On Friday, June 4, 2021 at 10:03:47 PM UTC+8 Emmanuel Charpentier wrote:
> Le samedi 29 mai 2021 à 01:16:21 UTC+2, [email protected] a écrit : > >> 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? >> > > Yep, with a bit of cut’n paste (since both foms can’t be obtained from the > same Mathematica installation) : > > sage: var("x, s") > (x, s) > sage: a="-I*(dirac_delta(s + 1) - dirac_delta(s - 1))*sqrt(1/2*pi)" # > text representatin of yours. > sage: b="-1/2*I*sqrt(2)*sqrt(pi)*(dirac_delta(s + 1) - dirac_delta(s - 1))" # > text representation of mine. > sage: bool(eval(a)==eval(b)) > True > > > > This should do it... > > Thanks a lot. It does the trick. HY > 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/d2402996-81a1-406e-8b0e-21f7eeb0ab5bn%40googlegroups.com.
