In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 29, 2005, 15:27:48)... |
In[2]:= | PD[Knot[10, 61]] |
Out[2]= | PD[X[8, 2, 9, 1], X[10, 4, 11, 3], X[2, 10, 3, 9], X[18, 12, 19, 11],
X[14, 7, 15, 8], X[16, 5, 17, 6], X[6, 15, 7, 16], X[4, 17, 5, 18],
X[20, 14, 1, 13], X[12, 20, 13, 19]] |
In[3]:= | GaussCode[Knot[10, 61]] |
Out[3]= | GaussCode[1, -3, 2, -8, 6, -7, 5, -1, 3, -2, 4, -10, 9, -5, 7, -6, 8,
-4, 10, -9] |
In[4]:= | DTCode[Knot[10, 61]] |
Out[4]= | DTCode[8, 10, 16, 14, 2, 18, 20, 6, 4, 12] |
In[5]:= | br = BR[Knot[10, 61]] |
Out[5]= | BR[4, {1, 1, 1, -2, 1, 1, 1, -2, -3, 2, -3}] |
In[6]:= | {First[br], Crossings[br]} |
Out[6]= | {4, 11} |
In[7]:= | BraidIndex[Knot[10, 61]] |
Out[7]= | 4 |
In[8]:= | Show[DrawMorseLink[Knot[10, 61]]] |
| |
Out[8]= | -Graphics- |
In[9]:= | (#[Knot[10, 61]]&) /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex} |
Out[9]= | {Reversible, {2, 3}, 3, 3, NotAvailable, 2} |
In[10]:= | alex = Alexander[Knot[10, 61]][t] |
Out[10]= | 2 5 6 2 3
7 - -- + -- - - - 6 t + 5 t - 2 t
3 2 t
t t |
In[11]:= | Conway[Knot[10, 61]][z] |
Out[11]= | 2 4 6
1 - 4 z - 7 z - 2 z |
In[12]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[12]= | {Knot[10, 61]} |
In[13]:= | {KnotDet[Knot[10, 61]], KnotSignature[Knot[10, 61]]} |
Out[13]= | {33, 4} |
In[14]:= | Jones[Knot[10, 61]][q] |
Out[14]= | -2 1 2 3 4 5 6 7 8
3 + q - - - 4 q + 4 q - 5 q + 5 q - 4 q + 3 q - 2 q + q
q |
In[15]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[15]= | {Knot[10, 61]} |
In[16]:= | A2Invariant[Knot[10, 61]][q] |
Out[16]= | -6 -4 2 4 6 8 14 24
2 + q + q + -- - q - 3 q - 2 q + 2 q + q
2
q |
In[17]:= | HOMFLYPT[Knot[10, 61]][a, z] |
Out[17]= | 2 2 2 4 4
-6 -4 5 2 3 z 3 z 8 z 4 z 4 z
4 + a + a - -- + 4 z + ---- - ---- - ---- + z + -- - ---- -
2 6 4 2 6 4
a a a a a a
4 6 6
5 z z z
---- - -- - --
2 4 2
a a a |
In[18]:= | Kauffman[Knot[10, 61]][a, z] |
Out[18]= | 2 2 2 2
-6 -4 5 6 z 8 z 2 z 2 z 2 z 6 z z
4 - a + a + -- - --- - --- - --- - 16 z + --- - ---- + ---- + -- -
2 5 3 a 10 8 6 4
a a a a a a a
2 3 3 3 3 3 4 4
24 z 2 z 6 z 17 z 26 z z 4 3 z 13 z
----- + ---- - ---- + ----- + ----- + -- + 17 z + ---- - ----- +
2 9 7 5 3 a 8 6
a a a a a a a
4 4 5 5 5 5 6 6
5 z 38 z 4 z 18 z 16 z 6 z 6 5 z 10 z
---- + ----- + ---- - ----- - ----- + ---- - 7 z + ---- - ----- -
4 2 7 5 3 a 6 4
a a a a a a a
6 7 7 8 8 9 9
22 z 5 z 5 z 8 3 z 4 z z z
----- + ---- - ---- + z + ---- + ---- + -- + --
2 5 a 4 2 3 a
a a a a a |
In[19]:= | {Vassiliev[2][Knot[10, 61]], Vassiliev[3][Knot[10, 61]]} |
Out[19]= | {-4, -5} |
In[20]:= | Kh[Knot[10, 61]][q, t] |
Out[20]= | 3
3 5 1 1 3 q 3 q 5 7
3 q + 2 q + ----- + ---- + ---- + - + ---- + 3 q t + 2 q t +
5 4 3 2 t t
q t q t q t
7 2 9 2 9 3 11 3 11 4 13 4 13 5
2 q t + 3 q t + 2 q t + 2 q t + q t + 2 q t + q t +
15 5 17 6
q t + q t |
In[21]:= | ColouredJones[Knot[10, 61], 2][q] |
Out[21]= | -8 -7 -6 4 -4 6 7 1 2 3
-11 + q - q - q + -- - q - -- + -- + - + 8 q + 5 q - 13 q +
5 3 2 q
q q q
4 5 6 7 8 9 11 12 13
7 q + 9 q - 13 q + 3 q + 9 q - 10 q + 7 q - 5 q - q +
14 15 17 18 19 20 21 22
5 q - 4 q + 3 q - 4 q + 2 q + q - 2 q + q |