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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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