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

**References**:**can't MATHEMATICA simplify simple expressions?***From:*Cole Turner <REMOVEcole.tuner@liwest.at>