In [1]:

    

import numpy as np
import sympy as sy
from sympy import I, exp


    

In [2]:

    

z = sy.symbols("z", real=False)
a,h,r1,s0,s1 = sy.symbols("a,h,r1,s0,s1")


    

In [3]:

    

pd = 0.76*np.exp(1j*0.28)
print np.conjugate(pd)
A2ndorder = (z-pd)*(z-np.conjugate(pd))
print sy.collect(sy.simplify(sy.expand(A2ndorder)), z)
Acl = A2ndorder*(z-a)
print sy.collect(sy.simplify(sy.expand(Acl)), z)


    

    




(0.730402133116-0.210030292909j)
z**2 - 1.46080426623237*z + 0.5776
-0.5776*a + z**3 + z**2*(-a - 1.46080426623237) + z*(1.46080426623237*a + 0.5776)

In [4]:

    

Acp = sy.poly(Acl, z)
Ap = sy.poly((z-1)*(z-0.76), z)
Bp = sy.poly(-.10*z + 0.14, z)
Rp = sy.poly(z+r1, z)
Sp = sy.poly(s0*z + s1, z)
dioph=(Ap*Rp+Bp*Sp-Acp).all_coeffs()


    

In [8]:

    

sol=sy.solve(dioph, (r1,s0,s1))
print sol[r1]
sol[r1]-1.76-0.10*sol[s1]


    

    




-1.92372666904173*a + 1.2932173366584






    
Out[8]:





-2.55546400366438*a + 0.235249605130106

In [ ]:

    




    

In [5]:

    

np.exp(-0.15)


    

    
Out[5]:





0.86070797642505781

In [7]:

    

argp=np.sqrt(3)*0.15
argp*180/np.pi


    

    
Out[7]:





14.885880176388383

In [8]:

    

0.4/(2*np.sqrt(2))


    

    
Out[8]:





0.1414213562373095

In [9]:

    

np.exp(-0.28)


    

    
Out[9]:





0.75578374145572547

In [10]:

    

0.28*180.0/np.pi


    

    
Out[10]:





16.04281826366305

In [14]:

    

hh=0.14
-1+hh+np.exp(-2*hh)


    

    
Out[14]:





-0.10421625854427452

In [15]:

    

1-(1+hh)*np.exp(-2*hh)


    

    
Out[15]:





0.13840653474047282

In [16]:

    

np.exp(-2*hh)


    

    
Out[16]:





0.75578374145572547

In [ ]:

    

sy.expand()