In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 17, 2005, 14:44:34)... |
In[2]:= | Crossings[Knot[10, 21]] |
Out[2]= | 10 |
In[3]:= | PD[Knot[10, 21]] |
Out[3]= | PD[X[1, 4, 2, 5], X[5, 14, 6, 15], X[3, 13, 4, 12], X[13, 3, 14, 2],
X[7, 16, 8, 17], X[11, 20, 12, 1], X[15, 6, 16, 7], X[19, 8, 20, 9],
X[9, 18, 10, 19], X[17, 10, 18, 11]] |
In[4]:= | GaussCode[Knot[10, 21]] |
Out[4]= | GaussCode[-1, 4, -3, 1, -2, 7, -5, 8, -9, 10, -6, 3, -4, 2, -7, 5, -10,
9, -8, 6] |
In[5]:= | BR[Knot[10, 21]] |
Out[5]= | BR[4, {-1, -1, -2, 1, -2, -2, -2, -2, 3, -2, 3}] |
In[6]:= | alex = Alexander[Knot[10, 21]][t] |
Out[6]= | 2 7 9 2 3
9 - -- + -- - - - 9 t + 7 t - 2 t
3 2 t
t t |
In[7]:= | Conway[Knot[10, 21]][z] |
Out[7]= | 2 4 6
1 + z - 5 z - 2 z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[10, 21], Knot[11, NonAlternating, 69]} |
In[9]:= | {KnotDet[Knot[10, 21]], KnotSignature[Knot[10, 21]]} |
Out[9]= | {45, -4} |
In[10]:= | J=Jones[Knot[10, 21]][q] |
Out[10]= | -10 2 3 6 7 7 7 5 4 2
1 + q - -- + -- - -- + -- - -- + -- - -- + -- - -
9 8 7 6 5 4 3 2 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[10, 21]} |
In[12]:= | A2Invariant[Knot[10, 21]][q] |
Out[12]= | -30 2 2 -14 3 -6
1 + q - --- - --- + q + --- + q
22 18 10
q q q |
In[13]:= | Kauffman[Knot[10, 21]][a, z] |
Out[13]= | 2 4 6 8 5 7 9 11 2 2
-a + 2 a + 3 a + a - 2 a z - a z + 3 a z + 2 a z + 4 a z -
4 2 6 2 8 2 12 2 3 3 5 3
3 a z - 14 a z - 5 a z - 2 a z + 5 a z + 3 a z +
7 3 11 3 2 4 4 4 6 4 8 4
2 a z - 4 a z - 4 a z + 4 a z + 20 a z + 9 a z -
10 4 12 4 3 5 5 5 9 5 11 5 2 6
2 a z + a z - 7 a z - 3 a z - 2 a z + 2 a z + a z -
4 6 6 6 8 6 10 6 3 7 5 7 7 7
6 a z - 14 a z - 5 a z + 2 a z + 2 a z - a z - a z +
9 7 4 8 6 8 8 8 5 9 7 9
2 a z + 2 a z + 4 a z + 2 a z + a z + a z |
In[14]:= | {Vassiliev[2][Knot[10, 21]], Vassiliev[3][Knot[10, 21]]} |
Out[14]= | {0, 0} |
In[15]:= | Kh[Knot[10, 21]][q, t] |
Out[15]= | 2 3 1 1 1 2 1 4
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ +
5 3 21 8 19 7 17 7 17 6 15 6 15 5
q q q t q t q t q t q t q t
2 3 4 4 3 3 4 2
------ + ------ + ------ + ------ + ----- + ----- + ----- + ---- +
13 5 13 4 11 4 11 3 9 3 9 2 7 2 7
q t q t q t q t q t q t q t q t
3 t t 2
---- + -- + - + q t
5 3 q
q t q |