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MathGroup Archive 2004

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Re: can't MATHEMATICA simplify simple expressions?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51526] Re: [mg51505] can't MATHEMATICA simplify simple expressions?
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Thu, 21 Oct 2004 22:20:41 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200410200521.BAA08484@smc.vnet.net>
  • Reply-to: murray at math.umass.edu
  • Sender: owner-wri-mathgroup at wolfram.com

Perhaps because the result would NOT necessarily be correct in the case 
that the number a is complex?

Example:

      a = -I;

Then

      a^3
   I

By definition, the principal value of (-1)^(3/2) is

      Exp[(3/2) Log[-1]]

that is,

      Exp[(3/2) (Log[Abs[-1]] + I Arg[-1])]

which, since Arg[-1], as Mathematica will tell you, is Pi, is:

      Exp[(3/2) I Pi]
   -I

Or:

      a = -1;
      {a^3, (a^2)^(3/2)}
   {-1, 1}

But:

      Clear[a]
      Simplify[(a^2)^(3/2), Element[a, Reals]]
   Abs[a]^3

      Simplify[(a^2)^(3/2), a > 0]
   a^3

Cole Turner wrote:
> if I enter:
> 
> FullSimplify [ (a^2)^(3/2) ]
> 
> (in correct MATHEMATICA syntax, the program does not yield the correct
> result, a^3 ... 
> 
> why is that?
> 
> thanks!

-- 
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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