Yes, presently the integral transforms code don't do any kind of table
lookups. They just try to compute the integral, and if the integral
can't be computed it can't give a result. In this case, the integral
itself is wrong and it should be fixed. This has been mentioned in
some other issues as well https://github.com/sympy/sympy/issues/13491,
https://github.com/sympy/sympy/issues/13606 (and probably others if
you search the tracker).

Such a project should also improve the other transforms as well, not
just Fourier. It would also be beneficial if integrate() itself were
improved, so that integrals that look like transforms always work
whenever a *_transform() call works.

Aaron Meurer

On Thu, Mar 26, 2020 at 3:38 PM Ondřej Čertík <[email protected]> wrote:
>
> Hi,
>
> Here is a great idea for a GSoC project:
>
> https://github.com/sympy/sympy/issues/2803#issuecomment-604697523
>
> Would any student be interested? I know at least one user who couldn't use 
> SymPy because of that. So fixing it would be very useful to a lot of people. 
> The scope of the GSoC project could be to get SymPy working with Fourier 
> transforms of many such functions including Piecewise and adding a nice page 
> to SymPy's documentation with examples.
>
> I'll be happy to mentor such a project.
>
> Ondrej
>
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