       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

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Paul Abbott                                      Phone:  61 8 6488 2734
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