PD Presentation: |
X1,11,2,10 X20,12,21,11 X21,3,22,2 X12,4,13,3 X13,23,14,22 X4,24,5,23 X5,15,6,14 X24,16,25,15 X25,7,26,6 X16,8,17,7 X17,27,18,26 X8,28,9,27 X9,19,10,18 X28,20,1,19 |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | TubePlot[TorusKnot[7, 3]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | Crossings[TorusKnot[7, 3]] |
Out[3]= | 14 |
In[4]:= | PD[TorusKnot[7, 3]] |
Out[4]= | PD[X[1, 11, 2, 10], X[20, 12, 21, 11], X[21, 3, 22, 2], X[12, 4, 13, 3],
> X[13, 23, 14, 22], X[4, 24, 5, 23], X[5, 15, 6, 14], X[24, 16, 25, 15],
> X[25, 7, 26, 6], X[16, 8, 17, 7], X[17, 27, 18, 26], X[8, 28, 9, 27],
> X[9, 19, 10, 18], X[28, 20, 1, 19]] |
In[5]:= | GaussCode[TorusKnot[7, 3]] |
Out[5]= | GaussCode[-1, 3, 4, -6, -7, 9, 10, -12, -13, 1, 2, -4, -5, 7, 8, -10, -11, 13,
> 14, -2, -3, 5, 6, -8, -9, 11, 12, -14] |
In[6]:= | BR[TorusKnot[7, 3]] |
Out[6]= | BR[3, {1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2}] |
In[7]:= | alex = Alexander[TorusKnot[7, 3]][t] |
Out[7]= | -6 -5 -3 -2 2 3 5 6
1 + t - t + t - t - t + t - t + t |
In[8]:= | Conway[TorusKnot[7, 3]][z] |
Out[8]= | 2 4 6 8 10 12
1 + 16 z + 60 z + 78 z + 44 z + 11 z + z |
In[9]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[9]= | {} |
In[10]:= | {KnotDet[TorusKnot[7, 3]], KnotSignature[TorusKnot[7, 3]]} |
Out[10]= | {1, 8} |
In[11]:= | J=Jones[TorusKnot[7, 3]][q] |
Out[11]= | 6 8 14
q + q - q |
In[12]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[12]= | {} |
In[13]:= | ColouredJones[TorusKnot[7, 3], 2][q] |
Out[13]= | 12 15 18 19 21 22 24 25 28 31 32 34 35
q + q + q - q + q - q + q - q - q - q + q - q + q -
37 38 40 41
> q + q - q + q |
In[14]:= | A2Invariant[TorusKnot[7, 3]][q] |
Out[14]= | 22 24 26 28 30 32 34 38 40 42 44
q + q + 2 q + 2 q + 2 q + q + q - q - 2 q - 2 q - 2 q -
46 56
> q + q |
In[15]:= | Kauffman[TorusKnot[7, 3]][a, z] |
Out[15]= | 2 2 2 3 3 4
5 16 12 16 z 16 z 10 z 76 z 66 z 60 z 60 z 6 z
--- + --- + --- - ---- - ---- - ----- - ----- - ----- + ----- + ----- + ---- +
16 14 12 15 13 16 14 12 15 13 16
a a a a a a a a a a a
4 4 5 5 6 6 6 7 7
138 z 132 z 78 z 78 z z 122 z 121 z 44 z 44 z
> ------ + ------ - ----- - ----- - --- - ------ - ------ + ----- + ----- +
14 12 15 13 16 14 12 15 13
a a a a a a a a a
8 8 9 9 10 10 11 11 12 12
55 z 55 z 11 z 11 z 12 z 12 z z z z z
> ----- + ----- - ----- - ----- - ------ - ------ + --- + --- + --- + ---
14 12 15 13 14 12 15 13 14 12
a a a a a a a a a a |
In[16]:= | {Vassiliev[2][TorusKnot[7, 3]], Vassiliev[3][TorusKnot[7, 3]]} |
Out[16]= | {16, 56} |
In[17]:= | Kh[TorusKnot[7, 3]][q, t] |
Out[17]= | 11 13 15 2 19 3 17 4 19 4 21 5 23 5 21 6
q + q + q t + q t + q t + q t + q t + q t + q t +
25 7 23 8 25 8 27 9 29 9
> q t + q t + q t + q t + q t |