       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>
• 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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