```
In [1]:
```%pylab inline
import sympy
sympy.init_printing()

```
```

```
In [8]:
```def mataf(h):
'Array flatten a matrix list of appropriate dimensions'
H=sympy.Matrix.hstack(*h[0])
for sor in range(1,len(h)):
H=sympy.Matrix.vstack(H,sympy.Matrix.hstack(*h[sor]))
return H

```
In [9]:
```S1=sympy.physics.matrices.msigma(1)
S2=sympy.physics.matrices.msigma(2)
S3=sympy.physics.matrices.msigma(3)
S0=S1*S1
N=0*S0
S=sympy.Matrix([[S1],[S2],[S3]])

```
In [10]:
```m,th,ph,kx,ky=sympy.symbols('m theta phi kx ky',positive=True)
t,t1,t2,t3,mz=sympy.symbols('t t1 t2 t3 mz',positive=True)

```
In [11]:
```a1=sympy.Matrix([[sqrt(3)],
[1]])/2
a2=sympy.Matrix([[-sqrt(3)],
[1]])/2
k=sympy.Matrix([[kx,ky]])

```
In [12]:
```U=mataf([[N,N,N,N,t*S0,t*S0],
[N,N,N,t*S0,t*S0,N],
[N,N,N,t*S0,N,t*S0],
[N,t*S0,t*S0,N,N,N],
[t*S0,t*S0,N,N,N,N],
[t*S0,N,t*S0,N,N,N]])
T1=mataf([[N,N,N,N,N,N],
[N,N,N,N,N,t*S0],
[N,N,N,N,N,N],
[N,N,N,N,N,N],
[N,N,N,N,N,N],
[N,N,N,N,N,N]])
T2=mataf([[N,N,N,t*S0,N,N],
[N,N,N,N,N,N],
[N,N,N,N,N,N],
[N,N,N,N,N,N],
[N,N,N,N,N,N],
[N,N,N,N,N,N]])
T3=mataf([[N,N,N,N,N,N],
[N,N,N,N,N,N],
[N,N,N,N,N,N],
[N,N,N,N,N,N],
[N,N,t*S0,N,N,N],
[N,N,N,N,N,N]])

```
In [ ]:
```