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Re: Simplification shortcomings?

  • To: mathgroup at
  • Subject: [mg24649] Re: Simplification shortcomings?
  • From: "Allan Hayes" <hay at>
  • Date: Mon, 31 Jul 2000 09:23:20 -0400 (EDT)
  • References: <8lsutf$>
  • Sender: owner-wri-mathgroup at


FullSimplify uses more information and tries harder than Simplify:

FullSimplify[(1 + Sqrt[5])/2 - Sqrt[(3 + Sqrt[5])/2]]


Allan Hayes
Mathematica Training and Consulting
Leicester UK
hay at
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Bob Harris" <nitlion at> wrote in message
news:8lsutf$27c at
> 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
> 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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