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

Computes a "random" element of a given order.

<p><p>

<h3>
Syntax:
</h3>
<pre>alpha := RandomElt(R [, l | b, deg | degl]);</pre>

<p>

<table>
<tr>
<td>element</td>
<td><pre>  alpha  </pre></td>
<td>of <tt> o</tt></td>
</tr>
<tr>
<td>ring</td>
<td><pre>  R  </pre></td>
<td>may be an order, an ideal, Z, a module, a polynomial algebra or an function field order.</td>
</tr>
<tr>
<td>list</td>
<td><pre>  l  </pre></td>
<td>of integers</td>
</tr>
<tr>
<td>integer</td>
<td><pre>  b  </pre></td>
<td>equivalent to l := [-b..b]</td>
</tr>
<tr>
<td>integer</td>
<td><pre>  deg  </pre></td>
<td>degree of a random element of the</td>
</tr>
<tr>
<td></td>
<td><pre>  polynomial algebra R  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  degl  </pre></td>
<td>of positive integers</td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
A "random" element aplpha with coefficients in l
will be returned (by default l := [-20,20]).
Of course, it is not possible to do a truly
random element from an infinite set.

If R is a polynomial algebra,
and you want to create a random element with a certain degree
deg, then you also have to give l or b as a parameter
to <tt> RandomElt</tt>. If deg is a list, then the degree
of alpha will be an element of deg.
If R is a function field order, then deg
is the range of the degree of the coefficients of
\alpha, and l the range of coefficients of these
coefficients (only for absolute extensions in the moment).
By default the degree is an integer
between 0 and 20.

<p><p>

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

<pre>
kash> o := Order(Z, 5, 3);
Generating polynomial: x^5 - 3

kash> RandomElt(o);
[19, 11, 5, -6, -18]
kash> RandomElt(o, 100);
[-29, 86, 87, 22, -77]
kash> RandomElt(o, [-1,1]);
> [-1, -1, -1, -1, 1]

</pre>

<p>


<hr>

<p>
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