9 8

9_7

9_9

(KnotPlot image)	See the full Rolfsen Knot Table. Visit 9 8's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 9 8 at Knotilus!

Knot presentations

Planar diagram presentation	X1425 X3849 X5,14,6,15 X9,1,10,18 X11,17,12,16 X15,13,16,12 X17,11,18,10 X13,6,14,7 X7283
Gauss code	-1, 9, -2, 1, -3, 8, -9, 2, -4, 7, -5, 6, -8, 3, -6, 5, -7, 4
Dowker-Thistlethwaite code	4 8 14 2 18 16 6 12 10
Conway Notation	[2412]

Minimum Braid Representative	A Morse Link Presentation	An Arc Presentation
Length is 10, width is 5, Braid index is 5		[{12, 2}, {1, 10}, {8, 11}, {10, 12}, {9, 3}, {2, 8}, {4, 9}, {3, 5}, {6, 4}, {5, 7}, {11, 6}, {7, 1}]

[edit Notes on presentations of 9 8]

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. Read more at http://katlas.org/wiki/KnotTheory.

In[3]:=

K = Knot["9 8"];

In[4]:=

PD[K]

KnotTheory::loading: Loading precomputed data in PD4Knots`.

Out[4]=

X1425 X3849 X5,14,6,15 X9,1,10,18 X11,17,12,16 X15,13,16,12 X17,11,18,10 X13,6,14,7 X7283

In[5]:=

GaussCode[K]

Out[5]=

-1, 9, -2, 1, -3, 8, -9, 2, -4, 7, -5, 6, -8, 3, -6, 5, -7, 4

In[6]:=

DTCode[K]

Out[6]=

4 8 14 2 18 16 6 12 10

(The path below may be different on your system)

In[7]:=

AppendTo[$Path, "C:/bin/LinKnot/"];

In[8]:=

ConwayNotation[K]

Out[8]=

[2412]

In[9]:=

br = BR[K]

KnotTheory::credits: The minimum braids representing the knots with up to 10 crossings were provided by Thomas Gittings. See arXiv:math.GT/0401051.

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 \textrm{BR}(5,\{-1,-1,2,-1,2,3,-2,-4,3,-4\})}

In[10]:=

{First[br], Crossings[br], BraidIndex[K]}

KnotTheory::credits: The braid index data known to KnotTheory` is taken from Charles Livingston's http://www.indiana.edu/~knotinfo/.

KnotTheory::loading: Loading precomputed data in IndianaData`.

Out[10]=

{ 5, 10, 5 }

In[11]:=

Show[BraidPlot[br]]

Out[11]=

-Graphics-

In[12]:=

Show[DrawMorseLink[K]]

KnotTheory::credits: "MorseLink was added to KnotTheory` by Siddarth Sankaran at the University of Toronto in the summer of 2005."

KnotTheory::credits: "DrawMorseLink was written by Siddarth Sankaran at the University of Toronto in the summer of 2005."

Out[12]=

-Graphics-

In[13]:=

ap = ArcPresentation[K]

Out[13]=

ArcPresentation[{12, 2}, {1, 10}, {8, 11}, {10, 12}, {9, 3}, {2, 8}, {4, 9}, {3, 5}, {6, 4}, {5, 7}, {11, 6}, {7, 1}]

In[14]:=

Draw[ap]

Out[14]=

-Graphics-

Three dimensional invariants

Symmetry type Reversible Unknotting number 2 3-genus 2 Bridge index 2 Super bridge index 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 \{4,6\}} Nakanishi index 1 Maximal Thurston-Bennequin number [-8][-3] Hyperbolic Volume 8.19235 A-Polynomial See Data:9 8/A-polynomial

[edit Notes for 9 8's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus 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} Topological 4 genus 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} Concordance genus 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} Rasmussen s-Invariant -2

[edit Notes for 9 8's four dimensional invariants]

