Re: [sage-support] Re: Symbolic Fourier transform in sagemath.

2021-05-28 Thread Hongyi Zhao
On Saturday, May 29, 2021 at 1:01:38 AM UTC+8 dim...@gmail.com wrote: > On Fri, May 28, 2021 at 5:38 PM Hongyi Zhao 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 >

Re: [sage-support] Re: Symbolic Fourier transform in sagemath.

2021-05-28 Thread Dima Pasechnik
On Fri, May 28, 2021 at 5:38 PM Hongyi Zhao 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,

[sage-support] Re: Symbolic Fourier transform in sagemath.

2021-05-28 Thread Hongyi Zhao
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) -

[sage-support] Re: memory leak in trivial calculation?

2021-05-28 Thread Emmanuel Charpentier
Nice one… Indeed: sage: f.expand()(y=i) -(3735/1394*I + 405/1394)*z^3 - (606/697*I - 942/697)*z^2 - (8681/6970*I + 15973/6970)*z + 1 sage: f.partial_fraction(y)(y=i) -(3735/1394*I + 405/1394)*z^3 - (606/697*I - 942/697)*z^2 - (8681/6970*I + 15973/6970)*z + 1 sage: f.simplify_full()(y=i)

[sage-support] Re: Symbolic Fourier transform in sagemath.

2021-05-28 Thread Emmanuel Charpentier
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: