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simplifying ^ fails, on exact numerical constants in Mathematica 5.0

• To: mathgroup at smc.vnet.net
• Subject: [mg61148] simplifying ^ fails, on exact numerical constants in Mathematica 5.0
• From: "Richard J. Fateman" <fateman at eecs.berkeley.edu>
• Date: Tue, 11 Oct 2005 03:22:17 -0400 (EDT)
• Organization: UC Berkeley
• Sender: owner-wri-mathgroup at wolfram.com

Consider
f[x_, y_, n_] :=  (x^n)^(y/n)

For x, y, positive rational numbers and n an integer
this should compute exactly the same as x^y.

And indeed this seems to be the case

for
f(1/4+1/10^18,  1/2,  n)

when n is 1,2,3 or 4.  But it comes up with a different
answer when n is 5 or more  (using Mathematica 5.0).

Are the answers different?  N[%-%%,1000] checks numerical
equality, but this gives an meprec error....

Simplify[..] does not simplify to zero.

FullSimplify does better, if you are willing to wait
long enough, (or n is small enough) and returns 0.

  Can a CAS do this right and fast?

RJF