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MathGroup Archive 2005

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Re: Simplify

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58679] Re: Simplify
  • From: Peter Pein <petsie at dordos.net>
  • Date: Thu, 14 Jul 2005 02:49:05 -0400 (EDT)
  • References: <db2g9i$djm$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

paulvonhippel at yahoo schrieb:
> 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, b=CF=B5Reals}]
>
> which should return one, I think, but doesn't.
>
> I'd be grateful for suggestions.
>
> Thanks!
> Paul
>
It's quite easy:

In[1]:=
$Assumptions = 1 > p > 0 < s && Element[b, Reals];
poly = p*(p - 1)*b^2 + s^2;
prod = Sqrt[poly]*Sqrt[1/poly];

In[4]:= Simplify[prod,
   s > Abs[b]*Sqrt[p*(1 - p)] ]

Out[4]= 1

In[5]:= Simplify[prod,
  s < Abs[b]*Sqrt[p*(1 - p)]]

Out[5]= -1

--
Peter Pein
Berlin
http://people.freenet.de/Peter_Berlin/


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