Fourier Transforms

[João Silva]

Hello,

I need a CAS for some symbolic work involving (among other things)
Fourier
transforms. As I'm already familiar with python, numpy, scipy and
matplotlib, sympy would be the obvious choice (I don't like maxima).
Although sympy seems quite advanced, it couldn't calculate the Fourier
transform of a gaussian function:

integrate(exp(-x**2)*exp(I*k*x), (x, -oo, oo))

which should be sqrt(pi)*exp(k**2/4)

Addicionally Dirac deltas seem unsupported:

integrate(exp(I*k*x), (x, -oo, oo)) returns nonsense.

integrate(cos(x)*exp(I*k*x), (x, -oo, oo)) exits with
PolynomialException: I
is no rational coefficient!

Are there plans to add this functionality, and is it easy to
implement?

Best regards,
João Silva

[Ondrej Certik]

Hi João!

Thanks for your interest. Yes, all of the things you mentioned are on our plan.

Fixing the integral should be as easy as adding a matching rule to our
integrate function.

Dirac delta functions are not yet supported, any contribution is
welcome, it'd be very useful.

If you use numpy/scipy etc. tools, it should be fairly easy for you to
implement such things. You can ask anytime, either here or on IRC for
help and someone will help you implement what you need.

Feel free to create new issues in our tracker with things you would
like to have and that don't work.

Ondrej