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

• To: mathgroup at smc.vnet.net
• Subject: [mg108136] Re: [mg108074] Why can't Mathematica tell when something is algebraically zero?
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Tue, 9 Mar 2010 06:21:13 -0500 (EST)
• References: <201003081109.GAA03756@smc.vnet.net>

On Mar 8, 2010, at 6:09 AM, 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.
>

   The expression is not identically zero when r is complex valued,  
and furthermore when r = 0 the first Sqrt expression is undefined so  
whole expression is not identically zero and Mathematica correctly  
reports that fact.  If you ask Mathematica so simplify the expression  
when r is a real number greater than zero you get your expected result:

(Debug) (Dialog) In[64]:= FullSimplify[r^2 Sqrt[(r^3+r+2)/r]-Sqrt[r^3  
(r^3+r+2)],r>0]
(Debug) (Dialog) Out[64]= 0

Best Regards,
	Sseziwa

• References:
  • Why can't Mathematica tell when something is algebraically zero?
    • From: mmdanziger <mmdanziger@gmail.com>