In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 29, 2005, 15:27:48)... |
In[2]:= | PD[Knot[10, 38]] |
Out[2]= | PD[X[1, 4, 2, 5], X[3, 10, 4, 11], X[5, 12, 6, 13], X[15, 18, 16, 19],
X[7, 17, 8, 16], X[17, 7, 18, 6], X[13, 20, 14, 1],
X[19, 14, 20, 15], X[11, 8, 12, 9], X[9, 2, 10, 3]] |
In[3]:= | GaussCode[Knot[10, 38]] |
Out[3]= | GaussCode[-1, 10, -2, 1, -3, 6, -5, 9, -10, 2, -9, 3, -7, 8, -4, 5, -6,
4, -8, 7] |
In[4]:= | DTCode[Knot[10, 38]] |
Out[4]= | DTCode[4, 10, 12, 16, 2, 8, 20, 18, 6, 14] |
In[5]:= | br = BR[Knot[10, 38]] |
Out[5]= | BR[5, {-1, -1, -1, -2, 1, -2, -2, -3, 2, 4, -3, 4}] |
In[6]:= | {First[br], Crossings[br]} |
Out[6]= | {5, 12} |
In[7]:= | BraidIndex[Knot[10, 38]] |
Out[7]= | 5 |
In[8]:= | Show[DrawMorseLink[Knot[10, 38]]] |
| |
Out[8]= | -Graphics- |
In[9]:= | (#[Knot[10, 38]]&) /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex} |
Out[9]= | {Reversible, 2, 2, 2, NotAvailable, 1} |
In[10]:= | alex = Alexander[Knot[10, 38]][t] |
Out[10]= | 4 15 2
-21 - -- + -- + 15 t - 4 t
2 t
t |
In[11]:= | Conway[Knot[10, 38]][z] |
Out[11]= | 2 4
1 - z - 4 z |
In[12]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[12]= | {Knot[10, 38], Knot[11, Alternating, 166]} |
In[13]:= | {KnotDet[Knot[10, 38]], KnotSignature[Knot[10, 38]]} |
Out[13]= | {59, -2} |
In[14]:= | Jones[Knot[10, 38]][q] |
Out[14]= | -9 3 5 7 9 10 9 7 5
-2 + q - -- + -- - -- + -- - -- + -- - -- + - + q
8 7 6 5 4 3 2 q
q q q q q q q |
In[15]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[15]= | {Knot[10, 38]} |
In[16]:= | A2Invariant[Knot[10, 38]][q] |
Out[16]= | -28 -26 -24 2 -20 -18 -16 2 2 -8 -6
q - q - q + --- - q + q + q - --- - --- + q + q -
22 14 10
q q q
-4 3 4
q + -- + q
2
q |
In[17]:= | HOMFLYPT[Knot[10, 38]][a, z] |
Out[17]= | 2 4 6 2 4 2 8 2 2 4 4 4 6 4
1 + a - 2 a + a + z - 3 a z + a z - a z - 2 a z - a z |
In[18]:= | Kauffman[Knot[10, 38]][a, z] |
Out[18]= | 2 4 6 7 9 2 2 2 4 2 6 2
1 - a - 2 a - a - a z - a z - 2 z + 2 a z + 8 a z + 2 a z +
10 2 3 3 3 5 3 7 3 9 3 4
2 a z - 2 a z + a z + 3 a z + 8 a z + 8 a z + z -
2 4 4 4 6 4 8 4 10 4 5 3 5
3 a z - 8 a z + 3 a z + 4 a z - 3 a z + 2 a z - 2 a z -
5 5 7 5 9 5 2 6 4 6 6 6
7 a z - 13 a z - 10 a z + 3 a z + 2 a z - 10 a z -
8 6 10 6 3 7 5 7 7 7 9 7 4 8
8 a z + a z + 3 a z + 3 a z + 3 a z + 3 a z + 2 a z +
6 8 8 8 5 9 7 9
5 a z + 3 a z + a z + a z |
In[19]:= | {Vassiliev[2][Knot[10, 38]], Vassiliev[3][Knot[10, 38]]} |
Out[19]= | {-1, 2} |
In[20]:= | Kh[Knot[10, 38]][q, t] |
Out[20]= | 2 4 1 2 1 3 2 4 3
-- + - + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
3 q 19 8 17 7 15 7 15 6 13 6 13 5 11 5
q q t q t q t q t q t q t q t
5 4 5 5 4 5 3 4 t
------ + ----- + ----- + ----- + ----- + ----- + ---- + ---- + - +
11 4 9 4 9 3 7 3 7 2 5 2 5 3 q
q t q t q t q t q t q t q t q t
3 2
q t + q t |
In[21]:= | ColouredJones[Knot[10, 38], 2][q] |
Out[21]= | -26 3 10 11 9 29 15 29 50 10
-10 + q - --- + --- - --- - --- + --- - --- - --- + --- - --- -
25 23 22 21 20 19 18 17 16
q q q q q q q q q
53 63 -13 71 64 13 72 51 17 53 31 11
--- + --- + q - --- + --- + --- - -- + -- + -- - -- + -- + -- -
15 14 12 11 10 9 8 7 6 5 4
q q q q q q q q q q q
28 15 4 2 3 4
-- + -- + - + 5 q + q - 2 q + q
3 2 q
q q |