Fourier Transforms in sage

[Oscar]

I wanted to calculate some Fourier transforms, and it seems like sage
doesn't have them. I was expecting something on the likes of
mathematica's command

sage: fourier_transform(exp(-I*omega0*t) , t, omega )
sqrt(2*pi)*dirac_delta(omega-omega0)

Am I completely missing how this is done in sage, or is it really missing?

Thank you,

Oscar Lazo.

[David Joyner]

They are in sympy, which is in Sage:
http://docs.sympy.org/dev/modules/integrals/integrals.html

> Thank you,
>
> Oscar Lazo.
>
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[Emmanuel Charpentier]

Beware of sympy for fourier transform of unintegrable functions :

This works :

sage: var("x,t,omega")
(x, t, omega)
sage: from sympy import fourier_transform, inverse_fourier_transform
sage: fourier_transform(e^-t^2,t,omega)._sage_()
sqrt(pi)*e^(-pi^2*omega^2)
sage: inverse_fourier_transform(fourier_transform(e^-t^2,t,omega)._sage_(),omega,t)._sage_()
e^(-t^2)

But :

sage: fourier_transform(sin(t),t,omega)._sage_()
0
sage: fourier_transform(sin(t),t,omega,noconds=False)
(0,
 And(Abs(periodic_argument(exp_polar(-I*pi)*polar_lift(omega)**2, oo)) < pi, Abs(periodic_argument(exp_polar(I*pi)*polar_lift(omega)**2, oo)) < pi))

Whereas one could expect a sum of Diracs. This issue is known to Sympy developers (see this question on stackoverflow and the resulting issue in sympy ticket system).

Maybe a similar ticket should be opened for Sage, which has, as far as I know, no way to represent a Dirac or a Heaviside function in SR...

HTH,

--
Emmanuel Charpentier