In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 17, 2005, 14:44:34)... |
In[2]:= | Crossings[TorusKnot[11, 2]] |
Out[2]= | 11 |
In[3]:= | PD[TorusKnot[11, 2]] |
Out[3]= | PD[X[5, 17, 6, 16], X[17, 7, 18, 6], X[7, 19, 8, 18], X[19, 9, 20, 8],
X[9, 21, 10, 20], X[21, 11, 22, 10], X[11, 1, 12, 22],
X[1, 13, 2, 12], X[13, 3, 14, 2], X[3, 15, 4, 14], X[15, 5, 16, 4]] |
In[4]:= | GaussCode[TorusKnot[11, 2]] |
Out[4]= | GaussCode[-8, 9, -10, 11, -1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11, 1,
-2, 3, -4, 5, -6, 7] |
In[5]:= | BR[TorusKnot[11, 2]] |
Out[5]= | BR[2, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}] |
In[6]:= | alex = Alexander[TorusKnot[11, 2]][t] |
Out[6]= | -5 -4 -3 -2 1 2 3 4 5
-1 + t - t + t - t + - + t - t + t - t + t
t |
In[7]:= | Conway[TorusKnot[11, 2]][z] |
Out[7]= | 2 4 6 8 10
1 + 15 z + 35 z + 28 z + 9 z + z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, Alternating, 367]} |
In[9]:= | {KnotDet[TorusKnot[11, 2]], KnotSignature[TorusKnot[11, 2]]} |
Out[9]= | {11, 10} |
In[10]:= | J=Jones[TorusKnot[11, 2]][q] |
Out[10]= | 5 7 8 9 10 11 12 13 14 15 16
q + q - q + q - q + q - q + q - q + q - q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, Alternating, 367]} |
In[12]:= | A2Invariant[TorusKnot[11, 2]][q] |
Out[12]= | 18 20 22 24 26 42 44 46
q + q + 2 q + q + q - q - q - q |
In[13]:= | Kauffman[TorusKnot[11, 2]][a, z] |
Out[13]= | 2 2 2
-5 6 z z z z z 5 z z 2 z 3 z
--- - --- + --- - --- + --- - --- + --- + --- + --- - ---- + ---- -
12 10 21 19 17 15 13 11 20 18 16
a a a a a a a a a a a
2 2 2 3 3 3 3 3 4
4 z 25 z 35 z z 3 z 6 z 10 z 20 z z
---- + ----- + ----- + --- - ---- + ---- - ----- - ----- + --- -
14 12 10 19 17 15 13 11 18
a a a a a a a a a
4 4 4 4 5 5 5 5 6
4 z 10 z 41 z 56 z z 5 z 15 z 21 z z
---- + ----- - ----- - ----- + --- - ---- + ----- + ----- + --- -
16 14 12 10 17 15 13 11 16
a a a a a a a a a
6 6 6 7 7 7 8 8 8 9
6 z 29 z 36 z z 7 z 8 z z 9 z 10 z z
---- + ----- + ----- + --- - ---- - ---- + --- - ---- - ----- + --- +
14 12 10 15 13 11 14 12 10 13
a a a a a a a a a a
9 10 10
z z z
--- + --- + ---
11 12 10
a a a |
In[14]:= | {Vassiliev[2][TorusKnot[11, 2]], Vassiliev[3][TorusKnot[11, 2]]} |
Out[14]= | {0, 55} |
In[15]:= | Kh[TorusKnot[11, 2]][q, t] |
Out[15]= | 9 11 13 2 17 3 17 4 21 5 21 6 25 7
q + q + q t + q t + q t + q t + q t + q t +
25 8 29 9 29 10 33 11
q t + q t + q t + q t |