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MathGroup Archive 2011

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simplification

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122188] simplification
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Wed, 19 Oct 2011 05:36:02 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hello to all.

I would appreciate your suggestions about simplifying further the
following lengthy expression.

ArcTan[(3*(Sqrt[3] + I*x - I*x^2)*(1 - x + x^2))/(-3 + I*Sqrt[3] - 3*x
- 3*I*Sqrt[3]*x + 3*x^2 + I*Sqrt[3]*x^2 - 6*x^3 -
      2*I*Sqrt[3]*x^4 - I*Sqrt[3*(1 - I*Sqrt[3])]*Sqrt[1 - x + x^2] +
I*Sqrt[3*(1 - I*Sqrt[3])]*x*Sqrt[1 - x + x^2] +
      I*Sqrt[3*(1 - I*Sqrt[3])]*x^2*Sqrt[1 - x + x^2] + 2*I*Sqrt[3*(1
- I*Sqrt[3])]*x^3*Sqrt[1 - x + x^2])]/
   Sqrt[3*(1 - I*Sqrt[3])] - ArcTan[(3*(Sqrt[3] - I*x + I*x^2)*(1 - x
+ x^2))/(3 + I*Sqrt[3] + 3*x - 3*I*Sqrt[3]*x - 3*x^2 +
      I*Sqrt[3]*x^2 + 6*x^3 - 2*I*Sqrt[3]*x^4 - I*Sqrt[3*(1 +
I*Sqrt[3])]*Sqrt[1 - x + x^2] +
      I*Sqrt[3*(1 + I*Sqrt[3])]*x*Sqrt[1 - x + x^2] + I*Sqrt[3*(1 +
I*Sqrt[3])]*x^2*Sqrt[1 - x + x^2] +
      2*I*Sqrt[3*(1 + I*Sqrt[3])]*x^3*Sqrt[1 - x + x^2])]/Sqrt[3*(1 +
I*Sqrt[3])] -
  (I*Log[(-I + Sqrt[3] - 2*I*x)^2*(I + Sqrt[3] + 2*I*x)^2])/
(2*Sqrt[3*(1 - I*Sqrt[3])]) +
  (I*Log[(-I + Sqrt[3] - 2*I*x)^2*(I + Sqrt[3] + 2*I*x)^2])/
(2*Sqrt[3*(1 + I*Sqrt[3])]) +
  (I*Log[(1 + x + x^2)*(11*I + 4*Sqrt[3] - 17*I*x - 4*Sqrt[3]*x +
11*I*x^2 + 4*Sqrt[3]*x^2 +
       10*I*Sqrt[1 - I*Sqrt[3]]*Sqrt[1 - x + x^2] - 8*I*Sqrt[1 -
I*Sqrt[3]]*x*Sqrt[1 - x + x^2])])/(2*Sqrt[3*(1 - I*Sqrt[3])]) -
  (I*Log[(1 + x + x^2)*(-11*I + 4*Sqrt[3] + 17*I*x - 4*Sqrt[3]*x -
11*I*x^2 + 4*Sqrt[3]*x^2 -
       10*I*Sqrt[1 + I*Sqrt[3]]*Sqrt[1 - x + x^2] + 8*I*Sqrt[1 +
I*Sqrt[3]]*x*Sqrt[1 - x + x^2])])/(2*Sqrt[3*(1 + I*Sqrt[3])])

Thanks in advance.
Dimitris



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