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^2+8 t-11+8 t^{-1} -2 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 1-2 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	{ 31, -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^3-2 q^2+3 q-4+5 q^{-1} -5 q^{-2} +5 q^{-3} -3 q^{-4} +2 q^{-5} - q^{-6} }
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^6+2 z^2 a^4+2 a^4-z^4 a^2-z^2 a^2-z^4-2 z^2-1+z^2 a^{-2} + a^{-2} }
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^2 z^8+z^8+2 a^3 z^7+4 a z^7+2 z^7 a^{-1} +2 a^4 z^6+z^6 a^{-2} -z^6+2 a^5 z^5-3 a^3 z^5-13 a z^5-8 z^5 a^{-1} +2 a^6 z^4-4 a^2 z^4-4 z^4 a^{-2} -6 z^4+a^7 z^3+2 a^3 z^3+11 a z^3+8 z^3 a^{-1} -2 a^6 z^2-3 a^4 z^2+2 a^2 z^2+4 z^2 a^{-2} +7 z^2-a^7 z-a^5 z-a^3 z-3 a z-2 z a^{-1} +a^6+2 a^4- 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^{20}-q^{18}+q^{16}+q^{12}+2 q^{10}+q^6-q^4- q^{-2} + q^{-4} + q^{-10} }
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^{100}-q^{98}+2 q^{96}-2 q^{94}-3 q^{88}+4 q^{86}-5 q^{84}+4 q^{82}-4 q^{80}+3 q^{76}-5 q^{74}+6 q^{72}-7 q^{70}+5 q^{68}-4 q^{66}+3 q^{62}-5 q^{60}+9 q^{58}-6 q^{56}+5 q^{54}-q^{52}-2 q^{50}+7 q^{48}-5 q^{46}+4 q^{44}+3 q^{42}-4 q^{40}+7 q^{38}-3 q^{36}-3 q^{34}+11 q^{32}-13 q^{30}+10 q^{28}-5 q^{26}-5 q^{24}+14 q^{22}-17 q^{20}+14 q^{18}-10 q^{16}+7 q^{12}-12 q^{10}+12 q^8-9 q^6+3 q^4+3 q^2-7+7 q^{-2} -3 q^{-4} -2 q^{-6} +8 q^{-8} -10 q^{-10} +7 q^{-12} -8 q^{-16} +14 q^{-18} -15 q^{-20} +10 q^{-22} -2 q^{-24} -6 q^{-26} +11 q^{-28} -11 q^{-30} +10 q^{-32} -3 q^{-34} - q^{-36} +3 q^{-38} -4 q^{-40} +3 q^{-42} - q^{-44} + q^{-46} }

Further Quantum Invariants

Further quantum knot invariants for 9_8.

A1 Invariants.

