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Re: Avoid long output, Real variables?

• To: mathgroup at smc.vnet.net
• Subject: [mg20474] Re: Avoid long output, Real variables?
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Wed, 27 Oct 1999 02:04:43 -0400
• References: <7v3ch5$5vu@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Bergervoet J.R.M. <bergervo at prl.philips.nl> wrote in message
news:7v3ch5$5vu at smc.vnet.net...
> 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
>

Jos,

We can put the assumption in locally,

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


    BesselK[0, Sqrt[x^2]]/Pi


--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565