Dear all,
I don't know if my problem is with the knowledge of fractionnal
decomposition itself or with symPy's implementation.
I start with the following code :
import sympy as sp
sp.var('s')
Hstab = 1/(s**3+s**2+5*s+4)
Hstab = sp.apart(Hstab)
display(Hstab)
The result is :
[image: Capture d’écran 2020-08-10 à 10.18.18.png]
Now I check another similar expression :
Hstab2 = 1/(s**3 + 2*s**2 + 5*s + 4)
Hstab2 = sp.apart(Hstab2,s)
display(Hstab2)
and I get :
[image: Capture d’écran 2020-08-10 à 10.21.14.png]
If now I check for the roots of the denominator for each case :
print("\n\nFirst case :")
P1=(1/Hstab).simplify()
display(P1)
for sol in sp.solve(P1,s):
display(sol.evalf())
print("\n\nSecond case :")
P2=(1/Hstab2).simplify()
display(P2)
for sol in sp.solve(P2,s):
display(sol.evalf())
I get :
[image: Capture d’écran 2020-08-10 à 10.26.18.png]
Which is very similar except that the real root of the first case is not
ass simple as the one of the second case. So I do not understand as I can't
see any mathematical impossibility, the two cases are very close.
Is there a way to reach the fractional decomposition for the first case ?
Thanks a lot,
Mike
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