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MathGroup Archive 2007

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Re: question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77847] Re: [mg77827] question
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Mon, 18 Jun 2007 06:58:23 -0400 (EDT)
  • Reply-to: hanlonr at cox.net

o = 2*Cos[Pi/48]*(1 - Cos[Pi/48]^2)^(1/2) + 2*Cos[Pi/48]^2 - 1;

ClearSystemCache[]

Timing[ToRadicals[
  RootReduce[(FullSimplify[#1, 
       ComplexityFunction -> (Count[{#1}, _Cos, Infinity] &)] &)[
    o]]]]

{20.088752000000014, 
   Sqrt[(1/2)*(2 + Sqrt[
            2 - Sqrt[3]])]}

ClearSystemCache[]

Timing[ToRadicals[
  RootReduce[Simplify[o /. 1 - Cos[x_]^2 -> Sin[x]^2]]]]

{0.0916960000000131, 
   Sqrt[(1/2)*(2 + Sqrt[
            2 - Sqrt[3]])]}

ClearSystemCache[]

Timing[o // TrigFactor // FullSimplify]

{2.2494800000000055, Cos[Pi/24] + 
     Sin[Pi/24]}

ClearSystemCache[]

Timing[o // TrigToExp // FullSimplify]

{2.2507500000000107, Cos[Pi/24] + 
     Sin[Pi/24]}

ClearSystemCache[]

Timing[o // TrigToExp // Simplify // RootReduce // ToRadicals]

{8.879419999999996, 
   Sqrt[(1/2)*(2 + Sqrt[
            2 - Sqrt[3]])]}

ClearSystemCache[]

Timing[o // TrigFactor // Simplify // RootReduce // ToRadicals]

{8.879437999999993, 
   Sqrt[(1/2)*(2 + Sqrt[
            2 - Sqrt[3]])]}


Bob Hanlon

---- dimitris <dimmechan at yahoo.com> wrote: 
> Two eforts in Mathematica 5.2 in order
> to simplify o below
> 
> o = 2*Cos[Pi/48]*(1 - Cos[Pi/48]^2)^(1/2) + 2*Cos[Pi/48]^2 - 1;
> 
> First leaving Mathematica do the job.
> 
> Timing[ToRadicals[RootReduce[(FullSimplify[#1, ComplexityFunction ->
> (Count[{#1}, _Cos, Infinity] & )] & )[o]]]]
> {43.031*Second, Sqrt[(1/2)*(2 + Sqrt[2 - Sqrt[3]])]}
> 
> Then help a bit Mathematica.
> I couldn't find a built in command to simplify 1 - Cos[Pi/48]^2 to
> Sin[Pi/48]^2. That's why the adding of a rule.
> 
> Timing[ToRadicals[RootReduce[Simplify[o /. 1 - Cos[Pi/48]^2 ->
> Sin[Pi/
> 48]^2]]]]
> {0.25*Second, Sqrt[(1/2)*(2 + Sqrt[2 - Sqrt[3]])]}
> 
> Any other suggestions will be highly appreciated.
> 
> Dimitris
> 
> 



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