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Simplification shortcomings?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg24621] Simplification shortcomings?
*From*: Bob Harris <nitlion at mindspring.com>
*Date*: Fri, 28 Jul 2000 17:23:59 -0400 (EDT)
*Organization*: MindSpring Enterprises
*Sender*: owner-wri-mathgroup at wolfram.com
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
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