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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="EltAbsLogHeight"></a>
EltAbsLogHeight
</h2>

Computes the absolute logarithmic height of an algebraic number.

<p><p>

<h3>
Syntax:
</h3>
<pre>h := EltAbsLogHeight(a);</pre>

<p>

<table>
<tr>
<td>real</td>
<td><pre>  h  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic element</td>
<td><pre>  a  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Let \alpha be an algebraic number. Denote by
 m_\alpha(t) = a_0 t^n + cdots + a_n
= a_0 \prod_{j=1}^n (t-\alpha^{(j)})

its minimal polynomial over Z. The absolute
logarithmic height of \alpha is defined by
 h(\alpha)
= frac{1}{n} \log \left(
a_0 \prod_{j=1}^n \max(1,|\alpha^{(j)}|) right).


<p><p>

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

<pre>

kash> o := Order(Z,4,7);
Generating polynomial: x^4 - 7

kash> a := Elt(o,[1,1,1,1]);
[1, 1, 1, 1]
kash> EltAbsLogHeight(a);
1.343819601921041250609358018785526704542243019136
kash> EltAbsLogHeight(a/100);
> 4.085309800568132385973058818275095989145577876487

</pre>

<p>


<hr>

<p>
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