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

The minimum of the ideal.

<p><p>

<h3>
Syntax:
</h3>
<pre>m:=IdealMin(I);</pre>

<p>

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

<p>


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

<p>

<h3>
Description:
</h3>
The intersection of the ideal with the coefficient ring
(which is Z for absolute ideals and the coefficient order
for relative ideals) defines an ideal over the coefficient
ring.

In case of absolute
ideals the principal generator of this ideal is returned
(which is the smallest positive rational integer in the
ideal), in case of relative ideals
the ideal itself is returned.

Iterative application of <tt> IdealMin</tt> to a relative ideal
eventually leads to the smallest positive rational integer in the
ideal.

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

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
for absolute ideals 
<pre>

kash> O := OrderMaximal(Order(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> I := Ideal(a);
<[1, 5, 1, 8, 0]>
kash> IdealMin(I);
> 3563523

</pre>

<p>


<hr>

<p>
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