Re: simplifying ^ fails, on exact numerical constants in Mathematica 5.0

*To*: mathgroup at smc.vnet.net*Subject*: [mg62025] Re: simplifying ^ fails, on exact numerical constants in Mathematica 5.0*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Wed, 9 Nov 2005 03:45:55 -0500 (EST)*Organization*: The University of Western Australia*References*: <difr5c$fdt$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <difr5c$fdt$1 at smc.vnet.net>, "Richard J. Fateman" <fateman at eecs.berkeley.edu> wrote: > 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 Indeed, FullSimplify[(x^n)^(y/n), Element[n, Integers] && x > 0 && y > 0] yields x^y. Moreover, for such parameters, one could code f as f[x_/; x >0, y_ /; y> 0, n_Integer] := x^y > 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). Not in Mathematica 5.2. > 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? Well, 5.2 does ok on this problem. Cheers, Paul _______________________________________________________________________ Paul Abbott Phone: 61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) AUSTRALIA http://physics.uwa.edu.au/~paul