On Fri, May 28, 2021 at 5:38 PM Hongyi Zhao <hongyi.z...@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
>
> 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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