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MathGroup Archive 2007

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Re: question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg80108] Re: question
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Mon, 13 Aug 2007 04:23:46 -0400 (EDT)
  • References: <f9mq4l$r0q$1@smc.vnet.net>

On 12    , 14:15, Bob Hanlon <hanl... at cox.net> wrote:
> $Version
>
> 6.0 for Mac OS X x86 (32-bit) (June 19, 2007)
>
> expr = FourierTransform[Sign[y]*Sign[a*y], y, q]
>
> (-Sqrt[2*Pi])*DiracDelta[q]*
>      UnitStep[-a] -
>    (I*Sqrt[2/Pi]*UnitStep[a]*
>         UnitStep[-a])/q +
>    Sqrt[2*Pi]*DiracDelta[q]*
>      UnitStep[a]
>
> Simplify[expr, a > 0]
>
> Sqrt[2*Pi]*DiracDelta[q]
>
> Assuming[{a > 0}, FourierTransform[Sign[y]*Sign[a*y], y, q]]
>
> Sqrt[2*Pi]*DiracDelta[q]
>
> Simplify[expr, a < 0]
>
> (-Sqrt[2*Pi])*DiracDelta[q]
>
> Assuming[{a < 0}, FourierTransform[Sign[y]*Sign[a*y], y, q]]
>
> (-Sqrt[2*Pi])*DiracDelta[q]
>
> x1 = FullSimplify[expr, a != 0]
>
> Sqrt[2*Pi]*DiracDelta[q]*
>      UnitStep[a] - Sqrt[2*Pi]*
>      DiracDelta[q]*UnitStep[-a]
>
> x2 = Assuming[{a != 0}, FourierTransform[Sign[y]*Sign[a*y], y, q]]
>
> 2*Sqrt[2*Pi]*DiracDelta[q]*
>      UnitStep[a] - Sqrt[2*Pi]*
>      DiracDelta[q]
>
> Simplify[x2 - x1, #] & /@ {a > 0, a < 0}
>
> {0,0}
>
> Bob Hanlon
>
>
>
> ---- dimitris <dimmec... at yahoo.com> wrote:
> > Let's see if Mathematica 6 has become better.
>
> > In Mathematica 5.2 (and as well 6; as it
> > was mentioned in a recent thread).
>
> > In[11]:=
> > FourierTransform[Sign[y]*Sign[y], y, q]
>
> > Out[11]=
> > Sqrt[2*Pi]*DiracDelta[q]
>
> > which is correct.
>
> > In Mathematica 5.2
>
> > In[5]:=
> > FourierTransform[Sign[y]*Sign[a*y], y, q]
>
> > Out[5]=
> > (1/q)*((I*(1 - E^(I*q*Sqrt[1/Integrate`NLtheoremDump`myMax[0,
> > 0]^2]*Integrate`NLtheoremDump`myMax[0, 0]^2) +
> >      E^(2*I*q*Sqrt[1/Integrate`NLtheoremDump`myMax[0,
> > 0]^2]*Integrate`NLtheoremDump`myMax[0, 0]^2))*Sqrt[2/Pi]*
> >     (2 + DiscreteDelta[a] - UnitStep[-a] - UnitStep[a]))/E^(I*q*Sqrt[1/
> > Integrate`NLtheoremDump`myMax[0, 0]^2]*
> >      Integrate`NLtheoremDump`myMax[0, 0]^2))
>
> > I think outputs like this is a mini nightmare for the developers.
>
> > What does version 6 returns?
>
> > Thanks
> > Dimitris-                               -
>
> -                               -

Much better in Mathematica 6 I believe!

Cheers,
Dimitris



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