Re: Simplification shortcomings?

*To*: mathgroup at smc.vnet.net*Subject*: [mg24649] Re: Simplification shortcomings?*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Mon, 31 Jul 2000 09:23:20 -0400 (EDT)*References*: <8lsutf$27c@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Bob, FullSimplify uses more information and tries harder than Simplify: FullSimplify[(1 + Sqrt[5])/2 - Sqrt[(3 + Sqrt[5])/2]] 0 -- Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "Bob Harris" <nitlion at mindspring.com> wrote in message news:8lsutf$27c at smc.vnet.net... > 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 > > > >