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: <firstname.lastname@example.org>
- 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:
> 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
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
> 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.
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)
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