Weight	Invariant
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^{13}+q^{11}-q^9+2 q^7+q- q^{-1} + q^{-3} - q^{-5} + q^{-7} }
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^{36}-q^{34}-q^{32}+2 q^{30}-2 q^{28}+3 q^{24}-4 q^{22}+4 q^{18}-3 q^{16}-q^{14}+3 q^{12}+q^{10}-2 q^8+3 q^4-q^2-2+4 q^{-2} -4 q^{-6} +3 q^{-8} +2 q^{-10} -4 q^{-12} + q^{-14} +3 q^{-16} -2 q^{-18} - q^{-20} + q^{-22} }
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^{69}+q^{67}+q^{65}-2 q^{61}+2 q^{57}-q^{51}-q^{49}-q^{47}+4 q^{45}+2 q^{43}-6 q^{41}-5 q^{39}+8 q^{37}+6 q^{35}-5 q^{33}-10 q^{31}+2 q^{29}+9 q^{27}+2 q^{25}-5 q^{23}-6 q^{21}+3 q^{19}+8 q^{17}+q^{15}-9 q^{13}-2 q^{11}+8 q^9+4 q^7-8 q^5-4 q^3+8 q+7 q^{-1} -5 q^{-3} -7 q^{-5} +3 q^{-7} +9 q^{-9} -10 q^{-13} -4 q^{-15} +7 q^{-17} +8 q^{-19} -4 q^{-21} -9 q^{-23} + q^{-25} +8 q^{-27} +3 q^{-29} -6 q^{-31} -5 q^{-33} +3 q^{-35} +4 q^{-37} -2 q^{-41} - q^{-43} + 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^{112}-q^{110}-q^{108}+4 q^{102}-2 q^{100}-2 q^{98}-2 q^{96}-2 q^{94}+9 q^{92}+q^{90}-q^{88}-7 q^{86}-9 q^{84}+12 q^{82}+10 q^{80}+5 q^{78}-14 q^{76}-24 q^{74}+9 q^{72}+23 q^{70}+21 q^{68}-15 q^{66}-44 q^{64}-6 q^{62}+29 q^{60}+42 q^{58}-46 q^{54}-25 q^{52}+9 q^{50}+40 q^{48}+23 q^{46}-20 q^{44}-27 q^{42}-17 q^{40}+12 q^{38}+24 q^{36}+10 q^{34}-6 q^{32}-25 q^{30}-14 q^{28}+14 q^{26}+25 q^{24}+7 q^{22}-21 q^{20}-22 q^{18}+9 q^{16}+31 q^{14}+9 q^{12}-22 q^{10}-27 q^8+7 q^6+36 q^4+12 q^2-19-33 q^{-2} -4 q^{-4} +34 q^{-6} +21 q^{-8} -5 q^{-10} -32 q^{-12} -20 q^{-14} +17 q^{-16} +22 q^{-18} +18 q^{-20} -13 q^{-22} -26 q^{-24} -7 q^{-26} +5 q^{-28} +26 q^{-30} +11 q^{-32} -10 q^{-34} -16 q^{-36} -19 q^{-38} +11 q^{-40} +18 q^{-42} +10 q^{-44} -2 q^{-46} -21 q^{-48} -7 q^{-50} +4 q^{-52} +12 q^{-54} +11 q^{-56} -7 q^{-58} -7 q^{-60} -5 q^{-62} + q^{-64} +6 q^{-66} + q^{-68} -2 q^{-72} - q^{-74} + q^{-76} }
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^{165}+q^{163}+q^{161}-2 q^{155}-2 q^{153}+2 q^{151}+4 q^{149}+q^{147}-6 q^{143}-7 q^{141}+q^{139}+9 q^{137}+10 q^{135}+q^{133}-11 q^{131}-17 q^{129}-6 q^{127}+18 q^{125}+28 q^{123}+8 q^{121}-24 q^{119}-37 q^{117}-18 q^{115}+31 q^{113}+62 q^{111}+26 q^{109}-44 q^{107}-84 q^{105}-45 q^{103}+49 q^{101}+113 q^{99}+72 q^{97}-51 q^{95}-138 q^{93}-107 q^{91}+36 q^{89}+156 q^{87}+136 q^{85}-q^{83}-145 q^{81}-163 q^{79}-38 q^{77}+119 q^{75}+163 q^{73}+73 q^{71}-63 q^{69}-142 q^{67}-102 q^{65}+12 q^{63}+99 q^{61}+100 q^{59}+32 q^{57}-45 q^{55}-87 q^{53}-63 q^{51}+3 q^{49}+61 q^{47}+72 q^{45}+31 q^{43}-37 q^{41}-79 q^{39}-46 q^{37}+29 q^{35}+75 q^{33}+53 q^{31}-24 q^{29}-82 q^{27}-54 q^{25}+31 q^{23}+89 q^{21}+60 q^{19}-33 q^{17}-100 q^{15}-70 q^{13}+34 q^{11}+111 q^9+87 q^7-24 q^5-118 q^3-103 q+4 q^{-1} +113 q^{-3} +123 q^{-5} +23 q^{-7} -97 q^{-9} -131 q^{-11} -53 q^{-13} +66 q^{-15} +128 q^{-17} +83 q^{-19} -27 q^{-21} -110 q^{-23} -98 q^{-25} -12 q^{-27} +71 q^{-29} +97 q^{-31} +48 q^{-33} -29 q^{-35} -77 q^{-37} -64 q^{-39} -11 q^{-41} +39 q^{-43} +61 q^{-45} +41 q^{-47} - q^{-49} -39 q^{-51} -48 q^{-53} -28 q^{-55} +4 q^{-57} +36 q^{-59} +43 q^{-61} +22 q^{-63} -13 q^{-65} -35 q^{-67} -34 q^{-69} -13 q^{-71} +18 q^{-73} +33 q^{-75} +25 q^{-77} -19 q^{-81} -24 q^{-83} -15 q^{-85} +6 q^{-87} +17 q^{-89} +14 q^{-91} +3 q^{-93} -5 q^{-95} -9 q^{-97} -7 q^{-99} + q^{-101} +4 q^{-103} +3 q^{-105} + q^{-107} -2 q^{-111} - q^{-113} + q^{-115} }

