9 17

9_16

9_18

Visit 9 17's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 9 17's page at Knotilus! Visit 9 17's page at the original Knot Atlas!

9 17 Quick Notes

9 17 Further Notes and Views

Knot presentations

Planar diagram presentation	X1425 X5,12,6,13 X3,11,4,10 X11,3,12,2 X7,14,8,15 X13,6,14,7 X15,18,16,1 X9,17,10,16 X17,9,18,8
Gauss code	-1, 4, -3, 1, -2, 6, -5, 9, -8, 3, -4, 2, -6, 5, -7, 8, -9, 7
Dowker-Thistlethwaite code	4 10 12 14 16 2 6 18 8
Conway Notation	[21312]

Three dimensional invariants

Symmetry type Reversible Unknotting number 2 3-genus 3 Bridge index 2 Super bridge index $\{4,7\}$ Nakanishi index 1 Maximal Thurston-Bennequin number [-8][-3] Hyperbolic Volume 9.47458 A-Polynomial See Data:9 17/A-polynomial

[edit Notes for 9 17's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus $1$ Topological 4 genus $1$ Concordance genus $3$ Rasmussen s-Invariant -2

[edit Notes for 9 17's four dimensional invariants]

Polynomial invariants

Alexander polynomial	$t^{3}-5t^{2}+9t-9+9t^{-1}-5t^{-2}+t^{-3}$
Conway polynomial	$z^{6}+z^{4}-2z^{2}+1$
2nd Alexander ideal (db, data sources)	$\{1\}$
Determinant and Signature	{ 39, -2 }
Jones polynomial	$q^{3}-2q^{2}+4q-5+6q^{-1}-7q^{-2}+6q^{-3}-4q^{-4}+3q^{-5}-q^{-6}$
HOMFLY-PT polynomial (db, data sources)	$a^{2}z^{6}-a^{4}z^{4}+4a^{2}z^{4}-2z^{4}-2a^{4}z^{2}+5a^{2}z^{2}+z^{2}a^{-2}-6z^{2}+2a^{2}+2a^{-2}-3$
Kauffman polynomial (db, data sources)	$a^{2}z^{8}+z^{8}+3a^{3}z^{7}+5az^{7}+2z^{7}a^{-1}+4a^{4}z^{6}+4a^{2}z^{6}+z^{6}a^{-2}+z^{6}+4a^{5}z^{5}-2a^{3}z^{5}-13az^{5}-7z^{5}a^{-1}+3a^{6}z^{4}-3a^{4}z^{4}-14a^{2}z^{4}-4z^{4}a^{-2}-12z^{4}+a^{7}z^{3}-3a^{5}z^{3}-4a^{3}z^{3}+6az^{3}+6z^{3}a^{-1}-2a^{6}z^{2}-a^{4}z^{2}+9a^{2}z^{2}+5z^{2}a^{-2}+13z^{2}+a^{5}z+3a^{3}z+az-za^{-1}-2a^{2}-2a^{-2}-3$
The A2 invariant	$-q^{18}+q^{16}+q^{12}+2q^{10}-q^{8}+q^{6}-2q^{4}-q^{-2}+q^{-4}+q^{-8}+q^{-10}$
The G2 invariant	$q^{100}-2q^{98}+3q^{96}-4q^{94}+q^{92}-3q^{88}+8q^{86}-9q^{84}+12q^{82}-9q^{80}+3q^{78}+4q^{76}-9q^{74}+14q^{72}-20q^{70}+17q^{68}-12q^{66}+q^{64}+10q^{62}-18q^{60}+22q^{58}-16q^{56}+8q^{54}+q^{52}-14q^{50}+16q^{48}-7q^{46}-2q^{44}+15q^{42}-18q^{40}+15q^{38}+3q^{36}-17q^{34}+30q^{32}-35q^{30}+26q^{28}-6q^{26}-14q^{24}+33q^{22}-38q^{20}+32q^{18}-16q^{16}-4q^{14}+15q^{12}-26q^{10}+22q^{8}-12q^{6}-4q^{4}+14q^{2}-17+10q^{-2}+3q^{-4}-17q^{-6}+23q^{-8}-24q^{-10}+11q^{-12}+5q^{-14}-21q^{-16}+32q^{-18}-27q^{-20}+17q^{-22}-q^{-24}-11q^{-26}+19q^{-28}-18q^{-30}+14q^{-32}-4q^{-34}-2q^{-36}+5q^{-38}-5q^{-40}+4q^{-42}-q^{-44}+q^{-46}$

Further Quantum Invariants

Further quantum knot invariants for 9_17.

