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MathGroup Archive 2000

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Re: Assumptions ignored?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25141] Re: [mg25061] Assumptions ignored?
  • From: BobHanlon at aol.com
  • Date: Sun, 10 Sep 2000 03:14:59 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 9/7/2000 10:55:01 PM, Jos.Bergervoet at philips.com writes:

>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 plain answer (without ifs and whens) to
>use it in further computations. How can it be obtained? (If
>possible, do not give answers about menus and mouseclicks, but
>just the lines of input to be typed. I'm not very fond of GUI's ;-)
>

You can either help it with additional (albeit redundant) assumptions

Simplify[Integrate[ x/Sqrt[x^2 + zp^2]^3,  {zp, z, Infinity}, 
    Assumptions -> {x > 0, z > 0, x^2 > 0, z^2 > 0} ], x > 0]

(1 - z/Sqrt[x^2 + z^2])/x

or more straightforwardly just turn off the generation of conditions

% == Simplify[Integrate[ x/Sqrt[x^2 + zp^2]^3, {zp, z, Infinity}, 
      GenerateConditions -> False ], x > 0]

True


Bob Hanlon


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