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<h2><a name="MatSymDiag"></a>
MatSymDiag
</h2>

missing shortdoc

<p><p>

<h3>
Syntax:
</h3>
<pre>L := MatSymDiag (A);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td></td>
</tr>
<tr>
<td>matrix</td>
<td><pre>  A  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Let A be a symmetric matrix over Z, Q or R. The
<tt> MatSymDiag</tt> function computes \Delta, T and \lambda
such that \Delta = \lambdaT^t AT is a diagonal matrix.
The diagonal entries of \Delta are squarefree integers if
the coefficient ring of A is Z or Q. When the
coefficient ring of A equals R each diagonal entry of
\Delta is \pm 1 or 0.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>

<pre>

kash> A := Mat(Z,[[2,3,4],[3,1,4],[4,4,0]]);
[2 3 4]
[3 1 4]
[4 4 0]
kash> L := MatSymDiag(A);;
kash> Delta := L[1];
[ 7  0  0]
[ 0 -1  0]
[ 0  0 -6]
kash> lambda := L[2];
14/1
kash> T := L[3];
[  1/2 -3/14  -2/7]
[    0   1/7  -1/7]
[    0     0   1/4]
kash> Delta;
[ 7  0  0]
[ 0 -1  0]
[ 0  0 -6]
kash> lambda * MatTrans(T) * A * T;
> [ 7  0  0]
[ 0 -1  0]
[ 0  0 -6]

</pre>

<p>


<hr>

<p>
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