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

Returns the denominator of an object.


<p><p>

<h3>
Syntax:
</h3>
<pre>d := Den( a );
d := Den(a, "rep");
d := Den( q );
I := Den( I );</pre>

<p>

<table>
<tr>
<td>integer</td>
<td><pre>  d  </pre></td>
<td></td>
</tr>
<tr>
<td>quotient field element or polynomial</td>
<td><pre>  d  </pre></td>
<td></td>
</tr>
<tr>
<td>rational</td>
<td><pre>  q  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic element</td>
<td><pre>  a  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic function field order element</td>
<td><pre>  a  </pre></td>
<td></td>
</tr>
<tr>
<td>quotient field element or polynomial</td>
<td><pre>  q  </pre></td>
<td></td>
</tr>
<tr>
<td>ideal</td>
<td><pre>  I  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
For a rational number or a rational function the function
returns the denominator of the rational argument.
The denominator of the algebraic number a is the smallest
natural number d such that dcdot a is an algebraic
integer. If you use <tt> Den(a, "rep")</tt> the
denominator in the representation of a is returned.
For an algebraic function field order element
see <tt> AlffEltDen</tt>.
The denominator of a fractional ideal \a is the smallest
positive integer d that dcdot \a is an integral ideal.


<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
An absolute example for an algebraic element: 
<pre>

kash> o := Order (x^3 - 23*x^2 + 146*x - 244);;
kash> a := Elt (o, [1/2,3/5,45/5657567]);
[28287835, 33945402, 450] / 56575670
kash> Den ( a );
56575670
kash> Den ( a, "rep" );
> 56575670

</pre>

<p>


<hr>

<p>
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