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^{20}-q^{18}+q^{16}+q^{12}+2 q^{10}+q^6-q^4- q^{-2} + q^{-4} + q^{-10} }
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^{52}-2 q^{50}+4 q^{48}-6 q^{46}+9 q^{44}-12 q^{42}+14 q^{40}-16 q^{38}+15 q^{36}-18 q^{34}+14 q^{32}-16 q^{30}+16 q^{28}-14 q^{26}+18 q^{24}-10 q^{22}+10 q^{20}+2 q^{18}-14 q^{16}+26 q^{14}-44 q^{12}+52 q^{10}-62 q^8+64 q^6-59 q^4+56 q^2-38+26 q^{-2} -7 q^{-4} -10 q^{-6} +24 q^{-8} -36 q^{-10} +41 q^{-12} -40 q^{-14} +36 q^{-16} -28 q^{-18} +19 q^{-20} -12 q^{-22} +6 q^{-24} -2 q^{-26} + q^{-28} }
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^{50}+q^{48}-2 q^{44}-q^{42}-2 q^{38}-2 q^{36}+2 q^{34}+3 q^{32}-q^{30}-q^{28}+3 q^{26}+3 q^{24}-3 q^{22}+q^{18}-q^{16}-q^{14}-q^8+2 q^6+3 q^4+3 q^{-2} + q^{-4} -3 q^{-6} - q^{-8} + q^{-10} + q^{-12} - q^{-14} - q^{-16} +2 q^{-18} + q^{-20} - q^{-22} - q^{-24} + q^{-28} }

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^{42}-q^{40}+2 q^{36}-3 q^{34}-3 q^{32}+2 q^{30}-2 q^{28}-3 q^{26}+5 q^{24}+2 q^{22}+4 q^{18}+2 q^{16}-q^{14}-q^{12}-4 q^6+q^4+3 q^2-2+ q^{-2} +3 q^{-4} -2 q^{-6} +2 q^{-10} -2 q^{-12} + q^{-14} + q^{-16} - q^{-18} + q^{-20} }
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^{27}-q^{25}-q^{23}+q^{21}+2 q^{17}+q^{15}+2 q^{13}+q^9-q^5-q- q^{-3} + q^{-5} + q^{-9} + q^{-13} }

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^{42}+q^{40}-2 q^{38}+2 q^{36}-3 q^{34}+3 q^{32}-4 q^{30}+4 q^{28}-3 q^{26}+3 q^{24}+4 q^{18}-4 q^{16}+7 q^{14}-7 q^{12}+8 q^{10}-8 q^8+6 q^6-5 q^4+3 q^2-2- q^{-2} +3 q^{-4} -4 q^{-6} +4 q^{-8} -4 q^{-10} +4 q^{-12} -3 q^{-14} +3 q^{-16} - q^{-18} + q^{-20} }
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^{68}-q^{64}-q^{62}+q^{60}+2 q^{58}-3 q^{54}-3 q^{52}+3 q^{48}+q^{46}-3 q^{44}-3 q^{42}+q^{40}+5 q^{38}+q^{36}-2 q^{34}-q^{32}+4 q^{30}+3 q^{28}-q^{26}-3 q^{24}+q^{22}+3 q^{20}-3 q^{16}-q^{14}+2 q^{12}-3 q^8-q^6+3 q^4+3 q^2-1-4 q^{-2} +5 q^{-6} +3 q^{-8} -3 q^{-10} -4 q^{-12} + q^{-14} +4 q^{-16} + q^{-18} -3 q^{-20} -2 q^{-22} +2 q^{-24} +2 q^{-26} - q^{-28} - q^{-30} + q^{-34} }

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^{100}-q^{98}+2 q^{96}-2 q^{94}-3 q^{88}+4 q^{86}-5 q^{84}+4 q^{82}-4 q^{80}+3 q^{76}-5 q^{74}+6 q^{72}-7 q^{70}+5 q^{68}-4 q^{66}+3 q^{62}-5 q^{60}+9 q^{58}-6 q^{56}+5 q^{54}-q^{52}-2 q^{50}+7 q^{48}-5 q^{46}+4 q^{44}+3 q^{42}-4 q^{40}+7 q^{38}-3 q^{36}-3 q^{34}+11 q^{32}-13 q^{30}+10 q^{28}-5 q^{26}-5 q^{24}+14 q^{22}-17 q^{20}+14 q^{18}-10 q^{16}+7 q^{12}-12 q^{10}+12 q^8-9 q^6+3 q^4+3 q^2-7+7 q^{-2} -3 q^{-4} -2 q^{-6} +8 q^{-8} -10 q^{-10} +7 q^{-12} -8 q^{-16} +14 q^{-18} -15 q^{-20} +10 q^{-22} -2 q^{-24} -6 q^{-26} +11 q^{-28} -11 q^{-30} +10 q^{-32} -3 q^{-34} - q^{-36} +3 q^{-38} -4 q^{-40} +3 q^{-42} - q^{-44} + q^{-46} }

.

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. Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.