A1 Invariants.

Weight	Invariant
1	$-q^{13}+2q^{11}-q^{9}+2q^{7}-q^{5}-q^{3}+q-q^{-1}+2q^{-3}-q^{-5}+q^{-7}$
2	$q^{36}-2q^{34}-q^{32}+4q^{30}-4q^{28}+q^{26}+7q^{24}-7q^{22}-q^{20}+7q^{18}-5q^{16}-4q^{14}+4q^{12}+2q^{10}-3q^{8}-q^{6}+6q^{4}-q^{2}-5+7q^{-2}+q^{-4}-8q^{-6}+4q^{-8}+4q^{-10}-6q^{-12}+q^{-14}+4q^{-16}-2q^{-18}-q^{-20}+q^{-22}$
3	$-q^{69}+2q^{67}+q^{65}-2q^{63}-2q^{61}+q^{59}+2q^{57}-5q^{55}+3q^{53}+7q^{51}-3q^{49}-12q^{47}+7q^{45}+17q^{43}-8q^{41}-22q^{39}+4q^{37}+24q^{35}-22q^{31}-8q^{29}+18q^{27}+12q^{25}-6q^{23}-17q^{21}+18q^{17}+7q^{15}-16q^{13}-13q^{11}+15q^{9}+16q^{7}-11q^{5}-21q^{3}+9q+22q^{-1}-2q^{-3}-23q^{-5}-4q^{-7}+23q^{-9}+11q^{-11}-19q^{-13}-15q^{-15}+12q^{-17}+18q^{-19}-4q^{-21}-18q^{-23}-q^{-25}+13q^{-27}+6q^{-29}-8q^{-31}-7q^{-33}+3q^{-35}+5q^{-37}-2q^{-41}-q^{-43}+q^{-45}$
4	$q^{112}-2q^{110}-q^{108}+2q^{106}+5q^{102}-4q^{100}-q^{98}-9q^{94}+9q^{92}+9q^{88}+q^{86}-28q^{84}+q^{82}+12q^{80}+36q^{78}+9q^{76}-60q^{74}-30q^{72}+17q^{70}+76q^{68}+39q^{66}-80q^{64}-74q^{62}-6q^{60}+96q^{58}+80q^{56}-50q^{54}-86q^{52}-55q^{50}+56q^{48}+93q^{46}+14q^{44}-44q^{42}-75q^{40}-14q^{38}+51q^{36}+57q^{34}+19q^{32}-56q^{30}-64q^{28}+q^{26}+70q^{24}+53q^{22}-30q^{20}-80q^{18}-29q^{16}+71q^{14}+66q^{12}-12q^{10}-85q^{8}-51q^{6}+64q^{4}+77q^{2}+18-78q^{-2}-78q^{-4}+34q^{-6}+76q^{-8}+58q^{-10}-45q^{-12}-91q^{-14}-18q^{-16}+40q^{-18}+85q^{-20}+13q^{-22}-64q^{-24}-52q^{-26}-16q^{-28}+64q^{-30}+50q^{-32}-7q^{-34}-38q^{-36}-52q^{-38}+12q^{-40}+38q^{-42}+27q^{-44}+q^{-46}-37q^{-48}-16q^{-50}+4q^{-52}+18q^{-54}+17q^{-56}-8q^{-58}-9q^{-60}-7q^{-62}+q^{-64}+7q^{-66}+q^{-68}-2q^{-72}-q^{-74}+q^{-76}$
5	$-q^{165}+2q^{163}+q^{161}-2q^{159}-3q^{155}-2q^{153}+3q^{151}+6q^{149}+3q^{147}+2q^{145}-6q^{143}-13q^{141}-9q^{139}+8q^{137}+27q^{135}+16q^{133}-9q^{131}-40q^{129}-46q^{127}+10q^{125}+78q^{123}+71q^{121}-7q^{119}-103q^{117}-128q^{115}-13q^{113}+159q^{111}+194q^{109}+37q^{107}-194q^{105}-279q^{103}-97q^{101}+218q^{99}+372q^{97}+176q^{95}-211q^{93}-442q^{91}-274q^{89}+152q^{87}+468q^{85}+377q^{83}-56q^{81}-433q^{79}-435q^{77}-72q^{75}+338q^{73}+439q^{71}+185q^{69}-189q^{67}-386q^{65}-271q^{63}+43q^{61}+283q^{59}+291q^{57}+103q^{55}-157q^{53}-285q^{51}-193q^{49}+43q^{47}+239q^{45}+251q^{43}+50q^{41}-205q^{39}-281q^{37}-101q^{35}+174q^{33}+292q^{31}+133q^{29}-160q^{27}-311q^{25}-151q^{23}+168q^{21}+325q^{19}+176q^{17}-153q^{15}-356q^{13}-214q^{11}+143q^{9}+372q^{7}+260q^{5}-95q^{3}-375q-322q^{-1}+27q^{-3}+348q^{-5}+369q^{-7}+69q^{-9}-286q^{-11}-391q^{-13}-169q^{-15}+186q^{-17}+376q^{-19}+257q^{-21}-64q^{-23}-313q^{-25}-300q^{-27}-65q^{-29}+206q^{-31}+300q^{-33}+166q^{-35}-81q^{-37}-244q^{-39}-212q^{-41}-42q^{-43}+146q^{-45}+211q^{-47}+122q^{-49}-43q^{-51}-154q^{-53}-147q^{-55}-50q^{-57}+76q^{-59}+132q^{-61}+90q^{-63}-3q^{-65}-79q^{-67}-92q^{-69}-44q^{-71}+27q^{-73}+66q^{-75}+55q^{-77}+9q^{-79}-31q^{-81}-41q^{-83}-26q^{-85}+5q^{-87}+24q^{-89}+21q^{-91}+5q^{-93}-6q^{-95}-11q^{-97}-9q^{-99}+q^{-101}+5q^{-103}+3q^{-105}+q^{-107}-2q^{-111}-q^{-113}+q^{-115}$

