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MathGroup Archive 1999

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Re: Avoid long output, Real variables?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg20521] Re: [mg20424] Avoid long output, Real variables?
  • From: BobHanlon at aol.com
  • Date: Wed, 27 Oct 1999 02:05:12 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Use the option Assumptions

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

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

Bob Hanlon

In a message dated 10/26/1999 8:48:21 AM, bergervo at prl.philips.nl writes:

>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).
>


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