In[3]:=

K = Knot["9 8"];

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 -2 t^2+8 t-11+8 t^{-1} -2 t^{-2} }

In[5]:=

Conway[K][z]

Out[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 1-2 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]=

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]=

{ 31, -2 }

In[8]:=

Jones[K][q]

KnotTheory::loading: Loading precomputed data in Jones4Knots`.

Out[8]=

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+3 q-4+5 q^{-1} -5 q^{-2} +5 q^{-3} -3 q^{-4} +2 q^{-5} - q^{-6} }

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^6+2 z^2 a^4+2 a^4-z^4 a^2-z^2 a^2-z^4-2 z^2-1+z^2 a^{-2} + a^{-2} }

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 a^2 z^8+z^8+2 a^3 z^7+4 a z^7+2 z^7 a^{-1} +2 a^4 z^6+z^6 a^{-2} -z^6+2 a^5 z^5-3 a^3 z^5-13 a z^5-8 z^5 a^{-1} +2 a^6 z^4-4 a^2 z^4-4 z^4 a^{-2} -6 z^4+a^7 z^3+2 a^3 z^3+11 a z^3+8 z^3 a^{-1} -2 a^6 z^2-3 a^4 z^2+2 a^2 z^2+4 z^2 a^{-2} +7 z^2-a^7 z-a^5 z-a^3 z-3 a z-2 z a^{-1} +a^6+2 a^4- a^{-2} -1}

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {8_14, 10_131,}

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}} ): {K11n60,}

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. Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.

In[3]:=

K = Knot["9 8"];

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 -2 t^2+8 t-11+8 t^{-1} -2 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^3-2 q^2+3 q-4+5 q^{-1} -5 q^{-2} +5 q^{-3} -3 q^{-4} +2 q^{-5} - q^{-6} } }

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]=

{8_14, 10_131,}

In[6]:=

DeleteCases[ Select[ AllKnots[], (J === Jones[#][q] || (J /. q -> 1/q) === Jones[#][q]) & ], K ]

KnotTheory::loading: Loading precomputed data in Jones4Knots11`.

Out[6]=

{K11n60,}

Vassiliev invariants

V2 and V3:

(0, -2)

V2,1 through V6,9:

V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9 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 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 -16} 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 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 48} 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 16} 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 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 -\frac{256}{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 \frac{32}{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 -48} 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 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 128} 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 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 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 344} 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 -\frac{224}{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 \frac{608}{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 \frac{104}{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 24}

V_2,1 through V_6,9 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 $r$). The squares with yellow highlighting are those on the "critical diagonals", where $j-2r=s+1$ or $j-2r=s-1$, where $s=$-2 is the signature of 9 8. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

\   r    \    j   \ -5 -4 -3 -2 -1 0 1 2 3 4 χ 7                   1 1 5                 1   -1 3               2 1   1 1             2 1     -1 -1           3 2       1 -3         3 3         0 -5       2 2           0 -7     1 3             2 -9   1 2               -1 -11   1                 1 -13 1                   -1

Integral Khovanov Homology (db, data source)

$\dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}$ $i=-3$ $i=-1$ $r=-5$ ${\mathbb {Z} }$ $r=-4$ ${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$ ${\mathbb {Z} }$ $r=-3$ ${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}$ ${\mathbb {Z} }$ $r=-2$ ${\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}^{2}$ ${\mathbb {Z} }^{2}$ $r=-1$ ${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{3}$ ${\mathbb {Z} }^{3}$ $r=0$ ${\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}^{2}$ ${\mathbb {Z} }^{3}$ $r=1$ ${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{2}$ ${\mathbb {Z} }^{2}$ $r=2$ ${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}^{2}$ ${\mathbb {Z} }^{2}$ $r=3$ ${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}$ ${\mathbb {Z} }$ $r=4$ ${\mathbb {Z} }_{2}$ ${\mathbb {Z} }$

The Coloured Jones Polynomials

The Coloured Jones Polynomials (in the $n+1$-dimensional representation of $sl(2)$)

