In [1]:

    

import numpy as np
import sympy as sy


    

In [3]:

    

s = sy.symbols('s', real=False)
h = sy.symbols('h')


    

In [4]:

    

Ac = sy.Matrix([[-2, -0.02, 0],[1,0,0], [0,2,0]])
Bc = sy.Matrix([[1],[0],[0]])
Cc = sy.Matrix([[0,0,2]])


    

In [11]:

    

sIminAc = s*sy.Matrix.eye(3) - Ac
charactPoly = sIminAc.det()
sIminAcinv = sIminAc.inv()
AA = sIminAcinv * charactPoly
for el in AA:
    print sy.simplify(sy.expand(el))


    

    




1.0*s**2
-0.02*s
0
s
s*(s**3 + 4*s**2 + 4.02*s + 0.04)/(s**2 + 2*s + 0.02)
0
2.00000000000000
(2*s**3 + 8*s**2 + 8.04*s + 0.08)/(s**2 + 2*s + 0.02)
s**2 + 2*s + 0.02

In [12]:

    

charactPoly


    

    
Out[12]:





s**3 + 2*s**2 + 0.02*s

In [13]:

    

q = sy.symbols('q')
Hq = (0.32*q**2 + 1.21*q+0.29)/(q**3 -2.82*q**2 + 2.64*q-0.82 )
sy.apart(Hq)


    

    
Out[13]:





46.2150617283951/(1.0*q - 0.82) - 45.8950617283951/(q - 1) + 10.1111111111111/(q - 1)**2

In [14]:

    

sy.together(- 45.8950617283951/(q - 1) + 10.1111111111111/(q - 1)**2)


    

    
Out[14]:





(-45.8950617283951*q + 56.0061728395062)/(q - 1)**2

In [ ]: