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

Returns the norm of an ideal.

<p><p>

<h3>
Syntax:
</h3>
<pre>n := IdealNorm(I);</pre>

<p>

<table>
<tr>
<td>ideal</td>
<td><pre>  I  </pre></td>
<td></td>
</tr>
<tr>
<td>rational number</td>
<td><pre>  n  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
If the ideal \a is an ideal over an absolute order O the
norm is the number of elements of the finite ring O/\a.

If the ideal \a is an ideal over a relative order the
relative norm of this ideal is returned which is the ideal
generated by the norms of all elements of the ideal \a.

Iterative application of <tt> IdealNorm</tt> eventually leads to
the absolute norm of an relative 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>
Computing the norm of 2*O + (1+rho)*O where O is the maximal order
of x^2-2 and rho^2 = 2.
<pre>

kash> O := OrderMaximal(Order(Poly(Zx, [1, 0, -2])));
Generating polynomial: x^2 - 2
Discriminant: 8 

kash> IdealNorm(Elt(O, [1 ,4])*O);
31
kash> IdealNorm (Elt (O,[3,6]/2)*O);
> 63/4

</pre>

<p>


<hr>

<p>
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