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
<http://stackoverflow.com/questions/21202244/fourier-transform-a-trig-function-in-sympy-returns-unexpected-result>
on stackoverflow and the resulting issue
<https://github.com/sympy/sympy/issues/2803> 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
Le vendredi 15 août 2014 23:04:08 UTC+2, David Joyner a écrit :
>
> On Fri, Aug 15, 2014 at 4:59 PM, Oscar <[email protected] <javascript:>>
> wrote:
> > 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?
> >
>
> 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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