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Re: Simplify
*To*: mathgroup at smc.vnet.net
*Subject*: [mg58678] Re: Simplify
*From*: David Bailey <dave at Remove_Thisdbailey.co.uk>
*Date*: Thu, 14 Jul 2005 02:49:04 -0400 (EDT)
*References*: <db2g9i$djm$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
paulvonhippel at yahoo wrote:
> I'm having some trouble getting an expression to simplify in an obvious
> way. (There seems to be a long tradition of users posting to this group
> with similar troubles.)
>
> The expression is
>
> poly = p (p - 1) b^2 + s^2
> prod = Sqrt [poly] Sqrt[1/poly]
> Simplify[prod, {0 < p < 1, s > 0, bÏµReals}]
>
> which should return one, I think, but doesn't.
>
> I'd be grateful for suggestions.
>
> Thanks!
> Paul
>
Hello,
There is indeed a long tradition of users posting questions about
Simplify and FullSimplify, however most of these are misunderstandings.
In your case it is easier to consider simplifying Sqrt[x]Sqrt[1/x]
(where x is your polynomial). This also fails unless you add the
assumption that x>0 (which implies that x is also Real):
Simplify[Sqrt[x]Sqrt[1/x],x>0]
To see why this assumption is necessary consider the case where x=-1.
You get Sqrt[-1]Sqrt[-1], which equals I*I, which is -1.
The other thing to remember about Simplify and FullSimplify is that
there is no guarantee of success, nor is the concept of the "simplest
form" well defined - so you don't always get complete simplification
even when it is valid.
David Bailey
http://www.dbaileyconsultancy.co.uk
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