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MathGroup Archive 2007

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Re: question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77851] Re: [mg77827] question
  • From: Carl Woll <carlw at wolfram.com>
  • Date: Mon, 18 Jun 2007 07:00:27 -0400 (EDT)
  • References: <200706171021.GAA02852@smc.vnet.net>

dimitris 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
>
>  
>
Try using Developer`TrigToRadicals:

In[2]:=
o//Developer`TrigToRadicals//RootReduce//ToRadicals
Out[2]=
Sqrt[(1/2)*(2 + Sqrt[2 - Sqrt[3]])]

Note that I deleted some error messages above that appear in version 
5.2, but not in version 6.

Carl Woll
Wolfram Research


  • References:
    • question
      • From: dimitris <dimmechan@yahoo.com>
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