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
>
>