$n$	$J_{n}$
2	$q^{10}-2q^{9}-q^{8}+6q^{7}-4q^{6}-6q^{5}+12q^{4}-3q^{3}-13q^{2}+16q+1-19q^{-1}+17q^{-2}+5q^{-3}-22q^{-4}+15q^{-5}+8q^{-6}-20q^{-7}+11q^{-8}+6q^{-9}-13q^{-10}+7q^{-11}+2q^{-12}-6q^{-13}+4q^{-14}-2q^{-16}+q^{-17}$
3	$q^{21}-2q^{20}-q^{19}+2q^{18}+5q^{17}-3q^{16}-9q^{15}+q^{14}+14q^{13}+2q^{12}-16q^{11}-9q^{10}+19q^{9}+14q^{8}-17q^{7}-20q^{6}+13q^{5}+24q^{4}-8q^{3}-26q^{2}+3q+26+4q^{-1}-25q^{-2}-9q^{-3}+22q^{-4}+16q^{-5}-21q^{-6}-19q^{-7}+15q^{-8}+26q^{-9}-14q^{-10}-24q^{-11}+6q^{-12}+27q^{-13}-7q^{-14}-17q^{-15}-q^{-16}+15q^{-17}-2q^{-18}-6q^{-19}+q^{-20}+2q^{-21}-3q^{-22}+2q^{-23}+3q^{-24}-3q^{-25}-3q^{-26}+2q^{-27}+4q^{-28}-3q^{-29}-q^{-30}+2q^{-32}-q^{-33}$
4	$q^{36}-2q^{35}-q^{34}+2q^{33}+q^{32}+6q^{31}-7q^{30}-7q^{29}+q^{27}+24q^{26}-6q^{25}-15q^{24}-11q^{23}-13q^{22}+43q^{21}+6q^{20}-7q^{19}-18q^{18}-43q^{17}+46q^{16}+12q^{15}+14q^{14}-3q^{13}-64q^{12}+34q^{11}-7q^{10}+27q^{9}+28q^{8}-60q^{7}+29q^{6}-44q^{5}+15q^{4}+55q^{3}-34q^{2}+42q-82-14q^{-1}+69q^{-2}-3q^{-3}+66q^{-4}-111q^{-5}-48q^{-6}+74q^{-7}+28q^{-8}+88q^{-9}-133q^{-10}-79q^{-11}+75q^{-12}+56q^{-13}+106q^{-14}-144q^{-15}-107q^{-16}+64q^{-17}+75q^{-18}+122q^{-19}-130q^{-20}-119q^{-21}+35q^{-22}+65q^{-23}+129q^{-24}-87q^{-25}-102q^{-26}+4q^{-27}+31q^{-28}+108q^{-29}-41q^{-30}-60q^{-31}-9q^{-32}-4q^{-33}+70q^{-34}-12q^{-35}-24q^{-36}-7q^{-37}-18q^{-38}+37q^{-39}-2q^{-40}-5q^{-41}-2q^{-42}-16q^{-43}+16q^{-44}+q^{-46}-8q^{-48}+5q^{-49}+q^{-51}-2q^{-53}+q^{-54}$
5	$q^{55}-2q^{54}-q^{53}+2q^{52}+q^{51}+2q^{50}+2q^{49}-5q^{48}-9q^{47}+5q^{45}+10q^{44}+13q^{43}-2q^{42}-20q^{41}-21q^{40}-4q^{39}+15q^{38}+32q^{37}+23q^{36}-12q^{35}-36q^{34}-35q^{33}-6q^{32}+31q^{31}+45q^{30}+23q^{29}-15q^{28}-42q^{27}-38q^{26}-q^{25}+25q^{24}+32q^{23}+23q^{22}-18q^{20}-23q^{19}-25q^{18}-21q^{17}+10q^{16}+48q^{15}+59q^{14}+26q^{13}-51q^{12}-104q^{11}-76q^{10}+36q^{9}+142q^{8}+136q^{7}-6q^{6}-166q^{5}-195q^{4}-42q^{3}+176q^{2}+256q+94-176q^{-1}-304q^{-2}-149q^{-3}+161q^{-4}+350q^{-5}+205q^{-6}-152q^{-7}-381q^{-8}-253q^{-9}+131q^{-10}+417q^{-11}+298q^{-12}-123q^{-13}-439q^{-14}-338q^{-15}+103q^{-16}+475q^{-17}+375q^{-18}-101q^{-19}-485q^{-20}-413q^{-21}+70q^{-22}+517q^{-23}+443q^{-24}-60q^{-25}-496q^{-26}-471q^{-27}+4q^{-28}+493q^{-29}+485q^{-30}+17q^{-31}-428q^{-32}-472q^{-33}-83q^{-34}+379q^{-35}+445q^{-36}+96q^{-37}-292q^{-38}-382q^{-39}-127q^{-40}+222q^{-41}+320q^{-42}+114q^{-43}-148q^{-44}-245q^{-45}-107q^{-46}+102q^{-47}+177q^{-48}+83q^{-49}-61q^{-50}-122q^{-51}-66q^{-52}+38q^{-53}+83q^{-54}+44q^{-55}-21q^{-56}-52q^{-57}-30q^{-58}+7q^{-59}+34q^{-60}+25q^{-61}-8q^{-62}-20q^{-63}-10q^{-64}-3q^{-65}+10q^{-66}+14q^{-67}-2q^{-68}-8q^{-69}-q^{-70}-4q^{-71}+2q^{-72}+6q^{-73}-q^{-74}-2q^{-75}-q^{-77}+2q^{-79}-q^{-80}$
