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MathGroup Archive 2000

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Re: How to keep things real?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25093] Re: [mg25084] How to keep things real?
  • From: Andrzej Kozlowski <andrzej at bekkoame.ne.jp>
  • Date: Fri, 8 Sep 2000 03:00:41 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In my opinion the answer to your question is this: the Assumptions mechanism
in Integrate generally does not work (except in a few special cases), and
as, far as I can remember, nobody from Wolfram Research has ever answered
any complaints about it.

On the other hand, the (mostly algebraic) mechanism of assumptions in
Simplify and FullSimplify works very nicely, even though it is still far
from perfect. Moreover, bugs, when reported have always been acknowledged
and, whenever possible, fixed.

In your case the following will give you the answer you want;


In[20]:=
Simplify[Integrate[ 1/Sqrt[x^2 + zp^2]^3, {zp, z, Infinity}], {x > 0, z >
0}]

Out[20]=
          z
1 - -------------
          2    2
    Sqrt[x  + z ]
-----------------
        2
       x


on 00.9.8 11:28 AM, Jos Bergervoet at bergervo at iaehv.iae.nl wrote:

> 
> With the following input:
> 
> Integrate[ x/Sqrt[x^2+zp^2]^3, {zp,z,Infinity},
> Assumptions -> {x>0, z>0} ]
> 
> I get:
> 
> 2    2             2
> Out[1]= x If[x  + z  >= 0 || Im[x ] != 0,   ...., .... ]
> 
> Why does this if-statement appear in the output? Why is Mathematica
> apparently ignoring my directive that x and z are positive?
> 
> The same happens with Assumptions -> {x \[Element] Reals,
> z \[Element] Reals}  and with combinations of these two versions.
> 
> I would like to have the answer without "if", to use it in
> subsequent computations. Is there a way to do this?
> 
> Thanks in advance,
> Jos
> 
> --
> Dr. Jozef R. Bergervoet                      Electromagnetism and EMC
> Philips Research Laboratories,             Eindhoven, The Netherlands
> Building WS01                                     FAX: +31-40-2742224
> E-mail: bergervo at natlab.research.philips.com    Phone: +31-40-2742403
> 
> 
> 

-- 
Andrzej Kozlowski
Toyama International University, JAPAN

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