A2 Invariants.

Weight	Invariant
1,0	$-q^{18}+q^{16}+q^{12}+2q^{10}-q^{8}+q^{6}-2q^{4}-q^{-2}+q^{-4}+q^{-8}+q^{-10}$
1,1	$q^{52}-4q^{50}+8q^{48}-12q^{46}+18q^{44}-28q^{42}+36q^{40}-40q^{38}+45q^{36}-56q^{34}+60q^{32}-56q^{30}+60q^{28}-50q^{26}+40q^{24}-16q^{22}-17q^{20}+44q^{18}-88q^{16}+114q^{14}-141q^{12}+160q^{10}-156q^{8}+148q^{6}-117q^{4}+92q^{2}-50+6q^{-2}+31q^{-4}-62q^{-6}+80q^{-8}-94q^{-10}+92q^{-12}-78q^{-14}+64q^{-16}-46q^{-18}+29q^{-20}-16q^{-22}+8q^{-24}-2q^{-26}+q^{-28}$
2,0	$q^{46}-q^{44}-q^{42}-q^{38}+2q^{34}+3q^{32}-2q^{30}+4q^{26}+2q^{24}-6q^{22}-q^{20}+3q^{18}-3q^{16}-3q^{14}+2q^{10}-2q^{8}+2q^{6}+4q^{4}+q^{2}+1+4q^{-2}-5q^{-6}+2q^{-10}-q^{-12}-3q^{-14}+q^{-16}+3q^{-18}-2q^{-22}+q^{-26}+q^{-28}$

A3 Invariants.

