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

The denominator of the ideal.

<p><p>

<h3>
Syntax:
</h3>
<pre>d := IdealDen(I);</pre>

<p>

<table>
<tr>
<td>ideal </td>
<td><pre>  I  </pre></td>
<td></td>
</tr>
<tr>
<td>integer </td>
<td><pre>  d  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#IdealIsIntegral">IdealIsIntegral</a>

<p>

<h3>
Description:
</h3>
The denominator of a fractional ideal \a is the smallest positive
integer d that d\a is an integral ideal. Integral ideals
are just fractional ideals with denominator 1 and have no
separate internal data structure.

Once computed the denominator is stored in the ideal data
structure so it has not to be computed again.

<p><p>

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

<pre>

kash> O := OrderMaximal(Poly(Zx,[1,4,1,-4,-3,7]));
Generating polynomial: x^5 + 4*x^4 + x^3 - 4*x^2 - 3*x + 7
Discriminant: 28442269 

kash> a := Elt(O,[1,5,1,8,0]);
[1, 5, 1, 8, 0]
kash> b := Elt(O,[3, 1,5,1,8]);
[3, 1, 5, 1, 8]
kash> I := Ideal(a, b);
<[1, 5, 1, 8, 0], [3, 1, 5, 1, 8]>
kash> IdealDen(I^-1);
> 3

</pre>

<p>


<hr>

<p>
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