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Re: FunctionExpand problem in version 6

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82056] Re: FunctionExpand problem in version 6
  • From: "Eric W. Weisstein" <eww at wolfram.com>
  • Date: Wed, 10 Oct 2007 04:34:47 -0400 (EDT)
  • References: <fefi66$jd3$1@smc.vnet.net>

Use Developer`TrigToRadicals:

Mathematica 6.0 for Mac OS X x86 (32-bit)
Copyright 1988-2007 Wolfram Research, Inc.

In[1]:= Developer`TrigToRadicals[Sin[Pi/13]]//InputForm

Out[1]//InputForm=
(-I/2)*((((-1 - Sqrt[13])/2 + I*Sqrt[7 + Sqrt[13] + (-1 + Sqrt[13])/
2])/2 +
    ((-1 + I*Sqrt[3])*(((-1 + Sqrt[13])/2 -
         I*Sqrt[7 - Sqrt[13] + (-1 - Sqrt[13])/2])/2 +
       (((-1 + I*Sqrt[3])/2 + (-1 + I*Sqrt[3])^2/4)*((-1 - Sqrt[13])/2
-
          I*Sqrt[7 + Sqrt[13] + (-1 + Sqrt[13])/2]))/2))/
     (2*(6 + (3*(-1 + I*Sqrt[3])*((-1 + Sqrt[13])/2 -
           I*Sqrt[7 - Sqrt[13] + (-1 - Sqrt[13])/2]))/4 +
        (3*(-1 + I*Sqrt[3])^2*((-1 + Sqrt[13])/2 +
           I*Sqrt[7 - Sqrt[13] + (-1 - Sqrt[13])/2]))/8 +
        ((-1 - Sqrt[13])/2 + I*Sqrt[7 + Sqrt[13] + (-1 + Sqrt[13])/2])/
2)^
       (1/3)) + ((-1 + I*Sqrt[3])^2*
      (6 + (3*(-1 + I*Sqrt[3])*((-1 + Sqrt[13])/2 -
           I*Sqrt[7 - Sqrt[13] + (-1 - Sqrt[13])/2]))/4 +
        (3*(-1 + I*Sqrt[3])^2*((-1 + Sqrt[13])/2 +
           I*Sqrt[7 - Sqrt[13] + (-1 - Sqrt[13])/2]))/8 +
        ((-1 - Sqrt[13])/2 + I*Sqrt[7 + Sqrt[13] + (-1 + Sqrt[13])/2])/
2)^
       (1/3))/4)/3 +
  (((1 + Sqrt[13])/2 + I*Sqrt[7 + Sqrt[13] + (-1 + Sqrt[13])/2])/2 -
    ((-1 + I*Sqrt[3])^2*(6 + (3*(-1 + I*Sqrt[3])^2*((-1 + Sqrt[13])/2
-
           I*Sqrt[7 - Sqrt[13] + (-1 - Sqrt[13])/2]))/8 +
        (3*(-1 + I*Sqrt[3])*((-1 + Sqrt[13])/2 +
           I*Sqrt[7 - Sqrt[13] + (-1 - Sqrt[13])/2]))/4 +
        ((-1 - Sqrt[13])/2 - I*Sqrt[7 + Sqrt[13] + (-1 + Sqrt[13])/2])/
2)^
       (1/3))/4 - ((-1 + I*Sqrt[3])*
      (((-1 + Sqrt[13])/2 + I*Sqrt[7 - Sqrt[13] + (-1 - Sqrt[13])/2])/
2 +
       (((-1 + I*Sqrt[3])/2 + (-1 + I*Sqrt[3])^2/4)*((-1 - Sqrt[13])/2
+
          I*Sqrt[7 + Sqrt[13] + (-1 + Sqrt[13])/2]))/2))/
     (2*(6 + (3*(-1 + I*Sqrt[3])^2*((-1 + Sqrt[13])/2 -
           I*Sqrt[7 - Sqrt[13] + (-1 - Sqrt[13])/2]))/8 +
        (3*(-1 + I*Sqrt[3])*((-1 + Sqrt[13])/2 +
           I*Sqrt[7 - Sqrt[13] + (-1 - Sqrt[13])/2]))/4 +
        ((-1 - Sqrt[13])/2 - I*Sqrt[7 + Sqrt[13] + (-1 + Sqrt[13])/2])/
2)^
       (1/3)))/3)

This (change) will I hope be better documented in the near future.

Best wishes,
-Eric

On Oct 9, 4:38 am, michael.p.crouc... at googlemail.com wrote:
> Hi All
>
> In version 5.2 If I do
>
> FunctionExpand[Sin[Pi/13]]
>
> I get a very complicated result involving lots of square roots.  This
> is also mentioned here:
>
> http://mathworld.wolfram.com/TrigonometryAnglesPi13.html
>
> But if I do the same thing in version 6.0 then I just get the result
>
> Sin[Pi/13]
>
> Which is not nearly as impressive.  What has changed with the
> FunctionExpand function in v6 that causes this and how do I get the
> original behaviour?



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