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
> defini
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, -
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
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)
-(373
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: