Simplify, FullSimplify, .....

• To: mathgroup at smc.vnet.net
• Subject: [mg50065] Simplify, FullSimplify, .....
• From: "Maurits Haverkort" <Haverkort at ph2.uni-koeln.de>
• Date: Fri, 13 Aug 2004 05:56:43 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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 useing Mathematic 5.0.1.0 on windows 2000, AMD processor

Best regards,

Maurits Haverkort

```

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