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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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