On Saturday, May 29, 2021 at 1:01:38 AM UTC+8 [email protected] wrote:
> On Fri, May 28, 2021 at 5:38 PM Hongyi Zhao <[email protected]> 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: 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 > Is there a convenient way to prove they are the equivalent forms in sage? HY > > > > > 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, [email protected] 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 > >>> > > -- > > You received this message because you are subscribed to the Google > Groups "sage-support" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to [email protected]. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-support/84095de0-8726-4194-a84f-f2f0c5c876c3n%40googlegroups.com. > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/6ab4a610-d772-4a21-8b96-739e6fde6130n%40googlegroups.com.
