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Re: Simplify

  • To: mathgroup at
  • Subject: [mg58678] Re: Simplify
  • From: David Bailey <dave at>
  • Date: Thu, 14 Jul 2005 02:49:04 -0400 (EDT)
  • References: <db2g9i$djm$>
  • Sender: owner-wri-mathgroup at

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, bϵReals}]
> which should return one, I think, but doesn't.
> I'd be grateful for suggestions.
> Thanks!
> Paul

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):


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

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