I am trying to replicate this:
https://math.stackexchange.com/questions/2280196/inverse-fourier-transform-of-a-partial-fraction-decomposition
with sympy.
With Mathematica I get just the same behavior as the above theory suggest.
With sympy I it looks wrong. At t<0, I get the result close to the correct
one for t>0. (I was not able to include all the assumptions in sympy).
Here is the sympy code:
import sympy as sym
sym.init_printing()
ω = sym.symbols('omega', real=True, positive=True)
R, λ = sym.symbols('R, lambda', complex=True)
t = sym.symbols('t', real=True, positive=True)
α = R/(sym.I*ω-λ)+sym.conjugate(R)/(sym.I*ω-sym.conjugate(λ))
α
sym.inverse_fourier_transform(α, ω, -t)
and the Mathematica:
a = InverseFourierTransform[ R/(I omega - lambda) + Conjugate[R]/(I omega
- Conjugate[lambda]), omega, t,
FourierParameters -> {1, -1}]
Simplify[a, {Re[lambda] < 0, t > 0}]
Is the sympy result really wrong?
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