Le vendredi 28 mai 2021 à 19:01:38 UTC+2, dim...@gmail.com a écrit :
> On Fri, May 28, 2021 at 5:38 PM Hongyi Zhao <hongy...@gmail.com> wrote:
> >
> >
> >
> > On Friday, May 28, 2021 at 8:19:07 PM UTC+8 Emmanuel Charpentier wrote:
> >>
> >> This can be computed “by hand” using (one of) the textbook
> definition(s) :
> >>
> >> sage: var("omega, s")
> >> (omega, s)
> >> sage: integrate(sin(x^2)*e^(-I*s*x), x, -oo, oo)
> >> 1/2*sqrt(2)*sqrt(pi)*cos(1/4*s^2) - 1/2*sqrt(2)*sqrt(pi)*sin(1/4*s^2)
> >>
> >> Both sympy and giac have implementations of this transform :
> >>
> >> sage: from sympy import fourier_transform, sympify
> >> sage: fourier_transform(*map(sympify, (sin(x^2),x, s)))._sage_()
> >> 1/2*sqrt(2)*sqrt(pi)*(cos(pi^2*s^2) - sin(pi^2*s^2))
> >> sage: libgiac.fourier(*map(lambda u:u._giac_(), (sin(x^2), x,
> s))).sage()
> >> 1/2*sqrt(2)*sqrt(pi)*(cos(1/4*s^2) - sin(1/4*s^2))
> >>
> >> which do not follow the same definitions… But beware : they may be more
> or less wrong :
> >>
> >> sage: integrate(sin(x)*e^(-I*s*x), x, -oo, oo).factor()
> >> undef # Wrong
> >> sage: fourier_transform(*map(sympify, (sin(x),x, s)))._sage_()
> >> 0 # Wrong AND misleading
> >> sage: libgiac.fourier(*map(lambda u:u._giac_(), (sin(x), x, s))).sage()
> >> I*pi*dirac_delta(s + 1) - I*pi*dirac_delta(s - 1) # Better...
> >>
> >> BTW:
> >>
> >> sage: mathematica.FourierTransform(sin(x^2), x, s).sage().factor()
> >> 1/2*cos(1/4*s^2) - 1/2*sin(1/4*s^2)
> >> sage: mathematica.FourierTransform(sin(x), x, s).sage().factor()
> >> -1/2*I*sqrt(2)*sqrt(pi)*(dirac_delta(s + 1) - dirac_delta(s - 1))
> >
> > But what I got is different from yours:
> >
> > sage: sage: var("omega, s")
> > (omega, s)
> > sage: mathematica.FourierTransform(sin(x), x, s).sage().factor()
> > -I*(dirac_delta(s + 1) - dirac_delta(s - 1))*Sqrt(1/2*pi)
>
> this depends of a version of Mathematica
This also depends on Trac#31756 <https://trac.sagemath.org/ticket/31756> ,
not in 9.3 but in 9.4.beta0 : up to 9.3, mathematica("Sqrt[x]").sage()
would give you Sqrt(x) (and not sqrt(x) as expected)…
HTH,
>
> > BTW:
> >
> > How to input the sage computation representation as the code style just
> like what you've posted?
> >
> > HY
> >
> >>
> >> HTH,
> >>
> >> Le dimanche 23 mai 2021 à 03:22:06 UTC+2, hongy...@gmail.com a écrit :
> >>>
> >>> It seems that all the Fourier transform methods implemented in
> sagemath is numeric, instead of symbolic/analytic.
> >>>
> >>> I want to know whether there are some symbolic/analytic Fourier
> transform functions, just as we can do in mathematica, in sagemath?
> >>>
> >>> I want to know if there are some symbolic/analytical Fourier transform
> functions available in sagemath, just as the ones in mathematica?
> >>>
> >>> Regards,
> >>> HY
> >>>
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>
>
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