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

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  • Subject: [mg108074] Why can't Mathematica tell when something is algebraically zero?
  • From: mmdanziger <mmdanziger at gmail.com>
  • Date: Mon, 8 Mar 2010 06:09:56 -0500 (EST)

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


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