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Re: Simplification shortcomings?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg24644] Re: [mg24621] Simplification shortcomings?
*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>
*Date*: Mon, 31 Jul 2000 09:23:17 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
on 7/28/00 11:23 PM, Bob Harris at nitlion at mindspring.com wrote:
> Howdy,
>
> I'm a relative novice to Mathematica. While working with it today, I had
> occasion to want to know if a result was equal to (1 + Sqrt[5])/2. The
> result was shown as Sqrt[(3 + Sqrt[5])/2]. After some pancil and paper
> work, I figured out that these two are equal. Or, I should say, that the
> former is one of the values that the latter can have.
>
> I was frustrated in my attempts to get Mathematica to answer that question
> for me. Simplify[(1 + Sqrt[5])/2 - Sqrt[(3 + Sqrt[5])/2]] didn't provide
> any improvement. Calculating this value to many decimal digits showed it
> was near zero (probably close enough that I could have applied the
> techniques shown in Scheinerman's recent article in American Mathematical
> Monthly). The only way I got Mathematica to show the equality was to square
> both numbers; Simplify[((1 + Sqrt[5])/2)^2 - (3 + Sqrt[5])/2] is zero.
>
> Is there any better way to do this? I have some other, more complicated
> numbers that I need to compare.
>
> Thanks,
> Bob Harris
>
>
>
>
>
Yes.
In[3]:=
FullSimplify[(1 + Sqrt[5])/2 - Sqrt[(3 + Sqrt[5])/2]]
Out[3]=
0
or
In[5]:=
RootReduce[(1 + Sqrt[5])/2 - Sqrt[(3 + Sqrt[5])/2]]
Out[5]=
0
(Actually FullSimplify uses RootReduce so it is the latter that really does
the job here).
Andrzej
--
Andrzej Kozlowski
Toyama International University, JAPAN
For Mathematica related links and resources try:
<http://www.sstreams.com/Mathematica/>
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