6	$q^{78}-2q^{77}-q^{76}+2q^{75}+q^{74}+2q^{73}-2q^{72}+4q^{71}-7q^{70}-9q^{69}+3q^{68}+4q^{67}+11q^{66}+2q^{65}+18q^{64}-14q^{63}-27q^{62}-13q^{61}-7q^{60}+17q^{59}+9q^{58}+63q^{57}+4q^{56}-31q^{55}-35q^{54}-43q^{53}-12q^{52}-20q^{51}+102q^{50}+44q^{49}+13q^{48}-15q^{47}-46q^{46}-48q^{45}-98q^{44}+82q^{43}+28q^{42}+44q^{41}+31q^{40}+23q^{39}+q^{38}-125q^{37}+53q^{36}-56q^{35}-29q^{34}-23q^{33}+66q^{32}+108q^{31}-21q^{30}+156q^{29}-69q^{28}-138q^{27}-225q^{26}-62q^{25}+105q^{24}+102q^{23}+401q^{22}+125q^{21}-99q^{20}-423q^{19}-337q^{18}-121q^{17}+55q^{16}+614q^{15}+465q^{14}+170q^{13}-432q^{12}-571q^{11}-483q^{10}-223q^{9}+629q^{8}+765q^{7}+569q^{6}-215q^{5}-622q^{4}-805q^{3}-624q^{2}+431q+904+938q^{-1}+123q^{-2}-493q^{-3}-993q^{-4}-1007q^{-5}+126q^{-6}+895q^{-7}+1200q^{-8}+455q^{-9}-285q^{-10}-1064q^{-11}-1303q^{-12}-171q^{-13}+830q^{-14}+1370q^{-15}+721q^{-16}-101q^{-17}-1098q^{-18}-1519q^{-19}-405q^{-20}+789q^{-21}+1508q^{-22}+926q^{-23}+22q^{-24}-1150q^{-25}-1701q^{-26}-591q^{-27}+772q^{-28}+1639q^{-29}+1118q^{-30}+135q^{-31}-1179q^{-32}-1854q^{-33}-792q^{-34}+682q^{-35}+1690q^{-36}+1297q^{-37}+325q^{-38}-1063q^{-39}-1883q^{-40}-992q^{-41}+428q^{-42}+1519q^{-43}+1347q^{-44}+556q^{-45}-737q^{-46}-1654q^{-47}-1048q^{-48}+99q^{-49}+1105q^{-50}+1136q^{-51}+653q^{-52}-342q^{-53}-1185q^{-54}-847q^{-55}-108q^{-56}+635q^{-57}+727q^{-58}+526q^{-59}-82q^{-60}-695q^{-61}-496q^{-62}-119q^{-63}+307q^{-64}+343q^{-65}+296q^{-66}+q^{-67}-361q^{-68}-207q^{-69}-46q^{-70}+151q^{-71}+118q^{-72}+125q^{-73}+2q^{-74}-190q^{-75}-59q^{-76}-2q^{-77}+85q^{-78}+31q^{-79}+48q^{-80}-q^{-81}-106q^{-82}-9q^{-83}+4q^{-84}+46q^{-85}+7q^{-86}+23q^{-87}+q^{-88}-55q^{-89}+2q^{-90}-2q^{-91}+21q^{-92}+13q^{-94}+2q^{-95}-24q^{-96}+4q^{-97}-4q^{-98}+8q^{-99}-q^{-100}+5q^{-101}+q^{-102}-8q^{-103}+3q^{-104}-2q^{-105}+2q^{-106}+q^{-108}-2q^{-110}+q^{-111}$
