T(29,2)

T(29,2) Quantum Invariants.

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["T(29,2)"];

In[4]:=

Alexander[K][t]

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

Out[4]=

t14−t13 + t12−t11 + t10−t9 + t8−t7 + t6−t5 + t4−t3 + t2−t + 1−t−1 + t−2−t−3 + t−4−t−5 + t−6−t−7 + t−8−t−9 + t−10−t−11 + t−12−t−13 + t−14

In[5]:=

Conway[K][z]

Out[5]=

z28 + 27z26 + 325z24 + 2300z22 + 10626z20 + 33649z18 + 74613z16 + 116280z14 + 125970z12 + 92378z10 + 43758z8 + 12376z6 + 1820z4 + 105z2 + 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]=

{ 29, 28 }

In[8]:=

Jones[K][q]

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

Out[8]=

−q43 + q42−q41 + q40−q39 + q38−q37 + q36−q35 + q34−q33 + q32−q31 + q30−q29 + q28−q27 + q26−q25 + q24−q23 + q22−q21 + q20−q19 + q18−q17 + q16 + q14

In[9]:=

HOMFLYPT[K][a, z]

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

Out[9]=

z28a−28−28z26a−28−z26a−30 + 351z24a−28 + 26z24a−30−2600z22a−28−300z22a−30 + 12650z20a−28 + 2024z20a−30−42504z18a−28−8855z18a−30 + 100947z16a−28 + 26334z16a−30−170544z14a−28−54264z14a−30 + 203490z12a−28 + 77520z12a−30−167960z10a−28−75582z10a−30 + 92378z8a−28 + 48620z8a−30−31824z6a−28−19448z6a−30 + 6188z4a−28 + 4368z4a−30−560z2a−28−455z2a−30 + 15a−28 + 14a−30

In[10]:=

Kauffman[K][a, z]

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

Out[10]=

z28a−28 + z28a−30 + z27a−29 + z27a−31−28z26a−28−27z26a−30 + z26a−32−26z25a−29−25z25a−31 + z25a−33 + 351z24a−28 + 326z24a−30−24z24a−32 + z24a−34 + 300z23a−29 + 276z23a−31−23z23a−33 + z23a−35−2600z22a−28−2324z22a−30 + 253z22a−32−22z22a−34 + z22a−36−2024z21a−29−1771z21a−31 + 231z21a−33−21z21a−35 + z21a−37 + 12650z20a−28 + 10879z20a−30−1540z20a−32 + 210z20a−34−20z20a−36 + z20a−38 + 8855z19a−29 + 7315z19a−31−1330z19a−33 + 190z19a−35−19z19a−37 + z19a−39−42504z18a−28−35189z18a−30 + 5985z18a−32−1140z18a−34 + 171z18a−36−18z18a−38 + z18a−40−26334z17a−29−20349z17a−31 + 4845z17a−33−969z17a−35 + 153z17a−37−17z17a−39 + z17a−41 + 100947z16a−28 + 80598z16a−30−15504z16a−32 + 3876z16a−34−816z16a−36 + 136z16a−38−16z16a−40 + z16a−42 + 54264z15a−29 + 38760z15a−31−11628z15a−33 + 3060z15a−35−680z15a−37 + 120z15a−39−15z15a−41 + z15a−43−170544z14a−28−131784z14a−30 + 27132z14a−32−8568z14a−34 + 2380z14a−36−560z14a−38 + 105z14a−40−14z14a−42 + z14a−44−77520z13a−29−50388z13a−31 + 18564z13a−33−6188z13a−35 + 1820z13a−37−455z13a−39 + 91z13a−41−13z13a−43 + z13a−45 + 203490z12a−28 + 153102z12a−30−31824z12a−32 + 12376z12a−34−4368z12a−36 + 1365z12a−38−364z12a−40 + 78z12a−42−12z12a−44 + z12a−46 + 75582z11a−29 + 43758z11a−31−19448z11a−33 + 8008z11a−35−3003z11a−37 + 1001z11a−39−286z11a−41 + 66z11a−43−11z11a−45 + z11a−47−167960z10a−28−124202z10a−30 + 24310z10a−32−11440z10a−34 + 5005z10a−36−2002z10a−38 + 715z10a−40−220z10a−42 + 55z10a−44−10z10a−46 + z10a−48−48620z9a−29−24310z9a−31 + 12870z9a−33−6435z9a−35 + 3003z9a−37−1287z9a−39 + 495z9a−41−165z9a−43 + 45z9a−45−9z9a−47 + z9a−49 + 92378z8a−28 + 68068z8a−30−11440z8a−32 + 6435z8a−34−3432z8a−36 + 1716z8a−38−792z8a−40 + 330z8a−42−120z8a−44 + 36z8a−46−8z8a−48 + z8a−50 + 19448z7a−29 + 8008z7a−31−5005z7a−33 + 3003z7a−35−1716z7a−37 + 924z7a−39−462z7a−41 + 210z7a−43−84z7a−45 + 28z7a−47−7z7a−49 + z7a−51−31824z6a−28−23816z6a−30 + 3003z6a−32−2002z6a−34 + 1287z6a−36−792z6a−38 + 462z6a−40−252z6a−42 + 126z6a−44−56z6a−46 + 21z6a−48−6z6a−50 + z6a−52−4368z5a−29−1365z5a−31 + 1001z5a−33−715z5a−35 + 495z5a−37−330z5a−39 + 210z5a−41−126z5a−43 + 70z5a−45−35z5a−47 + 15z5a−49−5z5a−51 + z5a−53 + 6188z4a−28 + 4823z4a−30−364z4a−32 + 286z4a−34−220z4a−36 + 165z4a−38−120z4a−40 + 84z4a−42−56z4a−44 + 35z4a−46−20z4a−48 + 10z4a−50−4z4a−52 + z4a−54 + 455z3a−29 + 91z3a−31−78z3a−33 + 66z3a−35−55z3a−37 + 45z3a−39−36z3a−41 + 28z3a−43−21z3a−45 + 15z3a−47−10z3a−49 + 6z3a−51−3z3a−53 + z3a−55−560z2a−28−469z2a−30 + 13z2a−32−12z2a−34 + 11z2a−36−10z2a−38 + 9z2a−40−8z2a−42 + 7z2a−44−6z2a−46 + 5z2a−48−4z2a−50 + 3z2a−52−2z2a−54 + z2a−56−14za−29−za−31 + za−33−za−35 + za−37−za−39 + za−41−za−43 + za−45−za−47 + za−49−za−51 + za−53−za−55 + za−57 + 15a−28 + 14a−30

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["T(29,2)"];

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]=

{ t14−t13 + t12−t11 + t10−t9 + t8−t7 + t6−t5 + t4−t3 + t2−t + 1−t−1 + t−2−t−3 + t−4−t−5 + t−6−t−7 + t−8−t−9 + t−10−t−11 + t−12−t−13 + t−14, −q43 + q42−q41 + q40−q39 + q38−q37 + q36−q35 + q34−q33 + q32−q31 + q30−q29 + q28−q27 + q26−q25 + q24−q23 + q22−q21 + q20−q19 + q18−q17 + q16 + q14 }

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]=

{}

In[6]:=

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

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

Out[6]=

{}