I read the proof here, http://books.google.co.in/books?id=WbZcqdvCEfwC&lpg=PP1&pg=PA26#v=onepage&q&f=false also >>> inverse_fourier_transform(DiracDelta(t),t,k,noconds=False) (1, True)
On 5 November 2013 10:04, Aaron Meurer <[email protected]> wrote: > I believe fourier_transform does use integration. But this is what the > integral returns > > In [15]: fourier_transform(f(x), x, z).rewrite(Integral).subs(f(x), 1) > Out[15]: > ∞ > ⌠ > ⎮ -2⋅ⅈ⋅π⋅x⋅z > ⎮ ℯ dx > ⌡ > -∞ > > In [16]: fourier_transform(f(x), x, z).rewrite(Integral).subs(f(x), > 1).doit() > Out[16]: > ⎧ │ ⎛ -ⅈ⋅π ⎞│ > │ ⎛ ⅈ⋅π ⎞│ > ⎪ │ ⎜ ───── ⎟│ > │ ⎜ ─── ⎟│ > ⎪ │ ⎜ 2 ⎟│ > π │ ⎜ 2 ⎟│ π > ⎪ 0 for │periodic_argument⎝ℯ ⋅polar_lift(z), ∞⎠│ < > ─ ∧ │periodic_argument⎝ℯ ⋅polar_lift(z), ∞⎠│ < ─ > ⎪ > 2 2 > ⎪ > ⎨∞ > ⎪⌠ > ⎪⎮ -2⋅ⅈ⋅π⋅x⋅z > ⎪⎮ ℯ dx otherwise > ⎪⌡ > ⎪-∞ > ⎩ > > So it can't get the result in terms of the Dirac delta function. In > fact, if you pass noconds=False to fourier_transform, you get those > same conditions. Actually, if I plug 0 into the conditions, I get nan > < pi/2, and if I plug any other real number, I get False. So I'm not > really sure about the result anyway. I was never clear what the > periodic_argument at oo was. I CCd Tom. Maybe he can answer. > > Aaron Meurer > > On Wed, Oct 30, 2013 at 3:32 PM, Pablo Puente <[email protected]> > wrote: > > Yes, this is a defect. > > > > I created in fact a Issue this week for it: > > https://code.google.com/p/sympy/issues/detail?id=4079 > > > > > > > > On Wednesday, October 30, 2013 12:03:32 PM UTC+1, Harsh Gupta wrote: > >> > >> >>> from sympy.integrals import transforms > >> >>> FT = fourier_transform > >> >>> from sympy.abc import x, k > >> >>> FT(1,x,k) > >> 0 > >> > >> Sympy evaluates the fourier transform of 1 as 0 though it is > >> dirac_delta(k). > >> Similarly sympy evaluates the fourier transform of powers of x as 0 as > >> well. > >> > >> http://mathworld.wolfram.com/FourierTransform1.html > >> > >> This might be arising because fourier transform of a 1 is not evaluated > by > >> direct integration > >> rather it is evaluated using a form of the generalized unit function. > >> > > -- > > You received this message because you are subscribed to the Google Groups > > "sympy" group. > > To unsubscribe from this group and stop receiving emails from it, send an > > email to [email protected]. > > To post to this group, send email to [email protected]. > > Visit this group at http://groups.google.com/group/sympy. > > For more options, visit https://groups.google.com/groups/opt_out. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > For more options, visit https://groups.google.com/groups/opt_out. > -- Harsh -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
