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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg108161] Re: [mg108074] Why can't Mathematica tell when something is algebraically
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Tue, 9 Mar 2010 06:25:46 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <201003081109.GAA03756@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

But it is NOT identically zero!  Try, for example:

   r^2 Sqrt[(r^3 + r + 2)/r] - Sqrt[r^3 (r^3 + r + 2)] /. r -> I


On 3/8/2010 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.
>
> Best,
> md
>

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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