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MathGroup Archive 1999

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Re: Avoid long output, Real variables?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg20465] Re: Avoid long output, Real variables?
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 27 Oct 1999 02:04:39 -0400
  • Organization: Universitaet Leipzig
  • References: <7v3ch5$5vu@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

in Mathematica 3. and 4. you can give the assumptions option

Integrate[E^(I*k*x)/Sqrt[1 + k^2]/(2*Pi), {k, -Infinity, Infinity}, 
  Assumptions -> {Im[x] == 0}]

Hope that helps
  Jens

"Bergervoet J.R.M." wrote:
> 
> Is it possible to tell Mathematica that a variable, x, is Real?
> I am looking for commands like those of some competing vendor:
>   assume(x, real)
>   assume(x>0)
> If I cannot declare x to be Real, I get clumsy answers. For
> instance, a Fourier transform which for real x is just:
> 
>   2 BesselK[0, x Sign[x]]
> 
> gives me instead a pretty long answer where the actual solution
> for real x is hardly recognizable between the rest:
> 
>   In[4]:=Integrate[E^(I*k*x)/Sqrt[1+k^2]/(2*Pi), {k,-Infinity,Infinity}]
> 
>   Out[4]= If[Im[x] == 0, 2 BesselK[0, x Sign[x]],
> 
>                     I k x
>                    E
>       Integrate[------------, {k, -Infinity, Infinity}]] / (2 Pi)
>                           2
>                 Sqrt[1 + k ]
>   In[5]:=
> 
> And it can get worse if several variables are involved. So I really
> hope that someone can teach me how to declare them Real (or positive).
> 
> Thanks in advance,
> Jos


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