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Re: Why can't Mathematica tell when something is algebraically zero?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg108127] Re: Why can't Mathematica tell when something is algebraically zero?
  • From: dh <dh at metrohm.com>
  • Date: Tue, 9 Mar 2010 06:19:35 -0500 (EST)
  • References: <hn2ltj$3kt$1@smc.vnet.net>

Hi,
Sqrt is a multivalued function. Therefore, your expression is not 
necessarily zero. If you are sure that all your variables are real and 
that you only want the main branch of Power, then you can use PowerExpand:
r^2 Sqrt[(r^3 + r + 2)/r] - Sqrt[r^3 (r^3 + r + 2)] // PowerExpand
Daniel

On 08.03.2010 12:09, mmdanziger wrote:
> This isn't the first time that I've encountered something like this in
> Mathematica but in my calculations I got a term like this:
>
> r^2 Sqrt[(r^3 + r + 2)/r] - Sqrt[r^3 (r^3 + r + 2)]
>
> Which is obviously identically zero.  For some reason Simplify or even
> FullSimplify can't figure this out.  Once you get dependent on
> Mathematica these things are pretty disturbing...you forget about your
> own knowledge because the program tells you that things are
> different.  Then you sit there like an idiot checking an algebraic
> identity that any beginning precalc student should be able to solve no
> problem.
>
> Is there any way to get Mathematica to "wake up" to these things?  It
> has such a powerful algebraic engine for most things, why can't it see
> something simple like the above?  Do you really have to manually
> override and tell the program when things should be zero?
>
> For the time being I'll just sift through and test things by hand but
> I can't believe that there isn't a better way.
>
> Best,
> md
>


-- 

Daniel Huber
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E-Mail:<mailto:dh at metrohm.com>
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