Weight	Invariant
0,1,0	$q^{42}-2q^{40}-q^{38}+4q^{36}-3q^{34}-2q^{32}+7q^{30}-q^{28}-5q^{26}+6q^{24}-2q^{22}-6q^{20}+3q^{18}+q^{16}+q^{12}+5q^{10}+3q^{8}-5q^{6}+q^{4}+3q^{2}-7-q^{-2}+4q^{-4}-5q^{-6}+q^{-8}+4q^{-10}-2q^{-12}+2q^{-14}+2q^{-16}-q^{-18}+q^{-20}$
1,0,0	$-q^{23}+q^{21}-q^{19}+2q^{17}+2q^{13}+q^{9}-q^{5}-2q-2q^{-3}+q^{-5}+2q^{-9}+q^{-11}+q^{-13}$

A4 Invariants.

Weight	Invariant
0,1,0,0	$q^{52}-q^{50}-2q^{48}+2q^{46}+q^{44}-4q^{42}-q^{40}+5q^{38}+2q^{36}-2q^{34}+3q^{32}+6q^{30}-3q^{28}-5q^{26}+q^{24}-3q^{22}-7q^{20}+2q^{18}+4q^{16}-q^{14}+3q^{12}+8q^{10}+3q^{8}-3q^{6}+2q^{4}+4q^{2}-4-5q^{-2}-q^{-6}-4q^{-8}-q^{-10}+q^{-12}+q^{-14}+q^{-16}+2q^{-18}+2q^{-20}+q^{-22}+q^{-24}+q^{-26}$
1,0,0,0	$-q^{28}+q^{26}-q^{24}+q^{22}+q^{20}+2q^{16}+2q^{12}+q^{8}-q^{6}-2q^{2}-2-q^{-2}-2q^{-4}+q^{-6}+2q^{-10}+2q^{-12}+q^{-14}+q^{-16}$

B2 Invariants.

Weight	Invariant
0,1	$-q^{42}+2q^{40}-3q^{38}+4q^{36}-5q^{34}+6q^{32}-7q^{30}+7q^{28}-5q^{26}+4q^{24}-2q^{20}+7q^{18}-9q^{16}+12q^{14}-13q^{12}+13q^{10}-13q^{8}+9q^{6}-7q^{4}+3q^{2}-1-3q^{-2}+6q^{-4}-7q^{-6}+7q^{-8}-6q^{-10}+6q^{-12}-4q^{-14}+4q^{-16}-q^{-18}+q^{-20}$
1,0	$q^{68}-2q^{64}-2q^{62}+q^{60}+4q^{58}+q^{56}-4q^{54}-4q^{52}+2q^{50}+7q^{48}+3q^{46}-5q^{44}-5q^{42}+2q^{40}+7q^{38}-q^{36}-7q^{34}-3q^{32}+5q^{30}+3q^{28}-4q^{26}-4q^{24}+3q^{22}+6q^{20}-3q^{16}+q^{14}+5q^{12}-5q^{8}-2q^{6}+5q^{4}+4q^{2}-4-8q^{-2}+8q^{-6}+3q^{-8}-6q^{-10}-6q^{-12}+3q^{-14}+6q^{-16}+q^{-18}-4q^{-20}-2q^{-22}+3q^{-24}+3q^{-26}-q^{-28}-q^{-30}+q^{-34}$

D4 Invariants.

Weight	Invariant
1,0,0,0	$q^{58}-2q^{56}+q^{54}-2q^{52}+4q^{50}-4q^{48}+3q^{46}-4q^{44}+7q^{42}-4q^{40}+4q^{38}-5q^{36}+4q^{34}-2q^{32}-q^{30}-5q^{26}+6q^{24}-6q^{22}+10q^{20}-8q^{18}+13q^{16}-7q^{14}+12q^{12}-8q^{10}+7q^{8}-6q^{6}+2q^{4}-5q^{2}-2-5q^{-4}+3q^{-6}-6q^{-8}+7q^{-10}-4q^{-12}+6q^{-14}-3q^{-16}+6q^{-18}-2q^{-20}+3q^{-22}-q^{-24}+q^{-26}$

G2 Invariants.

