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Re: Another question on Assuming

• To: mathgroup at smc.vnet.net
• Subject: [mg85915] Re: [mg85866] Another question on Assuming
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Wed, 27 Feb 2008 04:33:27 -0500 (EST)
• References: <200802261242.HAA22491@smc.vnet.net>

On 26 Feb 2008, at 13:42, Kevin J. McCann wrote:

> The first example in the Mathematica Help on Assuming is (in part)
>
> Assuming[a > 0, Refine[Sqrt[a^2]]]
>
> which results in the answer a, as it should; however if I type instead
>
> Assuming[a > 0, Sqrt[a^2]]
>
> I get back Sqrt[a^2]], but I should get a, since there is no other
> correct answer, because the assumption that a > 0 implies that it a  
> is a
> positive real.
>
> Bug?
>
> Kevin
> -- 
>
> Kevin J. McCann
> Research Associate Professor
> JCET/Physics
> Physics Building
> University of Maryland, Baltimore County
> 1000 Hilltop Circle
> Baltimore, MD 21250
>

This is not a bug but a design feature. Assuming works only with  
functions such as Simplify, Refine, Integrate, Limit etc.,  that have  
Assumptions among their options (the one exception is PowerExpand).   
You've got to use one of such functions, so, for example,  even this  
will work:

Assuming[a > 0, Limit[Sqrt[a^2], x -> b]]

a

However, in the case of a function like Sqrt, which does admit the  
Assumptions option (in fact, it admits no options) Assuming does  
nothing at all.

Andrzej Kozlowski

• References:
  • Another question on Assuming
    • From: "Kevin J. McCann" <Kevin.McCann@umbc.edu>