 q^{36}+4 q^{34}+6 q^{32}+4 q^{30}+3 q^{28}-2 q^{26}-4 q^{24}-5 q^{22}-5 q^{20}-3 q^{18}+4 q^{14}+4 q^{12}+5 q^{10}+2 q^8+1- q^{-2} } |
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^{46}+q^{42}-q^{38}-2 q^{36}-2 q^{34}-2 q^{32}-3 q^{30}+2 q^{24}+2 q^{22}+4 q^{20}+3 q^{18}+2 q^{16}+2 q^{14}-q^{10}-2 q^8-q^6-q^4+2+ q^{-2} + q^{-4} } |
| 1,0,0 | 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^{29}-q^{27}-2 q^{25}-q^{23}+2 q^{19}+3 q^{17}+3 q^{15}+2 q^{13}-q^9-2 q^7-q^5+q+ q^{-1} + q^{-3} } |
A4 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0,0 | 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^{60}+q^{58}+2 q^{56}+2 q^{54}+q^{52}-q^{50}-3 q^{48}-6 q^{46}-7 q^{44}-6 q^{42}-4 q^{40}-q^{38}+2 q^{36}+6 q^{34}+6 q^{32}+5 q^{30}+4 q^{28}+3 q^{26}+q^{22}+q^{20}+q^{18}+q^{16}+q^{14}-2 q^{10}-2 q^8-q^6-q^4+2+2 q^{-2} + q^{-4} + q^{-6} } |
| 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^{36}-q^{34}-2 q^{32}-2 q^{30}-q^{28}+2 q^{24}+3 q^{22}+4 q^{20}+3 q^{18}+2 q^{16}-q^{12}-2 q^{10}-2 q^8-q^6+q^2+1+ q^{-2} + q^{-4} } |
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^{46}-q^{42}-q^{38}+q^{30}+2 q^{26}+2 q^{22}+q^{18}-q^{10}-q^6+q^4+ q^{-2} + q^{-4} } |
| 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^{76}+q^{68}-q^{64}-q^{62}-q^{58}-2 q^{56}-q^{54}-q^{48}+q^{42}+q^{38}+q^{34}+q^{32}+q^{30}+q^{26}+2 q^{24}+q^{22}+q^{16}-q^{12}-q^{10}-q^4+1+ q^{-2} + q^{-6} } |
D4 Invariants.
| Weight | Invariant |
|---|---|
| 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^{62}+q^{58}+q^{54}-q^{52}-q^{50}-2 q^{48}-3 q^{46}-3 q^{44}-4 q^{42}-2 q^{40}-2 q^{38}+q^{36}+q^{34}+4 q^{32}+4 q^{30}+6 q^{28}+4 q^{26}+4 q^{24}+2 q^{22}+q^{20}-2 q^{16}-2 q^{14}-3 q^{12}-q^{10}-2 q^8+q^2+2+ q^{-2} + q^{-4} + q^{-6} } |
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^{108}+q^{104}-q^{102}-q^{96}+q^{94}-q^{92}-q^{90}-q^{88}-q^{86}-q^{82}-4 q^{80}-4 q^{70}+q^{68}+3 q^{66}-q^{62}-q^{60}+3 q^{58}+5 q^{56}+2 q^{54}-q^{52}+q^{50}+3 q^{48}+4 q^{46}-2 q^{42}+q^{40}+3 q^{38}+q^{36}-q^{34}-2 q^{30}+q^{28}-3 q^{24}-q^{20}-q^{18}+q^{16}-q^{14}-q^{12}-q^8+q^6+2+ q^{-4} + q^{-6} + q^{-10} } |
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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]:=
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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["10 140"];
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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^2-2 t+3-2 t^{-1} + t^{-2} } |
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^4+2 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 \left\{2,t^2+t+1\right\}} |
In[7]:=
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{KnotDet[K], KnotSignature[K]}
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Out[7]=
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{ 9, 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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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- q^{-1} + q^{-2} - q^{-3} +2 q^{-4} - q^{-5} + q^{-6} - q^{-7} } |
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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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^2 a^6-2 a^6+z^4 a^4+4 z^2 a^4+4 a^4-z^2 a^2-2 a^2+1} |
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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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^6 z^8+a^4 z^8+a^7 z^7+2 a^5 z^7+a^3 z^7-6 a^6 z^6-6 a^4 z^6-6 a^7 z^5-11 a^5 z^5-5 a^3 z^5+11 a^6 z^4+12 a^4 z^4+a^2 z^4+10 a^7 z^3+16 a^5 z^3+6 a^3 z^3-8 a^6 z^2-12 a^4 z^2-4 a^2 z^2-4 a^7 z-6 a^5 z-2 a^3 z+2 a^6+4 a^4+2 a^2+1} |
"Similar" Knots (within the Atlas)
Same Alexander/Conway Polynomial: {8_20, K11n73, K11n74,}
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}} ): {}
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["10 140"];
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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 t^2-2 t+3-2 t^{-1} + 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 1- q^{-1} + q^{-2} - q^{-3} +2 q^{-4} - q^{-5} + q^{-6} - q^{-7} } } |
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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{8_20, K11n73, K11n74,} |
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: | (2, -4) |
| 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 10 140. 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
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+1+2 q^{-1} -2 q^{-2} +3 q^{-4} -2 q^{-5} + q^{-7} -2 q^{-8} + q^{-9} - q^{-11} +2 q^{-12} - q^{-13} +2 q^{-15} -2 q^{-16} - q^{-17} +2 q^{-18} - q^{-19} - q^{-20} + q^{-21} } |
| 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^3+2 q+2-4 q^{-1} -2 q^{-2} +4 q^{-3} +5 q^{-4} -5 q^{-5} -5 q^{-6} +4 q^{-7} +6 q^{-8} -4 q^{-9} -5 q^{-10} +3 q^{-11} +6 q^{-12} -3 q^{-13} -5 q^{-14} +2 q^{-15} +5 q^{-16} -2 q^{-17} -5 q^{-18} +5 q^{-20} -4 q^{-22} - q^{-23} +4 q^{-24} + q^{-25} -2 q^{-26} - q^{-27} +2 q^{-28} - q^{-30} + q^{-32} - q^{-33} -2 q^{-34} + q^{-35} +2 q^{-36} -2 q^{-38} + q^{-40} + q^{-41} - q^{-42} } |
| 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^3-2 q^2-2 q+4 q^{-1} +7 q^{-2} -5 q^{-3} -6 q^{-4} -4 q^{-5} +6 q^{-6} +12 q^{-7} -4 q^{-8} -7 q^{-9} -8 q^{-10} +4 q^{-11} +14 q^{-12} -3 q^{-13} -6 q^{-14} -7 q^{-15} +3 q^{-16} +11 q^{-17} -4 q^{-18} -4 q^{-19} -5 q^{-20} +3 q^{-21} +9 q^{-22} -3 q^{-23} -2 q^{-24} -5 q^{-25} + q^{-26} +7 q^{-27} - q^{-28} -5 q^{-30} -2 q^{-31} +4 q^{-32} +3 q^{-34} -2 q^{-35} -4 q^{-36} +5 q^{-39} +2 q^{-40} -3 q^{-41} -3 q^{-42} -2 q^{-43} +3 q^{-44} +5 q^{-45} -3 q^{-47} -3 q^{-48} - q^{-49} +4 q^{-50} - q^{-53} -2 q^{-54} +3 q^{-55} -2 q^{-56} +4 q^{-60} -2 q^{-61} - q^{-62} - q^{-63} - q^{-64} +3 q^{-65} - q^{-68} - q^{-69} + q^{-70} } |
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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