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MathGroup Archive 2004

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Re: Simplify, FullSimplify, .....

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50132] Re: Simplify, FullSimplify, .....
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Tue, 17 Aug 2004 05:00:41 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <cfi949$4r4$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

eqn = -(a^2*(4*(-6 + a^2)*pd\[Pi]^2 - 3*a^2*pd\[Sigma]^2)*
     (4*Sqrt[3]*(-12 + a^4)*pd\[Pi]^2 - 12*a^2*(-2 + a^2)*
       pd\[Pi]*pd\[Sigma] + 3*Sqrt[3]*a^2*(-4 + a^2)*pd\[Sigma]^2))/
   (6*Sqrt[-4*a^2*(-6 + a^2)*pd\[Pi]^2 + 3*a^4*pd\[Sigma]^2]*
    (4*(-12 + a^4)*pd\[Pi]^2 - 4*Sqrt[3]*a^2*(-2 + a^2)*
      pd\[Pi]*pd\[Sigma] + 3*a^2*(-4 + a^2)*pd\[Sigma]^2));

and

((Numerator[eqn]^2/Denominator[eqn]^2 // FullSimplify // Expand) //. 
        a^4*b_ + a^4*c_ :> a^4*(4*b + 4*c)/4 /. 
      a_ + Rational[1, 4]*b_ :> (4*a + b)/4) // Sqrt

Regards
  Jens


Maurits Haverkort wrote:
> 
> Dear all
> 
> Mathematica is almost perfect, since most of my algebra problems it can
> solve, but once in a while it does not. I want to simplify the following
> equation:
> 
> \!\(\(-\(\(a\^2\ \((4\ \((\(-6\) + a\^2)\)\ pd\[Pi]\^2 -
> 3\ a\^2\ pd\[Sigma]\^2)\)\ \((4\ \@3\ \((\(-12\) +
> a\^4)\)\ pd\[Pi]\^2 -
> 12\ a\^2\ \((\(-2\) + a\^2)\)\ pd\[Pi]\ pd\[Sigma] +
> 3\ \@3\ a\^2\ \((\(-4\) +
> a\^2)\)\ pd\[Sigma]\^2)\)\)\/\(6\ \@\(\(-4\)\ a\^2\ \
> \((\(-6\) + a\^2)\)\ pd\[Pi]\^2 + 3\ a\^4\ pd\[Sigma]\^2\)\ \((4\ \((\(-12\)
> \
> + a\^4)\)\ pd\[Pi]\^2 -
> 4\ \@3\ a\^2\ \((\(-2\) + a\^2)\)\ pd\[Pi]\ pd\[Sigma] +
> 3\ a\^2\ \((\(-4\) + a\^2)\)\ pd\[Sigma]\^2)\)\)\)\)\)
> 
> Furhter more I know that:
> \!\({{a, pd\[Sigma], pd\[Pi]} \[Element] Reals, a > 0, pd\[Sigma] < 0,
> pd\[Pi] > 0, a < \@3}\)
> 
> I also know that the equation I want to simplify is equal to:
> 
> \!\(1\/2\ \@\(8\ a\^2\ pd\[Pi]\^2 + a\^4\ \((\(-\(\(4\ pd\[Pi]\^2\)\/3\)\) +
> \
> pd\[Sigma]\^2)\)\)\)
> 
> How can I simplify this equation with Mathematica?
> 
> I tried:
> 
> \!\(FullSimplify[\(-\(\(a\^2\ \((4\ \((\(-6\) + a\^2)\)\ pd\[Pi]\^2 -
> 3\ a\^2\ pd\[Sigma]\^2)\)\ \((4\ \@3\ \((\(-12\) +
> a\^4)\)\ pd\[Pi]\^2 -
> 12\ a\^2\ \((\(-2\) + a\^2)\)\ pd\[Pi]\ pd\[Sigma] +
> 3\ \@3\ a\^2\ \((\(-4\) +
> a\^2)\)\ pd\[Sigma]\^2)\)\)\/\(6\ \@\(\(-4\)\ a\^2\ \((\
> \(-6\) + a\^2)\)\ pd\[Pi]\^2 + 3\ a\^4\ pd\[Sigma]\^2\)\ \((4\ \((\(-12\) +
> a\^4)\)\ pd\[Pi]\^2 -
> 4\ \@3\ a\^2\ \((\(-2\) + a\^2)\)\ pd\[Pi]\ pd\[Sigma] +
> 3\ a\^2\ \((\(-4\) + a\^2)\)\ pd\[Sigma]\^2)\)\)\)\), {{a,
> pd\[Sigma], pd\[Pi]} \[Element] Reals, a > 0, pd\[Sigma] < 0,
> pd\[Pi] > 0, a < \@3}]\)
> 
> But that did not do anything.
> 
> I have some more equations alike, for wich I do not know the answer, so if
> there is a way to let Mathematica do my algebra better I would be glad.
> 
> I am using Mathematica 5.0.1.0 on windows 2000, AMD processor
> 
> Best regards,
> 
> Maurits Haverkort


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