Weight

Invariant

1,0

$q^{100}-2q^{98}+3q^{96}-4q^{94}+q^{92}-3q^{88}+8q^{86}-9q^{84}+12q^{82}-9q^{80}+3q^{78}+4q^{76}-9q^{74}+14q^{72}-20q^{70}+17q^{68}-12q^{66}+q^{64}+10q^{62}-18q^{60}+22q^{58}-16q^{56}+8q^{54}+q^{52}-14q^{50}+16q^{48}-7q^{46}-2q^{44}+15q^{42}-18q^{40}+15q^{38}+3q^{36}-17q^{34}+30q^{32}-35q^{30}+26q^{28}-6q^{26}-14q^{24}+33q^{22}-38q^{20}+32q^{18}-16q^{16}-4q^{14}+15q^{12}-26q^{10}+22q^{8}-12q^{6}-4q^{4}+14q^{2}-17+10q^{-2}+3q^{-4}-17q^{-6}+23q^{-8}-24q^{-10}+11q^{-12}+5q^{-14}-21q^{-16}+32q^{-18}-27q^{-20}+17q^{-22}-q^{-24}-11q^{-26}+19q^{-28}-18q^{-30}+14q^{-32}-4q^{-34}-2q^{-36}+5q^{-38}-5q^{-40}+4q^{-42}-q^{-44}+q^{-46}$

.

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 17"];

In[4]:=

Alexander[K][t]

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

Out[4]=

$t^{3}-5t^{2}+9t-9+9t^{-1}-5t^{-2}+t^{-3}$

In[5]:=

Conway[K][z]

Out[5]=

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

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]=

$\{1\}$

In[7]:=

{KnotDet[K], KnotSignature[K]}

Out[7]=

{ 39, -2 }

In[8]:=

Jones[K][q]

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

Out[8]=

$q^{3}-2q^{2}+4q-5+6q^{-1}-7q^{-2}+6q^{-3}-4q^{-4}+3q^{-5}-q^{-6}$

In[9]:=

HOMFLYPT[K][a, z]

KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.

Out[9]=

$a^{2}z^{6}-a^{4}z^{4}+4a^{2}z^{4}-2z^{4}-2a^{4}z^{2}+5a^{2}z^{2}+z^{2}a^{-2}-6z^{2}+2a^{2}+2a^{-2}-3$

In[10]:=

Kauffman[K][a, z]

KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.

Out[10]=

$a^{2}z^{8}+z^{8}+3a^{3}z^{7}+5az^{7}+2z^{7}a^{-1}+4a^{4}z^{6}+4a^{2}z^{6}+z^{6}a^{-2}+z^{6}+4a^{5}z^{5}-2a^{3}z^{5}-13az^{5}-7z^{5}a^{-1}+3a^{6}z^{4}-3a^{4}z^{4}-14a^{2}z^{4}-4z^{4}a^{-2}-12z^{4}+a^{7}z^{3}-3a^{5}z^{3}-4a^{3}z^{3}+6az^{3}+6z^{3}a^{-1}-2a^{6}z^{2}-a^{4}z^{2}+9a^{2}z^{2}+5z^{2}a^{-2}+13z^{2}+a^{5}z+3a^{3}z+az-za^{-1}-2a^{2}-2a^{-2}-3$

Vassiliev invariants

V2 and V3:

(-2, 0)

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 $-8$ $0$ $32$ ${\frac {116}{3}}$ ${\frac {28}{3}}$ $0$ $32$ $32$ $0$ $-{\frac {256}{3}}$ $0$ $-{\frac {928}{3}}$ $-{\frac {224}{3}}$ $-{\frac {4951}{15}}$ $-{\frac {1796}{15}}$ $-{\frac {2764}{45}}$ ${\frac {7}{9}}$ ${\frac {89}{15}}$

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 $t^{r}q^{j}$ are shown, along with their alternating sums $\chi$ (fixed $j$, 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 17. 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								3	1		2
1							2	1			-1
-1						4	3				1
-3					4	3					-1
-5				2	3						-1
-7			2	4							2
-9		1	2								-1
-11		2									2
-13	1										-1

Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session.