7	$q^{105}-2q^{104}-q^{103}+2q^{102}+q^{101}+2q^{100}-2q^{99}+2q^{97}-7q^{96}-6q^{95}+2q^{94}+4q^{93}+13q^{92}+4q^{91}+9q^{89}-18q^{88}-23q^{87}-16q^{86}-9q^{85}+27q^{84}+25q^{83}+21q^{82}+41q^{81}-6q^{80}-34q^{79}-47q^{78}-74q^{77}-2q^{76}+20q^{75}+33q^{74}+98q^{73}+51q^{72}+22q^{71}-21q^{70}-120q^{69}-68q^{68}-47q^{67}-37q^{66}+88q^{65}+66q^{64}+87q^{63}+92q^{62}-60q^{61}-30q^{60}-55q^{59}-106q^{58}+8q^{57}-47q^{56}-9q^{55}+86q^{54}-21q^{53}+89q^{52}+111q^{51}+24q^{50}+113q^{49}-87q^{48}-194q^{47}-160q^{46}-282q^{45}-37q^{44}+189q^{43}+276q^{42}+518q^{41}+280q^{40}-60q^{39}-308q^{38}-739q^{37}-585q^{36}-217q^{35}+169q^{34}+857q^{33}+926q^{32}+616q^{31}+119q^{30}-826q^{29}-1166q^{28}-1039q^{27}-577q^{26}+584q^{25}+1262q^{24}+1432q^{23}+1110q^{22}-168q^{21}-1154q^{20}-1689q^{19}-1640q^{18}-385q^{17}+837q^{16}+1754q^{15}+2101q^{14}+1008q^{13}-356q^{12}-1635q^{11}-2413q^{10}-1596q^{9}-248q^{8}+1313q^{7}+2554q^{6}+2137q^{5}+897q^{4}-861q^{3}-2540q^{2}-2550q-1529+315q^{-1}+2369q^{-2}+2843q^{-3}+2130q^{-4}+271q^{-5}-2121q^{-6}-3031q^{-7}-2635q^{-8}-832q^{-9}+1789q^{-10}+3125q^{-11}+3072q^{-12}+1371q^{-13}-1466q^{-14}-3167q^{-15}-3425q^{-16}-1833q^{-17}+1156q^{-18}+3174q^{-19}+3717q^{-20}+2229q^{-21}-889q^{-22}-3187q^{-23}-3968q^{-24}-2553q^{-25}+684q^{-26}+3226q^{-27}+4189q^{-28}+2816q^{-29}-538q^{-30}-3284q^{-31}-4403q^{-32}-3058q^{-33}+419q^{-34}+3389q^{-35}+4638q^{-36}+3272q^{-37}-328q^{-38}-3462q^{-39}-4848q^{-40}-3538q^{-41}+154q^{-42}+3524q^{-43}+5082q^{-44}+3800q^{-45}+52q^{-46}-3449q^{-47}-5191q^{-48}-4102q^{-49}-422q^{-50}+3238q^{-51}+5228q^{-52}+4359q^{-53}+816q^{-54}-2844q^{-55}-5022q^{-56}-4488q^{-57}-1295q^{-58}+2267q^{-59}+4638q^{-60}+4470q^{-61}+1682q^{-62}-1637q^{-63}-4014q^{-64}-4185q^{-65}-1941q^{-66}+945q^{-67}+3259q^{-68}+3730q^{-69}+2007q^{-70}-391q^{-71}-2460q^{-72}-3070q^{-73}-1872q^{-74}-39q^{-75}+1705q^{-76}+2370q^{-77}+1579q^{-78}+275q^{-79}-1070q^{-80}-1693q^{-81}-1208q^{-82}-357q^{-83}+616q^{-84}+1104q^{-85}+816q^{-86}+339q^{-87}-303q^{-88}-659q^{-89}-498q^{-90}-258q^{-91}+136q^{-92}+358q^{-93}+242q^{-94}+156q^{-95}-44q^{-96}-161q^{-97}-78q^{-98}-92q^{-99}+13q^{-100}+72q^{-101}-12q^{-102}+26q^{-103}-14q^{-104}-15q^{-105}+62q^{-106}-2q^{-107}+6q^{-108}+3q^{-109}-59q^{-110}-11q^{-111}-22q^{-112}-6q^{-113}+65q^{-114}+20q^{-115}+12q^{-116}-q^{-117}-42q^{-118}-5q^{-119}-19q^{-120}-13q^{-121}+34q^{-122}+13q^{-123}+10q^{-124}+3q^{-125}-20q^{-126}-8q^{-128}-9q^{-129}+14q^{-130}+2q^{-131}+4q^{-132}+4q^{-133}-8q^{-134}+q^{-135}-3q^{-136}-2q^{-137}+5q^{-138}-q^{-139}+2q^{-141}-2q^{-142}-q^{-144}+2q^{-146}-q^{-147}$

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.

9_7 9_9