${\textrm {Include}}({\textrm {ColouredJonesM.mhtml}})$

In[1]:=	<< KnotTheory`
Loading KnotTheory` (version of August 17, 2005, 14:44:34)...
In[2]:=	Crossings[Knot[9, 17]]
Out[2]=	9
In[3]:=	PD[Knot[9, 17]]
Out[3]=	PD[X[1, 4, 2, 5], X[5, 12, 6, 13], X[3, 11, 4, 10], X[11, 3, 12, 2], X[7, 14, 8, 15], X[13, 6, 14, 7], X[15, 18, 16, 1], X[9, 17, 10, 16], X[17, 9, 18, 8]]
In[4]:=	GaussCode[Knot[9, 17]]
Out[4]=	GaussCode[-1, 4, -3, 1, -2, 6, -5, 9, -8, 3, -4, 2, -6, 5, -7, 8, -9, 7]
In[5]:=	BR[Knot[9, 17]]
Out[5]=	BR[4, {1, -2, 1, -2, -2, -2, 3, -2, 3}]
In[6]:=	alex = Alexander[Knot[9, 17]][t]
Out[6]=	-3 5 9 2 3 -9 + t - -- + - + 9 t - 5 t + t 2 t t
In[7]:=	Conway[Knot[9, 17]][z]
Out[7]=	2 4 6 1 - 2 z + z + z
In[8]:=	Select[AllKnots[], (alex === Alexander[#][t])&]
Out[8]=	{Knot[9, 17]}
In[9]:=	{KnotDet[Knot[9, 17]], KnotSignature[Knot[9, 17]]}
Out[9]=	{39, -2}
In[10]:=	J=Jones[Knot[9, 17]][q]
Out[10]=	-6 3 4 6 7 6 2 3 -5 - q + -- - -- + -- - -- + - + 4 q - 2 q + q 5 4 3 2 q q q q q
In[11]:=	Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]
Out[11]=	{Knot[9, 17]}
In[12]:=	A2Invariant[Knot[9, 17]][q]
Out[12]=	-18 -16 -12 2 -8 -6 2 2 4 8 10 -q + q + q + --- - q + q - -- - q + q + q + q 10 4 q q
In[13]:=	Kauffman[Knot[9, 17]][a, z]
Out[13]=	2 2 2 z 3 5 2 5 z 2 2 -3 - -- - 2 a - - + a z + 3 a z + a z + 13 z + ---- + 9 a z - 2 a 2 a a 3 4 2 6 2 6 z 3 3 3 5 3 7 3 4 a z - 2 a z + ---- + 6 a z - 4 a z - 3 a z + a z - 12 z - a 4 5 4 z 2 4 4 4 6 4 7 z 5 3 5 ---- - 14 a z - 3 a z + 3 a z - ---- - 13 a z - 2 a z + 2 a a 6 7 5 5 6 z 2 6 4 6 2 z 7 3 7 4 a z + z + -- + 4 a z + 4 a z + ---- + 5 a z + 3 a z + 2 a a 8 2 8 z + a z
In[14]:=	{Vassiliev[2][Knot[9, 17]], Vassiliev[3][Knot[9, 17]]}
Out[14]=	{0, 0}
In[15]:=	Kh[Knot[9, 17]][q, t]
Out[15]=	3 4 1 2 1 2 2 4 2 -- + - + ------ + ------ + ----- + ----- + ----- + ----- + ----- + 3 q 13 5 11 4 9 4 9 3 7 3 7 2 5 2 q q t q t q t q t q t q t q t 3 4 3 t 2 3 2 3 3 5 3 7 4 ---- + ---- + --- + 2 q t + q t + 3 q t + q t + q t + q t 5 3 q q t q t